Subgroups — C₅×#13121 #11935841

Order 1280.

382 conjugacy classes of subgroups.

The subgroup lattice has 342 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, complemented
2	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₅×#1374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1374	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₄×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
17	C₅×C₄⋊C₁₆	—	2	2	no	—
18	C₅×C₂²⋊C₁₆	—	2	2	no	—
19	C₅×C₂²⋊C₁₆	—	2	2	no	—
20	C₅×#346	—	2	2	no	—
21	C₅×#336	C₄	1	1	yes	characteristic
22	C₅×#336	C₄	1	1	yes	characteristic
23	#13121	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₅×C₈	—	2	1	no	—
26	C₂²×C₅×C₈	—	2	1	no	—
27	C₂²×C₅×C₈	—	2	1	no	—
28	C₂²×C₅×C₈	—	2	1	no	—
29	C₂²×C₅×C₈	—	2	1	no	—
30	C₂²×C₅×C₈	—	2	1	no	—
31	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
35	C₂×C₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
37	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₅×C₁₆	—	2	1	no	—
40	C₂×C₅×C₁₆	—	2	1	no	—
41	C₂×C₅×C₁₆	—	2	1	no	—
42	C₂×C₅×C₁₆	—	2	1	no	—
43	C₂×C₅×C₁₆	—	2	1	no	—
44	C₂×C₅×C₁₆	—	2	1	no	—
45	C₂×C₅×C₁₆	—	2	1	no	—
46	C₂×C₅×C₁₆	—	2	1	no	—
47	C₂×C₅×C₁₆	—	2	1	no	—
48	C₂×C₅×C₁₆	—	2	1	no	—
49	C₂×C₅×C₁₆	D₄	1	2	yes	—
50	C₂×C₅×C₁₆	D₄	1	2	yes	—
51	C₅×C₂²⋊C₈	—	2	2	no	—
52	C₄×C₅×C₈	—	2	1	no	—
53	C₄×C₅×C₈	—	2	1	no	—
54	C₄×C₅×C₈	—	2	1	no	—
55	C₄×C₅×C₈	—	2	1	no	—
56	C₅×#95	C₈	1	1	yes	characteristic
57	C₅×#95	C₈	1	1	yes	characteristic
58	C₂×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic
60	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic
61	C₂×#346	C₂×C₅	1	1	yes	characteristic, complemented
62	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
63	#1374	C₂×C₅	1	1	yes	characteristic, complemented
64	#1374	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
66	C₂²×C₄×C₅	—	2	1	no	—
67	C₂²×C₄×C₅	—	2	1	no	—
68	C₂²×C₄×C₅	—	2	1	no	—
69	C₂²×C₄×C₅	—	2	1	no	—
70	C₂²×C₄×C₅	—	2	1	no	—
71	C₂²×C₄×C₅	—	2	1	no	—
72	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
74	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
75	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₅×C₈	—	2	1	no	—
79	C₂×C₅×C₈	—	2	1	no	—
80	C₂×C₅×C₈	—	2	1	no	—
81	C₂×C₅×C₈	—	2	1	no	—
82	C₂×C₅×C₈	—	2	1	no	—
83	C₂×C₅×C₈	—	2	1	no	—
84	C₂×C₅×C₈	—	2	1	no	—
85	C₂×C₅×C₈	—	2	1	no	—
86	C₂×C₅×C₈	—	4	1	no	—
87	C₂×C₅×C₈	—	4	1	no	—
88	C₂×C₅×C₈	—	4	1	no	—
89	C₂×C₅×C₈	—	4	1	no	—
90	C₂×C₅×C₈	M₁₆	1	2	yes	—
91	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
