Subgroups — C₇×#34430 #13211646

Order 1792.

1966 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic
2	C₇×#2383	C₂	1	2	yes	maximal
3	C₇×#2382	C₂	1	2	yes	maximal, complemented
4	C₇×#2373	C₂	1	2	yes	maximal
5	C₇×#2370	C₂	1	2	yes	maximal, complemented
6	C₇×#2362	C₂	1	1	yes	maximal, characteristic
7	C₇×#2362	C₂	1	1	yes	maximal, characteristic
8	C₇×#2360	C₂	1	1	yes	maximal, characteristic
9	C₇×#2360	C₂	1	1	yes	maximal, characteristic
10	C₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2336	C₂	1	2	yes	maximal, complemented
15	C₇×#2334	C₂	1	2	yes	maximal
16	C₇×#2334	C₂	1	2	yes	maximal
17	C₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2330	C₂	1	2	yes	maximal, complemented
19	C₇×#2327	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2317	C₂	1	1	yes	maximal, characteristic
21	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2298	C₂	1	1	yes	maximal, characteristic
24	C₇×#541	C₄	1	16	yes	complemented
25	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#126	C₂²	1	2	yes	—
27	C₂×C₇×#126	C₂²	1	2	yes	—
28	C₂×C₇×#125	C₂²	1	1	yes	characteristic
29	C₂×C₇×#125	C₂²	1	2	yes	—
30	C₂×C₇×#125	C₂²	1	2	yes	—
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊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	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×#117	C₂²	1	1	yes	characteristic
40	C₂×C₇×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₇×#391	C₂²	1	1	yes	characteristic
43	C₇×#391	C₂²	1	1	yes	characteristic
44	C₇×#391	C₂²	1	1	yes	characteristic
45	C₇×#391	C₂²	1	1	yes	characteristic
46	C₇×#389	C₂²	1	1	yes	characteristic
47	C₇×#389	C₂²	1	1	yes	characteristic
48	C₇×#389	C₂²	1	2	yes	—
49	C₇×#389	C₂²	1	2	yes	—
50	C₇×#389	C₂²	1	2	yes	—
51	C₇×#389	C₂²	1	2	yes	—
52	C₇×#389	C₂²	1	2	yes	—
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#389	C₂²	1	1	yes	characteristic
55	C₇×#389	C₂²	1	2	yes	—
56	C₇×#389	C₂²	1	2	yes	—
57	C₇×#389	C₂²	1	2	yes	—
58	C₇×#389	C₂²	1	2	yes	—
59	C₇×#389	C₂²	1	2	yes	—
60	C₇×#389	C₂²	1	2	yes	—
61	C₇×#389	C₂²	1	2	yes	—
62	C₇×#388	C₂²	1	1	yes	characteristic
63	C₇×#388	C₂²	1	1	yes	characteristic
64	C₇×#388	C₂²	1	1	yes	characteristic
65	C₇×#388	C₂²	1	1	yes	characteristic
66	C₇×#388	C₂²	1	2	yes	—
67	C₇×#388	C₂²	1	2	yes	—
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#387	C₂²	1	1	yes	characteristic
71	C₇×#387	C₂²	1	1	yes	characteristic
72	C₇×#387	C₂²	1	1	yes	characteristic
73	C₇×#387	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
90	C₇×#385	C₂²	1	2	yes	—
91	C₇×#385	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#384	C₂²	1	1	yes	characteristic
95	C₇×#384	C₂²	1	1	yes	characteristic
96	C₇×#384	C₂²	1	2	yes	—
97	C₇×#383	C₂²	1	2	yes	—
98	C₇×#382	C₂²	1	1	yes	characteristic
99	C₇×#382	C₂²	1	1	yes	characteristic
100	C₇×#382	C₂²	1	2	yes	—
101	C₇×#382	C₂²	1	2	yes	—
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	2	yes	—
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	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
114	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
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	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₇×#376	C₂²	1	1	yes	characteristic
122	C₇×#376	C₂²	1	2	yes	—
123	C₄³×C₇	C₂²	1	1	yes	characteristic
124	#34430	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	2	yes	—
