Subgroups — (C₁₉⋊C₃)⋊#63118 #28414830

Order 14820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#63118	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₁₉⋊C₃)⋊#261	—	5	1	no	maximal, Hall
5	C₅×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic
6	D₁₃×C₁₉⋊C₃	D₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	(C₁₉⋊C₃)⋊Dic₅	—	13	1	no	maximal, Hall
9	C₁₉⋊#261	—	5	1	no	Hall
10	C₃×#63118	—	19	1	no	maximal, Hall
11	C₁₃×C₁₉⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₁₉⋊C₃	—	13	1	no	—
13	C₁₉×D₁₃	C₃×D₅	1	1	yes	characteristic
14	C₃×C₅×D₁₃	—	38	1	no	—
15	Dic₉₅	—	13	1	no	Hall
16	C₅×C₁₉⋊C₃	#261	1	1	yes	characteristic, complemented, Hall
17	#63118	—	19	1	no	Hall
18	C₁₃×C₁₉	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
19	(C₁₉⋊C₃)⋊C₄	—	65	1	no	Hall
20	C₃×C₅×C₁₃	—	38	1	no	Hall
21	C₂×C₅×C₁₉	—	13	1	no	—
22	C₃×#261	—	95	1	no	Hall
23	C₅×D₁₃	D₁₉⋊C₃	1	1	yes	characteristic
24	C₂×C₁₉⋊C₃	—	13	1	no	—
25	C₅×C₁₉	C₃×#261	1	1	yes	characteristic, complemented, Hall
26	C₃×D₁₃	—	38	1	no	—
27	Dic₁₉	—	65	1	no	Hall
28	C₅×C₁₃	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
29	C₃×Dic₅	—	247	1	no	Hall
30	C₁₉⋊C₃	#63118	1	1	yes	characteristic, complemented, Hall
31	#261	—	95	1	no	Hall
32	C₃×C₁₃	—	38	1	no	Hall
33	C₂×C₁₉	—	13	1	no	—
34	C₂×C₃×C₅	—	494	1	no	—
35	D₁₃	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic
36	Dic₅	—	247	1	no	Hall
37	C₁₉	C₃×#63118	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	—	38	1	no	Hall
39	C₁₃	(C₁₉⋊C₃)⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	1235	1	no	Hall
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	494	1	no	—
43	C₅	(C₁₉⋊C₃)⋊#261	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	1235	1	no	Sylow
45	C₃	—	38	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₃×C₁₉	C₃×C₄
prime radical	C₅×D₁₃×C₁₉⋊C₃	C₂
cosocle	C₅×C₁₉×D₁₃	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₉⋊#63118	C₃	semidirect
3. C₅×C₁₃×C₁₉⋊C₃	C₄	semidirect
7. C₅×C₁₃×C₁₉	C₃×C₄	semidirect
11. C₁₃×C₁₉⋊C₃	Dic₅	semidirect
16. C₅×C₁₉⋊C₃	#261	semidirect
18. C₁₃×C₁₉	C₃×Dic₅	semidirect
25. C₅×C₁₉	C₃×#261	semidirect
28. C₅×C₁₃	(C₁₉⋊C₃)⋊C₄	semidirect
30. C₁₉⋊C₃	#63118	semidirect
37. C₁₉	C₃×#63118	semidirect
39. C₁₃	(C₁₉⋊C₃)⋊Dic₅	semidirect
43. C₅	(C₁₉⋊C₃)⋊#261	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₃×C₁₉⋊C₃	2
C₁₉⋊#63118	3
(C₁₉⋊C₃)⋊#261	5
(C₁₉⋊C₃)⋊Dic₅	13
C₃×#63118	19

Subgroups — (C19⋊C3)⋊#63118 #28414830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₁₉⋊C₃)⋊#63118 #28414830