Subgroups — #12097255

Order 1280.

1110 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65128	C₂	1	1	yes	maximal, characteristic
2	C₂×#64997	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×#64978	C₂	1	1	yes	maximal, characteristic
5	#10605486	C₂	1	1	yes	maximal, characteristic
6	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601260	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600626	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600626	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600550	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600271	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599454	C₂	1	1	yes	maximal, characteristic
13	#10599453	C₂	1	1	yes	maximal, characteristic
14	#10599447	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599446	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#676	C₂²	1	1	yes	characteristic
17	C₂²×#676	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
20	C₂×#4018	C₂²	1	1	yes	characteristic
21	C₂×#4018	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×#97	C₂²	1	1	yes	characteristic
25	C₂×C₅×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×#3947	C₂²	1	1	yes	characteristic
29	C₂×#3947	C₂²	1	1	yes	characteristic
30	C₂×#3947	C₂²	1	1	yes	characteristic
31	C₂×#3947	C₂²	1	1	yes	characteristic
32	C₂×#3946	C₂²	1	1	yes	characteristic
33	C₂×#3946	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
36	#65278	C₄	1	2	yes	—
37	#65261	C₄	1	2	yes	—
38	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
39	C₄×#683	C₂²	1	1	yes	characteristic
40	C₄×#683	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₂×#3935	C₂²	1	1	yes	characteristic
43	C₂×#3935	C₂²	1	1	yes	characteristic
44	C₂×C₄×#168	C₂²	1	1	yes	characteristic
45	#65128	C₄	1	8	yes	complemented
46	#64997	—	2	4	no	—
47	D₅×#97	—	2	4	no	—
48	#64978	C₄	1	8	yes	complemented
49	#64957	C₄	1	2	yes	—
50	#64936	C₄	1	2	yes	—
51	C₅×#336	C₂²	1	1	yes	characteristic
52	C₅×#336	C₂²	1	1	yes	characteristic
53	#64770	C₂²	1	1	yes	characteristic
54	#64770	C₂²	1	1	yes	characteristic
55	#64770	C₂²	1	1	yes	characteristic
56	#64770	C₂²	1	1	yes	characteristic
57	#64744	C₂²	1	1	yes	characteristic
58	#64744	C₂²	1	1	yes	characteristic
59	#20436	—	5	1	no	maximal, Sylow
60	C₂²×C₄×D₅	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×#685	C₂×C₄	1	2	yes	—
71	C₂×#685	C₂×C₄	1	1	yes	characteristic
72	C₂×#685	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
74	C₂×#683	C₂×C₄	1	2	yes	—
75	C₂×#683	C₂×C₄	1	2	yes	—
76	C₂×#683	C₂×C₄	1	2	yes	—
77	C₂×#683	C₂×C₄	1	1	yes	characteristic
