Subgroups — C₃²×D₁₃×C₅₃ #27137178

Order 12402.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₃×C₅₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₃×C₅₃	C₂×C₃	1	4	yes	complemented
4	D₁₃×C₅₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃²×C₅₃	—	13	1	no	maximal, Hall
6	C₁₃×C₅₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₅₃	D₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₅₃	—	13	4	no	—
9	C₃²×D₁₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅₃	C₃×D₁₃	1	4	yes	direct product factor
11	C₃²×C₁₃	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅₃	—	13	1	no	Hall
13	C₃×D₁₃	C₃×C₅₃	1	4	yes	direct product factor
14	C₅₃	C₃²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₃	C₂×C₃×C₅₃	1	4	yes	complemented
16	D₁₃	C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²	—	13	1	no	Hall
18	C₁₃	C₂×C₃²×C₅₃	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	13	4	no	—
21	C₃	C₃×D₁₃×C₅₃	1	4	yes	direct product factor
22	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃²×C₅₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₅₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃²×C₅₃

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.