Subgroups — C₅×#3946 #11716640

Order 800.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅²	C₂²	1	1	yes	characteristic
5	C₂×C₅×Dic₅	C₄	1	1	yes	characteristic
6	C₂×C₅×Dic₅	C₄	1	1	yes	characteristic
7	C₅²×C₈	—	2	1	no	—
8	C₅×#168	—	2	1	no	—
9	C₅×C₄⋊C₈	—	5	1	no	maximal
10	#3946	C₅	1	1	yes	maximal, characteristic, direct product factor
11	C₂²×C₅²	C₂×C₄	1	1	yes	characteristic
12	C₄×C₅²	D₄	1	1	yes	characteristic
13	C₄×C₅²	Q₈	1	1	yes	characteristic
14	C₅×Dic₅	—	2	1	no	—
15	C₅×Dic₅	C₈	1	2	yes	complemented
16	C₂×C₅×C₈	—	2	2	no	—
17	C₂×C₅×C₈	—	5	1	no	—
18	C₂×C₅×C₈	D₅	1	1	yes	characteristic
19	C₂×C₅×C₈	C₂×C₅	1	1	yes	characteristic
20	C₄²×C₅	—	5	1	no	—
21	C₄×Dic₅	C₂×C₅	1	1	yes	characteristic
22	C₂×#168	C₂×C₅	1	1	yes	characteristic
23	C₂×C₅²	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₅²	C₂×C₈	1	1	yes	characteristic
25	C₂×C₅²	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₅	—	2	2	no	—
27	C₂×C₄×C₅	—	5	1	no	—
28	C₂×C₄×C₅	—	5	1	no	—
29	C₂×C₄×C₅	C₂×D₅	1	1	yes	characteristic
30	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
31	C₂×Dic₅	C₄×C₅	1	1	yes	characteristic
32	C₂×Dic₅	C₄×C₅	1	1	yes	characteristic
33	C₅×C₈	—	2	4	no	—
34	C₅×C₈	—	2	1	no	—
35	C₅×C₈	—	2	1	no	—
36	C₅×C₈	—	10	1	no	—
37	#168	—	2	1	no	—
38	C₄⋊C₈	—	5	1	no	Sylow
39	C₅²	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₅	—	2	2	no	—
41	C₂²×C₅	C₄×D₅	1	1	yes	characteristic
42	C₂²×C₅	C₂×C₄×C₅	1	1	yes	characteristic
43	C₄×C₅	—	2	2	no	—
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	—	5	2	no	—
46	C₄×C₅	—	10	1	no	—
47	C₄×C₅	Dic₁₀	1	1	yes	characteristic
48	C₄×C₅	C₂²⋊D₅	1	1	yes	characteristic
49	C₄×C₅	C₅×D₄	1	1	yes	characteristic
50	C₄×C₅	C₅×Q₈	1	1	yes	characteristic
51	Dic₅	—	2	1	no	—
52	Dic₅	C₅×C₈	1	2	yes	complemented
53	C₂×C₈	—	5	1	no	—
54	C₂×C₈	C₅×D₅	1	1	yes	characteristic
55	C₄²	—	5	1	no	—
56	C₂×C₅	—	2	2	no	—
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	2	2	no	—
59	C₂×C₅	C₈×D₅	1	1	yes	characteristic
60	C₂×C₅	#676	1	1	yes	characteristic
61	C₂×C₅	#683	1	1	yes	characteristic
62	C₂×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₅	C₂×C₅×C₈	1	1	yes	characteristic
64	C₂×C₅	C₅×M₁₆	1	1	yes	characteristic
65	C₂×C₄	—	5	1	no	—
66	C₂×C₄	—	5	1	no	—
67	C₂×C₄	C₂×C₅×D₅	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	—	10	1	no	—
70	C₅	—	2	2	no	—
71	C₅	#3946	1	1	yes	characteristic, direct product factor
72	C₅	C₅×C₄⋊C₈	1	1	yes	characteristic, complemented
73	C₂²	C₄×C₅×D₅	1	1	yes	characteristic
74	C₄	—	5	2	no	—
75	C₄	—	10	1	no	—
76	C₄	C₅×Dic₁₀	1	1	yes	characteristic
77	C₄	C₅×C₂²⋊D₅	1	1	yes	characteristic
78	C₂	C₅×C₈×D₅	1	1	yes	characteristic
79	C₂	C₅×#676	1	1	yes	characteristic
80	C₂	C₅×#683	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₅
commutator	C₂×C₅	C₂×C₅×C₈
Frattini	C₂×C₄	C₂×C₅×D₅
Fitting	C₂×C₅²×C₈	C₂
socle, prime radical	C₂²×C₅²	C₂×C₄
cosocle	C₂×C₄×C₅	C₂²×C₅
hypercenter	C₂×C₅×C₈	D₅
hypocenter	C₅	C₅×C₄⋊C₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈

Complements

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

N	H ≅ G/N	type
10. #3946	C₅	direct (N × H)
15. C₅×Dic₅	C₈	semidirect
39. C₅²	C₄⋊C₈	semidirect
52. Dic₅	C₅×C₈	semidirect
71. C₅	#3946	direct (N × H)
72. C₅	C₅×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₈	2
C₄×C₅×Dic₅	2
C₂×C₅×#168	2
C₅×C₄⋊C₈	5
#3946	5

Subgroups — C5×#3946 #11716640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3946 #11716640