Subgroups — C₃⋊D₃₄₉₅ #35230463

Order 20970.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₄₉₅	—	3	4	no	maximal
3	C₃⋊D₆₉₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₂₃₃	D₃	1	4	yes	complemented
5	D₁₁₆₅	—	9	1	no	Hall
6	C₃²×C₂₃₃	D₅	1	1	yes	characteristic, complemented, Hall
7	D₆₉₉	—	15	4	no	—
8	C₅×C₂₃₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₂₃₃	D₁₅	1	4	yes	complemented
10	D₂₃₃	—	45	1	no	Hall
11	C₂₃₃	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊D₁₅	—	233	1	no	maximal, Hall
13	C₃²×C₅	D₂₃₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	699	4	no	—
15	C₃⋊D₃	—	1165	1	no	Hall
16	C₃×C₅	D₆₉₉	1	4	yes	complemented
17	D₅	—	2097	1	no	Hall
18	C₃²	D₁₁₆₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	3495	4	no	—
20	C₅	C₃⋊D₆₉₉	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₃₄₉₅	1	4	yes	complemented
22	C₂	—	10485	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₂₃₃	C₂
LCS	G ▷ C₃²×C₅×C₂₃₃
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.