129	C₇×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
130	C₇×#126	C₂×C₄	1	16	yes	—
131	C₇×#126	C₂×C₄	1	16	yes	—
132	C₇×#125	C₂×C₄	1	8	yes	complemented
133	C₇×#125	C₂×C₄	1	16	yes	complemented
134	C₇×#125	C₂×C₄	1	16	yes	complemented
135	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
136	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
137	C₄×C₇×Q₈	—	4	2	no	—
138	C₄×C₇×Q₈	—	4	2	no	—
139	C₄×C₇×Q₈	—	4	2	no	—
140	C₄×C₇×Q₈	—	4	2	no	—
141	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
142	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
143	C₇×#117	—	4	2	no	—
144	C₇×#117	C₂×C₄	1	8	yes	—
145	C₂×C₇×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
187	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₇	C₂³	1	2	yes	—
204	C₂×C₄²×C₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	1	yes	characteristic
210	C₇×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
217	C₇×#95	C₂³	1	1	yes	characteristic
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₂×#541	C₂×C₇	1	1	yes	characteristic
242	#2383	C₂×C₇	1	2	yes	—
243	#2382	C₂×C₇	1	2	yes	complemented
244	#2373	C₂×C₇	1	2	yes	—
245	#2370	C₂×C₇	1	2	yes	complemented
246	#2362	C₂×C₇	1	1	yes	characteristic
247	#2362	C₂×C₇	1	1	yes	characteristic
248	#2360	C₂×C₇	1	1	yes	characteristic
249	#2360	C₂×C₇	1	1	yes	characteristic
250	#2356	C₂×C₇	1	1	yes	characteristic, complemented
251	#2355	C₂×C₇	1	1	yes	characteristic, complemented
252	#2351	C₂×C₇	1	1	yes	characteristic, complemented
253	Q₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
254	#2336	C₂×C₇	1	2	yes	complemented
255	#2334	C₂×C₇	1	2	yes	—
256	#2334	C₂×C₇	1	2	yes	—
257	#2330	C₂×C₇	1	1	yes	characteristic, complemented
258	#2330	C₂×C₇	1	2	yes	complemented
259	#2327	C₂×C₇	1	1	yes	characteristic, complemented
260	#2317	C₂×C₇	1	1	yes	characteristic
261	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
262	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
263	#2298	C₂×C₇	1	1	yes	characteristic
264	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	2	no	—
268	C₂×C₇×Q₈	—	2	2	no	—
269	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
270	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
271	C₂²×C₄×C₇	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	4	2	no	—
274	C₂²×C₄×C₇	—	4	2	no	—
275	C₂²×C₄×C₇	—	4	2	no	—
276	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	4	no	—
306	C₇×C₄⋊C₄	—	4	2	no	—
307	C₇×C₄⋊C₄	—	4	2	no	—
308	C₇×C₄⋊C₄	—	4	2	no	—
309	C₇×C₄⋊C₄	—	4	2	no	—
310	C₇×C₄⋊C₄	—	4	2	no	—
311	C₇×C₄⋊C₄	—	4	2	no	—
312	C₇×C₄⋊C₄	—	4	1	no	—
313	C₇×C₄⋊C₄	—	4	1	no	—
314	C₇×C₄⋊C₄	—	4	2	no	—
315	C₇×C₄⋊C₄	—	4	2	no	—
316	C₇×C₄⋊C₄	—	4	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	C₂²×C₄	1	4	yes	—
321	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
322	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
323	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
324	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
325	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
326	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
327	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
328	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
329	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
330	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
331	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	4	1	no	—
