Subgroups — #2960×D₇₉ #35152628

Order 20224.

1982 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533×D₇₉	C₂	1	1	yes	maximal, characteristic
2	#23772335	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772334	C₂	1	1	yes	maximal, characteristic, complemented
4	#23772333	C₂	1	2	yes	maximal, complemented
5	#23772332	C₂	1	2	yes	maximal, complemented
6	#23772331	C₂	1	4	yes	maximal, complemented
7	#23772330	C₂	1	1	yes	maximal, characteristic, complemented
8	#23772329	C₂	1	4	yes	maximal, complemented
9	#446×D₇₉	C₂	1	4	yes	maximal, complemented
10	C₈×Q₈×D₇₉	C₂	1	4	yes	maximal, complemented
11	#424×D₇₉	C₂	1	2	yes	maximal
12	#423×D₇₉	C₂	1	1	yes	maximal, characteristic
13	#405×D₇₉	C₂	1	2	yes	maximal
14	C₂×C₄×C₈×D₇₉	C₂	1	1	yes	maximal, characteristic
15	C₇₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×M₁₆×D₇₉	C₂²	1	2	yes	—
17	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
19	#19099120	C₂²	1	1	yes	characteristic
20	#19099119	C₄	1	2	yes	—
21	#19099118	C₄	1	2	yes	—
22	#19099117	C₂²	1	4	yes	—
23	#19099116	C₂²	1	2	yes	—
24	#19099115	C₄	1	4	yes	—
25	C₄⋊Q₈×D₇₉	C₄	1	2	yes	—
26	#125×D₇₉	C₄	1	2	yes	—
27	C₂²⋊Q₈×D₇₉	C₄	1	4	yes	—
28	C₄×Q₈×D₇₉	C₂²	1	4	yes	—
29	#117×D₇₉	C₂²	1	2	yes	—
30	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
31	#19098694	C₂²	1	4	yes	complemented
32	#19098693	C₂²	1	4	yes	complemented
33	#19098692	C₂²	1	8	yes	complemented
34	#19098691	C₂²	1	8	yes	complemented
35	#19098690	C₂²	1	4	yes	complemented
36	Q₈×C₇₉⋊C₈	C₂²	1	4	yes	complemented
37	C₈×Dic₁₅₈	C₂²	1	8	yes	complemented
38	C₈×Dic₁₅₈	C₂²	1	4	yes	complemented
39	#19098687	C₂²	1	4	yes	complemented
40	#19098687	C₂²	1	8	yes	complemented
41	#19098591	C₂²	1	2	yes	—
42	#19098590	C₂²	1	2	yes	—
43	#19098589	C₂²	1	2	yes	—
44	#19098588	C₂²	1	8	yes	—
45	#19098587	C₂²	1	1	yes	characteristic
46	#19098586	C₂²	1	2	yes	—
47	#19098585	C₂²	1	4	yes	—
48	C₄⋊C₈×D₇₉	C₂²	1	4	yes	—
49	C₄⋊C₈×D₇₉	C₂²	1	8	yes	—
50	#19098521	C₂²	1	2	yes	—
51	#19098520	C₂²	1	4	yes	—
52	#19098519	C₂²	1	2	yes	—
53	#19098518	C₂²	1	2	yes	—
54	#19098517	C₂²	1	4	yes	—
55	#97×D₇₉	C₂²	1	4	yes	—
56	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
57	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
58	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
59	C₄×C₈×D₇₉	C₂²	1	2	yes	—
60	C₄×C₈×D₇₉	C₂²	1	2	yes	—
61	C₄×C₈×D₇₉	C₂²	1	2	yes	—
62	C₄×C₈×D₇₉	C₂²	1	2	yes	—
63	C₄×C₈×D₇₉	C₂²	1	4	yes	—
