Subgroups — C₅×#86626 #14483036

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 1556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5824	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5677	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5656	C₂	1	2	yes	maximal, complemented
9	C₅×#5655	C₂	1	2	yes	maximal, complemented
10	C₅×#5632	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5627	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5610	C₂	1	2	yes	maximal, complemented
13	C₅×#5606	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5599	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5596	C₂	1	2	yes	maximal, complemented
16	C₅×#5590	C₂	1	2	yes	maximal, complemented
17	C₅×#5586	C₂	1	2	yes	maximal, complemented
18	C₅×#5554	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#5552	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#5490	C₂	1	2	yes	maximal, complemented
23	C₂×C₅×#67⋊C₄	C₂	1	2	yes	maximal, complemented
24	C₅×D₄×#41	—	3	1	no	maximal, Hall
25	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₅×#67	C₂²	1	2	yes	—
28	C₂²×C₅×#67	C₂²	1	2	yes	complemented
29	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
30	C₅×D₃×#41	—	2	8	no	—
31	C₂×C₅×#239	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#237	—	2	8	no	—
34	C₂×C₅×#237	C₂²	1	1	yes	characteristic
35	C₂×C₅×#237	C₂²	1	2	yes	complemented
36	C₂×C₅×#237	C₂²	1	2	yes	complemented
37	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×#237	C₂²	1	2	yes	complemented
41	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×D₃×D₄	C₂²	1	2	yes	complemented
44	C₂×C₅×#235	C₂²	1	2	yes	complemented
45	C₂×C₅×#235	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
47	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#123	C₂²	1	2	yes	complemented
52	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#121	C₂²	1	2	yes	complemented
54	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#120	C₂²	1	2	yes	complemented
56	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
59	C₅×#953	C₂²	1	2	yes	complemented
60	C₅×#946	C₂²	1	1	yes	characteristic, complemented
61	C₅×#944	C₂²	1	1	yes	characteristic, complemented
62	C₅×#940	C₂²	1	1	yes	characteristic, complemented
63	C₅×#940	C₂²	1	2	yes	complemented
64	C₅×#939	C₂²	1	2	yes	complemented
65	C₅×#939	C₂²	1	2	yes	complemented
66	C₅×#939	C₂²	1	2	yes	complemented
67	C₅×#939	C₂²	1	2	yes	complemented
68	C₅×#938	C₂²	1	1	yes	characteristic, complemented
69	C₅×#937	C₂²	1	2	yes	complemented
70	C₅×#937	C₂²	1	2	yes	complemented
71	C₅×#935	C₂²	1	2	yes	complemented
72	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
73	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
74	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
75	C₅×#930	C₂²	1	2	yes	complemented
76	C₅×#930	C₂²	1	1	yes	characteristic, complemented
77	C₅×#929	C₂²	1	2	yes	complemented
78	C₄×C₅×#67	C₂²	1	1	yes	characteristic
79	C₄×C₅×#67	C₂²	1	2	yes	complemented
80	C₄×C₅×#67	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
82	C₅×#924	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
84	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
85	C₅×#897	C₂²	1	1	yes	characteristic, complemented
86	C₅×#896	C₂²	1	2	yes	complemented
87	C₅×#896	C₂²	1	2	yes	complemented
88	C₅×#895	C₂²	1	1	yes	characteristic, complemented
89	C₅×#894	C₂²	1	2	yes	complemented
90	C₅×#893	C₂²	1	1	yes	characteristic, complemented
91	C₅×#893	C₂²	1	2	yes	complemented
92	C₅×#892	C₂²	1	1	yes	characteristic, complemented
93	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	C₅×#888	C₂²	1	2	yes	complemented
95	C₅×#887	C₂²	1	1	yes	characteristic, complemented
96	C₅×#886	C₂²	1	2	yes	complemented
97	C₅×#885	C₂²	1	2	yes	complemented
98	C₅×#885	C₂²	1	2	yes	complemented
99	C₅×#884	C₂²	1	2	yes	complemented
100	C₅×#884	C₂²	1	2	yes	complemented
101	C₅×#884	C₂²	1	2	yes	complemented
102	C₅×#884	C₂²	1	2	yes	complemented
103	C₅×#883	C₂²	1	2	yes	complemented
104	C₅×#882	C₂²	1	2	yes	complemented
105	C₅×#882	C₂²	1	2	yes	complemented
106	C₅×#67⋊C₄	C₂²	1	1	yes	characteristic
107	C₅×#67⋊C₄	C₂²	1	2	yes	—
108	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
109	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
110	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
111	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
112	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
113	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
114	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
115	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
116	C₅×#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₅×#878	C₂²	1	2	yes	complemented
120	C₅×#878	C₂²	1	2	yes	complemented
121	C₅×#877	C₂²	1	2	yes	complemented
122	C₅×#875	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
124	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
125	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
126	#86626	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
127	C₂²×C₅×#41	—	3	1	no	—
128	C₂²×C₅×#41	—	3	1	no	—
129	C₅×#550	—	3	1	no	—
130	C₅×D₄×Q₈	—	3	1	no	—
131	C₅×#548	—	3	1	no	—
132	C₅×#548	—	3	1	no	—
133	C₅×#547	—	3	1	no	—
134	C₅×#547	—	3	2	no	—
135	C₅×#546	—	3	2	no	—
136	C₅×#546	—	3	1	no	—
137	C₅×#546	—	3	2	no	—
138	C₅×#546	D₃	1	1	yes	characteristic, complemented
139	C₅×D₄²	—	3	1	no	—
140	C₅×D₄²	—	3	2	no	—
141	C₅×#532	—	3	1	no	—
142	C₅×#532	—	3	2	no	—
143	C₅×#525	—	3	2	no	—
144	C₅×#525	—	3	1	no	—
145	C₅×#525	—	3	1	no	—
146	C₅×#525	—	3	2	no	—
147	C₄×C₅×#41	—	3	1	no	—
148	C₂×C₄×C₅×D₄	—	3	1	no	—
149	C₂×C₄×C₅×D₄	—	3	2	no	—
150	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
151	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
152	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
153	C₂³×C₅×D₃	C₂³	1	2	yes	—
154	C₃×C₅×#41	—	2	4	no	—
155	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₅×D₄	—	2	4	no	—
157	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
159	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
160	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
162	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
164	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
165	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
166	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
167	C₂×C₅×#67	—	2	8	no	—
168	C₂×C₅×#67	—	2	8	no	—
169	C₂×C₅×#67	C₂³	1	2	yes	—
170	C₂×C₅×#67	C₂³	1	2	yes	—
171	C₂×C₅×#67	C₂³	1	2	yes	—
172	C₂×C₅×#67	C₂³	1	1	yes	characteristic
173	C₂×C₅×#67	C₂³	1	2	yes	—
174	C₂×C₅×#67	C₂³	1	2	yes	—
175	C₂×C₅×#67	C₂³	1	2	yes	—
176	C₂×C₅×#67	C₂³	1	2	yes	—
177	C₂×C₅×#67	C₂³	1	2	yes	—
178	C₂×C₅×#67	C₂³	1	2	yes	—
179	C₂×C₅×#67	C₂³	1	2	yes	—
180	C₂×C₅×#67	C₂³	1	1	yes	characteristic
181	C₂²×C₅×Dic₃	—	2	8	no	—
182	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
183	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
184	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
185	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
186	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
187	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
188	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
189	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
190	C₅×#239	—	2	4	no	—
191	C₅×D₃×Q₈	—	2	4	no	—
192	C₅×#237	—	2	4	no	—
193	C₅×#237	—	2	8	no	—
194	C₅×#237	—	2	8	no	—
195	C₅×#237	—	2	8	no	—
196	C₅×#237	—	2	4	no	—
197	C₅×#237	—	2	4	no	—
198	C₅×#237	D₄	1	8	yes	complemented
199	C₅×D₃×D₄	—	2	4	no	—
200	C₅×D₃×D₄	—	2	8	no	—
201	C₅×D₃×D₄	—	2	4	no	—
202	C₅×#235	—	2	8	no	—
203	C₅×#235	—	2	4	no	—
204	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
205	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
206	C₂×C₅×D₁₂	C₂³	1	2	yes	—
207	C₂×C₅×D₁₂	C₂³	1	2	yes	—
