Subgroups — #23761438

Order 10112.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098943	C₂	1	1	yes	maximal, characteristic
2	#19098384	C₂	1	1	yes	maximal, characteristic
3	#364×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₁₆	—	2	1	no	—
5	C₂×Dic₃₁₆	—	2	1	no	—
6	#14579161	C₄	1	2	yes	—
7	#14579101	—	2	1	no	—
8	M₃₂×C₇₉	—	2	1	no	—
9	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₅₈	—	2	2	no	—
11	Dic₃₁₆	—	4	1	no	—
12	Dic₃₁₆	—	4	1	no	—
13	Dic₃₁₆	—	4	1	no	—
14	Dic₃₁₆	—	4	1	no	—
15	C₄⋊Dic₇₉	—	4	2	no	—
16	C₇₉⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
19	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₇₉	—	4	1	no	—
21	C₂×C₄×C₇₉	—	2	1	no	—
22	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₇₉	—	4	2	no	—
24	Dic₁₅₈	—	4	2	no	—
25	Dic₁₅₈	—	4	2	no	—
26	C₈×C₇₉	D₈	1	1	yes	characteristic
27	C₈×C₇₉	D₈	1	1	yes	characteristic
28	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
29	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
30	C₂²×C₇₉	#100	1	1	yes	characteristic
31	C₄×C₇₉	—	2	2	no	—
32	C₄×C₇₉	#102	1	1	yes	characteristic
33	C₄×C₇₉	#102	1	1	yes	characteristic
34	Dic₇₉	—	8	2	no	—
35	C₂×C₇₉	—	2	1	no	—
36	C₂×C₇₉	#331	1	1	yes	characteristic
37	#1358	—	79	1	no	maximal, Sylow
38	C₇₉	#1358	1	1	yes	characteristic, complemented, Sylow
39	#494	—	79	1	no	—
40	#364	—	79	1	no	—
41	#364	D₇₉	1	1	yes	characteristic
42	C₂×Q₁₆	—	158	1	no	—
43	C₂×Q₁₆	—	158	1	no	—
44	C₄⋊Q₈	—	79	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	158	1	no	—
47	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
48	C₂×Q₈	—	158	2	no	—
49	Q₁₆	—	316	1	no	—
50	Q₁₆	—	316	1	no	—
51	Q₁₆	—	316	1	no	—
52	Q₁₆	—	316	1	no	—
53	C₂×C₈	D₃₁₆	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
55	C₄⋊C₄	—	316	2	no	—
56	C₄²	C₄×D₇₉	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	316	1	no	—
59	Q₈	—	316	2	no	—
60	Q₈	—	316	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	316	2	no	—
63	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
64	C₈	#11929609	1	1	yes	characteristic
65	C₈	D₆₃₂	1	1	yes	characteristic
66	C₈	#11929611	1	1	yes	characteristic
67	C₈	#11929613	1	1	yes	characteristic
68	C₂²	#14579077	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	632	2	no	—
71	C₄	#14579081	1	1	yes	characteristic
72	C₄	#14579083	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#19098306	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098306
commutator	C₄²×C₇₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#364×C₇₉	C₂
socle	C₂×C₇₉	#331
prime radical	C₂²×C₇₉	#100
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#364	D₇₉
hypocenter	C₇₉	#1358
LCS	G ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
38. C₇₉	#1358	semidirect