Subgroups — C₅×#86151 #14484123

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×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5708	C₂	1	2	yes	maximal, complemented
3	C₅×#5705	C₂	1	2	yes	maximal, complemented
4	C₅×#5694	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5690	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5671	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5661	C₂	1	2	yes	maximal, complemented
9	C₅×#5659	C₂	1	2	yes	maximal, complemented
10	C₅×#5639	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5616	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5612	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5578	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#5557	C₂	1	2	yes	maximal, complemented
17	C₅×#5557	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#5547	C₂	1	2	yes	maximal, complemented
19	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#5528	C₂	1	2	yes	maximal, complemented
21	C₅×D₃×#117	C₂	1	2	yes	maximal, complemented
22	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#3475	—	3	1	no	maximal, Hall
25	C₂×C₅×#239	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	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×C₅×#126	C₂²	1	2	yes	complemented
31	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#124	C₂²	1	1	yes	characteristic
33	C₃×C₅×#123	C₂²	1	2	yes	complemented
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
39	C₃×C₅×#117	C₂²	1	2	yes	complemented
40	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
41	C₅×#946	C₂²	1	1	yes	characteristic
42	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₅×#944	C₂²	1	1	yes	characteristic, complemented
44	C₅×#939	C₂²	1	2	yes	complemented
45	C₅×#938	C₂²	1	2	yes	—
46	C₅×#938	C₂²	1	1	yes	characteristic
47	C₅×#937	C₂²	1	2	yes	—
48	C₅×#936	C₂²	1	1	yes	characteristic
49	C₅×#936	C₂²	1	2	yes	complemented
50	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×C₅×#67	C₂²	1	1	yes	characteristic
52	C₄×C₅×#67	C₂²	1	1	yes	characteristic
53	C₄×C₅×#67	C₂²	1	2	yes	—
54	C₄×C₅×#67	C₂²	1	2	yes	complemented
55	C₄×C₅×#67	C₂²	1	1	yes	characteristic, complemented
56	C₄×C₅×#67	C₂²	1	2	yes	complemented
57	C₄×C₅×#67	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₅×#67	C₂²	1	2	yes	complemented
59	C₅×#926	C₂²	1	1	yes	characteristic, complemented
60	C₅×#926	C₂²	1	1	yes	characteristic, complemented
61	C₅×#926	C₂²	1	2	yes	complemented
62	C₅×#898	C₂²	1	2	yes	complemented
63	C₅×#897	C₂²	1	1	yes	characteristic
64	C₅×#897	C₂²	1	2	yes	complemented
65	C₅×#897	C₂²	1	1	yes	characteristic, complemented
66	C₅×#896	C₂²	1	2	yes	—
67	C₅×#896	C₂²	1	2	yes	complemented
68	C₅×#896	C₂²	1	2	yes	complemented
69	C₅×#894	C₂²	1	2	yes	—
70	C₅×#894	C₂²	1	2	yes	complemented
71	C₅×#893	C₂²	1	1	yes	characteristic
72	C₅×#893	C₂²	1	1	yes	characteristic
73	C₅×#893	C₂²	1	2	yes	complemented
74	C₅×#892	C₂²	1	2	yes	—
75	C₅×#892	C₂²	1	2	yes	—
76	C₅×#892	C₂²	1	2	yes	complemented
77	C₅×#892	C₂²	1	1	yes	characteristic, complemented
78	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₅×#890	C₂²	1	1	yes	characteristic, complemented
82	C₅×#890	C₂²	1	2	yes	complemented
83	C₅×#889	C₂²	1	2	yes	complemented
84	C₅×#889	C₂²	1	2	yes	complemented
85	C₅×#888	C₂²	1	1	yes	characteristic, complemented
86	C₅×#885	C₂²	1	2	yes	complemented
87	C₅×#884	C₂²	1	2	yes	—
88	C₅×#884	C₂²	1	2	yes	complemented
89	C₅×#883	C₂²	1	2	yes	—
90	C₅×#883	C₂²	1	2	yes	—
91	C₅×#883	C₂²	1	2	yes	—
92	C₅×#883	C₂²	1	2	yes	complemented
93	C₅×#883	C₂²	1	2	yes	complemented
94	C₅×#882	C₂²	1	2	yes	—
95	C₅×#67⋊C₄	C₂²	1	2	yes	—
96	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₅×#879	C₂²	1	2	yes	complemented
100	C₅×#879	C₂²	1	2	yes	complemented
101	C₅×#879	C₂²	1	2	yes	complemented
102	C₅×#879	C₂²	1	2	yes	complemented
103	C₅×#878	C₂²	1	2	yes	complemented
104	C₅×#877	C₂²	1	2	yes	complemented
105	C₅×#877	C₂²	1	2	yes	complemented
106	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
107	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
108	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
109	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
110	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
111	C₅×#872	C₂²	1	1	yes	characteristic
112	C₅×#872	C₂²	1	2	yes	—
113	C₅×#872	C₂²	1	2	yes	complemented
114	C₅×#872	C₂²	1	1	yes	characteristic, complemented
115	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
116	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
117	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
118	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
119	C₄×C₅×Dic₆	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	#86151	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	2	no	—
