Subgroups — C₁₃×C₁₉×#3874 #49150239

Order 37050.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₅×C₁₃×C₁₉	—	3	1	no	maximal, Hall
3	C₅²×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₁₉×#3874	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₅×C₁₃×C₁₉	—	3	1	no	—
6	C₂×C₅×C₁₃×C₁₉	—	15	1	no	—
7	C₁₃×#3874	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	D₃×C₁₃×C₁₉	—	25	1	no	maximal, Hall
9	C₁₉×C₅²⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₅×C₁₃×C₁₉	—	3	1	no	—
11	C₅×C₁₃×C₁₉	—	3	1	no	—
12	C₁₃×C₅²⋊C₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
13	C₅×D₅×C₁₉	—	3	1	no	Hall
14	C₃×C₁₃×C₁₉	—	25	1	no	Hall
15	C₅×D₅×C₁₃	—	3	1	no	Hall
16	C₂×C₁₃×C₁₉	—	15	1	no	Hall
17	C₅²×C₁₉	D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₁₃	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₁₃×C₁₉	#3874	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₉	—	15	1	no	—
21	D₅×C₁₉	—	3	1	no	—
22	#3874	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₅×C₁₃	—	15	1	no	—
24	D₅×C₁₃	—	3	1	no	—
25	D₃×C₁₉	—	25	1	no	Hall
26	C₅×C₁₉	—	3	1	no	—
27	C₅×C₁₉	—	3	1	no	—
28	D₃×C₁₃	—	25	1	no	Hall
29	C₅²⋊C₃	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₅×C₁₃	—	3	1	no	—
31	C₅×C₁₃	—	3	1	no	—
32	C₃×C₁₉	—	25	1	no	Hall
33	C₅×D₅	—	3	1	no	Hall
34	C₃×C₁₃	—	25	1	no	Hall
35	C₂×C₁₉	—	15	1	no	Hall
36	C₂×C₁₃	—	15	1	no	Hall
37	C₅²	D₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
38	C₁₉	C₁₃×#3874	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₃	C₁₉×#3874	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₅	—	15	1	no	—
41	D₅	—	3	1	no	—
42	D₃	—	25	1	no	Hall
43	C₅	—	3	1	no	—
44	C₅	—	3	1	no	—
45	C₃	—	25	1	no	Sylow
46	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₉	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×C₅²⋊C₃	C₂	semidirect
3. C₅²×C₁₃×C₁₉	D₃	semidirect
4. C₁₉×#3874	C₁₃	direct (N × H)
7. C₁₃×#3874	C₁₉	direct (N × H)
9. C₁₉×C₅²⋊C₃	C₂×C₁₃	semidirect
12. C₁₃×C₅²⋊C₃	C₂×C₁₉	semidirect
17. C₅²×C₁₉	D₃×C₁₃	semidirect
18. C₅²×C₁₃	D₃×C₁₉	semidirect
19. C₁₃×C₁₉	#3874	direct (N × H)
22. #3874	C₁₃×C₁₉	direct (N × H)
29. C₅²⋊C₃	C₂×C₁₃×C₁₉	semidirect
37. C₅²	D₃×C₁₃×C₁₉	semidirect
38. C₁₉	C₁₃×#3874	direct (N × H)
39. C₁₃	C₁₉×#3874	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×C₅²⋊C₃	2
C₅×D₅×C₁₃×C₁₉	3
C₁₉×#3874	13
C₁₃×#3874	19
D₃×C₁₃×C₁₉	25

Subgroups — C13×C19×#3874 #49150239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₉×#3874 #49150239