Subgroups — #23761467

Order 10112.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098384	C₂	1	1	yes	maximal, characteristic
2	#19098339	C₂	1	1	yes	maximal, characteristic
3	#364×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579101	—	2	1	no	—
5	C₂×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
7	M₃₂×C₇₉	—	2	1	no	—
8	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
9	C₇₉⋊C₁₆	—	2	1	no	—
10	C₇₉⋊C₁₆	—	4	1	no	—
11	C₇₉⋊C₁₆	C₈	1	2	yes	—
12	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
14	C₄²×C₇₉	Q₈	1	1	yes	characteristic
15	C₁₆×C₇₉	—	4	1	no	—
16	C₂×C₄×C₇₉	—	2	1	no	—
17	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₇₉	M₁₆	1	1	yes	characteristic
20	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
21	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
22	C₂²×C₇₉	#108	1	1	yes	characteristic
23	C₄×C₇₉	—	4	1	no	—
24	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₇₉	#106	1	1	yes	characteristic
26	C₂×C₇₉	—	2	1	no	—
27	C₂×C₇₉	#334	1	1	yes	characteristic
28	#1369	—	79	1	no	maximal, Sylow
29	C₇₉	#1369	1	1	yes	characteristic, complemented, Sylow
30	#364	—	79	1	no	—
31	#364	D₇₉	1	1	yes	characteristic
32	#346	—	79	1	no	—
33	M₃₂	—	2	1	no	—
34	M₃₂	—	158	1	no	—
35	C₂×C₁₆	—	79	1	no	—
36	C₂×C₁₆	—	79	1	no	—
37	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
38	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
40	C₄²	Dic₁₅₈	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	316	1	no	—
43	C₁₆	—	79	2	no	—
44	C₁₆	—	158	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
47	C₈	C₈×D₇₉	1	1	yes	characteristic
48	C₈	#11929607	1	1	yes	characteristic
49	C₈	#11929611	1	1	yes	characteristic
50	C₈	#11929612	1	1	yes	characteristic
51	C₂²	#14579096	1	1	yes	characteristic
52	C₄	—	4	1	no	—
53	C₄	Dic₇₉⋊C₈	1	1	yes	characteristic
54	C₄	#14579092	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#19098313	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14579092
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#364×C₇₉	C₂
socle	C₂×C₇₉	#334
prime radical	C₂²×C₇₉	#108
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#364	D₇₉
hypocenter	C₇₉	#1369
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
29. C₇₉	#1369	semidirect