130	C₅×#552	—	3	1	no	—
131	C₅×#552	—	3	1	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	D₃	1	1	yes	characteristic, complemented
142	C₅×#525	—	3	2	no	—
143	C₄×C₅×#41	—	3	1	no	—
144	C₄×C₅×#41	—	3	1	no	—
145	C₄×C₅×#41	—	3	1	no	—
146	C₂×C₄×C₅×D₄	—	3	1	no	—
147	C₂×C₅×#117	—	3	2	no	—
148	C₂³×C₅×D₃	C₂³	1	2	yes	—
149	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
152	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂×C₅×#67	C₂³	1	2	yes	—
157	C₂×C₅×#67	C₂³	1	1	yes	characteristic
158	C₂×C₅×#67	C₂³	1	2	yes	—
159	C₂×C₅×#67	C₂³	1	1	yes	characteristic
160	C₂×C₅×#67	C₂³	1	2	yes	—
161	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
162	C₅×#239	—	2	4	no	—
163	C₅×D₃×D₄	—	2	4	no	—
164	C₅×#235	—	2	4	no	—
165	C₅×#235	—	2	4	no	—
166	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
167	C₂×C₅×D₁₂	C₂³	1	2	yes	—
168	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
169	C₂×C₄×C₅×D₃	—	2	8	no	—
170	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
171	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
172	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
174	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
176	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
177	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
178	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
188	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₃×C₄²×C₅	C₂³	1	2	yes	—
200	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
201	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₅×#217	C₂³	1	2	yes	—
203	C₅×#217	C₂³	1	2	yes	—
204	C₅×#217	C₂³	1	2	yes	—
205	C₅×#217	C₂³	1	2	yes	—
206	C₅×#217	C₂³	1	1	yes	characteristic
207	C₅×#217	C₂³	1	2	yes	—
208	C₅×#217	C₂³	1	1	yes	characteristic
209	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
210	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
214	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
216	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
226	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
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	1	yes	characteristic
233	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
242	C₄×C₅×Dic₃	C₂³	1	2	yes	—
243	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×C₅×Dic₃	C₂³	1	2	yes	—
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	2	yes	—
250	C₄×C₅×Dic₃	C₂³	1	2	yes	—
251	C₄×C₅×Dic₃	C₂³	1	2	yes	—
252	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
253	#5708	C₂×C₅	1	2	yes	complemented
254	#5705	C₂×C₅	1	2	yes	complemented
255	#5694	C₂×C₅	1	1	yes	characteristic, complemented
256	#5690	C₂×C₅	1	1	yes	characteristic, complemented
257	#5676	C₂×C₅	1	1	yes	characteristic, complemented
258	#5671	C₂×C₅	1	1	yes	characteristic, complemented
259	#5661	C₂×C₅	1	2	yes	complemented
260	#5659	C₂×C₅	1	2	yes	complemented
261	#5639	C₂×C₅	1	1	yes	characteristic, complemented
262	#5631	C₂×C₅	1	1	yes	characteristic, complemented
263	#5616	C₂×C₅	1	1	yes	characteristic, complemented
264	#5612	C₂×C₅	1	1	yes	characteristic, complemented
265	#5578	C₂×C₅	1	1	yes	characteristic, complemented
266	C₄×#239	C₂×C₅	1	1	yes	characteristic, complemented
267	#5557	C₂×C₅	1	2	yes	complemented
268	#5557	C₂×C₅	1	1	yes	characteristic, complemented
269	#5547	C₂×C₅	1	2	yes	complemented
270	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
271	#5528	C₂×C₅	1	2	yes	complemented
272	D₃×#117	C₂×C₅	1	2	yes	complemented
273	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
274	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
275	C₂×C₅×#41	—	3	1	no	—
276	C₂×C₅×#41	—	3	1	no	—
277	C₂×C₅×#41	—	3	1	no	—
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	C₂×D₃	1	2	yes	complemented
288	C₅×#125	—	3	2	no	—
289	C₅×#125	—	3	2	no	—
290	C₅×#125	—	3	2	no	—
291	C₅×#125	—	3	1	no	—
292	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
293	C₅×#124	—	3	1	no	—
294	C₅×#124	—	3	2	no	—
295	C₅×#124	—	3	2	no	—
296	C₅×#124	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	2	yes	complemented
305	C₅×C₂²⋊Q₈	—	3	1	no	—
306	C₅×C₂²⋊Q₈	—	3	2	no	—
307	C₅×C₂²⋊Q₈	—	3	2	no	—
308	C₅×C₂²⋊Q₈	—	3	2	no	—
309	C₅×C₂²⋊Q₈	—	3	1	no	—
310	C₅×C₂²⋊Q₈	—	3	1	no	—
311	C₅×C₂²⋊Q₈	—	3	2	no	—
312	C₅×C₂²⋊Q₈	—	3	2	no	—
313	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
314	C₅×#121	—	3	2	no	—
315	C₅×#121	—	3	1	no	—
316	C₅×#121	—	3	2	no	—
317	C₅×#121	—	3	2	no	—
318	C₅×#121	—	3	2	no	—
319	C₅×#121	C₂×D₃	1	1	yes	characteristic
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	1	no	—
327	C₄×C₅×Q₈	—	3	2	no	—
328	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
329	C₄×C₅×D₄	—	3	1	no	—
330	C₄×C₅×D₄	—	3	2	no	—
331	C₄×C₅×D₄	—	3	1	no	—
332	C₄×C₅×D₄	—	3	1	no	—
333	C₄×C₅×D₄	—	3	2	no	—
