Subgroups — #34314604

Order 20224.

776 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23764199	C₂	1	1	yes	maximal, characteristic, complemented
2	#23764199	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764015	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764015	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763966	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763966	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763698	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763698	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763693	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763693	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763585	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763580	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763471	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763384	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#2392	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
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×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
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×#14579072	C₂²	1	1	yes	characteristic
33	C₂×#14579072	C₂²	1	1	yes	characteristic
34	#19098318	C₂²	1	1	yes	characteristic
35	#19098318	C₂²	1	1	yes	characteristic
36	#19098318	C₂²	1	1	yes	characteristic
37	#19098318	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	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
48	#398×C₇₉	C₄	1	1	yes	characteristic
49	#397×C₇₉	C₄	1	1	yes	characteristic
50	#396×C₇₉	C₄	1	1	yes	characteristic
51	#396×C₇₉	C₄	1	1	yes	characteristic
52	#394×C₇₉	C₄	1	1	yes	characteristic
53	#394×C₇₉	C₄	1	1	yes	characteristic
54	#394×C₇₉	C₄	1	1	yes	characteristic
55	#392×C₇₉	C₄	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₇₉	C₂²	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	C₂×#11929608	—	4	1	no	—
60	C₂×#11929608	—	4	1	no	—
61	C₂×#11929608	—	4	1	no	—
62	C₂²×C₇₉⋊C₈	—	4	1	no	—
63	C₂²×C₇₉⋊C₈	—	4	1	no	—
64	C₂²×C₇₉⋊C₈	—	4	1	no	—
65	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
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	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
74	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
75	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
76	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
77	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
78	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
79	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
80	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
81	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
82	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
83	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
84	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
85	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
86	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
87	#14579072	—	4	1	no	—
88	#14579072	—	4	1	no	—
89	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₇₉	—	4	1	no	—
96	C₄×D₄×C₇₉	—	4	1	no	—
97	C₄×D₄×C₇₉	—	4	1	no	—
98	C₄×D₄×C₇₉	—	4	1	no	—
99	C₄×D₄×C₇₉	—	4	1	no	—
100	C₄×D₄×C₇₉	—	4	1	no	—
101	#117×C₇₉	—	4	1	no	—
102	#117×C₇₉	—	4	1	no	—
