Subgroups — C₂×C₇×#2510 #13211966

Order 1792.

2658 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2510	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₇×#401	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic
11	C₂×C₇×#386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#383	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#95	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₇×#401	C₂²	1	8	yes	complemented
37	C₇×#400	C₂²	1	8	yes	complemented
38	C₇×#397	C₂²	1	8	yes	complemented
39	C₇×#397	C₂²	1	8	yes	complemented
40	C₇×#388	C₂²	1	8	yes	complemented
41	C₇×#388	C₂²	1	8	yes	complemented
42	C₇×#387	C₂²	1	8	yes	complemented
43	C₇×#386	C₂²	1	8	yes	—
44	C₇×#386	C₂²	1	8	yes	—
45	C₇×#386	C₂²	1	8	yes	—
46	C₇×#385	C₂²	1	8	yes	complemented
47	C₇×#383	C₂²	1	8	yes	complemented
48	C₇×#380	C₂²	1	8	yes	complemented
49	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
50	C₂×C₇×#95	C₂²	1	1	yes	characteristic
51	C₂×C₇×#95	C₂²	1	1	yes	characteristic
52	C₂×C₇×#95	C₂²	1	1	yes	characteristic
53	C₂×C₇×#95	C₂²	1	1	yes	characteristic
54	C₂×C₇×#95	C₂²	1	1	yes	characteristic
55	C₂×C₇×#95	C₂²	1	1	yes	characteristic
56	C₂×C₇×#95	C₂²	1	1	yes	characteristic
57	C₂×C₇×#95	C₂²	1	1	yes	characteristic
58	C₂×C₇×#95	C₂²	1	1	yes	characteristic
59	C₂×C₇×#95	C₂²	1	1	yes	characteristic
60	C₂×C₇×#95	C₂²	1	1	yes	characteristic
61	C₂×C₇×#95	C₂²	1	1	yes	characteristic
62	C₂×C₇×#95	C₂²	1	1	yes	characteristic
63	C₂×C₇×#95	C₂²	1	1	yes	characteristic
64	C₂×C₇×#95	C₂²	1	1	yes	characteristic
65	C₂×C₇×#95	C₂²	1	1	yes	characteristic
66	C₂×C₇×#95	C₂²	1	8	yes	complemented
67	C₂×#2510	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁵×C₇	C₂³	1	1	yes	characteristic
69	C₂⁵×C₇	C₂³	1	1	yes	characteristic
70	C₂²×C₇×D₄	—	2	4	no	—
71	C₂²×C₇×D₄	—	2	4	no	—
72	C₂²×C₇×D₄	—	2	4	no	—
73	C₂²×C₇×D₄	C₂³	1	4	yes	—
74	C₂³×C₄×C₇	—	2	4	no	—
75	C₂³×C₄×C₇	—	2	4	no	—
76	C₂³×C₄×C₇	—	2	4	no	—
77	C₂³×C₄×C₇	—	2	4	no	—
78	C₂³×C₄×C₇	—	2	4	no	—
79	C₂³×C₄×C₇	—	4	2	no	—
80	C₂³×C₄×C₇	—	4	2	no	—
81	C₂³×C₄×C₇	—	4	2	no	—
82	C₂³×C₄×C₇	—	4	2	no	—
83	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇	C₂³	1	4	yes	—
95	C₂³×C₄×C₇	C₂³	1	4	yes	—
96	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	C₂³	1	4	yes	—
99	C₂×C₇×C₄⋊C₄	—	2	4	no	—
100	C₂×C₇×C₄⋊C₄	—	4	2	no	—
101	C₂×C₇×C₄⋊C₄	—	4	2	no	—
102	C₂×C₇×C₄⋊C₄	—	4	2	no	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
112	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
113	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
114	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
115	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
