Subgroups — C₇×#34477 #13211693

Order 1792.

2568 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#550	C₂	1	1	yes	maximal, characteristic
2	C₇×#2380	C₂	1	2	yes	maximal, complemented
3	C₇×#2377	C₂	1	2	yes	maximal, complemented
4	C₇×#2366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2364	C₂	1	2	yes	maximal, complemented
6	C₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2353	C₂	1	2	yes	maximal, complemented
10	C₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2333	C₂	1	2	yes	maximal, complemented
14	C₇×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2328	C₂	1	2	yes	maximal, complemented
16	C₇×#2325	C₂	1	2	yes	maximal, complemented
17	C₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2318	C₂	1	2	yes	maximal, complemented
20	C₇×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₇×#550	C₄	1	16	yes	complemented
27	C₂×C₇×#127	C₂²	1	1	yes	characteristic
28	C₂×C₇×#127	C₂²	1	2	yes	—
29	C₂×C₇×#121	C₂²	1	1	yes	characteristic
30	C₂×C₇×#121	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	2	yes	—
32	C₂×C₇×#121	C₂²	1	2	yes	—
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
38	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
43	C₂×C₇×#117	C₂²	1	1	yes	characteristic
44	C₂×C₇×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
47	C₇×#391	C₂²	1	1	yes	characteristic
48	C₇×#391	C₂²	1	1	yes	characteristic
49	C₇×#391	C₂²	1	1	yes	characteristic
50	C₇×#391	C₂²	1	1	yes	characteristic
51	C₇×#390	C₂²	1	1	yes	characteristic
52	C₇×#390	C₂²	1	1	yes	characteristic
53	C₇×#390	C₂²	1	1	yes	characteristic
54	C₇×#390	C₂²	1	1	yes	characteristic
55	C₇×#390	C₂²	1	2	yes	—
56	C₇×#390	C₂²	1	2	yes	—
57	C₇×#390	C₂²	1	2	yes	—
58	C₇×#389	C₂²	1	1	yes	characteristic
59	C₇×#389	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	2	yes	—
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×#387	C₂²	1	1	yes	characteristic
68	C₇×#387	C₂²	1	1	yes	characteristic
69	C₇×#387	C₂²	1	2	yes	—
70	C₇×#387	C₂²	1	2	yes	—
71	C₇×#387	C₂²	1	2	yes	—
72	C₇×#387	C₂²	1	2	yes	—
73	C₇×#387	C₂²	1	2	yes	—
74	C₇×#386	C₂²	1	1	yes	characteristic
75	C₇×#386	C₂²	1	1	yes	characteristic
76	C₇×#386	C₂²	1	2	yes	—
77	C₇×#386	C₂²	1	2	yes	—
78	C₇×#386	C₂²	1	2	yes	—
79	C₇×#386	C₂²	1	2	yes	—
80	C₇×#386	C₂²	1	2	yes	—
81	C₇×#386	C₂²	1	2	yes	—
82	C₇×#386	C₂²	1	2	yes	—
83	C₇×#386	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×#386	C₂²	1	2	yes	—
93	C₇×#386	C₂²	1	2	yes	—
94	C₇×#386	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	1	yes	characteristic
96	C₇×#385	C₂²	1	1	yes	characteristic
97	C₇×#385	C₂²	1	2	yes	—
98	C₇×#385	C₂²	1	2	yes	—
99	C₇×#383	C₂²	1	2	yes	—
100	C₇×#383	C₂²	1	2	yes	—
101	C₇×#382	C₂²	1	2	yes	—
102	C₇×#382	C₂²	1	1	yes	characteristic
103	C₇×#381	C₂²	1	2	yes	—
104	C₇×#381	C₂²	1	2	yes	—
105	C₇×#380	C₂²	1	1	yes	characteristic
106	C₇×#380	C₂²	1	2	yes	—
107	C₇×#380	C₂²	1	2	yes	—
108	C₇×#380	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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₇×#376	C₂²	1	1	yes	characteristic
121	C₇×#376	C₂²	1	2	yes	—
122	C₂×C₇×#95	C₂²	1	2	yes	—
123	C₂×C₇×#95	C₂²	1	2	yes	—
124	#34477	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂×C₇×#41	—	4	2	no	—
126	C₂×C₇×#41	—	4	2	no	—
127	C₂×C₇×#41	—	4	2	no	—
128	C₂×C₇×#41	—	4	2	no	—
129	C₂×C₇×#41	C₂×C₄	1	8	yes	complemented
130	C₂×C₇×#41	C₂×C₄	1	8	yes	complemented
131	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
