Subgroups — #23763017

Order 10112.

192 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	#19098966	C₂	1	2	yes	maximal
3	#19098942	C₂	1	2	yes	maximal
4	C₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#500×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929614	—	2	4	no	—
7	#14579161	C₂²	1	2	yes	—
8	#14579095	—	2	2	no	—
9	#14579094	—	2	4	no	—
10	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
13	#107×C₇₉	—	2	2	no	—
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	2	2	no	—
16	#11929614	—	4	8	no	—
17	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
18	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₂×Q₈×C₇₉	—	2	2	no	—
22	C₂×C₈×C₇₉	D₄	1	2	yes	—
23	C₄⋊C₄×C₇₉	—	2	2	no	—
24	C₄⋊C₄×C₇₉	—	2	2	no	—
25	C₄²×C₇₉	C₂³	1	1	yes	characteristic
26	Q₈×C₇₉	—	4	4	no	—
27	C₂×C₄×C₇₉	—	4	2	no	—
28	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₇₉	—	4	2	no	—
32	Dic₁₅₈	—	4	4	no	—
33	C₈×C₇₉	Q₁₆	1	4	yes	complemented
34	C₇₉⋊C₈	D₈	1	4	yes	—
35	C₇₉⋊C₈	Q₁₆	1	4	yes	complemented
36	C₂²×C₇₉	#127	1	1	yes	characteristic
37	C₄×C₇₉	—	8	2	no	—
38	C₄×C₇₉	C₂×D₈	1	2	yes	—
39	C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
40	C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
41	Dic₇₉	—	8	2	no	—
42	C₂×C₇₉	#493	1	1	yes	characteristic
43	C₂×C₇₉	#494	1	1	yes	characteristic
44	C₂×C₇₉	#494	1	1	yes	characteristic
45	#1713	—	79	1	no	maximal, Sylow
46	C₇₉	#1713	1	1	yes	characteristic, complemented, Sylow
47	#500	—	79	2	no	—
48	#500	—	79	1	no	—
49	#500	D₇₉	1	1	yes	characteristic
50	#494	—	79	2	no	—
51	C₈²	—	79	1	no	—
52	C₂×Q₁₆	—	158	4	no	—
53	C₄⋊Q₈	—	79	2	no	—
54	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
55	#107	—	2	2	no	—
56	#107	—	158	4	no	—
57	#107	—	158	2	no	—
58	C₄×C₈	—	79	1	no	—
59	C₄×C₈	—	79	1	no	—
60	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
61	C₂×Q₈	—	2	2	no	—
62	C₂×Q₈	—	158	2	no	—
63	Q₁₆	—	316	8	no	—
64	C₂×C₈	—	79	2	no	—
65	C₂×C₈	—	79	2	no	—
66	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	2	2	no	—
69	C₄⋊C₄	—	158	2	no	—
70	C₄⋊C₄	—	158	2	no	—
71	C₄²	C₂²×D₇₉	1	1	yes	characteristic
72	Q₈	—	4	4	no	—
73	Q₈	—	316	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	316	2	no	—
76	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
77	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
79	C₈	—	79	4	no	—
80	C₈	—	79	4	no	—
81	C₈	#11929614	1	4	yes	complemented
82	C₂²	#14579157	1	1	yes	characteristic
83	C₄	—	8	2	no	—
84	C₄	—	632	2	no	—
85	C₄	D₈×D₇₉	1	2	yes	—
86	C₄	Q₁₆×D₇₉	1	2	yes	—
87	C₄	C₂×#11929614	1	2	yes	—
88	C₂	#19098938	1	1	yes	characteristic
89	C₂	#19098941	1	1	yes	characteristic
90	C₂	#19098942	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14579157
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#500×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#127
hypercenter	#500	D₇₉
hypocenter	C₇₉	#1713
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

Complements

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

N	H ≅ G/N	type
33. C₈×C₇₉	Q₁₆	semidirect
35. C₇₉⋊C₈	Q₁₆	semidirect
46. C₇₉	#1713	semidirect
81. C₈	#11929614	semidirect