78	C₂×#683	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
80	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₂²×#168	C₂³	1	1	yes	characteristic
84	C₂²×#168	C₂³	1	1	yes	characteristic
85	C₂²×#168	C₂³	1	1	yes	characteristic
86	C₂²×#168	C₂³	1	1	yes	characteristic
87	C₂×#676	—	2	2	no	—
88	C₂×#676	—	2	2	no	—
89	C₂×#676	—	2	2	no	—
90	C₂×#676	—	2	2	no	—
91	C₂×#676	C₂×C₄	1	4	yes	—
92	C₂×#676	C₂×C₄	1	4	yes	—
93	C₂×C₈×D₅	—	2	2	no	—
94	C₂×C₈×D₅	—	2	2	no	—
95	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
96	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
97	C₂×C₈×D₅	D₄	1	4	yes	—
98	C₂×C₈×D₅	Q₈	1	4	yes	—
99	#4018	—	2	2	no	—
100	#4018	—	2	2	no	—
101	#4018	C₂×C₄	1	4	yes	—
102	#4018	C₂×C₄	1	4	yes	—
103	C₄²×D₅	—	2	2	no	—
104	C₄²×D₅	—	2	2	no	—
105	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
106	C₅×#97	—	2	2	no	—
107	C₅×#97	—	2	2	no	—
108	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
109	C₅×#95	C₂×C₄	1	2	yes	—
110	#3963	C₂×C₄	1	2	yes	—
111	#3963	C₂×C₄	1	2	yes	—
112	#3963	C₂×C₄	1	2	yes	—
113	#3947	—	2	2	no	—
114	#3947	—	2	2	no	—
115	#3947	—	2	2	no	—
116	#3947	C₂×C₄	1	4	yes	complemented
117	#3946	C₂×C₄	1	4	yes	complemented
118	#3946	C₂×C₄	1	4	yes	complemented
119	C₈×Dic₅	—	2	2	no	—
120	C₈×Dic₅	C₂×C₄	1	4	yes	complemented
121	C₄⋊#168	C₂×C₄	1	4	yes	complemented
122	#3935	—	2	2	no	—
123	#3935	C₂×C₄	1	4	yes	complemented
124	C₄×#168	—	2	2	no	—
125	C₂×#424	—	5	1	no	—
126	C₂×#405	—	5	1	no	—
127	C₂×#405	—	5	1	no	—
128	C₂²×#97	—	5	1	no	—
129	#2296	—	5	1	no	—
130	#1771	—	5	1	no	—
131	#1771	—	5	1	no	—
132	#1771	—	5	1	no	—
133	#1771	—	5	1	no	—
134	#1770	—	5	1	no	—
135	#1770	—	5	1	no	—
136	#1770	—	5	1	no	—
137	#1770	D₅	1	1	yes	characteristic, complemented
138	#1729	—	5	1	no	—
139	#1728	—	5	1	no	—
140	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₂²×Dic₅	C₂²×C₄	1	2	yes	—
147	C₂²×Dic₅	C₂²×C₄	1	2	yes	—
148	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅	—	2	4	no	—
152	C₂×C₄×D₅	—	4	2	no	—
153	C₂×C₄×D₅	—	4	2	no	—
154	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
155	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
156	C₂×C₄×D₅	C₂×D₄	1	2	yes	—
157	C₂×C₄×D₅	C₂×Q₈	1	2	yes	—
158	C₂×C₄×D₅	#41	1	2	yes	—
159	C₂×C₄×D₅	#41	1	2	yes	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
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	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
171	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
172	C₅×C₄⋊C₄	—	4	2	no	—
173	C₄²×C₅	—	2	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	C₂²×C₄	1	2	yes	—
178	C₄²×C₅	C₂²×C₄	1	2	yes	—
179	#685	—	2	4	no	—