334	C₄×C₅×D₄	—	3	1	no	—
335	C₄×C₅×D₄	—	3	2	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	1	no	—
340	C₄×C₅×D₄	—	3	2	no	—
341	C₄×C₅×D₄	—	3	2	no	—
342	C₄×C₅×D₄	—	3	1	no	—
343	C₄×C₅×D₄	—	3	1	no	—
344	C₄×C₅×D₄	—	3	1	no	—
345	C₄×C₅×D₄	—	3	1	no	—
346	C₄×C₅×D₄	—	3	2	no	—
347	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
348	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
349	C₅×#117	—	3	2	no	—
350	C₅×#117	—	3	1	no	—
351	C₅×#117	—	3	1	no	—
352	C₅×#117	—	3	2	no	—
353	C₅×#117	—	3	2	no	—
354	C₅×#117	—	3	2	no	—
355	C₅×#117	—	3	1	no	—
356	C₅×#117	—	3	2	no	—
357	C₅×#117	—	3	2	no	—
358	C₅×#117	—	3	1	no	—
359	C₅×#117	—	3	2	no	—
360	C₅×#117	—	3	1	no	—
361	C₅×#117	—	3	2	no	—
362	C₅×#117	C₂×D₃	1	2	yes	complemented
363	C₂×C₅×C₄⋊C₄	—	3	1	no	—
364	C₂×C₅×C₄⋊C₄	—	3	2	no	—
365	C₂×C₅×C₄⋊C₄	—	3	2	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	1	no	—
370	C₂×C₄²×C₅	—	3	2	no	—
371	C₂×C₄²×C₅	—	3	2	no	—
372	C₂×C₄²×C₅	—	3	1	no	—
373	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
374	#3475	—	3	1	no	Sylow
375	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
376	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
381	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
383	C₃×C₅×Q₈	—	2	2	no	—
384	C₃×C₅×D₄	—	2	2	no	—
385	C₃×C₅×D₄	—	4	2	no	—
386	C₂×C₃×C₄×C₅	—	2	4	no	—
387	C₂×C₃×C₄×C₅	—	2	2	no	—
388	C₂×C₃×C₄×C₅	—	2	2	no	—
389	C₂×C₃×C₄×C₅	—	4	1	no	—
390	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
391	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
392	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
393	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
394	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
399	C₅×#67	—	2	2	no	—
400	C₅×#67	—	2	4	no	—
401	C₅×#67	—	2	4	no	—
402	C₅×#67	—	2	2	no	—
403	C₅×#67	—	4	2	no	—
404	C₂×C₅×Dic₃	—	2	4	no	—
405	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
406	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
410	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
411	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
412	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
414	C₅×D₁₂	—	2	2	no	—
415	C₅×D₁₂	—	2	4	no	—
416	C₅×D₁₂	#41	1	4	yes	complemented
417	C₄×C₅×D₃	—	2	4	no	—
418	C₄×C₅×D₃	—	2	4	no	—
419	C₄×C₅×D₃	—	2	4	no	—
420	C₄×C₅×D₃	—	2	4	no	—
421	C₄×C₅×D₃	—	2	2	no	—
422	C₄×C₅×D₃	—	2	2	no	—
423	C₄×C₅×D₃	—	2	2	no	—
424	C₄×C₅×D₃	—	2	4	no	—
425	C₄×C₅×D₃	—	4	1	no	—
426	C₄×C₅×D₃	—	4	2	no	—
427	C₄×C₅×D₃	—	4	2	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×#239	C₂²×C₅	1	1	yes	characteristic
434	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
435	C₂×#235	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×#126	C₂²×C₅	1	2	yes	complemented
439	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₃×#124	C₂²×C₅	1	1	yes	characteristic
441	C₃×#123	C₂²×C₅	1	2	yes	complemented
442	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
443	C₃×#121	C₂²×C₅	1	1	yes	characteristic
444	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
445	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
446	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
447	C₃×#117	C₂²×C₅	1	2	yes	complemented
448	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
449	#946	C₂²×C₅	1	1	yes	characteristic
450	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
451	#944	C₂²×C₅	1	1	yes	characteristic, complemented
452	#939	C₂²×C₅	1	2	yes	complemented
453	#938	C₂²×C₅	1	2	yes	—
454	#938	C₂²×C₅	1	1	yes	characteristic
455	#937	C₂²×C₅	1	2	yes	—
456	#936	C₂²×C₅	1	1	yes	characteristic
457	#936	C₂²×C₅	1	2	yes	complemented
458	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
459	C₄×#67	C₂²×C₅	1	1	yes	characteristic
460	C₄×#67	C₂²×C₅	1	1	yes	characteristic
461	C₄×#67	C₂²×C₅	1	2	yes	—
462	C₄×#67	C₂²×C₅	1	2	yes	complemented
463	C₄×#67	C₂²×C₅	1	1	yes	characteristic, complemented
464	C₄×#67	C₂²×C₅	1	2	yes	complemented
465	C₄×#67	C₂²×C₅	1	1	yes	characteristic, complemented
466	C₄×#67	C₂²×C₅	1	2	yes	complemented
467	#926	C₂²×C₅	1	1	yes	characteristic, complemented
468	#926	C₂²×C₅	1	1	yes	characteristic, complemented
469	#926	C₂²×C₅	1	2	yes	complemented
470	#898	C₂²×C₅	1	2	yes	complemented
471	#897	C₂²×C₅	1	1	yes	characteristic
472	#897	C₂²×C₅	1	2	yes	complemented
473	#897	C₂²×C₅	1	1	yes	characteristic, complemented
474	#896	C₂²×C₅	1	2	yes	—
475	#896	C₂²×C₅	1	2	yes	complemented
476	#896	C₂²×C₅	1	2	yes	complemented
477	#894	C₂²×C₅	1	2	yes	—
478	#894	C₂²×C₅	1	2	yes	complemented
479	#893	C₂²×C₅	1	1	yes	characteristic
480	#893	C₂²×C₅	1	1	yes	characteristic
481	#893	C₂²×C₅	1	2	yes	complemented
482	#892	C₂²×C₅	1	2	yes	—
483	#892	C₂²×C₅	1	2	yes	—
484	#892	C₂²×C₅	1	2	yes	complemented
485	#892	C₂²×C₅	1	1	yes	characteristic, complemented
