Subgroups — C₂×C₄₁×D₇₅ #27134181

Order 12300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₇₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₂₅×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×D₂₅	—	3	1	no	maximal, Hall
4	C₃×C₂₅×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₅×C₄₁	—	5	1	no	maximal
6	C₄₁×D₂₅	—	3	2	no	—
7	C₂×C₂₅×C₄₁	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₅×C₄₁	D₅	1	1	yes	characteristic
9	D₁₅×C₄₁	—	5	2	no	—
10	C₂₅×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₄₁	—	15	1	no	—
12	C₃×C₅×C₄₁	C₂×D₅	1	1	yes	characteristic
13	C₂×D₃×C₄₁	—	25	1	no	Hall
14	C₂×C₅×C₄₁	D₁₅	1	1	yes	characteristic
15	D₅×C₄₁	—	15	2	no	—
16	C₂×D₇₅	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₄₁	D₂₅	1	1	yes	characteristic, complemented
18	D₃×C₄₁	—	25	2	no	—
19	C₅×C₄₁	C₂×D₁₅	1	1	yes	characteristic
20	C₂²×C₄₁	—	75	1	no	Hall
21	C₂×C₃×C₂₅	C₂×C₄₁	1	1	yes	characteristic, complemented
22	D₇₅	C₂×C₄₁	1	2	yes	direct product factor
23	C₃×C₄₁	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
24	C₂×D₂₅	—	3	1	no	Hall
25	C₂×C₄₁	—	75	2	no	—
26	C₂×C₄₁	D₇₅	1	1	yes	characteristic, direct product factor
27	C₃×C₂₅	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₅	—	5	1	no	—
29	C₂×C₂₅	D₃×C₄₁	1	1	yes	characteristic, complemented
30	D₂₅	—	3	2	no	—
31	C₄₁	C₂×D₇₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×C₅	D₅×C₄₁	1	1	yes	characteristic
33	D₁₅	—	5	2	no	—
34	C₂₅	C₂×D₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	15	1	no	—
36	C₃×C₅	C₂×D₅×C₄₁	1	1	yes	characteristic
37	C₂×D₃	—	25	1	no	Hall
38	C₂×C₅	D₁₅×C₄₁	1	1	yes	characteristic
39	D₅	—	15	2	no	—
40	C₂×C₃	C₄₁×D₂₅	1	1	yes	characteristic, complemented
41	D₃	—	25	2	no	—
42	C₅	C₂×D₁₅×C₄₁	1	1	yes	characteristic
43	C₂²	—	75	1	no	Sylow
44	C₃	C₂×C₄₁×D₂₅	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	75	2	no	—
46	C₂	C₄₁×D₇₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₁	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂²×C₄₁
Frattini	C₅	C₂×D₁₅×C₄₁
Fitting	C₂×C₃×C₂₅×C₄₁	C₂
socle	C₂×C₃×C₅×C₄₁	D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₂×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×D₇₅	C₂	direct (N × H)
2. C₂×C₃×C₂₅×C₄₁	C₂	semidirect
4. C₃×C₂₅×C₄₁	C₂²	semidirect
7. C₂×C₂₅×C₄₁	D₃	semidirect
10. C₂₅×C₄₁	C₂×D₃	semidirect
16. C₂×D₇₅	C₄₁	direct (N × H)
17. C₂×C₃×C₄₁	D₂₅	semidirect
21. C₂×C₃×C₂₅	C₂×C₄₁	semidirect
22. D₇₅	C₂×C₄₁	direct (N × H)
23. C₃×C₄₁	C₂×D₂₅	semidirect
26. C₂×C₄₁	D₇₅	direct (N × H)
27. C₃×C₂₅	C₂²×C₄₁	semidirect
29. C₂×C₂₅	D₃×C₄₁	semidirect
31. C₄₁	C₂×D₇₅	direct (N × H)
34. C₂₅	C₂×D₃×C₄₁	semidirect
40. C₂×C₃	C₄₁×D₂₅	semidirect
44. C₃	C₂×C₄₁×D₂₅	semidirect
46. C₂	C₄₁×D₇₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×D₇₅	2
C₂×C₃×C₂₅×C₄₁	2
C₂×C₄₁×D₂₅	3
C₂×D₁₅×C₄₁	5
C₂×D₇₅	41

Subgroups — C2×C41×D75 #27134181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×D₇₅ #27134181