Subgroups — #11716613

Order 800.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#1039	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#168	C₂	1	2	yes	maximal
3	C₂×C₄×C₅²	C₂²	1	1	yes	characteristic
4	C₂×#1039	C₄	1	1	yes	characteristic
5	C₂×#1039	C₄	1	1	yes	characteristic
6	C₅×#168	—	2	2	no	—
7	#3946	—	5	2	no	maximal
8	C₂²×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₄×C₅²	D₄	1	1	yes	characteristic
10	C₄×C₅²	Q₈	1	1	yes	characteristic
11	#1039	—	2	1	no	—
12	#1039	C₈	1	2	yes	complemented
13	C₂×C₅×C₈	—	5	2	no	—
14	C₄×Dic₅	—	5	2	no	—
15	C₄×Dic₅	—	10	2	no	—
16	C₂×#168	D₅	1	2	yes	—
17	C₂×C₅²	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₅²	C₂×C₈	1	1	yes	characteristic
19	C₂×C₅²	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₅	—	2	2	no	—
21	C₂×C₄×C₅	C₂×D₅	1	2	yes	—
22	C₂×Dic₅	—	5	2	no	—
23	C₂×Dic₅	—	5	2	no	—
24	C₂×Dic₅	—	10	2	no	—
25	C₂×Dic₅	—	10	2	no	—
26	C₅×C₈	—	10	2	no	—
27	#168	—	2	2	no	—
28	C₄⋊C₈	—	25	1	no	Sylow
29	C₅²	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₅	—	2	2	no	—
31	C₂²×C₅	C₄×D₅	1	2	yes	—
32	C₄×C₅	—	2	2	no	—
33	C₄×C₅	—	2	2	no	—
34	C₄×C₅	Dic₁₀	1	2	yes	—
35	C₄×C₅	C₂²⋊D₅	1	2	yes	—
36	Dic₅	—	5	4	no	—
37	Dic₅	—	10	4	no	—
38	Dic₅	—	10	4	no	—
39	Dic₅	—	10	2	no	—
40	C₂×C₈	—	5	2	no	—
41	C₄²	—	25	1	no	—
42	C₂×C₅	—	2	2	no	—
43	C₂×C₅	—	2	2	no	—
44	C₂×C₅	—	2	2	no	—
45	C₂×C₅	C₈×D₅	1	2	yes	—
46	C₂×C₅	#676	1	2	yes	—
47	C₂×C₅	#683	1	2	yes	—
48	C₂×C₄	—	25	1	no	—
49	C₂×C₄	—	25	1	no	—
50	C₂×C₄	D₅²	1	1	yes	characteristic
51	C₈	—	10	2	no	—
52	C₅	—	2	2	no	—
53	C₅	#3946	1	2	yes	complemented
54	C₂²	#6036	1	1	yes	characteristic
55	C₄	—	25	2	no	—
56	C₄	—	50	1	no	—
57	C₄	#6037	1	1	yes	characteristic
58	C₄	#6039	1	1	yes	characteristic
59	C₂	#87767	1	1	yes	characteristic
60	C₂	#87769	1	1	yes	characteristic
61	C₂	#87781	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₅²
commutator	C₂×C₅²	C₂×C₈
Fitting, cosocle	C₂×C₄×C₅²	C₂²
socle, prime radical	C₂²×C₅²	C₂×C₄
hypocenter	C₅²	C₄⋊C₈
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
12. #1039	C₈	semidirect
29. C₅²	C₄⋊C₈	semidirect
53. C₅	#3946	semidirect

Maximal subgroups

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

subgroup	index
C₄×#1039	2
C₂×C₅×#168	2
#3946	5