Subgroups — C₇×#34974 #13212190

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2532	C₂	1	2	yes	maximal, complemented
2	C₇×#2529	C₂	1	2	yes	maximal, complemented
3	C₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2508	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2491	C₂	1	1	yes	maximal, characteristic
7	C₇×#2479	C₂	1	2	yes	maximal, complemented
8	C₇×#2474	C₂	1	2	yes	maximal, complemented
9	C₇×#2451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2426	C₂	1	1	yes	maximal, characteristic
12	C₇×#2423	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2396	C₂	1	2	yes	maximal, complemented
14	C₇×#2395	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#126	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×#124	C₂	1	2	yes	maximal, complemented
19	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic
21	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#126	C₂²	1	2	yes	—
26	C₂×C₇×#124	C₂²	1	1	yes	characteristic
27	C₂×C₇×#124	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
36	C₂×C₇×#117	C₂²	1	1	yes	characteristic
37	C₂×C₇×#117	C₂²	1	1	yes	characteristic
38	C₂×C₇×#117	C₂²	1	2	yes	—
39	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
40	C₇×#400	C₂²	1	2	yes	—
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#399	C₂²	1	2	yes	—
43	C₇×#399	C₂²	1	2	yes	—
44	C₇×#398	C₂²	1	2	yes	—
45	C₇×#398	C₂²	1	2	yes	—
46	C₇×#398	C₂²	1	2	yes	—
47	C₇×#397	C₂²	1	2	yes	—
48	C₇×#397	C₂²	1	2	yes	—
49	C₇×#397	C₂²	1	2	yes	—
50	C₇×#396	C₂²	1	2	yes	—
51	C₇×#396	C₂²	1	2	yes	—
52	C₇×#395	C₂²	1	2	yes	—
53	C₇×#394	C₂²	1	2	yes	—
54	C₇×#394	C₂²	1	2	yes	—
55	C₇×#393	C₂²	1	2	yes	—
56	C₇×#391	C₂²	1	1	yes	characteristic
57	C₇×#391	C₂²	1	1	yes	characteristic
58	C₇×#391	C₂²	1	2	yes	—
59	C₇×#391	C₂²	1	2	yes	—
60	C₇×#390	C₂²	1	2	yes	—
61	C₇×#390	C₂²	1	1	yes	characteristic
62	C₇×#390	C₂²	1	1	yes	characteristic
63	C₇×#390	C₂²	1	1	yes	characteristic
64	C₇×#390	C₂²	1	1	yes	characteristic
65	C₇×#389	C₂²	1	1	yes	characteristic
66	C₇×#389	C₂²	1	1	yes	characteristic
67	C₇×#389	C₂²	1	1	yes	characteristic
68	C₇×#389	C₂²	1	1	yes	characteristic
69	C₇×#389	C₂²	1	1	yes	characteristic
70	C₇×#389	C₂²	1	2	yes	—
71	C₇×#389	C₂²	1	1	yes	characteristic
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	—
75	C₇×#388	C₂²	1	2	yes	—
76	C₇×#388	C₂²	1	2	yes	—
77	C₇×#388	C₂²	1	2	yes	—
78	C₇×#388	C₂²	1	2	yes	—
79	C₇×#388	C₂²	1	2	yes	—
80	C₇×#388	C₂²	1	2	yes	—
81	C₇×#388	C₂²	1	2	yes	—
82	C₇×#388	C₂²	1	2	yes	—
83	C₇×#388	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×#386	C₂²	1	2	yes	—
89	C₇×#385	C₂²	1	2	yes	—
90	C₇×#384	C₂²	1	1	yes	characteristic
91	C₇×#383	C₂²	1	2	yes	—
92	C₇×#382	C₂²	1	1	yes	characteristic
93	C₇×#382	C₂²	1	2	yes	—
94	C₇×#380	C₂²	1	1	yes	characteristic
95	C₇×#380	C₂²	1	1	yes	characteristic
