Subgroups — C₇×#62815 #13240031

Order 1792.

7210 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	4	yes	maximal, complemented
2	C₇×#3511	C₂	1	4	yes	maximal, complemented
3	C₇×#3510	C₂	1	4	yes	maximal, complemented
4	C₇×#3509	C₂	1	2	yes	maximal, complemented
5	C₇×#3508	C₂	1	2	yes	maximal, complemented
6	C₇×#3507	C₂	1	4	yes	maximal, complemented
7	C₇×#3506	C₂	1	4	yes	maximal, complemented
8	C₇×#3505	C₂	1	8	yes	maximal, complemented
9	C₇×#3480	C₂	1	8	yes	maximal, complemented
10	C₇×#3475	C₂	1	8	yes	maximal, complemented
11	C₇×#3455	C₂	1	4	yes	maximal, complemented
12	C₇×#3449	C₂	1	2	yes	maximal, complemented
13	C₇×#3444	C₂	1	4	yes	maximal, complemented
14	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3428	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₇×#41	C₂²	1	2	yes	—
20	C₇×#559	C₂²	1	16	yes	complemented
21	C₇×#559	C₂²	1	8	yes	complemented
22	C₇×#557	C₂²	1	8	yes	complemented
23	C₇×#556	C₂²	1	8	yes	complemented
24	C₇×#556	C₂²	1	8	yes	complemented
25	C₇×#556	C₂²	1	16	yes	complemented
26	C₇×#555	C₂²	1	8	yes	complemented
27	C₇×#554	C₂²	1	8	yes	complemented
28	C₇×#553	C₂²	1	16	yes	complemented
29	C₇×#553	C₂²	1	16	yes	complemented
30	C₇×#553	C₂²	1	32	yes	complemented
31	C₇×#552	C₂²	1	16	yes	complemented
32	C₇×#552	C₂²	1	16	yes	complemented
33	C₇×#551	C₂²	1	32	yes	complemented
34	C₇×#550	C₂²	1	8	yes	complemented
35	C₇×#548	C₂²	1	16	yes	complemented
36	C₇×#547	C₂²	1	8	yes	complemented
37	C₇×#546	C₂²	1	16	yes	complemented
38	C₇×#542	C₂²	1	16	yes	complemented
39	C₇×#541	C₂²	1	8	yes	complemented
40	C₇×#540	C₂²	1	8	yes	complemented
41	C₇×#539	C₂²	1	16	yes	complemented
42	C₇×#538	C₂²	1	16	yes	complemented
43	C₇×#537	C₂²	1	8	yes	complemented
44	C₇×#536	C₂²	1	4	yes	—
45	C₇×#536	C₂²	1	4	yes	complemented
46	C₇×#535	C₂²	1	4	yes	—
47	C₇×#535	C₂²	1	4	yes	complemented
48	C₇×#534	C₂²	1	8	yes	—
49	C₇×#533	C₂²	1	2	yes	complemented
50	C₇×#533	C₂²	1	2	yes	complemented
51	C₇×#533	C₂²	1	4	yes	complemented
52	C₇×#533	C₂²	1	4	yes	complemented
53	C₇×#533	C₂²	1	2	yes	complemented
54	C₇×#533	C₂²	1	2	yes	complemented
55	C₇×#533	C₂²	1	8	yes	complemented
56	C₇×#532	C₂²	1	2	yes	—
57	C₇×#532	C₂²	1	2	yes	—
58	C₇×#532	C₂²	1	4	yes	—
59	C₇×#532	C₂²	1	4	yes	complemented
60	C₇×#532	C₂²	1	2	yes	complemented
61	C₇×#532	C₂²	1	2	yes	complemented
62	C₇×#532	C₂²	1	8	yes	complemented
63	C₇×#532	C₂²	1	8	yes	complemented
64	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
66	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
67	C₇×#529	C₂²	1	16	yes	complemented
68	C₇×#529	C₂²	1	16	yes	complemented
69	C₇×#529	C₂²	1	16	yes	complemented
70	C₇×#529	C₂²	1	32	yes	complemented
71	C₂×C₇×#125	C₂²	1	2	yes	complemented
72	C₂×C₇×#124	C₂²	1	2	yes	complemented
73	C₇×#525	C₂²	1	8	yes	—
74	C₇×#525	C₂²	1	8	yes	complemented
75	C₇×#525	C₂²	1	16	yes	complemented
76	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
77	C₂×C₇×#121	C₂²	1	4	yes	—
78	C₇×#520	C₂²	1	8	yes	complemented
79	C₇×#520	C₂²	1	8	yes	complemented
80	C₇×#519	C₂²	1	4	yes	complemented
81	C₇×#518	C₂²	1	8	yes	—
82	C₇×#518	C₂²	1	4	yes	complemented
83	C₄×C₇×#41	C₂²	1	4	yes	—
84	C₄×C₇×#41	C₂²	1	2	yes	—
85	C₄×C₇×#41	C₂²	1	2	yes	—
86	C₄×C₇×#41	C₂²	1	4	yes	complemented
87	C₄×C₇×#41	C₂²	1	2	yes	complemented
88	C₄×C₇×#41	C₂²	1	2	yes	complemented
89	C₄×C₇×#41	C₂²	1	8	yes	complemented
90	C₄×C₇×#41	C₂²	1	8	yes	complemented
91	C₄×C₇×#41	C₂²	1	16	yes	complemented
92	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
93	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
94	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
95	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
96	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
97	C₂×C₇×#117	C₂²	1	1	yes	characteristic
98	C₂×C₇×#117	C₂²	1	2	yes	—
99	C₂×C₇×#117	C₂²	1	2	yes	complemented
100	C₂×C₇×#117	C₂²	1	8	yes	complemented
101	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
102	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
103	#62815	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂×C₇×#41	—	2	8	no	—
105	C₂×C₇×#41	—	2	16	no	—
106	C₂×C₇×#41	C₂³	1	2	yes	—
107	C₂×C₇×#41	C₂³	1	2	yes	—
108	C₂×C₇×#41	C₂³	1	4	yes	—
109	C₂×C₇×#41	C₂³	1	2	yes	—
110	C₂×C₇×#41	C₂³	1	4	yes	—
111	C₂×C₇×#41	C₂³	1	2	yes	—
112	C₂×C₇×#41	C₂³	1	4	yes	—
113	C₂×C₇×#41	C₂³	1	4	yes	—
114	C₂×C₇×#41	C₂³	1	16	yes	—
