Subgroups — C₇×#34431 #13211647

Order 1792.

2382 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic
2	C₇×#2377	C₂	1	2	yes	maximal, complemented
3	C₇×#2376	C₂	1	2	yes	maximal, complemented
4	C₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2361	C₂	1	2	yes	maximal, complemented
9	C₇×#2359	C₂	1	2	yes	maximal, complemented
10	C₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2335	C₂	1	2	yes	maximal, complemented
15	C₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2328	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2325	C₂	1	2	yes	maximal, complemented
18	C₇×#2324	C₂	1	2	yes	maximal, complemented
19	C₇×#2322	C₂	1	2	yes	maximal, complemented
20	C₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×#127	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, complemented
24	C₇×#540	C₄	1	16	yes	complemented
25	C₂×C₇×#127	C₂²	1	1	yes	characteristic
26	C₂×C₇×#125	C₂²	1	1	yes	characteristic
27	C₂×C₇×#123	C₂²	1	2	yes	—
28	C₂×C₇×#123	C₂²	1	2	yes	—
29	C₂×C₇×#121	C₂²	1	2	yes	—
30	C₂×C₇×#121	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	1	yes	characteristic
32	C₂×C₇×#121	C₂²	1	2	yes	—
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
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	2	yes	—
38	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
39	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₇×#117	C₂²	1	1	yes	characteristic
44	C₂×C₇×#117	C₂²	1	2	yes	—
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
48	C₇×#390	C₂²	1	2	yes	—
49	C₇×#390	C₂²	1	1	yes	characteristic
50	C₇×#390	C₂²	1	1	yes	characteristic
51	C₇×#390	C₂²	1	2	yes	—
52	C₇×#390	C₂²	1	2	yes	—
53	C₇×#390	C₂²	1	2	yes	—
54	C₇×#390	C₂²	1	1	yes	characteristic
55	C₇×#390	C₂²	1	1	yes	characteristic
56	C₇×#389	C₂²	1	1	yes	characteristic
57	C₇×#389	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
62	C₇×#389	C₂²	1	1	yes	characteristic
63	C₇×#389	C₂²	1	2	yes	—
64	C₇×#388	C₂²	1	1	yes	characteristic
65	C₇×#388	C₂²	1	1	yes	characteristic
66	C₇×#388	C₂²	1	1	yes	characteristic
67	C₇×#388	C₂²	1	1	yes	characteristic
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#388	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×#387	C₂²	1	1	yes	characteristic
77	C₇×#387	C₂²	1	1	yes	characteristic
78	C₇×#387	C₂²	1	1	yes	characteristic
79	C₇×#387	C₂²	1	1	yes	characteristic
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×#386	C₂²	1	2	yes	—
85	C₇×#386	C₂²	1	2	yes	—
86	C₇×#386	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×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	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×#385	C₂²	1	2	yes	—
100	C₇×#384	C₂²	1	1	yes	characteristic
101	C₇×#384	C₂²	1	1	yes	characteristic
102	C₇×#382	C₂²	1	1	yes	characteristic
103	C₇×#382	C₂²	1	1	yes	characteristic
104	C₇×#381	C₂²	1	2	yes	—
105	C₇×#380	C₂²	1	2	yes	—
106	C₇×#380	C₂²	1	2	yes	—
107	C₇×#380	C₂²	1	2	yes	—
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	2	yes	—
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	2	yes	—