96	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
103	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₇×#376	C₂²	1	1	yes	characteristic
119	C₇×#376	C₂²	1	1	yes	characteristic
120	C₄³×C₇	C₂²	1	1	yes	characteristic
121	C₄³×C₇	C₂²	1	1	yes	characteristic
122	C₄³×C₇	C₂²	1	2	yes	—
123	#34974	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	2	yes	—
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₇×D₄	C₂³	1	2	yes	—
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	2	yes	—
132	C₇×C₄⋊Q₈	—	2	4	no	—
133	C₇×#126	—	2	8	no	—
134	C₇×#124	—	2	4	no	—
135	C₇×#124	—	2	8	no	—
136	C₇×C₂²⋊Q₈	—	2	4	no	—
137	C₇×#121	—	2	4	no	—
138	C₄×C₇×Q₈	—	2	4	no	—
139	C₄×C₇×Q₈	—	2	4	no	—
140	C₄×C₇×Q₈	—	2	4	no	—
141	C₄×C₇×Q₈	—	4	4	no	—
142	C₄×C₇×D₄	—	2	4	no	—
143	C₄×C₇×D₄	—	4	4	no	—
144	C₇×#117	—	2	4	no	—
145	C₇×#117	—	2	4	no	—
146	C₇×#117	—	4	4	no	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	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	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	—	2	4	no	—
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₇×#95	C₂³	1	1	yes	characteristic
214	C₇×#95	C₂³	1	1	yes	characteristic
215	C₇×#95	C₂³	1	1	yes	characteristic
216	C₇×#95	C₂³	1	1	yes	characteristic
217	C₇×#95	C₂³	1	1	yes	characteristic
218	C₇×#95	C₂³	1	1	yes	characteristic
219	C₇×#95	C₂³	1	1	yes	characteristic
220	C₇×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	2	yes	—
238	C₇×#95	C₂³	1	2	yes	—
239	#2532	C₂×C₇	1	2	yes	complemented
240	#2529	C₂×C₇	1	2	yes	complemented
241	#2512	C₂×C₇	1	1	yes	characteristic, complemented
242	#2508	C₂×C₇	1	1	yes	characteristic, complemented
243	#2495	C₂×C₇	1	1	yes	characteristic, complemented
244	#2491	C₂×C₇	1	1	yes	characteristic
245	#2479	C₂×C₇	1	2	yes	complemented
246	#2474	C₂×C₇	1	2	yes	complemented
247	#2451	C₂×C₇	1	1	yes	characteristic, complemented
248	#2448	C₂×C₇	1	1	yes	characteristic, complemented
249	#2426	C₂×C₇	1	1	yes	characteristic
250	#2423	C₂×C₇	1	1	yes	characteristic, complemented
251	#2396	C₂×C₇	1	2	yes	complemented
252	#2395	C₂×C₇	1	2	yes	complemented
253	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
254	C₄×#126	C₂×C₇	1	2	yes	complemented
255	C₄×#124	C₂×C₇	1	1	yes	characteristic, complemented
256	C₄×#124	C₂×C₇	1	2	yes	complemented
257	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
258	C₄×#121	C₂×C₇	1	1	yes	characteristic
259	#2293	C₂×C₇	1	1	yes	characteristic, complemented
260	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
261	C₄×#117	C₂×C₇	1	1	yes	characteristic, complemented
262	C₂⁴×C₇	C₂⁴	1	2	yes	—
263	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₇×Q₈	—	2	2	no	—
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	4	no	—
267	C₂×C₇×Q₈	—	2	4	no	—
268	C₂×C₇×Q₈	—	4	2	no	—
