Subgroups — D₅×C₂₃×D₅₅ #38760794

Order 25300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₂₃×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×C₅⋊D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×D₅₅	—	5	1	no	maximal
6	D₅×D₁₁×C₂₃	—	5	1	no	maximal
7	C₂₃×D₅₅	—	5	1	no	—
8	C₂₃×D₅₅	—	5	1	no	—
9	C₂₃×D₅₅	—	10	2	no	—
10	C₂₃×D₅₅	D₅	1	1	yes	characteristic, direct product factor
11	D₅×C₁₁×C₂₃	D₅	1	1	yes	characteristic, complemented
12	C₅×D₁₁×C₂₃	—	5	1	no	—
13	C₂×C₅×C₁₁×C₂₃	—	5	1	no	—
14	D₅²×C₂₃	—	11	1	no	maximal, Hall
15	C₅×C₁₁×C₂₃	—	2	2	no	—
16	C₅×C₁₁×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented
17	C₅×C₁₁×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented
18	C₂₃×C₅⋊D₅	—	11	1	no	—
19	C₅×D₅×C₂₃	—	11	1	no	—
20	C₅×D₅×C₂₃	D₁₁	1	1	yes	characteristic, complemented
21	D₅×D₅₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×D₁₁×C₂₃	—	25	1	no	Hall
23	C₅²×C₂₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₅⋊D₅₅	C₂×C₂₃	1	1	yes	characteristic, complemented
25	C₅×D₅₅	C₂×C₂₃	1	1	yes	characteristic, complemented
26	C₅×D₅×C₁₁	C₂×C₂₃	1	1	yes	characteristic, complemented
27	C₂×C₁₁×C₂₃	—	5	1	no	—
28	D₁₁×C₂₃	—	5	1	no	—
29	D₁₁×C₂₃	—	25	1	no	—
30	C₂×D₅×C₂₃	—	55	1	no	—
31	C₂×D₅×C₂₃	—	55	1	no	—
32	C₅²×C₁₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
33	C₁₁×C₂₃	D₅²	1	1	yes	characteristic, complemented, Hall
34	C₂×C₅×C₂₃	—	5	1	no	—
35	C₂×C₅×C₂₃	—	55	1	no	—
36	D₅×C₂₃	—	11	1	no	—
37	D₅×C₂₃	—	55	1	no	—
38	D₅×C₂₃	—	55	1	no	—
39	D₅×C₂₃	—	110	2	no	—
40	D₅×C₂₃	D₅₅	1	1	yes	characteristic, direct product factor
41	C₂×D₅₅	—	5	1	no	—
42	D₅×D₁₁	—	5	1	no	—
43	C₅×C₂₃	—	2	2	no	—
44	C₅×C₂₃	D₅×D₁₁	1	1	yes	characteristic, complemented
45	C₅×C₂₃	C₂×D₅₅	1	1	yes	characteristic, complemented
46	C₂×C₅×C₁₁	—	5	1	no	—
47	D₅₅	—	5	1	no	—
48	D₅₅	—	5	1	no	—
49	D₅₅	—	10	2	no	—
50	D₅₅	D₅×C₂₃	1	1	yes	characteristic, direct product factor
51	C₅×D₁₁	—	5	1	no	—
52	D₅×C₁₁	D₅×C₂₃	1	1	yes	characteristic, complemented
53	D₅²	—	11	1	no	Hall
54	C₂²×C₂₃	—	275	1	no	Hall
55	C₅×C₁₁	—	2	2	no	—
56	C₅×C₁₁	C₂×D₅×C₂₃	1	1	yes	characteristic, complemented
57	C₅×C₁₁	C₂×D₅×C₂₃	1	1	yes	characteristic, complemented
58	C₅⋊D₅	—	11	1	no	—
59	C₅×D₅	—	11	1	no	—
60	C₅×D₅	D₁₁×C₂₃	1	1	yes	characteristic, complemented
61	C₂×C₂₃	—	5	1	no	—
62	C₂×C₂₃	—	275	1	no	—
63	C₂×C₂₃	—	55	1	no	—
64	C₂×D₁₁	—	25	1	no	Hall
65	C₅²	C₂×D₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
66	C₂₃	D₅×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₁₁	—	5	1	no	—
68	D₁₁	—	5	1	no	—
69	D₁₁	—	25	1	no	—
70	C₂×D₅	—	55	1	no	—
71	C₂×D₅	—	55	1	no	—
72	C₁₁	D₅²×C₂₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	5	1	no	—
74	C₂×C₅	—	55	1	no	—
75	D₅	—	11	1	no	—
76	D₅	—	55	1	no	—
77	D₅	—	55	1	no	—
78	D₅	—	110	2	no	—
79	D₅	C₂₃×D₅₅	1	1	yes	characteristic, direct product factor
80	C₅	—	2	2	no	—
81	C₅	D₅×D₁₁×C₂₃	1	1	yes	characteristic, complemented
82	C₅	C₂×C₂₃×D₅₅	1	1	yes	characteristic, complemented
83	C₂²	—	275	1	no	Sylow
84	C₂	—	5	1	no	—
85	C₂	—	275	1	no	—
86	C₂	—	55	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₅×D₅₅
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₂₃	C₂²
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×C₁₁×C₂₃	C₂	semidirect
2. C₅×C₂₃×D₅₅	C₂	semidirect
3. C₂₃×C₅⋊D₅₅	C₂	semidirect
4. C₅²×C₁₁×C₂₃	C₂²	semidirect
10. C₂₃×D₅₅	D₅	direct (N × H)
11. D₅×C₁₁×C₂₃	D₅	semidirect
16. C₅×C₁₁×C₂₃	C₂×D₅	semidirect
17. C₅×C₁₁×C₂₃	C₂×D₅	semidirect
20. C₅×D₅×C₂₃	D₁₁	semidirect
21. D₅×D₅₅	C₂₃	direct (N × H)
23. C₅²×C₂₃	C₂×D₁₁	semidirect
24. C₅⋊D₅₅	C₂×C₂₃	semidirect
25. C₅×D₅₅	C₂×C₂₃	semidirect
26. C₅×D₅×C₁₁	C₂×C₂₃	semidirect
32. C₅²×C₁₁	C₂²×C₂₃	semidirect
33. C₁₁×C₂₃	D₅²	semidirect
40. D₅×C₂₃	D₅₅	direct (N × H)
44. C₅×C₂₃	D₅×D₁₁	semidirect
45. C₅×C₂₃	C₂×D₅₅	semidirect
50. D₅₅	D₅×C₂₃	direct (N × H)
52. D₅×C₁₁	D₅×C₂₃	semidirect
56. C₅×C₁₁	C₂×D₅×C₂₃	semidirect
57. C₅×C₁₁	C₂×D₅×C₂₃	semidirect
60. C₅×D₅	D₁₁×C₂₃	semidirect
65. C₅²	C₂×D₁₁×C₂₃	semidirect
66. C₂₃	D₅×D₅₅	direct (N × H)
72. C₁₁	D₅²×C₂₃	semidirect
79. D₅	C₂₃×D₅₅	direct (N × H)
81. C₅	D₅×D₁₁×C₂₃	semidirect
82. C₅	C₂×C₂₃×D₅₅	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×C₂₃	2
C₅×C₂₃×D₅₅	2
C₂₃×C₅⋊D₅₅	2
C₂×C₂₃×D₅₅	5
D₅×D₁₁×C₂₃	5
D₅²×C₂₃	11
D₅×D₅₅	23

Subgroups — D5×C23×D55 #38760794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₂₃×D₅₅ #38760794