Subgroups — C₂×C₃₁×D₂₆₁ #44569049

Order 32364.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₂₆₁
commutator, cosocle, hypocenter	C₉×C₂₉	C₂²×C₃₁
Frattini	C₃	C₂×C₃₁×D₈₇
Fitting	C₂×C₉×C₂₉×C₃₁	C₂
socle	C₂×C₃×C₂₉×C₃₁	D₃
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₂₆₁	C₂	direct (N × H)
2. C₂×C₉×C₂₉×C₃₁	C₂	semidirect
4. C₉×C₂₉×C₃₁	C₂²	semidirect
9. C₂×C₂₉×C₃₁	D₉	semidirect
12. C₂×D₂₆₁	C₃₁	direct (N × H)
13. C₂₉×C₃₁	C₂×D₉	semidirect
14. C₂×C₉×C₃₁	D₂₉	semidirect
16. C₂×C₉×C₂₉	C₂×C₃₁	semidirect
17. D₂₆₁	C₂×C₃₁	direct (N × H)
20. C₉×C₃₁	C₂×D₂₉	semidirect
21. C₉×C₂₉	C₂²×C₃₁	semidirect
31. C₂×C₃₁	D₂₆₁	direct (N × H)
32. C₂×C₂₉	D₉×C₃₁	semidirect
35. C₃₁	C₂×D₂₆₁	direct (N × H)
36. C₂₉	C₂×D₉×C₃₁	semidirect
37. C₂×C₉	C₃₁×D₂₉	semidirect
40. C₉	C₂×C₃₁×D₂₉	semidirect
46. C₂	C₃₁×D₂₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×D₂₆₁	2
C₂×C₉×C₂₉×C₃₁	2
C₂×C₃₁×D₈₇	3
C₂×D₉×C₃₁	29
C₂×D₂₆₁	31

Subgroups — C2×C31×D261 #44569049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×D₂₆₁ #44569049