Subgroups — D₅×C₁₉×D₃₁ #26044530

Order 11780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₉×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×D₃₁	—	5	1	no	maximal, Hall
6	C₂×C₁₉×C₃₁	—	5	1	no	—
7	C₁₉×D₃₁	—	5	1	no	—
8	C₁₉×D₃₁	D₅	1	1	yes	characteristic, direct product factor
9	D₅×D₃₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₁₉	—	31	1	no	maximal, Hall
12	D₁₅₅	C₂×C₁₉	1	1	yes	characteristic, complemented
13	C₅×D₃₁	C₂×C₁₉	1	1	yes	characteristic, complemented
14	D₅×C₃₁	C₂×C₁₉	1	1	yes	characteristic, complemented
15	C₂×C₅×C₁₉	—	31	1	no	—
16	D₅×C₁₉	—	31	1	no	—
17	D₅×C₁₉	D₃₁	1	1	yes	characteristic, direct product factor
18	C₅×C₃₁	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃₁	—	5	1	no	Hall
20	C₅×C₁₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₉	—	155	1	no	Hall
22	C₂×C₃₁	—	5	1	no	—
23	D₃₁	—	5	1	no	—
24	D₃₁	D₅×C₁₉	1	1	yes	characteristic, direct product factor
25	C₂×C₁₉	—	5	1	no	—
26	C₂×C₁₉	—	31	1	no	—
27	C₂×C₁₉	—	155	1	no	—
28	C₃₁	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₅	—	31	1	no	Hall
30	C₁₉	D₅×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	—	31	1	no	—
32	D₅	—	31	1	no	—
33	D₅	C₁₉×D₃₁	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₁₉×D₃₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	155	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	31	1	no	—
38	C₂	—	155	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₅×D₃₁
commutator, cosocle, hypocenter	C₅×C₃₁	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₃₁	C₂²
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₁₅₅	C₂	semidirect
2. D₅×C₁₉×C₃₁	C₂	semidirect
3. C₅×C₁₉×D₃₁	C₂	semidirect
4. C₅×C₁₉×C₃₁	C₂²	semidirect
8. C₁₉×D₃₁	D₅	direct (N × H)
9. D₅×D₃₁	C₁₉	direct (N × H)
10. C₁₉×C₃₁	C₂×D₅	semidirect
12. D₁₅₅	C₂×C₁₉	semidirect
13. C₅×D₃₁	C₂×C₁₉	semidirect
14. D₅×C₃₁	C₂×C₁₉	semidirect
17. D₅×C₁₉	D₃₁	direct (N × H)
18. C₅×C₃₁	C₂²×C₁₉	semidirect
20. C₅×C₁₉	C₂×D₃₁	semidirect
24. D₃₁	D₅×C₁₉	direct (N × H)
28. C₃₁	C₂×D₅×C₁₉	semidirect
30. C₁₉	D₅×D₃₁	direct (N × H)
33. D₅	C₁₉×D₃₁	direct (N × H)
34. C₅	C₂×C₁₉×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₁₅₅	2
D₅×C₁₉×C₃₁	2
C₅×C₁₉×D₃₁	2
C₂×C₁₉×D₃₁	5
D₅×D₃₁	19
C₂×D₅×C₁₉	31

Subgroups — D5×C19×D31 #26044530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₉×D₃₁ #26044530