Subgroups — C₂×D₆₇₅ #72210163

Order 2700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₆₇₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₂₅	—	3	1	no	maximal
4	C₂₅×C₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₃₅	—	5	1	no	maximal
6	C₂×C₉×C₂₅	D₃	1	1	yes	characteristic
7	D₂₂₅	—	3	2	no	—
8	C₂×D₇₅	—	9	1	no	—
9	C₂×C₅×C₂₇	D₅	1	1	yes	characteristic
10	D₁₃₅	—	5	2	no	—
11	C₉×C₂₅	C₂×D₃	1	1	yes	characteristic
12	C₂×D₄₅	—	15	1	no	—
13	C₂×C₃×C₂₅	D₉	1	1	yes	characteristic
14	D₇₅	—	9	2	no	—
15	C₅×C₂₇	C₂×D₅	1	1	yes	characteristic
16	C₂×D₂₇	—	25	1	no	Hall
17	C₂×D₂₅	—	27	1	no	Hall
18	C₂×C₅×C₉	D₁₅	1	1	yes	characteristic
19	D₄₅	—	15	2	no	—
20	C₃×C₂₅	C₂×D₉	1	1	yes	characteristic
21	C₂×D₁₅	—	45	1	no	—
22	C₂×C₂₇	D₂₅	1	1	yes	characteristic, complemented
23	D₂₇	—	25	2	no	—
24	C₂×C₂₅	D₂₇	1	1	yes	characteristic, complemented
25	D₂₅	—	27	2	no	—
26	C₅×C₉	C₂×D₁₅	1	1	yes	characteristic
27	C₂×D₉	—	75	1	no	—
28	C₂×C₃×C₅	D₄₅	1	1	yes	characteristic
29	D₁₅	—	45	2	no	—
30	C₂₇	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
31	C₂₅	C₂×D₂₇	1	1	yes	characteristic, complemented, Sylow
32	C₂×D₅	—	135	1	no	—
33	C₂×C₉	D₇₅	1	1	yes	characteristic
34	D₉	—	75	2	no	—
35	C₃×C₅	C₂×D₄₅	1	1	yes	characteristic
36	C₂×D₃	—	225	1	no	—
37	C₂×C₅	D₁₃₅	1	1	yes	characteristic
38	D₅	—	135	2	no	—
39	C₉	C₂×D₇₅	1	1	yes	characteristic
40	C₂×C₃	D₂₂₅	1	1	yes	characteristic
41	D₃	—	225	2	no	—
42	C₅	C₂×D₁₃₅	1	1	yes	characteristic
43	C₂²	—	675	1	no	Sylow
44	C₃	C₂×D₂₂₅	1	1	yes	characteristic
45	C₂	—	675	2	no	—
46	C₂	D₆₇₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₆₇₅
commutator, cosocle, hypocenter	C₂₅×C₂₇	C₂²
Frattini	C₅×C₉	C₂×D₁₅
Fitting	C₂×C₂₅×C₂₇	C₂
socle	C₂×C₃×C₅	D₄₅
LCS	G ▷ C₂₅×C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₅×C₂₇	C₂	semidirect
2. D₆₇₅	C₂	direct (N × H)
4. C₂₅×C₂₇	C₂²	semidirect
22. C₂×C₂₇	D₂₅	semidirect
24. C₂×C₂₅	D₂₇	semidirect
30. C₂₇	C₂×D₂₅	semidirect
31. C₂₅	C₂×D₂₇	semidirect
46. C₂	D₆₇₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₅×C₂₇	2
D₆₇₅	2
C₂×D₂₂₅	3
C₂×D₁₃₅	5

Subgroups — C2×D675 #72210163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₆₇₅ #72210163