Subgroups — C₃×Dic₂₅₇₃ #44525243

Order 30876.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₁×C₈₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₅₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₃₁×C₈₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×C₈₃	C₂×C₃	1	1	yes	characteristic
5	C₃₁×C₈₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₈₃	—	31	1	no	maximal, Hall
7	C₂×C₃×C₈₃	D₃₁	1	1	yes	characteristic
8	C₃×Dic₃₁	—	83	1	no	maximal, Hall
9	Dic₈₃	—	31	1	no	Hall
10	C₃×C₈₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₃₁	D₈₃	1	1	yes	characteristic
12	C₂×C₈₃	C₃×D₃₁	1	1	yes	characteristic
13	Dic₃₁	—	83	1	no	Hall
14	C₃×C₃₁	Dic₈₃	1	1	yes	characteristic, complemented, Hall
15	C₈₃	C₃×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃₁	C₃×D₈₃	1	1	yes	characteristic
17	C₃₁	C₃×Dic₈₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2573	1	no	Hall
19	C₂×C₃	D₂₅₇₃	1	1	yes	characteristic
20	C₄	—	2573	1	no	Sylow
21	C₃	Dic₂₅₇₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₂₅₇₃	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.