64	#533×C₇₉	C₂²	1	1	yes	characteristic
65	#446×C₇₉	C₂²	1	4	yes	complemented
66	C₈×Q₈×C₇₉	C₂²	1	4	yes	complemented
67	#424×C₇₉	C₂²	1	2	yes	—
68	#423×C₇₉	C₂²	1	1	yes	characteristic
69	#405×C₇₉	C₂²	1	2	yes	—
70	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
71	C₂×Q₈×D₇₉	C₂×C₄	1	4	yes	—
72	C₂²×C₄×D₇₉	C₂×C₄	1	2	yes	—
73	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
74	C₂×#11929608	C₂³	1	2	yes	—
75	C₂×#11929607	C₂³	1	4	yes	—
76	M₁₆×D₇₉	—	2	8	no	—
77	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₇₉	—	2	4	no	—
80	C₂×C₈×D₇₉	Q₈	1	8	yes	complemented
81	C₂×C₈×D₇₉	C₂³	1	2	yes	—
82	C₂×C₈×D₇₉	C₂³	1	2	yes	—
83	C₂×C₈×D₇₉	C₂³	1	4	yes	—
84	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
86	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
88	#14579161	C₂×C₄	1	2	yes	—
89	#14579160	C₂×C₄	1	4	yes	—
90	#14579160	C₂×C₄	1	4	yes	—
91	#14579159	C₂×C₄	1	4	yes	—
92	#14579153	C₂×C₄	1	2	yes	—
93	#14579152	C₂×C₄	1	4	yes	—
94	#14579151	C₂×C₄	1	8	yes	—
95	#14579141	C₂×C₄	1	4	yes	—
96	#14579140	C₂×C₄	1	4	yes	—
97	#14579139	C₂×C₄	1	8	yes	—
98	#14579138	C₂×C₄	1	8	yes	—
99	#14579137	C₂×C₄	1	4	yes	—
100	Q₈×Dic₇₉	C₂×C₄	1	4	yes	—
101	C₄×Dic₁₅₈	C₂³	1	4	yes	—
102	C₄×Dic₁₅₈	C₂³	1	8	yes	—
103	#14579126	C₂×C₄	1	4	yes	—
104	#14579126	C₂×C₄	1	8	yes	—
105	#14579120	C₂³	1	2	yes	—
106	#14579119	C₂×C₄	1	4	yes	—
107	#14579118	C₂³	1	4	yes	—
108	#14579117	C₂×C₄	1	4	yes	—
109	C₄⋊C₄×D₇₉	C₂×C₄	1	4	yes	—
110	C₄⋊C₄×D₇₉	C₂×C₄	1	8	yes	—
111	C₄⋊C₄×D₇₉	C₂×C₄	1	4	yes	—
112	C₂²⋊C₄×D₇₉	C₂×C₄	1	4	yes	—
113	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
114	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
115	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
116	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
117	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
118	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
119	C₄²×D₇₉	C₂³	1	2	yes	—
120	C₄²×D₇₉	C₂³	1	2	yes	—
121	C₄²×D₇₉	C₂³	1	4	yes	—
122	C₄⋊(C₇₉⋊C₈)	C₂³	1	8	yes	—
123	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
124	Dic₇₉⋊C₈	C₂³	1	8	yes	—
125	Dic₇₉⋊C₈	C₂³	1	8	yes	—
126	Dic₇₉⋊C₈	C₂³	1	8	yes	—
127	#14579072	C₂³	1	4	yes	—
128	#14579071	C₂³	1	4	yes	—
129	#14579071	C₂³	1	4	yes	—
130	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
131	C₄×C₇₉⋊C₈	C₂³	1	4	yes	—
132	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
133	C₈×Dic₇₉	C₂³	1	2	yes	—
134	C₈×Dic₇₉	C₂³	1	4	yes	—
