Subgroups — #12107548

Order 1280.

712 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#4044	C₂	1	1	yes	maximal, characteristic
2	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
3	#10601243	C₂	1	1	yes	maximal, characteristic
4	#10601240	C₂	1	1	yes	maximal, characteristic, complemented
5	#10600603	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600601	C₂	1	1	yes	maximal, characteristic
7	#10600601	C₂	1	1	yes	maximal, characteristic
8	Dic₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#683	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600574	C₂	1	1	yes	maximal, characteristic
11	#10600276	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599451	C₂	1	1	yes	maximal, characteristic
13	#10599408	C₂	1	1	yes	maximal, characteristic
14	#10599406	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599400	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#676	C₂²	1	1	yes	characteristic
17	C₂×#4044	C₄	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#97	C₂²	1	1	yes	characteristic
20	C₂×C₅×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×#3952	C₂²	1	1	yes	characteristic
24	C₂×#3952	C₂²	1	1	yes	characteristic
25	C₂×#3952	C₂²	1	1	yes	characteristic
26	C₂×#3947	C₂²	1	1	yes	characteristic
27	C₂×#3947	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	#65279	C₄	1	1	yes	characteristic
33	#65270	C₄	1	1	yes	characteristic
34	#65267	C₄	1	1	yes	characteristic
35	C₄×#685	C₂²	1	1	yes	characteristic
36	C₄×#685	C₂²	1	1	yes	characteristic
37	C₄×#685	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
39	C₄×#683	C₂²	1	1	yes	characteristic
40	C₄²×Dic₅	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₂×#3935	C₂²	1	1	yes	characteristic
43	#64959	C₄	1	1	yes	characteristic
44	#64958	C₄	1	1	yes	characteristic
45	#64943	C₄	1	1	yes	characteristic
46	#64940	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	#64744	C₂²	1	1	yes	characteristic
56	#64744	C₂²	1	1	yes	characteristic
57	#64744	C₂²	1	1	yes	characteristic
58	#64744	C₂²	1	1	yes	characteristic
59	#21667	—	5	1	no	maximal, Sylow
60	C₂²×C₄×D₅	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	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×#685	C₂×C₄	1	1	yes	characteristic
71	C₂×#685	C₂×C₄	1	1	yes	characteristic
72	C₂×#685	C₂×C₄	1	1	yes	characteristic
73	C₂×#685	C₂×C₄	1	1	yes	characteristic
74	C₂×#685	C₂×C₄	1	1	yes	characteristic
75	C₂×#685	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×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	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₅	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	C₂²×#168	C₂³	1	1	yes	characteristic
91	C₂×#676	—	2	2	no	—
92	C₂×#676	—	2	2	no	—
93	C₂×#676	—	2	2	no	—
94	#4044	—	2	4	no	—
95	C₅×C₄⋊C₈	—	2	2	no	—
96	C₅×#97	—	2	2	no	—
97	C₅×#97	—	2	2	no	—
98	C₄×C₅×C₈	—	2	2	no	—
99	C₅×#95	C₂×C₄	1	1	yes	characteristic
100	C₅×#95	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	#3963	C₂×C₄	1	1	yes	characteristic
110	#3963	C₂×C₄	1	1	yes	characteristic
111	#3952	—	2	2	no	—
112	#3952	—	2	2	no	—
113	#3952	—	2	2	no	—
114	#3947	—	2	2	no	—
115	#3947	—	2	2	no	—
116	#3946	—	2	2	no	—
117	C₈×Dic₅	—	2	2	no	—
118	C₈×Dic₅	—	2	2	no	—
119	C₈×Dic₅	—	2	2	no	—
120	C₄⋊#168	—	2	2	no	—
121	#3935	—	2	2	no	—
