Subgroups — #34314784

Order 20224.

696 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23766684	C₂	1	1	yes	maximal, characteristic
2	#23764338	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764334	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764016	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764010	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764009	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764003	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763698	C₂	1	1	yes	maximal, characteristic
9	#23763583	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763583	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763582	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763582	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763518	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763518	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1870	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11929608	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
18	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₇₉⋊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×#14579071	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
29	#19098501	C₄	1	1	yes	characteristic
30	#19098501	C₄	1	1	yes	characteristic
31	#19098488	C₄	1	1	yes	characteristic
32	#19098488	C₄	1	1	yes	characteristic
33	#19098477	C₄	1	1	yes	characteristic
34	#19098477	C₄	1	1	yes	characteristic
35	#19098475	C₄	1	1	yes	characteristic
36	#19098475	C₄	1	1	yes	characteristic
37	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
41	#19098409	C₂²	1	1	yes	characteristic
42	#19098318	C₂²	1	1	yes	characteristic
43	#19098318	C₂²	1	1	yes	characteristic
44	#19098317	C₂²	1	1	yes	characteristic
45	#19098317	C₂²	1	1	yes	characteristic
46	#19098317	C₂²	1	1	yes	characteristic
47	#19098317	C₂²	1	1	yes	characteristic
48	#19098317	C₂²	1	1	yes	characteristic
49	#19098317	C₂²	1	1	yes	characteristic
50	#19098317	C₂²	1	1	yes	characteristic
51	#19098317	C₂²	1	1	yes	characteristic
52	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
57	#336×C₇₉	C₂²	1	1	yes	characteristic
58	#336×C₇₉	C₂²	1	1	yes	characteristic
59	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
60	C₂×#11929608	—	4	1	no	—
61	C₂×#11929608	—	4	1	no	—
62	C₂×#11929608	—	4	1	no	—
63	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₄×Dic₁₅₈	—	4	1	no	—
68	C₄×Dic₁₅₈	—	4	1	no	—
69	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
84	Dic₇₉⋊C₈	—	4	1	no	—
85	Dic₇₉⋊C₈	—	4	1	no	—
86	Dic₇₉⋊C₈	—	4	1	no	—
87	Dic₇₉⋊C₈	—	4	1	no	—
88	Dic₇₉⋊C₈	—	4	1	no	—
89	Dic₇₉⋊C₈	—	4	1	no	—
