Subgroups — C₇×#62834 #13240050

Order 1792.

7900 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3558	C₂	1	8	yes	maximal, complemented
2	C₇×#3549	C₂	1	2	yes	maximal, complemented
3	C₇×#3548	C₂	1	2	yes	maximal, complemented
4	C₇×#3546	C₂	1	8	yes	maximal, complemented
5	C₇×#3537	C₂	1	4	yes	maximal, complemented
6	C₇×#3519	C₂	1	8	yes	maximal, complemented
7	C₇×#3511	C₂	1	4	yes	maximal, complemented
8	C₇×#3508	C₂	1	4	yes	maximal, complemented
9	C₇×#3506	C₂	1	4	yes	maximal, complemented
10	C₇×#3498	C₂	1	4	yes	maximal, complemented
11	C₇×#3496	C₂	1	4	yes	maximal, complemented
12	C₇×#3488	C₂	1	8	yes	maximal, complemented
13	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#532	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×H(5,𝔽₂)	C₂²	1	8	yes	complemented
16	C₂²×C₇×#41	C₂²	1	4	yes	complemented
17	C₇×#562	C₂²	1	8	yes	complemented
18	C₇×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₇×#560	C₂²	1	16	yes	complemented
20	C₇×#559	C₂²	1	16	yes	complemented
21	C₇×#556	C₂²	1	8	yes	complemented
22	C₇×#555	C₂²	1	4	yes	complemented
23	C₇×#555	C₂²	1	8	yes	complemented
24	C₇×#554	C₂²	1	8	yes	complemented
25	C₇×#553	C₂²	1	16	yes	complemented
26	C₇×#553	C₂²	1	16	yes	complemented
27	C₇×#550	C₂²	1	16	yes	complemented
28	C₇×#550	C₂²	1	8	yes	complemented
29	C₇×#550	C₂²	1	8	yes	complemented
30	C₇×#548	C₂²	1	16	yes	complemented
31	C₇×#547	C₂²	1	8	yes	complemented
32	C₇×#547	C₂²	1	8	yes	complemented
33	C₇×#546	C₂²	1	16	yes	complemented
34	C₇×#546	C₂²	1	32	yes	complemented
35	C₇×#546	C₂²	1	16	yes	complemented
36	C₇×#546	C₂²	1	16	yes	complemented
37	C₇×D₄²	C₂²	1	16	yes	complemented
38	C₇×D₄²	C₂²	1	16	yes	complemented
39	C₇×D₄²	C₂²	1	4	yes	complemented
40	C₇×D₄²	C₂²	1	8	yes	complemented
41	C₇×D₄²	C₂²	1	16	yes	complemented
42	C₇×D₄²	C₂²	1	8	yes	complemented
43	C₇×#542	C₂²	1	16	yes	complemented
44	C₇×#540	C₂²	1	8	yes	complemented
45	C₇×#540	C₂²	1	8	yes	complemented
46	C₇×#538	C₂²	1	16	yes	complemented
47	C₇×#538	C₂²	1	32	yes	complemented
48	C₇×#537	C₂²	1	8	yes	complemented
49	C₇×#537	C₂²	1	16	yes	complemented
50	C₇×#535	C₂²	1	8	yes	complemented
51	C₇×#535	C₂²	1	16	yes	complemented
52	C₇×#535	C₂²	1	16	yes	complemented
53	C₇×#535	C₂²	1	8	yes	complemented
54	C₇×#534	C₂²	1	16	yes	complemented
55	C₇×#533	C₂²	1	2	yes	complemented
56	C₇×#533	C₂²	1	1	yes	characteristic, complemented
57	C₇×#533	C₂²	1	4	yes	complemented
58	C₇×#532	C₂²	1	4	yes	complemented
59	C₇×#532	C₂²	1	4	yes	complemented
60	C₇×#532	C₂²	1	4	yes	complemented
61	C₇×#532	C₂²	1	4	yes	complemented
62	C₇×#532	C₂²	1	4	yes	complemented
63	C₇×#532	C₂²	1	4	yes	complemented
64	C₇×#532	C₂²	1	4	yes	complemented
65	C₇×#532	C₂²	1	4	yes	complemented
66	C₇×#532	C₂²	1	2	yes	complemented
67	C₇×#532	C₂²	1	1	yes	characteristic, complemented
68	C₇×#532	C₂²	1	8	yes	complemented
69	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
70	C₂×C₇×#127	C₂²	1	2	yes	complemented
71	C₂×C₇×#127	C₂²	1	4	yes	complemented
72	C₇×#529	C₂²	1	4	yes	complemented
73	C₇×#529	C₂²	1	4	yes	complemented
74	C₇×#529	C₂²	1	4	yes	complemented
75	C₂×C₇×#124	C₂²	1	4	yes	complemented
76	C₇×#525	C₂²	1	4	yes	complemented
77	C₇×#525	C₂²	1	2	yes	complemented
78	C₇×#525	C₂²	1	16	yes	complemented
79	C₂×C₇×#121	C₂²	1	4	yes	complemented
80	C₂×C₇×#121	C₂²	1	4	yes	complemented
81	C₂×C₇×#121	C₂²	1	16	yes	complemented
82	C₇×#520	C₂²	1	8	yes	complemented
83	C₇×#518	C₂²	1	8	yes	complemented
84	C₄×C₇×#41	C₂²	1	4	yes	complemented
85	C₄×C₇×#41	C₂²	1	2	yes	complemented
86	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
87	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
88	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
89	#62834	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₇×H(5,𝔽₂)	—	4	32	no	—
