Subgroups — #34258450

Order 20224.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772549	C₂	1	1	yes	maximal, characteristic, complemented
2	#23772511	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762272	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762265	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762244	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762237	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762224	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762219	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#23762171	C₂	1	1	yes	maximal, characteristic, complemented
12	#23761839	C₂	1	1	yes	maximal, characteristic, complemented
13	#23761813	C₂	1	1	yes	maximal, characteristic, complemented
14	#23761695	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3102	C₂	1	1	yes	maximal, characteristic
16	#19098694	C₂²	1	1	yes	characteristic
17	Q₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
18	Q₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	#19098641	—	2	1	no	—
21	#19098641	C₂²	1	1	yes	characteristic
22	#19098635	—	2	1	no	—
23	D₄×C₇₉⋊C₈	—	2	1	no	—
24	D₄×C₇₉⋊C₈	—	2	1	no	—
25	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
26	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
27	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
28	#19098624	—	2	1	no	—
29	#19098616	—	2	1	no	—
30	#19098616	C₂²	1	1	yes	characteristic
31	#19098590	—	2	1	no	—
32	#19098587	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
34	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
35	C₄×#11929608	C₂²	1	1	yes	characteristic
36	#19098314	C₂²	1	1	yes	characteristic
37	#19098314	C₂²	1	1	yes	characteristic
38	#19098314	C₂²	1	1	yes	characteristic
39	#19098314	C₂²	1	1	yes	characteristic
40	Q₈⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
42	Q₈⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
43	Q₈⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
44	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
45	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
46	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
47	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
48	#19098285	C₂²	1	1	yes	characteristic
49	#19098285	C₂²	1	1	yes	characteristic
50	#19098284	C₂²	1	1	yes	characteristic
51	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
52	#529×C₇₉	C₂²	1	1	yes	characteristic
53	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
54	#485×C₇₉	C₄	1	1	yes	characteristic
55	#482×C₇₉	C₄	1	1	yes	characteristic
56	#479×C₇₉	C₄	1	1	yes	characteristic
57	#478×C₇₉	C₄	1	1	yes	characteristic
58	#464×C₇₉	C₄	1	1	yes	characteristic
59	#463×C₇₉	C₄	1	1	yes	characteristic
60	#452×C₇₉	C₄	1	1	yes	characteristic
61	#449×C₇₉	C₄	1	1	yes	characteristic
62	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
63	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
64	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
66	#431×C₇₉	C₂²	1	1	yes	characteristic
67	C₂×#11929608	—	2	1	no	—
68	C₂×#11929608	—	2	1	no	—
69	C₂×#11929608	—	2	1	no	—
70	C₂²×C₇₉⋊C₈	—	2	1	no	—
71	C₂²×C₇₉⋊C₈	—	2	1	no	—
72	C₂²×C₇₉⋊C₈	—	2	1	no	—
73	C₂²×C₇₉⋊C₈	—	2	1	no	—
74	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
79	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
80	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
81	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
82	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
84	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
85	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
86	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
87	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
88	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
89	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
91	C₂²⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
92	#14579072	—	2	1	no	—
93	#14579072	—	2	1	no	—
