Subgroups — C₂×C₃²×C₅⋊D₁₅₅ #42124984

Order 27900.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅⋊D₁₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅⋊D₁₅₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₁₅₅	—	5	6	no	maximal
6	C₃×C₅⋊D₁₅₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅²×C₃₁	C₂×C₃	1	4	yes	complemented
8	C₂×C₅⋊D₁₅₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×D₁₅₅	—	5	12	no	—
10	C₂×C₃²×C₅×C₃₁	D₅	1	6	yes	complemented
11	C₃×C₅²×C₃₁	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃×D₁₅₅	—	5	24	no	—
13	C₂×C₅²×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₅⋊D₁₅₅	C₂×C₃²	1	2	yes	direct product factor
15	C₃²×C₅×C₃₁	C₂×D₅	1	6	yes	complemented
16	C₂×C₃²×D₃₁	—	25	1	no	Hall
17	C₂×C₃×C₅×C₃₁	C₃×D₅	1	24	yes	complemented
18	C₃×D₁₅₅	—	5	48	no	—
19	C₂×C₃²×C₅⋊D₅	—	31	1	no	maximal, Hall
20	C₅²×C₃₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
21	C₂×D₁₅₅	—	5	6	no	—
22	C₂×C₃²×C₃₁	C₅⋊D₅	1	1	yes	characteristic, complemented
23	C₃²×D₃₁	—	25	2	no	—
24	C₃×C₅×C₃₁	C₂×C₃×D₅	1	24	yes	complemented
25	C₂×C₃²×C₅²	D₃₁	1	1	yes	characteristic, complemented
26	C₃²×C₅⋊D₅	—	31	2	no	—
27	C₂×C₃×D₃₁	—	25	4	no	—
28	C₂×C₅×C₃₁	C₃²×D₅	1	6	yes	complemented
29	D₁₅₅	—	5	12	no	—
30	C₂×C₃×C₅⋊D₅	—	31	4	no	—
31	C₃²×C₃₁	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₅²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₃₁	C₃×C₅⋊D₅	1	4	yes	complemented
34	C₃×D₃₁	—	25	8	no	—
35	C₂×C₃²×D₅	—	155	6	no	—
36	C₅×C₃₁	C₂×C₃²×D₅	1	6	yes	complemented
37	C₂×C₃×C₅²	C₃×D₃₁	1	4	yes	complemented
38	C₃×C₅⋊D₅	—	31	8	no	—
39	C₂×D₃₁	—	25	1	no	Hall
40	C₂×C₅⋊D₅	—	31	1	no	Hall
41	C₃×C₃₁	C₂×C₃×C₅⋊D₅	1	4	yes	complemented
42	C₂×C₃²×C₅	D₁₅₅	1	6	yes	complemented
43	C₃²×D₅	—	155	12	no	—
44	C₃×C₅²	C₂×C₃×D₃₁	1	4	yes	complemented
45	C₂×C₃₁	C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented
46	D₃₁	—	25	2	no	—
47	C₂×C₃×D₅	—	155	24	no	—
48	C₂×C₅²	C₃²×D₃₁	1	1	yes	characteristic, complemented
49	C₅⋊D₅	—	31	2	no	—
50	C₃²×C₅	C₂×D₁₅₅	1	6	yes	complemented
51	C₂²×C₃²	—	775	1	no	Hall
52	C₃₁	C₂×C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₃×C₅	C₃×D₁₅₅	1	24	yes	complemented
54	C₃×D₅	—	155	48	no	—
55	C₅²	C₂×C₃²×D₃₁	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₅	—	155	6	no	—
57	C₂×C₃²	—	775	2	no	—
