Subgroups — C₇×#34920 #13212136

Order 1792.

1692 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2590	C₂	1	2	yes	maximal
2	C₇×#2588	C₂	1	2	yes	maximal
3	C₇×#2584	C₂	1	1	yes	maximal, characteristic
4	C₇×#2581	C₂	1	1	yes	maximal, characteristic
5	C₇×#2565	C₂	1	1	yes	maximal, characteristic
6	C₇×#2550	C₂	1	1	yes	maximal, characteristic
7	C₇×#2520	C₂	1	2	yes	maximal
8	C₇×#2508	C₂	1	1	yes	maximal, characteristic
9	C₇×#2506	C₂	1	1	yes	maximal, characteristic
10	C₇×#2462	C₂	1	2	yes	maximal
11	C₇×#2453	C₂	1	1	yes	maximal, characteristic
12	C₇×#2451	C₂	1	1	yes	maximal, characteristic
13	C₇×#2402	C₂	1	2	yes	maximal
14	C₇×#2399	C₂	1	2	yes	maximal
15	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
16	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic
17	C₄×C₇×#125	C₂	1	2	yes	maximal
18	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic
19	C₇×#2295	C₂	1	2	yes	maximal
20	C₇×#2295	C₂	1	1	yes	maximal, characteristic
21	C₇×#2295	C₂	1	1	yes	maximal, characteristic
22	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
23	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#125	C₂²	1	1	yes	characteristic
26	C₂×C₇×#125	C₂²	1	2	yes	—
27	C₂×C₇×#125	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
35	C₇×#400	C₂²	1	2	yes	—
36	C₇×#400	C₂²	1	2	yes	—
37	C₇×#400	C₂²	1	2	yes	—
38	C₇×#400	C₂²	1	2	yes	—
39	C₇×#398	C₂²	1	2	yes	—
40	C₇×#398	C₂²	1	2	yes	—
41	C₇×#398	C₂²	1	2	yes	—
42	C₇×#398	C₂²	1	2	yes	—
43	C₇×#398	C₂²	1	2	yes	—
44	C₇×#398	C₂²	1	2	yes	—
45	C₇×#398	C₂²	1	2	yes	—
46	C₇×#398	C₂²	1	2	yes	—
47	C₇×#395	C₂²	1	2	yes	—
48	C₇×#395	C₂²	1	2	yes	—
49	C₇×#395	C₂²	1	2	yes	—
50	C₇×#395	C₂²	1	2	yes	—
51	C₇×#391	C₂²	1	2	yes	—
52	C₇×#391	C₂²	1	1	yes	characteristic
53	C₇×#391	C₂²	1	1	yes	characteristic
54	C₇×#391	C₂²	1	1	yes	characteristic
55	C₇×#391	C₂²	1	1	yes	characteristic
56	C₇×#391	C₂²	1	2	yes	—
57	C₇×#391	C₂²	1	2	yes	—
58	C₇×#389	C₂²	1	1	yes	characteristic
59	C₇×#389	C₂²	1	1	yes	characteristic
60	C₇×#389	C₂²	1	2	yes	—
61	C₇×#389	C₂²	1	1	yes	characteristic
62	C₇×#389	C₂²	1	1	yes	characteristic
63	C₇×#389	C₂²	1	2	yes	—
64	C₇×#389	C₂²	1	1	yes	characteristic
65	C₇×#389	C₂²	1	1	yes	characteristic
66	C₇×#389	C₂²	1	1	yes	characteristic
67	C₇×#389	C₂²	1	1	yes	characteristic
68	C₇×#389	C₂²	1	1	yes	characteristic
69	C₇×#389	C₂²	1	1	yes	characteristic
70	C₇×#389	C₂²	1	2	yes	—
71	C₇×#389	C₂²	1	2	yes	—
72	C₇×#389	C₂²	1	2	yes	—
73	C₇×#387	C₂²	1	2	yes	—
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#384	C₂²	1	1	yes	characteristic
90	C₇×#382	C₂²	1	2	yes	—
91	C₇×#382	C₂²	1	1	yes	characteristic
92	C₇×#382	C₂²	1	1	yes	characteristic
93	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
101	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
117	C₇×#376	C₂²	1	2	yes	—
118	C₇×#376	C₂²	1	2	yes	—
119	C₄³×C₇	C₂²	1	1	yes	characteristic
