Subgroups — #34258331

Order 20224.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 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	#23772424	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762265	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762258	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762237	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762230	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762224	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#23762189	C₂	1	1	yes	maximal, characteristic, complemented
12	#23761825	C₂	1	1	yes	maximal, characteristic, complemented
13	#23761808	C₂	1	1	yes	maximal, characteristic, complemented
14	#23761700	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3105	C₂	1	1	yes	maximal, characteristic
16	#19098694	C₂²	1	1	yes	characteristic, complemented
17	Q₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
18	#19098641	—	2	1	no	—
19	#19098641	C₂²	1	1	yes	characteristic, complemented
20	#19098635	—	2	1	no	—
21	D₄×C₇₉⋊C₈	—	2	1	no	—
22	D₄×C₇₉⋊C₈	—	2	1	no	—
23	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
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, complemented
28	#19098624	—	2	1	no	—
29	#19098616	C₂²	1	1	yes	characteristic
30	#19098616	C₂²	1	1	yes	characteristic
31	#19098616	C₂²	1	1	yes	characteristic
32	#19098590	—	2	1	no	—
33	#19098587	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
35	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
36	#19098316	C₂²	1	1	yes	characteristic, complemented
37	#19098316	C₂²	1	1	yes	characteristic, complemented
38	#19098314	C₂²	1	1	yes	characteristic, complemented
39	#19098314	C₂²	1	1	yes	characteristic, complemented
40	Q₈⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	Q₈⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
42	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
43	D₄⋊(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, complemented
47	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
48	#19098285	C₂²	1	1	yes	characteristic, complemented
49	#19098285	C₂²	1	1	yes	characteristic, complemented
50	#19098284	C₂²	1	1	yes	characteristic, complemented
51	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	#529×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
54	#484×C₇₉	C₄	1	1	yes	characteristic
55	#481×C₇₉	C₄	1	1	yes	characteristic
56	#478×C₇₉	C₄	1	1	yes	characteristic
57	#478×C₇₉	C₄	1	1	yes	characteristic
58	#463×C₇₉	C₄	1	1	yes	characteristic
59	#463×C₇₉	C₄	1	1	yes	characteristic
60	#450×C₇₉	C₄	1	1	yes	characteristic
61	#447×C₇₉	C₄	1	1	yes	characteristic
62	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
63	C₄×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
64	C₄×D₈×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	C₂²×C₇₉⋊C₈	—	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)	D₄	1	1	yes	characteristic
79	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
80	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
82	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
84	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
