Subgroups — C₅×#85841 #14484141

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5829	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5824	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5580	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5578	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5556	C₂	1	2	yes	maximal, complemented
9	C₅×#5554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5547	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5540	C₂	1	2	yes	maximal, complemented
13	C₅×#5539	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5538	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#5532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#5531	C₂	1	2	yes	maximal, complemented
18	C₅×#5529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#5527	C₂	1	2	yes	maximal, complemented
20	C₅×#5479	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#5479	C₂	1	2	yes	maximal, complemented
22	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅×#872	C₂	1	2	yes	maximal, complemented
24	C₅×#3475	—	3	1	no	maximal, Hall
25	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
26	C₂×C₅×#237	C₂²	1	1	yes	characteristic
27	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×#235	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
30	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
35	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
36	C₃×C₅×#117	C₂²	1	2	yes	complemented
37	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
39	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
40	C₅×#947	C₂²	1	1	yes	characteristic
41	C₅×#946	C₂²	1	1	yes	characteristic
42	C₅×#946	C₂²	1	1	yes	characteristic, complemented
43	C₅×#944	C₂²	1	1	yes	characteristic, complemented
44	C₅×#939	C₂²	1	2	yes	—
45	C₅×#939	C₂²	1	2	yes	complemented
46	C₅×#937	C₂²	1	2	yes	—
47	C₅×#935	C₂²	1	2	yes	complemented
48	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
49	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
50	C₅×#930	C₂²	1	1	yes	characteristic
51	C₅×#930	C₂²	1	2	yes	—
52	C₅×#929	C₂²	1	2	yes	—
53	C₅×#929	C₂²	1	2	yes	complemented
54	C₅×#929	C₂²	1	2	yes	complemented
55	C₄×C₅×#67	C₂²	1	1	yes	characteristic
56	C₄×C₅×#67	C₂²	1	1	yes	characteristic
57	C₄×C₅×#67	C₂²	1	2	yes	—
58	C₄×C₅×#67	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₅×#67	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₅×#67	C₂²	1	2	yes	complemented
61	C₄×C₅×#67	C₂²	1	2	yes	complemented
62	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
63	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
64	C₅×#926	C₂²	1	1	yes	characteristic, complemented
65	C₅×#924	C₂²	1	1	yes	characteristic, complemented
66	C₅×#924	C₂²	1	2	yes	complemented
67	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
68	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
70	C₅×#898	C₂²	1	2	yes	complemented
71	C₅×#898	C₂²	1	2	yes	complemented
72	C₅×#897	C₂²	1	1	yes	characteristic
73	C₅×#896	C₂²	1	2	yes	—
74	C₅×#896	C₂²	1	2	yes	complemented
75	C₅×#895	C₂²	1	1	yes	characteristic
76	C₅×#894	C₂²	1	2	yes	—
77	C₅×#894	C₂²	1	2	yes	complemented
78	C₅×#893	C₂²	1	1	yes	characteristic
79	C₅×#892	C₂²	1	1	yes	characteristic, complemented
80	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	C₅×#890	C₂²	1	1	yes	characteristic, complemented
82	C₅×#889	C₂²	1	2	yes	complemented
83	C₅×#889	C₂²	1	2	yes	complemented
84	C₅×#888	C₂²	1	1	yes	characteristic, complemented
85	C₅×#887	C₂²	1	1	yes	characteristic, complemented
86	C₅×#886	C₂²	1	2	yes	—
87	C₅×#885	C₂²	1	2	yes	complemented
88	C₅×#884	C₂²	1	2	yes	complemented
89	C₅×#883	C₂²	1	2	yes	—
90	C₅×#882	C₂²	1	2	yes	—
91	C₅×#67⋊C₄	C₂²	1	2	yes	—
92	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
93	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
94	C₅×#879	C₂²	1	2	yes	complemented
95	C₅×#878	C₂²	1	2	yes	complemented
96	C₅×#878	C₂²	1	2	yes	complemented
97	C₅×#877	C₂²	1	2	yes	complemented
98	C₅×#876	C₂²	1	2	yes	complemented
99	C₅×#876	C₂²	1	2	yes	complemented
100	C₅×#876	C₂²	1	2	yes	complemented
101	C₅×#875	C₂²	1	1	yes	characteristic
102	C₅×#875	C₂²	1	2	yes	complemented
103	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
104	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
105	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
106	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
107	C₅×#872	C₂²	1	1	yes	characteristic
108	C₅×#872	C₂²	1	2	yes	—
109	C₅×#872	C₂²	1	2	yes	—
110	C₅×#872	C₂²	1	2	yes	—
111	C₅×#872	C₂²	1	2	yes	complemented
112	C₅×#872	C₂²	1	2	yes	complemented
113	C₅×#872	C₂²	1	2	yes	complemented
114	C₅×#872	C₂²	1	2	yes	complemented
115	C₅×#872	C₂²	1	1	yes	characteristic, complemented
116	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
117	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
118	C₅×#870	C₂²	1	2	yes	complemented
119	C₅×#870	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
124	#85841	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#556	—	3	1	no	—
126	C₅×#555	—	3	1	no	—
127	C₅×#554	—	3	1	no	—
128	C₅×#553	—	3	2	no	—
129	C₅×#552	—	3	1	no	—
130	C₅×#552	—	3	1	no	—
131	C₅×#552	—	3	2	no	—
132	C₅×#551	—	3	2	no	—
133	C₅×#551	—	3	2	no	—
134	C₅×#547	—	3	1	no	—
135	C₅×#546	—	3	1	no	—
136	C₅×#546	—	3	1	no	—
137	C₅×#533	—	3	1	no	—
138	C₅×#529	—	3	1	no	—
139	C₅×#529	—	3	2	no	—
140	C₅×#529	—	3	2	no	—
141	C₅×#529	—	3	1	no	—
142	C₅×#525	—	3	2	no	—
143	C₄×C₅×#41	—	3	1	no	—
144	C₄×C₅×#41	—	3	1	no	—
145	C₄×C₅×#41	D₃	1	1	yes	characteristic, complemented
146	C₂×C₄×C₅×D₄	—	3	1	no	—
147	C₂×C₅×#117	—	3	2	no	—
148	C₂³×C₅×D₃	C₂³	1	2	yes	—
149	C₃×C₅×#41	—	2	4	no	—
150	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
152	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
154	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
155	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
158	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
159	C₂×C₅×#67	C₂³	1	2	yes	—
160	C₂×C₅×#67	C₂³	1	2	yes	—
161	C₂×C₅×#67	C₂³	1	1	yes	characteristic
162	C₂×C₅×#67	C₂³	1	1	yes	characteristic
163	C₂×C₅×#67	C₂³	1	2	yes	—
164	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
165	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
166	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
167	C₅×#237	—	2	4	no	—
