Subgroups — C₅×Dic₁₇₁₁ #46803750

Order 34220.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₉×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₇₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₉×C₅₉	C₂×C₅	1	1	yes	characteristic
5	C₂₉×C₅₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×Dic₅₉	—	29	1	no	maximal, Hall
7	C₂×C₅×C₅₉	D₂₉	1	1	yes	characteristic
8	C₅×Dic₂₉	—	59	1	no	maximal, Hall
9	C₅×C₅₉	Dic₂₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₂₉	D₅₉	1	1	yes	characteristic
11	Dic₅₉	—	29	1	no	Hall
12	C₅×C₂₉	Dic₅₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₉	C₅×D₂₉	1	1	yes	characteristic
14	Dic₂₉	—	59	1	no	Hall
15	C₅₉	C₅×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₉	C₅×D₅₉	1	1	yes	characteristic
17	C₂₉	C₅×Dic₅₉	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	1711	1	no	Hall
19	C₂×C₅	D₁₇₁₁	1	1	yes	characteristic
20	C₅	Dic₁₇₁₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1711	1	no	Sylow
22	C₂	C₅×D₁₇₁₁	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.