Subgroups — C₇×#35030 #13212246

Order 1792.

1964 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2653	C₂	1	2	yes	maximal, complemented
6	C₇×#2650	C₂	1	2	yes	maximal, complemented
7	C₇×#2574	C₂	1	2	yes	maximal, complemented
8	C₇×#2572	C₂	1	2	yes	maximal, complemented
9	C₇×#2514	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2510	C₂	1	2	yes	maximal, complemented
11	C₇×#2489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2444	C₂	1	2	yes	maximal, complemented
14	C₇×#2442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2436	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2416	C₂	1	1	yes	maximal, characteristic
18	C₇×#2409	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2325	C₂	1	2	yes	maximal, complemented
20	C₇×#2318	C₂	1	2	yes	maximal, complemented
21	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#125	C₂²	1	1	yes	characteristic
26	C₂×C₇×#124	C₂²	1	1	yes	characteristic
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#121	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	2	yes	—
32	C₂×C₇×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
41	C₇×#401	C₂²	1	2	yes	—
42	C₇×#400	C₂²	1	2	yes	—
43	C₇×#400	C₂²	1	2	yes	—
44	C₇×#400	C₂²	1	2	yes	—
45	C₇×#398	C₂²	1	2	yes	—
46	C₇×#397	C₂²	1	2	yes	—
47	C₇×#397	C₂²	1	2	yes	—
48	C₇×#397	C₂²	1	2	yes	—
49	C₇×#397	C₂²	1	2	yes	—
50	C₇×#396	C₂²	1	2	yes	—
51	C₇×#395	C₂²	1	2	yes	—
52	C₇×#394	C₂²	1	2	yes	—
53	C₇×#394	C₂²	1	2	yes	—
54	C₇×#393	C₂²	1	2	yes	—
55	C₇×#393	C₂²	1	2	yes	—
56	C₇×#393	C₂²	1	2	yes	—
57	C₇×#391	C₂²	1	2	yes	—
58	C₇×#391	C₂²	1	1	yes	characteristic
59	C₇×#391	C₂²	1	1	yes	characteristic
60	C₇×#391	C₂²	1	1	yes	characteristic
61	C₇×#391	C₂²	1	1	yes	characteristic
62	C₇×#391	C₂²	1	1	yes	characteristic
63	C₇×#391	C₂²	1	1	yes	characteristic
64	C₇×#391	C₂²	1	2	yes	—
65	C₇×#391	C₂²	1	1	yes	characteristic
66	C₇×#391	C₂²	1	1	yes	characteristic
67	C₇×#390	C₂²	1	1	yes	characteristic
68	C₇×#390	C₂²	1	1	yes	characteristic
69	C₇×#389	C₂²	1	1	yes	characteristic
70	C₇×#389	C₂²	1	1	yes	characteristic
71	C₇×#389	C₂²	1	1	yes	characteristic
72	C₇×#389	C₂²	1	1	yes	characteristic
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	—
75	C₇×#388	C₂²	1	2	yes	—
76	C₇×#388	C₂²	1	2	yes	—
77	C₇×#388	C₂²	1	2	yes	—
78	C₇×#388	C₂²	1	2	yes	—
79	C₇×#388	C₂²	1	2	yes	—
80	C₇×#388	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×#386	C₂²	1	2	yes	—
88	C₇×#386	C₂²	1	2	yes	—
89	C₇×#386	C₂²	1	2	yes	—
90	C₇×#386	C₂²	1	2	yes	—
91	C₇×#386	C₂²	1	2	yes	—
92	C₇×#386	C₂²	1	2	yes	—
93	C₇×#386	C₂²	1	2	yes	—
94	C₇×#386	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	—
97	C₇×#385	C₂²	1	2	yes	—
98	C₇×#385	C₂²	1	2	yes	—
99	C₇×#383	C₂²	1	2	yes	—
100	C₇×#383	C₂²	1	2	yes	—
101	C₇×#382	C₂²	1	1	yes	characteristic