94	C₄×C₇₉⋊C₈	—	2	1	no	—
95	C₄×C₇₉⋊C₈	—	2	1	no	—
96	C₄×C₇₉⋊C₈	—	2	1	no	—
97	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
98	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×#41×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
106	#126×C₇₉	—	2	1	no	—
107	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
108	#124×C₇₉	C₂×C₄	1	1	yes	characteristic
109	#123×C₇₉	—	2	1	no	—
110	C₂²⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
111	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₇₉	—	2	1	no	—
116	C₄×D₄×C₇₉	—	2	1	no	—
117	C₄×D₄×C₇₉	—	2	1	no	—
118	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
121	#117×C₇₉	—	2	1	no	—
122	#117×C₇₉	—	2	1	no	—
123	#117×C₇₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₇₉	—	2	1	no	—
125	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
126	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
127	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
128	#106×C₇₉	C₂×C₄	1	1	yes	characteristic
129	#106×C₇₉	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
132	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
133	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
134	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
135	#103×C₇₉	C₂×C₄	1	1	yes	characteristic
136	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
137	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
144	#11929608	—	4	2	no	—
145	#11929608	—	8	1	no	—
146	#11929608	—	8	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	—	8	1	no	—
154	C₂×C₇₉⋊C₈	—	8	1	no	—
155	C₂×C₇₉⋊C₈	—	8	1	no	—
156	C₂×C₇₉⋊C₈	—	8	1	no	—
157	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
161	#41×C₇₉	—	2	2	no	—
162	#41×C₇₉	—	2	2	no	—
163	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×D₄×C₇₉	—	2	1	no	—
166	C₂×D₄×C₇₉	—	2	1	no	—
167	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₉	—	2	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	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
176	Q₁₆×C₇₉	—	2	2	no	—
177	SD₁₆×C₇₉	—	2	2	no	—
178	SD₁₆×C₇₉	—	2	2	no	—
179	D₈×C₇₉	—	2	2	no	—
180	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₇₉	—	2	1	no	—
185	C₄⋊C₄×C₇₉	—	2	1	no	—
186	C₄⋊C₄×C₇₉	—	2	1	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	2	1	no	—
189	C₄⋊C₄×C₇₉	—	2	1	no	—
190	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
199	C₂²⋊C₄×C₇₉	—	2	1	no	—
200	C₂²⋊C₄×C₇₉	—	2	1	no	—
201	C₂²⋊C₄×C₇₉	—	2	1	no	—
202	C₄²×C₇₉	—	2	1	no	—
203	C₄²×C₇₉	—	2	1	no	—
204	C₄²×C₇₉	—	2	1	no	—
205	C₄²×C₇₉	—	2	1	no	—
206	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₇₉	#41	1	1	yes	characteristic
209	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
210	C₂³×C₇₉	—	2	1	no	—
211	C₂³×C₇₉	—	2	1	no	—
212	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₇₉	—	2	1	no	—
214	Q₈×C₇₉	—	2	1	no	—
215	Q₈×C₇₉	—	2	1	no	—
216	Q₈×C₇₉	#131	1	2	yes	—
217	D₄×C₇₉	—	2	4	no	—
218	D₄×C₇₉	—	2	1	no	—
219	D₄×C₇₉	—	2	1	no	—
220	D₄×C₇₉	—	2	1	no	—
221	D₄×C₇₉	—	8	1	no	—
222	D₄×C₇₉	#131	1	2	yes	—
223	C₂×C₄×C₇₉	—	2	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	—	4	1	no	—
235	C₂×C₄×C₇₉	—	4	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	—	8	1	no	—
240	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
246	C₈×C₇₉	—	2	1	no	—
247	C₈×C₇₉	—	2	1	no	—
248	C₈×C₇₉	—	2	1	no	—
249	C₈×C₇₉	—	2	1	no	—
250	C₇₉⋊C₈	—	2	2	no	—
251	C₇₉⋊C₈	—	2	1	no	—
252	C₇₉⋊C₈	—	2	1	no	—
253	C₇₉⋊C₈	—	2	1	no	—
254	C₇₉⋊C₈	—	2	1	no	—
255	C₇₉⋊C₈	—	4	1	no	—
256	C₇₉⋊C₈	—	4	1	no	—
257	C₇₉⋊C₈	—	4	1	no	—
258	C₇₉⋊C₈	—	4	1	no	—
259	C₇₉⋊C₈	—	4	1	no	—
260	C₂²×C₇₉	—	2	1	no	—
261	C₂²×C₇₉	—	2	2	no	—
262	C₂²×C₇₉	—	2	1	no	—
263	C₂²×C₇₉	—	2	1	no	—
264	C₂²×C₇₉	—	4	1	no	—
265	C₂²×C₇₉	—	4	1	no	—
266	C₂²×C₇₉	—	4	1	no	—
267	C₂²×C₇₉	—	4	1	no	—
268	C₂²×C₇₉	—	4	1	no	—
269	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₇₉	—	2	1	no	—
271	C₄×C₇₉	—	2	2	no	—
272	C₄×C₇₉	—	2	1	no	—
273	C₄×C₇₉	—	2	1	no	—
274	C₄×C₇₉	—	2	1	no	—
275	C₄×C₇₉	—	4	1	no	—
