Subgroups — C₅×#17829 #11940549

Order 1280.

610 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	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#2925	C₂	1	2	yes	maximal
3	C₅×#1572	C₂	1	4	yes	maximal, complemented
4	C₅×#1570	C₂	1	2	yes	maximal, complemented
5	C₅×#1568	C₂	1	2	yes	maximal, complemented
6	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1564	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#41	C₂²	1	1	yes	characteristic
10	C₅×C₈×Q₈	C₄	1	1	yes	characteristic
11	C₅×C₈×Q₈	C₄	1	1	yes	characteristic
12	C₅×C₈×D₄	C₄	1	2	yes	—
13	C₅×C₈×D₄	C₄	1	1	yes	characteristic
14	C₅×C₈×D₄	C₄	1	2	yes	—
15	C₅×C₈×D₄	C₄	1	1	yes	characteristic
16	C₅×#433	—	2	4	no	—
17	C₅×#432	C₂²	1	4	yes	—
18	C₅×#431	C₂²	1	4	yes	—
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₅×#431	C₂²	1	2	yes	—
21	C₅×#423	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
23	C₅×#408	—	2	2	no	—
24	C₅×#405	—	2	2	no	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₅×#335	C₂²	1	1	yes	characteristic
28	C₅×#335	C₂²	1	1	yes	characteristic
29	C₅×#335	C₂²	1	2	yes	—
30	C₅×#335	C₂²	1	2	yes	—
31	C₅×#335	C₂²	1	2	yes	—
32	C₅×#334	C₂²	1	4	yes	—
33	C₅×#334	C₂²	1	4	yes	—
34	#17829	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₅×#41	D₄	1	1	yes	characteristic
36	C₂×C₅×M₁₆	—	2	2	no	—
37	C₂²×C₅×C₈	—	2	2	no	—
38	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
40	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
42	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
43	C₄×C₅×Q₈	Q₈	1	1	yes	characteristic
44	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
45	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
46	C₄×C₅×D₄	Q₈	1	2	yes	—
47	C₄×C₅×D₄	Q₈	1	1	yes	characteristic
48	C₅×#117	D₄	1	1	yes	characteristic
49	C₅×#117	D₄	1	2	yes	—
50	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂³	1	2	yes	—
52	C₅×C₄⋊C₈	—	2	2	no	—
53	C₅×C₄⋊C₈	—	2	2	no	—
54	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
58	C₅×C₄⋊C₈	C₂³	1	2	yes	—
59	C₅×C₄⋊C₈	C₂³	1	2	yes	—
60	C₅×C₄⋊C₈	C₂³	1	4	yes	—
61	C₅×C₂²⋊C₈	—	2	4	no	—
62	C₅×C₂²⋊C₈	—	2	4	no	—
63	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₅×#97	—	2	4	no	—
67	C₄×C₅×C₈	—	2	4	no	—
68	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
70	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
71	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
72	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×C₈	C₂³	1	2	yes	—
74	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₈×#41	C₂×C₅	1	1	yes	characteristic
76	#2925	C₂×C₅	1	2	yes	—
77	#1572	C₂×C₅	1	4	yes	complemented
78	#1570	C₂×C₅	1	2	yes	complemented
79	#1568	C₂×C₅	1	2	yes	complemented
80	#1567	C₂×C₅	1	1	yes	characteristic, complemented
81	#1564	C₂×C₅	1	2	yes	complemented
82	C₂×#335	C₂×C₅	1	1	yes	characteristic, complemented
83	C₅×#41	—	2	2	no	—
84	C₅×#41	—	2	2	no	—
85	C₂×C₅×Q₈	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
87	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
93	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₅×M₁₆	—	4	4	no	—
95	C₂×C₅×C₈	—	2	2	no	—
96	C₂×C₅×C₈	—	2	4	no	—
97	C₂×C₅×C₈	—	2	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₂×C₅×C₈	—	4	1	no	—
101	C₂×C₅×C₈	—	4	2	no	—
102	C₂×C₅×C₈	—	4	4	no	—
103	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
107	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
109	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
110	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
111	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
112	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
113	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
114	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
115	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
116	C₄²×C₅	C₂²×C₄	1	2	yes	—
117	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂×D₄	1	2	yes	—
