Subgroups — Dic₁₃×C₄₅₇ #37557708

Order 23764.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄₅₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₄₅₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₄₅₇	—	13	1	no	maximal, Hall
4	C₂×C₄₅₇	D₁₃	1	1	yes	characteristic
5	C₄₅₇	Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
6	Dic₁₃	C₄₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃	C₂×C₄₅₇	1	1	yes	characteristic
8	C₁₃	C₄×C₄₅₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	13	1	no	Sylow
10	C₂	D₁₃×C₄₅₇	1	1	yes	characteristic

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.