Subgroups — C₇×#34800 #13212016

Order 1792.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2532	C₂	1	2	yes	maximal, complemented
2	C₇×#2526	C₂	1	2	yes	maximal, complemented
3	C₇×#2518	C₂	1	2	yes	maximal, complemented
4	C₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2508	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2500	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2485	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2459	C₂	1	2	yes	maximal, complemented
11	C₇×#2439	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2414	C₂	1	1	yes	maximal, characteristic
13	C₇×#2398	C₂	1	2	yes	maximal, complemented
14	C₇×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#124	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2298	C₂	1	2	yes	maximal, complemented
20	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#124	C₂²	1	2	yes	—
26	C₂×C₇×#121	C₂²	1	1	yes	characteristic
27	C₂×C₇×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
35	C₂×C₇×#117	C₂²	1	2	yes	—
36	C₂×C₇×#117	C₂²	1	1	yes	characteristic
37	C₂×C₇×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
40	C₇×#400	C₂²	1	2	yes	—
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#398	C₂²	1	2	yes	—
43	C₇×#397	C₂²	1	2	yes	—
44	C₇×#397	C₂²	1	2	yes	—
45	C₇×#397	C₂²	1	2	yes	—
46	C₇×#396	C₂²	1	2	yes	—
47	C₇×#396	C₂²	1	2	yes	—
48	C₇×#394	C₂²	1	2	yes	—
49	C₇×#394	C₂²	1	2	yes	—
50	C₇×#394	C₂²	1	2	yes	—
51	C₇×#394	C₂²	1	2	yes	—
52	C₇×#394	C₂²	1	2	yes	—
53	C₇×#393	C₂²	1	2	yes	—
54	C₇×#393	C₂²	1	2	yes	—
55	C₇×#392	C₂²	1	2	yes	—
56	C₇×#391	C₂²	1	2	yes	—
57	C₇×#391	C₂²	1	2	yes	—
58	C₇×#390	C₂²	1	1	yes	characteristic
59	C₇×#390	C₂²	1	2	yes	—
60	C₇×#390	C₂²	1	1	yes	characteristic
61	C₇×#390	C₂²	1	1	yes	characteristic
62	C₇×#390	C₂²	1	1	yes	characteristic
63	C₇×#389	C₂²	1	1	yes	characteristic
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	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
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×#388	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×#386	C₂²	1	2	yes	—
87	C₇×#386	C₂²	1	2	yes	—
88	C₇×#384	C₂²	1	1	yes	characteristic
89	C₇×#383	C₂²	1	2	yes	—
90	C₇×#382	C₂²	1	1	yes	characteristic
91	C₇×#382	C₂²	1	1	yes	characteristic
92	C₇×#382	C₂²	1	2	yes	—
93	C₇×#381	C₂²	1	2	yes	—
94	C₇×#380	C₂²	1	1	yes	characteristic
95	C₇×#380	C₂²	1	1	yes	characteristic
96	C₇×#380	C₂²	1	1	yes	characteristic
97	C₇×#380	C₂²	1	1	yes	characteristic
98	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
109	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
119	C₇×#376	C₂²	1	2	yes	—
120	C₇×#376	C₂²	1	2	yes	—
121	C₄³×C₇	C₂²	1	2	yes	—
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#34800	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	2	yes	—
125	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₇×D₄	C₂³	1	2	yes	—
128	C₂²×C₇×D₄	C₂³	1	2	yes	—