135	C₈×Dic₇₉	C₂³	1	2	yes	—
136	C₈×Dic₇₉	C₂³	1	4	yes	—
137	C₈×Dic₇₉	C₂³	1	2	yes	—
138	C₈×Dic₇₉	C₂³	1	2	yes	—
139	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
140	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
143	#125×C₇₉	C₂×C₄	1	2	yes	—
144	C₂²⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
145	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
146	#117×C₇₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
149	C₄⋊C₈×C₇₉	C₂³	1	8	yes	—
150	#97×C₇₉	C₂³	1	4	yes	—
151	C₄×C₈×C₇₉	C₂³	1	2	yes	—
152	C₄×C₈×C₇₉	C₂³	1	4	yes	—
153	C₄×C₈×C₇₉	C₂³	1	2	yes	—
154	C₂³×D₇₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×Dic₁₅₈	C₂²×C₄	1	8	yes	—
156	C₂×Dic₁₅₈	C₂²×C₄	1	4	yes	—
157	Q₈×D₇₉	—	2	16	no	—
158	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
159	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₇₉	—	2	8	no	—
161	C₂×C₄×D₇₉	C₂²×C₄	1	8	yes	—
162	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
163	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
164	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
165	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
168	C₂×C₄×D₇₉	C₂×Q₈	1	4	yes	—
169	C₂×C₄×D₇₉	#41	1	4	yes	—
170	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
172	#11929608	—	2	4	no	—
173	#11929607	—	2	8	no	—
174	C₂×C₇₉⋊C₈	—	2	2	no	—
175	C₂×C₇₉⋊C₈	C₂×Q₈	1	4	yes	complemented
176	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
177	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
178	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
179	C₂×C₇₉⋊C₈	C₂⁴	1	1	yes	characteristic
180	C₈×D₇₉	—	2	4	no	—
181	C₈×D₇₉	—	2	4	no	—
182	C₈×D₇₉	—	2	8	no	—
183	C₈×D₇₉	C₂×Q₈	1	4	yes	—
184	C₈×D₇₉	C₂×Q₈	1	4	yes	—
185	C₈×D₇₉	C₂×Q₈	1	4	yes	complemented
186	C₈×D₇₉	C₂×Q₈	1	4	yes	complemented
187	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
188	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
189	C₄⋊Dic₇₉	C₂²×C₄	1	8	yes	—
190	Dic₇₉⋊C₄	C₂²×C₄	1	8	yes	—
191	Dic₇₉⋊C₄	C₂²×C₄	1	8	yes	—
192	Dic₇₉⋊C₄	C₂²×C₄	1	8	yes	—
193	Dic₇₉⋊C₄	C₂²×C₄	1	8	yes	—
194	C₂²⋊Dic₇₉	C₂²×C₄	1	4	yes	—
195	(C₂×D₇₉)⋊C₄	C₂²×C₄	1	8	yes	—
196	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
199	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
200	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
201	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
202	C₄×Dic₇₉	C₂²×C₄	1	8	yes	—
