Subgroups — C₂×C₇×#2505 #13211964

Order 1792.

2486 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2505	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
11	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
13	C₂×C₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#380	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₇×#95	C₂	1	1	yes	maximal, characteristic
17	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂²×C₇×C₄⋊C₄	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₄⋊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×#400	C₂²	1	8	yes	complemented
37	C₇×#400	C₂²	1	8	yes	complemented
38	C₇×#400	C₂²	1	8	yes	complemented
39	C₇×#398	C₂²	1	8	yes	complemented
40	C₇×#389	C₂²	1	8	yes	complemented
41	C₇×#387	C₂²	1	8	yes	complemented
42	C₇×#387	C₂²	1	8	yes	complemented
43	C₇×#385	C₂²	1	8	yes	—
44	C₇×#385	C₂²	1	8	yes	—
45	C₇×#385	C₂²	1	8	yes	—
46	C₇×#385	C₂²	1	8	yes	—
47	C₇×#382	C₂²	1	8	yes	complemented
48	C₇×#380	C₂²	1	8	yes	—
49	C₄×C₇×C₂²⋊C₄	C₂²	1	8	yes	—
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	8	yes	—
64	C₂×C₇×#95	C₂²	1	1	yes	characteristic
65	C₂×C₇×#95	C₂²	1	1	yes	characteristic
66	C₂×C₇×#95	C₂²	1	1	yes	characteristic
67	C₂×#2505	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁵×C₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇	—	2	4	no	—
70	C₂³×C₄×C₇	—	2	4	no	—
71	C₂³×C₄×C₇	—	2	4	no	—
72	C₂³×C₄×C₇	—	2	4	no	—
73	C₂³×C₄×C₇	—	2	4	no	—
74	C₂³×C₄×C₇	—	4	2	no	—
75	C₂³×C₄×C₇	—	4	2	no	—
76	C₂³×C₄×C₇	—	4	2	no	—
77	C₂³×C₄×C₇	—	4	2	no	—
78	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
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	4	yes	—
89	C₂³×C₄×C₇	C₂³	1	4	yes	—
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	C₂×C₇×C₄⋊C₄	—	2	4	no	—
96	C₂×C₇×C₄⋊C₄	—	2	4	no	—
97	C₂×C₇×C₄⋊C₄	—	2	4	no	—
98	C₂×C₇×C₄⋊C₄	—	4	2	no	—
99	C₂×C₇×C₄⋊C₄	—	4	2	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	—	4	2	no	—
104	C₂×C₇×C₄⋊C₄	—	4	2	no	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
118	C₂×C₇×C₂²⋊C₄	Q₈	1	8	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×C₄²×C₇	—	2	4	no	—
124	C₂×C₄²×C₇	—	4	2	no	—
125	C₂×C₄²×C₇	C₂³	1	4	yes	—
126	C₂×C₄²×C₇	C₂³	1	4	yes	—
127	C₇×#95	C₂³	1	4	yes	—
128	C₇×#95	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	#2505	C₂×C₇	1	16	yes	direct product factor
144	C₂×#400	C₂×C₇	1	1	yes	characteristic, complemented
145	C₂×#400	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂×#400	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#398	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂×#389	C₂×C₇	1	1	yes	characteristic, complemented
149	C₂×#387	C₂×C₇	1	1	yes	characteristic, complemented
150	C₂×#387	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂×#385	C₂×C₇	1	1	yes	characteristic
152	C₂×#385	C₂×C₇	1	1	yes	characteristic
153	C₂×#385	C₂×C₇	1	1	yes	characteristic
154	C₂×#385	C₂×C₇	1	1	yes	characteristic
155	C₂×#382	C₂×C₇	1	1	yes	characteristic, complemented
156	C₂×#380	C₂×C₇	1	1	yes	characteristic
157	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
