Subgroups — C₂×C₅×#1940 #11943862

Order 1280.

1182 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₅×#1940	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#336	C₂	1	2	yes	maximal
7	C₂³×C₅×C₈	C₂²	1	2	yes	—
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₅×C₄⋊C₄	C₄	1	2	yes	—
11	C₂²×C₄²×C₅	C₂²	1	2	yes	—
12	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	—	2	8	no	—
14	C₂×C₅×C₄⋊C₈	—	2	4	no	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	8	yes	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
17	C₂×C₅×#97	—	2	4	no	—
18	C₂×C₅×#97	C₂²	1	4	yes	—
19	C₄×C₅×C₄⋊C₄	C₄	1	4	yes	—
20	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
21	C₂×C₅×#95	C₄	1	1	yes	characteristic
22	C₂×C₅×#95	C₄	1	1	yes	characteristic
23	C₅×#336	C₂²	1	8	yes	—
24	C₂×#1940	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
26	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂²×C₅×C₈	—	2	2	no	—
31	C₂²×C₅×C₈	—	2	2	no	—
32	C₂²×C₅×C₈	—	2	2	no	—
33	C₂²×C₅×C₈	—	2	2	no	—
34	C₂²×C₅×C₈	—	2	4	no	—
35	C₂²×C₅×C₈	—	2	4	no	—
36	C₂²×C₅×C₈	—	2	4	no	—
37	C₂²×C₅×C₈	D₄	1	4	yes	—
38	C₂²×C₅×C₈	Q₈	1	4	yes	—
39	C₂²×C₅×C₈	C₂³	1	4	yes	—
40	C₂²×C₅×C₈	C₂³	1	2	yes	—
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂×C₅×C₄⋊C₄	—	2	8	no	—
43	C₂×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
44	C₂×C₄²×C₅	—	2	4	no	—
45	C₂×C₄²×C₅	—	2	4	no	—
46	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₅	D₄	1	4	yes	—
49	C₂×C₄²×C₅	Q₈	1	4	yes	—
50	C₂×C₄²×C₅	C₂³	1	4	yes	—
51	C₂×C₄²×C₅	C₂³	1	2	yes	—
52	C₅×C₄⋊C₈	—	2	16	no	—
53	C₅×C₄⋊C₈	—	2	8	no	—
54	C₅×#97	—	2	8	no	—
55	C₅×#95	C₂×C₄	1	4	yes	—
56	C₅×#95	C₂×C₄	1	4	yes	—
57	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
58	C₂²×C₄⋊C₈	C₂×C₅	1	2	yes	—
59	C₂²×#97	C₂×C₅	1	1	yes	characteristic
60	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
61	#1940	C₂×C₅	1	8	yes	direct product factor
62	C₂×#336	C₂×C₅	1	2	yes	—
63	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅	—	2	4	no	—
65	C₂²×C₄×C₅	—	2	4	no	—
66	C₂²×C₄×C₅	—	2	4	no	—
67	C₂²×C₄×C₅	—	2	4	no	—
68	C₂²×C₄×C₅	—	2	4	no	—
69	C₂²×C₄×C₅	—	2	4	no	—
70	C₂²×C₄×C₅	—	2	4	no	—
71	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
72	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
73	C₂²×C₄×C₅	M₁₆	1	8	yes	—
74	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
83	C₂²×C₄×C₅	#41	1	2	yes	—
84	C₂²×C₄×C₅	#41	1	2	yes	—
85	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
86	C₂×C₅×C₈	—	2	8	no	—
87	C₂×C₅×C₈	—	2	8	no	—
88	C₂×C₅×C₈	—	2	2	no	—
89	C₂×C₅×C₈	—	2	2	no	—
90	C₂×C₅×C₈	—	2	2	no	—
91	C₂×C₅×C₈	—	2	2	no	—
92	C₂×C₅×C₈	—	2	4	no	—
93	C₂×C₅×C₈	—	2	4	no	—
94	C₂×C₅×C₈	—	2	4	no	—
95	C₂×C₅×C₈	—	4	8	no	—
96	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
97	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
98	C₅×C₄⋊C₄	—	2	16	no	—
99	C₄²×C₅	—	2	8	no	—
100	C₄²×C₅	—	2	4	no	—
101	C₄²×C₅	—	2	4	no	—
102	C₄²×C₅	C₄⋊C₄	1	8	yes	—
103	C₄²×C₅	C₂×D₄	1	4	yes	—
104	C₄²×C₅	C₂×Q₈	1	4	yes	—
105	C₂³×C₈	C₂²×C₅	1	2	yes	—
106	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
107	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₄⋊C₄	C₄×C₅	1	2	yes	—
109	C₂²×C₄²	C₂²×C₅	1	2	yes	—
110	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₄⋊C₈	—	2	8	no	—
112	C₂×C₄⋊C₈	—	2	4	no	—
113	C₂×C₄⋊C₈	C₂²×C₅	1	8	yes	—
114	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
115	C₂×#97	—	2	4	no	—
116	C₂×#97	C₂²×C₅	1	4	yes	—
117	C₄×C₄⋊C₄	C₄×C₅	1	4	yes	—
118	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
119	C₂×#95	C₄×C₅	1	1	yes	characteristic
120	C₂×#95	C₄×C₅	1	1	yes	characteristic