115	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
116	C₂²×C₇×Q₈	C₂³	1	2	yes	—
117	C₂²×C₇×Q₈	C₂³	1	4	yes	—
118	C₂²×C₇×D₄	C₂³	1	2	yes	—
119	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
120	C₂²×C₇×D₄	C₂³	1	4	yes	—
121	C₂²×C₇×D₄	C₂³	1	2	yes	—
122	C₂²×C₇×D₄	C₂³	1	4	yes	—
123	C₂³×C₄×C₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₇	C₂³	1	4	yes	—
125	C₂³×C₄×C₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₇	C₂³	1	4	yes	—
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
132	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
134	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
135	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
136	C₇×#127	C₂³	1	2	yes	—
137	C₇×#127	C₂³	1	2	yes	—
138	C₇×#127	C₂³	1	4	yes	—
139	C₇×#127	C₂³	1	8	yes	—
140	C₇×#126	C₂³	1	32	yes	—
141	C₇×#126	C₂³	1	32	yes	—
142	C₇×#126	C₂³	1	32	yes	—
143	C₇×#125	C₂³	1	4	yes	—
144	C₇×#125	C₂³	1	4	yes	—
145	C₇×#125	C₂³	1	8	yes	—
146	C₇×#125	C₂³	1	16	yes	—
147	C₇×#125	C₂³	1	32	yes	—
148	C₇×#124	C₂³	1	4	yes	—
149	C₇×#124	C₂³	1	4	yes	—
150	C₇×#124	C₂³	1	8	yes	—
151	C₇×#124	C₂³	1	16	yes	—
152	C₇×#124	C₂³	1	32	yes	—
153	C₇×#124	C₂³	1	8	yes	—
154	C₇×#124	C₂³	1	8	yes	—
155	C₇×#123	C₂³	1	16	yes	—
156	C₇×#123	C₂³	1	16	yes	—
157	C₇×#123	C₂³	1	32	yes	—
158	C₇×#123	C₂³	1	32	yes	—
159	C₇×#123	C₂³	1	32	yes	—
160	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
161	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
162	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
163	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
164	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
165	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
166	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
167	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
168	C₇×#121	C₂³	1	8	yes	—
169	C₇×#121	C₂³	1	8	yes	—
170	C₇×#121	C₂³	1	8	yes	—
171	C₇×#121	C₂³	1	8	yes	—
172	C₇×#121	C₂³	1	16	yes	—
173	C₇×#121	C₂³	1	16	yes	—
174	C₇×#121	C₂³	1	16	yes	—
175	C₇×#121	C₂³	1	32	yes	—
176	C₇×#121	C₂³	1	32	yes	—
177	C₇×#120	C₂³	1	16	yes	—
178	C₇×#120	C₂³	1	16	yes	—
179	C₄×C₇×Q₈	C₂³	1	4	yes	—
180	C₄×C₇×Q₈	C₂³	1	4	yes	—
181	C₄×C₇×Q₈	C₂³	1	4	yes	—
182	C₄×C₇×Q₈	C₂³	1	4	yes	—
183	C₄×C₇×Q₈	C₂³	1	8	yes	—
184	C₄×C₇×Q₈	C₂³	1	8	yes	—
185	C₄×C₇×Q₈	C₂³	1	8	yes	—
186	C₄×C₇×Q₈	C₂³	1	8	yes	—
187	C₄×C₇×Q₈	C₂³	1	16	yes	—
188	C₄×C₇×Q₈	C₂³	1	16	yes	—
189	C₄×C₇×Q₈	C₂³	1	16	yes	—
190	C₄×C₇×D₄	C₂³	1	8	yes	—
191	C₄×C₇×D₄	C₂³	1	8	yes	—
192	C₄×C₇×D₄	C₂³	1	8	yes	—
193	C₄×C₇×D₄	C₂³	1	8	yes	—
194	C₄×C₇×D₄	C₂³	1	4	yes	—
195	C₄×C₇×D₄	C₂³	1	4	yes	—
196	C₄×C₇×D₄	C₂³	1	4	yes	—
197	C₄×C₇×D₄	C₂³	1	4	yes	—
198	C₄×C₇×D₄	C₂³	1	8	yes	—
199	C₄×C₇×D₄	C₂³	1	8	yes	—
200	C₄×C₇×D₄	C₂³	1	8	yes	—
201	C₄×C₇×D₄	C₂³	1	8	yes	—
202	C₄×C₇×D₄	C₂³	1	32	yes	—
203	C₄×C₇×D₄	C₂³	1	32	yes	—
204	C₄×C₇×D₄	C₂³	1	16	yes	—
205	C₄×C₇×D₄	C₂³	1	16	yes	—
206	C₄×C₇×D₄	C₂³	1	32	yes	—
207	C₄×C₇×D₄	C₂³	1	32	yes	—
208	C₄×C₇×D₄	C₂³	1	16	yes	—
209	C₇×#117	C₂³	1	2	yes	—
210	C₇×#117	C₂³	1	4	yes	—
211	C₇×#117	C₂³	1	2	yes	—
212	C₇×#117	C₂³	1	2	yes	—
213	C₇×#117	C₂³	1	2	yes	—
214	C₇×#117	C₂³	1	4	yes	—
215	C₇×#117	C₂³	1	4	yes	—
216	C₇×#117	C₂³	1	4	yes	—
217	C₇×#117	C₂³	1	8	yes	—
218	C₇×#117	C₂³	1	4	yes	—
219	C₇×#117	C₂³	1	4	yes	—
220	C₇×#117	C₂³	1	16	yes	—
221	C₇×#117	C₂³	1	16	yes	—
222	C₇×#117	C₂³	1	16	yes	—
223	C₇×#117	C₂³	1	16	yes	—
224	C₇×#117	C₂³	1	32	yes	—
225	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
226	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
227	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
228	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
229	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
230	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
231	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
232	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
234	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
235	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
236	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
237	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₇	C₂³	1	2	yes	—
240	C₂×C₄²×C₇	C₂³	1	2	yes	—
241	C₂×C₄²×C₇	C₂³	1	2	yes	—
242	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₇	C₂³	1	2	yes	—
247	C₂×C₄²×C₇	C₂³	1	4	yes	—
248	C₂×C₄²×C₇	C₂³	1	8	yes	—
249	C₂×C₄²×C₇	C₂³	1	4	yes	—
