Subgroups — #34288765

Order 20224.

854 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098621	C₂	1	2	yes	maximal
2	C₄×#14579120	C₂	1	1	yes	maximal, characteristic
3	#23763551	C₂	1	1	yes	maximal, characteristic, complemented
4	#23763551	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763518	C₂	1	2	yes	maximal, complemented
6	#23763382	C₂	1	2	yes	maximal
7	#23763380	C₂	1	1	yes	maximal, characteristic
8	#23763256	C₂	1	2	yes	maximal, complemented
9	#23763255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579120	C₂²	1	1	yes	characteristic
13	C₂×#14579120	C₂²	1	1	yes	characteristic
14	#19098621	—	2	8	no	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
20	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
22	C₂×#14579071	C₂²	1	2	yes	—
23	C₂×C₈×Dic₇₉	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₇₉	C₄	1	1	yes	characteristic
25	C₄×C₄⋊Dic₇₉	C₄	1	1	yes	characteristic
26	C₄×C₄⋊Dic₇₉	C₄	1	1	yes	characteristic
27	C₄×C₄⋊Dic₇₉	C₄	1	1	yes	characteristic
28	C₄×C₂²⋊Dic₇₉	C₄	1	1	yes	characteristic
29	C₄×C₂²⋊Dic₇₉	C₄	1	1	yes	characteristic
30	C₄×C₂²⋊Dic₇₉	C₄	1	1	yes	characteristic
31	C₄×C₂²⋊Dic₇₉	C₄	1	1	yes	characteristic
32	#19098409	C₂²	1	1	yes	characteristic
33	#19098409	C₂²	1	1	yes	characteristic
34	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
35	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
36	#19098318	C₂²	1	2	yes	—
37	#19098317	C₂²	1	2	yes	—
38	#19098317	C₂²	1	2	yes	—
39	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
43	#336×C₇₉	C₂²	1	2	yes	—
44	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
46	#14579120	—	2	2	no	—
47	#14579120	—	2	2	no	—
48	#14579120	D₄	1	4	yes	—
49	#14579120	Q₈	1	4	yes	—
50	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
70	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
71	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
72	Dic₇₉⋊C₈	—	2	4	no	—
73	Dic₇₉⋊C₈	—	2	4	no	—
74	Dic₇₉⋊C₈	—	2	4	no	—
75	Dic₇₉⋊C₈	—	2	4	no	—
76	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
77	#14579071	—	2	4	no	—
78	C₈×Dic₇₉	—	2	4	no	—
79	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
81	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
82	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
83	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
84	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
85	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
86	C₇₉⋊#95	C₂×C₄	1	1	yes	characteristic
87	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
89	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
91	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₇₉	—	2	2	no	—
93	C₂×C₄²×C₇₉	—	2	2	no	—
94	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₉	—	2	2	no	—
99	C₄⋊C₈×C₇₉	—	2	2	no	—
100	C₂²⋊C₈×C₇₉	—	2	4	no	—
101	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₂×C₇₉⋊C₈	—	2	2	no	—
