Subgroups — #23761460

Order 10112.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098965	C₂	1	1	yes	maximal, characteristic
2	#19098384	C₂	1	1	yes	maximal, characteristic
3	#364×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579153	C₄	1	2	yes	—
5	#14579101	—	2	1	no	—
6	#14579095	—	2	1	no	—
7	#14579093	—	2	1	no	—
8	M₃₂×C₇₉	—	2	1	no	—
9	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₇₉	—	2	2	no	—
11	Dic₇₉⋊C₄	—	4	2	no	—
12	C₇₉⋊C₁₆	—	4	1	no	—
13	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
15	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₉	—	4	1	no	—
17	C₂×C₄×C₇₉	—	2	1	no	—
18	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₇₉	—	4	2	no	—
20	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
21	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
22	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
23	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
24	C₂²×C₇₉	#100	1	1	yes	characteristic
25	C₄×C₇₉	—	4	1	no	—
26	C₄×C₇₉	#103	1	1	yes	characteristic
27	C₄×C₇₉	#103	1	1	yes	characteristic
28	Dic₇₉	—	8	2	no	—
29	C₂×C₇₉	—	2	1	no	—
30	C₂×C₇₉	#333	1	1	yes	characteristic
31	#1366	—	79	1	no	maximal, Sylow
32	C₇₉	#1366	1	1	yes	characteristic, complemented, Sylow
33	#499	—	79	1	no	—
34	#364	—	79	1	no	—
35	#364	D₇₉	1	1	yes	characteristic
36	#125	—	79	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	158	1	no	—
39	#107	—	158	1	no	—
40	#106	—	158	1	no	—
41	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
42	C₂×C₈	D₃₁₆	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
44	C₄⋊C₄	—	316	2	no	—
45	C₄⋊C₄	—	158	2	no	—
46	C₄²	C₄×D₇₉	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	316	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	316	2	no	—
51	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
52	C₈	#11929612	1	1	yes	characteristic
53	C₈	#11929613	1	1	yes	characteristic
54	C₈	#11929614	1	1	yes	characteristic
55	C₈	Dic₃₁₆	1	1	yes	characteristic
56	C₂²	#14579077	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	632	2	no	—
59	C₄	#14579084	1	1	yes	characteristic
60	C₄	#14579086	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#19098311	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098311
commutator	C₄²×C₇₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#364×C₇₉	C₂
socle	C₂×C₇₉	#333
prime radical	C₂²×C₇₉	#100
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#364	D₇₉
hypocenter	C₇₉	#1366
LCS	G ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
32. C₇₉	#1366	semidirect