Subgroups — C₃×C₅×C₃⋊C₈ #67104

Order 360.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₈	—	3	1	no	maximal
3	C₅×C₃⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃²×C₅	C₄	1	1	yes	characteristic
5	C₃×C₃⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₄×C₅	—	2	1	no	—
7	C₃×C₄×C₅	D₃	1	1	yes	characteristic
8	C₃×C₄×C₅	C₂×C₃	1	1	yes	characteristic
9	C₃²×C₅	C₈	1	1	yes	characteristic, complemented, Hall
10	C₅×C₈	—	3	1	no	Hall
11	C₃²×C₄	C₂×C₅	1	1	yes	characteristic
12	C₂×C₃×C₅	—	2	1	no	—
13	C₂×C₃×C₅	Dic₃	1	1	yes	characteristic
14	C₂×C₃×C₅	C₃×C₄	1	1	yes	characteristic
15	C₃×C₈	—	3	1	no	—
16	C₃⋊C₈	C₃×C₅	1	1	yes	characteristic, direct product factor
17	C₄×C₅	C₃×D₃	1	1	yes	characteristic
18	C₂×C₃²	C₄×C₅	1	1	yes	characteristic
19	C₃×C₅	—	2	1	no	—
20	C₃×C₅	C₃⋊C₈	1	1	yes	characteristic, direct product factor
21	C₃×C₅	C₃×C₈	1	1	yes	characteristic, complemented
22	C₃×C₄	—	2	1	no	—
23	C₃×C₄	C₅×D₃	1	1	yes	characteristic
24	C₃×C₄	C₂×C₃×C₅	1	1	yes	characteristic
25	C₂×C₅	C₃×Dic₃	1	1	yes	characteristic
26	C₃²	C₅×C₈	1	1	yes	characteristic, complemented, Sylow
27	C₈	—	3	1	no	Sylow
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	C₅×Dic₃	1	1	yes	characteristic
30	C₂×C₃	C₃×C₄×C₅	1	1	yes	characteristic
31	C₅	C₃×C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	C₃×C₅×D₃	1	1	yes	characteristic
33	C₃	—	2	1	no	—
34	C₃	C₅×C₃⋊C₈	1	1	yes	characteristic, direct product factor
35	C₃	C₃×C₅×C₈	1	1	yes	characteristic, complemented
36	C₂	C₃×C₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₅	D₃
commutator, hypocenter	C₃	C₃×C₅×C₈
Frattini	C₄	C₃×C₅×D₃
Fitting	C₃²×C₄×C₅	C₂
socle, prime radical	C₂×C₃²×C₅	C₄
cosocle	C₃×C₄	C₂×C₃×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₄×C₅

Complements

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

N	H ≅ G/N	type
3. C₅×C₃⋊C₈	C₃	direct (N × H)
5. C₃×C₃⋊C₈	C₅	direct (N × H)
9. C₃²×C₅	C₈	semidirect
16. C₃⋊C₈	C₃×C₅	direct (N × H)
20. C₃×C₅	C₃⋊C₈	direct (N × H)
21. C₃×C₅	C₃×C₈	semidirect
26. C₃²	C₅×C₈	semidirect
31. C₅	C₃×C₃⋊C₈	direct (N × H)
34. C₃	C₅×C₃⋊C₈	direct (N × H)
35. C₃	C₃×C₅×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄×C₅	2
C₃×C₅×C₈	3
C₅×C₃⋊C₈	3
C₃×C₃⋊C₈	5

Subgroups — C3×C5×C3⋊C8 #67104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₃⋊C₈ #67104