203	C₄×Dic₇₉	C₂⁴	1	2	yes	—
204	C₄×Dic₇₉	C₂⁴	1	4	yes	—
205	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
206	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
207	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
208	M₁₆×C₇₉	—	2	4	no	—
209	C₂×C₈×C₇₉	—	2	2	no	—
210	C₂×C₈×C₇₉	C₂×Q₈	1	4	yes	complemented
211	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
212	C₂×C₈×C₇₉	C₂⁴	1	4	yes	—
213	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
214	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
215	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
217	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
218	C₂²⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
219	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
220	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₇₉	C₂⁴	1	2	yes	—
222	C₄²×C₇₉	C₂⁴	1	4	yes	—
223	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
224	C₂²×D₇₉	—	2	4	no	—
225	C₂²×D₇₉	C₄×Q₈	1	4	yes	—
226	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
227	C₂²×D₇₉	C₂³×C₄	1	1	yes	characteristic
228	Q₈×C₇₉	—	2	8	no	—
229	C₂×C₄×C₇₉	—	2	4	no	—
230	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₇₉	C₂³×C₄	1	8	yes	—
232	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
235	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
237	C₂×Dic₇₉	—	2	4	no	—
238	C₂×Dic₇₉	C₄×Q₈	1	4	yes	—
239	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
240	C₂×Dic₇₉	C₂³×C₄	1	8	yes	—
241	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
242	C₂×Dic₇₉	C₂³×C₄	1	1	yes	characteristic
243	C₂×Dic₇₉	C₂³×C₄	1	2	yes	—
244	C₄×D₇₉	—	2	4	no	—
245	C₄×D₇₉	—	2	16	no	—
246	C₄×D₇₉	—	2	4	no	—
247	C₄×D₇₉	—	2	4	no	—
248	C₄×D₇₉	C₄×Q₈	1	4	yes	—
249	C₄×D₇₉	C₄×Q₈	1	4	yes	—
250	C₄×D₇₉	#131	1	8	yes	—
251	C₄×D₇₉	C₂²×Q₈	1	2	yes	—
252	C₄×D₇₉	C₂²×Q₈	1	2	yes	—
253	C₄×D₇₉	C₂×#41	1	2	yes	—
254	C₄×D₇₉	C₂×#41	1	2	yes	—
255	Dic₁₅₈	—	2	8	no	—
256	Dic₁₅₈	—	2	16	no	—
257	C₈×C₇₉	—	2	2	no	—
258	C₈×C₇₉	—	2	4	no	—
259	C₈×C₇₉	C₂²×Q₈	1	2	yes	—
260	C₈×C₇₉	C₂²×Q₈	1	2	yes	—
261	C₇₉⋊C₈	—	2	2	no	—
262	C₇₉⋊C₈	—	2	4	no	—
263	C₇₉⋊C₈	C₂²×Q₈	1	2	yes	—
264	C₇₉⋊C₈	C₂²×Q₈	1	2	yes	—
265	C₂²×C₇₉	—	2	2	no	—
266	C₂²×C₇₉	C₂×C₄×Q₈	1	2	yes	—
267	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
268	C₂×D₇₉	—	2	2	no	—
269	C₂×D₇₉	—	2	8	no	—
270	C₂×D₇₉	C₂×C₄×Q₈	1	2	yes	—
271	C₂×D₇₉	C₂×C₄×Q₈	1	2	yes	—
272	C₂×D₇₉	C₂×#131	1	4	yes	—
273	C₄×C₇₉	—	2	2	no	—