168	C₅×D₃×D₄	—	2	4	no	—
169	C₅×#235	—	2	4	no	—
170	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
171	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
172	C₂×C₅×D₁₂	C₂³	1	2	yes	—
173	C₂×C₄×C₅×D₃	—	2	8	no	—
174	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
178	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
179	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
180	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
185	C₂×C₅×Dic₆	C₂³	1	2	yes	—
186	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₃×C₄²×C₅	C₂³	1	2	yes	—
196	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₃×C₄²×C₅	C₂³	1	2	yes	—
198	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₃×C₄²×C₅	C₂³	1	2	yes	—
200	C₅×#217	C₂³	1	2	yes	—
201	C₅×#217	C₂³	1	2	yes	—
202	C₅×#217	C₂³	1	1	yes	characteristic
203	C₅×#217	C₂³	1	2	yes	—
204	C₅×#217	C₂³	1	1	yes	characteristic
205	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
206	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
207	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
208	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
213	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
214	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
215	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
217	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
220	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
222	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
226	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
228	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
229	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
231	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
232	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
233	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
235	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
237	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
240	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
241	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
242	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
243	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×C₅×Dic₃	C₂³	1	2	yes	—
245	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
246	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
247	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
250	C₄×C₅×Dic₃	C₂³	1	2	yes	—
251	C₄×C₅×Dic₃	C₂³	1	2	yes	—
252	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
253	#5829	C₂×C₅	1	1	yes	characteristic, complemented
254	#5824	C₂×C₅	1	1	yes	characteristic, complemented
255	#5581	C₂×C₅	1	1	yes	characteristic, complemented
256	#5580	C₂×C₅	1	1	yes	characteristic, complemented
257	#5578	C₂×C₅	1	1	yes	characteristic, complemented
258	#5568	C₂×C₅	1	1	yes	characteristic, complemented
259	#5556	C₂×C₅	1	2	yes	complemented
260	#5554	C₂×C₅	1	1	yes	characteristic, complemented
261	#5547	C₂×C₅	1	2	yes	complemented
262	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
263	#5540	C₂×C₅	1	2	yes	complemented
264	#5539	C₂×C₅	1	1	yes	characteristic, complemented
265	#5538	C₂×C₅	1	2	yes	complemented
266	C₄×#237	C₂×C₅	1	1	yes	characteristic, complemented
267	#5532	C₂×C₅	1	1	yes	characteristic, complemented
268	#5531	C₂×C₅	1	2	yes	complemented
269	#5529	C₂×C₅	1	1	yes	characteristic, complemented
270	#5527	C₂×C₅	1	2	yes	complemented
271	#5479	C₂×C₅	1	1	yes	characteristic, complemented
272	#5479	C₂×C₅	1	2	yes	complemented
273	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
274	C₂×#872	C₂×C₅	1	2	yes	complemented
275	C₂×C₅×#41	—	3	1	no	—
276	C₂×C₅×#41	—	3	1	no	—
277	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
278	C₂²×C₅×D₄	—	3	1	no	—
279	C₂³×C₄×C₅	—	3	2	no	—
280	C₅×C₄⋊Q₈	—	3	1	no	—
281	C₅×C₄⋊Q₈	—	3	1	no	—
282	C₅×#126	—	3	2	no	—
283	C₅×#126	—	3	2	no	—
284	C₅×#126	—	3	2	no	—
285	C₅×#126	—	3	2	no	—
286	C₅×#126	—	3	2	no	—
287	C₅×#126	—	3	2	no	—
288	C₅×#125	—	3	2	no	—
289	C₅×#125	—	3	2	no	—
290	C₅×#125	—	3	1	no	—
291	C₅×#125	—	3	2	no	—
292	C₅×#125	—	3	1	no	—
293	C₅×#124	—	3	1	no	—
294	C₅×#124	—	3	2	no	—
295	C₅×#124	—	3	1	no	—
296	C₅×#124	—	3	2	no	—
297	C₅×#123	—	3	2	no	—
298	C₅×#123	—	3	2	no	—
299	C₅×#123	—	3	2	no	—
300	C₅×#123	—	3	2	no	—
301	C₅×#123	—	3	2	no	—
302	C₅×#123	—	3	2	no	—
303	C₅×#123	—	3	2	no	—
304	C₅×#123	—	3	2	no	—
305	C₅×C₂²⋊Q₈	—	3	1	no	—
306	C₅×C₂²⋊Q₈	—	3	1	no	—
307	C₅×C₂²⋊Q₈	—	3	1	no	—
308	C₅×C₂²⋊Q₈	—	3	2	no	—
309	C₅×C₂²⋊Q₈	—	3	2	no	—
310	C₅×C₂²⋊Q₈	—	3	2	no	—
311	C₅×C₂²⋊Q₈	—	3	1	no	—
312	C₅×C₂²⋊Q₈	—	3	2	no	—
313	C₅×C₂²⋊Q₈	—	3	2	no	—
314	C₅×#121	—	3	2	no	—
315	C₅×#121	—	3	2	no	—
316	C₅×#121	—	3	2	no	—
317	C₅×#121	—	3	1	no	—
318	C₅×#121	—	3	1	no	—
319	C₅×#121	—	3	2	no	—
320	C₅×#120	—	3	2	no	—
321	C₅×#120	—	3	2	no	—
322	C₄×C₅×Q₈	—	3	1	no	—
323	C₄×C₅×Q₈	—	3	1	no	—
324	C₄×C₅×Q₈	—	3	1	no	—
325	C₄×C₅×Q₈	—	3	1	no	—
326	C₄×C₅×Q₈	—	3	2	no	—
327	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
328	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
329	C₄×C₅×D₄	—	3	1	no	—
330	C₄×C₅×D₄	—	3	1	no	—
331	C₄×C₅×D₄	—	3	2	no	—
332	C₄×C₅×D₄	—	3	1	no	—
333	C₄×C₅×D₄	—	3	1	no	—
334	C₄×C₅×D₄	—	3	2	no	—
335	C₄×C₅×D₄	—	3	1	no	—
336	C₄×C₅×D₄	—	3	1	no	—
337	C₄×C₅×D₄	—	3	2	no	—
338	C₄×C₅×D₄	—	3	1	no	—
339	C₄×C₅×D₄	—	3	2	no	—
340	C₄×C₅×D₄	—	3	2	no	—
341	C₄×C₅×D₄	—	3	1	no	—
342	C₄×C₅×D₄	—	3	1	no	—
343	C₄×C₅×D₄	—	3	1	no	—
344	C₄×C₅×D₄	—	3	2	no	—
345	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
346	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
347	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
348	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
349	C₅×#117	—	3	1	no	—
350	C₅×#117	—	3	1	no	—
351	C₅×#117	—	3	2	no	—
352	C₅×#117	—	3	1	no	—
353	C₅×#117	—	3	2	no	—
354	C₅×#117	—	3	2	no	—
355	C₅×#117	—	3	2	no	—
356	C₅×#117	—	3	2	no	—
357	C₅×#117	—	3	2	no	—
358	C₅×#117	—	3	2	no	—
359	C₅×#117	—	3	2	no	—
360	C₅×#117	—	3	1	no	—
361	C₅×#117	C₂×D₃	1	2	yes	complemented
362	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
363	C₂×C₅×C₄⋊C₄	—	3	2	no	—
364	C₂×C₅×C₄⋊C₄	—	3	2	no	—
365	C₂×C₅×C₄⋊C₄	—	3	1	no	—
366	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
367	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
368	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
369	C₂×C₄²×C₅	—	3	2	no	—
370	C₂×C₄²×C₅	—	3	1	no	—