276	C₄×C₇₉	—	4	1	no	—
277	C₄×C₇₉	—	4	1	no	—
278	C₄×C₇₉	—	4	1	no	—
279	C₄×C₇₉	—	4	1	no	—
280	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
281	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
282	C₄×C₇₉	#577	1	1	yes	characteristic
283	C₄×C₇₉	#577	1	1	yes	characteristic
284	#17927	—	79	1	no	maximal, Sylow
285	C₂×C₇₉	—	4	1	no	—
286	C₂×C₇₉	—	4	2	no	—
287	C₂×C₇₉	—	8	1	no	—
288	C₂×C₇₉	#2929	1	1	yes	characteristic
289	C₂×C₇₉	#2952	1	1	yes	characteristic
290	C₂×C₇₉	#2956	1	1	yes	characteristic
291	#3102	D₇₉	1	1	yes	characteristic
292	#2993	—	79	1	no	—
293	#2988	—	79	1	no	—
294	#1587	—	79	1	no	—
295	#1586	—	79	1	no	—
296	#1583	—	79	1	no	—
297	#1582	—	79	1	no	—
298	#1580	—	79	1	no	—
299	#1579	—	79	1	no	—
300	C₈×SD₁₆	—	79	1	no	—
301	C₈×SD₁₆	—	79	1	no	—
302	#1570	—	79	1	no	—
303	#1489	—	79	1	no	—
304	#1483	—	79	1	no	—
305	#1453	—	79	1	no	—
306	C₇₉	#17927	1	1	yes	characteristic, complemented, Sylow
307	#529	C₂×D₇₉	1	1	yes	characteristic
308	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
309	#485	Dic₇₉	1	1	yes	characteristic
310	#482	Dic₇₉	1	1	yes	characteristic
311	#479	Dic₇₉	1	1	yes	characteristic
312	#478	Dic₇₉	1	1	yes	characteristic
313	#464	Dic₇₉	1	1	yes	characteristic
314	#463	Dic₇₉	1	1	yes	characteristic
315	#452	Dic₇₉	1	1	yes	characteristic
316	#449	Dic₇₉	1	1	yes	characteristic
317	#446	—	79	1	no	—
318	C₈×Q₈	—	79	1	no	—
319	C₈×Q₈	—	79	1	no	—
320	C₈×Q₈	—	79	1	no	—
321	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
322	C₄×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
323	C₄×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
324	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
325	#436	—	79	1	no	—
326	#436	—	158	1	no	—
327	#435	—	158	1	no	—
328	C₈×D₄	—	79	1	no	—
329	C₈×D₄	—	79	1	no	—
330	C₈×D₄	—	79	1	no	—
331	C₈×D₄	—	158	1	no	—
332	C₈×D₄	—	158	1	no	—
333	#433	—	158	1	no	—
334	#431	—	79	1	no	—
335	#431	—	158	1	no	—
336	#431	C₂×D₇₉	1	1	yes	characteristic
337	#424	—	158	1	no	—
338	#423	—	79	1	no	—
339	C₂×C₄⋊C₈	—	79	1	no	—
340	C₂×C₄⋊C₈	—	158	1	no	—
341	C₄×M₁₆	—	79	1	no	—
342	#334	—	79	1	no	—
343	#334	—	79	1	no	—
344	#334	—	79	1	no	—
345	#334	—	79	1	no	—
346	Q₈⋊C₈	—	79	1	no	—
347	Q₈⋊C₈	—	79	1	no	—
348	Q₈⋊C₈	—	79	1	no	—
349	Q₈⋊C₈	—	79	1	no	—
350	D₄⋊C₈	—	79	1	no	—
351	D₄⋊C₈	—	79	1	no	—
352	D₄⋊C₈	—	79	1	no	—
353	D₄⋊C₈	—	79	1	no	—
354	#322	—	79	1	no	—
355	#322	—	79	1	no	—
356	#322	—	79	1	no	—
357	C₈²	—	79	1	no	—
358	C₂×#41	C₂×Dic₇₉	1	1	yes	characteristic
359	C₂×Q₁₆	C₂×Dic₇₉	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
361	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
362	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
363	C₂×M₁₆	—	158	1	no	—
364	C₂×M₁₆	—	158	1	no	—
365	C₂×M₁₆	—	158	1	no	—
366	C₂²×C₈	—	158	1	no	—
367	C₂²×C₈	—	158	1	no	—
368	C₂²×C₈	—	158	1	no	—
369	C₂²×C₈	—	158	1	no	—
370	#126	—	2	1	no	—
371	#125	C₂×Dic₇₉	1	1	yes	characteristic
372	#124	C₂×Dic₇₉	1	1	yes	characteristic
373	#123	—	2	1	no	—
374	C₂²⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
375	#121	C₂×Dic₇₉	1	1	yes	characteristic
376	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
377	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
378	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
383	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
384	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	C₂×Dic₇₉	1	1	yes	characteristic
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
390	#107	C₂×Dic₇₉	1	1	yes	characteristic
391	#107	C₂×Dic₇₉	1	1	yes	characteristic
392	#106	C₂×Dic₇₉	1	1	yes	characteristic
393	#106	C₂×Dic₇₉	1	1	yes	characteristic
394	C₄⋊C₈	—	79	1	no	—
395	C₄⋊C₈	—	79	1	no	—
396	C₄⋊C₈	—	79	1	no	—
397	C₄⋊C₈	—	79	1	no	—
398	C₄⋊C₈	—	79	1	no	—
399	C₄⋊C₈	—	79	1	no	—
400	C₄⋊C₈	—	158	1	no	—
401	C₄⋊C₈	—	158	1	no	—
402	C₄⋊C₈	—	158	1	no	—
403	C₄⋊C₈	—	158	1	no	—
404	C₄⋊C₈	—	158	1	no	—
405	C₄⋊C₈	—	158	1	no	—
406	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
