Subgroups — #12109514

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10613960	C₂	1	1	yes	maximal, characteristic
2	C₅×#1798	C₂	1	1	yes	maximal, characteristic
3	#10602376	C₂	1	1	yes	maximal, characteristic
4	#10601238	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601236	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601235	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601235	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600708	C₂	1	1	yes	maximal, characteristic
9	#10600707	C₂	1	1	yes	maximal, characteristic
10	#10600706	C₂	1	1	yes	maximal, characteristic
11	#10600705	C₂	1	1	yes	maximal, characteristic
12	#10599406	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599405	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599403	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599402	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊C₈	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×#3946	C₂²	1	1	yes	characteristic
30	C₂×#3946	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
33	#65270	C₄	1	1	yes	characteristic
34	#65270	C₄	1	1	yes	characteristic
35	#65270	C₄	1	1	yes	characteristic
36	#65270	C₄	1	1	yes	characteristic
37	#65240	C₄	1	1	yes	characteristic
38	#65240	C₄	1	1	yes	characteristic
39	#65240	C₄	1	1	yes	characteristic
40	#65240	C₄	1	1	yes	characteristic
41	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
43	#65221	C₂²	1	1	yes	characteristic
44	C₄²×Dic₅	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊#168	C₂²	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	#21929	—	5	1	no	maximal, Sylow
60	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₅×#117	—	2	2	no	—
66	C₅×#117	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	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×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
87	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
89	C₂²×#168	C₂³	1	1	yes	characteristic
90	C₂²×#168	C₂³	1	1	yes	characteristic
91	C₂²×#168	C₂³	1	1	yes	characteristic
92	C₂²×#168	C₂³	1	1	yes	characteristic
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×C₄⋊C₈	—	2	2	no	—
95	C₅×C₂²⋊C₈	—	4	1	no	—
96	C₅×C₂²⋊C₈	—	4	1	no	—
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	—	4	1	no	—
110	C₂²⋊#168	—	4	1	no	—
111	#3947	—	4	1	no	—
112	#3947	—	4	1	no	—
113	#3946	—	4	1	no	—
114	#3946	—	4	1	no	—
115	#3946	—	4	1	no	—
116	#3946	—	4	1	no	—
117	C₈×Dic₅	—	4	1	no	—
118	C₈×Dic₅	—	4	1	no	—
119	C₄⋊#168	—	2	2	no	—
120	C₄⋊#168	—	2	2	no	—
121	#2298	—	5	1	no	—
122	#1924	—	5	1	no	—
123	#1924	—	5	1	no	—
124	#1923	—	5	1	no	—
125	#1923	—	5	1	no	—
126	#1917	—	5	1	no	—
127	#1917	—	5	1	no	—
128	#1916	—	5	1	no	—
129	#1916	—	5	1	no	—
130	#1842	—	5	1	no	—
131	#1831	—	5	1	no	—
132	#1798	—	5	1	no	—
133	#1798	D₅	1	1	yes	characteristic
134	#1768	—	5	1	no	—
135	#1768	—	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	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₂²⋊C₄	—	2	2	no	—
172	C₅×C₂²⋊C₄	—	2	2	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	#41	1	2	yes	—
176	C₄²×C₅	#41	1	2	yes	—
177	C₂²⋊Dic₅	—	2	2	no	—
178	C₂²⋊Dic₅	—	2	2	no	—
179	C₂²⋊Dic₅	—	4	1	no	—
180	C₂²⋊Dic₅	—	4	1	no	—
181	C₄⋊Dic₅	—	2	2	no	—
182	C₄⋊Dic₅	—	2	2	no	—
183	C₄⋊Dic₅	—	4	1	no	—
184	C₄⋊Dic₅	—	4	1	no	—
185	C₄×Dic₅	—	2	1	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	2	no	—
194	C₄×Dic₅	—	2	2	no	—
195	C₄×Dic₅	—	4	1	no	—
196	C₄×Dic₅	—	4	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	—	2	1	no	—
205	C₂×#168	—	2	1	no	—
206	C₂×#168	—	2	1	no	—
207	C₂×#168	—	2	1	no	—
208	C₂×#168	—	2	1	no	—
209	C₂×#117	C₂×D₅	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	5	1	no	—
211	C₂×C₄⋊C₈	—	5	1	no	—
212	C₂×C₄⋊C₈	—	5	1	no	—
213	C₂×C₄⋊C₈	—	5	1	no	—
214	C₂×C₄⋊C₈	—	5	1	no	—
