Subgroups — C₇×#35025 #13212241

Order 1792.

2176 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2861	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2651	C₂	1	2	yes	maximal, complemented
6	C₇×#2648	C₂	1	2	yes	maximal, complemented
7	C₇×#2593	C₂	1	2	yes	maximal, complemented
8	C₇×#2554	C₂	1	2	yes	maximal, complemented
9	C₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2480	C₂	1	2	yes	maximal, complemented
12	C₇×#2448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2418	C₂	1	2	yes	maximal, complemented
17	C₇×#2417	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2408	C₂	1	1	yes	maximal, characteristic
19	C₇×#2321	C₂	1	2	yes	maximal, complemented
20	C₇×#2312	C₂	1	2	yes	maximal, complemented
21	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₇×#126	C₂²	1	2	yes	complemented
26	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×#124	C₂²	1	1	yes	characteristic
29	C₂×C₇×#123	C₂²	1	2	yes	complemented
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₇×#121	C₂²	1	1	yes	characteristic
33	C₂×C₇×#121	C₂²	1	1	yes	characteristic
34	C₂×C₇×#120	C₂²	1	2	yes	—
35	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
39	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
44	C₇×#400	C₂²	1	2	yes	complemented
45	C₇×#399	C₂²	1	2	yes	complemented
46	C₇×#398	C₂²	1	2	yes	complemented
47	C₇×#398	C₂²	1	2	yes	complemented
48	C₇×#397	C₂²	1	2	yes	complemented
49	C₇×#397	C₂²	1	2	yes	complemented
50	C₇×#397	C₂²	1	2	yes	complemented
51	C₇×#397	C₂²	1	2	yes	complemented
52	C₇×#396	C₂²	1	2	yes	complemented
53	C₇×#396	C₂²	1	2	yes	complemented
54	C₇×#394	C₂²	1	2	yes	—
55	C₇×#394	C₂²	1	2	yes	—
56	C₇×#394	C₂²	1	2	yes	—
57	C₇×#394	C₂²	1	2	yes	complemented
58	C₇×#394	C₂²	1	2	yes	complemented
59	C₇×#392	C₂²	1	2	yes	—
60	C₇×#391	C₂²	1	1	yes	characteristic, complemented
61	C₇×#391	C₂²	1	1	yes	characteristic, complemented
62	C₇×#390	C₂²	1	2	yes	—
63	C₇×#390	C₂²	1	1	yes	characteristic
64	C₇×#390	C₂²	1	1	yes	characteristic
65	C₇×#390	C₂²	1	1	yes	characteristic
66	C₇×#390	C₂²	1	1	yes	characteristic
67	C₇×#390	C₂²	1	1	yes	characteristic
68	C₇×#390	C₂²	1	1	yes	characteristic
69	C₇×#390	C₂²	1	2	yes	—
70	C₇×#390	C₂²	1	1	yes	characteristic
71	C₇×#390	C₂²	1	1	yes	characteristic
72	C₇×#390	C₂²	1	2	yes	complemented
73	C₇×#390	C₂²	1	2	yes	complemented
74	C₇×#389	C₂²	1	1	yes	characteristic, complemented
75	C₇×#389	C₂²	1	1	yes	characteristic, complemented
76	C₇×#389	C₂²	1	1	yes	characteristic, complemented
77	C₇×#389	C₂²	1	1	yes	characteristic, complemented
78	C₇×#388	C₂²	1	2	yes	complemented
79	C₇×#388	C₂²	1	2	yes	complemented
80	C₇×#388	C₂²	1	2	yes	complemented
81	C₇×#388	C₂²	1	2	yes	complemented
82	C₇×#388	C₂²	1	2	yes	complemented
83	C₇×#388	C₂²	1	2	yes	complemented
84	C₇×#388	C₂²	1	2	yes	complemented
85	C₇×#388	C₂²	1	2	yes	complemented
86	C₇×#388	C₂²	1	2	yes	complemented
87	C₇×#388	C₂²	1	2	yes	complemented
88	C₇×#388	C₂²	1	2	yes	complemented
89	C₇×#388	C₂²	1	2	yes	complemented
90	C₇×#388	C₂²	1	2	yes	complemented
91	C₇×#388	C₂²	1	2	yes	complemented
92	C₇×#388	C₂²	1	2	yes	complemented
93	C₇×#388	C₂²	1	2	yes	complemented
94	C₇×#388	C₂²	1	2	yes	complemented
95	C₇×#387	C₂²	1	2	yes	complemented
96	C₇×#386	C₂²	1	2	yes	—
97	C₇×#386	C₂²	1	2	yes	complemented
98	C₇×#386	C₂²	1	2	yes	complemented
99	C₇×#386	C₂²	1	2	yes	complemented
100	C₇×#385	C₂²	1	2	yes	—
101	C₇×#385	C₂²	1	2	yes	—
102	C₇×#382	C₂²	1	1	yes	characteristic, complemented
103	C₇×#380	C₂²	1	1	yes	characteristic
104	C₇×#380	C₂²	1	2	yes	—
105	C₇×#380	C₂²	1	2	yes	—
106	C₇×#380	C₂²	1	1	yes	characteristic, complemented
