Subgroups — #12252412

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10610280	C₂	1	1	yes	maximal, characteristic
2	C₅×#2164	C₂	1	1	yes	maximal, characteristic, complemented
3	#10600676	C₂	1	1	yes	maximal, characteristic, complemented
4	#10600077	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600069	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600069	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599900	C₂	1	1	yes	maximal, characteristic
9	#10599900	C₂	1	1	yes	maximal, characteristic
10	#10599886	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599885	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599866	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599865	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599845	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599844	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4053	C₄	1	1	yes	characteristic
17	C₂×#4047	C₂²	1	1	yes	characteristic
18	#65856	C₄	1	1	yes	characteristic
19	C₅×#405	C₂²	1	1	yes	characteristic
20	M₁₆×Dic₅	C₄	1	1	yes	characteristic
21	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
22	#65286	C₄	1	1	yes	characteristic
23	C₂×#3930	C₂²	1	1	yes	characteristic
24	C₂×#3930	C₂²	1	1	yes	characteristic
25	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
26	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
27	#64997	C₄	1	1	yes	characteristic
28	#64997	C₄	1	1	yes	characteristic
29	#64996	C₄	1	1	yes	characteristic
30	#64996	C₄	1	1	yes	characteristic
31	#64978	C₂²	1	1	yes	characteristic
32	#64978	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₅×#346	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
41	C₂²⋊#672	C₂²	1	1	yes	characteristic
42	C₂²⋊#672	C₂²	1	1	yes	characteristic
43	#64727	C₂²	1	1	yes	characteristic
44	#64727	C₂²	1	1	yes	characteristic
45	#64727	C₂²	1	1	yes	characteristic
46	#64727	C₂²	1	1	yes	characteristic
47	#64722	C₂²	1	1	yes	characteristic
48	#64722	C₂²	1	1	yes	characteristic
49	#64721	C₂²	1	1	yes	characteristic
50	#64721	C₂²	1	1	yes	characteristic
51	#64721	C₂²	1	1	yes	characteristic
52	#64721	C₂²	1	1	yes	characteristic
53	C₁₆×Dic₅	C₂²	1	1	yes	characteristic
54	C₁₆×Dic₅	C₂²	1	1	yes	characteristic
55	C₄⋊#672	C₂²	1	1	yes	characteristic
56	C₄⋊#672	C₂²	1	1	yes	characteristic
57	#64681	C₂²	1	1	yes	characteristic
58	C₄×#672	C₂²	1	1	yes	characteristic
59	#33423	—	5	1	no	maximal, Sylow
60	C₂×#709	C₂×C₄	1	1	yes	characteristic
61	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₅×#117	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
65	C₂×#681	C₂×C₄	1	1	yes	characteristic
66	C₂²×#168	C₂×C₄	1	1	yes	characteristic
67	#4053	—	2	4	no	—
68	#4047	—	2	2	no	—
69	#4047	—	2	2	no	—
70	C₂×#676	C₂×C₄	1	1	yes	characteristic
71	C₂×#676	C₂×C₄	1	1	yes	characteristic
72	C₂×#676	C₂×C₄	1	1	yes	characteristic
73	C₂×#676	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
78	#4039	C₈	1	1	yes	characteristic
79	#4039	C₈	1	1	yes	characteristic
