Subgroups — C₃×D₁₅₃₃ #22604155

Order 9198.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅₃₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₅₁₁	—	3	1	no	maximal
4	C₃×C₇×C₇₃	—	2	1	no	—
5	C₃×C₇×C₇₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₂₁₉	—	7	1	no	maximal, Hall
8	D₅₁₁	—	3	1	no	Hall
9	C₃²×C₇₃	D₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₁₉	—	7	1	no	—
12	C₃×D₇₃	—	21	1	no	—
13	C₃×C₇₃	—	2	1	no	—
14	C₃×C₇₃	C₃×D₇	1	1	yes	characteristic, complemented
15	C₃×C₇₃	D₂₁	1	1	yes	characteristic, complemented
16	D₇₃	—	21	1	no	Hall
17	C₃×D₂₁	—	73	1	no	maximal, Hall
18	C₇₃	C₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₇	D₇₃	1	1	yes	characteristic, complemented, Hall
20	D₂₁	—	73	1	no	—
21	C₃×D₇	—	219	1	no	—
22	C₃×C₇	—	2	1	no	—
23	C₃×C₇	C₃×D₇₃	1	1	yes	characteristic, complemented
24	C₃×C₇	D₂₁₉	1	1	yes	characteristic, complemented
25	C₃×D₃	—	511	1	no	Hall
26	D₇	—	219	1	no	Hall
27	C₃²	D₅₁₁	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₃×D₂₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	1533	1	no	—
30	D₃	—	511	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₅₁₁	1	1	yes	characteristic, complemented
33	C₃	D₁₅₃₃	1	1	yes	characteristic, direct product factor
34	C₂	—	1533	1	no	Sylow

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