Subgroups — #23761571

Order 10112.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098356	C₂	1	2	yes	maximal
2	#490×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#14579076	—	2	2	no	—
4	#127×C₇₉	C₂²	1	1	yes	characteristic
5	#125×C₇₉	C₄	1	1	yes	characteristic, complemented
6	#102×C₇₉	—	2	2	no	—
7	#97×C₇₉	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊Dic₇₉	—	4	2	no	—
9	C₂×D₄×C₇₉	—	4	1	no	—
10	C₂×D₄×C₇₉	D₄	1	2	yes	—
11	C₂×C₈×C₇₉	—	2	1	no	—
12	C₄⋊C₄×C₇₉	—	2	1	no	—
13	C₄⋊C₄×C₇₉	—	4	1	no	—
14	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₇₉	—	2	2	no	—
16	D₄×C₇₉	—	4	2	no	—
17	D₄×C₇₉	—	8	2	no	—
18	C₂×C₄×C₇₉	—	2	1	no	—
19	C₂×C₄×C₇₉	—	4	1	no	—
20	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₇₉	—	8	2	no	—
22	C₈×C₇₉	—	4	1	no	—
23	C₂²×C₇₉	—	4	2	no	—
24	C₂²×C₇₉	—	8	2	no	—
25	C₂²×C₇₉	#99	1	1	yes	characteristic
26	C₄×C₇₉	—	2	1	no	—
27	C₄×C₇₉	—	4	1	no	—
28	C₄×C₇₉	—	8	1	no	—
29	Dic₇₉	—	16	2	no	—
30	C₂×C₇₉	—	2	1	no	—
31	C₂×C₇₉	—	8	2	no	—
32	C₂×C₇₉	#354	1	1	yes	characteristic
33	#1412	—	79	1	no	maximal, Sylow
34	C₇₉	#1412	1	1	yes	characteristic, complemented, Sylow
35	#490	D₇₉	1	1	yes	characteristic
36	#353	—	79	2	no	—
37	#127	C₂×D₇₉	1	1	yes	characteristic
38	#125	Dic₇₉	1	1	yes	characteristic, complemented
39	#102	—	2	2	no	—
40	#99	—	158	2	no	—
41	#97	Dic₇₉	1	1	yes	characteristic, complemented
42	C₂×D₄	—	4	1	no	—
43	C₂×D₄	C₂²⋊D₇₉	1	2	yes	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	316	2	no	—
48	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
49	C₂³	—	2	2	no	—
50	D₄	—	4	2	no	—
51	D₄	—	8	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	632	2	no	—
55	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
56	C₈	—	4	1	no	—
57	C₂²	—	4	2	no	—
58	C₂²	—	8	2	no	—
59	C₂²	#14579076	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	1264	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	8	2	no	—
66	C₂	#19098358	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098358
commutator	C₄²×C₇₉	C₂×C₄
Frattini	#127	C₂×D₇₉
Fitting	#490×C₇₉	C₂
socle	C₂×C₇₉	#354
prime radical, cosocle	#127×C₇₉	C₂²
hypercenter	#490	D₇₉
hypocenter	C₇₉	#1412
LCS	G ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #490

Complements

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

N	H ≅ G/N	type
5. #125×C₇₉	C₄	semidirect
7. #97×C₇₉	C₄	semidirect
34. C₇₉	#1412	semidirect
38. #125	Dic₇₉	semidirect
41. #97	Dic₇₉	semidirect