Subgroups — Dic₁₅×C₅₆₉ #46802468

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	Dic₅×C₅₆₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₅₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₃×C₅₆₉	—	5	1	no	maximal, Hall
5	C₂×C₅×C₅₆₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅₆₉	D₅	1	1	yes	characteristic
7	C₅×C₅₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₄×C₅₆₉	—	15	1	no	Hall
9	C₃×C₅₆₉	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅₆₉	D₁₅	1	1	yes	characteristic
11	C₅₆₉	Dic₁₅	1	1	yes	characteristic, direct product factor, Sylow
12	Dic₁₅	C₅₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅	C₂×C₅₆₉	1	1	yes	characteristic
14	Dic₅	—	3	1	no	Hall
15	C₃×C₅	C₄×C₅₆₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	5	1	no	Hall
17	C₂×C₅	D₃×C₅₆₉	1	1	yes	characteristic
18	C₂×C₃	D₅×C₅₆₉	1	1	yes	characteristic
19	C₅	Dic₃×C₅₆₉	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	15	1	no	Sylow
21	C₃	Dic₅×C₅₆₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₁₅×C₅₆₉	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.