Subgroups — #13100126

Order 1600.

69 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#11716579	C₂	1	2	yes	maximal, complemented
3	C₅×C₈×D₅	C₄	1	1	yes	characteristic
4	C₅²×C₁₆	C₄	1	1	yes	characteristic
5	C₅×#672	C₂²	1	1	yes	characteristic
6	#64842	—	5	1	no	maximal
7	#64719	—	5	1	no	maximal
8	C₄×C₅×D₅	C₈	1	1	yes	characteristic
9	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
10	C₅×#168	C₈	1	1	yes	characteristic
11	C₂×C₅×C₁₆	—	5	1	no	—
12	D₅×C₁₆	D₅	1	1	yes	characteristic
13	#3928	—	5	2	no	—
14	#3926	—	5	2	no	—
15	C₂×C₅×D₅	C₁₆	1	1	yes	characteristic
16	C₄×C₅²	C₂×C₈	1	1	yes	characteristic
17	C₅×Dic₅	C₁₆	1	1	yes	characteristic
18	C₂×C₅×C₈	—	5	1	no	—
19	C₈×D₅	Dic₅	1	1	yes	characteristic
20	C₅×C₁₆	—	4	1	no	—
21	C₅×C₁₆	—	5	1	no	—
22	C₅×C₁₆	Dic₅	1	1	yes	characteristic
23	C₅×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
24	#672	C₂×D₅	1	1	yes	characteristic
25	M₆₄	—	25	1	no	Sylow
26	C₂×C₅²	C₂×C₁₆	1	1	yes	characteristic
27	C₅×D₅	—	2	1	no	—
28	C₂×C₄×C₅	—	5	1	no	—
29	C₄×D₅	#168	1	1	yes	characteristic
30	C₅×C₈	—	4	1	no	—
31	C₅×C₈	—	5	1	no	—
32	C₅×C₈	C₂×Dic₅	1	1	yes	characteristic
33	C₅×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
34	#168	#168	1	1	yes	characteristic
35	C₂×C₁₆	—	5	1	no	—
36	C₃₂	—	25	2	no	—
37	C₅²	M₆₄	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₅	—	5	1	no	—
39	C₂×D₅	#672	1	1	yes	characteristic
40	C₄×C₅	—	4	1	no	—
41	C₄×C₅	—	5	1	no	—
42	C₄×C₅	C₂×#168	1	1	yes	characteristic
43	C₄×C₅	D₅⋊C₈	1	1	yes	characteristic
44	Dic₅	#672	1	1	yes	characteristic
45	C₂×C₈	—	5	1	no	—
46	C₁₆	—	5	1	no	—
47	C₁₆	#1042	1	1	yes	characteristic
48	C₂×C₅	—	4	1	no	—
49	C₂×C₅	—	10	1	no	—
50	C₂×C₅	C₂×#672	1	1	yes	characteristic
51	C₂×C₅	D₅⋊C₁₆	1	1	yes	characteristic
52	D₅	—	2	1	no	—
53	C₂×C₄	—	5	1	no	—
54	C₈	—	5	1	no	—
55	C₈	C₂×#1042	1	1	yes	characteristic
56	C₅	—	4	1	no	—
57	C₅	#64719	1	1	yes	characteristic, complemented
58	C₅	#64842	1	1	yes	characteristic, complemented
59	C₂²	—	5	1	no	—
60	C₄	—	5	1	no	—
61	C₄	D₅⋊#168	1	1	yes	characteristic
62	C₂	—	10	1	no	—
63	C₂	D₅⋊#672	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×#1042
commutator, socle	C₂×C₅²	C₂×C₁₆
Fitting	C₅²×C₁₆	C₄
prime radical	C₂×C₅×D₅	C₁₆
cosocle	C₅×#672	C₂²
hypercenter	C₁₆	#1042
hypocenter	C₅²	M₆₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
2. #11716579	C₂	semidirect
37. C₅²	M₆₄	semidirect
57. C₅	#64719	semidirect
58. C₅	#64842	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×C₁₆	2
#11716579	2
#64842	5
#64719	5