Subgroups — C₂×C₅×C₉×Q₁₆ #13084622

Order 1440.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₉	C₂	1	2	yes	maximal
2	C₅×C₉×Q₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×Q₁₆	C₃	1	1	yes	maximal, characteristic
5	C₅×Q₈×C₉	—	2	2	no	—
6	C₅×Q₈×C₉	C₂²	1	4	yes	—
7	C₂×C₄×C₅×C₉	—	2	2	no	—
8	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
9	C₅×C₈×C₉	C₂²	1	2	yes	—
10	C₂×C₉×Q₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×Q₈	C₂×C₃	1	2	yes	—
12	C₃×C₅×Q₁₆	C₂×C₃	1	4	yes	—
13	C₂×C₃×C₅×C₈	C₂×C₃	1	1	yes	characteristic
14	C₂²×C₅×C₉	D₄	1	1	yes	characteristic
15	C₄×C₅×C₉	—	2	4	no	—
16	C₄×C₅×C₉	D₄	1	1	yes	characteristic
17	C₄×C₅×C₉	C₂³	1	1	yes	characteristic
18	C₂×C₅×Q₁₆	C₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×Q₈×C₉	C₂×C₅	1	2	yes	—
20	C₉×Q₁₆	C₂×C₅	1	4	yes	direct product factor
21	C₂×C₈×C₉	C₂×C₅	1	1	yes	characteristic
22	C₃×C₅×Q₈	—	2	2	no	—
23	C₃×C₅×Q₈	C₂²×C₃	1	4	yes	—
24	C₂×C₃×C₄×C₅	—	2	2	no	—
25	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
26	C₃×C₅×C₈	C₂²×C₃	1	2	yes	—
27	C₂×C₃×Q₁₆	C₃×C₅	1	1	yes	characteristic
28	C₂×C₅×C₉	Q₁₆	1	2	yes	direct product factor
29	C₂×C₅×C₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₅×Q₈	C₂×C₉	1	2	yes	—
31	C₅×Q₁₆	C₂×C₉	1	4	yes	direct product factor
32	C₂×C₅×C₈	C₂×C₉	1	1	yes	characteristic
33	Q₈×C₉	—	2	2	no	—
34	Q₈×C₉	C₂²×C₅	1	4	yes	—
35	C₂×C₄×C₉	—	2	2	no	—
36	C₂×C₄×C₉	C₂²×C₅	1	1	yes	characteristic
37	C₈×C₉	C₂²×C₅	1	2	yes	—
38	C₂²×C₃×C₅	C₃×D₄	1	1	yes	characteristic
39	C₃×C₄×C₅	—	2	4	no	—
40	C₃×C₄×C₅	C₃×D₄	1	1	yes	characteristic
41	C₃×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
42	C₂×C₃×Q₈	C₂×C₃×C₅	1	2	yes	—
43	C₃×Q₁₆	C₂×C₃×C₅	1	4	yes	—
44	C₂×C₃×C₈	C₂×C₃×C₅	1	1	yes	characteristic
45	C₅×C₉	C₂×Q₁₆	1	1	yes	characteristic, direct product factor, Hall
46	C₅×Q₈	—	2	2	no	—
47	C₅×Q₈	C₂²×C₉	1	4	yes	—
48	C₂×C₄×C₅	—	2	2	no	—
49	C₂×C₄×C₅	C₂²×C₉	1	1	yes	characteristic
50	C₅×C₈	C₂²×C₉	1	2	yes	—
51	C₂²×C₉	C₅×D₄	1	1	yes	characteristic
52	C₄×C₉	—	2	4	no	—
53	C₄×C₉	C₅×D₄	1	1	yes	characteristic
54	C₄×C₉	C₂³×C₅	1	1	yes	characteristic
55	C₂×Q₁₆	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃×C₅	C₃×Q₁₆	1	2	yes	—
57	C₂×C₃×C₅	C₂×C₃×D₄	1	1	yes	characteristic
58	C₃×Q₈	—	2	2	no	—
59	C₃×Q₈	C₂²×C₃×C₅	1	4	yes	—
60	C₂×C₃×C₄	—	2	2	no	—
