Subgroups — C₂×C₃×D₁₃₁₅ #30628880

Order 15780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₂₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₂₆₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₂₆₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₂₆₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₃₁₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₂₆₃	D₅	1	1	yes	characteristic, complemented
9	C₃×D₂₆₃	—	5	2	no	—
10	C₅×C₂₆₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₂₆₃	—	5	1	no	Hall
12	C₃×C₂₆₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₆₃	C₃×D₅	1	1	yes	characteristic, complemented
14	D₂₆₃	—	5	2	no	—
15	C₂₆₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₅	—	263	1	no	maximal, Hall
17	C₂×C₃×C₅	D₂₆₃	1	1	yes	characteristic, complemented
18	C₃×D₅	—	263	2	no	—
19	C₂×D₅	—	263	1	no	Hall
20	C₃×C₅	C₂×D₂₆₃	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃	—	1315	1	no	Hall
22	C₂×C₅	C₃×D₂₆₃	1	1	yes	characteristic, complemented
23	D₅	—	263	2	no	—
24	C₂×C₃	—	1315	2	no	—
25	C₂×C₃	D₁₃₁₅	1	1	yes	characteristic, direct product factor
26	C₅	C₂×C₃×D₂₆₃	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	1315	1	no	Sylow
28	C₃	C₂×D₁₃₁₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	1315	2	no	—
30	C₂	C₃×D₁₃₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₃₁₅
commutator, cosocle, hypocenter	C₅×C₂₆₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₂₆₃	C₂
LCS	G ▷ C₅×C₂₆₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃₁₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₂₆₃	C₂	semidirect
3. C₂×D₁₃₁₅	C₃	direct (N × H)
4. C₃×C₅×C₂₆₃	C₂²	semidirect
6. C₂×C₅×C₂₆₃	C₂×C₃	semidirect
7. D₁₃₁₅	C₂×C₃	direct (N × H)
8. C₂×C₃×C₂₆₃	D₅	semidirect
10. C₅×C₂₆₃	C₂²×C₃	semidirect
12. C₃×C₂₆₃	C₂×D₅	semidirect
13. C₂×C₂₆₃	C₃×D₅	semidirect
15. C₂₆₃	C₂×C₃×D₅	semidirect
17. C₂×C₃×C₅	D₂₆₃	semidirect
20. C₃×C₅	C₂×D₂₆₃	semidirect
22. C₂×C₅	C₃×D₂₆₃	semidirect
25. C₂×C₃	D₁₃₁₅	direct (N × H)
26. C₅	C₂×C₃×D₂₆₃	semidirect
28. C₃	C₂×D₁₃₁₅	direct (N × H)
30. C₂	C₃×D₁₃₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₁₃₁₅	2
C₂×C₃×C₅×C₂₆₃	2
C₂×D₁₃₁₅	3
C₂×C₃×D₂₆₃	5
C₂×C₃×D₅	263

Subgroups — C2×C3×D1315 #30628880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₃₁₅ #30628880