Subgroups — #13100136

Order 1600.

85 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716839	C₂	1	2	yes	maximal
2	C₅×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#87849	—	2	2	no	—
4	C₅×C₈×D₅	C₂²	1	1	yes	characteristic
5	C₅²×C₁₆	C₄	1	1	yes	characteristic
6	C₅×#672	C₄	1	1	yes	characteristic
7	#64851	—	5	1	no	maximal
8	#64726	—	5	1	no	maximal
9	C₄×C₅×D₅	D₄	1	1	yes	characteristic
10	#6032	—	4	2	no	—
11	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
12	C₅×#168	Q₈	1	1	yes	characteristic
13	#3996	—	5	2	no	—
14	C₂×C₅×C₁₆	—	5	1	no	—
15	#3951	—	5	2	no	—
16	D₅×C₁₆	D₅	1	1	yes	characteristic
17	C₂×C₅×D₅	Q₁₆	1	1	yes	characteristic
18	C₄×C₅²	C₄⋊C₄	1	1	yes	characteristic
19	C₅×Dic₅	D₈	1	1	yes	characteristic
20	#700	—	10	2	no	—
21	C₂×C₅×C₈	—	5	1	no	—
22	#681	—	10	2	no	—
23	C₈×D₅	C₂×D₅	1	1	yes	characteristic
24	C₅×C₁₆	—	4	1	no	—
25	C₅×C₁₆	—	5	1	no	—
26	C₅×C₁₆	Dic₅	1	1	yes	characteristic
27	C₅×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
28	#672	Dic₅	1	1	yes	characteristic
29	#368	—	25	1	no	Sylow
30	C₂×C₅²	#107	1	1	yes	characteristic
31	C₅×D₅	—	2	1	no	—
32	C₂×C₄×C₅	—	5	1	no	—
33	C₄×D₅	D₂₀	1	1	yes	characteristic
34	#170	—	20	2	no	—
35	C₅×C₈	—	4	1	no	—
36	C₅×C₈	—	5	1	no	—
37	C₅×C₈	C₂×Dic₅	1	1	yes	characteristic
38	C₅×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
39	#168	—	20	2	no	—
40	#168	Dic₁₀	1	1	yes	characteristic
41	C₂×C₁₆	—	5	1	no	—
42	#108	—	25	2	no	—
43	C₅²	#368	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₅	—	5	1	no	—
45	C₂×D₅	Dic₂₀	1	1	yes	characteristic
46	C₄×C₅	—	4	1	no	—
47	C₄×C₅	—	5	1	no	—
48	C₄×C₅	C₄⋊Dic₅	1	1	yes	characteristic
49	C₄×C₅	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
50	Dic₅	D₄₀	1	1	yes	characteristic
51	M₁₆	—	50	2	no	—
52	C₂×C₈	—	5	1	no	—
53	C₁₆	—	5	1	no	—
54	C₁₆	#1042	1	1	yes	characteristic
55	C₂×C₅	—	4	1	no	—
56	C₂×C₅	—	10	1	no	—
57	C₂×C₅	#3950	1	1	yes	characteristic
58	C₂×C₅	#3994	1	1	yes	characteristic
59	D₅	—	2	1	no	—
60	C₂×C₄	—	5	1	no	—
61	C₈	—	5	1	no	—
62	C₈	—	100	2	no	—
63	C₈	C₂×#1042	1	1	yes	characteristic
64	C₅	—	4	1	no	—
65	C₅	#64726	1	1	yes	characteristic, complemented
66	C₅	#64851	1	1	yes	characteristic, complemented
67	C₂²	—	5	1	no	—
68	C₄	—	5	1	no	—
69	C₄	C₄⋊#1042	1	1	yes	characteristic
70	C₂	—	10	1	no	—
71	C₂	#11716837	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716837
commutator	C₅²×C₈	C₂×C₄
Frattini	C₈	C₂×#1042
Fitting	C₅²×C₁₆	C₄
socle	C₂×C₅²	#107
prime radical	C₂×C₅×D₅	Q₁₆
cosocle	C₅×C₈×D₅	C₂²
hypercenter	C₁₆	#1042
hypocenter	C₅²	#368
LCS	G ▷ C₅²×C₈ ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
43. C₅²	#368	semidirect
65. C₅	#64726	semidirect
66. C₅	#64851	semidirect

Maximal subgroups

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

subgroup	index
#11716839	2
C₅×D₅×C₁₆	2
#64851	5
#64726	5