Subgroups — #23765687

Order 10112.

120 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	#19098390	C₂	1	2	yes	maximal
3	#19098388	C₂	1	2	yes	maximal
4	#19098339	C₂	1	1	yes	maximal, characteristic
5	#499×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579161	—	2	1	no	—
7	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
8	#14579095	—	2	1	no	—
9	#14579095	C₂²	1	2	yes	—
10	#125×C₇₉	—	2	1	no	—
11	#107×C₇₉	C₂²	1	1	yes	characteristic
12	#107×C₇₉	C₂²	1	1	yes	characteristic
13	#106×C₇₉	—	2	1	no	—
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	4	1	no	—
16	C₄⋊Dic₇₉	—	2	2	no	—
17	C₄⋊Dic₇₉	—	4	1	no	—
18	C₇₉⋊C₁₆	Q₈	1	4	yes	complemented
19	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₇₉	—	2	1	no	—
22	C₄⋊C₄×C₇₉	—	2	1	no	—
23	C₄⋊C₄×C₇₉	—	4	1	no	—
24	C₄⋊C₄×C₇₉	—	4	1	no	—
25	C₄²×C₇₉	D₄	1	1	yes	characteristic
26	C₂×C₄×C₇₉	—	4	1	no	—
27	C₂×C₄×C₇₉	—	4	1	no	—
28	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₇₉	—	4	2	no	—
32	Dic₁₅₈	—	8	2	no	—
33	C₈×C₇₉	Q₁₆	1	2	yes	—
34	C₈×C₇₉	C₂×Q₈	1	2	yes	—
35	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₇₉	—	2	1	no	—
37	C₄×C₇₉	—	2	1	no	—
38	C₄×C₇₉	—	8	1	no	—
39	C₄×C₇₉	—	8	1	no	—
40	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
41	C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
42	Dic₇₉	—	8	2	no	—
43	C₂×C₇₉	#500	1	1	yes	characteristic
44	C₂×C₇₉	#509	1	1	yes	characteristic
45	C₂×C₇₉	#510	1	1	yes	characteristic
46	#2255	—	79	1	no	maximal, Sylow
47	C₇₉	#2255	1	1	yes	characteristic, complemented, Sylow
48	#500	—	79	1	no	—
49	#499	D₇₉	1	1	yes	characteristic
50	#367	—	79	2	no	—
51	#366	—	79	2	no	—
52	#346	—	79	1	no	—
53	C₄⋊Q₈	—	158	1	no	—
54	#125	—	2	1	no	—
55	C₂×C₁₆	—	79	2	no	—
56	#107	—	79	2	no	—
57	#107	—	158	1	no	—
58	#107	C₂×D₇₉	1	1	yes	characteristic
59	#107	C₂×D₇₉	1	1	yes	characteristic
60	#106	—	2	1	no	—
61	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
62	C₂×Q₈	—	316	1	no	—
63	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
65	C₄⋊C₄	—	2	1	no	—
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₄⋊C₄	—	316	1	no	—
70	C₄⋊C₄	—	158	2	no	—
71	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
72	C₁₆	—	79	4	no	—
73	Q₈	—	632	2	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	316	2	no	—
77	C₂×C₄	#11929609	1	1	yes	characteristic
78	C₂×C₄	#11929609	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
80	C₈	#11929614	1	2	yes	—
81	C₈	Q₈×D₇₉	1	2	yes	—
82	C₂²	C₂×#11929609	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	8	1	no	—
87	C₄	—	632	2	no	—
88	C₄	#14579159	1	1	yes	characteristic
89	C₄	C₂×#11929614	1	1	yes	characteristic
90	C₂	#19098966	1	1	yes	characteristic
91	C₂	#19098998	1	1	yes	characteristic
92	C₂	#19099003	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#499×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	#499	D₇₉
hypocenter	C₇₉	#2255
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
18. C₇₉⋊C₁₆	Q₈	semidirect
47. C₇₉	#2255	semidirect