92	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
93	C₂×C₅×C₈	#41	1	1	yes	characteristic
94	C₂×C₅×C₈	#41	1	1	yes	characteristic
95	C₂×C₅×C₈	#41	1	1	yes	characteristic
96	C₂×C₅×C₈	#41	1	1	yes	characteristic
97	C₅×C₂²⋊C₄	—	2	2	no	—
98	C₅×C₂²⋊C₄	—	2	2	no	—
99	C₄²×C₅	—	2	1	no	—
100	C₄²×C₅	—	2	1	no	—
101	C₄²×C₅	—	2	1	no	—
102	C₄²×C₅	—	2	1	no	—
103	C₅×C₁₆	—	2	2	no	—
104	C₅×C₁₆	—	2	2	no	—
105	C₅×C₁₆	—	4	1	no	—
106	C₅×C₁₆	—	4	1	no	—
107	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
110	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₂²⋊C₈	C₄×C₅	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
115	C₄×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
116	C₄⋊C₁₆	—	2	2	no	—
117	C₂²⋊C₁₆	—	2	2	no	—
118	C₂²⋊C₁₆	—	2	2	no	—
119	#346	—	2	2	no	—
120	#336	C₄×C₅	1	1	yes	characteristic
121	#336	C₄×C₅	1	1	yes	characteristic
122	C₂³×C₅	—	2	1	no	—
123	C₂³×C₅	—	2	1	no	—
124	C₂³×C₅	—	2	1	no	—
125	C₂³×C₅	—	2	1	no	—
126	C₂³×C₅	—	2	1	no	—
127	C₂³×C₅	—	2	1	no	—
128	C₂³×C₅	M₃₂	1	2	yes	—
129	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
130	C₂×C₄×C₅	—	2	1	no	—
131	C₂×C₄×C₅	—	2	1	no	—
132	C₂×C₄×C₅	—	2	1	no	—
133	C₂×C₄×C₅	—	2	1	no	—
134	C₂×C₄×C₅	—	2	1	no	—
135	C₂×C₄×C₅	—	2	1	no	—
136	C₂×C₄×C₅	—	2	1	no	—
137	C₂×C₄×C₅	—	2	1	no	—
138	C₂×C₄×C₅	—	2	1	no	—
139	C₂×C₄×C₅	—	2	1	no	—
140	C₂×C₄×C₅	—	2	1	no	—
141	C₂×C₄×C₅	—	2	1	no	—
142	C₂×C₄×C₅	—	2	1	no	—
143	C₂×C₄×C₅	—	2	1	no	—
144	C₂×C₄×C₅	—	4	1	no	—
145	C₂×C₄×C₅	—	4	1	no	—
146	C₂×C₄×C₅	—	4	1	no	—
147	C₂×C₄×C₅	—	4	1	no	—
148	C₂×C₄×C₅	M₃₂	1	2	yes	—
149	C₂×C₄×C₅	#117	1	1	yes	characteristic
150	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₅	#131	1	1	yes	characteristic
154	C₂×C₄×C₅	#131	1	1	yes	characteristic
155	C₅×C₈	—	2	2	no	—
156	C₅×C₈	—	4	1	no	—
157	C₅×C₈	—	4	1	no	—
158	C₅×C₈	#121	1	1	yes	characteristic
159	C₅×C₈	#123	1	1	yes	characteristic
160	C₅×C₈	#124	1	1	yes	characteristic
161	C₅×C₈	#126	1	1	yes	characteristic
162	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	—	2	1	no	—
165	C₂²×C₈	—	2	1	no	—
166	C₂²×C₈	—	2	1	no	—
167	C₂²×C₈	—	2	1	no	—
168	C₂²×C₈	—	2	1	no	—
169	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	C₅×C₈	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	C₅×C₈	1	1	yes	characteristic
175	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂×C₁₆	—	2	1	no	—
178	C₂×C₁₆	—	2	1	no	—
179	C₂×C₁₆	—	2	1	no	—
180	C₂×C₁₆	—	2	1	no	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	2	1	no	—
184	C₂×C₁₆	—	2	1	no	—
185	C₂×C₁₆	—	2	1	no	—
186	C₂×C₁₆	—	2	1	no	—
