Subgroups — #12065019

Order 1280.

814 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611009	C₂	1	1	yes	maximal, characteristic
2	#10610254	C₂	1	1	yes	maximal, characteristic
3	C₄×#4047	C₂	1	1	yes	maximal, characteristic
4	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601536	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598868	C₂	1	1	yes	maximal, characteristic, complemented
9	#10598865	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	#10598840	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4047	C₄	1	2	yes	—
17	C₄×#709	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	#65417	C₄	1	2	yes	—
22	#65416	C₄	1	2	yes	—
23	#65390	C₄	1	2	yes	—
24	#65214	C₂²	1	1	yes	characteristic
25	C₄×#681	C₂²	1	1	yes	characteristic
26	C₄×#681	C₂²	1	1	yes	characteristic
27	#65125	C₄	1	2	yes	—
28	#65117	C₄	1	2	yes	—
29	#65018	C₄	1	2	yes	—
30	#65017	C₄	1	2	yes	—
31	#64995	C₄	1	2	yes	—
32	#64990	C₄	1	2	yes	—
33	#64978	C₄	1	2	yes	—
34	#64978	C₄	1	2	yes	—
35	C₄×#676	C₂²	1	1	yes	characteristic
36	C₄×#676	C₂²	1	1	yes	characteristic
37	C₄×#676	C₂²	1	1	yes	characteristic
38	C₄×#676	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
48	C₅×#322	C₂²	1	1	yes	characteristic
49	C₅×C₈²	C₂²	1	1	yes	characteristic
50	C₅×C₈²	C₂²	1	1	yes	characteristic
51	#64675	C₂²	1	1	yes	characteristic
52	#64675	C₂²	1	1	yes	characteristic
53	#64674	C₂²	1	1	yes	characteristic
54	#64674	C₂²	1	1	yes	characteristic
55	#64674	C₂²	1	1	yes	characteristic
56	#64674	C₂²	1	1	yes	characteristic
57	#64674	C₂²	1	1	yes	characteristic
58	#64674	C₂²	1	1	yes	characteristic
59	C₈×#168	C₂²	1	1	yes	characteristic
60	C₈×#168	C₂²	1	1	yes	characteristic
61	C₈×#168	C₂²	1	1	yes	characteristic
62	C₈×#168	C₂²	1	1	yes	characteristic
63	#17335	—	5	1	no	maximal, Sylow
64	C₂×#709	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
66	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
71	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
72	#4072	C₂×C₄	1	1	yes	characteristic
73	C₂×#681	C₂×C₄	1	2	yes	—
74	C₂×#681	C₂×C₄	1	2	yes	—
75	#4047	—	2	8	no	—
76	C₂×#676	C₂×C₄	1	2	yes	—
77	C₂×#676	C₂×C₄	1	2	yes	—
78	C₂×#676	C₂×C₄	1	2	yes	—
79	C₂×#676	C₂×C₄	1	2	yes	—
80	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
81	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
82	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
83	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
84	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
85	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
86	#4018	C₂×C₄	1	1	yes	characteristic
87	#4018	C₂×C₄	1	1	yes	characteristic
88	C₄²×D₅	C₂³	1	1	yes	characteristic
89	C₄²×D₅	C₂³	1	1	yes	characteristic
90	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
92	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
93	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₅×#97	C₂×C₄	1	2	yes	—
95	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂²⋊#168	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	#3952	C₂×C₄	1	2	yes	—
107	#3947	C₂×C₄	1	2	yes	—
108	#3947	C₂×C₄	1	2	yes	—
109	#3947	C₂×C₄	1	2	yes	—
110	#3947	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	#3946	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	C₈×Dic₅	C₂×C₄	1	2	yes	—
119	C₄⋊#168	C₂×C₄	1	2	yes	—
120	#3935	C₂×C₄	1	2	yes	—