91	C₂×C₇×#41	—	4	16	no	—
92	C₂×C₇×#41	C₂³	1	8	yes	—
93	C₂×C₇×#41	C₂³	1	4	yes	—
94	C₂×C₇×#41	C₂³	1	8	yes	—
95	C₂×C₇×#41	C₂³	1	8	yes	—
96	C₂×C₇×#41	C₂³	1	8	yes	—
97	C₂×C₇×#41	C₂³	1	16	yes	—
98	C₂×C₇×#41	C₂³	1	16	yes	—
99	C₂×C₇×#41	C₂³	1	2	yes	—
100	C₂²×C₇×Q₈	C₂³	1	4	yes	—
101	C₂²×C₇×D₄	C₂³	1	4	yes	—
102	C₂²×C₇×D₄	C₂³	1	8	yes	—
103	C₂²×C₇×D₄	C₂³	1	4	yes	—
104	C₂²×C₇×D₄	C₂³	1	32	yes	—
105	C₂²×C₇×D₄	C₂³	1	16	yes	—
106	C₂²×C₇×D₄	C₂³	1	16	yes	—
107	C₂²×C₇×D₄	C₂³	1	4	yes	—
108	C₂²×C₇×D₄	C₂³	1	8	yes	—
109	C₂³×C₄×C₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₇	C₂³	1	8	yes	—
111	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
112	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₇×#127	C₂³	1	4	yes	—
119	C₇×#127	C₂³	1	4	yes	—
120	C₇×#127	C₂³	1	4	yes	—
121	C₇×#127	C₂³	1	4	yes	—
122	C₇×#127	C₂³	1	16	yes	—
123	C₇×#127	C₂³	1	8	yes	—
124	C₇×#127	C₂³	1	1	yes	characteristic
125	C₇×#127	C₂³	1	16	yes	—
126	C₇×#126	C₂³	1	8	yes	—
127	C₇×#126	C₂³	1	32	yes	—
128	C₇×#125	C₂³	1	4	yes	—
129	C₇×#125	C₂³	1	2	yes	—
130	C₇×#125	C₂³	1	8	yes	—
131	C₇×#124	C₂³	1	8	yes	—
132	C₇×#124	C₂³	1	8	yes	—
133	C₇×#124	C₂³	1	8	yes	—
134	C₇×#124	C₂³	1	8	yes	—
135	C₇×#124	C₂³	1	4	yes	—
136	C₇×#124	C₂³	1	2	yes	—
137	C₇×#124	C₂³	1	16	yes	—
138	C₇×#124	C₂³	1	16	yes	—
139	C₇×#124	C₂³	1	32	yes	—
140	C₇×#123	C₂³	1	8	yes	—
141	C₇×#123	C₂³	1	4	yes	—
142	C₇×#123	C₂³	1	32	yes	—
143	C₇×#123	C₂³	1	32	yes	—
144	C₇×#123	C₂³	1	32	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
151	C₇×#121	C₂³	1	4	yes	—
152	C₇×#121	C₂³	1	8	yes	—
153	C₇×#121	C₂³	1	8	yes	—
154	C₇×#121	C₂³	1	8	yes	—
155	C₇×#121	C₂³	1	8	yes	—
156	C₇×#121	C₂³	1	8	yes	—
157	C₇×#121	C₂³	1	8	yes	—
158	C₇×#121	C₂³	1	8	yes	—
159	C₇×#121	C₂³	1	8	yes	—
160	C₇×#121	C₂³	1	32	yes	—
161	C₇×#121	C₂³	1	16	yes	—
162	C₇×#121	C₂³	1	16	yes	—
163	C₇×#121	C₂³	1	32	yes	—
164	C₇×#121	C₂³	1	4	yes	—
165	C₇×#121	C₂³	1	4	yes	—
166	C₇×#121	C₂³	1	16	yes	—
167	C₇×#121	C₂³	1	16	yes	—
168	C₇×#121	C₂³	1	16	yes	—
169	C₇×#121	C₂³	1	32	yes	—
170	C₇×#121	C₂³	1	32	yes	—
171	C₇×#121	C₂³	1	32	yes	—
172	C₇×#120	C₂³	1	4	yes	—
173	C₇×#120	C₂³	1	32	yes	—
174	C₇×#120	C₂³	1	16	yes	—
175	C₇×#120	C₂³	1	32	yes	—
176	C₇×#120	C₂³	1	16	yes	—
177	C₇×#120	C₂³	1	32	yes	—
178	C₄×C₇×Q₈	C₂³	1	4	yes	—
179	C₄×C₇×Q₈	C₂³	1	4	yes	—
180	C₄×C₇×Q₈	C₂³	1	4	yes	—
181	C₄×C₇×Q₈	C₂³	1	16	yes	—
182	C₄×C₇×D₄	C₂³	1	8	yes	—
183	C₄×C₇×D₄	C₂³	1	8	yes	—
184	C₄×C₇×D₄	C₂³	1	8	yes	—
185	C₄×C₇×D₄	C₂³	1	8	yes	—
186	C₄×C₇×D₄	C₂³	1	8	yes	—
187	C₄×C₇×D₄	C₂³	1	8	yes	—
188	C₄×C₇×D₄	C₂³	1	8	yes	—
189	C₄×C₇×D₄	C₂³	1	8	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	4	yes	—
194	C₄×C₇×D₄	C₂³	1	4	yes	—
195	C₄×C₇×D₄	C₂³	1	4	yes	—
196	C₄×C₇×D₄	C₂³	1	32	yes	—
197	C₄×C₇×D₄	C₂³	1	16	yes	—
198	C₄×C₇×D₄	C₂³	1	32	yes	—
199	C₄×C₇×D₄	C₂³	1	16	yes	—
200	C₇×#117	C₂³	1	4	yes	—
201	C₇×#117	C₂³	1	4	yes	—
202	C₇×#117	C₂³	1	2	yes	—
203	C₇×#117	C₂³	1	8	yes	—
204	C₇×#117	C₂³	1	8	yes	—
205	C₇×#117	C₂³	1	16	yes	—
206	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
209	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
210	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
211	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	—
212	C₂×C₄²×C₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₇	C₂³	1	4	yes	—
220	#3558	C₂×C₇	1	8	yes	complemented
221	#3549	C₂×C₇	1	2	yes	complemented
222	#3548	C₂×C₇	1	2	yes	complemented
223	#3546	C₂×C₇	1	8	yes	complemented
224	#3537	C₂×C₇	1	4	yes	complemented
225	#3519	C₂×C₇	1	8	yes	complemented
226	#3511	C₂×C₇	1	4	yes	complemented
227	#3508	C₂×C₇	1	4	yes	complemented
228	#3506	C₂×C₇	1	4	yes	complemented
229	#3498	C₂×C₇	1	4	yes	complemented
230	#3496	C₂×C₇	1	4	yes	complemented
231	#3488	C₂×C₇	1	8	yes	complemented
232	#3444	C₂×C₇	1	1	yes	characteristic, complemented
