Subgroups — D₅×#1567 #12068299

Order 1280.

854 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#423	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
4	#10601284	C₂	1	2	yes	maximal, complemented
5	#10600524	C₂	1	1	yes	maximal, characteristic, complemented
6	#10599362	C₂	1	4	yes	maximal, complemented
7	D₅×#335	C₂	1	4	yes	maximal, complemented
8	C₂×D₅×M₁₆	—	2	2	no	—
9	C₂²×C₈×D₅	C₄	1	2	yes	—
10	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
11	C₅×#423	C₂²	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	#65407	—	2	2	no	—
14	C₂×C₈×Dic₅	C₄	1	2	yes	—
15	#65213	C₂²	1	2	yes	—
16	C₂×C₄×#168	C₂²	1	1	yes	characteristic
17	#65126	—	2	2	no	—
18	#65126	C₂²	1	4	yes	—
19	D₅×C₄⋊C₈	—	2	2	no	—
20	D₅×C₄⋊C₈	C₂²	1	4	yes	—
21	C₄×C₈×D₅	C₄	1	1	yes	characteristic
22	C₄×C₈×D₅	C₄	1	1	yes	characteristic
23	C₄×C₈×D₅	C₄	1	1	yes	characteristic
24	C₄×C₈×D₅	C₄	1	1	yes	characteristic
25	C₄×C₈×D₅	C₂²	1	2	yes	—
26	C₄×C₈×D₅	C₂²	1	2	yes	—
27	C₅×#335	C₂²	1	4	yes	complemented
28	#64699	C₂²	1	8	yes	complemented
29	#64678	C₂²	1	4	yes	complemented
30	C₂×#1567	—	5	1	no	maximal, Sylow
31	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
34	C₂×C₅×M₁₆	—	2	2	no	—
35	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
40	C₂×#681	—	2	2	no	—
41	C₂²×#168	C₂×C₄	1	2	yes	—
42	D₅×M₁₆	—	4	8	no	—
43	C₂×#676	—	2	4	no	—
44	C₂×C₈×D₅	—	2	8	no	—
45	C₂×C₈×D₅	—	2	4	no	—
46	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
50	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₅	D₄	1	1	yes	characteristic
53	C₄²×D₅	D₄	1	1	yes	characteristic
54	C₄²×D₅	Q₈	1	1	yes	characteristic
55	C₄²×D₅	Q₈	1	1	yes	characteristic
56	C₄²×D₅	C₂³	1	1	yes	characteristic
57	C₄²×D₅	C₂³	1	1	yes	characteristic
58	C₅×C₄⋊C₈	—	2	2	no	—
59	C₅×C₄⋊C₈	C₂³	1	4	yes	—
60	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×C₈	C₂³	1	2	yes	—
63	#3946	—	2	4	no	—
64	#3946	—	2	4	no	—
65	C₈×Dic₅	C₂×C₄	1	2	yes	—
66	C₈×Dic₅	C₂×C₄	1	2	yes	—
67	C₈×Dic₅	C₂×C₄	1	2	yes	—
68	C₈×Dic₅	C₂×C₄	1	2	yes	—
69	C₄⋊#168	—	2	2	no	—
70	C₄⋊#168	C₂³	1	4	yes	—
71	C₄×#168	C₂×C₄	1	1	yes	characteristic
72	C₄×#168	C₂×C₄	1	1	yes	characteristic
73	C₄×#168	C₂³	1	2	yes	—
74	C₂×#423	—	5	2	no	—
75	C₂²×C₄×C₈	—	5	1	no	—
76	#1567	—	5	2	no	—
77	#1567	—	5	1	no	—
78	#1567	—	5	4	no	—
79	#1567	D₅	1	1	yes	characteristic, direct product factor
80	C₂×#335	—	5	4	no	—
81	C₂³×D₅	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
85	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₅	—	2	4	no	—
89	C₂×C₄×D₅	—	2	4	no	—
90	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₅	D₈	1	4	yes	—
97	C₂×C₄×D₅	Q₁₆	1	4	yes	—
98	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
104	C₅×M₁₆	—	4	4	no	—
105	C₂×C₅×C₈	—	2	4	no	—
106	C₂×C₅×C₈	—	2	4	no	—
107	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
