Subgroups — C₂×C₉×C₃₁×C₅⋊D₅ #42124589

Order 27900.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁×C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₃₁×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic
4	C₅²×C₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₅×C₃₁	—	5	6	no	maximal
6	C₃×C₃₁×C₅⋊D₅	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃₁×C₅⋊D₅	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×D₅×C₃₁	—	5	12	no	—
10	C₂×C₅×C₉×C₃₁	D₅	1	6	yes	complemented
11	C₃×C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×D₅×C₃₁	—	5	6	no	—
13	C₂×C₅²×C₃₁	C₂×C₉	1	1	yes	characteristic, complemented
14	C₃₁×C₅⋊D₅	C₂×C₉	1	2	yes	direct product factor
15	C₅×C₉×C₃₁	C₂×D₅	1	6	yes	complemented
16	C₂²×C₉×C₃₁	—	25	1	no	Hall
17	C₂×C₃×C₅×C₃₁	C₃×D₅	1	6	yes	—
18	C₃×D₅×C₃₁	—	5	12	no	—
19	C₂×C₉×C₅⋊D₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₅²×C₃₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×D₅×C₃₁	—	5	6	no	—
22	C₂×C₉×C₃₁	—	25	2	no	—
23	C₂×C₉×C₃₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor
24	C₃×C₅×C₃₁	C₂×C₃×D₅	1	6	yes	—
25	C₂×C₅²×C₉	C₂×C₃₁	1	1	yes	characteristic, complemented
26	C₉×C₅⋊D₅	C₂×C₃₁	1	2	yes	direct product factor
27	C₂²×C₃×C₃₁	—	25	1	no	—
28	C₂×C₅×C₃₁	C₉×D₅	1	6	yes	complemented
29	D₅×C₃₁	—	5	12	no	—
30	C₂×C₃×C₅⋊D₅	C₃×C₃₁	1	1	yes	characteristic
31	C₉×C₃₁	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
32	C₅²×C₉	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₃₁	—	25	2	no	—
34	C₂×C₃×C₃₁	C₃×C₅⋊D₅	1	1	yes	characteristic
35	C₂×C₉×D₅	—	5	6	no	—
36	C₅×C₃₁	C₂×C₉×D₅	1	6	yes	complemented
37	C₂×C₃×C₅²	C₂×C₃×C₃₁	1	1	yes	characteristic
38	C₃×C₅⋊D₅	C₂×C₃×C₃₁	1	2	yes	—
39	C₂²×C₃₁	—	25	1	no	Hall
40	C₂×C₅⋊D₅	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
41	C₃×C₃₁	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic
42	C₂×C₅×C₉	D₅×C₃₁	1	6	yes	complemented
43	C₉×D₅	—	5	12	no	—
44	C₃×C₅²	C₂²×C₃×C₃₁	1	1	yes	characteristic
45	C₂×C₃₁	—	25	2	no	—
46	C₂×C₃₁	C₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
47	C₂×C₃×D₅	—	5	6	no	—
48	C₂×C₅²	C₂×C₉×C₃₁	1	1	yes	characteristic, complemented
49	C₅⋊D₅	C₂×C₉×C₃₁	1	2	yes	direct product factor
50	C₅×C₉	C₂×D₅×C₃₁	1	6	yes	complemented
51	C₂²×C₉	—	25	1	no	Hall
52	C₃₁	C₂×C₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₃×C₅	C₃×D₅×C₃₁	1	6	yes	—
54	C₃×D₅	—	5	12	no	—
55	C₅²	C₂²×C₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₅	—	5	6	no	—
57	C₂×C₉	—	25	2	no	—
58	C₂×C₉	C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor
59	C₃×C₅	C₂×C₃×D₅×C₃₁	1	6	yes	—
60	C₂²×C₃	—	25	1	no	—
61	C₂×C₅	C₉×D₅×C₃₁	1	6	yes	complemented
62	D₅	—	5	12	no	—
63	C₉	C₂×C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	25	2	no	—
65	C₂×C₃	C₃×C₃₁×C₅⋊D₅	1	1	yes	characteristic
66	C₅	C₂×C₉×D₅×C₃₁	1	6	yes	complemented
67	C₂²	—	25	1	no	Sylow
68	C₃	C₂×C₃×C₃₁×C₅⋊D₅	1	1	yes	characteristic
69	C₂	—	25	2	no	—
70	C₂	C₉×C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉×C₃₁	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₉×C₃₁
Frattini	C₃	C₂×C₃×C₃₁×C₅⋊D₅
Fitting	C₂×C₅²×C₉×C₃₁	C₂
socle	C₂×C₃×C₅²×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₃₁×C₅⋊D₅	C₃
cosocle	C₃×C₅²	C₂²×C₃×C₃₁
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₉×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₉×C₃₁×C₅⋊D₅	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₃₁	C₂	semidirect
4. C₅²×C₉×C₃₁	C₂²	semidirect
8. C₂×C₃₁×C₅⋊D₅	C₉	direct (N × H)
10. C₂×C₅×C₉×C₃₁	D₅	semidirect
13. C₂×C₅²×C₃₁	C₂×C₉	semidirect
14. C₃₁×C₅⋊D₅	C₂×C₉	direct (N × H)
15. C₅×C₉×C₃₁	C₂×D₅	semidirect
19. C₂×C₉×C₅⋊D₅	C₃₁	direct (N × H)
20. C₅²×C₃₁	C₂²×C₉	semidirect
23. C₂×C₉×C₃₁	C₅⋊D₅	direct (N × H)
25. C₂×C₅²×C₉	C₂×C₃₁	semidirect
26. C₉×C₅⋊D₅	C₂×C₃₁	direct (N × H)
28. C₂×C₅×C₃₁	C₉×D₅	semidirect
31. C₉×C₃₁	C₂×C₅⋊D₅	direct (N × H)
32. C₅²×C₉	C₂²×C₃₁	semidirect
36. C₅×C₃₁	C₂×C₉×D₅	semidirect
40. C₂×C₅⋊D₅	C₉×C₃₁	direct (N × H)
42. C₂×C₅×C₉	D₅×C₃₁	semidirect
46. C₂×C₃₁	C₉×C₅⋊D₅	direct (N × H)
48. C₂×C₅²	C₂×C₉×C₃₁	semidirect
49. C₅⋊D₅	C₂×C₉×C₃₁	direct (N × H)
50. C₅×C₉	C₂×D₅×C₃₁	semidirect
52. C₃₁	C₂×C₉×C₅⋊D₅	direct (N × H)
55. C₅²	C₂²×C₉×C₃₁	semidirect
58. C₂×C₉	C₃₁×C₅⋊D₅	direct (N × H)
61. C₂×C₅	C₉×D₅×C₃₁	semidirect
63. C₉	C₂×C₃₁×C₅⋊D₅	direct (N × H)
66. C₅	C₂×C₉×D₅×C₃₁	semidirect
70. C₂	C₉×C₃₁×C₅⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₃₁×C₅⋊D₅	2
C₂×C₅²×C₉×C₃₁	2
C₂×C₃×C₃₁×C₅⋊D₅	3
C₂×C₉×D₅×C₃₁	5
C₂×C₉×C₅⋊D₅	31

Subgroups — C2×C9×C31×C5⋊D5 #42124589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₃₁×C₅⋊D₅ #42124589