Subgroups — #23765308

Order 10112.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₇₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	Dic₇₉⋊C₁₆	C₂	1	2	yes	maximal
4	#19098338	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₁₅₈	C₄	1	1	yes	characteristic
7	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
8	C₄⋊(C₇₉⋊C₈)	C₄	1	1	yes	characteristic
9	Dic₇₉⋊C₈	C₄	1	2	yes	—
10	C₈×Dic₇₉	C₂²	1	2	yes	—
11	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₅₈	C₈	1	1	yes	characteristic
15	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
16	C₄⋊Dic₇₉	C₈	1	1	yes	characteristic
17	Dic₇₉⋊C₄	C₈	1	2	yes	—
18	C₄×Dic₇₉	C₂×C₄	1	2	yes	—
19	C₇₉⋊C₁₆	—	2	2	no	—
20	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
22	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₇₉	—	2	1	no	—
24	C₁₆×C₇₉	Q₈	1	2	yes	complemented
25	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₇₉	C₂×C₈	1	2	yes	—
29	C₂×Dic₇₉	C₂×C₈	1	2	yes	—
30	Dic₁₅₈	—	2	2	no	—
31	C₈×C₇₉	—	2	1	no	—
32	C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
33	C₈×C₇₉	#41	1	1	yes	characteristic
34	C₇₉⋊C₈	—	2	2	no	—
35	C₂²×C₇₉	C₂²×C₈	1	1	yes	characteristic
36	C₄×C₇₉	—	2	1	no	—
37	C₄×C₇₉	M₃₂	1	2	yes	—
38	C₄×C₇₉	C₄×Q₈	1	1	yes	characteristic
39	C₄×C₇₉	#131	1	1	yes	characteristic
40	Dic₇₉	—	2	2	no	—
41	Dic₇₉	—	2	2	no	—
42	C₂×C₇₉	C₈×Q₈	1	1	yes	characteristic
43	C₂×C₇₉	C₂×M₃₂	1	1	yes	characteristic
44	C₂×C₇₉	#504	1	1	yes	characteristic
45	#2183	—	79	1	no	maximal, Sylow
46	C₇₉	#2183	1	1	yes	characteristic, complemented, Sylow
47	C₈×Q₈	—	79	1	no	—
48	C₄⋊C₁₆	—	79	2	no	—
49	C₄⋊C₁₆	—	79	1	no	—
50	#346	—	79	2	no	—
51	C₄×C₁₆	D₇₉	1	1	yes	characteristic
52	C₄×Q₈	—	79	1	no	—
53	C₂×C₁₆	—	79	2	no	—
54	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
55	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
56	C₄⋊C₈	—	79	2	no	—
57	C₄⋊C₈	—	79	1	no	—
58	C₄×C₈	—	79	2	no	—
59	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
60	C₂×Q₈	—	79	1	no	—
61	C₂×C₈	—	79	2	no	—
62	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
63	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
64	C₄⋊C₄	—	79	2	no	—
65	C₄⋊C₄	—	79	1	no	—
66	C₄²	—	79	2	no	—
67	C₄²	C₄×D₇₉	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	158	2	no	—
70	C₁₆	Dic₁₅₈	1	2	yes	complemented
71	Q₈	—	158	2	no	—
72	C₂×C₄	—	79	2	no	—
73	C₂×C₄	—	79	2	no	—
74	C₂×C₄	C₈×D₇₉	1	1	yes	characteristic
75	C₂×C₄	C₈×D₇₉	1	1	yes	characteristic
76	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	158	2	no	—
79	C₈	C₂×Dic₁₅₈	1	1	yes	characteristic
80	C₈	#11929624	1	1	yes	characteristic
81	C₂²	C₂×C₈×D₇₉	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	158	2	no	—
84	C₄	—	158	2	no	—
85	C₄	#14579100	1	2	yes	—
86	C₄	C₄×Dic₁₅₈	1	1	yes	characteristic
87	C₄	#14579167	1	1	yes	characteristic
88	C₂	C₈×Dic₁₅₈	1	1	yes	characteristic
89	C₂	C₂×#14579100	1	1	yes	characteristic
90	C₂	#19098979	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₉
commutator, socle, prime radical	C₂²×C₇₉	C₂²×C₈
Fitting	C₄×C₁₆×C₇₉	C₂
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#2183
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
24. C₁₆×C₇₉	Q₈	semidirect
46. C₇₉	#2183	semidirect
70. C₁₆	Dic₁₅₈	semidirect