Subgroups — D₅×#1278 #11988790

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#431	C₂	1	1	yes	maximal, characteristic
2	C₄×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	C₅×#1278	C₂	1	1	yes	maximal, characteristic, complemented
5	#10598230	C₂	1	1	yes	maximal, characteristic, complemented
6	#10598158	C₂	1	1	yes	maximal, characteristic, complemented
7	#10598147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅×M₁₆	C₄	1	2	yes	—
9	C₂²×C₈×D₅	—	2	1	no	—
10	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
11	C₅×#431	C₂²	1	1	yes	characteristic
12	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	M₁₆×Dic₅	C₄	1	2	yes	—
15	C₂×C₈×Dic₅	—	2	1	no	—
16	#65214	C₂²	1	1	yes	characteristic
17	C₄×#681	C₂²	1	1	yes	characteristic
18	C₂×C₄×#168	C₂²	1	1	yes	characteristic
19	#65122	C₄	1	2	yes	—
20	D₅×C₄⋊C₈	C₄	1	2	yes	—
21	D₅×C₂²⋊C₈	—	2	1	no	—
22	#65007	—	2	1	no	—
23	#64996	—	2	1	no	—
24	D₅×#97	—	2	1	no	—
25	C₄×#676	—	2	1	no	—
26	#64974	—	2	1	no	—
27	C₄×C₈×D₅	—	2	1	no	—
28	C₄×C₈×D₅	—	2	1	no	—
29	C₄×C₈×D₅	—	2	1	no	—
30	C₄×C₈×D₅	—	2	1	no	—
31	C₄×C₈×D₅	C₄	1	2	yes	—
32	C₄×C₈×D₅	C₄	1	2	yes	—
33	C₂×#1278	—	5	1	no	maximal, Sylow
34	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
37	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
38	C₂²×C₅×C₈	—	2	1	no	—
39	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
42	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
43	C₂×#681	C₂×C₄	1	2	yes	—
44	C₂²×#168	—	2	1	no	—
45	D₅×M₁₆	—	2	4	no	—
46	D₅×M₁₆	C₈	1	8	yes	complemented
47	C₂×#676	—	2	2	no	—
48	C₂×C₈×D₅	—	2	8	no	—
49	C₂×C₈×D₅	—	2	2	no	—
50	C₂×C₈×D₅	—	2	2	no	—
51	C₂×C₈×D₅	—	2	2	no	—
52	C₂×C₈×D₅	—	2	2	no	—
53	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₅	D₄	1	1	yes	characteristic
58	C₄²×D₅	D₄	1	1	yes	characteristic
59	C₄²×D₅	D₄	1	1	yes	characteristic
60	C₄²×D₅	D₄	1	1	yes	characteristic
61	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₅×C₂²⋊C₈	—	2	1	no	—
63	C₅×#97	—	2	1	no	—
64	C₄×C₅×C₈	—	2	1	no	—
65	C₄×C₅×C₈	—	2	1	no	—
66	C₄×C₅×C₈	—	2	1	no	—
67	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
68	C₂²⋊#168	—	2	1	no	—
69	#3952	—	2	2	no	—
70	#3947	—	2	2	no	—
71	#3946	—	2	2	no	—
72	C₈×Dic₅	—	2	2	no	—
73	C₈×Dic₅	—	2	2	no	—
74	C₈×Dic₅	—	2	2	no	—
75	C₈×Dic₅	—	2	2	no	—
76	C₄⋊#168	C₂×C₄	1	2	yes	—
77	#3935	—	2	1	no	—
78	C₄×#168	—	2	1	no	—
79	C₄×#168	—	2	1	no	—
80	C₄×#168	—	2	1	no	—
81	C₄×#168	C₂×C₄	1	2	yes	—
82	C₂×#431	—	5	1	no	—
83	C₂×C₄×M₁₆	—	5	1	no	—
84	C₂²×C₄×C₈	—	5	1	no	—
85	#1278	—	5	1	no	—
86	#1278	—	5	1	no	—
87	#1278	—	5	1	no	—
88	#1278	D₅	1	1	yes	characteristic, direct product factor
89	C₂³×D₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