274	C₄×C₇₉	—	2	8	no	—
275	C₄×C₇₉	C₂×C₄×Q₈	1	2	yes	—
276	C₄×C₇₉	C₂×#131	1	4	yes	—
277	C₄×C₇₉	C₂³×Q₈	1	1	yes	characteristic
278	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
279	Dic₇₉	—	2	8	no	—
280	Dic₇₉	—	2	2	no	—
281	Dic₇₉	C₂×C₄×Q₈	1	2	yes	—
282	Dic₇₉	C₂×C₄×Q₈	1	2	yes	—
283	Dic₇₉	C₂×#131	1	4	yes	—
284	C₂×#2960	—	79	1	no	maximal, Sylow
285	C₂×C₇₉	—	2	2	no	—
286	C₂×C₇₉	C₂²×C₄×Q₈	1	1	yes	characteristic
287	C₂×C₇₉	C₂²×#131	1	2	yes	—
288	D₇₉	—	2	2	no	—
289	D₇₉	#2960	1	4	yes	direct product factor
290	C₂×#533	—	79	1	no	—
291	#2960	—	79	4	no	—
292	#2960	—	79	4	no	—
293	#2960	—	79	2	no	—
294	#2960	—	79	1	no	—
295	#2960	—	79	2	no	—
296	#2960	—	79	1	no	—
297	#2960	—	79	1	no	—
298	#2960	D₇₉	1	1	yes	characteristic, direct product factor
299	C₂×#446	—	79	4	no	—
300	C₂×C₈×Q₈	—	79	4	no	—
301	C₂×#424	—	79	2	no	—
302	C₂×#423	—	79	1	no	—
303	C₂×#405	—	79	2	no	—
304	C₂²×C₄×C₈	—	79	1	no	—
305	C₇₉	C₂×#2960	1	1	yes	characteristic, complemented, Sylow
306	C₂²×M₁₆	—	79	2	no	—
307	C₂³×C₈	—	79	1	no	—
308	C₂³×C₈	—	79	1	no	—
309	#533	—	79	2	no	—
310	#533	—	79	2	no	—
311	#533	—	79	4	no	—
312	#533	—	79	4	no	—
313	#533	—	79	2	no	—
314	#533	—	79	1	no	—
315	#533	C₂×D₇₉	1	1	yes	characteristic
316	C₂×C₄⋊Q₈	—	79	2	no	—
317	C₂×#125	—	79	2	no	—
318	C₂×C₂²⋊Q₈	—	79	4	no	—
319	C₂×C₄×Q₈	—	79	4	no	—
320	C₂×#117	—	79	2	no	—
321	C₂²×C₄²	—	79	1	no	—
322	#446	—	79	4	no	—
323	#446	—	79	4	no	—
324	#446	—	79	8	no	—
325	#446	—	79	8	no	—
326	#446	—	79	4	no	—
327	#446	C₂×D₇₉	1	4	yes	complemented
328	C₈×Q₈	—	79	4	no	—
329	C₈×Q₈	—	79	8	no	—
330	C₈×Q₈	—	79	4	no	—
331	C₈×Q₈	—	79	8	no	—
332	C₈×Q₈	—	79	4	no	—
333	C₈×Q₈	C₂×D₇₉	1	4	yes	complemented
334	#424	—	79	2	no	—
335	#424	—	79	2	no	—
336	#424	—	79	2	no	—
337	#424	—	79	8	no	—
338	#424	C₂×D₇₉	1	2	yes	—
339	#423	—	79	2	no	—
340	#423	—	79	1	no	—
341	#423	—	79	4	no	—
342	#423	C₂×D₇₉	1	1	yes	characteristic
343	C₂×C₄⋊C₈	—	79	4	no	—
344	C₂×C₄⋊C₈	—	79	8	no	—
345	#405	—	79	2	no	—
346	#405	—	79	2	no	—
347	#405	—	79	2	no	—
348	#405	—	79	4	no	—
349	#405	—	79	4	no	—
350	#405	C₂×D₇₉	1	2	yes	—
351	C₂×#97	—	79	4	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	2	no	—
356	C₂×C₄×C₈	—	79	2	no	—
357	C₂×C₄×C₈	—	79	2	no	—
358	C₂×C₄×C₈	—	79	2	no	—
359	C₂×C₄×C₈	—	79	4	no	—
360	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
361	C₂²×Q₈	—	79	4	no	—
362	C₂³×C₄	—	79	1	no	—
363	C₂³×C₄	—	79	2	no	—
364	C₂×M₁₆	—	79	2	no	—