119	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₅	C₂×Q₈	1	2	yes	—
121	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₅	C₂⁴	1	1	yes	characteristic
123	C₄×#41	C₂²×C₅	1	1	yes	characteristic
124	C₈×Q₈	C₄×C₅	1	1	yes	characteristic
125	C₈×Q₈	C₄×C₅	1	1	yes	characteristic
126	C₈×D₄	C₄×C₅	1	1	yes	characteristic
127	C₈×D₄	C₄×C₅	1	2	yes	—
128	C₈×D₄	C₄×C₅	1	1	yes	characteristic
129	C₈×D₄	C₄×C₅	1	2	yes	—
130	#433	—	2	4	no	—
131	#432	C₂²×C₅	1	4	yes	—
132	#431	C₂²×C₅	1	4	yes	—
133	#431	C₂²×C₅	1	1	yes	characteristic
134	#431	C₂²×C₅	1	2	yes	—
135	#423	C₂²×C₅	1	2	yes	—
136	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
137	#408	—	2	2	no	—
138	#405	—	2	2	no	—
139	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
141	#335	C₂²×C₅	1	1	yes	characteristic
142	#335	C₂²×C₅	1	1	yes	characteristic
143	#335	C₂²×C₅	1	2	yes	—
144	#335	C₂²×C₅	1	2	yes	—
145	#335	C₂²×C₅	1	2	yes	—
146	#334	C₂²×C₅	1	4	yes	—
147	#334	C₂²×C₅	1	4	yes	—
148	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
149	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₅×Q₈	—	2	2	no	—
151	C₅×D₄	—	2	4	no	—
152	C₅×D₄	—	2	2	no	—
153	C₂×C₄×C₅	—	2	1	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	1	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	4	1	no	—
160	C₂×C₄×C₅	—	4	2	no	—
161	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	#135	1	2	yes	—
168	C₂×C₄×C₅	#135	1	2	yes	—
169	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
172	C₅×C₈	—	2	2	no	—
173	C₅×C₈	—	2	1	no	—
174	C₅×C₈	—	2	1	no	—
175	C₅×C₈	—	2	2	no	—
176	C₅×C₈	—	2	1	no	—
177	C₅×C₈	—	4	2	no	—
178	C₅×C₈	—	4	2	no	—
179	C₅×C₈	—	4	4	no	—
180	C₅×C₈	#131	1	2	yes	—
181	C₂×#41	C₅×D₄	1	1	yes	characteristic
182	C₂×M₁₆	—	2	2	no	—
183	C₂²×C₈	—	2	2	no	—
184	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
186	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
187	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
188	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
189	C₄×Q₈	C₅×Q₈	1	1	yes	characteristic
190	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
191	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
192	C₄×D₄	C₅×Q₈	1	2	yes	—
193	C₄×D₄	C₅×Q₈	1	1	yes	characteristic
194	#117	C₅×D₄	1	1	yes	characteristic
195	#117	C₅×D₄	1	2	yes	—
196	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
197	C₂×C₄²	C₂³×C₅	1	2	yes	—
198	C₄⋊C₈	—	2	2	no	—
199	C₄⋊C₈	—	2	2	no	—
200	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
201	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
202	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
203	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
204	C₄⋊C₈	C₂³×C₅	1	2	yes	—
205	C₄⋊C₈	C₂³×C₅	1	2	yes	—
206	C₄⋊C₈	C₂³×C₅	1	4	yes	—
207	C₂²⋊C₈	—	2	4	no	—
208	C₂²⋊C₈	—	2	4	no	—
209	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
210	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
211	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
212	#97	—	2	4	no	—
213	C₄×C₈	—	2	4	no	—
214	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
215	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
216	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
217	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
218	C₄×C₈	C₂³×C₅	1	2	yes	—
219	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
220	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₅	—	2	1	no	—
222	C₂²×C₅	—	2	1	no	—
223	C₂²×C₅	—	2	2	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	—	2	2	no	—
226	C₂²×C₅	#427	1	2	yes	—
227	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₅	—	2	1	no	—
229	C₄×C₅	—	2	2	no	—
230	C₄×C₅	—	2	2	no	—
231	C₄×C₅	—	2	1	no	—
232	C₄×C₅	—	2	1	no	—
233	C₄×C₅	—	2	2	no	—
234	C₄×C₅	#427	1	2	yes	—
235	C₄×C₅	C₂×#131	1	1	yes	characteristic
236	C₄×C₅	#568	1	1	yes	characteristic
237	C₄×C₅	C₂×#135	1	1	yes	characteristic