180	#685	C₄²	1	4	yes	—
181	#685	C₄²	1	4	yes	—
182	C₄⋊Dic₅	—	4	2	no	—
183	#683	—	2	4	no	—
184	#683	—	4	2	no	—
185	#683	—	4	2	no	—
186	#683	C₄²	1	4	yes	—
187	#683	C₄²	1	4	yes	—
188	C₄×Dic₅	—	2	1	no	—
189	C₄×Dic₅	—	2	1	no	—
190	C₄×Dic₅	—	2	1	no	—
191	C₄×Dic₅	—	2	1	no	—
192	C₄×Dic₅	—	2	4	no	—
193	C₄×Dic₅	C₂²×C₄	1	2	yes	—
194	C₄×Dic₅	C₂²×C₄	1	2	yes	—
195	C₂×#168	—	2	1	no	—
196	C₂×#168	—	2	1	no	—
197	C₂×#168	—	2	1	no	—
198	C₂×#168	—	2	1	no	—
199	C₂×#168	—	2	1	no	—
200	C₂×#168	—	2	1	no	—
201	C₂×#168	C₂²×C₄	1	2	yes	—
202	C₂×#168	C₂²×C₄	1	2	yes	—
203	C₂×#168	C₂²×C₄	1	2	yes	—
204	C₂×#168	C₂²×C₄	1	2	yes	—
205	C₂×#168	C₂×D₄	1	2	yes	—
206	C₂×#168	C₂×Q₈	1	2	yes	—
207	#676	—	2	8	no	—
208	#676	—	2	8	no	—
209	C₈×D₅	—	2	8	no	—
210	C₈×D₅	C₄⋊C₄	1	16	yes	complemented
211	C₂²×M₁₆	—	5	1	no	—
212	C₂²×M₁₆	—	5	1	no	—
213	C₂³×C₈	—	5	1	no	—
214	C₂³×C₈	—	5	1	no	—
215	C₂×#117	—	5	1	no	—
216	C₂×#117	—	5	1	no	—
217	C₂²×C₄²	—	5	1	no	—
218	#424	—	5	8	no	—
219	C₂×C₄⋊C₈	—	5	1	no	—
220	C₂×C₄⋊C₈	—	5	1	no	—
221	C₂×C₄⋊C₈	—	5	1	no	—
222	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
223	#405	—	5	8	no	—
224	#405	—	10	4	no	—
225	C₂×#97	—	5	1	no	—
226	C₂×#97	—	5	1	no	—
227	C₂×#97	—	5	1	no	—
228	C₂×#97	—	5	1	no	—
229	C₂×#97	—	5	1	no	—
230	C₂×#97	—	5	1	no	—
231	C₂×#97	—	10	4	no	—
232	C₂×#97	C₂×D₅	1	1	yes	characteristic
233	C₂×#97	C₂×D₅	1	1	yes	characteristic
234	C₂×C₄×C₈	—	5	1	no	—
235	C₂×C₄×C₈	—	5	1	no	—
236	C₂×C₄×C₈	—	5	1	no	—
237	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
238	#389	—	5	2	no	—
239	#389	—	5	2	no	—
240	#385	—	5	2	no	—
241	#385	—	5	2	no	—
242	C₄×C₄⋊C₄	—	5	1	no	—
243	C₄×C₄⋊C₄	—	5	1	no	—
244	C₄×C₄⋊C₄	—	5	1	no	—
245	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
246	#336	—	5	1	no	—
247	#336	—	5	1	no	—
248	#336	—	5	1	no	—
249	#336	—	5	1	no	—
250	#336	—	5	1	no	—
251	#336	—	5	1	no	—
252	#336	C₂×D₅	1	1	yes	characteristic
253	#336	C₂×D₅	1	1	yes	characteristic
254	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂²×D₅	—	2	2	no	—
256	C₂²×D₅	—	2	2	no	—
257	C₂²×D₅	C₂×C₄²	1	2	yes	—
258	C₂²×D₅	C₄×D₄	1	2	yes	—
259	C₂²×D₅	C₄×Q₈	1	2	yes	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
269	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
270	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
276	C₂×Dic₅	—	2	2	no	—
277	C₂×Dic₅	—	2	2	no	—
278	C₂×Dic₅	—	2	2	no	—
279	C₂×Dic₅	—	2	2	no	—
280	C₂×Dic₅	—	2	2	no	—
281	C₂×Dic₅	—	2	2	no	—
282	C₂×Dic₅	—	2	2	no	—
283	C₂×Dic₅	—	2	2	no	—
284	C₂×Dic₅	C₂×C₄²	1	2	yes	—
285	C₂×Dic₅	C₂×C₄²	1	2	yes	—
286	C₂×Dic₅	C₂×C₄²	1	2	yes	—
287	C₂×Dic₅	C₄×D₄	1	2	yes	—
288	C₂×Dic₅	C₄×Q₈	1	2	yes	—