233	C₂×#532	C₂×C₇	1	2	yes	complemented
234	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₇	C₂⁴	1	8	yes	—
236	C₂⁴×C₇	C₂⁴	1	16	yes	—
237	C₇×#41	—	2	32	no	—
238	C₇×#41	—	2	16	no	—
239	C₇×#41	—	4	16	no	—
240	C₇×#41	—	4	4	no	—
241	C₇×#41	—	4	16	no	—
242	C₇×#41	—	4	16	no	—
243	C₇×#41	—	4	32	no	—
244	C₇×#41	—	4	32	no	—
245	C₂×C₇×Q₈	—	4	8	no	—
246	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
247	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
248	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
249	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
250	C₂×C₇×D₄	—	2	16	no	—
251	C₂×C₇×D₄	—	4	8	no	—
252	C₂×C₇×D₄	—	4	16	no	—
253	C₂×C₇×D₄	—	4	8	no	—
254	C₂×C₇×D₄	—	4	32	no	—
255	C₂×C₇×D₄	—	4	32	no	—
256	C₂×C₇×D₄	—	4	16	no	—
257	C₂×C₇×D₄	—	4	64	no	—
258	C₂×C₇×D₄	C₂⁴	1	8	yes	—
259	C₂×C₇×D₄	C₂⁴	1	16	yes	—
260	C₂×C₇×D₄	C₂⁴	1	8	yes	—
261	C₂×C₇×D₄	C₂⁴	1	4	yes	—
262	C₂×C₇×D₄	C₂⁴	1	8	yes	—
263	C₂×C₇×D₄	C₂⁴	1	8	yes	—
264	C₂×C₇×D₄	C₂⁴	1	8	yes	—
265	C₂×C₇×D₄	C₂⁴	1	2	yes	—
266	C₂×C₇×D₄	C₂⁴	1	4	yes	—
267	C₂×C₇×D₄	C₂⁴	1	8	yes	—
268	C₂×C₇×D₄	C₂⁴	1	16	yes	—
269	C₂×C₇×D₄	C₂⁴	1	8	yes	—
270	C₂×C₇×D₄	C₂⁴	1	32	yes	—
271	C₂×C₇×D₄	C₂⁴	1	16	yes	—
272	C₂×C₇×D₄	C₂⁴	1	32	yes	—
273	C₂²×C₄×C₇	—	2	8	no	—
274	C₂²×C₄×C₇	—	4	2	no	—
275	C₂²×C₄×C₇	—	4	16	no	—
276	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
285	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
293	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
304	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
305	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
306	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
307	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
308	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
309	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
310	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
311	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
312	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
313	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
314	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
315	C₄²×C₇	C₂⁴	1	1	yes	characteristic
316	C₄²×C₇	C₂⁴	1	1	yes	characteristic
317	C₄²×C₇	C₂⁴	1	2	yes	—
318	C₄²×C₇	C₂⁴	1	2	yes	—
319	C₄²×C₇	C₂⁴	1	1	yes	characteristic
320	C₄²×C₇	C₂⁴	1	2	yes	—
321	C₄²×C₇	C₂⁴	1	2	yes	—
322	C₄²×C₇	C₂⁴	1	2	yes	—
323	C₄²×C₇	C₂⁴	1	2	yes	—
324	C₄²×C₇	C₂⁴	1	1	yes	characteristic
325	C₄²×C₇	C₂⁴	1	4	yes	—
326	C₄²×C₇	C₂⁴	1	8	yes	—
327	C₄²×C₇	C₂⁴	1	16	yes	—
328	C₂×H(5,𝔽₂)	C₂²×C₇	1	8	yes	complemented
329	C₂²×#41	C₂²×C₇	1	4	yes	complemented
330	#562	C₂²×C₇	1	8	yes	complemented
331	H(3,𝔽₄)	C₂²×C₇	1	8	yes	complemented
332	#560	C₂²×C₇	1	16	yes	complemented
333	#559	C₂²×C₇	1	16	yes	complemented
334	#556	C₂²×C₇	1	8	yes	complemented
335	#555	C₂²×C₇	1	4	yes	complemented
336	#555	C₂²×C₇	1	8	yes	complemented
337	#554	C₂²×C₇	1	8	yes	complemented
338	#553	C₂²×C₇	1	16	yes	complemented
339	#553	C₂²×C₇	1	16	yes	complemented
340	#550	C₂²×C₇	1	16	yes	complemented
341	#550	C₂²×C₇	1	8	yes	complemented
342	#550	C₂²×C₇	1	8	yes	complemented
343	#548	C₂²×C₇	1	16	yes	complemented
344	#547	C₂²×C₇	1	8	yes	complemented
345	#547	C₂²×C₇	1	8	yes	complemented
346	#546	C₂²×C₇	1	16	yes	complemented
347	#546	C₂²×C₇	1	32	yes	complemented
348	#546	C₂²×C₇	1	16	yes	complemented
349	#546	C₂²×C₇	1	16	yes	complemented
350	D₄²	C₂²×C₇	1	16	yes	complemented
351	D₄²	C₂²×C₇	1	16	yes	complemented
352	D₄²	C₂²×C₇	1	4	yes	complemented
353	D₄²	C₂²×C₇	1	8	yes	complemented
354	D₄²	C₂²×C₇	1	16	yes	complemented
355	D₄²	C₂²×C₇	1	8	yes	complemented
356	#542	C₂²×C₇	1	16	yes	complemented
357	#540	C₂²×C₇	1	8	yes	complemented
358	#540	C₂²×C₇	1	8	yes	complemented
359	#538	C₂²×C₇	1	16	yes	complemented
