Subgroups — C₅×C₂₉×Dic₆₁ #47978043

Order 35380.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₉×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₉×Dic₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₉×C₆₁	C₂×C₅	1	1	yes	characteristic
5	C₂₉×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×Dic₆₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₆₁	C₂×C₂₉	1	1	yes	characteristic
8	C₄×C₅×C₂₉	—	61	1	no	maximal, Hall
9	C₅×C₆₁	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₂₉	D₆₁	1	1	yes	characteristic
11	Dic₆₁	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₂₉	Dic₆₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₆₁	C₂×C₅×C₂₉	1	1	yes	characteristic
14	C₄×C₂₉	—	61	1	no	Hall
15	C₆₁	C₄×C₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₉	C₅×D₆₁	1	1	yes	characteristic
17	C₂₉	C₅×Dic₆₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₄×C₅	—	61	1	no	Hall
19	C₂×C₅	C₂₉×D₆₁	1	1	yes	characteristic
20	C₅	C₂₉×Dic₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	61	1	no	Sylow
22	C₂	C₅×C₂₉×D₆₁	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.