58	C₂×C₃²	C₅⋊D₁₅₅	1	1	yes	characteristic, direct product factor
59	C₃×C₅	C₂×C₃×D₁₅₅	1	24	yes	complemented
60	C₂²×C₃	—	775	4	no	—
61	C₂×C₅	C₃²×D₁₅₅	1	6	yes	complemented
62	D₅	—	155	12	no	—
63	C₃²	C₂×C₅⋊D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	775	8	no	—
65	C₂×C₃	C₃×C₅⋊D₁₅₅	1	4	yes	direct product factor
66	C₅	C₂×C₃²×D₁₅₅	1	6	yes	complemented
67	C₂²	—	775	1	no	Sylow
68	C₃	C₂×C₃×C₅⋊D₁₅₅	1	4	yes	direct product factor
69	C₂	—	775	2	no	—
70	C₂	C₃²×C₅⋊D₁₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	C₅⋊D₁₅₅
commutator, cosocle, hypocenter	C₅²×C₃₁	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₃₁	C₂
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅⋊D₁₅₅	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₃₁	C₂	semidirect
3. C₂×C₃×C₅⋊D₁₅₅	C₃	direct (N × H)
4. C₃²×C₅²×C₃₁	C₂²	semidirect
6. C₃×C₅⋊D₁₅₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅²×C₃₁	C₂×C₃	semidirect
8. C₂×C₅⋊D₁₅₅	C₃²	direct (N × H)
10. C₂×C₃²×C₅×C₃₁	D₅	semidirect
11. C₃×C₅²×C₃₁	C₂²×C₃	semidirect
13. C₂×C₅²×C₃₁	C₂×C₃²	semidirect
14. C₅⋊D₁₅₅	C₂×C₃²	direct (N × H)
15. C₃²×C₅×C₃₁	C₂×D₅	semidirect
17. C₂×C₃×C₅×C₃₁	C₃×D₅	semidirect
20. C₅²×C₃₁	C₂²×C₃²	semidirect
22. C₂×C₃²×C₃₁	C₅⋊D₅	semidirect
24. C₃×C₅×C₃₁	C₂×C₃×D₅	semidirect
25. C₂×C₃²×C₅²	D₃₁	semidirect
28. C₂×C₅×C₃₁	C₃²×D₅	semidirect
31. C₃²×C₃₁	C₂×C₅⋊D₅	semidirect
32. C₃²×C₅²	C₂×D₃₁	semidirect
33. C₂×C₃×C₃₁	C₃×C₅⋊D₅	semidirect
36. C₅×C₃₁	C₂×C₃²×D₅	semidirect
37. C₂×C₃×C₅²	C₃×D₃₁	semidirect
41. C₃×C₃₁	C₂×C₃×C₅⋊D₅	semidirect
42. C₂×C₃²×C₅	D₁₅₅	semidirect
44. C₃×C₅²	C₂×C₃×D₃₁	semidirect
45. C₂×C₃₁	C₃²×C₅⋊D₅	semidirect
48. C₂×C₅²	C₃²×D₃₁	semidirect
50. C₃²×C₅	C₂×D₁₅₅	semidirect
52. C₃₁	C₂×C₃²×C₅⋊D₅	semidirect
53. C₂×C₃×C₅	C₃×D₁₅₅	semidirect
55. C₅²	C₂×C₃²×D₃₁	semidirect
58. C₂×C₃²	C₅⋊D₁₅₅	direct (N × H)
59. C₃×C₅	C₂×C₃×D₁₅₅	semidirect
61. C₂×C₅	C₃²×D₁₅₅	semidirect
63. C₃²	C₂×C₅⋊D₁₅₅	direct (N × H)
65. C₂×C₃	C₃×C₅⋊D₁₅₅	direct (N × H)
66. C₅	C₂×C₃²×D₁₅₅	semidirect
68. C₃	C₂×C₃×C₅⋊D₁₅₅	direct (N × H)
70. C₂	C₃²×C₅⋊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
C₃²×C₅⋊D₁₅₅	2
C₂×C₃²×C₅²×C₃₁	2
C₂×C₃×C₅⋊D₁₅₅	3
C₂×C₃²×D₁₅₅	5
C₂×C₃²×C₅⋊D₅	31

Subgroups — C2×C32×C5⋊D155 #42124984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅⋊D₁₅₅ #42124984