Subgroups — #34314436

Order 20224.

680 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23766659	C₂	1	1	yes	maximal, characteristic
2	#23764199	C₂	1	1	yes	maximal, characteristic
3	#23764122	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764117	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764016	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764010	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764009	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764003	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763962	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763962	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763583	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763583	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763382	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763382	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1870	C₂	1	1	yes	maximal, characteristic
16	C₂×#14579120	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₇₉⋊C₈)	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×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×#14579072	C₂²	1	1	yes	characteristic
29	C₂×#14579071	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
31	#19098502	C₄	1	1	yes	characteristic
32	#19098499	C₄	1	1	yes	characteristic
33	#19098493	C₄	1	1	yes	characteristic
34	#19098491	C₄	1	1	yes	characteristic
35	#19098491	C₄	1	1	yes	characteristic
36	#19098488	C₄	1	1	yes	characteristic
37	#19098477	C₄	1	1	yes	characteristic
38	#19098477	C₄	1	1	yes	characteristic
39	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊Dic₇₉	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×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
63	#14579120	—	4	1	no	—
64	#14579120	—	4	1	no	—
65	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
67	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₇₉⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊Dic₇₉	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×C₄×Dic₇₉	C₂³	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	C₄⋊(C₇₉⋊C₈)	—	4	1	no	—
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	C₂²⋊(C₇₉⋊C₈)	—	4	1	no	—
94	#14579072	—	4	1	no	—
95	#14579071	—	4	1	no	—
96	C₈×Dic₇₉	—	4	1	no	—
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	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
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	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	C₄⋊Dic₇₉	—	4	1	no	—
147	C₄⋊Dic₇₉	—	4	1	no	—
148	Dic₇₉⋊C₄	—	2	2	no	—
149	Dic₇₉⋊C₄	—	4	1	no	—
150	Dic₇₉⋊C₄	—	4	1	no	—
151	Dic₇₉⋊C₄	—	4	1	no	—
152	C₂²⋊Dic₇₉	—	2	2	no	—
153	C₂²⋊Dic₇₉	—	2	2	no	—
154	C₂²⋊Dic₇₉	—	4	1	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	C₄×Dic₇₉	—	2	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	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×D₄×C₇₉	—	4	1	no	—
171	C₂×D₄×C₇₉	—	4	1	no	—
172	C₂×D₄×C₇₉	—	4	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	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
190	M₁₆×C₇₉	—	4	4	no	—
191	C₂×C₈×C₇₉	—	2	1	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	C₄⋊C₄×C₇₉	—	4	1	no	—
204	C₂²⋊C₄×C₇₉	—	4	1	no	—
205	C₂²⋊C₄×C₇₉	—	4	1	no	—
206	C₄²×C₇₉	—	2	1	no	—
207	C₄²×C₇₉	—	2	1	no	—
208	C₂³×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	C₂³×C₄	1	1	yes	characteristic
223	D₄×C₇₉	—	4	4	no	—
224	C₂×C₄×C₇₉	—	2	1	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	—	4	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	H(5,𝔽₂)	1	1	yes	characteristic
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	2₋¹⁺⁴	1	1	yes	characteristic
249	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
250	C₂×Dic₇₉	—	2	1	no	—
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	#131	1	2	yes	—
274	C₈×C₇₉	—	4	1	no	—
275	C₈×C₇₉	—	4	1	no	—
276	C₈×C₇₉	—	4	1	no	—
277	C₈×C₇₉	—	4	1	no	—
278	C₇₉⋊C₈	—	4	1	no	—
279	C₇₉⋊C₈	—	4	1	no	—
280	C₇₉⋊C₈	—	4	1	no	—
281	C₇₉⋊C₈	—	4	1	no	—
282	C₂²×C₇₉	—	4	1	no	—