365	C₂×M₁₆	—	79	4	no	—
366	C₂×M₁₆	—	158	8	no	—
367	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
368	C₂²×C₈	—	79	1	no	—
369	C₂²×C₈	—	79	8	no	—
370	C₂²×C₈	—	79	1	no	—
371	C₂²×C₈	—	79	1	no	—
372	C₂²×C₈	—	79	1	no	—
373	C₂²×C₈	—	79	1	no	—
374	C₂²×C₈	—	79	1	no	—
375	C₂²×C₈	—	79	2	no	—
376	C₂²×C₈	—	79	2	no	—
377	C₂²×C₈	—	79	4	no	—
378	C₂²×C₈	—	158	4	no	—
379	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
380	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
381	C₄⋊Q₈	—	79	4	no	—
382	C₄⋊Q₈	—	79	4	no	—
383	C₄⋊Q₈	—	79	4	no	—
384	C₄⋊Q₈	—	79	2	no	—
385	C₄⋊Q₈	C₄×D₇₉	1	2	yes	—
386	#125	—	79	8	no	—
387	#125	—	79	4	no	—
388	#125	—	79	2	no	—
389	#125	C₄×D₇₉	1	2	yes	—
390	C₂²⋊Q₈	—	79	4	no	—
391	C₂²⋊Q₈	—	79	4	no	—
392	C₂²⋊Q₈	—	79	8	no	—
393	C₂²⋊Q₈	—	79	4	no	—
394	C₂²⋊Q₈	—	79	8	no	—
395	C₂²⋊Q₈	C₄×D₇₉	1	4	yes	—
396	C₄×Q₈	—	79	4	no	—
397	C₄×Q₈	—	79	4	no	—
398	C₄×Q₈	—	79	8	no	—
399	C₄×Q₈	—	79	8	no	—
400	C₄×Q₈	—	79	4	no	—
401	C₄×Q₈	C₂²×D₇₉	1	4	yes	—
402	#117	—	79	2	no	—
403	#117	—	79	4	no	—
404	#117	—	79	4	no	—
405	#117	—	79	4	no	—
406	#117	C₂²×D₇₉	1	2	yes	—
407	C₂×C₄⋊C₄	—	79	4	no	—
408	C₂×C₄⋊C₄	—	79	8	no	—
409	C₂×C₄⋊C₄	—	79	4	no	—
410	C₂×C₂²⋊C₄	—	79	4	no	—
411	C₂×C₄²	—	79	2	no	—
412	C₂×C₄²	—	79	1	no	—
413	C₂×C₄²	—	79	1	no	—
414	C₂×C₄²	—	79	1	no	—
415	C₂×C₄²	—	79	1	no	—
416	C₂×C₄²	—	79	1	no	—
417	C₂×C₄²	—	79	4	no	—
418	C₂×C₄²	—	79	2	no	—
419	C₂×C₄²	—	79	2	no	—
420	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
421	C₄⋊C₈	—	79	8	no	—
422	C₄⋊C₈	—	79	8	no	—
423	C₄⋊C₈	—	79	8	no	—
424	C₄⋊C₈	—	79	4	no	—
425	C₄⋊C₈	—	79	8	no	—
426	C₄⋊C₈	C₂²×D₇₉	1	4	yes	—
427	C₄⋊C₈	C₂²×D₇₉	1	8	yes	—
428	#97	—	79	4	no	—
429	#97	—	79	4	no	—
430	#97	—	79	4	no	—
431	#97	C₂²×D₇₉	1	4	yes	—
432	C₄×C₈	—	79	2	no	—
433	C₄×C₈	—	79	2	no	—
434	C₄×C₈	—	79	2	no	—
435	C₄×C₈	—	79	4	no	—
436	C₄×C₈	—	79	2	no	—
437	C₄×C₈	—	79	4	no	—
438	C₄×C₈	—	79	2	no	—
439	C₄×C₈	—	79	2	no	—
440	C₄×C₈	—	79	4	no	—
441	C₄×C₈	C₂²×D₇₉	1	2	yes	—
442	C₄×C₈	C₂²×D₇₉	1	2	yes	—
443	C₄×C₈	C₂²×D₇₉	1	4	yes	—
444	C₂⁴	—	79	1	no	—
445	C₂×Q₈	—	79	8	no	—
446	C₂×Q₈	—	79	4	no	—
447	C₂×Q₈	—	158	16	no	—
448	C₂×Q₈	C₂×C₄×D₇₉	1	4	yes	—
449	C₂²×C₄	—	79	1	no	—
450	C₂²×C₄	—	79	4	no	—
451	C₂²×C₄	—	79	4	no	—
452	C₂²×C₄	—	79	1	no	—
453	C₂²×C₄	—	79	1	no	—
454	C₂²×C₄	—	79	1	no	—
455	C₂²×C₄	—	79	2	no	—
456	C₂²×C₄	—	79	1	no	—
457	C₂²×C₄	—	79	2	no	—
458	C₂²×C₄	—	79	2	no	—
459	C₂²×C₄	—	79	2	no	—
460	C₂²×C₄	—	79	2	no	—
