Subgroups — D₉×C₃₁×D₂₉ #44569041

Order 32364.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₂₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₃₁×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₃₁×D₂₉	—	3	1	no	maximal
5	C₉×C₂₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₈₇	—	3	1	no	—
7	D₃×C₂₉×C₃₁	—	3	1	no	—
8	C₃×C₃₁×D₂₉	D₃	1	1	yes	characteristic
9	C₂×C₃₁×D₂₉	—	9	1	no	Hall
10	C₃×C₂₉×C₃₁	C₂×D₃	1	1	yes	characteristic
11	C₂×C₂₉×C₃₁	—	9	1	no	—
12	C₃₁×D₂₉	—	9	1	no	—
13	C₃₁×D₂₉	D₉	1	1	yes	characteristic, direct product factor
14	C₂×D₉×C₃₁	—	29	1	no	maximal, Hall
15	D₉×D₂₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂₉×C₃₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₉×C₃₁	—	29	1	no	—
18	D₉×C₃₁	—	29	1	no	—
19	D₉×C₃₁	D₂₉	1	1	yes	characteristic, direct product factor
20	D₂₆₁	C₂×C₃₁	1	1	yes	characteristic, complemented
21	C₉×D₂₉	C₂×C₃₁	1	1	yes	characteristic, complemented
22	D₉×C₂₉	C₂×C₃₁	1	1	yes	characteristic, complemented
23	C₂×D₃×C₃₁	—	87	1	no	—
24	D₃×D₂₉	—	3	1	no	—
25	C₉×C₃₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
26	C₉×C₂₉	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₃₁	—	29	1	no	—
28	D₃×C₃₁	—	3	1	no	—
29	D₃×C₃₁	—	87	1	no	—
30	D₈₇	—	3	1	no	—
31	C₃×D₂₉	D₃×C₃₁	1	1	yes	characteristic
32	D₃×C₂₉	—	3	1	no	—
33	C₂²×C₃₁	—	261	1	no	Hall
34	C₂×D₂₉	—	9	1	no	Hall
35	C₃×C₃₁	D₃×D₂₉	1	1	yes	characteristic
36	C₃×C₂₉	C₂×D₃×C₃₁	1	1	yes	characteristic
37	C₂×C₃₁	—	261	1	no	—
38	C₂×C₃₁	—	9	1	no	—
39	C₂×C₃₁	—	29	1	no	—
40	C₂×C₂₉	—	9	1	no	—
41	D₂₉	—	9	1	no	—
42	D₂₉	D₉×C₃₁	1	1	yes	characteristic, direct product factor
43	C₂×D₉	—	29	1	no	Hall
44	C₃₁	D₉×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂₉	C₂×D₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	29	1	no	—
47	D₉	—	29	1	no	—
48	D₉	C₃₁×D₂₉	1	1	yes	characteristic, direct product factor
49	C₂×D₃	—	87	1	no	—
50	C₉	C₂×C₃₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	29	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	87	1	no	—
54	C₂²	—	261	1	no	Sylow
55	C₃	D₃×C₃₁×D₂₉	1	1	yes	characteristic
56	C₂	—	261	1	no	—
57	C₂	—	9	1	no	—
58	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₉×D₂₉
commutator, cosocle, hypocenter	C₉×C₂₉	C₂²×C₃₁
Frattini	C₃	D₃×C₃₁×D₂₉
Fitting	C₉×C₂₉×C₃₁	C₂²
socle	C₃×C₂₉×C₃₁	C₂×D₃
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₂₆₁	C₂	semidirect
2. D₉×C₂₉×C₃₁	C₂	semidirect
3. C₉×C₃₁×D₂₉	C₂	semidirect
5. C₉×C₂₉×C₃₁	C₂²	semidirect
13. C₃₁×D₂₉	D₉	direct (N × H)
15. D₉×D₂₉	C₃₁	direct (N × H)
16. C₂₉×C₃₁	C₂×D₉	semidirect
19. D₉×C₃₁	D₂₉	direct (N × H)
20. D₂₆₁	C₂×C₃₁	semidirect
21. C₉×D₂₉	C₂×C₃₁	semidirect
22. D₉×C₂₉	C₂×C₃₁	semidirect
25. C₉×C₃₁	C₂×D₂₉	semidirect
26. C₉×C₂₉	C₂²×C₃₁	semidirect
42. D₂₉	D₉×C₃₁	direct (N × H)
44. C₃₁	D₉×D₂₉	direct (N × H)
45. C₂₉	C₂×D₉×C₃₁	semidirect
48. D₉	C₃₁×D₂₉	direct (N × H)
50. C₉	C₂×C₃₁×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×D₂₆₁	2
D₉×C₂₉×C₃₁	2
C₉×C₃₁×D₂₉	2
D₃×C₃₁×D₂₉	3
C₂×D₉×C₃₁	29
D₉×D₂₉	31

Subgroups — D9×C31×D29 #44569041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₃₁×D₂₉ #44569041