371	C₂×C₄²×C₅	—	3	1	no	—
372	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
373	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
374	#3475	—	3	1	no	Sylow
375	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
376	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
377	C₂²×C₅×D₃	—	2	4	no	—
378	C₂²×C₅×D₃	—	2	4	no	—
379	C₂²×C₅×D₃	—	4	2	no	—
380	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
381	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
383	C₃×C₅×Q₈	—	2	2	no	—
384	C₃×C₅×D₄	—	2	4	no	—
385	C₃×C₅×D₄	#41	1	4	yes	complemented
386	C₂×C₃×C₄×C₅	—	2	4	no	—
387	C₂×C₃×C₄×C₅	—	2	4	no	—
388	C₂×C₃×C₄×C₅	—	2	2	no	—
389	C₂×C₃×C₄×C₅	—	2	2	no	—
390	C₂×C₃×C₄×C₅	—	4	2	no	—
391	C₂×C₃×C₄×C₅	—	4	1	no	—
392	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
393	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
394	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
395	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
396	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
397	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
398	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
399	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
400	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
401	C₅×#67	—	2	4	no	—
402	C₅×#67	—	2	4	no	—
403	C₅×#67	—	2	2	no	—
404	C₅×#67	—	2	2	no	—
405	C₅×#67	—	4	2	no	—
406	C₂×C₅×Dic₃	—	2	4	no	—
407	C₂×C₅×Dic₃	—	2	4	no	—
408	C₂×C₅×Dic₃	—	4	2	no	—
409	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
410	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
411	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
413	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
414	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
417	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
418	C₅×D₁₂	—	2	2	no	—
419	C₅×D₁₂	—	2	2	no	—
420	C₅×D₁₂	—	4	2	no	—
421	C₄×C₅×D₃	—	2	4	no	—
422	C₄×C₅×D₃	—	2	4	no	—
423	C₄×C₅×D₃	—	2	2	no	—
424	C₄×C₅×D₃	—	2	2	no	—
425	C₄×C₅×D₃	—	2	2	no	—
426	C₄×C₅×D₃	—	2	4	no	—
427	C₄×C₅×D₃	—	4	1	no	—
428	C₄×C₅×D₃	—	4	1	no	—
429	C₄×C₅×D₃	#41	1	4	yes	complemented
430	C₅×Dic₆	—	2	2	no	—
431	C₅×Dic₆	—	2	2	no	—
432	C₅×Dic₆	—	4	2	no	—
433	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
434	C₂×#237	C₂²×C₅	1	1	yes	characteristic
435	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
436	C₂×#235	C₂²×C₅	1	1	yes	characteristic
437	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
438	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
439	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
441	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
442	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
443	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
444	C₃×#117	C₂²×C₅	1	2	yes	complemented
445	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
446	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
447	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
448	#947	C₂²×C₅	1	1	yes	characteristic
449	#946	C₂²×C₅	1	1	yes	characteristic
450	#946	C₂²×C₅	1	1	yes	characteristic, complemented
451	#944	C₂²×C₅	1	1	yes	characteristic, complemented
452	#939	C₂²×C₅	1	2	yes	—
453	#939	C₂²×C₅	1	2	yes	complemented
454	#937	C₂²×C₅	1	2	yes	—
455	#935	C₂²×C₅	1	2	yes	complemented
456	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
457	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
458	#930	C₂²×C₅	1	1	yes	characteristic
459	#930	C₂²×C₅	1	2	yes	—
460	#929	C₂²×C₅	1	2	yes	—
461	#929	C₂²×C₅	1	2	yes	complemented
462	#929	C₂²×C₅	1	2	yes	complemented
463	C₄×#67	C₂²×C₅	1	1	yes	characteristic
464	C₄×#67	C₂²×C₅	1	1	yes	characteristic
465	C₄×#67	C₂²×C₅	1	2	yes	—
466	C₄×#67	C₂²×C₅	1	1	yes	characteristic, complemented
467	C₄×#67	C₂²×C₅	1	1	yes	characteristic, complemented
468	C₄×#67	C₂²×C₅	1	2	yes	complemented
469	C₄×#67	C₂²×C₅	1	2	yes	complemented
470	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
471	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
472	#926	C₂²×C₅	1	1	yes	characteristic, complemented
473	#924	C₂²×C₅	1	1	yes	characteristic, complemented
474	#924	C₂²×C₅	1	2	yes	complemented
475	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
476	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
477	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
478	#898	C₂²×C₅	1	2	yes	complemented
479	#898	C₂²×C₅	1	2	yes	complemented
480	#897	C₂²×C₅	1	1	yes	characteristic
481	#896	C₂²×C₅	1	2	yes	—
482	#896	C₂²×C₅	1	2	yes	complemented
483	#895	C₂²×C₅	1	1	yes	characteristic
484	#894	C₂²×C₅	1	2	yes	—
485	#894	C₂²×C₅	1	2	yes	complemented
486	#893	C₂²×C₅	1	1	yes	characteristic
487	#892	C₂²×C₅	1	1	yes	characteristic, complemented
488	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
489	#890	C₂²×C₅	1	1	yes	characteristic, complemented
490	#889	C₂²×C₅	1	2	yes	complemented
491	#889	C₂²×C₅	1	2	yes	complemented
492	#888	C₂²×C₅	1	1	yes	characteristic, complemented
493	#887	C₂²×C₅	1	1	yes	characteristic, complemented
494	#886	C₂²×C₅	1	2	yes	—
495	#885	C₂²×C₅	1	2	yes	complemented
496	#884	C₂²×C₅	1	2	yes	complemented
497	#883	C₂²×C₅	1	2	yes	—
498	#882	C₂²×C₅	1	2	yes	—
499	#67⋊C₄	C₂²×C₅	1	2	yes	—
500	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
501	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
502	#879	C₂²×C₅	1	2	yes	complemented
503	#878	C₂²×C₅	1	2	yes	complemented
504	#878	C₂²×C₅	1	2	yes	complemented
505	#877	C₂²×C₅	1	2	yes	complemented
506	#876	C₂²×C₅	1	2	yes	complemented
507	#876	C₂²×C₅	1	2	yes	complemented
508	#876	C₂²×C₅	1	2	yes	complemented
509	#875	C₂²×C₅	1	1	yes	characteristic
510	#875	C₂²×C₅	1	2	yes	complemented
511	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
512	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
513	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
514	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
515	#872	C₂²×C₅	1	1	yes	characteristic
516	#872	C₂²×C₅	1	2	yes	—
517	#872	C₂²×C₅	1	2	yes	—
518	#872	C₂²×C₅	1	2	yes	—
519	#872	C₂²×C₅	1	2	yes	complemented
520	#872	C₂²×C₅	1	2	yes	complemented
521	#872	C₂²×C₅	1	2	yes	complemented
522	#872	C₂²×C₅	1	2	yes	complemented
523	#872	C₂²×C₅	1	1	yes	characteristic, complemented
524	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
525	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
