Subgroups — #34305307

Order 20224.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098624	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098530	C₂	1	1	yes	maximal, characteristic
3	#23764015	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764015	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764015	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764008	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763585	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763580	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763471	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763380	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763312	C₂	1	1	yes	maximal, characteristic
12	#23763184	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763178	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763162	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#2297	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	#19098624	—	2	4	no	—
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
23	#19098530	—	2	4	no	—
24	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×#14579072	C₂²	1	1	yes	characteristic
35	C₂×#14579072	C₂²	1	1	yes	characteristic
36	C₂×#14579072	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
38	#19098318	C₂²	1	1	yes	characteristic
39	#19098318	C₂²	1	1	yes	characteristic
40	#19098318	C₂²	1	1	yes	characteristic
41	#19098318	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098318	C₂²	1	1	yes	characteristic
45	#19098318	C₂²	1	1	yes	characteristic
46	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
49	#391×C₇₉	C₄	1	1	yes	characteristic
50	#391×C₇₉	C₄	1	1	yes	characteristic
51	#390×C₇₉	C₄	1	1	yes	characteristic
52	#390×C₇₉	C₄	1	1	yes	characteristic
53	#386×C₇₉	C₄	1	1	yes	characteristic
54	#386×C₇₉	C₄	1	1	yes	characteristic
55	#386×C₇₉	C₄	1	1	yes	characteristic
56	#386×C₇₉	C₄	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
61	C₂×#11929608	—	2	2	no	—
62	C₂×#11929608	—	2	2	no	—
63	C₂×#11929608	—	4	1	no	—
64	C₂²×C₇₉⋊C₈	—	2	2	no	—
65	C₂²×C₇₉⋊C₈	—	2	2	no	—
66	C₂²×C₇₉⋊C₈	—	4	1	no	—
67	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
75	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
76	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
77	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
78	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
79	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
81	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
82	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
83	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
84	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
85	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
86	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
87	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
88	C₂²⋊(C₇₉⋊C₈)	D₄	1	4	yes	—
89	#14579072	—	2	2	no	—
90	#14579072	—	4	1	no	—
91	#14579072	—	4	1	no	—
92	C₄×C₇₉⋊C₈	—	2	2	no	—
93	C₂×#41×C₇₉	—	2	2	no	—
94	C₂×#41×C₇₉	—	2	2	no	—
95	C₂×#41×C₇₉	—	2	2	no	—
96	C₂×#41×C₇₉	—	2	2	no	—
97	C₂×#41×C₇₉	—	4	1	no	—
