Subgroups — C₃⋊D₅₂₉₅ #44540939

Order 31770.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₉₅	—	3	4	no	maximal
3	C₃⋊D₁₀₅₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₅₃	D₃	1	4	yes	complemented
5	D₁₇₆₅	—	9	1	no	Hall
6	C₃²×C₃₅₃	D₅	1	1	yes	characteristic, complemented, Hall
7	D₁₀₅₉	—	15	4	no	—
8	C₅×C₃₅₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₅₃	D₁₅	1	4	yes	complemented
10	D₃₅₃	—	45	1	no	Hall
11	C₃₅₃	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊D₁₅	—	353	1	no	maximal, Hall
13	C₃²×C₅	D₃₅₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	1059	4	no	—
15	C₃⋊D₃	—	1765	1	no	Hall
16	C₃×C₅	D₁₀₅₉	1	4	yes	complemented
17	D₅	—	3177	1	no	Hall
18	C₃²	D₁₇₆₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	5295	4	no	—
20	C₅	C₃⋊D₁₀₅₉	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₅₂₉₅	1	4	yes	complemented
22	C₂	—	15885	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₃₅₃	C₂
LCS	G ▷ C₃²×C₅×C₃₅₃
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.