526	#870	C₂²×C₅	1	2	yes	complemented
527	#870	C₂²×C₅	1	1	yes	characteristic, complemented
528	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
529	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
530	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
531	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
532	C₂⁴×C₅	—	3	2	no	—
533	C₅×#41	—	2	4	no	—
534	C₅×#41	—	6	4	no	—
535	C₅×#41	—	6	4	no	—
536	C₂×C₅×Q₈	—	3	1	no	—
537	C₂×C₅×Q₈	—	3	1	no	—
538	C₂×C₅×Q₈	—	3	2	no	—
539	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
540	C₂×C₅×D₄	—	3	1	no	—
541	C₂×C₅×D₄	—	3	2	no	—
542	C₂×C₅×D₄	—	3	1	no	—
543	C₂×C₅×D₄	—	3	2	no	—
544	C₂×C₅×D₄	—	3	2	no	—
545	C₂×C₅×D₄	—	3	1	no	—
546	C₂×C₅×D₄	—	3	1	no	—
547	C₂×C₅×D₄	—	3	2	no	—
548	C₂×C₅×D₄	—	6	4	no	—
549	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
550	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
551	C₂²×C₄×C₅	—	3	1	no	—
552	C₂²×C₄×C₅	—	3	2	no	—
553	C₂²×C₄×C₅	—	3	2	no	—
554	C₂²×C₄×C₅	—	3	2	no	—
555	C₂²×C₄×C₅	—	3	1	no	—
556	C₂²×C₄×C₅	—	3	1	no	—
557	C₂²×C₄×C₅	—	3	2	no	—
558	C₂²×C₄×C₅	—	3	2	no	—
559	C₂²×C₄×C₅	—	3	1	no	—
560	C₂²×C₄×C₅	—	3	2	no	—
561	C₂²×C₄×C₅	—	3	1	no	—
562	C₂²×C₄×C₅	—	3	1	no	—
563	C₂²×C₄×C₅	—	6	8	no	—
564	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
565	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
566	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
567	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
568	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
569	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
570	C₅×C₄⋊C₄	—	3	1	no	—
571	C₅×C₄⋊C₄	—	3	1	no	—
572	C₅×C₄⋊C₄	—	3	2	no	—
573	C₅×C₄⋊C₄	—	3	2	no	—
574	C₅×C₄⋊C₄	—	3	2	no	—
575	C₅×C₄⋊C₄	—	3	2	no	—
576	C₅×C₄⋊C₄	—	3	2	no	—
577	C₅×C₄⋊C₄	—	3	2	no	—
578	C₅×C₄⋊C₄	—	3	1	no	—
579	C₅×C₄⋊C₄	—	3	2	no	—
580	C₅×C₄⋊C₄	—	3	1	no	—
581	C₅×C₄⋊C₄	—	3	1	no	—
582	C₅×C₄⋊C₄	—	3	1	no	—
583	C₅×C₄⋊C₄	—	3	2	no	—
584	C₅×C₄⋊C₄	—	3	2	no	—
585	C₅×C₄⋊C₄	—	3	1	no	—
586	C₅×C₄⋊C₄	—	3	1	no	—
587	C₅×C₄⋊C₄	—	3	2	no	—
588	C₅×C₄⋊C₄	—	3	2	no	—
589	C₅×C₄⋊C₄	—	3	2	no	—
590	C₅×C₄⋊C₄	—	3	2	no	—
591	C₅×C₄⋊C₄	—	3	2	no	—
592	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
593	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
594	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
595	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
596	C₅×C₂²⋊C₄	—	3	2	no	—
597	C₅×C₂²⋊C₄	—	3	2	no	—
598	C₅×C₂²⋊C₄	—	3	1	no	—
599	C₅×C₂²⋊C₄	—	3	1	no	—
600	C₅×C₂²⋊C₄	—	3	2	no	—
601	C₅×C₂²⋊C₄	—	3	1	no	—
602	C₅×C₂²⋊C₄	—	3	1	no	—
603	C₅×C₂²⋊C₄	—	3	2	no	—
604	C₅×C₂²⋊C₄	—	3	2	no	—
605	C₅×C₂²⋊C₄	—	3	2	no	—
606	C₅×C₂²⋊C₄	—	3	2	no	—
607	C₅×C₂²⋊C₄	—	3	2	no	—
608	C₅×C₂²⋊C₄	—	3	2	no	—
609	C₅×C₂²⋊C₄	—	3	2	no	—
610	C₅×C₂²⋊C₄	—	3	2	no	—
611	C₅×C₂²⋊C₄	—	3	1	no	—
612	C₅×C₂²⋊C₄	—	3	2	no	—
613	C₅×C₂²⋊C₄	—	3	1	no	—
614	C₅×C₂²⋊C₄	—	3	2	no	—
615	C₅×C₂²⋊C₄	—	3	2	no	—
616	C₅×C₂²⋊C₄	—	3	2	no	—
617	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
618	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
619	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
620	C₄²×C₅	—	3	2	no	—
621	C₄²×C₅	—	3	2	no	—
622	C₄²×C₅	—	3	1	no	—
623	C₄²×C₅	—	3	1	no	—
624	C₄²×C₅	—	3	1	no	—
625	C₄²×C₅	—	3	1	no	—
626	C₄²×C₅	—	3	1	no	—
627	C₄²×C₅	—	3	1	no	—
628	C₄²×C₅	—	3	2	no	—
629	C₄²×C₅	C₂²×D₃	1	2	yes	—
630	C₄²×C₅	C₂²×D₃	1	2	yes	—
631	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
632	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
633	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
634	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
635	C₄²×C₅	C₂²×D₃	1	2	yes	—
636	#556	—	3	1	no	—
637	#555	—	3	1	no	—
638	#554	—	3	1	no	—
639	#553	—	3	2	no	—
640	#552	—	3	1	no	—
641	#552	—	3	1	no	—
642	#552	—	3	2	no	—
643	#551	—	3	2	no	—
644	#551	—	3	2	no	—
645	#547	—	3	1	no	—
646	#546	—	3	1	no	—
647	#546	—	3	1	no	—
648	#533	—	3	1	no	—
649	#529	—	3	1	no	—
650	#529	—	3	2	no	—
651	#529	—	3	2	no	—
652	#529	—	3	1	no	—
653	#525	—	3	2	no	—
654	C₄×#41	—	3	1	no	—
655	C₄×#41	—	3	1	no	—
656	C₄×#41	C₅×D₃	1	1	yes	characteristic, complemented
657	C₂×C₄×D₄	—	3	1	no	—
658	C₂×#117	—	3	2	no	—
659	C₂²×C₃×C₅	—	2	2	no	—
660	C₂²×C₃×C₅	—	2	2	no	—
661	C₂²×C₃×C₅	—	2	1	no	—
662	C₂²×C₃×C₅	—	2	1	no	—
663	C₂²×C₃×C₅	—	2	1	no	—
664	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
665	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
666	C₂×C₅×D₃	—	2	1	no	—
667	C₂×C₅×D₃	—	2	1	no	—
668	C₂×C₅×D₃	—	2	2	no	—
669	C₂×C₅×D₃	—	2	1	no	—
670	C₂×C₅×D₃	—	2	1	no	—
671	C₂×C₅×D₃	—	2	2	no	—
672	C₂×C₅×D₃	—	2	1	no	—
673	C₂×C₅×D₃	—	2	2	no	—
674	C₂×C₅×D₃	—	4	8	no	—
675	C₂×C₅×D₃	C₂×#41	1	2	yes	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	2	no	—
678	C₃×C₄×C₅	—	2	1	no	—
679	C₃×C₄×C₅	—	2	2	no	—
680	C₃×C₄×C₅	—	2	2	no	—
681	C₃×C₄×C₅	—	2	1	no	—
682	C₃×C₄×C₅	—	2	1	no	—
683	C₃×C₄×C₅	C₂×#41	1	2	yes	—
684	C₃×C₄×C₅	C₂×#41	1	2	yes	—
685	C₅×Dic₃	—	2	1	no	—
686	C₅×Dic₃	—	2	2	no	—
687	C₅×Dic₃	—	2	2	no	—
688	C₅×Dic₃	—	2	1	no	—
689	C₅×Dic₃	—	2	1	no	—
690	C₅×Dic₃	—	2	1	no	—
691	C₅×Dic₃	—	2	2	no	—
692	C₅×Dic₃	—	2	1	no	—
693	C₅×Dic₃	C₂×#41	1	2	yes	—
694	C₂³×D₃	C₂³×C₅	1	2	yes	—
695	C₃×#41	—	2	4	no	—
696	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
697	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
698	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
699	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
700	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
701	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
702	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
703	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
704	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
705	C₂×#67	C₂³×C₅	1	2	yes	—
706	C₂×#67	C₂³×C₅	1	2	yes	—
707	C₂×#67	C₂³×C₅	1	1	yes	characteristic
708	C₂×#67	C₂³×C₅	1	1	yes	characteristic
709	C₂×#67	C₂³×C₅	1	2	yes	—
710	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
711	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
712	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
713	#237	—	2	4	no	—
714	D₃×D₄	—	2	4	no	—
715	#235	—	2	4	no	—
716	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
717	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
718	C₂×D₁₂	C₂³×C₅	1	2	yes	—
719	C₂×C₄×D₃	—	2	8	no	—
720	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
