Subgroups — C₃⋊#14524208 #20266641

Order 6498.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11762245	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
3	#14524208	—	3	1	no	maximal
4	C₃×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
5	#11762245	—	2	1	no	—
6	#11762245	D₃	1	1	yes	characteristic, complemented
7	C₁₉×D₁₉	—	3	1	no	Hall
8	C₁₉²	C₃×D₃	1	1	yes	characteristic, complemented, Sylow
9	C₃⋊(D₁₉⋊C₃)	—	19	1	no	maximal
10	D₃×C₁₉⋊C₃	—	19	1	no	maximal
11	C₃×C₁₉⋊C₃	—	19	1	no	—
12	C₃×C₁₉⋊C₃	—	19	1	no	—
13	C₃×C₁₉⋊C₃	—	38	9	no	—
14	D₅₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
15	D₃×C₁₉	—	19	1	no	—
16	C₂×C₁₉⋊C₃	—	57	1	no	—
17	D₁₉⋊C₃	—	57	1	no	—
18	C₃×C₁₉	—	2	9	no	—
19	C₃×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
20	C₃×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
21	C₁₉⋊C₃	—	19	1	no	—
22	C₁₉⋊C₃	—	19	1	no	—
23	C₁₉⋊C₃	—	38	9	no	—
24	C₁₉⋊C₃	—	38	18	no	—
25	C₁₉⋊C₃	—	38	1	no	—
26	C₁₉⋊C₃	—	38	1	no	—
27	C₂×C₁₉	—	57	1	no	—
28	D₁₉	—	3	1	no	—
29	C₁₉	—	2	9	no	—
30	C₁₉	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
31	C₁₉	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
32	C₃×D₃	—	361	1	no	Hall
33	C₃²	—	361	1	no	Sylow
34	C₂×C₃	—	1083	1	no	—
35	D₃	—	19	1	no	—
36	C₃	—	361	1	no	—
37	C₃	—	722	1	no	—
38	C₃	#14524208	1	1	yes	characteristic, complemented
39	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₉²	C₂×C₃
LCS	G ▷ C₃×C₁₉²
UCS	C₁

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