93	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₅	—	2	4	no	—
97	C₂×C₄×D₅	—	2	4	no	—
98	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
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	C₂×C₈	1	4	yes	—
111	C₂×C₄×D₅	M₁₆	1	4	yes	—
112	C₅×M₁₆	—	2	2	no	—
113	C₅×M₁₆	C₂×C₈	1	4	yes	complemented
114	C₂×C₅×C₈	—	2	4	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₅	C₄²	1	1	yes	characteristic
123	C₄×Dic₅	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
129	C₄×Dic₅	C₂²⋊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	C₂×C₈	1	4	yes	complemented
136	C₂×#168	—	2	4	no	—
137	C₂×#168	—	2	2	no	—
138	C₂×#168	—	2	2	no	—
139	C₂×#168	—	2	2	no	—
140	#676	—	2	8	no	—
141	C₈×D₅	—	2	8	no	—
142	C₈×D₅	—	2	8	no	—
143	C₈×D₅	—	2	8	no	—
144	C₈×D₅	—	4	4	no	—
145	C₂²×M₁₆	—	5	2	no	—
146	C₂³×C₈	—	10	1	no	—
147	C₂²×C₄²	—	5	1	no	—
148	#431	—	5	1	no	—
149	#431	—	5	2	no	—
150	#431	—	10	1	no	—
151	#431	—	10	1	no	—
152	#431	C₂×D₅	1	1	yes	characteristic
153	C₂×C₄⋊C₈	—	5	2	no	—
154	C₂×C₂²⋊C₈	—	10	1	no	—
155	C₄×M₁₆	—	5	2	no	—
156	C₄×M₁₆	—	5	1	no	—
157	C₄×M₁₆	—	10	1	no	—
158	C₄×M₁₆	—	10	1	no	—
159	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
160	C₂×#97	—	10	1	no	—
161	C₂×C₄×C₈	—	5	1	no	—
162	C₂×C₄×C₈	—	5	2	no	—
163	C₂×C₄×C₈	—	5	2	no	—
164	C₂×C₄×C₈	—	10	1	no	—
165	C₂×C₄×C₈	—	10	1	no	—
166	C₂×C₄×C₈	—	10	1	no	—
167	C₂×C₄×C₈	—	10	1	no	—
168	C₂×C₄×C₈	—	10	1	no	—
169	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
170	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×D₅	—	2	2	no	—
172	C₂²×D₅	—	2	2	no	—
173	C₂²×D₅	#95	1	1	yes	characteristic
174	C₂²×D₅	#95	1	1	yes	characteristic
175	C₂²×D₅	C₄⋊C₈	1	4	yes	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	C₂×C₄²	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×C₂²⋊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	C₂²×C₈	1	2	yes	—
185	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
186	C₂×Dic₅	—	2	2	no	—
187	C₂×Dic₅	—	2	2	no	—
188	C₂×Dic₅	#95	1	1	yes	characteristic
189	C₂×Dic₅	#95	1	1	yes	characteristic
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	C₄⋊C₈	1	4	yes	—
195	C₄×D₅	—	2	2	no	—
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	2	no	—
201	C₄×D₅	C₄×C₈	1	2	yes	—
202	C₄×D₅	C₄×C₈	1	2	yes	—
203	C₄×D₅	#97	1	2	yes	—
204	C₄×D₅	#97	1	2	yes	—
205	C₄×D₅	C₂²⋊C₈	1	4	yes	—
206	C₄×D₅	C₂²⋊C₈	1	4	yes	—
207	C₄×D₅	#104	1	4	yes	—
208	C₄×D₅	#108	1	4	yes	—
209	C₅×C₈	—	2	4	no	—
210	C₅×C₈	—	2	4	no	—
211	C₅×C₈	—	4	2	no	—
212	#168	—	2	4	no	—
213	#168	—	2	4	no	—
214	#168	—	4	2	no	—
215	C₂³×C₄	—	5	1	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂³×C₄	—	5	1	no	—
218	C₂×M₁₆	—	5	2	no	—
219	C₂×M₁₆	—	5	8	no	—
220	C₂×M₁₆	—	10	2	no	—
221	C₂×M₁₆	—	10	4	no	—
