Subgroups — C₁₉⋊#90866 #22580378

Order 8892.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×D₃₉	—	6	2	no	—
4	C₁₉⋊#261	—	9	1	no	maximal, Hall
5	C₃×C₁₃×C₁₉	—	2	2	no	—
6	C₁₉⋊#157	—	13	1	no	maximal, Hall
7	C₁₉×D₁₃	—	9	1	no	—
8	#90866	—	19	1	no	maximal, Hall
9	C₃⋊D₃×C₁₉	—	13	1	no	—
10	C₁₃×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
11	C₃⋊D₃₉	D₁₉	1	1	yes	characteristic
12	C₃²×C₁₉	#261	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₉	—	78	2	no	—
15	D₃₉	—	6	2	no	—
16	Dic₁₉	—	117	1	no	Hall
17	C₃×C₁₉	—	2	2	no	—
18	#261	—	171	1	no	Hall
19	C₃×C₁₃	—	2	2	no	—
20	C₂×C₁₉	—	117	1	no	—
21	#157	—	247	1	no	Hall
22	D₁₃	—	9	1	no	—
23	C₁₉	#90866	1	1	yes	characteristic, complemented, Sylow
24	C₃⋊D₃	—	13	1	no	—
25	C₁₃	C₁₉⋊#157	1	1	yes	characteristic, complemented, Sylow
26	C₃²	C₁₉⋊#261	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	78	2	no	—
28	C₄	—	2223	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	117	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃×C₁₉	C₄
LCS	G ▷ C₃²×C₁₃×C₁₉
UCS	C₁

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