Subgroups — C₇×#34434 #13211650

Order 1792.

1974 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic
2	C₇×#2381	C₂	1	2	yes	maximal, complemented
3	C₇×#2378	C₂	1	2	yes	maximal
4	C₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2365	C₂	1	2	yes	maximal, complemented
9	C₇×#2362	C₂	1	2	yes	maximal
10	C₇×#2347	C₂	1	1	yes	maximal, characteristic
11	C₇×#2347	C₂	1	1	yes	maximal, characteristic
12	C₇×#2345	C₂	1	1	yes	maximal, characteristic
13	C₇×#2344	C₂	1	1	yes	maximal, characteristic
14	C₇×#2336	C₂	1	2	yes	maximal, complemented
15	C₇×#2336	C₂	1	2	yes	maximal, complemented
16	C₇×#2332	C₂	1	2	yes	maximal
17	C₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2323	C₂	1	2	yes	maximal
20	C₇×#2314	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×#544	C₄	1	16	yes	complemented
25	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊Q₈	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	1	yes	characteristic
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
34	C₂×C₄×C₇×Q₈	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×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₇×#391	C₂²	1	2	yes	—
40	C₇×#391	C₂²	1	2	yes	—
41	C₇×#391	C₂²	1	2	yes	—
42	C₇×#391	C₂²	1	2	yes	—
43	C₇×#391	C₂²	1	2	yes	—
44	C₇×#391	C₂²	1	2	yes	—
45	C₇×#389	C₂²	1	1	yes	characteristic
46	C₇×#389	C₂²	1	1	yes	characteristic
47	C₇×#389	C₂²	1	2	yes	—
48	C₇×#389	C₂²	1	1	yes	characteristic
49	C₇×#389	C₂²	1	1	yes	characteristic
50	C₇×#389	C₂²	1	2	yes	—
51	C₇×#389	C₂²	1	2	yes	—
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#389	C₂²	1	2	yes	—
55	C₇×#389	C₂²	1	1	yes	characteristic
56	C₇×#389	C₂²	1	1	yes	characteristic
57	C₇×#389	C₂²	1	2	yes	—
58	C₇×#389	C₂²	1	2	yes	—
59	C₇×#388	C₂²	1	1	yes	characteristic
60	C₇×#388	C₂²	1	1	yes	characteristic
61	C₇×#388	C₂²	1	1	yes	characteristic
62	C₇×#388	C₂²	1	1	yes	characteristic
63	C₇×#388	C₂²	1	2	yes	—
64	C₇×#388	C₂²	1	2	yes	—
65	C₇×#388	C₂²	1	2	yes	—
66	C₇×#388	C₂²	1	2	yes	—
67	C₇×#388	C₂²	1	2	yes	—
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#387	C₂²	1	1	yes	characteristic
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	2	yes	—
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#387	C₂²	1	2	yes	—
91	C₇×#384	C₂²	1	1	yes	characteristic
92	C₇×#383	C₂²	1	2	yes	—
93	C₇×#383	C₂²	1	2	yes	—
94	C₇×#382	C₂²	1	1	yes	characteristic
95	C₇×#381	C₂²	1	2	yes	—
96	C₇×#380	C₂²	1	1	yes	characteristic
97	C₇×#380	C₂²	1	1	yes	characteristic
98	C₇×#380	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	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	2	yes	—
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
117	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
118	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₇×#376	C₂²	1	1	yes	characteristic
123	C₄³×C₇	C₂²	1	1	yes	characteristic
124	#34434	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₇×Q₈	C₂³	1	2	yes	—
126	C₂²×C₇×Q₈	C₂³	1	2	yes	—
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	—
130	C₇×C₄⋊Q₈	C₂×C₄	1	8	yes	—
131	C₇×C₄⋊Q₈	C₂×C₄	1	16	yes	—
132	C₇×#125	C₂×C₄	1	8	yes	—
133	C₇×#125	C₂×C₄	1	16	yes	—
134	C₇×#125	C₂×C₄	1	8	yes	—
135	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
136	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
137	C₄×C₇×Q₈	—	4	4	no	—
138	C₄×C₇×Q₈	—	4	4	no	—
139	C₇×#117	—	4	4	no	—
140	C₇×#117	C₂×C₄	1	8	yes	—
141	C₇×#117	C₂×C₄	1	8	yes	—
142	C₂×C₇×C₄⋊C₄	C₂×C₄	1	8	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	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	2	yes	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₇	C₂³	1	2	yes	—
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	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	1	yes	characteristic
205	C₇×#95	C₂³	1	1	yes	characteristic
206	C₇×#95	C₂³	1	1	yes	characteristic
207	C₇×#95	C₂³	1	1	yes	characteristic
208	C₇×#95	C₂³	1	1	yes	characteristic
209	C₇×#95	C₂³	1	1	yes	characteristic
210	C₇×#95	C₂³	1	2	yes	—
211	C₇×#95	C₂³	1	1	yes	characteristic
212	C₇×#95	C₂³	1	1	yes	characteristic