114	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₄⋊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	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	C₂×C₇×#95	C₂²	1	2	yes	—
123	C₄³×C₇	C₂²	1	1	yes	characteristic
124	#34431	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	C₂²×C₇×D₄	C₂³	1	2	yes	—
130	C₂²×C₇×D₄	C₂³	1	2	yes	—
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₇	C₂³	1	2	yes	—
139	C₇×#127	C₂×C₄	1	8	yes	complemented
140	C₇×#125	C₂×C₄	1	8	yes	complemented
141	C₇×#123	C₂×C₄	1	16	yes	complemented
142	C₇×#123	C₂×C₄	1	16	yes	complemented
143	C₇×#121	C₂×C₄	1	16	yes	complemented
144	C₇×#121	C₂×C₄	1	16	yes	complemented
145	C₇×#121	C₂×C₄	1	8	yes	complemented
146	C₇×#121	C₂×C₄	1	8	yes	complemented
147	C₄×C₇×D₄	—	4	4	no	—
148	C₄×C₇×D₄	—	4	4	no	—
149	C₄×C₇×D₄	—	4	2	no	—
150	C₄×C₇×D₄	—	4	2	no	—
151	C₄×C₇×D₄	—	4	2	no	—
152	C₄×C₇×D₄	—	4	2	no	—
153	C₄×C₇×D₄	—	4	4	no	—
154	C₄×C₇×D₄	—	4	4	no	—
155	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
156	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
157	C₇×#117	—	4	4	no	—
158	C₇×#117	—	4	2	no	—
159	C₇×#117	C₂×C₄	1	8	yes	complemented
160	C₂×C₇×C₄⋊C₄	—	4	4	no	—
161	C₂×C₇×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
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	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	1	yes	characteristic
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₄⋊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×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₇	C₂³	1	2	yes	—
220	C₂×C₄²×C₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₇×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
228	C₇×#95	C₂³	1	1	yes	characteristic
229	C₇×#95	C₂³	1	1	yes	characteristic
230	C₇×#95	C₂³	1	1	yes	characteristic
231	C₇×#95	C₂³	1	1	yes	characteristic
232	C₇×#95	C₂³	1	1	yes	characteristic
233	C₇×#95	C₂³	1	1	yes	characteristic
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	1	yes	characteristic
237	C₇×#95	C₂³	1	1	yes	characteristic
238	C₇×#95	C₂³	1	1	yes	characteristic
239	C₇×#95	C₂³	1	2	yes	—
240	C₇×#95	C₂³	1	2	yes	—
241	C₇×#95	C₂³	1	2	yes	—
242	C₇×#95	C₂³	1	1	yes	characteristic
243	C₇×#95	C₂³	1	2	yes	—
244	C₇×#95	C₂³	1	2	yes	—
245	C₇×#95	C₂³	1	2	yes	—
246	C₇×#95	C₂³	1	2	yes	—
247	C₂×#540	C₂×C₇	1	1	yes	characteristic
248	#2377	C₂×C₇	1	2	yes	complemented
249	#2376	C₂×C₇	1	2	yes	complemented
250	#2363	C₂×C₇	1	1	yes	characteristic, complemented
251	#2363	C₂×C₇	1	1	yes	characteristic, complemented
252	#2361	C₂×C₇	1	1	yes	characteristic, complemented
253	#2361	C₂×C₇	1	1	yes	characteristic, complemented
254	#2361	C₂×C₇	1	2	yes	complemented
255	#2359	C₂×C₇	1	2	yes	complemented
256	#2357	C₂×C₇	1	1	yes	characteristic, complemented
257	#2354	C₂×C₇	1	1	yes	characteristic, complemented
258	#2349	C₂×C₇	1	1	yes	characteristic, complemented
259	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
260	#2335	C₂×C₇	1	2	yes	complemented
261	#2330	C₂×C₇	1	1	yes	characteristic, complemented
262	#2328	C₂×C₇	1	1	yes	characteristic, complemented
263	#2325	C₂×C₇	1	2	yes	complemented
264	#2324	C₂×C₇	1	2	yes	complemented
265	#2322	C₂×C₇	1	2	yes	complemented