250	C₂×C₄²×C₇	C₂³	1	4	yes	—
251	C₂×C₄²×C₇	C₂³	1	4	yes	—
252	C₂×C₄²×C₇	C₂³	1	16	yes	—
253	#3512	C₂×C₇	1	4	yes	complemented
254	#3511	C₂×C₇	1	4	yes	complemented
255	#3510	C₂×C₇	1	4	yes	complemented
256	#3509	C₂×C₇	1	2	yes	complemented
257	#3508	C₂×C₇	1	2	yes	complemented
258	#3507	C₂×C₇	1	4	yes	complemented
259	#3506	C₂×C₇	1	4	yes	complemented
260	#3505	C₂×C₇	1	8	yes	complemented
261	#3480	C₂×C₇	1	8	yes	complemented
262	#3475	C₂×C₇	1	8	yes	complemented
263	#3455	C₂×C₇	1	4	yes	complemented
264	#3449	C₂×C₇	1	2	yes	complemented
265	#3444	C₂×C₇	1	4	yes	complemented
266	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
267	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
268	#3428	C₂×C₇	1	2	yes	complemented
269	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
270	C₂⁴×C₇	C₂⁴	1	4	yes	—
271	C₂⁴×C₇	C₂⁴	1	2	yes	—
272	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
273	C₇×#41	—	2	8	no	—
274	C₇×#41	—	2	16	no	—
275	C₇×#41	—	2	8	no	—
276	C₇×#41	—	2	16	no	—
277	C₇×#41	—	2	8	no	—
278	C₇×#41	—	2	16	no	—
279	C₇×#41	—	2	8	no	—
280	C₇×#41	—	2	16	no	—
281	C₇×#41	—	4	32	no	—
282	C₂×C₇×Q₈	—	2	8	no	—
283	C₂×C₇×Q₈	—	2	4	no	—
284	C₂×C₇×Q₈	—	4	8	no	—
285	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
286	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
287	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
288	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
289	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
290	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
291	C₂×C₇×D₄	—	2	8	no	—
292	C₂×C₇×D₄	—	2	16	no	—
293	C₂×C₇×D₄	—	2	8	no	—
294	C₂×C₇×D₄	—	2	4	no	—
295	C₂×C₇×D₄	—	4	8	no	—
296	C₂×C₇×D₄	C₂⁴	1	4	yes	—
297	C₂×C₇×D₄	C₂⁴	1	8	yes	—
298	C₂×C₇×D₄	C₂⁴	1	4	yes	—
299	C₂×C₇×D₄	C₂⁴	1	8	yes	—
300	C₂×C₇×D₄	C₂⁴	1	2	yes	—
301	C₂×C₇×D₄	C₂⁴	1	4	yes	—
302	C₂×C₇×D₄	C₂⁴	1	8	yes	—
303	C₂×C₇×D₄	C₂⁴	1	2	yes	—
304	C₂×C₇×D₄	C₂⁴	1	4	yes	—
305	C₂×C₇×D₄	C₂⁴	1	32	yes	—
306	C₂×C₇×D₄	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₇	—	2	16	no	—
308	C₂²×C₄×C₇	—	2	8	no	—
309	C₂²×C₄×C₇	—	4	4	no	—
310	C₂²×C₄×C₇	—	4	8	no	—
311	C₂²×C₄×C₇	#41	1	8	yes	complemented
312	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
319	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
321	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
322	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
327	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
328	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
329	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
335	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
336	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
337	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
338	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
339	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
340	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
341	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
342	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
343	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
344	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
345	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
346	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
347	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
348	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
349	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
350	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
351	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
352	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
353	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
354	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
355	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
356	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
357	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
358	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
359	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
360	C₄²×C₇	C₂⁴	1	1	yes	characteristic
361	C₄²×C₇	C₂⁴	1	1	yes	characteristic
362	C₄²×C₇	C₂⁴	1	4	yes	—
363	C₄²×C₇	C₂⁴	1	8	yes	—
364	C₄²×C₇	C₂⁴	1	1	yes	characteristic
365	C₄²×C₇	C₂⁴	1	1	yes	characteristic
366	C₄²×C₇	C₂⁴	1	2	yes	—
367	C₄²×C₇	C₂⁴	1	2	yes	—
368	C₄²×C₇	C₂⁴	1	8	yes	—
