Subgroups — C₂×C₁₃²×C₁₁⋊C₅ #32915768

Order 18590.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁×C₁₃²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₃²	—	11	1	no	maximal, Hall
5	C₂×C₁₃×C₁₁⋊C₅	C₁₃	1	14	yes	maximal, direct product factor
6	C₅×C₁₃²	—	11	1	no	Hall
7	C₁₃×C₁₁⋊C₅	C₂×C₁₃	1	14	yes	direct product factor
8	C₂×C₁₃²	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₁×C₁₃	C₅×C₁₃	1	14	yes	complemented
10	C₁₃²	C₂×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
11	C₁₁×C₁₃	C₂×C₅×C₁₃	1	14	yes	complemented
12	C₂×C₅×C₁₃	—	11	14	no	—
13	C₂×C₁₁⋊C₅	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₁₃	—	11	14	no	—
15	C₁₁⋊C₅	C₂×C₁₃²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	C₁₃×C₁₁⋊C₅	1	14	yes	direct product factor
17	C₂×C₁₁	C₅×C₁₃²	1	1	yes	characteristic, complemented, Hall
18	C₁₃	C₂×C₁₃×C₁₁⋊C₅	1	14	yes	direct product factor
19	C₁₁	C₂×C₅×C₁₃²	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	11	1	no	Hall
21	C₅	—	11	1	no	Sylow
22	C₂	C₁₃²×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₃²	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₁₃²
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃²	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₃²

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.