Subgroups — C₅×Dic₁₃×C₁₉⋊C₃ #28414739

Order 14820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×Dic₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₃×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₃×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₅×C₁₉⋊C₃	—	13	1	no	maximal, Hall
9	C₁₉×Dic₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×Dic₁₃	—	19	1	no	maximal, Hall
11	C₁₃×C₁₉⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₁₉⋊C₃	D₁₃	1	1	yes	characteristic
13	C₂×C₁₃×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
14	C₂×C₃×C₅×C₁₃	—	19	1	no	—
15	C₄×C₅×C₁₉	—	13	1	no	Hall
16	C₅×C₁₉⋊C₃	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₅×Dic₁₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃×C₁₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
19	C₄×C₁₉⋊C₃	—	13	1	no	Hall
20	C₃×C₅×C₁₃	—	19	1	no	Hall
21	C₂×C₅×C₁₉	C₃×D₁₃	1	1	yes	characteristic
22	C₃×Dic₁₃	—	19	1	no	Hall
23	C₂×C₅×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
24	C₂×C₁₉⋊C₃	C₅×D₁₃	1	1	yes	characteristic
25	C₅×C₁₉	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₃	—	19	1	no	—
27	C₄×C₁₉	—	13	1	no	Hall
28	C₅×C₁₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄×C₅	—	247	1	no	Hall
30	C₁₉⋊C₃	C₅×Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
31	Dic₁₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₁₃	—	19	1	no	Hall
33	C₂×C₁₉	C₃×C₅×D₁₃	1	1	yes	characteristic
34	C₂×C₃×C₅	—	19	1	no	—
35	C₂×C₁₃	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
36	C₄×C₅	—	13	1	no	Hall
37	C₁₉	C₃×C₅×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	—	19	1	no	Hall
39	C₁₃	C₄×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	247	1	no	Hall
41	C₂×C₅	D₁₃×C₁₉⋊C₃	1	1	yes	characteristic
42	C₂×C₃	—	19	1	no	—
43	C₅	Dic₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	13	1	no	Sylow
45	C₃	—	19	1	no	Sylow
46	C₂	C₅×D₁₃×C₁₉⋊C₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₉×Dic₁₃	C₃	semidirect
3. C₅×C₁₃×C₁₉⋊C₃	C₄	semidirect
4. Dic₁₃×C₁₉⋊C₃	C₅	direct (N × H)
7. C₅×C₁₃×C₁₉	C₃×C₄	semidirect
9. C₁₉×Dic₁₃	C₃×C₅	semidirect
11. C₁₃×C₁₉⋊C₃	C₄×C₅	semidirect
16. C₅×C₁₉⋊C₃	Dic₁₃	direct (N × H)
17. C₅×Dic₁₃	C₁₉⋊C₃	direct (N × H)
18. C₁₃×C₁₉	C₃×C₄×C₅	semidirect
25. C₅×C₁₉	C₃×Dic₁₃	semidirect
28. C₅×C₁₃	C₄×C₁₉⋊C₃	semidirect
30. C₁₉⋊C₃	C₅×Dic₁₃	direct (N × H)
31. Dic₁₃	C₅×C₁₉⋊C₃	direct (N × H)
37. C₁₉	C₃×C₅×Dic₁₃	semidirect
39. C₁₃	C₄×C₅×C₁₉⋊C₃	semidirect
43. C₅	Dic₁₃×C₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₃×C₁₉⋊C₃	2
C₅×C₁₉×Dic₁₃	3
Dic₁₃×C₁₉⋊C₃	5
C₄×C₅×C₁₉⋊C₃	13
C₃×C₅×Dic₁₃	19

Subgroups — C5×Dic13×C19⋊C3 #28414739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₁₃×C₁₉⋊C₃ #28414739