Subgroups — #34176167

Order 20224.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761611	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉⋊C₆₄	—	2	2	no	—
4	C₂×C₃₂×C₇₉	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₇₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₇₉	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₇₉	C₈	1	1	yes	characteristic
10	C₃₂×C₇₉	—	2	1	no	—
11	C₃₂×C₇₉	D₄	1	1	yes	characteristic
12	C₃₂×C₇₉	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₇₉	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₇₉	C₁₆	1	1	yes	characteristic
16	C₁₆×C₇₉	—	2	1	no	—
17	C₁₆×C₇₉	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆×C₇₉	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₇₉	—	2	1	no	—
20	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
21	C₈×C₇₉	C₃₂	1	2	yes	—
22	C₈×C₇₉	C₄⋊C₈	1	1	yes	characteristic
23	C₈×C₇₉	M₃₂	1	1	yes	characteristic
24	C₂²×C₇₉	M₆₄	1	1	yes	characteristic
25	C₄×C₇₉	—	2	2	no	—
26	C₄×C₇₉	C₄⋊C₁₆	1	1	yes	characteristic
27	C₄×C₇₉	C₂×C₃₂	1	1	yes	characteristic
28	#7544	—	79	1	no	maximal, Sylow
29	C₂×C₇₉	—	2	1	no	—
30	C₂×C₇₉	C₄⋊C₃₂	1	1	yes	characteristic
31	M₁₂₈	—	79	2	no	—
32	C₄×C₃₂	D₇₉	1	1	yes	characteristic
33	C₇₉	#7544	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃₂	Dic₇₉	1	1	yes	characteristic
35	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
36	C₄×C₁₆	Dic₇₉	1	1	yes	characteristic
37	C₆₄	—	158	2	no	—
38	C₂×C₁₆	C₇₉⋊C₈	1	1	yes	characteristic
39	C₂×C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
40	C₄×C₈	C₇₉⋊C₈	1	1	yes	characteristic
41	C₃₂	—	2	1	no	—
42	C₃₂	Dic₁₅₈	1	1	yes	characteristic
43	C₃₂	D₃₁₆	1	1	yes	characteristic
44	C₂×C₈	C₇₉⋊C₁₆	1	1	yes	characteristic
45	C₂×C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
46	C₄²	C₇₉⋊C₁₆	1	1	yes	characteristic
47	C₁₆	—	2	1	no	—
48	C₁₆	C₄⋊Dic₇₉	1	1	yes	characteristic
49	C₁₆	#11929608	1	1	yes	characteristic
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₂×C₇₉⋊C₁₆	1	1	yes	characteristic
52	C₈	C₇₉⋊C₃₂	1	2	yes	—
53	C₈	C₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
54	C₈	#14579101	1	1	yes	characteristic
55	C₂²	#19098397	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	C₄⋊(C₇₉⋊C₁₆)	1	1	yes	characteristic
58	C₄	C₂×C₇₉⋊C₃₂	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	C₄⋊(C₇₉⋊C₃₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	D₃₁₆
commutator	C₄×C₇₉	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₇₉
Fitting	C₄×C₃₂×C₇₉	C₂
socle	C₂×C₇₉	C₄⋊C₃₂
prime radical	C₂²×C₇₉	M₆₄
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	C₄×C₃₂	D₇₉
hypocenter	C₇₉	#7544
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
33. C₇₉	#7544	semidirect

Maximal subgroups

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

subgroup	index
#23761611	2
C₄×C₃₂×C₇₉	2
#7544	79