103	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊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	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
126	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
127	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
128	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
129	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
130	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
131	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
132	#11929608	—	4	4	no	—
133	C₂×C₇₉⋊C₈	—	2	1	no	—
134	C₂×C₇₉⋊C₈	—	2	1	no	—
135	C₂×C₇₉⋊C₈	—	2	1	no	—
136	C₂×C₇₉⋊C₈	—	2	1	no	—
137	C₂×C₇₉⋊C₈	—	2	1	no	—
138	C₂×C₇₉⋊C₈	—	2	1	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	—	4	4	no	—
158	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
159	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
160	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×D₄×C₇₉	—	2	2	no	—
162	C₂×D₄×C₇₉	—	2	2	no	—
163	C₂×D₄×C₇₉	—	4	1	no	—
164	C₂×D₄×C₇₉	—	4	1	no	—
165	C₂×D₄×C₇₉	—	4	1	no	—
166	C₂×D₄×C₇₉	—	4	1	no	—
167	C₂×D₄×C₇₉	—	4	1	no	—
168	C₂×D₄×C₇₉	—	4	1	no	—
169	C₂×D₄×C₇₉	—	4	1	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	1	no	—
173	C₂²×C₄×C₇₉	—	2	1	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	2	1	no	—
178	C₂²×C₄×C₇₉	—	2	1	no	—
179	C₂²×C₄×C₇₉	—	2	1	no	—
180	C₂²×C₄×C₇₉	—	2	1	no	—
181	C₂²×C₄×C₇₉	—	2	1	no	—
182	C₂²×C₄×C₇₉	—	2	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	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
200	C₄⋊C₄×C₇₉	—	4	1	no	—
201	C₄⋊C₄×C₇₉	—	4	1	no	—
202	C₄⋊C₄×C₇₉	—	4	1	no	—
203	C₄⋊C₄×C₇₉	—	4	1	no	—
204	C₄⋊C₄×C₇₉	—	4	1	no	—
205	C₄⋊C₄×C₇₉	—	4	1	no	—
206	C₄⋊C₄×C₇₉	—	4	1	no	—
207	C₂²⋊C₄×C₇₉	—	2	2	no	—
208	C₂²⋊C₄×C₇₉	—	4	1	no	—
209	C₂²⋊C₄×C₇₉	—	4	1	no	—
210	C₂²⋊C₄×C₇₉	—	4	1	no	—
211	C₂²⋊C₄×C₇₉	—	4	1	no	—
212	C₂²⋊C₄×C₇₉	—	4	1	no	—
213	C₂²⋊C₄×C₇₉	—	4	1	no	—
214	C₂²⋊C₄×C₇₉	—	4	1	no	—
215	C₂²⋊C₄×C₇₉	—	4	1	no	—
216	C₂²⋊C₄×C₇₉	—	4	1	no	—
217	C₂²⋊C₄×C₇₉	—	4	1	no	—
218	C₂²⋊C₄×C₇₉	—	4	1	no	—
219	C₄²×C₇₉	—	2	1	no	—
220	C₄²×C₇₉	—	2	1	no	—
221	C₄²×C₇₉	—	2	1	no	—
222	C₄²×C₇₉	—	2	1	no	—
223	C₄²×C₇₉	—	2	1	no	—
224	C₄²×C₇₉	—	2	1	no	—
225	C₄²×C₇₉	—	2	1	no	—
226	C₄²×C₇₉	—	2	1	no	—
227	C₂³×C₇₉	—	2	1	no	—
228	C₂³×C₇₉	—	2	1	no	—
229	C₂³×C₇₉	—	2	1	no	—
230	C₂³×C₇₉	—	2	1	no	—
231	C₂³×C₇₉	—	2	1	no	—
232	C₂³×C₇₉	—	2	1	no	—
233	C₂³×C₇₉	—	2	1	no	—
234	C₂³×C₇₉	—	2	1	no	—
235	C₂³×C₇₉	—	2	1	no	—
236	C₂³×C₇₉	—	2	1	no	—
237	C₂³×C₇₉	—	2	1	no	—
238	C₂³×C₇₉	—	2	1	no	—
239	C₂³×C₇₉	—	2	1	no	—
240	C₂³×C₇₉	—	2	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	#131	1	2	yes	—
248	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
249	D₄×C₇₉	—	4	4	no	—
250	D₄×C₇₉	—	4	4	no	—
251	D₄×C₇₉	—	4	4	no	—
252	C₂×C₄×C₇₉	—	2	1	no	—
253	C₂×C₄×C₇₉	—	2	1	no	—
254	C₂×C₄×C₇₉	—	2	1	no	—
255	C₂×C₄×C₇₉	—	2	1	no	—
256	C₂×C₄×C₇₉	—	2	1	no	—
257	C₂×C₄×C₇₉	—	2	1	no	—
258	C₂×C₄×C₇₉	—	2	1	no	—
259	C₂×C₄×C₇₉	—	2	1	no	—
260	C₂×C₄×C₇₉	—	2	1	no	—
261	C₂×C₄×C₇₉	—	2	1	no	—
262	C₂×C₄×C₇₉	—	2	1	no	—
263	C₂×C₄×C₇₉	—	2	1	no	—
264	C₂×C₄×C₇₉	—	2	1	no	—
265	C₂×C₄×C₇₉	—	2	1	no	—
266	C₂×C₄×C₇₉	—	2	1	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	1	no	—
274	C₂×C₄×C₇₉	—	2	1	no	—
275	C₂×C₄×C₇₉	—	2	1	no	—
276	C₂×C₄×C₇₉	—	2	1	no	—
277	C₂×C₄×C₇₉	—	2	1	no	—
278	C₂×C₄×C₇₉	—	2	1	no	—
279	C₂×C₄×C₇₉	—	2	1	no	—
280	C₂×C₄×C₇₉	—	2	1	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	—	4	1	no	—
