Subgroups — C₅×C₁₁⋊C₅×Dic₃₁ #46802011

Order 34100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊C₅×Dic₃₁	C₅	1	5	yes	maximal, direct product factor
4	C₅×C₁₁×Dic₃₁	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×C₁₁⋊C₅	C₂×C₅	1	5	yes	—
6	C₂×C₅×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₅²×Dic₃₁	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented
9	C₃₁×C₁₁⋊C₅	C₄×C₅	1	5	yes	complemented
10	C₂×C₅²×C₃₁	—	11	1	no	—
11	C₁₁×Dic₃₁	C₅²	1	1	yes	characteristic, complemented, Hall
12	C₄×C₅×C₁₁⋊C₅	—	31	1	no	maximal, Hall
13	C₅²×C₃₁	—	11	1	no	Hall
14	C₂×C₁₁×C₃₁	C₂×C₅²	1	1	yes	characteristic
15	C₅×Dic₃₁	—	11	5	no	—
16	C₅×Dic₃₁	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
17	C₂×C₅×C₁₁⋊C₅	D₃₁	1	1	yes	characteristic
18	C₁₁×C₃₁	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₃₁	—	11	5	no	—
20	C₂×C₅×C₃₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic
21	C₅×C₁₁⋊C₅	Dic₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₄×C₅×C₁₁	—	31	1	no	—
23	C₄×C₁₁⋊C₅	—	31	5	no	—
24	C₅×C₃₁	—	11	5	no	—
25	C₅×C₃₁	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented
26	Dic₃₁	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₁₁	C₅×D₃₁	1	1	yes	characteristic
28	C₂×C₁₁⋊C₅	C₅×D₃₁	1	5	yes	—
29	C₄×C₅²	—	341	1	no	Hall
30	C₂×C₃₁	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic
31	C₅×C₁₁	C₅×Dic₃₁	1	1	yes	characteristic, complemented
32	C₁₁⋊C₅	C₅×Dic₃₁	1	5	yes	direct product factor
33	C₂×C₅²	—	11	1	no	—
34	C₄×C₁₁	—	31	1	no	Hall
35	C₃₁	C₄×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
36	C₅²	—	11	1	no	Sylow
37	C₂×C₁₁	C₅²×D₃₁	1	1	yes	characteristic
38	C₄×C₅	—	31	1	no	—
39	C₄×C₅	—	341	5	no	—
40	C₁₁	C₅²×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	11	5	no	—
42	C₂×C₅	C₁₁⋊C₅×D₃₁	1	1	yes	characteristic
43	C₅	—	11	5	no	—
44	C₅	C₁₁⋊C₅×Dic₃₁	1	1	yes	characteristic, direct product factor
45	C₄	—	31	1	no	Sylow
46	C₂	C₅×C₁₁⋊C₅×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₁₁⋊C₅×D₃₁
commutator, hypocenter	C₁₁×C₃₁	C₄×C₅²
Frattini	C₂	C₅×C₁₁⋊C₅×D₃₁
Fitting, socle	C₂×C₅×C₁₁×C₃₁	C₂×C₅
prime radical	C₂×C₅×C₃₁×C₁₁⋊C₅	C₂
cosocle	C₂×C₁₁×C₃₁	C₂×C₅²
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₃₁×C₁₁⋊C₅	C₄	semidirect
3. C₁₁⋊C₅×Dic₃₁	C₅	direct (N × H)
4. C₅×C₁₁×Dic₃₁	C₅	semidirect
8. C₅×C₁₁×C₃₁	C₄×C₅	semidirect
9. C₃₁×C₁₁⋊C₅	C₄×C₅	semidirect
11. C₁₁×Dic₃₁	C₅²	semidirect
16. C₅×Dic₃₁	C₁₁⋊C₅	direct (N × H)
18. C₁₁×C₃₁	C₄×C₅²	semidirect
21. C₅×C₁₁⋊C₅	Dic₃₁	direct (N × H)
25. C₅×C₃₁	C₄×C₁₁⋊C₅	semidirect
26. Dic₃₁	C₅×C₁₁⋊C₅	direct (N × H)
31. C₅×C₁₁	C₅×Dic₃₁	semidirect
32. C₁₁⋊C₅	C₅×Dic₃₁	direct (N × H)
35. C₃₁	C₄×C₅×C₁₁⋊C₅	semidirect
40. C₁₁	C₅²×Dic₃₁	semidirect
44. C₅	C₁₁⋊C₅×Dic₃₁	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×C₃₁×C₁₁⋊C₅	2
C₁₁⋊C₅×Dic₃₁	5
C₅×C₁₁×Dic₃₁	5
C₅²×Dic₃₁	11
C₄×C₅×C₁₁⋊C₅	31

Subgroups — C5×C11⋊C5×Dic31 #46802011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁⋊C₅×Dic₃₁ #46802011