116	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₄²×C₇	—	2	4	no	—
126	C₂×C₄²×C₇	—	4	2	no	—
127	C₂×C₄²×C₇	C₂³	1	4	yes	—
128	C₂×C₄²×C₇	C₂³	1	4	yes	—
129	C₇×#95	C₂³	1	4	yes	—
130	C₇×#95	C₂³	1	4	yes	—
131	C₇×#95	C₂³	1	4	yes	—
132	C₇×#95	C₂³	1	4	yes	—
133	C₇×#95	C₂³	1	4	yes	—
134	C₇×#95	C₂³	1	4	yes	—
135	C₇×#95	C₂³	1	4	yes	—
136	C₇×#95	C₂³	1	4	yes	—
137	C₇×#95	C₂³	1	4	yes	—
138	C₇×#95	C₂³	1	4	yes	—
139	C₇×#95	C₂³	1	4	yes	—
140	C₇×#95	C₂³	1	4	yes	—
141	C₇×#95	C₂³	1	4	yes	—
142	C₇×#95	C₂³	1	4	yes	—
143	C₇×#95	C₂³	1	4	yes	—
144	C₇×#95	C₂³	1	4	yes	—
145	#2510	C₂×C₇	1	16	yes	direct product factor
146	C₂×#401	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#400	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂×#397	C₂×C₇	1	1	yes	characteristic, complemented
149	C₂×#397	C₂×C₇	1	1	yes	characteristic, complemented
150	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂×#388	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂×#387	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂×#386	C₂×C₇	1	1	yes	characteristic
154	C₂×#386	C₂×C₇	1	1	yes	characteristic
155	C₂×#386	C₂×C₇	1	1	yes	characteristic
156	C₂×#385	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂×#383	C₂×C₇	1	1	yes	characteristic, complemented
158	C₂×#380	C₂×C₇	1	1	yes	characteristic, complemented
159	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
160	C₂²×#95	C₂×C₇	1	1	yes	characteristic, complemented
161	C₂⁴×C₇	—	2	2	no	—
162	C₂⁴×C₇	—	2	2	no	—
163	C₂⁴×C₇	—	2	2	no	—
164	C₂⁴×C₇	—	2	2	no	—
165	C₂⁴×C₇	—	2	2	no	—
166	C₂⁴×C₇	—	2	2	no	—
167	C₂⁴×C₇	—	2	2	no	—
168	C₂⁴×C₇	—	2	2	no	—
169	C₂⁴×C₇	—	2	2	no	—
170	C₂⁴×C₇	—	2	2	no	—
171	C₂⁴×C₇	—	2	2	no	—
172	C₂⁴×C₇	#41	1	4	yes	—
173	C₂⁴×C₇	#41	1	4	yes	—
174	C₂⁴×C₇	#41	1	4	yes	—
175	C₂⁴×C₇	C₂⁴	1	2	yes	—
176	C₂⁴×C₇	C₂⁴	1	2	yes	—
177	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
178	C₂×C₇×D₄	—	2	8	no	—
179	C₂×C₇×D₄	—	2	8	no	—
180	C₂×C₇×D₄	—	2	8	no	—
181	C₂×C₇×D₄	—	4	16	no	—
182	C₂²×C₄×C₇	—	2	2	no	—
183	C₂²×C₄×C₇	—	2	2	no	—
184	C₂²×C₄×C₇	—	2	2	no	—
185	C₂²×C₄×C₇	—	2	2	no	—
186	C₂²×C₄×C₇	—	2	2	no	—
187	C₂²×C₄×C₇	—	2	2	no	—
188	C₂²×C₄×C₇	—	2	2	no	—
189	C₂²×C₄×C₇	—	2	2	no	—
190	C₂²×C₄×C₇	—	2	2	no	—
191	C₂²×C₄×C₇	—	2	2	no	—
192	C₂²×C₄×C₇	—	2	2	no	—
193	C₂²×C₄×C₇	—	2	2	no	—
194	C₂²×C₄×C₇	—	2	2	no	—
195	C₂²×C₄×C₇	—	2	2	no	—
196	C₂²×C₄×C₇	—	2	2	no	—
197	C₂²×C₄×C₇	—	2	2	no	—
198	C₂²×C₄×C₇	—	2	8	no	—
199	C₂²×C₄×C₇	—	2	8	no	—
200	C₂²×C₄×C₇	—	2	8	no	—
201	C₂²×C₄×C₇	—	2	2	no	—
202	C₂²×C₄×C₇	—	2	2	no	—
203	C₂²×C₄×C₇	—	2	2	no	—
204	C₂²×C₄×C₇	—	2	2	no	—
205	C₂²×C₄×C₇	—	2	2	no	—
206	C₂²×C₄×C₇	—	2	2	no	—
207	C₂²×C₄×C₇	—	2	2	no	—
208	C₂²×C₄×C₇	—	2	2	no	—