266	#2317	C₂×C₇	1	1	yes	characteristic, complemented
267	C₄×#127	C₂×C₇	1	1	yes	characteristic, complemented
268	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
269	#2298	C₂×C₇	1	1	yes	characteristic, complemented
270	C₂⁴×C₇	C₂⁴	1	2	yes	—
271	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
272	C₂⁴×C₇	C₂⁴	1	2	yes	—
273	C₂×C₇×D₄	—	2	2	no	—
274	C₂×C₇×D₄	—	2	2	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	C₂×C₇×D₄	—	4	2	no	—
281	C₂×C₇×D₄	—	4	2	no	—
282	C₂×C₇×D₄	—	4	2	no	—
283	C₂×C₇×D₄	—	4	2	no	—
284	C₂×C₇×D₄	—	4	2	no	—
285	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
286	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
287	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
288	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
289	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
290	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
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	4	no	—
295	C₂²×C₄×C₇	—	4	2	no	—
296	C₂²×C₄×C₇	—	4	2	no	—
297	C₂²×C₄×C₇	—	4	2	no	—
298	C₂²×C₄×C₇	—	4	2	no	—
299	C₂²×C₄×C₇	—	4	2	no	—
300	C₂²×C₄×C₇	—	4	2	no	—
301	C₂²×C₄×C₇	—	4	2	no	—
302	C₂²×C₄×C₇	—	4	2	no	—
303	C₂²×C₄×C₇	—	4	2	no	—
304	C₂²×C₄×C₇	—	4	2	no	—
305	C₂²×C₄×C₇	—	4	2	no	—
306	C₂²×C₄×C₇	—	4	2	no	—
307	C₂²×C₄×C₇	—	4	2	no	—
308	C₂²×C₄×C₇	—	4	2	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	C₂²×C₄	1	4	yes	—
313	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
314	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
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	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	4	no	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	4	2	no	—
343	C₇×C₄⋊C₄	—	4	2	no	—
344	C₇×C₄⋊C₄	—	4	2	no	—
345	C₇×C₄⋊C₄	—	4	1	no	—
346	C₇×C₄⋊C₄	—	4	1	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	C₂²×C₄	1	4	yes	—
353	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
354	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
355	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
356	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
357	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
358	C₇×C₂²⋊C₄	—	2	4	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	2	2	no	—
361	C₇×C₂²⋊C₄	—	2	4	no	—
362	C₇×C₂²⋊C₄	—	4	1	no	—
363	C₇×C₂²⋊C₄	—	4	1	no	—
364	C₇×C₂²⋊C₄	—	4	2	no	—
365	C₇×C₂²⋊C₄	—	4	2	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	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
376	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
377	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
378	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
379	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
380	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
381	C₄²×C₇	—	2	4	no	—
382	C₄²×C₇	—	2	2	no	—
383	C₄²×C₇	—	2	2	no	—
384	C₄²×C₇	—	2	2	no	—
385	C₄²×C₇	—	2	2	no	—
386	C₄²×C₇	—	2	2	no	—
387	C₄²×C₇	—	2	2	no	—
388	C₄²×C₇	—	4	2	no	—
389	C₄²×C₇	—	4	1	no	—
390	C₄²×C₇	—	4	1	no	—
391	C₄²×C₇	—	4	2	no	—
392	C₄²×C₇	—	4	2	no	—
393	C₄²×C₇	—	4	2	no	—
394	C₄²×C₇	C₂²×C₄	1	4	yes	—