222	C₂×M₁₆	C₄×D₅	1	2	yes	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	10	2	no	—
225	C₂²×C₈	—	10	2	no	—
226	C₂²×C₈	—	10	2	no	—
227	C₂²×C₈	—	10	8	no	—
228	C₂²×C₈	—	10	2	no	—
229	C₂²×C₈	—	10	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	—	5	1	no	—
240	C₂×C₄²	—	5	1	no	—
241	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
242	C₄⋊C₈	—	5	2	no	—
243	C₄⋊C₈	—	10	2	no	—
244	C₄⋊C₈	C₄×D₅	1	2	yes	—
245	C₂²⋊C₈	—	2	1	no	—
246	C₂²⋊C₈	—	10	2	no	—
247	C₂²⋊C₈	—	10	1	no	—
248	#97	—	2	1	no	—
249	#97	—	10	2	no	—
250	#97	—	10	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	5	2	no	—
255	C₄×C₈	—	10	2	no	—
256	C₄×C₈	—	10	2	no	—
257	C₄×C₈	—	10	2	no	—
258	C₄×C₈	—	10	2	no	—
259	C₄×C₈	—	10	1	no	—
260	C₄×C₈	—	10	1	no	—
261	C₄×C₈	—	10	1	no	—
262	C₄×C₈	C₄×D₅	1	2	yes	—
263	C₂²×C₅	—	2	1	no	—
264	C₂²×C₅	—	2	1	no	—
265	C₂²×C₅	C₂×#95	1	1	yes	characteristic
266	C₂²×C₅	C₂×C₄⋊C₈	1	2	yes	—
267	C₂×D₅	—	2	1	no	—
268	C₂×D₅	—	2	1	no	—
269	C₂×D₅	—	2	8	no	—
270	C₂×D₅	#336	1	2	yes	—
271	C₂×D₅	#336	1	2	yes	—
272	C₂×D₅	#339	1	2	yes	—
273	C₂×D₅	#341	1	2	yes	—
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
277	C₄×C₅	C₂×#97	1	1	yes	characteristic
278	C₄×C₅	C₂×C₂²⋊C₈	1	2	yes	—
279	C₄×C₅	C₂×#104	1	2	yes	—
280	C₄×C₅	C₂×#108	1	2	yes	—
281	Dic₅	—	2	1	no	—
282	Dic₅	—	2	1	no	—
283	Dic₅	#336	1	2	yes	—
284	Dic₅	#336	1	2	yes	—
285	Dic₅	#339	1	2	yes	—
286	Dic₅	#341	1	2	yes	—
287	C₂⁴	—	5	1	no	—
288	C₂²×C₄	—	5	1	no	—
289	C₂²×C₄	—	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	4	no	—
296	C₂²×C₄	—	5	4	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	4	no	—
306	C₂²×C₄	—	10	4	no	—
307	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
309	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
310	M₁₆	—	2	2	no	—
311	M₁₆	—	5	4	no	—
312	M₁₆	—	10	8	no	—
313	M₁₆	—	10	2	no	—
314	M₁₆	C₈×D₅	1	4	yes	complemented
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	10	8	no	—
320	C₂×C₈	—	10	8	no	—
321	C₂×C₈	—	10	8	no	—
322	C₂×C₈	—	10	4	no	—
323	C₂×C₈	—	10	2	no	—
324	C₂×C₈	—	10	2	no	—
325	C₂×C₈	—	10	2	no	—
326	C₂×C₈	—	20	4	no	—
327	C₄²	—	5	1	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	C₂×C₄×D₅	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
341	C₄²	D₄×D₅	1	1	yes	characteristic
342	C₄²	D₄×D₅	1	1	yes	characteristic
343	C₂×C₅	—	2	2	no	—
344	C₂×C₅	C₂×#336	1	1	yes	characteristic
345	C₂×C₅	C₂×#339	1	1	yes	characteristic
346	C₂×C₅	C₂×#341	1	1	yes	characteristic
347	D₅	—	2	2	no	—
348	D₅	#1278	1	4	yes	direct product factor
349	C₂³	—	5	1	no	—
350	C₂³	—	5	4	no	—
351	C₂³	—	5	1	no	—
352	C₂³	—	10	2	no	—
353	C₂³	—	10	2	no	—
354	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	5	4	no	—
358	C₂×C₄	—	5	1	no	—
359	C₂×C₄	—	5	1	no	—
