Subgroups — #34175938

Order 20224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761536	C₂	1	1	yes	maximal, characteristic
2	#23761468	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1368	C₂	1	1	yes	maximal, characteristic
4	#19098397	C₄	1	1	yes	characteristic
5	#19098397	C₄	1	1	yes	characteristic
6	#19098384	—	2	1	no	—
7	#346×C₇₉	C₂²	1	1	yes	characteristic
8	#334×C₇₉	—	2	1	no	—
9	#14579101	—	4	1	no	—
10	C₇₉⋊C₃₂	—	2	1	no	—
11	C₇₉⋊C₃₂	C₈	1	2	yes	complemented
12	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₇₉	Q₈	1	1	yes	characteristic
14	C₄⋊C₈×C₇₉	—	4	1	no	—
15	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
16	C₇₉⋊C₁₆	—	8	1	no	—
17	C₂×C₈×C₇₉	—	8	1	no	—
18	C₂×C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₇₉	SD₁₆	1	1	yes	characteristic
20	C₄²×C₇₉	SD₁₆	1	1	yes	characteristic
21	C₁₆×C₇₉	—	2	1	no	—
22	C₁₆×C₇₉	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₇₉	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₇₉	—	2	1	no	—
25	C₂×C₄×C₇₉	#106	1	1	yes	characteristic
26	C₈×C₇₉	—	2	1	no	—
27	C₈×C₇₉	—	16	1	no	—
28	C₈×C₇₉	C₄⋊C₈	1	1	yes	characteristic
29	C₈×C₇₉	#108	1	1	yes	characteristic
30	C₂²×C₇₉	#365	1	1	yes	characteristic
31	C₄×C₇₉	—	4	1	no	—
32	C₄×C₇₉	#334	1	1	yes	characteristic
33	C₄×C₇₉	#365	1	1	yes	characteristic
34	#7457	—	79	1	no	maximal, Sylow
35	C₂×C₇₉	—	2	1	no	—
36	C₂×C₇₉	#1368	1	1	yes	characteristic
37	#1398	—	79	1	no	—
38	#1369	—	79	1	no	—
39	#1368	D₇₉	1	1	yes	characteristic
40	C₇₉	#7457	1	1	yes	characteristic, complemented, Sylow
41	M₆₄	—	79	1	no	—
42	M₆₄	—	79	1	no	—
43	#364	—	158	1	no	—
44	#346	C₂×D₇₉	1	1	yes	characteristic
45	#334	—	2	1	no	—
46	M₃₂	—	316	1	no	—
47	C₂×C₁₆	Dic₁₅₈	1	1	yes	characteristic
48	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
49	C₄⋊C₈	—	4	1	no	—
50	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
51	C₃₂	—	79	2	no	—
52	C₃₂	—	158	1	no	—
53	C₂×C₈	—	8	1	no	—
54	C₂×C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
55	C₂×C₈	#11929611	1	1	yes	characteristic
56	C₄²	#11929612	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	632	1	no	—
59	C₁₆	C₈×D₇₉	1	1	yes	characteristic
60	C₁₆	#11929607	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#14579092	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	16	1	no	—
65	C₈	Dic₇₉⋊C₈	1	1	yes	characteristic
66	C₈	#14579096	1	1	yes	characteristic
67	C₂²	#19098385	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#19098313	1	1	yes	characteristic
70	C₄	#19098387	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#23761465	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23761465
commutator	C₁₆×C₇₉	C₂×C₈
Frattini	#346	C₂×D₇₉
Fitting	C₇₉×#1368	C₂
socle	C₂×C₇₉	#1368
prime radical	C₂²×C₇₉	#365
cosocle	#346×C₇₉	C₂²
hypercenter	#1368	D₇₉
hypocenter	C₇₉	#7457
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #1368

Complements

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

N	H ≅ G/N	type
11. C₇₉⋊C₃₂	C₈	semidirect
40. C₇₉	#7457	semidirect

Maximal subgroups

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

subgroup	index
#23761536	2
#23761468	2
C₇₉×#1368	2
#7457	79