Subgroups — C₅₃×D₁₆₅ #31775821

Order 17490.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₃×D₅₅	—	3	1	no	maximal, Hall
3	C₅₃×D₃₃	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₅₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₅₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₅×C₅₃	—	11	1	no	maximal, Hall
7	D₁₁×C₅₃	—	15	1	no	Hall
8	C₃×C₅×C₅₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₅₃	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₅×C₅₃	—	33	1	no	Hall
11	D₁₆₅	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₅₃	—	55	1	no	Hall
13	C₅×C₅₃	D₃₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₁	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅₃	D₅₅	1	1	yes	characteristic, complemented, Hall
16	D₅₅	—	3	1	no	Hall
17	C₂×C₅₃	—	165	1	no	Hall
18	D₃₃	—	5	1	no	Hall
19	C₅×C₁₁	D₃×C₅₃	1	1	yes	characteristic, complemented, Hall
20	C₅₃	D₁₆₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₁	D₅×C₅₃	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	11	1	no	Hall
23	D₁₁	—	15	1	no	Hall
24	C₃×C₅	D₁₁×C₅₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁	D₁₅×C₅₃	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	33	1	no	Hall
27	D₃	—	55	1	no	Hall
28	C₅	C₅₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₅₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	165	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₃	D₁₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₁	C₂×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₅₃	C₂
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ 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.