90	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
91	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
92	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
93	#14579071	—	4	1	no	—
94	C₈×Dic₇₉	—	4	1	no	—
95	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
96	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
97	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₇₉	—	4	1	no	—
111	C₂×M₁₆×C₇₉	—	4	1	no	—
112	C₂×M₁₆×C₇₉	—	4	1	no	—
113	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₇₉	—	4	1	no	—
118	C₄×D₄×C₇₉	—	4	1	no	—
119	C₂×C₄⋊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	C₂²⋊C₈×C₇₉	—	4	1	no	—
124	C₂²⋊C₈×C₇₉	—	4	1	no	—
125	C₂²⋊C₈×C₇₉	—	4	1	no	—
126	C₂×Dic₁₅₈	—	2	2	no	—
127	C₂×Dic₁₅₈	—	4	1	no	—
128	C₂×Dic₁₅₈	—	4	1	no	—
129	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
137	#11929608	—	4	4	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	C₄⋊Dic₇₉	—	4	1	no	—
151	Dic₇₉⋊C₄	—	4	1	no	—
152	Dic₇₉⋊C₄	—	4	1	no	—
153	C₂²⋊Dic₇₉	—	2	2	no	—
154	C₂²⋊Dic₇₉	—	2	2	no	—
155	C₂²⋊Dic₇₉	—	4	1	no	—
156	C₂²⋊Dic₇₉	—	4	1	no	—
157	C₂²⋊Dic₇₉	—	4	1	no	—
158	C₂²⋊Dic₇₉	—	4	1	no	—
159	C₂²⋊Dic₇₉	—	4	1	no	—
160	C₂²⋊Dic₇₉	—	4	1	no	—
161	C₄×Dic₇₉	—	2	1	no	—
162	C₄×Dic₇₉	—	2	1	no	—
163	C₄×Dic₇₉	—	2	1	no	—
164	C₄×Dic₇₉	—	2	1	no	—
165	C₄×Dic₇₉	—	2	1	no	—
166	C₄×Dic₇₉	—	2	1	no	—
167	C₄×Dic₇₉	—	2	1	no	—
168	C₄×Dic₇₉	—	2	1	no	—
169	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
170	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
171	C₂×D₄×C₇₉	—	4	1	no	—
172	C₂×D₄×C₇₉	—	4	1	no	—
173	C₂×D₄×C₇₉	—	4	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	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
191	M₁₆×C₇₉	—	4	4	no	—
192	C₂×C₈×C₇₉	—	2	1	no	—
193	C₂×C₈×C₇₉	—	2	1	no	—
194	C₂×C₈×C₇₉	—	2	1	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₂×C₈×C₇₉	—	2	1	no	—
197	C₂×C₈×C₇₉	—	2	1	no	—
198	C₂×C₈×C₇₉	—	2	1	no	—
199	C₂×C₈×C₇₉	—	2	1	no	—
200	C₂×C₈×C₇₉	—	2	1	no	—
201	C₂×C₈×C₇₉	—	2	1	no	—
202	C₂×C₈×C₇₉	—	2	1	no	—
203	C₂×C₈×C₇₉	—	2	1	no	—
204	C₄⋊C₄×C₇₉	—	4	1	no	—
205	C₂²⋊C₄×C₇₉	—	4	1	no	—
206	C₂²⋊C₄×C₇₉	—	4	1	no	—
207	C₄²×C₇₉	—	2	1	no	—
208	C₄²×C₇₉	—	2	1	no	—
209	C₂³×C₇₉	—	2	1	no	—
210	C₂³×C₇₉	—	2	1	no	—
211	C₂³×C₇₉	—	2	1	no	—
212	C₂³×C₇₉	—	2	1	no	—
213	C₂³×C₇₉	—	2	1	no	—
214	C₂³×C₇₉	—	2	1	no	—
215	C₂³×C₇₉	—	2	1	no	—
216	C₂³×C₇₉	—	2	1	no	—
217	C₂³×C₇₉	—	2	1	no	—
218	C₂³×C₇₉	—	2	1	no	—
219	C₂³×C₇₉	—	2	1	no	—
220	C₂³×C₇₉	—	2	1	no	—
221	C₂³×C₇₉	—	2	1	no	—
222	C₂³×C₇₉	—	2	1	no	—
223	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
224	D₄×C₇₉	—	4	4	no	—
225	C₂×C₄×C₇₉	—	2	1	no	—
226	C₂×C₄×C₇₉	—	2	1	no	—
227	C₂×C₄×C₇₉	—	2	1	no	—
228	C₂×C₄×C₇₉	—	2	1	no	—