395	C₄²×C₇	C₂²×C₄	1	4	yes	—
396	#540	C₄×C₇	1	16	yes	complemented
397	C₂×#127	C₂²×C₇	1	1	yes	characteristic
398	C₂×#125	C₂²×C₇	1	1	yes	characteristic
399	C₂×#123	C₂²×C₇	1	2	yes	—
400	C₂×#123	C₂²×C₇	1	2	yes	—
401	C₂×#121	C₂²×C₇	1	2	yes	—
402	C₂×#121	C₂²×C₇	1	1	yes	characteristic
403	C₂×#121	C₂²×C₇	1	1	yes	characteristic
404	C₂×#121	C₂²×C₇	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
411	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
415	C₂×#117	C₂²×C₇	1	1	yes	characteristic
416	C₂×#117	C₂²×C₇	1	2	yes	—
417	C₂×#117	C₂²×C₇	1	1	yes	characteristic
418	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
419	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
420	#390	C₂²×C₇	1	2	yes	—
421	#390	C₂²×C₇	1	1	yes	characteristic
422	#390	C₂²×C₇	1	1	yes	characteristic
423	#390	C₂²×C₇	1	2	yes	—
424	#390	C₂²×C₇	1	2	yes	—
425	#390	C₂²×C₇	1	2	yes	—
426	#390	C₂²×C₇	1	1	yes	characteristic
427	#390	C₂²×C₇	1	1	yes	characteristic
428	#389	C₂²×C₇	1	1	yes	characteristic
429	#389	C₂²×C₇	1	1	yes	characteristic
430	#389	C₂²×C₇	1	2	yes	—
431	#389	C₂²×C₇	1	2	yes	—
432	#389	C₂²×C₇	1	2	yes	—
433	#389	C₂²×C₇	1	1	yes	characteristic
434	#389	C₂²×C₇	1	1	yes	characteristic
435	#389	C₂²×C₇	1	2	yes	—
436	#388	C₂²×C₇	1	2	yes	—
437	#388	C₂²×C₇	1	2	yes	—
438	#388	C₂²×C₇	1	1	yes	characteristic
439	#388	C₂²×C₇	1	2	yes	—
440	#388	C₂²×C₇	1	1	yes	characteristic
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	#388	C₂²×C₇	1	1	yes	characteristic
447	#388	C₂²×C₇	1	1	yes	characteristic
448	#387	C₂²×C₇	1	2	yes	—
449	#387	C₂²×C₇	1	2	yes	—
450	#387	C₂²×C₇	1	1	yes	characteristic
451	#387	C₂²×C₇	1	2	yes	—
452	#387	C₂²×C₇	1	2	yes	—
453	#387	C₂²×C₇	1	1	yes	characteristic
454	#387	C₂²×C₇	1	1	yes	characteristic
455	#387	C₂²×C₇	1	1	yes	characteristic
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	#386	C₂²×C₇	1	2	yes	—
461	#386	C₂²×C₇	1	2	yes	—
462	#386	C₂²×C₇	1	2	yes	—
463	#386	C₂²×C₇	1	2	yes	—
464	#385	C₂²×C₇	1	2	yes	—
465	#385	C₂²×C₇	1	2	yes	—
466	#385	C₂²×C₇	1	2	yes	—
467	#385	C₂²×C₇	1	2	yes	—
468	#385	C₂²×C₇	1	2	yes	—
469	#385	C₂²×C₇	1	2	yes	—
470	#385	C₂²×C₇	1	2	yes	—
471	#385	C₂²×C₇	1	2	yes	—
472	#384	C₂²×C₇	1	1	yes	characteristic
473	#384	C₂²×C₇	1	1	yes	characteristic
474	#382	C₂²×C₇	1	1	yes	characteristic
475	#382	C₂²×C₇	1	1	yes	characteristic
476	#381	C₂²×C₇	1	2	yes	—
477	#380	C₂²×C₇	1	2	yes	—
478	#380	C₂²×C₇	1	2	yes	—
479	#380	C₂²×C₇	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
482	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
483	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
485	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
486	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
492	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
493	#376	C₂²×C₇	1	1	yes	characteristic
494	C₂×#95	C₂²×C₇	1	2	yes	—
495	C₄³	C₂²×C₇	1	1	yes	characteristic
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	—	2	1	no	—
498	C₂³×C₇	—	2	2	no	—
499	C₂³×C₇	—	2	1	no	—
500	C₂³×C₇	—	2	1	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	—	2	1	no	—
506	C₂³×C₇	—	2	2	no	—
507	C₂³×C₇	—	2	2	no	—