133	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₇×D₄	C₂³	1	2	yes	—
135	C₂²×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂²×C₇×D₄	C₂³	1	2	yes	—
138	C₂²×C₇×D₄	C₂³	1	2	yes	—
139	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
140	C₂²×C₇×D₄	C₂³	1	2	yes	—
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₇	C₂³	1	2	yes	—
149	C₂³×C₄×C₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₇	C₂³	1	2	yes	—
152	C₇×#127	C₂×C₄	1	8	yes	complemented
153	C₇×#127	C₂×C₄	1	16	yes	complemented
154	C₇×#121	C₂×C₄	1	8	yes	complemented
155	C₇×#121	C₂×C₄	1	8	yes	complemented
156	C₇×#121	C₂×C₄	1	16	yes	complemented
157	C₇×#121	C₂×C₄	1	16	yes	complemented
158	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
159	C₄×C₇×D₄	—	4	4	no	—
160	C₄×C₇×D₄	—	4	2	no	—
161	C₄×C₇×D₄	—	4	2	no	—
162	C₄×C₇×D₄	—	4	2	no	—
163	C₄×C₇×D₄	—	4	2	no	—
164	C₄×C₇×D₄	—	4	4	no	—
165	C₄×C₇×D₄	—	4	4	no	—
166	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
167	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
168	C₇×#117	—	4	2	no	—
169	C₇×#117	—	4	2	no	—
170	C₂×C₇×C₄⋊C₄	—	4	2	no	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	—	4	2	no	—
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	1	yes	characteristic
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	2	yes	—
223	C₇×#95	C₂³	1	1	yes	characteristic
224	C₇×#95	C₂³	1	1	yes	characteristic
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	1	yes	characteristic
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	1	yes	characteristic
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
242	C₇×#95	C₂³	1	2	yes	—
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	C₇×#95	C₂³	1	1	yes	characteristic
248	C₇×#95	C₂³	1	2	yes	—
249	C₇×#95	C₂³	1	2	yes	—
250	C₂×#550	C₂×C₇	1	1	yes	characteristic
251	#2380	C₂×C₇	1	2	yes	complemented
252	#2377	C₂×C₇	1	2	yes	complemented
253	#2366	C₂×C₇	1	1	yes	characteristic, complemented
254	#2364	C₂×C₇	1	2	yes	complemented
255	#2363	C₂×C₇	1	1	yes	characteristic, complemented
256	#2361	C₂×C₇	1	1	yes	characteristic, complemented
257	#2356	C₂×C₇	1	1	yes	characteristic, complemented
258	#2353	C₂×C₇	1	2	yes	complemented
259	#2352	C₂×C₇	1	1	yes	characteristic, complemented
260	#2339	C₂×C₇	1	1	yes	characteristic, complemented
261	#2339	C₂×C₇	1	1	yes	characteristic, complemented
262	#2333	C₂×C₇	1	2	yes	complemented
263	#2328	C₂×C₇	1	2	yes	complemented
264	#2328	C₂×C₇	1	1	yes	characteristic, complemented
265	#2325	C₂×C₇	1	2	yes	complemented
266	#2324	C₂×C₇	1	1	yes	characteristic, complemented
267	#2320	C₂×C₇	1	1	yes	characteristic, complemented
268	#2318	C₂×C₇	1	2	yes	complemented
269	#2311	C₂×C₇	1	1	yes	characteristic, complemented
270	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
271	#2297	C₂×C₇	1	1	yes	characteristic, complemented
272	#2290	C₂×C₇	1	1	yes	characteristic, complemented
273	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
274	C₂⁴×C₇	C₂⁴	1	2	yes	—
275	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
276	C₂⁴×C₇	C₂⁴	1	2	yes	—
277	C₇×#41	—	4	16	no	—
278	C₇×#41	—	4	16	no	—
279	C₂×C₇×Q₈	—	2	2	no	—
280	C₂×C₇×Q₈	—	2	2	no	—
281	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	2	2	no	—
284	C₂×C₇×D₄	—	2	2	no	—
285	C₂×C₇×D₄	—	2	2	no	—
286	C₂×C₇×D₄	—	4	2	no	—
287	C₂×C₇×D₄	—	4	2	no	—
288	C₂×C₇×D₄	—	4	2	no	—
289	C₂×C₇×D₄	—	4	2	no	—
290	C₂×C₇×D₄	—	4	2	no	—
291	C₂×C₇×D₄	—	4	2	no	—
292	C₂×C₇×D₄	—	4	2	no	—
293	C₂×C₇×D₄	—	4	1	no	—