360	#538	C₂²×C₇	1	32	yes	complemented
361	#537	C₂²×C₇	1	8	yes	complemented
362	#537	C₂²×C₇	1	16	yes	complemented
363	#535	C₂²×C₇	1	8	yes	complemented
364	#535	C₂²×C₇	1	16	yes	complemented
365	#535	C₂²×C₇	1	16	yes	complemented
366	#535	C₂²×C₇	1	8	yes	complemented
367	#534	C₂²×C₇	1	16	yes	complemented
368	#533	C₂²×C₇	1	2	yes	complemented
369	#533	C₂²×C₇	1	1	yes	characteristic, complemented
370	#533	C₂²×C₇	1	4	yes	complemented
371	#532	C₂²×C₇	1	4	yes	complemented
372	#532	C₂²×C₇	1	4	yes	complemented
373	#532	C₂²×C₇	1	4	yes	complemented
374	#532	C₂²×C₇	1	4	yes	complemented
375	#532	C₂²×C₇	1	4	yes	complemented
376	#532	C₂²×C₇	1	4	yes	complemented
377	#532	C₂²×C₇	1	4	yes	complemented
378	#532	C₂²×C₇	1	4	yes	complemented
379	#532	C₂²×C₇	1	2	yes	complemented
380	#532	C₂²×C₇	1	1	yes	characteristic, complemented
381	#532	C₂²×C₇	1	8	yes	complemented
382	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
383	C₂×#127	C₂²×C₇	1	2	yes	complemented
384	C₂×#127	C₂²×C₇	1	4	yes	complemented
385	#529	C₂²×C₇	1	4	yes	complemented
386	#529	C₂²×C₇	1	4	yes	complemented
387	#529	C₂²×C₇	1	4	yes	complemented
388	C₂×#124	C₂²×C₇	1	4	yes	complemented
389	#525	C₂²×C₇	1	4	yes	complemented
390	#525	C₂²×C₇	1	2	yes	complemented
391	#525	C₂²×C₇	1	16	yes	complemented
392	C₂×#121	C₂²×C₇	1	4	yes	complemented
393	C₂×#121	C₂²×C₇	1	4	yes	complemented
394	C₂×#121	C₂²×C₇	1	16	yes	complemented
395	#520	C₂²×C₇	1	8	yes	complemented
396	#518	C₂²×C₇	1	8	yes	complemented
397	C₄×#41	C₂²×C₇	1	4	yes	complemented
398	C₄×#41	C₂²×C₇	1	2	yes	complemented
399	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
400	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
401	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
402	C₂³×C₇	—	2	4	no	—
403	C₂³×C₇	—	2	16	no	—
404	C₂³×C₇	—	4	1	no	—
405	C₂³×C₇	—	4	8	no	—
406	C₂³×C₇	—	4	8	no	—
407	C₂³×C₇	—	4	32	no	—
408	C₂³×C₇	—	4	16	no	—
409	C₂³×C₇	C₂⁵	1	4	yes	—
410	C₂³×C₇	C₂⁵	1	16	yes	—
411	C₂³×C₇	C₂⁵	1	1	yes	characteristic
412	C₂³×C₇	C₂⁵	1	2	yes	—
413	C₇×Q₈	—	2	16	no	—
414	C₇×Q₈	—	2	8	no	—
415	C₇×Q₈	—	4	8	no	—
416	C₇×Q₈	—	4	2	no	—
417	C₇×D₄	—	2	16	no	—
418	C₇×D₄	—	2	32	no	—
419	C₇×D₄	—	2	16	no	—
420	C₇×D₄	—	2	16	no	—
421	C₇×D₄	—	2	8	no	—
422	C₇×D₄	—	2	16	no	—
423	C₇×D₄	—	2	16	no	—
424	C₇×D₄	—	4	32	no	—
425	C₇×D₄	—	4	32	no	—
426	C₇×D₄	—	4	8	no	—
427	C₇×D₄	—	4	16	no	—
428	C₇×D₄	—	4	8	no	—
429	C₇×D₄	—	4	16	no	—
430	C₇×D₄	—	4	2	no	—
431	C₇×D₄	—	4	4	no	—
432	C₂×C₄×C₇	—	2	4	no	—
433	C₂×C₄×C₇	—	2	4	no	—
434	C₂×C₄×C₇	—	2	4	no	—
435	C₂×C₄×C₇	—	2	4	no	—
436	C₂×C₄×C₇	—	2	4	no	—
437	C₂×C₄×C₇	—	2	32	no	—
438	C₂×C₄×C₇	—	2	16	no	—
439	C₂×C₄×C₇	—	2	4	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	8	no	—
442	C₂×C₄×C₇	—	4	1	no	—
443	C₂×C₄×C₇	—	4	2	no	—
444	C₂×C₄×C₇	—	4	8	no	—
445	C₂×C₄×C₇	—	4	16	no	—
446	C₂×C₄×C₇	—	4	32	no	—
447	C₂×C₄×C₇	H(5,𝔽₂)	1	8	yes	complemented
448	C₂×C₄×C₇	C₂⁵	1	4	yes	—
449	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
450	C₂×C₄×C₇	C₂⁵	1	2	yes	—
451	C₂×C₄×C₇	C₂⁵	1	2	yes	—
452	C₂×C₄×C₇	C₂⁵	1	2	yes	—
453	C₂×C₄×C₇	C₂⁵	1	16	yes	—
454	C₂×C₄×C₇	C₂⁵	1	8	yes	—
455	C₂×C₄×C₇	C₂⁵	1	2	yes	—
456	C₂×C₄×C₇	C₂⁵	1	2	yes	—
457	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
458	H(5,𝔽₂)	—	4	32	no	—
459	C₂×#41	—	4	16	no	—
460	C₂×#41	C₂³×C₇	1	4	yes	—
461	C₂×#41	C₂³×C₇	1	8	yes	—
462	C₂×#41	C₂³×C₇	1	2	yes	—
463	C₂×#41	C₂³×C₇	1	16	yes	—
464	C₂×#41	C₂³×C₇	1	8	yes	—
465	C₂×#41	C₂³×C₇	1	8	yes	—
466	C₂×#41	C₂³×C₇	1	8	yes	—
467	C₂×#41	C₂³×C₇	1	16	yes	—
468	C₂²×Q₈	C₂³×C₇	1	4	yes	—
469	C₂²×D₄	C₂³×C₇	1	4	yes	—
470	C₂²×D₄	C₂³×C₇	1	4	yes	—
471	C₂²×D₄	C₂³×C₇	1	8	yes	—
472	C₂²×D₄	C₂³×C₇	1	8	yes	—
473	C₂²×D₄	C₂³×C₇	1	32	yes	—
474	C₂²×D₄	C₂³×C₇	1	16	yes	—
475	C₂²×D₄	C₂³×C₇	1	4	yes	—
476	C₂²×D₄	C₂³×C₇	1	16	yes	—