121	#3935	C₂×C₄	1	2	yes	—
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	C₄×#168	C₂³	1	1	yes	characteristic
128	#2965	—	5	1	no	—
129	#2965	—	5	1	no	—
130	C₄×#131	—	5	1	no	—
131	#1455	—	5	1	no	—
132	#1455	—	5	1	no	—
133	#1453	—	5	1	no	—
134	#1453	—	5	1	no	—
135	#1451	—	5	1	no	—
136	#1451	—	5	1	no	—
137	#1450	—	5	1	no	—
138	C₈×M₁₆	—	5	1	no	—
139	C₈×M₁₆	—	5	1	no	—
140	C₈×M₁₆	—	5	1	no	—
141	C₈×M₁₆	D₅	1	1	yes	characteristic, complemented
142	C₂×C₈²	—	5	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	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
148	#709	—	2	4	no	—
149	C₂×D₂₀	C₄²	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
156	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
157	C₅×M₁₆	—	2	4	no	—
158	C₂×C₅×C₈	—	2	4	no	—
159	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
160	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
161	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
163	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
164	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
165	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₅	C₂⁴	1	1	yes	characteristic
169	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
170	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
171	#685	C₄²	1	1	yes	characteristic
172	#685	C₄²	1	1	yes	characteristic
173	#685	C₄²	1	1	yes	characteristic
174	#685	C₄²	1	1	yes	characteristic
175	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
176	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
177	#683	C₄²	1	1	yes	characteristic
178	#683	C₄²	1	1	yes	characteristic
179	#683	C₄²	1	1	yes	characteristic
180	#683	C₄²	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	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
187	#681	—	2	4	no	—
188	#681	—	2	4	no	—
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	C₂×#168	C₂²×C₄	1	2	yes	—
193	C₂×#168	C₂²×C₄	1	2	yes	—
194	C₂×#168	C₂²×C₄	1	2	yes	—
195	#676	—	2	4	no	—
196	#676	—	2	4	no	—
197	#676	—	2	4	no	—
198	#676	—	2	4	no	—
199	C₈×D₅	—	2	4	no	—
200	C₈×D₅	—	2	4	no	—
201	C₈×D₅	—	2	4	no	—
202	C₈×D₅	M₁₆	1	8	yes	complemented
203	C₂×#131	—	5	2	no	—
204	C₄×#41	—	5	1	no	—
205	#446	—	5	2	no	—
206	#446	—	5	2	no	—
207	#436	—	5	2	no	—
208	#436	—	5	2	no	—
209	#435	—	5	2	no	—
210	#435	—	5	2	no	—
211	#435	—	5	2	no	—
212	#435	—	5	2	no	—
213	#431	—	5	1	no	—
214	#431	—	5	1	no	—
215	#431	—	5	1	no	—
216	#431	—	5	1	no	—
217	#431	—	5	1	no	—
218	#431	C₂×D₅	1	1	yes	characteristic
219	#405	—	5	2	no	—
220	#405	—	5	2	no	—
221	#405	—	5	2	no	—
222	C₄×M₁₆	—	5	1	no	—
223	C₄×M₁₆	—	5	1	no	—
224	C₄×M₁₆	—	5	1	no	—
225	C₄×M₁₆	—	5	1	no	—
226	C₄×M₁₆	—	5	1	no	—
227	C₄×M₁₆	—	5	1	no	—
228	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
229	C₂×C₄×C₈	—	5	1	no	—
230	C₂×C₄×C₈	—	5	1	no	—
231	C₂×C₄×C₈	—	5	1	no	—
232	C₂×C₄×C₈	—	5	1	no	—
233	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
234	#322	—	5	1	no	—
235	#322	—	5	1	no	—
236	#322	—	5	1	no	—
237	#322	—	5	1	no	—
238	#322	—	5	1	no	—
239	#322	—	5	1	no	—
240	#322	—	5	1	no	—
241	#322	—	5	1	no	—
242	#322	C₂×D₅	1	1	yes	characteristic
243	#322	C₂×D₅	1	1	yes	characteristic
244	C₈²	—	5	1	no	—
245	C₈²	—	5	1	no	—
246	C₈²	—	5	1	no	—
247	C₈²	—	5	1	no	—
248	C₈²	C₂×D₅	1	1	yes	characteristic
249	C₈²	C₂×D₅	1	1	yes	characteristic
250	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
