Subgroups — C₇×#20553 #13197769

Order 1792.

870 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#424	C₂	1	1	yes	maximal, characteristic
3	C₇×#2298	C₂	1	1	yes	maximal, characteristic
4	C₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1753	C₂	1	1	yes	maximal, characteristic
13	C₇×#1753	C₂	1	1	yes	maximal, characteristic
14	C₇×#1752	C₂	1	1	yes	maximal, characteristic
15	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×#117	C₂²	1	1	yes	characteristic
19	C₇×#433	C₄	1	8	yes	complemented
20	C₇×#424	C₄	1	8	yes	complemented
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#97	C₂²	1	1	yes	characteristic
30	C₂×C₇×#97	C₂²	1	1	yes	characteristic
31	C₂×C₇×#97	C₂²	1	1	yes	characteristic
32	C₂×C₇×#97	C₂²	1	1	yes	characteristic
33	C₂×C₇×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#388	C₄	1	2	yes	—
40	C₇×#388	C₄	1	2	yes	—
41	C₇×#387	C₄	1	2	yes	—
42	C₇×#387	C₄	1	2	yes	—
43	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₇×#376	C₂²	1	1	yes	characteristic
48	C₄³×C₇	C₂²	1	1	yes	characteristic
49	C₇×#336	C₂²	1	1	yes	characteristic
50	C₇×#336	C₂²	1	1	yes	characteristic
51	C₇×#336	C₂²	1	1	yes	characteristic
52	C₇×#336	C₂²	1	1	yes	characteristic
53	C₇×#336	C₂²	1	1	yes	characteristic
54	C₇×#336	C₂²	1	1	yes	characteristic
55	C₇×#336	C₂²	1	1	yes	characteristic
56	C₇×#336	C₂²	1	1	yes	characteristic
57	#20553	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₇×M₁₆	—	4	1	no	—
60	C₂×C₇×M₁₆	—	4	1	no	—
61	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
62	C₂²×C₇×C₈	—	4	1	no	—
63	C₂²×C₇×C₈	—	4	1	no	—
64	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₇×#117	C₂×C₄	1	4	yes	—
74	C₇×#117	C₂×C₄	1	4	yes	—
75	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
91	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
92	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
93	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
94	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
95	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
96	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
97	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
98	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
99	C₇×#97	—	4	1	no	—
100	C₇×#97	—	4	1	no	—
101	C₇×#97	—	4	1	no	—
102	C₇×#97	—	4	1	no	—
103	C₇×#97	C₂×C₄	1	4	yes	—
104	C₄×C₇×C₈	—	4	1	no	—
105	C₄×C₇×C₈	—	4	1	no	—
106	C₄×C₇×C₈	—	4	1	no	—
107	C₄×C₇×C₈	—	4	1	no	—
108	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
109	C₇×#95	C₂×C₄	1	2	yes	—
110	C₇×#95	C₂×C₄	1	2	yes	—
111	C₇×#95	C₂×C₄	1	2	yes	—
112	C₇×#95	C₂×C₄	1	2	yes	—
113	C₇×#95	C₂×C₄	1	2	yes	—
114	C₇×#95	C₂×C₄	1	2	yes	—
115	C₂×#433	C₂×C₇	1	1	yes	characteristic
116	C₂×#424	C₂×C₇	1	1	yes	characteristic
117	#2298	C₂×C₇	1	1	yes	characteristic
118	#1771	C₂×C₇	1	1	yes	characteristic, complemented
119	#1771	C₂×C₇	1	1	yes	characteristic, complemented
120	#1770	C₂×C₇	1	1	yes	characteristic, complemented
121	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
122	#1768	C₂×C₇	1	1	yes	characteristic, complemented
123	#1768	C₂×C₇	1	1	yes	characteristic, complemented
124	#1767	C₂×C₇	1	1	yes	characteristic, complemented
125	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
126	#1753	C₂×C₇	1	1	yes	characteristic
127	#1753	C₂×C₇	1	1	yes	characteristic
