Subgroups — Dic₅×C₄⋊C₁₆ #12014607

Order 1280.

438 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₅	C₂	1	2	yes	maximal
3	C₄×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#672	C₂	1	1	yes	maximal, characteristic
5	#10598295	C₂	1	2	yes	maximal
6	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
12	C₂²×#672	C₂²	1	2	yes	—
13	C₄²×Dic₅	C₄	1	1	yes	characteristic
14	C₂×C₄×#168	C₄	1	1	yes	characteristic
15	C₅×C₄⋊C₁₆	C₄	1	4	yes	complemented
16	C₁₆×Dic₅	—	2	4	no	—
17	C₄⋊#672	C₄	1	4	yes	complemented
18	C₄×C₄⋊C₁₆	—	5	1	no	maximal, Sylow
19	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
21	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₅	C₈	1	2	yes	—
23	C₂×C₄×Dic₅	C₈	1	2	yes	—
24	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×#168	C₂×C₄	1	1	yes	characteristic
27	C₂²×#168	C₂×C₄	1	1	yes	characteristic
28	C₂×C₅×C₁₆	—	2	2	no	—
29	C₂×C₅×C₁₆	—	2	2	no	—
30	C₂×C₅×C₁₆	C₂×C₄	1	4	yes	—
31	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
32	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
33	C₈×Dic₅	—	2	1	no	—
34	C₈×Dic₅	—	2	1	no	—
35	C₈×Dic₅	—	2	2	no	—
36	C₈×Dic₅	—	2	2	no	—
37	C₈×Dic₅	D₄	1	2	yes	—
38	C₈×Dic₅	Q₈	1	2	yes	—
39	C₂×#672	—	2	2	no	—
40	C₂×#672	—	2	2	no	—
41	C₂×#672	C₂×C₄	1	4	yes	—
42	C₄×#168	C₈	1	4	yes	—
43	C₂×C₄⋊C₁₆	—	5	1	no	—
44	C₂×C₄⋊C₁₆	D₅	1	1	yes	characteristic
45	C₂×C₄×C₁₆	—	5	2	no	—
46	C₄²×C₈	—	5	1	no	—
47	#1374	—	5	2	no	—
48	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
49	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
51	C₂²×Dic₅	C₂×C₈	1	2	yes	—
52	C₂²×Dic₅	C₂×C₈	1	2	yes	—
53	C₂×C₅×C₈	—	2	1	no	—
54	C₂×C₅×C₈	—	2	1	no	—
55	C₂×C₅×C₈	C₄²	1	2	yes	—
56	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
59	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₅×C₈	#41	1	1	yes	characteristic
61	C₂×C₅×C₈	#41	1	1	yes	characteristic
62	C₄²×C₅	C₄²	1	2	yes	—
63	C₄²×C₅	C₂×C₈	1	2	yes	—
64	C₄×Dic₅	—	2	1	no	—
65	C₄×Dic₅	—	2	1	no	—
66	C₄×Dic₅	—	2	4	no	—
67	C₄×Dic₅	C₁₆	1	8	yes	complemented
68	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
69	C₄×Dic₅	M₁₆	1	2	yes	—
70	C₂×#168	—	2	1	no	—
71	C₂×#168	—	2	1	no	—
72	C₂×#168	C₄⋊C₄	1	2	yes	—
73	C₂×#168	C₂×C₈	1	2	yes	—
74	C₂×#168	C₂×C₈	1	2	yes	—
75	C₂×#168	M₁₆	1	2	yes	—
76	C₅×C₁₆	—	2	4	no	—
77	#672	—	2	4	no	—
78	C₂²×C₁₆	—	5	2	no	—
79	C₂²×C₁₆	C₂×D₅	1	2	yes	—
80	C₂×C₄×C₈	—	5	1	no	—
81	C₂×C₄×C₈	—	5	1	no	—
82	C₂×C₄×C₈	—	5	1	no	—
83	C₂×C₄×C₈	—	5	1	no	—
84	C₂×C₄×C₈	—	5	1	no	—
85	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
86	C₄³	—	5	1	no	—
87	C₄⋊C₁₆	—	5	4	no	—
88	C₄⋊C₁₆	Dic₅	1	4	yes	direct product factor
89	C₄×C₁₆	—	10	4	no	—
90	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