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	1	yes	characteristic
215	C₇×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	1	yes	characteristic
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	1	yes	characteristic
237	C₇×#95	C₂³	1	2	yes	—
238	C₂×#544	C₂×C₇	1	1	yes	characteristic
239	#2381	C₂×C₇	1	2	yes	complemented
240	#2378	C₂×C₇	1	2	yes	—
241	#2370	C₂×C₇	1	1	yes	characteristic, complemented
242	#2370	C₂×C₇	1	1	yes	characteristic, complemented
243	#2369	C₂×C₇	1	1	yes	characteristic, complemented
244	#2365	C₂×C₇	1	2	yes	complemented
245	#2365	C₂×C₇	1	1	yes	characteristic, complemented
246	#2362	C₂×C₇	1	2	yes	—
247	#2347	C₂×C₇	1	1	yes	characteristic
248	#2347	C₂×C₇	1	1	yes	characteristic
249	#2345	C₂×C₇	1	1	yes	characteristic
250	#2344	C₂×C₇	1	1	yes	characteristic
251	#2336	C₂×C₇	1	2	yes	complemented
252	#2336	C₂×C₇	1	2	yes	complemented
253	#2332	C₂×C₇	1	2	yes	—
254	#2331	C₂×C₇	1	1	yes	characteristic, complemented
255	#2330	C₂×C₇	1	1	yes	characteristic, complemented
256	#2323	C₂×C₇	1	2	yes	—
257	#2314	C₂×C₇	1	1	yes	characteristic
258	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
259	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
260	#2298	C₂×C₇	1	1	yes	characteristic
261	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₇×Q₈	—	4	2	no	—
263	C₂×C₇×Q₈	—	4	2	no	—
264	C₂×C₇×Q₈	—	4	2	no	—
265	C₂×C₇×Q₈	—	4	2	no	—
266	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
267	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
268	C₂²×C₄×C₇	—	2	2	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	4	2	no	—
271	C₂²×C₄×C₇	—	4	2	no	—
272	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
273	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂⁴	1	2	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	2	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
287	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	4	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	4	1	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	1	no	—
310	C₇×C₄⋊C₄	—	4	2	no	—
311	C₇×C₄⋊C₄	—	4	2	no	—
312	C₇×C₄⋊C₄	—	4	2	no	—
313	C₇×C₄⋊C₄	—	4	2	no	—
314	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
315	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
316	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
317	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
318	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
319	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
320	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
321	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
322	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
323	C₇×C₄⋊C₄	C₂²×C₄	1	8	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×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	4	2	no	—
330	C₇×C₂²⋊C₄	—	4	1	no	—
331	C₇×C₂²⋊C₄	—	4	1	no	—
332	C₇×C₂²⋊C₄	—	4	2	no	—
333	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
334	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
335	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
336	C₄²×C₇	—	2	4	no	—
337	C₄²×C₇	—	2	2	no	—
338	C₄²×C₇	—	2	2	no	—
339	C₄²×C₇	—	2	2	no	—
340	C₄²×C₇	—	2	2	no	—
341	C₄²×C₇	—	2	2	no	—
342	C₄²×C₇	—	2	2	no	—
343	C₄²×C₇	—	4	2	no	—
344	C₄²×C₇	—	4	1	no	—
345	C₄²×C₇	—	4	2	no	—
346	C₄²×C₇	—	4	2	no	—
347	C₄²×C₇	—	4	2	no	—
348	C₄²×C₇	—	4	1	no	—
349	C₄²×C₇	—	4	2	no	—
350	C₄²×C₇	—	4	2	no	—
351	C₄²×C₇	—	4	2	no	—
352	C₄²×C₇	—	4	2	no	—
353	C₄²×C₇	—	4	2	no	—
354	C₄²×C₇	C₂²×C₄	1	8	yes	—
355	C₄²×C₇	C₂²×C₄	1	4	yes	—
356	C₄²×C₇	C₂²×C₄	1	4	yes	—
357	#544	C₄×C₇	1	16	yes	complemented
358	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
359	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
360	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
361	C₂×#125	C₂²×C₇	1	1	yes	characteristic
362	C₂×#125	C₂²×C₇	1	2	yes	—
363	C₂×#125	C₂²×C₇	1	1	yes	characteristic
364	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
366	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