721	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
723	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
724	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
725	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
726	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
727	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
728	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
729	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
730	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
731	C₂×Dic₆	C₂³×C₅	1	2	yes	—
732	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
733	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
734	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
735	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
736	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
737	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
738	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
739	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
740	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
741	C₃×C₄²	C₂³×C₅	1	2	yes	—
742	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
743	C₃×C₄²	C₂³×C₅	1	2	yes	—
744	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
745	C₃×C₄²	C₂³×C₅	1	2	yes	—
746	#217	C₂³×C₅	1	2	yes	—
747	#217	C₂³×C₅	1	2	yes	—
748	#217	C₂³×C₅	1	1	yes	characteristic
749	#217	C₂³×C₅	1	2	yes	—
750	#217	C₂³×C₅	1	1	yes	characteristic
751	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
752	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
753	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
754	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
755	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
756	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
757	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
758	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
759	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
760	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
761	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
762	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
763	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
764	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
765	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
766	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
767	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
768	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
769	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
770	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
771	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
772	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
773	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
774	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
775	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
776	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
777	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
778	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
779	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
780	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
781	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
782	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
784	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
785	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
786	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
787	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
788	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
789	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
790	C₄×Dic₃	C₂³×C₅	1	2	yes	—
791	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
792	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
793	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
794	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
795	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
796	C₄×Dic₃	C₂³×C₅	1	2	yes	—
797	C₄×Dic₃	C₂³×C₅	1	2	yes	—
798	C₂³×C₅	—	3	1	no	—
799	C₂³×C₅	—	3	2	no	—
800	C₂³×C₅	—	3	1	no	—
801	C₂³×C₅	—	6	4	no	—
802	C₂³×C₅	—	6	4	no	—
803	C₂³×C₅	—	12	2	no	—
804	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
805	C₂³×C₅	C₂³×D₃	1	2	yes	—
806	C₅×Q₈	—	2	2	no	—
807	C₅×Q₈	—	6	2	no	—
808	C₅×Q₈	—	6	2	no	—
809	C₅×Q₈	—	12	2	no	—
810	C₅×D₄	—	2	4	no	—
811	C₅×D₄	—	6	2	no	—
812	C₅×D₄	—	6	2	no	—
813	C₅×D₄	—	6	2	no	—
814	C₅×D₄	—	6	4	no	—
815	C₅×D₄	—	6	4	no	—
816	C₅×D₄	—	6	2	no	—
817	C₅×D₄	—	12	2	no	—
818	C₅×D₄	—	12	2	no	—
819	C₅×D₄	#235	1	4	yes	complemented
820	C₂×C₄×C₅	—	2	4	no	—
821	C₂×C₄×C₅	—	2	2	no	—
822	C₂×C₄×C₅	—	2	4	no	—
823	C₂×C₄×C₅	—	2	2	no	—
824	C₂×C₄×C₅	—	3	1	no	—
825	C₂×C₄×C₅	—	3	4	no	—
826	C₂×C₄×C₅	—	3	1	no	—
827	C₂×C₄×C₅	—	3	1	no	—
828	C₂×C₄×C₅	—	3	1	no	—
829	C₂×C₄×C₅	—	3	2	no	—
830	C₂×C₄×C₅	—	3	1	no	—
831	C₂×C₄×C₅	—	3	2	no	—
832	C₂×C₄×C₅	—	3	1	no	—
833	C₂×C₄×C₅	—	3	2	no	—
834	C₂×C₄×C₅	—	4	1	no	—
835	C₂×C₄×C₅	—	4	2	no	—
836	C₂×C₄×C₅	—	6	4	no	—
837	C₂×C₄×C₅	—	6	4	no	—
838	C₂×C₄×C₅	—	6	4	no	—
839	C₂×C₄×C₅	—	6	4	no	—
840	C₂×C₄×C₅	—	6	2	no	—
841	C₂×C₄×C₅	—	6	2	no	—
842	C₂×C₄×C₅	—	6	4	no	—
843	C₂×C₄×C₅	—	6	2	no	—
844	C₂×C₄×C₅	—	12	1	no	—
845	C₂×C₄×C₅	—	12	1	no	—
846	C₂×C₄×C₅	—	12	2	no	—
847	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
848	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
849	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
850	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
851	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
852	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
853	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
854	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
855	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
856	C₂×#41	—	3	1	no	—
857	C₂×#41	—	3	1	no	—
858	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
859	C₂²×D₄	—	3	1	no	—
860	C₂³×C₄	—	3	2	no	—
861	C₄⋊Q₈	—	3	1	no	—
862	C₄⋊Q₈	—	3	1	no	—
863	#126	—	3	2	no	—
864	#126	—	3	2	no	—
865	#126	—	3	2	no	—
866	#126	—	3	2	no	—
867	#126	—	3	2	no	—
868	#126	—	3	2	no	—
869	#125	—	3	2	no	—
870	#125	—	3	1	no	—
871	#125	—	3	2	no	—
872	#125	—	3	2	no	—
873	#125	—	3	1	no	—
874	#124	—	3	1	no	—