477	C₂³×C₄	C₂³×C₇	1	2	yes	—
478	C₂³×C₄	C₂³×C₇	1	8	yes	—
479	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
481	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
482	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
483	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
484	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
485	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
486	#127	C₂³×C₇	1	4	yes	—
487	#127	C₂³×C₇	1	4	yes	—
488	#127	C₂³×C₇	1	4	yes	—
489	#127	C₂³×C₇	1	4	yes	—
490	#127	C₂³×C₇	1	16	yes	—
491	#127	C₂³×C₇	1	8	yes	—
492	#127	C₂³×C₇	1	1	yes	characteristic
493	#127	C₂³×C₇	1	16	yes	—
494	#126	C₂³×C₇	1	8	yes	—
495	#126	C₂³×C₇	1	32	yes	—
496	#125	C₂³×C₇	1	4	yes	—
497	#125	C₂³×C₇	1	2	yes	—
498	#125	C₂³×C₇	1	8	yes	—
499	#124	C₂³×C₇	1	8	yes	—
500	#124	C₂³×C₇	1	8	yes	—
501	#124	C₂³×C₇	1	8	yes	—
502	#124	C₂³×C₇	1	8	yes	—
503	#124	C₂³×C₇	1	4	yes	—
504	#124	C₂³×C₇	1	2	yes	—
505	#124	C₂³×C₇	1	16	yes	—
506	#124	C₂³×C₇	1	16	yes	—
507	#124	C₂³×C₇	1	32	yes	—
508	#123	C₂³×C₇	1	8	yes	—
509	#123	C₂³×C₇	1	4	yes	—
510	#123	C₂³×C₇	1	32	yes	—
511	#123	C₂³×C₇	1	32	yes	—
512	#123	C₂³×C₇	1	32	yes	—
513	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
514	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
515	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
516	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
517	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
518	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
519	#121	C₂³×C₇	1	4	yes	—
520	#121	C₂³×C₇	1	8	yes	—
521	#121	C₂³×C₇	1	8	yes	—
522	#121	C₂³×C₇	1	8	yes	—
523	#121	C₂³×C₇	1	8	yes	—
524	#121	C₂³×C₇	1	8	yes	—
525	#121	C₂³×C₇	1	8	yes	—
526	#121	C₂³×C₇	1	8	yes	—
527	#121	C₂³×C₇	1	8	yes	—
528	#121	C₂³×C₇	1	32	yes	—
529	#121	C₂³×C₇	1	16	yes	—
530	#121	C₂³×C₇	1	16	yes	—
531	#121	C₂³×C₇	1	32	yes	—
532	#121	C₂³×C₇	1	4	yes	—
533	#121	C₂³×C₇	1	4	yes	—
534	#121	C₂³×C₇	1	16	yes	—
535	#121	C₂³×C₇	1	16	yes	—
536	#121	C₂³×C₇	1	16	yes	—
537	#121	C₂³×C₇	1	32	yes	—
538	#121	C₂³×C₇	1	32	yes	—
539	#121	C₂³×C₇	1	32	yes	—
540	#120	C₂³×C₇	1	4	yes	—
541	#120	C₂³×C₇	1	32	yes	—
542	#120	C₂³×C₇	1	16	yes	—
543	#120	C₂³×C₇	1	32	yes	—
544	#120	C₂³×C₇	1	16	yes	—
545	#120	C₂³×C₇	1	32	yes	—
546	C₄×Q₈	C₂³×C₇	1	4	yes	—
547	C₄×Q₈	C₂³×C₇	1	4	yes	—
548	C₄×Q₈	C₂³×C₇	1	4	yes	—
549	C₄×Q₈	C₂³×C₇	1	16	yes	—
550	C₄×D₄	C₂³×C₇	1	8	yes	—
551	C₄×D₄	C₂³×C₇	1	8	yes	—
552	C₄×D₄	C₂³×C₇	1	8	yes	—
553	C₄×D₄	C₂³×C₇	1	8	yes	—
554	C₄×D₄	C₂³×C₇	1	8	yes	—
555	C₄×D₄	C₂³×C₇	1	8	yes	—
556	C₄×D₄	C₂³×C₇	1	8	yes	—
557	C₄×D₄	C₂³×C₇	1	8	yes	—
558	C₄×D₄	C₂³×C₇	1	8	yes	—
559	C₄×D₄	C₂³×C₇	1	8	yes	—
560	C₄×D₄	C₂³×C₇	1	8	yes	—
561	C₄×D₄	C₂³×C₇	1	4	yes	—
562	C₄×D₄	C₂³×C₇	1	4	yes	—
563	C₄×D₄	C₂³×C₇	1	4	yes	—
564	C₄×D₄	C₂³×C₇	1	32	yes	—
565	C₄×D₄	C₂³×C₇	1	16	yes	—
566	C₄×D₄	C₂³×C₇	1	32	yes	—
567	C₄×D₄	C₂³×C₇	1	16	yes	—
568	#117	C₂³×C₇	1	4	yes	—
569	#117	C₂³×C₇	1	4	yes	—
570	#117	C₂³×C₇	1	2	yes	—
571	#117	C₂³×C₇	1	8	yes	—
572	#117	C₂³×C₇	1	8	yes	—
573	#117	C₂³×C₇	1	16	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	—
580	C₂×C₄²	C₂³×C₇	1	2	yes	—
581	C₂×C₄²	C₂³×C₇	1	2	yes	—
582	C₂×C₄²	C₂³×C₇	1	4	yes	—
583	C₂×C₄²	C₂³×C₇	1	2	yes	—
584	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₇	1	2	yes	—
586	C₂×C₄²	C₂³×C₇	1	2	yes	—
587	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
588	C₂²×C₇	—	2	2	no	—
589	C₂²×C₇	—	2	2	no	—
590	C₂²×C₇	—	2	2	no	—
591	C₂²×C₇	—	2	16	no	—
592	C₂²×C₇	—	2	8	no	—
593	C₂²×C₇	—	2	16	no	—
594	C₂²×C₇	—	2	1	no	—
595	C₂²×C₇	—	2	4	no	—
596	C₂²×C₇	—	2	16	no	—
597	C₂²×C₇	—	4	4	no	—
598	C₂²×C₇	—	8	16	no	—
599	C₂²×C₇	—	16	16	no	—
600	C₂²×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
601	C₂²×C₇	C₂⁶	1	1	yes	characteristic
602	C₄×C₇	—	2	2	no	—
603	C₄×C₇	—	2	2	no	—
