Subgroups — D₅×D₁₅×C₃₇ #26012919

Order 11100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅²×C₃₇	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₁₅×C₃₇	—	5	1	no	maximal
7	D₃×D₅×C₃₇	—	5	1	no	maximal
8	C₃₇×C₅⋊D₅	—	3	1	no	—
9	C₅×D₅×C₃₇	—	3	1	no	—
10	C₅×D₅×C₃₇	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₃₇	—	5	1	no	—
12	D₁₅×C₃₇	—	5	1	no	—
13	D₁₅×C₃₇	—	5	1	no	—
14	D₁₅×C₃₇	—	10	2	no	—
15	D₁₅×C₃₇	D₅	1	1	yes	characteristic, direct product factor
16	C₅×D₃×C₃₇	—	5	1	no	—
17	C₃×D₅×C₃₇	D₅	1	1	yes	characteristic, complemented
18	C₅²×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₅×C₃₇	—	15	1	no	—
20	C₂×D₅×C₃₇	—	15	1	no	—
21	C₃×C₅×C₃₇	—	2	2	no	—
22	C₃×C₅×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented
24	C₂×D₃×C₃₇	—	25	1	no	Hall
25	C₂×C₅×C₃₇	—	5	1	no	—
26	C₂×C₅×C₃₇	—	15	1	no	—
27	D₅×C₃₇	—	3	1	no	—
28	D₅×C₃₇	—	15	1	no	—
29	D₅×C₃₇	—	15	1	no	—
30	D₅×C₃₇	—	30	2	no	—
31	D₅×C₃₇	D₁₅	1	1	yes	characteristic, direct product factor
32	D₅×D₁₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₃×C₃₇	—	5	1	no	—
34	D₃×C₃₇	—	5	1	no	—
35	D₃×C₃₇	—	25	1	no	—
36	C₅×C₃₇	—	2	2	no	—
37	C₅×C₃₇	D₃×D₅	1	1	yes	characteristic, complemented
38	C₅×C₃₇	C₂×D₁₅	1	1	yes	characteristic, complemented
39	C₃⋊(C₅⋊D₅)	C₂×C₃₇	1	1	yes	characteristic, complemented
40	C₅×D₁₅	C₂×C₃₇	1	1	yes	characteristic, complemented
41	C₃×C₅×D₅	C₂×C₃₇	1	1	yes	characteristic, complemented
42	C₂²×C₃₇	—	75	1	no	Hall
43	C₃×C₃₇	D₅²	1	1	yes	characteristic, complemented, Hall
44	D₅²	—	3	1	no	Hall
45	C₃×C₅²	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃₇	—	5	1	no	—
47	C₂×C₃₇	—	15	1	no	—
48	C₂×C₃₇	—	75	1	no	—
49	C₂×D₁₅	—	5	1	no	—
50	D₃×D₅	—	5	1	no	—
51	C₅⋊D₅	—	3	1	no	—
52	C₅×D₅	—	3	1	no	—
53	C₅×D₅	D₃×C₃₇	1	1	yes	characteristic, complemented
54	C₃₇	D₅×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×C₃×C₅	—	5	1	no	—
56	D₁₅	—	5	1	no	—
57	D₁₅	—	5	1	no	—
58	D₁₅	—	10	2	no	—
59	D₁₅	D₅×C₃₇	1	1	yes	characteristic, direct product factor
60	C₃×D₅	D₅×C₃₇	1	1	yes	characteristic, complemented
61	C₅×D₃	—	5	1	no	—
62	C₅²	C₂×D₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	15	1	no	—
64	C₂×D₅	—	15	1	no	—
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	C₂×D₅×C₃₇	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×D₅×C₃₇	1	1	yes	characteristic, complemented
68	C₂×D₃	—	25	1	no	Hall
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	15	1	no	—
71	D₅	—	3	1	no	—
72	D₅	—	15	1	no	—
73	D₅	—	15	1	no	—
74	D₅	—	30	2	no	—
75	D₅	D₁₅×C₃₇	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	5	1	no	—
77	D₃	—	5	1	no	—
78	D₃	—	25	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₃×D₅×C₃₇	1	1	yes	characteristic, complemented
81	C₅	C₂×D₁₅×C₃₇	1	1	yes	characteristic, complemented
82	C₂²	—	75	1	no	Sylow
83	C₃	D₅²×C₃₇	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	15	1	no	—
86	C₂	—	75	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	D₅×D₁₅
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₇	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃₇×C₃⋊(C₅⋊D₅)	C₂	semidirect
2. C₅×D₁₅×C₃₇	C₂	semidirect
3. C₃×C₅×D₅×C₃₇	C₂	semidirect
5. C₃×C₅²×C₃₇	C₂²	semidirect
10. C₅×D₅×C₃₇	D₃	semidirect
15. D₁₅×C₃₇	D₅	direct (N × H)
17. C₃×D₅×C₃₇	D₅	semidirect
18. C₅²×C₃₇	C₂×D₃	semidirect
22. C₃×C₅×C₃₇	C₂×D₅	semidirect
23. C₃×C₅×C₃₇	C₂×D₅	semidirect
31. D₅×C₃₇	D₁₅	direct (N × H)
32. D₅×D₁₅	C₃₇	direct (N × H)
37. C₅×C₃₇	D₃×D₅	semidirect
38. C₅×C₃₇	C₂×D₁₅	semidirect
39. C₃⋊(C₅⋊D₅)	C₂×C₃₇	semidirect
40. C₅×D₁₅	C₂×C₃₇	semidirect
41. C₃×C₅×D₅	C₂×C₃₇	semidirect
43. C₃×C₃₇	D₅²	semidirect
45. C₃×C₅²	C₂²×C₃₇	semidirect
53. C₅×D₅	D₃×C₃₇	semidirect
54. C₃₇	D₅×D₁₅	direct (N × H)
59. D₁₅	D₅×C₃₇	direct (N × H)
60. C₃×D₅	D₅×C₃₇	semidirect
62. C₅²	C₂×D₃×C₃₇	semidirect
66. C₃×C₅	C₂×D₅×C₃₇	semidirect
67. C₃×C₅	C₂×D₅×C₃₇	semidirect
75. D₅	D₁₅×C₃₇	direct (N × H)
80. C₅	D₃×D₅×C₃₇	semidirect
81. C₅	C₂×D₁₅×C₃₇	semidirect
83. C₃	D₅²×C₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₇×C₃⋊(C₅⋊D₅)	2
C₅×D₁₅×C₃₇	2
C₃×C₅×D₅×C₃₇	2
D₅²×C₃₇	3
C₂×D₁₅×C₃₇	5
D₃×D₅×C₃₇	5
D₅×D₁₅	37

Subgroups — D5×D15×C37 #26012919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₅×C₃₇ #26012919