Subgroups — #23761603

Order 10112.

50 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
2	#19098393	C₂	1	1	yes	maximal, characteristic
3	#368×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579097	—	2	1	no	—
5	C₇₉⋊C₃₂	C₄	1	2	yes	—
6	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
7	#108×C₇₉	—	2	1	no	—
8	#11929608	—	4	1	no	—
9	M₁₆×C₇₉	—	4	1	no	—
10	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
11	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
14	C₈×C₇₉	—	8	1	no	—
15	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
17	C₇₉⋊C₈	—	8	1	no	—
18	C₂²×C₇₉	Q₃₂	1	1	yes	characteristic
19	C₄×C₇₉	#107	1	1	yes	characteristic
20	C₄×C₇₉	D₁₆	1	1	yes	characteristic
21	C₂×C₇₉	—	2	1	no	—
22	C₂×C₇₉	#366	1	1	yes	characteristic
23	#1425	—	79	1	no	maximal, Sylow
24	C₇₉	#1425	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	79	1	no	—
26	#368	—	79	1	no	—
27	#368	D₇₉	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	158	1	no	—
31	C₃₂	—	79	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	316	1	no	—
34	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
35	C₁₆	Dic₁₅₈	1	1	yes	characteristic
36	C₁₆	C₄×D₇₉	1	1	yes	characteristic
37	C₂×C₄	#11929609	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	632	1	no	—
40	C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
41	C₈	#11929614	1	1	yes	characteristic
42	C₂²	#14579107	1	1	yes	characteristic
43	C₄	#14579094	1	1	yes	characteristic
44	C₄	#14579102	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#19098388	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14579102
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting	#368×C₇₉	C₂
socle	C₂×C₇₉	#366
prime radical	C₂²×C₇₉	Q₃₂
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	#368	D₇₉
hypocenter	C₇₉	#1425
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
24. C₇₉	#1425	semidirect