107	C₇×#379	C₂²	1	2	yes	—
108	C₇×#379	C₂²	1	2	yes	—
109	C₇×#379	C₂²	1	2	yes	—
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
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	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
122	C₄³×C₇	C₂²	1	1	yes	characteristic, complemented
123	#35025	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂⁵×C₇	C₂³	1	2	yes	—
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₇×D₄	—	2	4	no	—
127	C₂²×C₇×D₄	—	4	2	no	—
128	C₂²×C₇×D₄	—	4	2	no	—
129	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
133	C₂²×C₇×D₄	C₂³	1	2	yes	—
134	C₂²×C₇×D₄	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₇×#126	—	4	4	no	—
143	C₇×#125	—	4	2	no	—
144	C₇×#124	—	4	2	no	—
145	C₇×#124	—	4	2	no	—
146	C₇×#123	—	4	4	no	—
147	C₇×C₂²⋊Q₈	—	2	4	no	—
148	C₇×C₂²⋊Q₈	—	4	2	no	—
149	C₇×#121	—	4	2	no	—
150	C₇×#121	—	4	2	no	—
151	C₇×#120	—	2	8	no	—
152	C₄×C₇×Q₈	—	4	2	no	—
153	C₄×C₇×D₄	—	2	4	no	—
154	C₄×C₇×D₄	—	2	4	no	—
155	C₄×C₇×D₄	—	2	4	no	—
156	C₂×C₇×C₄⋊C₄	—	4	2	no	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
176	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
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	1	yes	characteristic
184	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
189	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	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	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	2	yes	—
208	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₄²×C₇	—	4	2	no	—
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	1	yes	characteristic
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	1	yes	characteristic
219	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₇	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	1	yes	characteristic
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	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	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	2	yes	—
243	C₇×#95	C₂³	1	2	yes	—
244	C₇×#95	C₂³	1	2	yes	—
245	#2861	C₂×C₇	1	1	yes	characteristic, complemented
246	#2860	C₂×C₇	1	1	yes	characteristic, complemented
247	#2854	C₂×C₇	1	1	yes	characteristic, complemented
248	#2850	C₂×C₇	1	1	yes	characteristic, complemented
249	#2651	C₂×C₇	1	2	yes	complemented
250	#2648	C₂×C₇	1	2	yes	complemented
251	#2593	C₂×C₇	1	2	yes	complemented
252	#2554	C₂×C₇	1	2	yes	complemented
253	#2513	C₂×C₇	1	1	yes	characteristic, complemented
254	#2490	C₂×C₇	1	1	yes	characteristic, complemented
255	#2480	C₂×C₇	1	2	yes	complemented
256	#2448	C₂×C₇	1	1	yes	characteristic, complemented
257	#2442	C₂×C₇	1	1	yes	characteristic, complemented
258	#2435	C₂×C₇	1	1	yes	characteristic, complemented
259	#2426	C₂×C₇	1	1	yes	characteristic, complemented
260	#2418	C₂×C₇	1	2	yes	complemented
261	#2417	C₂×C₇	1	1	yes	characteristic, complemented
262	#2408	C₂×C₇	1	1	yes	characteristic
263	#2321	C₂×C₇	1	2	yes	complemented
264	#2312	C₂×C₇	1	2	yes	complemented
265	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
266	C₂×#390	C₂×C₇	1	1	yes	characteristic, complemented
267	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
268	C₂⁴×C₇	—	2	4	no	—
269	C₂⁴×C₇	—	2	4	no	—
270	C₂⁴×C₇	—	2	4	no	—
271	C₂⁴×C₇	—	4	2	no	—
272	C₂⁴×C₇	—	4	2	no	—
273	C₂⁴×C₇	—	4	2	no	—
274	C₂⁴×C₇	—	4	2	no	—
275	C₂⁴×C₇	C₂⁴	1	2	yes	—
276	C₂⁴×C₇	C₂⁴	1	2	yes	—
277	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
278	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
279	C₂×C₇×Q₈	—	2	2	no	—
280	C₂×C₇×Q₈	—	2	2	no	—