120	C₄³×C₇	C₂²	1	2	yes	—
121	C₄³×C₇	C₂²	1	1	yes	characteristic
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#34920	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×Q₈	C₂³	1	2	yes	—
126	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₇×C₄⋊Q₈	—	2	4	no	—
128	C₇×#125	—	2	8	no	—
129	C₇×#125	—	2	4	no	—
130	C₇×#125	—	2	4	no	—
131	C₄×C₇×Q₈	—	2	4	no	—
132	C₄×C₇×Q₈	—	2	4	no	—
133	C₄×C₇×Q₈	—	2	4	no	—
134	C₄×C₇×Q₈	—	2	8	no	—
135	C₄×C₇×Q₈	—	2	4	no	—
136	C₄×C₇×Q₈	—	2	4	no	—
137	C₄×C₇×Q₈	Q₈	1	8	yes	complemented
138	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₇×#95	C₂³	1	2	yes	—
202	C₇×#95	C₂³	1	2	yes	—
203	C₇×#95	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	2	yes	—
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	C₇×#95	C₂³	1	2	yes	—
208	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	1	yes	characteristic
210	C₇×#95	C₂³	1	1	yes	characteristic
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	1	yes	characteristic
213	C₇×#95	C₂³	1	1	yes	characteristic
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	1	yes	characteristic
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	1	yes	characteristic
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
222	C₇×#95	C₂³	1	2	yes	—
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	#2590	C₂×C₇	1	2	yes	—
235	#2588	C₂×C₇	1	2	yes	—
236	#2584	C₂×C₇	1	1	yes	characteristic
237	#2581	C₂×C₇	1	1	yes	characteristic
238	#2565	C₂×C₇	1	1	yes	characteristic
239	#2550	C₂×C₇	1	1	yes	characteristic
240	#2520	C₂×C₇	1	2	yes	—
241	#2508	C₂×C₇	1	1	yes	characteristic
242	#2506	C₂×C₇	1	1	yes	characteristic
243	#2462	C₂×C₇	1	2	yes	—
244	#2453	C₂×C₇	1	1	yes	characteristic
245	#2451	C₂×C₇	1	1	yes	characteristic
246	#2402	C₂×C₇	1	2	yes	—
247	#2399	C₂×C₇	1	2	yes	—
248	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
249	C₄×#125	C₂×C₇	1	1	yes	characteristic
250	C₄×#125	C₂×C₇	1	1	yes	characteristic
251	C₄×#125	C₂×C₇	1	2	yes	—
252	#2295	C₂×C₇	1	2	yes	—
253	#2295	C₂×C₇	1	1	yes	characteristic
254	#2295	C₂×C₇	1	1	yes	characteristic
255	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic
256	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic
257	C₂×C₇×Q₈	—	2	2	no	—
258	C₂×C₇×Q₈	—	2	2	no	—
259	C₂×C₇×Q₈	—	2	2	no	—
260	C₂×C₇×Q₈	—	2	2	no	—
261	C₂×C₇×Q₈	—	2	2	no	—
262	C₂×C₇×Q₈	—	2	4	no	—
263	C₂×C₇×Q₈	—	2	4	no	—
264	C₂×C₇×Q₈	—	4	2	no	—
265	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	2	no	—
292	C₇×C₄⋊C₄	—	2	2	no	—
293	C₇×C₄⋊C₄	—	2	4	no	—
294	C₇×C₄⋊C₄	—	2	4	no	—
295	C₇×C₄⋊C₄	—	2	4	no	—
296	C₇×C₄⋊C₄	—	2	2	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	2	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	4	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	4	no	—
303	C₇×C₄⋊C₄	—	2	4	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	4	no	—
