Subgroups — C₅×Dic₁₇₀₇ #46802467

Order 34140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₅₆₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅₆₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₅₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₇₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₅₆₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅₆₉	C₂×C₅	1	1	yes	characteristic
7	C₅×C₅₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₅₆₉	—	3	1	no	Hall
9	C₃×C₅₆₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅₆₉	C₅×D₃	1	1	yes	characteristic
11	C₅₆₉	C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
12	C₅×Dic₃	—	569	1	no	maximal, Hall
13	C₂×C₃×C₅	D₅₆₉	1	1	yes	characteristic
14	C₄×C₅	—	1707	1	no	Hall
15	C₃×C₅	Dic₅₆₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	569	1	no	Hall
17	C₂×C₅	D₁₇₀₇	1	1	yes	characteristic
18	C₂×C₃	C₅×D₅₆₉	1	1	yes	characteristic
19	C₅	Dic₁₇₀₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	1707	1	no	Sylow
21	C₃	C₅×Dic₅₆₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₅×D₁₇₀₇	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.