128	#1752	C₂×C₇	1	1	yes	characteristic
129	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
130	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	1	no	—
133	C₂²×C₄×C₇	—	2	1	no	—
134	C₂²×C₄×C₇	—	2	1	no	—
135	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
147	C₇×M₁₆	—	4	4	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	1	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	—	2	1	no	—
154	C₂×C₇×C₈	—	2	1	no	—
155	C₂×C₇×C₈	—	2	1	no	—
156	C₂×C₇×C₈	—	2	1	no	—
157	C₂×C₇×C₈	—	2	1	no	—
158	C₂×C₇×C₈	—	2	1	no	—
159	C₂×C₇×C₈	—	2	1	no	—
160	C₂×C₇×C₈	—	2	1	no	—
161	C₂×C₇×C₈	—	2	1	no	—
162	C₂×C₇×C₈	—	2	1	no	—
163	C₂×C₇×C₈	—	2	1	no	—
164	C₂×C₇×C₈	—	4	4	no	—
165	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
170	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
173	C₇×C₄⋊C₄	—	2	4	no	—
174	C₇×C₄⋊C₄	—	4	2	no	—
175	C₇×C₄⋊C₄	C₄²	1	4	yes	—
176	C₇×C₄⋊C₄	C₄²	1	4	yes	—
177	C₇×C₂²⋊C₄	—	2	4	no	—
178	C₇×C₂²⋊C₄	—	4	2	no	—
179	C₇×C₂²⋊C₄	C₄²	1	4	yes	—
180	C₇×C₂²⋊C₄	C₄²	1	4	yes	—
181	C₄²×C₇	—	2	4	no	—
182	C₄²×C₇	—	2	1	no	—
183	C₄²×C₇	—	2	1	no	—
184	C₄²×C₇	—	2	1	no	—
185	C₄²×C₇	—	2	1	no	—
186	C₄²×C₇	—	2	1	no	—
187	C₄²×C₇	—	2	1	no	—
188	C₄²×C₇	—	2	1	no	—
189	C₄²×C₇	—	2	1	no	—
190	C₄²×C₇	—	4	2	no	—
191	C₄²×C₇	C₂²×C₄	1	2	yes	—
192	C₄²×C₇	C₂²×C₄	1	2	yes	—
193	C₄²×C₇	C₂²×C₄	1	2	yes	—
194	C₄²×C₇	C₂²×C₄	1	2	yes	—
195	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
197	C₂×#117	C₂²×C₇	1	1	yes	characteristic
198	#433	C₄×C₇	1	8	yes	complemented
199	#424	C₄×C₇	1	8	yes	complemented
200	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
206	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
207	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
208	C₂×#97	C₂²×C₇	1	1	yes	characteristic
209	C₂×#97	C₂²×C₇	1	1	yes	characteristic
210	C₂×#97	C₂²×C₇	1	1	yes	characteristic
211	C₂×#97	C₂²×C₇	1	1	yes	characteristic
212	C₂×#97	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
217	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
218	#388	C₄×C₇	1	2	yes	—
219	#388	C₄×C₇	1	2	yes	—
220	#387	C₄×C₇	1	2	yes	—
221	#387	C₄×C₇	1	2	yes	—
222	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
224	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
225	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
226	#376	C₂²×C₇	1	1	yes	characteristic
227	C₄³	C₂²×C₇	1	1	yes	characteristic
228	#336	C₂²×C₇	1	1	yes	characteristic
229	#336	C₂²×C₇	1	1	yes	characteristic
230	#336	C₂²×C₇	1	1	yes	characteristic
231	#336	C₂²×C₇	1	1	yes	characteristic
232	#336	C₂²×C₇	1	1	yes	characteristic
233	#336	C₂²×C₇	1	1	yes	characteristic
234	#336	C₂²×C₇	1	1	yes	characteristic
235	#336	C₂²×C₇	1	1	yes	characteristic
236	C₂³×C₇	—	2	1	no	—
237	C₂³×C₇	—	2	1	no	—
238	C₂³×C₇	—	2	2	no	—
239	C₂³×C₇	—	2	2	no	—
240	C₂³×C₇	C₂×C₄²	1	2	yes	—
241	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	—	2	1	no	—
245	C₂×C₄×C₇	—	2	2	no	—
246	C₂×C₄×C₇	—	2	2	no	—
247	C₂×C₄×C₇	—	2	2	no	—
248	C₂×C₄×C₇	—	2	2	no	—
249	C₂×C₄×C₇	—	2	2	no	—
250	C₂×C₄×C₇	—	2	2	no	—
251	C₂×C₄×C₇	—	2	2	no	—
252	C₂×C₄×C₇	—	2	2	no	—
253	C₂×C₄×C₇	—	2	2	no	—
254	C₂×C₄×C₇	—	2	2	no	—
255	C₂×C₄×C₇	—	2	2	no	—
256	C₂×C₄×C₇	—	2	2	no	—
257	C₂×C₄×C₇	—	2	2	no	—
258	C₂×C₄×C₇	—	2	2	no	—
259	C₂×C₄×C₇	—	2	2	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	2	2	no	—