158	C₂²×#95	C₂×C₇	1	1	yes	characteristic
159	C₂⁴×C₇	—	2	2	no	—
160	C₂⁴×C₇	—	2	2	no	—
161	C₂⁴×C₇	—	2	2	no	—
162	C₂⁴×C₇	—	2	2	no	—
163	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
164	C₂⁴×C₇	#41	1	4	yes	—
165	C₂⁴×C₇	#41	1	4	yes	—
166	C₂⁴×C₇	C₂⁴	1	2	yes	—
167	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₇	—	2	2	no	—
169	C₂²×C₄×C₇	—	2	2	no	—
170	C₂²×C₄×C₇	—	2	2	no	—
171	C₂²×C₄×C₇	—	2	2	no	—
172	C₂²×C₄×C₇	—	2	2	no	—
173	C₂²×C₄×C₇	—	2	2	no	—
174	C₂²×C₄×C₇	—	2	2	no	—
175	C₂²×C₄×C₇	—	2	2	no	—
176	C₂²×C₄×C₇	—	2	2	no	—
177	C₂²×C₄×C₇	—	2	2	no	—
178	C₂²×C₄×C₇	—	2	2	no	—
179	C₂²×C₄×C₇	—	2	2	no	—
180	C₂²×C₄×C₇	—	2	2	no	—
181	C₂²×C₄×C₇	—	2	2	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	8	no	—
189	C₂²×C₄×C₇	—	2	8	no	—
190	C₂²×C₄×C₇	—	2	8	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	2	no	—
199	C₂²×C₄×C₇	—	2	2	no	—
200	C₂²×C₄×C₇	—	2	2	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	8	no	—
210	C₂²×C₄×C₇	—	2	8	no	—
211	C₂²×C₄×C₇	—	4	4	no	—
212	C₂²×C₄×C₇	—	4	4	no	—
213	C₂²×C₄×C₇	—	4	4	no	—
214	C₂²×C₄×C₇	—	4	4	no	—
215	C₂²×C₄×C₇	—	4	16	no	—
216	C₂²×C₄×C₇	—	4	16	no	—
217	C₂²×C₄×C₇	—	4	16	no	—
218	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
219	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
220	C₂²×C₄×C₇	#41	1	4	yes	—
221	C₂²×C₄×C₇	#41	1	4	yes	—
222	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₇	C₂⁴	1	2	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	C₇×C₄⋊C₄	—	2	8	no	—
237	C₇×C₄⋊C₄	—	2	8	no	—
238	C₇×C₄⋊C₄	—	2	8	no	—
239	C₇×C₄⋊C₄	—	4	4	no	—
240	C₇×C₄⋊C₄	—	4	4	no	—
241	C₇×C₄⋊C₄	—	4	4	no	—
242	C₇×C₄⋊C₄	—	4	4	no	—
243	C₇×C₄⋊C₄	—	4	4	no	—
244	C₇×C₄⋊C₄	—	4	4	no	—
245	C₇×C₄⋊C₄	—	4	4	no	—
246	C₇×C₂²⋊C₄	—	2	8	no	—
247	C₇×C₂²⋊C₄	—	2	8	no	—
248	C₇×C₂²⋊C₄	—	2	8	no	—
249	C₇×C₂²⋊C₄	C₂×Q₈	1	16	yes	—
250	C₄²×C₇	—	2	8	no	—
251	C₄²×C₇	—	4	4	no	—
252	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
253	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
254	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
269	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
270	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
271	#400	C₂²×C₇	1	8	yes	complemented
272	#400	C₂²×C₇	1	8	yes	complemented
273	#400	C₂²×C₇	1	8	yes	complemented
274	#398	C₂²×C₇	1	8	yes	complemented
275	#389	C₂²×C₇	1	8	yes	complemented
276	#387	C₂²×C₇	1	8	yes	complemented
277	#387	C₂²×C₇	1	8	yes	complemented
278	#385	C₂²×C₇	1	8	yes	—
279	#385	C₂²×C₇	1	8	yes	—
280	#385	C₂²×C₇	1	8	yes	—
281	#385	C₂²×C₇	1	8	yes	—
282	#382	C₂²×C₇	1	8	yes	complemented
283	#380	C₂²×C₇	1	8	yes	—
284	C₄×C₂²⋊C₄	C₂²×C₇	1	8	yes	—
285	C₂×#95	C₂²×C₇	1	1	yes	characteristic
286	C₂×#95	C₂²×C₇	1	1	yes	characteristic
287	C₂×#95	C₂²×C₇	1	1	yes	characteristic
288	C₂×#95	C₂²×C₇	1	1	yes	characteristic
289	C₂×#95	C₂²×C₇	1	1	yes	characteristic
290	C₂×#95	C₂²×C₇	1	1	yes	characteristic
291	C₂×#95	C₂²×C₇	1	1	yes	characteristic
292	C₂×#95	C₂²×C₇	1	1	yes	characteristic
293	C₂×#95	C₂²×C₇	1	1	yes	characteristic
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	8	yes	—
