Subgroups — #13104143

Order 1600.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716920	C₂	1	2	yes	maximal
2	#11716882	C₂	1	1	yes	maximal, characteristic
3	#11716794	C₂	1	4	yes	maximal, complemented
4	#87872	—	2	2	no	—
5	C₈×C₅⋊D₅	C₂²	1	1	yes	characteristic
6	C₅×Dic₂₀	—	2	2	no	—
7	#87775	C₂²	1	4	yes	—
8	#87765	C₂²	1	2	yes	—
9	C₄×C₅⋊D₅	D₄	1	1	yes	characteristic
10	C₅×Dic₁₀	—	2	4	no	—
11	#6039	—	4	2	no	—
12	#6036	—	4	2	no	—
13	C₅²×C₈	D₄	1	1	yes	characteristic
14	#6029	C₂³	1	1	yes	characteristic
15	D₅×Q₁₆	—	10	2	no	—
16	D₅⋊C₁₆	—	10	1	no	—
17	C₂×C₅⋊D₅	D₈	1	1	yes	characteristic
18	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
19	#1039	D₈	1	1	yes	characteristic
20	C₅×Dic₅	—	4	4	no	—
21	Q₈×D₅	—	10	4	no	—
22	C₅×Q₁₆	—	10	2	no	—
23	#689	—	10	4	no	—
24	Dic₂₀	—	2	2	no	—
25	C₈×D₅	—	10	1	no	—
26	C₈×D₅	—	10	2	no	—
27	#674	—	10	2	no	—
28	C₂×Q₃₂	—	25	1	no	maximal, Sylow
29	C₂×C₅²	C₂×D₈	1	1	yes	characteristic
30	C₅⋊D₅	Q₃₂	1	2	yes	complemented
31	C₅×Q₈	—	10	4	no	—
32	C₄×D₅	—	10	1	no	—
33	C₄×D₅	—	10	2	no	—
34	C₄×D₅	—	20	4	no	—
35	Dic₁₀	—	2	4	no	—
36	Dic₁₀	—	20	4	no	—
37	C₅×C₈	—	2	1	no	—
38	C₅×C₈	—	2	2	no	—
39	#168	—	10	1	no	—
40	#168	—	10	2	no	—
41	C₂×Q₁₆	—	25	2	no	—
42	Q₃₂	—	25	4	no	—
43	C₂×C₁₆	—	25	1	no	—
44	C₅²	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₅	—	10	1	no	—
46	C₂×D₅	—	10	2	no	—
47	C₄×C₅	—	2	2	no	—
48	C₄×C₅	—	2	1	no	—
49	C₄×C₅	—	20	4	no	—
50	Dic₅	—	4	4	no	—
51	Dic₅	—	10	2	no	—
52	Dic₅	—	10	1	no	—
53	C₂×Q₈	—	50	2	no	—
54	Q₁₆	—	10	2	no	—
55	Q₁₆	—	25	4	no	—
56	C₂×C₈	—	25	1	no	—
57	C₁₆	—	25	2	no	—
58	C₂×C₅	—	2	2	no	—
59	C₂×C₅	—	2	1	no	—
60	D₅	—	10	2	no	—
61	D₅	—	10	4	no	—
62	Q₈	—	10	4	no	—
63	Q₈	—	100	2	no	—
64	C₂×C₄	—	25	1	no	—
65	C₂×C₄	—	100	2	no	—
66	C₈	—	25	1	no	—
67	C₈	D₅²⋊C₂	1	1	yes	characteristic
68	C₅	—	2	2	no	—
69	C₅	—	2	1	no	—
70	C₂²	—	25	1	no	—
71	C₄	—	20	4	no	—
72	C₄	—	25	1	no	—
73	C₄	C₂×D₅²⋊C₂	1	1	yes	characteristic
74	C₂	—	25	2	no	—
75	C₂	#11717383	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11717383
commutator, cosocle	#6029	C₂³
Frattini	C₄	C₂×D₅²⋊C₂
Fitting	C₅²×C₈	D₄
socle	C₂×C₅²	C₂×D₈
prime radical	C₂×C₅⋊D₅	D₈
hypercenter	C₈	D₅²⋊C₂
hypocenter	C₅²	C₂×Q₃₂
LCS	G ▷ #6029 ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
3. #11716794	C₂	semidirect
30. C₅⋊D₅	Q₃₂	semidirect
44. C₅²	C₂×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
#11716920	2
#11716882	2
#11716794	2
C₂×Q₃₂	25