360	C₂×C₄	—	5	1	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	4	no	—
363	C₂×C₄	—	5	4	no	—
364	C₂×C₄	—	5	2	no	—
365	C₂×C₄	—	5	2	no	—
366	C₂×C₄	—	5	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	5	4	no	—
369	C₂×C₄	—	5	4	no	—
370	C₂×C₄	—	5	1	no	—
371	C₂×C₄	—	5	1	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	—	10	2	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	—	10	2	no	—
380	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
381	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
382	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
383	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
384	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
385	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
386	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
387	C₂×C₄	D₅×M₁₆	1	2	yes	—
388	C₈	—	2	4	no	—
389	C₈	—	2	4	no	—
390	C₈	—	4	2	no	—
391	C₈	—	10	4	no	—
392	C₈	—	10	4	no	—
393	C₈	—	20	2	no	—
394	C₅	C₂×#1278	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	5	2	no	—
398	C₂²	—	5	2	no	—
399	C₂²	—	5	2	no	—
400	C₂²	—	5	2	no	—
401	C₂²	—	10	8	no	—
402	C₂²	—	10	1	no	—
403	C₂²	—	10	1	no	—
404	C₂²	D₅×#95	1	1	yes	characteristic
405	C₂²	D₅×C₄⋊C₈	1	2	yes	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	5	2	no	—
409	C₄	—	5	2	no	—
410	C₄	—	5	2	no	—
411	C₄	—	5	2	no	—
412	C₄	—	10	1	no	—
413	C₄	—	10	1	no	—
414	C₄	C₄×C₈×D₅	1	1	yes	characteristic
415	C₄	D₅×#97	1	1	yes	characteristic
416	C₄	D₅×C₂²⋊C₈	1	2	yes	—
417	C₄	D₅×#104	1	2	yes	—
418	C₄	D₅×#108	1	2	yes	—
419	C₂	—	2	2	no	—
420	C₂	—	5	4	no	—
421	C₂	—	10	2	no	—
422	C₂	D₅×#336	1	1	yes	characteristic
423	C₂	D₅×#339	1	1	yes	characteristic
424	C₂	D₅×#341	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₅
commutator	C₄×C₅	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₅×#1278	C₂
socle	C₂²×C₅	C₂×#95
prime radical	C₂³×D₅	C₄⋊C₄
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	#1278	D₅
hypocenter	C₅	C₂×#1278
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1278

Complements

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

N	H ≅ G/N	type
4. C₅×#1278	C₂	semidirect
5. #10598230	C₂	semidirect
6. #10598158	C₂	semidirect
7. #10598147	C₂	semidirect
46. D₅×M₁₆	C₈	semidirect
88. #1278	D₅	direct (N × H)
113. C₅×M₁₆	C₂×C₈	semidirect
135. #681	C₂×C₈	semidirect
314. M₁₆	C₈×D₅	semidirect
348. D₅	#1278	direct (N × H)
394. C₅	C₂×#1278	semidirect

Maximal subgroups

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

subgroup	index
D₅×#431	2
C₄×D₅×M₁₆	2
C₂×C₄×C₈×D₅	2
C₅×#1278	2
#10598230	2
#10598158	2
#10598147	2
C₂×#1278	5

Subgroups — D5×#1278 #11988790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#1278 #11988790