Subgroups — C₅×C₇₁×C₃⋊D₁₅ #44544092

Order 31950.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₅×C₇₁	—	3	4	no	maximal
3	C₇₁×C₃⋊D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₃⋊D₃×C₇₁	—	5	1	no	maximal
5	C₃×C₅²×C₇₁	D₃	1	4	yes	complemented
6	C₅×D₅×C₇₁	—	9	1	no	Hall
7	C₃²×C₅×C₇₁	—	2	2	no	—
8	C₃²×C₅×C₇₁	D₅	1	1	yes	characteristic, complemented
9	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
10	D₁₅×C₇₁	—	3	4	no	—
11	C₅×D₃×C₇₁	—	15	4	no	—
12	C₅²×C₇₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊D₃×C₇₁	—	5	1	no	Hall
14	C₃×C₅×C₇₁	—	2	8	no	—
15	C₃×C₅×C₇₁	C₅×D₃	1	4	yes	complemented
16	C₃×C₅×C₇₁	D₁₅	1	4	yes	complemented
17	C₂×C₅×C₇₁	—	45	1	no	—
18	D₅×C₇₁	—	9	1	no	—
19	C₃²×C₇₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
20	C₅×C₃⋊D₁₅	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	D₃×C₇₁	—	15	4	no	—
22	C₅×C₇₁	—	2	2	no	—
23	C₅×C₇₁	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
24	C₅×C₇₁	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
25	C₃²×C₅²	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇₁	C₅×D₁₅	1	4	yes	complemented
27	C₅×D₁₅	—	3	4	no	—
28	C₂×C₇₁	—	45	1	no	Hall
29	C₃⋊D₁₅	C₅×C₇₁	1	1	yes	characteristic, direct product factor
30	C₅×C₃⋊D₃	—	5	1	no	—
31	C₃×C₅²	D₃×C₇₁	1	4	yes	complemented
32	C₇₁	C₅×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₅×D₅	—	9	1	no	Hall
34	C₃²×C₅	—	2	2	no	—
35	C₃²×C₅	D₅×C₇₁	1	1	yes	characteristic, complemented
36	C₃²×C₅	C₂×C₅×C₇₁	1	1	yes	characteristic, complemented
37	D₁₅	—	3	4	no	—
38	C₅×D₃	—	15	4	no	—
39	C₅²	C₃⋊D₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
40	C₃⋊D₃	—	5	1	no	Hall
41	C₃×C₅	—	2	8	no	—
42	C₃×C₅	C₅×D₃×C₇₁	1	4	yes	complemented
43	C₃×C₅	D₁₅×C₇₁	1	4	yes	complemented
44	C₂×C₅	—	45	1	no	—
45	D₅	—	9	1	no	—
46	C₃²	C₅×D₅×C₇₁	1	1	yes	characteristic, complemented, Sylow
47	D₃	—	15	4	no	—
48	C₅	—	2	2	no	—
49	C₅	C₅×C₃⋊D₃×C₇₁	1	1	yes	characteristic, complemented
50	C₅	C₇₁×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
51	C₃	C₅×D₁₅×C₇₁	1	4	yes	complemented
52	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇₁	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂×C₅×C₇₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇₁	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅×C₇₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇₁	C₂	semidirect
3. C₇₁×C₃⋊D₁₅	C₅	direct (N × H)
5. C₃×C₅²×C₇₁	D₃	semidirect
8. C₃²×C₅×C₇₁	D₅	semidirect
9. C₃²×C₅×C₇₁	C₂×C₅	semidirect
12. C₅²×C₇₁	C₃⋊D₃	semidirect
15. C₃×C₅×C₇₁	C₅×D₃	semidirect
16. C₃×C₅×C₇₁	D₁₅	semidirect
19. C₃²×C₇₁	C₅×D₅	semidirect
20. C₅×C₃⋊D₁₅	C₇₁	direct (N × H)
23. C₅×C₇₁	C₅×C₃⋊D₃	semidirect
24. C₅×C₇₁	C₃⋊D₁₅	direct (N × H)
25. C₃²×C₅²	C₂×C₇₁	semidirect
26. C₃×C₇₁	C₅×D₁₅	semidirect
29. C₃⋊D₁₅	C₅×C₇₁	direct (N × H)
31. C₃×C₅²	D₃×C₇₁	semidirect
32. C₇₁	C₅×C₃⋊D₁₅	direct (N × H)
35. C₃²×C₅	D₅×C₇₁	semidirect
36. C₃²×C₅	C₂×C₅×C₇₁	semidirect
39. C₅²	C₃⋊D₃×C₇₁	semidirect
42. C₃×C₅	C₅×D₃×C₇₁	semidirect
43. C₃×C₅	D₁₅×C₇₁	semidirect
46. C₃²	C₅×D₅×C₇₁	semidirect
49. C₅	C₅×C₃⋊D₃×C₇₁	semidirect
50. C₅	C₇₁×C₃⋊D₁₅	direct (N × H)
51. C₃	C₅×D₁₅×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²×C₇₁	2
C₅×D₁₅×C₇₁	3
C₇₁×C₃⋊D₁₅	5
C₅×C₃⋊D₃×C₇₁	5
C₅×C₃⋊D₁₅	71

Subgroups — C5×C71×C3⋊D15 #44544092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇₁×C₃⋊D₁₅ #44544092