486	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
487	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
488	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
489	#890	C₂²×C₅	1	1	yes	characteristic, complemented
490	#890	C₂²×C₅	1	2	yes	complemented
491	#889	C₂²×C₅	1	2	yes	complemented
492	#889	C₂²×C₅	1	2	yes	complemented
493	#888	C₂²×C₅	1	1	yes	characteristic, complemented
494	#885	C₂²×C₅	1	2	yes	complemented
495	#884	C₂²×C₅	1	2	yes	—
496	#884	C₂²×C₅	1	2	yes	complemented
497	#883	C₂²×C₅	1	2	yes	—
498	#883	C₂²×C₅	1	2	yes	—
499	#883	C₂²×C₅	1	2	yes	—
500	#883	C₂²×C₅	1	2	yes	complemented
501	#883	C₂²×C₅	1	2	yes	complemented
502	#882	C₂²×C₅	1	2	yes	—
503	#67⋊C₄	C₂²×C₅	1	2	yes	—
504	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
505	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
506	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
507	#879	C₂²×C₅	1	2	yes	complemented
508	#879	C₂²×C₅	1	2	yes	complemented
509	#879	C₂²×C₅	1	2	yes	complemented
510	#879	C₂²×C₅	1	2	yes	complemented
511	#878	C₂²×C₅	1	2	yes	complemented
512	#877	C₂²×C₅	1	2	yes	complemented
513	#877	C₂²×C₅	1	2	yes	complemented
514	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
515	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
516	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
517	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
518	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
519	#872	C₂²×C₅	1	1	yes	characteristic
520	#872	C₂²×C₅	1	2	yes	—
521	#872	C₂²×C₅	1	2	yes	complemented
522	#872	C₂²×C₅	1	1	yes	characteristic, complemented
523	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
524	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
525	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
526	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
527	C₄×Dic₆	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	—	6	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	1	yes	characteristic
550	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
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	2	no	—
560	C₂²×C₄×C₅	—	3	1	no	—
561	C₂²×C₄×C₅	—	3	1	no	—
562	C₂²×C₄×C₅	—	3	2	no	—
563	C₂²×C₄×C₅	—	3	2	no	—
564	C₂²×C₄×C₅	—	3	1	no	—
565	C₂²×C₄×C₅	—	6	8	no	—
566	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
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	1	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	1	no	—
580	C₅×C₄⋊C₄	—	3	1	no	—
581	C₅×C₄⋊C₄	—	3	2	no	—
582	C₅×C₄⋊C₄	—	3	2	no	—
583	C₅×C₄⋊C₄	—	3	2	no	—
584	C₅×C₄⋊C₄	—	3	1	no	—
585	C₅×C₄⋊C₄	—	3	1	no	—
586	C₅×C₄⋊C₄	—	3	2	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	C₂²×D₃	1	2	yes	—
591	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
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	2	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	2	no	—
603	C₅×C₂²⋊C₄	—	3	1	no	—
604	C₅×C₂²⋊C₄	—	3	1	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	C₂²×D₃	1	2	yes	—
616	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
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	2	no	—
623	C₄²×C₅	—	3	2	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	1	no	—
629	C₄²×C₅	—	3	1	no	—
630	C₄²×C₅	—	3	2	no	—
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	2	no	—
641	#552	—	3	1	no	—
642	#552	—	3	1	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	C₅×D₃	1	1	yes	characteristic, complemented
653	#525	—	3	2	no	—
654	C₄×#41	—	3	1	no	—
655	C₄×#41	—	3	1	no	—
656	C₄×#41	—	3	1	no	—
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	1	no	—
661	C₂²×C₃×C₅	—	2	1	no	—
662	C₂²×C₃×C₅	—	2	2	no	—
663	C₂²×C₃×C₅	—	2	2	no	—
664	C₂²×C₃×C₅	—	2	1	no	—
665	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
666	C₂×C₅×D₃	—	2	2	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	1	no	—
672	C₂×C₅×D₃	—	2	1	no	—
673	C₂×C₅×D₃	—	4	8	no	—
674	C₂×C₅×D₃	C₂×#41	1	2	yes	—
675	C₂×C₅×D₃	C₂×#41	1	4	yes	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	1	no	—
678	C₃×C₄×C₅	—	2	2	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	2	no	—
686	C₅×Dic₃	—	2	1	no	—
687	C₅×Dic₃	—	2	1	no	—
688	C₅×Dic₃	—	2	2	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	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
696	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
697	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
698	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
699	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
700	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
701	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
702	C₂×#67	C₂³×C₅	1	2	yes	—
703	C₂×#67	C₂³×C₅	1	1	yes	characteristic
704	C₂×#67	C₂³×C₅	1	2	yes	—