369	C₄²×C₇	C₂⁴	1	2	yes	—
370	C₄²×C₇	C₂⁴	1	2	yes	—
371	C₄²×C₇	C₂⁴	1	32	yes	—
372	C₄²×C₇	C₂⁴	1	8	yes	—
373	C₄²×C₇	C₂⁴	1	4	yes	—
374	C₄²×C₇	C₂⁴	1	2	yes	—
375	C₄²×C₇	C₂⁴	1	2	yes	—
376	C₄²×C₇	C₂⁴	1	8	yes	—
377	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
378	C₂²×#41	C₂²×C₇	1	2	yes	—
379	#559	C₂²×C₇	1	16	yes	complemented
380	#559	C₂²×C₇	1	8	yes	complemented
381	#557	C₂²×C₇	1	8	yes	complemented
382	#556	C₂²×C₇	1	8	yes	complemented
383	#556	C₂²×C₇	1	8	yes	complemented
384	#556	C₂²×C₇	1	16	yes	complemented
385	#555	C₂²×C₇	1	8	yes	complemented
386	#554	C₂²×C₇	1	8	yes	complemented
387	#553	C₂²×C₇	1	16	yes	complemented
388	#553	C₂²×C₇	1	16	yes	complemented
389	#553	C₂²×C₇	1	32	yes	complemented
390	#552	C₂²×C₇	1	16	yes	complemented
391	#552	C₂²×C₇	1	16	yes	complemented
392	#551	C₂²×C₇	1	32	yes	complemented
393	#550	C₂²×C₇	1	8	yes	complemented
394	#548	C₂²×C₇	1	16	yes	complemented
395	#547	C₂²×C₇	1	8	yes	complemented
396	#546	C₂²×C₇	1	16	yes	complemented
397	#542	C₂²×C₇	1	16	yes	complemented
398	#541	C₂²×C₇	1	8	yes	complemented
399	#540	C₂²×C₇	1	8	yes	complemented
400	#539	C₂²×C₇	1	16	yes	complemented
401	#538	C₂²×C₇	1	16	yes	complemented
402	#537	C₂²×C₇	1	8	yes	complemented
403	#536	C₂²×C₇	1	4	yes	—
404	#536	C₂²×C₇	1	4	yes	complemented
405	#535	C₂²×C₇	1	4	yes	—
406	#535	C₂²×C₇	1	4	yes	complemented
407	#534	C₂²×C₇	1	8	yes	—
408	#533	C₂²×C₇	1	2	yes	complemented
409	#533	C₂²×C₇	1	2	yes	complemented
410	#533	C₂²×C₇	1	4	yes	complemented
411	#533	C₂²×C₇	1	4	yes	complemented
412	#533	C₂²×C₇	1	2	yes	complemented
413	#533	C₂²×C₇	1	2	yes	complemented
414	#533	C₂²×C₇	1	8	yes	complemented
415	#532	C₂²×C₇	1	2	yes	—
416	#532	C₂²×C₇	1	2	yes	—
417	#532	C₂²×C₇	1	4	yes	—
418	#532	C₂²×C₇	1	4	yes	complemented
419	#532	C₂²×C₇	1	2	yes	complemented
420	#532	C₂²×C₇	1	2	yes	complemented
421	#532	C₂²×C₇	1	8	yes	complemented
422	#532	C₂²×C₇	1	8	yes	complemented
423	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
424	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
425	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
426	#529	C₂²×C₇	1	16	yes	complemented
427	#529	C₂²×C₇	1	16	yes	complemented
428	#529	C₂²×C₇	1	16	yes	complemented
429	#529	C₂²×C₇	1	32	yes	complemented
430	C₂×#125	C₂²×C₇	1	2	yes	complemented
431	C₂×#124	C₂²×C₇	1	2	yes	complemented
432	#525	C₂²×C₇	1	8	yes	—
433	#525	C₂²×C₇	1	8	yes	complemented
434	#525	C₂²×C₇	1	16	yes	complemented
435	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
436	C₂×#121	C₂²×C₇	1	4	yes	—
437	#520	C₂²×C₇	1	8	yes	complemented
438	#520	C₂²×C₇	1	8	yes	complemented
439	#519	C₂²×C₇	1	4	yes	complemented
440	#518	C₂²×C₇	1	8	yes	—
441	#518	C₂²×C₇	1	4	yes	complemented
442	C₄×#41	C₂²×C₇	1	4	yes	—
443	C₄×#41	C₂²×C₇	1	2	yes	—
444	C₄×#41	C₂²×C₇	1	2	yes	—
445	C₄×#41	C₂²×C₇	1	4	yes	complemented
446	C₄×#41	C₂²×C₇	1	2	yes	complemented
447	C₄×#41	C₂²×C₇	1	2	yes	complemented
448	C₄×#41	C₂²×C₇	1	8	yes	complemented
449	C₄×#41	C₂²×C₇	1	8	yes	complemented
450	C₄×#41	C₂²×C₇	1	16	yes	complemented
451	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
452	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
453	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
454	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
455	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
456	C₂×#117	C₂²×C₇	1	1	yes	characteristic
457	C₂×#117	C₂²×C₇	1	2	yes	—
458	C₂×#117	C₂²×C₇	1	2	yes	complemented
459	C₂×#117	C₂²×C₇	1	8	yes	complemented
460	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
461	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
462	C₂³×C₇	—	2	4	no	—
463	C₂³×C₇	—	2	8	no	—
464	C₂³×C₇	—	4	2	no	—
465	C₂³×C₇	—	4	4	no	—
466	C₂³×C₇	—	4	8	no	—
467	C₂³×C₇	C₂×#41	1	4	yes	—
468	C₂³×C₇	C₂⁵	1	4	yes	—
469	C₂³×C₇	C₂⁵	1	8	yes	—
470	C₂³×C₇	C₂⁵	1	1	yes	characteristic
471	C₂³×C₇	C₂⁵	1	1	yes	characteristic
472	C₂³×C₇	C₂⁵	1	1	yes	characteristic
473	C₇×Q₈	—	2	4	no	—
474	C₇×Q₈	—	2	8	no	—
475	C₇×Q₈	—	2	8	no	—
476	C₇×Q₈	—	2	4	no	—
477	C₇×Q₈	—	2	16	no	—
478	C₇×Q₈	—	4	8	no	—
479	C₇×D₄	—	2	8	no	—
480	C₇×D₄	—	2	16	no	—
481	C₇×D₄	—	2	8	no	—
482	C₇×D₄	—	2	16	no	—
483	C₇×D₄	—	2	4	no	—
484	C₇×D₄	—	2	8	no	—
485	C₇×D₄	—	2	4	no	—
486	C₇×D₄	—	2	8	no	—
487	C₇×D₄	—	2	16	no	—
488	C₇×D₄	—	4	8	no	—
489	C₇×D₄	—	4	32	no	—
490	C₂×C₄×C₇	—	2	8	no	—
491	C₂×C₄×C₇	—	2	4	no	—