281	C₂×C₇×Q₈	—	2	2	no	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	2	2	no	—
284	C₂×C₇×D₄	—	2	4	no	—
285	C₂×C₇×D₄	—	2	4	no	—
286	C₂×C₇×D₄	—	2	4	no	—
287	C₂×C₇×D₄	—	2	2	no	—
288	C₂×C₇×D₄	—	2	2	no	—
289	C₂×C₇×D₄	—	2	2	no	—
290	C₂×C₇×D₄	—	2	2	no	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	2	no	—
293	C₂×C₇×D₄	—	4	2	no	—
294	C₂×C₇×D₄	—	4	2	no	—
295	C₂×C₇×D₄	—	4	16	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	#41	1	4	yes	—
301	C₂²×C₄×C₇	—	2	2	no	—
302	C₂²×C₄×C₇	—	2	2	no	—
303	C₂²×C₄×C₇	—	2	2	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	4	no	—
306	C₂²×C₄×C₇	—	2	2	no	—
307	C₂²×C₄×C₇	—	2	2	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
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	—	4	1	no	—
313	C₂²×C₄×C₇	—	4	1	no	—
314	C₂²×C₄×C₇	—	4	1	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	2	no	—
319	C₂²×C₄×C₇	—	4	2	no	—
320	C₂²×C₄×C₇	#41	1	4	yes	—
321	C₂²×C₄×C₇	#41	1	4	yes	—
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
329	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	4	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	2	no	—
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	—	2	4	no	—
351	C₇×C₄⋊C₄	—	4	2	no	—
352	C₇×C₄⋊C₄	—	4	2	no	—
353	C₇×C₄⋊C₄	—	4	2	no	—
354	C₇×C₄⋊C₄	—	4	2	no	—
355	C₇×C₄⋊C₄	—	4	2	no	—
356	C₇×C₄⋊C₄	—	4	2	no	—
357	C₇×C₄⋊C₄	—	4	2	no	—
358	C₇×C₄⋊C₄	—	4	2	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	2	2	no	—
361	C₇×C₂²⋊C₄	—	2	2	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	—	2	4	no	—
364	C₇×C₂²⋊C₄	—	2	4	no	—
365	C₇×C₂²⋊C₄	—	2	4	no	—
366	C₇×C₂²⋊C₄	—	2	4	no	—
367	C₇×C₂²⋊C₄	—	2	4	no	—
368	C₇×C₂²⋊C₄	—	2	4	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	4	no	—
372	C₇×C₂²⋊C₄	—	2	4	no	—
373	C₇×C₂²⋊C₄	—	2	4	no	—
374	C₇×C₂²⋊C₄	—	2	4	no	—
375	C₇×C₂²⋊C₄	—	4	2	no	—
376	C₇×C₂²⋊C₄	—	4	2	no	—
377	C₇×C₂²⋊C₄	—	4	2	no	—
378	C₇×C₂²⋊C₄	—	4	2	no	—
379	C₇×C₂²⋊C₄	—	4	2	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	2	no	—
385	C₇×C₂²⋊C₄	—	4	2	no	—
386	C₇×C₂²⋊C₄	—	4	2	no	—
387	C₇×C₂²⋊C₄	—	4	2	no	—
388	C₇×C₂²⋊C₄	—	4	2	no	—
389	C₇×C₂²⋊C₄	—	4	2	no	—
390	C₇×C₂²⋊C₄	—	4	2	no	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	—	2	2	no	—
396	C₄²×C₇	—	2	2	no	—
397	C₄²×C₇	—	2	2	no	—
398	C₄²×C₇	—	2	2	no	—
399	C₄²×C₇	—	4	1	no	—
400	C₄²×C₇	—	4	1	no	—
401	C₄²×C₇	—	4	1	no	—
402	C₄²×C₇	—	4	1	no	—
403	C₄²×C₇	—	4	2	no	—
404	C₄²×C₇	—	4	1	no	—
405	C₄²×C₇	—	4	2	no	—
406	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
407	C₂×#126	C₂²×C₇	1	2	yes	complemented
408	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
409	C₂×#124	C₂²×C₇	1	1	yes	characteristic
410	C₂×#124	C₂²×C₇	1	1	yes	characteristic
411	C₂×#123	C₂²×C₇	1	2	yes	complemented
412	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
414	C₂×#121	C₂²×C₇	1	1	yes	characteristic
415	C₂×#121	C₂²×C₇	1	1	yes	characteristic
416	C₂×#120	C₂²×C₇	1	2	yes	—
417	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
418	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
421	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
423	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
424	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
425	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
426	#400	C₂²×C₇	1	2	yes	complemented
427	#399	C₂²×C₇	1	2	yes	complemented
428	#398	C₂²×C₇	1	2	yes	complemented
429	#398	C₂²×C₇	1	2	yes	complemented
430	#397	C₂²×C₇	1	2	yes	complemented
431	#397	C₂²×C₇	1	2	yes	complemented
432	#397	C₂²×C₇	1	2	yes	complemented
433	#397	C₂²×C₇	1	2	yes	complemented
434	#396	C₂²×C₇	1	2	yes	complemented