102	C₇×#382	C₂²	1	2	yes	—
103	C₇×#381	C₂²	1	2	yes	—
104	C₇×#381	C₂²	1	2	yes	—
105	C₇×#380	C₂²	1	1	yes	characteristic
106	C₇×#380	C₂²	1	1	yes	characteristic
107	C₇×#380	C₂²	1	2	yes	—
108	C₇×#380	C₂²	1	2	yes	—
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	1	yes	characteristic
113	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₂×C₇×#95	C₂²	1	2	yes	—
121	C₂×C₇×#95	C₂²	1	2	yes	—
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#35030	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	—	2	4	no	—
125	C₂²×C₇×Q₈	—	4	2	no	—
126	C₂²×C₇×Q₈	—	4	2	no	—
127	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₇×Q₈	C₂³	1	2	yes	—
130	C₂²×C₇×D₄	C₂³	1	2	yes	—
131	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
133	C₂²×C₇×D₄	C₂³	1	2	yes	—
134	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₇×#125	—	4	2	no	—
144	C₇×#124	—	4	2	no	—
145	C₇×#124	—	4	2	no	—
146	C₇×C₂²⋊Q₈	—	4	2	no	—
147	C₇×C₂²⋊Q₈	—	4	2	no	—
148	C₇×#121	—	2	8	no	—
149	C₇×#121	—	2	4	no	—
150	C₇×#121	—	4	2	no	—
151	C₄×C₇×D₄	—	2	4	no	—
152	C₄×C₇×D₄	—	2	4	no	—
153	C₄×C₇×D₄	—	2	4	no	—
154	C₄×C₇×D₄	—	2	8	no	—
155	C₄×C₇×D₄	—	4	2	no	—
156	C₂×C₇×C₄⋊C₄	—	4	2	no	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₄²×C₇	—	4	2	no	—
196	C₂×C₄²×C₇	—	4	2	no	—
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	2	yes	—
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	1	yes	characteristic
220	C₇×#95	C₂³	1	1	yes	characteristic
221	C₇×#95	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	1	yes	characteristic
223	C₇×#95	C₂³	1	1	yes	characteristic
224	C₇×#95	C₂³	1	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	2	yes	—
238	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	2	yes	—
240	C₇×#95	C₂³	1	2	yes	—
241	C₇×#95	C₂³	1	2	yes	—
242	#2863	C₂×C₇	1	1	yes	characteristic, complemented
243	#2861	C₂×C₇	1	1	yes	characteristic, complemented
244	#2855	C₂×C₇	1	1	yes	characteristic, complemented
245	#2850	C₂×C₇	1	1	yes	characteristic, complemented
246	#2653	C₂×C₇	1	2	yes	complemented
247	#2650	C₂×C₇	1	2	yes	complemented
248	#2574	C₂×C₇	1	2	yes	complemented
249	#2572	C₂×C₇	1	2	yes	complemented
250	#2514	C₂×C₇	1	1	yes	characteristic, complemented
251	#2510	C₂×C₇	1	2	yes	complemented
252	#2489	C₂×C₇	1	1	yes	characteristic, complemented
253	#2447	C₂×C₇	1	1	yes	characteristic, complemented
254	#2444	C₂×C₇	1	2	yes	complemented
255	#2442	C₂×C₇	1	1	yes	characteristic, complemented
256	#2436	C₂×C₇	1	1	yes	characteristic, complemented
257	#2427	C₂×C₇	1	1	yes	characteristic, complemented
258	#2416	C₂×C₇	1	1	yes	characteristic
259	#2409	C₂×C₇	1	1	yes	characteristic, complemented
260	#2325	C₂×C₇	1	2	yes	complemented
261	#2318	C₂×C₇	1	2	yes	complemented
262	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