98	C₂×#41×C₇₉	—	4	1	no	—
99	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
108	#117×C₇₉	—	2	2	no	—
109	#117×C₇₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₇₉	—	4	1	no	—
123	C₂×C₄²×C₇₉	—	4	1	no	—
124	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
130	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
131	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
132	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
133	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
134	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
135	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
136	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
137	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
138	#11929608	—	4	4	no	—
139	C₂×C₇₉⋊C₈	—	2	1	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	—	2	1	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₂×C₇₉⋊C₈	—	2	1	no	—
144	C₂×C₇₉⋊C₈	—	2	1	no	—
145	C₂×C₇₉⋊C₈	—	2	1	no	—
146	C₂×C₇₉⋊C₈	—	2	1	no	—
147	C₂×C₇₉⋊C₈	—	2	1	no	—
148	C₂×C₇₉⋊C₈	—	2	1	no	—
149	C₂×C₇₉⋊C₈	—	2	1	no	—
150	C₂×C₇₉⋊C₈	—	2	1	no	—
151	C₂×C₇₉⋊C₈	—	2	1	no	—
152	C₂×C₇₉⋊C₈	—	2	1	no	—
153	C₂×C₇₉⋊C₈	—	2	1	no	—
154	C₂×C₇₉⋊C₈	—	2	1	no	—
155	C₂×C₇₉⋊C₈	—	2	1	no	—
156	C₂×C₇₉⋊C₈	—	2	1	no	—
157	C₂×C₇₉⋊C₈	—	2	1	no	—
158	C₂×C₇₉⋊C₈	—	2	1	no	—
159	C₂×C₇₉⋊C₈	—	2	1	no	—
160	C₂×C₇₉⋊C₈	—	2	1	no	—
161	C₂×C₇₉⋊C₈	—	4	4	no	—
162	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
163	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
164	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
165	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
166	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
167	#41×C₇₉	—	4	4	no	—
168	#41×C₇₉	—	4	4	no	—
169	#41×C₇₉	—	4	4	no	—
170	#41×C₇₉	—	4	4	no	—
171	C₂×Q₈×C₇₉	—	2	2	no	—
172	C₂×Q₈×C₇₉	—	2	2	no	—
173	C₂×Q₈×C₇₉	—	4	1	no	—
174	C₂×D₄×C₇₉	—	2	2	no	—
175	C₂×D₄×C₇₉	—	2	2	no	—
176	C₂×D₄×C₇₉	—	2	2	no	—
177	C₂×D₄×C₇₉	—	2	2	no	—
178	C₂×D₄×C₇₉	—	2	2	no	—
179	C₂×D₄×C₇₉	—	2	2	no	—
180	C₂×D₄×C₇₉	—	4	1	no	—
181	C₂×D₄×C₇₉	—	4	1	no	—
182	C₂×D₄×C₇₉	—	4	1	no	—
183	C₂²×C₄×C₇₉	—	2	1	no	—
184	C₂²×C₄×C₇₉	—	2	1	no	—
185	C₂²×C₄×C₇₉	—	2	1	no	—
186	C₂²×C₄×C₇₉	—	2	1	no	—
187	C₂²×C₄×C₇₉	—	2	1	no	—
188	C₂²×C₄×C₇₉	—	2	1	no	—
189	C₂²×C₄×C₇₉	—	2	1	no	—
190	C₂²×C₄×C₇₉	—	2	1	no	—
191	C₂²×C₄×C₇₉	—	2	2	no	—
192	C₂²×C₄×C₇₉	—	2	1	no	—
193	C₂²×C₄×C₇₉	—	2	1	no	—
194	C₂²×C₄×C₇₉	—	2	1	no	—
195	C₂²×C₄×C₇₉	—	2	1	no	—
196	C₂²×C₄×C₇₉	—	2	1	no	—
197	C₂²×C₄×C₇₉	—	2	1	no	—
198	C₂²×C₄×C₇₉	—	4	1	no	—
199	C₂²×C₄×C₇₉	—	4	1	no	—
200	C₂²×C₄×C₇₉	—	4	1	no	—
201	C₂²×C₄×C₇₉	—	4	1	no	—
202	C₂²×C₄×C₇₉	—	4	1	no	—
203	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₇₉	#41	1	2	yes	—
216	C₂²×C₄×C₇₉	#41	1	2	yes	—
217	C₂²×C₄×C₇₉	#41	1	2	yes	—
218	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₇₉	—	2	2	no	—
220	C₄⋊C₄×C₇₉	—	2	2	no	—
221	C₂²⋊C₄×C₇₉	—	2	2	no	—
222	C₂²⋊C₄×C₇₉	—	2	2	no	—
223	C₂²⋊C₄×C₇₉	—	2	2	no	—
224	C₂²⋊C₄×C₇₉	—	2	2	no	—
225	C₂²⋊C₄×C₇₉	—	4	1	no	—
226	C₂²⋊C₄×C₇₉	—	4	1	no	—
227	C₂²⋊C₄×C₇₉	—	4	1	no	—
228	C₂²⋊C₄×C₇₉	—	4	1	no	—
229	C₂²⋊C₄×C₇₉	—	4	1	no	—
230	C₂²⋊C₄×C₇₉	—	4	1	no	—
231	C₄²×C₇₉	—	2	1	no	—
