Subgroups — C₂×C₅₉×C₂₄₃ #72205652

Order 28674.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×C₈₁	C₃	1	1	yes	maximal, characteristic
2	C₂×C₂₇×C₅₉	C₉	1	1	yes	characteristic
3	C₅₉×C₂₄₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅₉×C₈₁	C₂×C₃	1	1	yes	characteristic
5	C₂₇×C₅₉	C₂×C₉	1	1	yes	characteristic
6	C₂×C₉×C₅₉	C₂₇	1	1	yes	characteristic
7	C₉×C₅₉	C₂×C₂₇	1	1	yes	characteristic
8	C₂×C₂₄₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅₉	C₈₁	1	1	yes	characteristic
10	C₂₄₃	C₂×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×C₅₉	C₂×C₈₁	1	1	yes	characteristic
12	C₂×C₈₁	C₃×C₅₉	1	1	yes	characteristic
13	C₂×C₅₉	C₂₄₃	1	1	yes	characteristic, direct product factor, Hall
14	C₈₁	C₂×C₃×C₅₉	1	1	yes	characteristic
15	C₅₉	C₂×C₂₄₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₇	C₉×C₅₉	1	1	yes	characteristic
17	C₂₇	C₂×C₉×C₅₉	1	1	yes	characteristic
18	C₂×C₉	C₂₇×C₅₉	1	1	yes	characteristic
19	C₉	C₂×C₂₇×C₅₉	1	1	yes	characteristic
20	C₂×C₃	C₅₉×C₈₁	1	1	yes	characteristic
21	C₃	C₂×C₅₉×C₈₁	1	1	yes	characteristic
22	C₂	C₅₉×C₂₄₃	1	1	yes	characteristic, direct product factor, Sylow

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.