Subgroups — #12116684

Order 1280.

864 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#4023	C₂	1	1	yes	maximal, characteristic
2	C₅×#1850	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#64770	C₂	1	1	yes	maximal, characteristic
5	#10601240	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601240	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601236	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600740	C₂	1	1	yes	maximal, characteristic
10	#10600703	C₂	1	1	yes	maximal, characteristic
11	#10600242	C₂	1	1	yes	maximal, characteristic
12	#10599404	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599404	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599400	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599389	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₂³×#168	C₂²	1	1	yes	characteristic
19	C₂×#4023	C₄	1	1	yes	characteristic
20	C₂×#4023	C₄	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
31	C₂²⋊C₄×Dic₅	C₄	1	1	yes	characteristic
32	C₂²⋊C₄×Dic₅	C₄	1	1	yes	characteristic
33	C₄×#683	C₂²	1	1	yes	characteristic
34	C₄×#683	C₂²	1	1	yes	characteristic
35	C₄²×Dic₅	C₂²	1	1	yes	characteristic
36	C₄²×Dic₅	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
39	#64938	C₄	1	1	yes	characteristic
40	#64938	C₄	1	1	yes	characteristic
41	#64937	C₄	1	1	yes	characteristic
42	#64937	C₄	1	1	yes	characteristic
43	C₅×#336	C₂²	1	1	yes	characteristic
44	C₅×#336	C₂²	1	1	yes	characteristic
45	#64770	C₂²	1	1	yes	characteristic
46	#64770	C₂²	1	1	yes	characteristic
47	#64770	C₂²	1	1	yes	characteristic
48	#64770	C₂²	1	1	yes	characteristic
49	#64770	C₂²	1	1	yes	characteristic
50	#64770	C₂²	1	1	yes	characteristic
51	#64770	C₂²	1	1	yes	characteristic
52	#64770	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	#22589	—	5	1	no	maximal, Sylow
60	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂³×Dic₅	C₂×C₄	1	1	yes	characteristic
62	C₂³×Dic₅	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	—	2	2	no	—
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₂²×C₅×C₈	—	4	1	no	—
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₂×#683	C₂×C₄	1	1	yes	characteristic
77	C₂×#683	C₂×C₄	1	1	yes	characteristic
78	C₂×#683	C₂×C₄	1	1	yes	characteristic
79	C₂×#683	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×Dic₅	—	2	2	no	—
81	C₂×C₄×Dic₅	—	2	2	no	—
82	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
93	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
94	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
95	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
96	C₂²×#168	—	2	2	no	—
97	C₂²×#168	—	2	2	no	—
98	C₂²×#168	—	4	1	no	—
99	C₂²×#168	C₂³	1	1	yes	characteristic
100	C₂²×#168	C₂³	1	1	yes	characteristic
101	C₂²×#168	C₂³	1	1	yes	characteristic
102	C₂²×#168	C₂³	1	1	yes	characteristic
103	#4023	—	2	4	no	—
104	#4023	C₈	1	8	yes	complemented
105	C₅×C₄⋊C₈	—	2	2	no	—
106	C₅×C₄⋊C₈	—	4	1	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×#95	C₂×C₄	1	1	yes	characteristic
109	C₅×#95	C₂×C₄	1	1	yes	characteristic
110	#3963	C₂×C₄	1	1	yes	characteristic
