Subgroups — C₂×C₅×D₃₀₅ #20259131

Order 6100.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃₀₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₃₀₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₅×D₆₁	—	5	1	no	maximal
6	C₂×C₅×C₆₁	—	2	2	no	—
7	C₂×C₅×C₆₁	D₅	1	1	yes	characteristic, complemented
8	C₂×C₅×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented
9	D₃₀₅	C₂×C₅	1	2	yes	direct product factor
10	C₅×D₆₁	—	5	2	no	—
11	C₅×C₆₁	—	2	2	no	—
12	C₅×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented
13	C₅×C₆₁	C₂²×C₅	1	1	yes	characteristic, complemented
14	C₂×D₆₁	—	5	1	no	Hall
15	C₂×C₆₁	C₅×D₅	1	1	yes	characteristic, complemented
16	D₆₁	—	5	2	no	—
17	C₂×C₅×D₅	—	61	1	no	maximal, Hall
18	C₆₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅²	D₆₁	1	1	yes	characteristic, complemented
20	C₅×D₅	—	61	2	no	—
21	C₅²	C₂×D₆₁	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₅	—	305	1	no	—
23	C₂×D₅	—	61	1	no	—
24	C₂×C₅	—	2	2	no	—
25	C₂×C₅	—	305	2	no	—
26	C₂×C₅	C₅×D₆₁	1	1	yes	characteristic, complemented
27	C₂×C₅	D₃₀₅	1	1	yes	characteristic, direct product factor
28	D₅	—	61	2	no	—
29	C₅	—	2	2	no	—
30	C₅	C₂×C₅×D₆₁	1	1	yes	characteristic, complemented
31	C₅	C₂×D₃₀₅	1	1	yes	characteristic, direct product factor
32	C₂²	—	305	1	no	Sylow
33	C₂	—	305	2	no	—
34	C₂	C₅×D₃₀₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₃₀₅
commutator, hypocenter	C₅×C₆₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₆₁	C₂
LCS	G ▷ C₅×C₆₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₃₀₅	C₂	direct (N × H)
2. C₂×C₅²×C₆₁	C₂	semidirect
3. C₅²×C₆₁	C₂²	semidirect
4. C₂×D₃₀₅	C₅	direct (N × H)
7. C₂×C₅×C₆₁	D₅	semidirect
8. C₂×C₅×C₆₁	C₂×C₅	semidirect
9. D₃₀₅	C₂×C₅	direct (N × H)
12. C₅×C₆₁	C₂×D₅	semidirect
13. C₅×C₆₁	C₂²×C₅	semidirect
15. C₂×C₆₁	C₅×D₅	semidirect
18. C₆₁	C₂×C₅×D₅	semidirect
19. C₂×C₅²	D₆₁	semidirect
21. C₅²	C₂×D₆₁	semidirect
26. C₂×C₅	C₅×D₆₁	semidirect
27. C₂×C₅	D₃₀₅	direct (N × H)
30. C₅	C₂×C₅×D₆₁	semidirect
31. C₅	C₂×D₃₀₅	direct (N × H)
34. C₂	C₅×D₃₀₅	direct (N × H)

Subgroups — C2×C5×D305 #20259131

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₃₀₅ #20259131