187	C₂×C₁₆	C₅×D₄	1	2	yes	—
188	C₂×C₁₆	C₅×D₄	1	2	yes	—
189	C₂²⋊C₈	—	2	2	no	—
190	C₄×C₈	—	2	1	no	—
191	C₄×C₈	—	2	1	no	—
192	C₄×C₈	—	2	1	no	—
193	C₄×C₈	—	2	1	no	—
194	#95	C₅×C₈	1	1	yes	characteristic
195	#95	C₅×C₈	1	1	yes	characteristic
196	C₂²×C₅	—	2	2	no	—
197	C₂²×C₅	—	2	2	no	—
198	C₂²×C₅	—	2	2	no	—
199	C₂²×C₅	—	4	1	no	—
200	C₂²×C₅	—	4	1	no	—
201	C₂²×C₅	—	4	1	no	—
202	C₂²×C₅	—	4	1	no	—
203	C₂²×C₅	#431	1	1	yes	characteristic
204	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
205	C₂²×C₅	C₈×D₄	1	1	yes	characteristic
206	C₂²×C₅	C₂×M₃₂	1	1	yes	characteristic
207	C₂²×C₅	C₂×M₃₂	1	1	yes	characteristic
208	C₂²×C₅	#504	1	1	yes	characteristic
209	C₂²×C₅	#504	1	1	yes	characteristic
210	C₄×C₅	—	2	2	no	—
211	C₄×C₅	—	4	1	no	—
212	C₄×C₅	—	4	1	no	—
213	C₄×C₅	—	4	1	no	—
214	C₄×C₅	—	4	1	no	—
215	C₄×C₅	#388	1	1	yes	characteristic
216	C₄×C₅	#433	1	1	yes	characteristic
217	C₄×C₅	#435	1	1	yes	characteristic
218	C₄×C₅	#436	1	1	yes	characteristic
219	C₂⁴	C₂×C₅×C₈	1	1	yes	characteristic
220	C₂²×C₄	—	2	1	no	—
221	C₂²×C₄	—	2	1	no	—
222	C₂²×C₄	—	2	1	no	—
223	C₂²×C₄	—	2	1	no	—
224	C₂²×C₄	—	2	1	no	—
225	C₂²×C₄	—	2	1	no	—
226	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
227	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
229	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
230	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
231	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
232	C₂×C₈	—	2	1	no	—
233	C₂×C₈	—	2	1	no	—
234	C₂×C₈	—	2	1	no	—
235	C₂×C₈	—	2	1	no	—
236	C₂×C₈	—	2	1	no	—
237	C₂×C₈	—	2	1	no	—
238	C₂×C₈	—	2	1	no	—
239	C₂×C₈	—	2	1	no	—
240	C₂×C₈	—	4	1	no	—
241	C₂×C₈	—	4	1	no	—
242	C₂×C₈	—	4	1	no	—
243	C₂×C₈	—	4	1	no	—
244	C₂×C₈	C₅×M₁₆	1	2	yes	—
245	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
246	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
247	C₂×C₈	C₅×#41	1	1	yes	characteristic
248	C₂×C₈	C₅×#41	1	1	yes	characteristic
249	C₂×C₈	C₅×#41	1	1	yes	characteristic
250	C₂×C₈	C₅×#41	1	1	yes	characteristic
251	C₂²⋊C₄	—	2	2	no	—
252	C₂²⋊C₄	—	2	2	no	—
253	C₄²	—	2	1	no	—
254	C₄²	—	2	1	no	—
255	C₄²	—	2	1	no	—
256	C₄²	—	2	1	no	—
257	C₁₆	—	2	2	no	—
258	C₁₆	—	2	2	no	—
259	C₁₆	—	4	1	no	—
260	C₁₆	—	4	1	no	—
261	C₂×C₅	—	4	2	no	—
262	C₂×C₅	#1923	1	1	yes	characteristic
263	C₂×C₅	#2163	1	1	yes	characteristic
264	C₂×C₅	#2164	1	1	yes	characteristic
265	C₂×C₅	#2168	1	1	yes	characteristic
266	C₂×C₅	#2168	1	1	yes	characteristic
267	C₂×C₅	#2168	1	1	yes	characteristic
268	C₂×C₅	#2169	1	1	yes	characteristic