604	C₄×C₇	—	2	8	no	—
605	C₄×C₇	—	2	16	no	—
606	C₄×C₇	—	2	2	no	—
607	C₄×C₇	—	2	1	no	—
608	C₄×C₇	—	2	4	no	—
609	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
610	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
611	C₄×C₇	#585	1	2	yes	—
612	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
613	C₂⁴	C₂⁴×C₇	1	8	yes	—
614	C₂⁴	C₂⁴×C₇	1	16	yes	—
615	#41	—	2	32	no	—
616	#41	—	2	16	no	—
617	#41	—	4	16	no	—
618	#41	—	4	4	no	—
619	#41	—	4	16	no	—
620	#41	—	4	16	no	—
621	#41	—	4	32	no	—
622	#41	—	4	32	no	—
623	C₂×Q₈	—	4	8	no	—
624	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
625	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
626	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
627	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
628	C₂×D₄	—	2	16	no	—
629	C₂×D₄	—	4	8	no	—
630	C₂×D₄	—	4	8	no	—
631	C₂×D₄	—	4	16	no	—
632	C₂×D₄	—	4	32	no	—
633	C₂×D₄	—	4	32	no	—
634	C₂×D₄	—	4	16	no	—
635	C₂×D₄	—	4	64	no	—
636	C₂×D₄	C₂⁴×C₇	1	8	yes	—
637	C₂×D₄	C₂⁴×C₇	1	16	yes	—
638	C₂×D₄	C₂⁴×C₇	1	8	yes	—
639	C₂×D₄	C₂⁴×C₇	1	4	yes	—
640	C₂×D₄	C₂⁴×C₇	1	8	yes	—
641	C₂×D₄	C₂⁴×C₇	1	8	yes	—
642	C₂×D₄	C₂⁴×C₇	1	8	yes	—
643	C₂×D₄	C₂⁴×C₇	1	2	yes	—
644	C₂×D₄	C₂⁴×C₇	1	4	yes	—
645	C₂×D₄	C₂⁴×C₇	1	8	yes	—
646	C₂×D₄	C₂⁴×C₇	1	16	yes	—
647	C₂×D₄	C₂⁴×C₇	1	8	yes	—
648	C₂×D₄	C₂⁴×C₇	1	32	yes	—
649	C₂×D₄	C₂⁴×C₇	1	16	yes	—
650	C₂×D₄	C₂⁴×C₇	1	32	yes	—
651	C₂²×C₄	—	2	8	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	16	no	—
654	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
663	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
664	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
667	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
668	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
669	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
671	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
672	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
673	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
674	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
675	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
676	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
677	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
678	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
679	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
680	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
681	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
682	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
683	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
684	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
685	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
686	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
687	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
688	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
689	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
690	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
691	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
692	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
693	C₄²	C₂⁴×C₇	1	1	yes	characteristic
694	C₄²	C₂⁴×C₇	1	1	yes	characteristic
695	C₄²	C₂⁴×C₇	1	2	yes	—
696	C₄²	C₂⁴×C₇	1	2	yes	—
697	C₄²	C₂⁴×C₇	1	1	yes	characteristic
698	C₄²	C₂⁴×C₇	1	2	yes	—
699	C₄²	C₂⁴×C₇	1	2	yes	—
700	C₄²	C₂⁴×C₇	1	2	yes	—
701	C₄²	C₂⁴×C₇	1	2	yes	—
702	C₄²	C₂⁴×C₇	1	1	yes	characteristic
703	C₄²	C₂⁴×C₇	1	4	yes	—
704	C₄²	C₂⁴×C₇	1	8	yes	—
705	C₄²	C₂⁴×C₇	1	16	yes	—
706	C₂×C₇	—	2	4	no	—
707	C₂×C₇	—	4	1	no	—
708	C₂×C₇	—	4	16	no	—
709	C₂×C₇	—	4	4	no	—
710	C₂×C₇	C₂²×H(5,𝔽₂)	1	2	yes	—
711	C₂×C₇	C₂×#585	1	1	yes	characteristic
712	C₂³	—	2	4	no	—
713	C₂³	—	2	16	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	8	no	—
