Subgroups — #29503113

Order 15162.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#87705	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊(C₁₉⋊D₁₉)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₁₉⋊C₃)⋊D₁₉	—	7	1	no	maximal, Hall
5	C₁₉×C₁₉⋊C₃	—	7	1	no	Hall
6	#11716328	—	19	1	no	maximal
7	ΓL(1,𝔽₈)⋊D₁₉	—	19	1	no	maximal
8	C₁₉⋊D₁₉	—	7	1	no	Hall
9	#87705	D₁₉	1	1	yes	characteristic, complemented
10	C₁₉×ΓL(1,𝔽₈)	—	19	1	no	—
11	C₁₉²	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
12	D₁₃₃	—	19	1	no	—
13	D₁₃₃	—	19	1	no	—
14	D₁₃₃	—	57	6	no	—
15	C₇×C₁₉	—	3	6	no	—
16	C₇×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
17	C₇×C₁₉	C₃×D₁₉	1	1	yes	characteristic, complemented
18	C₃×D₁₉	—	133	1	no	—
19	D₁₉⋊C₃	—	133	1	no	—
20	C₃×C₁₉	—	133	1	no	—
21	C₁₉⋊C₃	—	7	1	no	—
22	AGL(1,𝔽₇)	—	361	1	no	Hall
23	D₁₉	—	133	1	no	—
24	D₁₉	—	133	1	no	—
25	D₁₉	—	399	6	no	—
26	ΓL(1,𝔽₈)	—	19	1	no	Hall
27	C₁₉	—	3	6	no	—
28	C₁₉	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
29	C₁₉	#11716328	1	1	yes	characteristic, complemented
30	D₇	—	361	1	no	Hall
31	C₇	(C₁₉⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃	—	2527	1	no	Hall
33	C₃	—	133	1	no	Sylow
34	C₂	—	2527	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉²	C₂×C₃
LCS	G ▷ C₇×C₁₉²
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.