215	C₂×C₄⋊C₈	—	5	1	no	—
216	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	—	5	1	no	—
219	C₂×C₂²⋊C₈	—	5	1	no	—
220	C₂×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
222	C₂×#97	—	5	1	no	—
223	C₂×#97	—	5	1	no	—
224	C₂×C₄×C₈	—	5	1	no	—
225	C₂×C₄×C₈	—	5	1	no	—
226	#388	—	5	1	no	—
227	#388	—	5	1	no	—
228	#388	—	5	1	no	—
229	#388	—	5	1	no	—
230	#387	—	5	1	no	—
231	#387	—	5	1	no	—
232	#387	—	5	1	no	—
233	#387	—	5	1	no	—
234	C₄×C₄⋊C₄	—	5	1	no	—
235	C₄×C₄⋊C₄	—	5	1	no	—
236	C₄×C₂²⋊C₄	—	5	1	no	—
237	C₄×C₂²⋊C₄	—	5	1	no	—
238	#376	—	5	1	no	—
239	C₄³	—	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	—	5	1	no	—
248	#336	—	5	1	no	—
249	#336	—	5	1	no	—
250	#336	C₂×D₅	1	1	yes	characteristic
251	#336	C₂×D₅	1	1	yes	characteristic
252	C₂³×C₅	—	2	1	no	—
253	C₂³×C₅	—	2	1	no	—
254	C₂³×C₅	—	2	1	no	—
255	C₂³×C₅	—	2	1	no	—
256	C₂³×C₅	—	2	1	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	2	1	no	—
259	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	4	1	no	—
274	C₂×C₄×C₅	—	4	1	no	—
275	C₂×C₄×C₅	—	4	1	no	—
276	C₂×C₄×C₅	—	4	1	no	—
277	C₂×C₄×C₅	#117	1	2	yes	—
278	C₂×C₄×C₅	#117	1	2	yes	—
279	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
282	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
284	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	1	no	—
305	C₂×Dic₅	—	2	1	no	—
306	C₂×Dic₅	—	2	1	no	—
307	C₂×Dic₅	#131	1	2	yes	—
308	C₂×Dic₅	#131	1	2	yes	—
309	C₅×C₈	—	4	1	no	—
310	C₅×C₈	—	4	1	no	—
311	C₅×C₈	—	4	1	no	—
312	C₅×C₈	—	4	1	no	—
313	#168	—	4	1	no	—
314	#168	—	4	1	no	—
315	#168	—	4	1	no	—
316	#168	—	4	1	no	—
317	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
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	#117	—	2	2	no	—
327	#117	—	2	2	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×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	5	1	no	—
335	C₂×C₂²⋊C₄	—	5	1	no	—
336	C₂×C₂²⋊C₄	—	5	1	no	—
337	C₂×C₂²⋊C₄	—	5	1	no	—
338	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
340	C₂×C₄²	—	5	1	no	—
341	C₂×C₄²	—	5	1	no	—
342	C₂×C₄²	—	5	1	no	—
343	C₂×C₄²	—	5	1	no	—
344	C₂×C₄²	—	5	1	no	—
345	C₂×C₄²	—	5	1	no	—
346	C₂×C₄²	—	5	1	no	—
347	C₂×C₄²	—	5	1	no	—
348	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
349	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
350	C₄⋊C₈	—	2	2	no	—
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	10	2	no	—
353	C₄⋊C₈	—	10	2	no	—
354	C₄⋊C₈	—	20	1	no	—
355	C₄⋊C₈	—	20	1	no	—
356	C₄⋊C₈	—	20	1	no	—
357	C₄⋊C₈	—	20	1	no	—
358	C₂²⋊C₈	—	4	1	no	—
359	C₂²⋊C₈	—	4	1	no	—
360	C₂²⋊C₈	—	20	1	no	—
361	C₂²⋊C₈	—	20	1	no	—
362	#97	—	20	1	no	—
363	#97	—	20	1	no	—
364	C₄×C₈	—	20	1	no	—
365	C₄×C₈	—	20	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	—	5	1	no	—
374	#95	—	5	1	no	—
375	#95	—	5	1	no	—
376	#95	—	5	1	no	—
377	#95	—	5	1	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	—	4	1	no	—
383	C₂²×C₅	—	4	1	no	—
384	C₂²×C₅	—	4	1	no	—
385	C₂²×C₅	C₂×#117	1	1	yes	characteristic
386	C₂²×C₅	#520	1	1	yes	characteristic
387	C₂²×C₅	#520	1	1	yes	characteristic
388	C₂²×C₅	C₂×#131	1	1	yes	characteristic
389	C₂²×C₅	C₂×#131	1	1	yes	characteristic
390	C₂²×C₅	#568	1	1	yes	characteristic
391	C₂²×C₅	#568	1	1	yes	characteristic
392	C₄×C₅	—	2	2	no	—
393	C₄×C₅	—	2	2	no	—
394	C₄×C₅	—	4	1	no	—
395	C₄×C₅	—	4	1	no	—
396	C₄×C₅	—	4	1	no	—
397	C₄×C₅	#540	1	1	yes	characteristic
398	C₄×C₅	#541	1	1	yes	characteristic
399	C₄×C₅	#542	1	1	yes	characteristic
400	C₄×C₅	#542	1	1	yes	characteristic
401	Dic₅	—	2	2	no	—
402	Dic₅	—	2	2	no	—
403	Dic₅	—	4	1	no	—
404	Dic₅	—	4	1	no	—
405	Dic₅	—	4	1	no	—
406	Dic₅	—	4	1	no	—
407	Dic₅	—	4	1	no	—
408	Dic₅	—	4	1	no	—
409	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	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	—	5	1	no	—
422	C₂²×C₄	—	5	1	no	—
423	C₂²×C₄	—	5	1	no	—
