Subgroups — #12064946

Order 1280.

772 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611013	C₂	1	1	yes	maximal, characteristic
2	D₅×#431	C₂	1	1	yes	maximal, characteristic
3	D₅×#431	C₂	1	1	yes	maximal, characteristic
4	C₅×#1454	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598864	C₂	1	1	yes	maximal, characteristic, complemented
9	#10598864	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598863	C₂	1	1	yes	maximal, characteristic, complemented
11	#10598862	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598861	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598860	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598840	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
17	C₅×#431	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₅×#431	C₂²	1	1	yes	characteristic
20	#65214	C₂²	1	1	yes	characteristic
21	#65214	C₂²	1	1	yes	characteristic
22	#65214	C₂²	1	1	yes	characteristic
23	#65126	C₄	1	2	yes	—
24	#65124	C₄	1	2	yes	—
25	#65122	C₄	1	2	yes	—
26	#65122	C₄	1	2	yes	—
27	D₅×C₄⋊C₈	C₄	1	2	yes	—
28	D₅×C₄⋊C₈	C₄	1	2	yes	—
29	#65015	C₄	1	2	yes	—
30	D₅×C₂²⋊C₈	C₄	1	2	yes	—
31	D₅×C₂²⋊C₈	C₄	1	2	yes	—
32	#65008	C₄	1	2	yes	—
33	#65007	C₄	1	2	yes	—
34	#65007	C₄	1	2	yes	—
35	C₄×#676	C₂²	1	1	yes	characteristic
36	C₄×#676	C₂²	1	1	yes	characteristic
37	#64974	C₂²	1	1	yes	characteristic
38	#64974	C₂²	1	1	yes	characteristic
39	#64974	C₂²	1	1	yes	characteristic
40	#64974	C₂²	1	1	yes	characteristic
41	#64974	C₂²	1	1	yes	characteristic
42	#64974	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
47	C₅×#322	C₂²	1	1	yes	characteristic, complemented
48	C₅×#322	C₂²	1	1	yes	characteristic, complemented
49	C₅×#322	C₂²	1	1	yes	characteristic, complemented
50	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
51	#64675	C₂²	1	1	yes	characteristic, complemented
52	#64675	C₂²	1	1	yes	characteristic, complemented
53	#64675	C₂²	1	1	yes	characteristic, complemented
54	#64674	C₂²	1	1	yes	characteristic, complemented
55	#64674	C₂²	1	1	yes	characteristic, complemented
56	#64674	C₂²	1	1	yes	characteristic, complemented
57	#64674	C₂²	1	1	yes	characteristic, complemented
58	#64674	C₂²	1	1	yes	characteristic, complemented
59	#64674	C₂²	1	1	yes	characteristic, complemented
60	C₈×#168	C₂²	1	1	yes	characteristic, complemented
61	C₈×#168	C₂²	1	1	yes	characteristic, complemented
62	C₈×#168	C₂²	1	1	yes	characteristic, complemented
63	#17326	—	5	1	no	maximal, Sylow
64	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₂×#676	C₂×C₄	1	2	yes	—
72	C₂×#676	C₂×C₄	1	2	yes	—
73	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
74	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
75	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
76	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
77	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
79	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
80	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₅	C₂³	1	1	yes	characteristic
84	C₄²×D₅	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
86	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