208	C₂×C₄×C₅×D₃	—	2	8	no	—
209	C₂×C₄×C₅×D₃	—	2	4	no	—
210	C₂×C₄×C₅×D₃	—	2	4	no	—
211	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
212	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
213	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
214	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
215	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
216	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
217	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
218	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
219	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
220	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
221	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
222	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
223	C₂×C₅×Dic₆	—	2	4	no	—
224	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
225	C₂×C₅×Dic₆	C₂³	1	2	yes	—
226	C₂×C₅×Dic₆	C₂³	1	2	yes	—
227	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
228	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
230	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
239	C₅×#217	C₂³	1	2	yes	—
240	C₅×#217	C₂³	1	1	yes	characteristic
241	C₅×#217	C₂³	1	2	yes	—
242	C₅×#217	C₂³	1	1	yes	characteristic
243	C₅×#217	C₂³	1	2	yes	—
244	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
245	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
246	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
247	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
248	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
249	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
250	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
251	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
252	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
253	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
254	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
255	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
256	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
257	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
258	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
259	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
260	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
261	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
262	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
263	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
264	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
265	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
266	C₄×C₅×Dic₃	C₂³	1	2	yes	—
267	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
268	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
269	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
270	C₄×C₅×Dic₃	C₂³	1	2	yes	—
271	C₄×C₅×Dic₃	C₂³	1	2	yes	—
272	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
273	C₂²×#237	C₂×C₅	1	1	yes	characteristic, complemented
274	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
275	#5824	C₂×C₅	1	1	yes	characteristic, complemented
276	D₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
277	#5677	C₂×C₅	1	1	yes	characteristic, complemented
278	#5668	C₂×C₅	1	1	yes	characteristic, complemented
279	#5656	C₂×C₅	1	2	yes	complemented
280	#5655	C₂×C₅	1	2	yes	complemented
281	#5632	C₂×C₅	1	1	yes	characteristic, complemented
282	#5627	C₂×C₅	1	1	yes	characteristic, complemented
283	#5610	C₂×C₅	1	2	yes	complemented
284	#5606	C₂×C₅	1	1	yes	characteristic, complemented
285	#5599	C₂×C₅	1	1	yes	characteristic, complemented
286	#5596	C₂×C₅	1	2	yes	complemented
287	#5590	C₂×C₅	1	2	yes	complemented
288	#5586	C₂×C₅	1	2	yes	complemented
289	#5554	C₂×C₅	1	1	yes	characteristic, complemented
290	#5552	C₂×C₅	1	1	yes	characteristic, complemented
291	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
292	C₄×#237	C₂×C₅	1	1	yes	characteristic, complemented
293	#5490	C₂×C₅	1	2	yes	complemented
294	C₂×#67⋊C₄	C₂×C₅	1	2	yes	complemented
295	C₂×C₅×#41	—	3	1	no	—
296	C₂×C₅×#41	—	3	1	no	—
297	C₂×C₅×#41	—	3	2	no	—
298	C₂×C₅×#41	—	3	2	no	—
299	C₂×C₅×#41	—	3	1	no	—
300	C₂×C₅×#41	—	3	1	no	—
301	C₂×C₅×#41	—	3	2	no	—
302	C₂×C₅×#41	—	3	1	no	—
303	C₂×C₅×#41	—	3	2	no	—
304	C₂×C₅×#41	—	3	1	no	—
305	C₂×C₅×#41	—	6	8	no	—
306	C₂×C₅×#41	—	6	8	no	—
307	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic, complemented
308	C₂²×C₅×Q₈	—	3	1	no	—
309	C₂²×C₅×Q₈	—	3	1	no	—
310	C₂²×C₅×D₄	—	3	2	no	—
311	C₂²×C₅×D₄	—	3	2	no	—
312	C₂²×C₅×D₄	—	3	1	no	—
313	C₂²×C₅×D₄	—	3	2	no	—
314	C₂²×C₅×D₄	—	3	1	no	—
315	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
316	C₂³×C₄×C₅	—	3	2	no	—
317	C₂³×C₄×C₅	—	3	2	no	—
318	C₂³×C₄×C₅	—	3	1	no	—
319	C₂³×C₄×C₅	—	3	1	no	—
320	C₅×C₄⋊Q₈	—	3	1	no	—
321	C₅×C₄⋊Q₈	—	3	2	no	—
322	C₅×#127	—	3	2	no	—
323	C₅×#127	—	3	1	no	—
324	C₅×#124	—	3	2	no	—
325	C₅×#124	—	3	2	no	—
326	C₅×#124	—	3	1	no	—
327	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
328	C₅×#123	—	3	2	no	—
329	C₅×#123	—	3	2	no	—
330	C₅×#123	—	3	2	no	—
331	C₅×#123	—	3	2	no	—
332	C₅×#123	—	3	2	no	—
333	C₅×#123	C₂×D₃	1	2	yes	complemented
334	C₅×C₂²⋊Q₈	—	3	1	no	—
335	C₅×C₂²⋊Q₈	—	3	1	no	—
336	C₅×C₂²⋊Q₈	—	3	2	no	—
337	C₅×C₂²⋊Q₈	—	3	2	no	—
338	C₅×C₂²⋊Q₈	—	3	1	no	—
339	C₅×C₂²⋊Q₈	—	3	2	no	—
340	C₅×C₂²⋊Q₈	—	3	2	no	—
341	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
342	C₅×#121	—	3	1	no	—
343	C₅×#121	—	3	2	no	—
344	C₅×#121	—	3	2	no	—
345	C₅×#121	—	3	2	no	—
346	C₅×#121	—	3	2	no	—
347	C₅×#121	—	3	1	no	—
348	C₅×#121	—	3	2	no	—
349	C₅×#121	—	3	1	no	—
350	C₅×#121	—	3	2	no	—
351	C₅×#121	—	3	2	no	—
352	C₅×#121	—	3	2	no	—
353	C₅×#121	—	3	2	no	—
354	C₅×#121	C₂×D₃	1	1	yes	characteristic, complemented
355	C₅×#121	C₂×D₃	1	2	yes	complemented
356	C₅×#120	—	3	2	no	—
357	C₅×#120	—	3	2	no	—
358	C₅×#120	—	3	2	no	—
359	C₅×#120	—	3	2	no	—
360	C₅×#120	—	3	2	no	—
361	C₅×#120	C₂×D₃	1	2	yes	complemented
362	C₄×C₅×Q₈	—	3	1	no	—
363	C₄×C₅×Q₈	—	3	1	no	—
364	C₄×C₅×D₄	—	3	1	no	—
365	C₄×C₅×D₄	—	3	1	no	—
366	C₄×C₅×D₄	—	3	2	no	—
367	C₄×C₅×D₄	—	3	1	no	—
368	C₄×C₅×D₄	—	3	1	no	—
369	C₄×C₅×D₄	—	3	2	no	—
370	C₄×C₅×D₄	—	3	1	no	—
371	C₄×C₅×D₄	—	3	2	no	—
372	C₄×C₅×D₄	—	3	1	no	—
373	C₄×C₅×D₄	—	3	2	no	—
374	C₄×C₅×D₄	—	3	2	no	—
375	C₄×C₅×D₄	—	3	2	no	—
376	C₄×C₅×D₄	—	3	1	no	—
377	C₄×C₅×D₄	—	3	2	no	—
378	C₄×C₅×D₄	—	3	2	no	—
379	C₄×C₅×D₄	—	3	2	no	—
380	C₄×C₅×D₄	—	3	2	no	—
381	C₄×C₅×D₄	—	3	2	no	—
382	C₄×C₅×D₄	—	3	2	no	—
383	C₄×C₅×D₄	—	3	1	no	—
384	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
385	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
386	C₅×#117	—	3	1	no	—
387	C₅×#117	—	3	2	no	—
388	C₂×C₅×C₄⋊C₄	—	3	2	no	—
389	C₂×C₅×C₄⋊C₄	—	3	1	no	—
390	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
391	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
392	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
393	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
394	C₂×C₄²×C₅	—	3	2	no	—
395	C₂×C₄²×C₅	—	3	1	no	—
396	D₄×#41	—	3	1	no	Sylow
397	C₂³×C₃×C₅	—	2	4	no	—
398	C₂³×C₃×C₅	—	2	4	no	—
399	C₂³×C₃×C₅	—	4	2	no	—
400	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
401	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
402	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
403	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
404	C₂²×C₅×D₃	—	2	4	no	—
405	C₂²×C₅×D₃	—	2	2	no	—
406	C₂²×C₅×D₃	—	2	2	no	—
407	C₂²×C₅×D₃	—	2	2	no	—
408	C₂²×C₅×D₃	—	2	2	no	—
409	C₂²×C₅×D₃	—	2	4	no	—
410	C₂²×C₅×D₃	—	4	1	no	—
411	C₂²×C₅×D₃	—	4	1	no	—
412	C₂²×C₅×D₃	—	4	2	no	—
413	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
414	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
417	C₃×C₅×Q₈	—	2	2	no	—
418	C₃×C₅×D₄	—	2	4	no	—
419	C₃×C₅×D₄	—	2	4	no	—
420	C₃×C₅×D₄	—	2	2	no	—
421	C₃×C₅×D₄	—	2	2	no	—
422	C₃×C₅×D₄	—	4	2	no	—
