Subgroups — D₅×#66472 #72269592

Order 3240.

1192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic
2	#13108537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#66472	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃⋊(C₃⋊(C₃⋊D₁₅))	C₄	1	1	yes	characteristic, complemented
5	C₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic
6	C₃⁴×D₅	C₄	1	1	yes	characteristic, complemented
7	C₂×#66472	—	5	1	no	maximal, Hall
8	D₅×C₃⋊(C₃⋊D₃)	—	6	20	no	—
9	C₃⁴×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	D₅×#157	—	9	10	no	maximal
11	C₂×C₃⋊(C₃⋊(C₃⋊D₃))	—	5	1	no	—
12	#66472	—	5	1	no	—
13	#66472	D₅	1	1	yes	characteristic, direct product factor
14	C₃⋊(C₃⋊D₁₅)	—	6	20	no	—
15	C₅×C₃⋊(C₃⋊D₃)	—	6	20	no	—
16	C₃³×D₅	—	2	20	no	—
17	D₅×C₃⋊D₃	—	9	10	no	—
18	D₅×C₃⋊D₃	—	18	60	no	—
19	#4379	—	9	10	no	—
20	C₅×#157	—	9	10	no	—
21	C₂×C₃⁴	—	5	1	no	—
22	C₃⋊(C₃⋊(C₃⋊D₃))	—	5	1	no	—
23	C₃⋊(C₃⋊(C₃⋊D₃))	C₂×D₅	1	1	yes	characteristic
24	C₃³×C₅	—	2	20	no	—
25	C₂×C₃⋊(C₃⋊D₃)	—	30	20	no	—
26	C₃⋊D₁₅	—	9	10	no	—
27	C₃⋊D₁₅	—	18	60	no	—
28	C₅×C₃⋊D₃	—	9	10	no	—
29	C₅×C₃⋊D₃	—	18	60	no	—
30	C₃²×D₅	—	2	60	no	—
31	C₃²×D₅	#157	1	10	yes	complemented
32	C₃⁴	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
33	C₂×#157	—	45	10	no	—
34	D₃×D₅	—	54	20	no	—
35	C₂×C₃³	—	10	20	no	—
36	C₃⋊(C₃⋊D₃)	—	6	20	no	—
37	C₃⋊(C₃⋊D₃)	—	30	20	no	—
38	C₃²×C₅	—	2	60	no	—
39	C₃²×C₅	C₂×#157	1	10	yes	complemented
40	C₄×D₅	—	81	1	no	Hall
41	C₂×C₃⋊D₃	—	45	10	no	—
42	C₂×C₃⋊D₃	—	90	60	no	—
43	#157	—	9	10	no	—
44	#157	—	45	10	no	—
45	D₁₅	—	54	20	no	—
46	C₃×D₅	—	2	20	no	—
47	C₅×D₃	—	54	20	no	—
48	C₃³	—	2	20	no	—
49	C₂×D₅	—	81	1	no	—
50	C₄×C₅	—	81	1	no	—
51	Dic₅	—	81	1	no	—
52	C₂×C₃²	—	5	10	no	—
53	C₂×C₃²	—	10	60	no	—
54	C₃⋊D₃	—	9	10	no	—
55	C₃⋊D₃	—	18	60	no	—
56	C₃⋊D₃	—	45	10	no	—
57	C₃⋊D₃	—	90	60	no	—
58	C₃×C₅	—	2	20	no	—
59	C₂×D₃	—	270	20	no	—
60	C₂×C₅	—	81	1	no	—
61	D₅	—	81	1	no	—
62	D₅	#66472	1	1	yes	characteristic, direct product factor
63	C₃²	—	2	60	no	—
64	C₃²	D₅×#157	1	10	yes	complemented
65	C₂×C₄	—	405	1	no	Sylow
66	C₂×C₃	—	10	20	no	—
67	D₃	—	270	20	no	—
68	D₃	—	54	20	no	—
69	C₅	C₂×#66472	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	405	1	no	—
71	C₄	—	81	1	no	—
72	C₄	—	405	1	no	—
73	C₃	—	2	20	no	—
74	C₂	—	5	1	no	—
75	C₂	—	81	1	no	—
76	C₂	—	405	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃⁴×C₅	C₂×C₄
prime radical	D₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂
cosocle	C₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂²
LCS	G ▷ C₃⁴×C₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #13108537	C₂	semidirect
3. C₅×#66472	C₂	semidirect
4. C₃⋊(C₃⋊(C₃⋊D₁₅))	C₄	semidirect
6. C₃⁴×D₅	C₄	semidirect
9. C₃⁴×C₅	C₂×C₄	semidirect
13. #66472	D₅	direct (N × H)
31. C₃²×D₅	#157	semidirect
32. C₃⁴	C₄×D₅	semidirect
39. C₃²×C₅	C₂×#157	semidirect
62. D₅	#66472	direct (N × H)
64. C₃²	D₅×#157	semidirect
69. C₅	C₂×#66472	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₃⋊(C₃⋊(C₃⋊D₃))	2
#13108537	2
C₅×#66472	2
C₂×#66472	5
D₅×#157	9

Subgroups — D5×#66472 #72269592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#66472 #72269592