435	#396	C₂²×C₇	1	2	yes	complemented
436	#394	C₂²×C₇	1	2	yes	—
437	#394	C₂²×C₇	1	2	yes	—
438	#394	C₂²×C₇	1	2	yes	—
439	#394	C₂²×C₇	1	2	yes	complemented
440	#394	C₂²×C₇	1	2	yes	complemented
441	#392	C₂²×C₇	1	2	yes	—
442	#391	C₂²×C₇	1	1	yes	characteristic, complemented
443	#391	C₂²×C₇	1	1	yes	characteristic, complemented
444	#390	C₂²×C₇	1	2	yes	—
445	#390	C₂²×C₇	1	1	yes	characteristic
446	#390	C₂²×C₇	1	1	yes	characteristic
447	#390	C₂²×C₇	1	1	yes	characteristic
448	#390	C₂²×C₇	1	1	yes	characteristic
449	#390	C₂²×C₇	1	1	yes	characteristic
450	#390	C₂²×C₇	1	1	yes	characteristic
451	#390	C₂²×C₇	1	2	yes	—
452	#390	C₂²×C₇	1	1	yes	characteristic
453	#390	C₂²×C₇	1	1	yes	characteristic
454	#390	C₂²×C₇	1	2	yes	complemented
455	#390	C₂²×C₇	1	2	yes	complemented
456	#389	C₂²×C₇	1	1	yes	characteristic, complemented
457	#389	C₂²×C₇	1	1	yes	characteristic, complemented
458	#389	C₂²×C₇	1	1	yes	characteristic, complemented
459	#389	C₂²×C₇	1	1	yes	characteristic, complemented
460	#388	C₂²×C₇	1	2	yes	complemented
461	#388	C₂²×C₇	1	2	yes	complemented
462	#388	C₂²×C₇	1	2	yes	complemented
463	#388	C₂²×C₇	1	2	yes	complemented
464	#388	C₂²×C₇	1	2	yes	complemented
465	#388	C₂²×C₇	1	2	yes	complemented
466	#388	C₂²×C₇	1	2	yes	complemented
467	#388	C₂²×C₇	1	2	yes	complemented
468	#388	C₂²×C₇	1	2	yes	complemented
469	#388	C₂²×C₇	1	2	yes	complemented
470	#388	C₂²×C₇	1	2	yes	complemented
471	#388	C₂²×C₇	1	2	yes	complemented
472	#388	C₂²×C₇	1	2	yes	complemented
473	#388	C₂²×C₇	1	2	yes	complemented
474	#388	C₂²×C₇	1	2	yes	complemented
475	#388	C₂²×C₇	1	2	yes	complemented
476	#388	C₂²×C₇	1	2	yes	complemented
477	#387	C₂²×C₇	1	2	yes	complemented
478	#386	C₂²×C₇	1	2	yes	—
479	#386	C₂²×C₇	1	2	yes	complemented
480	#386	C₂²×C₇	1	2	yes	complemented
481	#386	C₂²×C₇	1	2	yes	complemented
482	#385	C₂²×C₇	1	2	yes	—
483	#385	C₂²×C₇	1	2	yes	—
484	#382	C₂²×C₇	1	1	yes	characteristic, complemented
485	#380	C₂²×C₇	1	2	yes	—
486	#380	C₂²×C₇	1	2	yes	—
487	#380	C₂²×C₇	1	1	yes	characteristic
488	#380	C₂²×C₇	1	1	yes	characteristic, complemented
489	#379	C₂²×C₇	1	2	yes	—
490	#379	C₂²×C₇	1	2	yes	—
491	#379	C₂²×C₇	1	2	yes	—
492	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
493	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
494	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
495	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
496	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
497	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
498	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
502	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
503	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
504	C₄³	C₂²×C₇	1	1	yes	characteristic, complemented
505	C₂³×C₇	—	2	1	no	—
506	C₂³×C₇	—	2	1	no	—
507	C₂³×C₇	—	2	1	no	—
508	C₂³×C₇	—	2	1	no	—
509	C₂³×C₇	—	2	1	no	—
510	C₂³×C₇	—	2	1	no	—
511	C₂³×C₇	—	2	1	no	—
512	C₂³×C₇	—	2	1	no	—
513	C₂³×C₇	—	2	1	no	—
514	C₂³×C₇	—	2	1	no	—
515	C₂³×C₇	—	2	2	no	—
516	C₂³×C₇	—	2	2	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	2	no	—
523	C₂³×C₇	—	2	2	no	—
524	C₂³×C₇	—	2	2	no	—
525	C₂³×C₇	—	2	2	no	—
526	C₂³×C₇	—	2	2	no	—
527	C₂³×C₇	—	2	2	no	—
528	C₂³×C₇	—	2	2	no	—
529	C₂³×C₇	—	4	8	no	—
530	C₂³×C₇	—	4	8	no	—
531	C₂³×C₇	—	4	8	no	—
532	C₂³×C₇	—	8	4	no	—
533	C₂³×C₇	—	8	4	no	—
534	C₂³×C₇	—	8	4	no	—
535	C₂³×C₇	—	8	4	no	—
536	C₂³×C₇	C₂×#41	1	2	yes	—
537	C₂³×C₇	C₂×#41	1	2	yes	—
538	C₂³×C₇	C₂×#41	1	2	yes	—
539	C₂³×C₇	C₂×#41	1	2	yes	—
540	C₂³×C₇	C₂⁵	1	1	yes	characteristic
541	C₇×Q₈	—	4	4	no	—
542	C₇×D₄	—	2	8	no	—
