Subgroups — #12107555

Order 1280.

702 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10605213	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₈×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
5	#10600708	C₂	1	1	yes	maximal, characteristic
6	#10600707	C₂	1	1	yes	maximal, characteristic
7	C₈×#683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#683	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600542	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600245	C₂	1	1	yes	maximal, characteristic
12	#10599449	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599407	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599405	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599401	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
25	C₂×#3947	C₂²	1	1	yes	characteristic
26	C₂×#3947	C₂²	1	1	yes	characteristic
27	C₂×#3946	C₂²	1	1	yes	characteristic
28	C₂×#3946	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
33	#65242	C₄	1	1	yes	characteristic
34	#65241	C₄	1	1	yes	characteristic
35	#65241	C₄	1	1	yes	characteristic
36	#65237	C₄	1	1	yes	characteristic
37	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
38	#65221	C₂²	1	1	yes	characteristic
39	C₄×#683	C₂²	1	1	yes	characteristic
40	C₄×#683	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₂×#3935	C₂²	1	1	yes	characteristic
43	C₅⋊#401	C₄	1	1	yes	characteristic
44	#64949	C₄	1	1	yes	characteristic
45	#64948	C₄	1	1	yes	characteristic
46	#64947	C₄	1	1	yes	characteristic
47	C₅×#336	C₂²	1	1	yes	characteristic
48	C₅×#336	C₂²	1	1	yes	characteristic
49	#64770	C₂²	1	1	yes	characteristic
50	#64770	C₂²	1	1	yes	characteristic
51	#64770	C₂²	1	1	yes	characteristic
52	#64770	C₂²	1	1	yes	characteristic
53	#64770	C₂²	1	1	yes	characteristic
54	#64770	C₂²	1	1	yes	characteristic
55	#64770	C₂²	1	1	yes	characteristic
56	#64770	C₂²	1	1	yes	characteristic
57	#64744	C₂²	1	1	yes	characteristic
58	#64744	C₂²	1	1	yes	characteristic
59	#21668	—	5	1	no	maximal, Sylow
60	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	—	2	2	no	—
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₂²×C₅×C₈	—	2	2	no	—
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₂×#683	C₂×C₄	1	1	yes	characteristic
79	C₂×#683	C₂×C₄	1	1	yes	characteristic
80	C₂×#683	C₂×C₄	1	1	yes	characteristic
81	C₂×#683	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
86	C₂²×#168	C₂³	1	1	yes	characteristic
87	C₂²×#168	C₂³	1	1	yes	characteristic
88	C₂²×#168	C₂³	1	1	yes	characteristic
89	C₂²×#168	C₂³	1	1	yes	characteristic
90	C₅×C₂²⋊C₈	—	2	2	no	—
91	C₄×C₅×C₈	—	2	2	no	—
92	C₄×C₅×C₈	—	2	2	no	—
93	C₅×#95	C₂×C₄	1	1	yes	characteristic
94	C₅×#95	C₂×C₄	1	1	yes	characteristic
95	#3963	C₂×C₄	1	1	yes	characteristic
96	#3963	C₂×C₄	1	1	yes	characteristic
97	#3963	C₂×C₄	1	1	yes	characteristic