91	C₂×C₄×C₅	—	2	2	no	—
92	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
93	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
94	C₂×C₄×C₅	C₂×C₁₆	1	4	yes	—
95	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
96	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₅	#117	1	1	yes	characteristic
98	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
100	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
101	C₂×Dic₅	—	2	2	no	—
102	C₂×Dic₅	—	2	2	no	—
103	C₂×Dic₅	C₄⋊C₈	1	4	yes	—
104	C₂×Dic₅	C₂×C₁₆	1	4	yes	—
105	C₂×Dic₅	C₂×C₁₆	1	4	yes	—
106	C₂×Dic₅	M₃₂	1	4	yes	—
107	C₅×C₈	—	2	2	no	—
108	C₅×C₈	C₄×D₄	1	1	yes	characteristic
109	C₅×C₈	C₄×D₄	1	1	yes	characteristic
110	C₅×C₈	C₄×Q₈	1	1	yes	characteristic
111	C₅×C₈	C₄×Q₈	1	1	yes	characteristic
112	#168	—	2	2	no	—
113	#168	C₄⋊C₈	1	4	yes	—
114	C₂²×C₈	—	5	1	no	—
115	C₂²×C₈	—	5	1	no	—
116	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
117	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
118	C₂×C₄²	—	5	2	no	—
119	C₂×C₄²	—	5	1	no	—
120	C₂×C₄²	—	5	2	no	—
121	C₂×C₄²	—	5	1	no	—
122	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
123	C₂×C₁₆	—	2	2	no	—
124	C₂×C₁₆	—	2	2	no	—
125	C₂×C₁₆	—	5	4	no	—
126	C₂×C₁₆	—	10	2	no	—
127	C₂×C₁₆	—	10	2	no	—
128	C₂×C₁₆	C₂×Dic₅	1	4	yes	—
129	C₄×C₈	—	5	2	no	—
130	C₄×C₈	—	5	2	no	—
131	C₄×C₈	—	5	4	no	—
132	C₄×C₈	—	10	2	no	—
133	C₄×C₈	—	10	2	no	—
134	C₄×C₈	—	10	1	no	—
135	C₄×C₈	—	10	1	no	—
136	C₄×C₈	C₄×D₅	1	2	yes	—
137	C₄×C₈	C₂×Dic₅	1	2	yes	—
138	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
139	C₂²×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
140	C₂²×C₅	#431	1	1	yes	characteristic
141	C₂²×C₅	C₂²×C₁₆	1	2	yes	—
142	C₂²×C₅	C₂×M₃₂	1	2	yes	—
143	C₄×C₅	—	2	2	no	—
144	C₄×C₅	C₄×C₁₆	1	4	yes	complemented
145	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
146	C₄×C₅	C₄×M₁₆	1	1	yes	characteristic
147	C₄×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
148	C₄×C₅	#431	1	1	yes	characteristic
149	Dic₅	—	2	4	no	—
150	Dic₅	C₄⋊C₁₆	1	8	yes	direct product factor
151	C₂²×C₄	—	5	2	no	—
152	C₂²×C₄	—	5	2	no	—
153	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
154	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
155	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	—	2	1	no	—
158	C₂×C₈	—	5	2	no	—
159	C₂×C₈	—	5	2	no	—
160	C₂×C₈	—	5	2	no	—
161	C₂×C₈	—	5	2	no	—
162	C₂×C₈	—	10	1	no	—
163	C₂×C₈	—	10	1	no	—
164	C₂×C₈	C₄×Dic₅	1	2	yes	—
165	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
166	C₂×C₈	D₄×D₅	1	1	yes	characteristic
167	C₂×C₈	#711	1	1	yes	characteristic
168	C₂×C₈	Q₈×D₅	1	1	yes	characteristic
169	C₂×C₈	#713	1	1	yes	characteristic
