Subgroups — #11989002

Order 1280.

616 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611013	C₂	1	1	yes	maximal, characteristic
2	C₂×#65124	C₂	1	1	yes	maximal, characteristic
3	C₄×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1283	C₂	1	1	yes	maximal, characteristic, complemented
5	#10598235	C₂	1	1	yes	maximal, characteristic, complemented
6	#10598197	C₂	1	1	yes	maximal, characteristic, complemented
7	#10598159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅×M₁₆	C₄	1	2	yes	—
9	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
10	C₅×#431	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	M₁₆×Dic₅	C₄	1	2	yes	—
14	C₂×#3952	C₄	1	2	yes	—
15	C₂×#3947	C₄	1	2	yes	—
16	#65214	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
18	C₄×#681	C₂²	1	1	yes	characteristic
19	#65126	—	2	1	no	—
20	#65124	—	2	1	no	—
21	#65124	—	2	1	no	—
22	#65124	—	2	1	no	—
23	#65124	—	2	1	no	—
24	#65124	—	2	1	no	—
25	#65015	C₄	1	2	yes	—
26	#65008	C₄	1	2	yes	—
27	#64996	—	2	1	no	—
28	D₅×#97	—	2	1	no	—
29	C₄×#676	—	2	1	no	—
30	C₄×#676	—	2	1	no	—
31	#64974	—	2	1	no	—
32	C₄×C₈×D₅	—	2	1	no	—
33	#7937	—	5	1	no	maximal, Sylow
34	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
38	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
43	C₂×#681	C₂×C₄	1	2	yes	—
44	C₂²×#168	C₂×C₄	1	2	yes	—
45	D₅×M₁₆	—	2	4	no	—
46	D₅×M₁₆	—	2	4	no	—
47	C₂×#676	—	2	2	no	—
48	C₂×#676	—	2	2	no	—
49	C₂×C₈×D₅	—	2	2	no	—
50	C₄²×D₅	D₄	1	1	yes	characteristic
51	C₄²×D₅	D₄	1	1	yes	characteristic
52	C₄²×D₅	D₄	1	1	yes	characteristic
53	C₄²×D₅	D₄	1	1	yes	characteristic
54	C₄²×D₅	D₄	1	1	yes	characteristic
55	C₄²×D₅	D₄	1	1	yes	characteristic
56	C₄²×D₅	Q₈	1	1	yes	characteristic
57	C₄²×D₅	Q₈	1	1	yes	characteristic
58	C₅×C₄⋊C₈	—	2	1	no	—
59	C₅×C₄⋊C₈	—	2	1	no	—
60	C₅×C₄⋊C₈	—	2	1	no	—
61	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
62	C₅×#97	—	2	1	no	—
63	C₄×C₅×C₈	—	2	1	no	—
64	C₄×C₅×C₈	—	2	1	no	—
65	C₂²⋊#168	C₂×C₄	1	2	yes	—
66	#3952	—	2	2	no	—
67	#3952	—	2	2	no	—
68	#3952	—	2	2	no	—
69	#3947	—	2	2	no	—
70	#3947	—	2	2	no	—
71	#3947	—	2	2	no	—
72	#3947	—	2	2	no	—
73	#3946	—	2	2	no	—
74	C₈×Dic₅	—	2	2	no	—
75	C₄⋊#168	—	2	1	no	—
76	C₄⋊#168	—	2	1	no	—
77	C₄⋊#168	—	2	1	no	—
78	#3935	—	2	1	no	—
79	C₄×#168	—	2	1	no	—
80	C₄×#168	—	2	1	no	—
81	#2920	—	5	1	no	—
82	C₂×#432	—	5	1	no	—
83	C₂×C₄×M₁₆	—	5	1	no	—
84	#1283	—	5	1	no	—
85	#1283	—	5	1	no	—
86	#1283	—	5	1	no	—
87	#1283	D₅	1	1	yes	characteristic, complemented
88	C₂³×D₅	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₅	C₄²	1	1	yes	characteristic
93	C₂²×Dic₅	C₄²	1	1	yes	characteristic
94	C₂²×Dic₅	C₄²	1	1	yes	characteristic
95	C₂×C₄×D₅	—	2	2	no	—
96	C₂×C₄×D₅	—	2	2	no	—
97	C₂×C₄×D₅	—	4	1	no	—
98	C₂×C₄×D₅	—	4	1	no	—
99	C₂×C₄×D₅	—	4	2	no	—
100	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