122	C₄×#126	—	5	1	no	—
123	#1924	—	5	1	no	—
124	#1924	—	5	1	no	—
125	#1923	—	5	1	no	—
126	#1917	—	5	1	no	—
127	#1917	—	5	1	no	—
128	#1916	—	5	1	no	—
129	#1839	—	5	1	no	—
130	#1771	—	5	1	no	—
131	#1770	D₅	1	1	yes	characteristic, complemented
132	C₈×C₄⋊C₄	—	5	1	no	—
133	#1753	—	5	1	no	—
134	#1753	—	5	1	no	—
135	#1753	—	5	1	no	—
136	C₄×#97	—	5	1	no	—
137	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×Dic₅	C₂²×C₄	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	C₂×C₄×D₅	—	2	1	no	—
153	C₂×C₄×D₅	—	2	1	no	—
154	C₂×C₄×D₅	—	2	1	no	—
155	C₂×C₄×D₅	—	2	1	no	—
156	C₂×C₄×D₅	—	2	1	no	—
157	C₂×C₄×D₅	—	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	#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×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	—	4	1	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	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	#685	—	2	2	no	—
179	#685	—	2	2	no	—
180	#685	—	2	2	no	—
181	#685	—	2	2	no	—
182	#685	—	4	1	no	—
183	#685	—	4	1	no	—
184	C₄⋊Dic₅	—	2	2	no	—
185	C₄⋊Dic₅	—	4	1	no	—
186	#683	—	2	2	no	—
187	#683	M₁₆	1	4	yes	complemented
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	C₄×Dic₅	—	2	2	no	—
195	C₄×Dic₅	—	2	2	no	—
196	C₄×Dic₅	—	4	1	no	—
197	C₄×Dic₅	—	4	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	#41	1	2	yes	—
209	C₂×#168	#41	1	2	yes	—
210	#676	—	4	4	no	—
211	C₂²×M₁₆	—	5	1	no	—
212	C₂×#126	—	5	1	no	—
213	C₂×C₄⋊C₈	—	5	1	no	—
214	C₂×C₄⋊C₈	—	5	1	no	—
215	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	—	5	1	no	—
217	C₂×C₂²⋊C₈	—	5	1	no	—
218	C₂×C₂²⋊C₈	—	5	1	no	—
219	C₂×#97	—	5	1	no	—
220	C₂×#97	—	5	1	no	—
221	C₂×#97	—	5	1	no	—
222	C₂×#97	C₂×D₅	1	1	yes	characteristic
223	C₂×#97	C₂×D₅	1	1	yes	characteristic
224	C₂×C₄×C₈	—	5	1	no	—
225	C₂×C₄×C₈	—	5	1	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
228	#388	—	5	1	no	—
229	#388	—	5	1	no	—
230	#388	—	5	1	no	—
231	#387	—	5	1	no	—
232	#387	—	5	1	no	—
233	#387	—	5	1	no	—
234	#383	—	5	1	no	—
235	C₄×C₄⋊C₄	—	5	1	no	—
236	C₄×C₄⋊C₄	—	5	1	no	—
237	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
238	C₄×C₂²⋊C₄	—	5	1	no	—
239	C₄×C₂²⋊C₄	—	5	1	no	—
240	C₄×C₂²⋊C₄	—	5	1	no	—
241	C₄³	—	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	—	5	1	no	—
251	#336	—	5	1	no	—
252	#336	C₂×D₅	1	1	yes	characteristic
253	#336	C₂×D₅	1	1	yes	characteristic
254	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂²×D₅	—	2	1	no	—
256	C₂²×D₅	—	2	1	no	—
257	C₂²×D₅	—	2	1	no	—
258	C₂²×D₅	—	2	1	no	—
259	C₂²×D₅	—	2	1	no	—
260	C₂²×D₅	—	2	1	no	—
261	C₂²×D₅	—	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	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
280	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
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	C₂×M₁₆	1	2	yes	—
305	C₂×Dic₅	C₂×M₁₆	1	2	yes	—
306	C₂×Dic₅	#131	1	2	yes	—
307	C₄×D₅	—	4	1	no	—
308	C₄×D₅	—	4	1	no	—
309	C₄×D₅	—	4	1	no	—
310	C₄×D₅	—	4	1	no	—
311	C₅×C₈	—	2	2	no	—
312	C₅×C₈	—	4	1	no	—
313	C₅×C₈	—	4	1	no	—
314	C₅×C₈	#126	1	4	yes	complemented
315	#168	—	2	2	no	—
316	#168	—	2	2	no	—
317	#168	—	4	1	no	—
318	#168	—	4	1	no	—
319	C₂³×C₄	—	5	1	no	—
320	C₂×M₁₆	—	10	2	no	—
321	C₂×M₁₆	—	10	2	no	—
322	C₂×M₁₆	—	10	2	no	—
323	C₂²×C₈	—	5	1	no	—
324	C₂²×C₈	—	5	1	no	—
325	C₂²×C₈	—	5	1	no	—