269	C₂×C₇×Q₈	#41	1	4	yes	—
270	C₂×C₇×D₄	—	2	4	no	—
271	C₂×C₇×D₄	—	2	2	no	—
272	C₂×C₇×D₄	—	2	4	no	—
273	C₂×C₇×D₄	—	2	2	no	—
274	C₂×C₇×D₄	—	2	2	no	—
275	C₂×C₇×D₄	—	4	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	4	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	4	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	2	no	—
287	C₂²×C₄×C₇	—	2	4	no	—
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	4	no	—
315	C₇×C₄⋊C₄	—	2	4	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	—	2	2	no	—
318	C₇×C₄⋊C₄	—	2	2	no	—
319	C₇×C₄⋊C₄	—	2	4	no	—
320	C₇×C₄⋊C₄	—	2	4	no	—
321	C₇×C₄⋊C₄	—	2	4	no	—
322	C₇×C₄⋊C₄	—	2	4	no	—
323	C₇×C₄⋊C₄	—	2	2	no	—
324	C₇×C₄⋊C₄	—	4	2	no	—
325	C₇×C₄⋊C₄	—	4	2	no	—
326	C₇×C₄⋊C₄	—	4	2	no	—
327	C₇×C₄⋊C₄	—	4	2	no	—
328	C₇×C₄⋊C₄	—	4	2	no	—
329	C₇×C₄⋊C₄	—	4	2	no	—
330	C₇×C₄⋊C₄	#41	1	4	yes	—
331	C₇×C₄⋊C₄	#41	1	4	yes	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	4	no	—
334	C₇×C₂²⋊C₄	—	2	2	no	—
335	C₇×C₂²⋊C₄	—	2	2	no	—
336	C₇×C₂²⋊C₄	—	2	4	no	—
337	C₇×C₂²⋊C₄	—	2	4	no	—
338	C₇×C₂²⋊C₄	—	2	4	no	—
339	C₇×C₂²⋊C₄	—	2	4	no	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	4	no	—
342	C₇×C₂²⋊C₄	—	2	4	no	—
343	C₇×C₂²⋊C₄	—	2	4	no	—
344	C₇×C₂²⋊C₄	—	2	4	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	4	2	no	—
347	C₇×C₂²⋊C₄	—	4	2	no	—
348	C₇×C₂²⋊C₄	—	4	2	no	—
349	C₇×C₂²⋊C₄	—	4	2	no	—
350	C₇×C₂²⋊C₄	#41	1	4	yes	—
351	C₄²×C₇	—	2	2	no	—
352	C₄²×C₇	—	2	2	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	—	2	2	no	—
355	C₄²×C₇	—	2	2	no	—
356	C₄²×C₇	—	2	2	no	—
357	C₄²×C₇	—	2	2	no	—
358	C₄²×C₇	—	2	4	no	—
359	C₄²×C₇	—	2	4	no	—
360	C₄²×C₇	—	2	2	no	—
361	C₄²×C₇	—	2	2	no	—
362	C₄²×C₇	—	2	4	no	—
363	C₄²×C₇	—	2	4	no	—
364	C₄²×C₇	—	2	2	no	—
365	C₄²×C₇	—	2	4	no	—
366	C₄²×C₇	—	2	2	no	—
367	C₄²×C₇	—	2	2	no	—
368	C₄²×C₇	—	2	4	no	—
369	C₄²×C₇	—	2	4	no	—
370	C₄²×C₇	—	2	2	no	—
371	C₄²×C₇	—	2	2	no	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	#41	1	4	yes	—
374	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
375	C₂×#126	C₂²×C₇	1	2	yes	—
376	C₂×#124	C₂²×C₇	1	1	yes	characteristic
377	C₂×#124	C₂²×C₇	1	2	yes	—
378	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
379	C₂×#121	C₂²×C₇	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
382	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
384	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
386	C₂×#117	C₂²×C₇	1	1	yes	characteristic
387	C₂×#117	C₂²×C₇	1	1	yes	characteristic
388	C₂×#117	C₂²×C₇	1	2	yes	—
389	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
390	#400	C₂²×C₇	1	2	yes	—
391	#400	C₂²×C₇	1	2	yes	—
392	#399	C₂²×C₇	1	2	yes	—
393	#399	C₂²×C₇	1	2	yes	—
394	#398	C₂²×C₇	1	2	yes	—
395	#398	C₂²×C₇	1	2	yes	—
396	#398	C₂²×C₇	1	2	yes	—
397	#397	C₂²×C₇	1	2	yes	—
398	#397	C₂²×C₇	1	2	yes	—
399	#397	C₂²×C₇	1	2	yes	—