111	#3963	C₂×C₄	1	1	yes	characteristic
112	#3963	C₂×C₄	1	1	yes	characteristic
113	#3963	C₂×C₄	1	1	yes	characteristic
114	#3963	C₂×C₄	1	1	yes	characteristic
115	#3963	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#168	—	2	2	no	—
117	C₈×Dic₅	—	2	2	no	—
118	C₈×Dic₅	—	2	2	no	—
119	C₈×Dic₅	—	4	1	no	—
120	C₈×Dic₅	—	4	1	no	—
121	C₄⋊#168	—	2	2	no	—
122	C₄⋊#168	—	4	1	no	—
123	C₄×#117	—	5	1	no	—
124	#1916	—	5	1	no	—
125	#1916	—	5	1	no	—
126	#1916	—	5	1	no	—
127	#1916	—	5	1	no	—
128	#1850	—	5	1	no	—
129	#1850	D₅	1	1	yes	characteristic
130	#1839	—	5	1	no	—
131	#1831	—	5	1	no	—
132	#1817	—	5	1	no	—
133	C₄×C₄⋊C₈	—	5	1	no	—
134	C₈×C₂²⋊C₄	—	5	1	no	—
135	C₈×C₂²⋊C₄	—	5	1	no	—
136	#1744	—	5	1	no	—
137	C₂×#336	—	5	1	no	—
138	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	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	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	#41	1	2	yes	—
149	C₂²×C₄×C₅	#41	1	2	yes	—
150	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
151	C₂²×Dic₅	—	2	2	no	—
152	C₂²×Dic₅	—	2	2	no	—
153	C₂²×Dic₅	—	2	2	no	—
154	C₂²×Dic₅	—	2	2	no	—
155	C₂²×Dic₅	—	4	1	no	—
156	C₂²×Dic₅	C₂×C₈	1	4	yes	—
157	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
158	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
159	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
163	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	4	4	no	—
177	C₂×C₅×C₈	#41	1	2	yes	—
178	C₅×C₂²⋊C₄	—	2	2	no	—
179	C₅×C₂²⋊C₄	C₂×C₈	1	4	yes	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	—	2	1	no	—
182	C₄²×C₅	—	2	1	no	—
183	C₄²×C₅	—	2	1	no	—
184	C₂²⋊Dic₅	C₂×C₈	1	4	yes	—
185	C₂²⋊Dic₅	M₁₆	1	4	yes	—
186	#683	—	2	2	no	—
187	#683	—	2	2	no	—
188	#683	C₂×C₈	1	4	yes	complemented
189	#683	C₂×C₈	1	4	yes	complemented
190	C₄×Dic₅	—	2	2	no	—
191	C₄×Dic₅	—	2	2	no	—
192	C₄×Dic₅	—	2	1	no	—
193	C₄×Dic₅	—	2	1	no	—
194	C₄×Dic₅	—	2	1	no	—
195	C₄×Dic₅	—	2	1	no	—
196	C₄×Dic₅	—	2	1	no	—
197	C₄×Dic₅	—	2	1	no	—
198	C₄×Dic₅	—	2	1	no	—
199	C₄×Dic₅	—	2	1	no	—
200	C₄×Dic₅	—	2	2	no	—
201	C₄×Dic₅	—	2	2	no	—
202	C₄×Dic₅	—	2	2	no	—
203	C₄×Dic₅	—	2	2	no	—
204	C₄×Dic₅	—	4	1	no	—
205	C₄×Dic₅	—	4	1	no	—
206	C₄×Dic₅	C₂×C₈	1	4	yes	complemented
207	C₄×Dic₅	C₂×C₈	1	4	yes	complemented
208	C₂×#168	—	2	1	no	—
209	C₂×#168	—	2	1	no	—
210	C₂×#168	—	2	1	no	—
211	C₂×#168	—	2	1	no	—
212	C₂×#168	—	2	1	no	—
213	C₂×#168	—	2	1	no	—
214	C₂×#168	—	2	1	no	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	4	4	no	—
220	C₂×#168	#41	1	2	yes	—
221	C₂³×C₈	—	5	1	no	—
222	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
223	C₂×#117	—	5	1	no	—
224	C₂×#117	—	5	1	no	—
225	C₂²×C₄²	—	5	1	no	—
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	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	—	5	1	no	—
231	C₂×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
232	C₂×C₄×C₈	—	5	1	no	—
233	C₂×C₄×C₈	—	5	1	no	—
234	C₂×C₄×C₈	—	5	1	no	—
235	C₂×C₄×C₈	—	5	1	no	—
236	C₄×C₄⋊C₄	—	5	1	no	—
237	C₄×C₄⋊C₄	—	5	1	no	—
238	C₄×C₄⋊C₄	—	5	1	no	—
239	C₄×C₄⋊C₄	—	5	1	no	—
240	C₄×C₂²⋊C₄	—	5	1	no	—
241	C₄×C₂²⋊C₄	—	5	1	no	—
