Subgroups — #45684304

Order 33174.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30658676	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₉⋊C₃)⋊D₉₇	C₃	1	1	yes	maximal, characteristic
3	C₁₉⋊C₃×C₉₇	C₂×C₃	1	1	yes	characteristic
4	D₁₈₄₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₉₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	D₉₇⋊C₉	—	19	1	no	maximal, Hall
7	C₉₇⋊C₉	—	19	1	no	Hall
8	C₃×D₉₇	—	19	1	no	—
9	AGL(1,𝔽₁₉)	—	97	1	no	maximal, Hall
10	C₃×C₉₇	—	19	1	no	—
11	D₉₇	—	19	1	no	Hall
12	#4296	—	97	1	no	Hall
13	D₁₉⋊C₃	—	97	1	no	—
14	C₉₇	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Sylow
15	C₁₉⋊C₃	D₉₇⋊C₃	1	1	yes	characteristic
16	D₁₉	—	97	1	no	Hall
17	C₁₉	D₉₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	1843	1	no	Hall
19	C₉	—	1843	1	no	Sylow
20	C₂×C₃	—	1843	1	no	—
21	C₃	—	19	1	no	—
22	C₂	—	1843	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₉×C₉₇	C₂×C₉
prime radical	(C₁₉⋊C₃)⋊D₉₇	C₃
cosocle	C₁₉⋊C₃×C₉₇	C₂×C₃
LCS	G ▷ C₁₉×C₉₇
UCS	C₁

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.