705	C₂×#67	C₂³×C₅	1	1	yes	characteristic
706	C₂×#67	C₂³×C₅	1	2	yes	—
707	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
708	#239	—	2	4	no	—
709	D₃×D₄	—	2	4	no	—
710	#235	—	2	4	no	—
711	#235	—	2	4	no	—
712	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
713	C₂×D₁₂	C₂³×C₅	1	2	yes	—
714	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
715	C₂×C₄×D₃	—	2	8	no	—
716	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
717	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
718	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
719	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
720	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
721	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
722	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
723	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
724	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
734	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
735	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
736	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
737	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
738	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
739	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
740	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
741	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
742	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
743	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
744	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
745	C₃×C₄²	C₂³×C₅	1	2	yes	—
746	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
747	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
748	#217	C₂³×C₅	1	2	yes	—
749	#217	C₂³×C₅	1	2	yes	—
750	#217	C₂³×C₅	1	2	yes	—
751	#217	C₂³×C₅	1	2	yes	—
752	#217	C₂³×C₅	1	1	yes	characteristic
753	#217	C₂³×C₅	1	2	yes	—
754	#217	C₂³×C₅	1	1	yes	characteristic
755	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
756	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
760	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
761	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
762	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
772	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
773	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
774	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
779	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
780	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
788	C₄×Dic₃	C₂³×C₅	1	2	yes	—
789	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
790	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
791	C₄×Dic₃	C₂³×C₅	1	2	yes	—
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	2	yes	—
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	2	yes	—
805	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
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	2	no	—
811	C₅×D₄	—	3	4	no	—
812	C₅×D₄	—	4	2	no	—
813	C₅×D₄	—	6	2	no	—
814	C₅×D₄	—	6	4	no	—
815	C₅×D₄	—	6	2	no	—
816	C₅×D₄	—	6	4	no	—
817	C₅×D₄	—	6	2	no	—
818	C₅×D₄	—	6	4	no	—
819	C₅×D₄	—	12	2	no	—
820	C₂×C₄×C₅	—	2	4	no	—
821	C₂×C₄×C₅	—	2	2	no	—
822	C₂×C₄×C₅	—	2	2	no	—
823	C₂×C₄×C₅	—	3	1	no	—
824	C₂×C₄×C₅	—	3	4	no	—
825	C₂×C₄×C₅	—	3	2	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	1	no	—
830	C₂×C₄×C₅	—	3	2	no	—
831	C₂×C₄×C₅	—	3	2	no	—
832	C₂×C₄×C₅	—	3	1	no	—
833	C₂×C₄×C₅	—	4	1	no	—
834	C₂×C₄×C₅	—	6	4	no	—
835	C₂×C₄×C₅	—	6	4	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	2	no	—
843	C₂×C₄×C₅	—	12	1	no	—
844	C₂×C₄×C₅	—	12	2	no	—
845	C₂×C₄×C₅	—	12	1	no	—
846	C₂×C₄×C₅	—	12	2	no	—
847	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
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	2	yes	—
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	—	3	1	no	—
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	C₂×C₅×D₃	1	2	yes	complemented
869	#125	—	3	2	no	—
870	#125	—	3	2	no	—
871	#125	—	3	1	no	—
872	#125	—	3	2	no	—
873	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
874	#124	—	3	1	no	—
875	#124	—	3	2	no	—
876	#124	—	3	2	no	—
877	#124	C₂×C₅×D₃	1	1	yes	characteristic
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	C₂×C₅×D₃	1	2	yes	complemented
886	C₂²⋊Q₈	—	3	1	no	—
887	C₂²⋊Q₈	—	3	2	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	C₂×C₅×D₃	1	1	yes	characteristic, complemented
895	#121	—	3	2	no	—
896	#121	—	3	2	no	—
897	#121	—	3	1	no	—
898	#121	—	3	2	no	—
899	#121	—	3	2	no	—
900	#121	C₂×C₅×D₃	1	1	yes	characteristic
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	1	no	—
908	C₄×Q₈	—	3	2	no	—
909	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
910	C₄×D₄	—	3	1	no	—
911	C₄×D₄	—	3	2	no	—