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₇×C₄⋊Q₈	—	2	4	no	—
137	C₇×#124	—	2	8	no	—
138	C₇×#121	—	2	4	no	—
139	C₇×#121	—	2	4	no	—
140	C₄×C₇×Q₈	—	4	4	no	—
141	C₄×C₇×D₄	—	2	4	no	—
142	C₄×C₇×D₄	—	2	4	no	—
143	C₄×C₇×D₄	—	2	4	no	—
144	C₄×C₇×D₄	—	2	4	no	—
145	C₄×C₇×D₄	—	4	4	no	—
146	C₄×C₇×D₄	—	4	4	no	—
147	C₇×#117	—	2	4	no	—
148	C₇×#117	—	2	4	no	—
149	C₇×#117	—	2	8	no	—
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	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
192	C₂×C₄²×C₇	—	2	4	no	—
193	C₂×C₄²×C₇	—	2	4	no	—
194	C₂×C₄²×C₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	2	yes	—
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	2	yes	—
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
226	C₇×#95	C₂³	1	1	yes	characteristic
227	C₇×#95	C₂³	1	1	yes	characteristic
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	#2532	C₂×C₇	1	2	yes	complemented
240	#2526	C₂×C₇	1	2	yes	complemented
241	#2518	C₂×C₇	1	2	yes	complemented
242	#2513	C₂×C₇	1	1	yes	characteristic, complemented
243	#2508	C₂×C₇	1	1	yes	characteristic, complemented
244	#2500	C₂×C₇	1	1	yes	characteristic, complemented
245	#2497	C₂×C₇	1	1	yes	characteristic, complemented
246	#2491	C₂×C₇	1	1	yes	characteristic, complemented
247	#2485	C₂×C₇	1	1	yes	characteristic, complemented
248	#2459	C₂×C₇	1	2	yes	complemented
249	#2439	C₂×C₇	1	1	yes	characteristic, complemented
250	#2414	C₂×C₇	1	1	yes	characteristic
251	#2398	C₂×C₇	1	2	yes	complemented
252	#2392	C₂×C₇	1	2	yes	complemented
253	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
254	C₄×#124	C₂×C₇	1	2	yes	complemented
255	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
256	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
257	#2298	C₂×C₇	1	2	yes	complemented
258	#2293	C₂×C₇	1	1	yes	characteristic, complemented
259	#2283	C₂×C₇	1	1	yes	characteristic, complemented
260	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
261	C₄×#117	C₂×C₇	1	1	yes	characteristic, complemented
262	C₂⁴×C₇	C₂⁴	1	2	yes	—
263	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₇×Q₈	—	2	4	no	—
266	C₂×C₇×Q₈	—	2	4	no	—
267	C₂×C₇×Q₈	—	4	2	no	—
268	C₂×C₇×D₄	—	2	2	no	—
269	C₂×C₇×D₄	—	2	2	no	—
270	C₂×C₇×D₄	—	2	4	no	—
271	C₂×C₇×D₄	—	2	4	no	—
272	C₂×C₇×D₄	—	2	2	no	—
273	C₂×C₇×D₄	—	2	2	no	—
274	C₂×C₇×D₄	—	2	4	no	—
275	C₂×C₇×D₄	—	2	2	no	—
276	C₂×C₇×D₄	—	2	2	no	—
277	C₂×C₇×D₄	—	4	2	no	—
278	C₂×C₇×D₄	—	4	2	no	—
279	C₂×C₇×D₄	—	4	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	2	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	2	no	—
287	C₂²×C₄×C₇	—	2	2	no	—
288	C₂²×C₄×C₇	—	2	4	no	—
289	C₂²×C₄×C₇	—	2	2	no	—
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	4	no	—
294	C₂²×C₄×C₇	—	2	2	no	—
295	C₂²×C₄×C₇	—	2	2	no	—
296	C₂²×C₄×C₇	—	2	2	no	—
297	C₂²×C₄×C₇	—	2	4	no	—
298	C₂²×C₄×C₇	—	4	1	no	—
299	C₂²×C₄×C₇	—	4	1	no	—
300	C₂²×C₄×C₇	#41	1	4	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₇×C₄⋊C₄	—	2	2	no	—