263	C₂×#391	C₂×C₇	1	1	yes	characteristic, complemented
264	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
265	C₂⁴×C₇	C₂⁴	1	2	yes	—
266	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
268	C₂×C₇×Q₈	—	2	4	no	—
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	2	2	no	—
271	C₂×C₇×Q₈	—	2	2	no	—
272	C₂×C₇×Q₈	—	2	2	no	—
273	C₂×C₇×Q₈	—	2	2	no	—
274	C₂×C₇×Q₈	—	2	2	no	—
275	C₂×C₇×Q₈	—	4	2	no	—
276	C₂×C₇×Q₈	—	4	2	no	—
277	C₂×C₇×Q₈	—	4	16	no	—
278	C₂×C₇×D₄	—	2	2	no	—
279	C₂×C₇×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	4	no	—
281	C₂×C₇×D₄	—	2	4	no	—
282	C₂×C₇×D₄	—	2	4	no	—
283	C₂×C₇×D₄	—	2	4	no	—
284	C₂×C₇×D₄	—	2	2	no	—
285	C₂×C₇×D₄	—	2	2	no	—
286	C₂×C₇×D₄	—	2	2	no	—
287	C₂×C₇×D₄	—	4	2	no	—
288	C₂×C₇×D₄	—	4	2	no	—
289	C₂×C₇×D₄	#41	1	4	yes	—
290	C₂²×C₄×C₇	—	2	2	no	—
291	C₂²×C₄×C₇	—	2	2	no	—
292	C₂²×C₄×C₇	—	2	2	no	—
293	C₂²×C₄×C₇	—	2	2	no	—
294	C₂²×C₄×C₇	—	2	4	no	—
295	C₂²×C₄×C₇	—	2	4	no	—
296	C₂²×C₄×C₇	—	2	2	no	—
297	C₂²×C₄×C₇	—	2	2	no	—
298	C₂²×C₄×C₇	—	2	2	no	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	2	no	—
302	C₂²×C₄×C₇	—	2	4	no	—
303	C₂²×C₄×C₇	—	4	1	no	—
304	C₂²×C₄×C₇	—	4	1	no	—
305	C₂²×C₄×C₇	—	4	1	no	—
306	C₂²×C₄×C₇	—	4	1	no	—
307	C₂²×C₄×C₇	—	4	1	no	—
308	C₂²×C₄×C₇	—	4	1	no	—
309	C₂²×C₄×C₇	—	4	2	no	—
310	C₂²×C₄×C₇	—	4	2	no	—
311	C₂²×C₄×C₇	—	4	2	no	—
312	C₂²×C₄×C₇	—	4	2	no	—
313	C₂²×C₄×C₇	—	4	2	no	—
314	C₂²×C₄×C₇	—	4	2	no	—
315	C₂²×C₄×C₇	#41	1	4	yes	—
316	C₂²×C₄×C₇	#41	1	4	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₇	C₂⁴	1	2	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	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	4	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	4	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	4	2	no	—
348	C₇×C₄⋊C₄	—	4	2	no	—
349	C₇×C₄⋊C₄	—	4	2	no	—
350	C₇×C₄⋊C₄	—	4	2	no	—
351	C₇×C₄⋊C₄	—	4	2	no	—
352	C₇×C₄⋊C₄	—	4	2	no	—
353	C₇×C₄⋊C₄	—	4	2	no	—
354	C₇×C₂²⋊C₄	—	2	2	no	—
355	C₇×C₂²⋊C₄	—	2	2	no	—
356	C₇×C₂²⋊C₄	—	2	4	no	—
357	C₇×C₂²⋊C₄	—	2	2	no	—
358	C₇×C₂²⋊C₄	—	2	2	no	—
359	C₇×C₂²⋊C₄	—	2	4	no	—
360	C₇×C₂²⋊C₄	—	2	2	no	—
361	C₇×C₂²⋊C₄	—	2	4	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	—	2	4	no	—
364	C₇×C₂²⋊C₄	—	2	4	no	—
365	C₇×C₂²⋊C₄	—	2	4	no	—
366	C₇×C₂²⋊C₄	—	4	2	no	—
367	C₇×C₂²⋊C₄	—	4	2	no	—
368	C₇×C₂²⋊C₄	—	4	2	no	—
369	C₇×C₂²⋊C₄	—	4	2	no	—
370	C₇×C₂²⋊C₄	—	4	2	no	—
371	C₇×C₂²⋊C₄	—	4	2	no	—
372	C₇×C₂²⋊C₄	—	4	2	no	—
373	C₇×C₂²⋊C₄	—	4	2	no	—
374	C₇×C₂²⋊C₄	—	4	2	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	2	no	—
377	C₄²×C₇	—	2	2	no	—
378	C₄²×C₇	—	2	4	no	—
379	C₄²×C₇	—	2	2	no	—
380	C₄²×C₇	—	2	2	no	—
381	C₄²×C₇	—	2	2	no	—
382	C₄²×C₇	—	2	2	no	—
383	C₄²×C₇	—	2	2	no	—
384	C₄²×C₇	—	4	1	no	—
385	C₄²×C₇	—	4	1	no	—
386	C₄²×C₇	—	4	1	no	—
387	C₄²×C₇	—	4	1	no	—
388	C₄²×C₇	—	4	1	no	—