283	C₂²×C₇₉	—	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	#518	1	1	yes	characteristic
297	C₂²×C₇₉	#520	1	1	yes	characteristic
298	C₂²×C₇₉	#520	1	1	yes	characteristic
299	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
300	C₂²×C₇₉	#568	1	1	yes	characteristic
301	C₂²×C₇₉	#568	1	1	yes	characteristic
302	C₂²×C₇₉	#568	1	1	yes	characteristic
303	C₄×C₇₉	—	4	1	no	—
304	C₄×C₇₉	—	4	1	no	—
305	C₄×C₇₉	—	4	1	no	—
306	C₄×C₇₉	—	4	1	no	—
307	C₄×C₇₉	#560	1	1	yes	characteristic
308	C₄×C₇₉	#562	1	1	yes	characteristic
309	C₄×C₇₉	#562	1	1	yes	characteristic
310	C₄×C₇₉	#563	1	1	yes	characteristic
311	Dic₇₉	—	2	2	no	—
312	Dic₇₉	—	4	1	no	—
313	Dic₇₉	—	4	1	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	#23321	—	79	1	no	maximal, Sylow
320	C₂×C₇₉	—	8	1	no	—
321	C₂×C₇₉	—	8	1	no	—
322	C₂×C₇₉	#2376	1	1	yes	characteristic
323	C₂×C₇₉	#2978	1	1	yes	characteristic
324	C₂×C₇₉	#2981	1	1	yes	characteristic
325	C₂×C₇₉	#2992	1	1	yes	characteristic
326	C₂×C₇₉	#2993	1	1	yes	characteristic
327	C₂×C₇₉	#2995	1	1	yes	characteristic
328	C₂×C₇₉	#2995	1	1	yes	characteristic
329	#2395	—	79	1	no	—
330	#1955	—	79	1	no	—
331	#1940	—	79	1	no	—
332	#1939	—	79	1	no	—
333	#1924	—	79	1	no	—
334	#1924	—	79	1	no	—
335	#1923	—	79	1	no	—
336	#1923	—	79	1	no	—
337	#1917	—	79	1	no	—
338	#1917	—	79	1	no	—
339	#1870	D₇₉	1	1	yes	characteristic
340	#1851	—	79	1	no	—
341	#1851	—	79	1	no	—
342	#1798	—	79	1	no	—
343	#1798	—	79	1	no	—
344	C₇₉	#23321	1	1	yes	characteristic, complemented, Sylow
345	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
346	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
347	C₂×#117	—	79	1	no	—
348	C₂×C₄⋊C₈	—	79	1	no	—
349	C₂×C₄⋊C₈	—	79	1	no	—
350	C₂×C₄⋊C₈	—	79	1	no	—
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×C₂²⋊C₈	—	79	1	no	—
356	C₂×C₂²⋊C₈	—	79	1	no	—
357	C₂×C₂²⋊C₈	—	79	1	no	—
358	C₂×C₂²⋊C₈	—	79	1	no	—
359	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
360	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
362	C₂×#97	—	79	1	no	—
363	C₂×#97	—	79	1	no	—
364	C₂×C₄×C₈	—	79	1	no	—
365	#400	—	79	1	no	—
366	#399	—	79	1	no	—
367	#398	—	79	1	no	—
368	#397	—	79	1	no	—
369	#397	—	79	1	no	—
370	#397	—	79	1	no	—
371	#394	—	79	1	no	—
372	#394	—	79	1	no	—
373	C₄×C₄⋊C₄	—	79	1	no	—
374	C₄×C₄⋊C₄	—	79	1	no	—
375	C₄×C₂²⋊C₄	—	79	1	no	—
376	C₄×C₂²⋊C₄	—	79	1	no	—
377	C₄×C₂²⋊C₄	—	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	C₂×D₇₉	1	1	yes	characteristic
387	#336	C₂×D₇₉	1	1	yes	characteristic
388	C₂²×D₄	C₄×D₇₉	1	1	yes	characteristic
389	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
390	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
391	C₂×M₁₆	—	4	1	no	—
392	C₂×M₁₆	—	4	1	no	—
393	C₂×M₁₆	—	4	1	no	—
394	C₂²×C₈	—	79	1	no	—
395	C₂²×C₈	—	79	1	no	—
396	C₂²×C₈	—	79	1	no	—
397	C₂²×C₈	—	79	1	no	—
398	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
399	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
401	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
402	C₄×D₄	—	4	1	no	—
403	C₄×D₄	—	4	1	no	—
404	#117	—	316	1	no	—
405	#117	—	316	1	no	—
406	C₂×C₄⋊C₄	—	79	1	no	—
407	C₂×C₄⋊C₄	—	79	1	no	—
408	C₂×C₄⋊C₄	—	79	1	no	—
409	C₂×C₄⋊C₄	—	79	1	no	—
410	C₂×C₄⋊C₄	—	79	1	no	—
411	C₂×C₄⋊C₄	—	79	1	no	—
412	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	79	1	no	—
414	C₂×C₂²⋊C₄	—	79	1	no	—
415	C₂×C₂²⋊C₄	—	79	1	no	—
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	C₄×D₇₉	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₄×D₇₉	1	1	yes	characteristic
423	C₂×C₄²	—	79	1	no	—
424	C₂×C₄²	—	79	1	no	—
425	C₂×C₄²	—	79	1	no	—
426	C₂×C₄²	—	79	1	no	—
427	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
428	C₄⋊C₈	—	316	1	no	—
429	C₄⋊C₈	—	316	1	no	—
430	C₄⋊C₈	—	316	1	no	—
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	C₂²⋊C₈	—	4	1	no	—
436	C₂²⋊C₈	—	4	1	no	—
437	C₂²⋊C₈	—	4	1	no	—
438	C₂²⋊C₈	—	316	1	no	—
439	C₂²⋊C₈	—	316	1	no	—
440	C₂²⋊C₈	—	316	1	no	—
441	C₂²⋊C₈	—	316	1	no	—
442	#97	—	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	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
