Subgroups — #23761502

Order 10112.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098601	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#14579120	—	2	2	no	—
4	#14579095	—	2	2	no	—
5	#14579093	C₄	1	4	yes	complemented
6	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
7	M₃₂×C₇₉	—	2	2	no	—
8	C₂×C₁₆×C₇₉	C₄	1	2	yes	complemented
9	C₄⋊Dic₇₉	—	2	4	no	—
10	C₂²⋊Dic₇₉	—	4	2	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	C₈×C₇₉	C₄²	1	1	yes	characteristic
25	C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₇₉	C₄⋊C₄	1	2	yes	—
27	C₂²×C₇₉	—	4	1	no	—
28	C₂²×C₇₉	#102	1	2	yes	—
29	C₂²×C₇₉	#107	1	1	yes	characteristic
30	C₄×C₇₉	#95	1	1	yes	characteristic
31	C₄×C₇₉	#103	1	2	yes	—
32	C₄×C₇₉	#106	1	1	yes	characteristic
33	Dic₇₉	—	8	4	no	—
34	C₂×C₇₉	—	2	2	no	—
35	C₂×C₇₉	—	2	1	no	—
36	C₂×C₇₉	#340	1	1	yes	characteristic
37	#1384	—	79	1	no	maximal, Sylow
38	C₇₉	#1384	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₃₂	D₇₉	1	1	yes	characteristic
40	#427	—	79	2	no	—
41	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
42	#117	—	158	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₇₉	1	2	yes	complemented
45	#107	—	158	2	no	—
46	#106	—	79	4	no	—
47	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
48	C₂×C₈	Dic₁₅₈	1	1	yes	characteristic
49	C₂×C₈	C₄×D₇₉	1	2	yes	—
50	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
52	C₄⋊C₄	—	158	4	no	—
53	C₂²⋊C₄	—	316	2	no	—
54	C₄²	—	316	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₆₃₂	1	1	yes	characteristic
57	C₂×C₄	—	316	4	no	—
58	C₂×C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
59	C₂×C₄	C₄⋊Dic₇₉	1	1	yes	characteristic
60	C₂×C₄	#11929613	1	2	yes	—
61	C₂×C₄	Dic₃₁₆	1	1	yes	characteristic
62	C₈	C₄×Dic₇₉	1	1	yes	characteristic
63	C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
64	C₈	Dic₇₉⋊C₄	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	#14579083	1	2	yes	—
67	C₂²	#14579095	1	1	yes	characteristic
68	C₄	—	632	4	no	—
69	C₄	C₇₉⋊#95	1	1	yes	characteristic
70	C₄	#14579086	1	2	yes	—
71	C₄	#14579093	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#19098326	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14579093
commutator	C₈×C₇₉	C₄²
Frattini	C₂²×C₈	C₂×D₇₉
Fitting	C₂×M₃₂×C₇₉	C₂
socle	C₂×C₇₉	#340
prime radical	C₂³×C₇₉	D₈
cosocle	C₂²×C₈×C₇₉	C₂²
hypercenter	C₂×M₃₂	D₇₉
hypocenter	C₇₉	#1384
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #14579093	C₄	semidirect
8. C₂×C₁₆×C₇₉	C₄	semidirect
38. C₇₉	#1384	semidirect
44. C₂×C₁₆	Dic₇₉	semidirect