Subgroups — #23761585

Order 10112.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098995	C₂	1	1	yes	maximal, characteristic
2	#19098393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579183	—	2	1	no	—
5	Dic₆₃₂	C₄	1	1	yes	characteristic
6	#14579106	—	2	1	no	—
7	D₁₂₆₄	C₄	1	1	yes	characteristic
8	#14579097	—	2	1	no	—
9	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
10	C₃₂×C₇₉	—	2	1	no	—
11	#11929624	—	4	1	no	—
12	Dic₃₁₆	—	2	1	no	—
13	#11929613	—	4	1	no	—
14	D₆₃₂	—	2	1	no	—
15	#11929608	—	4	1	no	—
16	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
17	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₇₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
20	C₂²⋊D₇₉	—	8	1	no	—
21	D₃₁₆	—	4	1	no	—
22	C₄×D₇₉	—	8	1	no	—
23	Dic₁₅₈	—	4	1	no	—
24	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
26	C₇₉⋊C₈	—	8	1	no	—
27	C₂²×C₇₉	SD₃₂	1	1	yes	characteristic
28	C₂×D₇₉	—	8	1	no	—
29	C₄×C₇₉	#102	1	1	yes	characteristic
30	C₄×C₇₉	D₁₆	1	1	yes	characteristic
31	Dic₇₉	—	8	1	no	—
32	C₂×C₇₉	—	2	1	no	—
33	C₂×C₇₉	#357	1	1	yes	characteristic
34	D₇₉	—	16	1	no	—
35	#1417	—	79	1	no	maximal, Sylow
36	C₇₉	#1417	1	1	yes	characteristic, complemented, Sylow
37	#508	—	79	1	no	—
38	C₂×C₃₂	D₇₉	1	1	yes	characteristic, complemented
39	#368	—	79	1	no	—
40	#135	—	158	1	no	—
41	Q₃₂	—	79	1	no	—
42	SD₃₂	—	158	1	no	—
43	D₁₆	—	79	1	no	—
44	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
45	#108	—	158	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	316	1	no	—
48	Q₁₆	—	158	1	no	—
49	SD₁₆	—	316	1	no	—
50	D₈	—	158	1	no	—
51	M₁₆	—	316	1	no	—
52	C₂×C₈	D₃₁₆	1	1	yes	characteristic
53	C₁₆	C₄×D₇₉	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
55	Q₈	—	316	1	no	—
56	D₄	—	316	1	no	—
57	D₄	—	632	1	no	—
58	C₂×C₄	—	632	1	no	—
59	C₂×C₄	D₆₃₂	1	1	yes	characteristic
60	C₈	—	632	1	no	—
61	C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
62	C₈	#11929613	1	1	yes	characteristic
63	C₂²	—	632	1	no	—
64	C₂²	#14579106	1	1	yes	characteristic
65	C₄	—	632	1	no	—
66	C₄	#14579083	1	1	yes	characteristic
67	C₄	D₁₂₆₄	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	1264	1	no	—
70	C₂	#19098365	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₂₆₄
commutator	C₁₆×C₇₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₉
Fitting	C₂×C₃₂×C₇₉	C₂
socle	C₂×C₇₉	#357
prime radical	#19098995	C₂
cosocle	C₂×C₁₆×C₇₉	C₂²
hypercenter	C₂×C₃₂	D₇₉
hypocenter	C₇₉	#1417
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #19098393	C₂	semidirect
3. C₂×C₃₂×C₇₉	C₂	semidirect
36. C₇₉	#1417	semidirect
38. C₂×C₃₂	D₇₉	semidirect