Subgroups — C₃⋊D₁₅×C₃₈₃ #46828107

Order 34470.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅×C₃₈₃	—	3	4	no	maximal
3	C₃⋊D₃×C₃₈₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₈₃	D₃	1	4	yes	complemented
5	D₅×C₃₈₃	—	9	1	no	Hall
6	C₃²×C₃₈₃	D₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₃₈₃	—	15	4	no	—
8	C₅×C₃₈₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₈₃	D₁₅	1	4	yes	complemented
10	C₂×C₃₈₃	—	45	1	no	Hall
11	C₃₈₃	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₃⋊D₁₅	C₃₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₅	C₂×C₃₈₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	3	4	no	—
15	C₃⋊D₃	—	5	1	no	Hall
16	C₃×C₅	D₃×C₃₈₃	1	4	yes	complemented
17	D₅	—	9	1	no	Hall
18	C₃²	D₅×C₃₈₃	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	15	4	no	—
20	C₅	C₃⋊D₃×C₃₈₃	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₁₅×C₃₈₃	1	4	yes	complemented
22	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₈₃	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂×C₃₈₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₈₃	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₃₈₃

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

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