209	C₂²×C₄×C₇	—	2	2	no	—
210	C₂²×C₄×C₇	—	2	2	no	—
211	C₂²×C₄×C₇	—	2	2	no	—
212	C₂²×C₄×C₇	—	2	2	no	—
213	C₂²×C₄×C₇	—	2	2	no	—
214	C₂²×C₄×C₇	—	2	2	no	—
215	C₂²×C₄×C₇	—	2	2	no	—
216	C₂²×C₄×C₇	—	2	2	no	—
217	C₂²×C₄×C₇	—	2	2	no	—
218	C₂²×C₄×C₇	—	2	2	no	—
219	C₂²×C₄×C₇	—	2	2	no	—
220	C₂²×C₄×C₇	—	2	2	no	—
221	C₂²×C₄×C₇	—	2	2	no	—
222	C₂²×C₄×C₇	—	2	8	no	—
223	C₂²×C₄×C₇	—	2	8	no	—
224	C₂²×C₄×C₇	—	4	4	no	—
225	C₂²×C₄×C₇	—	4	4	no	—
226	C₂²×C₄×C₇	—	4	4	no	—
227	C₂²×C₄×C₇	—	4	4	no	—
228	C₂²×C₄×C₇	—	4	16	no	—
229	C₂²×C₄×C₇	—	4	16	no	—
230	C₂²×C₄×C₇	—	4	16	no	—
231	C₂²×C₄×C₇	#41	1	4	yes	—
232	C₂²×C₄×C₇	#41	1	4	yes	—
233	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
246	C₇×C₄⋊C₄	—	2	8	no	—
247	C₇×C₄⋊C₄	—	4	4	no	—
248	C₇×C₄⋊C₄	—	4	4	no	—
249	C₇×C₄⋊C₄	—	4	4	no	—
250	C₇×C₂²⋊C₄	—	2	8	no	—
251	C₇×C₂²⋊C₄	—	2	8	no	—
252	C₇×C₂²⋊C₄	—	2	8	no	—
253	C₇×C₂²⋊C₄	—	2	8	no	—
254	C₇×C₂²⋊C₄	—	2	8	no	—
255	C₇×C₂²⋊C₄	—	4	4	no	—
256	C₇×C₂²⋊C₄	—	4	4	no	—
257	C₇×C₂²⋊C₄	—	4	4	no	—
258	C₇×C₂²⋊C₄	—	4	4	no	—
259	C₄²×C₇	—	2	8	no	—
260	C₄²×C₇	—	4	4	no	—
261	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
263	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
264	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
274	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
278	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
279	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
280	#401	C₂²×C₇	1	8	yes	complemented
281	#400	C₂²×C₇	1	8	yes	complemented
282	#397	C₂²×C₇	1	8	yes	complemented
283	#397	C₂²×C₇	1	8	yes	complemented
284	#388	C₂²×C₇	1	8	yes	complemented
285	#388	C₂²×C₇	1	8	yes	complemented
286	#387	C₂²×C₇	1	8	yes	complemented
287	#386	C₂²×C₇	1	8	yes	—
288	#386	C₂²×C₇	1	8	yes	—
289	#386	C₂²×C₇	1	8	yes	—
290	#385	C₂²×C₇	1	8	yes	complemented
291	#383	C₂²×C₇	1	8	yes	complemented
292	#380	C₂²×C₇	1	8	yes	complemented
293	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
294	C₂×#95	C₂²×C₇	1	1	yes	characteristic
295	C₂×#95	C₂²×C₇	1	1	yes	characteristic
296	C₂×#95	C₂²×C₇	1	1	yes	characteristic
297	C₂×#95	C₂²×C₇	1	1	yes	characteristic
298	C₂×#95	C₂²×C₇	1	1	yes	characteristic
299	C₂×#95	C₂²×C₇	1	1	yes	characteristic
300	C₂×#95	C₂²×C₇	1	1	yes	characteristic
301	C₂×#95	C₂²×C₇	1	1	yes	characteristic
302	C₂×#95	C₂²×C₇	1	1	yes	characteristic
303	C₂×#95	C₂²×C₇	1	1	yes	characteristic
304	C₂×#95	C₂²×C₇	1	1	yes	characteristic
305	C₂×#95	C₂²×C₇	1	1	yes	characteristic
306	C₂×#95	C₂²×C₇	1	1	yes	characteristic
307	C₂×#95	C₂²×C₇	1	1	yes	characteristic
308	C₂×#95	C₂²×C₇	1	1	yes	characteristic
309	C₂×#95	C₂²×C₇	1	1	yes	characteristic
310	C₂×#95	C₂²×C₇	1	8	yes	complemented