98	#3963	C₂×C₄	1	1	yes	characteristic
99	#3963	C₂×C₄	1	1	yes	characteristic
100	#3963	C₂×C₄	1	1	yes	characteristic
101	#3963	C₂×C₄	1	1	yes	characteristic
102	#3963	C₂×C₄	1	1	yes	characteristic
103	#3963	C₂×C₄	1	1	yes	characteristic
104	#3963	C₂×C₄	1	1	yes	characteristic
105	#3963	C₂×C₄	1	1	yes	characteristic
106	#3963	C₂×C₄	1	1	yes	characteristic
107	#3963	C₂×C₄	1	1	yes	characteristic
108	#3963	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊#168	—	2	2	no	—
110	C₂²⋊#168	—	2	2	no	—
111	#3947	—	2	2	no	—
112	#3947	—	2	2	no	—
113	#3946	—	2	2	no	—
114	#3946	—	2	2	no	—
115	C₈×Dic₅	—	2	2	no	—
116	C₈×Dic₅	—	2	2	no	—
117	C₈×Dic₅	—	2	2	no	—
118	C₈×Dic₅	—	2	2	no	—
119	C₄⋊#168	—	2	2	no	—
120	#3935	—	2	2	no	—
121	#2401	—	5	1	no	—
122	#1924	—	5	1	no	—
123	#1924	—	5	1	no	—
124	#1924	—	5	1	no	—
125	#1917	—	5	1	no	—
126	#1917	—	5	1	no	—
127	#1917	—	5	1	no	—
128	#1840	—	5	1	no	—
129	C₈×C₄⋊C₄	—	5	1	no	—
130	C₈×C₄⋊C₄	—	5	1	no	—
131	C₈×C₄⋊C₄	—	5	1	no	—
132	C₈×C₂²⋊C₄	—	5	1	no	—
133	C₈×C₂²⋊C₄	—	5	1	no	—
134	C₈×C₂²⋊C₄	D₅	1	1	yes	characteristic
135	#1726	—	5	1	no	—
136	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	4	4	no	—
166	C₂×C₅×C₈	#41	1	2	yes	—
167	C₂×C₅×C₈	#41	1	2	yes	—
168	C₂×C₅×C₈	#41	1	2	yes	—
169	C₂×C₅×C₈	#41	1	2	yes	—
170	C₅×C₂²⋊C₄	—	2	2	no	—
171	C₅×C₂²⋊C₄	—	2	2	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₂²⋊Dic₅	—	2	2	no	—
177	C₂²⋊Dic₅	—	2	2	no	—
178	C₂²⋊Dic₅	—	2	2	no	—
179	C₂²⋊Dic₅	—	2	2	no	—
180	C₄⋊Dic₅	—	2	2	no	—
181	C₄⋊Dic₅	—	2	2	no	—
182	#683	—	2	2	no	—
183	#683	—	2	2	no	—
184	#683	—	2	2	no	—
185	#683	—	2	2	no	—
186	C₄×Dic₅	—	2	1	no	—
187	C₄×Dic₅	—	2	1	no	—
188	C₄×Dic₅	—	2	1	no	—
189	C₄×Dic₅	—	2	1	no	—
190	C₄×Dic₅	—	2	1	no	—
191	C₄×Dic₅	—	2	1	no	—
192	C₄×Dic₅	—	2	1	no	—
193	C₄×Dic₅	—	2	1	no	—
194	C₂×#168	—	2	1	no	—
195	C₂×#168	—	2	1	no	—
196	C₂×#168	—	2	1	no	—
197	C₂×#168	—	2	1	no	—
198	C₂×#168	—	2	1	no	—
199	C₂×#168	—	2	1	no	—
200	C₂×#168	—	2	1	no	—
201	C₂×#168	—	2	1	no	—
202	C₂×#168	—	2	1	no	—
203	C₂×#168	—	2	1	no	—
204	C₂×#168	#41	1	2	yes	—
205	C₂×#168	#41	1	2	yes	—
206	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
207	C₂×C₄⋊C₈	—	5	1	no	—
208	C₂×C₄⋊C₈	—	5	1	no	—
209	C₂×C₄⋊C₈	—	5	1	no	—
210	C₂×C₂²⋊C₈	—	5	1	no	—
211	C₂×C₂²⋊C₈	—	5	1	no	—
212	C₂×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
213	C₂×#97	—	5	1	no	—
214	C₂×#97	—	5	1	no	—
215	C₂×#97	—	5	1	no	—
216	C₂×C₄×C₈	—	5	1	no	—
217	C₂×C₄×C₈	—	5	1	no	—
218	C₂×C₄×C₈	—	5	1	no	—
219	C₂×C₄×C₈	—	5	1	no	—
220	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
222	#401	—	5	1	no	—
223	#400	—	5	1	no	—
224	#400	—	5	1	no	—
225	#400	—	5	1	no	—
226	#397	—	5	1	no	—
227	#397	—	5	1	no	—
228	#397	—	5	1	no	—
229	#396	—	5	1	no	—
230	C₄×C₄⋊C₄	—	5	1	no	—
231	C₄×C₄⋊C₄	—	5	1	no	—
232	C₄×C₄⋊C₄	—	5	1	no	—
233	C₄×C₂²⋊C₄	—	5	1	no	—