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	C₂³×C₇	—	2	8	no	—
303	C₂³×C₇	—	2	8	no	—
304	C₂³×C₇	—	2	8	no	—
305	C₂³×C₇	—	2	8	no	—
306	C₂³×C₇	—	2	8	no	—
307	C₂³×C₇	—	2	8	no	—
308	C₂³×C₇	—	2	2	no	—
309	C₂³×C₇	—	2	2	no	—
310	C₂³×C₇	—	2	2	no	—
311	C₂³×C₇	—	2	2	no	—
312	C₂³×C₇	#125	1	16	yes	—
313	C₂³×C₇	C₂²×Q₈	1	4	yes	—
314	C₂³×C₇	C₂²×Q₈	1	2	yes	—
315	C₂³×C₇	C₂×#41	1	4	yes	—
316	C₂³×C₇	C₂×#41	1	4	yes	—
317	C₂³×C₇	C₂×#41	1	2	yes	—
318	C₂³×C₇	C₂×#41	1	2	yes	—
319	C₂³×C₇	C₂×#41	1	2	yes	—
320	C₂³×C₇	C₂×#41	1	2	yes	—
321	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
322	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
323	C₂³×C₇	C₂⁵	1	1	yes	characteristic
324	C₂×C₄×C₇	—	2	8	no	—
325	C₂×C₄×C₇	—	2	8	no	—
326	C₂×C₄×C₇	—	2	8	no	—
327	C₂×C₄×C₇	—	2	8	no	—
328	C₂×C₄×C₇	—	2	2	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	2	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	2	2	no	—
338	C₂×C₄×C₇	—	2	2	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	2	no	—
341	C₂×C₄×C₇	—	2	2	no	—
342	C₂×C₄×C₇	—	2	2	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	2	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	2	no	—
348	C₂×C₄×C₇	—	2	2	no	—
349	C₂×C₄×C₇	—	2	2	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	—	4	16	no	—
367	C₂×C₄×C₇	—	4	16	no	—
368	C₂×C₄×C₇	—	4	16	no	—
369	C₂×C₄×C₇	—	4	4	no	—
370	C₂×C₄×C₇	—	4	4	no	—
371	C₂×C₄×C₇	—	4	4	no	—
372	C₂×C₄×C₇	—	4	4	no	—
373	C₂×C₄×C₇	—	4	4	no	—
374	C₂×C₄×C₇	—	4	4	no	—
375	C₂×C₄×C₇	—	4	4	no	—
376	C₂×C₄×C₇	—	4	4	no	—
377	C₂×C₄×C₇	—	4	4	no	—
378	C₂×C₄×C₇	—	4	4	no	—
379	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
380	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
381	C₂×C₄×C₇	C₂×#41	1	4	yes	—
382	C₂×C₄×C₇	C₂×#41	1	4	yes	—
383	C₂⁵	C₂³×C₇	1	1	yes	characteristic
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	—	2	4	no	—
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	—	2	4	no	—
388	C₂³×C₄	—	2	4	no	—
389	C₂³×C₄	—	4	2	no	—
390	C₂³×C₄	—	4	2	no	—
391	C₂³×C₄	—	4	2	no	—
392	C₂³×C₄	—	4	2	no	—
393	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₇	1	4	yes	—
404	C₂³×C₄	C₂³×C₇	1	4	yes	—
405	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₇	1	4	yes	—
410	C₂×C₄⋊C₄	—	2	4	no	—
411	C₂×C₄⋊C₄	—	2	4	no	—
412	C₂×C₄⋊C₄	—	2	4	no	—
413	C₂×C₄⋊C₄	—	4	2	no	—
414	C₂×C₄⋊C₄	—	4	2	no	—
415	C₂×C₄⋊C₄	—	4	2	no	—
416	C₂×C₄⋊C₄	—	4	2	no	—
417	C₂×C₄⋊C₄	—	4	2	no	—
418	C₂×C₄⋊C₄	—	4	2	no	—
419	C₂×C₄⋊C₄	—	4	2	no	—
420	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
423	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₂²⋊C₄	—	2	4	no	—
432	C₂×C₂²⋊C₄	—	2	4	no	—
433	C₂×C₂²⋊C₄	C₇×Q₈	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
438	C₂×C₄²	—	2	4	no	—
439	C₂×C₄²	—	4	2	no	—
440	C₂×C₄²	C₂³×C₇	1	4	yes	—
441	C₂×C₄²	C₂³×C₇	1	4	yes	—
442	#95	C₂³×C₇	1	4	yes	—
443	#95	C₂³×C₇	1	4	yes	—
444	#95	C₂³×C₇	1	4	yes	—
445	#95	C₂³×C₇	1	4	yes	—
446	#95	C₂³×C₇	1	4	yes	—
447	#95	C₂³×C₇	1	4	yes	—
448	#95	C₂³×C₇	1	4	yes	—
449	#95	C₂³×C₇	1	4	yes	—
450	#95	C₂³×C₇	1	4	yes	—