875	#124	—	3	2	no	—
876	#124	—	3	1	no	—
877	#124	—	3	2	no	—
878	#123	—	3	2	no	—
879	#123	—	3	2	no	—
880	#123	—	3	2	no	—
881	#123	—	3	2	no	—
882	#123	—	3	2	no	—
883	#123	—	3	2	no	—
884	#123	—	3	2	no	—
885	#123	—	3	2	no	—
886	C₂²⋊Q₈	—	3	1	no	—
887	C₂²⋊Q₈	—	3	1	no	—
888	C₂²⋊Q₈	—	3	1	no	—
889	C₂²⋊Q₈	—	3	2	no	—
890	C₂²⋊Q₈	—	3	2	no	—
891	C₂²⋊Q₈	—	3	1	no	—
892	C₂²⋊Q₈	—	3	2	no	—
893	C₂²⋊Q₈	—	3	2	no	—
894	C₂²⋊Q₈	—	3	2	no	—
895	#121	—	3	2	no	—
896	#121	—	3	2	no	—
897	#121	—	3	2	no	—
898	#121	—	3	1	no	—
899	#121	—	3	1	no	—
900	#121	—	3	2	no	—
901	#120	—	3	2	no	—
902	#120	—	3	2	no	—
903	C₄×Q₈	—	3	1	no	—
904	C₄×Q₈	—	3	1	no	—
905	C₄×Q₈	—	3	1	no	—
906	C₄×Q₈	—	3	1	no	—
907	C₄×Q₈	—	3	2	no	—
908	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
909	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
910	C₄×D₄	—	3	1	no	—
911	C₄×D₄	—	3	1	no	—
912	C₄×D₄	—	3	2	no	—
913	C₄×D₄	—	3	2	no	—
914	C₄×D₄	—	3	1	no	—
915	C₄×D₄	—	3	1	no	—
916	C₄×D₄	—	3	1	no	—
917	C₄×D₄	—	3	1	no	—
918	C₄×D₄	—	3	2	no	—
919	C₄×D₄	—	3	1	no	—
920	C₄×D₄	—	3	2	no	—
921	C₄×D₄	—	3	2	no	—
922	C₄×D₄	—	3	1	no	—
923	C₄×D₄	—	3	1	no	—
924	C₄×D₄	—	3	1	no	—
925	C₄×D₄	—	3	2	no	—
926	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
927	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
928	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
929	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
930	#117	—	3	1	no	—
931	#117	—	3	1	no	—
932	#117	—	3	2	no	—
933	#117	—	3	1	no	—
934	#117	—	3	2	no	—
935	#117	—	3	2	no	—
936	#117	—	3	2	no	—
937	#117	—	3	2	no	—
938	#117	—	3	2	no	—
939	#117	—	3	2	no	—
940	#117	—	3	2	no	—
941	#117	—	3	1	no	—
942	#117	C₂×C₅×D₃	1	2	yes	complemented
943	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
944	C₂×C₄⋊C₄	—	3	2	no	—
945	C₂×C₄⋊C₄	—	3	2	no	—
946	C₂×C₄⋊C₄	—	3	1	no	—
947	C₂×C₂²⋊C₄	—	3	2	no	—
948	C₂×C₂²⋊C₄	—	3	2	no	—
949	C₂×C₂²⋊C₄	—	3	2	no	—
950	C₂×C₄²	—	3	2	no	—
951	C₂×C₄²	—	3	1	no	—
952	C₂×C₄²	—	3	1	no	—
953	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
954	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
955	C₂×C₃×C₅	—	2	4	no	—
956	C₂×C₃×C₅	—	4	1	no	—
957	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
958	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
959	C₂×C₃×C₅	#585	1	1	yes	characteristic
960	C₅×D₃	—	2	2	no	—
961	C₅×D₃	—	4	1	no	—
962	C₅×D₃	—	4	2	no	—
963	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
964	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
965	C₂²×D₃	—	2	4	no	—
966	C₂²×D₃	—	2	4	no	—
967	C₂²×D₃	—	4	2	no	—
968	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
969	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
970	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
971	C₃×Q₈	—	2	2	no	—
972	C₃×D₄	—	2	4	no	—
973	C₃×D₄	C₅×#41	1	4	yes	complemented
974	C₂×C₃×C₄	—	2	4	no	—
975	C₂×C₃×C₄	—	2	4	no	—
976	C₂×C₃×C₄	—	2	2	no	—
977	C₂×C₃×C₄	—	2	2	no	—
978	C₂×C₃×C₄	—	4	2	no	—
979	C₂×C₃×C₄	—	4	1	no	—
980	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
981	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
982	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
983	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
984	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
985	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
986	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
987	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
988	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
989	#67	—	2	4	no	—
990	#67	—	2	4	no	—
991	#67	—	2	2	no	—
992	#67	—	2	2	no	—
993	#67	—	4	2	no	—
994	C₂×Dic₃	—	2	4	no	—
995	C₂×Dic₃	—	2	4	no	—
996	C₂×Dic₃	—	4	2	no	—
997	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
998	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
999	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1000	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1001	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1002	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1003	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1004	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1005	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1006	D₁₂	—	2	2	no	—
1007	D₁₂	—	2	2	no	—
1008	D₁₂	—	4	2	no	—
1009	C₄×D₃	—	2	4	no	—
1010	C₄×D₃	—	2	4	no	—
1011	C₄×D₃	—	2	2	no	—
1012	C₄×D₃	—	2	2	no	—
1013	C₄×D₃	—	2	2	no	—
1014	C₄×D₃	—	2	4	no	—
1015	C₄×D₃	—	4	1	no	—
1016	C₄×D₃	—	4	1	no	—
1017	C₄×D₃	C₅×#41	1	4	yes	complemented
1018	Dic₆	—	2	2	no	—
1019	Dic₆	—	2	2	no	—
1020	Dic₆	—	4	2	no	—
1021	C₂²×C₅	—	2	2	no	—
1022	C₂²×C₅	—	2	2	no	—
1023	C₂²×C₅	—	2	1	no	—
1024	C₂²×C₅	—	2	1	no	—
1025	C₂²×C₅	—	2	1	no	—
1026	C₂²×C₅	—	3	2	no	—
1027	C₂²×C₅	—	6	1	no	—
1028	C₂²×C₅	—	6	1	no	—
1029	C₂²×C₅	—	6	1	no	—
1030	C₂²×C₅	—	6	2	no	—
1031	C₂²×C₅	—	6	2	no	—
1032	C₂²×C₅	—	6	1	no	—
1033	C₂²×C₅	—	6	1	no	—
1034	C₂²×C₅	—	6	2	no	—
1035	C₂²×C₅	—	12	8	no	—
1036	C₂²×C₅	C₂×#235	1	4	yes	—
1037	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1038	C₄×C₅	—	2	1	no	—
1039	C₄×C₅	—	2	2	no	—
1040	C₄×C₅	—	2	2	no	—
1041	C₄×C₅	—	2	1	no	—
1042	C₄×C₅	—	2	1	no	—
1043	C₄×C₅	—	2	1	no	—
1044	C₄×C₅	—	2	2	no	—
1045	C₄×C₅	—	3	2	no	—
1046	C₄×C₅	—	6	1	no	—
1047	C₄×C₅	—	6	1	no	—
1048	C₄×C₅	—	6	2	no	—
1049	C₄×C₅	—	6	2	no	—
1050	C₄×C₅	—	6	1	no	—
1051	C₄×C₅	—	6	1	no	—
1052	C₄×C₅	—	6	2	no	—
1053	C₄×C₅	—	6	1	no	—
1054	C₄×C₅	C₂×#235	1	2	yes	—
1055	C₄×C₅	D₃×#41	1	2	yes	—
1056	C₂⁴	—	3	2	no	—
1057	#41	—	2	4	no	—
1058	#41	—	6	4	no	—
1059	#41	—	6	4	no	—
1060	C₂×Q₈	—	3	1	no	—
1061	C₂×Q₈	—	3	1	no	—
1062	C₂×Q₈	—	3	2	no	—
1063	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
1064	C₂×D₄	—	3	1	no	—
1065	C₂×D₄	—	3	2	no	—
1066	C₂×D₄	—	3	1	no	—
1067	C₂×D₄	—	3	2	no	—
1068	C₂×D₄	—	3	2	no	—
1069	C₂×D₄	—	3	1	no	—
1070	C₂×D₄	—	3	1	no	—
1071	C₂×D₄	—	3	2	no	—
1072	C₂×D₄	—	6	4	no	—
1073	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
1074	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1075	C₂²×C₄	—	3	1	no	—
1076	C₂²×C₄	—	3	2	no	—
1077	C₂²×C₄	—	3	2	no	—
1078	C₂²×C₄	—	3	2	no	—
1079	C₂²×C₄	—	3	1	no	—
1080	C₂²×C₄	—	3	1	no	—
1081	C₂²×C₄	—	3	1	no	—
1082	C₂²×C₄	—	3	2	no	—
1083	C₂²×C₄	—	3	2	no	—
1084	C₂²×C₄	—	3	2	no	—
1085	C₂²×C₄	—	3	1	no	—
1086	C₂²×C₄	—	3	1	no	—
1087	C₂²×C₄	—	6	8	no	—
