Subgroups — C₁₁⋊C₅×#90673 #38733249

Order 24860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×D₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊C₅×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#90673	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×D₁₁₃	C₂×C₅	1	1	yes	characteristic
5	C₅×#90673	—	11	1	no	maximal, Hall
6	C₁₁×C₁₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₁₁₃	—	11	1	no	—
8	C₅×C₁₁₃	—	11	1	no	Hall
9	#90673	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
10	D₁₁₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic
11	C₄×C₁₁⋊C₅	—	113	1	no	maximal, Hall
12	C₁₁₃	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₁⋊C₅	—	113	1	no	—
14	C₁₁⋊C₅	#90673	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁	—	113	1	no	Hall
16	C₂×C₁₁	—	113	1	no	—
17	C₄×C₅	—	1243	1	no	Hall
18	C₁₁	C₅×#90673	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	1243	1	no	—
20	C₅	—	11	1	no	Sylow
21	C₄	—	113	1	no	Sylow
22	C₂	—	113	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₁₁₃	C₄×C₅
prime radical	C₁₁⋊C₅×D₁₁₃	C₂
cosocle	C₁₁×D₁₁₃	C₂×C₅
LCS	G ▷ C₁₁×C₁₁₃
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.