289	C₄×D₅	—	4	8	no	—
290	C₄×D₅	C₂×C₄⋊C₄	1	4	yes	—
291	C₄×D₅	#117	1	4	yes	—
292	C₄×D₅	C₄×D₄	1	4	yes	—
293	C₄×D₅	C₄×Q₈	1	4	yes	—
294	C₅×C₈	—	2	2	no	—
295	C₅×C₈	—	2	2	no	—
296	C₅×C₈	—	2	2	no	—
297	C₅×C₈	C₂×C₄⋊C₄	1	4	yes	—
298	#168	—	2	2	no	—
299	#168	—	2	2	no	—
300	#168	—	2	2	no	—
301	#168	C₂×C₄⋊C₄	1	4	yes	—
302	C₂³×C₄	—	5	1	no	—
303	C₂³×C₄	—	5	2	no	—
304	C₂×M₁₆	—	5	4	no	—
305	C₂×M₁₆	—	5	4	no	—
306	C₂×M₁₆	—	10	2	no	—
307	C₂×M₁₆	—	10	2	no	—
308	C₂×M₁₆	—	10	2	no	—
309	C₂×M₁₆	—	10	2	no	—
310	C₂²×C₈	—	5	1	no	—
311	C₂²×C₈	—	5	4	no	—
312	C₂²×C₈	—	5	4	no	—
313	C₂²×C₈	—	5	4	no	—
314	C₂²×C₈	—	5	1	no	—
315	C₂²×C₈	—	5	1	no	—
316	C₂²×C₈	—	5	1	no	—
317	C₂²×C₈	—	5	4	no	—
318	C₂²×C₈	—	10	2	no	—
319	C₂²×C₈	—	10	2	no	—
320	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
321	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
322	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
323	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
324	#117	—	5	4	no	—
325	#117	—	5	4	no	—
326	#117	—	10	2	no	—
327	#117	—	10	2	no	—
328	C₂×C₄⋊C₄	—	5	1	no	—
329	C₂×C₄⋊C₄	—	5	1	no	—
330	C₂×C₄⋊C₄	—	5	2	no	—
331	C₂×C₄⋊C₄	—	5	2	no	—
332	C₂×C₄⋊C₄	—	5	2	no	—
333	C₂×C₄⋊C₄	—	5	2	no	—
334	C₂×C₄⋊C₄	C₄×D₅	1	2	yes	—
335	C₂×C₂²⋊C₄	—	5	1	no	—
336	C₂×C₂²⋊C₄	—	5	1	no	—
337	C₂×C₂²⋊C₄	—	5	2	no	—
338	C₂×C₄²	—	5	1	no	—
339	C₂×C₄²	—	5	2	no	—
340	C₂×C₄²	—	5	1	no	—
341	C₂×C₄²	—	5	1	no	—
342	C₂×C₄²	—	10	2	no	—
343	C₂×C₄²	—	10	2	no	—
344	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
345	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
346	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
347	C₄⋊C₈	—	5	4	no	—
348	C₄⋊C₈	—	5	4	no	—
349	C₄⋊C₈	—	5	4	no	—
350	C₄⋊C₈	C₄×D₅	1	4	yes	complemented
351	#97	—	2	2	no	—
352	#97	—	2	2	no	—
353	#97	—	5	4	no	—
354	#97	—	5	4	no	—
355	#97	—	10	2	no	—
356	#97	—	10	2	no	—
357	#97	—	10	2	no	—
358	#97	—	10	2	no	—
359	C₄×C₈	—	5	4	no	—
360	C₄×C₈	—	10	2	no	—
361	C₄×C₈	—	10	2	no	—
362	C₄×C₈	C₄×D₅	1	4	yes	complemented
363	#95	—	5	2	no	—
364	#95	—	5	2	no	—
365	#95	—	5	2	no	—
366	#95	C₄×D₅	1	2	yes	—
367	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
368	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
370	C₂²×C₅	#568	1	2	yes	—
371	C₂²×C₅	#568	1	2	yes	—
372	C₂×D₅	—	2	2	no	—
373	C₂×D₅	—	2	2	no	—
374	C₂×D₅	—	2	4	no	—
375	C₂×D₅	—	2	4	no	—
376	C₂×D₅	C₄×C₄⋊C₄	1	4	yes	—
377	C₄×C₅	—	2	2	no	—
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
382	C₄×C₅	C₂×#117	1	1	yes	characteristic
383	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
384	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
385	Dic₅	—	2	2	no	—
