Subgroups — #23763034

Order 10112.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098959	C₂	1	2	yes	maximal
2	#19098943	C₂	1	1	yes	maximal, characteristic
3	#19098913	C₂	1	2	yes	maximal
4	#19098284	C₂	1	1	yes	maximal, characteristic
5	#498×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₁₆	—	2	2	no	—
7	#14579161	C₂²	1	1	yes	characteristic
8	#14579161	C₂²	1	1	yes	characteristic
9	#14579092	—	2	4	no	—
10	#14579085	—	2	4	no	—
11	C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
13	#106×C₇₉	—	2	2	no	—
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	2	1	no	—
16	C₂×Dic₁₅₈	—	2	1	no	—
17	Dic₃₁₆	—	4	4	no	—
18	C₂×C₇₉⋊C₈	D₄	1	4	yes	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₂×Q₈×C₇₉	—	2	2	no	—
22	C₂×C₈×C₇₉	D₄	1	2	yes	—
23	C₄⋊C₄×C₇₉	—	2	2	no	—
24	C₄⋊C₄×C₇₉	—	2	2	no	—
25	C₄²×C₇₉	C₂³	1	1	yes	characteristic
26	Q₈×C₇₉	—	4	4	no	—
27	C₂×C₄×C₇₉	—	4	2	no	—
28	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₇₉	—	4	1	no	—
31	C₂×Dic₇₉	—	4	1	no	—
32	Dic₁₅₈	—	4	2	no	—
33	Dic₁₅₈	—	4	2	no	—
34	C₈×C₇₉	SD₁₆	1	4	yes	—
35	C₇₉⋊C₈	—	2	4	no	—
36	C₂²×C₇₉	#127	1	1	yes	characteristic
37	C₄×C₇₉	—	8	2	no	—
38	C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
39	C₄×C₇₉	#137	1	4	yes	—
40	Dic₇₉	—	8	1	no	—
41	Dic₇₉	—	8	1	no	—
42	C₂×C₇₉	#492	1	1	yes	characteristic
43	C₂×C₇₉	#497	1	2	yes	—
44	#1716	—	79	1	no	maximal, Sylow
45	C₇₉	#1716	1	1	yes	characteristic, complemented, Sylow
46	#498	—	79	2	no	—
47	#498	D₇₉	1	1	yes	characteristic
48	#494	—	79	1	no	—
49	#487	—	79	2	no	—
50	#322	—	79	1	no	—
51	C₂×Q₁₆	—	158	2	no	—
52	C₄⋊Q₈	—	79	1	no	—
53	C₄⋊Q₈	—	79	1	no	—
54	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
55	#106	—	2	2	no	—
56	#106	—	158	4	no	—
57	#103	—	158	4	no	—
58	C₄×C₈	—	79	2	no	—
59	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
60	C₂×Q₈	—	2	2	no	—
61	C₂×Q₈	—	158	1	no	—
62	C₂×Q₈	—	158	1	no	—
63	Q₁₆	—	316	4	no	—
64	C₂×C₈	—	79	4	no	—
65	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	158	2	no	—
69	C₄⋊C₄	—	158	2	no	—
70	C₄²	C₂²×D₇₉	1	1	yes	characteristic
71	Q₈	—	4	4	no	—
72	Q₈	—	316	2	no	—
73	Q₈	—	316	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	316	1	no	—
76	C₂×C₄	—	316	1	no	—
77	C₂×C₄	D₄×D₇₉	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
79	C₈	—	158	4	no	—
80	C₈	#11929611	1	4	yes	—
81	C₂²	#14579157	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	632	1	no	—
84	C₄	—	632	1	no	—
85	C₄	C₂×#11929611	1	2	yes	—
86	C₄	#14579190	1	4	yes	—
87	C₂	#19098937	1	1	yes	characteristic
88	C₂	#19098954	1	2	yes	—

	subgroup	G/H
center	C₂²	#14579157
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#498×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#127
hypercenter	#498	D₇₉
hypocenter	C₇₉	#1716
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
45. C₇₉	#1716	semidirect