912	C₄×D₄	—	3	2	no	—
913	C₄×D₄	—	3	1	no	—
914	C₄×D₄	—	3	1	no	—
915	C₄×D₄	—	3	1	no	—
916	C₄×D₄	—	3	2	no	—
917	C₄×D₄	—	3	1	no	—
918	C₄×D₄	—	3	2	no	—
919	C₄×D₄	—	3	1	no	—
920	C₄×D₄	—	3	1	no	—
921	C₄×D₄	—	3	2	no	—
922	C₄×D₄	—	3	2	no	—
923	C₄×D₄	—	3	1	no	—
924	C₄×D₄	—	3	2	no	—
925	C₄×D₄	—	3	1	no	—
926	C₄×D₄	—	3	1	no	—
927	C₄×D₄	—	3	1	no	—
928	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
929	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
930	#117	—	3	2	no	—
931	#117	—	3	1	no	—
932	#117	—	3	1	no	—
933	#117	—	3	2	no	—
934	#117	—	3	2	no	—
935	#117	—	3	2	no	—
936	#117	—	3	1	no	—
937	#117	—	3	2	no	—
938	#117	—	3	2	no	—
939	#117	—	3	1	no	—
940	#117	—	3	2	no	—
941	#117	—	3	1	no	—
942	#117	—	3	2	no	—
943	#117	C₂×C₅×D₃	1	2	yes	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	2	no	—
952	C₂×C₄²	—	3	1	no	—
953	C₂×C₄²	—	3	1	no	—
954	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
955	C₂×C₃×C₅	—	4	2	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	—	2	4	no	—
962	C₅×D₃	—	4	1	no	—
963	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
964	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
965	C₂²×D₃	—	2	4	no	—
966	C₂²×D₃	—	2	4	no	—
967	C₂²×D₃	—	4	2	no	—
968	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
969	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
970	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
971	C₃×Q₈	—	2	2	no	—
972	C₃×D₄	—	2	2	no	—
973	C₃×D₄	—	4	2	no	—
974	C₂×C₃×C₄	—	2	4	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	2	2	no	—
977	C₂×C₃×C₄	—	4	1	no	—
978	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
979	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
980	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
981	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
982	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
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	1	yes	characteristic
987	#67	—	2	2	no	—
988	#67	—	2	4	no	—
989	#67	—	2	4	no	—
990	#67	—	2	2	no	—
991	#67	—	4	2	no	—
992	C₂×Dic₃	—	2	4	no	—
993	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
994	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
995	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
996	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
997	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
998	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
999	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1000	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1001	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1002	D₁₂	—	2	2	no	—
1003	D₁₂	—	2	4	no	—
1004	D₁₂	C₅×#41	1	4	yes	complemented
1005	C₄×D₃	—	2	4	no	—
1006	C₄×D₃	—	2	4	no	—
1007	C₄×D₃	—	2	4	no	—
1008	C₄×D₃	—	2	4	no	—
1009	C₄×D₃	—	2	2	no	—
1010	C₄×D₃	—	2	2	no	—
1011	C₄×D₃	—	2	2	no	—
1012	C₄×D₃	—	2	4	no	—
1013	C₄×D₃	—	4	1	no	—
1014	C₄×D₃	—	4	2	no	—
1015	C₄×D₃	—	4	2	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	1	no	—
1023	C₂²×C₅	—	2	1	no	—
1024	C₂²×C₅	—	2	2	no	—
1025	C₂²×C₅	—	2	1	no	—
1026	C₂²×C₅	—	2	2	no	—
1027	C₂²×C₅	—	3	2	no	—
1028	C₂²×C₅	—	3	4	no	—
1029	C₂²×C₅	—	6	2	no	—
1030	C₂²×C₅	—	6	1	no	—
1031	C₂²×C₅	—	6	2	no	—
1032	C₂²×C₅	—	6	1	no	—
1033	C₂²×C₅	—	6	1	no	—
1034	C₂²×C₅	—	6	1	no	—
1035	C₂²×C₅	—	6	1	no	—
1036	C₂²×C₅	—	12	8	no	—
1037	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1038	C₄×C₅	—	2	2	no	—
1039	C₄×C₅	—	2	1	no	—
1040	C₄×C₅	—	2	1	no	—
1041	C₄×C₅	—	2	2	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	2	no	—
1047	C₄×C₅	—	6	1	no	—
1048	C₄×C₅	—	6	1	no	—
1049	C₄×C₅	—	6	1	no	—
1050	C₄×C₅	—	6	2	no	—
1051	C₄×C₅	—	6	1	no	—
1052	C₄×C₅	—	6	2	no	—
1053	C₄×C₅	—	6	1	no	—
1054	C₄×C₅	D₃×#41	1	2	yes	—
1055	C₄×C₅	D₃×#41	1	2	yes	—
1056	C₂⁴	—	3	2	no	—
1057	#41	—	6	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	1	yes	characteristic
1074	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
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	2	no	—
1080	C₂²×C₄	—	3	1	no	—
1081	C₂²×C₄	—	3	1	no	—
1082	C₂²×C₄	—	3	1	no	—
1083	C₂²×C₄	—	3	2	no	—
1084	C₂²×C₄	—	3	2	no	—
1085	C₂²×C₄	—	3	1	no	—
1086	C₂²×C₄	—	3	2	no	—
1087	C₂²×C₄	—	3	2	no	—
1088	C₂²×C₄	—	3	1	no	—
1089	C₂²×C₄	—	6	8	no	—
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	1	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	1	no	—
1104	C₄⋊C₄	—	3	1	no	—
1105	C₄⋊C₄	—	3	2	no	—
1106	C₄⋊C₄	—	3	2	no	—
1107	C₄⋊C₄	—	3	2	no	—
1108	C₄⋊C₄	—	3	1	no	—
1109	C₄⋊C₄	—	3	1	no	—
1110	C₄⋊C₄	—	3	2	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	—	3	2	no	—
1113	C₄⋊C₄	—	3	2	no	—
1114	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1115	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
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	2	no	—
