Subgroups — C₂×C₃×C₁₇×D₁₅₅ #44539401

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₁₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇×D₃₁	—	5	1	no	maximal, Hall
6	C₁₇×D₁₅₅	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₁₇×D₃₁	—	5	2	no	—
9	C₂×C₃×C₁₇×C₃₁	D₅	1	1	yes	characteristic, complemented
10	C₅×C₁₇×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×D₃₁	—	5	1	no	Hall
12	C₂×C₃×D₁₅₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₇×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₇×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
15	C₁₇×D₃₁	—	5	2	no	—
16	C₂×C₃×D₅×C₁₇	—	31	1	no	maximal, Hall
17	C₂×C₃×C₅×C₃₁	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₃×D₁₅₅	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×D₁₅₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₁₇×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅×C₁₇	D₃₁	1	1	yes	characteristic, complemented
22	C₃×D₅×C₁₇	—	31	2	no	—
23	C₃×C₅×C₃₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₃₁	—	5	1	no	Hall
25	C₂×D₅×C₁₇	—	31	1	no	Hall
26	C₂×C₅×C₃₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
27	D₁₅₅	C₂×C₃×C₁₇	1	2	yes	direct product factor
28	C₃×C₅×C₁₇	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₃×C₁₇	—	155	1	no	Hall
30	C₂×C₃×C₃₁	D₅×C₁₇	1	1	yes	characteristic, complemented
31	C₃×D₃₁	—	5	2	no	—
32	C₂×C₅×C₁₇	C₃×D₃₁	1	1	yes	characteristic, complemented
33	D₅×C₁₇	—	31	2	no	—
34	C₅×C₃₁	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃₁	—	5	1	no	Hall
36	C₂×C₃×C₁₇	—	155	2	no	—
37	C₂×C₃×C₁₇	D₁₅₅	1	1	yes	characteristic, direct product factor
38	C₃×C₃₁	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₁₇	—	155	1	no	Hall
41	C₂×C₃₁	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented
42	D₃₁	—	5	2	no	—
43	C₂×C₃×D₅	—	31	1	no	Hall
44	C₃×C₁₇	C₂×D₁₅₅	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₁₇	—	155	2	no	—
46	C₂×C₁₇	C₃×D₁₅₅	1	1	yes	characteristic, direct product factor
47	C₃₁	C₂×C₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	C₁₇×D₃₁	1	1	yes	characteristic, complemented
49	C₃×D₅	—	31	2	no	—
50	C₂×D₅	—	31	1	no	Hall
51	C₁₇	C₂×C₃×D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	C₂×C₁₇×D₃₁	1	1	yes	characteristic, complemented, Hall
53	C₂²×C₃	—	155	1	no	Hall
54	C₂×C₅	C₃×C₁₇×D₃₁	1	1	yes	characteristic, complemented
55	D₅	—	31	2	no	—
56	C₂×C₃	—	155	2	no	—
57	C₂×C₃	C₁₇×D₁₅₅	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×C₁₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	155	1	no	Sylow
60	C₃	C₂×C₁₇×D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	155	2	no	—
62	C₂	C₃×C₁₇×D₁₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₁₅₅
commutator, cosocle, hypocenter	C₅×C₃₁	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇×C₃₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₁₅₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₇×C₃₁	C₂	semidirect
3. C₂×C₁₇×D₁₅₅	C₃	direct (N × H)
4. C₃×C₅×C₁₇×C₃₁	C₂²	semidirect
6. C₁₇×D₁₅₅	C₂×C₃	direct (N × H)
7. C₂×C₅×C₁₇×C₃₁	C₂×C₃	semidirect
9. C₂×C₃×C₁₇×C₃₁	D₅	semidirect
10. C₅×C₁₇×C₃₁	C₂²×C₃	semidirect
12. C₂×C₃×D₁₅₅	C₁₇	direct (N × H)
13. C₃×C₁₇×C₃₁	C₂×D₅	semidirect
14. C₂×C₁₇×C₃₁	C₃×D₅	semidirect
17. C₂×C₃×C₅×C₃₁	C₂×C₁₇	semidirect
18. C₃×D₁₅₅	C₂×C₁₇	direct (N × H)
19. C₂×D₁₅₅	C₃×C₁₇	direct (N × H)
20. C₁₇×C₃₁	C₂×C₃×D₅	semidirect
21. C₂×C₃×C₅×C₁₇	D₃₁	semidirect
23. C₃×C₅×C₃₁	C₂²×C₁₇	semidirect
26. C₂×C₅×C₃₁	C₂×C₃×C₁₇	semidirect
27. D₁₅₅	C₂×C₃×C₁₇	direct (N × H)
28. C₃×C₅×C₁₇	C₂×D₃₁	semidirect
30. C₂×C₃×C₃₁	D₅×C₁₇	semidirect
32. C₂×C₅×C₁₇	C₃×D₃₁	semidirect
34. C₅×C₃₁	C₂²×C₃×C₁₇	semidirect
37. C₂×C₃×C₁₇	D₁₅₅	direct (N × H)
38. C₃×C₃₁	C₂×D₅×C₁₇	semidirect
39. C₅×C₁₇	C₂×C₃×D₃₁	semidirect
41. C₂×C₃₁	C₃×D₅×C₁₇	semidirect
44. C₃×C₁₇	C₂×D₁₅₅	direct (N × H)
46. C₂×C₁₇	C₃×D₁₅₅	direct (N × H)
47. C₃₁	C₂×C₃×D₅×C₁₇	semidirect
48. C₂×C₃×C₅	C₁₇×D₃₁	semidirect
51. C₁₇	C₂×C₃×D₁₅₅	direct (N × H)
52. C₃×C₅	C₂×C₁₇×D₃₁	semidirect
54. C₂×C₅	C₃×C₁₇×D₃₁	semidirect
57. C₂×C₃	C₁₇×D₁₅₅	direct (N × H)
58. C₅	C₂×C₃×C₁₇×D₃₁	semidirect
60. C₃	C₂×C₁₇×D₁₅₅	direct (N × H)
62. C₂	C₃×C₁₇×D₁₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₇×D₁₅₅	2
C₂×C₃×C₅×C₁₇×C₃₁	2
C₂×C₁₇×D₁₅₅	3
C₂×C₃×C₁₇×D₃₁	5
C₂×C₃×D₁₅₅	17
C₂×C₃×D₅×C₁₇	31

Subgroups — C2×C3×C17×D155 #44539401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₇×D₁₅₅ #44539401