335	C₇×C₂²⋊C₄	—	4	1	no	—
336	C₇×C₂²⋊C₄	—	4	2	no	—
337	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
338	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
339	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
340	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
341	C₄²×C₇	—	2	2	no	—
342	C₄²×C₇	—	2	2	no	—
343	C₄²×C₇	—	2	2	no	—
344	C₄²×C₇	—	2	4	no	—
345	C₄²×C₇	—	2	2	no	—
346	C₄²×C₇	—	2	2	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	4	2	no	—
349	C₄²×C₇	—	4	1	no	—
350	C₄²×C₇	—	4	2	no	—
351	C₄²×C₇	—	4	2	no	—
352	C₄²×C₇	—	4	1	no	—
353	C₄²×C₇	—	4	2	no	—
354	C₄²×C₇	—	4	2	no	—
355	C₄²×C₇	—	4	2	no	—
356	C₄²×C₇	—	4	2	no	—
357	C₄²×C₇	—	4	2	no	—
358	C₄²×C₇	C₂²×C₄	1	4	yes	—
359	C₄²×C₇	C₂²×C₄	1	4	yes	—
360	C₄²×C₇	C₂²×C₄	1	8	yes	—
361	C₄²×C₇	C₂²×C₄	1	8	yes	—
362	#541	C₄×C₇	1	16	yes	complemented
363	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
364	C₂×#126	C₂²×C₇	1	2	yes	—
365	C₂×#126	C₂²×C₇	1	2	yes	—
366	C₂×#125	C₂²×C₇	1	1	yes	characteristic
367	C₂×#125	C₂²×C₇	1	2	yes	—
368	C₂×#125	C₂²×C₇	1	2	yes	—
369	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
374	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
375	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
376	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
377	C₂×#117	C₂²×C₇	1	1	yes	characteristic
378	C₂×#117	C₂²×C₇	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
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	#389	C₂²×C₇	1	1	yes	characteristic
385	#389	C₂²×C₇	1	1	yes	characteristic
386	#389	C₂²×C₇	1	2	yes	—
387	#389	C₂²×C₇	1	2	yes	—
388	#389	C₂²×C₇	1	2	yes	—
389	#389	C₂²×C₇	1	2	yes	—
390	#389	C₂²×C₇	1	2	yes	—
391	#389	C₂²×C₇	1	1	yes	characteristic
392	#389	C₂²×C₇	1	1	yes	characteristic
393	#389	C₂²×C₇	1	2	yes	—
394	#389	C₂²×C₇	1	2	yes	—
395	#389	C₂²×C₇	1	2	yes	—
396	#389	C₂²×C₇	1	2	yes	—
397	#389	C₂²×C₇	1	2	yes	—
398	#389	C₂²×C₇	1	2	yes	—
399	#389	C₂²×C₇	1	2	yes	—
400	#388	C₂²×C₇	1	1	yes	characteristic
401	#388	C₂²×C₇	1	1	yes	characteristic
402	#388	C₂²×C₇	1	2	yes	—
403	#388	C₂²×C₇	1	2	yes	—
404	#388	C₂²×C₇	1	2	yes	—
405	#388	C₂²×C₇	1	2	yes	—
406	#388	C₂²×C₇	1	1	yes	characteristic
407	#388	C₂²×C₇	1	1	yes	characteristic
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	1	yes	characteristic
415	#387	C₂²×C₇	1	2	yes	—
416	#387	C₂²×C₇	1	2	yes	—
417	#387	C₂²×C₇	1	2	yes	—
418	#387	C₂²×C₇	1	2	yes	—
419	#387	C₂²×C₇	1	2	yes	—
420	#387	C₂²×C₇	1	2	yes	—
421	#387	C₂²×C₇	1	1	yes	characteristic
422	#387	C₂²×C₇	1	2	yes	—
423	#387	C₂²×C₇	1	2	yes	—
424	#387	C₂²×C₇	1	2	yes	—
425	#387	C₂²×C₇	1	2	yes	—
426	#387	C₂²×C₇	1	1	yes	characteristic
427	#387	C₂²×C₇	1	1	yes	characteristic
428	#385	C₂²×C₇	1	2	yes	—
429	#385	C₂²×C₇	1	2	yes	—
430	#385	C₂²×C₇	1	2	yes	—
431	#385	C₂²×C₇	1	2	yes	—
432	#384	C₂²×C₇	1	1	yes	characteristic
433	#384	C₂²×C₇	1	1	yes	characteristic
434	#384	C₂²×C₇	1	2	yes	—
435	#383	C₂²×C₇	1	2	yes	—
436	#382	C₂²×C₇	1	1	yes	characteristic
437	#382	C₂²×C₇	1	1	yes	characteristic
438	#382	C₂²×C₇	1	2	yes	—
439	#382	C₂²×C₇	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
459	#376	C₂²×C₇	1	1	yes	characteristic
460	#376	C₂²×C₇	1	2	yes	—
461	C₄³	C₂²×C₇	1	1	yes	characteristic
462	C₂³×C₇	—	2	1	no	—
463	C₂³×C₇	—	2	1	no	—
464	C₂³×C₇	—	2	1	no	—
465	C₂³×C₇	—	2	1	no	—
466	C₂³×C₇	—	2	1	no	—
467	C₂³×C₇	—	2	1	no	—
