Subgroups — C₁₁×D₉×D₂₅ #23754753

Order 9900.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₉×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₁×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₁×D₂₅	—	3	1	no	maximal
5	C₉×C₁₁×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×C₁₁×D₉	—	5	1	no	maximal
7	C₁₁×D₇₅	—	3	1	no	—
8	D₃×C₁₁×C₂₅	—	3	1	no	—
9	C₃×C₁₁×D₂₅	D₃	1	1	yes	characteristic
10	C₂×C₁₁×D₂₅	—	9	1	no	Hall
11	C₁₁×D₄₅	—	5	1	no	—
12	C₅×C₁₁×D₉	D₅	1	1	yes	characteristic
13	C₉×D₅×C₁₁	—	5	1	no	—
14	D₉×D₂₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₁₁×C₂₅	C₂×D₃	1	1	yes	characteristic
16	D₃×D₅×C₁₁	—	15	1	no	—
17	C₂×C₁₁×C₂₅	—	9	1	no	—
18	C₁₁×D₂₅	—	9	1	no	—
19	C₁₁×D₂₅	D₉	1	1	yes	characteristic, direct product factor
20	C₅×C₉×C₁₁	C₂×D₅	1	1	yes	characteristic
21	D₂₂₅	C₂×C₁₁	1	1	yes	characteristic, complemented
22	C₉×D₂₅	C₂×C₁₁	1	1	yes	characteristic, complemented
23	D₉×C₂₅	C₂×C₁₁	1	1	yes	characteristic, complemented
24	C₂×C₁₁×D₉	—	25	1	no	Hall
25	C₁₁×D₁₅	—	15	1	no	—
26	C₅×D₃×C₁₁	—	3	1	no	—
27	C₃×D₅×C₁₁	—	5	1	no	—
28	D₃×D₂₅	—	3	1	no	—
29	C₁₁×C₂₅	C₂×D₉	1	1	yes	characteristic, complemented, Hall
30	C₉×C₂₅	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
31	C₂×D₅×C₁₁	—	45	1	no	—
32	C₂×C₉×C₁₁	—	25	1	no	—
33	C₁₁×D₉	—	25	1	no	—
34	C₁₁×D₉	D₂₅	1	1	yes	characteristic, direct product factor
35	D₅×D₉	—	5	1	no	—
36	C₃×C₅×C₁₁	D₃×D₅	1	1	yes	characteristic
37	D₇₅	—	3	1	no	—
38	C₃×D₂₅	D₃×C₁₁	1	1	yes	characteristic
39	D₃×C₂₅	—	3	1	no	—
40	C₂×D₃×C₁₁	—	75	1	no	—
41	C₂×C₅×C₁₁	—	9	1	no	—
42	D₅×C₁₁	—	5	1	no	—
43	D₅×C₁₁	—	45	1	no	—
44	C₂×D₂₅	—	9	1	no	Hall
45	C₉×C₁₁	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
46	D₄₅	—	5	1	no	—
47	C₉×D₅	—	5	1	no	—
48	C₅×D₉	D₅×C₁₁	1	1	yes	characteristic
49	C₃×C₂₅	C₂×D₃×C₁₁	1	1	yes	characteristic
50	C₂×C₃×C₁₁	—	25	1	no	—
51	D₃×C₁₁	—	3	1	no	—
52	D₃×C₁₁	—	75	1	no	—
53	D₃×D₅	—	15	1	no	—
54	C₅×C₁₁	D₅×D₉	1	1	yes	characteristic
55	C₂×C₂₅	—	9	1	no	—
56	D₂₅	—	9	1	no	—
57	D₂₅	C₁₁×D₉	1	1	yes	characteristic, direct product factor
58	C₅×C₉	C₂×D₅×C₁₁	1	1	yes	characteristic
59	C₂²×C₁₁	—	225	1	no	Hall
60	C₂×D₉	—	25	1	no	Hall
61	C₃×C₁₁	D₃×D₂₅	1	1	yes	characteristic
62	D₁₅	—	15	1	no	—
63	C₃×D₅	—	5	1	no	—
64	C₅×D₃	—	3	1	no	—
65	C₂₅	C₂×C₁₁×D₉	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₁₁	—	9	1	no	—
67	C₂×C₁₁	—	25	1	no	—
68	C₂×C₁₁	—	225	1	no	—
69	C₂×D₅	—	45	1	no	—
70	C₂×C₉	—	25	1	no	—
71	D₉	—	25	1	no	—
72	D₉	C₁₁×D₂₅	1	1	yes	characteristic, direct product factor
73	C₃×C₅	D₃×D₅×C₁₁	1	1	yes	characteristic
74	C₂×D₃	—	75	1	no	—
75	C₁₁	D₉×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂×C₅	—	9	1	no	—
77	D₅	—	5	1	no	—
78	D₅	—	45	1	no	—
79	C₉	C₂×C₁₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	25	1	no	—
81	D₃	—	3	1	no	—
82	D₃	—	75	1	no	—
83	C₅	D₅×C₁₁×D₉	1	1	yes	characteristic
84	C₂²	—	225	1	no	Sylow
85	C₃	D₃×C₁₁×D₂₅	1	1	yes	characteristic
86	C₂	—	9	1	no	—
87	C₂	—	25	1	no	—
88	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₉×D₂₅
commutator, cosocle, hypocenter	C₉×C₂₅	C₂²×C₁₁
Frattini	C₃×C₅	D₃×D₅×C₁₁
Fitting	C₉×C₁₁×C₂₅	C₂²
socle	C₃×C₅×C₁₁	D₃×D₅
LCS	G ▷ C₉×C₂₅
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₂₂₅	C₂	semidirect
2. C₁₁×D₉×C₂₅	C₂	semidirect
3. C₉×C₁₁×D₂₅	C₂	semidirect
5. C₉×C₁₁×C₂₅	C₂²	semidirect
14. D₉×D₂₅	C₁₁	direct (N × H)
19. C₁₁×D₂₅	D₉	direct (N × H)
21. D₂₂₅	C₂×C₁₁	semidirect
22. C₉×D₂₅	C₂×C₁₁	semidirect
23. D₉×C₂₅	C₂×C₁₁	semidirect
29. C₁₁×C₂₅	C₂×D₉	semidirect
30. C₉×C₂₅	C₂²×C₁₁	semidirect
34. C₁₁×D₉	D₂₅	direct (N × H)
45. C₉×C₁₁	C₂×D₂₅	semidirect
57. D₂₅	C₁₁×D₉	direct (N × H)
65. C₂₅	C₂×C₁₁×D₉	semidirect
72. D₉	C₁₁×D₂₅	direct (N × H)
75. C₁₁	D₉×D₂₅	direct (N × H)
79. C₉	C₂×C₁₁×D₂₅	semidirect

Subgroups — C11×D9×D25 #23754753

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×D₉×D₂₅ #23754753