Subgroups — #23765643

Order 10112.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098940	C₂	1	1	yes	maximal, characteristic
2	#19098363	C₂	1	4	yes	maximal, complemented
3	#19098339	C₂	1	1	yes	maximal, characteristic, complemented
4	#499×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₆₃₂	—	2	1	no	—
6	C₂×D₆₃₂	C₂²	1	2	yes	—
7	#14579158	—	2	1	no	—
8	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
9	#125×C₇₉	—	2	1	no	—
10	#107×C₇₉	C₂²	1	2	yes	—
11	#106×C₇₉	—	2	1	no	—
12	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×D₃₁₆	—	2	2	no	—
14	C₂×D₃₁₆	—	4	2	no	—
15	D₆₃₂	—	2	4	no	—
16	D₆₃₂	—	4	2	no	—
17	C₇₉⋊C₁₆	—	2	2	no	—
18	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₇₉	—	2	2	no	—
21	C₄⋊C₄×C₇₉	—	4	2	no	—
22	C₄²×C₇₉	D₄	1	1	yes	characteristic
23	C₂²×D₇₉	—	4	2	no	—
24	C₂×C₄×C₇₉	—	4	2	no	—
25	C₂×C₄×C₇₉	D₈	1	2	yes	—
26	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
27	D₃₁₆	—	4	2	no	—
28	D₃₁₆	—	4	2	no	—
29	D₃₁₆	—	8	4	no	—
30	C₈×C₇₉	SD₁₆	1	2	yes	—
31	C₈×C₇₉	#41	1	2	yes	—
32	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
33	C₂×D₇₉	—	8	2	no	—
34	C₂×D₇₉	—	8	4	no	—
35	C₄×C₇₉	—	2	2	no	—
36	C₄×C₇₉	—	8	2	no	—
37	C₄×C₇₉	#124	1	1	yes	characteristic
38	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
39	C₂×C₇₉	#486	1	1	yes	characteristic
40	C₂×C₇₉	#509	1	2	yes	—
41	D₇₉	—	16	2	no	—
42	#2244	—	79	1	no	maximal, Sylow
43	C₇₉	#2244	1	1	yes	characteristic, complemented, Sylow
44	#499	D₇₉	1	1	yes	characteristic, complemented
45	#493	—	79	1	no	—
46	#357	—	79	4	no	—
47	#346	—	79	1	no	—
48	C₂×D₈	—	79	2	no	—
49	C₂×D₈	—	158	1	no	—
50	#127	—	158	1	no	—
51	#125	—	2	1	no	—
52	C₂×C₁₆	—	79	2	no	—
53	#107	C₂×D₇₉	1	2	yes	—
54	#106	—	2	1	no	—
55	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
56	C₂×D₄	—	316	2	no	—
57	C₂×D₄	—	158	2	no	—
58	D₈	—	316	2	no	—
59	D₈	—	158	4	no	—
60	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	4	2	no	—
64	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
65	C₁₆	—	158	2	no	—
66	C₂³	—	316	2	no	—
67	D₄	—	316	2	no	—
68	D₄	—	316	2	no	—
69	D₄	—	632	4	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	#11929609	1	2	yes	—
72	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
73	C₈	#11929611	1	2	yes	—
74	C₈	#11929625	1	2	yes	—
75	C₂²	—	632	2	no	—
76	C₂²	—	632	4	no	—
77	C₂²	C₂×#11929609	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	8	2	no	—
80	C₄	#14579150	1	1	yes	characteristic
81	C₄	C₂×#11929611	1	1	yes	characteristic
82	C₂	—	1264	2	no	—
83	C₂	#19098911	1	1	yes	characteristic
84	C₂	#19098998	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#499×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	#19098940	C₂
hypercenter	#499	D₇₉
hypocenter	C₇₉	#2244
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
2. #19098363	C₂	semidirect
3. #19098339	C₂	semidirect
4. #499×C₇₉	C₂	semidirect
43. C₇₉	#2244	semidirect
44. #499	D₇₉	semidirect