Subgroups — D₅×#1388 #12014229

Order 1280.

554 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅×#108	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×#108	C₂	1	1	yes	maximal, characteristic
4	C₅×#1388	C₂	1	1	yes	maximal, characteristic, complemented
5	#10598312	C₂	1	1	yes	maximal, characteristic, complemented
6	#10598225	C₂	1	1	yes	maximal, characteristic, complemented
7	#10598224	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅×M₁₆	—	2	1	no	—
9	C₂×D₅×M₁₆	—	2	1	no	—
10	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₅×#108	C₂²	1	1	yes	characteristic
13	C₂×C₅×#108	C₂²	1	1	yes	characteristic
14	C₂×#3954	—	2	1	no	—
15	C₂×#3954	—	2	1	no	—
16	C₂×#3951	C₂²	1	1	yes	characteristic
17	C₂×#3951	C₂²	1	1	yes	characteristic
18	C₂×#3944	C₂²	1	1	yes	characteristic
19	D₅×M₃₂	—	2	1	no	—
20	D₅×M₃₂	—	2	1	no	—
21	D₅×M₃₂	C₄	1	2	yes	—
22	D₅×M₃₂	C₄	1	2	yes	—
23	C₂×#3930	—	2	1	no	—
24	C₂×D₅×C₁₆	—	2	1	no	—
25	D₅×#108	—	2	1	no	—
26	D₅×#108	—	2	1	no	—
27	D₅×#108	—	2	1	no	—
28	D₅×#108	—	2	1	no	—
29	D₅×#108	C₄	1	2	yes	—
30	D₅×#108	C₄	1	2	yes	—
31	D₅×#108	C₄	1	2	yes	—
32	D₅×#108	C₄	1	2	yes	—
33	C₂×#1388	—	5	1	no	maximal, Sylow
34	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
35	C₂×C₅×M₁₆	—	2	1	no	—
36	C₂×C₅×M₁₆	—	2	1	no	—
37	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
38	C₂×#681	—	2	1	no	—
39	C₂×#681	—	2	1	no	—
40	C₂²×#168	D₄	1	1	yes	characteristic
41	D₅×M₁₆	—	2	2	no	—
42	D₅×M₁₆	—	2	2	no	—
43	D₅×M₁₆	—	2	2	no	—
44	D₅×M₁₆	—	2	2	no	—
45	D₅×M₁₆	—	4	1	no	—
46	D₅×M₁₆	—	4	1	no	—
47	D₅×M₁₆	—	4	1	no	—
48	D₅×M₁₆	—	4	1	no	—
49	C₂×#676	—	4	1	no	—
50	C₂×#676	—	4	1	no	—
51	C₂×C₈×D₅	—	4	1	no	—
52	C₂×C₈×D₅	—	4	1	no	—
53	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₅	D₄	1	1	yes	characteristic
60	C₂×C₈×D₅	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅	D₄	1	1	yes	characteristic
62	C₂×C₈×D₅	D₄	1	1	yes	characteristic
63	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
64	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
65	C₅×M₃₂	—	2	1	no	—
66	C₅×M₃₂	C₂×C₄	1	2	yes	—
67	C₂×C₅×C₁₆	—	2	1	no	—
68	C₅×#108	—	2	1	no	—
69	C₅×#108	—	2	1	no	—
70	C₅×#108	C₂×C₄	1	2	yes	—
71	C₅×#108	C₂×C₄	1	2	yes	—
72	#3954	—	2	2	no	—
73	#3954	—	2	2	no	—
74	#3954	—	2	2	no	—
75	#3954	—	2	2	no	—
76	#3951	—	2	1	no	—
77	#3951	—	2	1	no	—
78	#3951	C₂×C₄	1	2	yes	—
79	#3951	C₂×C₄	1	2	yes	—
80	#3944	—	2	1	no	—
81	#3944	C₂×C₄	1	2	yes	—
82	C₂×#672	—	2	1	no	—
83	#3930	—	2	2	no	—
84	#3930	—	2	2	no	—
85	D₅×C₁₆	—	2	2	no	—
86	D₅×C₁₆	—	2	2	no	—
87	C₂²×M₃₂	—	5	1	no	—