112	C₅×M₁₆	—	2	2	no	—
113	C₅×M₁₆	M₁₆	1	4	yes	complemented
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	4	2	no	—
118	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₄×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
125	C₄×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
126	C₄×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
127	C₄×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
128	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
134	#681	—	2	2	no	—
135	#681	M₁₆	1	4	yes	complemented
136	C₂×#168	—	2	2	no	—
137	C₂×#168	—	2	2	no	—
138	C₂×#168	—	2	2	no	—
139	C₂×#168	—	4	2	no	—
140	#676	—	2	8	no	—
141	#676	—	4	4	no	—
142	C₈×D₅	—	2	8	no	—
143	C₂²×M₁₆	—	5	2	no	—
144	C₂²×C₄²	—	5	1	no	—
145	#432	—	5	2	no	—
146	#432	—	10	1	no	—
147	#432	—	10	1	no	—
148	#432	—	10	1	no	—
149	#432	—	10	1	no	—
150	#432	—	10	1	no	—
151	#431	—	5	1	no	—
152	#431	—	10	1	no	—
153	#431	C₂×D₅	1	1	yes	characteristic
154	#423	—	10	1	no	—
155	C₂×C₄⋊C₈	—	5	1	no	—
156	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
157	#407	—	5	2	no	—
158	C₂×C₂²⋊C₈	—	5	2	no	—
159	C₄×M₁₆	—	5	2	no	—
160	C₄×M₁₆	—	5	1	no	—
161	C₄×M₁₆	—	10	1	no	—
162	C₄×M₁₆	—	10	1	no	—
163	C₄×M₁₆	—	10	1	no	—
164	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
165	C₂×#97	—	5	2	no	—
166	C₂×#97	—	10	1	no	—
167	C₂×C₄×C₈	—	10	1	no	—
168	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
169	C₂²×D₅	—	2	1	no	—
170	C₂²×D₅	—	2	1	no	—
171	C₂²×D₅	—	2	2	no	—
172	C₂²×D₅	—	4	1	no	—
173	C₂²×D₅	#95	1	1	yes	characteristic
174	C₂²×D₅	#95	1	1	yes	characteristic
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	4	1	no	—
178	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
185	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
186	C₂×Dic₅	—	2	1	no	—
187	C₂×Dic₅	—	2	1	no	—
188	C₂×Dic₅	—	4	1	no	—
189	C₂×Dic₅	—	4	1	no	—
190	C₂×Dic₅	#95	1	1	yes	characteristic
191	C₂×Dic₅	#95	1	1	yes	characteristic
192	C₂×Dic₅	#95	1	1	yes	characteristic
193	C₂×Dic₅	#95	1	1	yes	characteristic
194	C₂×Dic₅	#95	1	1	yes	characteristic
195	C₂×Dic₅	#95	1	1	yes	characteristic
196	C₄×D₅	—	2	2	no	—
197	C₄×D₅	—	2	2	no	—
198	C₄×D₅	—	2	2	no	—
199	C₄×D₅	—	2	2	no	—
200	C₄×D₅	—	2	1	no	—
201	C₄×D₅	—	2	1	no	—
202	C₄×D₅	—	2	1	no	—
203	C₄×D₅	—	2	1	no	—
204	C₄×D₅	—	2	2	no	—
205	C₄×D₅	—	2	2	no	—
206	C₄×D₅	—	4	1	no	—
207	C₄×D₅	—	4	1	no	—
208	C₄×D₅	—	4	1	no	—
209	C₄×D₅	—	4	1	no	—
210	C₅×C₈	—	2	4	no	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	—	4	2	no	—
213	#168	—	2	4	no	—
214	#168	—	4	2	no	—
215	#168	—	4	2	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂³×C₄	—	5	1	no	—
218	C₂³×C₄	—	5	1	no	—
219	C₂×M₁₆	—	5	2	no	—
220	C₂×M₁₆	—	10	2	no	—
221	C₂×M₁₆	—	10	2	no	—
222	C₂×M₁₆	—	10	4	no	—
223	C₂×M₁₆	—	10	4	no	—
224	C₂×M₁₆	C₄×D₅	1	2	yes	—
225	C₂²×C₈	—	5	2	no	—
226	C₂²×C₈	—	10	2	no	—