1088	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1089	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1090	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1091	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1092	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1093	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1094	C₄⋊C₄	—	3	1	no	—
1095	C₄⋊C₄	—	3	1	no	—
1096	C₄⋊C₄	—	3	2	no	—
1097	C₄⋊C₄	—	3	2	no	—
1098	C₄⋊C₄	—	3	2	no	—
1099	C₄⋊C₄	—	3	2	no	—
1100	C₄⋊C₄	—	3	2	no	—
1101	C₄⋊C₄	—	3	2	no	—
1102	C₄⋊C₄	—	3	1	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	1	no	—
1105	C₄⋊C₄	—	3	1	no	—
1106	C₄⋊C₄	—	3	1	no	—
1107	C₄⋊C₄	—	3	2	no	—
1108	C₄⋊C₄	—	3	2	no	—
1109	C₄⋊C₄	—	3	1	no	—
1110	C₄⋊C₄	—	3	1	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	—	3	2	no	—
1113	C₄⋊C₄	—	3	2	no	—
1114	C₄⋊C₄	—	3	2	no	—
1115	C₄⋊C₄	—	3	2	no	—
1116	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1117	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1118	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1119	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1120	C₂²⋊C₄	—	3	2	no	—
1121	C₂²⋊C₄	—	3	2	no	—
1122	C₂²⋊C₄	—	3	1	no	—
1123	C₂²⋊C₄	—	3	1	no	—
1124	C₂²⋊C₄	—	3	2	no	—
1125	C₂²⋊C₄	—	3	1	no	—
1126	C₂²⋊C₄	—	3	1	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	2	no	—
1129	C₂²⋊C₄	—	3	2	no	—
1130	C₂²⋊C₄	—	3	2	no	—
1131	C₂²⋊C₄	—	3	2	no	—
1132	C₂²⋊C₄	—	3	2	no	—
1133	C₂²⋊C₄	—	3	2	no	—
1134	C₂²⋊C₄	—	3	2	no	—
1135	C₂²⋊C₄	—	3	1	no	—
1136	C₂²⋊C₄	—	3	2	no	—
1137	C₂²⋊C₄	—	3	1	no	—
1138	C₂²⋊C₄	—	3	2	no	—
1139	C₂²⋊C₄	—	3	2	no	—
1140	C₂²⋊C₄	—	3	2	no	—
1141	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1142	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1143	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1144	C₄²	—	3	1	no	—
1145	C₄²	—	3	2	no	—
1146	C₄²	—	3	1	no	—
1147	C₄²	—	3	2	no	—
1148	C₄²	—	3	2	no	—
1149	C₄²	—	3	1	no	—
1150	C₄²	—	3	1	no	—
1151	C₄²	—	3	1	no	—
1152	C₄²	—	3	1	no	—
1153	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1154	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1155	C₄²	C₂²×C₅×D₃	1	2	yes	—
1156	C₄²	C₂²×C₅×D₃	1	2	yes	—
1157	C₄²	C₂²×C₅×D₃	1	2	yes	—
1158	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1159	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1160	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
1161	C₂²×C₃	—	2	2	no	—
1162	C₂²×C₃	—	2	2	no	—
1163	C₂²×C₃	—	2	1	no	—
1164	C₂²×C₃	—	2	1	no	—
1165	C₂²×C₃	—	2	1	no	—
1166	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
1167	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1168	C₂×D₃	—	2	1	no	—
1169	C₂×D₃	—	2	1	no	—
1170	C₂×D₃	—	2	2	no	—
1171	C₂×D₃	—	2	1	no	—
1172	C₂×D₃	—	2	1	no	—
1173	C₂×D₃	—	2	2	no	—
1174	C₂×D₃	—	2	1	no	—
1175	C₂×D₃	—	2	2	no	—
1176	C₂×D₃	—	4	8	no	—
1177	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1178	C₃×C₄	—	2	1	no	—
1179	C₃×C₄	—	2	2	no	—
1180	C₃×C₄	—	2	1	no	—
1181	C₃×C₄	—	2	2	no	—
1182	C₃×C₄	—	2	2	no	—
1183	C₃×C₄	—	2	1	no	—
1184	C₃×C₄	—	2	1	no	—
1185	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1186	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1187	Dic₃	—	2	1	no	—
1188	Dic₃	—	2	2	no	—
1189	Dic₃	—	2	2	no	—
1190	Dic₃	—	2	1	no	—
1191	Dic₃	—	2	1	no	—
1192	Dic₃	—	2	1	no	—
1193	Dic₃	—	2	2	no	—
1194	Dic₃	—	2	1	no	—
1195	Dic₃	C₂×C₅×#41	1	2	yes	—
1196	C₂×C₅	—	2	4	no	—
1197	C₂×C₅	—	4	1	no	—
1198	C₂×C₅	—	6	2	no	—
1199	C₂×C₅	—	12	2	no	—
1200	C₂×C₅	—	12	1	no	—
1201	C₂×C₅	C₂²×#235	1	1	yes	characteristic
1202	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1203	C₂×C₅	#5964	1	1	yes	characteristic
1204	C₂³	—	3	1	no	—
1205	C₂³	—	3	2	no	—
1206	C₂³	—	3	1	no	—
1207	C₂³	—	6	4	no	—
1208	C₂³	—	6	4	no	—
1209	C₂³	—	12	2	no	—
1210	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1211	C₂³	C₂³×C₅×D₃	1	2	yes	—
1212	Q₈	—	2	2	no	—
1213	Q₈	—	6	2	no	—
1214	Q₈	—	6	2	no	—
1215	Q₈	—	12	2	no	—
1216	D₄	—	2	4	no	—
1217	D₄	—	6	2	no	—
1218	D₄	—	6	2	no	—
1219	D₄	—	6	2	no	—
1220	D₄	—	6	4	no	—
1221	D₄	—	6	4	no	—
1222	D₄	—	6	2	no	—
1223	D₄	—	12	2	no	—
1224	D₄	—	12	2	no	—
1225	D₄	C₅×#235	1	4	yes	complemented
1226	C₂×C₄	—	2	4	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	4	no	—
1229	C₂×C₄	—	2	2	no	—
1230	C₂×C₄	—	3	1	no	—
1231	C₂×C₄	—	3	4	no	—
1232	C₂×C₄	—	3	1	no	—
1233	C₂×C₄	—	3	1	no	—
1234	C₂×C₄	—	3	1	no	—
1235	C₂×C₄	—	3	2	no	—
1236	C₂×C₄	—	3	1	no	—
1237	C₂×C₄	—	3	2	no	—
1238	C₂×C₄	—	3	1	no	—
1239	C₂×C₄	—	3	2	no	—
1240	C₂×C₄	—	4	1	no	—
1241	C₂×C₄	—	4	2	no	—
1242	C₂×C₄	—	6	4	no	—
1243	C₂×C₄	—	6	4	no	—
1244	C₂×C₄	—	6	4	no	—
1245	C₂×C₄	—	6	4	no	—
1246	C₂×C₄	—	6	2	no	—
1247	C₂×C₄	—	6	2	no	—
1248	C₂×C₄	—	6	4	no	—
1249	C₂×C₄	—	6	2	no	—
1250	C₂×C₄	—	12	1	no	—
1251	C₂×C₄	—	12	1	no	—
1252	C₂×C₄	—	12	2	no	—
1253	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1254	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1255	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1256	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1257	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1258	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1259	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1260	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1261	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1262	C₂×C₃	—	2	4	no	—
1263	C₂×C₃	—	4	1	no	—
1264	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1265	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1266	C₂×C₃	C₅×#585	1	1	yes	characteristic
1267	D₃	—	2	2	no	—
1268	D₃	—	4	2	no	—
1269	D₃	—	4	1	no	—
1270	C₅	#85841	1	1	yes	characteristic, direct product factor, Sylow
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	2	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	3	2	no	—
1277	C₂²	—	6	1	no	—
1278	C₂²	—	6	1	no	—
1279	C₂²	—	6	1	no	—
1280	C₂²	—	6	2	no	—
1281	C₂²	—	6	2	no	—
1282	C₂²	—	6	1	no	—
1283	C₂²	—	6	1	no	—
1284	C₂²	—	6	2	no	—
1285	C₂²	—	12	8	no	—
1286	C₂²	C₂×C₅×#235	1	4	yes	—
1287	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1288	C₄	—	2	1	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	3	2	no	—
1296	C₄	—	6	1	no	—
1297	C₄	—	6	1	no	—
1298	C₄	—	6	2	no	—
1299	C₄	—	6	2	no	—
1300	C₄	—	6	1	no	—
1301	C₄	—	6	1	no	—
1302	C₄	—	6	2	no	—
1303	C₄	—	6	1	no	—
1304	C₄	C₂×C₅×#235	1	2	yes	—
1305	C₄	C₅×D₃×#41	1	2	yes	—
1306	C₃	C₅×#3475	1	1	yes	characteristic, complemented, Sylow
1307	C₂	—	2	4	no	—
1308	C₂	—	4	1	no	—