80	#4033	C₈	1	1	yes	characteristic
81	#4033	C₈	1	1	yes	characteristic
82	#4027	C₈	1	1	yes	characteristic
83	#4027	C₈	1	1	yes	characteristic
84	#4027	C₈	1	1	yes	characteristic
85	#4027	C₈	1	1	yes	characteristic
86	#4018	C₂×C₄	1	1	yes	characteristic
87	#4018	C₂×C₄	1	1	yes	characteristic
88	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
89	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
94	C₅×#97	C₂×C₄	1	1	yes	characteristic
95	C₅×#97	C₂×C₄	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	#3947	C₂×C₄	1	1	yes	characteristic
99	#3947	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
104	C₈×Dic₅	C₂³	1	1	yes	characteristic
105	C₈×Dic₅	C₂³	1	1	yes	characteristic
106	C₂×#672	C₂³	1	1	yes	characteristic
107	C₂×#672	C₂³	1	1	yes	characteristic
108	C₂×#672	C₂³	1	1	yes	characteristic
109	C₂×#672	C₂³	1	1	yes	characteristic
110	#3935	C₂×C₄	1	1	yes	characteristic
111	#3935	C₂×C₄	1	1	yes	characteristic
112	C₄×#168	C₂×C₄	1	1	yes	characteristic
113	C₄×#168	C₂×C₄	1	1	yes	characteristic
114	#3930	—	2	2	no	—
115	#3930	—	2	2	no	—
116	D₅×C₁₆	—	2	2	no	—
117	D₅×C₁₆	—	2	2	no	—
118	C₄×#131	—	5	1	no	—
119	#2164	—	5	1	no	—
120	#2164	—	5	1	no	—
121	#2164	—	5	1	no	—
122	#2164	D₅	1	1	yes	characteristic, complemented
123	#2163	—	5	1	no	—
124	#2163	—	5	1	no	—
125	#2162	—	5	1	no	—
126	#2162	—	5	1	no	—
127	#2150	—	5	1	no	—
128	C₂×C₄⋊C₁₆	—	5	1	no	—
129	#2113	—	5	1	no	—
130	#2113	—	5	1	no	—
131	#2108	—	5	1	no	—
132	#2108	—	5	1	no	—
133	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
136	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
137	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
138	#709	—	2	2	no	—
139	#709	—	2	2	no	—
140	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
141	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
143	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₀	C₂×C₈	1	1	yes	characteristic
148	C₅×M₁₆	—	2	2	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
155	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
158	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
159	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
161	#685	C₂×C₈	1	1	yes	characteristic
162	#685	C₂×C₈	1	1	yes	characteristic
163	#685	C₂×C₈	1	1	yes	characteristic
164	#685	C₂×C₈	1	1	yes	characteristic
165	#683	C₂×C₈	1	1	yes	characteristic
166	#683	C₂×C₈	1	1	yes	characteristic
167	#683	C₂×C₈	1	1	yes	characteristic
168	#683	C₂×C₈	1	1	yes	characteristic
169	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
170	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
171	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
172	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
176	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
177	#681	—	2	2	no	—
178	C₂×#168	—	2	2	no	—
179	C₂×#168	C₂²×C₄	1	1	yes	characteristic
180	C₂×#168	C₂²×C₄	1	1	yes	characteristic
181	C₂×#168	C₂²×C₄	1	1	yes	characteristic
182	C₂×#168	C₂²×C₄	1	1	yes	characteristic
183	#676	—	2	2	no	—
184	#676	—	2	2	no	—