389	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
390	C₂×#125	C₂²×C₇	1	1	yes	characteristic
391	C₂×#124	C₂²×C₇	1	1	yes	characteristic
392	C₂×#124	C₂²×C₇	1	1	yes	characteristic
393	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
394	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
395	C₂×#121	C₂²×C₇	1	2	yes	—
396	C₂×#121	C₂²×C₇	1	1	yes	characteristic
397	C₂×#121	C₂²×C₇	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
399	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
404	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
405	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
406	#401	C₂²×C₇	1	2	yes	—
407	#400	C₂²×C₇	1	2	yes	—
408	#400	C₂²×C₇	1	2	yes	—
409	#400	C₂²×C₇	1	2	yes	—
410	#398	C₂²×C₇	1	2	yes	—
411	#397	C₂²×C₇	1	2	yes	—
412	#397	C₂²×C₇	1	2	yes	—
413	#397	C₂²×C₇	1	2	yes	—
414	#397	C₂²×C₇	1	2	yes	—
415	#396	C₂²×C₇	1	2	yes	—
416	#395	C₂²×C₇	1	2	yes	—
417	#394	C₂²×C₇	1	2	yes	—
418	#394	C₂²×C₇	1	2	yes	—
419	#393	C₂²×C₇	1	2	yes	—
420	#393	C₂²×C₇	1	2	yes	—
421	#393	C₂²×C₇	1	2	yes	—
422	#391	C₂²×C₇	1	2	yes	—
423	#391	C₂²×C₇	1	1	yes	characteristic
424	#391	C₂²×C₇	1	1	yes	characteristic
425	#391	C₂²×C₇	1	1	yes	characteristic
426	#391	C₂²×C₇	1	1	yes	characteristic
427	#391	C₂²×C₇	1	1	yes	characteristic
428	#391	C₂²×C₇	1	1	yes	characteristic
429	#391	C₂²×C₇	1	2	yes	—
430	#391	C₂²×C₇	1	1	yes	characteristic
431	#391	C₂²×C₇	1	1	yes	characteristic
432	#390	C₂²×C₇	1	1	yes	characteristic
433	#390	C₂²×C₇	1	1	yes	characteristic
434	#389	C₂²×C₇	1	1	yes	characteristic
435	#389	C₂²×C₇	1	1	yes	characteristic
436	#389	C₂²×C₇	1	1	yes	characteristic
437	#389	C₂²×C₇	1	1	yes	characteristic
438	#388	C₂²×C₇	1	2	yes	—
439	#388	C₂²×C₇	1	2	yes	—
440	#388	C₂²×C₇	1	2	yes	—
441	#388	C₂²×C₇	1	2	yes	—
442	#388	C₂²×C₇	1	2	yes	—
443	#388	C₂²×C₇	1	2	yes	—
444	#388	C₂²×C₇	1	2	yes	—
445	#388	C₂²×C₇	1	2	yes	—
446	#387	C₂²×C₇	1	2	yes	—
447	#387	C₂²×C₇	1	2	yes	—
448	#387	C₂²×C₇	1	2	yes	—
449	#387	C₂²×C₇	1	2	yes	—
450	#387	C₂²×C₇	1	2	yes	—
451	#387	C₂²×C₇	1	2	yes	—
452	#386	C₂²×C₇	1	2	yes	—
453	#386	C₂²×C₇	1	2	yes	—
454	#386	C₂²×C₇	1	2	yes	—
455	#386	C₂²×C₇	1	2	yes	—
456	#386	C₂²×C₇	1	2	yes	—
457	#386	C₂²×C₇	1	2	yes	—
458	#386	C₂²×C₇	1	2	yes	—
459	#386	C₂²×C₇	1	2	yes	—
460	#385	C₂²×C₇	1	2	yes	—
461	#385	C₂²×C₇	1	2	yes	—
462	#385	C₂²×C₇	1	2	yes	—
463	#385	C₂²×C₇	1	2	yes	—
464	#383	C₂²×C₇	1	2	yes	—
465	#383	C₂²×C₇	1	2	yes	—
466	#382	C₂²×C₇	1	2	yes	—
467	#382	C₂²×C₇	1	1	yes	characteristic
468	#381	C₂²×C₇	1	2	yes	—
469	#381	C₂²×C₇	1	2	yes	—
470	#380	C₂²×C₇	1	2	yes	—
471	#380	C₂²×C₇	1	2	yes	—
472	#380	C₂²×C₇	1	1	yes	characteristic
473	#380	C₂²×C₇	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
481	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
