Subgroups — C₂×C₁₁×D₃₁⋊C₂₅ #46801949

Order 34100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₃₁⋊C₂₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₃₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₃₁⋊C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₁×D₃₁	C₅	1	1	yes	maximal, characteristic
5	C₅×C₁₁×D₃₁	C₂×C₅	1	2	yes	—
6	C₂×C₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₂×D₃₁⋊C₂₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₃₁	C₂²×C₅	1	1	yes	characteristic
9	C₂×C₃₁⋊C₂₅	C₂×C₁₁	1	1	yes	characteristic, complemented
10	D₃₁⋊C₂₅	C₂×C₁₁	1	2	yes	direct product factor
11	C₂×C₁₁×D₃₁	C₂₅	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₁×C₂₅	—	31	1	no	maximal, Hall
13	C₃₁⋊C₂₅	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁×C₃₁	C₂×C₂₅	1	1	yes	characteristic, complemented
15	C₁₁×D₃₁	C₂×C₂₅	1	2	yes	complemented
16	C₂×C₅×D₃₁	C₅×C₁₁	1	1	yes	characteristic
17	C₂×C₁₁×C₂₅	—	31	2	no	—
18	C₂×C₁₁×C₂₅	—	31	1	no	—
19	C₁₁×C₃₁	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic
21	C₅×D₃₁	C₂×C₅×C₁₁	1	2	yes	—
22	C₁₁×C₂₅	—	31	1	no	Hall
23	C₂²×C₅×C₁₁	—	31	1	no	—
24	C₅×C₃₁	C₂²×C₅×C₁₁	1	1	yes	characteristic
25	C₂×D₃₁	C₁₁×C₂₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₁₁	—	31	2	no	—
27	C₂×C₅×C₁₁	D₃₁⋊C₅	1	1	yes	characteristic
28	C₂²×C₂₅	—	31	1	no	Hall
29	C₂×C₃₁	C₂×C₁₁×C₂₅	1	1	yes	characteristic, complemented
30	D₃₁	C₂×C₁₁×C₂₅	1	2	yes	complemented
31	C₅×C₁₁	C₂×D₃₁⋊C₅	1	1	yes	characteristic
32	C₂×C₂₅	—	31	2	no	—
33	C₂×C₂₅	—	31	1	no	—
34	C₂²×C₁₁	—	31	1	no	Hall
35	C₃₁	C₂²×C₁₁×C₂₅	1	1	yes	characteristic, complemented, Sylow
36	C₂₅	—	31	1	no	Sylow
37	C₂×C₁₁	—	31	2	no	—
38	C₂×C₁₁	D₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor
39	C₂²×C₅	—	31	1	no	—
40	C₁₁	C₂×D₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	—	31	2	no	—
42	C₂×C₅	C₁₁×D₃₁⋊C₅	1	1	yes	characteristic
43	C₅	C₂×C₁₁×D₃₁⋊C₅	1	1	yes	characteristic
44	C₂²	—	31	1	no	Sylow
45	C₂	—	31	2	no	—
46	C₂	C₁₁×D₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	D₃₁⋊C₅
commutator, hypocenter	C₃₁	C₂²×C₁₁×C₂₅
Frattini	C₅	C₂×C₁₁×D₃₁⋊C₅
Fitting, socle	C₂×C₅×C₁₁×C₃₁	C₂×C₅
prime radical	C₂×C₅×C₁₁×D₃₁	C₅
cosocle	C₅×C₃₁	C₂²×C₅×C₁₁
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₃₁⋊C₂₅	C₂	direct (N × H)
2. C₂×C₁₁×C₃₁⋊C₂₅	C₂	semidirect
3. C₁₁×C₃₁⋊C₂₅	C₂²	semidirect
7. C₂×D₃₁⋊C₂₅	C₁₁	direct (N × H)
9. C₂×C₃₁⋊C₂₅	C₂×C₁₁	semidirect
10. D₃₁⋊C₂₅	C₂×C₁₁	direct (N × H)
11. C₂×C₁₁×D₃₁	C₂₅	semidirect
13. C₃₁⋊C₂₅	C₂²×C₁₁	semidirect
14. C₂×C₁₁×C₃₁	C₂×C₂₅	semidirect
15. C₁₁×D₃₁	C₂×C₂₅	semidirect
19. C₁₁×C₃₁	C₂²×C₂₅	semidirect
25. C₂×D₃₁	C₁₁×C₂₅	semidirect
29. C₂×C₃₁	C₂×C₁₁×C₂₅	semidirect
30. D₃₁	C₂×C₁₁×C₂₅	semidirect
35. C₃₁	C₂²×C₁₁×C₂₅	semidirect
38. C₂×C₁₁	D₃₁⋊C₂₅	direct (N × H)
40. C₁₁	C₂×D₃₁⋊C₂₅	direct (N × H)
46. C₂	C₁₁×D₃₁⋊C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₃₁⋊C₂₅	2
C₂×C₁₁×C₃₁⋊C₂₅	2
C₂×C₅×C₁₁×D₃₁	5
C₂×D₃₁⋊C₂₅	11
C₂²×C₁₁×C₂₅	31

Subgroups — C2×C11×D31⋊C25 #46801949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₃₁⋊C₂₅ #46801949