423	C₃×C₅×D₄	C₂×D₄	1	4	yes	complemented
424	C₂×C₃×C₄×C₅	—	2	4	no	—
425	C₂×C₃×C₄×C₅	—	2	2	no	—
426	C₂×C₃×C₄×C₅	—	2	2	no	—
427	C₂×C₃×C₄×C₅	—	4	2	no	—
428	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
429	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
430	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
431	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
432	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
433	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
434	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
435	C₅×#67	—	2	4	no	—
436	C₅×#67	—	2	4	no	—
437	C₅×#67	—	2	4	no	—
438	C₅×#67	—	2	4	no	—
439	C₅×#67	—	2	4	no	—
440	C₅×#67	—	2	4	no	—
441	C₅×#67	—	2	4	no	—
442	C₅×#67	—	2	2	no	—
443	C₅×#67	—	2	4	no	—
444	C₅×#67	—	4	2	no	—
445	C₅×#67	C₂×D₄	1	8	yes	complemented
446	C₅×#67	#41	1	4	yes	complemented
447	C₂×C₅×Dic₃	—	2	4	no	—
448	C₂×C₅×Dic₃	—	2	4	no	—
449	C₂×C₅×Dic₃	—	2	2	no	—
450	C₂×C₅×Dic₃	—	2	2	no	—
451	C₂×C₅×Dic₃	—	2	4	no	—
452	C₂×C₅×Dic₃	—	2	4	no	—
453	C₂×C₅×Dic₃	—	2	4	no	—
454	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	complemented
455	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
456	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
457	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
458	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
459	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
460	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
461	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
462	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
463	C₅×D₁₂	—	2	4	no	—
464	C₅×D₁₂	—	2	2	no	—
465	C₅×D₁₂	—	2	2	no	—
466	C₅×D₁₂	—	4	2	no	—
467	C₄×C₅×D₃	—	2	2	no	—
468	C₄×C₅×D₃	—	2	2	no	—
469	C₄×C₅×D₃	—	2	2	no	—
470	C₄×C₅×D₃	—	2	2	no	—
471	C₄×C₅×D₃	—	2	2	no	—
472	C₄×C₅×D₃	—	2	4	no	—
473	C₄×C₅×D₃	—	2	4	no	—
474	C₄×C₅×D₃	—	2	2	no	—
475	C₄×C₅×D₃	—	2	4	no	—
476	C₄×C₅×D₃	—	2	2	no	—
477	C₄×C₅×D₃	—	4	1	no	—
478	C₄×C₅×D₃	C₂×D₄	1	4	yes	complemented
479	C₅×Dic₆	—	2	2	no	—
480	C₅×Dic₆	—	2	4	no	—
481	C₅×Dic₆	—	2	4	no	—
482	C₅×Dic₆	C₂×D₄	1	4	yes	complemented
483	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
484	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
485	C₂²×#67	C₂²×C₅	1	2	yes	—
486	C₂²×#67	C₂²×C₅	1	2	yes	complemented
487	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
488	D₃×#41	—	2	8	no	—
489	C₂×#239	C₂²×C₅	1	1	yes	characteristic, complemented
490	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
491	C₂×#237	—	2	8	no	—
492	C₂×#237	C₂²×C₅	1	1	yes	characteristic
493	C₂×#237	C₂²×C₅	1	2	yes	complemented
494	C₂×#237	C₂²×C₅	1	2	yes	complemented
495	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
496	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
497	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
498	C₂×#237	C₂²×C₅	1	2	yes	complemented
499	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
500	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
501	C₂×D₃×D₄	C₂²×C₅	1	2	yes	complemented
502	C₂×#235	C₂²×C₅	1	2	yes	complemented
503	C₂×#235	C₂²×C₅	1	1	yes	characteristic, complemented
504	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
505	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
506	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
507	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
508	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
509	C₃×#123	C₂²×C₅	1	2	yes	complemented
510	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
511	C₃×#121	C₂²×C₅	1	2	yes	complemented
512	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
513	C₃×#120	C₂²×C₅	1	2	yes	complemented
514	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
515	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
516	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
517	#953	C₂²×C₅	1	2	yes	complemented
518	#946	C₂²×C₅	1	1	yes	characteristic, complemented
519	#944	C₂²×C₅	1	1	yes	characteristic, complemented
520	#940	C₂²×C₅	1	1	yes	characteristic, complemented
521	#940	C₂²×C₅	1	2	yes	complemented
522	#939	C₂²×C₅	1	2	yes	complemented
523	#939	C₂²×C₅	1	2	yes	complemented
524	#939	C₂²×C₅	1	2	yes	complemented
525	#939	C₂²×C₅	1	2	yes	complemented
526	#938	C₂²×C₅	1	1	yes	characteristic, complemented
527	#937	C₂²×C₅	1	2	yes	complemented
528	#937	C₂²×C₅	1	2	yes	complemented
529	#935	C₂²×C₅	1	2	yes	complemented
530	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
531	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
532	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
533	#930	C₂²×C₅	1	2	yes	complemented
534	#930	C₂²×C₅	1	1	yes	characteristic, complemented
535	#929	C₂²×C₅	1	2	yes	complemented
536	C₄×#67	C₂²×C₅	1	1	yes	characteristic
537	C₄×#67	C₂²×C₅	1	2	yes	complemented
538	C₄×#67	C₂²×C₅	1	1	yes	characteristic, complemented
539	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
540	#924	C₂²×C₅	1	1	yes	characteristic, complemented
541	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
542	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
543	#897	C₂²×C₅	1	1	yes	characteristic, complemented
544	#896	C₂²×C₅	1	2	yes	complemented
545	#896	C₂²×C₅	1	2	yes	complemented
546	#895	C₂²×C₅	1	1	yes	characteristic, complemented
547	#894	C₂²×C₅	1	2	yes	complemented
548	#893	C₂²×C₅	1	1	yes	characteristic, complemented
549	#893	C₂²×C₅	1	2	yes	complemented
550	#892	C₂²×C₅	1	1	yes	characteristic, complemented
551	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
552	#888	C₂²×C₅	1	2	yes	complemented
553	#887	C₂²×C₅	1	1	yes	characteristic, complemented
554	#886	C₂²×C₅	1	2	yes	complemented
555	#885	C₂²×C₅	1	2	yes	complemented
556	#885	C₂²×C₅	1	2	yes	complemented
557	#884	C₂²×C₅	1	2	yes	complemented
558	#884	C₂²×C₅	1	2	yes	complemented
559	#884	C₂²×C₅	1	2	yes	complemented
560	#884	C₂²×C₅	1	2	yes	complemented
561	#883	C₂²×C₅	1	2	yes	complemented
562	#882	C₂²×C₅	1	2	yes	complemented
563	#882	C₂²×C₅	1	2	yes	complemented
564	#67⋊C₄	C₂²×C₅	1	2	yes	—
565	#67⋊C₄	C₂²×C₅	1	1	yes	characteristic
566	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
567	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
568	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
569	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
570	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
571	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
572	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
573	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
574	#67⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
575	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
576	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
577	#878	C₂²×C₅	1	2	yes	complemented
578	#878	C₂²×C₅	1	2	yes	complemented
579	#877	C₂²×C₅	1	2	yes	complemented
580	#875	C₂²×C₅	1	1	yes	characteristic, complemented
581	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
582	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
583	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
584	C₂⁴×C₅	—	3	1	no	—
585	C₂⁴×C₅	—	3	2	no	—
586	C₂⁴×C₅	—	3	1	no	—
587	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
588	C₅×#41	—	2	4	no	—
589	C₅×#41	—	3	8	no	—
590	C₅×#41	—	6	8	no	—
591	C₅×#41	—	6	4	no	—
592	C₅×#41	—	6	8	no	—
593	C₅×#41	—	6	8	no	—
594	C₅×#41	—	6	4	no	—
595	C₅×#41	—	6	4	no	—
596	C₅×#41	—	6	8	no	—
597	C₅×#41	—	6	4	no	—
598	C₅×#41	—	6	4	no	—
599	C₂×C₅×Q₈	—	3	1	no	—
600	C₂×C₅×Q₈	—	3	2	no	—
601	C₂×C₅×Q₈	—	3	2	no	—
602	C₂×C₅×Q₈	—	3	1	no	—
603	C₂×C₅×Q₈	—	6	4	no	—
604	C₂×C₅×Q₈	—	6	4	no	—
605	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
606	C₂×C₅×D₄	—	2	4	no	—
607	C₂×C₅×D₄	—	3	1	no	—
608	C₂×C₅×D₄	—	3	2	no	—
609	C₂×C₅×D₄	—	3	2	no	—
610	C₂×C₅×D₄	—	3	2	no	—