311	C₂³×C₇	—	2	8	no	—
312	C₂³×C₇	—	2	8	no	—
313	C₂³×C₇	—	2	8	no	—
314	C₂³×C₇	—	2	8	no	—
315	C₂³×C₇	—	2	8	no	—
316	C₂³×C₇	—	2	8	no	—
317	C₂³×C₇	—	2	2	no	—
318	C₂³×C₇	—	2	2	no	—
319	C₂³×C₇	—	2	2	no	—
320	C₂³×C₇	—	2	2	no	—
321	C₂³×C₇	—	2	2	no	—
322	C₂³×C₇	—	2	2	no	—
323	C₂³×C₇	—	2	2	no	—
324	C₂³×C₇	—	2	2	no	—
325	C₂³×C₇	—	2	2	no	—
326	C₂³×C₇	—	2	2	no	—
327	C₂³×C₇	—	2	2	no	—
328	C₂³×C₇	—	4	4	no	—
329	C₂³×C₇	—	4	4	no	—
330	C₂³×C₇	—	4	4	no	—
331	C₂³×C₇	—	4	4	no	—
332	C₂³×C₇	—	4	4	no	—
333	C₂³×C₇	—	4	4	no	—
334	C₂³×C₇	—	4	4	no	—
335	C₂³×C₇	#126	1	16	yes	—
336	C₂³×C₇	C₂×#41	1	4	yes	—
337	C₂³×C₇	C₂×#41	1	4	yes	—
338	C₂³×C₇	C₂×#41	1	4	yes	—
339	C₂³×C₇	C₂×#41	1	2	yes	—
340	C₂³×C₇	C₂×#41	1	2	yes	—
341	C₂³×C₇	C₂×#41	1	2	yes	—
342	C₂³×C₇	C₂×#41	1	2	yes	—
343	C₂³×C₇	C₂×#41	1	2	yes	—
344	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
345	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
346	C₂³×C₇	C₂⁵	1	1	yes	characteristic
347	C₇×D₄	—	4	16	no	—
348	C₂×C₄×C₇	—	2	8	no	—
349	C₂×C₄×C₇	—	2	8	no	—
350	C₂×C₄×C₇	—	2	2	no	—
351	C₂×C₄×C₇	—	2	2	no	—
352	C₂×C₄×C₇	—	2	2	no	—
353	C₂×C₄×C₇	—	2	2	no	—
354	C₂×C₄×C₇	—	2	2	no	—
355	C₂×C₄×C₇	—	2	2	no	—
356	C₂×C₄×C₇	—	2	2	no	—
357	C₂×C₄×C₇	—	2	2	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	2	no	—
360	C₂×C₄×C₇	—	2	2	no	—
361	C₂×C₄×C₇	—	2	2	no	—
362	C₂×C₄×C₇	—	2	2	no	—
363	C₂×C₄×C₇	—	2	2	no	—
364	C₂×C₄×C₇	—	2	2	no	—
365	C₂×C₄×C₇	—	2	2	no	—
366	C₂×C₄×C₇	—	2	2	no	—
367	C₂×C₄×C₇	—	2	2	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	2	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	2	no	—
377	C₂×C₄×C₇	—	2	2	no	—
378	C₂×C₄×C₇	—	2	2	no	—
379	C₂×C₄×C₇	—	2	2	no	—
380	C₂×C₄×C₇	—	2	2	no	—
381	C₂×C₄×C₇	—	2	2	no	—
382	C₂×C₄×C₇	—	2	2	no	—
383	C₂×C₄×C₇	—	2	2	no	—
384	C₂×C₄×C₇	—	2	2	no	—
385	C₂×C₄×C₇	—	2	2	no	—
386	C₂×C₄×C₇	—	2	2	no	—
387	C₂×C₄×C₇	—	4	16	no	—
388	C₂×C₄×C₇	—	4	16	no	—
389	C₂×C₄×C₇	—	4	16	no	—
390	C₂×C₄×C₇	—	4	4	no	—
391	C₂×C₄×C₇	—	4	4	no	—
392	C₂×C₄×C₇	—	4	4	no	—
393	C₂×C₄×C₇	—	4	4	no	—
394	C₂×C₄×C₇	—	4	4	no	—
395	C₂×C₄×C₇	—	4	4	no	—
396	C₂×C₄×C₇	—	4	4	no	—
397	C₂×C₄×C₇	—	4	4	no	—
398	C₂×C₄×C₇	—	4	4	no	—
399	C₂×C₄×C₇	—	4	4	no	—
400	C₂×C₄×C₇	—	4	4	no	—
401	C₂×C₄×C₇	C₂×#41	1	4	yes	—
402	C₂×C₄×C₇	C₂×#41	1	4	yes	—
403	C₂⁵	C₂³×C₇	1	1	yes	characteristic
404	C₂⁵	C₂³×C₇	1	1	yes	characteristic
405	C₂²×D₄	—	2	4	no	—
406	C₂²×D₄	—	2	4	no	—
407	C₂²×D₄	—	2	4	no	—
408	C₂²×D₄	C₂³×C₇	1	4	yes	—
409	C₂³×C₄	—	2	4	no	—
410	C₂³×C₄	—	2	4	no	—
411	C₂³×C₄	—	2	4	no	—
412	C₂³×C₄	—	2	4	no	—
413	C₂³×C₄	—	2	4	no	—
414	C₂³×C₄	—	4	2	no	—
415	C₂³×C₄	—	4	2	no	—
416	C₂³×C₄	—	4	2	no	—
417	C₂³×C₄	—	4	2	no	—
