Subgroups — #23761584

Order 10112.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098393	C₂	1	1	yes	maximal, characteristic, complemented
3	#508×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579097	—	2	1	no	—
5	C₇₉⋊C₃₂	—	2	1	no	—
6	#135×C₇₉	—	2	1	no	—
7	Q₃₂×C₇₉	C₄	1	1	yes	characteristic
8	SD₃₂×C₇₉	—	2	1	no	—
9	D₁₆×C₇₉	C₄	1	1	yes	characteristic
10	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
11	#11929608	—	4	1	no	—
12	#41×C₇₉	—	4	1	no	—
13	Q₁₆×C₇₉	—	2	1	no	—
14	SD₁₆×C₇₉	—	4	1	no	—
15	D₈×C₇₉	—	2	1	no	—
16	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
17	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₇₉	D₄	1	1	yes	characteristic
19	Q₈×C₇₉	—	4	1	no	—
20	D₄×C₇₉	—	4	1	no	—
21	D₄×C₇₉	—	8	1	no	—
22	C₂×C₄×C₇₉	—	8	1	no	—
23	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
24	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
26	C₇₉⋊C₈	—	8	1	no	—
27	C₂²×C₇₉	—	8	1	no	—
28	C₂²×C₇₉	SD₃₂	1	1	yes	characteristic
29	C₄×C₇₉	—	8	1	no	—
30	C₄×C₇₉	#102	1	1	yes	characteristic
31	C₄×C₇₉	D₁₆	1	1	yes	characteristic
32	C₂×C₇₉	—	2	1	no	—
33	C₂×C₇₉	—	16	1	no	—
34	C₂×C₇₉	#357	1	1	yes	characteristic
35	#1417	—	79	1	no	maximal, Sylow
36	C₇₉	#1417	1	1	yes	characteristic, complemented, Sylow
37	#508	D₇₉	1	1	yes	characteristic
38	C₂×C₃₂	—	79	1	no	—
39	#368	—	79	1	no	—
40	#135	—	2	1	no	—
41	Q₃₂	Dic₇₉	1	1	yes	characteristic
42	SD₃₂	—	2	1	no	—
43	D₁₆	Dic₇₉	1	1	yes	characteristic
44	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
45	#108	—	158	1	no	—
46	C₃₂	—	158	1	no	—
47	#41	—	4	1	no	—
48	Q₁₆	—	2	1	no	—
49	SD₁₆	—	4	1	no	—
50	D₈	—	2	1	no	—
51	M₁₆	—	316	1	no	—
52	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
53	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
55	Q₈	—	4	1	no	—
56	D₄	—	4	1	no	—
57	D₄	—	8	1	no	—
58	C₂×C₄	—	8	1	no	—
59	C₂×C₄	#11929609	1	1	yes	characteristic
60	C₈	—	632	1	no	—
61	C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
62	C₈	#11929612	1	1	yes	characteristic
63	C₂²	—	8	1	no	—
64	C₂²	#14579105	1	1	yes	characteristic
65	C₄	—	8	1	no	—
66	C₄	#14579082	1	1	yes	characteristic
67	C₄	#14579102	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	16	1	no	—
70	C₂	#19098364	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14579102
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting, prime radical	#508×C₇₉	C₂
socle	C₂×C₇₉	#357
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	#508	D₇₉
hypocenter	C₇₉	#1417
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. C₂×C₇₉⋊C₃₂	C₂	semidirect
2. #19098393	C₂	semidirect
36. C₇₉	#1417	semidirect