Subgroups — C₂×C₃×C₅×D₁₅₅ #22604943

Order 9300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₁₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×C₅×D₃₁	—	5	1	no	maximal
7	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₁₅₅	C₂×C₃	1	2	yes	direct product factor
9	C₂×C₃×C₅×C₃₁	—	2	2	no	—
10	C₂×C₃×C₅×C₃₁	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₁₅₅	C₂×C₅	1	2	yes	direct product factor
13	C₃×C₅×D₃₁	—	5	2	no	—
14	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₅₅	C₃×C₅	1	1	yes	characteristic, direct product factor
16	C₂×C₅×D₃₁	—	5	1	no	—
17	C₃×C₅×C₃₁	—	2	2	no	—
18	C₃×C₅×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂×C₃×D₃₁	—	5	1	no	Hall
21	C₂×C₅×C₃₁	—	2	2	no	—
22	C₂×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
23	C₂×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	D₁₅₅	C₂×C₃×C₅	1	2	yes	direct product factor
25	C₅×D₃₁	—	5	2	no	—
26	C₂×C₃×C₅×D₅	—	31	1	no	maximal, Hall
27	C₂×C₃×C₃₁	C₅×D₅	1	1	yes	characteristic, complemented
28	C₃×D₃₁	—	5	2	no	—
29	C₅×C₃₁	—	2	2	no	—
30	C₅×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented
31	C₅×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅²	D₃₁	1	1	yes	characteristic, complemented
33	C₃×C₅×D₅	—	31	2	no	—
34	C₂×D₃₁	—	5	1	no	Hall
35	C₂×C₅×D₅	—	31	1	no	Hall
36	C₃×C₃₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic, complemented
39	D₃₁	—	5	2	no	—
40	C₂²×C₃×C₅	—	155	1	no	—
41	C₂×C₃×D₅	—	31	1	no	—
42	C₂×C₅²	C₃×D₃₁	1	1	yes	characteristic, complemented
43	C₅×D₅	—	31	2	no	—
44	C₃₁	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₅	—	155	2	no	—
47	C₂×C₃×C₅	C₅×D₃₁	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅	D₁₅₅	1	1	yes	characteristic, direct product factor
49	C₃×D₅	—	31	2	no	—
50	C₅²	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	—	155	1	no	—
52	C₂×D₅	—	31	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₂×C₅×D₃₁	1	1	yes	characteristic, complemented
55	C₃×C₅	C₂×D₁₅₅	1	1	yes	characteristic, direct product factor
56	C₂²×C₃	—	155	1	no	Hall
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	155	2	no	—
59	C₂×C₅	C₃×C₅×D₃₁	1	1	yes	characteristic, complemented
60	C₂×C₅	C₃×D₁₅₅	1	1	yes	characteristic, direct product factor
61	D₅	—	31	2	no	—
62	C₂×C₃	—	155	2	no	—
63	C₂×C₃	C₅×D₁₅₅	1	1	yes	characteristic, direct product factor
64	C₅	—	2	2	no	—
65	C₅	C₂×C₃×C₅×D₃₁	1	1	yes	characteristic, complemented
66	C₅	C₂×C₃×D₁₅₅	1	1	yes	characteristic, direct product factor
67	C₂²	—	155	1	no	Sylow
68	C₃	C₂×C₅×D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	—	155	2	no	—
70	C₂	C₃×C₅×D₁₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₁₅₅
commutator, hypocenter	C₅×C₃₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₁₅₅	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₃₁	C₂	semidirect
3. C₂×C₅×D₁₅₅	C₃	direct (N × H)
4. C₃×C₅²×C₃₁	C₂²	semidirect
5. C₂×C₃×D₁₅₅	C₅	direct (N × H)
7. C₂×C₅²×C₃₁	C₂×C₃	semidirect
8. C₅×D₁₅₅	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₃₁	D₅	semidirect
11. C₂×C₃×C₅×C₃₁	C₂×C₅	semidirect
12. C₃×D₁₅₅	C₂×C₅	direct (N × H)
14. C₅²×C₃₁	C₂²×C₃	semidirect
15. C₂×D₁₅₅	C₃×C₅	direct (N × H)
18. C₃×C₅×C₃₁	C₂×D₅	semidirect
19. C₃×C₅×C₃₁	C₂²×C₅	semidirect
22. C₂×C₅×C₃₁	C₃×D₅	semidirect
23. C₂×C₅×C₃₁	C₂×C₃×C₅	semidirect
24. D₁₅₅	C₂×C₃×C₅	direct (N × H)
27. C₂×C₃×C₃₁	C₅×D₅	semidirect
30. C₅×C₃₁	C₂×C₃×D₅	semidirect
31. C₅×C₃₁	C₂²×C₃×C₅	semidirect
32. C₂×C₃×C₅²	D₃₁	semidirect
36. C₃×C₃₁	C₂×C₅×D₅	semidirect
37. C₃×C₅²	C₂×D₃₁	semidirect
38. C₂×C₃₁	C₃×C₅×D₅	semidirect
42. C₂×C₅²	C₃×D₃₁	semidirect
44. C₃₁	C₂×C₃×C₅×D₅	semidirect
47. C₂×C₃×C₅	C₅×D₃₁	semidirect
48. C₂×C₃×C₅	D₁₅₅	direct (N × H)
50. C₅²	C₂×C₃×D₃₁	semidirect
54. C₃×C₅	C₂×C₅×D₃₁	semidirect
55. C₃×C₅	C₂×D₁₅₅	direct (N × H)
59. C₂×C₅	C₃×C₅×D₃₁	semidirect
60. C₂×C₅	C₃×D₁₅₅	direct (N × H)
63. C₂×C₃	C₅×D₁₅₅	direct (N × H)
65. C₅	C₂×C₃×C₅×D₃₁	semidirect
66. C₅	C₂×C₃×D₁₅₅	direct (N × H)
68. C₃	C₂×C₅×D₁₅₅	direct (N × H)
70. C₂	C₃×C₅×D₁₅₅	direct (N × H)

Subgroups — C2×C3×C5×D155 #22604943

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×D₁₅₅ #22604943