232	C₄²×C₇₉	—	2	1	no	—
233	C₄²×C₇₉	—	2	1	no	—
234	C₄²×C₇₉	—	2	1	no	—
235	C₄²×C₇₉	—	2	1	no	—
236	C₄²×C₇₉	—	2	1	no	—
237	C₄²×C₇₉	—	2	1	no	—
238	C₄²×C₇₉	—	2	1	no	—
239	C₄²×C₇₉	—	4	1	no	—
240	C₄²×C₇₉	—	4	1	no	—
241	C₂³×C₇₉	—	2	1	no	—
242	C₂³×C₇₉	—	2	1	no	—
243	C₂³×C₇₉	—	2	1	no	—
244	C₂³×C₇₉	—	2	1	no	—
245	C₂³×C₇₉	—	2	1	no	—
246	C₂³×C₇₉	—	2	1	no	—
247	C₂³×C₇₉	—	2	1	no	—
248	C₂³×C₇₉	—	2	1	no	—
249	C₂³×C₇₉	—	2	1	no	—
250	C₂³×C₇₉	—	2	1	no	—
251	C₂³×C₇₉	—	2	1	no	—
252	C₂³×C₇₉	—	2	1	no	—
253	C₂³×C₇₉	—	2	1	no	—
254	C₂³×C₇₉	—	2	1	no	—
255	C₂³×C₇₉	—	2	1	no	—
256	C₂³×C₇₉	—	2	1	no	—
257	C₂³×C₇₉	—	2	1	no	—
258	C₂³×C₇₉	—	2	1	no	—
259	C₂³×C₇₉	—	2	1	no	—
260	C₂³×C₇₉	#117	1	2	yes	—
261	C₂³×C₇₉	C₄×D₄	1	2	yes	—
262	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
263	Q₈×C₇₉	—	4	4	no	—
264	D₄×C₇₉	—	4	4	no	—
265	D₄×C₇₉	—	4	4	no	—
266	D₄×C₇₉	—	4	4	no	—
267	C₂×C₄×C₇₉	—	2	1	no	—
268	C₂×C₄×C₇₉	—	2	1	no	—
269	C₂×C₄×C₇₉	—	2	1	no	—
270	C₂×C₄×C₇₉	—	2	1	no	—
271	C₂×C₄×C₇₉	—	2	1	no	—
272	C₂×C₄×C₇₉	—	2	1	no	—
273	C₂×C₄×C₇₉	—	2	2	no	—
274	C₂×C₄×C₇₉	—	2	2	no	—
275	C₂×C₄×C₇₉	—	2	2	no	—
276	C₂×C₄×C₇₉	—	2	2	no	—
277	C₂×C₄×C₇₉	—	2	2	no	—
278	C₂×C₄×C₇₉	—	2	2	no	—
279	C₂×C₄×C₇₉	—	2	2	no	—
280	C₂×C₄×C₇₉	—	2	2	no	—
281	C₂×C₄×C₇₉	—	2	1	no	—
282	C₂×C₄×C₇₉	—	2	1	no	—
283	C₂×C₄×C₇₉	—	2	1	no	—
284	C₂×C₄×C₇₉	—	2	1	no	—
285	C₂×C₄×C₇₉	—	2	1	no	—
286	C₂×C₄×C₇₉	—	2	1	no	—
287	C₂×C₄×C₇₉	—	2	1	no	—
288	C₂×C₄×C₇₉	—	2	1	no	—
289	C₂×C₄×C₇₉	—	2	1	no	—
290	C₂×C₄×C₇₉	—	2	1	no	—
291	C₂×C₄×C₇₉	—	2	1	no	—
292	C₂×C₄×C₇₉	—	2	1	no	—
293	C₂×C₄×C₇₉	—	2	1	no	—
294	C₂×C₄×C₇₉	—	2	1	no	—
295	C₂×C₄×C₇₉	—	2	1	no	—
296	C₂×C₄×C₇₉	—	2	1	no	—
297	C₂×C₄×C₇₉	—	2	1	no	—
298	C₂×C₄×C₇₉	—	2	1	no	—
299	C₂×C₄×C₇₉	—	2	1	no	—
300	C₂×C₄×C₇₉	—	2	1	no	—
301	C₂×C₄×C₇₉	—	2	1	no	—
302	C₂×C₄×C₇₉	—	2	1	no	—
303	C₂×C₄×C₇₉	—	2	1	no	—
304	C₂×C₄×C₇₉	—	2	1	no	—
305	C₂×C₄×C₇₉	—	4	4	no	—
306	C₂×C₄×C₇₉	—	4	4	no	—
307	C₂×C₄×C₇₉	—	4	1	no	—
308	C₂×C₄×C₇₉	—	4	1	no	—
309	C₂×C₄×C₇₉	—	4	1	no	—
310	C₂×C₄×C₇₉	—	4	1	no	—
311	C₂×C₄×C₇₉	#117	1	2	yes	—
312	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
313	C₂×C₄×C₇₉	#131	1	2	yes	—
314	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
320	C₇₉⋊C₈	—	2	2	no	—
321	C₇₉⋊C₈	—	2	2	no	—
322	C₇₉⋊C₈	—	4	1	no	—
323	C₇₉⋊C₈	—	4	1	no	—
324	C₇₉⋊C₈	—	4	1	no	—
325	C₇₉⋊C₈	—	4	1	no	—
326	C₇₉⋊C₈	—	4	1	no	—
327	C₇₉⋊C₈	—	4	1	no	—
328	C₂²×C₇₉	—	2	2	no	—
329	C₂²×C₇₉	—	2	2	no	—
330	C₂²×C₇₉	—	2	2	no	—
331	C₂²×C₇₉	—	2	2	no	—
332	C₂²×C₇₉	—	2	2	no	—
333	C₂²×C₇₉	—	2	2	no	—
334	C₂²×C₇₉	—	4	1	no	—
335	C₂²×C₇₉	—	4	1	no	—
336	C₂²×C₇₉	—	4	1	no	—
337	C₂²×C₇₉	—	4	1	no	—
338	C₂²×C₇₉	—	4	1	no	—
339	C₂²×C₇₉	—	4	1	no	—
340	C₂²×C₇₉	—	4	1	no	—
341	C₂²×C₇₉	—	4	1	no	—
342	C₂²×C₇₉	—	4	1	no	—
343	C₂²×C₇₉	—	4	1	no	—
344	C₂²×C₇₉	—	4	1	no	—
345	C₂²×C₇₉	—	4	1	no	—
346	C₂²×C₇₉	—	4	1	no	—
347	C₂²×C₇₉	—	4	1	no	—
348	C₂²×C₇₉	—	4	1	no	—
349	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
350	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
351	C₂²×C₇₉	#518	1	1	yes	characteristic
352	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
353	C₂²×C₇₉	#568	1	1	yes	characteristic
354	C₂²×C₇₉	#568	1	1	yes	characteristic