113	C₂×C₇₉⋊C₈	—	2	2	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₄⋊Dic₇₉	—	2	2	no	—
116	C₄⋊Dic₇₉	—	2	2	no	—
117	C₄⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
118	C₄⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
119	C₂²⋊Dic₇₉	—	2	2	no	—
120	C₂²⋊Dic₇₉	—	2	2	no	—
121	C₂²⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
122	C₂²⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
123	C₄×Dic₇₉	—	2	2	no	—
124	C₄×Dic₇₉	—	2	2	no	—
125	C₄×Dic₇₉	—	2	2	no	—
126	C₄×Dic₇₉	—	2	2	no	—
127	C₄×Dic₇₉	—	2	1	no	—
128	C₄×Dic₇₉	—	2	1	no	—
129	C₄×Dic₇₉	—	4	1	no	—
130	C₄×Dic₇₉	—	4	1	no	—
131	C₄×Dic₇₉	—	4	1	no	—
132	C₄×Dic₇₉	—	4	1	no	—
133	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
134	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
135	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
136	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
137	C₄×Dic₇₉	#41	1	2	yes	—
138	C₄×Dic₇₉	#41	1	2	yes	—
139	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	—	2	1	no	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	—	2	2	no	—
146	C₂²×C₄×C₇₉	—	2	2	no	—
147	C₂²×C₄×C₇₉	—	2	2	no	—
148	C₂²×C₄×C₇₉	—	4	1	no	—
149	C₂²×C₄×C₇₉	—	4	1	no	—
150	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
157	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₇₉	—	2	2	no	—
159	C₂×C₈×C₇₉	—	2	2	no	—
160	C₂×C₈×C₇₉	—	2	2	no	—
161	C₂×C₈×C₇₉	—	2	2	no	—
162	C₂×C₈×C₇₉	—	2	2	no	—
163	C₂×C₈×C₇₉	—	2	2	no	—
164	C₄²×C₇₉	—	2	2	no	—
165	C₄²×C₇₉	—	2	2	no	—
166	C₄²×C₇₉	—	2	1	no	—
167	C₄²×C₇₉	—	2	1	no	—
168	C₄²×C₇₉	#41	1	2	yes	—
169	C₄²×C₇₉	#41	1	2	yes	—
170	C₂³×C₇₉	—	2	1	no	—
171	C₂³×C₇₉	—	2	1	no	—
172	C₂³×C₇₉	—	2	1	no	—
173	C₂³×C₇₉	—	2	1	no	—
174	C₂³×C₇₉	—	2	1	no	—
175	C₂³×C₇₉	—	2	1	no	—
176	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
177	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₇₉	—	2	1	no	—
179	C₂×C₄×C₇₉	—	2	1	no	—
180	C₂×C₄×C₇₉	—	2	1	no	—
181	C₂×C₄×C₇₉	—	2	1	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	2	2	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	2	1	no	—
187	C₂×C₄×C₇₉	—	2	1	no	—
188	C₂×C₄×C₇₉	—	2	1	no	—
189	C₂×C₄×C₇₉	—	2	1	no	—
190	C₂×C₄×C₇₉	—	2	1	no	—
191	C₂×C₄×C₇₉	—	2	1	no	—
192	C₂×C₄×C₇₉	—	4	4	no	—
193	C₂×C₄×C₇₉	—	4	4	no	—
194	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×C₄×C₇₉	#117	1	2	yes	—
196	C₂×C₄×C₇₉	#117	1	2	yes	—
197	C₂×C₄×C₇₉	#131	1	2	yes	—
198	C₂×C₄×C₇₉	#131	1	2	yes	—
199	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
205	C₂×Dic₇₉	—	2	1	no	—
206	C₂×Dic₇₉	—	2	1	no	—
207	C₂×Dic₇₉	—	2	1	no	—
208	C₂×Dic₇₉	—	2	1	no	—
209	C₂×Dic₇₉	—	2	1	no	—
210	C₂×Dic₇₉	—	2	1	no	—
211	C₂×Dic₇₉	—	2	1	no	—
212	C₂×Dic₇₉	—	2	1	no	—
213	C₂×Dic₇₉	—	2	1	no	—
214	C₂×Dic₇₉	—	2	1	no	—
215	C₂×Dic₇₉	—	2	1	no	—
216	C₂×Dic₇₉	—	2	1	no	—
217	C₂×Dic₇₉	—	2	1	no	—
218	C₂×Dic₇₉	—	2	1	no	—
219	C₂×Dic₇₉	—	2	1	no	—
220	C₂×Dic₇₉	—	2	1	no	—
