Subgroups — D₁₅×D₁₈₅ #26012921

Order 11100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₁₈₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₁₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₈₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₁₈₅	—	5	1	no	maximal
7	D₁₅×D₃₇	—	5	1	no	maximal
8	C₅⋊D₁₈₅	—	3	1	no	—
9	C₅×D₁₈₅	D₃	1	1	yes	characteristic, complemented
10	C₅×D₅×C₃₇	—	3	1	no	—
11	D₅₅₅	—	5	1	no	—
12	D₅₅₅	—	5	1	no	—
13	D₅₅₅	—	10	2	no	—
14	D₁₅×C₃₇	D₅	1	1	yes	characteristic, complemented
15	C₅×D₃×C₃₇	—	5	1	no	—
16	C₃×D₁₈₅	D₅	1	1	yes	characteristic, complemented
17	C₃×C₅×D₃₇	—	5	1	no	—
18	C₅²×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₈₅	—	15	1	no	—
20	D₅×D₃₇	—	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	D₃×D₃₇	—	25	1	no	Hall
25	C₂×C₅×C₃₇	—	15	1	no	—
26	D₁₈₅	—	15	1	no	—
27	D₁₈₅	—	15	1	no	—
28	D₁₈₅	—	30	2	no	—
29	D₁₈₅	D₁₅	1	1	yes	characteristic, direct product factor
30	C₅×D₃₇	—	5	1	no	—
31	D₅×C₃₇	—	3	1	no	—
32	D₅×D₁₅	—	37	1	no	maximal, Hall
33	D₁₁₁	—	25	1	no	—
34	C₃×D₃₇	—	5	1	no	—
35	D₃×C₃₇	—	5	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)	—	37	1	no	—
40	C₅×D₁₅	D₃₇	1	1	yes	characteristic, complemented
41	C₃×C₅×D₅	—	37	1	no	—
42	C₂×D₃₇	—	75	1	no	Hall
43	C₃×C₃₇	D₅²	1	1	yes	characteristic, complemented, Hall
44	D₅²	—	111	1	no	Hall
45	C₃×C₅²	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃₇	—	15	1	no	—
47	D₃₇	—	5	1	no	—
48	D₃₇	—	75	1	no	—
49	C₂×D₁₅	—	185	1	no	—
50	D₃×D₅	—	185	1	no	—
51	C₅⋊D₅	—	111	1	no	—
52	C₅×D₅	—	3	1	no	—
53	C₅×D₅	—	37	1	no	—
54	C₃₇	D₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₅	—	185	1	no	—
56	D₁₅	—	370	2	no	—
57	D₁₅	—	185	1	no	—
58	D₁₅	—	185	1	no	—
59	D₁₅	D₁₈₅	1	1	yes	characteristic, direct product factor
60	C₃×D₅	—	37	1	no	—
61	C₅×D₃	—	5	1	no	—
62	C₅²	D₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	555	1	no	—
64	C₂×D₅	—	555	1	no	—
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₃₇	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×D₁₈₅	1	1	yes	characteristic, complemented
68	C₂×D₃	—	925	1	no	Hall
69	C₂×C₅	—	15	1	no	—
70	C₂×C₅	—	185	1	no	—
71	D₅	—	3	1	no	—
72	D₅	—	37	1	no	—
73	D₅	—	555	1	no	—
74	D₅	—	555	1	no	—
75	D₅	—	1110	2	no	—
76	C₂×C₃	—	185	1	no	—
77	D₃	—	5	1	no	—
78	D₃	—	925	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₁₅×D₃₇	1	1	yes	characteristic, complemented
81	C₅	D₃×D₁₈₅	1	1	yes	characteristic, complemented
82	C₂²	—	2775	1	no	Sylow
83	C₃	D₅×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	15	1	no	—
85	C₂	—	185	1	no	—
86	C₂	—	2775	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₁₈₅)	C₂	semidirect
2. C₅×D₁₅×C₃₇	C₂	semidirect
3. C₃×C₅×D₁₈₅	C₂	semidirect
5. C₃×C₅²×C₃₇	C₂²	semidirect
9. C₅×D₁₈₅	D₃	semidirect
14. D₁₅×C₃₇	D₅	semidirect
16. C₃×D₁₈₅	D₅	semidirect
18. C₅²×C₃₇	C₂×D₃	semidirect
22. C₃×C₅×C₃₇	C₂×D₅	semidirect
23. C₃×C₅×C₃₇	C₂×D₅	semidirect
29. D₁₈₅	D₁₅	direct (N × H)
37. C₅×C₃₇	D₃×D₅	semidirect
38. C₅×C₃₇	C₂×D₁₅	semidirect
40. C₅×D₁₅	D₃₇	semidirect
43. C₃×C₃₇	D₅²	semidirect
45. C₃×C₅²	C₂×D₃₇	semidirect
54. C₃₇	D₅×D₁₅	semidirect
59. D₁₅	D₁₈₅	direct (N × H)
62. C₅²	D₃×D₃₇	semidirect
66. C₃×C₅	D₅×D₃₇	semidirect
67. C₃×C₅	C₂×D₁₈₅	semidirect
80. C₅	D₁₅×D₃₇	semidirect
81. C₅	D₃×D₁₈₅	semidirect
83. C₃	D₅×D₁₈₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₅⋊D₁₈₅)	2
C₅×D₁₅×C₃₇	2
C₃×C₅×D₁₈₅	2
D₅×D₁₈₅	3
D₃×D₁₈₅	5
D₁₅×D₃₇	5
D₅×D₁₅	37

Subgroups — D15×D185 #26012921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×D₁₈₅ #26012921