286	C₂×C₄×C₇₉	—	4	1	no	—
287	C₂×C₄×C₇₉	—	4	1	no	—
288	C₂×C₄×C₇₉	—	4	1	no	—
289	C₂×C₄×C₇₉	—	4	1	no	—
290	C₂×C₄×C₇₉	—	4	1	no	—
291	C₂×C₄×C₇₉	—	4	1	no	—
292	C₂×C₄×C₇₉	—	4	1	no	—
293	C₂×C₄×C₇₉	—	4	1	no	—
294	C₂×C₄×C₇₉	—	4	1	no	—
295	C₂×C₄×C₇₉	—	4	1	no	—
296	C₂×C₄×C₇₉	—	4	1	no	—
297	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
303	C₇₉⋊C₈	—	4	1	no	—
304	C₇₉⋊C₈	—	4	1	no	—
305	C₇₉⋊C₈	—	4	1	no	—
306	C₇₉⋊C₈	—	4	1	no	—
307	C₇₉⋊C₈	—	4	1	no	—
308	C₇₉⋊C₈	—	4	1	no	—
309	C₇₉⋊C₈	—	4	1	no	—
310	C₇₉⋊C₈	—	4	1	no	—
311	C₂²×C₇₉	—	2	2	no	—
312	C₂²×C₇₉	—	2	2	no	—
313	C₂²×C₇₉	—	2	2	no	—
314	C₂²×C₇₉	—	4	1	no	—
315	C₂²×C₇₉	—	4	1	no	—
316	C₂²×C₇₉	—	4	1	no	—
317	C₂²×C₇₉	—	4	1	no	—
318	C₂²×C₇₉	—	4	1	no	—
319	C₂²×C₇₉	—	4	1	no	—
320	C₂²×C₇₉	—	4	1	no	—
321	C₂²×C₇₉	—	4	1	no	—
322	C₂²×C₇₉	—	4	1	no	—
323	C₂²×C₇₉	—	4	1	no	—
324	C₂²×C₇₉	—	4	1	no	—
325	C₂²×C₇₉	—	4	1	no	—
326	C₂²×C₇₉	—	4	1	no	—
327	C₂²×C₇₉	—	4	1	no	—
328	C₂²×C₇₉	—	4	1	no	—
329	C₂²×C₇₉	—	4	1	no	—
330	C₂²×C₇₉	—	4	1	no	—
331	C₂²×C₇₉	—	4	1	no	—
332	C₂²×C₇₉	#518	1	1	yes	characteristic
333	C₂²×C₇₉	#518	1	1	yes	characteristic
334	C₂²×C₇₉	#520	1	1	yes	characteristic
335	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
336	C₂²×C₇₉	#568	1	1	yes	characteristic
337	C₂²×C₇₉	#568	1	1	yes	characteristic
338	C₂²×C₇₉	#568	1	1	yes	characteristic
339	C₄×C₇₉	—	4	1	no	—
340	C₄×C₇₉	—	4	1	no	—
341	C₄×C₇₉	—	4	1	no	—
342	C₄×C₇₉	—	4	1	no	—
343	C₄×C₇₉	—	4	1	no	—
344	C₄×C₇₉	—	4	1	no	—
345	C₄×C₇₉	—	4	1	no	—
346	C₄×C₇₉	—	4	1	no	—
347	C₄×C₇₉	—	4	1	no	—
348	C₄×C₇₉	—	4	1	no	—
349	C₄×C₇₉	—	4	1	no	—
350	C₄×C₇₉	#560	1	1	yes	characteristic
351	C₄×C₇₉	#560	1	1	yes	characteristic
352	C₄×C₇₉	#562	1	1	yes	characteristic
353	C₄×C₇₉	#562	1	1	yes	characteristic
354	#23335	—	79	1	no	maximal, Sylow
355	C₂×C₇₉	—	4	2	no	—
356	C₂×C₇₉	—	8	1	no	—
357	C₂×C₇₉	—	8	1	no	—
358	C₂×C₇₉	#2377	1	1	yes	characteristic
359	C₂×C₇₉	#2976	1	1	yes	characteristic
360	C₂×C₇₉	#2976	1	1	yes	characteristic
361	C₂×C₇₉	#2978	1	1	yes	characteristic
362	C₂×C₇₉	#2980	1	1	yes	characteristic
363	C₂×C₇₉	#2992	1	1	yes	characteristic
364	C₂×C₇₉	#2995	1	1	yes	characteristic
365	#2392	D₇₉	1	1	yes	characteristic
366	#1955	—	79	1	no	—
367	#1955	—	79	1	no	—
368	#1924	—	79	1	no	—
369	#1924	—	79	1	no	—
370	#1917	—	79	1	no	—
371	#1917	—	79	1	no	—
372	#1870	—	79	1	no	—
373	#1870	—	79	1	no	—
374	#1869	—	79	1	no	—
375	#1869	—	79	1	no	—
376	#1851	—	79	1	no	—
377	#1850	—	79	1	no	—
378	#1818	—	79	1	no	—
379	#1798	—	79	1	no	—
380	C₇₉	#23335	1	1	yes	characteristic, complemented, Sylow
381	C₂²×M₁₆	—	79	1	no	—
382	C₂³×C₈	—	79	1	no	—
383	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
386	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
387	C₂×C₄⋊C₈	—	79	1	no	—
388	C₂×C₄⋊C₈	—	79	1	no	—
389	C₂×C₄⋊C₈	—	79	1	no	—
390	C₂×C₄⋊C₈	—	79	1	no	—
391	C₂×C₂²⋊C₈	—	79	1	no	—
392	C₂×C₂²⋊C₈	—	79	1	no	—
393	C₂×C₂²⋊C₈	—	79	1	no	—
394	C₂×C₂²⋊C₈	—	79	1	no	—
395	C₂×C₂²⋊C₈	—	79	1	no	—
396	C₂×C₂²⋊C₈	—	79	1	no	—
397	C₂×C₂²⋊C₈	—	79	1	no	—
398	C₂×C₂²⋊C₈	—	79	1	no	—
399	C₂×C₂²⋊C₈	—	79	1	no	—
400	C₂×C₂²⋊C₈	—	79	1	no	—
401	C₂×#97	—	79	1	no	—
402	C₂×#97	—	79	1	no	—
403	#398	Dic₇₉	1	1	yes	characteristic
404	#397	Dic₇₉	1	1	yes	characteristic
405	#396	Dic₇₉	1	1	yes	characteristic
406	#396	Dic₇₉	1	1	yes	characteristic
407	#394	Dic₇₉	1	1	yes	characteristic