251	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
252	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
262	C₂²⋊D₅	—	2	2	no	—
263	C₂²⋊D₅	—	2	2	no	—
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	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
270	D₂₀	—	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	C₂×M₁₆	1	4	yes	—
277	Dic₁₀	—	2	2	no	—
278	C₅×C₈	—	2	2	no	—
279	C₅×C₈	—	2	2	no	—
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	2	2	no	—
282	C₅×C₈	C₂×M₁₆	1	4	yes	—
283	C₅×C₈	#131	1	4	yes	complemented
284	#168	—	2	2	no	—
285	#168	—	2	2	no	—
286	#168	—	2	2	no	—
287	#168	—	2	2	no	—
288	#168	C₂×M₁₆	1	4	yes	—
289	#168	#131	1	4	yes	complemented
290	C₂×#41	—	5	1	no	—
291	#131	—	10	8	no	—
292	C₂×M₁₆	—	5	2	no	—
293	C₂×M₁₆	—	5	2	no	—
294	C₂×M₁₆	—	5	2	no	—
295	C₂×M₁₆	—	5	2	no	—
296	C₂×M₁₆	—	5	2	no	—
297	C₂×M₁₆	—	5	2	no	—
298	C₂×M₁₆	C₄×D₅	1	2	yes	—
299	C₂²×C₈	—	5	2	no	—
300	C₂²×C₈	—	5	2	no	—
301	C₂²×C₈	—	5	2	no	—
302	C₂²×C₈	—	5	2	no	—
303	C₂²×C₈	C₄×D₅	1	2	yes	—
304	C₄×Q₈	—	5	1	no	—
305	C₄×Q₈	—	5	1	no	—
306	C₄×D₄	—	5	1	no	—
307	C₄×D₄	—	5	1	no	—
308	C₄×D₄	—	5	1	no	—
309	C₄×D₄	—	5	1	no	—
310	C₄×D₄	—	5	1	no	—
311	C₄×D₄	—	5	1	no	—
312	#117	—	5	1	no	—
313	#117	—	5	1	no	—
314	#117	—	5	1	no	—
315	C₂×C₄²	—	5	1	no	—
316	C₂×C₄²	—	5	1	no	—
317	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
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	C₂²⋊C₈	—	5	2	no	—
325	C₂²⋊C₈	—	5	2	no	—
326	C₂²⋊C₈	—	5	2	no	—
327	C₂²⋊C₈	—	5	2	no	—
328	C₂²⋊C₈	—	5	2	no	—
329	C₂²⋊C₈	C₄×D₅	1	2	yes	—
330	#97	—	5	2	no	—
331	#97	—	5	2	no	—
332	#97	—	5	2	no	—
333	#97	—	5	2	no	—
334	#97	—	5	2	no	—
335	#97	—	5	2	no	—
336	#97	C₄×D₅	1	2	yes	—
337	C₄×C₈	—	5	2	no	—
338	C₄×C₈	—	5	2	no	—
339	C₄×C₈	—	5	2	no	—
340	C₄×C₈	—	5	2	no	—
341	C₄×C₈	—	5	1	no	—
342	C₄×C₈	—	5	1	no	—
343	C₄×C₈	—	5	1	no	—
344	C₄×C₈	—	5	1	no	—
345	C₄×C₈	—	5	1	no	—
346	C₄×C₈	—	5	1	no	—
347	C₄×C₈	C₄×D₅	1	2	yes	—
348	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
349	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
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	C₂²×C₅	—	2	1	no	—
355	C₂²×C₅	—	2	1	no	—
356	C₂²×C₅	—	2	1	no	—
357	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
358	C₂×D₅	—	2	1	no	—
359	C₂×D₅	—	2	1	no	—
360	C₂×D₅	—	2	1	no	—
361	C₂×D₅	—	2	1	no	—
362	C₂×D₅	—	2	1	no	—
363	C₂×D₅	C₄×M₁₆	1	2	yes	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	1	no	—
367	C₄×C₅	C₂²×M₁₆	1	2	yes	—
368	C₄×C₅	C₂×#131	1	2	yes	—
369	C₄×C₅	C₂×#131	1	2	yes	—
370	Dic₅	—	2	1	no	—
371	Dic₅	—	2	1	no	—
372	Dic₅	—	2	1	no	—
373	Dic₅	—	2	1	no	—
374	Dic₅	—	2	1	no	—
375	Dic₅	C₄×M₁₆	1	2	yes	—
376	#41	—	10	4	no	—
377	C₂×Q₈	—	5	1	no	—
378	C₂×D₄	—	5	1	no	—
379	C₂×D₄	—	5	1	no	—
380	C₂×D₄	—	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	C₂×C₄×D₅	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
390	M₁₆	—	2	4	no	—
391	M₁₆	—	10	4	no	—
392	M₁₆	—	10	4	no	—
393	M₁₆	—	10	4	no	—
394	M₁₆	—	10	4	no	—
395	M₁₆	—	10	4	no	—
396	M₁₆	—	10	4	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	5	2	no	—
399	C₂×C₈	—	5	2	no	—
400	C₂×C₈	—	5	8	no	—
401	C₂×C₈	—	5	2	no	—
402	C₂×C₈	—	5	2	no	—
403	C₂×C₈	—	5	2	no	—
404	C₂×C₈	—	5	2	no	—
405	C₂×C₈	—	10	4	no	—
406	C₂×C₈	—	10	4	no	—
407	C₂×C₈	—	10	4	no	—
408	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