355	C₂²×C₇₉	#568	1	1	yes	characteristic
356	C₄×C₇₉	—	2	2	no	—
357	C₄×C₇₉	—	2	2	no	—
358	C₄×C₇₉	—	2	2	no	—
359	C₄×C₇₉	—	4	1	no	—
360	C₄×C₇₉	—	4	1	no	—
361	C₄×C₇₉	—	4	1	no	—
362	C₄×C₇₉	—	4	1	no	—
363	C₄×C₇₉	—	4	1	no	—
364	C₄×C₇₉	—	4	1	no	—
365	C₄×C₇₉	—	4	1	no	—
366	C₄×C₇₉	—	4	1	no	—
367	C₄×C₇₉	#546	1	1	yes	characteristic
368	C₄×C₇₉	#546	1	1	yes	characteristic
369	C₄×C₇₉	#551	1	1	yes	characteristic
370	C₄×C₇₉	#551	1	1	yes	characteristic
371	#22561	—	79	1	no	maximal, Sylow
372	C₂×C₇₉	—	4	2	no	—
373	C₂×C₇₉	—	4	2	no	—
374	C₂×C₇₉	—	8	1	no	—
375	C₂×C₇₉	#2342	1	1	yes	characteristic
376	C₂×C₇₉	#2923	1	1	yes	characteristic
377	C₂×C₇₉	#2925	1	1	yes	characteristic
378	C₂×C₇₉	#2932	1	1	yes	characteristic
379	C₂×C₇₉	#2935	1	1	yes	characteristic
380	C₂×C₇₉	#2976	1	1	yes	characteristic
381	C₂×C₇₉	#2978	1	1	yes	characteristic
382	C₂×#433	—	79	1	no	—
383	C₂×#408	—	79	1	no	—
384	#2297	D₇₉	1	1	yes	characteristic
385	#1924	—	79	1	no	—
386	#1924	—	79	1	no	—
387	#1924	—	79	1	no	—
388	#1923	—	79	1	no	—
389	#1851	—	79	1	no	—
390	#1850	—	79	1	no	—
391	#1818	—	79	1	no	—
392	#1797	—	79	1	no	—
393	#1780	—	79	1	no	—
394	#1753	—	79	1	no	—
395	#1752	—	79	1	no	—
396	#1749	—	79	1	no	—
397	C₇₉	#22561	1	1	yes	characteristic, complemented, Sylow
398	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
399	C₂²×M₁₆	—	79	1	no	—
400	C₂³×C₈	—	79	1	no	—
401	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
402	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
403	#433	—	158	4	no	—
404	C₂×C₄⋊C₈	—	79	1	no	—
405	C₂×C₄⋊C₈	—	79	1	no	—
406	C₂×C₄⋊C₈	—	79	1	no	—
407	C₂×C₄⋊C₈	—	79	1	no	—
408	#408	—	158	4	no	—
409	C₂×C₂²⋊C₈	—	79	1	no	—
410	C₂×C₂²⋊C₈	—	79	1	no	—
411	C₂×C₂²⋊C₈	—	79	1	no	—
412	C₂×C₂²⋊C₈	—	79	1	no	—
413	C₂×C₂²⋊C₈	—	79	1	no	—
414	C₂×C₂²⋊C₈	—	79	1	no	—
415	C₂×C₂²⋊C₈	—	79	1	no	—
416	C₂×C₂²⋊C₈	—	79	1	no	—
417	C₂×C₂²⋊C₈	—	79	1	no	—
418	C₂×C₂²⋊C₈	—	79	1	no	—
419	C₂×#97	—	79	1	no	—
420	C₂×#97	—	79	1	no	—
421	C₂×#97	—	79	1	no	—
422	C₂×C₄×C₈	—	79	1	no	—
423	#391	Dic₇₉	1	1	yes	characteristic
424	#391	Dic₇₉	1	1	yes	characteristic
425	#390	Dic₇₉	1	1	yes	characteristic
426	#390	Dic₇₉	1	1	yes	characteristic
427	#386	Dic₇₉	1	1	yes	characteristic
428	#386	Dic₇₉	1	1	yes	characteristic
429	#386	Dic₇₉	1	1	yes	characteristic
430	#386	Dic₇₉	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
433	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
435	#336	—	79	1	no	—
436	#336	—	79	1	no	—
437	#336	—	79	1	no	—
438	#336	—	79	1	no	—
439	#336	—	79	1	no	—
440	#336	—	79	1	no	—
441	#336	—	79	1	no	—
442	#336	—	79	1	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	—	4	1	no	—
448	C₂×#41	—	4	1	no	—
449	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
450	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
451	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
452	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
453	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
454	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
455	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
456	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