400	#396	C₂²×C₇	1	2	yes	—
401	#396	C₂²×C₇	1	2	yes	—
402	#395	C₂²×C₇	1	2	yes	—
403	#394	C₂²×C₇	1	2	yes	—
404	#394	C₂²×C₇	1	2	yes	—
405	#393	C₂²×C₇	1	2	yes	—
406	#391	C₂²×C₇	1	2	yes	—
407	#391	C₂²×C₇	1	1	yes	characteristic
408	#391	C₂²×C₇	1	1	yes	characteristic
409	#391	C₂²×C₇	1	2	yes	—
410	#390	C₂²×C₇	1	2	yes	—
411	#390	C₂²×C₇	1	1	yes	characteristic
412	#390	C₂²×C₇	1	1	yes	characteristic
413	#390	C₂²×C₇	1	1	yes	characteristic
414	#390	C₂²×C₇	1	1	yes	characteristic
415	#389	C₂²×C₇	1	1	yes	characteristic
416	#389	C₂²×C₇	1	1	yes	characteristic
417	#389	C₂²×C₇	1	2	yes	—
418	#389	C₂²×C₇	1	1	yes	characteristic
419	#389	C₂²×C₇	1	1	yes	characteristic
420	#389	C₂²×C₇	1	1	yes	characteristic
421	#389	C₂²×C₇	1	1	yes	characteristic
422	#388	C₂²×C₇	1	2	yes	—
423	#388	C₂²×C₇	1	2	yes	—
424	#388	C₂²×C₇	1	2	yes	—
425	#388	C₂²×C₇	1	2	yes	—
426	#388	C₂²×C₇	1	2	yes	—
427	#388	C₂²×C₇	1	2	yes	—
428	#388	C₂²×C₇	1	2	yes	—
429	#388	C₂²×C₇	1	2	yes	—
430	#388	C₂²×C₇	1	2	yes	—
431	#388	C₂²×C₇	1	2	yes	—
432	#388	C₂²×C₇	1	2	yes	—
433	#388	C₂²×C₇	1	2	yes	—
434	#387	C₂²×C₇	1	2	yes	—
435	#387	C₂²×C₇	1	2	yes	—
436	#387	C₂²×C₇	1	2	yes	—
437	#387	C₂²×C₇	1	2	yes	—
438	#386	C₂²×C₇	1	2	yes	—
439	#385	C₂²×C₇	1	2	yes	—
440	#384	C₂²×C₇	1	1	yes	characteristic
441	#383	C₂²×C₇	1	2	yes	—
442	#382	C₂²×C₇	1	1	yes	characteristic
443	#382	C₂²×C₇	1	2	yes	—
444	#380	C₂²×C₇	1	1	yes	characteristic
445	#380	C₂²×C₇	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
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	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
461	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
463	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
466	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
467	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
468	#376	C₂²×C₇	1	1	yes	characteristic
469	#376	C₂²×C₇	1	1	yes	characteristic
470	C₄³	C₂²×C₇	1	2	yes	—
471	C₄³	C₂²×C₇	1	1	yes	characteristic
472	C₄³	C₂²×C₇	1	1	yes	characteristic
473	C₂³×C₇	—	2	1	no	—
474	C₂³×C₇	—	2	1	no	—
475	C₂³×C₇	—	2	1	no	—
476	C₂³×C₇	—	2	1	no	—
477	C₂³×C₇	—	2	1	no	—
478	C₂³×C₇	—	2	1	no	—
479	C₂³×C₇	—	2	2	no	—
480	C₂³×C₇	—	2	2	no	—
481	C₂³×C₇	—	2	2	no	—
482	C₂³×C₇	—	2	2	no	—
483	C₂³×C₇	—	2	2	no	—
484	C₂³×C₇	—	2	2	no	—
485	C₂³×C₇	—	2	2	no	—
486	C₂³×C₇	C₂×#41	1	2	yes	—
487	C₂³×C₇	C₂⁵	1	1	yes	characteristic
488	C₇×Q₈	—	2	8	no	—
489	C₇×Q₈	—	4	8	no	—
490	C₇×D₄	—	4	8	no	—
491	C₇×D₄	—	4	4	no	—
492	C₂×C₄×C₇	—	2	8	no	—
493	C₂×C₄×C₇	—	2	1	no	—
494	C₂×C₄×C₇	—	2	1	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	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	2	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	1	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	1	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	1	no	—
