Subgroups — #12252405

Order 1280.

600 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	D₅×#405	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	#10600078	C₂	1	1	yes	maximal, characteristic, complemented
5	#10600078	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600068	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600067	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599899	C₂	1	1	yes	maximal, characteristic
9	D₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
10	#10599887	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599887	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×D₅×M₁₆	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
18	D₅×#117	C₄	1	1	yes	characteristic
19	C₅×#405	C₂²	1	1	yes	characteristic
20	#65411	C₄	1	1	yes	characteristic
21	#65390	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	D₅×#97	C₄	1	1	yes	characteristic
30	D₅×#97	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, complemented
36	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
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, complemented
40	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
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, complemented
48	#64722	C₂²	1	1	yes	characteristic, complemented
49	#64721	C₂²	1	1	yes	characteristic, complemented
50	#64721	C₂²	1	1	yes	characteristic, complemented
51	#64721	C₂²	1	1	yes	characteristic, complemented
52	#64721	C₂²	1	1	yes	characteristic, complemented
53	C₁₆×Dic₅	C₂²	1	1	yes	characteristic, complemented
54	C₁₆×Dic₅	C₂²	1	1	yes	characteristic, complemented
55	C₄⋊#672	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊#672	C₂²	1	1	yes	characteristic, complemented
57	#64681	C₂²	1	1	yes	characteristic, complemented
58	C₄×#672	C₂²	1	1	yes	characteristic, complemented
59	#33422	—	5	1	no	maximal, Sylow
60	C₂²×C₄×D₅	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	#4072	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	D₅×M₁₆	—	2	4	no	—
68	C₂×#676	C₂×C₄	1	1	yes	characteristic
69	C₂×#676	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₅	—	2	2	no	—
71	C₂×C₈×D₅	—	2	2	no	—
72	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅	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	#4038	C₈	1	1	yes	characteristic
79	#4038	C₈	1	1	yes	characteristic
80	D₅×C₄⋊C₄	C₈	1	1	yes	characteristic
81	D₅×C₄⋊C₄	C₈	1	1	yes	characteristic
82	D₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
83	D₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
84	#4023	C₈	1	1	yes	characteristic
85	#4023	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	#3947	C₂×C₄	1	1	yes	characteristic
101	#3947	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	C₂×#405	—	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	#2151	—	5	1	no	—
128	#2151	—	5	1	no	—
129	#2112	—	5	1	no	—
130	C₂×C₂²⋊C₁₆	—	5	1	no	—
131	#2108	—	5	1	no	—
132	#2108	—	5	1	no	—
133	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₅	—	2	2	no	—
137	C₂×C₄×D₅	—	2	2	no	—
138	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
140	C₂×C₄×D₅	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	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
146	C₅×M₁₆	—	2	2	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
154	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
155	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
156	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
157	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
160	C₂²⋊Dic₅	C₂×C₈	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	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