418	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₇	1	4	yes	—
430	C₂³×C₄	C₂³×C₇	1	4	yes	—
431	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₇	1	4	yes	—
434	C₂×C₄⋊C₄	—	2	4	no	—
435	C₂×C₄⋊C₄	—	4	2	no	—
436	C₂×C₄⋊C₄	—	4	2	no	—
437	C₂×C₄⋊C₄	—	4	2	no	—
438	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
442	C₂×C₂²⋊C₄	—	2	4	no	—
443	C₂×C₂²⋊C₄	—	2	4	no	—
444	C₂×C₂²⋊C₄	—	2	4	no	—
445	C₂×C₂²⋊C₄	—	2	4	no	—
446	C₂×C₂²⋊C₄	—	2	4	no	—
447	C₂×C₂²⋊C₄	—	4	2	no	—
448	C₂×C₂²⋊C₄	—	4	2	no	—
449	C₂×C₂²⋊C₄	—	4	2	no	—
450	C₂×C₂²⋊C₄	—	4	2	no	—
451	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
460	C₂×C₄²	—	2	4	no	—
461	C₂×C₄²	—	4	2	no	—
462	C₂×C₄²	C₂³×C₇	1	4	yes	—
463	C₂×C₄²	C₂³×C₇	1	4	yes	—
464	#95	C₂³×C₇	1	4	yes	—
465	#95	C₂³×C₇	1	4	yes	—
466	#95	C₂³×C₇	1	4	yes	—
467	#95	C₂³×C₇	1	4	yes	—
468	#95	C₂³×C₇	1	4	yes	—
469	#95	C₂³×C₇	1	4	yes	—
470	#95	C₂³×C₇	1	4	yes	—
471	#95	C₂³×C₇	1	4	yes	—
472	#95	C₂³×C₇	1	4	yes	—
473	#95	C₂³×C₇	1	4	yes	—
474	#95	C₂³×C₇	1	4	yes	—
475	#95	C₂³×C₇	1	4	yes	—
476	#95	C₂³×C₇	1	4	yes	—
477	#95	C₂³×C₇	1	4	yes	—
478	#95	C₂³×C₇	1	4	yes	—
479	#95	C₂³×C₇	1	4	yes	—
480	C₂²×C₇	—	2	4	no	—
481	C₂²×C₇	—	2	4	no	—
482	C₂²×C₇	—	2	4	no	—
483	C₂²×C₇	—	2	4	no	—
484	C₂²×C₇	—	2	4	no	—
485	C₂²×C₇	—	2	4	no	—
486	C₂²×C₇	—	2	32	no	—
487	C₂²×C₇	—	4	2	no	—
488	C₂²×C₇	—	4	2	no	—
489	C₂²×C₇	—	4	2	no	—
490	C₂²×C₇	—	4	2	no	—
491	C₂²×C₇	—	4	2	no	—
492	C₂²×C₇	—	4	2	no	—
493	C₂²×C₇	—	4	2	no	—
494	C₂²×C₇	—	8	8	no	—
495	C₂²×C₇	C₂×#126	1	8	yes	—
496	C₂²×C₇	C₂×#126	1	4	yes	—
497	C₂²×C₇	#529	1	4	yes	—
498	C₂²×C₇	#538	1	4	yes	—
499	C₂²×C₇	#551	1	4	yes	—
500	C₂²×C₇	#551	1	4	yes	—
501	C₂²×C₇	#553	1	4	yes	—
502	C₂²×C₇	#553	1	4	yes	—
503	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
504	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
505	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
506	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
507	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
508	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
510	C₄×C₇	—	2	4	no	—
511	C₄×C₇	—	2	4	no	—
512	C₄×C₇	—	4	2	no	—
513	C₄×C₇	—	4	2	no	—
514	C₄×C₇	—	4	2	no	—
515	C₄×C₇	—	4	2	no	—
516	C₄×C₇	—	4	2	no	—
517	C₄×C₇	—	4	2	no	—
518	C₄×C₇	—	4	2	no	—
519	C₄×C₇	—	4	2	no	—
520	C₄×C₇	—	4	2	no	—
521	C₄×C₇	—	4	2	no	—
522	C₄×C₇	—	4	2	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	2	no	—
531	C₂⁴	—	2	2	no	—
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	2	2	no	—
534	C₂⁴	C₇×#41	1	4	yes	—
535	C₂⁴	C₇×#41	1	4	yes	—
536	C₂⁴	C₇×#41	1	4	yes	—
537	C₂⁴	C₂⁴×C₇	1	2	yes	—
538	C₂⁴	C₂⁴×C₇	1	2	yes	—