456	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	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	—	79	1	no	—
473	C₂²×C₄	—	79	1	no	—
474	C₂²×C₄	—	79	1	no	—
475	C₂²×C₄	—	79	1	no	—
476	C₂²×C₄	—	79	1	no	—
477	C₂²×C₄	—	79	1	no	—
478	C₂²×C₄	—	79	1	no	—
479	C₂²×C₄	—	79	1	no	—
480	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
484	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
485	M₁₆	—	4	4	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	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	—	158	1	no	—
499	C₂×C₈	—	158	1	no	—
500	C₂×C₈	—	158	1	no	—
501	C₂×C₈	—	158	1	no	—
502	C₂×C₈	—	158	1	no	—
503	C₂×C₈	—	158	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	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	316	1	no	—
512	C₄⋊C₄	—	316	1	no	—
513	C₄⋊C₄	—	316	1	no	—
514	C₄⋊C₄	—	316	1	no	—
515	C₄⋊C₄	—	316	1	no	—
516	C₄⋊C₄	—	158	2	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	316	1	no	—
520	C₂²⋊C₄	—	316	1	no	—
521	C₂²⋊C₄	—	316	1	no	—
522	C₂²⋊C₄	—	316	1	no	—
523	C₂²⋊C₄	—	316	1	no	—
524	C₂²⋊C₄	—	316	1	no	—
525	C₂²⋊C₄	—	158	2	no	—
526	C₂²⋊C₄	—	158	2	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	158	1	no	—
530	C₄²	—	158	1	no	—
531	C₄²	—	158	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	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	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	C₂²×C₄×D₇₉	1	1	yes	characteristic
552	D₄	—	4	4	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	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	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	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	—	79	2	no	—
574	C₂×C₄	—	158	1	no	—
575	C₂×C₄	—	158	1	no	—
576	C₂×C₄	—	158	1	no	—
577	C₂×C₄	—	158	1	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	#14579206	1	1	yes	characteristic
598	C₂×C₄	#14579206	1	1	yes	characteristic
599	C₂×C₄	#14579206	1	1	yes	characteristic
600	C₂×C₄	#14579206	1	1	yes	characteristic
601	C₂×C₄	#14579208	1	1	yes	characteristic
602	C₂×C₄	#14579208	1	1	yes	characteristic
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	316	1	no	—
608	C₈	—	316	1	no	—
609	C₈	—	316	1	no	—
610	C₈	—	316	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	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	#19099036	1	1	yes	characteristic
626	C₂²	#19099042	1	1	yes	characteristic
627	C₂²	#19099042	1	1	yes	characteristic
628	C₂²	#131×D₇₉	1	1	yes	characteristic
629	C₂²	#19099328	1	1	yes	characteristic
630	C₂²	#19099329	1	1	yes	characteristic
631	C₂²	#19099329	1	1	yes	characteristic
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	316	1	no	—
637	C₄	—	316	1	no	—
638	C₄	—	316	1	no	—
639	C₄	—	316	1	no	—
640	C₄	—	316	1	no	—
641	C₄	—	316	1	no	—
642	C₄	—	316	1	no	—
643	C₄	—	158	2	no	—
644	C₄	#19099302	1	1	yes	characteristic
645	C₄	#19099308	1	1	yes	characteristic
646	C₄	#19099308	1	1	yes	characteristic
647	C₄	#19099316	1	1	yes	characteristic
648	C₂	—	8	1	no	—
649	C₂	—	8	1	no	—
650	C₂	#23766543	1	1	yes	characteristic
651	C₂	#23772460	1	1	yes	characteristic
652	C₂	#23772473	1	1	yes	characteristic
653	C₂	#23772535	1	1	yes	characteristic
654	C₂	#23772546	1	1	yes	characteristic
655	C₂	#23772564	1	1	yes	characteristic
656	C₂	#23772566	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	#23321
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
3. #23764122	C₂	semidirect
4. #23764117	C₂	semidirect
5. #23764016	C₂	semidirect
6. #23764010	C₂	semidirect
7. #23764009	C₂	semidirect
8. #23764003	C₂	semidirect
9. #23763962	C₂	semidirect
10. #23763962	C₂	semidirect
11. #23763583	C₂	semidirect
12. #23763583	C₂	semidirect
13. #23763382	C₂	semidirect
14. #23763382	C₂	semidirect
344. C₇₉	#23321	semidirect

Maximal subgroups

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

subgroup	index
#23766659	2
#23764199	2
#23764122	2
#23764117	2
#23764016	2
#23764010	2
#23764009	2
#23764003	2
#23763962	2
#23763583	2
#23763382	2
C₇₉×#1870	2
#23321	79