185	#676	—	2	2	no	—
186	#676	M₁₆	1	4	yes	—
187	C₈×D₅	—	2	2	no	—
188	C₈×D₅	—	2	2	no	—
189	C₈×D₅	—	2	1	no	—
190	C₈×D₅	—	2	1	no	—
191	C₈×D₅	#41	1	2	yes	—
192	C₈×D₅	#41	1	2	yes	—
193	C₅×C₁₆	—	2	1	no	—
194	C₅×C₁₆	—	2	1	no	—
195	C₅×C₁₆	—	2	1	no	—
196	C₅×C₁₆	—	2	1	no	—
197	#672	—	2	1	no	—
198	#672	—	2	1	no	—
199	#672	—	2	1	no	—
200	#672	—	2	1	no	—
201	C₂×#131	—	5	1	no	—
202	C₂×#131	—	5	1	no	—
203	C₄×#41	—	5	1	no	—
204	C₂×M₃₂	—	5	1	no	—
205	C₂×M₃₂	—	5	1	no	—
206	C₂²×C₁₆	—	5	1	no	—
207	C₂²×C₁₆	—	5	1	no	—
208	#405	—	5	1	no	—
209	#405	—	5	1	no	—
210	#405	—	5	1	no	—
211	#405	—	5	1	no	—
212	#405	—	5	1	no	—
213	#405	C₂×D₅	1	1	yes	characteristic
214	C₄×M₁₆	—	5	1	no	—
215	C₄×M₁₆	—	5	1	no	—
216	C₄×M₁₆	—	5	1	no	—
217	C₂×C₄×C₈	—	5	1	no	—
218	C₂×C₄×C₈	—	5	1	no	—
219	C₂×C₄×C₈	—	5	1	no	—
220	C₄⋊C₁₆	—	5	1	no	—
221	C₄⋊C₁₆	—	5	1	no	—
222	C₄⋊C₁₆	—	5	1	no	—
223	C₄⋊C₁₆	—	5	1	no	—
224	C₄⋊C₁₆	—	5	1	no	—
225	C₄⋊C₁₆	—	5	1	no	—
226	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic
227	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic
228	C₂²⋊C₁₆	—	5	1	no	—
229	C₂²⋊C₁₆	—	5	1	no	—
230	C₂²⋊C₁₆	—	5	1	no	—
231	C₂²⋊C₁₆	—	5	1	no	—
232	C₂²⋊C₁₆	—	5	1	no	—
233	C₂²⋊C₁₆	—	5	1	no	—
234	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic
235	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic
236	#346	—	5	1	no	—
237	#346	—	5	1	no	—
238	#346	—	5	1	no	—
239	#346	C₂×D₅	1	1	yes	characteristic
240	C₄×C₁₆	—	5	1	no	—
241	C₄×C₁₆	—	5	1	no	—
242	C₄×C₁₆	—	5	1	no	—
243	C₄×C₁₆	C₂×D₅	1	1	yes	characteristic
244	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
245	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
246	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂²⋊D₅	—	2	2	no	—
256	C₂²⋊D₅	—	2	2	no	—
257	C₂×Dic₅	—	2	2	no	—
258	C₂×Dic₅	—	4	1	no	—
259	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
260	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
261	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
262	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
263	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
264	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
265	D₂₀	—	2	2	no	—
266	C₄×D₅	—	2	1	no	—
267	C₄×D₅	—	2	1	no	—
268	C₄×D₅	—	2	2	no	—
269	C₄×D₅	—	2	2	no	—
270	C₄×D₅	—	4	1	no	—
271	C₄×D₅	—	4	1	no	—
272	C₄×D₅	#117	1	2	yes	—
273	C₄×D₅	C₂×M₁₆	1	2	yes	—
274	Dic₁₀	—	2	2	no	—
275	C₅×C₈	—	2	1	no	—
276	C₅×C₈	—	2	1	no	—
277	C₅×C₈	C₂×M₁₆	1	2	yes	—
278	C₅×C₈	C₂×#41	1	1	yes	characteristic
279	C₅×C₈	C₂×#41	1	1	yes	characteristic
280	#168	—	2	1	no	—
281	#168	—	2	1	no	—
282	#168	#117	1	2	yes	—
283	#168	C₂×M₁₆	1	2	yes	—
284	C₂×#41	—	5	1	no	—
285	#131	—	10	2	no	—
286	#131	—	10	2	no	—
287	#131	—	10	4	no	—
288	C₂×M₁₆	—	5	1	no	—
289	C₂×M₁₆	—	5	1	no	—
290	C₂×M₁₆	—	5	1	no	—
291	C₂×M₁₆	—	5	1	no	—
292	C₂×M₁₆	—	5	1	no	—
293	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
294	C₂²×C₈	—	5	1	no	—
295	C₂²×C₈	—	5	1	no	—
296	C₂²×C₈	—	5	1	no	—
297	C₂²×C₈	—	5	1	no	—
298	C₂²×C₈	—	5	1	no	—