539	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	4	16	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	8	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	2	8	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	8	no	—
585	C₂²×C₄	—	2	8	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	16	no	—
591	C₂²×C₄	—	4	16	no	—
592	C₂²×C₄	—	4	16	no	—
593	C₂²×C₄	C₇×#41	1	4	yes	—
594	C₂²×C₄	C₇×#41	1	4	yes	—
595	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	4	4	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	2	8	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	4	4	no	—
621	C₄²	—	2	8	no	—
622	C₄²	—	4	4	no	—
623	C₂×C₇	—	2	8	no	—
624	C₂×C₇	—	8	2	no	—
625	C₂×C₇	#2510	1	8	yes	direct product factor
626	C₂×C₇	C₂²×#126	1	1	yes	characteristic
627	C₂×C₇	C₂×#529	1	1	yes	characteristic
628	C₂×C₇	C₂×#538	1	1	yes	characteristic
629	C₂×C₇	C₂×#551	1	1	yes	characteristic
630	C₂×C₇	C₂×#551	1	1	yes	characteristic
631	C₂×C₇	C₂×#553	1	1	yes	characteristic
632	C₂×C₇	C₂×#553	1	1	yes	characteristic
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	8	no	—
638	C₂³	—	2	8	no	—
639	C₂³	—	2	8	no	—
640	C₂³	—	2	8	no	—
641	C₂³	—	2	8	no	—
642	C₂³	—	2	8	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	4	no	—
652	C₂³	—	4	4	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	4	no	—
656	C₂³	—	4	4	no	—
657	C₂³	C₇×#126	1	16	yes	—
658	C₂³	C₂×C₇×#41	1	4	yes	—
659	C₂³	C₂×C₇×#41	1	4	yes	—
660	C₂³	C₂×C₇×#41	1	4	yes	—
661	C₂³	C₂×C₇×#41	1	2	yes	—
662	C₂³	C₂×C₇×#41	1	2	yes	—
663	C₂³	C₂×C₇×#41	1	2	yes	—
664	C₂³	C₂×C₇×#41	1	2	yes	—
665	C₂³	C₂×C₇×#41	1	2	yes	—
666	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
667	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
668	C₂³	C₂⁵×C₇	1	1	yes	characteristic
669	D₄	—	4	16	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	8	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	16	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	4	16	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	C₂×C₇×#41	1	4	yes	—
724	C₂×C₄	C₂×C₇×#41	1	4	yes	—
725	C₇	C₂×#2510	1	1	yes	characteristic, direct product factor, Sylow
726	C₂²	—	2	32	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	8	8	no	—
741	C₂²	C₂×C₇×#126	1	8	yes	—
742	C₂²	C₂×C₇×#126	1	4	yes	—
743	C₂²	C₇×#529	1	4	yes	—
744	C₂²	C₇×#538	1	4	yes	—
745	C₂²	C₇×#551	1	4	yes	—
746	C₂²	C₇×#551	1	4	yes	—
747	C₂²	C₇×#553	1	4	yes	—
748	C₂²	C₇×#553	1	4	yes	—
749	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
750	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
751	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
752	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
753	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