322	C₇×C₄⋊C₄	—	2	2	no	—
323	C₇×C₄⋊C₄	—	2	2	no	—
324	C₇×C₄⋊C₄	—	2	4	no	—
325	C₇×C₄⋊C₄	—	2	4	no	—
326	C₇×C₄⋊C₄	—	2	2	no	—
327	C₇×C₄⋊C₄	—	2	2	no	—
328	C₇×C₄⋊C₄	—	2	2	no	—
329	C₇×C₄⋊C₄	—	2	2	no	—
330	C₇×C₄⋊C₄	—	2	2	no	—
331	C₇×C₄⋊C₄	—	2	4	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	4	2	no	—
334	C₇×C₄⋊C₄	—	4	2	no	—
335	C₇×C₄⋊C₄	—	4	2	no	—
336	C₇×C₄⋊C₄	—	4	2	no	—
337	C₇×C₄⋊C₄	—	4	2	no	—
338	C₇×C₄⋊C₄	—	4	2	no	—
339	C₇×C₄⋊C₄	#41	1	4	yes	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	2	no	—
342	C₇×C₂²⋊C₄	—	2	4	no	—
343	C₇×C₂²⋊C₄	—	2	4	no	—
344	C₇×C₂²⋊C₄	—	2	4	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	2	2	no	—
347	C₇×C₂²⋊C₄	—	2	4	no	—
348	C₇×C₂²⋊C₄	—	2	2	no	—
349	C₇×C₂²⋊C₄	—	2	2	no	—
350	C₇×C₂²⋊C₄	—	2	2	no	—
351	C₇×C₂²⋊C₄	—	2	4	no	—
352	C₇×C₂²⋊C₄	—	2	4	no	—
353	C₇×C₂²⋊C₄	—	2	4	no	—
354	C₇×C₂²⋊C₄	—	2	4	no	—
355	C₇×C₂²⋊C₄	—	4	2	no	—
356	C₇×C₂²⋊C₄	—	4	2	no	—
357	C₇×C₂²⋊C₄	—	4	2	no	—
358	C₇×C₂²⋊C₄	—	4	2	no	—
359	C₇×C₂²⋊C₄	—	4	2	no	—
360	C₇×C₂²⋊C₄	—	4	2	no	—
361	C₇×C₂²⋊C₄	—	4	2	no	—
362	C₇×C₂²⋊C₄	#41	1	4	yes	—
363	C₄²×C₇	—	2	2	no	—
364	C₄²×C₇	—	2	2	no	—
365	C₄²×C₇	—	2	2	no	—
366	C₄²×C₇	—	2	2	no	—
367	C₄²×C₇	—	2	2	no	—
368	C₄²×C₇	—	2	2	no	—
369	C₄²×C₇	—	2	4	no	—
370	C₄²×C₇	—	2	4	no	—
371	C₄²×C₇	—	2	4	no	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	—	2	2	no	—
374	C₄²×C₇	—	2	4	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	4	no	—
377	C₄²×C₇	—	2	4	no	—
378	C₄²×C₇	—	2	2	no	—
379	C₄²×C₇	—	4	2	no	—
380	C₄²×C₇	—	4	1	no	—
381	C₄²×C₇	#41	1	4	yes	—
382	C₄²×C₇	#41	1	4	yes	—
383	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
384	C₂×#124	C₂²×C₇	1	2	yes	—
385	C₂×#121	C₂²×C₇	1	1	yes	characteristic
386	C₂×#121	C₂²×C₇	1	1	yes	characteristic
387	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
388	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
390	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
391	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
393	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
394	C₂×#117	C₂²×C₇	1	2	yes	—
395	C₂×#117	C₂²×C₇	1	1	yes	characteristic
396	C₂×#117	C₂²×C₇	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
399	#400	C₂²×C₇	1	2	yes	—
400	#400	C₂²×C₇	1	2	yes	—
401	#398	C₂²×C₇	1	2	yes	—
402	#397	C₂²×C₇	1	2	yes	—
403	#397	C₂²×C₇	1	2	yes	—
404	#397	C₂²×C₇	1	2	yes	—
405	#396	C₂²×C₇	1	2	yes	—
406	#396	C₂²×C₇	1	2	yes	—
407	#394	C₂²×C₇	1	2	yes	—
408	#394	C₂²×C₇	1	2	yes	—
409	#394	C₂²×C₇	1	2	yes	—
410	#394	C₂²×C₇	1	2	yes	—
411	#394	C₂²×C₇	1	2	yes	—
412	#393	C₂²×C₇	1	2	yes	—
413	#393	C₂²×C₇	1	2	yes	—
414	#392	C₂²×C₇	1	2	yes	—
415	#391	C₂²×C₇	1	2	yes	—
416	#391	C₂²×C₇	1	2	yes	—
417	#390	C₂²×C₇	1	1	yes	characteristic
418	#390	C₂²×C₇	1	2	yes	—
419	#390	C₂²×C₇	1	1	yes	characteristic
420	#390	C₂²×C₇	1	1	yes	characteristic
421	#390	C₂²×C₇	1	1	yes	characteristic
422	#389	C₂²×C₇	1	1	yes	characteristic
423	#389	C₂²×C₇	1	1	yes	characteristic