269	C₂³	—	2	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	C₅×M₃₂	1	2	yes	—
276	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	4	1	no	—
292	C₂×C₄	—	4	1	no	—
293	C₂×C₄	—	4	1	no	—
294	C₂×C₄	—	4	1	no	—
295	C₂×C₄	C₅×M₃₂	1	2	yes	—
296	C₂×C₄	C₅×#117	1	1	yes	characteristic
297	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
298	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
299	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
300	C₂×C₄	C₅×#131	1	1	yes	characteristic
301	C₂×C₄	C₅×#131	1	1	yes	characteristic
302	C₈	—	2	2	no	—
303	C₈	—	4	1	no	—
304	C₈	—	4	1	no	—
305	C₈	C₅×#121	1	1	yes	characteristic
306	C₈	C₅×#123	1	1	yes	characteristic
307	C₈	C₅×#124	1	1	yes	characteristic
308	C₈	C₅×#126	1	1	yes	characteristic
309	C₅	#13121	1	1	yes	characteristic, direct product factor, Sylow
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	4	1	no	—
314	C₂²	—	4	1	no	—
315	C₂²	—	4	1	no	—
316	C₂²	—	4	1	no	—
317	C₂²	C₅×#431	1	1	yes	characteristic
318	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
319	C₂²	C₅×C₈×D₄	1	1	yes	characteristic
320	C₂²	C₂×C₅×M₃₂	1	1	yes	characteristic
321	C₂²	C₂×C₅×M₃₂	1	1	yes	characteristic
322	C₂²	C₅×#504	1	1	yes	characteristic
323	C₂²	C₅×#504	1	1	yes	characteristic
324	C₄	—	2	2	no	—
325	C₄	—	4	1	no	—
326	C₄	—	4	1	no	—
327	C₄	—	4	1	no	—
328	C₄	—	4	1	no	—
329	C₄	C₅×#388	1	1	yes	characteristic
330	C₄	C₅×#433	1	1	yes	characteristic
331	C₄	C₅×#435	1	1	yes	characteristic
332	C₄	C₅×#436	1	1	yes	characteristic
333	C₂	—	4	2	no	—
334	C₂	C₅×#1923	1	1	yes	characteristic
335	C₂	C₅×#2163	1	1	yes	characteristic
336	C₂	C₅×#2164	1	1	yes	characteristic
337	C₂	C₅×#2168	1	1	yes	characteristic
338	C₂	C₅×#2168	1	1	yes	characteristic
339	C₂	C₅×#2168	1	1	yes	characteristic
340	C₂	C₅×#2169	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅×C₈	C₂³
commutator	C₂³	C₂²×C₅×C₈
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂³×C₅	C₂²×C₈
prime radical	C₂⁴×C₅	C₂×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₄⋊C₁₆	C₂	semidirect
4. C₂×C₅×#346	C₂	semidirect
6. C₅×#1374	C₂	semidirect
7. C₅×#1374	C₂	semidirect
23. #13121	C₅	direct (N × H)
58. C₂×C₄⋊C₁₆	C₂×C₅	semidirect
61. C₂×#346	C₂×C₅	semidirect
63. #1374	C₂×C₅	semidirect
64. #1374	C₂×C₅	semidirect
309. C₅	#13121	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×C₄⋊C₁₆	2
C₂×C₅×C₂²⋊C₁₆	2
C₂×C₅×#346	2
C₅×C₈×C₂²⋊C₄	2
C₅×#1374	2
#13121	5

Subgroups — C5×#13121 #11935841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13121 #11935841