229	C₂×C₄×C₇₉	—	2	1	no	—
230	C₂×C₄×C₇₉	—	2	1	no	—
231	C₂×C₄×C₇₉	—	2	1	no	—
232	C₂×C₄×C₇₉	—	2	1	no	—
233	C₂×C₄×C₇₉	—	2	1	no	—
234	C₂×C₄×C₇₉	—	2	1	no	—
235	C₂×C₄×C₇₉	—	2	1	no	—
236	C₂×C₄×C₇₉	—	2	1	no	—
237	C₂×C₄×C₇₉	—	4	1	no	—
238	C₂×C₄×C₇₉	—	4	1	no	—
239	C₂×C₄×C₇₉	—	4	1	no	—
240	C₂×C₄×C₇₉	—	4	1	no	—
241	C₂×C₄×C₇₉	—	4	1	no	—
242	C₂×C₄×C₇₉	—	4	1	no	—
243	C₂×C₄×C₇₉	—	4	1	no	—
244	C₂×C₄×C₇₉	—	4	1	no	—
245	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
249	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
250	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
251	C₂×Dic₇₉	—	2	1	no	—
252	C₂×Dic₇₉	—	2	1	no	—
253	C₂×Dic₇₉	—	2	1	no	—
254	C₂×Dic₇₉	—	2	1	no	—
255	C₂×Dic₇₉	—	2	1	no	—
256	C₂×Dic₇₉	—	2	1	no	—
257	C₂×Dic₇₉	—	2	1	no	—
258	C₂×Dic₇₉	—	2	1	no	—
259	C₂×Dic₇₉	—	2	1	no	—
260	C₂×Dic₇₉	—	2	1	no	—
261	C₂×Dic₇₉	—	2	1	no	—
262	C₂×Dic₇₉	—	2	1	no	—
263	C₂×Dic₇₉	—	2	1	no	—
264	C₂×Dic₇₉	—	2	1	no	—
265	C₂×Dic₇₉	—	2	1	no	—
266	C₂×Dic₇₉	—	2	1	no	—
267	C₂×Dic₇₉	—	2	1	no	—
268	C₂×Dic₇₉	—	2	1	no	—
269	C₂×Dic₇₉	—	2	1	no	—
270	C₂×Dic₇₉	—	2	1	no	—
271	C₂×Dic₇₉	—	2	1	no	—
272	C₂×Dic₇₉	—	2	1	no	—
273	C₂×Dic₇₉	—	2	1	no	—
274	C₂×Dic₇₉	#131	1	2	yes	—
275	Dic₁₅₈	—	4	4	no	—
276	C₈×C₇₉	—	4	1	no	—
277	C₈×C₇₉	—	4	1	no	—
278	C₈×C₇₉	—	4	1	no	—
279	C₈×C₇₉	—	4	1	no	—
280	C₇₉⋊C₈	—	4	1	no	—
281	C₇₉⋊C₈	—	4	1	no	—
282	C₇₉⋊C₈	—	4	1	no	—
283	C₇₉⋊C₈	—	4	1	no	—
284	C₂²×C₇₉	—	4	1	no	—
285	C₂²×C₇₉	—	4	1	no	—
286	C₂²×C₇₉	—	4	1	no	—
287	C₂²×C₇₉	—	4	1	no	—
288	C₂²×C₇₉	—	4	1	no	—
289	C₂²×C₇₉	—	4	1	no	—
290	C₂²×C₇₉	—	4	1	no	—
291	C₂²×C₇₉	—	4	1	no	—
292	C₂²×C₇₉	—	4	1	no	—
293	C₂²×C₇₉	—	4	1	no	—
294	C₂²×C₇₉	—	4	1	no	—
295	C₂²×C₇₉	—	4	1	no	—
296	C₂²×C₇₉	—	4	1	no	—
297	C₂²×C₇₉	—	4	1	no	—
298	C₂²×C₇₉	#518	1	1	yes	characteristic
299	C₂²×C₇₉	#520	1	1	yes	characteristic
300	C₂²×C₇₉	#520	1	1	yes	characteristic
301	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
302	C₂²×C₇₉	#568	1	1	yes	characteristic
303	C₂²×C₇₉	#568	1	1	yes	characteristic
304	C₂²×C₇₉	#568	1	1	yes	characteristic
305	C₄×C₇₉	—	4	1	no	—
306	C₄×C₇₉	—	4	1	no	—
307	C₄×C₇₉	—	4	1	no	—
308	C₄×C₇₉	—	4	1	no	—
309	C₄×C₇₉	H(3,𝔽₄)	1	1	yes	characteristic
310	C₄×C₇₉	#562	1	1	yes	characteristic
311	C₄×C₇₉	#562	1	1	yes	characteristic
312	C₄×C₇₉	#563	1	1	yes	characteristic
313	Dic₇₉	—	2	2	no	—
314	Dic₇₉	—	4	1	no	—
315	Dic₇₉	—	4	1	no	—
316	Dic₇₉	—	4	1	no	—
317	Dic₇₉	—	4	1	no	—
318	Dic₇₉	—	4	1	no	—
319	Dic₇₉	—	4	1	no	—
320	Dic₇₉	—	4	1	no	—
321	#23351	—	79	1	no	maximal, Sylow
322	C₂×C₇₉	—	8	1	no	—
323	C₂×C₇₉	—	8	1	no	—
324	C₂×C₇₉	#2379	1	1	yes	characteristic
325	C₂×C₇₉	#2976	1	1	yes	characteristic
326	C₂×C₇₉	#2978	1	1	yes	characteristic
327	C₂×C₇₉	#2993	1	1	yes	characteristic