424	#389	C₂²×C₇	1	2	yes	—
425	#389	C₂²×C₇	1	1	yes	characteristic
426	#389	C₂²×C₇	1	1	yes	characteristic
427	#389	C₂²×C₇	1	1	yes	characteristic
428	#389	C₂²×C₇	1	1	yes	characteristic
429	#388	C₂²×C₇	1	2	yes	—
430	#388	C₂²×C₇	1	2	yes	—
431	#388	C₂²×C₇	1	2	yes	—
432	#388	C₂²×C₇	1	2	yes	—
433	#388	C₂²×C₇	1	2	yes	—
434	#388	C₂²×C₇	1	2	yes	—
435	#388	C₂²×C₇	1	2	yes	—
436	#388	C₂²×C₇	1	2	yes	—
437	#388	C₂²×C₇	1	2	yes	—
438	#388	C₂²×C₇	1	2	yes	—
439	#388	C₂²×C₇	1	2	yes	—
440	#388	C₂²×C₇	1	2	yes	—
441	#387	C₂²×C₇	1	2	yes	—
442	#387	C₂²×C₇	1	2	yes	—
443	#387	C₂²×C₇	1	2	yes	—
444	#387	C₂²×C₇	1	2	yes	—
445	#386	C₂²×C₇	1	2	yes	—
446	#386	C₂²×C₇	1	2	yes	—
447	#384	C₂²×C₇	1	1	yes	characteristic
448	#383	C₂²×C₇	1	2	yes	—
449	#382	C₂²×C₇	1	1	yes	characteristic
450	#382	C₂²×C₇	1	1	yes	characteristic
451	#382	C₂²×C₇	1	2	yes	—
452	#381	C₂²×C₇	1	2	yes	—
453	#380	C₂²×C₇	1	1	yes	characteristic
454	#380	C₂²×C₇	1	1	yes	characteristic
455	#380	C₂²×C₇	1	1	yes	characteristic
456	#380	C₂²×C₇	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
464	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
465	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
466	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
469	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
472	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
474	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
475	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
476	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
478	#376	C₂²×C₇	1	2	yes	—
479	#376	C₂²×C₇	1	2	yes	—
480	C₄³	C₂²×C₇	1	1	yes	characteristic
481	C₄³	C₂²×C₇	1	2	yes	—
482	C₂³×C₇	—	2	1	no	—
483	C₂³×C₇	—	2	1	no	—
484	C₂³×C₇	—	2	1	no	—
485	C₂³×C₇	—	2	1	no	—
486	C₂³×C₇	—	2	1	no	—
487	C₂³×C₇	—	2	1	no	—
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	2	no	—
495	C₂³×C₇	—	2	2	no	—
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	—	2	2	no	—
498	C₂³×C₇	—	2	2	no	—
499	C₂³×C₇	—	2	2	no	—
500	C₂³×C₇	—	2	2	no	—
501	C₂³×C₇	C₂×#41	1	2	yes	—
502	C₂³×C₇	C₂×#41	1	2	yes	—
503	C₂³×C₇	C₂⁵	1	1	yes	characteristic
504	C₇×Q₈	—	4	8	no	—
505	C₇×D₄	—	2	8	no	—
506	C₇×D₄	—	4	8	no	—
507	C₇×D₄	—	4	8	no	—
508	C₇×D₄	—	4	4	no	—
509	C₂×C₄×C₇	—	2	1	no	—
510	C₂×C₄×C₇	—	2	1	no	—
511	C₂×C₄×C₇	—	2	1	no	—
512	C₂×C₄×C₇	—	2	1	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	2	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	8	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	1	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	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	2	no	—
539	C₂×C₄×C₇	—	2	1	no	—
540	C₂×C₄×C₇	—	2	1	no	—
541	C₂×C₄×C₇	—	2	1	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	2	no	—
545	C₂×C₄×C₇	—	2	2	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	1	no	—
550	C₂×C₄×C₇	—	2	1	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	1	no	—
553	C₂×C₄×C₇	—	2	2	no	—