543	C₇×D₄	—	4	8	no	—
544	C₇×D₄	—	4	4	no	—
545	C₇×D₄	—	4	4	no	—
546	C₇×D₄	—	8	4	no	—
547	C₇×D₄	—	8	4	no	—
548	C₂×C₄×C₇	—	2	1	no	—
549	C₂×C₄×C₇	—	2	1	no	—
550	C₂×C₄×C₇	—	2	1	no	—
551	C₂×C₄×C₇	—	2	1	no	—
552	C₂×C₄×C₇	—	2	1	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	8	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	1	no	—
561	C₂×C₄×C₇	—	2	1	no	—
562	C₂×C₄×C₇	—	2	2	no	—
563	C₂×C₄×C₇	—	2	2	no	—
564	C₂×C₄×C₇	—	2	2	no	—
565	C₂×C₄×C₇	—	2	2	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	1	no	—
571	C₂×C₄×C₇	—	2	2	no	—
572	C₂×C₄×C₇	—	2	1	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	1	no	—
576	C₂×C₄×C₇	—	2	1	no	—
577	C₂×C₄×C₇	—	2	1	no	—
578	C₂×C₄×C₇	—	2	1	no	—
579	C₂×C₄×C₇	—	2	1	no	—
580	C₂×C₄×C₇	—	2	2	no	—
581	C₂×C₄×C₇	—	2	2	no	—
582	C₂×C₄×C₇	—	2	2	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	2	no	—
587	C₂×C₄×C₇	—	2	1	no	—
588	C₂×C₄×C₇	—	2	1	no	—
589	C₂×C₄×C₇	—	2	2	no	—
590	C₂×C₄×C₇	—	2	2	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	2	no	—
595	C₂×C₄×C₇	—	2	1	no	—
596	C₂×C₄×C₇	—	2	2	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	4	4	no	—
599	C₂×C₄×C₇	—	4	4	no	—
600	C₂×C₄×C₇	—	4	4	no	—
601	C₂×C₄×C₇	—	4	4	no	—
602	C₂×C₄×C₇	—	4	4	no	—
603	C₂×C₄×C₇	—	8	4	no	—
604	C₂×C₄×C₇	C₂×#41	1	2	yes	—
605	C₂×C₄×C₇	C₂×#41	1	2	yes	—
606	C₂×C₄×C₇	C₂×#41	1	2	yes	—
607	C₂×C₄×C₇	C₂×#41	1	2	yes	—
608	C₂×C₄×C₇	C₂×#41	1	2	yes	—
609	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
610	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
611	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
612	C₂⁵	C₂³×C₇	1	2	yes	—
613	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
614	C₂²×D₄	—	2	4	no	—
615	C₂²×D₄	—	4	2	no	—
616	C₂²×D₄	—	4	2	no	—
617	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₇	1	2	yes	—
621	C₂²×D₄	C₂³×C₇	1	2	yes	—
622	C₂²×D₄	C₂³×C₇	1	2	yes	—
623	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₇	1	2	yes	—
628	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
630	#126	—	4	4	no	—
631	#125	—	4	2	no	—
632	#124	—	4	2	no	—
633	#124	—	4	2	no	—
634	#123	—	4	4	no	—
635	C₂²⋊Q₈	—	2	4	no	—
636	C₂²⋊Q₈	—	4	2	no	—
637	#121	—	4	2	no	—
638	#121	—	4	2	no	—
639	#120	—	2	8	no	—
640	C₄×Q₈	—	4	2	no	—
641	C₄×D₄	—	2	4	no	—
642	C₄×D₄	—	2	4	no	—
643	C₄×D₄	—	2	4	no	—
644	C₂×C₄⋊C₄	—	4	2	no	—
645	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₂²⋊C₄	—	2	8	no	—
664	C₂×C₂²⋊C₄	—	4	4	no	—
665	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
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	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
697	C₂×C₄²	—	4	2	no	—
698	C₂×C₄²	—	4	2	no	—
699	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₇	1	2	yes	—
708	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₇	1	2	yes	—
710	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
714	#95	C₂³×C₇	1	1	yes	characteristic
715	#95	C₂³×C₇	1	1	yes	characteristic
716	#95	C₂³×C₇	1	1	yes	characteristic
717	#95	C₂³×C₇	1	1	yes	characteristic
718	#95	C₂³×C₇	1	1	yes	characteristic
719	#95	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
726	#95	C₂³×C₇	1	2	yes	—
727	#95	C₂³×C₇	1	2	yes	—
728	#95	C₂³×C₇	1	2	yes	—
729	#95	C₂³×C₇	1	2	yes	—
730	#95	C₂³×C₇	1	2	yes	—
731	#95	C₂³×C₇	1	2	yes	—
732	#95	C₂³×C₇	1	2	yes	—
733	C₂²×C₇	—	2	2	no	—
734	C₂²×C₇	—	2	2	no	—
735	C₂²×C₇	—	2	2	no	—
736	C₂²×C₇	—	2	2	no	—
737	C₂²×C₇	—	2	2	no	—
738	C₂²×C₇	—	2	2	no	—
739	C₂²×C₇	—	2	2	no	—
740	C₂²×C₇	—	2	2	no	—
741	C₂²×C₇	—	2	2	no	—
742	C₂²×C₇	—	4	1	no	—
743	C₂²×C₇	—	4	1	no	—
744	C₂²×C₇	—	4	1	no	—
745	C₂²×C₇	—	4	1	no	—
746	C₂²×C₇	—	4	2	no	—