367	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
368	C₂×#117	C₂²×C₇	1	2	yes	—
369	C₂×#117	C₂²×C₇	1	1	yes	characteristic
370	C₂×#117	C₂²×C₇	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
372	#391	C₂²×C₇	1	2	yes	—
373	#391	C₂²×C₇	1	2	yes	—
374	#391	C₂²×C₇	1	2	yes	—
375	#391	C₂²×C₇	1	2	yes	—
376	#391	C₂²×C₇	1	2	yes	—
377	#391	C₂²×C₇	1	2	yes	—
378	#389	C₂²×C₇	1	1	yes	characteristic
379	#389	C₂²×C₇	1	1	yes	characteristic
380	#389	C₂²×C₇	1	2	yes	—
381	#389	C₂²×C₇	1	1	yes	characteristic
382	#389	C₂²×C₇	1	1	yes	characteristic
383	#389	C₂²×C₇	1	2	yes	—
384	#389	C₂²×C₇	1	2	yes	—
385	#389	C₂²×C₇	1	1	yes	characteristic
386	#389	C₂²×C₇	1	1	yes	characteristic
387	#389	C₂²×C₇	1	2	yes	—
388	#389	C₂²×C₇	1	1	yes	characteristic
389	#389	C₂²×C₇	1	1	yes	characteristic
390	#389	C₂²×C₇	1	2	yes	—
391	#389	C₂²×C₇	1	2	yes	—
392	#388	C₂²×C₇	1	2	yes	—
393	#388	C₂²×C₇	1	2	yes	—
394	#388	C₂²×C₇	1	1	yes	characteristic
395	#388	C₂²×C₇	1	2	yes	—
396	#388	C₂²×C₇	1	2	yes	—
397	#388	C₂²×C₇	1	1	yes	characteristic
398	#388	C₂²×C₇	1	2	yes	—
399	#388	C₂²×C₇	1	2	yes	—
400	#388	C₂²×C₇	1	1	yes	characteristic
401	#388	C₂²×C₇	1	1	yes	characteristic
402	#387	C₂²×C₇	1	2	yes	—
403	#387	C₂²×C₇	1	2	yes	—
404	#387	C₂²×C₇	1	2	yes	—
405	#387	C₂²×C₇	1	2	yes	—
406	#387	C₂²×C₇	1	2	yes	—
407	#387	C₂²×C₇	1	2	yes	—
408	#387	C₂²×C₇	1	2	yes	—
409	#387	C₂²×C₇	1	2	yes	—
410	#387	C₂²×C₇	1	2	yes	—
411	#387	C₂²×C₇	1	2	yes	—
412	#387	C₂²×C₇	1	1	yes	characteristic
413	#387	C₂²×C₇	1	1	yes	characteristic
414	#387	C₂²×C₇	1	2	yes	—
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	2	yes	—
422	#387	C₂²×C₇	1	1	yes	characteristic
423	#387	C₂²×C₇	1	1	yes	characteristic
424	#384	C₂²×C₇	1	1	yes	characteristic
425	#383	C₂²×C₇	1	2	yes	—
426	#383	C₂²×C₇	1	2	yes	—
427	#382	C₂²×C₇	1	1	yes	characteristic
428	#381	C₂²×C₇	1	2	yes	—
429	#380	C₂²×C₇	1	1	yes	characteristic
430	#380	C₂²×C₇	1	1	yes	characteristic
431	#380	C₂²×C₇	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
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	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
455	#376	C₂²×C₇	1	1	yes	characteristic
456	C₄³	C₂²×C₇	1	1	yes	characteristic
457	C₂³×C₇	—	2	1	no	—
458	C₂³×C₇	—	2	1	no	—
459	C₂³×C₇	—	2	1	no	—
460	C₂³×C₇	—	2	1	no	—
461	C₂³×C₇	—	2	1	no	—
462	C₂³×C₇	—	2	1	no	—
463	C₂³×C₇	C₂³×C₄	1	2	yes	—
464	C₂³×C₇	C₂⁵	1	1	yes	characteristic
465	C₇×Q₈	—	4	8	no	—
466	C₇×Q₈	—	4	8	no	—
467	C₂×C₄×C₇	—	2	1	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	1	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	1	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	1	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	1	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	1	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	2	no	—
485	C₂×C₄×C₇	—	2	1	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	8	no	—
490	C₂×C₄×C₇	—	2	2	no	—
491	C₂×C₄×C₇	—	2	1	no	—
492	C₂×C₄×C₇	—	2	2	no	—
493	C₂×C₄×C₇	—	2	1	no	—
494	C₂×C₄×C₇	—	2	2	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	1	no	—
499	C₂×C₄×C₇	—	2	1	no	—
500	C₂×C₄×C₇	—	2	1	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	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	2	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	4	8	no	—
521	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
522	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
523	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
524	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
525	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
527	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
528	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
529	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
530	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
531	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
532	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
533	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
