Subgroups — D₅×D₁₅₁⋊C₅ #28419087

Order 15100.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(D₁₅₁⋊C₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₅₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₅₁⋊C₅	—	5	1	no	maximal
7	D₇₅₅	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅×D₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented
9	D₅×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂×C₁₅₁⋊C₅	—	5	1	no	—
11	D₁₅₁⋊C₅	—	2	2	no	—
12	D₁₅₁⋊C₅	—	5	1	no	—
13	D₁₅₁⋊C₅	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₁₅₁	C₂²×C₅	1	1	yes	characteristic, complemented
15	C₁₅₁⋊C₅	—	2	2	no	—
16	C₁₅₁⋊C₅	C₂×D₅	1	1	yes	characteristic, complemented
17	C₂×D₁₅₁	—	5	1	no	Hall
18	C₂×C₁₅₁	—	5	1	no	—
19	D₁₅₁	—	5	1	no	—
20	D₁₅₁	C₅×D₅	1	1	yes	characteristic, complemented
21	C₁₅₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₅×D₅	—	151	1	no	maximal, Hall
23	C₂×C₅²	—	151	1	no	—
24	C₅×D₅	—	302	1	no	—
25	C₅×D₅	—	151	1	no	—
26	C₅²	—	302	1	no	Sylow
27	C₂²×C₅	—	755	1	no	—
28	C₂×D₅	—	151	1	no	—
29	C₂×C₅	—	302	2	no	—
30	C₂×C₅	—	151	1	no	—
31	C₂×C₅	—	151	1	no	—
32	C₂×C₅	—	1510	1	no	—
33	C₂×C₅	—	755	1	no	—
34	D₅	—	151	1	no	—
35	D₅	D₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor
36	C₅	—	302	1	no	—
37	C₅	—	604	2	no	—
38	C₅	C₂×D₁₅₁⋊C₅	1	1	yes	characteristic, complemented
39	C₂²	—	755	1	no	Sylow
40	C₂	—	5	1	no	—
41	C₂	—	151	1	no	—
42	C₂	—	755	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₅₁	C₂²×C₅
LCS	G ▷ C₅×C₁₅₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅×C₁₅₁⋊C₅	C₂	semidirect
2. C₅⋊(D₁₅₁⋊C₅)	C₂	semidirect
3. C₅×D₁₅₁⋊C₅	C₂	semidirect
4. C₅×C₁₅₁⋊C₅	C₂²	semidirect
5. D₅×D₁₅₁	C₅	semidirect
7. D₇₅₅	C₂×C₅	semidirect
8. C₅×D₁₅₁	C₂×C₅	semidirect
9. D₅×C₁₅₁	C₂×C₅	semidirect
13. D₁₅₁⋊C₅	D₅	direct (N × H)
14. C₅×C₁₅₁	C₂²×C₅	semidirect
16. C₁₅₁⋊C₅	C₂×D₅	semidirect
20. D₁₅₁	C₅×D₅	semidirect
21. C₁₅₁	C₂×C₅×D₅	semidirect
35. D₅	D₁₅₁⋊C₅	direct (N × H)
38. C₅	C₂×D₁₅₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₁₅₁⋊C₅	2
C₅⋊(D₁₅₁⋊C₅)	2
C₅×D₁₅₁⋊C₅	2
D₅×D₁₅₁	5
C₂×D₁₅₁⋊C₅	5
C₂×C₅×D₅	151

Subgroups — D5×D151⋊C5 #28419087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₅₁⋊C₅ #28419087