328	C₂×C₇₉	#2993	1	1	yes	characteristic
329	C₂×C₇₉	#2995	1	1	yes	characteristic
330	C₂×C₇₉	#2995	1	1	yes	characteristic
331	#2398	—	79	1	no	—
332	#1985	—	79	1	no	—
333	#1984	—	79	1	no	—
334	#1924	—	79	1	no	—
335	#1924	—	79	1	no	—
336	#1923	—	79	1	no	—
337	#1923	—	79	1	no	—
338	#1870	—	79	1	no	—
339	#1870	D₇₉	1	1	yes	characteristic
340	#1851	—	79	1	no	—
341	#1851	—	79	1	no	—
342	#1851	—	79	1	no	—
343	#1851	—	79	1	no	—
344	#1832	—	79	1	no	—
345	#1832	—	79	1	no	—
346	C₇₉	#23351	1	1	yes	characteristic, complemented, Sylow
347	C₂²×M₁₆	—	79	1	no	—
348	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
349	C₂×C₄×Q₈	—	79	1	no	—
350	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
351	C₂×C₄⋊C₈	—	79	1	no	—
352	C₂×C₄⋊C₈	—	79	1	no	—
353	C₂×C₄⋊C₈	—	79	1	no	—
354	C₂×C₄⋊C₈	—	79	1	no	—
355	C₂×C₄⋊C₈	—	79	1	no	—
356	C₂×C₄⋊C₈	—	79	1	no	—
357	C₂×C₂²⋊C₈	—	79	1	no	—
358	C₂×C₂²⋊C₈	—	79	1	no	—
359	C₂×C₂²⋊C₈	—	79	1	no	—
360	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
363	C₂×#97	—	79	1	no	—
364	C₂×C₄×C₈	—	79	1	no	—
365	#400	—	79	1	no	—
366	#400	—	79	1	no	—
367	#397	—	79	1	no	—
368	#397	—	79	1	no	—
369	#394	—	79	1	no	—
370	#394	—	79	1	no	—
371	#393	—	79	1	no	—
372	#393	—	79	1	no	—
373	C₄×C₂²⋊C₄	—	79	1	no	—
374	C₄×C₂²⋊C₄	—	79	1	no	—
375	C₄×C₂²⋊C₄	—	79	1	no	—
376	C₄×C₂²⋊C₄	—	79	1	no	—
377	#376	—	79	1	no	—
378	#336	—	79	1	no	—
379	#336	—	79	1	no	—
380	#336	—	79	1	no	—
381	#336	—	79	1	no	—
382	#336	—	79	1	no	—
383	#336	—	79	1	no	—
384	#336	—	79	1	no	—
385	#336	—	79	1	no	—
386	#336	—	79	1	no	—
387	#336	—	79	1	no	—
388	#336	C₂×D₇₉	1	1	yes	characteristic
389	#336	C₂×D₇₉	1	1	yes	characteristic
390	C₂²×Q₈	—	79	1	no	—
391	C₂²×D₄	C₄×D₇₉	1	1	yes	characteristic
392	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
393	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
394	C₂×M₁₆	—	4	1	no	—
395	C₂×M₁₆	—	4	1	no	—
396	C₂×M₁₆	—	4	1	no	—
397	C₂×M₁₆	—	316	1	no	—
398	C₂×M₁₆	—	316	1	no	—
399	C₂×M₁₆	—	316	1	no	—
400	C₂²×C₈	—	79	1	no	—
401	C₂²×C₈	—	79	1	no	—
402	C₂²×C₈	—	79	1	no	—
403	C₂²×C₈	—	79	1	no	—
404	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
405	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
406	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
407	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
408	C₄×Q₈	—	316	1	no	—
409	C₄×Q₈	—	316	1	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	—	4	1	no	—
412	C₂×C₄⋊C₄	—	79	1	no	—
413	C₂×C₄⋊C₄	—	79	1	no	—
414	C₂×C₄⋊C₄	—	79	1	no	—
415	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	79	1	no	—
417	C₂×C₂²⋊C₄	—	79	1	no	—
418	C₂×C₂²⋊C₄	—	79	1	no	—
419	C₂×C₂²⋊C₄	—	79	1	no	—
420	C₂×C₂²⋊C₄	—	79	1	no	—