306	C₇×C₄⋊C₄	—	2	4	no	—
307	C₇×C₄⋊C₄	—	2	4	no	—
308	C₇×C₄⋊C₄	—	2	4	no	—
309	C₇×C₄⋊C₄	—	2	4	no	—
310	C₇×C₄⋊C₄	—	2	4	no	—
311	C₇×C₄⋊C₄	—	2	4	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	4	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	—	4	2	no	—
318	C₇×C₄⋊C₄	—	4	2	no	—
319	C₇×C₄⋊C₄	—	4	2	no	—
320	C₇×C₄⋊C₄	—	4	2	no	—
321	C₇×C₄⋊C₄	C₂×Q₈	1	8	yes	—
322	C₇×C₄⋊C₄	C₂×Q₈	1	4	yes	—
323	C₇×C₄⋊C₄	#41	1	4	yes	—
324	C₇×C₄⋊C₄	#41	1	4	yes	—
325	C₄²×C₇	—	2	2	no	—
326	C₄²×C₇	—	2	2	no	—
327	C₄²×C₇	—	2	4	no	—
328	C₄²×C₇	—	2	2	no	—
329	C₄²×C₇	—	2	2	no	—
330	C₄²×C₇	—	2	4	no	—
331	C₄²×C₇	—	2	2	no	—
332	C₄²×C₇	—	2	2	no	—
333	C₄²×C₇	—	2	2	no	—
334	C₄²×C₇	—	2	2	no	—
335	C₄²×C₇	—	2	4	no	—
336	C₄²×C₇	—	2	4	no	—
337	C₄²×C₇	—	2	4	no	—
338	C₄²×C₇	—	2	2	no	—
339	C₄²×C₇	—	2	2	no	—
340	C₄²×C₇	—	2	2	no	—
341	C₄²×C₇	—	2	2	no	—
342	C₄²×C₇	—	2	2	no	—
343	C₄²×C₇	—	2	4	no	—
344	C₄²×C₇	—	4	1	no	—
345	C₄²×C₇	—	4	2	no	—
346	C₄²×C₇	—	4	1	no	—
347	C₄²×C₇	—	4	1	no	—
348	C₄²×C₇	C₂×Q₈	1	8	yes	—
349	C₄²×C₇	C₂×Q₈	1	4	yes	—
350	C₄²×C₇	#41	1	4	yes	—
351	C₄²×C₇	#41	1	4	yes	—
352	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
353	C₂×#125	C₂²×C₇	1	1	yes	characteristic
354	C₂×#125	C₂²×C₇	1	1	yes	characteristic
355	C₂×#125	C₂²×C₇	1	2	yes	—
356	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
357	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
361	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
362	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
363	#400	C₂²×C₇	1	2	yes	—
364	#400	C₂²×C₇	1	2	yes	—
365	#400	C₂²×C₇	1	2	yes	—
366	#400	C₂²×C₇	1	2	yes	—
367	#398	C₂²×C₇	1	2	yes	—
368	#398	C₂²×C₇	1	2	yes	—
369	#398	C₂²×C₇	1	2	yes	—
370	#398	C₂²×C₇	1	2	yes	—
371	#398	C₂²×C₇	1	2	yes	—
372	#398	C₂²×C₇	1	2	yes	—
373	#398	C₂²×C₇	1	2	yes	—
374	#398	C₂²×C₇	1	2	yes	—
375	#395	C₂²×C₇	1	2	yes	—
376	#395	C₂²×C₇	1	2	yes	—
377	#395	C₂²×C₇	1	2	yes	—
378	#395	C₂²×C₇	1	2	yes	—
379	#391	C₂²×C₇	1	2	yes	—
380	#391	C₂²×C₇	1	1	yes	characteristic
381	#391	C₂²×C₇	1	1	yes	characteristic
382	#391	C₂²×C₇	1	1	yes	characteristic
383	#391	C₂²×C₇	1	1	yes	characteristic
384	#391	C₂²×C₇	1	2	yes	—
385	#391	C₂²×C₇	1	2	yes	—
386	#389	C₂²×C₇	1	1	yes	characteristic
387	#389	C₂²×C₇	1	2	yes	—
388	#389	C₂²×C₇	1	1	yes	characteristic
389	#389	C₂²×C₇	1	2	yes	—
390	#389	C₂²×C₇	1	1	yes	characteristic
391	#389	C₂²×C₇	1	1	yes	characteristic
392	#389	C₂²×C₇	1	1	yes	characteristic
393	#389	C₂²×C₇	1	1	yes	characteristic
394	#389	C₂²×C₇	1	2	yes	—
395	#389	C₂²×C₇	1	2	yes	—
396	#389	C₂²×C₇	1	1	yes	characteristic
397	#389	C₂²×C₇	1	1	yes	characteristic
398	#389	C₂²×C₇	1	2	yes	—
399	#389	C₂²×C₇	1	1	yes	characteristic
400	#389	C₂²×C₇	1	1	yes	characteristic
401	#387	C₂²×C₇	1	2	yes	—
402	#387	C₂²×C₇	1	2	yes	—
403	#387	C₂²×C₇	1	2	yes	—
404	#387	C₂²×C₇	1	2	yes	—