611	C₂×C₅×D₄	—	3	1	no	—
612	C₂×C₅×D₄	—	3	2	no	—
613	C₂×C₅×D₄	—	3	2	no	—
614	C₂×C₅×D₄	—	3	2	no	—
615	C₂×C₅×D₄	—	3	2	no	—
616	C₂×C₅×D₄	—	3	2	no	—
617	C₂×C₅×D₄	—	3	2	no	—
618	C₂×C₅×D₄	—	3	2	no	—
619	C₂×C₅×D₄	—	3	1	no	—
620	C₂×C₅×D₄	—	3	2	no	—
621	C₂×C₅×D₄	—	3	1	no	—
622	C₂×C₅×D₄	—	3	2	no	—
623	C₂×C₅×D₄	—	6	8	no	—
624	C₂×C₅×D₄	—	6	4	no	—
625	C₂×C₅×D₄	—	6	8	no	—
626	C₂×C₅×D₄	—	6	8	no	—
627	C₂×C₅×D₄	—	6	4	no	—
628	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
629	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
630	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
631	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
632	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
633	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
634	C₂²×C₄×C₅	—	3	2	no	—
635	C₂²×C₄×C₅	—	3	1	no	—
636	C₂²×C₄×C₅	—	3	2	no	—
637	C₂²×C₄×C₅	—	3	2	no	—
638	C₂²×C₄×C₅	—	3	1	no	—
639	C₂²×C₄×C₅	—	3	1	no	—
640	C₂²×C₄×C₅	—	3	2	no	—
641	C₂²×C₄×C₅	—	3	2	no	—
642	C₂²×C₄×C₅	—	3	2	no	—
643	C₂²×C₄×C₅	—	3	1	no	—
644	C₂²×C₄×C₅	—	3	1	no	—
645	C₂²×C₄×C₅	—	3	1	no	—
646	C₂²×C₄×C₅	—	3	1	no	—
647	C₂²×C₄×C₅	—	3	1	no	—
648	C₂²×C₄×C₅	—	3	2	no	—
649	C₂²×C₄×C₅	—	3	2	no	—
650	C₂²×C₄×C₅	—	3	1	no	—
651	C₂²×C₄×C₅	—	3	2	no	—
652	C₂²×C₄×C₅	—	3	1	no	—
653	C₂²×C₄×C₅	—	3	1	no	—
654	C₂²×C₄×C₅	—	6	8	no	—
655	C₂²×C₄×C₅	—	6	4	no	—
656	C₂²×C₄×C₅	—	6	4	no	—
657	C₂²×C₄×C₅	—	6	8	no	—
658	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
659	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
660	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
661	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
662	C₅×C₄⋊C₄	—	3	1	no	—
663	C₅×C₄⋊C₄	—	3	1	no	—
664	C₅×C₄⋊C₄	—	3	2	no	—
665	C₅×C₄⋊C₄	—	3	2	no	—
666	C₅×C₄⋊C₄	—	3	2	no	—
667	C₅×C₄⋊C₄	—	3	1	no	—
668	C₅×C₄⋊C₄	—	3	2	no	—
669	C₅×C₄⋊C₄	—	3	2	no	—
670	C₅×C₄⋊C₄	—	3	1	no	—
671	C₅×C₄⋊C₄	—	3	2	no	—
672	C₅×C₄⋊C₄	—	3	2	no	—
673	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
674	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
675	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
676	C₅×C₂²⋊C₄	—	3	1	no	—
677	C₅×C₂²⋊C₄	—	3	1	no	—
678	C₅×C₂²⋊C₄	—	3	2	no	—
679	C₅×C₂²⋊C₄	—	3	2	no	—
680	C₅×C₂²⋊C₄	—	3	2	no	—
681	C₅×C₂²⋊C₄	—	3	1	no	—
682	C₅×C₂²⋊C₄	—	3	1	no	—
683	C₅×C₂²⋊C₄	—	3	2	no	—
684	C₅×C₂²⋊C₄	—	3	1	no	—
685	C₅×C₂²⋊C₄	—	3	2	no	—
686	C₅×C₂²⋊C₄	—	3	2	no	—
687	C₅×C₂²⋊C₄	—	3	1	no	—
688	C₅×C₂²⋊C₄	—	3	2	no	—
689	C₅×C₂²⋊C₄	—	3	2	no	—
690	C₅×C₂²⋊C₄	—	3	2	no	—
691	C₅×C₂²⋊C₄	—	3	2	no	—
692	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
693	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
694	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
695	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
696	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
697	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
698	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
699	C₄²×C₅	—	3	1	no	—
700	C₄²×C₅	—	3	2	no	—
701	C₄²×C₅	—	3	1	no	—
702	C₄²×C₅	—	3	2	no	—
703	C₄²×C₅	—	3	2	no	—
704	C₄²×C₅	—	3	1	no	—
705	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
706	C₂²×#41	—	3	1	no	—
707	C₂²×#41	—	3	1	no	—
708	#550	—	3	1	no	—
709	D₄×Q₈	—	3	1	no	—
710	#548	—	3	1	no	—
711	#548	—	3	1	no	—
712	#547	—	3	1	no	—
713	#547	—	3	2	no	—
714	#546	—	3	2	no	—
715	#546	—	3	1	no	—
716	#546	—	3	2	no	—
717	#546	C₅×D₃	1	1	yes	characteristic, complemented
718	D₄²	—	3	1	no	—
719	D₄²	—	3	2	no	—
720	#532	—	3	1	no	—
721	#532	—	3	2	no	—
722	#525	—	3	2	no	—
723	#525	—	3	1	no	—
724	#525	—	3	1	no	—
725	#525	—	3	2	no	—
726	C₄×#41	—	3	1	no	—
727	C₂×C₄×D₄	—	3	1	no	—
728	C₂×C₄×D₄	—	3	2	no	—
729	C₂²×C₃×C₅	—	2	1	no	—
730	C₂²×C₃×C₅	—	2	2	no	—
731	C₂²×C₃×C₅	—	2	2	no	—
732	C₂²×C₃×C₅	—	2	1	no	—
733	C₂²×C₃×C₅	—	2	2	no	—
734	C₂²×C₃×C₅	—	2	1	no	—
735	C₂²×C₃×C₅	—	2	2	no	—
736	C₂²×C₃×C₅	—	2	1	no	—
737	C₂²×C₃×C₅	—	2	2	no	—
738	C₂²×C₃×C₅	—	2	1	no	—
739	C₂²×C₃×C₅	—	4	8	no	—
740	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
741	C₂²×C₃×C₅	C₂×#41	1	2	yes	complemented
742	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
743	C₂×C₅×D₃	—	2	1	no	—
744	C₂×C₅×D₃	—	2	1	no	—
745	C₂×C₅×D₃	—	2	1	no	—
746	C₂×C₅×D₃	—	2	1	no	—
747	C₂×C₅×D₃	—	2	2	no	—
748	C₂×C₅×D₃	—	2	1	no	—
749	C₂×C₅×D₃	—	2	1	no	—
750	C₂×C₅×D₃	—	2	2	no	—
751	C₂×C₅×D₃	—	2	1	no	—
752	C₂×C₅×D₃	—	2	2	no	—
753	C₂×C₅×D₃	—	4	4	no	—
754	C₂×C₅×D₃	—	4	8	no	—
755	C₂×C₅×D₃	—	4	4	no	—
756	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
757	C₂×C₅×D₃	C₂×#41	1	2	yes	complemented
758	C₃×C₄×C₅	—	2	1	no	—
759	C₃×C₄×C₅	—	2	2	no	—
760	C₃×C₄×C₅	—	2	1	no	—
761	C₃×C₄×C₅	—	2	1	no	—
762	C₃×C₄×C₅	—	2	1	no	—
763	C₃×C₄×C₅	—	2	2	no	—
764	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
765	C₅×Dic₃	—	2	1	no	—
766	C₅×Dic₃	—	2	2	no	—
767	C₅×Dic₃	—	2	1	no	—
768	C₅×Dic₃	—	2	2	no	—
769	C₅×Dic₃	—	2	1	no	—
770	C₅×Dic₃	C₂²×D₄	1	4	yes	—
771	C₅×Dic₃	C₂²×D₄	1	2	yes	—
772	C₅×Dic₃	C₂×#41	1	2	yes	complemented
773	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
774	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
775	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
776	C₂³×D₃	C₂³×C₅	1	2	yes	—
777	C₃×#41	—	2	4	no	—
778	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
779	C₂×C₃×D₄	—	2	4	no	—
780	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
781	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
782	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
783	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
784	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
785	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
786	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
787	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
788	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
789	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
790	C₂×#67	—	2	8	no	—
791	C₂×#67	—	2	8	no	—
792	C₂×#67	C₂³×C₅	1	2	yes	—
793	C₂×#67	C₂³×C₅	1	2	yes	—
794	C₂×#67	C₂³×C₅	1	2	yes	—
795	C₂×#67	C₂³×C₅	1	1	yes	characteristic
796	C₂×#67	C₂³×C₅	1	2	yes	—
797	C₂×#67	C₂³×C₅	1	2	yes	—
798	C₂×#67	C₂³×C₅	1	2	yes	—
799	C₂×#67	C₂³×C₅	1	2	yes	—
800	C₂×#67	C₂³×C₅	1	2	yes	—
801	C₂×#67	C₂³×C₅	1	2	yes	—
802	C₂×#67	C₂³×C₅	1	2	yes	—
803	C₂×#67	C₂³×C₅	1	1	yes	characteristic
804	C₂²×Dic₃	—	2	8	no	—
805	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
806	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
807	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
808	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
809	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
810	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
811	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
812	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
813	#239	—	2	4	no	—
814	D₃×Q₈	—	2	4	no	—
815	#237	—	2	4	no	—
816	#237	—	2	8	no	—
817	#237	—	2	8	no	—
818	#237	—	2	8	no	—
819	#237	—	2	4	no	—
820	#237	—	2	4	no	—
821	#237	C₅×D₄	1	8	yes	complemented
822	D₃×D₄	—	2	4	no	—
823	D₃×D₄	—	2	8	no	—
824	D₃×D₄	—	2	4	no	—
825	#235	—	2	8	no	—
826	#235	—	2	4	no	—
827	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
828	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
829	C₂×D₁₂	C₂³×C₅	1	2	yes	—
830	C₂×D₁₂	C₂³×C₅	1	2	yes	—
831	C₂×C₄×D₃	—	2	8	no	—
832	C₂×C₄×D₃	—	2	4	no	—
833	C₂×C₄×D₃	—	2	4	no	—
834	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
835	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
836	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
837	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
838	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
839	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
840	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
841	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