89	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
90	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
91	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₂²⋊#168	C₂×C₄	1	2	yes	—
98	C₂²⋊#168	C₂×C₄	1	2	yes	—
99	C₂²⋊#168	C₂×C₄	1	2	yes	—
100	#3952	C₂×C₄	1	2	yes	—
101	#3952	C₂×C₄	1	2	yes	—
102	#3952	C₂×C₄	1	2	yes	—
103	#3952	C₂×C₄	1	2	yes	—
104	#3952	C₂×C₄	1	2	yes	—
105	#3952	C₂×C₄	1	2	yes	—
106	#3947	C₂×C₄	1	2	yes	—
107	#3947	C₂×C₄	1	2	yes	—
108	#3946	C₂×C₄	1	2	yes	—
109	#3946	C₂×C₄	1	2	yes	—
110	#3946	C₂×C₄	1	2	yes	—
111	#3946	C₂×C₄	1	2	yes	—
112	#3946	C₂×C₄	1	2	yes	—
113	#3946	C₂×C₄	1	2	yes	—
114	C₈×Dic₅	C₂×C₄	1	2	yes	—
115	C₈×Dic₅	C₂×C₄	1	2	yes	—
116	C₈×Dic₅	C₂×C₄	1	2	yes	—
117	C₈×Dic₅	C₂×C₄	1	2	yes	—
118	C₄⋊#168	C₂×C₄	1	2	yes	—
119	C₄⋊#168	C₂×C₄	1	2	yes	—
120	C₄⋊#168	C₂×C₄	1	2	yes	—
121	C₄×#168	C₂³	1	1	yes	characteristic
122	C₄×#168	C₂³	1	1	yes	characteristic
123	C₄×#168	C₂³	1	1	yes	characteristic
124	C₄×#168	C₂³	1	1	yes	characteristic
125	C₄×#168	C₂³	1	1	yes	characteristic
126	C₄×#168	C₂³	1	1	yes	characteristic
127	#2920	—	5	1	no	—
128	C₂×#431	—	5	1	no	—
129	C₂×#431	—	5	1	no	—
130	#1454	—	5	1	no	—
131	#1454	—	5	1	no	—
132	#1454	—	5	1	no	—
133	#1454	D₅	1	1	yes	characteristic, complemented
134	#1452	—	5	1	no	—
135	#1452	—	5	1	no	—
136	#1451	—	5	1	no	—
137	#1451	—	5	1	no	—
138	#1450	—	5	1	no	—
139	#1450	—	5	1	no	—
140	C₈×M₁₆	—	5	1	no	—
141	C₈×M₁₆	—	5	1	no	—
142	C₂³×D₅	C₄²	1	1	yes	characteristic
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×Dic₅	C₄²	1	1	yes	characteristic
147	C₂²×Dic₅	C₄²	1	1	yes	characteristic
148	C₂²×Dic₅	C₄²	1	1	yes	characteristic
149	C₂×C₄×D₅	—	2	4	no	—
150	C₂×C₄×D₅	—	2	4	no	—
151	C₂×C₄×D₅	—	4	2	no	—
152	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
153	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
154	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
155	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
156	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
157	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
170	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₅	C₂⁴	1	1	yes	characteristic
174	C₄×Dic₅	C₄²	1	1	yes	characteristic
175	C₄×Dic₅	C₄²	1	1	yes	characteristic
176	C₄×Dic₅	C₄²	1	1	yes	characteristic
177	C₄×Dic₅	C₄²	1	1	yes	characteristic
178	C₄×Dic₅	C₄²	1	1	yes	characteristic
179	C₄×Dic₅	C₄²	1	1	yes	characteristic
180	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
181	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
182	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
183	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
184	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
185	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
186	C₂×#168	C₂²×C₄	1	2	yes	—
187	C₂×#168	C₂²×C₄	1	2	yes	—
188	C₂×#168	C₂²×C₄	1	2	yes	—
189	C₂×#168	C₂²×C₄	1	2	yes	—
190	C₂×#168	C₂²×C₄	1	2	yes	—
191	C₂×#168	C₂²×C₄	1	2	yes	—
192	#676	—	2	4	no	—
193	#676	—	2	4	no	—
194	C₈×D₅	—	2	4	no	—
195	C₈×D₅	—	2	4	no	—
196	C₈×D₅	—	4	2	no	—
197	C₈×D₅	—	4	2	no	—
198	C₂²×C₄²	—	5	1	no	—
199	#432	—	5	2	no	—
200	#432	—	5	2	no	—
