Subgroups — #22580238

Order 8892.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984641	C₂	1	1	yes	maximal, characteristic
2	#261×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#14555740	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₁₉×#261	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
7	C₄×#4296	—	13	1	no	maximal, Hall
8	C₁₉×D₁₃	C₂×C₉	1	1	yes	characteristic
9	#261⋊C₉	—	19	1	no	maximal, Hall
10	C₂×#4296	—	13	1	no	—
11	C₁₃×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	D₁₃⋊C₉	—	19	1	no	—
13	C₄×C₁₉⋊C₃	—	13	1	no	—
14	#4296	—	13	1	no	Hall
15	C₃×#261	—	19	1	no	—
16	C₁₃⋊C₉	—	19	1	no	Hall
17	C₂×C₁₉⋊C₃	—	13	1	no	—
18	C₃×D₁₃	—	19	1	no	—
19	C₄×C₁₉	—	13	1	no	Hall
20	C₁₉⋊C₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic
21	#261	#4296	1	1	yes	characteristic, complemented, Hall
22	C₃×C₁₃	—	19	1	no	—
23	C₂×C₁₉	—	13	1	no	—
24	C₄×C₉	—	247	1	no	Hall
25	D₁₃	C₂×#4296	1	1	yes	characteristic
26	C₁₉	#261⋊C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	247	1	no	—
28	C₁₃	C₄×#4296	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	247	1	no	—
30	C₉	—	247	1	no	Sylow
31	C₂×C₃	—	247	1	no	—
32	C₄	—	13	1	no	Sylow
33	C₃	—	19	1	no	—
34	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₉	C₄×C₉
LCS	G ▷ C₁₃×C₁₉
UCS	C₁

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