510	C₂×C₄×C₇	—	2	1	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	1	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	1	no	—
532	C₂×C₄×C₇	—	2	1	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	1	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	2	no	—
539	C₂×C₄×C₇	—	2	1	no	—
540	C₂×C₄×C₇	—	2	1	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	4	4	no	—
543	C₂×C₄×C₇	—	4	4	no	—
544	C₂×C₄×C₇	—	4	8	no	—
545	C₂×C₄×C₇	C₂×#41	1	2	yes	—
546	C₂×C₄×C₇	C₂×#41	1	2	yes	—
547	C₂×C₄×C₇	C₂×#41	1	2	yes	—
548	C₂×C₄×C₇	C₂×#41	1	2	yes	—
549	C₂×C₄×C₇	C₂×#41	1	4	yes	—
550	C₂×C₄×C₇	C₂×#41	1	2	yes	—
551	C₂×C₄×C₇	C₂×#41	1	4	yes	—
552	C₂×C₄×C₇	C₂×#41	1	2	yes	—
553	C₂×C₄×C₇	C₂×#41	1	2	yes	—
554	C₂×C₄×C₇	C₂×#41	1	2	yes	—
555	C₂×C₄×C₇	C₂×#41	1	2	yes	—
556	C₂×C₄×C₇	C₂×#41	1	2	yes	—
557	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
558	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
559	C₂²×Q₈	C₂³×C₇	1	2	yes	—
560	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₇	1	2	yes	—
563	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₇	1	2	yes	—
565	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
567	C₄⋊Q₈	—	2	4	no	—
568	#126	—	2	8	no	—
569	#124	—	2	4	no	—
570	#124	—	2	8	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	#121	—	2	4	no	—
573	C₄×Q₈	—	2	4	no	—
574	C₄×Q₈	—	2	4	no	—
575	C₄×Q₈	—	2	4	no	—
576	C₄×Q₈	—	4	4	no	—
577	C₄×D₄	—	2	4	no	—
578	C₄×D₄	—	4	4	no	—
579	#117	—	2	4	no	—
580	#117	—	2	4	no	—
581	#117	—	4	4	no	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
624	C₂×C₄²	—	2	4	no	—
625	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₇	1	2	yes	—
627	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₇	1	2	yes	—
632	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₇	1	2	yes	—
634	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₇	1	2	yes	—
637	C₂×C₄²	C₂³×C₇	1	2	yes	—
638	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₇	1	2	yes	—
641	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
648	#95	C₂³×C₇	1	1	yes	characteristic
649	#95	C₂³×C₇	1	1	yes	characteristic
650	#95	C₂³×C₇	1	1	yes	characteristic
651	#95	C₂³×C₇	1	1	yes	characteristic
652	#95	C₂³×C₇	1	1	yes	characteristic
653	#95	C₂³×C₇	1	1	yes	characteristic
654	#95	C₂³×C₇	1	1	yes	characteristic
655	#95	C₂³×C₇	1	1	yes	characteristic
656	#95	C₂³×C₇	1	2	yes	—
657	#95	C₂³×C₇	1	2	yes	—
658	#95	C₂³×C₇	1	2	yes	—
659	#95	C₂³×C₇	1	2	yes	—
660	#95	C₂³×C₇	1	2	yes	—
661	#95	C₂³×C₇	1	2	yes	—
662	#95	C₂³×C₇	1	2	yes	—
663	#95	C₂³×C₇	1	2	yes	—
664	#95	C₂³×C₇	1	2	yes	—
665	#95	C₂³×C₇	1	2	yes	—
666	#95	C₂³×C₇	1	2	yes	—
667	#95	C₂³×C₇	1	2	yes	—
668	#95	C₂³×C₇	1	2	yes	—
669	#95	C₂³×C₇	1	2	yes	—
670	#95	C₂³×C₇	1	2	yes	—
671	#95	C₂³×C₇	1	2	yes	—
672	#95	C₂³×C₇	1	2	yes	—
673	#95	C₂³×C₇	1	2	yes	—
