Subgroups — C₅×#13189 #11935909

Order 1280.

534 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₂²⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅×C₈	C₂²	1	2	yes	—
6	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
7	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
8	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
9	C₅×C₈×D₄	—	2	2	no	—
10	C₅×C₈×D₄	—	2	2	no	—
11	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×C₄⋊C₁₆	—	2	2	no	—
15	C₅×C₂²⋊C₁₆	—	2	8	no	—
16	C₄×C₅×C₁₆	—	2	2	no	—
17	#13189	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×D₄	C₈	1	1	yes	characteristic
19	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
20	C₂²×C₅×C₈	—	2	4	no	—
21	C₂²×C₅×C₈	—	2	2	no	—
22	C₂²×C₅×C₈	—	2	2	no	—
23	C₂²×C₅×C₈	—	2	4	no	—
24	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
27	C₄×C₅×D₄	—	2	2	no	—
28	C₄×C₅×D₄	—	2	2	no	—
29	C₂×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₄	C₈	1	2	yes	—
31	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂×C₅×C₁₆	—	2	2	no	—
33	C₂×C₅×C₁₆	—	2	2	no	—
34	C₂×C₅×C₁₆	—	2	4	no	—
35	C₂×C₅×C₁₆	—	2	2	no	—
36	C₂×C₅×C₁₆	D₄	1	4	yes	complemented
37	C₅×C₄⋊C₈	—	2	2	no	—
38	C₅×C₂²⋊C₈	—	2	4	no	—
39	C₄×C₅×C₈	D₄	1	2	yes	—
40	C₄×C₅×C₈	D₄	1	2	yes	—
41	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
42	C₂×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
43	C₂×C₂²⋊C₁₆	C₂×C₅	1	4	yes	complemented
44	C₂×C₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
45	C₂⁴×C₅	C₂×C₈	1	2	yes	—
46	C₂×C₅×D₄	—	2	2	no	—
47	C₂×C₅×D₄	—	2	2	no	—
48	C₂×C₅×D₄	C₁₆	1	4	yes	complemented
49	C₂²×C₄×C₅	—	2	2	no	—
50	C₂²×C₄×C₅	—	2	4	no	—
51	C₂²×C₄×C₅	—	2	2	no	—
52	C₂²×C₄×C₅	—	2	4	no	—
53	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
54	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₅×C₈	—	2	2	no	—
58	C₂×C₅×C₈	—	2	2	no	—
59	C₂×C₅×C₈	—	2	4	no	—
60	C₂×C₅×C₈	—	4	4	no	—
61	C₂×C₅×C₈	—	4	2	no	—
62	C₂×C₅×C₈	—	4	2	no	—
63	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
64	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
65	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
66	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
67	C₂×C₅×C₈	#41	1	2	yes	—
68	C₅×C₄⋊C₄	—	2	2	no	—
69	C₅×C₂²⋊C₄	—	2	4	no	—
70	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₅	M₁₆	1	2	yes	—
72	C₅×C₁₆	—	2	4	no	—
73	C₅×C₁₆	—	4	2	no	—
74	C₂³×C₈	C₂²×C₅	1	2	yes	—
75	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
76	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
77	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
78	C₈×D₄	—	2	2	no	—
79	C₈×D₄	—	2	2	no	—
80	C₂×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
81	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	—
82	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
83	C₄⋊C₁₆	—	2	2	no	—
84	C₂²⋊C₁₆	—	2	8	no	—
85	C₄×C₁₆	—	2	2	no	—
86	C₂³×C₅	—	2	2	no	—
87	C₂³×C₅	—	2	4	no	—
88	C₂³×C₅	—	2	2	no	—
89	C₂³×C₅	—	2	4	no	—
90	C₂³×C₅	C₂×C₁₆	1	4	yes	—
91	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
92	C₅×D₄	—	2	8	no	—
93	C₂×C₄×C₅	—	2	2	no	—
94	C₂×C₄×C₅	—	2	2	no	—
95	C₂×C₄×C₅	—	2	4	no	—
96	C₂×C₄×C₅	—	4	2	no	—
97	C₂×C₄×C₅	—	4	2	no	—
98	C₂×C₄×C₅	—	4	4	no	—
99	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
100	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
101	C₂×C₄×C₅	C₂×C₁₆	1	2	yes	—
102	C₂×C₄×C₅	M₃₂	1	2	yes	—
103	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₅	#131	1	2	yes	—
107	C₅×C₈	—	2	2	no	—
108	C₅×C₈	—	4	2	no	—
109	C₅×C₈	#121	1	2	yes	—
110	C₅×C₈	#124	1	1	yes	characteristic
111	C₅×C₈	#127	1	1	yes	characteristic
112	C₂²×D₄	C₅×C₈	1	1	yes	characteristic
113	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
114	C₂²×C₈	—	2	4	no	—
115	C₂²×C₈	—	2	2	no	—
116	C₂²×C₈	—	2	2	no	—
117	C₂²×C₈	—	2	4	no	—
118	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
119	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
120	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
121	C₄×D₄	—	2	2	no	—
122	C₄×D₄	—	2	2	no	—
123	C₂×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
124	C₂×C₂²⋊C₄	C₅×C₈	1	2	yes	—
125	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