294	C₂×C₇×D₄	—	4	1	no	—
295	C₂×C₇×D₄	—	4	2	no	—
296	C₂×C₇×D₄	—	4	2	no	—
297	C₂×C₇×D₄	—	4	2	no	—
298	C₂×C₇×D₄	—	4	2	no	—
299	C₂×C₇×D₄	—	4	2	no	—
300	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
301	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
302	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
303	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
304	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
305	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
306	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
307	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
308	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
309	C₂²×C₄×C₇	—	2	2	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	2	no	—
314	C₂²×C₄×C₇	—	2	4	no	—
315	C₂²×C₄×C₇	—	4	1	no	—
316	C₂²×C₄×C₇	—	4	1	no	—
317	C₂²×C₄×C₇	—	4	1	no	—
318	C₂²×C₄×C₇	—	4	1	no	—
319	C₂²×C₄×C₇	—	4	1	no	—
320	C₂²×C₄×C₇	—	4	2	no	—
321	C₂²×C₄×C₇	—	4	2	no	—
322	C₂²×C₄×C₇	—	4	2	no	—
323	C₂²×C₄×C₇	—	4	2	no	—
324	C₂²×C₄×C₇	—	4	2	no	—
325	C₂²×C₄×C₇	—	4	2	no	—
326	C₂²×C₄×C₇	—	4	2	no	—
327	C₂²×C₄×C₇	—	4	2	no	—
328	C₂²×C₄×C₇	—	4	2	no	—
329	C₂²×C₄×C₇	—	4	2	no	—
330	C₂²×C₄×C₇	—	4	2	no	—
331	C₂²×C₄×C₇	—	4	2	no	—
332	C₂²×C₄×C₇	—	4	2	no	—
333	C₂²×C₄×C₇	—	4	2	no	—
334	C₂²×C₄×C₇	—	4	2	no	—
335	C₂²×C₄×C₇	—	4	2	no	—
336	C₂²×C₄×C₇	—	4	2	no	—
337	C₂²×C₄×C₇	—	4	2	no	—
338	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
339	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
340	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
341	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	2	no	—
363	C₇×C₄⋊C₄	—	2	2	no	—
364	C₇×C₄⋊C₄	—	2	2	no	—
365	C₇×C₄⋊C₄	—	2	2	no	—
366	C₇×C₄⋊C₄	—	4	2	no	—
367	C₇×C₄⋊C₄	—	4	1	no	—
368	C₇×C₄⋊C₄	—	4	1	no	—
369	C₇×C₄⋊C₄	—	4	1	no	—
370	C₇×C₄⋊C₄	—	4	2	no	—
371	C₇×C₄⋊C₄	—	4	2	no	—
372	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
373	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
374	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
375	C₇×C₂²⋊C₄	—	2	4	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	4	2	no	—
378	C₇×C₂²⋊C₄	—	4	2	no	—
379	C₇×C₂²⋊C₄	—	4	1	no	—
380	C₇×C₂²⋊C₄	—	4	2	no	—
381	C₇×C₂²⋊C₄	—	4	2	no	—
382	C₇×C₂²⋊C₄	—	4	2	no	—
383	C₇×C₂²⋊C₄	—	4	2	no	—
384	C₇×C₂²⋊C₄	—	4	1	no	—
385	C₇×C₂²⋊C₄	—	4	1	no	—
386	C₇×C₂²⋊C₄	—	4	1	no	—
387	C₇×C₂²⋊C₄	—	4	1	no	—
388	C₇×C₂²⋊C₄	—	4	2	no	—
389	C₇×C₂²⋊C₄	—	4	2	no	—
390	C₇×C₂²⋊C₄	—	4	2	no	—
391	C₇×C₂²⋊C₄	—	4	2	no	—
392	C₇×C₂²⋊C₄	—	4	2	no	—
393	C₇×C₂²⋊C₄	—	4	2	no	—
394	C₇×C₂²⋊C₄	—	4	2	no	—
395	C₇×C₂²⋊C₄	—	4	2	no	—
396	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
397	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
398	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
399	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
400	C₄²×C₇	—	2	2	no	—
401	C₄²×C₇	—	2	2	no	—
402	C₄²×C₇	—	2	2	no	—
403	C₄²×C₇	—	2	4	no	—
404	C₄²×C₇	—	2	2	no	—
405	C₄²×C₇	—	4	1	no	—
406	C₄²×C₇	—	4	1	no	—
407	C₄²×C₇	—	4	2	no	—
408	C₄²×C₇	—	4	2	no	—
409	C₄²×C₇	—	4	2	no	—
410	C₄²×C₇	C₂²×C₄	1	8	yes	—
411	C₄²×C₇	C₂²×C₄	1	4	yes	—
412	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
413	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
414	#550	C₄×C₇	1	16	yes	complemented
415	C₂×#127	C₂²×C₇	1	1	yes	characteristic
416	C₂×#127	C₂²×C₇	1	2	yes	—
417	C₂×#121	C₂²×C₇	1	1	yes	characteristic
418	C₂×#121	C₂²×C₇	1	2	yes	—
419	C₂×#121	C₂²×C₇	1	2	yes	—
