Subgroups — D₃×C₁₁×D₃₁⋊C₅ #35205708

Order 20460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃⋊(D₃₁⋊C₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₁×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₃₁⋊C₅	—	3	1	no	maximal, Hall
5	C₃×C₁₁×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₁×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₁₁×D₃₁⋊C₅	—	3	1	no	—
8	C₁₁×D₃₁⋊C₅	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₁₁×ΓL(1,𝔽₃₂)	—	3	1	no	—
10	C₁₁×D₉₃	C₂×C₅	1	1	yes	characteristic, complemented
11	D₃×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₁₁×D₃₁	C₂×C₅	1	1	yes	characteristic, complemented
13	D₃×D₃₁⋊C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₁₁×ΓL(1,𝔽₃₂)	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×D₃₁	—	3	1	no	Hall
16	C₃×C₁₁×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃⋊(D₃₁⋊C₅)	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₃×ΓL(1,𝔽₃₂)	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₃×D₃₁⋊C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₂×C₁₁×C₃₁	—	3	1	no	—
21	C₁₁×D₃₁	—	3	1	no	—
22	C₁₁×D₃₁	C₅×D₃	1	1	yes	characteristic, complemented
23	C₂×C₅×D₃×C₁₁	—	31	1	no	maximal, Hall
24	C₂×D₃₁⋊C₅	—	3	1	no	Hall
25	C₃×ΓL(1,𝔽₃₂)	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
26	D₃×D₃₁	C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₁₁×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₅×C₁₁	—	31	1	no	—
29	C₅×D₃×C₁₁	—	31	1	no	—
30	C₅×D₃×C₁₁	—	31	1	no	—
31	C₂×ΓL(1,𝔽₃₂)	—	3	1	no	—
32	D₃₁⋊C₅	—	3	1	no	—
33	D₃₁⋊C₅	D₃×C₁₁	1	1	yes	characteristic, direct product factor
34	C₂²×C₅×C₁₁	—	93	1	no	Hall
35	D₉₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
36	C₃×D₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
37	D₃×C₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
38	C₃×C₅×C₁₁	—	31	1	no	Hall
39	ΓL(1,𝔽₃₂)	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃×C₁₁	—	31	1	no	Hall
41	C₂×D₃₁	—	3	1	no	Hall
42	C₂×C₅×C₁₁	—	31	1	no	—
43	C₂×C₅×C₁₁	—	93	1	no	—
44	C₂×C₅×C₁₁	—	93	1	no	—
45	C₃×C₃₁	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₁	—	31	1	no	—
47	D₃×C₁₁	—	31	1	no	—
48	D₃×C₁₁	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
49	C₂×C₃₁	—	3	1	no	—
50	D₃₁	—	3	1	no	—
51	D₃₁	C₅×D₃×C₁₁	1	1	yes	characteristic, complemented
52	C₂×C₅×D₃	—	31	1	no	Hall
53	C₅×C₁₁	—	31	1	no	Hall
54	C₂²×C₁₁	—	93	1	no	Hall
55	C₃×C₁₁	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
56	C₃₁	C₂×C₅×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃×C₅	—	31	1	no	—
58	C₅×D₃	—	31	1	no	—
59	C₅×D₃	—	31	1	no	—
60	C₂×C₁₁	—	3	1	no	—
61	C₂×C₁₁	—	31	1	no	—
62	C₂×C₁₁	—	93	1	no	—
63	C₂²×C₅	—	93	1	no	Hall
64	C₃×C₅	—	31	1	no	Hall
65	C₂×D₃	—	31	1	no	Hall
66	C₁₁	D₃×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₅	—	31	1	no	—
68	C₂×C₅	—	93	1	no	—
69	C₂×C₅	—	93	1	no	—
70	C₂×C₃	—	31	1	no	—
71	D₃	—	31	1	no	—
72	D₃	C₁₁×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
73	C₅	—	31	1	no	Sylow
74	C₂²	—	93	1	no	Sylow
75	C₃	C₂×C₁₁×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	31	1	no	—
78	C₂	—	93	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₃×D₃₁⋊C₅
commutator, cosocle, hypocenter	C₃×C₃₁	C₂²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₃₁	C₂²×C₅
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₃⋊(D₃₁⋊C₅)	C₂	semidirect
2. D₃×C₁₁×ΓL(1,𝔽₃₂)	C₂	semidirect
3. C₃×C₁₁×D₃₁⋊C₅	C₂	semidirect
5. C₃×C₁₁×ΓL(1,𝔽₃₂)	C₂²	semidirect
6. D₃×C₁₁×D₃₁	C₅	semidirect
8. C₁₁×D₃₁⋊C₅	D₃	direct (N × H)
10. C₁₁×D₉₃	C₂×C₅	semidirect
11. D₃×C₁₁×C₃₁	C₂×C₅	semidirect
12. C₃×C₁₁×D₃₁	C₂×C₅	semidirect
13. D₃×D₃₁⋊C₅	C₁₁	direct (N × H)
14. C₁₁×ΓL(1,𝔽₃₂)	C₂×D₃	semidirect
16. C₃×C₁₁×C₃₁	C₂²×C₅	semidirect
17. C₃⋊(D₃₁⋊C₅)	C₂×C₁₁	semidirect
18. D₃×ΓL(1,𝔽₃₂)	C₂×C₁₁	semidirect
19. C₃×D₃₁⋊C₅	C₂×C₁₁	semidirect
22. C₁₁×D₃₁	C₅×D₃	semidirect
25. C₃×ΓL(1,𝔽₃₂)	C₂²×C₁₁	semidirect
26. D₃×D₃₁	C₅×C₁₁	semidirect
27. C₁₁×C₃₁	C₂×C₅×D₃	semidirect
33. D₃₁⋊C₅	D₃×C₁₁	direct (N × H)
35. D₉₃	C₂×C₅×C₁₁	semidirect
36. C₃×D₃₁	C₂×C₅×C₁₁	semidirect
37. D₃×C₃₁	C₂×C₅×C₁₁	semidirect
39. ΓL(1,𝔽₃₂)	C₂×D₃×C₁₁	semidirect
45. C₃×C₃₁	C₂²×C₅×C₁₁	semidirect
48. D₃×C₁₁	D₃₁⋊C₅	direct (N × H)
51. D₃₁	C₅×D₃×C₁₁	semidirect
55. C₃×C₁₁	C₂×D₃₁⋊C₅	semidirect
56. C₃₁	C₂×C₅×D₃×C₁₁	semidirect
66. C₁₁	D₃×D₃₁⋊C₅	direct (N × H)
72. D₃	C₁₁×D₃₁⋊C₅	direct (N × H)
75. C₃	C₂×C₁₁×D₃₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₃⋊(D₃₁⋊C₅)	2
D₃×C₁₁×ΓL(1,𝔽₃₂)	2
C₃×C₁₁×D₃₁⋊C₅	2
C₂×C₁₁×D₃₁⋊C₅	3
D₃×C₁₁×D₃₁	5
D₃×D₃₁⋊C₅	11
C₂×C₅×D₃×C₁₁	31

Subgroups — D3×C11×D31⋊C5 #35205708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₁×D₃₁⋊C₅ #35205708