108	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
109	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₅	C₂⁴	1	1	yes	characteristic
113	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
116	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
120	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
123	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
124	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
125	#681	—	4	4	no	—
126	C₂×#168	—	2	4	no	—
127	C₂×#168	—	2	4	no	—
128	C₂×#168	C₂²×C₄	1	2	yes	—
129	C₂×#168	C₂²×C₄	1	2	yes	—
130	#676	—	4	8	no	—
131	C₈×D₅	—	2	4	no	—
132	C₈×D₅	—	2	4	no	—
133	C₈×D₅	—	2	4	no	—
134	C₈×D₅	—	4	8	no	—
135	C₈×D₅	M₁₆	1	8	yes	complemented
136	C₂²×M₁₆	—	10	2	no	—
137	C₂³×C₈	—	5	2	no	—
138	C₂²×C₄²	—	5	1	no	—
139	#423	—	5	2	no	—
140	#423	—	5	4	no	—
141	#423	—	10	2	no	—
142	#423	—	10	2	no	—
143	#423	C₂×D₅	1	2	yes	—
144	C₂×C₄⋊C₈	—	5	4	no	—
145	C₂×C₄⋊C₈	—	10	2	no	—
146	C₂×C₄×C₈	—	5	2	no	—
147	C₂×C₄×C₈	—	5	1	no	—
148	C₂×C₄×C₈	—	5	1	no	—
149	C₂×C₄×C₈	—	5	1	no	—
150	C₂×C₄×C₈	—	5	1	no	—
151	C₂×C₄×C₈	—	5	1	no	—
152	C₂×C₄×C₈	—	5	2	no	—
153	C₂×C₄×C₈	—	5	2	no	—
154	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
155	#335	—	5	8	no	—
156	#335	—	5	4	no	—
157	#335	C₂×D₅	1	4	yes	complemented
158	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×D₅	—	2	2	no	—
160	C₂²×D₅	—	2	2	no	—
161	C₂²×D₅	#107	1	4	yes	—
162	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
171	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
174	C₂×Dic₅	—	2	2	no	—
175	C₂×Dic₅	—	2	2	no	—
176	C₂×Dic₅	#107	1	4	yes	—
177	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₄×D₅	—	2	2	no	—
184	C₄×D₅	—	2	2	no	—
185	C₄×D₅	—	2	2	no	—
186	C₄×D₅	—	2	2	no	—
187	C₄×D₅	—	2	2	no	—
188	C₄×D₅	—	2	2	no	—
189	C₄×D₅	#107	1	4	yes	—
190	C₄×D₅	#107	1	4	yes	—
191	C₄×D₅	#108	1	4	yes	—
192	C₄×D₅	C₂×M₁₆	1	4	yes	—
193	C₄×D₅	C₂×D₈	1	2	yes	—
194	C₄×D₅	C₂×D₈	1	2	yes	—
195	C₄×D₅	C₂×Q₁₆	1	2	yes	—
196	C₄×D₅	C₂×Q₁₆	1	2	yes	—
197	C₅×C₈	—	2	2	no	—
198	C₅×C₈	—	4	4	no	—
199	C₅×C₈	C₂×M₁₆	1	4	yes	complemented
200	#168	—	2	2	no	—
201	#168	—	4	4	no	—
202	#168	C₂×M₁₆	1	4	yes	complemented
203	C₂³×C₄	—	5	1	no	—
204	C₂³×C₄	—	5	1	no	—
205	C₂³×C₄	—	5	1	no	—
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	10	4	no	—
208	C₂×M₁₆	—	10	2	no	—
209	C₂×M₁₆	—	20	8	no	—
210	C₂²×C₈	—	5	2	no	—
211	C₂²×C₈	—	5	2	no	—
212	C₂²×C₈	—	5	2	no	—
213	C₂²×C₈	—	5	2	no	—
214	C₂²×C₈	—	5	2	no	—
215	C₂²×C₈	—	10	8	no	—
216	C₂²×C₈	—	10	4	no	—
217	C₂²×C₈	C₄×D₅	1	2	yes	—
218	C₂×C₄²	—	5	1	no	—
219	C₂×C₄²	—	5	1	no	—
220	C₂×C₄²	—	5	1	no	—
221	C₂×C₄²	—	5	1	no	—
222	C₂×C₄²	—	5	1	no	—
223	C₂×C₄²	—	5	1	no	—
224	C₂×C₄²	—	5	1	no	—
225	C₂×C₄²	—	5	1	no	—
226	C₂×C₄²	—	5	1	no	—
227	C₂×C₄²	—	5	1	no	—