492	C₂×C₄×C₇	—	2	8	no	—
493	C₂×C₄×C₇	—	2	16	no	—
494	C₂×C₄×C₇	—	2	16	no	—
495	C₂×C₄×C₇	—	2	8	no	—
496	C₂×C₄×C₇	—	2	4	no	—
497	C₂×C₄×C₇	—	2	4	no	—
498	C₂×C₄×C₇	—	2	4	no	—
499	C₂×C₄×C₇	—	2	16	no	—
500	C₂×C₄×C₇	—	4	4	no	—
501	C₂×C₄×C₇	—	4	8	no	—
502	C₂×C₄×C₇	—	4	2	no	—
503	C₂×C₄×C₇	—	4	2	no	—
504	C₂×C₄×C₇	—	4	2	no	—
505	C₂×C₄×C₇	—	4	8	no	—
506	C₂×C₄×C₇	—	4	32	no	—
507	C₂×C₄×C₇	C₂×#41	1	4	yes	—
508	C₂×C₄×C₇	C₂×#41	1	4	yes	—
509	C₂×C₄×C₇	C₂×#41	1	4	yes	—
510	C₂×C₄×C₇	C₂×#41	1	4	yes	—
511	C₂×C₄×C₇	C₂×#41	1	4	yes	—
512	C₂×C₄×C₇	C₂×#41	1	4	yes	—
513	C₂×C₄×C₇	C₂⁵	1	2	yes	—
514	C₂×C₄×C₇	C₂⁵	1	8	yes	—
515	C₂×C₄×C₇	C₂⁵	1	2	yes	—
516	C₂×C₄×C₇	C₂⁵	1	4	yes	—
517	C₂×C₄×C₇	C₂⁵	1	8	yes	—
518	C₂×C₄×C₇	C₂⁵	1	16	yes	—
519	C₂×C₄×C₇	C₂⁵	1	2	yes	—
520	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
521	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
522	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
523	C₂×C₄×C₇	C₂⁵	1	2	yes	—
524	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
525	C₂×#41	—	2	8	no	—
526	C₂×#41	—	2	16	no	—
527	C₂×#41	C₂³×C₇	1	2	yes	—
528	C₂×#41	C₂³×C₇	1	2	yes	—
529	C₂×#41	C₂³×C₇	1	4	yes	—
530	C₂×#41	C₂³×C₇	1	2	yes	—
531	C₂×#41	C₂³×C₇	1	4	yes	—
532	C₂×#41	C₂³×C₇	1	2	yes	—
533	C₂×#41	C₂³×C₇	1	4	yes	—
534	C₂×#41	C₂³×C₇	1	4	yes	—
535	C₂×#41	C₂³×C₇	1	16	yes	—
536	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₇	1	2	yes	—
538	C₂²×Q₈	C₂³×C₇	1	4	yes	—
539	C₂²×D₄	C₂³×C₇	1	2	yes	—
540	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₇	1	4	yes	—
542	C₂²×D₄	C₂³×C₇	1	2	yes	—
543	C₂²×D₄	C₂³×C₇	1	4	yes	—
544	C₂³×C₄	C₂³×C₇	1	4	yes	—
545	C₂³×C₄	C₂³×C₇	1	2	yes	—
546	C₂³×C₄	C₂³×C₇	1	2	yes	—
547	C₂³×C₄	C₂³×C₇	1	4	yes	—
548	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
552	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
553	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
554	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
555	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
556	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
557	#127	C₂³×C₇	1	2	yes	—
558	#127	C₂³×C₇	1	2	yes	—
559	#127	C₂³×C₇	1	4	yes	—
560	#127	C₂³×C₇	1	8	yes	—
561	#126	C₂³×C₇	1	32	yes	—
562	#126	C₂³×C₇	1	32	yes	—
563	#126	C₂³×C₇	1	32	yes	—
564	#125	C₂³×C₇	1	4	yes	—
565	#125	C₂³×C₇	1	4	yes	—
566	#125	C₂³×C₇	1	8	yes	—
567	#125	C₂³×C₇	1	16	yes	—
568	#125	C₂³×C₇	1	32	yes	—
569	#124	C₂³×C₇	1	4	yes	—
570	#124	C₂³×C₇	1	4	yes	—
571	#124	C₂³×C₇	1	8	yes	—
572	#124	C₂³×C₇	1	16	yes	—
573	#124	C₂³×C₇	1	32	yes	—
574	#124	C₂³×C₇	1	8	yes	—
575	#124	C₂³×C₇	1	8	yes	—
576	#123	C₂³×C₇	1	16	yes	—
577	#123	C₂³×C₇	1	16	yes	—
578	#123	C₂³×C₇	1	32	yes	—
579	#123	C₂³×C₇	1	32	yes	—
580	#123	C₂³×C₇	1	32	yes	—
581	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
582	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
583	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
584	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
585	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
586	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
587	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
588	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
589	#121	C₂³×C₇	1	8	yes	—
590	#121	C₂³×C₇	1	8	yes	—
591	#121	C₂³×C₇	1	8	yes	—
592	#121	C₂³×C₇	1	8	yes	—
593	#121	C₂³×C₇	1	16	yes	—
594	#121	C₂³×C₇	1	16	yes	—
595	#121	C₂³×C₇	1	16	yes	—
596	#121	C₂³×C₇	1	32	yes	—
597	#121	C₂³×C₇	1	32	yes	—
598	#120	C₂³×C₇	1	16	yes	—
599	#120	C₂³×C₇	1	16	yes	—
600	C₄×Q₈	C₂³×C₇	1	4	yes	—
601	C₄×Q₈	C₂³×C₇	1	4	yes	—
602	C₄×Q₈	C₂³×C₇	1	4	yes	—
603	C₄×Q₈	C₂³×C₇	1	4	yes	—
604	C₄×Q₈	C₂³×C₇	1	8	yes	—
605	C₄×Q₈	C₂³×C₇	1	8	yes	—
606	C₄×Q₈	C₂³×C₇	1	8	yes	—
607	C₄×Q₈	C₂³×C₇	1	8	yes	—
608	C₄×Q₈	C₂³×C₇	1	16	yes	—
609	C₄×Q₈	C₂³×C₇	1	16	yes	—
610	C₄×Q₈	C₂³×C₇	1	16	yes	—
611	C₄×D₄	C₂³×C₇	1	8	yes	—
612	C₄×D₄	C₂³×C₇	1	8	yes	—
613	C₄×D₄	C₂³×C₇	1	8	yes	—
614	C₄×D₄	C₂³×C₇	1	8	yes	—
615	C₄×D₄	C₂³×C₇	1	4	yes	—
616	C₄×D₄	C₂³×C₇	1	4	yes	—
617	C₄×D₄	C₂³×C₇	1	4	yes	—
618	C₄×D₄	C₂³×C₇	1	4	yes	—
619	C₄×D₄	C₂³×C₇	1	8	yes	—
620	C₄×D₄	C₂³×C₇	1	8	yes	—
621	C₄×D₄	C₂³×C₇	1	8	yes	—
622	C₄×D₄	C₂³×C₇	1	8	yes	—
623	C₄×D₄	C₂³×C₇	1	32	yes	—
624	C₄×D₄	C₂³×C₇	1	32	yes	—
625	C₄×D₄	C₂³×C₇	1	16	yes	—
626	C₄×D₄	C₂³×C₇	1	16	yes	—
627	C₄×D₄	C₂³×C₇	1	32	yes	—
628	C₄×D₄	C₂³×C₇	1	32	yes	—
629	C₄×D₄	C₂³×C₇	1	16	yes	—
630	#117	C₂³×C₇	1	2	yes	—