408	#394	Dic₇₉	1	1	yes	characteristic
409	#394	Dic₇₉	1	1	yes	characteristic
410	#392	Dic₇₉	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
413	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
414	#336	—	79	1	no	—
415	#336	—	79	1	no	—
416	#336	—	79	1	no	—
417	#336	—	79	1	no	—
418	#336	—	79	1	no	—
419	#336	—	79	1	no	—
420	#336	—	79	1	no	—
421	#336	—	79	1	no	—
422	#336	—	79	1	no	—
423	#336	—	79	1	no	—
424	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
425	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
426	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
427	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
428	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
429	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
430	C₂×M₁₆	—	316	1	no	—
431	C₂×M₁₆	—	316	1	no	—
432	C₂×M₁₆	—	316	1	no	—
433	C₂²×C₈	—	316	1	no	—
434	C₂²×C₈	—	316	1	no	—
435	C₂²×C₈	—	316	1	no	—
436	C₂²×C₈	—	79	1	no	—
437	C₂²×C₈	—	79	1	no	—
438	C₂²×C₈	—	79	1	no	—
439	C₂²×C₈	—	79	1	no	—
440	C₂²×C₈	—	79	1	no	—
441	C₂²×C₈	—	79	1	no	—
442	C₂²×C₈	—	79	1	no	—
443	C₂²×C₈	—	79	1	no	—
444	C₄×D₄	—	4	1	no	—
445	C₄×D₄	—	4	1	no	—
446	C₄×D₄	—	4	1	no	—
447	C₄×D₄	—	4	1	no	—
448	C₄×D₄	—	4	1	no	—
449	C₄×D₄	—	4	1	no	—
450	#117	—	4	1	no	—
451	#117	—	4	1	no	—
452	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
471	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
472	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
473	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
474	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
475	C₄⋊C₈	—	316	1	no	—
476	C₄⋊C₈	—	316	1	no	—
477	C₄⋊C₈	—	316	1	no	—
478	C₄⋊C₈	—	316	1	no	—
479	C₂²⋊C₈	—	316	1	no	—
480	C₂²⋊C₈	—	316	1	no	—
481	C₂²⋊C₈	—	316	1	no	—
482	C₂²⋊C₈	—	316	1	no	—
483	C₂²⋊C₈	—	316	1	no	—
484	C₂²⋊C₈	—	316	1	no	—
485	C₂²⋊C₈	—	316	1	no	—
486	C₂²⋊C₈	—	316	1	no	—
487	C₂²⋊C₈	—	316	1	no	—
488	C₂²⋊C₈	—	316	1	no	—
489	#97	—	316	1	no	—
490	#97	—	316	1	no	—
491	#95	C₂×Dic₇₉	1	1	yes	characteristic
492	#95	C₂×Dic₇₉	1	1	yes	characteristic
493	#95	C₂×Dic₇₉	1	1	yes	characteristic
494	#95	C₂×Dic₇₉	1	1	yes	characteristic
495	#95	C₂×Dic₇₉	1	1	yes	characteristic
496	#95	C₂×Dic₇₉	1	1	yes	characteristic
497	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
498	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
499	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	4	1	no	—
503	C₂×D₄	—	4	1	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	—	4	1	no	—
506	C₂×D₄	—	4	1	no	—
507	C₂×D₄	—	4	1	no	—
508	C₂×D₄	—	4	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
528	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
529	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
530	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
531	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
532	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
533	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
534	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
535	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
536	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
537	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
538	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
539	M₁₆	—	316	4	no	—
540	C₂×C₈	—	316	4	no	—
541	C₂×C₈	—	158	1	no	—
542	C₂×C₈	—	158	1	no	—
543	C₂×C₈	—	158	1	no	—
