Subgroups — D₉×C₂₉×D₃₁ #44569037

Order 32364.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₂₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₉×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₂₉×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₂₉×D₃₁	—	3	1	no	maximal
5	C₉×C₂₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₉₃	—	3	1	no	—
7	D₃×C₂₉×C₃₁	—	3	1	no	—
8	C₃×C₂₉×D₃₁	D₃	1	1	yes	characteristic
9	C₂×C₂₉×D₃₁	—	9	1	no	Hall
10	C₃×C₂₉×C₃₁	C₂×D₃	1	1	yes	characteristic
11	C₂×C₂₉×C₃₁	—	9	1	no	—
12	C₂₉×D₃₁	—	9	1	no	—
13	C₂₉×D₃₁	D₉	1	1	yes	characteristic, direct product factor
14	D₉×D₃₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×D₉×C₂₉	—	31	1	no	maximal, Hall
16	C₂₉×C₃₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	D₂₇₉	C₂×C₂₉	1	1	yes	characteristic, complemented
18	C₉×D₃₁	C₂×C₂₉	1	1	yes	characteristic, complemented
19	D₉×C₃₁	C₂×C₂₉	1	1	yes	characteristic, complemented
20	C₂×C₉×C₂₉	—	31	1	no	—
21	D₉×C₂₉	—	31	1	no	—
22	D₉×C₂₉	D₃₁	1	1	yes	characteristic, direct product factor
23	D₃×D₃₁	—	3	1	no	—
24	C₂×D₃×C₂₉	—	93	1	no	—
25	C₉×C₃₁	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
26	C₉×C₂₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
27	D₉₃	—	3	1	no	—
28	C₃×D₃₁	D₃×C₂₉	1	1	yes	characteristic
29	D₃×C₃₁	—	3	1	no	—
30	C₂×C₃×C₂₉	—	31	1	no	—
31	D₃×C₂₉	—	3	1	no	—
32	D₃×C₂₉	—	93	1	no	—
33	C₂×D₃₁	—	9	1	no	Hall
34	C₂²×C₂₉	—	279	1	no	Hall
35	C₃×C₃₁	C₂×D₃×C₂₉	1	1	yes	characteristic
36	C₃×C₂₉	D₃×D₃₁	1	1	yes	characteristic
37	C₂×C₃₁	—	9	1	no	—
38	D₃₁	—	9	1	no	—
39	D₃₁	D₉×C₂₉	1	1	yes	characteristic, direct product factor
40	C₂×C₂₉	—	9	1	no	—
41	C₂×C₂₉	—	279	1	no	—
42	C₂×C₂₉	—	31	1	no	—
43	C₂×D₉	—	31	1	no	Hall
44	C₃₁	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
45	C₂₉	D₉×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₉	—	31	1	no	—
47	D₉	—	31	1	no	—
48	D₉	C₂₉×D₃₁	1	1	yes	characteristic, direct product factor
49	C₂×D₃	—	93	1	no	—
50	C₉	C₂×C₂₉×D₃₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	31	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	93	1	no	—
54	C₂²	—	279	1	no	Sylow
55	C₃	D₃×C₂₉×D₃₁	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	279	1	no	—
58	C₂	—	31	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₉×D₃₁
commutator, cosocle, hypocenter	C₉×C₃₁	C₂²×C₂₉
Frattini	C₃	D₃×C₂₉×D₃₁
Fitting	C₉×C₂₉×C₃₁	C₂²
socle	C₃×C₂₉×C₃₁	C₂×D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₂₇₉	C₂	semidirect
2. D₉×C₂₉×C₃₁	C₂	semidirect
3. C₉×C₂₉×D₃₁	C₂	semidirect
5. C₉×C₂₉×C₃₁	C₂²	semidirect
13. C₂₉×D₃₁	D₉	direct (N × H)
14. D₉×D₃₁	C₂₉	direct (N × H)
16. C₂₉×C₃₁	C₂×D₉	semidirect
17. D₂₇₉	C₂×C₂₉	semidirect
18. C₉×D₃₁	C₂×C₂₉	semidirect
19. D₉×C₃₁	C₂×C₂₉	semidirect
22. D₉×C₂₉	D₃₁	direct (N × H)
25. C₉×C₃₁	C₂²×C₂₉	semidirect
26. C₉×C₂₉	C₂×D₃₁	semidirect
39. D₃₁	D₉×C₂₉	direct (N × H)
44. C₃₁	C₂×D₉×C₂₉	semidirect
45. C₂₉	D₉×D₃₁	direct (N × H)
48. D₉	C₂₉×D₃₁	direct (N × H)
50. C₉	C₂×C₂₉×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×D₂₇₉	2
D₉×C₂₉×C₃₁	2
C₉×C₂₉×D₃₁	2
D₃×C₂₉×D₃₁	3
D₉×D₃₁	29
C₂×D₉×C₂₉	31

Subgroups — D9×C29×D31 #44569037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₂₉×D₃₁ #44569037