326	C₂²×C₈	—	5	1	no	—
327	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
328	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
329	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
330	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
331	#126	—	10	4	no	—
332	C₂×C₄⋊C₄	—	5	1	no	—
333	C₂×C₄⋊C₄	—	5	1	no	—
334	C₂×C₄⋊C₄	—	5	1	no	—
335	C₂×C₄⋊C₄	—	5	1	no	—
336	C₂×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	5	1	no	—
339	C₂×C₂²⋊C₄	—	5	1	no	—
340	C₂×C₂²⋊C₄	—	5	1	no	—
341	C₂×C₂²⋊C₄	—	5	1	no	—
342	C₂×C₂²⋊C₄	—	5	1	no	—
343	C₂×C₂²⋊C₄	—	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	—	5	1	no	—
349	C₂×C₄²	—	5	1	no	—
350	C₂×C₄²	—	5	1	no	—
351	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
352	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
354	C₄⋊C₈	—	2	2	no	—
355	C₄⋊C₈	—	10	2	no	—
356	C₄⋊C₈	—	10	2	no	—
357	C₂²⋊C₈	—	10	2	no	—
358	C₂²⋊C₈	—	10	2	no	—
359	C₂²⋊C₈	—	10	2	no	—
360	#97	—	2	2	no	—
361	#97	—	2	2	no	—
362	#97	—	10	2	no	—
363	#97	—	10	2	no	—
364	#97	—	10	2	no	—
365	C₄×C₈	—	2	2	no	—
366	C₄×C₈	—	10	2	no	—
367	C₄×C₈	—	10	2	no	—
368	C₄×C₈	—	10	2	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	#95	—	5	1	no	—
379	#95	C₄×D₅	1	1	yes	characteristic
380	#95	C₄×D₅	1	1	yes	characteristic
381	C₂²×C₅	C₄×#41	1	1	yes	characteristic
382	C₂²×C₅	C₄×#41	1	1	yes	characteristic
383	C₂²×C₅	C₄×#41	1	1	yes	characteristic
384	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
385	C₂²×C₅	C₂×#131	1	1	yes	characteristic
386	C₂²×C₅	#568	1	1	yes	characteristic
387	C₂²×C₅	#568	1	1	yes	characteristic
388	C₂×D₅	—	4	1	no	—
389	C₂×D₅	—	4	1	no	—
390	C₂×D₅	—	4	1	no	—
391	C₂×D₅	—	4	1	no	—
392	C₂×D₅	—	4	1	no	—
393	C₂×D₅	—	4	1	no	—
394	C₂×D₅	—	4	1	no	—
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	4	1	no	—
397	C₄×C₅	—	4	1	no	—
398	C₄×C₅	—	4	1	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	C₂×#126	1	1	yes	characteristic
402	C₄×C₅	#529	1	1	yes	characteristic
403	C₄×C₅	#529	1	1	yes	characteristic
404	C₄×C₅	#529	1	1	yes	characteristic
405	Dic₅	—	2	2	no	—
406	Dic₅	—	2	2	no	—
407	Dic₅	—	2	2	no	—
408	Dic₅	—	4	1	no	—
409	Dic₅	—	4	1	no	—
410	Dic₅	—	4	1	no	—
411	Dic₅	—	4	1	no	—
412	C₂⁴	—	5	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	—	10	1	no	—
421	C₂²×C₄	—	10	1	no	—
422	C₂²×C₄	—	10	1	no	—
423	C₂²×C₄	—	10	1	no	—
424	C₂²×C₄	—	10	1	no	—
425	C₂²×C₄	—	10	1	no	—
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	C₂×C₄×D₅	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
432	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
433	M₁₆	—	20	4	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	—	5	2	no	—
443	C₂×C₈	—	5	2	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	C₂×C₈	#709	1	2	yes	—
455	C₂×C₈	#709	1	2	yes	—
456	C₂×C₈	#711	1	2	yes	—
457	C₂×C₈	#713	1	2	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	5	4	no	—
461	C₄⋊C₄	—	10	2	no	—
462	C₄⋊C₄	—	10	2	no	—
463	C₄⋊C₄	—	20	1	no	—
464	C₂²⋊C₄	—	10	2	no	—
465	C₂²⋊C₄	—	10	2	no	—
466	C₂²⋊C₄	—	10	2	no	—
467	C₂²⋊C₄	—	10	2	no	—
468	C₂²⋊C₄	—	20	1	no	—
469	C₂²⋊C₄	—	20	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	10	2	no	—
477	C₄²	—	10	2	no	—
478	C₄²	—	10	1	no	—
479	C₄²	—	10	1	no	—
480	C₄²	—	10	1	no	—
481	C₄²	—	10	1	no	—
482	C₄²	—	10	1	no	—
483	C₄²	—	10	1	no	—