238	C₄×C₅	C₂×#135	1	1	yes	characteristic
239	#41	—	2	2	no	—
240	#41	—	2	2	no	—
241	C₂×Q₈	C₅×C₄⋊C₄	1	1	yes	characteristic
242	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
243	C₂×D₄	C₅×C₄⋊C₄	1	1	yes	characteristic
244	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
246	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
247	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
249	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
250	M₁₆	—	4	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	4	1	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	4	4	no	—
259	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
261	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
262	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
263	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
265	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
266	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
267	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
268	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
269	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
270	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
271	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
272	C₄²	C₂²×C₄×C₅	1	2	yes	—
273	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₄²	C₂×C₅×D₄	1	2	yes	—
275	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
276	C₄²	C₂×C₅×Q₈	1	2	yes	—
277	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
278	C₄²	C₂⁴×C₅	1	1	yes	characteristic
279	C₂×C₅	—	2	2	no	—
280	C₂×C₅	—	4	2	no	—
281	C₂×C₅	#2906	1	1	yes	characteristic
282	C₂×C₅	C₂×#427	1	1	yes	characteristic
283	C₂×C₅	#2916	1	1	yes	characteristic
284	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
285	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
286	Q₈	—	2	2	no	—
287	D₄	—	2	4	no	—
288	D₄	—	2	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
298	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
300	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
301	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
302	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
303	C₂×C₄	C₅×#135	1	2	yes	—
304	C₂×C₄	C₅×#135	1	2	yes	—
305	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
306	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
307	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
308	C₈	—	2	2	no	—
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₈	—	2	2	no	—
312	C₈	—	2	1	no	—
313	C₈	—	4	2	no	—
314	C₈	—	4	2	no	—
315	C₈	—	4	4	no	—
316	C₈	C₅×#131	1	2	yes	—
317	C₅	#17829	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	C₅×#427	1	2	yes	—
324	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
325	C₄	—	2	1	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	2	no	—
331	C₄	C₅×#427	1	2	yes	—
332	C₄	C₂×C₅×#131	1	1	yes	characteristic
333	C₄	C₅×#568	1	1	yes	characteristic
334	C₄	C₂×C₅×#135	1	1	yes	characteristic
335	C₄	C₂×C₅×#135	1	1	yes	characteristic
336	C₂	—	2	2	no	—
337	C₂	—	4	2	no	—
338	C₂	C₅×#2906	1	1	yes	characteristic
339	C₂	C₂×C₅×#427	1	1	yes	characteristic
340	C₂	C₅×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×C₅×#41	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1572	C₂	semidirect
4. C₅×#1570	C₂	semidirect
5. C₅×#1568	C₂	semidirect
6. C₅×#1567	C₂	semidirect
7. C₅×#1564	C₂	semidirect
8. C₂×C₅×#335	C₂	semidirect
34. #17829	C₅	direct (N × H)
77. #1572	C₂×C₅	semidirect
78. #1570	C₂×C₅	semidirect
79. #1568	C₂×C₅	semidirect
80. #1567	C₂×C₅	semidirect
81. #1564	C₂×C₅	semidirect
82. C₂×#335	C₂×C₅	semidirect
317. C₅	#17829	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₈×#41	2
C₅×#2925	2
C₅×#1572	2
C₅×#1570	2
C₅×#1568	2
C₅×#1567	2
C₅×#1564	2
C₂×C₅×#335	2
#17829	5

Subgroups — C5×#17829 #11940549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17829 #11940549