747	C₂²×C₇	—	4	2	no	—
748	C₂²×C₇	—	4	2	no	—
749	C₂²×C₇	—	4	2	no	—
750	C₂²×C₇	—	4	2	no	—
751	C₂²×C₇	—	4	2	no	—
752	C₂²×C₇	—	4	2	no	—
753	C₂²×C₇	—	4	2	no	—
754	C₂²×C₇	—	4	2	no	—
755	C₂²×C₇	—	4	2	no	—
756	C₂²×C₇	—	4	2	no	—
757	C₂²×C₇	—	4	2	no	—
758	C₂²×C₇	—	4	2	no	—
759	C₂²×C₇	—	4	2	no	—
760	C₂²×C₇	—	8	16	no	—
761	C₂²×C₇	#529	1	4	yes	—
762	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
763	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
764	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
765	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
766	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
767	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
768	C₂²×C₇	#585	1	1	yes	characteristic
769	C₄×C₇	—	2	2	no	—
770	C₄×C₇	—	2	2	no	—
771	C₄×C₇	—	2	2	no	—
772	C₄×C₇	—	2	2	no	—
773	C₄×C₇	—	2	2	no	—
774	C₄×C₇	—	4	1	no	—
775	C₄×C₇	—	4	2	no	—
776	C₄×C₇	—	4	1	no	—
777	C₄×C₇	—	4	2	no	—
778	C₄×C₇	—	4	1	no	—
779	C₄×C₇	—	4	1	no	—
780	C₄×C₇	—	4	2	no	—
781	C₄×C₇	—	4	2	no	—
782	C₄×C₇	—	4	1	no	—
783	C₄×C₇	—	4	2	no	—
784	C₄×C₇	—	4	1	no	—
785	C₄×C₇	—	4	1	no	—
786	C₄×C₇	—	4	2	no	—
787	C₄×C₇	#538	1	4	yes	—
788	C₂⁴	—	2	4	no	—
789	C₂⁴	—	2	4	no	—
790	C₂⁴	—	2	4	no	—
791	C₂⁴	—	4	2	no	—
792	C₂⁴	—	4	2	no	—
793	C₂⁴	—	4	2	no	—
794	C₂⁴	—	4	2	no	—
795	C₂⁴	C₂⁴×C₇	1	2	yes	—
796	C₂⁴	C₂⁴×C₇	1	2	yes	—
797	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
798	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
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	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	16	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	C₇×#41	1	4	yes	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	4	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	1	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	1	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	C₇×#41	1	4	yes	—
841	C₂²×C₄	C₇×#41	1	4	yes	—
842	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
844	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	4	2	no	—
872	C₄⋊C₄	—	4	2	no	—
873	C₄⋊C₄	—	4	2	no	—
874	C₄⋊C₄	—	4	2	no	—
875	C₄⋊C₄	—	4	2	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	4	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	2	no	—
899	C₂²⋊C₄	—	4	2	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	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	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	4	1	no	—
920	C₄²	—	4	1	no	—
921	C₄²	—	4	1	no	—
922	C₄²	—	4	1	no	—
923	C₄²	—	4	2	no	—
924	C₄²	—	4	2	no	—
925	C₄²	—	4	1	no	—
926	C₂×C₇	—	2	4	no	—
927	C₂×C₇	—	4	2	no	—
928	C₂×C₇	—	8	2	no	—
929	C₂×C₇	—	8	2	no	—
930	C₂×C₇	C₂×#529	1	1	yes	characteristic
931	C₂×C₇	C₂×#538	1	1	yes	characteristic
932	C₂×C₇	#3460	1	1	yes	characteristic
933	C₂×C₇	#3505	1	1	yes	characteristic
934	C₂×C₇	#3508	1	1	yes	characteristic
935	C₂×C₇	#3514	1	1	yes	characteristic
936	C₂×C₇	#3519	1	1	yes	characteristic
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	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	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	4	8	no	—
962	C₂³	—	4	8	no	—
963	C₂³	—	4	8	no	—
964	C₂³	—	8	4	no	—
965	C₂³	—	8	4	no	—
966	C₂³	—	8	4	no	—
967	C₂³	—	8	4	no	—
968	C₂³	C₂×C₇×#41	1	2	yes	—
969	C₂³	C₂×C₇×#41	1	2	yes	—
970	C₂³	C₂×C₇×#41	1	2	yes	—
971	C₂³	C₂×C₇×#41	1	2	yes	—
972	C₂³	C₂⁵×C₇	1	1	yes	characteristic
973	Q₈	—	4	4	no	—
974	D₄	—	2	8	no	—
975	D₄	—	4	8	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	4	no	—
978	D₄	—	8	4	no	—
