Subgroups — #12070550

Order 1280.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10614260	C₂	1	1	yes	maximal, characteristic
2	#10614253	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611020	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601541	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600528	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600519	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599019	C₂	1	2	yes	maximal, complemented
9	#10599009	C₂	1	2	yes	maximal, complemented
10	#10598945	C₂	1	2	yes	maximal, complemented
11	#10598944	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	#65811	C₂²	1	1	yes	characteristic
14	C₅×#431	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	#65527	C₄	1	2	yes	—
17	#65316	C₄	1	1	yes	characteristic
18	C₄×#688	C₂²	1	2	yes	—
19	#65313	C₂²	1	2	yes	—
20	#65310	C₄	1	1	yes	characteristic
21	#65304	C₄	1	1	yes	characteristic
22	C₄×#686	C₂²	1	2	yes	—
23	#65300	—	2	2	no	—
24	D₄×#168	C₂²	1	2	yes	—
25	#65297	C₄	1	1	yes	characteristic
26	#65292	C₄	1	2	yes	—
27	#65215	—	2	1	no	—
28	#65214	C₂²	1	1	yes	characteristic
29	#65214	C₂²	1	1	yes	characteristic
30	#65213	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#168	—	2	1	no	—
32	#65127	C₂²	1	2	yes	—
33	#65123	C₂²	1	2	yes	—
34	#65016	—	2	2	no	—
35	#64977	—	2	1	no	—
36	C₈×D₂₀	—	2	1	no	—
37	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
41	#64700	C₂²	1	2	yes	—
42	#64699	C₂²	1	2	yes	—
43	#64679	C₂²	1	2	yes	—
44	#64679	C₂²	1	2	yes	—
45	#64674	C₂²	1	2	yes	—
46	#64674	C₂²	1	2	yes	—
47	#18022	—	5	1	no	maximal, Sylow
48	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
49	C₂×#709	—	2	1	no	—
50	C₂²×C₅×C₈	—	2	1	no	—
51	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
52	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
53	C₄×C₅×D₄	—	2	1	no	—
54	C₄×C₅×D₄	—	2	1	no	—
55	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
56	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₅×#117	—	2	1	no	—
58	C₅×#117	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	—	2	1	no	—
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₂×#688	C₂×C₄	1	2	yes	—
62	C₂×#686	C₂×C₄	1	2	yes	—
63	#4076	—	2	1	no	—
64	#4076	C₂×C₄	1	2	yes	—
65	C₂×#681	—	2	1	no	—
66	C₂²×#168	—	2	2	no	—
67	C₂×#676	—	2	2	no	—
68	C₂×C₈×D₅	—	2	2	no	—
69	#4021	—	2	1	no	—
70	#4020	C₂×C₄	1	1	yes	characteristic
71	C₄×D₂₀	—	2	1	no	—
72	C₄×D₂₀	C₂³	1	2	yes	—
73	#4015	C₂×C₄	1	1	yes	characteristic
74	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₅×C₂²⋊C₈	—	2	1	no	—
77	C₄×C₅×C₈	—	2	1	no	—
78	C₄×C₅×C₈	—	2	1	no	—
79	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
81	#3967	C₂×C₄	1	2	yes	—
82	#3964	C₂×C₄	1	2	yes	—
83	C₂²⋊#168	—	2	2	no	—
84	C₂²⋊#168	C₂×C₄	1	2	yes	—
85	C₂²⋊#168	D₄	1	2	yes	—
86	#3952	—	2	2	no	—
87	#3952	—	2	2	no	—
88	#3941	C₂×C₄	1	2	yes	—
89	#3941	C₂×C₄	1	2	yes	—
90	#3940	C₂×C₄	1	2	yes	—
91	#3939	C₂×C₄	1	2	yes	—
92	C₄⋊#168	—	2	1	no	—
93	C₄⋊#168	—	2	2	no	—
94	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
96	C₄⋊#168	D₄	1	1	yes	characteristic
97	C₄⋊#168	D₄	1	1	yes	characteristic
98	C₄⋊#168	C₂³	1	2	yes	—
99	#3935	—	2	2	no	—
100	C₄×#168	C₂³	1	2	yes	—
101	C₄×#168	C₂³	1	2	yes	—
102	#3106	—	5	1	no	—
103	#2990	—	5	1	no	—
104	#2979	—	5	1	no	—
105	#1592	—	5	2	no	—
106	#1582	—	5	2	no	—
107	#1581	—	5	2	no	—
108	#1580	—	5	2	no	—
109	#1574	—	5	1	no	—
110	#1492	—	5	1	no	—
111	#1476	D₅	1	1	yes	characteristic, complemented
112	#1452	—	5	1	no	—
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	4	1	no	—
115	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	#41	1	1	yes	characteristic
124	C₂×C₂²⋊D₅	—	2	2	no	—
125	#709	—	8	1	no	—
126	#709	—	8	1	no	—
127	C₂×D₂₀	—	2	1	no	—
128	C₂×D₂₀	—	2	1	no	—
129	C₂×D₂₀	C₂²×C₄	1	2	yes	—