227	C₂²×C₈	C₄×D₅	1	2	yes	—
228	C₂×C₄²	—	5	1	no	—
229	C₂×C₄²	—	5	1	no	—
230	C₂×C₄²	—	5	1	no	—
231	C₂×C₄²	—	5	1	no	—
232	C₂×C₄²	—	5	1	no	—
233	C₂×C₄²	—	5	1	no	—
234	C₂×C₄²	—	5	1	no	—
235	C₂×C₄²	—	5	1	no	—
236	C₂×C₄²	—	5	1	no	—
237	C₂×C₄²	—	5	1	no	—
238	C₂×C₄²	—	5	1	no	—
239	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	10	2	no	—
244	C₄⋊C₈	—	10	1	no	—
245	C₄⋊C₈	—	10	1	no	—
246	C₄⋊C₈	—	10	1	no	—
247	C₂²⋊C₈	—	5	2	no	—
248	C₂²⋊C₈	—	10	2	no	—
249	C₂²⋊C₈	—	10	2	no	—
250	C₂²⋊C₈	—	10	2	no	—
251	C₂²⋊C₈	C₄×D₅	1	2	yes	—
252	#97	—	2	1	no	—
253	#97	—	10	2	no	—
254	#97	—	10	2	no	—
255	#97	—	10	2	no	—
256	#97	—	10	2	no	—
257	#97	—	10	1	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	10	2	no	—
261	C₄×C₈	—	10	1	no	—
262	C₄×C₈	—	10	1	no	—
263	C₂²×C₅	—	2	1	no	—
264	C₂²×C₅	—	2	1	no	—
265	C₂²×C₅	C₂×#95	1	1	yes	characteristic
266	C₂²×C₅	C₄×M₁₆	1	1	yes	characteristic
267	C₂²×C₅	C₄×M₁₆	1	1	yes	characteristic
268	C₂×D₅	—	2	1	no	—
269	C₂×D₅	—	2	1	no	—
270	C₂×D₅	—	2	1	no	—
271	C₂×D₅	—	2	1	no	—
272	C₂×D₅	—	2	1	no	—
273	C₂×D₅	—	4	2	no	—
274	C₂×D₅	—	4	2	no	—
275	C₂×D₅	#344	1	2	yes	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	#407	1	2	yes	—
280	C₄×C₅	#413	1	1	yes	characteristic
281	C₄×C₅	#413	1	1	yes	characteristic
282	C₄×C₅	#423	1	2	yes	—
283	Dic₅	—	2	1	no	—
284	Dic₅	—	2	1	no	—
285	Dic₅	—	2	1	no	—
286	Dic₅	—	2	1	no	—
287	Dic₅	—	2	1	no	—
288	Dic₅	—	2	1	no	—
289	C₂⁴	—	5	1	no	—
290	C₂²×C₄	—	5	1	no	—
291	C₂²×C₄	—	5	1	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	5	1	no	—
294	C₂²×C₄	—	5	1	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	1	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	1	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	10	2	no	—
306	C₂²×C₄	—	10	2	no	—
307	C₂²×C₄	—	20	1	no	—
308	C₂²×C₄	—	20	1	no	—
309	C₂²×C₄	—	20	2	no	—
310	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
313	M₁₆	—	2	2	no	—
314	M₁₆	—	5	4	no	—
315	M₁₆	—	10	8	no	—
316	M₁₆	—	10	2	no	—
317	M₁₆	—	20	4	no	—
318	M₁₆	#676	1	4	yes	complemented
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	10	8	no	—
324	C₂×C₈	—	10	2	no	—
325	C₂×C₈	—	10	2	no	—
326	C₂×C₈	—	10	2	no	—
327	C₂×C₈	—	20	2	no	—
328	C₄²	—	5	1	no	—
329	C₄²	—	5	1	no	—
330	C₄²	—	5	1	no	—
331	C₄²	—	5	1	no	—
332	C₄²	—	5	1	no	—
333	C₄²	—	5	1	no	—
334	C₄²	—	5	1	no	—
335	C₄²	—	5	1	no	—
336	C₄²	—	5	1	no	—
337	C₄²	—	5	1	no	—
338	C₄²	—	5	1	no	—
339	C₄²	—	5	1	no	—
340	C₄²	D₄×D₅	1	1	yes	characteristic
341	C₄²	D₄×D₅	1	1	yes	characteristic
342	C₄²	D₄×D₅	1	1	yes	characteristic
343	C₄²	Q₈×D₅	1	1	yes	characteristic
344	C₂×C₅	—	2	1	no	—
345	C₂×C₅	—	2	1	no	—
346	C₂×C₅	#1728	1	1	yes	characteristic
347	C₂×C₅	#1742	1	1	yes	characteristic
348	C₂×C₅	C₂×#344	1	1	yes	characteristic
349	D₅	—	2	2	no	—
350	D₅	—	4	1	no	—
351	C₂³	—	5	1	no	—
352	C₂³	—	5	1	no	—