979	D₄	—	8	4	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	8	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	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	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	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	4	4	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	8	4	no	—
1036	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1037	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1038	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1039	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1040	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1041	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1042	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1043	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1044	C₇	#35025	1	1	yes	characteristic, direct product factor, Sylow
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	8	16	no	—
1073	C₂²	C₇×#529	1	4	yes	—
1074	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1075	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1076	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1077	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1078	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1079	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1080	C₂²	C₇×#585	1	1	yes	characteristic
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	C₇×#538	1	4	yes	—
1100	C₂	—	2	4	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	8	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	C₂×C₇×#529	1	1	yes	characteristic
1105	C₂	C₂×C₇×#538	1	1	yes	characteristic
1106	C₂	C₇×#3460	1	1	yes	characteristic
1107	C₂	C₇×#3505	1	1	yes	characteristic
1108	C₂	C₇×#3508	1	1	yes	characteristic
1109	C₂	C₇×#3514	1	1	yes	characteristic
1110	C₂	C₇×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₇×#2408	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2861	C₂	semidirect
2. C₇×#2860	C₂	semidirect
3. C₇×#2854	C₂	semidirect
4. C₇×#2850	C₂	semidirect
5. C₇×#2651	C₂	semidirect
6. C₇×#2648	C₂	semidirect
7. C₇×#2593	C₂	semidirect
8. C₇×#2554	C₂	semidirect
9. C₇×#2513	C₂	semidirect
10. C₇×#2490	C₂	semidirect
11. C₇×#2480	C₂	semidirect
12. C₇×#2448	C₂	semidirect
13. C₇×#2442	C₂	semidirect
14. C₇×#2435	C₂	semidirect
15. C₇×#2426	C₂	semidirect
16. C₇×#2418	C₂	semidirect
17. C₇×#2417	C₂	semidirect
19. C₇×#2321	C₂	semidirect
20. C₇×#2312	C₂	semidirect
21. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₇×#390	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
25. C₂×C₇×#126	C₂²	semidirect
26. C₂×C₇×#125	C₂²	semidirect
29. C₂×C₇×#123	C₂²	semidirect
31. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₄×C₇×Q₈	C₂²	semidirect
43. C₂²×C₄²×C₇	C₂²	semidirect
44. C₇×#400	C₂²	semidirect
45. C₇×#399	C₂²	semidirect
46. C₇×#398	C₂²	semidirect
47. C₇×#398	C₂²	semidirect
48. C₇×#397	C₂²	semidirect
49. C₇×#397	C₂²	semidirect
50. C₇×#397	C₂²	semidirect
51. C₇×#397	C₂²	semidirect
52. C₇×#396	C₂²	semidirect
53. C₇×#396	C₂²	semidirect
57. C₇×#394	C₂²	semidirect
58. C₇×#394	C₂²	semidirect
60. C₇×#391	C₂²	semidirect
61. C₇×#391	C₂²	semidirect
72. C₇×#390	C₂²	semidirect
73. C₇×#390	C₂²	semidirect
74. C₇×#389	C₂²	semidirect
75. C₇×#389	C₂²	semidirect
76. C₇×#389	C₂²	semidirect
77. C₇×#389	C₂²	semidirect
78. C₇×#388	C₂²	semidirect
79. C₇×#388	C₂²	semidirect
80. C₇×#388	C₂²	semidirect
81. C₇×#388	C₂²	semidirect
82. C₇×#388	C₂²	semidirect
83. C₇×#388	C₂²	semidirect
84. C₇×#388	C₂²	semidirect
85. C₇×#388	C₂²	semidirect
86. C₇×#388	C₂²	semidirect
87. C₇×#388	C₂²	semidirect