88	C₂²×#108	—	5	1	no	—
89	C₂²×#108	—	5	1	no	—
90	#1388	—	5	1	no	—
91	#1388	—	5	1	no	—
92	#1388	—	5	1	no	—
93	#1388	D₅	1	1	yes	characteristic, direct product factor
94	C₂³×D₅	Q₁₆	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×Dic₅	Q₁₆	1	1	yes	characteristic
97	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₅	D₈	1	1	yes	characteristic
104	C₂×C₄×D₅	D₈	1	1	yes	characteristic
105	C₂×C₄×D₅	SD₁₆	1	1	yes	characteristic
106	C₂×C₄×D₅	SD₁₆	1	1	yes	characteristic
107	C₂×C₄×D₅	SD₁₆	1	1	yes	characteristic
108	C₂×C₄×D₅	SD₁₆	1	1	yes	characteristic
109	C₅×M₁₆	—	2	2	no	—
110	C₅×M₁₆	—	2	2	no	—
111	C₅×M₁₆	—	4	1	no	—
112	C₅×M₁₆	—	4	1	no	—
113	C₂×C₅×C₈	—	4	1	no	—
114	C₂×C₅×C₈	—	4	1	no	—
115	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
121	#681	—	2	2	no	—
122	#681	—	2	2	no	—
123	#681	—	4	1	no	—
124	#681	—	4	1	no	—
125	C₂×#168	—	4	1	no	—
126	C₂×#168	—	4	1	no	—
127	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
132	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
133	#676	—	4	2	no	—
134	#676	—	4	2	no	—
135	#676	—	4	2	no	—
136	#676	—	4	2	no	—
137	C₈×D₅	—	4	2	no	—
138	C₈×D₅	—	4	2	no	—
139	C₈×D₅	—	4	2	no	—
140	C₈×D₅	—	4	2	no	—
141	C₈×D₅	C₄²	1	1	yes	characteristic
142	C₈×D₅	C₄²	1	1	yes	characteristic
143	C₈×D₅	C₄²	1	1	yes	characteristic
144	C₈×D₅	C₄²	1	1	yes	characteristic
145	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
146	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
147	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
148	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
149	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
150	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
151	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
152	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
153	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
154	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
155	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
156	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
157	C₅×C₁₆	—	2	2	no	—
158	#672	—	2	2	no	—
159	C₂²×M₁₆	—	10	1	no	—
160	C₂²×M₁₆	—	10	1	no	—
161	C₂³×C₈	—	5	1	no	—
162	C₂×M₃₂	—	5	1	no	—
163	C₂×M₃₂	—	5	2	no	—
164	C₂×M₃₂	—	5	2	no	—
165	C₂×M₃₂	—	10	1	no	—
166	C₂×M₃₂	—	10	1	no	—
167	C₂×M₃₂	—	10	1	no	—
168	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
169	C₂²×C₁₆	—	10	1	no	—
170	C₂×#108	—	5	1	no	—
171	C₂×#108	—	5	1	no	—
172	C₂×#108	—	5	2	no	—
173	C₂×#108	—	5	2	no	—
174	C₂×#108	—	5	2	no	—
175	C₂×#108	—	5	2	no	—
176	C₂×#108	—	10	1	no	—