121	#336	C₂²×C₅	1	8	yes	—
122	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
123	C₂³×C₅	C₄×D₄	1	2	yes	—
124	C₂³×C₅	C₄×Q₈	1	2	yes	—
125	C₂³×C₅	C₂×M₁₆	1	4	yes	—
126	C₂³×C₅	#131	1	4	yes	—
127	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
128	C₂×C₄×C₅	—	2	4	no	—
129	C₂×C₄×C₅	—	2	4	no	—
130	C₂×C₄×C₅	—	2	4	no	—
131	C₂×C₄×C₅	—	2	4	no	—
132	C₂×C₄×C₅	—	2	8	no	—
133	C₂×C₄×C₅	—	2	8	no	—
134	C₂×C₄×C₅	—	2	16	no	—
135	C₂×C₄×C₅	—	2	4	no	—
136	C₂×C₄×C₅	—	2	4	no	—
137	C₂×C₄×C₅	—	2	4	no	—
138	C₂×C₄×C₅	—	4	8	no	—
139	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
140	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
141	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₅	#121	1	4	yes	—
145	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
146	C₂×C₄×C₅	#125	1	4	yes	—
147	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
148	C₂×C₄×C₅	C₂×M₁₆	1	8	yes	—
149	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
155	C₅×C₈	—	2	4	no	—
156	C₅×C₈	—	2	4	no	—
157	C₅×C₈	—	4	4	no	—
158	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
159	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
160	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
161	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
162	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	—	2	2	no	—
166	C₂²×C₈	—	2	2	no	—
167	C₂²×C₈	—	2	4	no	—
168	C₂²×C₈	—	2	4	no	—
169	C₂²×C₈	—	2	4	no	—
170	C₂²×C₈	C₅×D₄	1	4	yes	—
171	C₂²×C₈	C₅×Q₈	1	4	yes	—
172	C₂²×C₈	C₂³×C₅	1	4	yes	—
173	C₂²×C₈	C₂³×C₅	1	2	yes	—
174	C₂²×C₈	C₂³×C₅	1	2	yes	—
175	C₂×C₄⋊C₄	—	2	8	no	—
176	C₂×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
177	C₂×C₄²	—	2	4	no	—
178	C₂×C₄²	—	2	4	no	—
179	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
180	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
181	C₂×C₄²	C₅×D₄	1	4	yes	—
182	C₂×C₄²	C₅×Q₈	1	4	yes	—
183	C₂×C₄²	C₂³×C₅	1	4	yes	—
184	C₂×C₄²	C₂³×C₅	1	2	yes	—
185	C₄⋊C₈	—	2	16	no	—
186	C₄⋊C₈	—	2	8	no	—
187	#97	—	2	8	no	—
188	#95	C₂×C₄×C₅	1	4	yes	—
189	#95	C₂×C₄×C₅	1	4	yes	—
190	C₂²×C₅	#389	1	4	yes	—
191	C₂²×C₅	#423	1	4	yes	—
192	C₂²×C₅	#424	1	4	yes	—
193	C₂²×C₅	#435	1	8	yes	—
194	C₂²×C₅	#446	1	8	yes	—
195	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
196	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
198	C₂²×C₅	C₂²×M₁₆	1	2	yes	—
199	C₂²×C₅	C₂×#131	1	2	yes	—
200	C₄×C₅	—	2	4	no	—
201	C₄×C₅	—	2	4	no	—
202	C₄×C₅	—	2	8	no	—
203	C₄×C₅	—	4	4	no	—
204	C₄×C₅	#389	1	4	yes	—
205	C₄×C₅	C₂×#121	1	1	yes	characteristic
206	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	C₄×C₅	C₂×#125	1	1	yes	characteristic
208	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
209	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	—	2	4	no	—
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	2	4	no	—
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	2	4	no	—
217	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
218	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
219	C₂²×C₄	C₅×M₁₆	1	8	yes	—
220	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
221	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
222	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
223	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
224	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
226	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
227	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
228	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
229	C₂²×C₄	C₅×#41	1	2	yes	—
230	C₂²×C₄	C₅×#41	1	2	yes	—