421	C₂×C₂²⋊C₄	—	79	1	no	—
422	C₂×C₂²⋊C₄	—	79	1	no	—
423	C₂×C₂²⋊C₄	—	79	1	no	—
424	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
426	C₂×C₄²	—	79	1	no	—
427	C₂×C₄²	—	79	1	no	—
428	C₂×C₄²	—	79	1	no	—
429	C₂×C₄²	—	79	1	no	—
430	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
431	C₄⋊C₈	—	316	1	no	—
432	C₄⋊C₈	—	316	1	no	—
433	C₄⋊C₈	—	316	1	no	—
434	C₄⋊C₈	—	316	1	no	—
435	C₄⋊C₈	—	316	1	no	—
436	C₄⋊C₈	—	316	1	no	—
437	C₂²⋊C₈	—	4	1	no	—
438	C₂²⋊C₈	—	4	1	no	—
439	C₂²⋊C₈	—	4	1	no	—
440	C₂²⋊C₈	—	316	1	no	—
441	C₂²⋊C₈	—	316	1	no	—
442	C₂²⋊C₈	—	316	1	no	—
443	#97	—	316	1	no	—
444	C₄×C₈	—	316	1	no	—
445	#95	—	79	1	no	—
446	#95	—	79	1	no	—
447	#95	—	79	1	no	—
448	#95	—	79	1	no	—
449	#95	—	79	1	no	—
450	#95	—	79	1	no	—
451	#95	—	79	1	no	—
452	#95	—	79	1	no	—
453	#95	—	79	1	no	—
454	#95	—	79	1	no	—
455	#95	—	79	1	no	—
456	#95	—	79	1	no	—
457	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
458	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
459	C₂×Q₈	—	316	1	no	—
460	C₂×Q₈	—	316	1	no	—
461	C₂×Q₈	—	158	2	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	79	1	no	—
478	C₂²×C₄	—	79	1	no	—
479	C₂²×C₄	—	79	1	no	—
480	C₂²×C₄	—	79	1	no	—
481	C₂²×C₄	—	79	1	no	—
482	C₂²×C₄	—	79	1	no	—
483	C₂²×C₄	—	79	1	no	—
484	C₂²×C₄	—	79	1	no	—
485	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
489	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
490	M₁₆	—	4	4	no	—
491	M₁₆	—	316	4	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	158	1	no	—
505	C₂×C₈	—	158	1	no	—
506	C₂×C₈	—	158	1	no	—
507	C₂×C₈	—	158	1	no	—
508	C₂×C₈	—	158	1	no	—
509	C₂×C₈	—	158	1	no	—
510	C₂×C₈	—	158	1	no	—
511	C₂×C₈	—	158	1	no	—
512	C₂×C₈	—	158	1	no	—
513	C₂×C₈	—	158	1	no	—
514	C₂×C₈	—	158	1	no	—
515	C₂×C₈	—	158	1	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	—	316	1	no	—
518	C₄⋊C₄	—	316	1	no	—
519	C₄⋊C₄	—	316	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	—	316	1	no	—
523	C₂²⋊C₄	—	316	1	no	—
524	C₂²⋊C₄	—	316	1	no	—
525	C₂²⋊C₄	—	316	1	no	—
526	C₂²⋊C₄	—	316	1	no	—
527	C₂²⋊C₄	—	316	1	no	—
528	C₂²⋊C₄	—	158	2	no	—
529	C₂²⋊C₄	—	158	2	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	158	1	no	—
533	C₄²	—	158	1	no	—
534	C₄²	—	158	1	no	—
535	C₄²	—	158	1	no	—
536	C₄²	—	158	1	no	—
537	C₄²	—	158	1	no	—
538	C₄²	—	158	1	no	—
539	C₄²	—	158	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
555	Q₈	—	316	4	no	—
556	D₄	—	4	4	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	79	2	no	—
578	C₂×C₄	—	158	1	no	—
579	C₂×C₄	—	158	1	no	—
580	C₂×C₄	—	158	1	no	—
581	C₂×C₄	—	158	1	no	—
582	C₂×C₄	—	158	1	no	—
583	C₂×C₄	—	158	1	no	—
584	C₂×C₄	—	158	1	no	—
585	C₂×C₄	—	158	1	no	—