405	#387	C₂²×C₇	1	2	yes	—
406	#387	C₂²×C₇	1	2	yes	—
407	#387	C₂²×C₇	1	2	yes	—
408	#387	C₂²×C₇	1	2	yes	—
409	#387	C₂²×C₇	1	2	yes	—
410	#387	C₂²×C₇	1	2	yes	—
411	#387	C₂²×C₇	1	2	yes	—
412	#387	C₂²×C₇	1	2	yes	—
413	#387	C₂²×C₇	1	2	yes	—
414	#387	C₂²×C₇	1	2	yes	—
415	#387	C₂²×C₇	1	2	yes	—
416	#387	C₂²×C₇	1	2	yes	—
417	#384	C₂²×C₇	1	1	yes	characteristic
418	#382	C₂²×C₇	1	1	yes	characteristic
419	#382	C₂²×C₇	1	1	yes	characteristic
420	#382	C₂²×C₇	1	2	yes	—
421	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
445	#376	C₂²×C₇	1	2	yes	—
446	#376	C₂²×C₇	1	2	yes	—
447	C₄³	C₂²×C₇	1	1	yes	characteristic
448	C₄³	C₂²×C₇	1	2	yes	—
449	C₄³	C₂²×C₇	1	1	yes	characteristic
450	C₄³	C₂²×C₇	1	1	yes	characteristic
451	C₂³×C₇	C₂⁵	1	1	yes	characteristic
452	C₇×Q₈	—	2	8	no	—
453	C₇×Q₈	—	2	8	no	—
454	C₇×Q₈	—	4	8	no	—
455	C₂×C₄×C₇	—	2	1	no	—
456	C₂×C₄×C₇	—	2	1	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	1	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	1	no	—
462	C₂×C₄×C₇	—	2	1	no	—
463	C₂×C₄×C₇	—	2	1	no	—
464	C₂×C₄×C₇	—	2	1	no	—
465	C₂×C₄×C₇	—	2	1	no	—
466	C₂×C₄×C₇	—	2	1	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	2	1	no	—
469	C₂×C₄×C₇	—	2	1	no	—
470	C₂×C₄×C₇	—	2	1	no	—
471	C₂×C₄×C₇	—	2	1	no	—
472	C₂×C₄×C₇	—	2	1	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	2	no	—
476	C₂×C₄×C₇	—	2	1	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	2	no	—
480	C₂×C₄×C₇	—	2	2	no	—
481	C₂×C₄×C₇	—	2	1	no	—
482	C₂×C₄×C₇	—	2	1	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	1	no	—
485	C₂×C₄×C₇	—	2	1	no	—
486	C₂×C₄×C₇	—	2	1	no	—
487	C₂×C₄×C₇	—	2	1	no	—
488	C₂×C₄×C₇	—	2	1	no	—
489	C₂×C₄×C₇	—	2	2	no	—
490	C₂×C₄×C₇	—	2	2	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	2	2	no	—
493	C₂×C₄×C₇	—	2	2	no	—
494	C₂×C₄×C₇	—	2	2	no	—
495	C₂×C₄×C₇	—	2	2	no	—
496	C₂×C₄×C₇	—	2	1	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	1	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	1	no	—
504	C₂×C₄×C₇	—	2	1	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
508	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
509	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
510	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
511	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
512	C₂×C₄×C₇	C₂×#41	1	2	yes	—
513	C₂×C₄×C₇	C₂×#41	1	2	yes	—
514	C₂×C₄×C₇	C₂×#41	1	2	yes	—
515	C₂×C₄×C₇	C₂×#41	1	2	yes	—
516	C₂×C₄×C₇	C₂×#41	1	4	yes	—
517	C₂×C₄×C₇	C₂×#41	1	2	yes	—
518	C₂×C₄×C₇	C₂×#41	1	2	yes	—
519	C₂×C₄×C₇	C₂×#41	1	2	yes	—
520	C₂×C₄×C₇	C₂×#41	1	2	yes	—
521	C₂×C₄×C₇	C₂×#41	1	2	yes	—
522	C₂×C₄×C₇	C₂×#41	1	2	yes	—
523	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
524	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₇	1	2	yes	—
526	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
527	C₄⋊Q₈	—	2	4	no	—
