Subgroups — #34176172

Order 20224.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#23761604	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1425	C₂	1	1	yes	maximal, characteristic
4	#19098393	—	2	1	no	—
5	C₇₉⋊C₆₄	C₄	1	2	yes	—
6	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
7	#368×C₇₉	—	2	1	no	—
8	#14579097	—	4	1	no	—
9	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
10	#108×C₇₉	—	4	1	no	—
11	C₃₂×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₇₉	Q₈	1	1	yes	characteristic
13	#11929608	—	8	1	no	—
14	M₁₆×C₇₉	—	8	1	no	—
15	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
16	C₁₆×C₇₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₇₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
19	C₈×C₇₉	—	16	1	no	—
20	C₈×C₇₉	#107	1	1	yes	characteristic
21	C₈×C₇₉	Q₃₂	1	1	yes	characteristic
22	C₇₉⋊C₈	—	16	1	no	—
23	C₂²×C₇₉	Q₆₄	1	1	yes	characteristic
24	C₄×C₇₉	#366	1	1	yes	characteristic
25	C₄×C₇₉	D₃₂	1	1	yes	characteristic
26	#7547	—	79	1	no	maximal, Sylow
27	C₂×C₇₉	—	2	1	no	—
28	C₂×C₇₉	#1423	1	1	yes	characteristic
29	C₂×C₆₄	—	79	1	no	—
30	#1425	—	79	1	no	—
31	#1425	D₇₉	1	1	yes	characteristic
32	C₇₉	#7547	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
34	#368	—	2	1	no	—
35	#368	—	158	1	no	—
36	C₆₄	—	79	2	no	—
37	C₂×C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#108	—	316	1	no	—
40	C₃₂	Dic₁₅₈	1	1	yes	characteristic
41	C₃₂	C₄×D₇₉	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	M₁₆	—	632	1	no	—
44	C₂×C₈	#11929609	1	1	yes	characteristic
45	C₁₆	Dic₇₉⋊C₄	1	1	yes	characteristic
46	C₁₆	#11929614	1	1	yes	characteristic
47	C₂×C₄	#14579102	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	1264	1	no	—
50	C₈	#14579094	1	1	yes	characteristic
51	C₈	#14579107	1	1	yes	characteristic
52	C₂²	#19098403	1	1	yes	characteristic
53	C₄	#19098388	1	1	yes	characteristic
54	C₄	#19098398	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#23761599	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19098398
commutator	C₃₂×C₇₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₉
Fitting	C₇₉×#1425	C₂
socle	C₂×C₇₉	#1423
prime radical	C₂²×C₇₉	Q₆₄
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	#1425	D₇₉
hypocenter	C₇₉	#7547
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
32. C₇₉	#7547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇₉⋊C₆₄	2
#23761604	2
C₇₉×#1425	2
#7547	79