Subgroups — C₃²×D₁₅₆₅ #43245249

Order 28170.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₅₆₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₃₁₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₁₃	C₂×C₃	1	4	yes	complemented
5	D₁₅₆₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₃₁₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃₁₃	—	5	4	no	—
8	C₅×C₃₁₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₁₃	C₃×D₅	1	4	yes	complemented
10	D₃₁₃	—	5	1	no	Hall
11	C₃₁₃	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
12	C₃²×D₅	—	313	1	no	maximal, Hall
13	C₃²×C₅	D₃₁₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅	—	313	4	no	—
15	C₂×C₃²	—	1565	1	no	Hall
16	C₃×C₅	C₃×D₃₁₃	1	4	yes	complemented
17	D₅	—	313	1	no	Hall
18	C₃²	D₁₅₆₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	1565	4	no	—
20	C₅	C₃²×D₃₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₃	C₃×D₁₅₆₅	1	4	yes	direct product factor
22	C₂	—	1565	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₅₆₅
commutator, cosocle, hypocenter	C₅×C₃₁₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₁₃	C₂
LCS	G ▷ C₅×C₃₁₃
UCS	C₁ ◁ C₃²

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.