461	C₂²×C₄	—	79	8	no	—
462	C₂²×C₄	—	158	8	no	—
463	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
464	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
465	M₁₆	—	2	4	no	—
466	M₁₆	—	158	8	no	—
467	M₁₆	—	158	4	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	79	4	no	—
470	C₂×C₈	—	79	1	no	—
471	C₂×C₈	—	79	1	no	—
472	C₂×C₈	—	79	4	no	—
473	C₂×C₈	—	79	4	no	—
474	C₂×C₈	—	79	4	no	—
475	C₂×C₈	—	79	4	no	—
476	C₂×C₈	—	79	2	no	—
477	C₂×C₈	—	79	4	no	—
478	C₂×C₈	—	158	4	no	—
479	C₂×C₈	—	158	4	no	—
480	C₂×C₈	—	158	8	no	—
481	C₂×C₈	—	158	2	no	—
482	C₂×C₈	Q₈×D₇₉	1	4	yes	complemented
483	C₂×C₈	C₂³×D₇₉	1	2	yes	—
484	C₂×C₈	C₂³×D₇₉	1	4	yes	—
485	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
486	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
487	C₄⋊C₄	—	79	8	no	—
488	C₄⋊C₄	—	79	8	no	—
489	C₄⋊C₄	—	79	8	no	—
490	C₄⋊C₄	—	79	8	no	—
491	C₄⋊C₄	—	79	4	no	—
492	C₄⋊C₄	—	79	8	no	—
493	C₄⋊C₄	—	79	4	no	—
494	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
495	C₄⋊C₄	C₂×C₄×D₇₉	1	8	yes	—
496	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
497	C₂²⋊C₄	—	79	4	no	—
498	C₂²⋊C₄	—	79	8	no	—
499	C₂²⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
500	C₄²	—	79	2	no	—
501	C₄²	—	79	4	no	—
502	C₄²	—	79	2	no	—
503	C₄²	—	79	2	no	—
504	C₄²	—	79	2	no	—
505	C₄²	—	79	1	no	—
506	C₄²	—	79	2	no	—
507	C₄²	—	79	1	no	—
508	C₄²	—	79	8	no	—
509	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
510	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
511	C₄²	C₂³×D₇₉	1	2	yes	—
512	C₄²	C₂³×D₇₉	1	4	yes	—
513	C₂³	—	79	1	no	—
514	C₂³	—	79	4	no	—
515	C₂³	—	79	1	no	—
516	C₂³	—	158	4	no	—
517	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
518	Q₈	—	2	8	no	—
519	Q₈	—	158	16	no	—
520	Q₈	—	158	8	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	79	4	no	—
523	C₂×C₄	—	79	1	no	—
524	C₂×C₄	—	79	1	no	—
525	C₂×C₄	—	79	2	no	—
526	C₂×C₄	—	79	4	no	—
527	C₂×C₄	—	79	4	no	—
528	C₂×C₄	—	79	8	no	—
529	C₂×C₄	—	79	2	no	—
530	C₂×C₄	—	79	2	no	—
531	C₂×C₄	—	79	2	no	—
532	C₂×C₄	—	79	2	no	—
533	C₂×C₄	—	79	2	no	—
534	C₂×C₄	—	79	8	no	—
535	C₂×C₄	—	158	4	no	—
536	C₂×C₄	—	158	4	no	—
537	C₂×C₄	—	158	16	no	—
538	C₂×C₄	—	158	4	no	—
539	C₂×C₄	—	158	4	no	—
540	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
541	C₂×C₄	C₂²×C₄×D₇₉	1	8	yes	—
542	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
543	C₂×C₄	C₂²×C₄×D₇₉	1	2	yes	—
544	C₂×C₄	C₂×Q₈×D₇₉	1	2	yes	—
