Subgroups — C₄×C₅×C₃⋊D₃ #67176

Order 360.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₃	—	3	4	no	maximal
5	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
6	C₅×C₃⋊D₃	C₄	1	2	yes	direct product factor
7	C₄×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×D₃	—	3	4	no	—
9	C₃×C₄×C₅	D₃	1	4	yes	complemented
10	C₅×Dic₃	—	3	4	no	—
11	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₄×C₅	—	9	1	no	Hall
13	C₂×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
14	C₃²×C₄	C₂×C₅	1	1	yes	characteristic, complemented
15	C₃⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅	C₂×D₃	1	4	yes	—
17	C₅×D₃	—	3	8	no	—
18	C₄×D₃	—	3	4	no	—
19	C₂²×C₅	—	9	1	no	—
20	C₄×C₅	—	9	1	no	—
21	C₄×C₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor
22	C₂×C₃²	C₂²×C₅	1	1	yes	characteristic
23	C₃⋊D₃	C₄×C₅	1	2	yes	direct product factor
24	C₃×C₅	C₄×D₃	1	4	yes	complemented
25	C₂×D₃	—	3	4	no	—
26	C₃×C₄	C₅×D₃	1	4	yes	complemented
27	Dic₃	—	3	4	no	—
28	C₂×C₅	—	9	2	no	—
29	C₂×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic
30	C₃²	C₂×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄	—	9	1	no	Sylow
32	C₂×C₃	C₂×C₅×D₃	1	4	yes	—
33	D₃	—	3	8	no	—
34	C₅	C₄×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	9	1	no	—
36	C₄	—	9	1	no	—
37	C₄	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
38	C₃	C₄×C₅×D₃	1	4	yes	complemented
39	C₂	—	9	2	no	—
40	C₂	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₄×C₅
Frattini	C₂	C₂×C₅×C₃⋊D₃
Fitting	C₃²×C₄×C₅	C₂
socle	C₂×C₃²×C₅	C₂²
prime radical	C₂×C₅×C₃⋊D₃	C₂
cosocle	C₂×C₃²	C₂²×C₅
LCS	G ▷ C₃²
UCS	C₁ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×C₅	C₂	semidirect
3. C₅×C₃⋊Dic₃	C₂	semidirect
6. C₅×C₃⋊D₃	C₄	direct (N × H)
7. C₄×C₃⋊D₃	C₅	direct (N × H)
9. C₃×C₄×C₅	D₃	semidirect
11. C₃²×C₅	C₂×C₄	semidirect
14. C₃²×C₄	C₂×C₅	semidirect
15. C₃⋊Dic₃	C₂×C₅	semidirect
21. C₄×C₅	C₃⋊D₃	direct (N × H)
23. C₃⋊D₃	C₄×C₅	direct (N × H)
24. C₃×C₅	C₄×D₃	semidirect
26. C₃×C₄	C₅×D₃	semidirect
30. C₃²	C₂×C₄×C₅	semidirect
34. C₅	C₄×C₃⋊D₃	direct (N × H)
37. C₄	C₅×C₃⋊D₃	direct (N × H)
38. C₃	C₄×C₅×D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₃⋊D₃	2
C₃²×C₄×C₅	2
C₅×C₃⋊Dic₃	2
C₄×C₅×D₃	3
C₄×C₃⋊D₃	5

Subgroups — C4×C5×C3⋊D3 #67176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₃⋊D₃ #67176