842	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
843	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
844	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
845	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
846	C₂×Dic₆	—	2	4	no	—
847	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
848	C₂×Dic₆	C₂³×C₅	1	2	yes	—
849	C₂×Dic₆	C₂³×C₅	1	2	yes	—
850	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
851	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
852	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
853	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
854	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
855	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
856	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
857	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
858	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
859	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
860	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
861	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
862	#217	C₂³×C₅	1	2	yes	—
863	#217	C₂³×C₅	1	1	yes	characteristic
864	#217	C₂³×C₅	1	2	yes	—
865	#217	C₂³×C₅	1	1	yes	characteristic
866	#217	C₂³×C₅	1	2	yes	—
867	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
868	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
869	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
870	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
871	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
872	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
873	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
874	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
875	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
876	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
877	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
878	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
879	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
880	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
881	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
882	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
883	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
884	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
885	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
886	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
887	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
888	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
889	C₄×Dic₃	C₂³×C₅	1	2	yes	—
890	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
891	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
892	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
893	C₄×Dic₃	C₂³×C₅	1	2	yes	—
894	C₄×Dic₃	C₂³×C₅	1	2	yes	—
895	C₂³×C₅	—	2	4	no	—
896	C₂³×C₅	—	2	4	no	—
897	C₂³×C₅	—	3	1	no	—
898	C₂³×C₅	—	3	1	no	—
899	C₂³×C₅	—	3	2	no	—
900	C₂³×C₅	—	3	1	no	—
901	C₂³×C₅	—	4	2	no	—
902	C₂³×C₅	—	6	2	no	—
903	C₂³×C₅	—	6	2	no	—
904	C₂³×C₅	—	6	4	no	—
905	C₂³×C₅	—	6	2	no	—
906	C₂³×C₅	—	6	4	no	—
907	C₂³×C₅	—	6	2	no	—
908	C₂³×C₅	—	12	2	no	—
909	C₂³×C₅	—	12	1	no	—
910	C₂³×C₅	—	12	1	no	—
911	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
912	C₂³×C₅	C₂³×D₃	1	2	yes	—
913	C₂³×C₅	C₂³×D₃	1	2	yes	—
914	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
915	C₅×Q₈	—	2	2	no	—
916	C₅×Q₈	—	3	4	no	—
917	C₅×Q₈	—	6	4	no	—
918	C₅×Q₈	—	6	4	no	—
919	C₅×Q₈	—	6	2	no	—
920	C₅×D₄	—	2	4	no	—
921	C₅×D₄	—	2	4	no	—
922	C₅×D₄	—	2	2	no	—
923	C₅×D₄	—	2	2	no	—
924	C₅×D₄	—	3	8	no	—
925	C₅×D₄	—	3	4	no	—
926	C₅×D₄	—	4	2	no	—
927	C₅×D₄	—	6	2	no	—
928	C₅×D₄	—	6	4	no	—
929	C₅×D₄	—	6	2	no	—
930	C₅×D₄	—	6	4	no	—
931	C₅×D₄	—	6	4	no	—
932	C₅×D₄	—	6	4	no	—
933	C₅×D₄	—	6	4	no	—
934	C₅×D₄	—	6	4	no	—
935	C₅×D₄	—	6	4	no	—
936	C₅×D₄	—	6	4	no	—
937	C₅×D₄	—	6	4	no	—
938	C₅×D₄	—	6	2	no	—
939	C₅×D₄	—	12	2	no	—
940	C₅×D₄	—	12	2	no	—
941	C₅×D₄	D₃×D₄	1	4	yes	complemented
942	C₂×C₄×C₅	—	2	4	no	—
943	C₂×C₄×C₅	—	2	2	no	—
944	C₂×C₄×C₅	—	2	2	no	—
945	C₂×C₄×C₅	—	3	8	no	—
946	C₂×C₄×C₅	—	3	1	no	—
947	C₂×C₄×C₅	—	3	1	no	—
948	C₂×C₄×C₅	—	3	2	no	—
949	C₂×C₄×C₅	—	3	4	no	—
950	C₂×C₄×C₅	—	3	2	no	—
951	C₂×C₄×C₅	—	3	1	no	—
952	C₂×C₄×C₅	—	3	1	no	—
953	C₂×C₄×C₅	—	3	1	no	—
954	C₂×C₄×C₅	—	3	2	no	—
955	C₂×C₄×C₅	—	4	2	no	—
956	C₂×C₄×C₅	—	6	2	no	—
957	C₂×C₄×C₅	—	6	4	no	—
958	C₂×C₄×C₅	—	6	4	no	—
959	C₂×C₄×C₅	—	6	2	no	—
960	C₂×C₄×C₅	—	6	4	no	—
961	C₂×C₄×C₅	—	6	2	no	—
962	C₂×C₄×C₅	—	6	2	no	—
963	C₂×C₄×C₅	—	6	2	no	—
964	C₂×C₄×C₅	—	6	2	no	—
965	C₂×C₄×C₅	—	6	4	no	—
966	C₂×C₄×C₅	—	6	2	no	—
967	C₂×C₄×C₅	—	6	4	no	—
968	C₂×C₄×C₅	—	6	4	no	—
969	C₂×C₄×C₅	—	6	4	no	—
970	C₂×C₄×C₅	—	6	4	no	—
971	C₂×C₄×C₅	—	6	2	no	—
972	C₂×C₄×C₅	—	6	2	no	—
973	C₂×C₄×C₅	—	12	1	no	—
974	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
975	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
976	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
977	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
978	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
979	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
980	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
981	C₂×#41	—	3	1	no	—
982	C₂×#41	—	3	1	no	—
983	C₂×#41	—	3	2	no	—
984	C₂×#41	—	3	2	no	—
985	C₂×#41	—	3	1	no	—
986	C₂×#41	—	3	1	no	—
987	C₂×#41	—	3	2	no	—
988	C₂×#41	—	3	1	no	—
989	C₂×#41	—	3	2	no	—
990	C₂×#41	—	3	1	no	—
991	C₂×#41	—	6	8	no	—
992	C₂×#41	—	6	8	no	—
993	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
994	C₂²×Q₈	—	3	1	no	—
995	C₂²×Q₈	—	3	1	no	—
996	C₂²×D₄	—	3	2	no	—
997	C₂²×D₄	—	3	2	no	—
998	C₂²×D₄	—	3	1	no	—
999	C₂²×D₄	—	3	2	no	—
1000	C₂²×D₄	—	3	1	no	—
1001	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
1002	C₂³×C₄	—	3	2	no	—
1003	C₂³×C₄	—	3	2	no	—
1004	C₂³×C₄	—	3	1	no	—
1005	C₂³×C₄	—	3	1	no	—
1006	C₄⋊Q₈	—	3	1	no	—
1007	C₄⋊Q₈	—	3	2	no	—
1008	#127	—	3	2	no	—
1009	#127	—	3	1	no	—
1010	#124	—	3	2	no	—
1011	#124	—	3	2	no	—
1012	#124	—	3	1	no	—
1013	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
1014	#123	—	3	2	no	—
1015	#123	—	3	2	no	—
1016	#123	—	3	2	no	—
1017	#123	—	3	2	no	—
1018	#123	—	3	2	no	—
1019	#123	C₂×C₅×D₃	1	2	yes	complemented
1020	C₂²⋊Q₈	—	3	1	no	—
1021	C₂²⋊Q₈	—	3	1	no	—
1022	C₂²⋊Q₈	—	3	2	no	—
1023	C₂²⋊Q₈	—	3	1	no	—
1024	C₂²⋊Q₈	—	3	2	no	—
1025	C₂²⋊Q₈	—	3	2	no	—
1026	C₂²⋊Q₈	—	3	2	no	—
1027	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
1028	#121	—	3	1	no	—
1029	#121	—	3	2	no	—
1030	#121	—	3	2	no	—
1031	#121	—	3	2	no	—
1032	#121	—	3	2	no	—
1033	#121	—	3	1	no	—
1034	#121	—	3	2	no	—
1035	#121	—	3	1	no	—
1036	#121	—	3	2	no	—
1037	#121	—	3	2	no	—
1038	#121	—	3	2	no	—
1039	#121	—	3	2	no	—
1040	#121	C₂×C₅×D₃	1	1	yes	characteristic, complemented
1041	#121	C₂×C₅×D₃	1	2	yes	complemented
1042	#120	—	3	2	no	—
1043	#120	—	3	2	no	—
1044	#120	—	3	2	no	—
1045	#120	—	3	2	no	—
1046	#120	—	3	2	no	—
1047	#120	C₂×C₅×D₃	1	2	yes	complemented
1048	C₄×Q₈	—	3	1	no	—
1049	C₄×Q₈	—	3	1	no	—
1050	C₄×D₄	—	3	1	no	—
1051	C₄×D₄	—	3	1	no	—
1052	C₄×D₄	—	3	2	no	—
1053	C₄×D₄	—	3	1	no	—
1054	C₄×D₄	—	3	1	no	—
1055	C₄×D₄	—	3	2	no	—
1056	C₄×D₄	—	3	1	no	—
1057	C₄×D₄	—	3	2	no	—
1058	C₄×D₄	—	3	1	no	—
1059	C₄×D₄	—	3	2	no	—
1060	C₄×D₄	—	3	2	no	—
1061	C₄×D₄	—	3	1	no	—
1062	C₄×D₄	—	3	2	no	—
1063	C₄×D₄	—	3	2	no	—
1064	C₄×D₄	—	3	2	no	—
1065	C₄×D₄	—	3	2	no	—
1066	C₄×D₄	—	3	2	no	—
1067	C₄×D₄	—	3	2	no	—
1068	C₄×D₄	—	3	2	no	—
1069	C₄×D₄	—	3	1	no	—
1070	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
1071	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
1072	#117	—	3	1	no	—
1073	#117	—	3	2	no	—
1074	C₂×C₄⋊C₄	—	3	2	no	—
1075	C₂×C₄⋊C₄	—	3	1	no	—
1076	C₂×C₂²⋊C₄	—	3	2	no	—
1077	C₂×C₂²⋊C₄	—	3	1	no	—
1078	C₂×C₂²⋊C₄	—	3	1	no	—
1079	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
1080	C₂×C₄²	—	3	2	no	—
