Subgroups — C₃₁×D₄₉₅ #44501661

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₆₅	—	3	1	no	maximal
3	C₃₁×D₉₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₃₁	D₃	1	1	yes	characteristic
5	C₃₁×D₅₅	—	9	1	no	Hall
6	C₉×C₁₁×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃₁×D₄₅	—	11	1	no	maximal, Hall
8	C₃₁×D₃₃	—	15	1	no	—
9	C₅×C₁₁×C₃₁	D₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₃₁	D₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	D₁₅	1	1	yes	characteristic
12	D₄₉₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	D₁₅×C₃₁	—	33	1	no	—
14	D₁₁×C₃₁	—	45	1	no	Hall
15	D₉×C₃₁	—	55	1	no	Hall
16	C₅×C₉×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₃₁	D₃₃	1	1	yes	characteristic
18	C₁₁×C₃₁	D₄₅	1	1	yes	characteristic, complemented, Hall
19	D₁₆₅	—	3	1	no	—
20	D₅×C₃₁	—	99	1	no	Hall
21	C₉×C₃₁	D₅₅	1	1	yes	characteristic, complemented, Hall
22	D₉₉	—	5	1	no	Hall
23	D₃×C₃₁	—	165	1	no	—
24	C₃×C₅×C₁₁	D₃×C₃₁	1	1	yes	characteristic
25	C₅×C₃₁	D₉₉	1	1	yes	characteristic, complemented, Hall
26	D₅₅	—	9	1	no	Hall
27	C₉×C₁₁	D₅×C₃₁	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	D₁₆₅	1	1	yes	characteristic
29	D₄₅	—	11	1	no	Hall
30	D₃₃	—	15	1	no	—
31	C₂×C₃₁	—	495	1	no	Hall
32	C₅×C₁₁	D₉×C₃₁	1	1	yes	characteristic, complemented, Hall
33	C₅×C₉	D₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	D₁₅×C₃₁	1	1	yes	characteristic
35	C₃₁	D₄₉₅	1	1	yes	characteristic, direct product factor, Sylow
36	D₁₅	—	33	1	no	—
37	D₁₁	—	45	1	no	Hall
38	D₉	—	55	1	no	Hall
39	C₃×C₅	C₃₁×D₃₃	1	1	yes	characteristic
40	C₁₁	C₃₁×D₄₅	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	99	1	no	Hall
42	C₉	C₃₁×D₅₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	165	1	no	—
44	C₅	C₃₁×D₉₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃₁×D₁₆₅	1	1	yes	characteristic
46	C₂	—	495	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	D₄₉₅
commutator, cosocle, hypocenter	C₅×C₉×C₁₁	C₂×C₃₁
Frattini	C₃	C₃₁×D₁₆₅
Fitting	C₅×C₉×C₁₁×C₃₁	C₂
socle	C₃×C₅×C₁₁×C₃₁	D₃
LCS	G ▷ C₅×C₉×C₁₁
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×C₃₁	C₂	semidirect
6. C₉×C₁₁×C₃₁	D₅	semidirect
9. C₅×C₁₁×C₃₁	D₉	semidirect
10. C₅×C₉×C₃₁	D₁₁	semidirect
12. D₄₉₅	C₃₁	direct (N × H)
16. C₅×C₉×C₁₁	C₂×C₃₁	semidirect
18. C₁₁×C₃₁	D₄₅	semidirect
21. C₉×C₃₁	D₅₅	semidirect
25. C₅×C₃₁	D₉₉	semidirect
27. C₉×C₁₁	D₅×C₃₁	semidirect
32. C₅×C₁₁	D₉×C₃₁	semidirect
33. C₅×C₉	D₁₁×C₃₁	semidirect
35. C₃₁	D₄₉₅	direct (N × H)
40. C₁₁	C₃₁×D₄₅	semidirect
42. C₉	C₃₁×D₅₅	semidirect
44. C₅	C₃₁×D₉₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₁×C₃₁	2
C₃₁×D₁₆₅	3
C₃₁×D₉₉	5
C₃₁×D₄₅	11
D₄₉₅	31

Subgroups — C31×D495 #44501661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×D₄₉₅ #44501661