508	C₂³×C₇	—	2	2	no	—
509	C₂³×C₇	—	2	1	no	—
510	C₂³×C₇	—	2	2	no	—
511	C₂³×C₇	—	2	1	no	—
512	C₂³×C₇	—	2	2	no	—
513	C₂³×C₇	—	2	2	no	—
514	C₂³×C₇	C₂³×C₄	1	2	yes	—
515	C₂³×C₇	C₂³×C₄	1	4	yes	—
516	C₂³×C₇	C₂³×C₄	1	4	yes	—
517	C₂³×C₇	C₂⁵	1	1	yes	characteristic
518	C₇×D₄	—	2	8	no	—
519	C₇×D₄	—	2	8	no	—
520	C₇×D₄	—	4	8	no	—
521	C₇×D₄	—	4	8	no	—
522	C₇×D₄	—	4	8	no	—
523	C₇×D₄	—	4	8	no	—
524	C₂×C₄×C₇	—	2	2	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	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	1	no	—
533	C₂×C₄×C₇	—	2	1	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	1	no	—
540	C₂×C₄×C₇	—	2	1	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	8	no	—
543	C₂×C₄×C₇	—	2	1	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	2	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	2	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	2	no	—
554	C₂×C₄×C₇	—	2	1	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	2	no	—
560	C₂×C₄×C₇	—	2	1	no	—
561	C₂×C₄×C₇	—	2	1	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	1	no	—
569	C₂×C₄×C₇	—	2	1	no	—
570	C₂×C₄×C₇	—	2	2	no	—
571	C₂×C₄×C₇	—	2	1	no	—
572	C₂×C₄×C₇	—	2	1	no	—
573	C₂×C₄×C₇	—	4	8	no	—
574	C₂×C₄×C₇	—	4	8	no	—
575	C₂×C₄×C₇	—	8	4	no	—
576	C₂×C₄×C₇	—	8	4	no	—
577	C₂×C₄×C₇	—	8	4	no	—
578	C₂×C₄×C₇	—	8	4	no	—
579	C₂×C₄×C₇	—	8	4	no	—
580	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
581	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
584	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
585	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
586	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
587	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
589	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
590	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
591	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
592	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
594	C₂²×D₄	C₂³×C₇	1	2	yes	—
595	C₂²×D₄	C₂³×C₇	1	2	yes	—
596	C₂²×D₄	C₂³×C₇	1	2	yes	—
597	C₂²×D₄	C₂³×C₇	1	2	yes	—
598	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₇	1	2	yes	—
600	C₂³×C₄	C₂³×C₇	1	2	yes	—
601	C₂³×C₄	C₂³×C₇	1	2	yes	—
602	C₂³×C₄	C₂³×C₇	1	2	yes	—
603	C₂³×C₄	C₂³×C₇	1	2	yes	—
604	C₂³×C₄	C₂³×C₇	1	2	yes	—
605	C₂³×C₄	C₂³×C₇	1	2	yes	—
606	#127	C₂×C₄×C₇	1	8	yes	complemented
607	#125	C₂×C₄×C₇	1	8	yes	complemented
608	#123	C₂×C₄×C₇	1	16	yes	complemented
609	#123	C₂×C₄×C₇	1	16	yes	complemented
610	#121	C₂×C₄×C₇	1	16	yes	complemented
611	#121	C₂×C₄×C₇	1	16	yes	complemented
612	#121	C₂×C₄×C₇	1	8	yes	complemented
613	#121	C₂×C₄×C₇	1	8	yes	complemented
614	C₄×D₄	—	4	4	no	—
615	C₄×D₄	—	4	4	no	—
616	C₄×D₄	—	4	2	no	—
617	C₄×D₄	—	4	2	no	—
618	C₄×D₄	—	4	2	no	—
619	C₄×D₄	—	4	2	no	—
620	C₄×D₄	—	4	4	no	—
621	C₄×D₄	—	4	4	no	—
622	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
623	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
624	#117	—	4	4	no	—
625	#117	—	4	2	no	—
626	#117	C₂×C₄×C₇	1	8	yes	complemented
627	C₂×C₄⋊C₄	—	4	4	no	—
628	C₂×C₄⋊C₄	—	4	2	no	—
629	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