386	Dic₅	—	2	2	no	—
387	Dic₅	—	4	2	no	—
388	Dic₅	—	4	2	no	—
389	Dic₅	C₄×C₄⋊C₄	1	4	yes	—
390	C₂⁴	—	5	1	no	—
391	C₂²×C₄	—	5	1	no	—
392	C₂²×C₄	—	5	2	no	—
393	C₂²×C₄	—	5	2	no	—
394	C₂²×C₄	—	5	2	no	—
395	C₂²×C₄	—	5	2	no	—
396	C₂²×C₄	—	5	2	no	—
397	C₂²×C₄	—	5	2	no	—
398	C₂²×C₄	—	5	1	no	—
399	C₂²×C₄	—	5	1	no	—
400	C₂²×C₄	—	5	2	no	—
401	C₂²×C₄	—	5	2	no	—
402	C₂²×C₄	—	10	4	no	—
403	C₂²×C₄	—	20	2	no	—
404	C₂²×C₄	—	20	2	no	—
405	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
406	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
407	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
409	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
410	M₁₆	—	10	8	no	—
411	M₁₆	—	10	8	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	5	2	no	—
419	C₂×C₈	—	5	2	no	—
420	C₂×C₈	—	5	2	no	—
421	C₂×C₈	—	5	16	no	—
422	C₂×C₈	—	5	2	no	—
423	C₂×C₈	—	5	2	no	—
424	C₂×C₈	—	5	2	no	—
425	C₂×C₈	—	10	8	no	—
426	C₂×C₈	—	10	1	no	—
427	C₂×C₈	—	10	1	no	—
428	C₂×C₈	—	10	1	no	—
429	C₂×C₈	—	10	1	no	—
430	C₂×C₈	—	10	1	no	—
431	C₂×C₈	—	10	1	no	—
432	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
433	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
434	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
435	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
436	C₂×C₈	D₄×D₅	1	2	yes	—
437	C₂×C₈	Q₈×D₅	1	2	yes	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	—	5	4	no	—
440	C₄⋊C₄	—	5	4	no	—
441	C₄⋊C₄	—	10	4	no	—
442	C₄⋊C₄	—	20	2	no	—
443	C₄⋊C₄	—	20	2	no	—
444	C₄⋊C₄	—	20	2	no	—
445	C₂²⋊C₄	—	5	4	no	—
446	C₂²⋊C₄	—	5	4	no	—
447	C₂²⋊C₄	—	10	4	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	5	2	no	—
453	C₄²	—	5	2	no	—
454	C₄²	—	10	4	no	—
455	C₄²	—	10	1	no	—
456	C₄²	—	10	1	no	—
457	C₄²	—	10	1	no	—
458	C₄²	—	10	1	no	—
459	C₄²	C₂×C₄×D₅	1	2	yes	—
460	C₄²	C₂×C₄×D₅	1	2	yes	—
461	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
462	C₂×C₅	#2875	1	1	yes	characteristic
463	C₂×C₅	#2875	1	1	yes	characteristic
464	C₂×C₅	#2930	1	2	yes	—
465	C₂×C₅	#2961	1	2	yes	—
466	D₅	—	2	4	no	—
467	C₂³	—	5	2	no	—
468	C₂³	—	5	2	no	—
469	C₂³	—	5	2	no	—
470	C₂³	—	10	2	no	—
471	C₂³	—	10	2	no	—
472	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	5	2	no	—
482	C₂×C₄	—	5	2	no	—
483	C₂×C₄	—	5	2	no	—
484	C₂×C₄	—	5	4	no	—
485	C₂×C₄	—	5	4	no	—
486	C₂×C₄	—	5	4	no	—
487	C₂×C₄	—	5	4	no	—
488	C₂×C₄	—	5	2	no	—
489	C₂×C₄	—	5	2	no	—
490	C₂×C₄	—	10	2	no	—
491	C₂×C₄	—	10	2	no	—
492	C₂×C₄	—	10	2	no	—
493	C₂×C₄	—	10	2	no	—
494	C₂×C₄	—	10	2	no	—
495	C₂×C₄	—	10	2	no	—
496	C₂×C₄	—	10	2	no	—
497	C₂×C₄	—	10	2	no	—
498	C₂×C₄	—	20	8	no	—
499	C₂×C₄	C₄²×D₅	1	2	yes	—
