Subgroups — D₅×C₃⋊(C₃⋊C₁₆) #13084699

Order 1440.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊#672)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₃⋊C₁₆	—	3	4	no	maximal
5	C₃²×C₄×D₅	C₄	1	1	yes	characteristic
6	C₃²×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₃²×#168	C₄	1	1	yes	characteristic
8	C₂×C₃⋊(C₃⋊C₁₆)	—	5	1	no	maximal, Hall
9	C₃×C₈×D₅	D₃	1	4	yes	—
10	C₃⋊#672	—	3	4	no	—
11	C₅×C₃⋊C₁₆	—	3	4	no	—
12	C₂×C₃²×D₅	C₈	1	1	yes	characteristic
13	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃²×Dic₅	C₈	1	1	yes	characteristic
15	D₅×C₁₆	—	9	1	no	Hall
16	C₂×C₃²×C₈	—	5	1	no	—
17	C₃⋊(C₃⋊C₁₆)	—	5	1	no	—
18	C₃⋊(C₃⋊C₁₆)	D₅	1	1	yes	characteristic, direct product factor
19	C₃×C₄×D₅	Dic₃	1	4	yes	—
20	C₃×C₅×C₈	C₂×D₃	1	4	yes	—
21	C₃×#168	Dic₃	1	4	yes	—
22	C₂×C₃⋊C₁₆	—	15	4	no	—
23	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
24	C₃²×D₅	C₁₆	1	2	yes	complemented
25	C₈×D₅	C₃⋊D₃	1	1	yes	characteristic
26	C₅×C₁₆	—	9	1	no	—
27	#672	—	9	1	no	—
28	C₂×C₃²×C₄	—	5	1	no	—
29	C₃²×C₈	—	5	1	no	—
30	C₃²×C₈	C₂×D₅	1	1	yes	characteristic
31	C₂×C₃×D₅	C₃⋊C₈	1	4	yes	—
32	C₃×C₄×C₅	C₂×Dic₃	1	4	yes	—
33	C₃×Dic₅	C₃⋊C₈	1	4	yes	—
34	C₂×C₃×C₈	—	5	4	no	—
35	C₃⋊C₁₆	—	3	4	no	—
36	C₃⋊C₁₆	—	15	4	no	—
37	C₃²×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
38	C₄×D₅	C₃⋊Dic₃	1	1	yes	characteristic
39	C₅×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
40	#168	C₃⋊Dic₃	1	1	yes	characteristic
41	C₂²×C₃²	—	5	1	no	—
42	C₃²×C₄	—	5	1	no	—
43	C₃²×C₄	C₄×D₅	1	1	yes	characteristic
44	C₂×C₁₆	—	45	1	no	Sylow
45	C₂×C₃×C₅	C₂×C₃⋊C₈	1	4	yes	—
46	C₃×D₅	C₃⋊C₁₆	1	8	yes	complemented
47	C₂×C₃×C₄	—	5	4	no	—
48	C₃×C₈	—	5	4	no	—
49	C₃×C₈	D₃×D₅	1	4	yes	—
50	C₂×D₅	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
51	C₄×C₅	C₂×C₃⋊Dic₃	1	1	yes	characteristic
52	Dic₅	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
53	C₂×C₃²	—	5	2	no	—
54	C₂×C₃²	C₈×D₅	1	1	yes	characteristic
55	C₂×C₈	—	5	1	no	—
56	C₁₆	—	9	1	no	—
57	C₁₆	—	45	1	no	—
58	C₃×C₅	C₂×C₃⋊C₁₆	1	4	yes	complemented
59	C₂²×C₃	—	5	4	no	—
60	C₃×C₄	—	5	4	no	—
61	C₃×C₄	D₅×Dic₃	1	4	yes	—
62	C₂×C₅	C₂×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
63	D₅	C₃⋊(C₃⋊C₁₆)	1	2	yes	direct product factor
64	C₃²	D₅×C₁₆	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	—	5	1	no	—
66	C₈	—	5	1	no	—
67	C₈	D₅×C₃⋊D₃	1	1	yes	characteristic
68	C₂×C₃	—	5	8	no	—
69	C₂×C₃	D₅×C₃⋊C₈	1	4	yes	—
70	C₅	C₂×C₃⋊(C₃⋊C₁₆)	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	5	1	no	—
72	C₄	—	5	1	no	—
73	C₄	D₅×C₃⋊Dic₃	1	1	yes	characteristic
74	C₃	D₅×C₃⋊C₁₆	1	4	yes	complemented
75	C₂	—	5	2	no	—
76	C₂	D₅×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₅×C₃⋊D₃
commutator, hypocenter	C₃²×C₅	C₂×C₁₆
Fitting, cosocle	C₃²×C₅×C₈	C₂²
socle	C₂×C₃²×C₅	C₂×C₈
prime radical	C₂×C₃²×D₅	C₈
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊#672)	C₂	semidirect
3. C₅×C₃⋊(C₃⋊C₁₆)	C₂	semidirect
18. C₃⋊(C₃⋊C₁₆)	D₅	direct (N × H)
24. C₃²×D₅	C₁₆	semidirect
37. C₃²×C₅	C₂×C₁₆	semidirect
46. C₃×D₅	C₃⋊C₁₆	semidirect
58. C₃×C₅	C₂×C₃⋊C₁₆	semidirect
63. D₅	C₃⋊(C₃⋊C₁₆)	direct (N × H)
64. C₃²	D₅×C₁₆	semidirect
70. C₅	C₂×C₃⋊(C₃⋊C₁₆)	semidirect
74. C₃	D₅×C₃⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₈×D₅	2
C₃⋊(C₃⋊#672)	2
C₅×C₃⋊(C₃⋊C₁₆)	2
D₅×C₃⋊C₁₆	3
C₂×C₃⋊(C₃⋊C₁₆)	5

Subgroups — D5×C3⋊(C3⋊C16) #13084699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₃⋊(C₃⋊C₁₆) #13084699