408	#103	C₂×Dic₇₉	1	1	yes	characteristic
409	#103	C₂×Dic₇₉	1	1	yes	characteristic
410	#103	C₂×Dic₇₉	1	1	yes	characteristic
411	#103	C₂×Dic₇₉	1	1	yes	characteristic
412	#102	C₂×Dic₇₉	1	1	yes	characteristic
413	#102	C₂×Dic₇₉	1	1	yes	characteristic
414	#102	C₂×Dic₇₉	1	1	yes	characteristic
415	#102	C₂×Dic₇₉	1	1	yes	characteristic
416	C₂²⋊C₈	—	79	1	no	—
417	C₂²⋊C₈	—	79	1	no	—
418	C₂²⋊C₈	—	158	1	no	—
419	C₂²⋊C₈	—	158	1	no	—
420	C₂²⋊C₈	—	158	1	no	—
421	C₂²⋊C₈	—	158	1	no	—
422	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
423	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
424	#97	—	158	1	no	—
425	#97	—	158	1	no	—
426	C₄×C₈	—	79	1	no	—
427	C₄×C₈	—	79	1	no	—
428	C₄×C₈	—	79	1	no	—
429	C₄×C₈	—	79	1	no	—
430	C₄×C₈	—	158	1	no	—
431	C₄×C₈	—	158	1	no	—
432	C₄×C₈	—	158	1	no	—
433	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
438	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
442	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
448	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
449	C₂²×C₄	#11929623	1	1	yes	characteristic
450	Q₁₆	—	2	2	no	—
451	SD₁₆	—	2	2	no	—
452	SD₁₆	—	2	2	no	—
453	D₈	—	2	2	no	—
454	M₁₆	—	316	2	no	—
455	M₁₆	—	632	1	no	—
456	M₁₆	—	632	1	no	—
457	C₂×C₈	—	79	1	no	—
458	C₂×C₈	—	79	1	no	—
459	C₂×C₈	—	79	1	no	—
460	C₂×C₈	—	79	1	no	—
461	C₂×C₈	—	632	1	no	—
462	C₂×C₈	—	632	1	no	—
463	C₂×C₈	—	632	1	no	—
464	C₂×C₈	—	632	1	no	—
465	C₂×C₈	—	158	1	no	—
466	C₂×C₈	—	158	1	no	—
467	C₂×C₈	—	158	1	no	—
468	C₂×C₈	—	158	1	no	—
469	C₂×C₈	—	158	1	no	—
470	C₂×C₈	—	158	1	no	—
471	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
472	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
473	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
474	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
498	C₄²	D₄×D₇₉	1	1	yes	characteristic
499	C₄²	#11929623	1	1	yes	characteristic
500	C₄²	C₂³×D₇₉	1	1	yes	characteristic
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	#14579168	1	2	yes	—
508	D₄	—	2	4	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	8	1	no	—
513	D₄	#14579168	1	2	yes	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
532	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
533	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
534	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
535	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
536	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	316	1	no	—
542	C₈	—	316	1	no	—
543	C₈	—	316	1	no	—
544	C₈	—	316	1	no	—
545	C₈	—	316	1	no	—
546	C₈	—	158	2	no	—
547	C₈	—	158	1	no	—
548	C₈	—	158	1	no	—
549	C₈	—	158	1	no	—
550	C₈	—	158	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	C₂×#14579168	1	1	yes	characteristic
572	C₄	C₂×#14579168	1	1	yes	characteristic
573	C₄	#19099370	1	1	yes	characteristic
574	C₄	#19099370	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	1	no	—
578	C₂	#23772095	1	1	yes	characteristic
579	C₂	#23772284	1	1	yes	characteristic
580	C₂	#23772310	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3102	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#449×C₇₉	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#3102	D₇₉
hypocenter	C₇₉	#17927
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
1. #23772549	C₂	semidirect
2. #23772511	C₂	semidirect
3. #23762272	C₂	semidirect
4. #23762265	C₂	semidirect
5. #23762244	C₂	semidirect
6. #23762237	C₂	semidirect
7. #23762224	C₂	semidirect
8. #23762219	C₂	semidirect
9. SD₁₆×C₇₉⋊C₈	C₂	semidirect
10. SD₁₆×C₇₉⋊C₈	C₂	semidirect
11. #23762171	C₂	semidirect
12. #23761839	C₂	semidirect
13. #23761813	C₂	semidirect
14. #23761695	C₂	semidirect
306. C₇₉	#17927	semidirect

Maximal subgroups

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

subgroup	index
#23772549	2
#23772511	2
#23762272	2
#23762265	2
#23762244	2
#23762237	2
#23762224	2
#23762219	2
SD₁₆×C₇₉⋊C₈	2
#23762171	2
#23761839	2
#23761813	2
#23761695	2
C₇₉×#3102	2
#17927	79