Subgroups — D₃×#4380 #11762169

Order 1080.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#4380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#4380	—	3	1	no	maximal
5	C₃⋊(C₃⋊D₁₅)	C₄	1	1	yes	characteristic, complemented
6	C₃×C₃⋊D₁₅	C₂²	1	1	yes	characteristic
7	C₃²×C₅×D₃	C₄	1	1	yes	characteristic, complemented
8	D₃×#157	—	5	1	no	maximal, Hall
9	C₂×C₃⋊D₁₅	—	3	1	no	—
10	D₃×D₁₅	—	6	2	no	—
11	#4380	—	3	1	no	—
12	#4380	D₃	1	1	yes	characteristic, direct product factor
13	C₃³×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
14	D₃×AGL(1,𝔽₅)	—	9	1	no	maximal
15	D₃×C₃⋊D₃	—	5	1	no	—
16	C₃⋊#157	—	5	1	no	—
17	C₃×#157	—	5	1	no	—
18	C₂×C₃²×C₅	—	3	1	no	—
19	C₃⋊D₁₅	—	3	1	no	—
20	C₃⋊D₁₅	—	6	2	no	—
21	C₃⋊D₁₅	—	12	2	no	—
22	C₃⋊D₁₅	C₂×D₃	1	1	yes	characteristic
23	C₃×D₁₅	—	6	2	no	—
24	C₃×C₅×D₃	—	2	2	no	—
25	C₂×#157	—	15	1	no	—
26	C₂×D₁₅	—	18	2	no	—
27	D₃×D₅	—	9	1	no	—
28	ΓL(1,𝔽₁₆)	—	9	1	no	—
29	C₃×AGL(1,𝔽₅)	—	9	1	no	—
30	C₃⋊(C₃⋊D₃)	—	5	1	no	—
31	C₃×C₃⋊D₃	—	5	1	no	—
32	C₃²×D₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
33	C₃²×C₅	—	2	2	no	—
34	C₃²×C₅	—	4	2	no	—
35	C₃²×C₅	C₄×D₃	1	1	yes	characteristic, complemented
36	C₂×AGL(1,𝔽₅)	—	27	1	no	Hall
37	C₂×C₃⋊D₃	—	15	1	no	—
38	D₃²	—	30	2	no	—
39	#157	—	5	1	no	—
40	#157	—	15	1	no	—
41	C₂×C₃×C₅	—	6	2	no	—
42	D₁₅	—	6	2	no	—
43	D₁₅	—	9	1	no	—
44	D₁₅	—	18	2	no	—
45	D₁₅	—	36	2	no	—
46	C₃×D₅	—	9	1	no	—
47	C₅×D₃	#157	1	1	yes	characteristic, complemented
48	C₃³	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
49	C₄×D₃	—	45	1	no	—
50	C₂×D₅	—	27	1	no	—
51	AGL(1,𝔽₅)	—	9	1	no	—
52	AGL(1,𝔽₅)	—	27	1	no	—
53	C₂×C₃²	—	3	1	no	—
54	C₃⋊D₃	—	5	1	no	—
55	C₃⋊D₃	—	15	1	no	—
56	C₃⋊D₃	—	30	2	no	—
57	C₃⋊D₃	—	60	2	no	—
58	C₃×D₃	—	2	2	no	—
59	C₃×D₃	—	30	2	no	—
60	C₃×C₅	—	2	2	no	—
61	C₃×C₅	—	4	2	no	—
62	C₃×C₅	C₂×#157	1	1	yes	characteristic, complemented
63	C₂×D₃	—	45	1	no	—
64	C₂×D₃	—	90	2	no	—
65	C₃×C₄	—	45	1	no	—
66	Dic₃	—	45	1	no	—
67	C₂×C₅	—	3	1	no	—
68	D₅	—	9	1	no	—
69	D₅	—	27	1	no	—
70	C₃²	—	2	2	no	—
71	C₃²	—	4	2	no	—
72	C₃²	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
73	C₂×C₄	—	135	1	no	Sylow
74	C₂×C₃	—	6	2	no	—
75	C₂×C₃	—	45	1	no	—
76	D₃	—	30	2	no	—
77	D₃	—	45	1	no	—
78	D₃	—	90	2	no	—
79	D₃	—	180	2	no	—
80	D₃	#4380	1	1	yes	characteristic, direct product factor
81	C₅	D₃×#157	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	135	1	no	—
83	C₄	—	45	1	no	—
84	C₄	—	135	1	no	—
85	C₃	—	2	2	no	—
86	C₃	—	4	2	no	—
87	C₃	C₂×#4380	1	1	yes	characteristic, complemented
88	C₂	—	3	1	no	—
89	C₂	—	45	1	no	—
90	C₂	—	135	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃³×C₅	C₂×C₄
prime radical	D₃×C₃⋊D₁₅	C₂
cosocle	C₃×C₃⋊D₁₅	C₂²
LCS	G ▷ C₃³×C₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃⋊#4380	C₂	semidirect
3. C₃×#4380	C₂	semidirect
5. C₃⋊(C₃⋊D₁₅)	C₄	semidirect
7. C₃²×C₅×D₃	C₄	semidirect
12. #4380	D₃	direct (N × H)
13. C₃³×C₅	C₂×C₄	semidirect
32. C₃²×D₃	AGL(1,𝔽₅)	semidirect
35. C₃²×C₅	C₄×D₃	semidirect
47. C₅×D₃	#157	semidirect
48. C₃³	C₂×AGL(1,𝔽₅)	semidirect
62. C₃×C₅	C₂×#157	semidirect
72. C₃²	D₃×AGL(1,𝔽₅)	semidirect
80. D₃	#4380	direct (N × H)
81. C₅	D₃×#157	semidirect
87. C₃	C₂×#4380	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₃⋊D₁₅	2
C₃⋊#4380	2
C₃×#4380	2
C₂×#4380	3
D₃×#157	5
D₃×AGL(1,𝔽₅)	9

Subgroups — D3×#4380 #11762169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#4380 #11762169