554	C₂×C₄×C₇	—	2	2	no	—
555	C₂×C₄×C₇	—	2	1	no	—
556	C₂×C₄×C₇	—	2	2	no	—
557	C₂×C₄×C₇	—	4	4	no	—
558	C₂×C₄×C₇	—	4	4	no	—
559	C₂×C₄×C₇	—	4	4	no	—
560	C₂×C₄×C₇	—	4	4	no	—
561	C₂×C₄×C₇	—	4	4	no	—
562	C₂×C₄×C₇	—	4	8	no	—
563	C₂×C₄×C₇	C₂×#41	1	2	yes	—
564	C₂×C₄×C₇	C₂×#41	1	2	yes	—
565	C₂×C₄×C₇	C₂×#41	1	2	yes	—
566	C₂×C₄×C₇	C₂×#41	1	2	yes	—
567	C₂×C₄×C₇	C₂×#41	1	4	yes	—
568	C₂×C₄×C₇	C₂×#41	1	2	yes	—
569	C₂×C₄×C₇	C₂×#41	1	2	yes	—
570	C₂×C₄×C₇	C₂×#41	1	2	yes	—
571	C₂×C₄×C₇	C₂×#41	1	2	yes	—
572	C₂×C₄×C₇	C₂×#41	1	2	yes	—
573	C₂×C₄×C₇	C₂×#41	1	2	yes	—
574	C₂×C₄×C₇	C₂×#41	1	2	yes	—
575	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
576	C₂²×Q₈	C₂³×C₇	1	2	yes	—
577	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₇	1	2	yes	—
580	C₂²×D₄	C₂³×C₇	1	2	yes	—
581	C₂³×C₄	C₂³×C₇	1	2	yes	—
582	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
588	C₄⋊Q₈	—	2	4	no	—
589	#124	—	2	8	no	—
590	#121	—	2	4	no	—
591	#121	—	2	4	no	—
592	C₄×Q₈	—	4	4	no	—
593	C₄×D₄	—	2	4	no	—
594	C₄×D₄	—	2	4	no	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	4	no	—
597	C₄×D₄	—	4	4	no	—
598	C₄×D₄	—	4	4	no	—
599	#117	—	2	4	no	—
600	#117	—	2	4	no	—
601	#117	—	2	8	no	—
602	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₄²	—	2	4	no	—
645	C₂×C₄²	—	2	4	no	—
646	C₂×C₄²	C₂³×C₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₇	1	2	yes	—
648	C₂×C₄²	C₂³×C₇	1	2	yes	—
649	C₂×C₄²	C₂³×C₇	1	2	yes	—
650	C₂×C₄²	C₂³×C₇	1	2	yes	—
651	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₇	1	2	yes	—
655	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
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	#95	C₂³×C₇	1	2	yes	—
667	#95	C₂³×C₇	1	2	yes	—
668	#95	C₂³×C₇	1	2	yes	—
669	#95	C₂³×C₇	1	2	yes	—
670	#95	C₂³×C₇	1	2	yes	—
671	#95	C₂³×C₇	1	2	yes	—
672	#95	C₂³×C₇	1	2	yes	—
673	#95	C₂³×C₇	1	2	yes	—
674	#95	C₂³×C₇	1	1	yes	characteristic
675	#95	C₂³×C₇	1	1	yes	characteristic
676	#95	C₂³×C₇	1	1	yes	characteristic
677	#95	C₂³×C₇	1	1	yes	characteristic
678	#95	C₂³×C₇	1	1	yes	characteristic
679	#95	C₂³×C₇	1	1	yes	characteristic
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	2	yes	—
682	#95	C₂³×C₇	1	2	yes	—
683	#95	C₂³×C₇	1	2	yes	—
684	#95	C₂³×C₇	1	2	yes	—
685	#95	C₂³×C₇	1	2	yes	—
686	#95	C₂³×C₇	1	2	yes	—
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	C₂²×C₇	—	2	2	no	—
692	C₂²×C₇	—	2	2	no	—
693	C₂²×C₇	—	2	2	no	—
694	C₂²×C₇	—	2	2	no	—
695	C₂²×C₇	—	2	2	no	—
696	C₂²×C₇	—	2	2	no	—
697	C₂²×C₇	—	4	1	no	—
698	C₂²×C₇	—	4	1	no	—
699	C₂²×C₇	—	4	1	no	—
700	C₂²×C₇	—	4	1	no	—
701	C₂²×C₇	—	4	1	no	—
702	C₂²×C₇	—	4	1	no	—
703	C₂²×C₇	—	4	1	no	—
704	C₂²×C₇	—	4	1	no	—
705	C₂²×C₇	—	4	2	no	—
706	C₂²×C₇	—	4	2	no	—
707	C₂²×C₇	—	4	2	no	—
708	C₂²×C₇	—	4	2	no	—
709	C₂²×C₇	—	4	2	no	—
710	C₂²×C₇	—	4	2	no	—
711	C₂²×C₇	—	4	2	no	—
712	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
713	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