675	C₂×C₄²	C₂³×C₇	1	2	yes	—
676	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₇	1	2	yes	—
683	C₂×C₄²	C₂³×C₇	1	2	yes	—
684	C₂×C₄²	C₂³×C₇	1	2	yes	—
685	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₇	1	2	yes	—
688	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
690	#95	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
695	#95	C₂³×C₇	1	1	yes	characteristic
696	#95	C₂³×C₇	1	1	yes	characteristic
697	#95	C₂³×C₇	1	1	yes	characteristic
698	#95	C₂³×C₇	1	1	yes	characteristic
699	#95	C₂³×C₇	1	1	yes	characteristic
700	#95	C₂³×C₇	1	1	yes	characteristic
701	#95	C₂³×C₇	1	2	yes	—
702	#95	C₂³×C₇	1	2	yes	—
703	#95	C₂³×C₇	1	1	yes	characteristic
704	#95	C₂³×C₇	1	1	yes	characteristic
705	#95	C₂³×C₇	1	1	yes	characteristic
706	#95	C₂³×C₇	1	2	yes	—
707	#95	C₂³×C₇	1	2	yes	—
708	#95	C₂³×C₇	1	2	yes	—
709	#95	C₂³×C₇	1	1	yes	characteristic
710	#95	C₂³×C₇	1	2	yes	—
711	#95	C₂³×C₇	1	2	yes	—
712	#95	C₂³×C₇	1	2	yes	—
713	#95	C₂³×C₇	1	2	yes	—
714	C₂²×C₇	—	2	2	no	—
715	C₂²×C₇	—	2	4	no	—
716	C₂²×C₇	—	2	4	no	—
717	C₂²×C₇	—	2	4	no	—
718	C₂²×C₇	—	2	4	no	—
719	C₂²×C₇	—	2	2	no	—
720	C₂²×C₇	—	2	2	no	—
721	C₂²×C₇	—	2	4	no	—
722	C₂²×C₇	—	2	4	no	—
723	C₂²×C₇	—	4	2	no	—
724	C₂²×C₇	—	4	1	no	—
725	C₂²×C₇	—	4	2	no	—
726	C₂²×C₇	—	4	1	no	—
727	C₂²×C₇	—	4	2	no	—
728	C₂²×C₇	—	4	2	no	—
729	C₂²×C₇	—	4	2	no	—
730	C₂²×C₇	—	4	1	no	—
731	C₂²×C₇	—	4	2	no	—
732	C₂²×C₇	—	4	2	no	—
733	C₂²×C₇	—	4	1	no	—
734	C₂²×C₇	—	4	2	no	—
735	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
736	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
737	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
739	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
740	C₂²×C₇	#585	1	1	yes	characteristic
741	C₂²×C₇	#585	1	1	yes	characteristic
742	C₄×C₇	—	2	2	no	—
743	C₄×C₇	—	2	2	no	—
744	C₄×C₇	—	2	2	no	—
745	C₄×C₇	—	2	4	no	—
746	C₄×C₇	—	2	4	no	—
747	C₄×C₇	—	2	2	no	—
748	C₄×C₇	—	2	2	no	—
749	C₄×C₇	—	2	2	no	—
750	C₄×C₇	—	2	2	no	—
751	C₄×C₇	—	4	2	no	—
752	C₄×C₇	—	4	1	no	—
753	C₄×C₇	—	4	2	no	—
754	C₄×C₇	—	4	2	no	—
755	C₄×C₇	—	4	1	no	—
756	C₄×C₇	—	4	1	no	—
757	C₄×C₇	—	4	1	no	—
758	C₄×C₇	—	4	1	no	—
759	C₄×C₇	—	4	2	no	—
760	C₄×C₇	—	4	1	no	—
761	C₄×C₇	#520	1	4	yes	—
762	C₂⁴	C₂⁴×C₇	1	2	yes	—
763	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
764	C₂⁴	C₂⁴×C₇	1	2	yes	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	2	no	—
773	C₂×D₄	—	4	2	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
778	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
779	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
780	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
781	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
782	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	—	4	2	no	—
796	C₂²×C₄	—	4	2	no	—
797	C₂²×C₄	—	4	2	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	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
805	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
806	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
807	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
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	2	yes	—