221	C₂×Dic₇₉	—	2	1	no	—
222	C₂×Dic₇₉	—	2	1	no	—
223	C₂×Dic₇₉	C₂×C₄⋊C₄	1	2	yes	—
224	C₂×Dic₇₉	C₂×C₄⋊C₄	1	2	yes	—
225	C₂×Dic₇₉	C₂×C₄⋊C₄	1	2	yes	—
226	C₂×Dic₇₉	C₂×C₄⋊C₄	1	2	yes	—
227	C₂×Dic₇₉	#117	1	2	yes	—
228	C₂×Dic₇₉	#117	1	2	yes	—
229	C₈×C₇₉	—	4	2	no	—
230	C₈×C₇₉	—	4	2	no	—
231	C₇₉⋊C₈	—	4	2	no	—
232	C₇₉⋊C₈	—	4	2	no	—
233	C₂²×C₇₉	—	2	2	no	—
234	C₂²×C₇₉	—	2	2	no	—
235	C₂²×C₇₉	—	2	2	no	—
236	C₂²×C₇₉	—	4	1	no	—
237	C₂²×C₇₉	—	4	1	no	—
238	C₂²×C₇₉	—	4	1	no	—
239	C₂²×C₇₉	—	4	1	no	—
240	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
241	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
242	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
243	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
244	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
245	C₂²×C₇₉	#568	1	1	yes	characteristic
246	C₂²×C₇₉	#568	1	1	yes	characteristic
247	C₄×C₇₉	—	2	2	no	—
248	C₄×C₇₉	—	2	2	no	—
249	C₄×C₇₉	—	4	1	no	—
250	C₄×C₇₉	—	4	1	no	—
251	C₄×C₇₉	#433	1	4	yes	complemented
252	C₄×C₇₉	#532	1	1	yes	characteristic
253	C₄×C₇₉	#532	1	1	yes	characteristic
254	C₄×C₇₉	#533	1	1	yes	characteristic
255	C₄×C₇₉	#533	1	1	yes	characteristic
256	Dic₇₉	—	2	2	no	—
257	Dic₇₉	—	2	2	no	—
258	Dic₇₉	—	2	2	no	—
259	Dic₇₉	—	2	2	no	—
260	Dic₇₉	—	2	2	no	—
261	Dic₇₉	—	2	2	no	—
262	Dic₇₉	—	4	1	no	—
263	Dic₇₉	—	4	1	no	—
264	#20812	—	79	1	no	maximal, Sylow
265	C₂×C₇₉	—	4	2	no	—
266	C₂×C₇₉	#2285	1	1	yes	characteristic
267	C₂×C₇₉	#2906	1	1	yes	characteristic
268	C₂×C₇₉	#2906	1	1	yes	characteristic
269	C₂×C₇₉	C₂×#433	1	1	yes	characteristic
270	C₂×C₇₉	#2921	1	1	yes	characteristic
271	C₂×C₇₉	#2925	1	1	yes	characteristic
272	C₂×C₇₉	#2925	1	1	yes	characteristic
273	C₂×#433	—	79	2	no	—
274	C₄×#117	—	79	1	no	—
275	#1842	—	79	1	no	—
276	#1842	—	79	1	no	—
277	#1832	—	79	2	no	—
278	#1798	—	79	2	no	—
279	#1797	—	79	1	no	—
280	#1797	D₇₉	1	1	yes	characteristic
281	#1768	—	79	2	no	—
282	#1767	—	79	1	no	—
283	C₄×C₄⋊C₈	—	79	1	no	—
284	C₇₉	#20812	1	1	yes	characteristic, complemented, Sylow
285	C₂×#117	—	79	1	no	—
286	C₂×#117	—	79	1	no	—
287	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
288	#433	—	158	8	no	—
289	C₂×C₄⋊C₈	—	79	2	no	—
290	C₂×C₄⋊C₈	—	79	2	no	—
291	C₂×C₄⋊C₈	—	79	2	no	—
292	C₂×C₄⋊C₈	—	79	2	no	—
293	C₂×C₄⋊C₈	—	79	1	no	—
294	C₂×C₄⋊C₈	—	79	1	no	—
295	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
296	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	—	79	2	no	—
298	C₂×C₂²⋊C₈	C₂×D₇₉	1	2	yes	—
299	C₂×#97	—	79	2	no	—
300	C₂×C₄×C₈	—	79	2	no	—
301	C₄×C₄⋊C₄	—	79	1	no	—
302	C₄×C₄⋊C₄	—	79	1	no	—
303	C₄×C₄⋊C₄	—	79	1	no	—
304	C₄×C₄⋊C₄	—	79	1	no	—
305	C₄×C₂²⋊C₄	—	79	1	no	—
306	C₄×C₂²⋊C₄	—	79	1	no	—
307	C₄×C₂²⋊C₄	—	79	1	no	—
308	C₄×C₂²⋊C₄	—	79	1	no	—
309	#376	—	79	1	no	—
310	#376	—	79	1	no	—
311	C₄³	—	79	1	no	—
312	C₄³	—	79	1	no	—
313	#336	—	79	2	no	—
314	#336	—	79	2	no	—
315	#336	—	79	2	no	—
316	#336	C₂×D₇₉	1	2	yes	—