484	C₄²	—	20	1	no	—
485	C₄²	—	20	1	no	—
486	C₂×C₅	C₄×#126	1	1	yes	characteristic
487	C₂×C₅	#2965	1	1	yes	characteristic
488	C₂×C₅	#2967	1	1	yes	characteristic
489	C₂×C₅	#2968	1	1	yes	characteristic
490	C₂×C₅	#2969	1	1	yes	characteristic
491	C₂×C₅	#2970	1	1	yes	characteristic
492	C₂×C₅	#2971	1	1	yes	characteristic
493	D₅	—	8	1	no	—
494	C₂³	—	10	1	no	—
495	C₂³	—	10	1	no	—
496	C₂³	—	10	1	no	—
497	C₂³	—	10	1	no	—
498	C₂³	—	10	1	no	—
499	C₂³	—	10	1	no	—
500	C₂³	—	10	1	no	—
501	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
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	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	5	2	no	—
520	C₂×C₄	—	5	2	no	—
521	C₂×C₄	—	5	2	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	—	10	1	no	—
540	C₂×C₄	—	20	1	no	—
541	C₂×C₄	—	20	1	no	—
542	C₂×C₄	—	20	1	no	—
543	C₂×C₄	—	20	1	no	—
544	C₂×C₄	D₅×M₁₆	1	2	yes	—
545	C₂×C₄	C₂×#709	1	1	yes	characteristic
546	C₂×C₄	C₂×#709	1	1	yes	characteristic
547	C₂×C₄	C₂×#711	1	1	yes	characteristic
548	C₂×C₄	C₂×#713	1	1	yes	characteristic
549	C₂×C₄	D₅×#41	1	1	yes	characteristic
550	C₂×C₄	D₅×#41	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	10	2	no	—
555	C₈	—	10	2	no	—
556	C₈	—	20	1	no	—
557	C₈	—	20	1	no	—
558	C₈	#4044	1	4	yes	complemented
559	C₅	#21667	1	1	yes	characteristic, complemented, Sylow
560	C₂²	—	20	1	no	—
561	C₂²	—	20	1	no	—
562	C₂²	—	20	1	no	—
563	C₂²	—	20	1	no	—
564	C₂²	—	20	1	no	—
565	C₂²	—	20	1	no	—
566	C₂²	—	20	1	no	—
567	C₂²	C₄×#709	1	1	yes	characteristic
568	C₂²	C₄×#711	1	1	yes	characteristic
569	C₂²	C₄×#713	1	1	yes	characteristic
570	C₂²	C₂×D₅×M₁₆	1	1	yes	characteristic
571	C₂²	#66079	1	1	yes	characteristic
572	C₂²	D₅×#131	1	1	yes	characteristic
573	C₂²	#66084	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	10	2	no	—
581	C₄	—	10	2	no	—
582	C₄	—	10	2	no	—
583	C₄	—	20	1	no	—
584	C₄	—	20	1	no	—
585	C₄	—	20	1	no	—
586	C₄	—	20	1	no	—
587	C₄	C₂×#4044	1	1	yes	characteristic
588	C₄	#65862	1	1	yes	characteristic
589	C₄	#65872	1	1	yes	characteristic
590	C₄	#65914	1	1	yes	characteristic
591	C₂	—	40	1	no	—
592	C₂	C₄×#4044	1	1	yes	characteristic
593	C₂	#10610213	1	1	yes	characteristic
594	C₂	#10610289	1	1	yes	characteristic
595	C₂	#10611251	1	1	yes	characteristic
596	C₂	#10611253	1	1	yes	characteristic
597	C₂	#10611669	1	1	yes	characteristic
598	C₂	#10611671	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₅×#1770	C₂
prime radical	C₂³×D₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1770	D₅
hypocenter	C₅	#21667
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #1770

Complements

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

N	H ≅ G/N	type
2. C₅×#1770	C₂	semidirect
4. #10601240	C₂	semidirect
5. #10600603	C₂	semidirect
8. Dic₅×#97	C₂	semidirect
9. C₈×#683	C₂	semidirect
11. #10600276	C₂	semidirect
14. #10599406	C₂	semidirect
15. #10599400	C₂	semidirect
131. #1770	D₅	semidirect
187. #683	M₁₆	semidirect
314. C₅×C₈	#126	semidirect
558. C₈	#4044	semidirect
559. C₅	#21667	semidirect

Maximal subgroups

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

subgroup	index
C₄×#4044	2
C₅×#1770	2
#10601243	2
#10601240	2
#10600603	2
#10600601	2
Dic₅×#97	2
C₈×#683	2
#10600574	2
#10600276	2
#10599451	2
#10599408	2
#10599406	2
#10599400	2
#21667	5