Subgroups — C₃⋊D₃₄₀₅ #35205346

Order 20430.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₄₀₅	—	3	4	no	maximal
3	C₃⋊D₆₈₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₂₂₇	D₃	1	4	yes	complemented
5	D₁₁₃₅	—	9	1	no	Hall
6	C₃²×C₂₂₇	D₅	1	1	yes	characteristic, complemented, Hall
7	D₆₈₁	—	15	4	no	—
8	C₅×C₂₂₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₂₂₇	D₁₅	1	4	yes	complemented
10	D₂₂₇	—	45	1	no	Hall
11	C₂₂₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊D₁₅	—	227	1	no	maximal, Hall
13	C₃²×C₅	D₂₂₇	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	681	4	no	—
15	C₃⋊D₃	—	1135	1	no	Hall
16	C₃×C₅	D₆₈₁	1	4	yes	complemented
17	D₅	—	2043	1	no	Hall
18	C₃²	D₁₁₃₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	3405	4	no	—
20	C₅	C₃⋊D₆₈₁	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₃₄₀₅	1	4	yes	complemented
22	C₂	—	10215	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₂₂₇	C₂
LCS	G ▷ C₃²×C₅×C₂₂₇
UCS	C₁

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.