482	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
483	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
484	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
485	C₂×#95	C₂²×C₇	1	2	yes	—
486	C₂×#95	C₂²×C₇	1	2	yes	—
487	C₄³	C₂²×C₇	1	1	yes	characteristic
488	C₂³×C₇	—	2	1	no	—
489	C₂³×C₇	—	2	1	no	—
490	C₂³×C₇	—	2	1	no	—
491	C₂³×C₇	—	2	1	no	—
492	C₂³×C₇	—	2	1	no	—
493	C₂³×C₇	—	2	1	no	—
494	C₂³×C₇	—	2	1	no	—
495	C₂³×C₇	—	2	1	no	—
496	C₂³×C₇	—	2	1	no	—
497	C₂³×C₇	—	2	1	no	—
498	C₂³×C₇	—	2	2	no	—
499	C₂³×C₇	—	2	2	no	—
500	C₂³×C₇	—	2	2	no	—
501	C₂³×C₇	—	2	2	no	—
502	C₂³×C₇	—	2	2	no	—
503	C₂³×C₇	—	2	2	no	—
504	C₂³×C₇	—	2	2	no	—
505	C₂³×C₇	C₂×#41	1	2	yes	—
506	C₂³×C₇	C₂×#41	1	2	yes	—
507	C₂³×C₇	C₂×#41	1	2	yes	—
508	C₂³×C₇	C₂×#41	1	2	yes	—
509	C₂³×C₇	C₂⁵	1	1	yes	characteristic
510	C₇×Q₈	—	4	8	no	—
511	C₇×Q₈	—	4	4	no	—
512	C₇×Q₈	—	4	4	no	—
513	C₇×D₄	—	2	8	no	—
514	C₇×D₄	—	4	8	no	—
515	C₇×D₄	—	4	4	no	—
516	C₇×D₄	—	8	4	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	1	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	8	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	1	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	1	no	—
535	C₂×C₄×C₇	—	2	1	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	1	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	1	no	—
545	C₂×C₄×C₇	—	2	1	no	—
546	C₂×C₄×C₇	—	2	1	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	1	no	—
549	C₂×C₄×C₇	—	2	1	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	1	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	2	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	2	no	—
557	C₂×C₄×C₇	—	2	2	no	—
558	C₂×C₄×C₇	—	2	2	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	1	no	—
561	C₂×C₄×C₇	—	2	2	no	—
562	C₂×C₄×C₇	—	2	1	no	—
563	C₂×C₄×C₇	—	2	1	no	—
564	C₂×C₄×C₇	—	2	1	no	—
565	C₂×C₄×C₇	—	2	1	no	—
566	C₂×C₄×C₇	—	2	2	no	—
567	C₂×C₄×C₇	—	2	1	no	—
568	C₂×C₄×C₇	—	2	2	no	—
569	C₂×C₄×C₇	—	2	2	no	—
570	C₂×C₄×C₇	—	4	4	no	—
571	C₂×C₄×C₇	—	4	4	no	—
572	C₂×C₄×C₇	—	4	4	no	—
573	C₂×C₄×C₇	—	4	4	no	—
574	C₂×C₄×C₇	—	4	8	no	—
575	C₂×C₄×C₇	—	4	4	no	—
576	C₂×C₄×C₇	—	8	4	no	—
577	C₂×C₄×C₇	—	8	4	no	—
578	C₂×C₄×C₇	C₂×#41	1	2	yes	—
579	C₂×C₄×C₇	C₂×#41	1	2	yes	—
580	C₂×C₄×C₇	C₂×#41	1	2	yes	—
581	C₂×C₄×C₇	C₂×#41	1	2	yes	—
582	C₂×C₄×C₇	C₂×#41	1	2	yes	—
583	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
584	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
586	C₂²×Q₈	—	2	4	no	—
587	C₂²×Q₈	—	4	2	no	—
588	C₂²×Q₈	—	4	2	no	—
589	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
590	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
591	C₂²×Q₈	C₂³×C₇	1	2	yes	—
592	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₇	1	2	yes	—
594	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₇	1	2	yes	—
