Subgroups — C₅⋊(C₁₁⋊D₂₅₃) #42123748

Order 27830.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁⋊D₂₅₃	—	5	1	no	maximal, Hall
3	C₁₁²×C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
4	D₁₂₆₅	—	11	12	no	maximal
5	C₅×C₁₁×C₂₃	D₁₁	1	12	yes	complemented
6	C₅⋊(C₁₁⋊D₁₁)	—	23	1	no	maximal, Hall
7	C₅×C₁₁²	D₂₃	1	1	yes	characteristic, complemented, Hall
8	D₂₅₃	—	55	12	no	—
9	C₁₁×C₂₃	D₅₅	1	12	yes	complemented
10	C₁₁⋊D₁₁	—	115	1	no	Hall
11	D₁₁₅	—	121	1	no	Hall
12	C₁₁²	D₁₁₅	1	1	yes	characteristic, complemented, Sylow
13	C₅×C₂₃	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
14	D₅₅	—	253	12	no	—
15	C₅×C₁₁	D₂₅₃	1	12	yes	complemented
16	D₂₃	—	605	1	no	Hall
17	C₂₃	C₅⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, complemented, Sylow
18	D₁₁	—	1265	12	no	—
19	C₁₁	D₁₂₆₅	1	12	yes	complemented
20	D₅	—	2783	1	no	Hall
21	C₅	C₁₁⋊D₂₅₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	13915	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁²×C₂₃	C₂
LCS	G ▷ C₅×C₁₁²×C₂₃
UCS	C₁

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.