201	#431	—	5	1	no	—
202	#431	—	5	1	no	—
203	#431	—	5	1	no	—
204	#431	—	5	2	no	—
205	#431	—	5	2	no	—
206	#431	—	5	2	no	—
207	#431	—	5	2	no	—
208	#431	—	5	1	no	—
209	#431	—	5	1	no	—
210	#431	—	5	1	no	—
211	#431	—	5	1	no	—
212	#431	—	5	1	no	—
213	#431	—	5	1	no	—
214	#431	C₂×D₅	1	1	yes	characteristic
215	#431	C₂×D₅	1	1	yes	characteristic
216	#431	C₂×D₅	1	1	yes	characteristic
217	#423	—	5	2	no	—
218	C₂×C₄⋊C₈	—	5	2	no	—
219	C₂×C₄⋊C₈	—	5	2	no	—
220	#407	—	5	2	no	—
221	C₂×C₂²⋊C₈	—	5	2	no	—
222	C₂×C₂²⋊C₈	—	5	2	no	—
223	C₄×M₁₆	—	5	1	no	—
224	C₄×M₁₆	—	5	1	no	—
225	C₂×C₄×C₈	—	5	1	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂×C₄×C₈	—	5	1	no	—
228	C₂×C₄×C₈	—	5	1	no	—
229	#322	—	5	1	no	—
230	#322	—	5	1	no	—
231	#322	—	5	1	no	—
232	#322	—	5	1	no	—
233	#322	—	5	1	no	—
234	#322	—	5	1	no	—
235	#322	—	5	1	no	—
236	#322	—	5	1	no	—
237	#322	—	5	1	no	—
238	#322	C₂×D₅	1	1	yes	characteristic, complemented
239	#322	C₂×D₅	1	1	yes	characteristic, complemented
240	#322	C₂×D₅	1	1	yes	characteristic, complemented
241	C₈²	—	5	1	no	—
242	C₈²	—	5	1	no	—
243	C₈²	—	5	1	no	—
244	C₈²	C₂×D₅	1	1	yes	characteristic, complemented
245	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
246	C₂²×D₅	—	2	2	no	—
247	C₂²×D₅	—	2	2	no	—
248	C₂²×D₅	—	4	1	no	—
249	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
250	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	2	2	no	—
262	C₂×Dic₅	—	4	1	no	—
263	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
264	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
265	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
266	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
267	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
268	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
269	C₄×D₅	—	2	2	no	—
270	C₄×D₅	—	2	2	no	—
271	C₄×D₅	—	2	2	no	—
272	C₄×D₅	—	2	2	no	—
273	C₄×D₅	—	2	2	no	—
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	2	2	no	—
276	C₄×D₅	—	2	2	no	—
277	C₄×D₅	—	4	1	no	—
278	C₄×D₅	—	4	1	no	—
279	C₄×D₅	#131	1	4	yes	—
280	C₄×D₅	#131	1	4	yes	—
281	C₅×C₈	—	2	2	no	—
282	C₅×C₈	—	2	2	no	—
283	C₅×C₈	—	2	2	no	—
284	C₅×C₈	—	2	2	no	—
285	C₅×C₈	—	2	2	no	—
286	C₅×C₈	—	2	2	no	—
287	#168	—	2	2	no	—
288	#168	—	2	2	no	—
289	#168	—	2	2	no	—
290	#168	—	2	2	no	—
291	#168	—	2	2	no	—
292	#168	—	2	2	no	—
293	C₂³×C₄	—	5	1	no	—
294	C₂³×C₄	—	5	1	no	—
295	C₂³×C₄	—	5	1	no	—
296	C₂×M₁₆	—	5	2	no	—
297	C₂×M₁₆	—	5	2	no	—
298	C₂²×C₈	—	5	2	no	—
299	C₂²×C₈	—	5	2	no	—
300	C₂²×C₈	—	5	2	no	—
301	C₂²×C₈	—	5	2	no	—
302	C₂×C₄²	—	5	1	no	—
303	C₂×C₄²	—	5	1	no	—
304	C₂×C₄²	—	5	1	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₂×C₄²	—	5	1	no	—
307	C₂×C₄²	—	5	1	no	—
308	C₂×C₄²	—	5	1	no	—
309	C₂×C₄²	—	5	1	no	—
310	C₂×C₄²	—	5	1	no	—
311	C₂×C₄²	—	5	1	no	—
312	C₂×C₄²	—	5	1	no	—
313	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
314	C₄⋊C₈	—	5	2	no	—
315	C₄⋊C₈	—	5	2	no	—
316	C₄⋊C₈	—	5	2	no	—
317	C₄⋊C₈	—	5	2	no	—
318	C₄⋊C₈	—	5	2	no	—
319	C₄⋊C₈	—	5	2	no	—
320	C₄⋊C₈	—	5	2	no	—
321	C₄⋊C₈	—	5	2	no	—
322	C₄⋊C₈	—	5	2	no	—
323	C₄⋊C₈	C₄×D₅	1	2	yes	—
324	C₄⋊C₈	C₄×D₅	1	2	yes	—
325	C₄⋊C₈	C₄×D₅	1	2	yes	—