228	C₂×C₄²	—	5	1	no	—
229	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
230	C₄⋊C₈	—	2	2	no	—
231	C₄⋊C₈	—	5	4	no	—
232	C₄⋊C₈	—	10	4	no	—
233	C₄⋊C₈	—	10	4	no	—
234	C₄⋊C₈	—	10	2	no	—
235	C₄⋊C₈	C₂²×D₅	1	4	yes	—
236	C₄×C₈	—	5	2	no	—
237	C₄×C₈	—	5	2	no	—
238	C₄×C₈	—	5	2	no	—
239	C₄×C₈	—	5	2	no	—
240	C₄×C₈	—	5	1	no	—
241	C₄×C₈	—	5	1	no	—
242	C₄×C₈	—	5	2	no	—
243	C₄×C₈	C₄×D₅	1	1	yes	characteristic
244	C₄×C₈	C₄×D₅	1	1	yes	characteristic
245	C₄×C₈	C₂²×D₅	1	2	yes	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	C₂×#107	1	2	yes	—
249	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
250	C₂×D₅	—	2	1	no	—
251	C₂×D₅	—	2	1	no	—
252	C₂×D₅	—	2	8	no	—
253	C₂×D₅	#423	1	2	yes	—
254	C₂×D₅	C₂×#107	1	2	yes	—
255	C₂×D₅	C₂×#107	1	2	yes	—
256	C₂×D₅	C₂×#108	1	2	yes	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	C₂×#107	1	2	yes	—
260	C₄×C₅	C₂×#108	1	2	yes	—
261	C₄×C₅	C₂²×M₁₆	1	2	yes	—
262	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
263	C₄×C₅	C₂²×Q₁₆	1	1	yes	characteristic
264	Dic₅	—	2	1	no	—
265	Dic₅	—	2	1	no	—
266	Dic₅	#423	1	2	yes	—
267	Dic₅	C₂×#107	1	2	yes	—
268	Dic₅	C₂×#107	1	2	yes	—
269	Dic₅	C₂×#108	1	2	yes	—
270	C₂⁴	—	5	1	no	—
271	C₂²×C₄	—	5	1	no	—
272	C₂²×C₄	—	5	1	no	—
273	C₂²×C₄	—	5	1	no	—
274	C₂²×C₄	—	5	1	no	—
275	C₂²×C₄	—	5	1	no	—
276	C₂²×C₄	—	5	1	no	—
277	C₂²×C₄	—	5	1	no	—
278	C₂²×C₄	—	5	4	no	—
279	C₂²×C₄	—	5	4	no	—
280	C₂²×C₄	—	5	1	no	—
281	C₂²×C₄	—	5	1	no	—
282	C₂²×C₄	—	5	1	no	—
283	C₂²×C₄	—	5	1	no	—
284	C₂²×C₄	—	5	1	no	—
285	C₂²×C₄	—	5	1	no	—
286	C₂²×C₄	—	5	1	no	—
287	C₂²×C₄	—	5	1	no	—
288	C₂²×C₄	—	10	4	no	—
289	C₂²×C₄	—	10	4	no	—
290	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
292	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
293	M₁₆	—	4	4	no	—
294	M₁₆	—	20	8	no	—
295	M₁₆	—	20	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	5	2	no	—
299	C₂×C₈	—	5	8	no	—
300	C₂×C₈	—	5	2	no	—
301	C₂×C₈	—	10	4	no	—
302	C₂×C₈	—	10	4	no	—
303	C₂×C₈	—	10	4	no	—
304	C₂×C₈	—	10	4	no	—
305	C₂×C₈	—	10	4	no	—
306	C₂×C₈	—	20	8	no	—
307	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
308	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
309	C₄²	—	5	1	no	—
310	C₄²	—	5	1	no	—
311	C₄²	—	5	1	no	—
312	C₄²	—	5	1	no	—
313	C₄²	—	5	1	no	—
314	C₄²	—	5	1	no	—
315	C₄²	—	5	1	no	—
316	C₄²	—	5	1	no	—
317	C₄²	—	5	1	no	—
318	C₄²	—	5	1	no	—
319	C₄²	—	5	1	no	—
320	C₄²	—	5	1	no	—
321	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
322	C₄²	D₄×D₅	1	1	yes	characteristic
323	C₄²	Q₈×D₅	1	1	yes	characteristic
324	C₄²	C₂³×D₅	1	1	yes	characteristic
325	C₂×C₅	—	2	2	no	—
326	C₂×C₅	C₂×#423	1	1	yes	characteristic
327	C₂×C₅	C₂²×#107	1	1	yes	characteristic
328	C₂×C₅	C₂²×#108	1	1	yes	characteristic
329	D₅	—	2	2	no	—
330	D₅	#1567	1	4	yes	direct product factor