631	#117	C₂³×C₇	1	4	yes	—
632	#117	C₂³×C₇	1	2	yes	—
633	#117	C₂³×C₇	1	2	yes	—
634	#117	C₂³×C₇	1	2	yes	—
635	#117	C₂³×C₇	1	4	yes	—
636	#117	C₂³×C₇	1	4	yes	—
637	#117	C₂³×C₇	1	4	yes	—
638	#117	C₂³×C₇	1	8	yes	—
639	#117	C₂³×C₇	1	4	yes	—
640	#117	C₂³×C₇	1	4	yes	—
641	#117	C₂³×C₇	1	16	yes	—
642	#117	C₂³×C₇	1	16	yes	—
643	#117	C₂³×C₇	1	16	yes	—
644	#117	C₂³×C₇	1	16	yes	—
645	#117	C₂³×C₇	1	32	yes	—
646	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
648	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
649	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
650	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
652	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
658	C₂×C₄²	C₂³×C₇	1	2	yes	—
659	C₂×C₄²	C₂³×C₇	1	4	yes	—
660	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₇	1	16	yes	—
662	C₂×C₄²	C₂³×C₇	1	4	yes	—
663	C₂×C₄²	C₂³×C₇	1	2	yes	—
664	C₂×C₄²	C₂³×C₇	1	2	yes	—
665	C₂×C₄²	C₂³×C₇	1	2	yes	—
666	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₇	1	8	yes	—
669	C₂×C₄²	C₂³×C₇	1	4	yes	—
670	C₂×C₄²	C₂³×C₇	1	4	yes	—
671	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
674	C₂²×C₇	—	2	2	no	—
675	C₂²×C₇	—	2	2	no	—
676	C₂²×C₇	—	2	2	no	—
677	C₂²×C₇	—	2	4	no	—
678	C₂²×C₇	—	2	8	no	—
679	C₂²×C₇	—	2	8	no	—
680	C₂²×C₇	—	2	16	no	—
681	C₂²×C₇	—	4	4	no	—
682	C₂²×C₇	—	4	8	no	—
683	C₂²×C₇	—	8	8	no	—
684	C₂²×C₇	C₂²×#41	1	2	yes	—
685	C₂²×C₇	C₂²×#41	1	2	yes	—
686	C₂²×C₇	C₂²×#41	1	2	yes	—
687	C₂²×C₇	C₂⁶	1	1	yes	characteristic
688	C₄×C₇	—	2	8	no	—
689	C₄×C₇	—	2	4	no	—
690	C₄×C₇	—	2	2	no	—
691	C₄×C₇	—	2	8	no	—
692	C₄×C₇	—	2	2	no	—
693	C₄×C₇	—	2	2	no	—
694	C₄×C₇	—	2	16	no	—
695	C₄×C₇	C₂²×#41	1	2	yes	—
696	C₄×C₇	C₂²×#41	1	2	yes	—
697	C₄×C₇	C₂²×#41	1	2	yes	—
698	C₄×C₇	C₂²×#41	1	2	yes	—
699	C₄×C₇	#585	1	4	yes	—
700	C₂⁴	C₂⁴×C₇	1	4	yes	—
701	C₂⁴	C₂⁴×C₇	1	2	yes	—
702	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
703	#41	—	2	8	no	—
704	#41	—	2	16	no	—
705	#41	—	2	8	no	—
706	#41	—	2	16	no	—
707	#41	—	2	8	no	—
708	#41	—	2	16	no	—
709	#41	—	2	8	no	—
710	#41	—	2	16	no	—
711	#41	—	4	32	no	—
712	C₂×Q₈	—	2	8	no	—
713	C₂×Q₈	—	2	4	no	—
714	C₂×Q₈	—	4	8	no	—
715	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
716	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
717	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
718	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
719	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
720	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
721	C₂×D₄	—	2	8	no	—
722	C₂×D₄	—	2	16	no	—
723	C₂×D₄	—	2	8	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	4	8	no	—
726	C₂×D₄	C₂⁴×C₇	1	4	yes	—
727	C₂×D₄	C₂⁴×C₇	1	8	yes	—
728	C₂×D₄	C₂⁴×C₇	1	4	yes	—
729	C₂×D₄	C₂⁴×C₇	1	8	yes	—
730	C₂×D₄	C₂⁴×C₇	1	2	yes	—
731	C₂×D₄	C₂⁴×C₇	1	4	yes	—
732	C₂×D₄	C₂⁴×C₇	1	8	yes	—
733	C₂×D₄	C₂⁴×C₇	1	2	yes	—
734	C₂×D₄	C₂⁴×C₇	1	4	yes	—
735	C₂×D₄	C₂⁴×C₇	1	32	yes	—
736	C₂×D₄	C₂⁴×C₇	1	8	yes	—
737	C₂²×C₄	—	2	16	no	—
738	C₂²×C₄	—	2	8	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	—	4	8	no	—
741	C₂²×C₄	C₇×#41	1	8	yes	complemented
742	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
749	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
751	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
752	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
754	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
758	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
759	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
767	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
768	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
770	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
771	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
772	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
773	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
775	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
777	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
779	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
780	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
781	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
782	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
784	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
785	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