754	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
755	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
756	C₄	—	2	4	no	—
757	C₄	—	2	4	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₂	—	2	8	no	—
770	C₂	—	8	2	no	—
771	C₂	C₇×#2510	1	8	yes	direct product factor
772	C₂	C₂²×C₇×#126	1	1	yes	characteristic
773	C₂	C₂×C₇×#529	1	1	yes	characteristic
774	C₂	C₂×C₇×#538	1	1	yes	characteristic
775	C₂	C₂×C₇×#551	1	1	yes	characteristic
776	C₂	C₂×C₇×#551	1	1	yes	characteristic
777	C₂	C₂×C₇×#553	1	1	yes	characteristic
778	C₂	C₂×C₇×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2510	C₂	direct (N × H)
2. C₂×C₇×#401	C₂	semidirect
3. C₂×C₇×#400	C₂	semidirect
4. C₂×C₇×#397	C₂	semidirect
5. C₂×C₇×#397	C₂	semidirect
6. C₂×C₇×#388	C₂	semidirect
7. C₂×C₇×#388	C₂	semidirect
8. C₂×C₇×#387	C₂	semidirect
12. C₂×C₇×#385	C₂	semidirect
13. C₂×C₇×#383	C₂	semidirect
14. C₂×C₇×#380	C₂	semidirect
15. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
16. C₂²×C₇×#95	C₂	semidirect
36. C₇×#401	C₂²	semidirect
37. C₇×#400	C₂²	semidirect
38. C₇×#397	C₂²	semidirect
39. C₇×#397	C₂²	semidirect
40. C₇×#388	C₂²	semidirect
41. C₇×#388	C₂²	semidirect
42. C₇×#387	C₂²	semidirect
46. C₇×#385	C₂²	semidirect
47. C₇×#383	C₂²	semidirect
48. C₇×#380	C₂²	semidirect
49. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
66. C₂×C₇×#95	C₂²	semidirect
67. C₂×#2510	C₇	direct (N × H)
145. #2510	C₂×C₇	direct (N × H)
146. C₂×#401	C₂×C₇	semidirect
147. C₂×#400	C₂×C₇	semidirect
148. C₂×#397	C₂×C₇	semidirect
149. C₂×#397	C₂×C₇	semidirect
150. C₂×#388	C₂×C₇	semidirect
151. C₂×#388	C₂×C₇	semidirect
152. C₂×#387	C₂×C₇	semidirect
156. C₂×#385	C₂×C₇	semidirect
157. C₂×#383	C₂×C₇	semidirect
158. C₂×#380	C₂×C₇	semidirect
159. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
160. C₂²×#95	C₂×C₇	semidirect
280. #401	C₂²×C₇	semidirect
281. #400	C₂²×C₇	semidirect
282. #397	C₂²×C₇	semidirect
283. #397	C₂²×C₇	semidirect
284. #388	C₂²×C₇	semidirect
285. #388	C₂²×C₇	semidirect
286. #387	C₂²×C₇	semidirect
290. #385	C₂²×C₇	semidirect
291. #383	C₂²×C₇	semidirect
292. #380	C₂²×C₇	semidirect
293. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
310. C₂×#95	C₂²×C₇	semidirect
625. C₂×C₇	#2510	direct (N × H)
725. C₇	C₂×#2510	direct (N × H)
771. C₂	C₇×#2510	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×#2510	2
C₂×C₇×#401	2
C₂×C₇×#400	2
C₂×C₇×#397	2
C₂×C₇×#388	2
C₂×C₇×#387	2
C₂×C₇×#386	2
C₂×C₇×#385	2
C₂×C₇×#383	2
C₂×C₇×#380	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂²×C₇×#95	2
C₂×#2510	7

Subgroups — C2×C7×#2510 #13211966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2510 #13211966