Subgroups — D₃×D₁₀₇₅ #27166360

Order 12900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₂₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₅×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₀₇₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₀₇₅	—	3	1	no	maximal, Hall
5	C₃×C₂₅×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₂₁₅	—	5	1	no	maximal
7	D₁₀₇₅	—	3	1	no	—
8	D₁₀₇₅	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₂₅×C₄₃	—	3	1	no	—
10	D₆₄₅	—	5	1	no	—
11	C₅×D₃×C₄₃	D₅	1	1	yes	characteristic
12	C₃×D₂₁₅	—	5	1	no	—
13	C₂₅×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₂₁₅	—	15	1	no	—
15	C₃×C₅×C₄₃	C₂×D₅	1	1	yes	characteristic
16	D₃×D₄₃	—	25	1	no	Hall
17	C₂×C₅×C₄₃	—	3	1	no	—
18	D₂₁₅	—	5	1	no	—
19	D₂₁₅	—	15	1	no	—
20	D₃×D₂₅	—	43	1	no	maximal, Hall
21	D₁₂₉	—	25	1	no	—
22	C₃×D₄₃	—	25	1	no	—
23	D₃×C₄₃	D₂₅	1	1	yes	characteristic, complemented
24	C₅×C₄₃	D₃×D₅	1	1	yes	characteristic
25	C₂×D₄₃	—	75	1	no	Hall
26	D₇₅	—	43	1	no	—
27	C₃×D₂₅	—	43	1	no	—
28	D₃×C₂₅	D₄₃	1	1	yes	characteristic, complemented
29	C₃×C₄₃	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
30	C₂×D₂₅	—	129	1	no	Hall
31	C₂×C₄₃	—	3	1	no	—
32	D₄₃	—	25	1	no	—
33	D₄₃	—	75	1	no	—
34	C₃×C₂₅	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
35	D₃×D₅	—	215	1	no	—
36	C₂×C₂₅	—	3	1	no	—
37	D₂₅	—	43	1	no	—
38	D₂₅	—	129	1	no	—
39	C₄₃	D₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
40	D₁₅	—	215	1	no	—
41	C₃×D₅	—	215	1	no	—
42	C₅×D₃	D₂₁₅	1	1	yes	characteristic
43	C₂₅	D₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	645	1	no	—
45	C₃×C₅	C₂×D₂₁₅	1	1	yes	characteristic
46	C₂×D₃	—	1075	1	no	Hall
47	C₂×C₅	—	3	1	no	—
48	D₅	—	645	1	no	—
49	D₅	—	215	1	no	—
50	C₂×C₃	—	1075	1	no	—
51	D₃	—	1075	1	no	—
52	D₃	D₁₀₇₅	1	1	yes	characteristic, direct product factor
53	C₅	D₃×D₂₁₅	1	1	yes	characteristic
54	C₂²	—	3225	1	no	Sylow
55	C₃	C₂×D₁₀₇₅	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	1075	1	no	—
58	C₂	—	3225	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₅×C₄₃	C₂²
Frattini	C₅	D₃×D₂₁₅
socle	C₃×C₅×C₄₃	C₂×D₅
LCS	G ▷ C₃×C₂₅×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₂₂₅	C₂	semidirect
2. D₃×C₂₅×C₄₃	C₂	semidirect
3. C₃×D₁₀₇₅	C₂	semidirect
5. C₃×C₂₅×C₄₃	C₂²	semidirect
8. D₁₀₇₅	D₃	direct (N × H)
13. C₂₅×C₄₃	C₂×D₃	semidirect
23. D₃×C₄₃	D₂₅	semidirect
28. D₃×C₂₅	D₄₃	semidirect
29. C₃×C₄₃	C₂×D₂₅	semidirect
34. C₃×C₂₅	C₂×D₄₃	semidirect
39. C₄₃	D₃×D₂₅	semidirect
43. C₂₅	D₃×D₄₃	semidirect
52. D₃	D₁₀₇₅	direct (N × H)
55. C₃	C₂×D₁₀₇₅	semidirect

Maximal subgroups

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

subgroup	index
D₃₂₂₅	2
D₃×C₂₅×C₄₃	2
C₃×D₁₀₇₅	2
C₂×D₁₀₇₅	3
D₃×D₂₁₅	5
D₃×D₂₅	43

Subgroups — D3×D1075 #27166360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₀₇₅ #27166360