Subgroups — #23761600

Order 10112.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098389	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#14579095	—	2	2	no	—
4	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
5	C₃₂×C₇₉	C₄	1	2	yes	complemented
6	C₄⋊Dic₇₉	—	4	2	no	—
7	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
8	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₇₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
11	C₂×Dic₇₉	—	8	2	no	—
12	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
14	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
15	C₄×C₇₉	#107	1	1	yes	characteristic
16	C₄×C₇₉	Q₃₂	1	1	yes	characteristic
17	Dic₇₉	—	16	2	no	—
18	C₂×C₇₉	#366	1	1	yes	characteristic
19	C₂×C₇₉	D₃₂	1	1	yes	characteristic
20	C₂×C₇₉	Q₆₄	1	1	yes	characteristic
21	#1423	—	79	1	no	maximal, Sylow
22	C₇₉	#1423	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃₂	D₇₉	1	1	yes	characteristic
24	#366	—	79	2	no	—
25	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
26	#107	—	158	2	no	—
27	C₃₂	Dic₇₉	1	2	yes	complemented
28	C₂×C₈	D₃₁₆	1	1	yes	characteristic
29	C₄⋊C₄	—	316	2	no	—
30	C₁₆	Dic₁₅₈	1	1	yes	characteristic
31	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
32	C₂×C₄	—	632	2	no	—
33	C₂×C₄	D₆₃₂	1	1	yes	characteristic
34	C₈	C₄⋊Dic₇₉	1	1	yes	characteristic
35	C₈	Dic₃₁₆	1	1	yes	characteristic
36	C₂²	D₁₂₆₄	1	1	yes	characteristic
37	C₄	—	1264	2	no	—
38	C₄	#14579095	1	1	yes	characteristic
39	C₄	Dic₆₃₂	1	1	yes	characteristic
40	C₂	#19098389	1	1	yes	characteristic
41	C₂	D₂₅₂₈	1	1	yes	characteristic
42	C₂	Dic₁₂₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₂₆₄
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting	C₂×C₃₂×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	D₁₆
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	C₂×C₃₂	D₇₉
hypocenter	C₇₉	#1423
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₇₉	C₄	semidirect
22. C₇₉	#1423	semidirect
27. C₃₂	Dic₇₉	semidirect