326	C₂²⋊C₈	—	5	2	no	—
327	C₂²⋊C₈	—	5	2	no	—
328	C₂²⋊C₈	—	5	2	no	—
329	C₂²⋊C₈	—	5	2	no	—
330	C₂²⋊C₈	—	5	2	no	—
331	C₂²⋊C₈	—	5	2	no	—
332	C₂²⋊C₈	—	5	2	no	—
333	C₂²⋊C₈	—	5	2	no	—
334	C₂²⋊C₈	—	5	2	no	—
335	C₂²⋊C₈	C₄×D₅	1	2	yes	—
336	C₂²⋊C₈	C₄×D₅	1	2	yes	—
337	C₂²⋊C₈	C₄×D₅	1	2	yes	—
338	#97	—	5	2	no	—
339	#97	—	5	2	no	—
340	C₄×C₈	—	5	2	no	—
341	C₄×C₈	—	5	2	no	—
342	C₄×C₈	—	5	2	no	—
343	C₄×C₈	—	5	2	no	—
344	C₄×C₈	—	5	1	no	—
345	C₄×C₈	—	5	1	no	—
346	C₄×C₈	—	5	1	no	—
347	C₄×C₈	—	5	1	no	—
348	C₄×C₈	—	5	1	no	—
349	C₄×C₈	—	5	1	no	—
350	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
351	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
352	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
353	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
354	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
356	C₂²×C₅	—	2	1	no	—
357	C₂²×C₅	—	2	1	no	—
358	C₂²×C₅	—	2	1	no	—
359	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
360	C₂×D₅	—	2	1	no	—
361	C₂×D₅	—	2	1	no	—
362	C₂×D₅	—	2	1	no	—
363	C₂×D₅	—	2	1	no	—
364	C₂×D₅	—	4	4	no	—
365	C₂×D₅	#405	1	2	yes	—
366	C₂×D₅	#405	1	2	yes	—
367	C₄×C₅	—	2	1	no	—
368	C₄×C₅	—	2	1	no	—
369	C₄×C₅	—	2	1	no	—
370	C₄×C₅	C₂×#131	1	2	yes	—
371	C₄×C₅	C₂×#131	1	2	yes	—
372	C₄×C₅	#568	1	2	yes	—
373	Dic₅	—	2	1	no	—
374	Dic₅	—	2	1	no	—
375	Dic₅	—	2	1	no	—
376	Dic₅	—	2	1	no	—
377	Dic₅	#405	1	2	yes	—
378	Dic₅	#405	1	2	yes	—
379	C₂⁴	—	5	1	no	—
380	C₂²×C₄	—	5	1	no	—
381	C₂²×C₄	—	5	1	no	—
382	C₂²×C₄	—	5	1	no	—
383	C₂²×C₄	—	5	1	no	—
384	C₂²×C₄	—	5	1	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	C₂²×C₄	—	5	1	no	—
388	C₂²×C₄	—	5	1	no	—
389	C₂²×C₄	—	5	1	no	—
390	C₂²×C₄	—	5	1	no	—
391	C₂²×C₄	—	5	1	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	5	1	no	—
394	C₂²×C₄	—	5	1	no	—
395	C₂²×C₄	—	10	4	no	—
396	C₂²×C₄	—	10	4	no	—
397	C₂²×C₄	—	20	2	no	—
398	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
401	M₁₆	—	10	4	no	—
402	M₁₆	—	10	4	no	—
403	C₂×C₈	—	5	2	no	—
404	C₂×C₈	—	5	2	no	—
405	C₂×C₈	—	5	2	no	—
406	C₂×C₈	—	5	2	no	—
407	C₂×C₈	—	5	2	no	—
408	C₂×C₈	—	5	2	no	—
409	C₂×C₈	—	10	4	no	—
410	C₂×C₈	—	10	4	no	—
411	C₂×C₈	—	20	2	no	—
412	C₂×C₈	—	20	2	no	—
413	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
414	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
415	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
419	C₄²	—	5	1	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	1	no	—
422	C₄²	—	5	1	no	—
423	C₄²	—	5	1	no	—
424	C₄²	—	5	1	no	—
425	C₄²	—	5	1	no	—
426	C₄²	—	5	1	no	—
427	C₄²	—	5	1	no	—
428	C₄²	—	5	1	no	—
429	C₄²	—	5	1	no	—
430	C₄²	—	5	1	no	—
431	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
432	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
433	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
434	C₄²	C₂³×D₅	1	1	yes	characteristic
435	C₂×C₅	—	4	1	no	—
436	C₂×C₅	C₂×#405	1	1	yes	characteristic
437	C₂×C₅	C₂×#405	1	1	yes	characteristic
438	C₂×C₅	#2873	1	1	yes	characteristic
439	D₅	—	2	2	no	—
440	D₅	—	2	2	no	—
441	C₂³	—	5	1	no	—
442	C₂³	—	5	1	no	—
443	C₂³	—	10	2	no	—
444	C₂³	—	10	2	no	—
445	C₂³	—	20	1	no	—