457	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
458	C₂×M₁₆	—	316	1	no	—
459	C₂×M₁₆	—	158	2	no	—
460	C₂×M₁₆	—	158	2	no	—
461	C₂²×C₈	—	316	1	no	—
462	C₂²×C₈	—	79	1	no	—
463	C₂²×C₈	—	79	1	no	—
464	C₂²×C₈	—	79	1	no	—
465	C₂²×C₈	—	79	1	no	—
466	C₂²×C₈	—	79	1	no	—
467	C₂²×C₈	—	79	1	no	—
468	C₂²×C₈	—	79	1	no	—
469	C₂²×C₈	—	79	1	no	—
470	C₂²×C₈	—	158	2	no	—
471	C₂²×C₈	—	158	2	no	—
472	#117	—	2	2	no	—
473	#117	—	2	2	no	—
474	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
486	C₂×C₄²	—	4	1	no	—
487	C₂×C₄²	—	4	1	no	—
488	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
489	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
490	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
491	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
492	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
493	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
494	C₄⋊C₈	—	316	1	no	—
495	C₄⋊C₈	—	316	1	no	—
496	C₄⋊C₈	—	158	2	no	—
497	C₄⋊C₈	—	158	2	no	—
498	C₂²⋊C₈	—	316	1	no	—
499	C₂²⋊C₈	—	316	1	no	—
500	C₂²⋊C₈	—	79	4	no	—
501	C₂²⋊C₈	—	158	2	no	—
502	C₂²⋊C₈	—	158	2	no	—
503	C₂²⋊C₈	—	158	2	no	—
504	C₂²⋊C₈	—	158	2	no	—
505	C₂²⋊C₈	—	158	2	no	—
506	C₂²⋊C₈	—	158	2	no	—
507	C₂²⋊C₈	—	158	2	no	—
508	#97	—	316	1	no	—
509	#97	—	316	1	no	—
510	#97	—	158	2	no	—
511	C₄×C₈	—	158	2	no	—
512	#95	C₂×Dic₇₉	1	1	yes	characteristic
513	#95	C₂×Dic₇₉	1	1	yes	characteristic
514	#95	C₂×Dic₇₉	1	1	yes	characteristic
515	#95	C₂×Dic₇₉	1	1	yes	characteristic
516	#95	C₂×Dic₇₉	1	1	yes	characteristic
517	#95	C₂×Dic₇₉	1	1	yes	characteristic
518	#95	C₂×Dic₇₉	1	1	yes	characteristic
519	#95	C₂×Dic₇₉	1	1	yes	characteristic
520	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
521	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
522	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	#41	—	4	4	no	—
526	#41	—	4	4	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	4	1	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	4	1	no	—
537	C₂×D₄	—	4	1	no	—
538	C₂×D₄	—	4	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	1	no	—
559	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
560	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
561	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
562	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
563	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
564	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
565	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
566	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
567	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
568	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
569	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
570	C₂²×C₄	D₄×D₇₉	1	2	yes	—
571	C₂²×C₄	#11929623	1	2	yes	—
572	C₂²×C₄	#11929624	1	2	yes	—
573	C₂²×C₄	#11929624	1	2	yes	—
574	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
575	M₁₆	—	316	4	no	—
576	C₂×C₈	—	316	4	no	—
577	C₂×C₈	—	79	2	no	—
578	C₂×C₈	—	79	2	no	—
579	C₂×C₈	—	158	1	no	—
580	C₂×C₈	—	158	1	no	—
581	C₂×C₈	—	158	1	no	—
582	C₂×C₈	—	158	1	no	—
583	C₂×C₈	—	158	1	no	—
584	C₂×C₈	—	158	1	no	—