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)	—	2	1	no	—
91	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
93	C₂²⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
94	#14579072	—	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	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂³×C₄×C₇₉	—	2	1	no	—
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	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
107	#126×C₇₉	—	2	1	no	—
108	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
109	#124×C₇₉	C₂×C₄	1	1	yes	characteristic
110	#123×C₇₉	—	2	1	no	—
111	C₂²⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
112	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
114	C₄×D₄×C₇₉	—	2	1	no	—
115	C₄×D₄×C₇₉	—	2	1	no	—
116	C₄×D₄×C₇₉	—	2	1	no	—
117	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
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	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
122	#117×C₇₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×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	#102×C₇₉	C₂×C₄	1	1	yes	characteristic
135	#102×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	—	8	1	no	—
145	#11929608	—	8	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	—	8	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	C₂⁴×C₇₉	—	2	1	no	—
162	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×D₄×C₇₉	—	2	2	no	—
164	C₂×D₄×C₇₉	—	2	2	no	—
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	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
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	—	8	1	no	—
177	C₂²×C₄×C₇₉	—	8	1	no	—
178	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
181	SD₁₆×C₇₉	—	2	2	no	—
182	SD₁₆×C₇₉	—	2	2	no	—
183	D₈×C₇₉	—	2	2	no	—
184	D₈×C₇₉	—	2	2	no	—
185	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₇₉	—	2	1	no	—
190	C₄⋊C₄×C₇₉	—	2	1	no	—
191	C₄⋊C₄×C₇₉	—	2	1	no	—
192	C₄⋊C₄×C₇₉	—	2	1	no	—
193	C₄⋊C₄×C₇₉	—	2	1	no	—
194	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₇₉	—	2	1	no	—
203	C₂²⋊C₄×C₇₉	—	2	1	no	—
204	C₂²⋊C₄×C₇₉	—	2	1	no	—
205	C₂²⋊C₄×C₇₉	—	2	1	no	—
206	C₂²⋊C₄×C₇₉	—	2	1	no	—
207	C₄²×C₇₉	—	2	1	no	—
208	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₇₉	#41	1	1	yes	characteristic
211	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
212	C₂³×C₇₉	—	2	4	no	—
213	C₂³×C₇₉	—	2	1	no	—
214	C₂³×C₇₉	—	2	1	no	—
215	C₂³×C₇₉	—	2	1	no	—
216	C₂³×C₇₉	—	8	1	no	—
217	C₂³×C₇₉	—	8	1	no	—
218	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
219	Q₈×C₇₉	—	2	1	no	—
220	Q₈×C₇₉	—	2	1	no	—
221	D₄×C₇₉	—	2	4	no	—
222	D₄×C₇₉	—	2	1	no	—
223	D₄×C₇₉	—	2	1	no	—
224	D₄×C₇₉	—	2	1	no	—
225	D₄×C₇₉	—	2	1	no	—
226	D₄×C₇₉	—	8	1	no	—
227	D₄×C₇₉	#131	1	2	yes	—
228	D₄×C₇₉	#131	1	2	yes	—
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	—	2	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	—	8	1	no	—
246	C₂×C₄×C₇₉	—	8	1	no	—
247	C₂×C₄×C₇₉	—	8	1	no	—
248	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
254	C₈×C₇₉	—	2	1	no	—
255	C₈×C₇₉	—	2	1	no	—
256	C₈×C₇₉	—	2	1	no	—
257	C₈×C₇₉	—	2	1	no	—
258	C₇₉⋊C₈	—	2	1	no	—