468	C₂³×C₇	C₂³×C₄	1	2	yes	—
469	C₂³×C₇	C₂⁵	1	1	yes	characteristic
470	C₇×Q₈	—	2	8	no	—
471	C₇×Q₈	—	2	8	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	1	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	1	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	2	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	2	no	—
486	C₂×C₄×C₇	—	2	2	no	—
487	C₂×C₄×C₇	—	2	1	no	—
488	C₂×C₄×C₇	—	2	2	no	—
489	C₂×C₄×C₇	—	2	2	no	—
490	C₂×C₄×C₇	—	2	1	no	—
491	C₂×C₄×C₇	—	2	1	no	—
492	C₂×C₄×C₇	—	2	1	no	—
493	C₂×C₄×C₇	—	2	1	no	—
494	C₂×C₄×C₇	—	2	8	no	—
495	C₂×C₄×C₇	—	2	1	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	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	2	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	1	no	—
504	C₂×C₄×C₇	—	2	1	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	1	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	1	no	—
510	C₂×C₄×C₇	—	2	2	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	1	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	1	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	8	4	no	—
526	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
527	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
528	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
529	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
530	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
531	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
532	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
533	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
534	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
535	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
536	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
538	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
539	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
540	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₇	1	2	yes	—
544	C₄⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
545	#126	C₂×C₄×C₇	1	16	yes	—
546	#126	C₂×C₄×C₇	1	16	yes	—
547	#125	C₂×C₄×C₇	1	8	yes	complemented
548	#125	C₂×C₄×C₇	1	16	yes	complemented
549	#125	C₂×C₄×C₇	1	16	yes	complemented
550	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
551	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
552	C₄×Q₈	—	4	2	no	—
553	C₄×Q₈	—	4	2	no	—
554	C₄×Q₈	—	4	2	no	—
555	C₄×Q₈	—	4	2	no	—
556	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
557	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
558	#117	—	4	2	no	—
559	#117	C₂×C₄×C₇	1	8	yes	—
560	C₂×C₄⋊C₄	—	4	2	no	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₇	1	2	yes	—
610	C₂×C₄²	C₂³×C₇	1	2	yes	—
611	C₂×C₄²	C₂³×C₇	1	2	yes	—
612	C₂×C₄²	C₂³×C₇	1	2	yes	—
613	C₂×C₄²	C₂³×C₇	1	2	yes	—
614	C₂×C₄²	C₂³×C₇	1	2	yes	—
615	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₇	1	2	yes	—
618	C₂×C₄²	C₂³×C₇	1	2	yes	—
619	C₂×C₄²	C₂³×C₇	1	2	yes	—
620	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₇	1	2	yes	—
624	#95	C₂³×C₇	1	1	yes	characteristic
625	#95	C₂³×C₇	1	2	yes	—
626	#95	C₂³×C₇	1	2	yes	—
627	#95	C₂³×C₇	1	1	yes	characteristic
628	#95	C₂³×C₇	1	1	yes	characteristic
629	#95	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	1	yes	characteristic
631	#95	C₂³×C₇	1	1	yes	characteristic
632	#95	C₂³×C₇	1	1	yes	characteristic
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	1	yes	characteristic