1123	C₂²⋊C₄	—	3	1	no	—
1124	C₂²⋊C₄	—	3	2	no	—
1125	C₂²⋊C₄	—	3	1	no	—
1126	C₂²⋊C₄	—	3	2	no	—
1127	C₂²⋊C₄	—	3	1	no	—
1128	C₂²⋊C₄	—	3	1	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	C₂²×C₅×D₃	1	2	yes	—
1140	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
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	2	no	—
1147	C₄²	—	3	1	no	—
1148	C₄²	—	3	2	no	—
1149	C₄²	—	3	2	no	—
1150	C₄²	—	3	2	no	—
1151	C₄²	—	3	1	no	—
1152	C₄²	—	3	1	no	—
1153	C₄²	—	3	1	no	—
1154	C₄²	—	3	1	no	—
1155	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1156	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
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	1	no	—
1163	C₂²×C₃	—	2	1	no	—
1164	C₂²×C₃	—	2	2	no	—
1165	C₂²×C₃	—	2	2	no	—
1166	C₂²×C₃	—	2	1	no	—
1167	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1168	C₂×D₃	—	2	2	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	1	no	—
1174	C₂×D₃	—	2	1	no	—
1175	C₂×D₃	—	4	8	no	—
1176	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1177	C₂×D₃	C₂×C₅×#41	1	4	yes	—
1178	C₃×C₄	—	2	1	no	—
1179	C₃×C₄	—	2	1	no	—
1180	C₃×C₄	—	2	2	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	2	no	—
1188	Dic₃	—	2	1	no	—
1189	Dic₃	—	2	1	no	—
1190	Dic₃	—	2	2	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	—	4	2	no	—
1197	C₂×C₅	—	4	1	no	—
1198	C₂×C₅	—	6	2	no	—
1199	C₂×C₅	—	6	4	no	—
1200	C₂×C₅	—	12	1	no	—
1201	C₂×C₅	C₂×D₃×#41	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	2	yes	—
1211	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1212	Q₈	—	2	2	no	—
1213	Q₈	—	6	2	no	—
1214	Q₈	—	6	2	no	—
1215	Q₈	—	12	2	no	—
1216	D₄	—	2	2	no	—
1217	D₄	—	3	4	no	—
1218	D₄	—	4	2	no	—
1219	D₄	—	6	2	no	—
1220	D₄	—	6	4	no	—
1221	D₄	—	6	2	no	—
1222	D₄	—	6	4	no	—
1223	D₄	—	6	2	no	—
1224	D₄	—	6	4	no	—
1225	D₄	—	12	2	no	—
1226	C₂×C₄	—	2	4	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	3	1	no	—
1230	C₂×C₄	—	3	4	no	—
1231	C₂×C₄	—	3	1	no	—
1232	C₂×C₄	—	3	2	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	—	4	1	no	—
1240	C₂×C₄	—	6	4	no	—
1241	C₂×C₄	—	6	4	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	2	no	—
1249	C₂×C₄	—	12	1	no	—
1250	C₂×C₄	—	12	2	no	—
1251	C₂×C₄	—	12	1	no	—
1252	C₂×C₄	—	12	2	no	—
1253	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
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	2	yes	—
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	—	4	2	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	—	2	4	no	—
1269	D₃	—	4	1	no	—
1270	C₅	#86151	1	1	yes	characteristic, direct product factor, Sylow
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	3	2	no	—
1278	C₂²	—	3	4	no	—
1279	C₂²	—	6	2	no	—
1280	C₂²	—	6	1	no	—
1281	C₂²	—	6	2	no	—
1282	C₂²	—	6	1	no	—
1283	C₂²	—	6	1	no	—
1284	C₂²	—	6	1	no	—
1285	C₂²	—	6	1	no	—
1286	C₂²	—	12	8	no	—
1287	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1288	C₄	—	2	2	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	2	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	3	2	no	—
1296	C₄	—	6	2	no	—
1297	C₄	—	6	1	no	—
1298	C₄	—	6	1	no	—
1299	C₄	—	6	1	no	—
1300	C₄	—	6	2	no	—
1301	C₄	—	6	1	no	—
1302	C₄	—	6	2	no	—
1303	C₄	—	6	1	no	—
1304	C₄	C₅×D₃×#41	1	2	yes	—
1305	C₄	C₅×D₃×#41	1	2	yes	—
1306	C₃	C₅×#3475	1	1	yes	characteristic, complemented, Sylow
1307	C₂	—	4	2	no	—
1308	C₂	—	4	1	no	—
1309	C₂	—	6	2	no	—
1310	C₂	—	6	4	no	—
1311	C₂	—	12	1	no	—
1312	C₂	C₂×C₅×D₃×#41	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×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#529	D₃
hypocenter	C₃	C₅×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#529

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#529	C₂	semidirect
2. C₅×#5708	C₂	semidirect
3. C₅×#5705	C₂	semidirect
4. C₅×#5694	C₂	semidirect
5. C₅×#5690	C₂	semidirect
6. C₅×#5676	C₂	semidirect
7. C₅×#5671	C₂	semidirect
8. C₅×#5661	C₂	semidirect
9. C₅×#5659	C₂	semidirect
10. C₅×#5639	C₂	semidirect
11. C₅×#5631	C₂	semidirect
12. C₅×#5616	C₂	semidirect
13. C₅×#5612	C₂	semidirect
14. C₅×#5578	C₂	semidirect
15. C₄×C₅×#239	C₂	semidirect
16. C₅×#5557	C₂	semidirect
17. C₅×#5557	C₂	semidirect
18. C₅×#5547	C₂	semidirect
19. C₄×C₅×D₃×D₄	C₂	semidirect
20. C₅×#5528	C₂	semidirect
21. C₅×D₃×#117	C₂	semidirect
22. C₄×C₅×#235	C₂	semidirect
23. C₄×C₅×#235	C₂	semidirect
30. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#125	C₂²	semidirect
33. C₃×C₅×#123	C₂²	semidirect
34. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×C₅×Q₈	C₂²	semidirect
38. C₃×C₄×C₅×D₄	C₂²	semidirect
39. C₃×C₅×#117	C₂²	semidirect
40. C₂×C₃×C₄²×C₅	C₂²	semidirect
42. C₅×Q₈×Dic₃	C₂²	semidirect
43. C₅×#944	C₂²	semidirect
44. C₅×#939	C₂²	semidirect
49. C₅×#936	C₂²	semidirect
54. C₄×C₅×#67	C₂²	semidirect
55. C₄×C₅×#67	C₂²	semidirect
