Subgroups — #34175933

Order 20224.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765679	C₂	1	1	yes	maximal, characteristic
2	#23761598	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1373	C₂	1	1	yes	maximal, characteristic
4	#19098965	—	2	1	no	—
5	#19098397	—	2	1	no	—
6	#19098391	C₄	1	2	yes	—
7	#19098389	—	2	1	no	—
8	#364×C₇₉	—	2	1	no	—
9	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
10	#14579153	—	4	1	no	—
11	#14579095	—	2	2	no	—
12	#14579093	—	4	1	no	—
13	C₇₉⋊C₃₂	—	4	1	no	—
14	M₃₂×C₇₉	—	4	1	no	—
15	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
17	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
18	C₄⋊Dic₇₉	—	4	2	no	—
19	Dic₇₉⋊C₄	—	8	2	no	—
20	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
22	C₄²×C₇₉	SD₁₆	1	1	yes	characteristic
23	C₁₆×C₇₉	—	2	1	no	—
24	C₁₆×C₇₉	—	8	1	no	—
25	C₁₆×C₇₉	SD₁₆	1	1	yes	characteristic
26	C₁₆×C₇₉	Q₁₆	1	1	yes	characteristic
27	C₂×C₄×C₇₉	—	2	1	no	—
28	C₂×C₄×C₇₉	#102	1	1	yes	characteristic
29	C₂×Dic₇₉	—	8	2	no	—
30	C₈×C₇₉	#101	1	1	yes	characteristic
31	C₈×C₇₉	#103	1	1	yes	characteristic
32	C₈×C₇₉	SD₃₂	1	1	yes	characteristic
33	C₈×C₇₉	Q₃₂	1	1	yes	characteristic
34	C₂²×C₇₉	#361	1	1	yes	characteristic
35	C₄×C₇₉	—	4	1	no	—
36	C₄×C₇₉	#332	1	1	yes	characteristic
37	C₄×C₇₉	#358	1	1	yes	characteristic
38	Dic₇₉	—	16	2	no	—
39	#7454	—	79	1	no	maximal, Sylow
40	C₂×C₇₉	—	2	1	no	—
41	C₂×C₇₉	#1365	1	1	yes	characteristic
42	#2253	—	79	1	no	—
43	#1422	—	79	1	no	—
44	#1373	D₇₉	1	1	yes	characteristic
45	C₇₉	#7454	1	1	yes	characteristic, complemented, Sylow
46	#499	—	158	1	no	—
47	M₆₄	—	158	1	no	—
48	#367	—	79	2	no	—
49	#366	—	158	1	no	—
50	#364	—	2	1	no	—
51	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic
52	#125	—	316	1	no	—
53	M₃₂	—	4	1	no	—
54	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
55	C₂×C₁₆	D₃₁₆	1	1	yes	characteristic
56	#107	—	158	2	no	—
57	#106	—	316	1	no	—
58	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
59	C₃₂	—	316	1	no	—
60	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
61	C₂×C₈	#11929609	1	1	yes	characteristic
62	C₄⋊C₄	—	316	2	no	—
63	C₄⋊C₄	—	632	2	no	—
64	C₄²	#11929611	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	8	1	no	—
67	C₁₆	#11929613	1	1	yes	characteristic
68	C₁₆	Dic₃₁₆	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	632	2	no	—
71	C₂×C₄	#14579081	1	1	yes	characteristic
72	C₈	#14579079	1	1	yes	characteristic
73	C₈	#14579086	1	1	yes	characteristic
74	C₈	#14579105	1	1	yes	characteristic
75	C₈	#14579107	1	1	yes	characteristic
76	C₂²	#19098375	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	1264	2	no	—
79	C₄	#19098310	1	1	yes	characteristic
80	C₄	#19098366	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#23761459	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23761459
commutator	C₂×C₁₆×C₇₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₇₉
Fitting	C₇₉×#1373	C₂
socle	C₂×C₇₉	#1365
prime radical	C₂²×C₇₉	#361
cosocle	C₄×C₁₆×C₇₉	C₂²
hypercenter	#1373	D₇₉
hypocenter	C₇₉	#7454
LCS	G ▷ C₂×C₁₆×C₇₉ ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
45. C₇₉	#7454	semidirect

Maximal subgroups

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

subgroup	index
#23765679	2
#23761598	2
C₇₉×#1373	2
#7454	79