534	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
535	C₂²×Q₈	C₂³×C₇	1	2	yes	—
536	C₂²×Q₈	C₂³×C₇	1	2	yes	—
537	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₇	1	2	yes	—
539	C₄⋊Q₈	C₂×C₄×C₇	1	8	yes	—
540	C₄⋊Q₈	C₂×C₄×C₇	1	8	yes	—
541	C₄⋊Q₈	C₂×C₄×C₇	1	16	yes	—
542	#125	C₂×C₄×C₇	1	8	yes	—
543	#125	C₂×C₄×C₇	1	16	yes	—
544	#125	C₂×C₄×C₇	1	8	yes	—
545	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	—
546	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	—
547	C₄×Q₈	—	4	4	no	—
548	C₄×Q₈	—	4	4	no	—
549	#117	—	4	4	no	—
550	#117	C₂×C₄×C₇	1	8	yes	—
551	#117	C₂×C₄×C₇	1	8	yes	—
552	C₂×C₄⋊C₄	C₂×C₄×C₇	1	8	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄²	C₂³×C₇	1	2	yes	—
594	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₇	1	2	yes	—
601	C₂×C₄²	C₂³×C₇	1	2	yes	—
602	C₂×C₄²	C₂³×C₇	1	2	yes	—
603	C₂×C₄²	C₂³×C₇	1	2	yes	—
604	C₂×C₄²	C₂³×C₇	1	2	yes	—
605	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇	1	2	yes	—
608	C₂×C₄²	C₂³×C₇	1	2	yes	—
609	C₂×C₄²	C₂³×C₇	1	2	yes	—
610	C₂×C₄²	C₂³×C₇	1	2	yes	—
611	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₇	1	2	yes	—
614	#95	C₂³×C₇	1	1	yes	characteristic
615	#95	C₂³×C₇	1	1	yes	characteristic
616	#95	C₂³×C₇	1	1	yes	characteristic
617	#95	C₂³×C₇	1	1	yes	characteristic
618	#95	C₂³×C₇	1	1	yes	characteristic
619	#95	C₂³×C₇	1	1	yes	characteristic
620	#95	C₂³×C₇	1	2	yes	—
621	#95	C₂³×C₇	1	1	yes	characteristic
622	#95	C₂³×C₇	1	1	yes	characteristic
623	#95	C₂³×C₇	1	2	yes	—
624	#95	C₂³×C₇	1	1	yes	characteristic
625	#95	C₂³×C₇	1	1	yes	characteristic
626	#95	C₂³×C₇	1	2	yes	—
627	#95	C₂³×C₇	1	2	yes	—
628	#95	C₂³×C₇	1	2	yes	—
629	#95	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	2	yes	—
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	2	yes	—
637	#95	C₂³×C₇	1	2	yes	—
638	#95	C₂³×C₇	1	2	yes	—
639	#95	C₂³×C₇	1	2	yes	—
640	#95	C₂³×C₇	1	2	yes	—
641	#95	C₂³×C₇	1	2	yes	—
642	#95	C₂³×C₇	1	2	yes	—
643	#95	C₂³×C₇	1	2	yes	—
644	#95	C₂³×C₇	1	1	yes	characteristic
645	#95	C₂³×C₇	1	2	yes	—
646	#95	C₂³×C₇	1	1	yes	characteristic
647	#95	C₂³×C₇	1	2	yes	—
648	C₂²×C₇	—	2	2	no	—
649	C₂²×C₇	—	2	2	no	—
650	C₂²×C₇	—	2	2	no	—
651	C₂²×C₇	—	4	1	no	—
652	C₂²×C₇	—	4	1	no	—
653	C₂²×C₇	—	4	1	no	—
654	C₂²×C₇	—	4	1	no	—
655	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
656	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
659	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
660	C₂²×C₇	#585	1	1	yes	characteristic
661	C₂²×C₇	#585	1	1	yes	characteristic
662	C₄×C₇	—	2	2	no	—
663	C₄×C₇	—	2	4	no	—
664	C₄×C₇	—	2	4	no	—
665	C₄×C₇	—	2	2	no	—
666	C₄×C₇	—	2	4	no	—
667	C₄×C₇	—	2	2	no	—
668	C₄×C₇	—	2	2	no	—
669	C₄×C₇	—	2	2	no	—
670	C₄×C₇	—	2	4	no	—
671	C₄×C₇	—	2	2	no	—
672	C₄×C₇	—	2	2	no	—
673	C₄×C₇	—	4	2	no	—
674	C₄×C₇	—	4	1	no	—
675	C₄×C₇	—	4	1	no	—
676	C₄×C₇	—	4	1	no	—
677	C₄×C₇	—	4	2	no	—
678	C₄×C₇	—	4	1	no	—
679	C₄×C₇	—	4	2	no	—
680	C₄×C₇	—	4	1	no	—
681	C₄×C₇	—	4	1	no	—
682	C₄×C₇	—	4	2	no	—
683	C₄×C₇	#519	1	4	yes	—
684	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	—	4	2	no	—
689	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
690	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
696	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
697	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
738	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
739	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
740	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
741	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
742	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
743	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
744	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
745	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
746	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
747	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
748	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
749	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	—	4	1	no	—
756	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
