Subgroups — C₂×C₉×D₅×C₁₂₁ #36344684

Order 21780.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅×C₁₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅×C₁₂₁	C₃	1	1	yes	maximal, characteristic
4	C₅×C₉×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₉×C₁₂₁	—	5	1	no	maximal, Hall
6	C₃×D₅×C₁₂₁	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₂₁	C₂×C₃	1	1	yes	characteristic
8	C₂×D₅×C₁₂₁	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₉×C₁₂₁	—	5	2	no	—
10	C₂×C₉×C₁₂₁	D₅	1	1	yes	characteristic, direct product factor
11	C₂×C₉×D₅×C₁₁	C₁₁	1	1	yes	maximal, characteristic
12	C₃×C₅×C₁₂₁	C₂²×C₃	1	1	yes	characteristic
13	C₂²×C₃×C₁₂₁	—	5	1	no	—
14	C₂×C₅×C₁₂₁	C₂×C₉	1	1	yes	characteristic, complemented
15	D₅×C₁₂₁	C₂×C₉	1	2	yes	direct product factor
16	C₉×C₁₂₁	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₉×C₁₁	C₂×C₁₁	1	1	yes	characteristic
18	C₉×D₅×C₁₁	C₂×C₁₁	1	2	yes	—
19	C₂×C₃×C₁₂₁	—	5	2	no	—
20	C₂×C₃×C₁₂₁	C₃×D₅	1	1	yes	characteristic
21	C₂×C₃×D₅×C₁₁	C₃×C₁₁	1	1	yes	characteristic
22	C₅×C₁₂₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
23	C₅×C₉×C₁₁	C₂²×C₁₁	1	1	yes	characteristic
24	C₂²×C₁₂₁	—	5	1	no	Hall
25	C₂²×C₉×C₁₁	—	5	1	no	—
26	C₃×C₁₂₁	C₂×C₃×D₅	1	1	yes	characteristic
27	C₂×C₃×C₅×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic
28	C₃×D₅×C₁₁	C₂×C₃×C₁₁	1	2	yes	—
29	C₂×C₁₂₁	—	5	2	no	—
30	C₂×C₁₂₁	C₉×D₅	1	1	yes	characteristic, direct product factor
31	C₂×D₅×C₁₁	C₉×C₁₁	1	1	yes	characteristic
32	C₂×C₉×C₁₁	—	5	2	no	—
33	C₂×C₉×C₁₁	D₅×C₁₁	1	1	yes	characteristic
34	C₂×C₉×D₅	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₅×C₁₁	C₂²×C₃×C₁₁	1	1	yes	characteristic
36	C₂²×C₃×C₁₁	—	5	1	no	—
37	C₁₂₁	C₂×C₉×D₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₅×C₁₁	C₂×C₉×C₁₁	1	1	yes	characteristic
39	D₅×C₁₁	C₂×C₉×C₁₁	1	2	yes	—
40	C₉×C₁₁	C₂×D₅×C₁₁	1	1	yes	characteristic
41	C₂×C₅×C₉	C₂×C₁₂₁	1	1	yes	characteristic, complemented
42	C₉×D₅	C₂×C₁₂₁	1	2	yes	direct product factor
43	C₂×C₃×C₁₁	—	5	2	no	—
44	C₂×C₃×C₁₁	C₃×D₅×C₁₁	1	1	yes	characteristic
45	C₂×C₃×D₅	C₃×C₁₂₁	1	1	yes	characteristic
46	C₅×C₁₁	C₂²×C₉×C₁₁	1	1	yes	characteristic
47	C₅×C₉	C₂²×C₁₂₁	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₁₁	—	5	1	no	—
49	C₂²×C₉	—	5	1	no	Hall
50	C₃×C₁₁	C₂×C₃×D₅×C₁₁	1	1	yes	characteristic
51	C₂×C₃×C₅	C₂×C₃×C₁₂₁	1	1	yes	characteristic
52	C₃×D₅	C₂×C₃×C₁₂₁	1	2	yes	—
53	C₂×C₁₁	—	5	2	no	—
54	C₂×C₁₁	C₉×D₅×C₁₁	1	1	yes	characteristic
55	C₂×D₅	C₉×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
56	C₂×C₉	—	5	2	no	—
57	C₂×C₉	D₅×C₁₂₁	1	1	yes	characteristic, direct product factor
58	C₃×C₅	C₂²×C₃×C₁₂₁	1	1	yes	characteristic
59	C₂²×C₃	—	5	1	no	—
60	C₁₁	C₂×C₉×D₅×C₁₁	1	1	yes	characteristic
61	C₂×C₅	C₂×C₉×C₁₂₁	1	1	yes	characteristic, complemented
62	D₅	C₂×C₉×C₁₂₁	1	2	yes	direct product factor
63	C₉	C₂×D₅×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	5	2	no	—
65	C₂×C₃	C₃×D₅×C₁₂₁	1	1	yes	characteristic
66	C₅	C₂²×C₉×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
67	C₂²	—	5	1	no	Sylow
68	C₃	C₂×C₃×D₅×C₁₂₁	1	1	yes	characteristic
69	C₂	—	5	2	no	—
70	C₂	C₉×D₅×C₁₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₂₁	D₅
commutator, hypocenter	C₅	C₂²×C₉×C₁₂₁
Frattini	C₃×C₁₁	C₂×C₃×D₅×C₁₁
Fitting	C₂×C₅×C₉×C₁₂₁	C₂
socle	C₂×C₃×C₅×C₁₁	C₂×C₃×C₁₁
prime radical	C₂×C₃×D₅×C₁₁	C₃×C₁₁
cosocle	C₃×C₅×C₁₁	C₂²×C₃×C₁₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₉×C₁₂₁

Complements

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

N	H ≅ G/N	type
1. C₉×D₅×C₁₂₁	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₂₁	C₂	semidirect
4. C₅×C₉×C₁₂₁	C₂²	semidirect
8. C₂×D₅×C₁₂₁	C₉	direct (N × H)
10. C₂×C₉×C₁₂₁	D₅	direct (N × H)
14. C₂×C₅×C₁₂₁	C₂×C₉	semidirect
15. D₅×C₁₂₁	C₂×C₉	direct (N × H)
16. C₉×C₁₂₁	C₂×D₅	direct (N × H)
22. C₅×C₁₂₁	C₂²×C₉	semidirect
30. C₂×C₁₂₁	C₉×D₅	direct (N × H)
34. C₂×C₉×D₅	C₁₂₁	direct (N × H)
37. C₁₂₁	C₂×C₉×D₅	direct (N × H)
41. C₂×C₅×C₉	C₂×C₁₂₁	semidirect
42. C₉×D₅	C₂×C₁₂₁	direct (N × H)
47. C₅×C₉	C₂²×C₁₂₁	semidirect
55. C₂×D₅	C₉×C₁₂₁	direct (N × H)
57. C₂×C₉	D₅×C₁₂₁	direct (N × H)
61. C₂×C₅	C₂×C₉×C₁₂₁	semidirect
62. D₅	C₂×C₉×C₁₂₁	direct (N × H)
63. C₉	C₂×D₅×C₁₂₁	direct (N × H)
66. C₅	C₂²×C₉×C₁₂₁	semidirect
70. C₂	C₉×D₅×C₁₂₁	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×D₅×C₁₂₁	2
C₂×C₅×C₉×C₁₂₁	2
C₂×C₃×D₅×C₁₂₁	3
C₂²×C₉×C₁₂₁	5
C₂×C₉×D₅×C₁₁	11

Subgroups — C2×C9×D5×C121 #36344684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₅×C₁₂₁ #36344684