Subgroups — D₁₅×#10597243 #31827672

Order 18150.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#10597243	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×#10597243	—	3	1	no	maximal, Hall
3	C₁₁²×D₁₅	C₅	1	1	yes	maximal, characteristic, complemented
4	D₃×#10597243	—	5	1	no	maximal
5	C₅×#10597243	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×#10597243	—	2	2	no	—
8	C₃×#10597243	D₅	1	1	yes	characteristic, complemented
9	D₁₅×C₁₁⋊C₅	—	11	12	no	maximal
10	D₅×C₁₁²	—	3	1	no	—
11	C₂×#10597243	—	15	1	no	—
12	C₃×C₅×C₁₁⋊C₅	—	11	12	no	—
13	D₃×C₁₁²	—	5	1	no	Hall
14	C₅×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
15	#10597243	—	2	2	no	—
16	#10597243	D₁₅	1	1	yes	characteristic, direct product factor
17	D₅×C₁₁⋊C₅	—	33	12	no	—
18	C₃×C₁₁²	C₅×D₅	1	1	yes	characteristic, complemented, Hall
19	C₁₁×D₁₅	C₁₁⋊C₅	1	12	yes	complemented
20	D₃×C₁₁⋊C₅	—	55	12	no	—
21	C₅×C₁₁⋊C₅	—	11	12	no	—
22	C₂×C₁₁²	—	15	1	no	Hall
23	C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	1	12	yes	complemented
24	C₃×C₁₁⋊C₅	—	11	12	no	—
25	C₃×C₁₁⋊C₅	—	22	24	no	—
26	C₅×D₁₅	—	121	1	no	Hall
27	C₁₁²	C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
28	D₅×C₁₁	—	3	12	no	—
29	C₂×C₁₁⋊C₅	—	165	12	no	—
30	C₃×C₅²	—	121	1	no	Hall
31	D₃×C₁₁	—	5	12	no	—
32	C₅×C₁₁	D₃×C₁₁⋊C₅	1	12	yes	complemented
33	C₁₁⋊C₅	—	11	12	no	—
34	C₁₁⋊C₅	—	22	24	no	—
35	C₅×D₅	—	363	1	no	Hall
36	C₃×C₁₁	D₅×C₁₁⋊C₅	1	12	yes	complemented
37	D₁₅	#10597243	1	1	yes	characteristic, direct product factor
38	C₅×D₃	—	605	1	no	—
39	C₅²	—	121	1	no	Sylow
40	C₂×C₁₁	—	15	12	no	—
41	C₃×C₅	—	121	1	no	—
42	C₃×C₅	—	242	2	no	—
43	C₃×C₅	C₂×#10597243	1	1	yes	characteristic, complemented
44	C₁₁	D₁₅×C₁₁⋊C₅	1	12	yes	complemented
45	C₂×C₅	—	1815	1	no	—
46	D₅	—	3	1	no	—
47	D₃	—	5	1	no	Hall
48	C₅	—	121	1	no	—
49	C₅	—	242	2	no	—
50	C₅	D₃×#10597243	1	1	yes	characteristic, complemented
51	C₃	D₅×#10597243	1	1	yes	characteristic, complemented, Sylow
52	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×#10597243	C₂	semidirect
3. C₁₁²×D₁₅	C₅	semidirect
5. C₅×#10597243	D₃	semidirect
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
8. C₃×#10597243	D₅	semidirect
14. C₅×C₁₁²	C₅×D₃	semidirect
16. #10597243	D₁₅	direct (N × H)
18. C₃×C₁₁²	C₅×D₅	semidirect
19. C₁₁×D₁₅	C₁₁⋊C₅	semidirect
23. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
27. C₁₁²	C₅×D₁₅	semidirect
32. C₅×C₁₁	D₃×C₁₁⋊C₅	semidirect
36. C₃×C₁₁	D₅×C₁₁⋊C₅	semidirect
37. D₁₅	#10597243	direct (N × H)
43. C₃×C₅	C₂×#10597243	semidirect
44. C₁₁	D₁₅×C₁₁⋊C₅	semidirect
50. C₅	D₃×#10597243	semidirect
51. C₃	D₅×#10597243	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#10597243	2
D₅×#10597243	3
C₁₁²×D₁₅	5
D₃×#10597243	5
D₁₅×C₁₁⋊C₅	11

Subgroups — D15×#10597243 #31827672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×#10597243 #31827672