Subgroups — C₂×C₅×D₁₅₆₅ #44531049

Order 31300.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₃₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×D₃₁₃	—	5	1	no	maximal
5	C₂×D₁₅₆₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×C₃₁₃	—	2	2	no	—
7	C₂×C₅×C₃₁₃	D₅	1	1	yes	characteristic, complemented
8	C₂×C₅×C₃₁₃	C₂×C₅	1	1	yes	characteristic, complemented
9	D₁₅₆₅	C₂×C₅	1	2	yes	direct product factor
10	C₅×D₃₁₃	—	5	2	no	—
11	C₅×C₃₁₃	—	2	2	no	—
12	C₅×C₃₁₃	C₂×D₅	1	1	yes	characteristic, complemented
13	C₅×C₃₁₃	C₂²×C₅	1	1	yes	characteristic, complemented
14	C₂×D₃₁₃	—	5	1	no	Hall
15	C₂×C₃₁₃	C₅×D₅	1	1	yes	characteristic, complemented
16	D₃₁₃	—	5	2	no	—
17	C₃₁₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×D₅	—	313	1	no	maximal, Hall
19	C₂×C₅²	D₃₁₃	1	1	yes	characteristic, complemented
20	C₅×D₅	—	313	2	no	—
21	C₅²	C₂×D₃₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₅	—	1565	1	no	—
23	C₂×D₅	—	313	1	no	—
24	C₂×C₅	—	2	2	no	—
25	C₂×C₅	—	1565	2	no	—
26	C₂×C₅	C₅×D₃₁₃	1	1	yes	characteristic, complemented
27	C₂×C₅	D₁₅₆₅	1	1	yes	characteristic, direct product factor
28	D₅	—	313	2	no	—
29	C₅	—	2	2	no	—
30	C₅	C₂×D₁₅₆₅	1	1	yes	characteristic, direct product factor
31	C₅	C₂×C₅×D₃₁₃	1	1	yes	characteristic, complemented
32	C₂²	—	1565	1	no	Sylow
33	C₂	—	1565	2	no	—
34	C₂	C₅×D₁₅₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₅₆₅
commutator, cosocle, hypocenter	C₅×C₃₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₁₃	C₂
LCS	G ▷ C₅×C₃₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅₆₅	C₂	direct (N × H)
2. C₂×C₅²×C₃₁₃	C₂	semidirect
3. C₅²×C₃₁₃	C₂²	semidirect
5. C₂×D₁₅₆₅	C₅	direct (N × H)
7. C₂×C₅×C₃₁₃	D₅	semidirect
8. C₂×C₅×C₃₁₃	C₂×C₅	semidirect
9. D₁₅₆₅	C₂×C₅	direct (N × H)
12. C₅×C₃₁₃	C₂×D₅	semidirect
13. C₅×C₃₁₃	C₂²×C₅	semidirect
15. C₂×C₃₁₃	C₅×D₅	semidirect
17. C₃₁₃	C₂×C₅×D₅	semidirect
19. C₂×C₅²	D₃₁₃	semidirect
21. C₅²	C₂×D₃₁₃	semidirect
26. C₂×C₅	C₅×D₃₁₃	semidirect
27. C₂×C₅	D₁₅₆₅	direct (N × H)
30. C₅	C₂×D₁₅₆₅	direct (N × H)
31. C₅	C₂×C₅×D₃₁₃	semidirect
34. C₂	C₅×D₁₅₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₁₅₆₅	2
C₂×C₅²×C₃₁₃	2
C₂×C₅×D₃₁₃	5
C₂×D₁₅₆₅	5
C₂×C₅×D₅	313

Subgroups — C2×C5×D1565 #44531049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₅₆₅ #44531049