88. C₇×#388	C₂²	semidirect
89. C₇×#388	C₂²	semidirect
90. C₇×#388	C₂²	semidirect
91. C₇×#388	C₂²	semidirect
92. C₇×#388	C₂²	semidirect
93. C₇×#388	C₂²	semidirect
94. C₇×#388	C₂²	semidirect
95. C₇×#387	C₂²	semidirect
97. C₇×#386	C₂²	semidirect
98. C₇×#386	C₂²	semidirect
99. C₇×#386	C₂²	semidirect
102. C₇×#382	C₂²	semidirect
106. C₇×#380	C₂²	semidirect
110. C₄×C₇×C₄⋊C₄	C₂²	semidirect
111. C₄×C₇×C₄⋊C₄	C₂²	semidirect
112. C₄×C₇×C₄⋊C₄	C₂²	semidirect
113. C₄×C₇×C₄⋊C₄	C₂²	semidirect
114. C₄×C₇×C₄⋊C₄	C₂²	semidirect
119. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
122. C₄³×C₇	C₂²	semidirect
123. #35025	C₇	direct (N × H)
245. #2861	C₂×C₇	semidirect
246. #2860	C₂×C₇	semidirect
247. #2854	C₂×C₇	semidirect
248. #2850	C₂×C₇	semidirect
249. #2651	C₂×C₇	semidirect
250. #2648	C₂×C₇	semidirect
251. #2593	C₂×C₇	semidirect
252. #2554	C₂×C₇	semidirect
253. #2513	C₂×C₇	semidirect
254. #2490	C₂×C₇	semidirect
255. #2480	C₂×C₇	semidirect
256. #2448	C₂×C₇	semidirect
257. #2442	C₂×C₇	semidirect
258. #2435	C₂×C₇	semidirect
259. #2426	C₂×C₇	semidirect
260. #2418	C₂×C₇	semidirect
261. #2417	C₂×C₇	semidirect
263. #2321	C₂×C₇	semidirect
264. #2312	C₂×C₇	semidirect
265. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
266. C₂×#390	C₂×C₇	semidirect
267. C₄²×D₄	C₂×C₇	semidirect
407. C₂×#126	C₂²×C₇	semidirect
408. C₂×#125	C₂²×C₇	semidirect
411. C₂×#123	C₂²×C₇	semidirect
413. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
417. C₂×C₄×Q₈	C₂²×C₇	semidirect
425. C₂²×C₄²	C₂²×C₇	semidirect
426. #400	C₂²×C₇	semidirect
427. #399	C₂²×C₇	semidirect
428. #398	C₂²×C₇	semidirect
429. #398	C₂²×C₇	semidirect
430. #397	C₂²×C₇	semidirect
431. #397	C₂²×C₇	semidirect
432. #397	C₂²×C₇	semidirect
433. #397	C₂²×C₇	semidirect
434. #396	C₂²×C₇	semidirect
435. #396	C₂²×C₇	semidirect
439. #394	C₂²×C₇	semidirect
440. #394	C₂²×C₇	semidirect
442. #391	C₂²×C₇	semidirect
443. #391	C₂²×C₇	semidirect
454. #390	C₂²×C₇	semidirect
455. #390	C₂²×C₇	semidirect
456. #389	C₂²×C₇	semidirect
457. #389	C₂²×C₇	semidirect
458. #389	C₂²×C₇	semidirect
459. #389	C₂²×C₇	semidirect
460. #388	C₂²×C₇	semidirect
461. #388	C₂²×C₇	semidirect
462. #388	C₂²×C₇	semidirect
463. #388	C₂²×C₇	semidirect
464. #388	C₂²×C₇	semidirect
465. #388	C₂²×C₇	semidirect
466. #388	C₂²×C₇	semidirect
467. #388	C₂²×C₇	semidirect
468. #388	C₂²×C₇	semidirect
469. #388	C₂²×C₇	semidirect
470. #388	C₂²×C₇	semidirect
471. #388	C₂²×C₇	semidirect
472. #388	C₂²×C₇	semidirect
473. #388	C₂²×C₇	semidirect
474. #388	C₂²×C₇	semidirect
475. #388	C₂²×C₇	semidirect
476. #388	C₂²×C₇	semidirect
477. #387	C₂²×C₇	semidirect
479. #386	C₂²×C₇	semidirect
480. #386	C₂²×C₇	semidirect
481. #386	C₂²×C₇	semidirect
484. #382	C₂²×C₇	semidirect
488. #380	C₂²×C₇	semidirect
492. C₄×C₄⋊C₄	C₂²×C₇	semidirect
493. C₄×C₄⋊C₄	C₂²×C₇	semidirect
494. C₄×C₄⋊C₄	C₂²×C₇	semidirect
495. C₄×C₄⋊C₄	C₂²×C₇	semidirect
496. C₄×C₄⋊C₄	C₂²×C₇	semidirect
501. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
502. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
503. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
504. C₄³	C₂²×C₇	semidirect
1044. C₇	#35025	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×#2861	2
C₇×#2860	2
C₇×#2854	2
C₇×#2850	2
C₇×#2651	2
C₇×#2648	2
C₇×#2593	2
C₇×#2554	2
C₇×#2513	2
C₇×#2490	2
C₇×#2480	2
C₇×#2448	2
C₇×#2442	2
C₇×#2435	2
C₇×#2426	2
C₇×#2418	2
C₇×#2417	2
C₇×#2408	2
C₇×#2321	2
C₇×#2312	2
C₄×C₇×C₂²⋊Q₈	2
C₂×C₇×#390	2
C₄²×C₇×D₄	2
#35025	7

Subgroups — C7×#35025 #13212241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35025 #13212241