Subgroups — C₇₁×C₁₃⋊D₁₃ #37562090

Order 23998.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₇₁	—	13	14	no	maximal
3	C₁₃×C₇₁	D₁₃	1	14	yes	complemented
4	C₁₃⋊D₁₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃²	C₂×C₇₁	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₇₁	—	169	1	no	Hall
7	C₇₁	C₁₃⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
8	D₁₃	—	13	14	no	—
9	C₁₃	D₁₃×C₇₁	1	14	yes	complemented
10	C₂	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	C₁₃⋊D₁₃
commutator, cosocle, hypocenter	C₁₃²	C₂×C₇₁
Frattini	C₁	G
Fitting, socle	C₁₃²×C₇₁	C₂
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₇₁

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.