420	C₂×#121	C₂²×C₇	1	1	yes	characteristic
421	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
428	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
429	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
430	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
431	C₂×#117	C₂²×C₇	1	1	yes	characteristic
432	C₂×#117	C₂²×C₇	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
434	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
435	#391	C₂²×C₇	1	1	yes	characteristic
436	#391	C₂²×C₇	1	1	yes	characteristic
437	#391	C₂²×C₇	1	1	yes	characteristic
438	#391	C₂²×C₇	1	1	yes	characteristic
439	#390	C₂²×C₇	1	1	yes	characteristic
440	#390	C₂²×C₇	1	1	yes	characteristic
441	#390	C₂²×C₇	1	2	yes	—
442	#390	C₂²×C₇	1	1	yes	characteristic
443	#390	C₂²×C₇	1	2	yes	—
444	#390	C₂²×C₇	1	2	yes	—
445	#390	C₂²×C₇	1	1	yes	characteristic
446	#389	C₂²×C₇	1	1	yes	characteristic
447	#389	C₂²×C₇	1	1	yes	characteristic
448	#388	C₂²×C₇	1	2	yes	—
449	#388	C₂²×C₇	1	2	yes	—
450	#388	C₂²×C₇	1	2	yes	—
451	#388	C₂²×C₇	1	2	yes	—
452	#388	C₂²×C₇	1	2	yes	—
453	#388	C₂²×C₇	1	1	yes	characteristic
454	#388	C₂²×C₇	1	1	yes	characteristic
455	#387	C₂²×C₇	1	1	yes	characteristic
456	#387	C₂²×C₇	1	2	yes	—
457	#387	C₂²×C₇	1	2	yes	—
458	#387	C₂²×C₇	1	2	yes	—
459	#387	C₂²×C₇	1	2	yes	—
460	#387	C₂²×C₇	1	2	yes	—
461	#387	C₂²×C₇	1	1	yes	characteristic
462	#386	C₂²×C₇	1	2	yes	—
463	#386	C₂²×C₇	1	2	yes	—
464	#386	C₂²×C₇	1	2	yes	—
465	#386	C₂²×C₇	1	2	yes	—
466	#386	C₂²×C₇	1	2	yes	—
467	#386	C₂²×C₇	1	2	yes	—
468	#386	C₂²×C₇	1	2	yes	—
469	#386	C₂²×C₇	1	2	yes	—
470	#386	C₂²×C₇	1	2	yes	—
471	#386	C₂²×C₇	1	1	yes	characteristic
472	#386	C₂²×C₇	1	2	yes	—
473	#386	C₂²×C₇	1	2	yes	—
474	#386	C₂²×C₇	1	2	yes	—
475	#386	C₂²×C₇	1	2	yes	—
476	#386	C₂²×C₇	1	2	yes	—
477	#386	C₂²×C₇	1	2	yes	—
478	#386	C₂²×C₇	1	2	yes	—
479	#386	C₂²×C₇	1	2	yes	—
480	#386	C₂²×C₇	1	2	yes	—
481	#386	C₂²×C₇	1	2	yes	—
482	#386	C₂²×C₇	1	1	yes	characteristic
483	#385	C₂²×C₇	1	2	yes	—
484	#385	C₂²×C₇	1	2	yes	—
485	#385	C₂²×C₇	1	1	yes	characteristic
486	#385	C₂²×C₇	1	1	yes	characteristic
487	#383	C₂²×C₇	1	2	yes	—
488	#383	C₂²×C₇	1	2	yes	—
489	#382	C₂²×C₇	1	2	yes	—
490	#382	C₂²×C₇	1	1	yes	characteristic
491	#381	C₂²×C₇	1	2	yes	—
492	#381	C₂²×C₇	1	2	yes	—
493	#380	C₂²×C₇	1	2	yes	—
494	#380	C₂²×C₇	1	2	yes	—
495	#380	C₂²×C₇	1	1	yes	characteristic
496	#380	C₂²×C₇	1	1	yes	characteristic
497	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
500	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
503	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
505	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
506	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
508	#376	C₂²×C₇	1	1	yes	characteristic
509	#376	C₂²×C₇	1	2	yes	—
510	C₂×#95	C₂²×C₇	1	2	yes	—
511	C₂×#95	C₂²×C₇	1	2	yes	—
512	C₂³×C₇	—	2	2	no	—
513	C₂³×C₇	—	2	1	no	—
514	C₂³×C₇	—	2	1	no	—
515	C₂³×C₇	—	2	1	no	—
516	C₂³×C₇	—	2	1	no	—
517	C₂³×C₇	—	2	2	no	—
518	C₂³×C₇	—	2	2	no	—
519	C₂³×C₇	—	2	2	no	—
520	C₂³×C₇	—	2	2	no	—
521	C₂³×C₇	—	2	2	no	—
522	C₂³×C₇	—	2	1	no	—
523	C₂³×C₇	—	2	1	no	—
524	C₂³×C₇	—	2	2	no	—
525	C₂³×C₇	—	2	1	no	—
526	C₂³×C₇	—	2	1	no	—
527	C₂³×C₇	—	2	2	no	—
528	C₂³×C₇	—	2	1	no	—
529	C₂³×C₇	—	2	2	no	—
530	C₂³×C₇	—	2	1	no	—
531	C₂³×C₇	—	2	2	no	—
532	C₂³×C₇	—	2	1	no	—
533	C₂³×C₇	—	2	2	no	—
534	C₂³×C₇	—	2	1	no	—
535	C₂³×C₇	—	2	2	no	—
536	C₂³×C₇	C₂³×C₄	1	2	yes	—
537	C₂³×C₇	C₂³×C₄	1	2	yes	—
538	C₂³×C₇	C₂³×C₄	1	4	yes	—
