Subgroups — D₁₅×#10597245 #31827673

Order 18150.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#10597245	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×#10597245	—	3	1	no	maximal, Hall
3	C₁₁²×D₁₅	C₅	1	1	yes	maximal, characteristic, complemented
4	D₃×#10597245	—	5	1	no	maximal
5	C₅×#10597245	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×#10597245	—	2	2	no	—
8	C₃×#10597245	D₅	1	1	yes	characteristic, complemented
9	D₁₅×C₁₁⋊C₅	—	11	2	no	maximal
10	D₅×C₁₁²	—	3	1	no	—
11	C₂×#10597245	—	15	1	no	—
12	C₃×C₅×C₁₁⋊C₅	—	11	2	no	—
13	D₃×C₁₁²	—	5	1	no	Hall
14	C₅×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
15	#10597245	—	2	2	no	—
16	#10597245	D₁₅	1	1	yes	characteristic, direct product factor
17	D₅×C₁₁⋊C₅	—	33	2	no	—
18	C₃×C₁₁²	C₅×D₅	1	1	yes	characteristic, complemented, Hall
19	C₁₁×D₁₅	—	5	2	no	—
20	C₁₁×D₁₅	C₁₁⋊C₅	1	2	yes	complemented
21	D₃×C₁₁⋊C₅	—	55	2	no	—
22	C₅×C₁₁⋊C₅	—	11	2	no	—
23	C₂×C₁₁²	—	15	1	no	Hall
24	C₃×C₅×C₁₁	—	5	2	no	—
25	C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	1	2	yes	complemented
26	C₃×C₁₁⋊C₅	—	11	2	no	—
27	C₃×C₁₁⋊C₅	—	22	4	no	—
28	C₅×D₁₅	—	121	1	no	Hall
29	C₁₁²	C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
30	D₅×C₁₁	—	3	2	no	—
31	D₅×C₁₁	—	15	2	no	—
32	C₂×C₁₁⋊C₅	—	165	2	no	—
33	C₃×C₅²	—	121	1	no	Hall
34	D₃×C₁₁	—	5	2	no	—
35	D₃×C₁₁	—	25	2	no	—
36	C₅×C₁₁	—	5	2	no	—
37	C₅×C₁₁	D₃×C₁₁⋊C₅	1	2	yes	complemented
38	C₁₁⋊C₅	—	11	2	no	—
39	C₁₁⋊C₅	—	22	4	no	—
40	C₅×D₅	—	363	1	no	Hall
41	C₃×C₁₁	—	5	2	no	—
42	C₃×C₁₁	D₅×C₁₁⋊C₅	1	2	yes	complemented
43	D₁₅	#10597245	1	1	yes	characteristic, direct product factor
44	C₅×D₃	—	605	1	no	—
45	C₅²	—	121	1	no	Sylow
46	C₂×C₁₁	—	15	2	no	—
47	C₂×C₁₁	—	75	2	no	—
48	C₃×C₅	—	121	1	no	—
49	C₃×C₅	—	242	2	no	—
50	C₃×C₅	C₂×#10597245	1	1	yes	characteristic, complemented
51	C₁₁	—	5	2	no	—
52	C₁₁	D₁₅×C₁₁⋊C₅	1	2	yes	complemented
53	C₂×C₅	—	1815	1	no	—
54	D₅	—	3	1	no	—
55	D₃	—	5	1	no	Hall
56	C₅	—	121	1	no	—
57	C₅	—	242	2	no	—
58	C₅	D₃×#10597245	1	1	yes	characteristic, complemented
59	C₃	D₅×#10597245	1	1	yes	characteristic, complemented, Sylow
60	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₁²	C₂×C₅
LCS	G ▷ C₃×C₅×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#10597245	C₂	semidirect
3. C₁₁²×D₁₅	C₅	semidirect
5. C₅×#10597245	D₃	semidirect
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
8. C₃×#10597245	D₅	semidirect
14. C₅×C₁₁²	C₅×D₃	semidirect
16. #10597245	D₁₅	direct (N × H)
18. C₃×C₁₁²	C₅×D₅	semidirect
20. C₁₁×D₁₅	C₁₁⋊C₅	semidirect
25. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
29. C₁₁²	C₅×D₁₅	semidirect
37. C₅×C₁₁	D₃×C₁₁⋊C₅	semidirect
42. C₃×C₁₁	D₅×C₁₁⋊C₅	semidirect
43. D₁₅	#10597245	direct (N × H)
50. C₃×C₅	C₂×#10597245	semidirect
52. C₁₁	D₁₅×C₁₁⋊C₅	semidirect
58. C₅	D₃×#10597245	semidirect
59. C₃	D₅×#10597245	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#10597245	2
D₅×#10597245	3
C₁₁²×D₁₅	5
D₃×#10597245	5
D₁₅×C₁₁⋊C₅	11

Subgroups — D15×#10597245 #31827673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×#10597245 #31827673