Subgroups — #23765641

Order 10112.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098965	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098364	C₂	1	4	yes	maximal, complemented
3	#19098339	C₂	1	1	yes	maximal, characteristic, complemented
4	#493×C₇₉	C₂	1	1	yes	maximal, characteristic
5	#14579153	—	2	1	no	—
6	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
7	#14579095	C₂²	1	2	yes	—
8	#14579093	—	2	1	no	—
9	C₂×D₈×C₇₉	—	2	1	no	—
10	C₂×D₈×C₇₉	C₂²	1	2	yes	—
11	#127×C₇₉	—	2	1	no	—
12	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₇₉	—	2	2	no	—
14	Dic₇₉⋊C₄	—	4	2	no	—
15	C₇₉⋊C₁₆	—	2	2	no	—
16	C₂×D₄×C₇₉	—	2	2	no	—
17	C₂×D₄×C₇₉	—	4	2	no	—
18	D₈×C₇₉	—	2	4	no	—
19	D₈×C₇₉	—	4	2	no	—
20	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
22	C₄²×C₇₉	D₄	1	1	yes	characteristic
23	C₂³×C₇₉	—	4	2	no	—
24	D₄×C₇₉	—	4	2	no	—
25	D₄×C₇₉	—	4	2	no	—
26	D₄×C₇₉	—	8	4	no	—
27	C₂×C₄×C₇₉	D₈	1	2	yes	—
28	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₇₉	—	4	2	no	—
30	C₈×C₇₉	SD₁₆	1	2	yes	—
31	C₈×C₇₉	#41	1	2	yes	—
32	C₂²×C₇₉	—	8	2	no	—
33	C₂²×C₇₉	—	8	4	no	—
34	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
35	C₄×C₇₉	—	2	2	no	—
36	C₄×C₇₉	#124	1	1	yes	characteristic
37	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
38	Dic₇₉	—	8	2	no	—
39	C₂×C₇₉	—	16	2	no	—
40	C₂×C₇₉	#486	1	1	yes	characteristic
41	C₂×C₇₉	#509	1	2	yes	—
42	#2244	—	79	1	no	maximal, Sylow
43	C₇₉	#2244	1	1	yes	characteristic, complemented, Sylow
44	#499	—	79	1	no	—
45	#493	D₇₉	1	1	yes	characteristic
46	#357	—	79	4	no	—
47	#346	—	79	1	no	—
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	C₂×D₇₉	1	2	yes	—
50	#127	—	2	1	no	—
51	#125	—	158	1	no	—
52	C₂×C₁₆	—	79	2	no	—
53	#107	—	79	2	no	—
54	#106	—	158	1	no	—
55	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	—	4	2	no	—
58	D₈	—	2	4	no	—
59	D₈	—	4	2	no	—
60	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
62	C₄⋊C₄	—	316	2	no	—
63	C₄⋊C₄	—	158	2	no	—
64	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
65	C₁₆	—	158	2	no	—
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	316	2	no	—
71	C₂×C₄	#11929609	1	2	yes	—
72	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
73	C₈	#11929612	1	2	yes	—
74	C₈	#11929623	1	2	yes	—
75	C₂²	—	8	2	no	—
76	C₂²	—	8	4	no	—
77	C₂²	C₂×#11929609	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	632	2	no	—
80	C₄	#14579148	1	1	yes	characteristic
81	C₄	C₂×#11929612	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	#19098909	1	1	yes	characteristic
84	C₂	#19098999	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting, prime radical	#493×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
hypercenter	#493	D₇₉
hypocenter	C₇₉	#2244
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. #19098965	C₂	semidirect
2. #19098364	C₂	semidirect
3. #19098339	C₂	semidirect
43. C₇₉	#2244	semidirect