786	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
787	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
788	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
789	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
790	C₄²	C₂⁴×C₇	1	4	yes	—
791	C₄²	C₂⁴×C₇	1	2	yes	—
792	C₄²	C₂⁴×C₇	1	1	yes	characteristic
793	C₄²	C₂⁴×C₇	1	1	yes	characteristic
794	C₄²	C₂⁴×C₇	1	4	yes	—
795	C₄²	C₂⁴×C₇	1	2	yes	—
796	C₄²	C₂⁴×C₇	1	8	yes	—
797	C₄²	C₂⁴×C₇	1	8	yes	—
798	C₄²	C₂⁴×C₇	1	1	yes	characteristic
799	C₄²	C₂⁴×C₇	1	1	yes	characteristic
800	C₄²	C₂⁴×C₇	1	2	yes	—
801	C₄²	C₂⁴×C₇	1	2	yes	—
802	C₄²	C₂⁴×C₇	1	8	yes	—
803	C₄²	C₂⁴×C₇	1	2	yes	—
804	C₄²	C₂⁴×C₇	1	2	yes	—
805	C₄²	C₂⁴×C₇	1	32	yes	—
806	C₄²	C₂⁴×C₇	1	8	yes	—
807	C₂×C₇	—	2	2	no	—
808	C₂×C₇	—	2	2	no	—
809	C₂×C₇	—	2	2	no	—
810	C₂×C₇	—	4	4	no	—
811	C₂×C₇	—	4	8	no	—
812	C₂×C₇	C₂³×#41	1	1	yes	characteristic
813	C₂×C₇	C₂×#585	1	2	yes	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	8	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	4	no	—
818	C₂³	—	4	8	no	—
819	C₂³	C₂×C₇×#41	1	4	yes	—
820	C₂³	C₂⁵×C₇	1	4	yes	—
821	C₂³	C₂⁵×C₇	1	8	yes	—
822	C₂³	C₂⁵×C₇	1	1	yes	characteristic
823	C₂³	C₂⁵×C₇	1	1	yes	characteristic
824	C₂³	C₂⁵×C₇	1	1	yes	characteristic
825	Q₈	—	2	4	no	—
826	Q₈	—	2	8	no	—
827	Q₈	—	2	8	no	—
828	Q₈	—	2	4	no	—
829	Q₈	—	2	16	no	—
830	Q₈	—	4	8	no	—
831	D₄	—	2	8	no	—
832	D₄	—	2	16	no	—
833	D₄	—	2	8	no	—
834	D₄	—	2	16	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	8	no	—
837	D₄	—	2	4	no	—
838	D₄	—	2	8	no	—
839	D₄	—	2	16	no	—
840	D₄	—	4	8	no	—
841	D₄	—	4	32	no	—
842	C₂×C₄	—	2	8	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	8	no	—
845	C₂×C₄	—	2	16	no	—
846	C₂×C₄	—	2	16	no	—
847	C₂×C₄	—	2	8	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	16	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	32	no	—
859	C₂×C₄	C₂×C₇×#41	1	4	yes	—
860	C₂×C₄	C₂×C₇×#41	1	4	yes	—
861	C₂×C₄	C₂×C₇×#41	1	4	yes	—
862	C₂×C₄	C₂×C₇×#41	1	4	yes	—
863	C₂×C₄	C₂×C₇×#41	1	4	yes	—
864	C₂×C₄	C₂×C₇×#41	1	4	yes	—
865	C₂×C₄	C₂⁵×C₇	1	8	yes	—
866	C₂×C₄	C₂⁵×C₇	1	2	yes	—
867	C₂×C₄	C₂⁵×C₇	1	2	yes	—
868	C₂×C₄	C₂⁵×C₇	1	4	yes	—
869	C₂×C₄	C₂⁵×C₇	1	8	yes	—
870	C₂×C₄	C₂⁵×C₇	1	16	yes	—
871	C₂×C₄	C₂⁵×C₇	1	2	yes	—
872	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
873	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
874	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
875	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
876	C₂×C₄	C₂⁵×C₇	1	2	yes	—
877	C₇	#62815	1	1	yes	characteristic, direct product factor, Sylow
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	8	no	—
884	C₂²	—	2	16	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	8	8	no	—
888	C₂²	C₂²×C₇×#41	1	2	yes	—
889	C₂²	C₂²×C₇×#41	1	2	yes	—
890	C₂²	C₂²×C₇×#41	1	2	yes	—
891	C₂²	C₂⁶×C₇	1	1	yes	characteristic
892	C₄	—	2	8	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	8	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	16	no	—
899	C₄	C₂²×C₇×#41	1	2	yes	—
900	C₄	C₂²×C₇×#41	1	2	yes	—
901	C₄	C₂²×C₇×#41	1	2	yes	—
902	C₄	C₂²×C₇×#41	1	2	yes	—
903	C₄	C₇×#585	1	4	yes	—
904	C₂	—	2	2	no	—
905	C₂	—	2	2	no	—
906	C₂	—	2	2	no	—
907	C₂	—	4	4	no	—
908	C₂	—	4	8	no	—
909	C₂	C₂³×C₇×#41	1	1	yes	characteristic
910	C₂	C₂×C₇×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
socle	C₂²×C₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3511	C₂	semidirect
3. C₇×#3510	C₂	semidirect
4. C₇×#3509	C₂	semidirect
5. C₇×#3508	C₂	semidirect
6. C₇×#3507	C₂	semidirect
7. C₇×#3506	C₂	semidirect
8. C₇×#3505	C₂	semidirect
9. C₇×#3480	C₂	semidirect
10. C₇×#3475	C₂	semidirect
11. C₇×#3455	C₂	semidirect
12. C₇×#3449	C₂	semidirect
13. C₇×#3444	C₂	semidirect
14. C₂×C₇×#533	C₂	semidirect
15. C₂×C₇×#532	C₂	semidirect
16. C₇×#3428	C₂	semidirect
17. C₂×C₄×C₇×#41	C₂	semidirect
20. C₇×#559	C₂²	semidirect
21. C₇×#559	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#556	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#555	C₂²	semidirect
27. C₇×#554	C₂²	semidirect
28. C₇×#553	C₂²	semidirect
29. C₇×#553	C₂²	semidirect
30. C₇×#553	C₂²	semidirect
31. C₇×#552	C₂²	semidirect
32. C₇×#552	C₂²	semidirect
33. C₇×#551	C₂²	semidirect
34. C₇×#550	C₂²	semidirect
35. C₇×#548	C₂²	semidirect
36. C₇×#547	C₂²	semidirect
37. C₇×#546	C₂²	semidirect
38. C₇×#542	C₂²	semidirect
39. C₇×#541	C₂²	semidirect
40. C₇×#540	C₂²	semidirect
