Subgroups — #23761459

Order 10112.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098968	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#335×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#14579161	—	2	1	no	—
5	C₂×C₇₉⋊C₁₆	—	2	1	no	—
6	#14579095	—	2	1	no	—
7	#14579095	C₄	1	2	yes	—
8	C₄⋊C₈×C₇₉	—	2	1	no	—
9	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₅₈	—	4	1	no	—
11	C₄⋊Dic₇₉	—	2	2	no	—
12	C₄⋊Dic₇₉	—	4	1	no	—
13	C₇₉⋊C₁₆	—	4	1	no	—
14	C₂×C₈×C₇₉	—	4	1	no	—
15	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
17	C₄²×C₇₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₇₉	—	4	2	no	—
22	Dic₁₅₈	—	8	2	no	—
23	C₈×C₇₉	—	2	1	no	—
24	C₈×C₇₉	—	8	1	no	—
25	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
26	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
27	C₂²×C₇₉	#102	1	1	yes	characteristic
28	C₄×C₇₉	—	2	1	no	—
29	C₄×C₇₉	#101	1	1	yes	characteristic
30	C₄×C₇₉	#103	1	1	yes	characteristic
31	C₄×C₇₉	SD₃₂	1	1	yes	characteristic
32	C₄×C₇₉	Q₃₂	1	1	yes	characteristic
33	Dic₇₉	—	8	2	no	—
34	C₂×C₇₉	#332	1	1	yes	characteristic
35	C₂×C₇₉	#358	1	1	yes	characteristic
36	C₂×C₇₉	#361	1	1	yes	characteristic
37	#1365	—	79	1	no	maximal, Sylow
38	C₇₉	#1365	1	1	yes	characteristic, complemented, Sylow
39	#500	—	79	1	no	—
40	C₄⋊C₁₆	—	79	1	no	—
41	#335	D₇₉	1	1	yes	characteristic
42	C₄⋊Q₈	—	158	1	no	—
43	C₂×C₁₆	—	158	1	no	—
44	#107	—	79	2	no	—
45	#107	—	158	1	no	—
46	C₄⋊C₈	—	2	1	no	—
47	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
48	C₂×Q₈	—	316	1	no	—
49	C₂×C₈	—	4	1	no	—
50	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
51	C₂×C₈	D₃₁₆	1	1	yes	characteristic
52	C₄⋊C₄	—	316	1	no	—
53	C₄⋊C₄	—	158	2	no	—
54	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
55	C₁₆	—	316	1	no	—
56	Q₈	—	632	2	no	—
57	C₂×C₄	—	316	2	no	—
58	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
59	C₂×C₄	#11929609	1	1	yes	characteristic
60	C₂×C₄	#11929611	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	8	1	no	—
63	C₈	#11929613	1	1	yes	characteristic
64	C₈	Dic₃₁₆	1	1	yes	characteristic
65	C₂²	#14579081	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	632	2	no	—
68	C₄	#14579079	1	1	yes	characteristic
69	C₄	#14579086	1	1	yes	characteristic
70	C₄	#14579105	1	1	yes	characteristic
71	C₄	#14579107	1	1	yes	characteristic
72	C₂	#19098310	1	1	yes	characteristic
73	C₂	#19098366	1	1	yes	characteristic
74	C₂	#19098375	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14579081
commutator	C₂×C₈×C₇₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#335×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#102
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#335	D₇₉
hypocenter	C₇₉	#1365
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
38. C₇₉	#1365	semidirect