Subgroups — #13104140

Order 1600.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716915	C₂	1	2	yes	maximal, complemented
2	#11716882	C₂	1	1	yes	maximal, characteristic, complemented
3	#11716792	C₂	1	4	yes	maximal, complemented
4	#87877	—	2	2	no	—
5	C₈×C₅⋊D₅	C₂²	1	1	yes	characteristic
6	C₅×D₄₀	—	2	2	no	—
7	#87770	C₂²	1	4	yes	complemented
8	#87765	C₂²	1	2	yes	complemented
9	C₂×D₅²	—	4	2	no	—
10	C₄×C₅⋊D₅	D₄	1	1	yes	characteristic
11	C₅×D₂₀	—	2	4	no	—
12	#6037	—	4	2	no	—
13	C₅²×C₈	D₄	1	1	yes	characteristic
14	#6029	C₂³	1	1	yes	characteristic
15	D₅×D₈	—	10	2	no	—
16	D₅⋊C₁₆	—	10	1	no	—
17	C₂×C₅⋊D₅	D₈	1	1	yes	characteristic
18	C₂×C₅×D₅	—	4	4	no	—
19	D₅²	—	8	4	no	—
20	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
21	#1039	D₈	1	1	yes	characteristic
22	D₄×D₅	—	10	4	no	—
23	C₅×D₈	—	10	2	no	—
24	#686	—	10	4	no	—
25	D₄₀	—	2	2	no	—
26	C₈×D₅	—	10	1	no	—
27	C₈×D₅	—	10	2	no	—
28	#674	—	10	2	no	—
29	C₂×D₁₆	—	25	1	no	maximal, Sylow
30	C₂×C₅²	C₂×D₈	1	1	yes	characteristic
31	C₅⋊D₅	D₁₆	1	2	yes	complemented
32	C₅×D₅	—	8	4	no	—
33	C₂²×D₅	—	20	4	no	—
34	C₅×D₄	—	10	4	no	—
35	C₂²⋊D₅	—	20	4	no	—
36	D₂₀	—	2	4	no	—
37	C₄×D₅	—	10	1	no	—
38	C₄×D₅	—	10	2	no	—
39	C₅×C₈	—	2	1	no	—
40	C₅×C₈	—	2	2	no	—
41	#168	—	10	1	no	—
42	#168	—	10	2	no	—
43	C₂×D₈	—	25	2	no	—
44	D₁₆	—	25	4	no	—
45	C₂×C₁₆	—	25	1	no	—
46	C₅²	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₅	—	20	4	no	—
48	C₂×D₅	—	4	4	no	—
49	C₂×D₅	—	10	1	no	—
50	C₂×D₅	—	10	2	no	—
51	C₂×D₅	—	40	8	no	—
52	C₄×C₅	—	2	1	no	—
53	C₄×C₅	—	2	2	no	—
54	Dic₅	—	10	1	no	—
55	Dic₅	—	10	2	no	—
56	C₂×D₄	—	50	2	no	—
57	D₈	—	10	2	no	—
58	D₈	—	25	4	no	—
59	C₂×C₈	—	25	1	no	—
60	C₁₆	—	25	2	no	—
61	C₂×C₅	—	2	2	no	—
62	C₂×C₅	—	2	1	no	—
63	C₂×C₅	—	40	4	no	—
64	D₅	—	8	4	no	—
65	D₅	—	10	2	no	—
66	D₅	—	10	4	no	—
67	C₂³	—	100	2	no	—
68	D₄	—	10	4	no	—
69	D₄	—	100	2	no	—
70	C₂×C₄	—	25	1	no	—
71	C₈	—	25	1	no	—
72	C₈	D₅²⋊C₂	1	1	yes	characteristic
73	C₅	—	2	2	no	—
74	C₅	—	2	1	no	—
75	C₂²	—	20	4	no	—
76	C₂²	—	25	1	no	—
77	C₂²	—	200	4	no	—
78	C₄	—	25	1	no	—
79	C₄	C₂×D₅²⋊C₂	1	1	yes	characteristic
80	C₂	—	25	2	no	—
81	C₂	—	40	4	no	—
82	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
hypercenter	C₈	D₅²⋊C₂
hypocenter	C₅²	C₂×D₁₆
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
1. #11716915	C₂	semidirect
2. #11716882	C₂	semidirect
3. #11716792	C₂	semidirect
7. #87770	C₂²	semidirect
8. #87765	C₂²	semidirect
31. C₅⋊D₅	D₁₆	semidirect
46. C₅²	C₂×D₁₆	semidirect

Maximal subgroups

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

subgroup	index
#11716915	2
#11716882	2
#11716792	2
C₂×D₁₆	25