500	C₂×C₄	C₄²×D₅	1	2	yes	—
501	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
502	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
503	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
504	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
505	C₂×C₄	D₅×#41	1	1	yes	characteristic
506	C₂×C₄	D₅×#41	1	1	yes	characteristic
507	C₈	—	2	2	no	—
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	5	4	no	—
511	C₈	—	10	2	no	—
512	C₈	—	10	2	no	—
513	C₈	—	10	2	no	—
514	C₈	D₅×C₄⋊C₄	1	4	yes	—
515	C₅	#20436	1	1	yes	characteristic, complemented, Sylow
516	C₂²	—	5	4	no	—
517	C₂²	—	10	2	no	—
518	C₂²	—	10	4	no	—
519	C₂²	—	10	2	no	—
520	C₂²	—	10	4	no	—
521	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
522	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
523	C₂²	C₄×Q₈×D₅	1	1	yes	characteristic
524	C₂²	#66079	1	2	yes	—
525	C₂²	#66084	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	5	4	no	—
531	C₄	—	10	2	no	—
532	C₄	—	10	2	no	—
533	C₄	—	20	2	no	—
534	C₄	—	20	2	no	—
535	C₄	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
536	C₄	D₅×#117	1	1	yes	characteristic
537	C₄	C₄×D₄×D₅	1	1	yes	characteristic
538	C₄	C₄×Q₈×D₅	1	1	yes	characteristic
539	C₂	—	10	4	no	—
540	C₂	C₄×D₅×C₄⋊C₄	1	1	yes	characteristic
541	C₂	#10610217	1	1	yes	characteristic
542	C₂	#10610281	1	1	yes	characteristic
543	C₂	#10611268	1	2	yes	—
544	C₂	#10611690	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#1770	C₂
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂³×D₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1770	D₅
hypocenter	C₅	#20436
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #1770

Complements

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

N	H ≅ G/N	type
6. C₅×#1770	C₂	semidirect
7. #10601260	C₂	semidirect
8. #10600626	C₂	semidirect
9. #10600626	C₂	semidirect
10. #10600550	C₂	semidirect
11. #10600271	C₂	semidirect
14. #10599447	C₂	semidirect
15. #10599446	C₂	semidirect
45. #65128	C₄	semidirect
48. #64978	C₄	semidirect
105. C₅×C₄⋊C₈	C₂×C₄	semidirect
108. C₄×C₅×C₈	C₂×C₄	semidirect
116. #3947	C₂×C₄	semidirect
117. #3946	C₂×C₄	semidirect
118. #3946	C₂×C₄	semidirect
120. C₈×Dic₅	C₂×C₄	semidirect
121. C₄⋊#168	C₂×C₄	semidirect
123. #3935	C₂×C₄	semidirect
137. #1770	D₅	semidirect
210. C₈×D₅	C₄⋊C₄	semidirect
350. C₄⋊C₈	C₄×D₅	semidirect
362. C₄×C₈	C₄×D₅	semidirect
515. C₅	#20436	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65128	2
C₂×#64997	2
C₂×D₅×#97	2
C₂×#64978	2
#10605486	2
C₅×#1770	2
#10601260	2
#10600626	2
#10600550	2
#10600271	2
#10599454	2
#10599453	2
#10599447	2
#10599446	2
#20436	5