596	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₇	1	2	yes	—
601	C₂³×C₄	C₂³×C₇	1	2	yes	—
602	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₇	1	2	yes	—
604	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
605	#125	—	4	2	no	—
606	#124	—	4	2	no	—
607	#124	—	4	2	no	—
608	C₂²⋊Q₈	—	4	2	no	—
609	C₂²⋊Q₈	—	4	2	no	—
610	#121	—	2	8	no	—
611	#121	—	2	4	no	—
612	#121	—	4	2	no	—
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	—	2	8	no	—
617	C₄×D₄	—	4	2	no	—
618	C₂×C₄⋊C₄	—	4	2	no	—
619	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₄²	—	4	2	no	—
658	C₂×C₄²	—	4	2	no	—
659	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₇	1	2	yes	—
664	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
673	#95	C₂³×C₇	1	2	yes	—
674	#95	C₂³×C₇	1	2	yes	—
675	#95	C₂³×C₇	1	2	yes	—
676	#95	C₂³×C₇	1	2	yes	—
677	#95	C₂³×C₇	1	2	yes	—
678	#95	C₂³×C₇	1	2	yes	—
679	#95	C₂³×C₇	1	2	yes	—
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	1	yes	characteristic
682	#95	C₂³×C₇	1	1	yes	characteristic
683	#95	C₂³×C₇	1	1	yes	characteristic
684	#95	C₂³×C₇	1	1	yes	characteristic
685	#95	C₂³×C₇	1	1	yes	characteristic
686	#95	C₂³×C₇	1	1	yes	characteristic
687	#95	C₂³×C₇	1	2	yes	—
688	#95	C₂³×C₇	1	2	yes	—
689	#95	C₂³×C₇	1	2	yes	—
690	#95	C₂³×C₇	1	2	yes	—
691	#95	C₂³×C₇	1	2	yes	—
692	#95	C₂³×C₇	1	2	yes	—
693	#95	C₂³×C₇	1	2	yes	—
694	#95	C₂³×C₇	1	2	yes	—
695	#95	C₂³×C₇	1	2	yes	—
696	#95	C₂³×C₇	1	2	yes	—
697	#95	C₂³×C₇	1	2	yes	—
698	#95	C₂³×C₇	1	2	yes	—
699	#95	C₂³×C₇	1	2	yes	—
700	#95	C₂³×C₇	1	2	yes	—
701	#95	C₂³×C₇	1	2	yes	—
702	#95	C₂³×C₇	1	2	yes	—
703	#95	C₂³×C₇	1	2	yes	—
704	C₂²×C₇	—	2	2	no	—
705	C₂²×C₇	—	2	2	no	—
706	C₂²×C₇	—	2	2	no	—
707	C₂²×C₇	—	2	2	no	—
708	C₂²×C₇	—	2	2	no	—
709	C₂²×C₇	—	2	2	no	—
710	C₂²×C₇	—	2	2	no	—
711	C₂²×C₇	—	2	2	no	—
712	C₂²×C₇	—	2	2	no	—
713	C₂²×C₇	—	4	1	no	—
714	C₂²×C₇	—	4	1	no	—
715	C₂²×C₇	—	4	1	no	—
716	C₂²×C₇	—	4	1	no	—
717	C₂²×C₇	—	4	2	no	—
718	C₂²×C₇	—	4	2	no	—
719	C₂²×C₇	—	4	2	no	—
720	C₂²×C₇	—	4	2	no	—
721	C₂²×C₇	—	4	2	no	—
722	C₂²×C₇	—	4	2	no	—
723	C₂²×C₇	—	4	2	no	—
724	C₂²×C₇	#529	1	4	yes	—
725	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
726	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
727	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
728	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
730	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
731	C₂²×C₇	#585	1	1	yes	characteristic
732	C₄×C₇	—	2	2	no	—
733	C₄×C₇	—	2	2	no	—
734	C₄×C₇	—	2	2	no	—
735	C₄×C₇	—	2	2	no	—
736	C₄×C₇	—	2	2	no	—
737	C₄×C₇	—	4	2	no	—
738	C₄×C₇	—	4	1	no	—
739	C₄×C₇	—	4	2	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	1	no	—
742	C₄×C₇	—	4	1	no	—
743	C₄×C₇	—	4	2	no	—
744	C₄×C₇	—	4	1	no	—
745	C₄×C₇	—	4	2	no	—
746	C₄×C₇	—	4	1	no	—