234	C₄×C₂²⋊C₄	—	5	1	no	—
235	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
236	#376	—	5	1	no	—
237	#336	—	5	1	no	—
238	#336	—	5	1	no	—
239	#336	—	5	1	no	—
240	#336	—	5	1	no	—
241	#336	—	5	1	no	—
242	#336	—	5	1	no	—
243	#336	—	5	1	no	—
244	#336	—	5	1	no	—
245	#336	—	5	1	no	—
246	#336	—	5	1	no	—
247	#336	C₂×D₅	1	1	yes	characteristic
248	#336	C₂×D₅	1	1	yes	characteristic
249	C₂³×C₅	—	2	1	no	—
250	C₂³×C₅	—	2	1	no	—
251	C₂³×C₅	—	2	1	no	—
252	C₂³×C₅	—	2	1	no	—
253	C₂³×C₅	—	2	1	no	—
254	C₂³×C₅	—	2	1	no	—
255	C₂³×C₅	#131	1	2	yes	—
256	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	1	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	4	1	no	—
272	C₂×C₄×C₅	—	4	1	no	—
273	C₂×C₄×C₅	—	4	1	no	—
274	C₂×C₄×C₅	—	4	1	no	—
275	C₂×C₄×C₅	#131	1	2	yes	—
276	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
282	C₂×Dic₅	—	2	1	no	—
283	C₂×Dic₅	—	2	1	no	—
284	C₂×Dic₅	—	2	1	no	—
285	C₂×Dic₅	—	2	1	no	—
286	C₂×Dic₅	—	2	1	no	—
287	C₂×Dic₅	—	2	1	no	—
288	C₂×Dic₅	—	2	1	no	—
289	C₂×Dic₅	—	2	1	no	—
290	C₂×Dic₅	—	2	1	no	—
291	C₂×Dic₅	—	2	1	no	—
292	C₂×Dic₅	—	2	1	no	—
293	C₂×Dic₅	—	2	1	no	—
294	C₂×Dic₅	—	2	1	no	—
295	C₂×Dic₅	—	2	1	no	—
296	C₂×Dic₅	—	2	1	no	—
297	C₂×Dic₅	—	2	1	no	—
298	C₂×Dic₅	—	2	1	no	—
299	C₂×Dic₅	—	2	1	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	1	no	—
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	—	2	1	no	—
304	C₂×Dic₅	#131	1	2	yes	—
305	C₂×Dic₅	#131	1	2	yes	—
306	C₅×C₈	—	2	2	no	—
307	C₅×C₈	—	4	1	no	—
308	C₅×C₈	—	4	1	no	—
309	C₅×C₈	#126	1	4	yes	—
310	#168	—	2	2	no	—
311	#168	—	2	2	no	—
312	#168	—	4	1	no	—
313	#168	—	4	1	no	—
314	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	2	2	no	—
318	C₂²×C₈	—	5	1	no	—
319	C₂²×C₈	—	5	1	no	—
320	C₂²×C₈	—	5	1	no	—
321	C₂²×C₈	—	5	1	no	—
322	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
323	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
324	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
326	C₂×C₄⋊C₄	—	5	1	no	—
327	C₂×C₄⋊C₄	—	5	1	no	—
328	C₂×C₄⋊C₄	—	5	1	no	—
329	C₂×C₄⋊C₄	—	5	1	no	—
330	C₂×C₄⋊C₄	—	5	1	no	—
331	C₂×C₄⋊C₄	—	5	1	no	—
332	C₂×C₂²⋊C₄	—	5	1	no	—
333	C₂×C₂²⋊C₄	—	5	1	no	—
334	C₂×C₂²⋊C₄	—	5	1	no	—
335	C₂×C₂²⋊C₄	—	5	1	no	—
336	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
338	C₂×C₄²	—	5	1	no	—
339	C₂×C₄²	—	5	1	no	—
340	C₂×C₄²	—	5	1	no	—
341	C₂×C₄²	—	5	1	no	—
342	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
343	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
344	C₄⋊C₈	—	10	2	no	—
345	C₄⋊C₈	—	10	2	no	—
346	C₄⋊C₈	—	10	2	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	10	2	no	—
349	C₂²⋊C₈	—	10	2	no	—
350	#97	—	10	2	no	—
351	#97	—	10	2	no	—
352	#97	—	10	2	no	—
353	C₄×C₈	—	2	2	no	—
354	C₄×C₈	—	2	2	no	—
355	C₄×C₈	—	10	2	no	—
356	C₄×C₈	—	10	2	no	—
357	C₄×C₈	—	10	2	no	—