56. C₄×C₅×#67	C₂²	semidirect
57. C₄×C₅×#67	C₂²	semidirect
58. C₄×C₅×#67	C₂²	semidirect
59. C₅×#926	C₂²	semidirect
60. C₅×#926	C₂²	semidirect
61. C₅×#926	C₂²	semidirect
62. C₅×#898	C₂²	semidirect
64. C₅×#897	C₂²	semidirect
65. C₅×#897	C₂²	semidirect
67. C₅×#896	C₂²	semidirect
68. C₅×#896	C₂²	semidirect
70. C₅×#894	C₂²	semidirect
73. C₅×#893	C₂²	semidirect
76. C₅×#892	C₂²	semidirect
77. C₅×#892	C₂²	semidirect
79. C₅×D₃×C₄⋊C₄	C₂²	semidirect
80. C₅×D₃×C₄⋊C₄	C₂²	semidirect
81. C₅×#890	C₂²	semidirect
82. C₅×#890	C₂²	semidirect
83. C₅×#889	C₂²	semidirect
84. C₅×#889	C₂²	semidirect
85. C₅×#888	C₂²	semidirect
86. C₅×#885	C₂²	semidirect
88. C₅×#884	C₂²	semidirect
92. C₅×#883	C₂²	semidirect
93. C₅×#883	C₂²	semidirect
99. C₅×#879	C₂²	semidirect
100. C₅×#879	C₂²	semidirect
101. C₅×#879	C₂²	semidirect
102. C₅×#879	C₂²	semidirect
103. C₅×#878	C₂²	semidirect
104. C₅×#877	C₂²	semidirect
105. C₅×#877	C₂²	semidirect
110. C₄×C₅×D₁₂	C₂²	semidirect
113. C₅×#872	C₂²	semidirect
114. C₅×#872	C₂²	semidirect
116. C₄²×C₅×D₃	C₂²	semidirect
117. C₄²×C₅×D₃	C₂²	semidirect
118. C₄²×C₅×D₃	C₂²	semidirect
119. C₄×C₅×Dic₆	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. #86151	C₅	direct (N × H)
141. C₅×#529	D₃	semidirect
252. C₃×#529	C₂×C₅	semidirect
253. #5708	C₂×C₅	semidirect
254. #5705	C₂×C₅	semidirect
255. #5694	C₂×C₅	semidirect
256. #5690	C₂×C₅	semidirect
257. #5676	C₂×C₅	semidirect
258. #5671	C₂×C₅	semidirect
259. #5661	C₂×C₅	semidirect
260. #5659	C₂×C₅	semidirect
261. #5639	C₂×C₅	semidirect
262. #5631	C₂×C₅	semidirect
263. #5616	C₂×C₅	semidirect
264. #5612	C₂×C₅	semidirect
265. #5578	C₂×C₅	semidirect
266. C₄×#239	C₂×C₅	semidirect
267. #5557	C₂×C₅	semidirect
268. #5557	C₂×C₅	semidirect
269. #5547	C₂×C₅	semidirect
270. C₄×D₃×D₄	C₂×C₅	semidirect
271. #5528	C₂×C₅	semidirect
272. D₃×#117	C₂×C₅	semidirect
273. C₄×#235	C₂×C₅	semidirect
274. C₄×#235	C₂×C₅	semidirect
287. C₅×#126	C₂×D₃	semidirect
292. C₅×#125	C₂×D₃	semidirect
304. C₅×#123	C₂×D₃	semidirect
313. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
328. C₄×C₅×Q₈	C₂×D₃	semidirect
348. C₄×C₅×D₄	C₂×D₃	semidirect
362. C₅×#117	C₂×D₃	semidirect
373. C₂×C₄²×C₅	C₂×D₃	semidirect
416. C₅×D₁₂	#41	semidirect
429. C₄×C₅×D₃	#41	semidirect
438. C₃×#126	C₂²×C₅	semidirect
439. C₃×#125	C₂²×C₅	semidirect
441. C₃×#123	C₂²×C₅	semidirect
442. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
444. C₃×C₄×Q₈	C₂²×C₅	semidirect
446. C₃×C₄×D₄	C₂²×C₅	semidirect
447. C₃×#117	C₂²×C₅	semidirect
448. C₂×C₃×C₄²	C₂²×C₅	semidirect
450. Q₈×Dic₃	C₂²×C₅	semidirect
451. #944	C₂²×C₅	semidirect
452. #939	C₂²×C₅	semidirect
457. #936	C₂²×C₅	semidirect
462. C₄×#67	C₂²×C₅	semidirect
463. C₄×#67	C₂²×C₅	semidirect
464. C₄×#67	C₂²×C₅	semidirect
465. C₄×#67	C₂²×C₅	semidirect
466. C₄×#67	C₂²×C₅	semidirect
467. #926	C₂²×C₅	semidirect
468. #926	C₂²×C₅	semidirect
469. #926	C₂²×C₅	semidirect
470. #898	C₂²×C₅	semidirect
472. #897	C₂²×C₅	semidirect
473. #897	C₂²×C₅	semidirect
475. #896	C₂²×C₅	semidirect
476. #896	C₂²×C₅	semidirect
478. #894	C₂²×C₅	semidirect
481. #893	C₂²×C₅	semidirect
484. #892	C₂²×C₅	semidirect
485. #892	C₂²×C₅	semidirect
487. D₃×C₄⋊C₄	C₂²×C₅	semidirect
488. D₃×C₄⋊C₄	C₂²×C₅	semidirect
489. #890	C₂²×C₅	semidirect
490. #890	C₂²×C₅	semidirect
491. #889	C₂²×C₅	semidirect
492. #889	C₂²×C₅	semidirect
493. #888	C₂²×C₅	semidirect
494. #885	C₂²×C₅	semidirect
496. #884	C₂²×C₅	semidirect
500. #883	C₂²×C₅	semidirect
501. #883	C₂²×C₅	semidirect
507. #879	C₂²×C₅	semidirect
508. #879	C₂²×C₅	semidirect
509. #879	C₂²×C₅	semidirect
510. #879	C₂²×C₅	semidirect
511. #878	C₂²×C₅	semidirect
512. #877	C₂²×C₅	semidirect
513. #877	C₂²×C₅	semidirect
518. C₄×D₁₂	C₂²×C₅	semidirect
521. #872	C₂²×C₅	semidirect
522. #872	C₂²×C₅	semidirect
524. C₄²×D₃	C₂²×C₅	semidirect
525. C₄²×D₃	C₂²×C₅	semidirect
526. C₄²×D₃	C₂²×C₅	semidirect
527. C₄×Dic₆	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
652. #529	C₅×D₃	semidirect
868. #126	C₂×C₅×D₃	semidirect
873. #125	C₂×C₅×D₃	semidirect
885. #123	C₂×C₅×D₃	semidirect
894. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
909. C₄×Q₈	C₂×C₅×D₃	semidirect
929. C₄×D₄	C₂×C₅×D₃	semidirect
943. #117	C₂×C₅×D₃	semidirect
954. C₂×C₄²	C₂×C₅×D₃	semidirect
1004. D₁₂	C₅×#41	semidirect
1017. C₄×D₃	C₅×#41	semidirect
1160. C₃×C₅	#3475	semidirect
1270. C₅	#86151	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×C₅×#529	2
C₅×#5708	2
C₅×#5705	2
C₅×#5694	2
C₅×#5690	2
C₅×#5676	2
C₅×#5671	2
C₅×#5661	2
C₅×#5659	2
C₅×#5639	2
C₅×#5631	2
C₅×#5616	2
C₅×#5612	2
C₅×#5578	2
C₄×C₅×#239	2
C₅×#5557	2
C₅×#5547	2
C₄×C₅×D₃×D₄	2
C₅×#5528	2
C₅×D₃×#117	2
C₄×C₅×#235	2
C₅×#3475	3
#86151	5

Subgroups — C5×#86151 #14484123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86151 #14484123