Subgroups — C₃×C₇₁×D₇₅ #44544022

Order 31950.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₁×D₇₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₂₅×C₇₁	—	3	1	no	maximal
4	C₃×D₁₅×C₇₁	—	5	1	no	maximal
5	C₃×C₂₅×C₇₁	—	2	1	no	—
6	C₃×C₂₅×C₇₁	D₃	1	1	yes	characteristic, complemented
7	C₃×C₂₅×C₇₁	C₂×C₃	1	1	yes	characteristic, complemented
8	D₂₅×C₇₁	—	3	1	no	Hall
9	C₃²×C₅×C₇₁	D₅	1	1	yes	characteristic
10	D₁₅×C₇₁	—	5	1	no	—
11	C₃×D₅×C₇₁	—	15	1	no	—
12	C₂₅×C₇₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₃×C₇₁	—	25	1	no	Hall
14	C₃×C₅×C₇₁	—	2	1	no	—
15	C₃×C₅×C₇₁	C₃×D₅	1	1	yes	characteristic
16	C₃×C₅×C₇₁	D₁₅	1	1	yes	characteristic
17	D₅×C₇₁	—	15	1	no	—
18	C₃²×C₇₁	D₂₅	1	1	yes	characteristic, complemented, Hall
19	C₃×D₇₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₃×C₇₁	—	75	1	no	—
21	D₃×C₇₁	—	25	1	no	—
22	C₅×C₇₁	C₃×D₁₅	1	1	yes	characteristic
23	C₃²×C₂₅	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇₁	—	2	1	no	—
25	C₃×C₇₁	C₃×D₂₅	1	1	yes	characteristic, complemented
26	C₃×C₇₁	D₇₅	1	1	yes	characteristic, direct product factor
27	D₇₅	C₃×C₇₁	1	1	yes	characteristic, direct product factor
28	C₃×D₂₅	—	3	1	no	—
29	C₂×C₇₁	—	75	1	no	Hall
30	C₃×D₁₅	—	5	1	no	—
31	C₃×C₂₅	—	2	1	no	—
32	C₃×C₂₅	D₃×C₇₁	1	1	yes	characteristic, complemented
33	C₃×C₂₅	C₂×C₃×C₇₁	1	1	yes	characteristic, complemented
34	C₇₁	C₃×D₇₅	1	1	yes	characteristic, direct product factor, Sylow
35	D₂₅	—	3	1	no	Hall
36	C₃²×C₅	D₅×C₇₁	1	1	yes	characteristic
37	D₁₅	—	5	1	no	—
38	C₃×D₅	—	15	1	no	—
39	C₂₅	C₃×D₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×D₃	—	25	1	no	Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₃×D₅×C₇₁	1	1	yes	characteristic
43	C₃×C₅	D₁₅×C₇₁	1	1	yes	characteristic
44	D₅	—	15	1	no	—
45	C₃²	D₂₅×C₇₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	75	1	no	—
47	D₃	—	25	1	no	—
48	C₅	C₃×D₁₅×C₇₁	1	1	yes	characteristic
49	C₃	—	2	1	no	—
50	C₃	C₃×D₂₅×C₇₁	1	1	yes	characteristic, complemented
51	C₃	C₇₁×D₇₅	1	1	yes	characteristic, direct product factor
52	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇₁	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂×C₃×C₇₁
Frattini	C₅	C₃×D₁₅×C₇₁
Fitting	C₃²×C₂₅×C₇₁	C₂
socle	C₃²×C₅×C₇₁	D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₃×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₅×C₇₁	C₂	semidirect
2. C₇₁×D₇₅	C₃	direct (N × H)
6. C₃×C₂₅×C₇₁	D₃	semidirect
7. C₃×C₂₅×C₇₁	C₂×C₃	semidirect
12. C₂₅×C₇₁	C₃×D₃	semidirect
18. C₃²×C₇₁	D₂₅	semidirect
19. C₃×D₇₅	C₇₁	direct (N × H)
23. C₃²×C₂₅	C₂×C₇₁	semidirect
25. C₃×C₇₁	C₃×D₂₅	semidirect
26. C₃×C₇₁	D₇₅	direct (N × H)
27. D₇₅	C₃×C₇₁	direct (N × H)
32. C₃×C₂₅	D₃×C₇₁	semidirect
33. C₃×C₂₅	C₂×C₃×C₇₁	semidirect
34. C₇₁	C₃×D₇₅	direct (N × H)
39. C₂₅	C₃×D₃×C₇₁	semidirect
45. C₃²	D₂₅×C₇₁	semidirect
50. C₃	C₃×D₂₅×C₇₁	semidirect
51. C₃	C₇₁×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
C₃²×C₂₅×C₇₁	2
C₇₁×D₇₅	3
C₃×D₂₅×C₇₁	3
C₃×D₁₅×C₇₁	5
C₃×D₇₅	71

Subgroups — C3×C71×D75 #44544022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇₁×D₇₅ #44544022