299	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
300	C₄×Q₈	—	5	1	no	—
301	C₄×Q₈	—	5	1	no	—
302	C₄×D₄	—	5	1	no	—
303	C₄×D₄	—	5	1	no	—
304	C₄×D₄	—	5	1	no	—
305	C₄×D₄	—	5	1	no	—
306	C₄×D₄	—	5	1	no	—
307	C₄×D₄	—	5	1	no	—
308	#117	—	5	1	no	—
309	#117	—	5	1	no	—
310	#117	C₄×D₅	1	1	yes	characteristic
311	C₂×C₄²	—	5	1	no	—
312	C₂×C₄²	—	5	1	no	—
313	C₂×C₄²	—	5	1	no	—
314	M₃₂	—	10	2	no	—
315	M₃₂	—	10	2	no	—
316	C₂×C₁₆	—	5	1	no	—
317	C₂×C₁₆	—	5	1	no	—
318	C₂×C₁₆	—	5	1	no	—
319	C₂×C₁₆	—	5	1	no	—
320	C₂×C₁₆	—	10	2	no	—
321	C₂×C₁₆	—	10	2	no	—
322	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
323	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
324	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
325	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
326	#97	—	5	1	no	—
327	#97	—	5	1	no	—
328	#97	—	5	1	no	—
329	#97	—	5	1	no	—
330	#97	C₄×D₅	1	1	yes	characteristic
331	#97	C₄×D₅	1	1	yes	characteristic
332	C₄×C₈	—	5	1	no	—
333	C₄×C₈	—	5	1	no	—
334	C₄×C₈	—	5	1	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	C₂²×D₅	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
342	C₂²×C₅	—	2	1	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
346	C₂×D₅	—	2	1	no	—
347	C₂×D₅	—	2	1	no	—
348	C₂×D₅	—	2	1	no	—
349	C₂×D₅	—	2	1	no	—
350	C₂×D₅	—	2	1	no	—
351	C₂×D₅	#431	1	2	yes	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	C₂×#117	1	1	yes	characteristic
358	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
359	Dic₅	—	2	1	no	—
360	Dic₅	—	2	1	no	—
361	Dic₅	—	2	1	no	—
362	Dic₅	—	2	1	no	—
363	Dic₅	#431	1	2	yes	—
364	Dic₅	#504	1	2	yes	—
365	#41	—	10	2	no	—
366	#41	—	10	2	no	—
367	C₂×Q₈	—	5	1	no	—
368	C₂×D₄	—	5	1	no	—
369	C₂×D₄	—	5	1	no	—
370	C₂×D₄	—	5	1	no	—
371	C₂²×C₄	—	5	1	no	—
372	C₂²×C₄	—	5	1	no	—
373	C₂²×C₄	—	5	1	no	—
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	1	no	—
376	C₂²×C₄	—	5	1	no	—
377	C₂²×C₄	—	5	1	no	—
378	C₂²×C₄	—	5	1	no	—
379	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
380	M₁₆	—	2	2	no	—
381	M₁₆	—	5	4	no	—
382	M₁₆	—	10	2	no	—
383	M₁₆	—	10	2	no	—
384	M₁₆	—	10	2	no	—
385	M₁₆	—	10	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	2	no	—
391	C₂×C₈	—	5	2	no	—
392	C₂×C₈	—	5	1	no	—
393	C₂×C₈	—	5	1	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	10	2	no	—
396	C₂×C₈	—	10	1	no	—
397	C₂×C₈	—	10	1	no	—
398	C₂×C₈	—	10	2	no	—
399	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
400	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
401	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
402	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
403	C₄⋊C₄	—	5	1	no	—
404	C₄⋊C₄	—	5	1	no	—
405	C₄⋊C₄	—	5	1	no	—
406	C₄⋊C₄	—	5	1	no	—
407	C₄⋊C₄	C₈×D₅	1	1	yes	characteristic
408	C₄⋊C₄	C₈×D₅	1	1	yes	characteristic
409	C₂²⋊C₄	—	5	1	no	—
410	C₂²⋊C₄	—	5	1	no	—
411	C₂²⋊C₄	—	5	1	no	—
412	C₂²⋊C₄	—	5	1	no	—
413	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
414	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
415	C₄²	—	5	1	no	—
416	C₄²	—	5	1	no	—
