Subgroups — #34175928

Order 20224.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765682	C₂	1	1	yes	maximal, characteristic
2	#23761476	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1422	C₂	1	1	yes	maximal, characteristic
4	#19098968	—	2	1	no	—
5	#19098391	—	2	1	no	—
6	#19098391	C₄	1	2	yes	—
7	#19098384	—	2	1	no	—
8	M₆₄×C₇₉	—	2	1	no	—
9	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
10	#14579161	—	4	1	no	—
11	#14579101	—	4	1	no	—
12	#14579095	—	2	2	no	—
13	#14579095	—	4	1	no	—
14	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
17	C₃₂×C₇₉	—	4	1	no	—
18	C₂×Dic₁₅₈	—	8	1	no	—
19	C₄⋊Dic₇₉	—	4	2	no	—
20	C₄⋊Dic₇₉	—	8	1	no	—
21	C₇₉⋊C₁₆	—	8	1	no	—
22	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
24	C₄²×C₇₉	SD₁₆	1	1	yes	characteristic
25	C₁₆×C₇₉	—	2	1	no	—
26	C₁₆×C₇₉	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₇₉	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₇₉	—	2	1	no	—
29	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
30	C₂×Dic₇₉	—	8	2	no	—
31	Dic₁₅₈	—	16	2	no	—
32	C₈×C₇₉	#101	1	1	yes	characteristic
33	C₈×C₇₉	#103	1	1	yes	characteristic
34	C₈×C₇₉	SD₃₂	1	1	yes	characteristic
35	C₈×C₇₉	Q₃₂	1	1	yes	characteristic
36	C₂²×C₇₉	#361	1	1	yes	characteristic
37	C₄×C₇₉	—	2	2	no	—
38	C₄×C₇₉	#332	1	1	yes	characteristic
39	C₄×C₇₉	#358	1	1	yes	characteristic
40	Dic₇₉	—	16	2	no	—
41	#7453	—	79	1	no	maximal, Sylow
42	C₂×C₇₉	—	2	1	no	—
43	C₂×C₇₉	#1365	1	1	yes	characteristic
44	#2254	—	79	1	no	—
45	#1422	D₇₉	1	1	yes	characteristic
46	#1373	—	79	1	no	—
47	C₇₉	#7453	1	1	yes	characteristic, complemented, Sylow
48	#500	—	158	1	no	—
49	M₆₄	—	2	1	no	—
50	#367	—	79	2	no	—
51	#367	—	158	1	no	—
52	#364	—	158	1	no	—
53	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic
54	C₄⋊Q₈	—	316	1	no	—
55	M₃₂	—	316	1	no	—
56	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
57	C₂×C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
58	#107	—	316	1	no	—
59	#107	—	158	2	no	—
60	C₄×C₈	D₃₁₆	1	1	yes	characteristic
61	C₃₂	—	4	1	no	—
62	C₂×Q₈	—	632	1	no	—
63	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
64	C₂×C₈	D₆₃₂	1	1	yes	characteristic
65	C₄⋊C₄	—	316	2	no	—
66	C₄⋊C₄	—	632	1	no	—
67	C₄²	#11929613	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	632	1	no	—
70	C₁₆	#11929612	1	1	yes	characteristic
71	C₁₆	#11929614	1	1	yes	characteristic
72	Q₈	—	1264	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	632	2	no	—
75	C₂×C₄	#14579083	1	1	yes	characteristic
76	C₈	#14579079	1	1	yes	characteristic
77	C₈	#14579084	1	1	yes	characteristic
78	C₈	#14579106	1	1	yes	characteristic
79	C₈	Dic₆₃₂	1	1	yes	characteristic
80	C₂²	#19098377	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	1264	2	no	—
83	C₄	#19098308	1	1	yes	characteristic
84	C₄	#19098368	1	1	yes	characteristic
85	C₂	—	2	1	no	—
86	C₂	#23761457	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23761457
commutator	C₂×C₁₆×C₇₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₇₉
Fitting	C₇₉×#1422	C₂
socle	C₂×C₇₉	#1365
prime radical	C₂²×C₇₉	#361
cosocle	C₄×C₁₆×C₇₉	C₂²
hypercenter	#1422	D₇₉
hypocenter	C₇₉	#7453
LCS	G ▷ C₂×C₁₆×C₇₉ ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
47. C₇₉	#7453	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23765682	2
#23761476	2
C₇₉×#1422	2
#7453	79