1081	C₂×C₄²	—	3	1	no	—
1082	C₂×C₃×C₅	—	2	2	no	—
1083	C₂×C₃×C₅	—	2	4	no	—
1084	C₂×C₃×C₅	—	4	1	no	—
1085	C₂×C₃×C₅	—	4	2	no	—
1086	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
1087	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
1088	C₂×C₃×C₅	#585	1	1	yes	characteristic
1089	C₅×D₃	—	2	2	no	—
1090	C₅×D₃	—	2	2	no	—
1091	C₅×D₃	—	4	2	no	—
1092	C₅×D₃	—	4	1	no	—
1093	C₂³×C₃	—	2	4	no	—
1094	C₂³×C₃	—	2	4	no	—
1095	C₂³×C₃	—	4	2	no	—
1096	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
1097	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
1098	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
1099	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
1100	C₂²×D₃	—	2	4	no	—
1101	C₂²×D₃	—	2	2	no	—
1102	C₂²×D₃	—	2	2	no	—
1103	C₂²×D₃	—	2	2	no	—
1104	C₂²×D₃	—	2	2	no	—
1105	C₂²×D₃	—	2	4	no	—
1106	C₂²×D₃	—	4	1	no	—
1107	C₂²×D₃	—	4	1	no	—
1108	C₂²×D₃	—	4	2	no	—
1109	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
1110	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
1111	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
1112	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
1113	C₃×Q₈	—	2	2	no	—
1114	C₃×D₄	—	2	4	no	—
1115	C₃×D₄	—	2	4	no	—
1116	C₃×D₄	—	2	2	no	—
1117	C₃×D₄	—	2	2	no	—
1118	C₃×D₄	—	4	2	no	—
1119	C₃×D₄	C₂×C₅×D₄	1	4	yes	complemented
1120	C₂×C₃×C₄	—	2	4	no	—
1121	C₂×C₃×C₄	—	2	2	no	—
1122	C₂×C₃×C₄	—	2	2	no	—
1123	C₂×C₃×C₄	—	4	2	no	—
1124	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1125	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1126	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1127	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1128	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1129	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1130	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1131	#67	—	2	4	no	—
1132	#67	—	2	4	no	—
1133	#67	—	2	4	no	—
1134	#67	—	2	4	no	—
1135	#67	—	2	4	no	—
1136	#67	—	2	4	no	—
1137	#67	—	2	4	no	—
1138	#67	—	2	2	no	—
1139	#67	—	2	4	no	—
1140	#67	—	4	2	no	—
1141	#67	C₂×C₅×D₄	1	8	yes	complemented
1142	#67	C₅×#41	1	4	yes	complemented
1143	C₂×Dic₃	—	2	4	no	—
1144	C₂×Dic₃	—	2	4	no	—
1145	C₂×Dic₃	—	2	2	no	—
1146	C₂×Dic₃	—	2	2	no	—
1147	C₂×Dic₃	—	2	4	no	—
1148	C₂×Dic₃	—	2	4	no	—
1149	C₂×Dic₃	—	2	4	no	—
1150	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	complemented
1151	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1152	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1153	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1154	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1155	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1156	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1157	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1158	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1159	D₁₂	—	2	4	no	—
1160	D₁₂	—	2	2	no	—
1161	D₁₂	—	2	2	no	—
1162	D₁₂	—	4	2	no	—
1163	C₄×D₃	—	2	2	no	—
1164	C₄×D₃	—	2	2	no	—
1165	C₄×D₃	—	2	2	no	—
1166	C₄×D₃	—	2	2	no	—
1167	C₄×D₃	—	2	2	no	—
1168	C₄×D₃	—	2	4	no	—
1169	C₄×D₃	—	2	4	no	—
1170	C₄×D₃	—	2	2	no	—
1171	C₄×D₃	—	2	4	no	—
1172	C₄×D₃	—	2	2	no	—
1173	C₄×D₃	—	4	1	no	—
1174	C₄×D₃	C₂×C₅×D₄	1	4	yes	complemented
1175	Dic₆	—	2	2	no	—
1176	Dic₆	—	2	4	no	—
1177	Dic₆	—	2	4	no	—
1178	Dic₆	C₂×C₅×D₄	1	4	yes	complemented
1179	C₂²×C₅	—	2	1	no	—
1180	C₂²×C₅	—	2	2	no	—
1181	C₂²×C₅	—	2	2	no	—
1182	C₂²×C₅	—	2	1	no	—
1183	C₂²×C₅	—	2	1	no	—
1184	C₂²×C₅	—	2	2	no	—
1185	C₂²×C₅	—	2	1	no	—
1186	C₂²×C₅	—	2	2	no	—
1187	C₂²×C₅	—	2	1	no	—
1188	C₂²×C₅	—	2	2	no	—
1189	C₂²×C₅	—	3	2	no	—
1190	C₂²×C₅	—	3	2	no	—
1191	C₂²×C₅	—	4	8	no	—
1192	C₂²×C₅	—	6	1	no	—
1193	C₂²×C₅	—	6	1	no	—
1194	C₂²×C₅	—	6	1	no	—
1195	C₂²×C₅	—	6	1	no	—
1196	C₂²×C₅	—	6	2	no	—
1197	C₂²×C₅	—	6	1	no	—
1198	C₂²×C₅	—	6	1	no	—
1199	C₂²×C₅	—	6	2	no	—
1200	C₂²×C₅	—	6	1	no	—
1201	C₂²×C₅	—	6	2	no	—
1202	C₂²×C₅	—	12	4	no	—
1203	C₂²×C₅	—	12	8	no	—
1204	C₂²×C₅	—	12	4	no	—
1205	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
1206	C₂²×C₅	D₃×#41	1	2	yes	complemented
1207	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1208	C₄×C₅	—	2	1	no	—
1209	C₄×C₅	—	2	1	no	—
1210	C₄×C₅	—	2	2	no	—
1211	C₄×C₅	—	2	1	no	—
1212	C₄×C₅	—	2	1	no	—
1213	C₄×C₅	—	2	2	no	—
1214	C₄×C₅	—	3	2	no	—
1215	C₄×C₅	—	3	4	no	—
1216	C₄×C₅	—	3	2	no	—
1217	C₄×C₅	—	6	1	no	—
1218	C₄×C₅	—	6	1	no	—
1219	C₄×C₅	—	6	2	no	—
1220	C₄×C₅	—	6	2	no	—
1221	C₄×C₅	—	6	1	no	—
1222	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
1223	C₂⁴	—	3	1	no	—
1224	C₂⁴	—	3	2	no	—
1225	C₂⁴	—	3	1	no	—
1226	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
1227	#41	—	2	4	no	—
1228	#41	—	3	8	no	—
1229	#41	—	6	8	no	—
1230	#41	—	6	4	no	—
1231	#41	—	6	8	no	—
1232	#41	—	6	8	no	—
1233	#41	—	6	4	no	—
1234	#41	—	6	4	no	—
1235	#41	—	6	8	no	—
1236	#41	—	6	4	no	—
1237	#41	—	6	4	no	—
1238	C₂×Q₈	—	3	1	no	—
1239	C₂×Q₈	—	3	2	no	—
1240	C₂×Q₈	—	3	2	no	—
1241	C₂×Q₈	—	3	1	no	—
1242	C₂×Q₈	—	6	4	no	—
1243	C₂×Q₈	—	6	4	no	—
1244	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
1245	C₂×D₄	—	2	4	no	—
1246	C₂×D₄	—	3	1	no	—
1247	C₂×D₄	—	3	2	no	—
1248	C₂×D₄	—	3	2	no	—
1249	C₂×D₄	—	3	2	no	—
1250	C₂×D₄	—	3	1	no	—
1251	C₂×D₄	—	3	2	no	—
1252	C₂×D₄	—	3	2	no	—
1253	C₂×D₄	—	3	2	no	—
1254	C₂×D₄	—	3	2	no	—
1255	C₂×D₄	—	3	2	no	—
1256	C₂×D₄	—	3	2	no	—
1257	C₂×D₄	—	3	2	no	—
1258	C₂×D₄	—	3	1	no	—
1259	C₂×D₄	—	3	2	no	—
1260	C₂×D₄	—	3	1	no	—
1261	C₂×D₄	—	3	2	no	—
1262	C₂×D₄	—	6	8	no	—
1263	C₂×D₄	—	6	4	no	—
1264	C₂×D₄	—	6	8	no	—
1265	C₂×D₄	—	6	8	no	—
1266	C₂×D₄	—	6	4	no	—
1267	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1268	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
1269	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
1270	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1271	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
1272	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1273	C₂²×C₄	—	3	2	no	—
1274	C₂²×C₄	—	3	1	no	—
1275	C₂²×C₄	—	3	2	no	—
1276	C₂²×C₄	—	3	2	no	—
1277	C₂²×C₄	—	3	1	no	—
1278	C₂²×C₄	—	3	1	no	—
1279	C₂²×C₄	—	3	2	no	—
1280	C₂²×C₄	—	3	2	no	—
1281	C₂²×C₄	—	3	2	no	—
1282	C₂²×C₄	—	3	1	no	—
1283	C₂²×C₄	—	3	1	no	—
1284	C₂²×C₄	—	3	1	no	—
1285	C₂²×C₄	—	3	1	no	—
1286	C₂²×C₄	—	3	1	no	—
1287	C₂²×C₄	—	3	2	no	—
1288	C₂²×C₄	—	3	2	no	—
1289	C₂²×C₄	—	3	1	no	—
1290	C₂²×C₄	—	3	2	no	—
1291	C₂²×C₄	—	3	1	no	—
1292	C₂²×C₄	—	3	1	no	—
1293	C₂²×C₄	—	6	8	no	—
1294	C₂²×C₄	—	6	4	no	—
1295	C₂²×C₄	—	6	4	no	—
1296	C₂²×C₄	—	6	8	no	—
1297	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1298	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1299	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1300	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1301	C₄⋊C₄	—	3	1	no	—
1302	C₄⋊C₄	—	3	1	no	—
1303	C₄⋊C₄	—	3	2	no	—
1304	C₄⋊C₄	—	3	2	no	—
1305	C₄⋊C₄	—	3	2	no	—
1306	C₄⋊C₄	—	3	1	no	—
1307	C₄⋊C₄	—	3	2	no	—
1308	C₄⋊C₄	—	3	2	no	—
1309	C₄⋊C₄	—	3	1	no	—
1310	C₄⋊C₄	—	3	2	no	—
1311	C₄⋊C₄	—	3	2	no	—
1312	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1313	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1314	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1315	C₂²⋊C₄	—	3	1	no	—
1316	C₂²⋊C₄	—	3	1	no	—
1317	C₂²⋊C₄	—	3	2	no	—
1318	C₂²⋊C₄	—	3	2	no	—
1319	C₂²⋊C₄	—	3	2	no	—
1320	C₂²⋊C₄	—	3	1	no	—
1321	C₂²⋊C₄	—	3	1	no	—
1322	C₂²⋊C₄	—	3	2	no	—
1323	C₂²⋊C₄	—	3	1	no	—
1324	C₂²⋊C₄	—	3	2	no	—
1325	C₂²⋊C₄	—	3	2	no	—
1326	C₂²⋊C₄	—	3	1	no	—
1327	C₂²⋊C₄	—	3	2	no	—
1328	C₂²⋊C₄	—	3	2	no	—
1329	C₂²⋊C₄	—	3	2	no	—
1330	C₂²⋊C₄	—	3	2	no	—
1331	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1332	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1333	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1334	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1335	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1336	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1337	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1338	C₄²	—	3	1	no	—
