Subgroups — C₂×C₃²×D₁₅₅ #19150184

Order 5580.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₅₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₃₁	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₃₁	C₂×C₃	1	4	yes	complemented
7	C₃×D₁₅₅	C₂×C₃	1	8	yes	direct product factor
8	C₂×D₁₅₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₃₁	D₅	1	1	yes	characteristic, complemented
10	C₃²×D₃₁	—	5	2	no	—
11	C₃×C₅×C₃₁	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃×D₃₁	—	5	4	no	—
13	C₂×C₅×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented
14	D₁₅₅	C₂×C₃²	1	2	yes	direct product factor
15	C₃²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₃₁	C₃×D₅	1	4	yes	complemented
17	C₃×D₃₁	—	5	8	no	—
18	C₂×C₃²×D₅	—	31	1	no	maximal, Hall
19	C₅×C₃₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₁	—	5	1	no	Hall
21	C₃×C₃₁	C₂×C₃×D₅	1	4	yes	complemented
22	C₂×C₃²×C₅	D₃₁	1	1	yes	characteristic, complemented
23	C₃²×D₅	—	31	2	no	—
24	C₂×C₃₁	C₃²×D₅	1	1	yes	characteristic, complemented
25	D₃₁	—	5	2	no	—
26	C₂×C₃×D₅	—	31	4	no	—
27	C₃²×C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₃²	—	155	1	no	Hall
29	C₃₁	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃×C₅	C₃×D₃₁	1	4	yes	complemented
31	C₃×D₅	—	31	8	no	—
32	C₂×D₅	—	31	1	no	Hall
33	C₂×C₃²	—	155	2	no	—
34	C₂×C₃²	D₁₅₅	1	1	yes	characteristic, direct product factor
35	C₃×C₅	C₂×C₃×D₃₁	1	4	yes	complemented
36	C₂²×C₃	—	155	4	no	—
37	C₂×C₅	C₃²×D₃₁	1	1	yes	characteristic, complemented
38	D₅	—	31	2	no	—
39	C₃²	C₂×D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	155	8	no	—
41	C₂×C₃	C₃×D₁₅₅	1	4	yes	direct product factor
42	C₅	C₂×C₃²×D₃₁	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	155	1	no	Sylow
44	C₃	C₂×C₃×D₁₅₅	1	4	yes	direct product factor
45	C₂	—	155	2	no	—
46	C₂	C₃²×D₁₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₁₅₅
commutator, hypocenter	C₅×C₃₁	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₃₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₅₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₃₁	C₂	semidirect
3. C₂×C₃×D₁₅₅	C₃	direct (N × H)
4. C₃²×C₅×C₃₁	C₂²	semidirect
6. C₂×C₃×C₅×C₃₁	C₂×C₃	semidirect
7. C₃×D₁₅₅	C₂×C₃	direct (N × H)
8. C₂×D₁₅₅	C₃²	direct (N × H)
9. C₂×C₃²×C₃₁	D₅	semidirect
11. C₃×C₅×C₃₁	C₂²×C₃	semidirect
13. C₂×C₅×C₃₁	C₂×C₃²	semidirect
14. D₁₅₅	C₂×C₃²	direct (N × H)
15. C₃²×C₃₁	C₂×D₅	semidirect
16. C₂×C₃×C₃₁	C₃×D₅	semidirect
19. C₅×C₃₁	C₂²×C₃²	semidirect
21. C₃×C₃₁	C₂×C₃×D₅	semidirect
22. C₂×C₃²×C₅	D₃₁	semidirect
24. C₂×C₃₁	C₃²×D₅	semidirect
27. C₃²×C₅	C₂×D₃₁	semidirect
29. C₃₁	C₂×C₃²×D₅	semidirect
30. C₂×C₃×C₅	C₃×D₃₁	semidirect
34. C₂×C₃²	D₁₅₅	direct (N × H)
35. C₃×C₅	C₂×C₃×D₃₁	semidirect
37. C₂×C₅	C₃²×D₃₁	semidirect
39. C₃²	C₂×D₁₅₅	direct (N × H)
41. C₂×C₃	C₃×D₁₅₅	direct (N × H)
42. C₅	C₂×C₃²×D₃₁	semidirect
44. C₃	C₂×C₃×D₁₅₅	direct (N × H)
46. C₂	C₃²×D₁₅₅	direct (N × H)

Subgroups — C2×C32×D155 #19150184

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×D₁₅₅ #19150184