Subgroups — C₅×C₃⋊D₉₃₉ #43245255

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	C₅×D₉₃₉	—	3	4	no	maximal
3	C₃⋊D₉₃₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₃₁₃	D₃	1	4	yes	complemented
5	C₅×D₃₁₃	—	9	1	no	Hall
6	C₃²×C₃₁₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₉₃₉	—	3	4	no	—
8	C₅×C₃₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₁₃	C₅×D₃	1	4	yes	complemented
10	D₃₁₃	—	9	1	no	Hall
11	C₃₁₃	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
12	C₅×C₃⋊D₃	—	313	1	no	maximal, Hall
13	C₃²×C₅	D₃₁₃	1	1	yes	characteristic, complemented, Hall
14	C₅×D₃	—	939	4	no	—
15	C₃⋊D₃	—	313	1	no	Hall
16	C₃×C₅	D₉₃₉	1	4	yes	complemented
17	C₂×C₅	—	2817	1	no	Hall
18	C₃²	C₅×D₃₁₃	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	939	4	no	—
20	C₅	C₃⋊D₉₃₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₅×D₉₃₉	1	4	yes	complemented
22	C₂	—	2817	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₉₃₉
commutator, cosocle, hypocenter	C₃²×C₃₁₃	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₁₃	C₂
LCS	G ▷ C₃²×C₃₁₃
UCS	C₁ ◁ C₅

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.