Subgroups — C₂×C₃×C₅×D₅₃₅ #44545708

Order 32100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₅₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₅×D₁₀₇	—	5	1	no	maximal
6	C₂×C₃×D₅₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×D₅₃₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₅²×C₁₀₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₅₃₅	C₂×C₅	1	2	yes	direct product factor
10	C₃×C₅×D₁₀₇	—	5	2	no	—
11	C₂×C₃×C₅×C₁₀₇	—	2	2	no	—
12	C₂×C₃×C₅×C₁₀₇	D₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×C₁₀₇	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅²×C₁₀₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×D₁₀₇	—	5	1	no	—
16	C₂×D₅₃₅	C₃×C₅	1	1	yes	characteristic, direct product factor
17	C₃×C₅×C₁₀₇	—	2	2	no	—
18	C₃×C₅×C₁₀₇	C₂×D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₁₀₇	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂×C₃×D₁₀₇	—	5	1	no	Hall
21	C₂×C₅×C₁₀₇	—	2	2	no	—
22	C₂×C₅×C₁₀₇	C₃×D₅	1	1	yes	characteristic, complemented
23	C₂×C₅×C₁₀₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	D₅₃₅	C₂×C₃×C₅	1	2	yes	direct product factor
25	C₅×D₁₀₇	—	5	2	no	—
26	C₂×C₃×C₁₀₇	C₅×D₅	1	1	yes	characteristic, complemented
27	C₃×D₁₀₇	—	5	2	no	—
28	C₅×C₁₀₇	—	2	2	no	—
29	C₅×C₁₀₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
30	C₅×C₁₀₇	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
31	C₂×D₁₀₇	—	5	1	no	Hall
32	C₃×C₁₀₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅×D₅	—	107	1	no	maximal, Hall
34	C₂×C₁₀₇	C₃×C₅×D₅	1	1	yes	characteristic, complemented
35	D₁₀₇	—	5	2	no	—
36	C₂×C₃×C₅²	D₁₀₇	1	1	yes	characteristic, complemented
37	C₃×C₅×D₅	—	107	2	no	—
38	C₁₀₇	C₂×C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₅×D₅	—	107	1	no	Hall
40	C₃×C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₃×C₅	—	535	1	no	—
42	C₂×C₃×D₅	—	107	1	no	—
43	C₂×C₅²	C₃×D₁₀₇	1	1	yes	characteristic, complemented
44	C₅×D₅	—	107	2	no	—
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₅	—	535	2	no	—
47	C₂×C₃×C₅	C₅×D₁₀₇	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅	D₅₃₅	1	1	yes	characteristic, direct product factor
49	C₃×D₅	—	107	2	no	—
50	C₅²	C₂×C₃×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	—	535	1	no	—
52	C₂×D₅	—	107	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₂×D₅₃₅	1	1	yes	characteristic, direct product factor
55	C₃×C₅	C₂×C₅×D₁₀₇	1	1	yes	characteristic, complemented
56	C₂²×C₃	—	535	1	no	Hall
57	C₂×C₅	—	2	2	no	—
58	C₂×C₅	—	535	2	no	—
59	C₂×C₅	C₃×C₅×D₁₀₇	1	1	yes	characteristic, complemented
60	C₂×C₅	C₃×D₅₃₅	1	1	yes	characteristic, direct product factor
61	D₅	—	107	2	no	—
62	C₂×C₃	—	535	2	no	—
63	C₂×C₃	C₅×D₅₃₅	1	1	yes	characteristic, direct product factor
64	C₅	—	2	2	no	—
65	C₅	C₂×C₃×D₅₃₅	1	1	yes	characteristic, direct product factor
66	C₅	C₂×C₃×C₅×D₁₀₇	1	1	yes	characteristic, complemented
67	C₂²	—	535	1	no	Sylow
68	C₃	C₂×C₅×D₅₃₅	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	—	535	2	no	—
70	C₂	C₃×C₅×D₅₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₅₃₅
commutator, cosocle, hypocenter	C₅×C₁₀₇	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₀₇	C₂
LCS	G ▷ C₅×C₁₀₇
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅₃₅	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₀₇	C₂	semidirect
3. C₂×C₅×D₅₃₅	C₃	direct (N × H)
4. C₃×C₅²×C₁₀₇	C₂²	semidirect
6. C₂×C₃×D₅₃₅	C₅	direct (N × H)
7. C₅×D₅₃₅	C₂×C₃	direct (N × H)
8. C₂×C₅²×C₁₀₇	C₂×C₃	semidirect
9. C₃×D₅₃₅	C₂×C₅	direct (N × H)
12. C₂×C₃×C₅×C₁₀₇	D₅	semidirect
13. C₂×C₃×C₅×C₁₀₇	C₂×C₅	semidirect
14. C₅²×C₁₀₇	C₂²×C₃	semidirect
16. C₂×D₅₃₅	C₃×C₅	direct (N × H)
18. C₃×C₅×C₁₀₇	C₂×D₅	semidirect
19. C₃×C₅×C₁₀₇	C₂²×C₅	semidirect
22. C₂×C₅×C₁₀₇	C₃×D₅	semidirect
23. C₂×C₅×C₁₀₇	C₂×C₃×C₅	semidirect
24. D₅₃₅	C₂×C₃×C₅	direct (N × H)
26. C₂×C₃×C₁₀₇	C₅×D₅	semidirect
29. C₅×C₁₀₇	C₂×C₃×D₅	semidirect
30. C₅×C₁₀₇	C₂²×C₃×C₅	semidirect
32. C₃×C₁₀₇	C₂×C₅×D₅	semidirect
34. C₂×C₁₀₇	C₃×C₅×D₅	semidirect
36. C₂×C₃×C₅²	D₁₀₇	semidirect
38. C₁₀₇	C₂×C₃×C₅×D₅	semidirect
40. C₃×C₅²	C₂×D₁₀₇	semidirect
43. C₂×C₅²	C₃×D₁₀₇	semidirect
47. C₂×C₃×C₅	C₅×D₁₀₇	semidirect
48. C₂×C₃×C₅	D₅₃₅	direct (N × H)
50. C₅²	C₂×C₃×D₁₀₇	semidirect
54. C₃×C₅	C₂×D₅₃₅	direct (N × H)
55. C₃×C₅	C₂×C₅×D₁₀₇	semidirect
59. C₂×C₅	C₃×C₅×D₁₀₇	semidirect
60. C₂×C₅	C₃×D₅₃₅	direct (N × H)
63. C₂×C₃	C₅×D₅₃₅	direct (N × H)
65. C₅	C₂×C₃×D₅₃₅	direct (N × H)
66. C₅	C₂×C₃×C₅×D₁₀₇	semidirect
68. C₃	C₂×C₅×D₅₃₅	direct (N × H)
70. C₂	C₃×C₅×D₅₃₅	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×C₅×D₅₃₅	2
C₂×C₃×C₅²×C₁₀₇	2
C₂×C₅×D₅₃₅	3
C₂×C₃×C₅×D₁₀₇	5
C₂×C₃×D₅₃₅	5
C₂×C₃×C₅×D₅	107

Subgroups — C2×C3×C5×D535 #44545708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×D₅₃₅ #44545708