126	C₂×C₁₆	—	2	2	no	—
127	C₂×C₁₆	—	2	2	no	—
128	C₂×C₁₆	—	2	4	no	—
129	C₂×C₁₆	—	2	2	no	—
130	C₂×C₁₆	C₅×D₄	1	4	yes	complemented
131	C₄⋊C₈	—	2	2	no	—
132	C₂²⋊C₈	—	2	4	no	—
133	C₄×C₈	C₅×D₄	1	2	yes	—
134	C₄×C₈	C₅×D₄	1	2	yes	—
135	C₂²×C₅	—	2	4	no	—
136	C₂²×C₅	—	2	8	no	—
137	C₂²×C₅	—	4	2	no	—
138	C₂²×C₅	—	4	4	no	—
139	C₂²×C₅	—	4	2	no	—
140	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
141	C₂²×C₅	C₈×D₄	1	2	yes	—
142	C₂²×C₅	C₂²×C₁₆	1	1	yes	characteristic
143	C₂²×C₅	C₂×M₃₂	1	1	yes	characteristic
144	C₂²×C₅	#504	1	2	yes	—
145	C₄×C₅	—	2	2	no	—
146	C₄×C₅	—	4	2	no	—
147	C₄×C₅	C₂²⋊C₁₆	1	4	yes	complemented
148	C₄×C₅	#390	1	1	yes	characteristic
149	C₄×C₅	#408	1	1	yes	characteristic
150	C₄×C₅	#436	1	2	yes	—
151	C₂⁴	C₂×C₅×C₈	1	2	yes	—
152	C₂×D₄	—	2	2	no	—
153	C₂×D₄	—	2	2	no	—
154	C₂×D₄	C₅×C₁₆	1	4	yes	complemented
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	2	4	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
160	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
161	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
162	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	2	4	no	—
166	C₂×C₈	—	4	4	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
170	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
171	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
172	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
173	C₂×C₈	C₅×#41	1	2	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₂²⋊C₄	—	2	4	no	—
176	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
177	C₄²	C₅×M₁₆	1	2	yes	—
178	C₁₆	—	2	4	no	—
179	C₁₆	—	4	2	no	—
180	C₂×C₅	—	4	4	no	—
181	C₂×C₅	#1954	1	1	yes	characteristic
182	C₂×C₅	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
183	C₂×C₅	#2113	1	1	yes	characteristic
184	C₂×C₅	D₄×C₁₆	1	2	yes	—
185	C₂×C₅	#2169	1	2	yes	—
186	C₂³	—	2	2	no	—
187	C₂³	—	2	4	no	—
188	C₂³	—	2	2	no	—
189	C₂³	—	2	4	no	—
190	C₂³	C₂×C₅×C₁₆	1	4	yes	—
191	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
192	D₄	—	2	8	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
200	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
201	C₂×C₄	C₂×C₅×C₁₆	1	2	yes	—
202	C₂×C₄	C₅×M₃₂	1	2	yes	—
203	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
205	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
206	C₂×C₄	C₅×#131	1	2	yes	—
207	C₈	—	2	2	no	—
208	C₈	—	4	2	no	—
209	C₈	C₅×#121	1	2	yes	—
210	C₈	C₅×#124	1	1	yes	characteristic
211	C₈	C₅×#127	1	1	yes	characteristic
212	C₅	#13189	1	1	yes	characteristic, direct product factor, Sylow
213	C₂²	—	2	4	no	—
214	C₂²	—	2	8	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	4	no	—
217	C₂²	—	4	2	no	—
218	C₂²	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
219	C₂²	C₅×C₈×D₄	1	2	yes	—
220	C₂²	C₂²×C₅×C₁₆	1	1	yes	characteristic
221	C₂²	C₂×C₅×M₃₂	1	1	yes	characteristic
222	C₂²	C₅×#504	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	4	2	no	—
225	C₄	C₅×C₂²⋊C₁₆	1	4	yes	complemented
226	C₄	C₅×#390	1	1	yes	characteristic
227	C₄	C₅×#408	1	1	yes	characteristic
228	C₄	C₅×#436	1	2	yes	—
229	C₂	—	4	4	no	—
230	C₂	C₅×#1954	1	1	yes	characteristic
231	C₂	C₂×C₅×C₂²⋊C₁₆	1	1	yes	characteristic
232	C₂	C₅×#2113	1	1	yes	characteristic
233	C₂	C₅×D₄×C₁₆	1	2	yes	—
234	C₂	C₅×#2169	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅×C₈	C₂³
commutator	C₂²	C₂²×C₅×C₁₆
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂³×C₅	C₂²×C₈
prime radical	C₂²×C₅×D₄	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₄⋊C₁₆	C₂	semidirect
3. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
4. C₂×C₄×C₅×C₁₆	C₂	semidirect
17. #13189	C₅	direct (N × H)
36. C₂×C₅×C₁₆	D₄	semidirect
42. C₂×C₄⋊C₁₆	C₂×C₅	semidirect
43. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
44. C₂×C₄×C₁₆	C₂×C₅	semidirect
48. C₂×C₅×D₄	C₁₆	semidirect
130. C₂×C₁₆	C₅×D₄	semidirect
147. C₄×C₅	C₂²⋊C₁₆	semidirect
154. C₂×D₄	C₅×C₁₆	semidirect
212. C₅	#13189	direct (N × H)
225. C₄	C₅×C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₈×D₄	2
C₂×C₅×C₄⋊C₁₆	2
C₂×C₅×C₂²⋊C₁₆	2
C₂×C₄×C₅×C₁₆	2
#13189	5

Subgroups — C5×#13189 #11935909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13189 #11935909