Subgroups — D₃×D₆₁⋊C₂₅ #32912901

Order 18300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(D₆₁⋊C₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₆₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₆₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₁⋊C₂₅	—	3	1	no	maximal, Hall
5	C₃×C₆₁⋊C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×D₆₁	C₅	1	1	yes	maximal, characteristic
7	C₂×C₆₁⋊C₂₅	—	3	1	no	—
8	D₆₁⋊C₂₅	—	3	1	no	—
9	D₆₁⋊C₂₅	D₃	1	1	yes	characteristic, direct product factor
10	C₅×D₁₈₃	C₂×C₅	1	1	yes	characteristic
11	C₅×D₃×C₆₁	C₂×C₅	1	1	yes	characteristic
12	C₃×C₅×D₆₁	C₂×C₅	1	1	yes	characteristic
13	C₆₁⋊C₂₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×D₆₁	—	3	1	no	—
15	C₃×C₅×C₆₁	C₂²×C₅	1	1	yes	characteristic
16	D₃×D₆₁	C₂₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₆₁	—	3	1	no	—
18	C₅×D₆₁	—	3	1	no	—
19	C₅×D₆₁	C₅×D₃	1	1	yes	characteristic
20	D₁₈₃	C₂×C₂₅	1	1	yes	characteristic, complemented
21	C₃×D₆₁	C₂×C₂₅	1	1	yes	characteristic, complemented
22	D₃×C₆₁	C₂×C₂₅	1	1	yes	characteristic, complemented
23	C₅×C₆₁	C₂×C₅×D₃	1	1	yes	characteristic
24	C₂×D₃×C₂₅	—	61	1	no	maximal, Hall
25	C₂×D₆₁	—	3	1	no	Hall
26	C₃×C₆₁	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₂₅	—	61	1	no	—
28	D₃×C₂₅	—	61	1	no	—
29	D₃×C₂₅	—	61	1	no	—
30	C₂×C₆₁	—	3	1	no	—
31	D₆₁	—	3	1	no	—
32	D₆₁	D₃×C₂₅	1	1	yes	characteristic, complemented
33	C₂²×C₂₅	—	183	1	no	Hall
34	C₃×C₂₅	—	61	1	no	Hall
35	C₆₁	C₂×D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₅×D₃	—	305	1	no	—
37	C₂×C₂₅	—	61	1	no	—
38	C₂×C₂₅	—	183	1	no	—
39	C₂×C₂₅	—	183	1	no	—
40	C₂×C₃×C₅	—	305	1	no	—
41	C₅×D₃	—	305	1	no	—
42	C₅×D₃	D₆₁⋊C₅	1	1	yes	characteristic
43	C₂₅	—	61	1	no	Sylow
44	C₂²×C₅	—	915	1	no	—
45	C₃×C₅	C₂×D₆₁⋊C₅	1	1	yes	characteristic
46	C₂×D₃	—	305	1	no	Hall
47	C₂×C₅	—	3	1	no	—
48	C₂×C₅	—	305	1	no	—
49	C₂×C₅	—	915	1	no	—
50	C₂×C₃	—	305	1	no	—
51	D₃	—	305	1	no	—
52	D₃	D₆₁⋊C₂₅	1	1	yes	characteristic, direct product factor
53	C₅	D₃×D₆₁⋊C₅	1	1	yes	characteristic
54	C₂²	—	915	1	no	Sylow
55	C₃	C₂×D₆₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	305	1	no	—
58	C₂	—	915	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₅	D₃×D₆₁⋊C₅
commutator, hypocenter	C₃×C₆₁	C₂²×C₂₅
Fitting, socle, cosocle	C₃×C₅×C₆₁	C₂²×C₅
prime radical	C₅×D₃×D₆₁	C₅
LCS	G ▷ C₃×C₆₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃⋊(D₆₁⋊C₂₅)	C₂	semidirect
2. D₃×C₆₁⋊C₂₅	C₂	semidirect
3. C₃×D₆₁⋊C₂₅	C₂	semidirect
5. C₃×C₆₁⋊C₂₅	C₂²	semidirect
9. D₆₁⋊C₂₅	D₃	direct (N × H)
13. C₆₁⋊C₂₅	C₂×D₃	semidirect
16. D₃×D₆₁	C₂₅	semidirect
20. D₁₈₃	C₂×C₂₅	semidirect
21. C₃×D₆₁	C₂×C₂₅	semidirect
22. D₃×C₆₁	C₂×C₂₅	semidirect
26. C₃×C₆₁	C₂²×C₂₅	semidirect
32. D₆₁	D₃×C₂₅	semidirect
35. C₆₁	C₂×D₃×C₂₅	semidirect
52. D₃	D₆₁⋊C₂₅	direct (N × H)
55. C₃	C₂×D₆₁⋊C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(D₆₁⋊C₂₅)	2
D₃×C₆₁⋊C₂₅	2
C₃×D₆₁⋊C₂₅	2
C₂×D₆₁⋊C₂₅	3
C₅×D₃×D₆₁	5
C₂×D₃×C₂₅	61

Subgroups — D3×D61⋊C25 #32912901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₆₁⋊C₂₅ #32912901