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	2	yes	—
637	#95	C₂³×C₇	1	1	yes	characteristic
638	#95	C₂³×C₇	1	1	yes	characteristic
639	#95	C₂³×C₇	1	1	yes	characteristic
640	#95	C₂³×C₇	1	2	yes	—
641	#95	C₂³×C₇	1	2	yes	—
642	#95	C₂³×C₇	1	1	yes	characteristic
643	#95	C₂³×C₇	1	2	yes	—
644	#95	C₂³×C₇	1	2	yes	—
645	#95	C₂³×C₇	1	2	yes	—
646	#95	C₂³×C₇	1	2	yes	—
647	#95	C₂³×C₇	1	2	yes	—
648	#95	C₂³×C₇	1	2	yes	—
649	#95	C₂³×C₇	1	1	yes	characteristic
650	#95	C₂³×C₇	1	2	yes	—
651	#95	C₂³×C₇	1	2	yes	—
652	#95	C₂³×C₇	1	2	yes	—
653	#95	C₂³×C₇	1	2	yes	—
654	#95	C₂³×C₇	1	2	yes	—
655	#95	C₂³×C₇	1	2	yes	—
656	C₂²×C₇	—	2	2	no	—
657	C₂²×C₇	—	2	2	no	—
658	C₂²×C₇	—	2	2	no	—
659	C₂²×C₇	—	4	1	no	—
660	C₂²×C₇	—	4	1	no	—
661	C₂²×C₇	—	4	1	no	—
662	C₂²×C₇	—	4	1	no	—
663	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
664	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
666	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
667	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
668	C₂²×C₇	#585	1	1	yes	characteristic
669	C₂²×C₇	#585	1	1	yes	characteristic
670	C₄×C₇	—	2	2	no	—
671	C₄×C₇	—	2	4	no	—
672	C₄×C₇	—	2	4	no	—
673	C₄×C₇	—	2	2	no	—
674	C₄×C₇	—	2	2	no	—
675	C₄×C₇	—	2	4	no	—
676	C₄×C₇	—	2	4	no	—
677	C₄×C₇	—	2	2	no	—
678	C₄×C₇	—	2	2	no	—
679	C₄×C₇	—	2	2	no	—
680	C₄×C₇	—	2	2	no	—
681	C₄×C₇	—	4	1	no	—
682	C₄×C₇	—	4	2	no	—
683	C₄×C₇	—	4	1	no	—
684	C₄×C₇	—	4	1	no	—
685	C₄×C₇	—	4	1	no	—
686	C₄×C₇	—	4	1	no	—
687	C₄×C₇	—	4	2	no	—
688	C₄×C₇	—	4	2	no	—
689	C₄×C₇	—	4	2	no	—
690	C₄×C₇	—	4	1	no	—
691	C₄×C₇	#520	1	4	yes	—
692	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
698	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₄⋊C₄	—	4	1	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
749	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
750	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
751	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
752	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
753	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
754	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
755	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
756	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
757	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
758	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
759	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
766	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
767	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
768	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	4	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	1	no	—
783	C₄²	—	4	2	no	—
784	C₄²	—	4	2	no	—
785	C₄²	—	4	1	no	—
786	C₄²	C₂²×C₄×C₇	1	4	yes	—
787	C₄²	C₂²×C₄×C₇	1	4	yes	—
788	C₄²	C₂²×C₄×C₇	1	8	yes	—
789	C₄²	C₂²×C₄×C₇	1	8	yes	—
790	C₂×C₇	—	4	2	no	—
791	C₂×C₇	C₂×#520	1	1	yes	characteristic
792	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
793	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
794	C₂×C₇	#3552	1	1	yes	characteristic
795	C₂×C₇	#3555	1	1	yes	characteristic
796	C₂×C₇	#3562	1	1	yes	characteristic
797	C₂×C₇	#3563	1	1	yes	characteristic
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	C₂³×C₄×C₇	1	2	yes	—
805	C₂³	C₂⁵×C₇	1	1	yes	characteristic
806	Q₈	—	2	8	no	—