61	C₂×C₃×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
62	C₃×C₈	C₂²×C₃×C₅	1	2	yes	—
63	C₂²×C₅	D₄×C₉	1	1	yes	characteristic
64	C₄×C₅	—	2	4	no	—
65	C₄×C₅	D₄×C₉	1	1	yes	characteristic
66	C₄×C₅	C₂³×C₉	1	1	yes	characteristic
67	C₂×C₉	C₅×Q₁₆	1	2	yes	direct product factor
68	C₂×C₉	C₂×C₅×D₄	1	1	yes	characteristic
69	C₂×Q₈	C₂×C₅×C₉	1	2	yes	—
70	Q₁₆	C₂×C₅×C₉	1	4	yes	direct product factor
71	C₂×C₈	C₂×C₅×C₉	1	1	yes	characteristic
72	C₃×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
73	C₂²×C₃	C₃×C₅×D₄	1	1	yes	characteristic
74	C₃×C₄	—	2	4	no	—
75	C₃×C₄	C₃×C₅×D₄	1	1	yes	characteristic
76	C₃×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
77	C₂×C₅	C₉×Q₁₆	1	2	yes	direct product factor
78	C₂×C₅	C₂×D₄×C₉	1	1	yes	characteristic
79	C₉	C₂×C₅×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
80	Q₈	—	2	2	no	—
81	Q₈	C₂²×C₅×C₉	1	4	yes	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	C₂²×C₅×C₉	1	1	yes	characteristic
84	C₈	C₂²×C₅×C₉	1	2	yes	—
85	C₂×C₃	C₃×C₅×Q₁₆	1	2	yes	—
86	C₂×C₃	C₂×C₃×C₅×D₄	1	1	yes	characteristic
87	C₅	C₂×C₉×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
88	C₂²	C₅×D₄×C₉	1	1	yes	characteristic
89	C₄	—	2	4	no	—
90	C₄	C₅×D₄×C₉	1	1	yes	characteristic
91	C₄	C₂³×C₅×C₉	1	1	yes	characteristic
92	C₃	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
93	C₂	C₅×C₉×Q₁₆	1	2	yes	direct product factor
94	C₂	C₂×C₅×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅×C₉	D₄
commutator	C₄	C₂³×C₅×C₉
Frattini, cosocle	C₃×C₄	C₂³×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₃×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₉ ◁ C₂×C₄×C₅×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₉×Q₁₆	C₂	direct (N × H)
10. C₂×C₉×Q₁₆	C₅	direct (N × H)
18. C₂×C₅×Q₁₆	C₉	direct (N × H)
20. C₉×Q₁₆	C₂×C₅	direct (N × H)
28. C₂×C₅×C₉	Q₁₆	direct (N × H)
31. C₅×Q₁₆	C₂×C₉	direct (N × H)
45. C₅×C₉	C₂×Q₁₆	direct (N × H)
55. C₂×Q₁₆	C₅×C₉	direct (N × H)
67. C₂×C₉	C₅×Q₁₆	direct (N × H)
70. Q₁₆	C₂×C₅×C₉	direct (N × H)
77. C₂×C₅	C₉×Q₁₆	direct (N × H)
79. C₉	C₂×C₅×Q₁₆	direct (N × H)
87. C₅	C₂×C₉×Q₁₆	direct (N × H)
93. C₂	C₅×C₉×Q₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₈×C₉	2
C₅×C₉×Q₁₆	2
C₂×C₅×C₈×C₉	2
C₂×C₃×C₅×Q₁₆	3
C₂×C₉×Q₁₆	5

Subgroups — C2×C5×C9×Q16 #13084622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉×Q₁₆ #13084622