528	#125	—	2	8	no	—
529	#125	—	2	4	no	—
530	#125	—	2	4	no	—
531	C₄×Q₈	—	2	4	no	—
532	C₄×Q₈	—	2	4	no	—
533	C₄×Q₈	—	2	4	no	—
534	C₄×Q₈	—	2	8	no	—
535	C₄×Q₈	—	2	4	no	—
536	C₄×Q₈	—	2	4	no	—
537	C₄×Q₈	C₇×Q₈	1	8	yes	complemented
538	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₇	1	2	yes	—
575	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₇	1	2	yes	—
581	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₇	1	2	yes	—
583	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
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	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₇	1	2	yes	—
593	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₇	1	2	yes	—
597	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₇	1	2	yes	—
599	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
601	#95	C₂³×C₇	1	2	yes	—
602	#95	C₂³×C₇	1	2	yes	—
603	#95	C₂³×C₇	1	2	yes	—
604	#95	C₂³×C₇	1	2	yes	—
605	#95	C₂³×C₇	1	2	yes	—
606	#95	C₂³×C₇	1	2	yes	—
607	#95	C₂³×C₇	1	2	yes	—
608	#95	C₂³×C₇	1	2	yes	—
609	#95	C₂³×C₇	1	1	yes	characteristic
610	#95	C₂³×C₇	1	1	yes	characteristic
611	#95	C₂³×C₇	1	2	yes	—
612	#95	C₂³×C₇	1	1	yes	characteristic
613	#95	C₂³×C₇	1	1	yes	characteristic
614	#95	C₂³×C₇	1	2	yes	—
615	#95	C₂³×C₇	1	1	yes	characteristic
616	#95	C₂³×C₇	1	2	yes	—
617	#95	C₂³×C₇	1	1	yes	characteristic
618	#95	C₂³×C₇	1	2	yes	—
619	#95	C₂³×C₇	1	2	yes	—
620	#95	C₂³×C₇	1	2	yes	—
621	#95	C₂³×C₇	1	2	yes	—
622	#95	C₂³×C₇	1	2	yes	—
623	#95	C₂³×C₇	1	2	yes	—
624	#95	C₂³×C₇	1	2	yes	—
625	#95	C₂³×C₇	1	2	yes	—
626	#95	C₂³×C₇	1	2	yes	—
627	#95	C₂³×C₇	1	2	yes	—
628	#95	C₂³×C₇	1	2	yes	—
629	#95	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
635	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
636	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
637	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
638	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
639	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
640	C₂²×C₇	#585	1	1	yes	characteristic
641	C₄×C₇	—	2	4	no	—
642	C₄×C₇	—	2	2	no	—
643	C₄×C₇	—	2	2	no	—
644	C₄×C₇	—	2	2	no	—
645	C₄×C₇	—	2	2	no	—
646	C₄×C₇	—	2	4	no	—
647	C₄×C₇	—	2	2	no	—
648	C₄×C₇	—	2	2	no	—
649	C₄×C₇	—	2	4	no	—
650	C₄×C₇	—	2	2	no	—
651	C₄×C₇	—	2	2	no	—
652	C₄×C₇	—	4	2	no	—
653	C₄×C₇	—	4	2	no	—
654	C₄×C₇	—	4	1	no	—
655	C₄×C₇	—	4	1	no	—
656	C₄×C₇	—	4	2	no	—
657	C₄×C₇	—	4	1	no	—
658	C₄×C₇	—	4	1	no	—
659	C₄×C₇	—	4	2	no	—
660	C₄×C₇	—	4	1	no	—
661	C₄×C₇	—	4	2	no	—
662	C₄×C₇	#533	1	4	yes	—
663	C₄×C₇	#557	1	4	yes	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	4	no	—
670	C₂×Q₈	—	2	4	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	—
673	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	C₂×C₇×Q₈	1	8	yes	—
729	C₄⋊C₄	C₂×C₇×Q₈	1	4	yes	—
730	C₄⋊C₄	C₇×#41	1	4	yes	—
