Subgroups — #23761466

Order 10112.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098314	C₂	1	2	yes	maximal
2	#346×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
4	C₂×C₁₆×C₇₉	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₇₉	C₄	1	1	yes	characteristic
6	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
7	C₂×C₇₉⋊C₈	—	4	2	no	—
8	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
10	C₄²×C₇₉	D₄	1	1	yes	characteristic
11	C₁₆×C₇₉	—	2	1	no	—
12	C₁₆×C₇₉	C₈	1	2	yes	complemented
13	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₇₉	SD₁₆	1	2	yes	—
15	C₈×C₇₉	—	2	1	no	—
16	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
17	C₈×C₇₉	M₁₆	1	1	yes	characteristic
18	C₇₉⋊C₈	—	8	2	no	—
19	C₂²×C₇₉	#106	1	1	yes	characteristic
20	C₄×C₇₉	—	2	2	no	—
21	C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₇₉	#108	1	1	yes	characteristic
23	C₂×C₇₉	#334	1	1	yes	characteristic
24	C₂×C₇₉	#365	1	2	yes	—
25	#1368	—	79	1	no	maximal, Sylow
26	C₇₉	#1368	1	1	yes	characteristic, complemented, Sylow
27	#346	D₇₉	1	1	yes	characteristic
28	#334	—	79	2	no	—
29	C₂×C₁₆	Dic₇₉	1	1	yes	characteristic
30	C₂×C₁₆	Dic₇₉	1	1	yes	characteristic
31	C₄⋊C₈	—	158	2	no	—
32	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
33	C₂×C₈	—	316	2	no	—
34	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
35	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
36	C₄²	D₃₁₆	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	C₇₉⋊C₈	1	2	yes	complemented
39	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
40	C₂×C₄	#11929613	1	2	yes	—
41	C₈	—	2	1	no	—
42	C₈	—	632	2	no	—
43	C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
44	C₈	#11929608	1	1	yes	characteristic
45	C₂²	#14579093	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
48	C₄	#14579097	1	1	yes	characteristic
49	C₂	#19098314	1	1	yes	characteristic
50	C₂	#19098386	1	2	yes	—

	subgroup	G/H
center	C₂²	#14579093
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#346×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#106
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#346	D₇₉
hypocenter	C₇₉	#1368
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₇₉	C₈	semidirect
26. C₇₉	#1368	semidirect
38. C₁₆	C₇₉⋊C₈	semidirect