177	C₂×#108	—	10	1	no	—
178	C₂×#108	—	10	1	no	—
179	C₂×#108	—	10	1	no	—
180	C₂×#108	—	10	1	no	—
181	C₂×#108	—	10	1	no	—
182	C₂×#108	C₂×D₅	1	1	yes	characteristic
183	C₂×#108	C₂×D₅	1	1	yes	characteristic
184	C₂³×C₅	C₂×Q₁₆	1	1	yes	characteristic
185	C₂²×D₅	—	4	2	no	—
186	C₂²×D₅	#103	1	1	yes	characteristic
187	C₂²×D₅	#103	1	1	yes	characteristic
188	C₂²×D₅	#103	1	1	yes	characteristic
189	C₂²×D₅	#103	1	1	yes	characteristic
190	C₂²×D₅	#107	1	1	yes	characteristic
191	C₂²×D₅	#107	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×Dic₅	#103	1	1	yes	characteristic
199	C₂×Dic₅	#103	1	1	yes	characteristic
200	C₂×Dic₅	#103	1	1	yes	characteristic
201	C₂×Dic₅	#103	1	1	yes	characteristic
202	C₂×Dic₅	#107	1	1	yes	characteristic
203	C₂×Dic₅	#107	1	1	yes	characteristic
204	C₄×D₅	#95	1	1	yes	characteristic
205	C₄×D₅	#95	1	1	yes	characteristic
206	C₄×D₅	#95	1	1	yes	characteristic
207	C₄×D₅	#95	1	1	yes	characteristic
208	C₄×D₅	#102	1	1	yes	characteristic
209	C₄×D₅	#102	1	1	yes	characteristic
210	C₄×D₅	#102	1	1	yes	characteristic
211	C₄×D₅	#102	1	1	yes	characteristic
212	C₄×D₅	#102	1	1	yes	characteristic
213	C₄×D₅	#102	1	1	yes	characteristic
214	C₄×D₅	#102	1	1	yes	characteristic
215	C₄×D₅	#102	1	1	yes	characteristic
216	C₄×D₅	#106	1	1	yes	characteristic
217	C₄×D₅	#106	1	1	yes	characteristic
218	C₄×D₅	#106	1	1	yes	characteristic
219	C₄×D₅	#106	1	1	yes	characteristic
220	C₅×C₈	—	4	2	no	—
221	C₅×C₈	—	4	2	no	—
222	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
223	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
226	#168	—	4	2	no	—
227	#168	—	4	2	no	—
228	#168	#95	1	1	yes	characteristic
229	#168	#95	1	1	yes	characteristic
230	#168	#95	1	1	yes	characteristic
231	#168	#95	1	1	yes	characteristic
232	C₂³×C₄	—	5	1	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	10	2	no	—
236	C₂×M₁₆	—	10	2	no	—
237	C₂×M₁₆	—	10	2	no	—
238	C₂×M₁₆	—	10	2	no	—
239	C₂×M₁₆	—	10	1	no	—
240	C₂×M₁₆	—	10	1	no	—
241	C₂×M₁₆	—	20	1	no	—
242	C₂×M₁₆	—	20	1	no	—
243	C₂×M₁₆	—	20	1	no	—
244	C₂×M₁₆	—	20	1	no	—
245	C₂×M₁₆	—	20	1	no	—
246	C₂×M₁₆	—	20	1	no	—
247	C₂²×C₈	—	5	1	no	—
248	C₂²×C₈	—	5	1	no	—
249	C₂²×C₈	—	5	1	no	—
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	5	1	no	—
252	C₂²×C₈	—	5	1	no	—
253	C₂²×C₈	—	5	1	no	—
254	C₂²×C₈	—	5	1	no	—
255	C₂²×C₈	—	5	1	no	—
256	C₂²×C₈	—	5	1	no	—
257	C₂²×C₈	—	5	1	no	—
258	C₂²×C₈	—	5	1	no	—
259	C₂²×C₈	—	5	1	no	—
260	C₂²×C₈	—	20	1	no	—
261	C₂²×C₈	—	20	1	no	—
262	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
263	M₃₂	—	2	1	no	—
264	M₃₂	—	5	2	no	—
