Subgroups — #23761590

Order 10112.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098397	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579097	—	2	1	no	—
5	C₇₉⋊C₃₂	—	2	1	no	—
6	C₂×D₈×C₇₉	—	2	1	no	—
7	D₁₆×C₇₉	—	2	1	no	—
8	D₁₆×C₇₉	C₄	1	2	yes	—
9	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
10	#11929608	—	4	1	no	—
11	C₂×D₄×C₇₉	—	4	1	no	—
12	D₈×C₇₉	—	2	2	no	—
13	D₈×C₇₉	—	4	1	no	—
14	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
15	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₉	D₄	1	1	yes	characteristic
17	C₂³×C₇₉	—	8	1	no	—
18	D₄×C₇₉	—	4	2	no	—
19	D₄×C₇₉	—	8	1	no	—
20	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
21	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
23	C₇₉⋊C₈	—	8	1	no	—
24	C₂²×C₇₉	—	8	2	no	—
25	C₂²×C₇₉	—	16	2	no	—
26	C₂²×C₇₉	SD₃₂	1	1	yes	characteristic
27	C₄×C₇₉	#102	1	1	yes	characteristic
28	C₄×C₇₉	D₁₆	1	1	yes	characteristic
29	C₂×C₇₉	—	2	1	no	—
30	C₂×C₇₉	—	16	2	no	—
31	C₂×C₇₉	#357	1	1	yes	characteristic
32	#1419	—	79	1	no	maximal, Sylow
33	C₇₉	#1419	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₁₆	D₇₉	1	1	yes	characteristic
35	M₆₄	—	79	1	no	—
36	#368	—	79	1	no	—
37	C₂×D₈	—	2	1	no	—
38	D₁₆	—	2	1	no	—
39	D₁₆	Dic₇₉	1	2	yes	—
40	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
41	#108	—	158	1	no	—
42	C₃₂	—	158	1	no	—
43	C₂×D₄	—	4	1	no	—
44	D₈	—	2	2	no	—
45	D₈	—	4	1	no	—
46	M₁₆	—	316	1	no	—
47	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
48	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
50	C₂³	—	8	1	no	—
51	D₄	—	4	2	no	—
52	D₄	—	8	1	no	—
53	C₂×C₄	#11929609	1	1	yes	characteristic
54	C₈	—	632	1	no	—
55	C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
56	C₈	#11929612	1	1	yes	characteristic
57	C₂²	—	8	2	no	—
58	C₂²	—	16	2	no	—
59	C₂²	#14579105	1	1	yes	characteristic
60	C₄	#14579082	1	1	yes	characteristic
61	C₄	#14579102	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	16	2	no	—
64	C₂	#19098364	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098364
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting, prime radical	C₂×D₁₆×C₇₉	C₂
socle	C₂×C₇₉	#357
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	C₂×D₁₆	D₇₉
hypocenter	C₇₉	#1419
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. #19098397	C₂	semidirect
2. #19098393	C₂	semidirect
33. C₇₉	#1419	semidirect