259	C₇₉⋊C₈	—	2	1	no	—
260	C₇₉⋊C₈	—	2	1	no	—
261	C₇₉⋊C₈	—	2	1	no	—
262	C₇₉⋊C₈	—	4	1	no	—
263	C₇₉⋊C₈	—	4	1	no	—
264	C₇₉⋊C₈	—	4	1	no	—
265	C₇₉⋊C₈	—	4	1	no	—
266	C₇₉⋊C₈	—	4	1	no	—
267	C₇₉⋊C₈	—	4	1	no	—
268	C₂²×C₇₉	—	2	1	no	—
269	C₂²×C₇₉	—	2	2	no	—
270	C₂²×C₇₉	—	2	2	no	—
271	C₂²×C₇₉	—	2	1	no	—
272	C₂²×C₇₉	—	2	1	no	—
273	C₂²×C₇₉	—	4	1	no	—
274	C₂²×C₇₉	—	4	1	no	—
275	C₂²×C₇₉	—	4	1	no	—
276	C₂²×C₇₉	—	4	1	no	—
277	C₂²×C₇₉	—	4	1	no	—
278	C₂²×C₇₉	—	4	1	no	—
279	C₂²×C₇₉	—	4	1	no	—
280	C₂²×C₇₉	—	8	4	no	—
281	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₇₉	—	2	1	no	—
283	C₄×C₇₉	—	2	1	no	—
284	C₄×C₇₉	—	2	1	no	—
285	C₄×C₇₉	—	2	1	no	—
286	C₄×C₇₉	—	4	1	no	—
287	C₄×C₇₉	—	4	1	no	—
288	C₄×C₇₉	—	4	1	no	—
289	C₄×C₇₉	—	4	1	no	—
290	C₄×C₇₉	—	4	1	no	—
291	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
292	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
293	C₄×C₇₉	#576	1	1	yes	characteristic
294	C₄×C₇₉	#577	1	1	yes	characteristic
295	#17918	—	79	1	no	maximal, Sylow
296	C₂×C₇₉	—	4	1	no	—
297	C₂×C₇₉	—	4	2	no	—
298	C₂×C₇₉	—	4	2	no	—
299	C₂×C₇₉	—	8	1	no	—
300	C₂×C₇₉	#2929	1	1	yes	characteristic
301	C₂×C₇₉	#2946	1	1	yes	characteristic
302	C₂×C₇₉	#2957	1	1	yes	characteristic
303	#3105	D₇₉	1	1	yes	characteristic
304	#2993	—	79	1	no	—
305	#2972	—	79	1	no	—
306	#1586	—	79	1	no	—
307	#1585	—	79	1	no	—
308	#1582	—	79	1	no	—
309	#1581	—	79	1	no	—
310	#1580	—	79	1	no	—
311	SD₁₆⋊C₈	—	79	1	no	—
312	C₈×SD₁₆	—	79	1	no	—
313	C₈×D₈	—	79	1	no	—
314	#1574	—	79	1	no	—
315	#1486	—	79	1	no	—
316	#1482	—	79	1	no	—
317	#1454	—	79	1	no	—
318	C₇₉	#17918	1	1	yes	characteristic, complemented, Sylow
319	#529	C₂×D₇₉	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
321	#484	Dic₇₉	1	1	yes	characteristic
322	#481	Dic₇₉	1	1	yes	characteristic
323	#478	Dic₇₉	1	1	yes	characteristic
324	#478	Dic₇₉	1	1	yes	characteristic
325	#463	Dic₇₉	1	1	yes	characteristic
326	#463	Dic₇₉	1	1	yes	characteristic
327	#450	Dic₇₉	1	1	yes	characteristic
328	#447	Dic₇₉	1	1	yes	characteristic
329	#446	—	79	1	no	—
330	C₈×Q₈	—	79	1	no	—
331	C₄×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
332	C₄×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
333	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
334	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
335	#436	—	79	1	no	—
336	#436	—	158	1	no	—
337	#435	—	158	1	no	—
338	C₈×D₄	—	79	1	no	—
339	C₈×D₄	—	79	1	no	—
340	C₈×D₄	—	79	1	no	—
341	C₈×D₄	—	79	1	no	—
342	C₈×D₄	—	79	1	no	—
343	C₈×D₄	—	158	1	no	—
344	C₈×D₄	—	158	1	no	—
345	#433	—	158	1	no	—
346	#431	—	79	1	no	—
347	#431	—	79	1	no	—
348	#431	—	79	1	no	—
349	#431	C₂×D₇₉	1	1	yes	characteristic
350	#424	—	158	1	no	—
351	#423	—	79	1	no	—
352	C₂×C₂²⋊C₈	—	158	1	no	—
353	C₂×C₂²⋊C₈	—	158	1	no	—
354	#335	—	79	1	no	—
355	#335	—	79	1	no	—
356	#334	—	79	1	no	—
357	#334	—	79	1	no	—
358	Q₈⋊C₈	—	79	1	no	—
359	Q₈⋊C₈	—	79	1	no	—
360	D₄⋊C₈	—	79	1	no	—
361	D₄⋊C₈	—	79	1	no	—
362	D₄⋊C₈	—	79	1	no	—
363	D₄⋊C₈	—	79	1	no	—
364	D₄⋊C₈	—	79	1	no	—
365	D₄⋊C₈	—	79	1	no	—
366	#322	—	79	1	no	—
367	#322	—	79	1	no	—
368	#322	—	79	1	no	—
369	C₈²	—	79	1	no	—
370	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
