Subgroups — C₁₃⋊C₃×C₁₂₁⋊C₅ #37556191

Order 23595.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₂₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×C₁₂₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₁⋊C₅	—	11	1	no	maximal
4	C₃×C₁₂₁⋊C₅	—	13	1	no	maximal, Hall
5	C₁₃×C₁₂₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₁₁⋊C₅	—	11	1	no	—
7	C₁₂₁⋊C₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×C₁₃⋊C₃	C₁₁⋊C₅	1	1	yes	characteristic
9	C₃×C₁₂₁	—	13	1	no	Hall
10	C₅×C₁₃⋊C₃	—	121	1	no	Hall
11	C₃×C₁₁⋊C₅	—	143	1	no	—
12	C₁₁×C₁₃	C₃×C₁₁⋊C₅	1	1	yes	characteristic
13	C₁₂₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₃	—	121	1	no	Hall
15	C₁₁⋊C₅	—	11	1	no	—
16	C₁₃⋊C₃	C₁₂₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₁₁	—	13	1	no	—
18	C₃×C₅	—	1573	1	no	Hall
19	C₁₃	C₃×C₁₂₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	C₁₃⋊C₃×C₁₁⋊C₅	1	1	yes	characteristic
21	C₅	—	121	1	no	Sylow
22	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₃×C₁₂₁	C₃×C₅
Frattini	C₁₁	C₁₃⋊C₃×C₁₁⋊C₅
socle	C₁₁×C₁₃	C₃×C₁₁⋊C₅
LCS	G ▷ C₁₃×C₁₂₁
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.