1339	C₄²	—	3	2	no	—
1340	C₄²	—	3	1	no	—
1341	C₄²	—	3	2	no	—
1342	C₄²	—	3	2	no	—
1343	C₄²	—	3	1	no	—
1344	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1345	C₃×C₅	D₄×#41	1	1	yes	characteristic, complemented, Hall
1346	C₂²×C₃	—	2	1	no	—
1347	C₂²×C₃	—	2	2	no	—
1348	C₂²×C₃	—	2	2	no	—
1349	C₂²×C₃	—	2	1	no	—
1350	C₂²×C₃	—	2	2	no	—
1351	C₂²×C₃	—	2	1	no	—
1352	C₂²×C₃	—	2	2	no	—
1353	C₂²×C₃	—	2	1	no	—
1354	C₂²×C₃	—	2	2	no	—
1355	C₂²×C₃	—	2	1	no	—
1356	C₂²×C₃	—	4	8	no	—
1357	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
1358	C₂²×C₃	C₂×C₅×#41	1	2	yes	complemented
1359	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1360	C₂×D₃	—	2	1	no	—
1361	C₂×D₃	—	2	1	no	—
1362	C₂×D₃	—	2	1	no	—
1363	C₂×D₃	—	2	1	no	—
1364	C₂×D₃	—	2	2	no	—
1365	C₂×D₃	—	2	1	no	—
1366	C₂×D₃	—	2	1	no	—
1367	C₂×D₃	—	2	2	no	—
1368	C₂×D₃	—	2	1	no	—
1369	C₂×D₃	—	2	2	no	—
1370	C₂×D₃	—	4	4	no	—
1371	C₂×D₃	—	4	8	no	—
1372	C₂×D₃	—	4	4	no	—
1373	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
1374	C₂×D₃	C₂×C₅×#41	1	2	yes	complemented
1375	C₃×C₄	—	2	1	no	—
1376	C₃×C₄	—	2	2	no	—
1377	C₃×C₄	—	2	1	no	—
1378	C₃×C₄	—	2	1	no	—
1379	C₃×C₄	—	2	1	no	—
1380	C₃×C₄	—	2	2	no	—
1381	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
1382	Dic₃	—	2	1	no	—
1383	Dic₃	—	2	2	no	—
1384	Dic₃	—	2	1	no	—
1385	Dic₃	—	2	2	no	—
1386	Dic₃	—	2	1	no	—
1387	Dic₃	C₂²×C₅×D₄	1	4	yes	—
1388	Dic₃	C₂²×C₅×D₄	1	2	yes	—
1389	Dic₃	C₂×C₅×#41	1	2	yes	complemented
1390	C₂×C₅	—	2	2	no	—
1391	C₂×C₅	—	2	4	no	—
1392	C₂×C₅	—	4	2	no	—
1393	C₂×C₅	—	4	1	no	—
1394	C₂×C₅	—	6	2	no	—
1395	C₂×C₅	—	6	2	no	—
1396	C₂×C₅	—	12	2	no	—
1397	C₂×C₅	—	12	1	no	—
1398	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
1399	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1400	C₂×C₅	#5966	1	1	yes	characteristic
1401	C₂³	—	2	4	no	—
1402	C₂³	—	2	4	no	—
1403	C₂³	—	3	1	no	—
1404	C₂³	—	3	1	no	—
1405	C₂³	—	3	2	no	—
1406	C₂³	—	3	1	no	—
1407	C₂³	—	4	2	no	—
1408	C₂³	—	6	2	no	—
1409	C₂³	—	6	2	no	—
1410	C₂³	—	6	4	no	—
1411	C₂³	—	6	2	no	—
1412	C₂³	—	6	4	no	—
1413	C₂³	—	6	2	no	—
1414	C₂³	—	12	2	no	—
1415	C₂³	—	12	1	no	—
1416	C₂³	—	12	1	no	—
1417	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1418	C₂³	C₂³×C₅×D₃	1	2	yes	—
1419	C₂³	C₂³×C₅×D₃	1	2	yes	—
1420	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1421	Q₈	—	2	2	no	—
1422	Q₈	—	3	4	no	—
1423	Q₈	—	6	4	no	—
1424	Q₈	—	6	4	no	—
1425	Q₈	—	6	2	no	—
1426	D₄	—	2	4	no	—
1427	D₄	—	2	4	no	—
1428	D₄	—	2	2	no	—
1429	D₄	—	2	2	no	—
1430	D₄	—	3	8	no	—
1431	D₄	—	3	4	no	—
1432	D₄	—	4	2	no	—
1433	D₄	—	6	4	no	—
1434	D₄	—	6	2	no	—
1435	D₄	—	6	4	no	—
1436	D₄	—	6	4	no	—
1437	D₄	—	6	2	no	—
1438	D₄	—	6	4	no	—
1439	D₄	—	6	4	no	—
1440	D₄	—	6	4	no	—
1441	D₄	—	6	4	no	—
1442	D₄	—	6	4	no	—
1443	D₄	—	6	4	no	—
1444	D₄	—	6	2	no	—
1445	D₄	—	12	2	no	—
1446	D₄	—	12	2	no	—
1447	D₄	C₅×D₃×D₄	1	4	yes	complemented
1448	C₂×C₄	—	2	4	no	—
1449	C₂×C₄	—	2	2	no	—
1450	C₂×C₄	—	2	2	no	—
1451	C₂×C₄	—	3	8	no	—
1452	C₂×C₄	—	3	1	no	—
1453	C₂×C₄	—	3	1	no	—
1454	C₂×C₄	—	3	2	no	—
1455	C₂×C₄	—	3	4	no	—
1456	C₂×C₄	—	3	2	no	—
1457	C₂×C₄	—	3	1	no	—
1458	C₂×C₄	—	3	1	no	—
1459	C₂×C₄	—	3	1	no	—
1460	C₂×C₄	—	3	2	no	—
1461	C₂×C₄	—	4	2	no	—
1462	C₂×C₄	—	6	2	no	—
1463	C₂×C₄	—	6	4	no	—
1464	C₂×C₄	—	6	4	no	—
1465	C₂×C₄	—	6	2	no	—
1466	C₂×C₄	—	6	4	no	—
1467	C₂×C₄	—	6	2	no	—
1468	C₂×C₄	—	6	2	no	—
1469	C₂×C₄	—	6	2	no	—
1470	C₂×C₄	—	6	2	no	—
1471	C₂×C₄	—	6	4	no	—
1472	C₂×C₄	—	6	2	no	—
1473	C₂×C₄	—	6	4	no	—
1474	C₂×C₄	—	6	4	no	—
1475	C₂×C₄	—	6	4	no	—
1476	C₂×C₄	—	6	4	no	—
1477	C₂×C₄	—	6	2	no	—
1478	C₂×C₄	—	6	2	no	—
1479	C₂×C₄	—	12	1	no	—
1480	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1481	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1482	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1483	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1484	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1485	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1486	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1487	C₂×C₃	—	2	2	no	—
1488	C₂×C₃	—	2	4	no	—
1489	C₂×C₃	—	4	1	no	—
1490	C₂×C₃	—	4	2	no	—
1491	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
1492	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1493	C₂×C₃	C₅×#585	1	1	yes	characteristic
1494	D₃	—	2	2	no	—
1495	D₃	—	2	2	no	—
1496	D₃	—	4	2	no	—
1497	D₃	—	4	1	no	—
1498	C₅	#86626	1	1	yes	characteristic, direct product factor, Sylow
1499	C₂²	—	2	1	no	—
1500	C₂²	—	2	2	no	—
1501	C₂²	—	2	2	no	—
1502	C₂²	—	2	1	no	—
1503	C₂²	—	2	1	no	—
1504	C₂²	—	2	2	no	—
1505	C₂²	—	2	1	no	—
1506	C₂²	—	2	2	no	—
1507	C₂²	—	2	1	no	—
1508	C₂²	—	2	2	no	—
1509	C₂²	—	3	2	no	—
1510	C₂²	—	3	2	no	—
1511	C₂²	—	4	8	no	—
1512	C₂²	—	6	1	no	—
1513	C₂²	—	6	1	no	—
1514	C₂²	—	6	1	no	—
1515	C₂²	—	6	1	no	—
1516	C₂²	—	6	2	no	—
1517	C₂²	—	6	1	no	—
1518	C₂²	—	6	1	no	—
1519	C₂²	—	6	2	no	—
1520	C₂²	—	6	1	no	—
1521	C₂²	—	6	2	no	—
1522	C₂²	—	12	4	no	—
1523	C₂²	—	12	8	no	—
1524	C₂²	—	12	4	no	—
1525	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
1526	C₂²	C₅×D₃×#41	1	2	yes	complemented
1527	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1528	C₄	—	2	1	no	—
1529	C₄	—	2	1	no	—
1530	C₄	—	2	2	no	—
1531	C₄	—	2	1	no	—
1532	C₄	—	2	1	no	—
1533	C₄	—	2	2	no	—
1534	C₄	—	3	2	no	—
1535	C₄	—	3	4	no	—
1536	C₄	—	3	2	no	—
1537	C₄	—	6	1	no	—
1538	C₄	—	6	1	no	—
1539	C₄	—	6	2	no	—
1540	C₄	—	6	2	no	—
1541	C₄	—	6	1	no	—
1542	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
1543	C₃	C₅×D₄×#41	1	1	yes	characteristic, complemented, Sylow
1544	C₂	—	2	2	no	—
1545	C₂	—	2	4	no	—
1546	C₂	—	4	2	no	—
1547	C₂	—	4	1	no	—
1548	C₂	—	6	2	no	—
1549	C₂	—	6	2	no	—
1550	C₂	—	12	2	no	—
1551	C₂	—	12	1	no	—
1552	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
1553	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1554	C₂	C₅×#5966	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#546	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#546	D₃
hypocenter	C₃	C₅×D₄×#41
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅×D₃×#41	C₂	semidirect
2. C₂²×C₅×#237	C₂	semidirect
3. C₃×C₅×#546	C₂	semidirect
4. C₅×#5824	C₂	semidirect
5. C₅×D₄×#67	C₂	semidirect
6. C₅×#5677	C₂	semidirect
7. C₅×#5668	C₂	semidirect
8. C₅×#5656	C₂	semidirect
9. C₅×#5655	C₂	semidirect
10. C₅×#5632	C₂	semidirect
11. C₅×#5627	C₂	semidirect
12. C₅×#5610	C₂	semidirect
13. C₅×#5606	C₂	semidirect
14. C₅×#5599	C₂	semidirect
15. C₅×#5596	C₂	semidirect
16. C₅×#5590	C₂	semidirect
17. C₅×#5586	C₂	semidirect
18. C₅×#5554	C₂	semidirect
19. C₅×#5552	C₂	semidirect
20. C₄×C₅×D₃×D₄	C₂	semidirect
21. C₄×C₅×#237	C₂	semidirect
22. C₅×#5490	C₂	semidirect
23. C₂×C₅×#67⋊C₄	C₂	semidirect
25. C₂×C₃×C₅×#41	C₂²	semidirect
26. C₂²×C₃×C₅×D₄	C₂²	semidirect
28. C₂²×C₅×#67	C₂²	semidirect
29. C₂³×C₅×Dic₃	C₂²	semidirect
31. C₂×C₅×#239	C₂²	semidirect
32. C₂×C₅×D₃×Q₈	C₂²	semidirect
35. C₂×C₅×#237	C₂²	semidirect
36. C₂×C₅×#237	C₂²	semidirect
37. C₂×C₅×#237	C₂²	semidirect
38. C₂×C₅×#237	C₂²	semidirect
39. C₂×C₅×#237	C₂²	semidirect
40. C₂×C₅×#237	C₂²	semidirect
42. C₂×C₅×D₃×D₄	C₂²	semidirect
43. C₂×C₅×D₃×D₄	C₂²	semidirect
44. C₂×C₅×#235	C₂²	semidirect
45. C₂×C₅×#235	C₂²	semidirect
46. C₂²×C₄×C₅×D₃	C₂²	semidirect
47. C₂²×C₄×C₅×D₃	C₂²	semidirect
48. C₂²×C₄×C₅×D₃	C₂²	semidirect
49. C₂²×C₅×Dic₆	C₂²	semidirect
50. C₃×C₅×#124	C₂²	semidirect
51. C₃×C₅×#123	C₂²	semidirect
52. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
53. C₃×C₅×#121	C₂²	semidirect
54. C₃×C₅×#121	C₂²	semidirect
55. C₃×C₅×#120	C₂²	semidirect
56. C₃×C₄×C₅×D₄	C₂²	semidirect
57. C₃×C₄×C₅×D₄	C₂²	semidirect
58. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
59. C₅×#953	C₂²	semidirect
60. C₅×#946	C₂²	semidirect
