Subgroups — C₂×D₅×C₁₁²⋊C₉ #36344909

Order 21780.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₁²⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₅×C₁₁²	C₃	1	1	yes	maximal, characteristic
4	C₅×C₁₁²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₁₁²⋊C₉	—	5	1	no	maximal, Hall
6	C₃×D₅×C₁₁²	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₁²	C₂×C₃	1	1	yes	characteristic
8	C₂×D₅×C₁₁²	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁²⋊C₉	—	5	2	no	—
10	C₂×C₁₁²⋊C₉	D₅	1	1	yes	characteristic, direct product factor
11	C₃×C₅×C₁₁²	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃×C₁₁²	—	5	1	no	—
13	C₂×C₅×C₁₁²	C₂×C₉	1	1	yes	characteristic, complemented
14	D₅×C₁₁²	C₂×C₉	1	2	yes	complemented
15	C₁₁²⋊C₉	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₁₁²	—	5	2	no	—
17	C₂×C₃×C₁₁²	C₃×D₅	1	1	yes	characteristic
18	C₂×C₃×D₅×C₁₁	—	3	4	no	—
19	C₅×C₁₁²	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₁₁²	—	5	1	no	Hall
21	C₃×C₁₁²	C₂×C₃×D₅	1	1	yes	characteristic
22	C₂×C₃×C₅×C₁₁	—	3	4	no	—
23	C₃×D₅×C₁₁	—	3	8	no	—
24	C₂×C₁₁²	—	5	2	no	—
25	C₂×C₁₁²	C₉×D₅	1	1	yes	characteristic, complemented
26	C₂×D₅×C₁₁	—	3	4	no	—
27	C₂×C₉×D₅	—	121	1	no	maximal, Hall
28	C₃×C₅×C₁₁	—	3	4	no	—
29	C₂²×C₃×C₁₁	—	15	4	no	—
30	C₁₁²	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅×C₁₁	—	3	4	no	—
32	D₅×C₁₁	—	3	8	no	—
33	C₂×C₅×C₉	—	121	1	no	—
34	C₉×D₅	—	121	2	no	—
35	C₂×C₃×C₁₁	—	3	4	no	—
36	C₂×C₃×C₁₁	—	15	8	no	—
37	C₂×C₃×D₅	C₁₁²⋊C₃	1	1	yes	characteristic
38	C₅×C₁₁	—	3	4	no	—
39	C₅×C₉	—	121	1	no	Hall
40	C₂²×C₁₁	—	15	4	no	—
41	C₂²×C₉	—	605	1	no	Hall
42	C₃×C₁₁	—	3	4	no	—
43	C₂×C₃×C₅	C₂×C₁₁²⋊C₃	1	1	yes	characteristic
44	C₃×D₅	C₂×C₁₁²⋊C₃	1	2	yes	—
45	C₂×C₁₁	—	3	4	no	—
46	C₂×C₁₁	—	15	8	no	—
47	C₂×D₅	C₁₁²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₉	—	605	2	no	—
49	C₂×C₉	—	121	1	no	—
50	C₃×C₅	C₂²×C₁₁²⋊C₃	1	1	yes	characteristic
51	C₂²×C₃	—	5	1	no	—
52	C₁₁	—	3	4	no	—
53	C₂×C₅	C₂×C₁₁²⋊C₉	1	1	yes	characteristic, complemented
54	D₅	C₂×C₁₁²⋊C₉	1	2	yes	direct product factor
55	C₉	—	121	1	no	Sylow
56	C₂×C₃	—	5	2	no	—
57	C₂×C₃	D₅×C₁₁²⋊C₃	1	1	yes	characteristic
58	C₅	C₂²×C₁₁²⋊C₉	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5	1	no	Sylow
60	C₃	C₂×D₅×C₁₁²⋊C₃	1	1	yes	characteristic
61	C₂	—	5	2	no	—
62	C₂	D₅×C₁₁²⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅×C₁₁²⋊C₃
commutator, hypocenter	C₅×C₁₁²	C₂²×C₉
Frattini	C₃	C₂×D₅×C₁₁²⋊C₃
Fitting, socle	C₂×C₃×C₅×C₁₁²	C₂×C₃
prime radical	C₂×C₃×D₅×C₁₁²	C₃
cosocle	C₃×C₅×C₁₁²	C₂²×C₃
LCS	G ▷ C₅×C₁₁²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₁²⋊C₉	C₂	semidirect
2. D₅×C₁₁²⋊C₉	C₂	direct (N × H)
4. C₅×C₁₁²⋊C₉	C₂²	semidirect
8. C₂×D₅×C₁₁²	C₉	semidirect
10. C₂×C₁₁²⋊C₉	D₅	direct (N × H)
13. C₂×C₅×C₁₁²	C₂×C₉	semidirect
14. D₅×C₁₁²	C₂×C₉	semidirect
15. C₁₁²⋊C₉	C₂×D₅	direct (N × H)
19. C₅×C₁₁²	C₂²×C₉	semidirect
25. C₂×C₁₁²	C₉×D₅	semidirect
30. C₁₁²	C₂×C₉×D₅	semidirect
47. C₂×D₅	C₁₁²⋊C₉	direct (N × H)
53. C₂×C₅	C₂×C₁₁²⋊C₉	semidirect
54. D₅	C₂×C₁₁²⋊C₉	direct (N × H)
58. C₅	C₂²×C₁₁²⋊C₉	semidirect
62. C₂	D₅×C₁₁²⋊C₉	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×C₁₁²⋊C₉	2
D₅×C₁₁²⋊C₉	2
C₂×C₃×D₅×C₁₁²	3
C₂²×C₁₁²⋊C₉	5
C₂×C₉×D₅	121

Subgroups — C2×D5×C112⋊C9 #36344909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₁₁²⋊C₉ #36344909