265	M₃₂	—	10	2	no	—
266	M₃₂	—	10	2	no	—
267	M₃₂	—	10	1	no	—
268	M₃₂	C₄×D₅	1	2	yes	—
269	C₂×C₁₆	—	2	1	no	—
270	C₂×C₁₆	—	10	2	no	—
271	C₂×C₁₆	—	10	2	no	—
272	C₂×C₁₆	—	10	1	no	—
273	#108	—	2	1	no	—
274	#108	—	2	1	no	—
275	#108	—	5	2	no	—
276	#108	—	5	2	no	—
277	#108	—	10	2	no	—
278	#108	—	10	2	no	—
279	#108	—	10	2	no	—
280	#108	—	10	2	no	—
281	#108	—	10	1	no	—
282	#108	—	10	1	no	—
283	#108	C₄×D₅	1	2	yes	—
284	#108	C₄×D₅	1	2	yes	—
285	C₂²×C₅	—	4	1	no	—
286	C₂²×C₅	C₂×#103	1	1	yes	characteristic
287	C₂²×C₅	C₂×#103	1	1	yes	characteristic
288	C₂²×C₅	C₂×#107	1	1	yes	characteristic
289	C₂×D₅	—	2	2	no	—
290	C₂×D₅	—	2	2	no	—
291	C₂×D₅	—	2	2	no	—
292	C₂×D₅	—	4	1	no	—
293	C₂×D₅	—	4	1	no	—
294	C₂×D₅	—	4	1	no	—
295	C₂×D₅	#340	1	1	yes	characteristic
296	C₂×D₅	#340	1	1	yes	characteristic
297	C₂×D₅	#340	1	1	yes	characteristic
298	C₂×D₅	#340	1	1	yes	characteristic
299	C₄×C₅	C₂×#95	1	1	yes	characteristic
300	C₄×C₅	C₂×#102	1	1	yes	characteristic
301	C₄×C₅	C₂×#102	1	1	yes	characteristic
302	C₄×C₅	C₂×#106	1	1	yes	characteristic
303	Dic₅	#340	1	1	yes	characteristic
304	Dic₅	#340	1	1	yes	characteristic
305	Dic₅	#340	1	1	yes	characteristic
306	Dic₅	#340	1	1	yes	characteristic
307	C₂⁴	—	5	1	no	—
308	C₂²×C₄	—	5	1	no	—
309	C₂²×C₄	—	5	1	no	—
310	C₂²×C₄	—	5	1	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	5	1	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	10	2	no	—
327	M₁₆	—	10	2	no	—
328	M₁₆	—	20	2	no	—
329	M₁₆	—	20	2	no	—
330	M₁₆	—	20	2	no	—
331	M₁₆	—	20	2	no	—
332	M₁₆	—	20	1	no	—
333	M₁₆	—	20	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	5	1	no	—
337	C₂×C₈	—	5	1	no	—
338	C₂×C₈	—	5	1	no	—
339	C₂×C₈	—	5	1	no	—
340	C₂×C₈	—	5	1	no	—
341	C₂×C₈	—	5	1	no	—
342	C₂×C₈	—	5	1	no	—
343	C₂×C₈	—	5	1	no	—
344	C₂×C₈	—	5	1	no	—
345	C₂×C₈	—	5	1	no	—
346	C₂×C₈	—	5	1	no	—
347	C₂×C₈	—	5	1	no	—
348	C₂×C₈	—	5	1	no	—
349	C₂×C₈	—	5	1	no	—
350	C₂×C₈	—	5	1	no	—
351	C₂×C₈	—	5	1	no	—
352	C₂×C₈	—	5	1	no	—
353	C₂×C₈	—	5	1	no	—
354	C₂×C₈	—	5	1	no	—
355	C₂×C₈	—	5	1	no	—
356	C₂×C₈	—	5	1	no	—
357	C₂×C₈	—	5	1	no	—
358	C₂×C₈	—	20	2	no	—
359	C₂×C₈	—	20	2	no	—
360	C₂×C₈	—	20	2	no	—
361	C₂×C₈	—	20	2	no	—
362	C₂×C₈	—	20	1	no	—
363	C₂×C₈	—	20	1	no	—
364	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
365	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
367	C₂×C₈	D₄×D₅	1	1	yes	characteristic
368	C₂×C₈	D₄×D₅	1	1	yes	characteristic
369	C₂×C₈	Q₈×D₅	1	1	yes	characteristic
370	C₁₆	—	2	2	no	—
371	C₁₆	—	10	2	no	—
372	C₂×C₅	—	2	1	no	—
373	C₂×C₅	—	2	1	no	—
374	C₂×C₅	—	2	1	no	—
