Subgroups — C₈×(C₅⋊D₅)⋊C₅ #14522162

Order 2000.

93 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×(C₅⋊D₅)⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₈×H(3,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	#6029⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₅⋊D₅)⋊C₅	C₄	1	1	yes	characteristic
5	C₄×H(3,𝔽₅)	C₂²	1	1	yes	characteristic
6	#1039⋊C₅	C₄	1	1	yes	characteristic
7	C₈×C₅⋊D₅	C₅	1	1	yes	maximal, characteristic, complemented
8	C₅×C₈×D₅	—	5	1	no	maximal
9	C₂×H(3,𝔽₅)	C₂×C₄	1	1	yes	characteristic
10	(C₅⋊D₅)⋊C₅	C₈	1	2	yes	direct product factor
11	C₄×C₅⋊D₅	C₂×C₅	1	1	yes	characteristic
12	C₄×C₅×D₅	—	5	1	no	—
13	C₅²×C₈	—	2	2	no	—
14	C₅²×C₈	D₅	1	1	yes	characteristic, complemented
15	C₅²×C₈	C₂×C₅	1	1	yes	characteristic, complemented
16	#6029	C₂×C₅	1	1	yes	characteristic, complemented
17	C₅×#168	—	5	1	no	—
18	H(3,𝔽₅)	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅⋊D₅	C₄×C₅	1	1	yes	characteristic
20	C₂×C₅×D₅	—	5	1	no	—
21	C₄×C₅²	—	2	2	no	—
22	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
23	C₄×C₅²	C₂²×C₅	1	1	yes	characteristic
24	#1039	C₄×C₅	1	1	yes	characteristic
25	C₅×Dic₅	—	5	1	no	—
26	C₂×C₅×C₈	—	25	1	no	—
27	C₈×D₅	—	5	1	no	—
28	C₈×D₅	—	25	1	no	—
29	C₂×C₅²	—	2	2	no	—
30	C₂×C₅²	C₄×D₅	1	1	yes	characteristic
31	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
32	C₅⋊D₅	C₅×C₈	1	2	yes	complemented
33	C₅×D₅	—	5	2	no	—
34	C₂×C₄×C₅	—	25	1	no	—
35	C₄×D₅	—	5	1	no	—
36	C₄×D₅	—	25	1	no	—
37	C₅×C₈	—	5	1	no	—
38	C₅×C₈	—	5	1	no	—
39	C₅×C₈	—	10	2	no	—
40	C₅×C₈	—	25	1	no	—
41	C₅×C₈	C₅×D₅	1	1	yes	characteristic
42	#168	—	5	1	no	—
43	#168	—	25	1	no	—
44	C₅²	—	2	2	no	—
45	C₅²	C₈×D₅	1	1	yes	characteristic, complemented
46	C₅²	C₂×C₅×C₈	1	1	yes	characteristic, complemented
47	C₂²×C₅	—	25	1	no	—
48	C₂×D₅	—	5	1	no	—
49	C₂×D₅	—	25	1	no	—
50	C₄×C₅	—	5	1	no	—
51	C₄×C₅	—	5	1	no	—
52	C₄×C₅	—	10	2	no	—
53	C₄×C₅	—	25	1	no	—
54	C₄×C₅	C₂×C₅×D₅	1	1	yes	characteristic
55	Dic₅	—	5	1	no	—
56	Dic₅	—	25	1	no	—
57	C₂×C₈	—	25	1	no	Sylow
58	C₂×C₅	—	5	1	no	—
59	C₂×C₅	—	5	1	no	—
60	C₂×C₅	—	10	2	no	—
61	C₂×C₅	—	25	2	no	—
62	C₂×C₅	C₄×C₅×D₅	1	1	yes	characteristic
63	D₅	—	5	2	no	—
64	D₅	—	25	2	no	—
65	C₂×C₄	—	25	1	no	—
66	C₈	—	25	1	no	—
67	C₈	(C₅⋊D₅)⋊C₅	1	1	yes	characteristic, direct product factor
68	C₅	—	5	1	no	—
69	C₅	—	5	1	no	—
70	C₅	—	10	2	no	—
71	C₅	C₅×C₈×D₅	1	1	yes	characteristic
72	C₂²	—	25	1	no	—
73	C₄	—	25	1	no	—
74	C₄	C₂×(C₅⋊D₅)⋊C₅	1	1	yes	characteristic
75	C₂	—	25	2	no	—
76	C₂	C₄×(C₅⋊D₅)⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	(C₅⋊D₅)⋊C₅
commutator, hypocenter	C₅²	C₂×C₅×C₈
Frattini	C₄×C₅	C₂×C₅×D₅
Fitting	C₈×H(3,𝔽₅)	C₂
socle	C₂×C₅	C₄×C₅×D₅
prime radical	C₂×(C₅⋊D₅)⋊C₅	C₄
cosocle	C₄×C₅²	C₂²×C₅
LCS	G ▷ C₅²
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₈×H(3,𝔽₅)	C₂	semidirect
3. #6029⋊C₅	C₂	semidirect
7. C₈×C₅⋊D₅	C₅	semidirect
10. (C₅⋊D₅)⋊C₅	C₈	direct (N × H)
14. C₅²×C₈	D₅	semidirect
15. C₅²×C₈	C₂×C₅	semidirect
16. #6029	C₂×C₅	semidirect
18. H(3,𝔽₅)	C₂×C₈	semidirect
32. C₅⋊D₅	C₅×C₈	semidirect
45. C₅²	C₈×D₅	semidirect
46. C₅²	C₂×C₅×C₈	semidirect
67. C₈	(C₅⋊D₅)⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×(C₅⋊D₅)⋊C₅	2
C₈×H(3,𝔽₅)	2
#6029⋊C₅	2
C₈×C₅⋊D₅	5
C₅×C₈×D₅	5

Subgroups — C8×(C5⋊D5)⋊C5 #14522162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×(C₅⋊D₅)⋊C₅ #14522162