41. C₇×#539	C₂²	semidirect
42. C₇×#538	C₂²	semidirect
43. C₇×#537	C₂²	semidirect
45. C₇×#536	C₂²	semidirect
47. C₇×#535	C₂²	semidirect
49. C₇×#533	C₂²	semidirect
50. C₇×#533	C₂²	semidirect
51. C₇×#533	C₂²	semidirect
52. C₇×#533	C₂²	semidirect
53. C₇×#533	C₂²	semidirect
54. C₇×#533	C₂²	semidirect
55. C₇×#533	C₂²	semidirect
59. C₇×#532	C₂²	semidirect
60. C₇×#532	C₂²	semidirect
61. C₇×#532	C₂²	semidirect
62. C₇×#532	C₂²	semidirect
63. C₇×#532	C₂²	semidirect
64. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
65. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
66. C₂×C₇×#127	C₂²	semidirect
67. C₇×#529	C₂²	semidirect
68. C₇×#529	C₂²	semidirect
69. C₇×#529	C₂²	semidirect
70. C₇×#529	C₂²	semidirect
71. C₂×C₇×#125	C₂²	semidirect
72. C₂×C₇×#124	C₂²	semidirect
74. C₇×#525	C₂²	semidirect
75. C₇×#525	C₂²	semidirect
78. C₇×#520	C₂²	semidirect
79. C₇×#520	C₂²	semidirect
80. C₇×#519	C₂²	semidirect
82. C₇×#518	C₂²	semidirect
86. C₄×C₇×#41	C₂²	semidirect
87. C₄×C₇×#41	C₂²	semidirect
88. C₄×C₇×#41	C₂²	semidirect
89. C₄×C₇×#41	C₂²	semidirect
90. C₄×C₇×#41	C₂²	semidirect
91. C₄×C₇×#41	C₂²	semidirect
92. C₂×C₄×C₇×Q₈	C₂²	semidirect
93. C₂×C₄×C₇×Q₈	C₂²	semidirect
95. C₂×C₄×C₇×D₄	C₂²	semidirect
96. C₂×C₄×C₇×D₄	C₂²	semidirect
99. C₂×C₇×#117	C₂²	semidirect
100. C₂×C₇×#117	C₂²	semidirect
102. C₂²×C₄²×C₇	C₂²	semidirect
103. #62815	C₇	direct (N × H)
253. #3512	C₂×C₇	semidirect
254. #3511	C₂×C₇	semidirect
255. #3510	C₂×C₇	semidirect
256. #3509	C₂×C₇	semidirect
257. #3508	C₂×C₇	semidirect
258. #3507	C₂×C₇	semidirect
259. #3506	C₂×C₇	semidirect
260. #3505	C₂×C₇	semidirect
261. #3480	C₂×C₇	semidirect
262. #3475	C₂×C₇	semidirect
263. #3455	C₂×C₇	semidirect
264. #3449	C₂×C₇	semidirect
265. #3444	C₂×C₇	semidirect
266. C₂×#533	C₂×C₇	semidirect
267. C₂×#532	C₂×C₇	semidirect
268. #3428	C₂×C₇	semidirect
269. C₂×C₄×#41	C₂×C₇	semidirect
311. C₂²×C₄×C₇	#41	semidirect
379. #559	C₂²×C₇	semidirect
380. #559	C₂²×C₇	semidirect
381. #557	C₂²×C₇	semidirect
382. #556	C₂²×C₇	semidirect
383. #556	C₂²×C₇	semidirect
384. #556	C₂²×C₇	semidirect
385. #555	C₂²×C₇	semidirect
386. #554	C₂²×C₇	semidirect
387. #553	C₂²×C₇	semidirect
388. #553	C₂²×C₇	semidirect
389. #553	C₂²×C₇	semidirect
390. #552	C₂²×C₇	semidirect
391. #552	C₂²×C₇	semidirect
392. #551	C₂²×C₇	semidirect
393. #550	C₂²×C₇	semidirect
394. #548	C₂²×C₇	semidirect
395. #547	C₂²×C₇	semidirect
396. #546	C₂²×C₇	semidirect
397. #542	C₂²×C₇	semidirect
398. #541	C₂²×C₇	semidirect
399. #540	C₂²×C₇	semidirect
400. #539	C₂²×C₇	semidirect
401. #538	C₂²×C₇	semidirect
402. #537	C₂²×C₇	semidirect
404. #536	C₂²×C₇	semidirect
406. #535	C₂²×C₇	semidirect
408. #533	C₂²×C₇	semidirect
409. #533	C₂²×C₇	semidirect
410. #533	C₂²×C₇	semidirect
411. #533	C₂²×C₇	semidirect
412. #533	C₂²×C₇	semidirect
413. #533	C₂²×C₇	semidirect
414. #533	C₂²×C₇	semidirect
418. #532	C₂²×C₇	semidirect
419. #532	C₂²×C₇	semidirect
420. #532	C₂²×C₇	semidirect
421. #532	C₂²×C₇	semidirect
422. #532	C₂²×C₇	semidirect
423. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
424. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
425. C₂×#127	C₂²×C₇	semidirect
426. #529	C₂²×C₇	semidirect
427. #529	C₂²×C₇	semidirect
428. #529	C₂²×C₇	semidirect
429. #529	C₂²×C₇	semidirect
430. C₂×#125	C₂²×C₇	semidirect
431. C₂×#124	C₂²×C₇	semidirect
433. #525	C₂²×C₇	semidirect
434. #525	C₂²×C₇	semidirect
437. #520	C₂²×C₇	semidirect
438. #520	C₂²×C₇	semidirect
439. #519	C₂²×C₇	semidirect
441. #518	C₂²×C₇	semidirect
445. C₄×#41	C₂²×C₇	semidirect
446. C₄×#41	C₂²×C₇	semidirect
447. C₄×#41	C₂²×C₇	semidirect
448. C₄×#41	C₂²×C₇	semidirect
449. C₄×#41	C₂²×C₇	semidirect
450. C₄×#41	C₂²×C₇	semidirect
451. C₂×C₄×Q₈	C₂²×C₇	semidirect
452. C₂×C₄×Q₈	C₂²×C₇	semidirect
454. C₂×C₄×D₄	C₂²×C₇	semidirect
455. C₂×C₄×D₄	C₂²×C₇	semidirect
458. C₂×#117	C₂²×C₇	semidirect
459. C₂×#117	C₂²×C₇	semidirect
461. C₂²×C₄²	C₂²×C₇	semidirect
741. C₂²×C₄	C₇×#41	semidirect
877. C₇	#62815	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3512	2
C₇×#3511	2
C₇×#3510	2
C₇×#3509	2
C₇×#3508	2
C₇×#3507	2
C₇×#3506	2
C₇×#3505	2
C₇×#3480	2
C₇×#3475	2
C₇×#3455	2
C₇×#3449	2
C₇×#3444	2
C₂×C₇×#533	2
C₂×C₇×#532	2
C₇×#3428	2
C₂×C₄×C₇×#41	2
#62815	7

Subgroups — C7×#62815 #13240031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62815 #13240031