747	C₄×C₇	—	4	2	no	—
748	C₄×C₇	—	4	2	no	—
749	C₄×C₇	—	4	1	no	—
750	C₄×C₇	—	4	1	no	—
751	C₄×C₇	#538	1	4	yes	—
752	C₂⁴	C₂⁴×C₇	1	2	yes	—
753	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
754	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
755	C₂×Q₈	—	2	4	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	2	2	no	—
759	C₂×Q₈	—	2	2	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	4	2	no	—
763	C₂×Q₈	—	4	2	no	—
764	C₂×Q₈	—	4	16	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	4	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	4	no	—
770	C₂×D₄	—	2	4	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	C₇×#41	1	4	yes	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	4	1	no	—
791	C₂²×C₄	—	4	1	no	—
792	C₂²×C₄	—	4	1	no	—
793	C₂²×C₄	—	4	1	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	—	4	2	no	—
796	C₂²×C₄	—	4	1	no	—
797	C₂²×C₄	—	4	1	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	C₇×#41	1	4	yes	—
803	C₂²×C₄	C₇×#41	1	4	yes	—
804	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	4	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	4	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	4	2	no	—
835	C₄⋊C₄	—	4	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	2	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	4	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	2	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	4	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	4	1	no	—
872	C₄²	—	4	1	no	—
873	C₄²	—	4	1	no	—
874	C₄²	—	4	1	no	—
875	C₄²	—	4	1	no	—
876	C₂×C₇	—	2	4	no	—
877	C₂×C₇	—	4	2	no	—
878	C₂×C₇	—	8	2	no	—
879	C₂×C₇	C₂×#529	1	1	yes	characteristic
880	C₂×C₇	C₂×#538	1	1	yes	characteristic
881	C₂×C₇	#3461	1	1	yes	characteristic
882	C₂×C₇	#3505	1	1	yes	characteristic
883	C₂×C₇	#3511	1	1	yes	characteristic
884	C₂×C₇	#3514	1	1	yes	characteristic
885	C₂×C₇	#3520	1	1	yes	characteristic
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	C₂×C₇×#41	1	2	yes	—
904	C₂³	C₂×C₇×#41	1	2	yes	—
905	C₂³	C₂×C₇×#41	1	2	yes	—
906	C₂³	C₂×C₇×#41	1	2	yes	—
907	C₂³	C₂⁵×C₇	1	1	yes	characteristic
908	Q₈	—	4	8	no	—
909	Q₈	—	4	4	no	—
910	Q₈	—	4	4	no	—
911	D₄	—	2	8	no	—
912	D₄	—	4	8	no	—
913	D₄	—	4	4	no	—
914	D₄	—	8	4	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	8	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	4	8	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	8	4	no	—
975	C₂×C₄	—	8	4	no	—
976	C₂×C₄	C₂×C₇×#41	1	2	yes	—
977	C₂×C₄	C₂×C₇×#41	1	2	yes	—
978	C₂×C₄	C₂×C₇×#41	1	2	yes	—
979	C₂×C₄	C₂×C₇×#41	1	2	yes	—
980	C₂×C₄	C₂×C₇×#41	1	2	yes	—
981	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
982	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
983	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