166	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
167	#683	C₂×C₈	1	1	yes	characteristic
168	#683	C₂×C₈	1	1	yes	characteristic
169	#683	C₂×C₈	1	1	yes	characteristic
170	#683	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	M₁₆	1	4	yes	—
185	C₈×D₅	—	2	2	no	—
186	C₈×D₅	—	2	2	no	—
187	C₈×D₅	—	2	1	no	—
188	C₈×D₅	—	2	1	no	—
189	C₈×D₅	—	2	2	no	—
190	C₈×D₅	—	2	2	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	C₂²×M₁₆	—	5	1	no	—
202	C₂³×C₈	—	5	1	no	—
203	C₂×#117	—	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	—	5	1	no	—
214	#405	—	5	1	no	—
215	#405	C₂×D₅	1	1	yes	characteristic
216	C₂×#97	—	5	1	no	—
217	C₂×#97	—	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, complemented
227	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
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, complemented
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, complemented
244	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
245	C₂²×D₅	—	2	2	no	—
246	C₂²×D₅	—	2	2	no	—
247	C₂²×D₅	—	4	1	no	—
248	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
249	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
258	C₂×Dic₅	—	2	2	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	C₄×D₅	—	2	2	no	—
266	C₄×D₅	—	2	2	no	—
267	C₄×D₅	—	2	2	no	—
268	C₄×D₅	—	2	1	no	—
269	C₄×D₅	—	2	1	no	—
270	C₄×D₅	—	2	2	no	—
271	C₄×D₅	—	4	1	no	—
272	C₄×D₅	—	4	1	no	—
273	C₄×D₅	#117	1	2	yes	—
274	C₄×D₅	C₂×M₁₆	1	2	yes	—
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	C₂³×C₄	—	5	1	no	—
285	C₂×M₁₆	—	5	1	no	—
286	C₂×M₁₆	—	5	1	no	—
287	C₂×M₁₆	—	5	1	no	—
288	C₂×M₁₆	—	10	4	no	—
289	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
290	C₂²×C₈	—	5	1	no	—
291	C₂²×C₈	—	5	1	no	—
292	C₂²×C₈	—	5	1	no	—
293	C₂²×C₈	—	5	1	no	—
294	C₂²×C₈	—	5	1	no	—
295	C₂²×C₈	—	5	1	no	—
296	C₂²×C₈	—	5	1	no	—
297	C₂²×C₈	—	10	2	no	—
298	C₂²×C₈	—	10	2	no	—
299	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
300	#117	—	5	1	no	—
301	#117	—	5	1	no	—
302	#117	—	5	1	no	—
303	#117	—	5	1	no	—
304	#117	—	5	1	no	—
305	#117	—	5	1	no	—
306	#117	—	5	1	no	—
307	#117	C₄×D₅	1	1	yes	characteristic
308	C₂×C₄⋊C₄	—	5	1	no	—
309	C₂×C₄⋊C₄	—	5	1	no	—
310	C₂×C₂²⋊C₄	—	5	1	no	—
311	C₂×C₂²⋊C₄	—	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	—	5	1	no	—
331	#97	—	5	1	no	—
332	#97	C₄×D₅	1	1	yes	characteristic
333	#97	C₄×D₅	1	1	yes	characteristic
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	—	4	4	no	—
351	C₂×D₅	#431	1	2	yes	—
352	C₂×D₅	#504	1	2	yes	—
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	—	2	1	no	—
358	C₄×C₅	C₂×#117	1	1	yes	characteristic
359	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
360	Dic₅	—	2	1	no	—
361	Dic₅	—	2	1	no	—
362	Dic₅	—	2	1	no	—
363	Dic₅	—	2	1	no	—
364	Dic₅	—	2	1	no	—
365	Dic₅	#431	1	2	yes	—
366	C₂⁴	—	5	1	no	—
367	C₂²×C₄	—	5	1	no	—
368	C₂²×C₄	—	5	1	no	—
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	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	—	10	2	no	—
377	C₂²×C₄	—	10	2	no	—
378	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
379	M₁₆	—	2	2	no	—
380	M₁₆	—	5	4	no	—
381	M₁₆	—	10	2	no	—
382	M₁₆	—	10	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	5	1	no	—
386	C₂×C₈	—	5	1	no	—
387	C₂×C₈	—	5	2	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	10	2	no	—
392	C₂×C₈	—	10	2	no	—
393	C₂×C₈	—	10	2	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	10	1	no	—
396	C₂×C₈	—	10	1	no	—
397	C₂×C₈	—	10	2	no	—
398	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
399	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
400	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
401	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
402	C₄⋊C₄	—	5	1	no	—