262	C₂×C₄×C₇	—	2	2	no	—
263	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
264	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
265	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
266	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
267	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
268	C₂×C₄×C₇	#131	1	4	yes	—
269	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
274	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
275	C₇×C₈	—	2	2	no	—
276	C₇×C₈	—	2	2	no	—
277	C₇×C₈	—	2	2	no	—
278	C₇×C₈	—	2	2	no	—
279	C₇×C₈	—	2	2	no	—
280	C₇×C₈	—	2	2	no	—
281	C₇×C₈	—	2	2	no	—
282	C₇×C₈	—	2	2	no	—
283	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
284	C₂×M₁₆	—	4	1	no	—
285	C₂×M₁₆	—	4	1	no	—
286	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
287	C₂²×C₈	—	4	1	no	—
288	C₂²×C₈	—	4	1	no	—
289	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
290	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
298	#117	C₂×C₄×C₇	1	4	yes	—
299	#117	C₂×C₄×C₇	1	4	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
302	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
308	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
309	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
310	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
316	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
317	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
318	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
319	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
320	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
321	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
322	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
323	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
324	#97	—	4	1	no	—
325	#97	—	4	1	no	—
326	#97	—	4	1	no	—
327	#97	—	4	1	no	—
328	#97	C₂×C₄×C₇	1	4	yes	—
329	C₄×C₈	—	4	1	no	—
330	C₄×C₈	—	4	1	no	—
331	C₄×C₈	—	4	1	no	—
332	C₄×C₈	—	4	1	no	—
333	C₄×C₈	C₂×C₄×C₇	1	4	yes	—
334	#95	C₂×C₄×C₇	1	2	yes	—
335	#95	C₂×C₄×C₇	1	2	yes	—
336	#95	C₂×C₄×C₇	1	2	yes	—
337	#95	C₂×C₄×C₇	1	2	yes	—
338	#95	C₂×C₄×C₇	1	2	yes	—
339	#95	C₂×C₄×C₇	1	2	yes	—
340	C₂²×C₇	—	2	2	no	—
341	C₂²×C₇	—	2	2	no	—
342	C₂²×C₇	—	2	2	no	—
343	C₂²×C₇	—	4	2	no	—
344	C₂²×C₇	—	4	2	no	—
345	C₂²×C₇	C₂²×C₄²	1	1	yes	characteristic
346	C₂²×C₇	#520	1	1	yes	characteristic
347	C₂²×C₇	#520	1	1	yes	characteristic
348	C₂²×C₇	C₂×#131	1	2	yes	—
349	C₂²×C₇	#568	1	2	yes	—
350	C₄×C₇	—	2	2	no	—
351	C₄×C₇	—	2	2	no	—
352	C₄×C₇	—	2	2	no	—
353	C₄×C₇	—	2	2	no	—
354	C₄×C₇	—	2	4	no	—
355	C₄×C₇	—	2	2	no	—
356	C₄×C₇	—	4	2	no	—
357	C₄×C₇	—	4	2	no	—
358	C₄×C₇	—	4	2	no	—
359	C₄×C₇	#518	1	1	yes	characteristic
360	C₄×C₇	#519	1	1	yes	characteristic
361	C₄×C₇	#520	1	1	yes	characteristic
362	C₄×C₇	#520	1	1	yes	characteristic
363	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
369	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
370	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
371	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
376	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
377	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
378	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	4	4	no	—
398	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