714	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
715	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
716	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
717	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂²×C₇	#585	1	1	yes	characteristic
719	C₄×C₇	—	2	2	no	—
720	C₄×C₇	—	2	2	no	—
721	C₄×C₇	—	2	2	no	—
722	C₄×C₇	—	2	2	no	—
723	C₄×C₇	—	2	2	no	—
724	C₄×C₇	—	2	4	no	—
725	C₄×C₇	—	2	2	no	—
726	C₄×C₇	—	4	1	no	—
727	C₄×C₇	—	4	2	no	—
728	C₄×C₇	—	4	1	no	—
729	C₄×C₇	—	4	2	no	—
730	C₄×C₇	—	4	2	no	—
731	C₄×C₇	—	4	1	no	—
732	C₄×C₇	—	4	1	no	—
733	C₄×C₇	—	4	2	no	—
734	C₄×C₇	—	4	1	no	—
735	C₄×C₇	—	4	2	no	—
736	C₄×C₇	—	4	2	no	—
737	C₄×C₇	#529	1	4	yes	—
738	C₄×C₇	#555	1	4	yes	—
739	C₂⁴	C₂⁴×C₇	1	2	yes	—
740	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
741	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
742	C₂×Q₈	—	2	4	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	4	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	4	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	C₇×#41	1	4	yes	—
778	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	C₇×#41	1	4	yes	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	C₇×#41	1	4	yes	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	4	no	—
847	C₄²	—	2	4	no	—
848	C₄²	—	2	4	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	4	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	4	no	—
854	C₄²	—	2	4	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	4	2	no	—
857	C₄²	—	4	1	no	—
858	C₄²	C₇×#41	1	4	yes	—
859	C₄²	C₇×#41	1	4	yes	—
860	C₂×C₇	—	4	2	no	—
861	C₂×C₇	—	4	2	no	—
862	C₂×C₇	—	8	2	no	—
863	C₂×C₇	C₂×#529	1	1	yes	characteristic
864	C₂×C₇	#3444	1	1	yes	characteristic
865	C₂×C₇	#3460	1	1	yes	characteristic
866	C₂×C₇	C₂×#555	1	1	yes	characteristic
867	C₂×C₇	#3475	1	1	yes	characteristic
868	C₂×C₇	#3480	1	1	yes	characteristic
869	C₂×C₇	#3481	1	1	yes	characteristic
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	C₂×C₇×#41	1	2	yes	—
890	C₂³	C₂×C₇×#41	1	2	yes	—
891	C₂³	C₂⁵×C₇	1	1	yes	characteristic
892	Q₈	—	4	8	no	—
893	D₄	—	2	8	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	4	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	8	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	4	4	no	—
946	C₂×C₄	—	4	4	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	C₂×C₇×#41	1	2	yes	—
952	C₂×C₄	C₂×C₇×#41	1	2	yes	—
953	C₂×C₄	C₂×C₇×#41	1	2	yes	—
954	C₂×C₄	C₂×C₇×#41	1	2	yes	—
955	C₂×C₄	C₂×C₇×#41	1	4	yes	—
956	C₂×C₄	C₂×C₇×#41	1	2	yes	—
957	C₂×C₄	C₂×C₇×#41	1	2	yes	—
958	C₂×C₄	C₂×C₇×#41	1	2	yes	—
959	C₂×C₄	C₂×C₇×#41	1	2	yes	—
960	C₂×C₄	C₂×C₇×#41	1	2	yes	—
961	C₂×C₄	C₂×C₇×#41	1	2	yes	—
962	C₂×C₄	C₂×C₇×#41	1	2	yes	—
963	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
964	C₇	#34800	1	1	yes	characteristic, direct product factor, Sylow
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
987	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
