Subgroups — C₃×Dic₃×C₆₅₉ #37557461

Order 23724.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₆₅₉	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₆₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄×C₆₅₉	—	3	1	no	maximal
4	C₃²×C₆₅₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₆₅₉	—	2	1	no	—
6	C₂×C₃×C₆₅₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₆₅₉	C₂×C₃	1	1	yes	characteristic
8	C₄×C₆₅₉	—	3	1	no	Hall
9	C₃×C₆₅₉	—	2	1	no	—
10	C₃×C₆₅₉	Dic₃	1	1	yes	characteristic, direct product factor
11	C₃×C₆₅₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₂×C₆₅₉	C₃×D₃	1	1	yes	characteristic
13	C₆₅₉	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃×Dic₃	C₆₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃²	C₂×C₆₅₉	1	1	yes	characteristic
16	C₃×C₄	—	3	1	no	—
17	Dic₃	C₃×C₆₅₉	1	1	yes	characteristic, direct product factor
18	C₃²	C₄×C₆₅₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	2	1	no	—
20	C₂×C₃	D₃×C₆₅₉	1	1	yes	characteristic
21	C₂×C₃	C₂×C₃×C₆₅₉	1	1	yes	characteristic
22	C₄	—	3	1	no	Sylow
23	C₃	—	2	1	no	—
24	C₃	C₃×C₄×C₆₅₉	1	1	yes	characteristic, complemented
25	C₃	Dic₃×C₆₅₉	1	1	yes	characteristic, direct product factor
26	C₂	C₃×D₃×C₆₅₉	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.