539	C₂³×C₇	C₂³×C₄	1	4	yes	—
540	C₂³×C₇	C₂⁵	1	1	yes	characteristic
541	C₇×Q₈	—	2	8	no	—
542	C₇×D₄	—	2	8	no	—
543	C₇×D₄	—	2	8	no	—
544	C₇×D₄	—	4	4	no	—
545	C₇×D₄	—	4	8	no	—
546	C₇×D₄	—	4	8	no	—
547	C₇×D₄	—	4	8	no	—
548	C₇×D₄	—	4	8	no	—
549	C₇×D₄	—	4	8	no	—
550	C₇×D₄	—	4	8	no	—
551	C₂×C₄×C₇	—	2	1	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	1	no	—
555	C₂×C₄×C₇	—	2	1	no	—
556	C₂×C₄×C₇	—	2	1	no	—
557	C₂×C₄×C₇	—	2	1	no	—
558	C₂×C₄×C₇	—	2	2	no	—
559	C₂×C₄×C₇	—	2	2	no	—
560	C₂×C₄×C₇	—	2	2	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	8	no	—
566	C₂×C₄×C₇	—	2	8	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	1	no	—
571	C₂×C₄×C₇	—	2	1	no	—
572	C₂×C₄×C₇	—	2	2	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	2	no	—
576	C₂×C₄×C₇	—	2	2	no	—
577	C₂×C₄×C₇	—	2	2	no	—
578	C₂×C₄×C₇	—	2	2	no	—
579	C₂×C₄×C₇	—	2	1	no	—
580	C₂×C₄×C₇	—	2	2	no	—
581	C₂×C₄×C₇	—	2	1	no	—
582	C₂×C₄×C₇	—	2	1	no	—
583	C₂×C₄×C₇	—	2	2	no	—
584	C₂×C₄×C₇	—	2	1	no	—
585	C₂×C₄×C₇	—	2	2	no	—
586	C₂×C₄×C₇	—	2	1	no	—
587	C₂×C₄×C₇	—	2	1	no	—
588	C₂×C₄×C₇	—	2	1	no	—
589	C₂×C₄×C₇	—	2	1	no	—
590	C₂×C₄×C₇	—	2	1	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	2	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	1	no	—
595	C₂×C₄×C₇	—	2	2	no	—
596	C₂×C₄×C₇	—	2	1	no	—
597	C₂×C₄×C₇	—	2	2	no	—
598	C₂×C₄×C₇	—	2	1	no	—
599	C₂×C₄×C₇	—	2	1	no	—
600	C₂×C₄×C₇	—	4	8	no	—
601	C₂×C₄×C₇	—	4	8	no	—
602	C₂×C₄×C₇	—	4	4	no	—
603	C₂×C₄×C₇	—	4	4	no	—
604	C₂×C₄×C₇	—	8	4	no	—
605	C₂×C₄×C₇	—	8	4	no	—
606	C₂×C₄×C₇	—	8	4	no	—
607	C₂×C₄×C₇	—	8	4	no	—
608	C₂×C₄×C₇	—	8	4	no	—
609	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
610	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
611	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
612	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
613	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
614	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
615	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
616	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
617	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
618	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
619	C₂×#41	—	4	2	no	—
620	C₂×#41	—	4	2	no	—
621	C₂×#41	—	4	2	no	—
622	C₂×#41	—	4	2	no	—
623	C₂×#41	C₂×C₄×C₇	1	8	yes	complemented
624	C₂×#41	C₂×C₄×C₇	1	8	yes	complemented
625	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
626	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
627	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
628	C₂²×D₄	C₂³×C₇	1	2	yes	—
629	C₂²×D₄	C₂³×C₇	1	2	yes	—
630	C₂²×D₄	C₂³×C₇	1	2	yes	—
631	C₂²×D₄	C₂³×C₇	1	2	yes	—
632	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
633	C₂²×D₄	C₂³×C₇	1	2	yes	—
634	C₂²×D₄	C₂³×C₇	1	2	yes	—
635	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
637	C₂³×C₄	C₂³×C₇	1	2	yes	—
638	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₇	1	2	yes	—
640	C₂³×C₄	C₂³×C₇	1	2	yes	—
641	C₂³×C₄	C₂³×C₇	1	2	yes	—
642	C₂³×C₄	C₂³×C₇	1	2	yes	—
643	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₇	1	2	yes	—
645	C₂³×C₄	C₂³×C₇	1	2	yes	—
646	#127	C₂×C₄×C₇	1	8	yes	complemented
647	#127	C₂×C₄×C₇	1	16	yes	complemented
648	#121	C₂×C₄×C₇	1	8	yes	complemented
649	#121	C₂×C₄×C₇	1	8	yes	complemented
650	#121	C₂×C₄×C₇	1	16	yes	complemented
651	#121	C₂×C₄×C₇	1	16	yes	complemented
652	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
653	C₄×D₄	—	4	4	no	—
654	C₄×D₄	—	4	2	no	—
