Subgroups — C₅×Dic₁₇×C₃₁⋊C₃ #44539271

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×Dic₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₇×C₃₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₇×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₇×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₇×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃₁×Dic₁₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₄×C₅×C₃₁⋊C₃	—	17	1	no	maximal, Hall
10	C₁₇×C₃₁⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
12	C₃×C₅×Dic₁₇	—	31	1	no	maximal, Hall
13	C₂×C₅×C₃₁⋊C₃	D₁₇	1	1	yes	characteristic
14	C₄×C₅×C₃₁	—	17	1	no	Hall
15	C₁₇×C₃₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₅×C₁₇	—	31	1	no	—
17	C₅×C₃₁⋊C₃	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₄×C₃₁⋊C₃	—	17	1	no	Hall
19	C₅×Dic₁₇	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₃₁	C₃×D₁₇	1	1	yes	characteristic
21	C₃×C₅×C₁₇	—	31	1	no	Hall
22	C₃×Dic₁₇	—	31	1	no	Hall
23	C₂×C₃₁⋊C₃	C₅×D₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	C₂×C₃₁⋊C₃	1	1	yes	characteristic
25	C₅×C₃₁	C₃×Dic₁₇	1	1	yes	characteristic, complemented, Hall
26	C₄×C₃₁	—	17	1	no	Hall
27	C₂×C₃×C₁₇	—	31	1	no	—
28	C₃₁⋊C₃	C₅×Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₇	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
30	Dic₁₇	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃₁	C₃×C₅×D₁₇	1	1	yes	characteristic
32	C₃×C₄×C₅	—	527	1	no	Hall
33	C₃×C₁₇	—	31	1	no	Hall
34	C₂×C₁₇	C₂×C₅×C₃₁⋊C₃	1	1	yes	characteristic
35	C₃₁	C₃×C₅×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	31	1	no	—
37	C₄×C₅	—	17	1	no	Hall
38	C₁₇	C₄×C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	31	1	no	Hall
40	C₃×C₄	—	527	1	no	Hall
41	C₂×C₅	D₁₇×C₃₁⋊C₃	1	1	yes	characteristic
42	C₂×C₃	—	31	1	no	—
43	C₅	Dic₁₇×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	17	1	no	Sylow
45	C₃	—	31	1	no	Sylow
46	C₂	C₅×D₁₇×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₇×C₃₁⋊C₃
commutator, hypocenter	C₁₇×C₃₁	C₃×C₄×C₅
Frattini	C₂	C₅×D₁₇×C₃₁⋊C₃
Fitting, socle	C₂×C₅×C₁₇×C₃₁	C₂×C₃
prime radical	C₂×C₅×C₁₇×C₃₁⋊C₃	C₂
cosocle	C₂×C₁₇×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₁₇×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₃₁×Dic₁₇	C₃	semidirect
3. C₅×C₁₇×C₃₁⋊C₃	C₄	semidirect
4. Dic₁₇×C₃₁⋊C₃	C₅	direct (N × H)
7. C₅×C₁₇×C₃₁	C₃×C₄	semidirect
8. C₃₁×Dic₁₇	C₃×C₅	semidirect
10. C₁₇×C₃₁⋊C₃	C₄×C₅	semidirect
15. C₁₇×C₃₁	C₃×C₄×C₅	semidirect
17. C₅×C₃₁⋊C₃	Dic₁₇	direct (N × H)
19. C₅×Dic₁₇	C₃₁⋊C₃	direct (N × H)
25. C₅×C₃₁	C₃×Dic₁₇	semidirect
28. C₃₁⋊C₃	C₅×Dic₁₇	direct (N × H)
29. C₅×C₁₇	C₄×C₃₁⋊C₃	semidirect
30. Dic₁₇	C₅×C₃₁⋊C₃	direct (N × H)
35. C₃₁	C₃×C₅×Dic₁₇	semidirect
38. C₁₇	C₄×C₅×C₃₁⋊C₃	semidirect
43. C₅	Dic₁₇×C₃₁⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₇×C₃₁⋊C₃	2
C₅×C₃₁×Dic₁₇	3
Dic₁₇×C₃₁⋊C₃	5
C₄×C₅×C₃₁⋊C₃	17
C₃×C₅×Dic₁₇	31

Subgroups — C5×Dic17×C31⋊C3 #44539271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₁₇×C₃₁⋊C₃ #44539271