585	C₂×C₈	—	158	1	no	—
586	C₂×C₈	—	158	1	no	—
587	C₂×C₈	—	158	1	no	—
588	C₂×C₈	—	158	1	no	—
589	C₂×C₈	—	158	1	no	—
590	C₂×C₈	—	158	1	no	—
591	C₂×C₈	—	158	1	no	—
592	C₂×C₈	—	158	1	no	—
593	C₂×C₈	—	158	1	no	—
594	C₂×C₈	—	158	1	no	—
595	C₂×C₈	—	158	1	no	—
596	C₂×C₈	—	158	1	no	—
597	C₂×C₈	—	158	1	no	—
598	C₂×C₈	—	158	1	no	—
599	C₂×C₈	—	158	1	no	—
600	C₂×C₈	—	158	1	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	4	1	no	—
622	C₄²	—	4	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	#14579120	1	2	yes	—
643	C₂³	D₄×Dic₇₉	1	2	yes	—
644	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
645	Q₈	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	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	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	#14579120	1	2	yes	—
694	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
695	C₂×C₄	#14579168	1	2	yes	—
696	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
697	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
698	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
699	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
700	C₂×C₄	#14579206	1	1	yes	characteristic
701	C₂×C₄	#14579206	1	1	yes	characteristic
702	C₈	—	316	1	no	—
703	C₈	—	316	1	no	—
704	C₈	—	316	1	no	—
705	C₈	—	316	1	no	—
706	C₈	—	316	1	no	—
707	C₈	—	316	1	no	—
708	C₈	—	158	2	no	—
709	C₈	—	158	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	C₂×#14579120	1	1	yes	characteristic
732	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
733	C₂²	#19099038	1	1	yes	characteristic
734	C₂²	C₂×#14579168	1	1	yes	characteristic
735	C₂²	#19099330	1	1	yes	characteristic
736	C₂²	#19099330	1	1	yes	characteristic
737	C₂²	#19099330	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	#19099203	1	1	yes	characteristic
750	C₄	#19099203	1	1	yes	characteristic
751	C₄	#19099239	1	1	yes	characteristic
752	C₄	#19099239	1	1	yes	characteristic
753	C₂	—	4	2	no	—
754	C₂	—	4	2	no	—
755	C₂	—	8	1	no	—
756	C₂	#23766249	1	1	yes	characteristic
757	C₂	#23772051	1	1	yes	characteristic
758	C₂	#23772066	1	1	yes	characteristic
759	C₂	#23772118	1	1	yes	characteristic
760	C₂	#23772144	1	1	yes	characteristic
761	C₂	#23772448	1	1	yes	characteristic
762	C₂	#23772462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#2297	C₂
prime radical	C₂²×#41×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2297	D₇₉
hypocenter	C₇₉	#22561
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2297

Complements

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

N	H ≅ G/N	type
1. C₂×#19098624	C₂	semidirect
3. #23764015	C₂	semidirect
4. #23764015	C₂	semidirect
5. #23764015	C₂	semidirect
6. #23764008	C₂	semidirect
7. #23763585	C₂	semidirect
8. #23763580	C₂	semidirect
9. #23763471	C₂	semidirect
10. #23763380	C₂	semidirect
12. #23763184	C₂	semidirect
13. #23763178	C₂	semidirect
14. #23763162	C₂	semidirect
397. C₇₉	#22561	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098624	2
C₂×#19098530	2
#23764015	2
#23764008	2
#23763585	2
#23763580	2
#23763471	2
#23763380	2
#23763312	2
#23763184	2
#23763178	2
#23763162	2
C₇₉×#2297	2
#22561	79