61. C₅×#944	C₂²	semidirect
62. C₅×#940	C₂²	semidirect
63. C₅×#940	C₂²	semidirect
64. C₅×#939	C₂²	semidirect
65. C₅×#939	C₂²	semidirect
66. C₅×#939	C₂²	semidirect
67. C₅×#939	C₂²	semidirect
68. C₅×#938	C₂²	semidirect
69. C₅×#937	C₂²	semidirect
70. C₅×#937	C₂²	semidirect
71. C₅×#935	C₂²	semidirect
72. C₅×D₄×Dic₃	C₂²	semidirect
73. C₅×D₄×Dic₃	C₂²	semidirect
74. C₅×D₄×Dic₃	C₂²	semidirect
75. C₅×#930	C₂²	semidirect
76. C₅×#930	C₂²	semidirect
77. C₅×#929	C₂²	semidirect
79. C₄×C₅×#67	C₂²	semidirect
80. C₄×C₅×#67	C₂²	semidirect
81. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
82. C₅×#924	C₂²	semidirect
83. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
84. C₂×C₄×C₅×Dic₃	C₂²	semidirect
85. C₅×#897	C₂²	semidirect
86. C₅×#896	C₂²	semidirect
87. C₅×#896	C₂²	semidirect
88. C₅×#895	C₂²	semidirect
89. C₅×#894	C₂²	semidirect
90. C₅×#893	C₂²	semidirect
91. C₅×#893	C₂²	semidirect
92. C₅×#892	C₂²	semidirect
93. C₅×D₃×C₄⋊C₄	C₂²	semidirect
94. C₅×#888	C₂²	semidirect
95. C₅×#887	C₂²	semidirect
96. C₅×#886	C₂²	semidirect
97. C₅×#885	C₂²	semidirect
98. C₅×#885	C₂²	semidirect
99. C₅×#884	C₂²	semidirect
100. C₅×#884	C₂²	semidirect
101. C₅×#884	C₂²	semidirect
102. C₅×#884	C₂²	semidirect
103. C₅×#883	C₂²	semidirect
104. C₅×#882	C₂²	semidirect
105. C₅×#882	C₂²	semidirect
108. C₅×#67⋊C₄	C₂²	semidirect
109. C₅×#67⋊C₄	C₂²	semidirect
110. C₅×#67⋊C₄	C₂²	semidirect
111. C₅×#67⋊C₄	C₂²	semidirect
112. C₅×#67⋊C₄	C₂²	semidirect
113. C₅×#67⋊C₄	C₂²	semidirect
114. C₅×#67⋊C₄	C₂²	semidirect
115. C₅×#67⋊C₄	C₂²	semidirect
116. C₅×#67⋊C₄	C₂²	semidirect
117. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
118. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
119. C₅×#878	C₂²	semidirect
120. C₅×#878	C₂²	semidirect
121. C₅×#877	C₂²	semidirect
122. C₅×#875	C₂²	semidirect
123. C₄×C₅×D₁₂	C₂²	semidirect
124. C₄²×C₅×D₃	C₂²	semidirect
125. C₄×C₅×Dic₆	C₂²	semidirect
126. #86626	C₅	direct (N × H)
138. C₅×#546	D₃	semidirect
198. C₅×#237	D₄	semidirect
272. C₂×D₃×#41	C₂×C₅	semidirect
273. C₂²×#237	C₂×C₅	semidirect
274. C₃×#546	C₂×C₅	semidirect
275. #5824	C₂×C₅	semidirect
276. D₄×#67	C₂×C₅	semidirect
277. #5677	C₂×C₅	semidirect
278. #5668	C₂×C₅	semidirect
279. #5656	C₂×C₅	semidirect
280. #5655	C₂×C₅	semidirect
281. #5632	C₂×C₅	semidirect
282. #5627	C₂×C₅	semidirect
283. #5610	C₂×C₅	semidirect
284. #5606	C₂×C₅	semidirect
285. #5599	C₂×C₅	semidirect
286. #5596	C₂×C₅	semidirect
287. #5590	C₂×C₅	semidirect
288. #5586	C₂×C₅	semidirect
289. #5554	C₂×C₅	semidirect
290. #5552	C₂×C₅	semidirect
291. C₄×D₃×D₄	C₂×C₅	semidirect
292. C₄×#237	C₂×C₅	semidirect
293. #5490	C₂×C₅	semidirect
294. C₂×#67⋊C₄	C₂×C₅	semidirect
307. C₂×C₅×#41	C₂×D₃	semidirect
315. C₂²×C₅×D₄	C₂×D₃	semidirect
327. C₅×#124	C₂×D₃	semidirect
333. C₅×#123	C₂×D₃	semidirect
341. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
354. C₅×#121	C₂×D₃	semidirect
355. C₅×#121	C₂×D₃	semidirect
361. C₅×#120	C₂×D₃	semidirect
384. C₄×C₅×D₄	C₂×D₃	semidirect
385. C₄×C₅×D₄	C₂×D₃	semidirect
393. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
423. C₃×C₅×D₄	C₂×D₄	semidirect
445. C₅×#67	C₂×D₄	semidirect
446. C₅×#67	#41	semidirect
454. C₂×C₅×Dic₃	C₂×D₄	semidirect
478. C₄×C₅×D₃	C₂×D₄	semidirect
482. C₅×Dic₆	C₂×D₄	semidirect
483. C₂×C₃×#41	C₂²×C₅	semidirect
484. C₂²×C₃×D₄	C₂²×C₅	semidirect
486. C₂²×#67	C₂²×C₅	semidirect
487. C₂³×Dic₃	C₂²×C₅	semidirect
489. C₂×#239	C₂²×C₅	semidirect
490. C₂×D₃×Q₈	C₂²×C₅	semidirect
493. C₂×#237	C₂²×C₅	semidirect
494. C₂×#237	C₂²×C₅	semidirect
495. C₂×#237	C₂²×C₅	semidirect
496. C₂×#237	C₂²×C₅	semidirect
497. C₂×#237	C₂²×C₅	semidirect
498. C₂×#237	C₂²×C₅	semidirect
500. C₂×D₃×D₄	C₂²×C₅	semidirect
501. C₂×D₃×D₄	C₂²×C₅	semidirect
502. C₂×#235	C₂²×C₅	semidirect
503. C₂×#235	C₂²×C₅	semidirect
504. C₂²×C₄×D₃	C₂²×C₅	semidirect
505. C₂²×C₄×D₃	C₂²×C₅	semidirect
506. C₂²×C₄×D₃	C₂²×C₅	semidirect
507. C₂²×Dic₆	C₂²×C₅	semidirect
508. C₃×#124	C₂²×C₅	semidirect
509. C₃×#123	C₂²×C₅	semidirect
510. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
511. C₃×#121	C₂²×C₅	semidirect
512. C₃×#121	C₂²×C₅	semidirect
513. C₃×#120	C₂²×C₅	semidirect
514. C₃×C₄×D₄	C₂²×C₅	semidirect
515. C₃×C₄×D₄	C₂²×C₅	semidirect
516. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
517. #953	C₂²×C₅	semidirect
518. #946	C₂²×C₅	semidirect
519. #944	C₂²×C₅	semidirect
520. #940	C₂²×C₅	semidirect
521. #940	C₂²×C₅	semidirect
522. #939	C₂²×C₅	semidirect
523. #939	C₂²×C₅	semidirect
524. #939	C₂²×C₅	semidirect
525. #939	C₂²×C₅	semidirect
526. #938	C₂²×C₅	semidirect
527. #937	C₂²×C₅	semidirect
528. #937	C₂²×C₅	semidirect
529. #935	C₂²×C₅	semidirect
530. D₄×Dic₃	C₂²×C₅	semidirect
531. D₄×Dic₃	C₂²×C₅	semidirect
532. D₄×Dic₃	C₂²×C₅	semidirect
533. #930	C₂²×C₅	semidirect
534. #930	C₂²×C₅	semidirect
535. #929	C₂²×C₅	semidirect
537. C₄×#67	C₂²×C₅	semidirect
538. C₄×#67	C₂²×C₅	semidirect
539. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
540. #924	C₂²×C₅	semidirect
541. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
542. C₂×C₄×Dic₃	C₂²×C₅	semidirect
543. #897	C₂²×C₅	semidirect
544. #896	C₂²×C₅	semidirect
545. #896	C₂²×C₅	semidirect
546. #895	C₂²×C₅	semidirect
547. #894	C₂²×C₅	semidirect
548. #893	C₂²×C₅	semidirect
549. #893	C₂²×C₅	semidirect
550. #892	C₂²×C₅	semidirect
551. D₃×C₄⋊C₄	C₂²×C₅	semidirect
552. #888	C₂²×C₅	semidirect
553. #887	C₂²×C₅	semidirect
554. #886	C₂²×C₅	semidirect
555. #885	C₂²×C₅	semidirect
556. #885	C₂²×C₅	semidirect
557. #884	C₂²×C₅	semidirect
558. #884	C₂²×C₅	semidirect
559. #884	C₂²×C₅	semidirect
560. #884	C₂²×C₅	semidirect
561. #883	C₂²×C₅	semidirect
562. #882	C₂²×C₅	semidirect
563. #882	C₂²×C₅	semidirect
566. #67⋊C₄	C₂²×C₅	semidirect
567. #67⋊C₄	C₂²×C₅	semidirect
568. #67⋊C₄	C₂²×C₅	semidirect
569. #67⋊C₄	C₂²×C₅	semidirect
570. #67⋊C₄	C₂²×C₅	semidirect
571. #67⋊C₄	C₂²×C₅	semidirect
572. #67⋊C₄	C₂²×C₅	semidirect
573. #67⋊C₄	C₂²×C₅	semidirect
574. #67⋊C₄	C₂²×C₅	semidirect
575. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
576. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
577. #878	C₂²×C₅	semidirect
578. #878	C₂²×C₅	semidirect
579. #877	C₂²×C₅	semidirect
580. #875	C₂²×C₅	semidirect
581. C₄×D₁₂	C₂²×C₅	semidirect
582. C₄²×D₃	C₂²×C₅	semidirect
583. C₄×Dic₆	C₂²×C₅	semidirect
717. #546	C₅×D₃	semidirect
741. C₂²×C₃×C₅	C₂×#41	semidirect
757. C₂×C₅×D₃	C₂×#41	semidirect
772. C₅×Dic₃	C₂×#41	semidirect
821. #237	C₅×D₄	semidirect
941. C₅×D₄	D₃×D₄	semidirect
993. C₂×#41	C₂×C₅×D₃	semidirect
1001. C₂²×D₄	C₂×C₅×D₃	semidirect
1013. #124	C₂×C₅×D₃	semidirect
1019. #123	C₂×C₅×D₃	semidirect
1027. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
1040. #121	C₂×C₅×D₃	semidirect
1041. #121	C₂×C₅×D₃	semidirect
1047. #120	C₂×C₅×D₃	semidirect
1070. C₄×D₄	C₂×C₅×D₃	semidirect
1071. C₄×D₄	C₂×C₅×D₃	semidirect
1079. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
1119. C₃×D₄	C₂×C₅×D₄	semidirect
1141. #67	C₂×C₅×D₄	semidirect
1142. #67	C₅×#41	semidirect
1150. C₂×Dic₃	C₂×C₅×D₄	semidirect
1174. C₄×D₃	C₂×C₅×D₄	semidirect
1178. Dic₆	C₂×C₅×D₄	semidirect
1206. C₂²×C₅	D₃×#41	semidirect
1345. C₃×C₅	D₄×#41	semidirect
1358. C₂²×C₃	C₂×C₅×#41	semidirect
1374. C₂×D₃	C₂×C₅×#41	semidirect
1389. Dic₃	C₂×C₅×#41	semidirect
1447. D₄	C₅×D₃×D₄	semidirect
1498. C₅	#86626	direct (N × H)
1526. C₂²	C₅×D₃×#41	semidirect
1543. C₃	C₅×D₄×#41	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×D₃×#41	2
C₂²×C₅×#237	2
C₃×C₅×#546	2
C₅×#5824	2
C₅×D₄×#67	2
C₅×#5677	2
C₅×#5668	2
C₅×#5656	2
C₅×#5655	2
C₅×#5632	2
C₅×#5627	2
C₅×#5610	2
C₅×#5606	2
C₅×#5599	2
C₅×#5596	2
C₅×#5590	2
C₅×#5586	2
C₅×#5554	2
C₅×#5552	2
C₄×C₅×D₃×D₄	2
C₄×C₅×#237	2
C₅×#5490	2
C₂×C₅×#67⋊C₄	2
C₅×D₄×#41	3
#86626	5

Subgroups — C5×#86626 #14483036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86626 #14483036