821	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	4	no	—
829	C₄⋊C₄	—	2	2	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	C₄⋊C₄	—	4	1	no	—
842	C₄⋊C₄	—	4	1	no	—
843	C₄⋊C₄	—	4	2	no	—
844	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
845	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
846	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
847	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
848	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
849	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	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	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	1	no	—
864	C₂²⋊C₄	—	4	1	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
868	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
869	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
870	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
871	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
872	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
873	C₄²	—	2	4	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	4	2	no	—
881	C₄²	—	4	2	no	—
882	C₄²	—	4	2	no	—
883	C₄²	—	4	2	no	—
884	C₄²	—	4	1	no	—
885	C₄²	—	4	1	no	—
886	C₄²	C₂²×C₄×C₇	1	4	yes	—
887	C₄²	C₂²×C₄×C₇	1	4	yes	—
888	C₂×C₇	—	4	2	no	—
889	C₂×C₇	—	4	4	no	—
890	C₂×C₇	—	4	4	no	—
891	C₂×C₇	C₂×#520	1	1	yes	characteristic
892	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
893	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
894	C₂×C₇	#3543	1	1	yes	characteristic
895	C₂×C₇	#3547	1	1	yes	characteristic
896	C₂×C₇	#3559	1	1	yes	characteristic
897	C₂×C₇	#3562	1	1	yes	characteristic
898	C₂³	—	2	2	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	C₂³×C₄×C₇	1	2	yes	—
917	C₂³	C₂³×C₄×C₇	1	4	yes	—
918	C₂³	C₂³×C₄×C₇	1	4	yes	—
919	C₂³	C₂⁵×C₇	1	1	yes	characteristic
920	D₄	—	2	8	no	—
921	D₄	—	2	8	no	—
922	D₄	—	4	8	no	—
923	D₄	—	4	8	no	—
924	D₄	—	4	8	no	—
925	D₄	—	4	8	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	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	8	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	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	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	4	8	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	8	4	no	—
978	C₂×C₄	—	8	4	no	—
979	C₂×C₄	—	8	4	no	—
980	C₂×C₄	—	8	4	no	—
981	C₂×C₄	—	8	4	no	—
982	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
984	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
990	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
991	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
992	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
993	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
994	C₇	#34431	1	1	yes	characteristic, direct product factor, Sylow
995	C₂²	—	2	2	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	4	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1017	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1018	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1019	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1020	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1021	C₂²	C₇×#585	1	1	yes	characteristic