242	C₄×C₂²⋊C₄	—	5	1	no	—
243	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
244	#376	—	5	1	no	—
245	#376	—	5	1	no	—
246	C₄³	—	5	1	no	—
247	C₄³	—	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	—	5	1	no	—
253	#336	—	5	1	no	—
254	#336	—	5	1	no	—
255	#336	—	5	1	no	—
256	#336	—	5	1	no	—
257	#336	—	5	1	no	—
258	#336	—	5	1	no	—
259	#336	—	5	1	no	—
260	#336	—	5	1	no	—
261	#336	—	5	1	no	—
262	#336	C₂×D₅	1	1	yes	characteristic
263	#336	C₂×D₅	1	1	yes	characteristic
264	C₂³×C₅	—	2	1	no	—
265	C₂³×C₅	—	2	1	no	—
266	C₂³×C₅	—	2	1	no	—
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	#117	1	2	yes	—
269	C₂³×C₅	C₂²×C₈	1	2	yes	—
270	C₂³×C₅	C₂×M₁₆	1	2	yes	—
271	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	#117	1	2	yes	—
289	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
290	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
291	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
297	C₂×Dic₅	—	2	1	no	—
298	C₂×Dic₅	—	2	1	no	—
299	C₂×Dic₅	—	2	1	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	1	no	—
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	—	2	1	no	—
304	C₂×Dic₅	—	2	1	no	—
305	C₂×Dic₅	—	2	1	no	—
306	C₂×Dic₅	—	2	1	no	—
307	C₂×Dic₅	—	2	1	no	—
308	C₂×Dic₅	—	2	1	no	—
309	C₂×Dic₅	—	2	1	no	—
310	C₂×Dic₅	—	2	1	no	—
311	C₂×Dic₅	—	2	8	no	—
312	C₂×Dic₅	—	2	1	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	—	2	1	no	—
315	C₂×Dic₅	—	4	4	no	—
316	C₂×Dic₅	C₂²×C₈	1	2	yes	—
317	C₂×Dic₅	C₂²×C₈	1	2	yes	—
318	C₂×Dic₅	C₂²×C₈	1	2	yes	—
319	C₂×Dic₅	C₂²×C₈	1	2	yes	—
320	C₂×Dic₅	C₂×M₁₆	1	2	yes	—
321	C₂×Dic₅	C₂×M₁₆	1	2	yes	—
322	C₂×Dic₅	#131	1	2	yes	—
323	C₅×C₈	—	2	2	no	—
324	C₅×C₈	—	4	1	no	—
325	C₅×C₈	—	4	1	no	—
326	C₅×C₈	—	4	1	no	—
327	#168	—	2	2	no	—
328	#168	—	4	1	no	—
329	#168	—	4	1	no	—
330	#168	—	4	1	no	—
331	C₂³×C₄	—	5	1	no	—
332	C₂³×C₄	—	5	1	no	—
333	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	4	1	no	—
337	C₂²×C₈	—	5	1	no	—
338	C₂²×C₈	—	5	1	no	—
339	C₂²×C₈	—	5	1	no	—
340	C₂²×C₈	—	5	1	no	—
341	C₂²×C₈	—	10	2	no	—
342	C₂²×C₈	—	10	2	no	—
343	C₂²×C₈	—	20	1	no	—
344	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
347	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
348	#117	—	5	8	no	—
349	#117	—	10	4	no	—
350	C₂×C₄⋊C₄	—	5	1	no	—
351	C₂×C₄⋊C₄	—	5	1	no	—
352	C₂×C₄⋊C₄	—	5	1	no	—
353	C₂×C₄⋊C₄	—	5	1	no	—
354	C₂×C₂²⋊C₄	—	5	1	no	—
355	C₂×C₂²⋊C₄	—	5	1	no	—
356	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
358	C₂×C₄²	—	5	1	no	—
359	C₂×C₄²	—	5	1	no	—
360	C₂×C₄²	—	5	1	no	—
361	C₂×C₄²	—	5	1	no	—
362	C₂×C₄²	—	5	1	no	—
363	C₂×C₄²	—	5	1	no	—
364	C₂×C₄²	—	5	1	no	—
365	C₂×C₄²	—	5	1	no	—
366	C₂×C₄²	—	5	1	no	—
367	C₂×C₄²	—	5	1	no	—
368	C₂×C₄²	—	5	1	no	—
369	C₂×C₄²	—	5	1	no	—
370	C₂×C₄²	—	5	1	no	—
371	C₂×C₄²	—	5	1	no	—
372	C₂×C₄²	—	10	2	no	—
373	C₂×C₄²	—	10	2	no	—
374	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
376	C₄⋊C₈	—	2	2	no	—
377	C₄⋊C₈	—	4	1	no	—
378	C₄⋊C₈	—	10	2	no	—
379	C₄⋊C₈	—	20	1	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	C₂²⋊C₈	—	10	2	no	—
382	C₄×C₈	—	10	2	no	—
383	C₄×C₈	—	10	2	no	—
384	C₄×C₈	—	20	1	no	—