353	C₂³	—	10	2	no	—
354	C₂³	—	10	1	no	—
355	C₂³	—	10	1	no	—
356	C₂³	—	20	1	no	—
357	C₂³	C₄²×D₅	1	1	yes	characteristic
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	1	no	—
363	C₂×C₄	—	5	1	no	—
364	C₂×C₄	—	5	1	no	—
365	C₂×C₄	—	5	1	no	—
366	C₂×C₄	—	5	1	no	—
367	C₂×C₄	—	10	2	no	—
368	C₂×C₄	—	10	2	no	—
369	C₂×C₄	—	10	1	no	—
370	C₂×C₄	—	10	1	no	—
371	C₂×C₄	—	10	1	no	—
372	C₂×C₄	—	10	1	no	—
373	C₂×C₄	—	10	1	no	—
374	C₂×C₄	—	10	1	no	—
375	C₂×C₄	—	10	2	no	—
376	C₂×C₄	—	10	2	no	—
377	C₂×C₄	—	10	2	no	—
378	C₂×C₄	—	10	2	no	—
379	C₂×C₄	—	20	1	no	—
380	C₂×C₄	—	20	1	no	—
381	C₂×C₄	—	20	1	no	—
382	C₂×C₄	—	20	1	no	—
383	C₂×C₄	—	20	1	no	—
384	C₂×C₄	—	20	1	no	—
385	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
386	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
387	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
389	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
390	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
391	C₂×C₄	C₂×#676	1	2	yes	—
392	C₂×C₄	D₅×M₁₆	1	2	yes	—
393	C₈	—	2	4	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	10	4	no	—
397	C₈	—	20	2	no	—
398	C₈	—	20	2	no	—
399	C₅	#7937	1	1	yes	characteristic, complemented, Sylow
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	5	2	no	—
403	C₂²	—	10	1	no	—
404	C₂²	—	10	1	no	—
405	C₂²	—	10	1	no	—
406	C₂²	—	10	1	no	—
407	C₂²	—	10	1	no	—
408	C₂²	—	20	2	no	—
409	C₂²	—	20	2	no	—
410	C₂²	D₅×#95	1	1	yes	characteristic
411	C₂²	C₄×#676	1	1	yes	characteristic
412	C₂²	#64996	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	10	1	no	—
417	C₄	—	10	1	no	—
418	C₄	—	10	1	no	—
419	C₄	—	10	1	no	—
420	C₄	—	10	1	no	—
421	C₄	—	10	1	no	—
422	C₄	#65015	1	2	yes	—
423	C₄	#65034	1	1	yes	characteristic
424	C₄	#65040	1	1	yes	characteristic
425	C₄	#65126	1	2	yes	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	10	2	no	—
429	C₂	—	20	1	no	—
430	C₂	#10599453	1	1	yes	characteristic
431	C₂	#10599782	1	1	yes	characteristic
432	C₂	D₅×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×C₂²⋊C₄
commutator	C₂³×C₅	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₅×#1283	C₂
socle	C₂²×C₅	C₂×#95
prime radical	C₂³×D₅	C₄²
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	#1283	D₅
hypocenter	C₅	#7937
LCS	G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1283

Complements

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

N	H ≅ G/N	type
4. C₅×#1283	C₂	semidirect
5. #10598235	C₂	semidirect
6. #10598197	C₂	semidirect
7. #10598159	C₂	semidirect
87. #1283	D₅	semidirect
113. C₅×M₁₆	M₁₆	semidirect
135. #681	M₁₆	semidirect
318. M₁₆	#676	semidirect
399. C₅	#7937	semidirect

Maximal subgroups

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

subgroup	index
#10611013	2
C₂×#65124	2
C₄×D₅×M₁₆	2
C₅×#1283	2
#10598235	2
#10598197	2
#10598159	2
#7937	5