655	C₄×D₄	—	4	2	no	—
656	C₄×D₄	—	4	2	no	—
657	C₄×D₄	—	4	2	no	—
658	C₄×D₄	—	4	4	no	—
659	C₄×D₄	—	4	4	no	—
660	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
661	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
662	#117	—	4	2	no	—
663	#117	—	4	2	no	—
664	C₂×C₄⋊C₄	—	4	2	no	—
665	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
704	C₂×C₄²	—	4	2	no	—
705	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₇	1	2	yes	—
709	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₇	1	2	yes	—
711	C₂×C₄²	C₂³×C₇	1	2	yes	—
712	C₂×C₄²	C₂³×C₇	1	2	yes	—
713	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₇	1	2	yes	—
717	#95	C₂³×C₇	1	1	yes	characteristic
718	#95	C₂³×C₇	1	1	yes	characteristic
719	#95	C₂³×C₇	1	2	yes	—
720	#95	C₂³×C₇	1	2	yes	—
721	#95	C₂³×C₇	1	2	yes	—
722	#95	C₂³×C₇	1	2	yes	—
723	#95	C₂³×C₇	1	2	yes	—
724	#95	C₂³×C₇	1	2	yes	—
725	#95	C₂³×C₇	1	1	yes	characteristic
726	#95	C₂³×C₇	1	2	yes	—
727	#95	C₂³×C₇	1	1	yes	characteristic
728	#95	C₂³×C₇	1	2	yes	—
729	#95	C₂³×C₇	1	1	yes	characteristic
730	#95	C₂³×C₇	1	1	yes	characteristic
731	#95	C₂³×C₇	1	1	yes	characteristic
732	#95	C₂³×C₇	1	1	yes	characteristic
733	#95	C₂³×C₇	1	2	yes	—
734	#95	C₂³×C₇	1	2	yes	—
735	#95	C₂³×C₇	1	1	yes	characteristic
736	#95	C₂³×C₇	1	2	yes	—
737	#95	C₂³×C₇	1	2	yes	—
738	#95	C₂³×C₇	1	2	yes	—
739	#95	C₂³×C₇	1	2	yes	—
740	#95	C₂³×C₇	1	2	yes	—
741	#95	C₂³×C₇	1	1	yes	characteristic
742	#95	C₂³×C₇	1	2	yes	—
743	#95	C₂³×C₇	1	2	yes	—
744	C₂²×C₇	—	2	2	no	—
745	C₂²×C₇	—	2	2	no	—
746	C₂²×C₇	—	2	4	no	—
747	C₂²×C₇	—	2	4	no	—
748	C₂²×C₇	—	2	2	no	—
749	C₂²×C₇	—	2	4	no	—
750	C₂²×C₇	—	2	2	no	—
751	C₂²×C₇	—	2	4	no	—
752	C₂²×C₇	—	2	2	no	—
753	C₂²×C₇	—	2	4	no	—
754	C₂²×C₇	—	2	2	no	—
755	C₂²×C₇	—	2	4	no	—
756	C₂²×C₇	—	4	1	no	—
757	C₂²×C₇	—	4	1	no	—
758	C₂²×C₇	—	4	2	no	—
759	C₂²×C₇	—	4	2	no	—
760	C₂²×C₇	—	4	1	no	—
761	C₂²×C₇	—	4	2	no	—
762	C₂²×C₇	—	4	2	no	—
763	C₂²×C₇	—	4	1	no	—
764	C₂²×C₇	—	4	1	no	—
765	C₂²×C₇	—	4	2	no	—
766	C₂²×C₇	—	4	1	no	—
767	C₂²×C₇	—	4	2	no	—
768	C₂²×C₇	—	4	2	no	—
769	C₂²×C₇	—	4	1	no	—
770	C₂²×C₇	—	4	2	no	—
771	C₂²×C₇	—	4	1	no	—
772	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
773	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
775	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂²×C₇	#585	1	1	yes	characteristic
777	C₂²×C₇	#585	1	1	yes	characteristic
778	C₂²×C₇	#585	1	1	yes	characteristic
779	C₄×C₇	—	2	2	no	—
780	C₄×C₇	—	2	2	no	—
781	C₄×C₇	—	2	4	no	—
782	C₄×C₇	—	2	2	no	—
783	C₄×C₇	—	2	4	no	—
784	C₄×C₇	—	2	2	no	—
785	C₄×C₇	—	2	2	no	—
786	C₄×C₇	—	4	1	no	—
787	C₄×C₇	—	4	1	no	—
788	C₄×C₇	—	4	1	no	—
789	C₄×C₇	—	4	1	no	—
790	C₄×C₇	—	4	1	no	—
791	C₄×C₇	—	4	2	no	—
792	C₄×C₇	—	4	2	no	—
793	C₄×C₇	—	4	1	no	—
794	C₄×C₇	—	4	2	no	—
795	C₄×C₇	—	4	2	no	—
796	C₄×C₇	—	4	1	no	—
797	C₄×C₇	#518	1	4	yes	—
798	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
799	C₂⁴	C₂⁴×C₇	1	2	yes	—
800	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
801	C₂⁴	C₂⁴×C₇	1	2	yes	—
802	#41	—	4	16	no	—
803	#41	—	4	16	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	1	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	1	no	—
825	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
826	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
827	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
828	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
829	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
