Subgroups — C₃²×C₅×D₄ #67186

Order 360.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₅	C₂	1	2	yes	maximal, complemented
2	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₄	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₅	—	2	2	no	—
5	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
6	C₃²×D₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅	C₂×C₃	1	8	yes	complemented
8	C₃×C₄×C₅	C₂×C₃	1	4	yes	complemented
9	C₃²×C₅	D₄	1	1	yes	characteristic, direct product factor, Hall
10	C₅×D₄	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₃²	C₂×C₅	1	2	yes	complemented
12	C₃²×C₄	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅	—	2	8	no	—
14	C₂×C₃×C₅	C₂²×C₃	1	4	yes	—
15	C₃×D₄	C₃×C₅	1	4	yes	direct product factor
16	C₂²×C₅	C₂×C₃²	1	2	yes	complemented
17	C₄×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₂×C₃²	—	2	2	no	—
19	C₂×C₃²	C₂²×C₅	1	1	yes	characteristic
20	C₃×C₅	C₃×D₄	1	4	yes	direct product factor
21	C₂²×C₃	C₂×C₃×C₅	1	8	yes	complemented
22	C₃×C₄	C₂×C₃×C₅	1	4	yes	complemented
23	C₂×C₅	—	2	2	no	—
24	C₂×C₅	C₂²×C₃²	1	1	yes	characteristic
25	C₃²	C₅×D₄	1	1	yes	characteristic, direct product factor, Sylow
26	D₄	C₃²×C₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	2	8	no	—
28	C₂×C₃	C₂²×C₃×C₅	1	4	yes	—
29	C₅	C₃²×D₄	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₂×C₃²×C₅	1	2	yes	complemented
31	C₄	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
32	C₃	C₃×C₅×D₄	1	4	yes	direct product factor
33	C₂	—	2	2	no	—
34	C₂	C₂²×C₃²×C₅	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²×C₅	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃²×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×C₅	C₂	semidirect
2. C₃²×C₄×C₅	C₂	semidirect
3. C₃×C₅×D₄	C₃	direct (N × H)
6. C₃²×D₄	C₅	direct (N × H)
7. C₂²×C₃×C₅	C₂×C₃	semidirect
8. C₃×C₄×C₅	C₂×C₃	semidirect
9. C₃²×C₅	D₄	direct (N × H)
10. C₅×D₄	C₃²	direct (N × H)
11. C₂²×C₃²	C₂×C₅	semidirect
12. C₃²×C₄	C₂×C₅	semidirect
15. C₃×D₄	C₃×C₅	direct (N × H)
16. C₂²×C₅	C₂×C₃²	semidirect
17. C₄×C₅	C₂×C₃²	semidirect
20. C₃×C₅	C₃×D₄	direct (N × H)
21. C₂²×C₃	C₂×C₃×C₅	semidirect
22. C₃×C₄	C₂×C₃×C₅	semidirect
25. C₃²	C₅×D₄	direct (N × H)
26. D₄	C₃²×C₅	direct (N × H)
29. C₅	C₃²×D₄	direct (N × H)
30. C₂²	C₂×C₃²×C₅	semidirect
31. C₄	C₂×C₃²×C₅	semidirect
32. C₃	C₃×C₅×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₅	2
C₃²×C₄×C₅	2
C₃×C₅×D₄	3
C₃²×D₄	5

Subgroups — C32×C5×D4 #67186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×D₄ #67186