Subgroups — C₅×D₅×D₄₃⋊C₃ #27166403

Order 12900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₅⋊(D₄₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅²×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×D₄₃⋊C₃	—	5	1	no	maximal
7	D₅×D₄₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×D₂₁₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅²×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅×C₄₃⋊C₃	—	5	1	no	—
12	C₅⋊(D₄₃⋊C₃)	C₂×C₅	1	1	yes	characteristic, complemented
13	D₅×C₄₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×D₄₃⋊C₃	—	2	2	no	—
15	C₅×D₄₃⋊C₃	—	5	1	no	—
16	C₅×D₄₃⋊C₃	D₅	1	1	yes	characteristic, direct product factor
17	C₅×D₄₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₄₃	—	5	1	no	—
20	D₅×D₄₃	C₃×C₅	1	1	yes	characteristic, complemented
21	C₅×C₄₃⋊C₃	—	2	2	no	—
22	C₅×C₄₃⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented
23	C₅×C₄₃⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented
24	C₂×D₄₃⋊C₃	—	5	1	no	Hall
25	C₂×C₅×C₄₃	—	5	1	no	—
26	D₂₁₅	C₂×C₃×C₅	1	1	yes	characteristic, complemented
27	C₅×D₄₃	—	2	2	no	—
28	C₅×D₄₃	—	5	1	no	—
29	C₅×D₄₃	C₃×D₅	1	1	yes	characteristic, complemented
30	C₅×D₄₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
31	D₅×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×D₅	—	43	1	no	maximal, Hall
33	C₂×C₄₃⋊C₃	—	5	1	no	—
34	D₄₃⋊C₃	—	5	1	no	—
35	D₄₃⋊C₃	C₅×D₅	1	1	yes	characteristic, direct product factor
36	C₅×C₄₃	—	2	2	no	—
37	C₅×C₄₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
38	C₅×C₄₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
39	C₂×D₄₃	—	5	1	no	Hall
40	C₂×C₃×C₅²	—	43	1	no	—
41	C₃×C₅×D₅	—	43	1	no	—
42	C₃×C₅×D₅	—	43	1	no	—
43	C₄₃⋊C₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
44	C₂×C₅×D₅	—	43	1	no	Hall
45	C₂×C₄₃	—	5	1	no	—
46	D₄₃	—	5	1	no	—
47	D₄₃	C₃×C₅×D₅	1	1	yes	characteristic, complemented
48	C₃×C₅²	—	43	1	no	Hall
49	C₂²×C₃×C₅	—	215	1	no	—
50	C₂×C₃×D₅	—	43	1	no	—
51	C₂×C₅²	—	43	1	no	—
52	C₅×D₅	—	43	1	no	—
53	C₅×D₅	D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
54	C₄₃	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₅	—	43	1	no	—
56	C₂×C₃×C₅	—	43	1	no	—
57	C₂×C₃×C₅	—	86	2	no	—
58	C₂×C₃×C₅	—	215	1	no	—
59	C₂×C₃×C₅	—	215	1	no	—
60	C₃×D₅	—	43	1	no	—
61	C₃×D₅	—	43	1	no	—
62	C₅²	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₅	—	215	1	no	—
64	C₂×D₅	—	43	1	no	—
65	C₃×C₅	—	43	1	no	—
66	C₃×C₅	—	43	1	no	—
67	C₃×C₅	—	86	2	no	—
68	C₂²×C₃	—	215	1	no	Hall
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	43	1	no	—
71	C₂×C₅	—	43	1	no	—
72	C₂×C₅	—	86	2	no	—
73	C₂×C₅	—	215	1	no	—
74	D₅	—	43	1	no	—
75	D₅	C₅×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	43	1	no	—
77	C₂×C₃	—	215	1	no	—
78	C₂×C₃	—	215	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₅×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
81	C₅	C₂×C₅×D₄₃⋊C₃	1	1	yes	characteristic, complemented
82	C₂²	—	215	1	no	Sylow
83	C₃	—	43	1	no	Sylow
84	C₂	—	5	1	no	—
85	C₂	—	43	1	no	—
86	C₂	—	215	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₅×D₄₃⋊C₃
commutator, cosocle, hypocenter	C₅×C₄₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₄₃	C₂²×C₃
LCS	G ▷ C₅×C₄₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×C₄₃⋊C₃	C₂	semidirect
2. C₅×C₅⋊(D₄₃⋊C₃)	C₂	semidirect
3. C₅²×D₄₃⋊C₃	C₂	semidirect
4. C₅×D₅×D₄₃	C₃	semidirect
5. C₅²×C₄₃⋊C₃	C₂²	semidirect
7. D₅×D₄₃⋊C₃	C₅	direct (N × H)
8. C₅×D₂₁₅	C₂×C₃	semidirect
9. C₅×D₅×C₄₃	C₂×C₃	semidirect
10. C₅²×D₄₃	C₂×C₃	semidirect
12. C₅⋊(D₄₃⋊C₃)	C₂×C₅	semidirect
13. D₅×C₄₃⋊C₃	C₂×C₅	semidirect
16. C₅×D₄₃⋊C₃	D₅	direct (N × H)
17. C₅×D₄₃⋊C₃	C₂×C₅	semidirect
18. C₅²×C₄₃	C₂²×C₃	semidirect
20. D₅×D₄₃	C₃×C₅	semidirect
22. C₅×C₄₃⋊C₃	C₂×D₅	semidirect
23. C₅×C₄₃⋊C₃	C₂²×C₅	semidirect
26. D₂₁₅	C₂×C₃×C₅	semidirect
29. C₅×D₄₃	C₃×D₅	semidirect
30. C₅×D₄₃	C₂×C₃×C₅	semidirect
31. D₅×C₄₃	C₂×C₃×C₅	semidirect
35. D₄₃⋊C₃	C₅×D₅	direct (N × H)
37. C₅×C₄₃	C₂×C₃×D₅	semidirect
38. C₅×C₄₃	C₂²×C₃×C₅	semidirect
43. C₄₃⋊C₃	C₂×C₅×D₅	semidirect
47. D₄₃	C₃×C₅×D₅	semidirect
53. C₅×D₅	D₄₃⋊C₃	direct (N × H)
54. C₄₃	C₂×C₃×C₅×D₅	semidirect
62. C₅²	C₂×D₄₃⋊C₃	semidirect
75. D₅	C₅×D₄₃⋊C₃	direct (N × H)
80. C₅	D₅×D₄₃⋊C₃	direct (N × H)
81. C₅	C₂×C₅×D₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×C₄₃⋊C₃	2
C₅×C₅⋊(D₄₃⋊C₃)	2
C₅²×D₄₃⋊C₃	2
C₅×D₅×D₄₃	3
C₂×C₅×D₄₃⋊C₃	5
D₅×D₄₃⋊C₃	5
C₂×C₃×C₅×D₅	43

Subgroups — C5×D5×D43⋊C3 #27166403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×D₄₃⋊C₃ #27166403