130	C₂×C₄×D₅	—	2	2	no	—
131	C₂×Dic₁₀	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	4	2	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
140	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
141	C₅×C₂²⋊C₄	—	2	1	no	—
142	C₅×C₂²⋊C₄	—	2	1	no	—
143	C₅×C₂²⋊C₄	—	2	1	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₅	#41	1	1	yes	characteristic
150	C₄²×C₅	C₂⁴	1	1	yes	characteristic
151	#688	—	4	2	no	—
152	#686	—	2	4	no	—
153	#685	—	2	2	no	—
154	#685	—	2	2	no	—
155	C₄⋊Dic₅	—	2	1	no	—
156	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
157	#681	—	8	1	no	—
158	C₂×#168	—	2	2	no	—
159	C₂×#168	—	8	2	no	—
160	C₂×#168	C₂²×C₄	1	2	yes	—
161	C₂×#168	C₂²×C₄	1	2	yes	—
162	C₂×#168	C₂×D₄	1	2	yes	—
163	C₂×#168	C₂×D₄	1	2	yes	—
164	#676	—	8	2	no	—
165	C₈×D₅	—	8	2	no	—
166	#532	—	5	1	no	—
167	C₄×#41	C₂×D₅	1	1	yes	characteristic
168	#482	—	5	2	no	—
169	#477	—	5	1	no	—
170	#476	—	5	1	no	—
171	#460	—	5	1	no	—
172	#459	—	5	1	no	—
173	#449	—	5	2	no	—
174	#446	—	5	2	no	—
175	C₄×SD₁₆	—	5	2	no	—
176	C₄×D₈	—	5	2	no	—
177	#436	—	5	2	no	—
178	#436	—	10	1	no	—
179	#435	—	10	2	no	—
180	C₈×D₄	—	5	2	no	—
181	C₈×D₄	—	5	2	no	—
182	C₈×D₄	—	10	1	no	—
183	#432	—	10	1	no	—
184	#431	—	5	1	no	—
185	#431	—	5	1	no	—
186	#431	C₂×D₅	1	1	yes	characteristic
187	#423	—	5	1	no	—
188	C₂×C₄⋊C₈	—	10	1	no	—
189	#408	—	10	2	no	—
190	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
191	#335	—	5	2	no	—
192	#334	—	5	2	no	—
193	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
194	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
195	D₄⋊C₈	—	5	2	no	—
196	D₄⋊C₈	—	5	2	no	—
197	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
198	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
199	#322	—	5	2	no	—
200	#322	—	5	2	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂²×D₅	—	2	2	no	—
204	C₅×Q₈	—	2	1	no	—
205	C₅×Q₈	—	2	1	no	—
206	C₅×D₄	—	2	1	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	#131	1	2	yes	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
227	C₂²⋊D₅	—	8	2	no	—
228	C₂×Dic₅	—	2	2	no	—
229	D₂₀	—	2	2	no	—
230	D₂₀	—	2	2	no	—
231	D₂₀	—	4	2	no	—
232	D₂₀	—	8	1	no	—
233	C₄×D₅	—	4	2	no	—
234	C₄×D₅	—	4	2	no	—
235	Dic₁₀	—	8	1	no	—
236	C₅×C₈	—	4	1	no	—
237	C₅×C₈	—	4	1	no	—
238	C₅×C₈	—	4	1	no	—
239	C₅×C₈	—	4	1	no	—
240	#168	—	2	2	no	—
241	#168	—	2	2	no	—
242	#168	—	2	2	no	—
243	#168	—	2	2	no	—
244	#168	—	4	2	no	—
245	C₂×#41	—	10	1	no	—
246	C₂×#41	C₄×D₅	1	1	yes	characteristic
247	C₂×SD₁₆	—	5	2	no	—
248	C₂×D₈	—	5	2	no	—
249	C₂×M₁₆	—	10	2	no	—
250	C₂×M₁₆	—	10	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	10	2	no	—
253	C₂²×C₈	—	10	2	no	—
254	C₄⋊Q₈	—	5	1	no	—
255	#127	—	5	1	no	—
256	#124	—	10	1	no	—
257	#121	—	5	2	no	—
258	#121	—	10	1	no	—
259	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
260	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	5	2	no	—
264	C₄×D₄	—	10	1	no	—
265	C₄×D₄	C₄×D₅	1	1	yes	characteristic
266	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
267	#117	—	2	1	no	—
268	#117	C₄×D₅	1	1	yes	characteristic
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
271	#107	—	5	2	no	—
272	#106	—	5	2	no	—
273	C₄⋊C₈	—	5	1	no	—
274	C₄⋊C₈	—	5	1	no	—
275	C₄⋊C₈	—	5	1	no	—
276	C₄⋊C₈	—	5	1	no	—
277	C₄⋊C₈	—	5	2	no	—
278	C₄⋊C₈	—	10	2	no	—
279	C₄⋊C₈	—	10	1	no	—
280	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
282	#103	—	5	2	no	—
283	#102	—	5	2	no	—
284	#102	—	5	2	no	—
285	#102	—	5	2	no	—
286	C₂²⋊C₈	—	2	1	no	—
287	C₂²⋊C₈	—	5	2	no	—
288	C₂²⋊C₈	—	5	2	no	—
289	C₂²⋊C₈	—	10	2	no	—
290	C₂²⋊C₈	—	10	2	no	—
291	C₂²⋊C₈	—	10	2	no	—
292	#97	—	10	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	5	2	no	—
296	C₄×C₈	—	5	2	no	—
297	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	—	4	1	no	—
