Subgroups — #12065054

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2922	C₂	1	1	yes	maximal, characteristic
2	#10614248	C₂	1	1	yes	maximal, characteristic
3	#10614248	C₂	1	1	yes	maximal, characteristic
4	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601536	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601536	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601535	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601534	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601533	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601532	C₂	1	1	yes	maximal, characteristic, complemented
12	#10600642	C₂	1	1	yes	maximal, characteristic, complemented
13	#10600641	C₂	1	1	yes	maximal, characteristic, complemented
14	#10600518	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₅×#433	C₄	1	2	yes	—
18	C₅×#433	C₄	1	2	yes	—
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₅×#431	C₂²	1	1	yes	characteristic
21	C₅×#431	C₂²	1	1	yes	characteristic
22	C₅×#431	C₂²	1	1	yes	characteristic
23	C₅×#424	C₄	1	2	yes	—
24	C₅×#408	C₄	1	2	yes	—
25	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	#65313	C₄	1	2	yes	—
28	#65313	C₄	1	2	yes	—
29	#65301	C₄	1	2	yes	—
30	#65301	C₄	1	2	yes	—
31	#65300	C₄	1	2	yes	—
32	#65300	C₄	1	2	yes	—
33	#65300	C₄	1	2	yes	—
34	#65300	C₄	1	2	yes	—
35	#65214	C₂²	1	1	yes	characteristic
36	#65214	C₂²	1	1	yes	characteristic
37	#65214	C₂²	1	1	yes	characteristic
38	#65214	C₂²	1	1	yes	characteristic
39	#65214	C₂²	1	1	yes	characteristic
40	#65214	C₂²	1	1	yes	characteristic
41	C₄×#681	C₂²	1	1	yes	characteristic
42	C₄×#681	C₂²	1	1	yes	characteristic
43	C₄×#681	C₂²	1	1	yes	characteristic
44	C₄×#681	C₂²	1	1	yes	characteristic
45	C₂×C₄×#168	C₂²	1	1	yes	characteristic
46	C₂×C₄×#168	C₂²	1	1	yes	characteristic
47	#64675	C₂²	1	1	yes	characteristic
48	#64675	C₂²	1	1	yes	characteristic
49	#64675	C₂²	1	1	yes	characteristic
50	#64675	C₂²	1	1	yes	characteristic
51	#64674	C₂²	1	1	yes	characteristic
52	#64674	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	#17340	—	5	1	no	maximal, Sylow
64	C₂×C₅×#41	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	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
70	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
71	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
75	C₅×#117	C₂×C₄	1	1	yes	characteristic
76	C₅×#117	C₂×C₄	1	1	yes	characteristic
77	C₅×#117	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×#681	C₂×C₄	1	2	yes	—
82	C₂×#681	C₂×C₄	1	2	yes	—
83	C₂×#681	C₂×C₄	1	2	yes	—
84	C₂×#681	C₂×C₄	1	2	yes	—
85	C₂²×#168	C₂×C₄	1	2	yes	—
86	C₂²×#168	C₂×C₄	1	2	yes	—
87	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
89	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
90	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
95	C₅×#97	C₂×C₄	1	2	yes	—
96	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
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	C₂²⋊#168	C₂×C₄	1	2	yes	—
102	C₂²⋊#168	C₂×C₄	1	2	yes	—
103	C₂²⋊#168	C₂×C₄	1	2	yes	—
104	C₂²⋊#168	C₂×C₄	1	2	yes	—
105	C₂²⋊#168	C₂×C₄	1	2	yes	—
106	C₂²⋊#168	C₂×C₄	1	2	yes	—
107	C₄⋊#168	C₂×C₄	1	2	yes	—
108	C₄⋊#168	C₂×C₄	1	2	yes	—
109	C₄⋊#168	C₂×C₄	1	2	yes	—
110	C₄⋊#168	C₂×C₄	1	2	yes	—
111	C₄⋊#168	C₂×C₄	1	2	yes	—