451	#95	C₂³×C₇	1	4	yes	—
452	#95	C₂³×C₇	1	4	yes	—
453	#95	C₂³×C₇	1	4	yes	—
454	#95	C₂³×C₇	1	4	yes	—
455	#95	C₂³×C₇	1	4	yes	—
456	#95	C₂³×C₇	1	4	yes	—
457	#95	C₂³×C₇	1	4	yes	—
458	C₂²×C₇	—	2	4	no	—
459	C₂²×C₇	—	2	4	no	—
460	C₂²×C₇	—	2	4	no	—
461	C₂²×C₇	—	2	4	no	—
462	C₂²×C₇	—	2	4	no	—
463	C₂²×C₇	—	2	4	no	—
464	C₂²×C₇	—	2	32	no	—
465	C₂²×C₇	C₂×#125	1	8	yes	—
466	C₂²×C₇	C₂×#125	1	4	yes	—
467	C₂²×C₇	#529	1	4	yes	—
468	C₂²×C₇	#538	1	4	yes	—
469	C₂²×C₇	#551	1	4	yes	—
470	C₂²×C₇	#551	1	4	yes	—
471	C₂²×C₇	#554	1	4	yes	—
472	C₂²×C₇	#554	1	4	yes	—
473	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
474	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
475	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
476	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
477	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
478	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₄×C₇	—	2	4	no	—
481	C₄×C₇	—	2	4	no	—
482	C₄×C₇	—	2	4	no	—
483	C₄×C₇	—	2	4	no	—
484	C₄×C₇	—	4	2	no	—
485	C₄×C₇	—	4	2	no	—
486	C₄×C₇	—	4	2	no	—
487	C₄×C₇	—	4	2	no	—
488	C₄×C₇	—	4	2	no	—
489	C₄×C₇	—	4	2	no	—
490	C₄×C₇	—	4	2	no	—
491	C₄×C₇	—	4	2	no	—
492	C₄×C₇	—	4	2	no	—
493	C₄×C₇	—	4	2	no	—
494	C₂⁴	—	2	2	no	—
495	C₂⁴	—	2	2	no	—
496	C₂⁴	—	2	2	no	—
497	C₂⁴	—	2	2	no	—
498	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
499	C₂⁴	C₇×#41	1	4	yes	—
500	C₂⁴	C₇×#41	1	4	yes	—
501	C₂⁴	C₂⁴×C₇	1	2	yes	—
502	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	8	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	2	8	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	2	8	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	16	no	—
551	C₂²×C₄	—	4	16	no	—
552	C₂²×C₄	—	4	16	no	—
553	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
554	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
555	C₂²×C₄	C₇×#41	1	4	yes	—
556	C₂²×C₄	C₇×#41	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	8	no	—
574	C₄⋊C₄	—	4	4	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	—	4	4	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	—	4	4	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	C₂×C₇×Q₈	1	16	yes	—
585	C₄²	—	2	8	no	—
586	C₄²	—	4	4	no	—
587	C₂×C₇	—	2	8	no	—
588	C₂×C₇	#2505	1	8	yes	direct product factor
589	C₂×C₇	C₂²×#125	1	1	yes	characteristic
590	C₂×C₇	C₂×#529	1	1	yes	characteristic
591	C₂×C₇	C₂×#538	1	1	yes	characteristic
592	C₂×C₇	C₂×#551	1	1	yes	characteristic
593	C₂×C₇	C₂×#551	1	1	yes	characteristic
594	C₂×C₇	C₂×#554	1	1	yes	characteristic
595	C₂×C₇	C₂×#554	1	1	yes	characteristic
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	8	no	—
604	C₂³	—	2	8	no	—
605	C₂³	—	2	8	no	—
606	C₂³	C₇×#125	1	16	yes	—
607	C₂³	C₂²×C₇×Q₈	1	4	yes	—
608	C₂³	C₂²×C₇×Q₈	1	2	yes	—
609	C₂³	C₂×C₇×#41	1	4	yes	—
610	C₂³	C₂×C₇×#41	1	4	yes	—
611	C₂³	C₂×C₇×#41	1	2	yes	—
612	C₂³	C₂×C₇×#41	1	2	yes	—
613	C₂³	C₂×C₇×#41	1	2	yes	—
614	C₂³	C₂×C₇×#41	1	2	yes	—
615	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
616	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