317	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
318	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
319	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
320	C₂²×C₈	—	79	2	no	—
321	C₂²×C₈	—	79	2	no	—
322	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
323	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
324	#117	—	79	4	no	—
325	#117	—	79	4	no	—
326	#117	—	158	2	no	—
327	#117	—	158	2	no	—
328	C₂×C₄⋊C₄	—	79	1	no	—
329	C₂×C₄⋊C₄	—	79	1	no	—
330	C₂×C₄⋊C₄	—	79	1	no	—
331	C₂×C₄⋊C₄	—	79	1	no	—
332	C₂×C₂²⋊C₄	—	79	1	no	—
333	C₂×C₂²⋊C₄	—	79	1	no	—
334	C₂×C₂²⋊C₄	—	79	1	no	—
335	C₂×C₂²⋊C₄	—	79	1	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	—	79	1	no	—
339	C₂×C₄²	—	79	1	no	—
340	C₂×C₄²	—	79	1	no	—
341	C₂×C₄²	—	79	1	no	—
342	C₂×C₄²	—	79	1	no	—
343	C₂×C₄²	—	79	1	no	—
344	C₂×C₄²	—	79	1	no	—
345	C₂×C₄²	—	79	1	no	—
346	C₂×C₄²	—	79	1	no	—
347	C₂×C₄²	—	79	1	no	—
348	C₂×C₄²	—	79	1	no	—
349	C₂×C₄²	—	79	1	no	—
350	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
351	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
352	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	158	4	no	—
357	C₄⋊C₈	—	158	4	no	—
358	C₄⋊C₈	—	158	4	no	—
359	C₄⋊C₈	—	158	4	no	—
360	C₄⋊C₈	—	158	2	no	—
361	C₄⋊C₈	—	158	2	no	—
362	C₂²⋊C₈	—	2	4	no	—
363	C₂²⋊C₈	—	158	4	no	—
364	#97	—	158	4	no	—
365	C₄×C₈	—	158	4	no	—
366	#95	—	79	1	no	—
367	#95	—	79	1	no	—
368	#95	—	79	1	no	—
369	#95	—	79	1	no	—
370	#95	—	79	1	no	—
371	#95	—	79	1	no	—
372	#95	—	79	1	no	—
373	#95	—	79	1	no	—
374	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	79	1	no	—
386	C₂²×C₄	—	79	1	no	—
387	C₂²×C₄	—	79	1	no	—
388	C₂²×C₄	—	79	1	no	—
389	C₂²×C₄	—	79	1	no	—
390	C₂²×C₄	—	79	1	no	—
391	C₂²×C₄	—	79	1	no	—
392	C₂²×C₄	—	79	1	no	—
393	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
398	C₂²×C₄	D₄×D₇₉	1	2	yes	—
399	C₂²×C₄	Q₈×D₇₉	1	2	yes	—
400	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	158	2	no	—
408	C₂×C₈	—	158	2	no	—
409	C₂×C₈	—	158	2	no	—
410	C₂×C₈	—	158	2	no	—
411	C₂×C₈	—	158	2	no	—
412	C₂×C₈	—	158	2	no	—
413	C₄⋊C₄	—	79	4	no	—
414	C₄⋊C₄	—	79	4	no	—
415	C₄⋊C₄	—	158	2	no	—
416	C₄⋊C₄	—	158	2	no	—
417	C₂²⋊C₄	—	79	4	no	—
418	C₂²⋊C₄	—	79	4	no	—
419	C₂²⋊C₄	—	158	2	no	—
420	C₂²⋊C₄	—	158	2	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	316	1	no	—
426	C₄²	—	316	1	no	—
427	C₄²	—	316	1	no	—
428	C₄²	—	316	1	no	—
429	C₄²	—	79	2	no	—
430	C₄²	—	79	2	no	—
431	C₄²	—	79	2	no	—
432	C₄²	—	79	2	no	—
433	C₄²	—	79	2	no	—
434	C₄²	—	79	2	no	—
435	C₄²	—	158	1	no	—
436	C₄²	—	158	1	no	—
437	C₄²	—	158	2	no	—
438	C₄²	—	158	2	no	—
439	C₄²	—	158	2	no	—
440	C₄²	—	158	2	no	—
441	C₄²	#11929623	1	2	yes	—
442	C₄²	#11929623	1	2	yes	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	C₄⋊C₄×D₇₉	1	2	yes	—
450	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	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	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	79	2	no	—
