Subgroups — C₅×Dic₁₇₃₉ #46851985

Order 34780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₇×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₇₃₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃₇×C₄₇	C₂×C₅	1	1	yes	characteristic
5	C₃₇×C₄₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×Dic₄₇	—	37	1	no	maximal, Hall
7	C₅×Dic₃₇	—	47	1	no	maximal, Hall
8	C₂×C₅×C₄₇	D₃₇	1	1	yes	characteristic
9	C₂×C₅×C₃₇	D₄₇	1	1	yes	characteristic
10	C₅×C₄₇	Dic₃₇	1	1	yes	characteristic, complemented, Hall
11	Dic₄₇	—	37	1	no	Hall
12	C₅×C₃₇	Dic₄₇	1	1	yes	characteristic, complemented, Hall
13	Dic₃₇	—	47	1	no	Hall
14	C₂×C₄₇	C₅×D₃₇	1	1	yes	characteristic
15	C₂×C₃₇	C₅×D₄₇	1	1	yes	characteristic
16	C₄₇	C₅×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	C₅×Dic₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	1739	1	no	Hall
19	C₂×C₅	D₁₇₃₉	1	1	yes	characteristic
20	C₅	Dic₁₇₃₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1739	1	no	Sylow
22	C₂	C₅×D₁₇₃₉	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.