Subgroups — D₂₅×D₁₀₉⋊C₃ #45658184

Order 32700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅⋊(D₁₀₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₅×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×D₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₅×D₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂₅×C₁₀₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×D₁₀₉⋊C₃	—	5	1	no	maximal
7	D₂₇₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₅×D₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₂₅×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅⋊(D₁₀₉⋊C₃)	—	5	1	no	—
11	D₅×C₁₀₉⋊C₃	—	5	1	no	—
12	C₅×D₁₀₉⋊C₃	D₅	1	1	yes	characteristic
13	C₂₅×C₁₀₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₁₀₉	—	5	1	no	—
15	C₅×C₁₀₉⋊C₃	C₂×D₅	1	1	yes	characteristic
16	C₂×D₁₀₉⋊C₃	—	25	1	no	Hall
17	D₅₄₅	—	5	1	no	—
18	C₅×D₁₀₉	C₃×D₅	1	1	yes	characteristic
19	D₅×C₁₀₉	—	5	1	no	—
20	C₂×C₁₀₉⋊C₃	—	25	1	no	—
21	D₁₀₉⋊C₃	—	25	1	no	—
22	D₁₀₉⋊C₃	D₂₅	1	1	yes	characteristic, direct product factor
23	C₅×C₁₀₉	C₂×C₃×D₅	1	1	yes	characteristic
24	C₂×D₁₀₉	—	25	1	no	Hall
25	C₁₀₉⋊C₃	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₂₅	—	109	1	no	maximal, Hall
27	C₂×C₁₀₉	—	25	1	no	—
28	D₁₀₉	—	25	1	no	—
29	D₁₀₉	C₃×D₂₅	1	1	yes	characteristic, complemented
30	C₂×C₃×C₂₅	—	109	1	no	—
31	C₃×D₂₅	—	109	1	no	—
32	C₃×D₂₅	—	109	1	no	—
33	C₁₀₉	C₂×C₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₂₅	—	109	1	no	Hall
35	C₃×C₂₅	—	109	1	no	Hall
36	C₂×C₃×D₅	—	545	1	no	—
37	C₂×C₂₅	—	109	1	no	—
38	D₂₅	—	109	1	no	—
39	D₂₅	D₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₅	—	109	1	no	—
41	C₃×D₅	—	545	1	no	—
42	C₃×D₅	—	545	1	no	—
43	C₂₅	C₂×D₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	545	1	no	—
45	C₃×C₅	—	109	1	no	—
46	C₂²×C₃	—	2725	1	no	Hall
47	C₂×C₅	—	109	1	no	—
48	D₅	—	5	1	no	—
49	D₅	—	545	1	no	—
50	C₂×C₃	—	109	1	no	—
51	C₂×C₃	—	2725	1	no	—
52	C₂×C₃	—	2725	1	no	—
53	C₅	D₅×D₁₀₉⋊C₃	1	1	yes	characteristic
54	C₂²	—	2725	1	no	Sylow
55	C₃	—	109	1	no	Sylow
56	C₂	—	25	1	no	—
57	C₂	—	109	1	no	—
58	C₂	—	2725	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂₅×C₁₀₉	C₂²×C₃
Frattini	C₅	D₅×D₁₀₉⋊C₃
socle	C₅×C₁₀₉	C₂×C₃×D₅
LCS	G ▷ C₂₅×C₁₀₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₅⋊(D₁₀₉⋊C₃)	C₂	semidirect
2. D₂₅×C₁₀₉⋊C₃	C₂	semidirect
3. C₂₅×D₁₀₉⋊C₃	C₂	semidirect
4. D₂₅×D₁₀₉	C₃	semidirect
5. C₂₅×C₁₀₉⋊C₃	C₂²	semidirect
7. D₂₇₂₅	C₂×C₃	semidirect
8. C₂₅×D₁₀₉	C₂×C₃	semidirect
9. D₂₅×C₁₀₉	C₂×C₃	semidirect
13. C₂₅×C₁₀₉	C₂²×C₃	semidirect
22. D₁₀₉⋊C₃	D₂₅	direct (N × H)
25. C₁₀₉⋊C₃	C₂×D₂₅	semidirect
29. D₁₀₉	C₃×D₂₅	semidirect
33. C₁₀₉	C₂×C₃×D₂₅	semidirect
39. D₂₅	D₁₀₉⋊C₃	direct (N × H)
43. C₂₅	C₂×D₁₀₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₅⋊(D₁₀₉⋊C₃)	2
D₂₅×C₁₀₉⋊C₃	2
C₂₅×D₁₀₉⋊C₃	2
D₂₅×D₁₀₉	3
D₅×D₁₀₉⋊C₃	5
C₂×C₃×D₂₅	109

Subgroups — D25×D109⋊C3 #45658184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₅×D₁₀₉⋊C₃ #45658184