373	C₂×SD₁₆	C₂×Dic₇₉	1	1	yes	characteristic
374	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
375	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
376	C₂×M₁₆	—	158	1	no	—
377	C₂×M₁₆	—	158	1	no	—
378	C₂²×C₈	—	158	1	no	—
379	C₂²×C₈	—	158	1	no	—
380	C₂²×C₈	—	158	1	no	—
381	C₂²×C₈	—	158	1	no	—
382	C₂²×C₈	—	158	1	no	—
383	#126	—	2	1	no	—
384	#125	C₂×Dic₇₉	1	1	yes	characteristic
385	#124	C₂×Dic₇₉	1	1	yes	characteristic
386	#123	—	2	1	no	—
387	C₂²⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
388	#121	C₂×Dic₇₉	1	1	yes	characteristic
389	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
394	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
395	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
396	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
397	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
398	#117	—	2	1	no	—
399	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
402	#107	C₂×Dic₇₉	1	1	yes	characteristic
403	#107	C₂×Dic₇₉	1	1	yes	characteristic
404	#106	C₂×Dic₇₉	1	1	yes	characteristic
405	#106	C₂×Dic₇₉	1	1	yes	characteristic
406	C₄⋊C₈	—	79	1	no	—
407	C₄⋊C₈	—	79	1	no	—
408	C₄⋊C₈	—	79	1	no	—
409	C₄⋊C₈	—	79	1	no	—
410	C₄⋊C₈	—	79	1	no	—
411	C₄⋊C₈	—	79	1	no	—
412	C₄⋊C₈	—	158	1	no	—
413	C₄⋊C₈	—	158	1	no	—
414	C₄⋊C₈	—	158	1	no	—
415	C₄⋊C₈	—	158	1	no	—
416	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
418	#103	C₂×Dic₇₉	1	1	yes	characteristic
419	#103	C₂×Dic₇₉	1	1	yes	characteristic
420	#102	C₂×Dic₇₉	1	1	yes	characteristic
421	#102	C₂×Dic₇₉	1	1	yes	characteristic
422	#102	C₂×Dic₇₉	1	1	yes	characteristic
423	#102	C₂×Dic₇₉	1	1	yes	characteristic
424	#102	C₂×Dic₇₉	1	1	yes	characteristic
425	#102	C₂×Dic₇₉	1	1	yes	characteristic
426	C₂²⋊C₈	—	79	1	no	—
427	C₂²⋊C₈	—	79	1	no	—
428	C₂²⋊C₈	—	158	1	no	—
429	C₂²⋊C₈	—	158	1	no	—
430	C₂²⋊C₈	—	158	1	no	—
431	C₂²⋊C₈	—	158	1	no	—
432	C₂²⋊C₈	—	158	1	no	—
433	C₂²⋊C₈	—	158	1	no	—
434	C₂²⋊C₈	—	158	1	no	—
435	C₂²⋊C₈	—	158	1	no	—
436	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
437	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
438	#97	—	158	1	no	—
439	C₄×C₈	—	79	1	no	—
440	C₄×C₈	—	79	1	no	—
441	C₄×C₈	—	79	1	no	—
442	C₄×C₈	—	79	1	no	—
443	C₄×C₈	—	158	1	no	—
444	C₄×C₈	—	158	1	no	—
445	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
446	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
447	C₂⁴	—	2	1	no	—
448	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
454	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
455	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	8	1	no	—
463	C₂²×C₄	—	8	1	no	—
464	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
465	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
466	C₂²×C₄	#11929623	1	1	yes	characteristic
467	SD₁₆	—	2	2	no	—
468	SD₁₆	—	2	2	no	—
469	D₈	—	2	2	no	—
470	D₈	—	2	2	no	—
471	M₁₆	—	632	1	no	—
472	M₁₆	—	632	1	no	—
473	C₂×C₈	—	79	1	no	—
474	C₂×C₈	—	79	1	no	—
475	C₂×C₈	—	79	1	no	—
476	C₂×C₈	—	79	1	no	—
477	C₂×C₈	—	632	1	no	—
478	C₂×C₈	—	632	1	no	—
479	C₂×C₈	—	632	1	no	—
480	C₂×C₈	—	632	1	no	—
481	C₂×C₈	—	632	1	no	—
482	C₂×C₈	—	158	1	no	—
483	C₂×C₈	—	158	1	no	—