112	C₄⋊#168	C₂×C₄	1	2	yes	—
113	#3935	C₂×C₄	1	2	yes	—
114	#3935	C₂×C₄	1	2	yes	—
115	#3935	C₂×C₄	1	2	yes	—
116	#3935	C₂×C₄	1	2	yes	—
117	C₄×#168	C₂×C₄	1	2	yes	—
118	C₄×#168	C₂×C₄	1	2	yes	—
119	C₄×#168	C₂³	1	1	yes	characteristic
120	C₄×#168	C₂³	1	1	yes	characteristic
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	#2965	—	5	1	no	—
128	#2965	—	5	1	no	—
129	#2922	D₅	1	1	yes	characteristic
130	#1455	—	5	1	no	—
131	#1454	—	5	1	no	—
132	#1454	—	5	1	no	—
133	#1453	—	5	1	no	—
134	#1453	—	5	1	no	—
135	#1453	—	5	1	no	—
136	#1452	—	5	1	no	—
137	#1451	—	5	1	no	—
138	#1451	—	5	1	no	—
139	#1450	—	5	1	no	—
140	C₈×M₁₆	—	5	1	no	—
141	C₈×M₁₆	—	5	1	no	—
142	C₅×#41	—	4	2	no	—
143	C₂×C₅×Q₈	C₄²	1	1	yes	characteristic
144	C₂×C₅×D₄	C₄²	1	1	yes	characteristic
145	C₂×C₅×D₄	C₄²	1	1	yes	characteristic
146	C₂×C₅×D₄	C₄²	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₅×M₁₆	—	4	2	no	—
157	C₂×C₅×C₈	—	4	2	no	—
158	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
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	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
165	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
166	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
168	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
172	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
173	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
174	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂⁴	1	1	yes	characteristic
184	#681	—	2	4	no	—
185	#681	—	2	4	no	—
186	#681	—	4	2	no	—
187	#681	—	4	2	no	—
188	C₂×#168	—	2	4	no	—
189	C₂×#168	—	4	2	no	—
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	C₂×#168	C₂²×C₄	1	2	yes	—
196	C₂×#168	C₂²×C₄	1	2	yes	—
197	C₂×#168	C₂²×C₄	1	2	yes	—
198	C₄×#41	C₂×D₅	1	1	yes	characteristic
199	#446	—	5	2	no	—
200	#446	—	5	2	no	—
201	#436	—	5	2	no	—
202	#436	—	5	2	no	—
203	#435	—	5	2	no	—
204	#435	—	5	2	no	—
205	#435	—	5	2	no	—
206	#435	—	5	2	no	—
207	#433	Dic₅	1	2	yes	—
208	#433	Dic₅	1	2	yes	—
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	—	5	1	no	—
215	#431	C₂×D₅	1	1	yes	characteristic
216	#431	C₂×D₅	1	1	yes	characteristic
217	#431	C₂×D₅	1	1	yes	characteristic
218	#431	C₂×D₅	1	1	yes	characteristic
219	#424	Dic₅	1	2	yes	—
220	#408	Dic₅	1	2	yes	—
221	C₄×M₁₆	—	5	1	no	—
222	C₄×M₁₆	—	5	1	no	—
223	C₄×M₁₆	—	5	1	no	—
224	C₄×M₁₆	—	5	1	no	—
225	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂×C₄×C₈	—	5	1	no	—
228	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
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	—	5	1	no	—
239	#322	—	5	1	no	—
240	#322	—	5	1	no	—
241	C₈²	—	5	1	no	—
242	C₈²	—	5	1	no	—
243	C₈²	—	5	1	no	—
244	C₈²	—	5	1	no	—
245	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
246	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
247	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
248	C₅×Q₈	—	4	1	no	—
249	C₅×D₄	—	4	1	no	—
250	C₅×D₄	—	4	1	no	—
251	C₅×D₄	—	4	1	no	—
252	C₂×C₄×C₅	—	2	2	no	—
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	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
273	C₅×C₈	—	2	2	no	—
274	C₅×C₈	—	2	2	no	—
275	C₅×C₈	—	2	2	no	—
276	C₅×C₈	—	2	2	no	—
277	#168	—	2	2	no	—
278	#168	—	2	2	no	—
279	#168	—	2	2	no	—
280	#168	—	2	2	no	—