1309	C₂	—	6	2	no	—
1310	C₂	—	12	2	no	—
1311	C₂	—	12	1	no	—
1312	C₂	C₂²×C₅×#235	1	1	yes	characteristic
1313	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1314	C₂	C₅×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
2. C₅×#5829	C₂	semidirect
3. C₅×#5824	C₂	semidirect
4. C₅×#5581	C₂	semidirect
5. C₅×#5580	C₂	semidirect
6. C₅×#5578	C₂	semidirect
7. C₅×#5568	C₂	semidirect
8. C₅×#5556	C₂	semidirect
9. C₅×#5554	C₂	semidirect
10. C₅×#5547	C₂	semidirect
11. C₄×C₅×D₃×D₄	C₂	semidirect
12. C₅×#5540	C₂	semidirect
13. C₅×#5539	C₂	semidirect
14. C₅×#5538	C₂	semidirect
15. C₄×C₅×#237	C₂	semidirect
16. C₅×#5532	C₂	semidirect
17. C₅×#5531	C₂	semidirect
18. C₅×#5529	C₂	semidirect
19. C₅×#5527	C₂	semidirect
20. C₅×#5479	C₂	semidirect
21. C₅×#5479	C₂	semidirect
22. C₄×C₅×#235	C₂	semidirect
23. C₂×C₅×#872	C₂	semidirect
30. C₃×C₄×C₅×Q₈	C₂²	semidirect
31. C₃×C₄×C₅×Q₈	C₂²	semidirect
34. C₃×C₄×C₅×D₄	C₂²	semidirect
35. C₃×C₄×C₅×D₄	C₂²	semidirect
36. C₃×C₅×#117	C₂²	semidirect
37. C₃×C₅×#117	C₂²	semidirect
38. C₂×C₃×C₄²×C₅	C₂²	semidirect
39. C₂×C₃×C₄²×C₅	C₂²	semidirect
42. C₅×#946	C₂²	semidirect
43. C₅×#944	C₂²	semidirect
45. C₅×#939	C₂²	semidirect
47. C₅×#935	C₂²	semidirect
53. C₅×#929	C₂²	semidirect
54. C₅×#929	C₂²	semidirect
58. C₄×C₅×#67	C₂²	semidirect
59. C₄×C₅×#67	C₂²	semidirect
60. C₄×C₅×#67	C₂²	semidirect
61. C₄×C₅×#67	C₂²	semidirect
64. C₅×#926	C₂²	semidirect
65. C₅×#924	C₂²	semidirect
66. C₅×#924	C₂²	semidirect
67. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
68. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
69. C₂×C₄×C₅×Dic₃	C₂²	semidirect
70. C₅×#898	C₂²	semidirect
71. C₅×#898	C₂²	semidirect
74. C₅×#896	C₂²	semidirect
77. C₅×#894	C₂²	semidirect
79. C₅×#892	C₂²	semidirect
81. C₅×#890	C₂²	semidirect
82. C₅×#889	C₂²	semidirect
83. C₅×#889	C₂²	semidirect
84. C₅×#888	C₂²	semidirect
85. C₅×#887	C₂²	semidirect
87. C₅×#885	C₂²	semidirect
88. C₅×#884	C₂²	semidirect
92. C₅×#67⋊C₄	C₂²	semidirect
94. C₅×#879	C₂²	semidirect
95. C₅×#878	C₂²	semidirect
96. C₅×#878	C₂²	semidirect
97. C₅×#877	C₂²	semidirect
98. C₅×#876	C₂²	semidirect
99. C₅×#876	C₂²	semidirect
100. C₅×#876	C₂²	semidirect
102. C₅×#875	C₂²	semidirect
106. C₄×C₅×D₁₂	C₂²	semidirect
111. C₅×#872	C₂²	semidirect
112. C₅×#872	C₂²	semidirect
113. C₅×#872	C₂²	semidirect
114. C₅×#872	C₂²	semidirect
115. C₅×#872	C₂²	semidirect
117. C₄²×C₅×D₃	C₂²	semidirect
118. C₅×#870	C₂²	semidirect
119. C₅×#870	C₂²	semidirect
120. C₄×C₅×Dic₆	C₂²	semidirect
121. C₄×C₅×Dic₆	C₂²	semidirect
122. C₄×C₅×Dic₆	C₂²	semidirect
123. C₄×C₅×Dic₆	C₂²	semidirect
124. #85841	C₅	direct (N × H)
145. C₄×C₅×#41	D₃	semidirect
252. C₃×C₄×#41	C₂×C₅	semidirect
253. #5829	C₂×C₅	semidirect
254. #5824	C₂×C₅	semidirect
255. #5581	C₂×C₅	semidirect
256. #5580	C₂×C₅	semidirect
257. #5578	C₂×C₅	semidirect
258. #5568	C₂×C₅	semidirect
259. #5556	C₂×C₅	semidirect
260. #5554	C₂×C₅	semidirect
261. #5547	C₂×C₅	semidirect
262. C₄×D₃×D₄	C₂×C₅	semidirect
263. #5540	C₂×C₅	semidirect
264. #5539	C₂×C₅	semidirect
265. #5538	C₂×C₅	semidirect
266. C₄×#237	C₂×C₅	semidirect
267. #5532	C₂×C₅	semidirect
268. #5531	C₂×C₅	semidirect
269. #5529	C₂×C₅	semidirect
270. #5527	C₂×C₅	semidirect
271. #5479	C₂×C₅	semidirect
272. #5479	C₂×C₅	semidirect
273. C₄×#235	C₂×C₅	semidirect
274. C₂×#872	C₂×C₅	semidirect
327. C₄×C₅×Q₈	C₂×D₃	semidirect
328. C₄×C₅×Q₈	C₂×D₃	semidirect
347. C₄×C₅×D₄	C₂×D₃	semidirect
348. C₄×C₅×D₄	C₂×D₃	semidirect
361. C₅×#117	C₂×D₃	semidirect
362. C₅×#117	C₂×D₃	semidirect
372. C₂×C₄²×C₅	C₂×D₃	semidirect
373. C₂×C₄²×C₅	C₂×D₃	semidirect
385. C₃×C₅×D₄	#41	semidirect
429. C₄×C₅×D₃	#41	semidirect
438. C₃×C₄×Q₈	C₂²×C₅	semidirect
439. C₃×C₄×Q₈	C₂²×C₅	semidirect
442. C₃×C₄×D₄	C₂²×C₅	semidirect
443. C₃×C₄×D₄	C₂²×C₅	semidirect
444. C₃×#117	C₂²×C₅	semidirect
445. C₃×#117	C₂²×C₅	semidirect
446. C₂×C₃×C₄²	C₂²×C₅	semidirect
447. C₂×C₃×C₄²	C₂²×C₅	semidirect
450. #946	C₂²×C₅	semidirect
451. #944	C₂²×C₅	semidirect
453. #939	C₂²×C₅	semidirect
455. #935	C₂²×C₅	semidirect
461. #929	C₂²×C₅	semidirect
462. #929	C₂²×C₅	semidirect
466. C₄×#67	C₂²×C₅	semidirect
467. C₄×#67	C₂²×C₅	semidirect
468. C₄×#67	C₂²×C₅	semidirect
469. C₄×#67	C₂²×C₅	semidirect
472. #926	C₂²×C₅	semidirect
473. #924	C₂²×C₅	semidirect
474. #924	C₂²×C₅	semidirect
475. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
476. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
477. C₂×C₄×Dic₃	C₂²×C₅	semidirect
478. #898	C₂²×C₅	semidirect
479. #898	C₂²×C₅	semidirect
482. #896	C₂²×C₅	semidirect
485. #894	C₂²×C₅	semidirect
487. #892	C₂²×C₅	semidirect
489. #890	C₂²×C₅	semidirect
490. #889	C₂²×C₅	semidirect
491. #889	C₂²×C₅	semidirect
492. #888	C₂²×C₅	semidirect
493. #887	C₂²×C₅	semidirect
495. #885	C₂²×C₅	semidirect
496. #884	C₂²×C₅	semidirect
500. #67⋊C₄	C₂²×C₅	semidirect
502. #879	C₂²×C₅	semidirect
503. #878	C₂²×C₅	semidirect
504. #878	C₂²×C₅	semidirect
505. #877	C₂²×C₅	semidirect
506. #876	C₂²×C₅	semidirect
507. #876	C₂²×C₅	semidirect
508. #876	C₂²×C₅	semidirect
510. #875	C₂²×C₅	semidirect
514. C₄×D₁₂	C₂²×C₅	semidirect
519. #872	C₂²×C₅	semidirect
520. #872	C₂²×C₅	semidirect
521. #872	C₂²×C₅	semidirect
522. #872	C₂²×C₅	semidirect
523. #872	C₂²×C₅	semidirect
525. C₄²×D₃	C₂²×C₅	semidirect
526. #870	C₂²×C₅	semidirect
527. #870	C₂²×C₅	semidirect
528. C₄×Dic₆	C₂²×C₅	semidirect
529. C₄×Dic₆	C₂²×C₅	semidirect
530. C₄×Dic₆	C₂²×C₅	semidirect
531. C₄×Dic₆	C₂²×C₅	semidirect
656. C₄×#41	C₅×D₃	semidirect
819. C₅×D₄	#235	semidirect
908. C₄×Q₈	C₂×C₅×D₃	semidirect
909. C₄×Q₈	C₂×C₅×D₃	semidirect
928. C₄×D₄	C₂×C₅×D₃	semidirect
929. C₄×D₄	C₂×C₅×D₃	semidirect
942. #117	C₂×C₅×D₃	semidirect
943. #117	C₂×C₅×D₃	semidirect
953. C₂×C₄²	C₂×C₅×D₃	semidirect
954. C₂×C₄²	C₂×C₅×D₃	semidirect
973. C₃×D₄	C₅×#41	semidirect
1017. C₄×D₃	C₅×#41	semidirect
1160. C₃×C₅	#3475	semidirect
1225. D₄	C₅×#235	semidirect
1270. C₅	#85841	direct (N × H)
1306. C₃	C₅×#3475	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₅×#5829	2
C₅×#5824	2
C₅×#5581	2
C₅×#5580	2
C₅×#5578	2
C₅×#5568	2
C₅×#5556	2
C₅×#5554	2
C₅×#5547	2
C₄×C₅×D₃×D₄	2
C₅×#5540	2
C₅×#5539	2
C₅×#5538	2
C₄×C₅×#237	2
C₅×#5532	2
C₅×#5531	2
C₅×#5529	2
C₅×#5527	2
C₅×#5479	2
C₄×C₅×#235	2
C₂×C₅×#872	2
C₅×#3475	3
#85841	5

Subgroups — C5×#85841 #14484141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#85841 #14484141