358	C₄×C₈	—	10	2	no	—
359	#95	—	5	1	no	—
360	#95	—	5	1	no	—
361	#95	—	5	1	no	—
362	#95	—	5	1	no	—
363	#95	—	5	1	no	—
364	#95	—	5	1	no	—
365	#95	—	5	1	no	—
366	#95	—	5	1	no	—
367	#95	—	5	1	no	—
368	#95	—	5	1	no	—
369	#95	—	5	1	no	—
370	#95	—	5	1	no	—
371	#95	—	5	1	no	—
372	#95	—	5	1	no	—
373	#95	C₄×D₅	1	1	yes	characteristic
374	#95	C₄×D₅	1	1	yes	characteristic
375	C₂²×C₅	—	2	2	no	—
376	C₂²×C₅	—	2	2	no	—
377	C₂²×C₅	—	2	2	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	—	4	1	no	—
382	C₂²×C₅	C₄×#41	1	1	yes	characteristic
383	C₂²×C₅	C₄×#41	1	1	yes	characteristic
384	C₂²×C₅	C₄×#41	1	1	yes	characteristic
385	C₂²×C₅	C₂×#131	1	1	yes	characteristic
386	C₂²×C₅	C₂×#131	1	1	yes	characteristic
387	C₂²×C₅	C₂×#131	1	1	yes	characteristic
388	C₂²×C₅	C₂×#131	1	1	yes	characteristic
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	4	1	no	—
391	C₄×C₅	—	4	1	no	—
392	C₄×C₅	—	4	1	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	C₂×#126	1	1	yes	characteristic
395	C₄×C₅	#529	1	1	yes	characteristic
396	C₄×C₅	#529	1	1	yes	characteristic
397	C₄×C₅	#529	1	1	yes	characteristic
398	Dic₅	—	2	2	no	—
399	Dic₅	—	2	2	no	—
400	Dic₅	—	4	1	no	—
401	Dic₅	—	4	1	no	—
402	Dic₅	—	4	1	no	—
403	Dic₅	—	4	1	no	—
404	Dic₅	—	4	1	no	—
405	Dic₅	—	4	1	no	—
406	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	5	1	no	—
414	C₂²×C₄	—	5	1	no	—
415	C₂²×C₄	—	5	1	no	—
416	C₂²×C₄	—	5	1	no	—
417	C₂²×C₄	—	5	1	no	—
418	C₂²×C₄	—	5	1	no	—
419	C₂²×C₄	—	5	1	no	—
420	C₂²×C₄	—	5	1	no	—
421	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
423	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	4	4	no	—
436	C₂×C₈	—	5	2	no	—
437	C₂×C₈	—	5	2	no	—
438	C₂×C₈	—	10	1	no	—
439	C₂×C₈	—	10	1	no	—
440	C₂×C₈	—	10	1	no	—
441	C₂×C₈	—	10	1	no	—
442	C₂×C₈	—	10	1	no	—
443	C₂×C₈	—	10	1	no	—
444	C₂×C₈	—	10	1	no	—
445	C₂×C₈	—	10	1	no	—
446	C₂×C₈	—	10	1	no	—
447	C₂×C₈	—	10	1	no	—
448	C₂×C₈	#709	1	2	yes	—
449	C₂×C₈	#709	1	2	yes	—
450	C₂×C₈	#711	1	2	yes	—
451	C₂×C₈	#711	1	2	yes	—
452	C₄⋊C₄	—	10	2	no	—
453	C₄⋊C₄	—	10	2	no	—
454	C₄⋊C₄	—	10	2	no	—
455	C₄⋊C₄	—	10	2	no	—
456	C₄⋊C₄	—	10	2	no	—
457	C₄⋊C₄	—	10	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	10	2	no	—
461	C₂²⋊C₄	—	10	2	no	—
462	C₂²⋊C₄	—	10	2	no	—
463	C₂²⋊C₄	—	10	2	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	10	1	no	—
469	C₄²	—	10	1	no	—
470	C₄²	—	10	1	no	—
471	C₄²	—	10	1	no	—
472	C₄²	—	10	1	no	—
473	C₄²	—	10	1	no	—
474	C₄²	—	10	1	no	—
475	C₄²	—	10	1	no	—
476	C₂×C₅	—	4	2	no	—
477	C₂×C₅	C₄×#126	1	1	yes	characteristic
478	C₂×C₅	#2966	1	1	yes	characteristic
479	C₂×C₅	#2966	1	1	yes	characteristic
480	C₂×C₅	#2966	1	1	yes	characteristic
481	C₂×C₅	#2966	1	1	yes	characteristic
482	C₂×C₅	#2966	1	1	yes	characteristic
483	C₂×C₅	#2966	1	1	yes	characteristic
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	#4047	1	2	yes	—