586	C₂×C₄	—	158	1	no	—
587	C₂×C₄	—	158	1	no	—
588	C₂×C₄	—	158	1	no	—
589	C₂×C₄	—	158	1	no	—
590	C₂×C₄	—	158	1	no	—
591	C₂×C₄	—	158	1	no	—
592	C₂×C₄	—	158	1	no	—
593	C₂×C₄	—	158	1	no	—
594	C₂×C₄	—	158	1	no	—
595	C₂×C₄	—	158	1	no	—
596	C₂×C₄	—	158	1	no	—
597	C₂×C₄	—	158	1	no	—
598	C₂×C₄	—	158	1	no	—
599	C₂×C₄	—	158	1	no	—
600	C₂×C₄	—	158	1	no	—
601	C₂×C₄	#14579206	1	1	yes	characteristic
602	C₂×C₄	#14579206	1	1	yes	characteristic
603	C₂×C₄	#14579206	1	1	yes	characteristic
604	C₂×C₄	#14579206	1	1	yes	characteristic
605	C₂×C₄	#14579208	1	1	yes	characteristic
606	C₂×C₄	#14579208	1	1	yes	characteristic
607	C₈	—	4	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	316	1	no	—
612	C₈	—	316	1	no	—
613	C₈	—	316	1	no	—
614	C₈	—	316	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	#19099036	1	1	yes	characteristic
630	C₂²	#19099042	1	1	yes	characteristic
631	C₂²	#19099042	1	1	yes	characteristic
632	C₂²	#131×D₇₉	1	1	yes	characteristic
633	C₂²	#19099328	1	1	yes	characteristic
634	C₂²	#19099329	1	1	yes	characteristic
635	C₂²	#19099329	1	1	yes	characteristic
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	316	1	no	—
641	C₄	—	316	1	no	—
642	C₄	—	316	1	no	—
643	C₄	—	316	1	no	—
644	C₄	—	316	1	no	—
645	C₄	—	316	1	no	—
646	C₄	—	316	1	no	—
647	C₄	—	158	2	no	—
648	C₄	#19099306	1	1	yes	characteristic
649	C₄	#19099308	1	1	yes	characteristic
650	C₄	#19099308	1	1	yes	characteristic
651	C₄	#19099316	1	1	yes	characteristic
652	C₂	—	8	1	no	—
653	C₂	—	8	1	no	—
654	C₂	#23766570	1	1	yes	characteristic
655	C₂	#23772443	1	1	yes	characteristic
656	C₂	#23772460	1	1	yes	characteristic
657	C₂	#23772542	1	1	yes	characteristic
658	C₂	#23772546	1	1	yes	characteristic
659	C₂	#23772564	1	1	yes	characteristic
660	C₂	#23772571	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1870	C₂
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1870	D₇₉
hypocenter	C₇₉	#23351
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1870

Complements

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

N	H ≅ G/N	type
2. #23764338	C₂	semidirect
3. #23764334	C₂	semidirect
4. #23764016	C₂	semidirect
5. #23764010	C₂	semidirect
6. #23764009	C₂	semidirect
7. #23764003	C₂	semidirect
9. #23763583	C₂	semidirect
10. #23763583	C₂	semidirect
11. #23763582	C₂	semidirect
12. #23763582	C₂	semidirect
13. #23763518	C₂	semidirect
14. #23763518	C₂	semidirect
346. C₇₉	#23351	semidirect

Maximal subgroups

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

subgroup	index
#23766684	2
#23764338	2
#23764334	2
#23764016	2
#23764010	2
#23764009	2
#23764003	2
#23763698	2
#23763583	2
#23763582	2
#23763518	2
C₇₉×#1870	2
#23351	79