399	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
400	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
401	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
402	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
403	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
404	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
405	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	C₄²×C₇	1	4	yes	—
409	C₄⋊C₄	C₄²×C₇	1	4	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	C₄²×C₇	1	4	yes	—
413	C₂²⋊C₄	C₄²×C₇	1	4	yes	—
414	C₄²	—	2	4	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	4	2	no	—
424	C₄²	C₂²×C₄×C₇	1	2	yes	—
425	C₄²	C₂²×C₄×C₇	1	2	yes	—
426	C₄²	C₂²×C₄×C₇	1	2	yes	—
427	C₄²	C₂²×C₄×C₇	1	2	yes	—
428	C₂×C₇	—	4	2	no	—
429	C₂×C₇	#2274	1	1	yes	characteristic
430	C₂×C₇	C₄×#131	1	1	yes	characteristic
431	C₂×C₇	#2875	1	1	yes	characteristic
432	C₂×C₇	#2992	1	2	yes	—
433	C₂×C₇	#2993	1	2	yes	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	C₂×C₄²×C₇	1	2	yes	—
439	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
462	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
463	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
464	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
465	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
466	C₂×C₄	C₇×#131	1	4	yes	—
467	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
468	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
469	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
472	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₇	#20553	1	1	yes	characteristic, direct product factor, Sylow
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂²×C₄²×C₇	1	1	yes	characteristic
488	C₂²	C₇×#520	1	1	yes	characteristic
489	C₂²	C₇×#520	1	1	yes	characteristic
490	C₂²	C₂×C₇×#131	1	2	yes	—
491	C₂²	C₇×#568	1	2	yes	—
492	C₄	—	2	4	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	C₇×#518	1	1	yes	characteristic
502	C₄	C₇×#519	1	1	yes	characteristic
503	C₄	C₇×#520	1	1	yes	characteristic
504	C₄	C₇×#520	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	C₇×#2274	1	1	yes	characteristic
507	C₂	C₄×C₇×#131	1	1	yes	characteristic
508	C₂	C₇×#2875	1	1	yes	characteristic
509	C₂	C₇×#2992	1	2	yes	—
510	C₂	C₇×#2993	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂⁴×C₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#1771	C₂	semidirect
5. C₇×#1771	C₂	semidirect
6. C₇×#1770	C₂	semidirect
7. C₇×C₈×C₄⋊C₄	C₂	semidirect
8. C₇×#1768	C₂	semidirect
9. C₇×#1768	C₂	semidirect
10. C₇×#1767	C₂	semidirect
11. C₄×C₇×C₄⋊C₈	C₂	semidirect
19. C₇×#433	C₄	semidirect
20. C₇×#424	C₄	semidirect
57. #20553	C₇	direct (N × H)
118. #1771	C₂×C₇	semidirect
119. #1771	C₂×C₇	semidirect
120. #1770	C₂×C₇	semidirect
121. C₈×C₄⋊C₄	C₂×C₇	semidirect
122. #1768	C₂×C₇	semidirect
123. #1768	C₂×C₇	semidirect
124. #1767	C₂×C₇	semidirect
125. C₄×C₄⋊C₈	C₂×C₇	semidirect
198. #433	C₄×C₇	semidirect
199. #424	C₄×C₇	semidirect
481. C₇	#20553	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#433	2
C₂×C₇×#424	2
C₇×#2298	2
C₇×#1771	2
C₇×#1770	2
C₇×C₈×C₄⋊C₄	2
C₇×#1768	2
C₇×#1767	2
C₄×C₇×C₄⋊C₈	2
C₇×#1753	2
C₇×#1752	2
C₇×C₈×C₂²⋊C₄	2
#20553	7

Subgroups — C7×#20553 #13197769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#20553 #13197769