Subgroups — #13099239

Order 1600.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#3926	C₂	1	2	yes	maximal, complemented
3	C₈×C₅⋊D₅	C₄	1	1	yes	characteristic
4	C₅²×C₁₆	C₂²	1	1	yes	characteristic
5	#87756	C₄	1	1	yes	characteristic
6	#64667	—	5	2	no	maximal
7	C₄×C₅⋊D₅	C₈	1	1	yes	characteristic
8	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
9	#6029	C₈	1	1	yes	characteristic
10	D₅×C₁₆	—	5	2	no	—
11	D₅×C₁₆	—	10	2	no	—
12	C₅×C₃₂	—	5	2	no	—
13	#3926	D₅	1	2	yes	complemented
14	C₂×C₅⋊D₅	C₁₆	1	1	yes	characteristic
15	C₄×C₅²	C₂×C₈	1	1	yes	characteristic
16	#1039	C₁₆	1	1	yes	characteristic
17	C₈×D₅	—	5	2	no	—
18	C₈×D₅	—	10	2	no	—
19	C₅×C₁₆	—	2	2	no	—
20	C₅×C₁₆	C₂×D₅	1	2	yes	—
21	#672	—	5	2	no	—
22	#672	—	10	2	no	—
23	M₆₄	—	25	1	no	Sylow
24	C₂×C₅²	C₂×C₁₆	1	1	yes	characteristic
25	C₅⋊D₅	—	2	1	no	—
26	C₄×D₅	—	5	2	no	—
27	C₄×D₅	—	10	2	no	—
28	C₅×C₈	—	2	2	no	—
29	C₅×C₈	C₄×D₅	1	2	yes	—
30	#168	—	5	2	no	—
31	#168	—	10	2	no	—
32	C₂×C₁₆	—	25	1	no	—
33	C₃₂	—	5	2	no	—
34	C₅²	M₆₄	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	5	2	no	—
36	C₂×D₅	—	10	2	no	—
37	C₄×C₅	—	2	2	no	—
38	C₄×C₅	C₈×D₅	1	2	yes	—
39	Dic₅	—	5	2	no	—
40	Dic₅	—	10	2	no	—
41	C₂×C₈	—	25	1	no	—
42	C₁₆	—	25	1	no	—
43	C₁₆	D₅²	1	1	yes	characteristic
44	C₂×C₅	—	2	2	no	—
45	C₂×C₅	D₅×C₁₆	1	2	yes	—
46	D₅	—	10	4	no	—
47	D₅	—	10	2	no	—
48	C₂×C₄	—	25	1	no	—
49	C₈	—	25	1	no	—
50	C₈	#6036	1	1	yes	characteristic
51	C₅	—	2	2	no	—
52	C₅	#64667	1	2	yes	complemented
53	C₂²	—	25	1	no	—
54	C₄	—	25	1	no	—
55	C₄	#87767	1	1	yes	characteristic
56	C₂	—	50	1	no	—
57	C₂	#11716583	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	D₅²
commutator, socle	C₂×C₅²	C₂×C₁₆
Fitting, cosocle	C₅²×C₁₆	C₂²
prime radical	C₂×C₅⋊D₅	C₁₆
hypocenter	C₅²	M₆₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×#3926	C₂	semidirect
13. #3926	D₅	semidirect
34. C₅²	M₆₄	semidirect
52. C₅	#64667	semidirect

Maximal subgroups

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

subgroup	index
C₁₆×C₅⋊D₅	2
C₅×#3926	2
#64667	5