Subgroups — D₁₁×D₂₂₅ #23754752

Order 9900.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₄₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₂₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₁₁×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₇₅	—	3	1	no	maximal
5	C₉×C₁₁×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₁×D₄₅	—	5	1	no	maximal
7	D₈₂₅	—	3	1	no	—
8	C₁₁×D₇₅	—	3	1	no	—
9	C₃×D₁₁×C₂₅	D₃	1	1	yes	characteristic
10	D₁₁×D₂₅	—	9	1	no	Hall
11	D₄₉₅	—	5	1	no	—
12	C₁₁×D₄₅	—	5	1	no	—
13	C₅×C₉×D₁₁	D₅	1	1	yes	characteristic
14	C₂×D₂₂₅	—	11	1	no	maximal, Hall
15	C₃×C₁₁×C₂₅	C₂×D₃	1	1	yes	characteristic
16	D₁₁×D₁₅	—	15	1	no	—
17	D₂₇₅	—	9	1	no	—
18	D₁₁×C₂₅	D₉	1	1	yes	characteristic, complemented
19	C₁₁×D₂₅	—	9	1	no	—
20	C₅×C₉×C₁₁	C₂×D₅	1	1	yes	characteristic
21	C₂×C₉×C₂₅	—	11	1	no	—
22	D₂₂₅	—	11	1	no	—
23	D₂₂₅	D₁₁	1	1	yes	characteristic, direct product factor
24	D₉×D₁₁	—	25	1	no	Hall
25	D₁₆₅	—	15	1	no	—
26	C₁₁×D₁₅	—	15	1	no	—
27	C₃×C₅×D₁₁	D₁₅	1	1	yes	characteristic
28	C₂×D₇₅	—	33	1	no	—
29	C₁₁×C₂₅	C₂×D₉	1	1	yes	characteristic, complemented, Hall
30	C₉×C₂₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
31	D₅×D₁₁	—	45	1	no	—
32	D₉₉	—	25	1	no	—
33	C₉×D₁₁	D₂₅	1	1	yes	characteristic, complemented
34	C₁₁×D₉	—	25	1	no	—
35	C₂×D₄₅	—	55	1	no	—
36	C₃×C₅×C₁₁	C₂×D₁₅	1	1	yes	characteristic
37	C₂×C₃×C₂₅	—	11	1	no	—
38	D₇₅	—	3	1	no	—
39	D₇₅	—	33	1	no	—
40	D₃×D₁₁	—	75	1	no	—
41	D₅₅	—	45	1	no	—
42	C₅×D₁₁	D₄₅	1	1	yes	characteristic
43	D₅×C₁₁	—	45	1	no	—
44	C₂×D₂₅	—	99	1	no	Hall
45	C₉×C₁₁	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
46	C₂×C₅×C₉	—	11	1	no	—
47	D₄₅	—	5	1	no	—
48	D₄₅	—	55	1	no	—
49	C₃×C₂₅	D₃×D₁₁	1	1	yes	characteristic
50	D₃₃	—	75	1	no	—
51	C₃×D₁₁	D₇₅	1	1	yes	characteristic
52	D₃×C₁₁	—	75	1	no	—
53	C₂×D₁₅	—	165	1	no	—
54	C₅×C₁₁	C₂×D₄₅	1	1	yes	characteristic
55	C₂×C₂₅	—	11	1	no	—
56	D₂₅	—	9	1	no	—
57	D₂₅	—	99	1	no	—
58	C₅×C₉	D₅×D₁₁	1	1	yes	characteristic
59	C₂×D₁₁	—	225	1	no	Hall
60	C₂×D₉	—	275	1	no	Hall
61	C₃×C₁₁	C₂×D₇₅	1	1	yes	characteristic
62	C₂×C₃×C₅	—	11	1	no	—
63	D₁₅	—	15	1	no	—
64	D₁₅	—	165	1	no	—
65	C₂₅	D₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₁₁	—	225	1	no	—
67	D₁₁	—	225	1	no	—
68	D₁₁	D₂₂₅	1	1	yes	characteristic, direct product factor
69	C₂×D₅	—	495	1	no	—
70	C₂×C₉	—	11	1	no	—
71	D₉	—	275	1	no	—
72	D₉	—	25	1	no	—
73	C₃×C₅	D₁₁×D₁₅	1	1	yes	characteristic
74	C₂×D₃	—	825	1	no	—
75	C₁₁	C₂×D₂₂₅	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₅	—	11	1	no	—
77	D₅	—	45	1	no	—
78	D₅	—	495	1	no	—
79	C₉	D₁₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	11	1	no	—
81	D₃	—	825	1	no	—
82	D₃	—	75	1	no	—
83	C₅	D₁₁×D₄₅	1	1	yes	characteristic
84	C₂²	—	2475	1	no	Sylow
85	C₃	D₁₁×D₇₅	1	1	yes	characteristic
86	C₂	—	11	1	no	—
87	C₂	—	2475	1	no	—
88	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₂₅	C₂²
Frattini	C₃×C₅	D₁₁×D₁₅
socle	C₃×C₅×C₁₁	C₂×D₁₅
LCS	G ▷ C₉×C₁₁×C₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₄₇₅	C₂	semidirect
2. C₁₁×D₂₂₅	C₂	semidirect
3. C₉×D₁₁×C₂₅	C₂	semidirect
5. C₉×C₁₁×C₂₅	C₂²	semidirect
18. D₁₁×C₂₅	D₉	semidirect
23. D₂₂₅	D₁₁	direct (N × H)
29. C₁₁×C₂₅	C₂×D₉	semidirect
30. C₉×C₂₅	C₂×D₁₁	semidirect
33. C₉×D₁₁	D₂₅	semidirect
45. C₉×C₁₁	C₂×D₂₅	semidirect
65. C₂₅	D₉×D₁₁	semidirect
68. D₁₁	D₂₂₅	direct (N × H)
75. C₁₁	C₂×D₂₂₅	semidirect
79. C₉	D₁₁×D₂₅	semidirect

Subgroups — D11×D225 #23754752

Conjugacy classes of subgroups

Complements

Subgroups — D₁₁×D₂₂₅ #23754752