Subgroups — C₃²×C₁₉⋊#261 #22580347

Order 8892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉⋊#261	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×D₁₃	C₂×C₃	1	4	yes	—
5	C₁₉⋊#261	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₁₉	C₃×C₄	1	4	yes	complemented
7	C₃²×Dic₁₉	—	13	1	no	maximal, Hall
8	C₁₉×D₁₃	C₂×C₃²	1	1	yes	characteristic
9	C₃²×#261	—	19	1	no	maximal, Hall
10	C₂×C₃²×C₁₉	—	13	1	no	—
11	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
12	C₃²×D₁₃	D₁₉	1	1	yes	characteristic
13	C₃×Dic₁₉	—	13	4	no	—
14	C₃²×C₁₉	#261	1	1	yes	characteristic, complemented, Hall
15	C₃×#261	—	19	4	no	—
16	C₃²×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₉	—	13	4	no	—
18	C₃×D₁₃	C₃×D₁₉	1	4	yes	—
19	Dic₁₉	—	13	1	no	Hall
20	C₃×C₁₉	C₃×#261	1	4	yes	complemented
21	#261	—	19	1	no	Hall
22	C₃×C₁₃	C₃×Dic₁₉	1	4	yes	complemented
23	C₂×C₁₉	—	13	1	no	—
24	C₃²×C₄	—	247	1	no	Hall
25	D₁₃	C₃²×D₁₉	1	1	yes	characteristic
26	C₁₉	C₃²×#261	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃²	—	13	1	no	—
28	C₁₃	C₃²×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	247	4	no	—
30	C₃²	C₁₉⋊#261	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	13	4	no	—
32	C₄	—	247	1	no	Sylow
33	C₃	C₃×C₁₉⋊#261	1	4	yes	direct product factor
34	C₂	—	13	1	no	—

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