385	C₄×C₈	—	20	1	no	—
386	#95	—	5	1	no	—
387	#95	—	5	1	no	—
388	#95	—	5	1	no	—
389	#95	—	5	1	no	—
390	#95	—	5	1	no	—
391	#95	—	5	1	no	—
392	#95	C₄×D₅	1	1	yes	characteristic
393	#95	C₄×D₅	1	1	yes	characteristic
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	2	2	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	#431	1	4	yes	—
401	C₂²×C₅	C₂×#117	1	1	yes	characteristic
402	C₂²×C₅	C₄×#41	1	1	yes	characteristic
403	C₂²×C₅	#520	1	1	yes	characteristic
404	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
405	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
406	C₂²×C₅	C₂×#131	1	1	yes	characteristic
407	C₂²×C₅	#568	1	1	yes	characteristic
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	2	2	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	#551	1	1	yes	characteristic
414	C₄×C₅	#551	1	1	yes	characteristic
415	C₄×C₅	#552	1	1	yes	characteristic
416	C₄×C₅	#552	1	1	yes	characteristic
417	Dic₅	—	2	2	no	—
418	Dic₅	—	2	2	no	—
419	Dic₅	—	2	2	no	—
420	Dic₅	—	2	2	no	—
421	Dic₅	—	2	2	no	—
422	Dic₅	—	2	2	no	—
423	Dic₅	—	2	2	no	—
424	Dic₅	—	4	1	no	—
425	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	5	1	no	—
431	C₂²×C₄	—	5	1	no	—
432	C₂²×C₄	—	5	1	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	1	no	—
435	C₂²×C₄	—	5	1	no	—
436	C₂²×C₄	—	5	1	no	—
437	C₂²×C₄	—	5	4	no	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	10	2	no	—
440	C₂²×C₄	—	10	2	no	—
441	C₂²×C₄	—	10	2	no	—
442	C₂²×C₄	—	10	2	no	—
443	C₂²×C₄	—	20	1	no	—
444	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
449	C₂²×C₄	#711	1	2	yes	—
450	C₂²×C₄	#713	1	2	yes	—
451	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	4	4	no	—
464	C₂×C₈	—	5	2	no	—
465	C₂×C₈	—	10	1	no	—
466	C₂×C₈	—	10	1	no	—
467	C₂×C₈	—	10	1	no	—
468	C₂×C₈	—	10	1	no	—
469	C₂×C₈	—	10	1	no	—
470	C₂×C₈	—	10	1	no	—
471	C₂×C₈	—	10	1	no	—
472	C₂×C₈	—	10	1	no	—
473	C₂×C₈	—	10	1	no	—
474	C₂×C₈	—	10	1	no	—
475	C₂×C₈	—	10	1	no	—
476	C₂×C₈	—	20	4	no	—
477	C₂×C₈	#711	1	2	yes	—
478	C₄⋊C₄	—	5	4	no	—
479	C₄⋊C₄	—	5	4	no	—
480	C₄⋊C₄	—	10	2	no	—
481	C₄⋊C₄	—	10	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	5	4	no	—
484	C₂²⋊C₄	—	5	4	no	—
485	C₂²⋊C₄	C₈×D₅	1	4	yes	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	5	4	no	—
491	C₄²	—	5	4	no	—
492	C₄²	—	10	2	no	—
493	C₄²	—	10	2	no	—
494	C₄²	—	10	2	no	—
495	C₄²	—	10	2	no	—
496	C₄²	—	10	1	no	—
497	C₄²	—	10	1	no	—
498	C₄²	—	10	1	no	—
499	C₄²	—	10	1	no	—
500	C₄²	—	10	1	no	—
501	C₄²	—	10	1	no	—
502	C₄²	—	10	1	no	—
503	C₄²	—	10	1	no	—
504	C₄²	—	10	2	no	—
505	C₄²	—	10	2	no	—
506	C₄²	—	20	1	no	—
507	C₄²	—	20	1	no	—
508	C₂×C₅	—	2	4	no	—
509	C₂×C₅	#2343	1	1	yes	characteristic
510	C₂×C₅	C₂×#431	1	1	yes	characteristic
511	C₂×C₅	#2924	1	1	yes	characteristic
512	C₂×C₅	C₈×#41	1	1	yes	characteristic
513	C₂×C₅	#2970	1	1	yes	characteristic
514	C₂×C₅	#2988	1	1	yes	characteristic
515	C₂×C₅	#2990	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	#4038	1	2	yes	—
521	C₂³	C₂×C₈×D₅	1	2	yes	—
522	C₂³	D₅×M₁₆	1	2	yes	—
523	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	5	2	no	—