674	C₂²×C₇	—	2	2	no	—
675	C₂²×C₇	—	2	2	no	—
676	C₂²×C₇	—	2	2	no	—
677	C₂²×C₇	—	4	1	no	—
678	C₂²×C₇	—	4	1	no	—
679	C₂²×C₇	—	4	1	no	—
680	C₂²×C₇	—	4	1	no	—
681	C₂²×C₇	—	4	2	no	—
682	C₂²×C₇	—	4	2	no	—
683	C₂²×C₇	—	4	2	no	—
684	C₂²×C₇	—	4	2	no	—
685	C₂²×C₇	—	4	2	no	—
686	C₂²×C₇	—	4	2	no	—
687	C₂²×C₇	—	4	2	no	—
688	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
689	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
690	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
691	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
692	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
693	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
695	C₄×C₇	—	2	4	no	—
696	C₄×C₇	—	2	2	no	—
697	C₄×C₇	—	2	2	no	—
698	C₄×C₇	—	2	4	no	—
699	C₄×C₇	—	2	2	no	—
700	C₄×C₇	—	2	2	no	—
701	C₄×C₇	—	2	2	no	—
702	C₄×C₇	—	2	2	no	—
703	C₄×C₇	—	4	1	no	—
704	C₄×C₇	—	4	2	no	—
705	C₄×C₇	—	4	1	no	—
706	C₄×C₇	—	4	2	no	—
707	C₄×C₇	—	4	1	no	—
708	C₄×C₇	—	4	2	no	—
709	C₄×C₇	—	4	1	no	—
710	C₄×C₇	—	4	1	no	—
711	C₄×C₇	—	4	1	no	—
712	C₄×C₇	—	4	2	no	—
713	C₄×C₇	—	4	2	no	—
714	C₄×C₇	#529	1	4	yes	—
715	C₄×C₇	#542	1	4	yes	—
716	C₂⁴	C₂⁴×C₇	1	2	yes	—
717	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	4	2	no	—
723	C₂×Q₈	C₇×#41	1	4	yes	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	C₇×#41	1	4	yes	—
785	C₄⋊C₄	C₇×#41	1	4	yes	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	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	C₇×#41	1	4	yes	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	4	no	—
813	C₄²	—	2	4	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	4	no	—
817	C₄²	—	2	4	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	4	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	4	no	—
823	C₄²	—	2	4	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	C₇×#41	1	4	yes	—
828	C₂×C₇	—	4	2	no	—
829	C₂×C₇	—	8	2	no	—
830	C₂×C₇	C₂×#529	1	1	yes	characteristic
831	C₂×C₇	#3444	1	1	yes	characteristic
832	C₂×C₇	C₂×#542	1	1	yes	characteristic
833	C₂×C₇	#3481	1	1	yes	characteristic
834	C₂×C₇	#3482	1	1	yes	characteristic
835	C₂×C₇	#3482	1	1	yes	characteristic
836	C₂×C₇	#3483	1	1	yes	characteristic
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	C₂×C₇×#41	1	2	yes	—
851	C₂³	C₂⁵×C₇	1	1	yes	characteristic
852	Q₈	—	2	8	no	—
853	Q₈	—	4	8	no	—
854	D₄	—	4	8	no	—
855	D₄	—	4	4	no	—
856	C₂×C₄	—	2	8	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	8	no	—
909	C₂×C₄	C₂×C₇×#41	1	2	yes	—
910	C₂×C₄	C₂×C₇×#41	1	2	yes	—
911	C₂×C₄	C₂×C₇×#41	1	2	yes	—
912	C₂×C₄	C₂×C₇×#41	1	2	yes	—
913	C₂×C₄	C₂×C₇×#41	1	4	yes	—
914	C₂×C₄	C₂×C₇×#41	1	2	yes	—
915	C₂×C₄	C₂×C₇×#41	1	4	yes	—
916	C₂×C₄	C₂×C₇×#41	1	2	yes	—
917	C₂×C₄	C₂×C₇×#41	1	2	yes	—
918	C₂×C₄	C₂×C₇×#41	1	2	yes	—
919	C₂×C₄	C₂×C₇×#41	1	2	yes	—
920	C₂×C₄	C₂×C₇×#41	1	2	yes	—
