Subgroups — C₅⋊((C₁₉⋊C₃)⋊D₁₉) #24925331

Order 10830.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(C₁₉⋊D₁₉)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	(C₁₉⋊C₃)⋊D₁₉	—	5	1	no	maximal, Hall
4	C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₁₉⋊D₁₉	—	5	1	no	Hall
7	C₃×D₉₅	—	19	1	no	maximal
8	C₅⋊(D₁₉⋊C₃)	—	19	1	no	maximal
9	C₁₉²	C₃×D₅	1	1	yes	characteristic, complemented, Sylow
10	C₃×C₅×C₁₉	—	19	1	no	—
11	C₅×C₁₉⋊C₃	D₁₉	1	1	yes	characteristic, complemented
12	D₉₅	—	19	1	no	—
13	D₉₅	—	19	1	no	—
14	D₉₅	—	57	6	no	—
15	C₃×D₁₉	—	95	1	no	—
16	D₁₉⋊C₃	—	95	1	no	—
17	C₅×C₁₉	—	3	6	no	—
18	C₅×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented
19	C₅×C₁₉	C₃×D₁₉	1	1	yes	characteristic, complemented
20	C₃×C₁₉	—	19	1	no	—
21	C₁₉⋊C₃	D₉₅	1	1	yes	characteristic, complemented
22	D₁₉	—	285	6	no	—
23	D₁₉	—	95	1	no	—
24	D₁₉	—	95	1	no	—
25	C₃×D₅	—	361	1	no	Hall
26	C₁₉	—	3	6	no	—
27	C₁₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
28	C₁₉	C₃×D₉₅	1	1	yes	characteristic, complemented
29	C₃×C₅	—	19	1	no	Hall
30	D₅	—	361	1	no	Hall
31	C₂×C₃	—	1805	1	no	Hall
32	C₅	(C₁₉⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
33	C₃	—	19	1	no	Sylow
34	C₂	—	1805	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉²	C₂×C₃
LCS	G ▷ C₅×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.