541	C₂×C₄	—	5	2	no	—
542	C₂×C₄	—	5	2	no	—
543	C₂×C₄	—	5	2	no	—
544	C₂×C₄	—	5	2	no	—
545	C₂×C₄	—	5	2	no	—
546	C₂×C₄	—	5	2	no	—
547	C₂×C₄	—	10	1	no	—
548	C₂×C₄	—	10	1	no	—
549	C₂×C₄	—	10	1	no	—
550	C₂×C₄	—	10	1	no	—
551	C₂×C₄	—	10	1	no	—
552	C₂×C₄	—	10	1	no	—
553	C₂×C₄	—	10	1	no	—
554	C₂×C₄	—	10	1	no	—
555	C₂×C₄	—	10	1	no	—
556	C₂×C₄	—	10	1	no	—
557	C₂×C₄	—	10	1	no	—
558	C₂×C₄	—	10	1	no	—
559	C₂×C₄	—	10	1	no	—
560	C₂×C₄	—	10	1	no	—
561	C₂×C₄	—	10	8	no	—
562	C₂×C₄	—	10	1	no	—
563	C₂×C₄	—	10	1	no	—
564	C₂×C₄	—	10	1	no	—
565	C₂×C₄	—	20	4	no	—
566	C₂×C₄	#4038	1	2	yes	—
567	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
568	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
569	C₂×C₄	C₂×#711	1	1	yes	characteristic
570	C₂×C₄	C₂×#711	1	1	yes	characteristic
571	C₂×C₄	#4144	1	1	yes	characteristic
572	C₂×C₄	C₂×#713	1	1	yes	characteristic
573	C₂×C₄	D₅×#41	1	1	yes	characteristic
574	C₂×C₄	#4150	1	1	yes	characteristic
575	C₈	—	2	2	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₈	—	10	2	no	—
580	C₈	—	20	1	no	—
581	C₈	—	20	1	no	—
582	C₈	—	20	1	no	—
583	C₅	#22589	1	1	yes	characteristic, complemented, Sylow
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	#65122	1	4	yes	—
591	C₂²	C₂×#4038	1	1	yes	characteristic
592	C₂²	C₄×#711	1	1	yes	characteristic
593	C₂²	#65880	1	1	yes	characteristic
594	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
595	C₂²	C₂×D₅×M₁₆	1	1	yes	characteristic
596	C₂²	D₅×#131	1	1	yes	characteristic
597	C₂²	#66084	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	10	2	no	—
604	C₄	—	10	2	no	—
605	C₄	—	10	2	no	—
606	C₄	—	10	2	no	—
607	C₄	—	10	2	no	—
608	C₄	—	10	2	no	—
609	C₄	—	10	2	no	—
610	C₄	—	20	1	no	—
611	C₄	#65921	1	1	yes	characteristic
612	C₄	#65971	1	1	yes	characteristic
613	C₄	#65976	1	1	yes	characteristic
614	C₄	#65984	1	1	yes	characteristic
615	C₂	—	2	4	no	—
616	C₂	#10606123	1	1	yes	characteristic
617	C₂	C₂×#65122	1	1	yes	characteristic
618	C₂	#10610803	1	1	yes	characteristic
619	C₂	C₈×#711	1	1	yes	characteristic
620	C₂	#10611136	1	1	yes	characteristic
621	C₂	#10611191	1	1	yes	characteristic
622	C₂	#10611193	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₈
Fitting	C₅×#1850	C₂
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1850	D₅
hypocenter	C₅	#22589
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #1850

Complements

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

N	H ≅ G/N	type
5. #10601240	C₂	semidirect
6. #10601240	C₂	semidirect
7. #10601236	C₂	semidirect
8. Dic₅×C₄⋊C₈	C₂	semidirect
12. #10599404	C₂	semidirect
13. #10599404	C₂	semidirect
14. #10599400	C₂	semidirect
15. #10599389	C₂	semidirect
104. #4023	C₈	semidirect
188. #683	C₂×C₈	semidirect
189. #683	C₂×C₈	semidirect
206. C₄×Dic₅	C₂×C₈	semidirect
207. C₄×Dic₅	C₂×C₈	semidirect
583. C₅	#22589	semidirect

Maximal subgroups

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

subgroup	index
C₄×#4023	2
C₅×#1850	2
C₈×C₂²⋊Dic₅	2
C₂×#64770	2
#10601240	2
#10601236	2
Dic₅×C₄⋊C₈	2
#10600740	2
#10600703	2
#10600242	2
#10599404	2
#10599400	2
#10599389	2
#22589	5