231	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
232	C₂×C₈	—	2	8	no	—
233	C₂×C₈	—	2	8	no	—
234	C₂×C₈	—	2	2	no	—
235	C₂×C₈	—	2	2	no	—
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	—	2	4	no	—
240	C₂×C₈	—	2	4	no	—
241	C₂×C₈	—	4	8	no	—
242	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
243	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
244	C₄⋊C₄	—	2	16	no	—
245	C₄²	—	2	8	no	—
246	C₄²	—	2	4	no	—
247	C₄²	—	2	4	no	—
248	C₄²	C₅×C₄⋊C₄	1	8	yes	—
249	C₄²	C₂×C₅×D₄	1	4	yes	—
250	C₄²	C₂×C₅×Q₈	1	4	yes	—
251	C₂×C₅	#1940	1	8	yes	direct product factor
252	C₂×C₅	C₂×#389	1	1	yes	characteristic
253	C₂×C₅	C₂×#423	1	1	yes	characteristic
254	C₂×C₅	C₂×#424	1	1	yes	characteristic
255	C₂×C₅	C₂×#435	1	2	yes	—
256	C₂×C₅	C₂×#446	1	2	yes	—
257	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
258	C₂³	C₄×C₅×D₄	1	2	yes	—
259	C₂³	C₄×C₅×Q₈	1	2	yes	—
260	C₂³	C₂×C₅×M₁₆	1	4	yes	—
261	C₂³	C₅×#131	1	4	yes	—
262	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
263	C₂×C₄	—	2	8	no	—
264	C₂×C₄	—	2	8	no	—
265	C₂×C₄	—	2	16	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	2	4	no	—
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	4	8	no	—
274	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
275	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
276	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
277	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
278	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
279	C₂×C₄	C₅×#121	1	4	yes	—
280	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
281	C₂×C₄	C₅×#125	1	4	yes	—
282	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
283	C₂×C₄	C₂×C₅×M₁₆	1	8	yes	—
284	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
285	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
286	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
287	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
288	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
289	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
290	C₈	—	2	4	no	—
291	C₈	—	2	4	no	—
292	C₈	—	4	4	no	—
293	C₅	C₂×#1940	1	1	yes	characteristic, direct product factor, Sylow
294	C₂²	C₅×#389	1	4	yes	—
295	C₂²	C₅×#423	1	4	yes	—
296	C₂²	C₅×#424	1	4	yes	—
297	C₂²	C₅×#435	1	8	yes	—
298	C₂²	C₅×#446	1	8	yes	—
299	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
300	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
301	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
302	C₂²	C₂²×C₅×M₁₆	1	2	yes	—
303	C₂²	C₂×C₅×#131	1	2	yes	—
304	C₄	—	2	4	no	—
305	C₄	—	2	4	no	—
306	C₄	—	2	8	no	—
307	C₄	—	4	4	no	—
308	C₄	C₅×#389	1	4	yes	—
309	C₄	C₂×C₅×#121	1	1	yes	characteristic
310	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
311	C₄	C₂×C₅×#125	1	1	yes	characteristic
312	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
313	C₂	C₅×#1940	1	8	yes	direct product factor
314	C₂	C₂×C₅×#389	1	1	yes	characteristic
315	C₂	C₂×C₅×#423	1	1	yes	characteristic
316	C₂	C₂×C₅×#424	1	1	yes	characteristic
317	C₂	C₂×C₅×#435	1	2	yes	—
318	C₂	C₂×C₅×#446	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₅	C₂³
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×#1940	C₂	direct (N × H)
24. C₂×#1940	C₅	direct (N × H)
61. #1940	C₂×C₅	direct (N × H)
251. C₂×C₅	#1940	direct (N × H)
293. C₅	C₂×#1940	direct (N × H)
313. C₂	C₅×#1940	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₄⋊C₈	2
C₂²×C₅×#97	2
C₂×C₄×C₅×C₄⋊C₄	2
C₅×#1940	2
C₂×C₅×#336	2
C₂×#1940	5

Subgroups — C2×C5×#1940 #11943862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1940 #11943862