Subgroups — C₃×C₈₉×Dic₂₉ #44526367

Order 30972.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₉×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×Dic₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₉×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₉×C₈₉	C₂×C₃	1	1	yes	characteristic
5	C₂₉×C₈₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₈₉	—	29	1	no	maximal, Hall
7	C₂×C₃×C₈₉	D₂₉	1	1	yes	characteristic
8	C₄×C₈₉	—	29	1	no	Hall
9	C₃×Dic₂₉	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₈₉	Dic₂₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₈₉	C₃×D₂₉	1	1	yes	characteristic
12	C₂×C₃×C₂₉	C₂×C₈₉	1	1	yes	characteristic
13	Dic₂₉	C₃×C₈₉	1	1	yes	characteristic, direct product factor, Hall
14	C₈₉	C₃×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₂₉	C₄×C₈₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₉	C₂×C₃×C₈₉	1	1	yes	characteristic
17	C₂₉	C₃×C₄×C₈₉	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	29	1	no	Hall
19	C₂×C₃	D₂₉×C₈₉	1	1	yes	characteristic
20	C₄	—	29	1	no	Sylow
21	C₃	C₈₉×Dic₂₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₂₉×C₈₉	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.