988	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
989	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
990	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
991	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
992	C₂²	C₇×#585	1	1	yes	characteristic
993	C₄	—	2	2	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	2	no	—
996	C₄	—	2	2	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	4	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	4	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	1	no	—
1006	C₄	—	4	1	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	2	no	—
1011	C₄	C₇×#529	1	4	yes	—
1012	C₄	C₇×#555	1	4	yes	—
1013	C₂	—	4	2	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	8	2	no	—
1016	C₂	C₂×C₇×#529	1	1	yes	characteristic
1017	C₂	C₇×#3444	1	1	yes	characteristic
1018	C₂	C₇×#3460	1	1	yes	characteristic
1019	C₂	C₂×C₇×#555	1	1	yes	characteristic
1020	C₂	C₇×#3475	1	1	yes	characteristic
1021	C₂	C₇×#3480	1	1	yes	characteristic
1022	C₂	C₇×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₇×#2414	C₂
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
1. C₇×#2532	C₂	semidirect
2. C₇×#2526	C₂	semidirect
3. C₇×#2518	C₂	semidirect
4. C₇×#2513	C₂	semidirect
5. C₇×#2508	C₂	semidirect
6. C₇×#2500	C₂	semidirect
7. C₇×#2497	C₂	semidirect
8. C₇×#2491	C₂	semidirect
9. C₇×#2485	C₂	semidirect
10. C₇×#2459	C₂	semidirect
11. C₇×#2439	C₂	semidirect
13. C₇×#2398	C₂	semidirect
14. C₇×#2392	C₂	semidirect
15. C₄×C₇×C₄⋊Q₈	C₂	semidirect
16. C₄×C₇×#124	C₂	semidirect
17. C₄×C₇×#121	C₂	semidirect
18. C₄×C₇×#121	C₂	semidirect
19. C₇×#2298	C₂	semidirect
20. C₇×#2293	C₂	semidirect
21. C₇×#2283	C₂	semidirect
22. C₄²×C₇×D₄	C₂	semidirect
23. C₄×C₇×#117	C₂	semidirect
123. #34800	C₇	direct (N × H)
239. #2532	C₂×C₇	semidirect
240. #2526	C₂×C₇	semidirect
241. #2518	C₂×C₇	semidirect
242. #2513	C₂×C₇	semidirect
243. #2508	C₂×C₇	semidirect
244. #2500	C₂×C₇	semidirect
245. #2497	C₂×C₇	semidirect
246. #2491	C₂×C₇	semidirect
247. #2485	C₂×C₇	semidirect
248. #2459	C₂×C₇	semidirect
249. #2439	C₂×C₇	semidirect
251. #2398	C₂×C₇	semidirect
252. #2392	C₂×C₇	semidirect
253. C₄×C₄⋊Q₈	C₂×C₇	semidirect
254. C₄×#124	C₂×C₇	semidirect
255. C₄×#121	C₂×C₇	semidirect
256. C₄×#121	C₂×C₇	semidirect
257. #2298	C₂×C₇	semidirect
258. #2293	C₂×C₇	semidirect
259. #2283	C₂×C₇	semidirect
260. C₄²×D₄	C₂×C₇	semidirect
261. C₄×#117	C₂×C₇	semidirect
964. C₇	#34800	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×#2532	2
C₇×#2526	2
C₇×#2518	2
C₇×#2513	2
C₇×#2508	2
C₇×#2500	2
C₇×#2497	2
C₇×#2491	2
C₇×#2485	2
C₇×#2459	2
C₇×#2439	2
C₇×#2414	2
C₇×#2398	2
C₇×#2392	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#124	2
C₄×C₇×#121	2
C₇×#2298	2
C₇×#2293	2
C₇×#2283	2
C₄²×C₇×D₄	2
C₄×C₇×#117	2
#34800	7

Subgroups — C7×#34800 #13212016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34800 #13212016