468	C₂×C₄	—	79	2	no	—
469	C₂×C₄	—	79	2	no	—
470	C₂×C₄	—	79	2	no	—
471	C₂×C₄	—	79	2	no	—
472	C₂×C₄	—	79	2	no	—
473	C₂×C₄	—	158	1	no	—
474	C₂×C₄	—	158	1	no	—
475	C₂×C₄	—	158	1	no	—
476	C₂×C₄	—	158	1	no	—
477	C₂×C₄	—	158	1	no	—
478	C₂×C₄	—	158	1	no	—
479	C₂×C₄	—	158	1	no	—
480	C₂×C₄	—	158	1	no	—
481	C₂×C₄	—	158	1	no	—
482	C₂×C₄	—	158	1	no	—
483	C₂×C₄	—	158	1	no	—
484	C₂×C₄	—	158	1	no	—
485	C₂×C₄	—	158	1	no	—
486	C₂×C₄	—	158	1	no	—
487	C₂×C₄	—	158	1	no	—
488	C₂×C₄	—	158	1	no	—
489	C₂×C₄	—	158	1	no	—
490	C₂×C₄	—	158	1	no	—
491	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
492	C₂×C₄	#14579117	1	2	yes	—
493	C₂×C₄	#14579117	1	2	yes	—
494	C₂×C₄	#14579167	1	2	yes	—
495	C₂×C₄	#14579169	1	2	yes	—
496	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
497	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
498	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
499	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
500	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
501	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₈	—	316	2	no	—
505	C₈	—	316	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
514	C₂²	#117×D₇₉	1	1	yes	characteristic
515	C₂²	C₂×#14579117	1	1	yes	characteristic
516	C₂²	C₂×#14579167	1	1	yes	characteristic
517	C₂²	C₂×#14579169	1	1	yes	characteristic
518	C₂²	#19099329	1	1	yes	characteristic
519	C₂²	#19099329	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	316	1	no	—
525	C₄	—	316	1	no	—
526	C₄	—	158	2	no	—
527	C₄	—	158	2	no	—
528	C₄	—	158	2	no	—
529	C₄	—	158	2	no	—
530	C₄	—	158	2	no	—
531	C₄	—	158	2	no	—
532	C₄	#19098621	1	4	yes	complemented
533	C₄	#19099108	1	1	yes	characteristic
534	C₄	#19099108	1	1	yes	characteristic
535	C₄	#19099115	1	1	yes	characteristic
536	C₄	#19099115	1	1	yes	characteristic
537	C₂	—	4	2	no	—
538	C₂	#23765802	1	1	yes	characteristic
539	C₂	#23771965	1	1	yes	characteristic
540	C₂	#23771969	1	1	yes	characteristic
541	C₂	C₂×#19098621	1	1	yes	characteristic
542	C₂	#23772035	1	1	yes	characteristic
543	C₂	#23772061	1	1	yes	characteristic
544	C₂	#23772067	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1797	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1797	D₇₉
hypocenter	C₇₉	#20812
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1797

Complements

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

N	H ≅ G/N	type
3. #23763551	C₂	semidirect
4. #23763551	C₂	semidirect
5. #23763518	C₂	semidirect
8. #23763256	C₂	semidirect
9. #23763255	C₂	semidirect
10. C₄⋊C₈×Dic₇₉	C₂	semidirect
251. C₄×C₇₉	#433	semidirect
284. C₇₉	#20812	semidirect
532. C₄	#19098621	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098621	2
C₄×#14579120	2
#23763551	2
#23763518	2
#23763382	2
#23763380	2
#23763256	2
#23763255	2
C₄⋊C₈×Dic₇₉	2
C₇₉×#1797	2
#20812	79