Subgroups — C₃²×Dic₂₈₉ #23780804

Order 10404.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₂₈₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₈₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₂₈₉	C₂×C₃	1	4	yes	—
5	Dic₂₈₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₈₉	C₃×C₄	1	4	yes	complemented
7	C₃²×Dic₁₇	—	17	1	no	maximal
8	C₂×C₂₈₉	C₂×C₃²	1	1	yes	characteristic
9	C₂×C₃²×C₁₇	D₁₇	1	1	yes	characteristic
10	C₂₈₉	C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₃×Dic₁₇	—	17	4	no	—
12	C₃²×C₁₇	Dic₁₇	1	1	yes	characteristic
13	C₂×C₃×C₁₇	C₃×D₁₇	1	4	yes	—
14	Dic₁₇	—	17	1	no	—
15	C₃×C₁₇	C₃×Dic₁₇	1	4	yes	—
16	C₃²×C₄	—	289	1	no	Hall
17	C₂×C₁₇	C₃²×D₁₇	1	1	yes	characteristic
18	C₂×C₃²	D₂₈₉	1	1	yes	characteristic
19	C₁₇	C₃²×Dic₁₇	1	1	yes	characteristic
20	C₃×C₄	—	289	4	no	—
21	C₃²	Dic₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃	C₃×D₂₈₉	1	4	yes	—
23	C₄	—	289	1	no	Sylow
24	C₃	C₃×Dic₂₈₉	1	4	yes	direct product factor
25	C₂	C₃²×D₂₈₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.