484	C₂×C₈	—	158	1	no	—
485	C₂×C₈	—	158	1	no	—
486	C₂×C₈	—	158	1	no	—
487	C₂×C₈	—	158	1	no	—
488	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
489	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
490	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
491	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
512	C₄²	D₄×D₇₉	1	1	yes	characteristic
513	C₄²	#11929623	1	1	yes	characteristic
514	C₄²	C₂³×D₇₉	1	1	yes	characteristic
515	C₂³	—	2	4	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	8	1	no	—
520	C₂³	—	8	1	no	—
521	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	8	1	no	—
530	D₄	#14579168	1	2	yes	—
531	D₄	#14579168	1	2	yes	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
552	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
553	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
554	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
555	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
556	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	316	1	no	—
562	C₈	—	316	1	no	—
563	C₈	—	316	1	no	—
564	C₈	—	316	1	no	—
565	C₈	—	316	1	no	—
566	C₈	—	316	1	no	—
567	C₈	—	158	1	no	—
568	C₈	—	158	1	no	—
569	C₈	—	158	1	no	—
570	C₈	—	158	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	4	no	—
584	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	C₂×#14579168	1	1	yes	characteristic
595	C₄	C₂×#14579168	1	1	yes	characteristic
596	C₄	#19099367	1	1	yes	characteristic
597	C₄	#19099373	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	#23772095	1	1	yes	characteristic
603	C₂	#23772233	1	1	yes	characteristic
604	C₂	#23772317	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×#3105	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#447×C₇₉	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#3105	D₇₉
hypocenter	C₇₉	#17918
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #23772549	C₂	semidirect
2. #23772424	C₂	semidirect
3. #23762265	C₂	semidirect
4. #23762258	C₂	semidirect
5. #23762237	C₂	semidirect
6. #23762230	C₂	semidirect
7. #23762224	C₂	semidirect
8. SD₁₆⋊(C₇₉⋊C₈)	C₂	semidirect
9. SD₁₆×C₇₉⋊C₈	C₂	semidirect
10. D₈×C₇₉⋊C₈	C₂	semidirect
11. #23762189	C₂	semidirect
12. #23761825	C₂	semidirect
13. #23761808	C₂	semidirect
14. #23761700	C₂	semidirect
16. #19098694	C₂²	semidirect
17. Q₈×C₇₉⋊C₈	C₂²	semidirect
19. #19098641	C₂²	semidirect
27. D₄×C₇₉⋊C₈	C₂²	semidirect
36. #19098316	C₂²	semidirect
37. #19098316	C₂²	semidirect
38. #19098314	C₂²	semidirect
39. #19098314	C₂²	semidirect
40. Q₈⋊(C₇₉⋊C₈)	C₂²	semidirect
41. Q₈⋊(C₇₉⋊C₈)	C₂²	semidirect
46. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
47. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
48. #19098285	C₂²	semidirect
49. #19098285	C₂²	semidirect
50. #19098284	C₂²	semidirect
51. C₈×C₇₉⋊C₈	C₂²	semidirect
318. C₇₉	#17918	semidirect

Maximal subgroups

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

subgroup	index
#23772549	2
#23772424	2
#23762265	2
#23762258	2
#23762237	2
#23762230	2
#23762224	2
SD₁₆⋊(C₇₉⋊C₈)	2
SD₁₆×C₇₉⋊C₈	2
D₈×C₇₉⋊C₈	2
#23762189	2
#23761825	2
#23761808	2
#23761700	2
C₇₉×#3105	2
#17918	79