446	C₂³	C₄²×D₅	1	1	yes	characteristic
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	5	1	no	—
451	C₂×C₄	—	5	1	no	—
452	C₂×C₄	—	5	4	no	—
453	C₂×C₄	—	5	4	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	1	no	—
456	C₂×C₄	—	5	1	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	10	2	no	—
459	C₂×C₄	—	10	2	no	—
460	C₂×C₄	—	10	2	no	—
461	C₂×C₄	—	10	2	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	10	2	no	—
464	C₂×C₄	—	10	2	no	—
465	C₂×C₄	—	10	2	no	—
466	C₂×C₄	—	10	2	no	—
467	C₂×C₄	—	10	2	no	—
468	C₂×C₄	—	20	1	no	—
469	C₂×C₄	—	20	1	no	—
470	C₂×C₄	—	20	1	no	—
471	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
472	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
473	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
474	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
475	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	2	2	no	—
483	C₈	—	10	2	no	—
484	C₈	—	10	2	no	—
485	C₈	—	10	2	no	—
486	C₈	—	10	2	no	—
487	C₈	—	10	2	no	—
488	C₈	—	10	2	no	—
489	C₅	#17326	1	1	yes	characteristic, complemented, Sylow
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	5	2	no	—
494	C₂²	—	5	2	no	—
495	C₂²	—	10	1	no	—
496	C₂²	—	10	1	no	—
497	C₂²	—	10	1	no	—
498	C₂²	—	10	1	no	—
499	C₂²	—	20	4	no	—
500	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	5	2	no	—
505	C₄	—	5	2	no	—
506	C₄	—	10	1	no	—
507	C₄	—	10	1	no	—
508	C₄	—	10	1	no	—
509	C₄	—	10	1	no	—
510	C₄	D₅×#131	1	2	yes	—
511	C₄	D₅×#131	1	2	yes	—
512	C₄	#66084	1	2	yes	—
513	C₂	—	4	1	no	—
514	C₂	—	10	2	no	—
515	C₂	—	10	2	no	—
516	C₂	D₅×#405	1	1	yes	characteristic
517	C₂	D₅×#405	1	1	yes	characteristic
518	C₂	#10610279	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#1454	C₂
prime radical	C₂³×D₅	C₄²
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1454	D₅
hypocenter	C₅	#17326
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #1454

Complements

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

N	H ≅ G/N	type
4. C₅×#1454	C₂	semidirect
5. #10601537	C₂	semidirect
6. #10601537	C₂	semidirect
7. #10601537	C₂	semidirect
8. #10598864	C₂	semidirect
9. #10598864	C₂	semidirect
10. #10598863	C₂	semidirect
11. #10598862	C₂	semidirect
12. #10598861	C₂	semidirect
13. #10598860	C₂	semidirect
14. #10598840	C₂	semidirect
15. C₈×#676	C₂	semidirect
47. C₅×#322	C₂²	semidirect
48. C₅×#322	C₂²	semidirect
49. C₅×#322	C₂²	semidirect
50. C₅×C₈²	C₂²	semidirect
51. #64675	C₂²	semidirect
52. #64675	C₂²	semidirect
53. #64675	C₂²	semidirect
54. #64674	C₂²	semidirect
55. #64674	C₂²	semidirect
56. #64674	C₂²	semidirect
57. #64674	C₂²	semidirect
58. #64674	C₂²	semidirect
59. #64674	C₂²	semidirect
60. C₈×#168	C₂²	semidirect
61. C₈×#168	C₂²	semidirect
62. C₈×#168	C₂²	semidirect
133. #1454	D₅	semidirect
238. #322	C₂×D₅	semidirect
239. #322	C₂×D₅	semidirect
240. #322	C₂×D₅	semidirect
244. C₈²	C₂×D₅	semidirect
489. C₅	#17326	semidirect

Maximal subgroups

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

subgroup	index
#10611013	2
D₅×#431	2
C₅×#1454	2
#10601537	2
#10598864	2
#10598863	2
#10598862	2
#10598861	2
#10598860	2
#10598840	2
C₈×#676	2
#17326	5