Subgroups — #23765680

Order 10112.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098968	C₂	1	1	yes	maximal, characteristic
2	#19098390	C₂	1	4	yes	maximal
3	C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#500×C₇₉	C₂	1	1	yes	maximal, characteristic
5	#14579161	—	2	1	no	—
6	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
7	#14579095	—	2	1	no	—
8	#14579095	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₇₉	—	2	1	no	—
10	#107×C₇₉	—	2	1	no	—
11	#107×C₇₉	C₂²	1	2	yes	—
12	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₅₈	—	4	1	no	—
14	C₄⋊Dic₇₉	—	2	2	no	—
15	C₄⋊Dic₇₉	—	4	1	no	—
16	C₇₉⋊C₁₆	Q₈	1	4	yes	complemented
17	C₂×Q₈×C₇₉	—	4	1	no	—
18	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₇₉	—	2	2	no	—
21	C₄⋊C₄×C₇₉	—	4	1	no	—
22	C₄²×C₇₉	D₄	1	1	yes	characteristic
23	Q₈×C₇₉	—	8	2	no	—
24	C₂×C₄×C₇₉	—	4	2	no	—
25	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
26	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₇₉	—	4	2	no	—
29	Dic₁₅₈	—	8	2	no	—
30	C₈×C₇₉	Q₁₆	1	2	yes	—
31	C₈×C₇₉	C₂×Q₈	1	2	yes	—
32	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
33	C₄×C₇₉	—	8	2	no	—
34	C₄×C₇₉	SD₃₂	1	2	yes	—
35	C₄×C₇₉	SD₃₂	1	2	yes	—
36	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
37	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
38	Dic₇₉	—	8	2	no	—
39	C₂×C₇₉	#500	1	1	yes	characteristic
40	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
41	C₂×C₇₉	C₂×SD₃₂	1	1	yes	characteristic
42	#2254	—	79	1	no	maximal, Sylow
43	C₇₉	#2254	1	1	yes	characteristic, complemented, Sylow
44	#500	—	79	1	no	—
45	#500	D₇₉	1	1	yes	characteristic
46	#367	—	79	4	no	—
47	C₄×C₁₆	—	79	1	no	—
48	C₄⋊Q₈	—	2	1	no	—
49	C₄⋊Q₈	—	158	1	no	—
50	C₂×C₁₆	—	79	2	no	—
51	#107	—	2	1	no	—
52	#107	—	79	2	no	—
53	#107	—	158	1	no	—
54	#107	C₂×D₇₉	1	2	yes	—
55	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
56	C₂×Q₈	—	4	1	no	—
57	C₂×Q₈	—	316	1	no	—
58	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
59	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
60	C₄⋊C₄	—	2	2	no	—
61	C₄⋊C₄	—	4	1	no	—
62	C₄⋊C₄	—	316	1	no	—
63	C₄⋊C₄	—	158	2	no	—
64	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
65	C₁₆	—	79	4	no	—
66	Q₈	—	8	2	no	—
67	Q₈	—	632	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	316	2	no	—
70	C₂×C₄	#11929609	1	1	yes	characteristic
71	C₂×C₄	#11929609	1	1	yes	characteristic
72	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
73	C₈	#11929614	1	2	yes	—
74	C₈	Q₈×D₇₉	1	2	yes	—
75	C₂²	C₂×#11929609	1	1	yes	characteristic
76	C₄	—	8	2	no	—
77	C₄	—	632	2	no	—
78	C₄	#14579104	1	2	yes	—
79	C₄	#14579105	1	2	yes	—
80	C₄	#14579159	1	1	yes	characteristic
81	C₄	C₂×#11929614	1	1	yes	characteristic
82	C₂	#19098966	1	1	yes	characteristic
83	C₂	C₂×#14579104	1	1	yes	characteristic
84	C₂	C₂×#14579105	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#500×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	#500	D₇₉
hypocenter	C₇₉	#2254
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
16. C₇₉⋊C₁₆	Q₈	semidirect
43. C₇₉	#2254	semidirect