Subgroups — C₂×D₃₂₂₅ #27166371

Order 12900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	D₃₂₂₅
commutator, cosocle, hypocenter	C₃×C₂₅×C₄₃	C₂²
Frattini	C₅	C₂×D₆₄₅
Fitting	C₂×C₃×C₂₅×C₄₃	C₂
socle	C₂×C₃×C₅×C₄₃	D₅
LCS	G ▷ C₃×C₂₅×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₃₂₂₅	C₂	direct (N × H)
2. C₂×C₃×C₂₅×C₄₃	C₂	semidirect
4. C₃×C₂₅×C₄₃	C₂²	semidirect
7. C₂×C₂₅×C₄₃	D₃	semidirect
10. C₂₅×C₄₃	C₂×D₃	semidirect
17. C₂×C₃×C₄₃	D₂₅	semidirect
21. C₂×C₃×C₂₅	D₄₃	semidirect
23. C₃×C₄₃	C₂×D₂₅	semidirect
25. C₂×C₄₃	D₇₅	semidirect
27. C₃×C₂₅	C₂×D₄₃	semidirect
29. C₂×C₂₅	D₁₂₉	semidirect
31. C₄₃	C₂×D₇₅	semidirect
34. C₂₅	C₂×D₁₂₉	semidirect
40. C₂×C₃	D₁₀₇₅	semidirect
44. C₃	C₂×D₁₀₇₅	semidirect
46. C₂	D₃₂₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₂₂₅	2
C₂×C₃×C₂₅×C₄₃	2
C₂×D₁₀₇₅	3
C₂×D₆₄₅	5
C₂×D₇₅	43

Subgroups — C2×D3225 #27166371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₂₂₅ #27166371