Subgroups — #23761492

Order 10112.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14579095	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₇₉	—	2	2	no	—
4	#14579095	—	2	2	no	—
5	#14579095	C₄	1	4	yes	complemented
6	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₇₉	—	2	2	no	—
8	C₂×C₁₆×C₇₉	C₄	1	2	yes	complemented
9	C₂²×Dic₇₉	—	4	2	no	—
10	C₄⋊Dic₇₉	—	2	4	no	—
11	C₄⋊Dic₇₉	—	4	2	no	—
12	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₇₉	D₄	1	2	yes	—
16	C₂×C₈×C₇₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₇₉	—	2	2	no	—
18	C₂³×C₇₉	D₈	1	1	yes	characteristic
19	C₂×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₇₉	SD₁₆	1	2	yes	—
22	C₂×C₄×C₇₉	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₇₉	—	4	4	no	—
24	C₂×Dic₇₉	—	8	2	no	—
25	C₂×Dic₇₉	—	8	2	no	—
26	C₈×C₇₉	C₄²	1	1	yes	characteristic
27	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₇₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₇₉	#102	1	2	yes	—
30	C₂²×C₇₉	#107	1	1	yes	characteristic
31	C₂²×C₇₉	D₁₆	1	1	yes	characteristic
32	C₂²×C₇₉	SD₃₂	1	2	yes	—
33	C₂²×C₇₉	Q₃₂	1	1	yes	characteristic
34	C₄×C₇₉	#95	1	1	yes	characteristic
35	C₄×C₇₉	#103	1	2	yes	—
36	C₄×C₇₉	#106	1	1	yes	characteristic
37	Dic₇₉	—	8	4	no	—
38	C₂×C₇₉	#340	1	1	yes	characteristic
39	C₂×C₇₉	#357	1	2	yes	—
40	C₂×C₇₉	#358	1	2	yes	—
41	C₂×C₇₉	#366	1	1	yes	characteristic
42	C₂×C₇₉	#367	1	1	yes	characteristic
43	#1380	—	79	1	no	maximal, Sylow
44	C₇₉	#1380	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₁₆	D₇₉	1	1	yes	characteristic
46	C₂×#107	—	79	2	no	—
47	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	158	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₇₉	1	2	yes	complemented
51	#107	—	79	4	no	—
52	#107	—	158	2	no	—
53	C₂²×C₄	—	316	2	no	—
54	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
55	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
56	C₂×C₈	C₄×D₇₉	1	2	yes	—
57	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
59	C₄⋊C₄	—	316	2	no	—
60	C₄⋊C₄	—	158	4	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₆₃₂	1	1	yes	characteristic
63	C₂×C₄	—	316	4	no	—
64	C₂×C₄	—	632	2	no	—
65	C₂×C₄	—	632	2	no	—
66	C₂×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
68	C₂×C₄	#11929613	1	2	yes	—
69	C₂×C₄	Dic₃₁₆	1	1	yes	characteristic
70	C₈	C₄×Dic₇₉	1	1	yes	characteristic
71	C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
72	C₈	Dic₇₉⋊C₄	1	2	yes	—
73	C₂²	#14579083	1	2	yes	—
74	C₂²	#14579095	1	1	yes	characteristic
75	C₂²	D₁₂₆₄	1	1	yes	characteristic
76	C₂²	#14579106	1	2	yes	—
77	C₂²	Dic₆₃₂	1	1	yes	characteristic
78	C₄	—	632	4	no	—
79	C₄	C₇₉⋊#95	1	1	yes	characteristic
80	C₄	#14579086	1	2	yes	—
81	C₄	#14579093	1	1	yes	characteristic
82	C₂	#19098326	1	1	yes	characteristic
83	C₂	#19098365	1	2	yes	—
84	C₂	#19098368	1	2	yes	—
85	C₂	#19098389	1	1	yes	characteristic
86	C₂	#19098391	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₆₃₂
commutator	C₈×C₇₉	C₄²
Frattini	C₂²×C₈	C₂×D₇₉
Fitting	C₂²×C₁₆×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	D₈
cosocle	C₂²×C₈×C₇₉	C₂²
hypercenter	C₂²×C₁₆	D₇₉
hypocenter	C₇₉	#1380
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #14579095	C₄	semidirect
8. C₂×C₁₆×C₇₉	C₄	semidirect
44. C₇₉	#1380	semidirect
50. C₂×C₁₆	Dic₇₉	semidirect