830	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
831	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
832	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
833	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	4	1	no	—
841	C₂²×C₄	—	4	1	no	—
842	C₂²×C₄	—	4	1	no	—
843	C₂²×C₄	—	4	1	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
864	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
865	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
866	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
867	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	4	2	no	—
892	C₄⋊C₄	—	4	1	no	—
893	C₄⋊C₄	—	4	1	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	1	no	—
897	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
898	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
899	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	4	1	no	—
903	C₂²⋊C₄	—	4	1	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	1	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	1	no	—
920	C₂²⋊C₄	—	4	1	no	—
921	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
922	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
923	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
924	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	4	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	4	1	no	—
931	C₄²	—	4	1	no	—
932	C₄²	—	4	2	no	—
933	C₄²	—	4	2	no	—
934	C₄²	—	4	2	no	—
935	C₄²	C₂²×C₄×C₇	1	8	yes	—
936	C₄²	C₂²×C₄×C₇	1	4	yes	—
937	C₂×C₇	—	4	2	no	—
938	C₂×C₇	—	4	2	no	—
939	C₂×C₇	—	4	4	no	—
940	C₂×C₇	—	4	4	no	—
941	C₂×C₇	C₂×#518	1	1	yes	characteristic
942	C₂×C₇	#3428	1	1	yes	characteristic
943	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
944	C₂×C₇	#3539	1	1	yes	characteristic
945	C₂×C₇	#3542	1	1	yes	characteristic
946	C₂×C₇	#3546	1	1	yes	characteristic
947	C₂×C₇	#3562	1	1	yes	characteristic
948	C₂³	—	2	2	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	1	no	—
972	C₂³	C₂³×C₄×C₇	1	2	yes	—
973	C₂³	C₂³×C₄×C₇	1	2	yes	—
974	C₂³	C₂³×C₄×C₇	1	4	yes	—
975	C₂³	C₂³×C₄×C₇	1	4	yes	—
976	C₂³	C₂⁵×C₇	1	1	yes	characteristic
977	Q₈	—	2	8	no	—
978	D₄	—	2	8	no	—
979	D₄	—	2	8	no	—
980	D₄	—	4	4	no	—
981	D₄	—	4	8	no	—
982	D₄	—	4	8	no	—
983	D₄	—	4	8	no	—
984	D₄	—	4	8	no	—
985	D₄	—	4	8	no	—
986	D₄	—	4	8	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	8	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	4	8	no	—
1037	C₂×C₄	—	4	8	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	8	4	no	—
1041	C₂×C₄	—	8	4	no	—
1042	C₂×C₄	—	8	4	no	—
1043	C₂×C₄	—	8	4	no	—
1044	C₂×C₄	—	8	4	no	—
1045	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1046	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1047	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1048	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
1049	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1050	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1051	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
1052	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1053	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1054	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1055	C₇	#34477	1	1	yes	characteristic, direct product factor, Sylow
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	4	no	—
1059	C₂²	—	2	4	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	4	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	4	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
