Subgroups — D₅×C₁₁×D₁₄₅ #44542088

Order 31900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₅⋊D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×D₁₄₅	—	5	1	no	maximal
6	D₅×C₁₁×D₂₉	—	5	1	no	maximal
7	C₁₁×D₁₄₅	—	5	1	no	—
8	C₁₁×D₁₄₅	—	5	1	no	—
9	C₁₁×D₁₄₅	—	10	2	no	—
10	C₁₁×D₁₄₅	D₅	1	1	yes	characteristic, direct product factor
11	D₅×C₁₁×C₂₉	D₅	1	1	yes	characteristic, complemented
12	C₅×C₁₁×D₂₉	—	5	1	no	—
13	C₂×C₅×C₁₁×C₂₉	—	5	1	no	—
14	D₅×D₁₄₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₁₁×C₂₉	—	2	2	no	—
16	C₅×C₁₁×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented
17	C₅×C₁₁×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented
18	C₅⋊D₁₄₅	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₅×D₁₄₅	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₅×D₅×C₂₉	C₂×C₁₁	1	1	yes	characteristic, complemented
21	C₂×C₁₁×D₂₉	—	25	1	no	Hall
22	D₅²×C₁₁	—	29	1	no	maximal, Hall
23	C₅²×C₂₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₁×C₂₉	—	5	1	no	—
25	C₁₁×D₂₉	—	5	1	no	—
26	C₁₁×D₂₉	—	25	1	no	—
27	C₂×D₁₄₅	—	5	1	no	—
28	D₅×D₂₉	—	5	1	no	—
29	C₁₁×C₅⋊D₅	—	29	1	no	—
30	C₅×D₅×C₁₁	—	29	1	no	—
31	C₅×D₅×C₁₁	D₂₉	1	1	yes	characteristic, complemented
32	C₁₁×C₂₉	D₅²	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₂₉	—	5	1	no	—
34	D₁₄₅	—	5	1	no	—
35	D₁₄₅	—	5	1	no	—
36	D₁₄₅	—	10	2	no	—
37	D₁₄₅	D₅×C₁₁	1	1	yes	characteristic, direct product factor
38	C₅×D₂₉	—	5	1	no	—
39	D₅×C₂₉	D₅×C₁₁	1	1	yes	characteristic, complemented
40	C₅²×C₁₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	C₂×D₅×C₁₁	—	145	1	no	—
42	C₂×D₅×C₁₁	—	145	1	no	—
43	C₅×C₂₉	—	2	2	no	—
44	C₅×C₂₉	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
45	C₅×C₂₉	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
46	C₂×D₂₉	—	25	1	no	Hall
47	C₂×C₅×C₁₁	—	5	1	no	—
48	C₂×C₅×C₁₁	—	145	1	no	—
49	D₅×C₁₁	—	29	1	no	—
50	D₅×C₁₁	—	290	2	no	—
51	D₅×C₁₁	—	145	1	no	—
52	D₅×C₁₁	—	145	1	no	—
53	D₅×C₁₁	D₁₄₅	1	1	yes	characteristic, direct product factor
54	D₅²	—	29	1	no	Hall
55	C₂×C₂₉	—	5	1	no	—
56	D₂₉	—	5	1	no	—
57	D₂₉	—	25	1	no	—
58	C₅×C₁₁	—	2	2	no	—
59	C₅×C₁₁	D₅×D₂₉	1	1	yes	characteristic, complemented
60	C₅×C₁₁	C₂×D₁₄₅	1	1	yes	characteristic, complemented
61	C₅⋊D₅	—	29	1	no	—
62	C₅×D₅	—	29	1	no	—
63	C₅×D₅	C₁₁×D₂₉	1	1	yes	characteristic, complemented
64	C₂²×C₁₁	—	725	1	no	Hall
65	C₂₉	D₅²×C₁₁	1	1	yes	characteristic, complemented, Sylow
66	C₅²	C₂×C₁₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₁₁	—	5	1	no	—
68	C₂×C₁₁	—	145	1	no	—
69	C₂×C₁₁	—	725	1	no	—
70	C₂×D₅	—	145	1	no	—
71	C₂×D₅	—	145	1	no	—
72	C₁₁	D₅×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₅	—	5	1	no	—
74	C₂×C₅	—	145	1	no	—
75	D₅	—	29	1	no	—
76	D₅	—	290	2	no	—
77	D₅	—	145	1	no	—
78	D₅	—	145	1	no	—
79	D₅	C₁₁×D₁₄₅	1	1	yes	characteristic, direct product factor
80	C₅	—	2	2	no	—
81	C₅	D₅×C₁₁×D₂₉	1	1	yes	characteristic, complemented
82	C₅	C₂×C₁₁×D₁₄₅	1	1	yes	characteristic, complemented
83	C₂²	—	725	1	no	Sylow
84	C₂	—	5	1	no	—
85	C₂	—	145	1	no	—
86	C₂	—	725	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₅×D₁₄₅
commutator, cosocle, hypocenter	C₅²×C₂₉	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₂₉	C₂²
LCS	G ▷ C₅²×C₂₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×C₁₁×C₂₉	C₂	semidirect
2. C₅×C₁₁×D₁₄₅	C₂	semidirect
3. C₁₁×C₅⋊D₁₄₅	C₂	semidirect
4. C₅²×C₁₁×C₂₉	C₂²	semidirect
10. C₁₁×D₁₄₅	D₅	direct (N × H)
11. D₅×C₁₁×C₂₉	D₅	semidirect
14. D₅×D₁₄₅	C₁₁	direct (N × H)
16. C₅×C₁₁×C₂₉	C₂×D₅	semidirect
17. C₅×C₁₁×C₂₉	C₂×D₅	semidirect
18. C₅⋊D₁₄₅	C₂×C₁₁	semidirect
19. C₅×D₁₄₅	C₂×C₁₁	semidirect
20. C₅×D₅×C₂₉	C₂×C₁₁	semidirect
23. C₅²×C₂₉	C₂²×C₁₁	semidirect
31. C₅×D₅×C₁₁	D₂₉	semidirect
32. C₁₁×C₂₉	D₅²	semidirect
37. D₁₄₅	D₅×C₁₁	direct (N × H)
39. D₅×C₂₉	D₅×C₁₁	semidirect
40. C₅²×C₁₁	C₂×D₂₉	semidirect
44. C₅×C₂₉	C₂×D₅×C₁₁	semidirect
45. C₅×C₂₉	C₂×D₅×C₁₁	semidirect
53. D₅×C₁₁	D₁₄₅	direct (N × H)
59. C₅×C₁₁	D₅×D₂₉	semidirect
60. C₅×C₁₁	C₂×D₁₄₅	semidirect
63. C₅×D₅	C₁₁×D₂₉	semidirect
65. C₂₉	D₅²×C₁₁	semidirect
66. C₅²	C₂×C₁₁×D₂₉	semidirect
72. C₁₁	D₅×D₁₄₅	direct (N × H)
79. D₅	C₁₁×D₁₄₅	direct (N × H)
81. C₅	D₅×C₁₁×D₂₉	semidirect
82. C₅	C₂×C₁₁×D₁₄₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×C₁₁×C₂₉	2
C₅×C₁₁×D₁₄₅	2
C₁₁×C₅⋊D₁₄₅	2
C₂×C₁₁×D₁₄₅	5
D₅×C₁₁×D₂₉	5
D₅×D₁₄₅	11
D₅²×C₁₁	29

Subgroups — D5×C11×D145 #44542088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁×D₁₄₅ #44542088