617	C₂³	C₂⁵×C₇	1	1	yes	characteristic
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	8	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	16	no	—
661	C₂×C₄	—	4	16	no	—
662	C₂×C₄	—	4	16	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
674	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
675	C₂×C₄	C₂×C₇×#41	1	4	yes	—
676	C₂×C₄	C₂×C₇×#41	1	4	yes	—
677	C₇	C₂×#2505	1	1	yes	characteristic, direct product factor, Sylow
678	C₂²	—	2	32	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	4	no	—
685	C₂²	C₂×C₇×#125	1	8	yes	—
686	C₂²	C₂×C₇×#125	1	4	yes	—
687	C₂²	C₇×#529	1	4	yes	—
688	C₂²	C₇×#538	1	4	yes	—
689	C₂²	C₇×#551	1	4	yes	—
690	C₂²	C₇×#551	1	4	yes	—
691	C₂²	C₇×#554	1	4	yes	—
692	C₂²	C₇×#554	1	4	yes	—
693	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
694	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
695	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
696	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
697	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
698	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
700	C₄	—	2	4	no	—
701	C₄	—	2	4	no	—
702	C₄	—	2	4	no	—
703	C₄	—	2	4	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₂	—	2	8	no	—
715	C₂	C₇×#2505	1	8	yes	direct product factor
716	C₂	C₂²×C₇×#125	1	1	yes	characteristic
717	C₂	C₂×C₇×#529	1	1	yes	characteristic
718	C₂	C₂×C₇×#538	1	1	yes	characteristic
719	C₂	C₂×C₇×#551	1	1	yes	characteristic
720	C₂	C₂×C₇×#551	1	1	yes	characteristic
721	C₂	C₂×C₇×#554	1	1	yes	characteristic
722	C₂	C₂×C₇×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
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×#2505	C₂	direct (N × H)
2. C₂×C₇×#400	C₂	semidirect
3. C₂×C₇×#400	C₂	semidirect
4. C₂×C₇×#400	C₂	semidirect
5. C₂×C₇×#398	C₂	semidirect
6. C₂×C₇×#389	C₂	semidirect
7. C₂×C₇×#387	C₂	semidirect
8. C₂×C₇×#387	C₂	semidirect
13. C₂×C₇×#382	C₂	semidirect
36. C₇×#400	C₂²	semidirect
37. C₇×#400	C₂²	semidirect
38. C₇×#400	C₂²	semidirect
39. C₇×#398	C₂²	semidirect
40. C₇×#389	C₂²	semidirect
41. C₇×#387	C₂²	semidirect
42. C₇×#387	C₂²	semidirect
47. C₇×#382	C₂²	semidirect
67. C₂×#2505	C₇	direct (N × H)
143. #2505	C₂×C₇	direct (N × H)
144. C₂×#400	C₂×C₇	semidirect
145. C₂×#400	C₂×C₇	semidirect
146. C₂×#400	C₂×C₇	semidirect
147. C₂×#398	C₂×C₇	semidirect
148. C₂×#389	C₂×C₇	semidirect
149. C₂×#387	C₂×C₇	semidirect
150. C₂×#387	C₂×C₇	semidirect
155. C₂×#382	C₂×C₇	semidirect
271. #400	C₂²×C₇	semidirect
272. #400	C₂²×C₇	semidirect
273. #400	C₂²×C₇	semidirect
274. #398	C₂²×C₇	semidirect
275. #389	C₂²×C₇	semidirect
276. #387	C₂²×C₇	semidirect
277. #387	C₂²×C₇	semidirect
282. #382	C₂²×C₇	semidirect
588. C₂×C₇	#2505	direct (N × H)
677. C₇	C₂×#2505	direct (N × H)
715. C₂	C₇×#2505	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×#2505	2
C₂×C₇×#400	2
C₂×C₇×#398	2
C₂×C₇×#389	2
C₂×C₇×#387	2
C₂×C₇×#385	2
C₂×C₇×#382	2
C₂×C₇×#380	2
C₂×C₄×C₇×C₂²⋊C₄	2
C₂²×C₇×#95	2
C₂×#2505	7

Subgroups — C2×C7×#2505 #13211964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2505 #13211964