545	C₂×C₄	#41×D₇₉	1	2	yes	—
546	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	2	4	no	—
549	C₈	—	79	2	no	—
550	C₈	—	79	2	no	—
551	C₈	—	158	2	no	—
552	C₈	—	158	4	no	—
553	C₈	C₂×Q₈×D₇₉	1	2	yes	—
554	C₈	C₂×Q₈×D₇₉	1	2	yes	—
555	C₂²	—	2	2	no	—
556	C₂²	—	79	4	no	—
557	C₂²	—	79	2	no	—
558	C₂²	—	79	2	no	—
559	C₂²	—	158	8	no	—
560	C₂²	—	158	2	no	—
561	C₂²	C₄×Q₈×D₇₉	1	2	yes	—
562	C₂²	C₂³×C₄×D₇₉	1	1	yes	characteristic
563	C₄	—	2	2	no	—
564	C₄	—	2	8	no	—
565	C₄	—	79	4	no	—
566	C₄	—	79	2	no	—
567	C₄	—	79	2	no	—
568	C₄	—	158	2	no	—
569	C₄	—	158	8	no	—
570	C₄	C₄×Q₈×D₇₉	1	2	yes	—
571	C₄	#131×D₇₉	1	4	yes	—
572	C₄	C₂²×Q₈×D₇₉	1	1	yes	characteristic
573	C₄	C₂×#41×D₇₉	1	1	yes	characteristic
574	C₂	—	2	2	no	—
575	C₂	—	79	4	no	—
576	C₂	—	158	2	no	—
577	C₂	C₂×C₄×Q₈×D₇₉	1	1	yes	characteristic
578	C₂	C₂×#131×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂³×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₇₉×#2960	C₂
prime radical	C₂³×D₇₉	C₂²×C₄
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	#2960	D₇₉
hypocenter	C₇₉	C₂×#2960
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #23772335	C₂	semidirect
3. #23772334	C₂	semidirect
4. #23772333	C₂	semidirect
5. #23772332	C₂	semidirect
6. #23772331	C₂	semidirect
7. #23772330	C₂	semidirect
8. #23772329	C₂	semidirect
9. #446×D₇₉	C₂	semidirect
10. C₈×Q₈×D₇₉	C₂	semidirect
15. C₇₉×#2960	C₂	semidirect
31. #19098694	C₂²	semidirect
32. #19098693	C₂²	semidirect
33. #19098692	C₂²	semidirect
34. #19098691	C₂²	semidirect
35. #19098690	C₂²	semidirect
36. Q₈×C₇₉⋊C₈	C₂²	semidirect
37. C₈×Dic₁₅₈	C₂²	semidirect
38. C₈×Dic₁₅₈	C₂²	semidirect
39. #19098687	C₂²	semidirect
40. #19098687	C₂²	semidirect
65. #446×C₇₉	C₂²	semidirect
66. C₈×Q₈×C₇₉	C₂²	semidirect
80. C₂×C₈×D₇₉	Q₈	semidirect
175. C₂×C₇₉⋊C₈	C₂×Q₈	semidirect
185. C₈×D₇₉	C₂×Q₈	semidirect
186. C₈×D₇₉	C₂×Q₈	semidirect
210. C₂×C₈×C₇₉	C₂×Q₈	semidirect
289. D₇₉	#2960	direct (N × H)
298. #2960	D₇₉	direct (N × H)
305. C₇₉	C₂×#2960	semidirect
327. #446	C₂×D₇₉	semidirect
333. C₈×Q₈	C₂×D₇₉	semidirect
482. C₂×C₈	Q₈×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#533×D₇₉	2
#23772335	2
#23772334	2
#23772333	2
#23772332	2
#23772331	2
#23772330	2
#23772329	2
#446×D₇₉	2
C₈×Q₈×D₇₉	2
#424×D₇₉	2
#423×D₇₉	2
#405×D₇₉	2
C₂×C₄×C₈×D₇₉	2
C₇₉×#2960	2
C₂×#2960	79

Subgroups — #2960×D79 #35152628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2960×D₇₉ #35152628