170	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
171	C₄²	—	5	8	no	—
172	C₄²	—	5	2	no	—
173	C₄²	—	5	2	no	—
174	C₄²	—	10	4	no	—
175	C₄²	—	10	1	no	—
176	C₄²	—	10	1	no	—
177	C₄²	C₈×D₅	1	2	yes	—
178	C₄²	C₄×Dic₅	1	2	yes	—
179	C₁₆	—	2	4	no	—
180	C₁₆	—	10	4	no	—
181	C₂×C₅	C₄×C₄⋊C₈	1	1	yes	characteristic
182	C₂×C₅	C₂×C₄×C₁₆	1	1	yes	characteristic
183	C₂×C₅	C₄×M₃₂	1	1	yes	characteristic
184	C₂×C₅	C₂×C₄⋊C₁₆	1	2	yes	—
185	C₂×C₅	#2162	1	2	yes	—
186	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	5	4	no	—
189	C₂×C₄	—	5	4	no	—
190	C₂×C₄	—	5	4	no	—
191	C₂×C₄	—	5	4	no	—
192	C₂×C₄	—	10	2	no	—
193	C₂×C₄	—	10	2	no	—
194	C₂×C₄	D₅×C₁₆	1	4	yes	—
195	C₂×C₄	C₈×Dic₅	1	2	yes	—
196	C₂×C₄	C₈×Dic₅	1	2	yes	—
197	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₄	#4038	1	1	yes	characteristic
199	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
200	C₂×C₄	D₅×M₁₆	1	1	yes	characteristic
201	C₂×C₄	D₅×M₁₆	1	1	yes	characteristic
202	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
203	C₈	—	2	2	no	—
204	C₈	—	5	4	no	—
205	C₈	—	10	2	no	—
206	C₈	#4033	1	1	yes	characteristic
207	C₈	#4039	1	1	yes	characteristic
208	C₈	D₄×Dic₅	1	1	yes	characteristic
209	C₈	Q₈×Dic₅	1	1	yes	characteristic
210	C₅	C₄×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
211	C₂²	D₅×C₄⋊C₈	1	1	yes	characteristic
212	C₂²	#65122	1	1	yes	characteristic
213	C₂²	C₂×D₅×C₁₆	1	2	yes	—
214	C₂²	D₅×M₃₂	1	2	yes	—
215	C₂²	C₂×C₈×Dic₅	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	5	8	no	—
218	C₄	—	10	4	no	—
219	C₄	C₁₆×Dic₅	1	4	yes	complemented
220	C₄	D₅×C₄⋊C₈	1	1	yes	characteristic
221	C₄	#65122	1	1	yes	characteristic
222	C₄	C₄⋊C₄×Dic₅	1	1	yes	characteristic
223	C₄	M₁₆×Dic₅	1	1	yes	characteristic
224	C₂	#10600067	1	2	yes	—
225	C₂	D₅×C₄⋊C₁₆	1	2	yes	—
226	C₂	Dic₅×C₄⋊C₈	1	1	yes	characteristic
227	C₂	C₂×C₁₆×Dic₅	1	1	yes	characteristic
228	C₂	Dic₅×M₃₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₅
commutator	C₂×C₅	C₂×C₄×C₁₆
Fitting	C₂×C₅×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₅	C₂²×C₈
cosocle	C₂²×C₅×C₈	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₅
hypocenter	C₅	C₄×C₄⋊C₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
15. C₅×C₄⋊C₁₆	C₄	semidirect
17. C₄⋊#672	C₄	semidirect
67. C₄×Dic₅	C₁₆	semidirect
88. C₄⋊C₁₆	Dic₅	direct (N × H)
144. C₄×C₅	C₄×C₁₆	semidirect
150. Dic₅	C₄⋊C₁₆	direct (N × H)
210. C₅	C₄×C₄⋊C₁₆	semidirect
219. C₄	C₁₆×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₄⋊C₁₆	2
C₂×C₁₆×Dic₅	2
C₄×C₈×Dic₅	2
C₂×C₄⋊#672	2
#10598295	2
C₄×C₄⋊C₁₆	5

Subgroups — Dic5×C4⋊C16 #12014607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×C₄⋊C₁₆ #12014607