375	C₂×C₅	C₂×#340	1	1	yes	characteristic
376	D₅	—	2	1	no	—
377	D₅	—	2	1	no	—
378	D₅	—	2	1	no	—
379	D₅	#1388	1	2	yes	direct product factor
380	C₂³	—	5	1	no	—
381	C₂³	—	5	1	no	—
382	C₂³	—	5	1	no	—
383	C₂³	—	5	1	no	—
384	C₂³	—	5	1	no	—
385	C₂³	—	5	1	no	—
386	C₂³	—	20	2	no	—
387	C₂³	D₅×Q₁₆	1	1	yes	characteristic
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	5	1	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
411	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
413	C₂×C₄	D₅×D₈	1	1	yes	characteristic
414	C₂×C₄	D₅×SD₁₆	1	1	yes	characteristic
415	C₂×C₄	D₅×SD₁₆	1	1	yes	characteristic
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	5	1	no	—
419	C₈	—	5	1	no	—
420	C₈	—	5	1	no	—
421	C₈	—	5	1	no	—
422	C₈	—	20	2	no	—
423	C₈	—	20	2	no	—
424	C₈	C₄²×D₅	1	1	yes	characteristic
425	C₈	D₅×C₂²⋊C₄	1	1	yes	characteristic
426	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
427	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
428	C₅	C₂×#1388	1	1	yes	characteristic, complemented, Sylow
429	C₂²	—	4	1	no	—
430	C₂²	—	5	1	no	—
431	C₂²	—	5	1	no	—
432	C₂²	—	5	1	no	—
433	C₂²	—	5	1	no	—
434	C₂²	—	10	2	no	—
435	C₂²	—	10	2	no	—
436	C₂²	—	10	2	no	—
437	C₂²	—	20	1	no	—
438	C₂²	—	20	1	no	—
439	C₂²	—	20	1	no	—
440	C₂²	D₅×#103	1	1	yes	characteristic
441	C₂²	D₅×#103	1	1	yes	characteristic
442	C₂²	D₅×#107	1	1	yes	characteristic
443	C₄	—	5	1	no	—
444	C₄	—	5	1	no	—
445	C₄	—	5	1	no	—
446	C₄	—	5	1	no	—
447	C₄	D₅×#95	1	1	yes	characteristic
448	C₄	D₅×#102	1	1	yes	characteristic
449	C₄	D₅×#102	1	1	yes	characteristic
450	C₄	D₅×#106	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	5	2	no	—
455	C₂	—	10	1	no	—
456	C₂	—	10	1	no	—
457	C₂	—	10	1	no	—
458	C₂	D₅×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₅×#102
commutator	C₅×C₈	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₅
Fitting	C₅×#1388	C₂
socle	C₂×C₅	C₂×#340
prime radical	C₂³×D₅	Q₁₆
cosocle	C₂²×C₅×C₈	C₂³
hypercenter	#1388	D₅
hypocenter	C₅	C₂×#1388
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1388

Complements

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

N	H ≅ G/N	type
4. C₅×#1388	C₂	semidirect
5. #10598312	C₂	semidirect
6. #10598225	C₂	semidirect
7. #10598224	C₂	semidirect
93. #1388	D₅	direct (N × H)
379. D₅	#1388	direct (N × H)
428. C₅	C₂×#1388	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×M₃₂	2
C₂×D₅×#108	2
C₅×#1388	2
#10598312	2
#10598225	2
#10598224	2
C₂×#1388	5

Subgroups — D5×#1388 #12014229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#1388 #12014229