331	C₂³	—	5	1	no	—
332	C₂³	—	5	1	no	—
333	C₂³	—	5	4	no	—
334	C₂³	—	10	2	no	—
335	C₂³	—	10	2	no	—
336	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	5	1	no	—
340	C₂×C₄	—	5	1	no	—
341	C₂×C₄	—	5	1	no	—
342	C₂×C₄	—	5	1	no	—
343	C₂×C₄	—	5	4	no	—
344	C₂×C₄	—	5	4	no	—
345	C₂×C₄	—	5	2	no	—
346	C₂×C₄	—	5	2	no	—
347	C₂×C₄	—	5	2	no	—
348	C₂×C₄	—	5	2	no	—
349	C₂×C₄	—	5	4	no	—
350	C₂×C₄	—	5	4	no	—
351	C₂×C₄	—	5	4	no	—
352	C₂×C₄	—	5	1	no	—
353	C₂×C₄	—	5	1	no	—
354	C₂×C₄	—	10	2	no	—
355	C₂×C₄	—	10	2	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	—	10	2	no	—
359	C₂×C₄	—	10	2	no	—
360	C₂×C₄	—	10	2	no	—
361	C₂×C₄	—	10	2	no	—
362	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
363	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
364	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
365	C₂×C₄	D₅×D₈	1	2	yes	—
366	C₂×C₄	D₅×Q₁₆	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	4	4	no	—
372	C₈	—	5	4	no	—
373	C₈	—	10	2	no	—
374	C₈	—	20	4	no	—
375	C₈	D₅×M₁₆	1	4	yes	complemented
376	C₅	C₂×#1567	1	1	yes	characteristic, complemented, Sylow
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	5	2	no	—
380	C₂²	—	5	2	no	—
381	C₂²	—	5	2	no	—
382	C₂²	—	5	2	no	—
383	C₂²	—	10	8	no	—
384	C₂²	—	10	1	no	—
385	C₂²	—	10	1	no	—
386	C₂²	D₅×#107	1	2	yes	—
387	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	5	2	no	—
391	C₄	—	5	2	no	—
392	C₄	—	5	2	no	—
393	C₄	—	5	2	no	—
394	C₄	—	10	1	no	—
395	C₄	—	10	1	no	—
396	C₄	D₅×#107	1	2	yes	—
397	C₄	D₅×#108	1	2	yes	—
398	C₄	C₂×D₅×M₁₆	1	2	yes	—
399	C₄	C₂×D₅×D₈	1	1	yes	characteristic
400	C₄	C₂×D₅×Q₁₆	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	5	4	no	—
403	C₂	—	10	2	no	—
404	C₂	D₅×#423	1	1	yes	characteristic
405	C₂	C₂×D₅×#107	1	1	yes	characteristic
406	C₂	C₂×D₅×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1567	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₄⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1567	D₅
hypocenter	C₅	C₂×#1567
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
3. C₅×#1567	C₂	semidirect
4. #10601284	C₂	semidirect
5. #10600524	C₂	semidirect
6. #10599362	C₂	semidirect
7. D₅×#335	C₂	semidirect
27. C₅×#335	C₂²	semidirect
28. #64699	C₂²	semidirect
29. #64678	C₂²	semidirect
79. #1567	D₅	direct (N × H)
135. C₈×D₅	M₁₆	semidirect
157. #335	C₂×D₅	semidirect
199. C₅×C₈	C₂×M₁₆	semidirect
202. #168	C₂×M₁₆	semidirect
330. D₅	#1567	direct (N × H)
375. C₈	D₅×M₁₆	semidirect
376. C₅	C₂×#1567	semidirect

Maximal subgroups

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

subgroup	index
D₅×#423	2
C₂×C₄×C₈×D₅	2
C₅×#1567	2
#10601284	2
#10600524	2
#10599362	2
D₅×#335	2
C₂×#1567	5

Subgroups — D5×#1567 #12068299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#1567 #12068299