Subgroups — C₃²×C₅×C₅₃⋊C₁₃ #44526517

Order 31005.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₅₃⋊C₁₃	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₅₃⋊C₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₅₃⋊C₁₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃²×C₅×C₅₃	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₅₃⋊C₁₃	C₃×C₅	1	4	yes	direct product factor
6	C₃×C₅×C₅₃	C₃×C₁₃	1	4	yes	complemented
7	C₅₃⋊C₁₃	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₅×C₁₃	—	53	1	no	maximal, Hall
9	C₃²×C₅₃	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₅×C₅₃	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₁₃	—	53	4	no	—
12	C₃×C₅₃	C₃×C₅×C₁₃	1	4	yes	complemented
13	C₃²×C₁₃	—	53	1	no	Hall
14	C₅×C₁₃	—	53	1	no	Hall
15	C₅₃	C₃²×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₃²×C₅	C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₁₃	—	53	4	no	—
18	C₃×C₅	C₃×C₅₃⋊C₁₃	1	4	yes	direct product factor
19	C₁₃	—	53	1	no	Sylow
20	C₃²	C₅×C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₃²×C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	C₃×C₅×C₅₃⋊C₁₃	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²×C₅	C₅₃⋊C₁₃
commutator, cosocle, hypocenter	C₅₃	C₃²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₅₃	C₁₃
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₃²×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.