984	C₇	#35030	1	1	yes	characteristic, direct product factor, Sylow
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	C₇×#529	1	4	yes	—
1006	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1007	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1008	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1009	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1010	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1011	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1012	C₂²	C₇×#585	1	1	yes	characteristic
1013	C₄	—	2	2	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	C₇×#538	1	4	yes	—
1033	C₂	—	2	4	no	—
1034	C₂	—	4	2	no	—
1035	C₂	—	8	2	no	—
1036	C₂	C₂×C₇×#529	1	1	yes	characteristic
1037	C₂	C₂×C₇×#538	1	1	yes	characteristic
1038	C₂	C₇×#3461	1	1	yes	characteristic
1039	C₂	C₇×#3505	1	1	yes	characteristic
1040	C₂	C₇×#3511	1	1	yes	characteristic
1041	C₂	C₇×#3514	1	1	yes	characteristic
1042	C₂	C₇×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₇×#2416	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2863	C₂	semidirect
2. C₇×#2861	C₂	semidirect
3. C₇×#2855	C₂	semidirect
4. C₇×#2850	C₂	semidirect
5. C₇×#2653	C₂	semidirect
6. C₇×#2650	C₂	semidirect
7. C₇×#2574	C₂	semidirect
8. C₇×#2572	C₂	semidirect
9. C₇×#2514	C₂	semidirect
10. C₇×#2510	C₂	semidirect
11. C₇×#2489	C₂	semidirect
12. C₇×#2447	C₂	semidirect
13. C₇×#2444	C₂	semidirect
14. C₇×#2442	C₂	semidirect
15. C₇×#2436	C₂	semidirect
16. C₇×#2427	C₂	semidirect
18. C₇×#2409	C₂	semidirect
19. C₇×#2325	C₂	semidirect
20. C₇×#2318	C₂	semidirect
21. C₄×C₇×#121	C₂	semidirect
22. C₂×C₇×#391	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
123. #35030	C₇	direct (N × H)
242. #2863	C₂×C₇	semidirect
243. #2861	C₂×C₇	semidirect
244. #2855	C₂×C₇	semidirect
245. #2850	C₂×C₇	semidirect
246. #2653	C₂×C₇	semidirect
247. #2650	C₂×C₇	semidirect
248. #2574	C₂×C₇	semidirect
249. #2572	C₂×C₇	semidirect
250. #2514	C₂×C₇	semidirect
251. #2510	C₂×C₇	semidirect
252. #2489	C₂×C₇	semidirect
253. #2447	C₂×C₇	semidirect
254. #2444	C₂×C₇	semidirect
255. #2442	C₂×C₇	semidirect
256. #2436	C₂×C₇	semidirect
257. #2427	C₂×C₇	semidirect
259. #2409	C₂×C₇	semidirect
260. #2325	C₂×C₇	semidirect
261. #2318	C₂×C₇	semidirect
262. C₄×#121	C₂×C₇	semidirect
263. C₂×#391	C₂×C₇	semidirect
264. C₄²×D₄	C₂×C₇	semidirect
984. C₇	#35030	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×#2863	2
C₇×#2861	2
C₇×#2855	2
C₇×#2850	2
C₇×#2653	2
C₇×#2650	2
C₇×#2574	2
C₇×#2572	2
C₇×#2514	2
C₇×#2510	2
C₇×#2489	2
C₇×#2447	2
C₇×#2444	2
C₇×#2442	2
C₇×#2436	2
C₇×#2427	2
C₇×#2416	2
C₇×#2409	2
C₇×#2325	2
C₇×#2318	2
C₄×C₇×#121	2
C₂×C₇×#391	2
C₄²×C₇×D₄	2
#35030	7

Subgroups — C7×#35030 #13212246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35030 #13212246