491	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	5	2	no	—
511	C₂×C₄	—	5	2	no	—
512	C₂×C₄	—	10	1	no	—
513	C₂×C₄	—	10	1	no	—
514	C₂×C₄	—	10	1	no	—
515	C₂×C₄	—	10	1	no	—
516	C₂×C₄	—	10	1	no	—
517	C₂×C₄	—	10	1	no	—
518	C₂×C₄	—	10	1	no	—
519	C₂×C₄	—	10	1	no	—
520	C₂×C₄	—	10	1	no	—
521	C₂×C₄	—	10	1	no	—
522	C₂×C₄	—	10	1	no	—
523	C₂×C₄	—	10	1	no	—
524	C₂×C₄	—	10	1	no	—
525	C₂×C₄	—	10	1	no	—
526	C₂×C₄	—	10	1	no	—
527	C₂×C₄	—	10	1	no	—
528	C₂×C₄	—	10	1	no	—
529	C₂×C₄	—	10	1	no	—
530	C₂×C₄	—	10	1	no	—
531	C₂×C₄	—	10	1	no	—
532	C₂×C₄	—	10	1	no	—
533	C₂×C₄	—	10	1	no	—
534	C₂×C₄	#4047	1	2	yes	—
535	C₂×C₄	C₂×#709	1	1	yes	characteristic
536	C₂×C₄	C₂×#709	1	1	yes	characteristic
537	C₂×C₄	C₂×#711	1	1	yes	characteristic
538	C₂×C₄	C₂×#711	1	1	yes	characteristic
539	C₂×C₄	D₅×#41	1	1	yes	characteristic
540	C₂×C₄	D₅×#41	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	10	2	no	—
545	C₈	—	10	2	no	—
546	C₈	—	20	1	no	—
547	C₈	—	20	1	no	—
548	C₈	#4025	1	4	yes	—
549	C₅	#21668	1	1	yes	characteristic, complemented, Sylow
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	C₄×#709	1	1	yes	characteristic
558	C₂²	C₄×#711	1	1	yes	characteristic
559	C₂²	C₄×#711	1	1	yes	characteristic
560	C₂²	C₂×#4047	1	1	yes	characteristic
561	C₂²	C₂×#4047	1	1	yes	characteristic
562	C₂²	D₅×#131	1	1	yes	characteristic
563	C₂²	D₅×#131	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	10	2	no	—
570	C₄	—	10	2	no	—
571	C₄	—	20	1	no	—
572	C₄	—	20	1	no	—
573	C₄	—	20	1	no	—
574	C₄	—	20	1	no	—
575	C₄	—	20	1	no	—
576	C₄	—	20	1	no	—
577	C₄	C₂×#4025	1	1	yes	characteristic
578	C₄	#65862	1	1	yes	characteristic
579	C₄	#65872	1	1	yes	characteristic
580	C₄	#65891	1	1	yes	characteristic
581	C₂	—	4	2	no	—
582	C₂	C₄×#4025	1	1	yes	characteristic
583	C₂	#10610179	1	1	yes	characteristic
584	C₂	#10610287	1	1	yes	characteristic
585	C₂	#10611131	1	1	yes	characteristic
586	C₂	#10611131	1	1	yes	characteristic
587	C₂	#10611131	1	1	yes	characteristic
588	C₂	#10611132	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×C₈×C₂²⋊C₄	C₂
prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₈×C₂²⋊C₄	D₅
hypocenter	C₅	#21668
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₈ ◁ C₈×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
7. C₈×#683	C₂	semidirect
8. C₈×#683	C₂	semidirect
9. C₈×C₄⋊Dic₅	C₂	semidirect
10. #10600542	C₂	semidirect
12. #10599449	C₂	semidirect
13. #10599407	C₂	semidirect
14. #10599405	C₂	semidirect
15. #10599401	C₂	semidirect
549. C₅	#21668	semidirect

Maximal subgroups

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

subgroup	index
#10605213	2
C₅×C₈×C₂²⋊C₄	2
C₈×C₂²⋊Dic₅	2
#10600708	2
#10600707	2
C₈×#683	2
C₈×C₄⋊Dic₅	2
#10600542	2
#10600245	2
#10599449	2
#10599407	2
#10599405	2
#10599401	2
#21668	5