716	C₂³	—	4	8	no	—
717	C₂³	—	4	32	no	—
718	C₂³	—	4	16	no	—
719	C₂³	C₂⁵×C₇	1	4	yes	—
720	C₂³	C₂⁵×C₇	1	16	yes	—
721	C₂³	C₂⁵×C₇	1	1	yes	characteristic
722	C₂³	C₂⁵×C₇	1	2	yes	—
723	Q₈	—	2	16	no	—
724	Q₈	—	2	8	no	—
725	Q₈	—	4	8	no	—
726	Q₈	—	4	2	no	—
727	D₄	—	2	16	no	—
728	D₄	—	2	32	no	—
729	D₄	—	2	16	no	—
730	D₄	—	2	16	no	—
731	D₄	—	2	8	no	—
732	D₄	—	2	16	no	—
733	D₄	—	2	16	no	—
734	D₄	—	4	32	no	—
735	D₄	—	4	32	no	—
736	D₄	—	4	8	no	—
737	D₄	—	4	16	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	16	no	—
740	D₄	—	4	2	no	—
741	D₄	—	4	4	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	32	no	—
748	C₂×C₄	—	2	16	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	8	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	8	no	—
755	C₂×C₄	—	4	16	no	—
756	C₂×C₄	—	4	32	no	—
757	C₂×C₄	C₇×H(5,𝔽₂)	1	8	yes	complemented
758	C₂×C₄	C₂⁵×C₇	1	4	yes	—
759	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
760	C₂×C₄	C₂⁵×C₇	1	2	yes	—
761	C₂×C₄	C₂⁵×C₇	1	2	yes	—
762	C₂×C₄	C₂⁵×C₇	1	2	yes	—
763	C₂×C₄	C₂⁵×C₇	1	16	yes	—
764	C₂×C₄	C₂⁵×C₇	1	8	yes	—
765	C₂×C₄	C₂⁵×C₇	1	2	yes	—
766	C₂×C₄	C₂⁵×C₇	1	2	yes	—
767	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
768	C₇	#62834	1	1	yes	characteristic, direct product factor, Sylow
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	16	no	—
773	C₂²	—	2	8	no	—
774	C₂²	—	2	16	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	16	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	8	16	no	—
780	C₂²	—	16	16	no	—
781	C₂²	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
782	C₂²	C₂⁶×C₇	1	1	yes	characteristic
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	16	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	4	no	—
790	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
791	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
792	C₄	C₇×#585	1	2	yes	—
793	C₂	—	2	4	no	—
794	C₂	—	4	1	no	—
795	C₂	—	4	16	no	—
796	C₂	—	4	4	no	—
797	C₂	C₂²×C₇×H(5,𝔽₂)	1	2	yes	—
798	C₂	C₂×C₇×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇×#3558	C₂	semidirect
2. C₇×#3549	C₂	semidirect
3. C₇×#3548	C₂	semidirect
4. C₇×#3546	C₂	semidirect
5. C₇×#3537	C₂	semidirect
6. C₇×#3519	C₂	semidirect
7. C₇×#3511	C₂	semidirect
8. C₇×#3508	C₂	semidirect
9. C₇×#3506	C₂	semidirect
10. C₇×#3498	C₂	semidirect
11. C₇×#3496	C₂	semidirect
12. C₇×#3488	C₂	semidirect
13. C₇×#3444	C₂	semidirect
14. C₂×C₇×#532	C₂	semidirect
15. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
16. C₂²×C₇×#41	C₂²	semidirect
17. C₇×#562	C₂²	semidirect
18. C₇×H(3,𝔽₄)	C₂²	semidirect
19. C₇×#560	C₂²	semidirect
20. C₇×#559	C₂²	semidirect
21. C₇×#556	C₂²	semidirect
22. C₇×#555	C₂²	semidirect
23. C₇×#555	C₂²	semidirect
24. C₇×#554	C₂²	semidirect
25. C₇×#553	C₂²	semidirect
26. C₇×#553	C₂²	semidirect
27. C₇×#550	C₂²	semidirect
28. C₇×#550	C₂²	semidirect
29. C₇×#550	C₂²	semidirect
30. C₇×#548	C₂²	semidirect
31. C₇×#547	C₂²	semidirect
32. C₇×#547	C₂²	semidirect
33. C₇×#546	C₂²	semidirect
34. C₇×#546	C₂²	semidirect
35. C₇×#546	C₂²	semidirect
36. C₇×#546	C₂²	semidirect
37. C₇×D₄²	C₂²	semidirect
38. C₇×D₄²	C₂²	semidirect
39. C₇×D₄²	C₂²	semidirect
40. C₇×D₄²	C₂²	semidirect
41. C₇×D₄²	C₂²	semidirect
42. C₇×D₄²	C₂²	semidirect
43. C₇×#542	C₂²	semidirect
44. C₇×#540	C₂²	semidirect
45. C₇×#540	C₂²	semidirect
46. C₇×#538	C₂²	semidirect
47. C₇×#538	C₂²	semidirect
48. C₇×#537	C₂²	semidirect
49. C₇×#537	C₂²	semidirect
50. C₇×#535	C₂²	semidirect
51. C₇×#535	C₂²	semidirect
52. C₇×#535	C₂²	semidirect
53. C₇×#535	C₂²	semidirect
54. C₇×#534	C₂²	semidirect
55. C₇×#533	C₂²	semidirect
56. C₇×#533	C₂²	semidirect
57. C₇×#533	C₂²	semidirect
58. C₇×#532	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. C₇×#532	C₂²	semidirect
65. C₇×#532	C₂²	semidirect