281	#168	—	2	2	no	—
282	#168	—	2	2	no	—
283	#168	—	2	2	no	—
284	#168	#131	1	4	yes	—
285	C₂×#41	C₂×Dic₅	1	1	yes	characteristic
286	C₂×M₁₆	—	5	2	no	—
287	C₂×M₁₆	—	5	2	no	—
288	C₂×M₁₆	—	5	2	no	—
289	C₂×M₁₆	—	5	2	no	—
290	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
291	C₂²×C₈	—	5	2	no	—
292	C₂²×C₈	—	5	2	no	—
293	C₂²×C₈	C₂×Dic₅	1	2	yes	—
294	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
295	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
296	C₄×D₄	C₄×D₅	1	1	yes	characteristic
297	C₄×D₄	C₄×D₅	1	1	yes	characteristic
298	C₄×D₄	C₄×D₅	1	1	yes	characteristic
299	C₄×D₄	C₄×D₅	1	1	yes	characteristic
300	C₄×D₄	C₄×D₅	1	1	yes	characteristic
301	C₄×D₄	C₄×D₅	1	1	yes	characteristic
302	#117	C₂×Dic₅	1	1	yes	characteristic
303	#117	C₂×Dic₅	1	1	yes	characteristic
304	#117	C₂×Dic₅	1	1	yes	characteristic
305	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
306	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
307	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
308	C₄⋊C₈	—	5	2	no	—
309	C₄⋊C₈	—	5	2	no	—
310	C₄⋊C₈	—	5	2	no	—
311	C₄⋊C₈	—	5	2	no	—
312	C₄⋊C₈	—	5	2	no	—
313	C₄⋊C₈	—	5	2	no	—
314	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
315	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
316	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
317	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
318	C₂²⋊C₈	—	5	2	no	—
319	C₂²⋊C₈	—	5	2	no	—
320	C₂²⋊C₈	—	5	2	no	—
321	C₂²⋊C₈	—	5	2	no	—
322	C₂²⋊C₈	—	5	2	no	—
323	C₂²⋊C₈	—	5	2	no	—
324	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
325	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
326	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
327	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
328	#97	—	5	2	no	—
329	#97	—	5	2	no	—
330	#97	—	5	2	no	—
331	#97	—	5	2	no	—
332	#97	C₂×Dic₅	1	2	yes	—
333	C₄×C₈	—	5	2	no	—
334	C₄×C₈	—	5	2	no	—
335	C₄×C₈	—	5	1	no	—
336	C₄×C₈	—	5	1	no	—
337	C₄×C₈	—	5	1	no	—
338	C₄×C₈	—	5	1	no	—
339	C₄×C₈	—	5	1	no	—
340	C₄×C₈	—	5	1	no	—
341	C₄×C₈	—	5	1	no	—
342	C₄×C₈	—	5	1	no	—
343	C₄×C₈	C₂×Dic₅	1	2	yes	—
344	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
345	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
346	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
347	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	—	2	1	no	—
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	C₄×C₅	—	2	1	no	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	2	1	no	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	1	no	—
367	C₄×C₅	C₂×#131	1	2	yes	—
368	C₄×C₅	#568	1	2	yes	—
369	C₄×C₅	#568	1	2	yes	—
370	#41	—	4	2	no	—
371	C₂×Q₈	C₄×Dic₅	1	1	yes	characteristic
372	C₂×D₄	C₄×Dic₅	1	1	yes	characteristic
373	C₂×D₄	C₄×Dic₅	1	1	yes	characteristic
374	C₂×D₄	C₄×Dic₅	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
381	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
382	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
383	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
384	M₁₆	—	4	2	no	—
385	M₁₆	—	10	4	no	—
386	M₁₆	—	10	4	no	—
387	M₁₆	—	20	2	no	—
388	M₁₆	—	20	2	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	5	2	no	—
391	C₂×C₈	—	5	2	no	—
392	C₂×C₈	—	5	2	no	—
393	C₂×C₈	—	5	2	no	—
394	C₂×C₈	—	5	2	no	—