305	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
306	C₂×D₅	—	4	2	no	—
307	C₂×D₅	—	4	2	no	—
308	C₂×D₅	—	4	2	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	4	1	no	—
313	C₄×C₅	—	4	1	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	#444	1	2	yes	—
316	C₄×C₅	C₂×#131	1	1	yes	characteristic
317	C₄×C₅	#568	1	1	yes	characteristic
318	C₄×C₅	#576	1	1	yes	characteristic
319	C₄×C₅	#577	1	1	yes	characteristic
320	Dic₅	—	4	2	no	—
321	#41	—	2	2	no	—
322	#41	—	4	1	no	—
323	#41	—	40	1	no	—
324	#41	—	40	1	no	—
325	C₂×Q₈	—	10	1	no	—
326	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	5	2	no	—
329	C₂×D₄	—	10	2	no	—
330	C₂×D₄	—	10	1	no	—
331	C₂×D₄	—	10	1	no	—
332	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	10	2	no	—
337	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
339	C₂²×C₄	#711	1	1	yes	characteristic
340	SD₁₆	—	20	2	no	—
341	D₈	—	10	4	no	—
342	M₁₆	—	40	2	no	—
343	M₁₆	—	40	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	5	2	no	—
350	C₂×C₈	—	5	2	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	10	2	no	—
354	C₂×C₈	—	40	2	no	—
355	C₂×C₈	—	40	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	10	1	no	—
360	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
361	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	10	2	no	—
366	C₂²⋊C₄	—	10	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
371	C₄²	D₄×D₅	1	1	yes	characteristic
372	C₄²	#711	1	1	yes	characteristic
373	C₄²	C₂³×D₅	1	1	yes	characteristic
374	C₂×C₅	—	4	1	no	—
375	C₂×C₅	—	4	2	no	—
376	C₂×C₅	#2933	1	1	yes	characteristic
377	C₂×C₅	#2946	1	1	yes	characteristic
378	C₂×C₅	C₂×#444	1	1	yes	characteristic
379	D₅	—	8	2	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	10	2	no	—
382	C₂³	#4027	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	2	1	no	—
385	Q₈	—	40	1	no	—
386	D₄	—	2	1	no	—
387	D₄	—	4	2	no	—
388	D₄	—	10	2	no	—
389	D₄	—	10	2	no	—
390	D₄	—	20	2	no	—
391	D₄	—	40	1	no	—
392	D₄	—	40	2	no	—
393	D₄	#4047	1	2	yes	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	20	2	no	—
408	C₂×C₄	—	20	2	no	—
409	C₂×C₄	#4027	1	1	yes	characteristic
410	C₂×C₄	#4027	1	1	yes	characteristic
411	C₂×C₄	#4027	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
414	C₂×C₄	C₂×#711	1	1	yes	characteristic
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	10	2	no	—
420	C₈	—	10	2	no	—
421	C₈	—	10	2	no	—
422	C₈	—	10	2	no	—
423	C₈	—	20	2	no	—
424	C₅	#18022	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	20	2	no	—
432	C₂²	—	20	2	no	—
433	C₂²	—	20	2	no	—
434	C₂²	C₂×#4027	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	20	2	no	—
442	C₄	#65112	1	2	yes	—
443	C₄	C₂×#4047	1	1	yes	characteristic
444	C₄	#66079	1	1	yes	characteristic
445	C₄	#66103	1	1	yes	characteristic
446	C₄	#66104	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	40	2	no	—
450	C₂	#10610327	1	1	yes	characteristic
451	C₂	#10610551	1	1	yes	characteristic
452	C₂	C₂×#65112	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×#1476	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#10614260	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1476	D₅
hypocenter	C₅	#18022
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
2. #10614253	C₂	semidirect
3. #10611020	C₂	semidirect
4. C₅×#1476	C₂	semidirect
5. #10601541	C₂	semidirect
6. #10600528	C₂	semidirect
7. #10600519	C₂	semidirect
8. #10599019	C₂	semidirect
9. #10599009	C₂	semidirect
10. #10598945	C₂	semidirect
11. #10598944	C₂	semidirect
111. #1476	D₅	semidirect
424. C₅	#18022	semidirect

Maximal subgroups

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

subgroup	index
#10614260	2
#10614253	2
#10611020	2
C₅×#1476	2
#10601541	2
#10600528	2
#10600519	2
#10599019	2
#10599009	2
#10598945	2
#10598944	2
#18022	5