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	—	5	1	no	—
408	C₄⋊C₄	C₈×D₅	1	1	yes	characteristic
409	C₄⋊C₄	C₈×D₅	1	1	yes	characteristic
410	C₂²⋊C₄	—	5	1	no	—
411	C₂²⋊C₄	—	5	1	no	—
412	C₂²⋊C₄	—	5	1	no	—
413	C₂²⋊C₄	—	5	1	no	—
414	C₂²⋊C₄	—	5	1	no	—
415	C₂²⋊C₄	—	5	1	no	—
416	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
417	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
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	—	5	1	no	—
424	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
425	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
426	C₁₆	—	2	1	no	—
427	C₁₆	—	2	1	no	—
428	C₁₆	—	2	1	no	—
429	C₁₆	—	2	1	no	—
430	C₁₆	—	10	1	no	—
431	C₁₆	—	10	1	no	—
432	C₁₆	—	10	1	no	—
433	C₁₆	—	10	1	no	—
434	C₂×C₅	—	4	1	no	—
435	C₂×C₅	C₂×#431	1	1	yes	characteristic
436	C₂×C₅	C₂×#504	1	1	yes	characteristic
437	C₂×C₅	#3407	1	1	yes	characteristic
438	D₅	—	2	2	no	—
439	D₅	—	2	2	no	—
440	C₂³	—	5	1	no	—
441	C₂³	—	5	1	no	—
442	C₂³	—	10	2	no	—
443	C₂³	—	10	2	no	—
444	C₂³	—	20	1	no	—
445	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	5	1	no	—
449	C₂×C₄	—	5	2	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	1	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	2	no	—
460	C₂×C₄	—	10	2	no	—
461	C₂×C₄	—	10	1	no	—
462	C₂×C₄	—	10	1	no	—
463	C₂×C₄	—	20	1	no	—
464	C₂×C₄	—	20	1	no	—
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	C₂×C₈×D₅	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
471	C₈	—	2	1	no	—
472	C₈	—	2	1	no	—
473	C₈	—	5	2	no	—
474	C₈	—	5	2	no	—
475	C₈	—	10	1	no	—
476	C₈	—	10	1	no	—
477	C₈	D₅×M₁₆	1	2	yes	—
478	C₈	D₅×#41	1	1	yes	characteristic
479	C₈	D₅×#41	1	1	yes	characteristic
480	C₅	#33422	1	1	yes	characteristic, complemented, Sylow
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	5	2	no	—
485	C₂²	—	5	2	no	—
486	C₂²	—	10	1	no	—
487	C₂²	—	10	1	no	—
488	C₂²	—	10	1	no	—
489	C₂²	—	10	1	no	—
490	C₂²	—	20	4	no	—
491	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	5	2	no	—
498	C₄	—	10	1	no	—
499	C₄	—	10	1	no	—
500	C₄	—	10	1	no	—
501	C₄	—	10	1	no	—
502	C₄	—	10	1	no	—
503	C₄	D₅×#117	1	1	yes	characteristic
504	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
505	C₂	—	4	1	no	—
506	C₂	—	10	2	no	—
507	C₂	—	10	2	no	—
508	C₂	D₅×#431	1	1	yes	characteristic
509	C₂	D₅×#504	1	1	yes	characteristic
510	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	C₂³×D₅	C₂×C₈
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2164	D₅
hypocenter	C₅	#33422
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. #10600078	C₂	semidirect
5. #10600078	C₂	semidirect
6. #10600068	C₂	semidirect
7. #10600067	C₂	semidirect
10. #10599887	C₂	semidirect
11. #10599887	C₂	semidirect
12. #10599866	C₂	semidirect
13. #10599865	C₂	semidirect
14. #10599845	C₂	semidirect
15. #10599844	C₂	semidirect
35. C₅×C₄⋊C₁₆	C₂²	semidirect
36. C₅×C₄⋊C₁₆	C₂²	semidirect
39. C₅×#346	C₂²	semidirect
40. C₄×C₅×C₁₆	C₂²	semidirect
47. #64722	C₂²	semidirect
48. #64722	C₂²	semidirect
49. #64721	C₂²	semidirect
50. #64721	C₂²	semidirect
51. #64721	C₂²	semidirect
52. #64721	C₂²	semidirect
53. C₁₆×Dic₅	C₂²	semidirect
54. C₁₆×Dic₅	C₂²	semidirect
55. C₄⋊#672	C₂²	semidirect
56. C₄⋊#672	C₂²	semidirect
57. #64681	C₂²	semidirect
58. C₄×#672	C₂²	semidirect
122. #2164	D₅	semidirect
226. C₄⋊C₁₆	C₂×D₅	semidirect
227. C₄⋊C₁₆	C₂×D₅	semidirect
239. #346	C₂×D₅	semidirect
243. C₄×C₁₆	C₂×D₅	semidirect
480. C₅	#33422	semidirect

Maximal subgroups

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

subgroup	index
D₅×#405	2
C₅×#2164	2
#10600676	2
#10600078	2
#10600068	2
#10600067	2
#10599899	2
D₅×C₂²⋊C₁₆	2
#10599887	2
#10599866	2
#10599865	2
#10599845	2
#10599844	2
#33422	5