1085	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1086	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1087	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1088	C₂²	C₇×#585	1	1	yes	characteristic
1089	C₂²	C₇×#585	1	1	yes	characteristic
1090	C₂²	C₇×#585	1	1	yes	characteristic
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	4	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	4	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	C₇×#518	1	4	yes	—
1110	C₂	—	4	2	no	—
1111	C₂	—	4	2	no	—
1112	C₂	—	4	4	no	—
1113	C₂	—	4	4	no	—
1114	C₂	C₂×C₇×#518	1	1	yes	characteristic
1115	C₂	C₇×#3428	1	1	yes	characteristic
1116	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1117	C₂	C₇×#3539	1	1	yes	characteristic
1118	C₂	C₇×#3542	1	1	yes	characteristic
1119	C₂	C₇×#3546	1	1	yes	characteristic
1120	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×#550	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×#2380	C₂	semidirect
3. C₇×#2377	C₂	semidirect
4. C₇×#2366	C₂	semidirect
5. C₇×#2364	C₂	semidirect
6. C₇×#2363	C₂	semidirect
7. C₇×#2361	C₂	semidirect
8. C₇×#2356	C₂	semidirect
9. C₇×#2353	C₂	semidirect
10. C₇×#2352	C₂	semidirect
11. C₇×#2339	C₂	semidirect
12. C₇×#2339	C₂	semidirect
13. C₇×#2333	C₂	semidirect
14. C₇×#2328	C₂	semidirect
15. C₇×#2328	C₂	semidirect
16. C₇×#2325	C₂	semidirect
17. C₇×#2324	C₂	semidirect
18. C₇×#2320	C₂	semidirect
19. C₇×#2318	C₂	semidirect
20. C₇×#2311	C₂	semidirect
21. C₄×C₇×#121	C₂	semidirect
22. C₇×#2297	C₂	semidirect
23. C₇×#2290	C₂	semidirect
26. C₇×#550	C₄	semidirect
124. #34477	C₇	direct (N × H)
129. C₂×C₇×#41	C₂×C₄	semidirect
130. C₂×C₇×#41	C₂×C₄	semidirect
152. C₇×#127	C₂×C₄	semidirect
153. C₇×#127	C₂×C₄	semidirect
154. C₇×#121	C₂×C₄	semidirect
155. C₇×#121	C₂×C₄	semidirect
156. C₇×#121	C₂×C₄	semidirect
157. C₇×#121	C₂×C₄	semidirect
158. C₄×C₇×Q₈	C₂×C₄	semidirect
166. C₄×C₇×D₄	C₂×C₄	semidirect
167. C₄×C₇×D₄	C₂×C₄	semidirect
251. #2380	C₂×C₇	semidirect
252. #2377	C₂×C₇	semidirect
253. #2366	C₂×C₇	semidirect
254. #2364	C₂×C₇	semidirect
255. #2363	C₂×C₇	semidirect
256. #2361	C₂×C₇	semidirect
257. #2356	C₂×C₇	semidirect
258. #2353	C₂×C₇	semidirect
259. #2352	C₂×C₇	semidirect
260. #2339	C₂×C₇	semidirect
261. #2339	C₂×C₇	semidirect
262. #2333	C₂×C₇	semidirect
263. #2328	C₂×C₇	semidirect
264. #2328	C₂×C₇	semidirect
265. #2325	C₂×C₇	semidirect
266. #2324	C₂×C₇	semidirect
267. #2320	C₂×C₇	semidirect
268. #2318	C₂×C₇	semidirect
269. #2311	C₂×C₇	semidirect
270. C₄×#121	C₂×C₇	semidirect
271. #2297	C₂×C₇	semidirect
272. #2290	C₂×C₇	semidirect
414. #550	C₄×C₇	semidirect
623. C₂×#41	C₂×C₄×C₇	semidirect
624. C₂×#41	C₂×C₄×C₇	semidirect
646. #127	C₂×C₄×C₇	semidirect
647. #127	C₂×C₄×C₇	semidirect
648. #121	C₂×C₄×C₇	semidirect
649. #121	C₂×C₄×C₇	semidirect
650. #121	C₂×C₄×C₇	semidirect
651. #121	C₂×C₄×C₇	semidirect
652. C₄×Q₈	C₂×C₄×C₇	semidirect
660. C₄×D₄	C₂×C₄×C₇	semidirect
661. C₄×D₄	C₂×C₄×C₇	semidirect
1055. C₇	#34477	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×#550	2
C₇×#2380	2
C₇×#2377	2
C₇×#2366	2
C₇×#2364	2
C₇×#2363	2
C₇×#2361	2
C₇×#2356	2
C₇×#2353	2
C₇×#2352	2
C₇×#2339	2
C₇×#2333	2
C₇×#2328	2
C₇×#2325	2
C₇×#2324	2
C₇×#2320	2
C₇×#2318	2
C₇×#2311	2
C₄×C₇×#121	2
C₇×#2297	2
C₇×#2290	2
#34477	7

Subgroups — C7×#34477 #13211693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34477 #13211693