Subgroups — C₃×C₅×Q₈×C₁₆ #14275216

Order 1920.

268 conjugacy classes of subgroups.

The subgroup lattice has 128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₄⋊C₁₆	C₂	1	3	yes	maximal
3	C₃×C₄×C₅×C₁₆	C₂	1	3	yes	maximal
4	C₅×Q₈×C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
6	C₂×C₃×C₅×C₁₆	C₂²	1	3	yes	—
7	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	C₃×C₅×C₄⋊C₈	C₄	1	3	yes	—
9	C₃×C₄×C₅×C₈	C₂²	1	3	yes	—
10	C₃×Q₈×C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₈×Q₈	C₂×C₃	1	1	yes	characteristic
12	C₅×C₄⋊C₁₆	C₂×C₃	1	3	yes	—
13	C₄×C₅×C₁₆	C₂×C₃	1	3	yes	—
14	C₂×C₃×C₅×Q₈	C₈	1	1	yes	characteristic
15	C₂×C₃×C₅×C₈	C₂×C₄	1	3	yes	—
16	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
17	C₃×C₅×C₄⋊C₄	C₈	1	3	yes	—
18	C₃×C₄²×C₅	C₂×C₄	1	3	yes	—
19	C₃×C₅×C₁₆	—	2	3	no	—
20	C₃×C₅×C₁₆	Q₈	1	2	yes	direct product factor
21	C₃×C₈×Q₈	C₂×C₅	1	1	yes	characteristic
22	C₃×C₄⋊C₁₆	C₂×C₅	1	3	yes	—
23	C₃×C₄×C₁₆	C₂×C₅	1	3	yes	—
24	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic
25	C₂×C₅×C₁₆	C₂²×C₃	1	3	yes	—
26	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
27	C₅×C₄⋊C₈	C₃×C₄	1	3	yes	—
28	C₄×C₅×C₈	C₂²×C₃	1	3	yes	—
29	Q₈×C₁₆	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₃×C₅×Q₈	C₁₆	1	4	yes	direct product factor
31	C₂×C₃×C₄×C₅	C₂×C₈	1	3	yes	—
32	C₂×C₃×C₄×C₅	C₂×C₈	1	3	yes	—
33	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
34	C₃×C₅×C₈	—	2	3	no	—
35	C₃×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
36	C₃×C₅×C₈	#41	1	1	yes	characteristic
37	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
38	C₂×C₃×C₁₆	C₂²×C₅	1	3	yes	—
39	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
40	C₃×C₄⋊C₈	C₄×C₅	1	3	yes	—
41	C₃×C₄×C₈	C₂²×C₅	1	3	yes	—
42	C₂×C₅×Q₈	C₃×C₈	1	1	yes	characteristic
43	C₂×C₅×C₈	C₂×C₃×C₄	1	3	yes	—
44	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
45	C₅×C₄⋊C₄	C₃×C₈	1	3	yes	—
46	C₄²×C₅	C₂×C₃×C₄	1	3	yes	—
47	C₅×C₁₆	—	2	3	no	—
48	C₅×C₁₆	C₃×Q₈	1	2	yes	direct product factor
49	C₈×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
50	C₄⋊C₁₆	C₂×C₃×C₅	1	3	yes	—
51	C₄×C₁₆	C₂×C₃×C₅	1	3	yes	—
52	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
53	C₃×C₄×C₅	—	2	3	no	—
54	C₃×C₄×C₅	C₂×C₁₆	1	6	yes	—
55	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
56	C₃×C₄×C₅	#131	1	1	yes	characteristic
57	C₂×C₃×Q₈	C₅×C₈	1	1	yes	characteristic
58	C₂×C₃×C₈	C₂×C₄×C₅	1	3	yes	—
59	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
60	C₃×C₄⋊C₄	C₅×C₈	1	3	yes	—
61	C₃×C₄²	C₂×C₄×C₅	1	3	yes	—
62	C₃×C₁₆	—	2	3	no	—
63	C₃×C₁₆	C₅×Q₈	1	2	yes	direct product factor
64	C₅×Q₈	C₃×C₁₆	1	4	yes	direct product factor
65	C₂×C₄×C₅	C₂×C₃×C₈	1	3	yes	—
66	C₂×C₄×C₅	C₂×C₃×C₈	1	3	yes	—
67	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
68	C₅×C₈	—	2	3	no	—
69	C₅×C₈	C₂×C₃×Q₈	1	1	yes	characteristic
70	C₅×C₈	C₃×#41	1	1	yes	characteristic
71	C₄×Q₈	C₃×C₄×C₅	1	1	yes	characteristic
72	C₂×C₁₆	C₂²×C₃×C₅	1	3	yes	—
73	C₂×C₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
74	C₄⋊C₈	C₃×C₄×C₅	1	3	yes	—