417	C₄²	—	5	1	no	—
418	C₄²	—	5	1	no	—
419	C₄²	—	5	1	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	1	no	—
422	C₄²	—	5	1	no	—
423	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
425	C₁₆	—	2	1	no	—
426	C₁₆	—	2	1	no	—
427	C₁₆	—	2	1	no	—
428	C₁₆	—	2	1	no	—
429	C₁₆	—	10	1	no	—
430	C₁₆	—	10	1	no	—
431	C₁₆	—	10	1	no	—
432	C₁₆	—	10	1	no	—
433	C₂×C₅	—	4	1	no	—
434	C₂×C₅	C₂×#431	1	1	yes	characteristic
435	C₂×C₅	C₂×#504	1	1	yes	characteristic
436	C₂×C₅	#3407	1	1	yes	characteristic
437	D₅	—	2	2	no	—
438	D₅	—	4	1	no	—
439	C₂³	—	5	1	no	—
440	C₂³	—	5	1	no	—
441	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
442	Q₈	—	10	2	no	—
443	D₄	—	10	2	no	—
444	D₄	—	10	2	no	—
445	D₄	—	10	2	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	5	1	no	—
449	C₂×C₄	—	5	1	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	2	no	—
452	C₂×C₄	—	5	1	no	—
453	C₂×C₄	—	5	1	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	1	no	—
456	C₂×C₄	—	10	2	no	—
457	C₂×C₄	—	10	2	no	—
458	C₂×C₄	—	10	2	no	—
459	C₂×C₄	—	10	1	no	—
460	C₂×C₄	—	10	1	no	—
461	C₂×C₄	—	20	1	no	—
462	C₂×C₄	—	20	1	no	—
463	C₂×C₄	—	20	1	no	—
464	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
465	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
466	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
467	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
468	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	5	2	no	—
473	C₈	—	5	2	no	—
474	C₈	—	10	1	no	—
475	C₈	—	10	1	no	—
476	C₈	D₅×M₁₆	1	2	yes	—
477	C₈	D₅×#41	1	1	yes	characteristic
478	C₈	D₅×#41	1	1	yes	characteristic
479	C₅	#33423	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	5	2	no	—
484	C₂²	—	10	1	no	—
485	C₂²	—	10	1	no	—
486	C₂²	—	10	1	no	—
487	C₂²	—	10	1	no	—
488	C₂²	—	10	1	no	—
489	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	5	2	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	D₅×#117	1	1	yes	characteristic
502	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	10	2	no	—
505	C₂	—	20	1	no	—
506	C₂	D₅×#431	1	1	yes	characteristic
507	C₂	D₅×#504	1	1	yes	characteristic
508	C₂	#10613743	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#2164	C₂
prime radical	C₂×#709	C₂×C₄
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2164	D₅
hypocenter	C₅	#33423
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. C₅×#2164	C₂	semidirect
3. #10600676	C₂	semidirect
4. #10600077	C₂	semidirect
5. D₅×C₄⋊C₁₆	C₂	semidirect
6. #10600069	C₂	semidirect
7. #10600069	C₂	semidirect
10. #10599886	C₂	semidirect
11. #10599885	C₂	semidirect
12. #10599866	C₂	semidirect
13. #10599865	C₂	semidirect
14. #10599845	C₂	semidirect
15. #10599844	C₂	semidirect
122. #2164	D₅	semidirect
479. C₅	#33423	semidirect

Maximal subgroups

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

subgroup	index
#10610280	2
C₅×#2164	2
#10600676	2
#10600077	2
D₅×C₄⋊C₁₆	2
#10600069	2
#10599900	2
#10599886	2
#10599885	2
#10599866	2
#10599865	2
#10599845	2
#10599844	2
#33423	5