921	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
922	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
923	C₇	#34974	1	1	yes	characteristic, direct product factor, Sylow
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	2	no	—
938	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
939	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
940	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
941	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
942	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
943	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
944	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	C₇×#529	1	4	yes	—
965	C₄	C₇×#542	1	4	yes	—
966	C₂	—	4	2	no	—
967	C₂	—	8	2	no	—
968	C₂	C₂×C₇×#529	1	1	yes	characteristic
969	C₂	C₇×#3444	1	1	yes	characteristic
970	C₂	C₂×C₇×#542	1	1	yes	characteristic
971	C₂	C₇×#3481	1	1	yes	characteristic
972	C₂	C₇×#3482	1	1	yes	characteristic
973	C₂	C₇×#3482	1	1	yes	characteristic
974	C₂	C₇×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2532	C₂	semidirect
2. C₇×#2529	C₂	semidirect
3. C₇×#2512	C₂	semidirect
4. C₇×#2508	C₂	semidirect
5. C₇×#2495	C₂	semidirect
7. C₇×#2479	C₂	semidirect
8. C₇×#2474	C₂	semidirect
9. C₇×#2451	C₂	semidirect
10. C₇×#2448	C₂	semidirect
12. C₇×#2423	C₂	semidirect
13. C₇×#2396	C₂	semidirect
14. C₇×#2395	C₂	semidirect
15. C₄×C₇×C₄⋊Q₈	C₂	semidirect
16. C₄×C₇×#126	C₂	semidirect
17. C₄×C₇×#124	C₂	semidirect
18. C₄×C₇×#124	C₂	semidirect
19. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
21. C₇×#2293	C₂	semidirect
22. C₄²×C₇×Q₈	C₂	semidirect
23. C₄×C₇×#117	C₂	semidirect
123. #34974	C₇	direct (N × H)
239. #2532	C₂×C₇	semidirect
240. #2529	C₂×C₇	semidirect
241. #2512	C₂×C₇	semidirect
242. #2508	C₂×C₇	semidirect
243. #2495	C₂×C₇	semidirect
245. #2479	C₂×C₇	semidirect
246. #2474	C₂×C₇	semidirect
247. #2451	C₂×C₇	semidirect
248. #2448	C₂×C₇	semidirect
250. #2423	C₂×C₇	semidirect
251. #2396	C₂×C₇	semidirect
252. #2395	C₂×C₇	semidirect
253. C₄×C₄⋊Q₈	C₂×C₇	semidirect
254. C₄×#126	C₂×C₇	semidirect
255. C₄×#124	C₂×C₇	semidirect
256. C₄×#124	C₂×C₇	semidirect
257. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
259. #2293	C₂×C₇	semidirect
260. C₄²×Q₈	C₂×C₇	semidirect
261. C₄×#117	C₂×C₇	semidirect
923. C₇	#34974	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2532	2
C₇×#2529	2
C₇×#2512	2
C₇×#2508	2
C₇×#2495	2
C₇×#2491	2
C₇×#2479	2
C₇×#2474	2
C₇×#2451	2
C₇×#2448	2
C₇×#2426	2
C₇×#2423	2
C₇×#2396	2
C₇×#2395	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#126	2
C₄×C₇×#124	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#121	2
C₇×#2293	2
C₄²×C₇×Q₈	2
C₄×C₇×#117	2
#34974	7

Subgroups — C7×#34974 #13212190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34974 #13212190