75	C₄×C₈	C₂²×C₃×C₅	1	3	yes	—
76	C₂×C₃×C₅	C₈×Q₈	1	1	yes	characteristic
77	C₂×C₃×C₅	C₂²×C₁₆	1	1	yes	characteristic
78	C₂×C₃×C₅	#504	1	1	yes	characteristic
79	C₃×Q₈	C₅×C₁₆	1	4	yes	direct product factor
80	C₂×C₃×C₄	C₂×C₅×C₈	1	3	yes	—
81	C₂×C₃×C₄	C₂×C₅×C₈	1	3	yes	—
82	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
83	C₃×C₈	—	2	3	no	—
84	C₃×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
85	C₃×C₈	C₅×#41	1	1	yes	characteristic
86	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
87	C₄×C₅	—	2	3	no	—
88	C₄×C₅	C₂×C₃×C₁₆	1	6	yes	—
89	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
90	C₄×C₅	C₃×#131	1	1	yes	characteristic
91	C₂×Q₈	C₃×C₅×C₈	1	1	yes	characteristic
92	C₂×C₈	C₂×C₃×C₄×C₅	1	3	yes	—
93	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
94	C₄⋊C₄	C₃×C₅×C₈	1	3	yes	—
95	C₄²	C₂×C₃×C₄×C₅	1	3	yes	—
96	C₁₆	—	2	3	no	—
97	C₁₆	C₃×C₅×Q₈	1	2	yes	direct product factor
98	C₃×C₅	Q₈×C₁₆	1	1	yes	characteristic, direct product factor, Hall
99	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
100	C₃×C₄	—	2	3	no	—
101	C₃×C₄	C₂×C₅×C₁₆	1	6	yes	—
102	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
103	C₃×C₄	C₅×#131	1	1	yes	characteristic
104	C₂×C₅	C₃×C₈×Q₈	1	1	yes	characteristic
105	C₂×C₅	C₂²×C₃×C₁₆	1	1	yes	characteristic
106	C₂×C₅	C₃×#504	1	1	yes	characteristic
107	Q₈	C₃×C₅×C₁₆	1	4	yes	direct product factor
108	C₂×C₄	C₂×C₃×C₅×C₈	1	3	yes	—
109	C₂×C₄	C₂×C₃×C₅×C₈	1	3	yes	—
110	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
111	C₈	—	2	3	no	—
112	C₈	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
113	C₈	C₃×C₅×#41	1	1	yes	characteristic
114	C₂×C₃	C₅×C₈×Q₈	1	1	yes	characteristic
115	C₂×C₃	C₂²×C₅×C₁₆	1	1	yes	characteristic
116	C₂×C₃	C₅×#504	1	1	yes	characteristic
117	C₅	C₃×Q₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
118	C₂²	C₂²×C₃×C₅×C₈	1	1	yes	characteristic
119	C₄	—	2	3	no	—
120	C₄	C₂×C₃×C₅×C₁₆	1	6	yes	—
121	C₄	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
122	C₄	C₃×C₅×#131	1	1	yes	characteristic
123	C₃	C₅×Q₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
124	C₂	C₃×C₅×C₈×Q₈	1	1	yes	characteristic
125	C₂	C₂²×C₃×C₅×C₁₆	1	1	yes	characteristic
126	C₂	C₃×C₅×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₅×C₁₆	C₂²
commutator	C₂	C₂²×C₃×C₅×C₁₆
Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×Q₈×C₁₆	C₃	direct (N × H)
10. C₃×Q₈×C₁₆	C₅	direct (N × H)
20. C₃×C₅×C₁₆	Q₈	direct (N × H)
29. Q₈×C₁₆	C₃×C₅	direct (N × H)
30. C₃×C₅×Q₈	C₁₆	direct (N × H)
48. C₅×C₁₆	C₃×Q₈	direct (N × H)
63. C₃×C₁₆	C₅×Q₈	direct (N × H)
64. C₅×Q₈	C₃×C₁₆	direct (N × H)
79. C₃×Q₈	C₅×C₁₆	direct (N × H)
97. C₁₆	C₃×C₅×Q₈	direct (N × H)
98. C₃×C₅	Q₈×C₁₆	direct (N × H)
107. Q₈	C₃×C₅×C₁₆	direct (N × H)
117. C₅	C₃×Q₈×C₁₆	direct (N × H)
123. C₃	C₅×Q₈×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₈×Q₈	2
C₃×C₅×C₄⋊C₁₆	2
C₃×C₄×C₅×C₁₆	2
C₅×Q₈×C₁₆	3
C₃×Q₈×C₁₆	5

Subgroups — C3×C5×Q8×C16 #14275216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×Q₈×C₁₆ #14275216