807	Q₈	—	2	8	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	8	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	8	4	no	—
862	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
863	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
864	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
865	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
866	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
867	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
868	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
869	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
870	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
871	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
872	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
873	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
874	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
875	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
876	C₇	#34430	1	1	yes	characteristic, direct product factor, Sylow
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
885	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
887	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
888	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
889	C₂²	C₇×#585	1	1	yes	characteristic
890	C₂²	C₇×#585	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	4	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	C₇×#520	1	4	yes	—
913	C₂	—	4	2	no	—
914	C₂	C₂×C₇×#520	1	1	yes	characteristic
915	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
916	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
917	C₂	C₇×#3552	1	1	yes	characteristic
918	C₂	C₇×#3555	1	1	yes	characteristic
919	C₂	C₇×#3562	1	1	yes	characteristic
920	C₂	C₇×#3563	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₇×#2382	C₂	semidirect
5. C₇×#2370	C₂	semidirect
10. C₇×#2356	C₂	semidirect
11. C₇×#2355	C₂	semidirect
12. C₇×#2351	C₂	semidirect
13. C₇×Q₈×C₄⋊C₄	C₂	semidirect
14. C₇×#2336	C₂	semidirect
17. C₇×#2330	C₂	semidirect
18. C₇×#2330	C₂	semidirect
19. C₇×#2327	C₂	semidirect
21. C₄×C₇×C₄⋊Q₈	C₂	semidirect
22. C₄×C₇×#125	C₂	semidirect
24. C₇×#541	C₄	semidirect
124. #34430	C₇	direct (N × H)
129. C₇×C₄⋊Q₈	C₂×C₄	semidirect
132. C₇×#125	C₂×C₄	semidirect
133. C₇×#125	C₂×C₄	semidirect
134. C₇×#125	C₂×C₄	semidirect
141. C₄×C₇×Q₈	C₂×C₄	semidirect
142. C₄×C₇×Q₈	C₂×C₄	semidirect
243. #2382	C₂×C₇	semidirect
245. #2370	C₂×C₇	semidirect
250. #2356	C₂×C₇	semidirect
251. #2355	C₂×C₇	semidirect
252. #2351	C₂×C₇	semidirect
253. Q₈×C₄⋊C₄	C₂×C₇	semidirect
254. #2336	C₂×C₇	semidirect
257. #2330	C₂×C₇	semidirect
258. #2330	C₂×C₇	semidirect
259. #2327	C₂×C₇	semidirect
261. C₄×C₄⋊Q₈	C₂×C₇	semidirect
262. C₄×#125	C₂×C₇	semidirect
362. #541	C₄×C₇	semidirect
544. C₄⋊Q₈	C₂×C₄×C₇	semidirect
547. #125	C₂×C₄×C₇	semidirect
548. #125	C₂×C₄×C₇	semidirect
549. #125	C₂×C₄×C₇	semidirect
556. C₄×Q₈	C₂×C₄×C₇	semidirect
557. C₄×Q₈	C₂×C₄×C₇	semidirect
876. C₇	#34430	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#541	2
C₇×#2383	2
C₇×#2382	2
C₇×#2373	2
C₇×#2370	2
C₇×#2362	2
C₇×#2360	2
C₇×#2356	2
C₇×#2355	2
C₇×#2351	2
C₇×Q₈×C₄⋊C₄	2
C₇×#2336	2
C₇×#2334	2
C₇×#2330	2
C₇×#2327	2
C₇×#2317	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#125	2
C₇×#2298	2
#34430	7

Subgroups — C7×#34430 #13211646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34430 #13211646