424	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
429	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
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	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	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	—	10	1	no	—
449	C₂×C₈	—	10	1	no	—
450	C₂×C₈	—	10	1	no	—
451	C₂×C₈	—	10	1	no	—
452	C₂×C₈	—	10	1	no	—
453	C₂×C₈	—	10	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	10	2	no	—
457	C₄⋊C₄	—	10	2	no	—
458	C₄⋊C₄	—	20	1	no	—
459	C₄⋊C₄	—	20	1	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	10	2	no	—
463	C₂²⋊C₄	—	10	2	no	—
464	C₂²⋊C₄	—	20	1	no	—
465	C₂²⋊C₄	—	20	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	10	2	no	—
469	C₄²	—	10	2	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	C₄²	—	10	1	no	—
477	C₄²	—	10	1	no	—
478	C₄²	—	20	1	no	—
479	C₄²	—	20	1	no	—
480	C₄²	#711	1	2	yes	—
481	C₄²	#711	1	2	yes	—
482	C₂×C₅	—	8	1	no	—
483	C₂×C₅	#2314	1	1	yes	characteristic
484	C₂×C₅	#2925	1	1	yes	characteristic
485	C₂×C₅	#2925	1	1	yes	characteristic
486	C₂×C₅	#2992	1	1	yes	characteristic
487	C₂×C₅	#2993	1	1	yes	characteristic
488	C₂×C₅	#2994	1	1	yes	characteristic
489	C₂×C₅	#2995	1	1	yes	characteristic
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
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	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	5	2	no	—
516	C₂×C₄	—	5	2	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	—	10	1	no	—
535	C₂×C₄	—	10	1	no	—
536	C₂×C₄	—	10	1	no	—
537	C₂×C₄	—	10	1	no	—
538	C₂×C₄	—	10	1	no	—
539	C₂×C₄	#4023	1	2	yes	—
540	C₂×C₄	#4023	1	2	yes	—
541	C₂×C₄	C₂×#711	1	1	yes	characteristic
542	C₂×C₄	C₂×#711	1	1	yes	characteristic
543	C₂×C₄	#4144	1	1	yes	characteristic
544	C₂×C₄	#4147	1	1	yes	characteristic
545	C₂×C₄	#4149	1	1	yes	characteristic
546	C₂×C₄	#4150	1	1	yes	characteristic
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	20	1	no	—
552	C₈	—	20	1	no	—
553	C₈	—	20	1	no	—
554	C₈	—	20	1	no	—
555	C₅	#21929	1	1	yes	characteristic, complemented, Sylow
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂×#4023	1	1	yes	characteristic
564	C₂²	#65838	1	1	yes	characteristic
565	C₂²	#65857	1	1	yes	characteristic
566	C₂²	D₅×#131	1	1	yes	characteristic
567	C₂²	D₅×#131	1	1	yes	characteristic
568	C₂²	#66084	1	1	yes	characteristic
569	C₂²	#66084	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	10	2	no	—
576	C₄	—	10	2	no	—
577	C₄	—	20	1	no	—
578	C₄	—	20	1	no	—
579	C₄	—	20	1	no	—
580	C₄	—	20	1	no	—
581	C₄	—	20	1	no	—
582	C₄	—	20	1	no	—
583	C₄	#65937	1	1	yes	characteristic
584	C₄	#65953	1	1	yes	characteristic
585	C₄	#65959	1	1	yes	characteristic
586	C₄	#65977	1	1	yes	characteristic
587	C₂	—	8	1	no	—
588	C₂	#10605599	1	1	yes	characteristic
589	C₂	#10610381	1	1	yes	characteristic
590	C₂	#10610381	1	1	yes	characteristic
591	C₂	#10610813	1	1	yes	characteristic
592	C₂	#10610814	1	1	yes	characteristic
593	C₂	#10611112	1	1	yes	characteristic
594	C₂	#10611113	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₅×#1798	C₂
prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1798	D₅
hypocenter	C₅	#21929
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #1798

Complements

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

N	H ≅ G/N	type
4. #10601238	C₂	semidirect
5. #10601236	C₂	semidirect
6. #10601235	C₂	semidirect
7. #10601235	C₂	semidirect
12. #10599406	C₂	semidirect
13. #10599405	C₂	semidirect
14. #10599403	C₂	semidirect
15. #10599402	C₂	semidirect
555. C₅	#21929	semidirect

Maximal subgroups

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

subgroup	index
#10613960	2
C₅×#1798	2
#10602376	2
#10601238	2
#10601236	2
#10601235	2
#10600708	2
#10600707	2
#10600706	2
#10600705	2
#10599406	2
#10599405	2
#10599403	2
#10599402	2
#21929	5