395	C₂×C₈	—	5	2	no	—
396	C₂×C₈	—	5	2	no	—
397	C₂×C₈	—	5	2	no	—
398	C₂×C₈	—	10	4	no	—
399	C₂×C₈	—	20	2	no	—
400	C₂×C₈	C₂²×Dic₅	1	2	yes	—
401	C₂×C₈	C₂²×Dic₅	1	2	yes	—
402	C₂×C₈	C₂²×Dic₅	1	2	yes	—
403	C₂×C₈	C₂²×Dic₅	1	2	yes	—
404	C₄⋊C₄	C₄×Dic₅	1	1	yes	characteristic
405	C₄⋊C₄	C₄×Dic₅	1	1	yes	characteristic
406	C₄⋊C₄	C₄×Dic₅	1	1	yes	characteristic
407	C₄⋊C₄	C₄×Dic₅	1	1	yes	characteristic
408	C₄⋊C₄	C₄×Dic₅	1	1	yes	characteristic
409	C₄⋊C₄	C₄×Dic₅	1	1	yes	characteristic
410	C₂²⋊C₄	C₄×Dic₅	1	1	yes	characteristic
411	C₂²⋊C₄	C₄×Dic₅	1	1	yes	characteristic
412	C₂²⋊C₄	C₄×Dic₅	1	1	yes	characteristic
413	C₂²⋊C₄	C₄×Dic₅	1	1	yes	characteristic
414	C₂²⋊C₄	C₄×Dic₅	1	1	yes	characteristic
415	C₂²⋊C₄	C₄×Dic₅	1	1	yes	characteristic
416	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
417	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
418	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
419	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
420	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
421	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
422	C₄²	C₂²×Dic₅	1	1	yes	characteristic
423	C₄²	C₂²×Dic₅	1	1	yes	characteristic
424	C₄²	C₂²×Dic₅	1	1	yes	characteristic
425	C₄²	C₂³×D₅	1	1	yes	characteristic
426	C₂×C₅	—	4	1	no	—
427	C₂×C₅	—	4	1	no	—
428	C₂×C₅	—	4	1	no	—
429	C₂×C₅	#2873	1	1	yes	characteristic
430	C₂×C₅	C₄×#131	1	1	yes	characteristic
431	C₂×C₅	#2875	1	1	yes	characteristic
432	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
433	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
434	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
435	Q₈	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	4	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
449	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
459	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	5	4	no	—
465	C₈	—	10	2	no	—
466	C₈	—	10	2	no	—
467	C₈	—	10	2	no	—
468	C₈	—	10	2	no	—
469	C₈	—	10	2	no	—
470	C₈	—	10	2	no	—
471	C₈	—	10	2	no	—
472	C₅	#17340	1	1	yes	characteristic, complemented, Sylow
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	C₂²×C₄×Dic₅	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	D₅×#131	1	2	yes	—
493	C₄	#66084	1	2	yes	—
494	C₄	#66153	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	#10613933	1	1	yes	characteristic
499	C₂	Dic₅×#131	1	1	yes	characteristic
500	C₂	#10615513	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#2922	C₂
prime radical	C₂×C₅×#41	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2922	D₅
hypocenter	C₅	#17340
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #2922

Complements

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

N	H ≅ G/N	type
4. #10601537	C₂	semidirect
5. #10601537	C₂	semidirect
6. #10601536	C₂	semidirect
7. #10601536	C₂	semidirect
8. #10601535	C₂	semidirect
9. #10601534	C₂	semidirect
10. #10601533	C₂	semidirect
11. #10601532	C₂	semidirect
12. #10600642	C₂	semidirect
13. #10600641	C₂	semidirect
14. #10600518	C₂	semidirect
15. C₈×#681	C₂	semidirect
472. C₅	#17340	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2922	2
#10614248	2
#10601537	2
#10601536	2
#10601535	2
#10601534	2
#10601533	2
#10601532	2
#10600642	2
#10600641	2
#10600518	2
C₈×#681	2
#17340	5