544	C₂×C₈	—	158	1	no	—
545	C₂×C₈	—	158	1	no	—
546	C₂×C₈	—	158	1	no	—
547	C₂×C₈	—	158	1	no	—
548	C₂×C₈	—	158	1	no	—
549	C₂×C₈	—	158	1	no	—
550	C₂×C₈	—	158	1	no	—
551	C₂×C₈	—	158	1	no	—
552	C₂×C₈	—	158	1	no	—
553	C₂×C₈	—	158	1	no	—
554	C₂×C₈	—	158	1	no	—
555	C₂×C₈	—	158	1	no	—
556	C₂×C₈	—	158	1	no	—
557	C₂×C₈	—	158	1	no	—
558	C₂×C₈	—	158	1	no	—
559	C₂×C₈	—	158	1	no	—
560	C₂×C₈	—	158	1	no	—
561	C₂×C₈	—	158	1	no	—
562	C₂×C₈	—	158	1	no	—
563	C₂×C₈	—	158	1	no	—
564	C₂×C₈	—	158	1	no	—
565	C₄⋊C₄	—	4	1	no	—
566	C₄⋊C₄	—	4	1	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	—	4	1	no	—
569	C₄⋊C₄	—	4	1	no	—
570	C₄⋊C₄	—	4	1	no	—
571	C₄⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	1	no	—
577	C₂²⋊C₄	—	4	1	no	—
578	C₂²⋊C₄	—	4	1	no	—
579	C₂²⋊C₄	—	4	1	no	—
580	C₂²⋊C₄	—	4	1	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	4	1	no	—
583	C₂²⋊C₄	—	4	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	#14579168	1	2	yes	—
613	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
614	D₄	—	4	4	no	—
615	D₄	—	4	4	no	—
616	D₄	—	4	4	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	#14579206	1	1	yes	characteristic
663	C₂×C₄	#14579206	1	1	yes	characteristic
664	C₂×C₄	#14579206	1	1	yes	characteristic
665	C₂×C₄	#14579206	1	1	yes	characteristic
666	C₂×C₄	#14579207	1	1	yes	characteristic
667	C₂×C₄	#14579208	1	1	yes	characteristic
668	C₈	—	316	1	no	—
669	C₈	—	316	1	no	—
670	C₈	—	316	1	no	—
671	C₈	—	316	1	no	—
672	C₈	—	316	1	no	—
673	C₈	—	316	1	no	—
674	C₈	—	316	1	no	—
675	C₈	—	316	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	#19099038	1	1	yes	characteristic
698	C₂²	#19099038	1	1	yes	characteristic
699	C₂²	#19099046	1	1	yes	characteristic
700	C₂²	C₂×#14579168	1	1	yes	characteristic
701	C₂²	#19099330	1	1	yes	characteristic
702	C₂²	#19099330	1	1	yes	characteristic
703	C₂²	#19099330	1	1	yes	characteristic
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	#19099301	1	1	yes	characteristic
716	C₄	#19099301	1	1	yes	characteristic
717	C₄	#19099308	1	1	yes	characteristic
718	C₄	#19099308	1	1	yes	characteristic
719	C₂	—	4	2	no	—
720	C₂	—	8	1	no	—
721	C₂	—	8	1	no	—
722	C₂	#23766557	1	1	yes	characteristic
723	C₂	#23772448	1	1	yes	characteristic
724	C₂	#23772448	1	1	yes	characteristic
725	C₂	#23772462	1	1	yes	characteristic
726	C₂	#23772471	1	1	yes	characteristic
727	C₂	#23772539	1	1	yes	characteristic
728	C₂	#23772570	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#2392	C₂
prime radical	#392×C₇₉	C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2392	D₇₉
hypocenter	C₇₉	#23335
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2392

Complements

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

N	H ≅ G/N	type
1. #23764199	C₂	semidirect
2. #23764199	C₂	semidirect
3. #23764015	C₂	semidirect
4. #23764015	C₂	semidirect
5. #23763966	C₂	semidirect
6. #23763966	C₂	semidirect
7. #23763698	C₂	semidirect
8. #23763698	C₂	semidirect
9. #23763693	C₂	semidirect
10. #23763693	C₂	semidirect
11. #23763585	C₂	semidirect
12. #23763580	C₂	semidirect
13. #23763471	C₂	semidirect
14. #23763384	C₂	semidirect
380. C₇₉	#23335	semidirect

Maximal subgroups

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

subgroup	index
#23764199	2
#23764015	2
#23763966	2
#23763698	2
#23763693	2
#23763585	2
#23763580	2
#23763471	2
#23763384	2
C₇₉×#2392	2
#23335	79