Subgroups — D₅×D₄₃₅ #22576487

Order 8700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₁₄₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₄₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₄₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₄₃₅	—	5	1	no	maximal
7	D₅×D₈₇	—	5	1	no	maximal
8	C₅⋊D₁₄₅	—	3	1	no	—
9	C₅×D₁₄₅	—	3	1	no	—
10	C₅×D₅×C₂₉	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₂₉	—	5	1	no	—
12	D₄₃₅	—	5	1	no	—
13	D₄₃₅	—	5	1	no	—
14	D₄₃₅	—	10	2	no	—
15	D₄₃₅	D₅	1	1	yes	characteristic, direct product factor
16	C₅×D₈₇	—	5	1	no	—
17	C₃×D₅×C₂₉	D₅	1	1	yes	characteristic, complemented
18	C₅²×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₄₅	—	15	1	no	—
20	D₅×D₂₉	—	15	1	no	—
21	C₃×C₅×C₂₉	—	2	2	no	—
22	C₃×C₅×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented
24	C₂×D₈₇	—	25	1	no	Hall
25	D₅×D₁₅	—	29	1	no	maximal, Hall
26	C₂×C₅×C₂₉	—	5	1	no	—
27	D₁₄₅	—	3	1	no	—
28	D₁₄₅	—	15	1	no	—
29	D₁₄₅	—	15	1	no	—
30	D₁₄₅	—	30	2	no	—
31	C₅×D₂₉	—	15	1	no	—
32	D₅×C₂₉	D₁₅	1	1	yes	characteristic, complemented
33	C₂×C₃×C₂₉	—	5	1	no	—
34	D₈₇	—	5	1	no	—
35	D₈₇	—	25	1	no	—
36	C₃⋊(C₅⋊D₅)	—	29	1	no	—
37	C₅×D₁₅	—	29	1	no	—
38	C₃×C₅×D₅	D₂₉	1	1	yes	characteristic, complemented
39	C₅×C₂₉	—	2	2	no	—
40	C₅×C₂₉	D₃×D₅	1	1	yes	characteristic, complemented
41	C₅×C₂₉	C₂×D₁₅	1	1	yes	characteristic, complemented
42	C₂×D₂₉	—	75	1	no	Hall
43	D₅²	—	87	1	no	Hall
44	C₃×C₂₉	D₅²	1	1	yes	characteristic, complemented, Hall
45	C₃×C₅²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
46	C₂×D₁₅	—	145	1	no	—
47	D₃×D₅	—	145	1	no	—
48	C₂×C₂₉	—	5	1	no	—
49	D₂₉	—	15	1	no	—
50	D₂₉	—	75	1	no	—
51	C₅⋊D₅	—	87	1	no	—
52	C₅×D₅	—	87	1	no	—
53	C₅×D₅	D₈₇	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅	—	5	1	no	—
55	D₁₅	—	29	1	no	—
56	D₁₅	—	290	2	no	—
57	D₁₅	—	145	1	no	—
58	D₁₅	—	145	1	no	—
59	C₃×D₅	D₁₄₅	1	1	yes	characteristic, complemented
60	C₅×D₃	—	145	1	no	—
61	C₂₉	D₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
62	C₅²	C₂×D₈₇	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	435	1	no	—
64	C₂×D₅	—	435	1	no	—
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₂₉	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×D₁₄₅	1	1	yes	characteristic, complemented
68	C₂×D₃	—	725	1	no	Hall
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	435	1	no	—
71	D₅	—	87	1	no	—
72	D₅	—	870	2	no	—
73	D₅	—	435	1	no	—
74	D₅	—	435	1	no	—
75	D₅	D₄₃₅	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	5	1	no	—
77	D₃	—	145	1	no	—
78	D₃	—	725	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₅×D₈₇	1	1	yes	characteristic, complemented
81	C₅	C₂×D₄₃₅	1	1	yes	characteristic, complemented
82	C₂²	—	2175	1	no	Sylow
83	C₃	D₅×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	2175	1	no	—
86	C₂	—	435	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₂₉	C₂²
LCS	G ▷ C₃×C₅²×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₁₄₅)	C₂	semidirect
2. C₅×D₄₃₅	C₂	semidirect
3. C₃×C₅×D₅×C₂₉	C₂	semidirect
5. C₃×C₅²×C₂₉	C₂²	semidirect
10. C₅×D₅×C₂₉	D₃	semidirect
15. D₄₃₅	D₅	direct (N × H)
17. C₃×D₅×C₂₉	D₅	semidirect
18. C₅²×C₂₉	C₂×D₃	semidirect
22. C₃×C₅×C₂₉	C₂×D₅	semidirect
23. C₃×C₅×C₂₉	C₂×D₅	semidirect
32. D₅×C₂₉	D₁₅	semidirect
38. C₃×C₅×D₅	D₂₉	semidirect
40. C₅×C₂₉	D₃×D₅	semidirect
41. C₅×C₂₉	C₂×D₁₅	semidirect
44. C₃×C₂₉	D₅²	semidirect
45. C₃×C₅²	C₂×D₂₉	semidirect
53. C₅×D₅	D₈₇	semidirect
59. C₃×D₅	D₁₄₅	semidirect
61. C₂₉	D₅×D₁₅	semidirect
62. C₅²	C₂×D₈₇	semidirect
66. C₃×C₅	D₅×D₂₉	semidirect
67. C₃×C₅	C₂×D₁₄₅	semidirect
75. D₅	D₄₃₅	direct (N × H)
80. C₅	D₅×D₈₇	semidirect
81. C₅	C₂×D₄₃₅	semidirect
83. C₃	D₅×D₁₄₅	semidirect

Subgroups — D5×D435 #22576487

Conjugacy classes of subgroups

Complements

Subgroups — D₅×D₄₃₅ #22576487