757	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
758	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	4	2	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	2	no	—
770	C₄²	—	4	2	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	1	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	1	no	—
777	C₄²	C₂²×C₄×C₇	1	8	yes	—
778	C₄²	C₂²×C₄×C₇	1	4	yes	—
779	C₄²	C₂²×C₄×C₇	1	4	yes	—
780	C₂×C₇	—	4	2	no	—
781	C₂×C₇	C₂×#519	1	1	yes	characteristic
782	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
784	C₂×C₇	#3552	1	1	yes	characteristic
785	C₂×C₇	#3555	1	1	yes	characteristic
786	C₂×C₇	#3559	1	1	yes	characteristic
787	C₂×C₇	#3565	1	1	yes	characteristic
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	C₂³×C₄×C₇	1	2	yes	—
795	C₂³	C₂⁵×C₇	1	1	yes	characteristic
796	Q₈	—	4	8	no	—
797	Q₈	—	4	8	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	8	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	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	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	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	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
853	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
854	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
855	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
856	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
857	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
858	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
859	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
860	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
861	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
862	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
863	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
864	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
865	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
866	C₇	#34434	1	1	yes	characteristic, direct product factor, Sylow
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
875	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
876	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
877	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
879	C₂²	C₇×#585	1	1	yes	characteristic
880	C₂²	C₇×#585	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	4	no	—
883	C₄	—	2	4	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	C₇×#519	1	4	yes	—
903	C₂	—	4	2	no	—
904	C₂	C₂×C₇×#519	1	1	yes	characteristic
905	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
906	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
907	C₂	C₇×#3552	1	1	yes	characteristic
908	C₂	C₇×#3555	1	1	yes	characteristic
909	C₂	C₇×#3559	1	1	yes	characteristic
910	C₂	C₇×#3565	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
2. C₇×#2381	C₂	semidirect
4. C₇×#2370	C₂	semidirect
5. C₇×#2370	C₂	semidirect
6. C₇×#2369	C₂	semidirect
7. C₇×#2365	C₂	semidirect
8. C₇×#2365	C₂	semidirect
14. C₇×#2336	C₂	semidirect
15. C₇×#2336	C₂	semidirect
17. C₇×#2331	C₂	semidirect
18. C₇×#2330	C₂	semidirect
21. C₄×C₇×C₄⋊Q₈	C₂	semidirect
22. C₄×C₇×#125	C₂	semidirect
24. C₇×#544	C₄	semidirect
124. #34434	C₇	direct (N × H)
239. #2381	C₂×C₇	semidirect
241. #2370	C₂×C₇	semidirect
242. #2370	C₂×C₇	semidirect
243. #2369	C₂×C₇	semidirect
244. #2365	C₂×C₇	semidirect
245. #2365	C₂×C₇	semidirect
251. #2336	C₂×C₇	semidirect
252. #2336	C₂×C₇	semidirect
254. #2331	C₂×C₇	semidirect
255. #2330	C₂×C₇	semidirect
258. C₄×C₄⋊Q₈	C₂×C₇	semidirect
259. C₄×#125	C₂×C₇	semidirect
357. #544	C₄×C₇	semidirect
866. C₇	#34434	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×#544	2
C₇×#2381	2
C₇×#2378	2
C₇×#2370	2
C₇×#2369	2
C₇×#2365	2
C₇×#2362	2
C₇×#2347	2
C₇×#2345	2
C₇×#2344	2
C₇×#2336	2
C₇×#2332	2
C₇×#2331	2
C₇×#2330	2
C₇×#2323	2
C₇×#2314	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#125	2
C₇×#2298	2
#34434	7

Subgroups — C7×#34434 #13211650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34434 #13211650