410	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
411	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
412	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
413	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
414	C₄⋊C₄	—	5	1	no	—
415	C₄⋊C₄	—	5	1	no	—
416	C₄⋊C₄	—	5	1	no	—
417	C₄⋊C₄	—	5	1	no	—
418	C₄⋊C₄	—	5	1	no	—
419	C₄⋊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	—	5	1	no	—
425	C₂²⋊C₄	—	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	—	5	1	no	—
432	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
433	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
434	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
435	C₄²	C₂³×D₅	1	1	yes	characteristic
436	C₂×C₅	—	4	1	no	—
437	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
438	C₂×C₅	C₄×#131	1	1	yes	characteristic
439	C₂×C₅	C₄×#131	1	1	yes	characteristic
440	D₅	—	2	2	no	—
441	D₅	—	4	1	no	—
442	C₂³	—	5	1	no	—
443	C₂³	—	5	1	no	—
444	C₂³	C₄²×D₅	1	1	yes	characteristic
445	Q₈	—	10	2	no	—
446	D₄	—	10	2	no	—
447	D₄	—	10	2	no	—
448	D₄	—	10	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	5	1	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	—	5	1	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	C₄²×D₅	1	1	yes	characteristic
465	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
466	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
468	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
470	C₈	—	2	2	no	—
471	C₈	—	2	2	no	—
472	C₈	—	2	2	no	—
473	C₈	—	2	2	no	—
474	C₈	—	5	4	no	—
475	C₈	—	5	4	no	—
476	C₈	—	10	2	no	—
477	C₈	—	10	2	no	—
478	C₈	—	10	2	no	—
479	C₈	—	10	2	no	—
480	C₈	#4047	1	4	yes	complemented
481	C₈	D₅×M₁₆	1	4	yes	—
482	C₅	#17335	1	1	yes	characteristic, complemented, Sylow
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	5	2	no	—
487	C₂²	—	10	1	no	—
488	C₂²	—	10	1	no	—
489	C₂²	—	10	1	no	—
490	C₂²	—	10	1	no	—
491	C₂²	—	10	1	no	—
492	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	5	2	no	—
497	C₄	—	10	1	no	—
498	C₄	—	10	1	no	—
499	C₄	—	10	1	no	—
500	C₄	—	10	1	no	—
501	C₄	—	10	1	no	—
502	C₄	C₂×#4047	1	2	yes	—
503	C₄	C₂×D₅×M₁₆	1	2	yes	—
504	C₄	D₅×#131	1	2	yes	—
505	C₂	—	4	1	no	—
506	C₂	—	10	2	no	—
507	C₂	—	20	1	no	—
508	C₂	C₄×#4047	1	1	yes	characteristic
509	C₂	C₄×D₅×M₁₆	1	1	yes	characteristic
510	C₂	#10610280	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Frattini	C₄²	C₂³×D₅
Fitting	C₅×C₈×M₁₆	C₂
prime radical	C₂×#709	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₈×M₁₆	D₅
hypocenter	C₅	#17335
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₅×C₈×M₁₆	C₂	semidirect
5. #10601536	C₂	semidirect
6. #10600642	C₂	semidirect
7. C₈×#681	C₂	semidirect
8. #10598868	C₂	semidirect
9. #10598865	C₂	semidirect
10. #10598863	C₂	semidirect
11. #10598862	C₂	semidirect
12. #10598840	C₂	semidirect
13. C₈×#676	C₂	semidirect
14. C₈×#676	C₂	semidirect
15. C₈²×D₅	C₂	semidirect
141. C₈×M₁₆	D₅	semidirect
202. C₈×D₅	M₁₆	semidirect
283. C₅×C₈	#131	semidirect
289. #168	#131	semidirect
480. C₈	#4047	semidirect
482. C₅	#17335	semidirect

Maximal subgroups

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

subgroup	index
#10611009	2
#10610254	2
C₄×#4047	2
C₅×C₈×M₁₆	2
#10601536	2
#10600642	2
C₈×#681	2
#10598868	2
#10598865	2
#10598863	2
#10598862	2
#10598840	2
C₈×#676	2
C₈²×D₅	2
#17335	5