66. C₇×#532	C₂²	semidirect
67. C₇×#532	C₂²	semidirect
68. C₇×#532	C₂²	semidirect
69. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
70. C₂×C₇×#127	C₂²	semidirect
71. C₂×C₇×#127	C₂²	semidirect
72. C₇×#529	C₂²	semidirect
73. C₇×#529	C₂²	semidirect
74. C₇×#529	C₂²	semidirect
75. C₂×C₇×#124	C₂²	semidirect
76. C₇×#525	C₂²	semidirect
77. C₇×#525	C₂²	semidirect
78. C₇×#525	C₂²	semidirect
79. C₂×C₇×#121	C₂²	semidirect
80. C₂×C₇×#121	C₂²	semidirect
81. C₂×C₇×#121	C₂²	semidirect
82. C₇×#520	C₂²	semidirect
83. C₇×#518	C₂²	semidirect
84. C₄×C₇×#41	C₂²	semidirect
85. C₄×C₇×#41	C₂²	semidirect
86. C₂×C₄×C₇×D₄	C₂²	semidirect
87. C₂×C₄×C₇×D₄	C₂²	semidirect
88. C₂²×C₄²×C₇	C₂²	semidirect
89. #62834	C₇	direct (N × H)
220. #3558	C₂×C₇	semidirect
221. #3549	C₂×C₇	semidirect
222. #3548	C₂×C₇	semidirect
223. #3546	C₂×C₇	semidirect
224. #3537	C₂×C₇	semidirect
225. #3519	C₂×C₇	semidirect
226. #3511	C₂×C₇	semidirect
227. #3508	C₂×C₇	semidirect
228. #3506	C₂×C₇	semidirect
229. #3498	C₂×C₇	semidirect
230. #3496	C₂×C₇	semidirect
231. #3488	C₂×C₇	semidirect
232. #3444	C₂×C₇	semidirect
233. C₂×#532	C₂×C₇	semidirect
328. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
329. C₂²×#41	C₂²×C₇	semidirect
330. #562	C₂²×C₇	semidirect
331. H(3,𝔽₄)	C₂²×C₇	semidirect
332. #560	C₂²×C₇	semidirect
333. #559	C₂²×C₇	semidirect
334. #556	C₂²×C₇	semidirect
335. #555	C₂²×C₇	semidirect
336. #555	C₂²×C₇	semidirect
337. #554	C₂²×C₇	semidirect
338. #553	C₂²×C₇	semidirect
339. #553	C₂²×C₇	semidirect
340. #550	C₂²×C₇	semidirect
341. #550	C₂²×C₇	semidirect
342. #550	C₂²×C₇	semidirect
343. #548	C₂²×C₇	semidirect
344. #547	C₂²×C₇	semidirect
345. #547	C₂²×C₇	semidirect
346. #546	C₂²×C₇	semidirect
347. #546	C₂²×C₇	semidirect
348. #546	C₂²×C₇	semidirect
349. #546	C₂²×C₇	semidirect
350. D₄²	C₂²×C₇	semidirect
351. D₄²	C₂²×C₇	semidirect
352. D₄²	C₂²×C₇	semidirect
353. D₄²	C₂²×C₇	semidirect
354. D₄²	C₂²×C₇	semidirect
355. D₄²	C₂²×C₇	semidirect
356. #542	C₂²×C₇	semidirect
357. #540	C₂²×C₇	semidirect
358. #540	C₂²×C₇	semidirect
359. #538	C₂²×C₇	semidirect
360. #538	C₂²×C₇	semidirect
361. #537	C₂²×C₇	semidirect
362. #537	C₂²×C₇	semidirect
363. #535	C₂²×C₇	semidirect
364. #535	C₂²×C₇	semidirect
365. #535	C₂²×C₇	semidirect
366. #535	C₂²×C₇	semidirect
367. #534	C₂²×C₇	semidirect
368. #533	C₂²×C₇	semidirect
369. #533	C₂²×C₇	semidirect
370. #533	C₂²×C₇	semidirect
371. #532	C₂²×C₇	semidirect
372. #532	C₂²×C₇	semidirect
373. #532	C₂²×C₇	semidirect
374. #532	C₂²×C₇	semidirect
375. #532	C₂²×C₇	semidirect
376. #532	C₂²×C₇	semidirect
377. #532	C₂²×C₇	semidirect
378. #532	C₂²×C₇	semidirect
379. #532	C₂²×C₇	semidirect
380. #532	C₂²×C₇	semidirect
381. #532	C₂²×C₇	semidirect
382. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
383. C₂×#127	C₂²×C₇	semidirect
384. C₂×#127	C₂²×C₇	semidirect
385. #529	C₂²×C₇	semidirect
386. #529	C₂²×C₇	semidirect
387. #529	C₂²×C₇	semidirect
388. C₂×#124	C₂²×C₇	semidirect
389. #525	C₂²×C₇	semidirect
390. #525	C₂²×C₇	semidirect
391. #525	C₂²×C₇	semidirect
392. C₂×#121	C₂²×C₇	semidirect
393. C₂×#121	C₂²×C₇	semidirect
394. C₂×#121	C₂²×C₇	semidirect
395. #520	C₂²×C₇	semidirect
396. #518	C₂²×C₇	semidirect
397. C₄×#41	C₂²×C₇	semidirect
398. C₄×#41	C₂²×C₇	semidirect
399. C₂×C₄×D₄	C₂²×C₇	semidirect
400. C₂×C₄×D₄	C₂²×C₇	semidirect
401. C₂²×C₄²	C₂²×C₇	semidirect
447. C₂×C₄×C₇	H(5,𝔽₂)	semidirect
757. C₂×C₄	C₇×H(5,𝔽₂)	semidirect
768. C₇	#62834	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×#3558	2
C₇×#3549	2
C₇×#3548	2
C₇×#3546	2
C₇×#3537	2
C₇×#3519	2
C₇×#3511	2
C₇×#3508	2
C₇×#3506	2
C₇×#3498	2
C₇×#3496	2
C₇×#3488	2
C₇×#3444	2
C₂×C₇×#532	2
#62834	7

Subgroups — C7×#62834 #13240050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62834 #13240050