1022	C₂²	C₇×#585	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	C₇×#520	1	4	yes	—
1043	C₂	—	4	2	no	—
1044	C₂	—	4	4	no	—
1045	C₂	—	4	4	no	—
1046	C₂	C₂×C₇×#520	1	1	yes	characteristic
1047	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1048	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1049	C₂	C₇×#3543	1	1	yes	characteristic
1050	C₂	C₇×#3547	1	1	yes	characteristic
1051	C₂	C₇×#3559	1	1	yes	characteristic
1052	C₂	C₇×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#540	C₂
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×#2377	C₂	semidirect
3. C₇×#2376	C₂	semidirect
4. C₇×#2363	C₂	semidirect
5. C₇×#2363	C₂	semidirect
6. C₇×#2361	C₂	semidirect
7. C₇×#2361	C₂	semidirect
8. C₇×#2361	C₂	semidirect
9. C₇×#2359	C₂	semidirect
10. C₇×#2357	C₂	semidirect
11. C₇×#2354	C₂	semidirect
12. C₇×#2349	C₂	semidirect
13. C₇×D₄×C₄⋊C₄	C₂	semidirect
14. C₇×#2335	C₂	semidirect
15. C₇×#2330	C₂	semidirect
16. C₇×#2328	C₂	semidirect
17. C₇×#2325	C₂	semidirect
18. C₇×#2324	C₂	semidirect
19. C₇×#2322	C₂	semidirect
20. C₇×#2317	C₂	semidirect
21. C₄×C₇×#127	C₂	semidirect
22. C₄×C₇×#125	C₂	semidirect
23. C₇×#2298	C₂	semidirect
24. C₇×#540	C₄	semidirect
124. #34431	C₇	direct (N × H)
139. C₇×#127	C₂×C₄	semidirect
140. C₇×#125	C₂×C₄	semidirect
141. C₇×#123	C₂×C₄	semidirect
142. C₇×#123	C₂×C₄	semidirect
143. C₇×#121	C₂×C₄	semidirect
144. C₇×#121	C₂×C₄	semidirect
145. C₇×#121	C₂×C₄	semidirect
146. C₇×#121	C₂×C₄	semidirect
155. C₄×C₇×D₄	C₂×C₄	semidirect
156. C₄×C₇×D₄	C₂×C₄	semidirect
159. C₇×#117	C₂×C₄	semidirect
248. #2377	C₂×C₇	semidirect
249. #2376	C₂×C₇	semidirect
250. #2363	C₂×C₇	semidirect
251. #2363	C₂×C₇	semidirect
252. #2361	C₂×C₇	semidirect
253. #2361	C₂×C₇	semidirect
254. #2361	C₂×C₇	semidirect
255. #2359	C₂×C₇	semidirect
256. #2357	C₂×C₇	semidirect
257. #2354	C₂×C₇	semidirect
258. #2349	C₂×C₇	semidirect
259. D₄×C₄⋊C₄	C₂×C₇	semidirect
260. #2335	C₂×C₇	semidirect
261. #2330	C₂×C₇	semidirect
262. #2328	C₂×C₇	semidirect
263. #2325	C₂×C₇	semidirect
264. #2324	C₂×C₇	semidirect
265. #2322	C₂×C₇	semidirect
266. #2317	C₂×C₇	semidirect
267. C₄×#127	C₂×C₇	semidirect
268. C₄×#125	C₂×C₇	semidirect
269. #2298	C₂×C₇	semidirect
396. #540	C₄×C₇	semidirect
606. #127	C₂×C₄×C₇	semidirect
607. #125	C₂×C₄×C₇	semidirect
608. #123	C₂×C₄×C₇	semidirect
609. #123	C₂×C₄×C₇	semidirect
610. #121	C₂×C₄×C₇	semidirect
611. #121	C₂×C₄×C₇	semidirect
612. #121	C₂×C₄×C₇	semidirect
613. #121	C₂×C₄×C₇	semidirect
622. C₄×D₄	C₂×C₄×C₇	semidirect
623. C₄×D₄	C₂×C₄×C₇	semidirect
626. #117	C₂×C₄×C₇	semidirect
994. C₇	#34431	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×#540	2
C₇×#2377	2
C₇×#2376	2
C₇×#2363	2
C₇×#2361	2
C₇×#2359	2
C₇×#2357	2
C₇×#2354	2
C₇×#2349	2
C₇×D₄×C₄⋊C₄	2
C₇×#2335	2
C₇×#2330	2
C₇×#2328	2
C₇×#2325	2
C₇×#2324	2
C₇×#2322	2
C₇×#2317	2
C₄×C₇×#127	2
C₄×C₇×#125	2
C₇×#2298	2
#34431	7

Subgroups — C7×#34431 #13211647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34431 #13211647