731	C₄⋊C₄	C₇×#41	1	4	yes	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	4	no	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	4	1	no	—
752	C₄²	—	4	2	no	—
753	C₄²	—	4	1	no	—
754	C₄²	—	4	1	no	—
755	C₄²	C₂×C₇×Q₈	1	8	yes	—
756	C₄²	C₂×C₇×Q₈	1	4	yes	—
757	C₄²	C₇×#41	1	4	yes	—
758	C₄²	C₇×#41	1	4	yes	—
759	C₂×C₇	C₂×#533	1	1	yes	characteristic
760	C₂×C₇	#3444	1	1	yes	characteristic
761	C₂×C₇	#3461	1	1	yes	characteristic
762	C₂×C₇	#3475	1	1	yes	characteristic
763	C₂×C₇	C₂×#557	1	1	yes	characteristic
764	C₂×C₇	Q₈×#41	1	1	yes	characteristic
765	C₂×C₇	#3482	1	1	yes	characteristic
766	C₂³	C₂⁵×C₇	1	1	yes	characteristic
767	Q₈	—	2	8	no	—
768	Q₈	—	2	8	no	—
769	Q₈	—	4	8	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
823	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
824	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
825	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
826	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
827	C₂×C₄	C₂×C₇×#41	1	2	yes	—
828	C₂×C₄	C₂×C₇×#41	1	2	yes	—
829	C₂×C₄	C₂×C₇×#41	1	2	yes	—
830	C₂×C₄	C₂×C₇×#41	1	2	yes	—
831	C₂×C₄	C₂×C₇×#41	1	4	yes	—
832	C₂×C₄	C₂×C₇×#41	1	2	yes	—
833	C₂×C₄	C₂×C₇×#41	1	2	yes	—
834	C₂×C₄	C₂×C₇×#41	1	2	yes	—
835	C₂×C₄	C₂×C₇×#41	1	2	yes	—
836	C₂×C₄	C₂×C₇×#41	1	2	yes	—
837	C₂×C₄	C₂×C₇×#41	1	2	yes	—
838	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
839	C₇	#34920	1	1	yes	characteristic, direct product factor, Sylow
840	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
841	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
842	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
843	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
844	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
845	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂²	C₇×#585	1	1	yes	characteristic
847	C₄	—	2	4	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	C₇×#533	1	4	yes	—
869	C₄	C₇×#557	1	4	yes	—
870	C₂	C₂×C₇×#533	1	1	yes	characteristic
871	C₂	C₇×#3444	1	1	yes	characteristic
872	C₂	C₇×#3461	1	1	yes	characteristic
873	C₂	C₇×#3475	1	1	yes	characteristic
874	C₂	C₂×C₇×#557	1	1	yes	characteristic
875	C₂	C₇×Q₈×#41	1	1	yes	characteristic
876	C₂	C₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle, prime radical	C₂³×C₇	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
123. #34920	C₇	direct (N × H)
137. C₄×C₇×Q₈	Q₈	semidirect
537. C₄×Q₈	C₇×Q₈	semidirect
839. C₇	#34920	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×#2590	2
C₇×#2588	2
C₇×#2584	2
C₇×#2581	2
C₇×#2565	2
C₇×#2550	2
C₇×#2520	2
C₇×#2508	2
C₇×#2506	2
C₇×#2462	2
C₇×#2453	2
C₇×#2451	2
C₇×#2402	2
C₇×#2399	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#125	2
C₇×#2295	2
C₄²×C₇×Q₈	2
#34920	7

Subgroups — C7×#34920 #13212136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34920 #13212136