Subgroups — #12106321

Order 1280.

924 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#123	C₂	1	1	yes	maximal, characteristic
2	C₂×#65301	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602404	C₂	1	1	yes	maximal, characteristic
5	#10602324	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600276	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600275	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600271	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600245	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600244	C₂	1	1	yes	maximal, characteristic, complemented
12	#10600243	C₂	1	1	yes	maximal, characteristic, complemented
13	#10600241	C₂	1	1	yes	maximal, characteristic, complemented
14	#10600241	C₂	1	1	yes	maximal, characteristic, complemented
15	#10600241	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#123	C₄	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂²×#681	C₂²	1	1	yes	characteristic
20	C₂²×#681	C₂²	1	1	yes	characteristic
21	C₂²×#681	C₂²	1	1	yes	characteristic
22	C₅×#388	C₄	1	1	yes	characteristic
23	C₅×#388	C₄	1	1	yes	characteristic
24	C₅×#387	C₄	1	1	yes	characteristic
25	C₅×#387	C₄	1	1	yes	characteristic
26	C₅×#386	C₄	1	1	yes	characteristic
27	C₅×#385	C₄	1	1	yes	characteristic
28	C₅×#381	C₄	1	1	yes	characteristic
29	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
39	#65301	—	2	4	no	—
40	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
43	C₄×#681	—	2	4	no	—
44	C₂×#3935	C₂²	1	1	yes	characteristic
45	C₂×#3935	C₂²	1	1	yes	characteristic
46	C₂×#3935	C₂²	1	1	yes	characteristic
47	C₂×C₄×#168	C₂²	1	1	yes	characteristic
48	C₂×C₄×#168	C₂²	1	1	yes	characteristic
49	C₂×C₄×#168	C₂²	1	1	yes	characteristic
50	C₂×C₄×#168	C₂²	1	1	yes	characteristic
51	#64744	C₂²	1	1	yes	characteristic
52	#64744	C₂²	1	1	yes	characteristic
53	#64744	C₂²	1	1	yes	characteristic
54	#64744	C₂²	1	1	yes	characteristic
55	#64744	C₂²	1	1	yes	characteristic
56	#64744	C₂²	1	1	yes	characteristic
57	#64744	C₂²	1	1	yes	characteristic
58	#64744	C₂²	1	1	yes	characteristic
59	#64744	C₂²	1	1	yes	characteristic
60	#64744	C₂²	1	1	yes	characteristic
61	#21565	—	5	1	no	maximal, Sylow
62	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₅×#123	—	2	4	no	—
68	C₄×C₅×D₄	—	2	2	no	—
69	C₄×C₅×D₄	—	2	2	no	—
70	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₅	—	2	2	no	—
84	C₂×C₄²×C₅	—	2	2	no	—
85	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₂×#681	—	2	2	no	—
93	C₂×#681	—	2	2	no	—
94	C₂×#681	—	2	2	no	—
95	C₂×#681	—	2	2	no	—
96	C₂×#681	—	2	2	no	—
97	C₂×#681	—	2	2	no	—
98	C₂×#681	—	2	2	no	—
99	C₂×#681	—	2	2	no	—
100	C₂×#681	D₄	1	4	yes	—
101	C₂²×#168	C₂³	1	1	yes	characteristic
102	C₂²×#168	C₂³	1	1	yes	characteristic
103	C₂²×#168	C₂³	1	1	yes	characteristic
104	C₂²×#168	C₂³	1	1	yes	characteristic
105	C₂²×#168	C₂³	1	1	yes	characteristic
106	C₂²×#168	C₂³	1	1	yes	characteristic
107	C₂²×#168	C₂³	1	1	yes	characteristic
108	C₂²×#168	C₂³	1	1	yes	characteristic
109	C₅×#95	C₂×C₄	1	1	yes	characteristic
110	C₅×#95	C₂×C₄	1	1	yes	characteristic
111	C₅×#95	C₂×C₄	1	1	yes	characteristic
112	C₅×#95	C₂×C₄	1	1	yes	characteristic
113	C₅×#95	C₂×C₄	1	1	yes	characteristic
114	C₅×#95	C₂×C₄	1	1	yes	characteristic
115	C₅×#95	C₂×C₄	1	1	yes	characteristic
116	C₅×#95	C₂×C₄	1	1	yes	characteristic
117	C₅×#95	C₂×C₄	1	1	yes	characteristic
118	C₅×#95	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊#168	—	2	2	no	—
120	C₂²⋊#168	—	2	2	no	—
121	C₂²⋊#168	—	2	2	no	—
122	C₂²⋊#168	—	2	2	no	—
123	C₂²⋊#168	—	2	2	no	—
124	C₄⋊#168	—	2	2	no	—
125	C₄⋊#168	—	2	2	no	—
126	C₄⋊#168	—	2	2	no	—
127	#3935	—	2	2	no	—
128	#3935	—	2	2	no	—
129	#3935	—	2	2	no	—
130	C₄×#168	—	2	2	no	—
131	C₄×#168	—	2	2	no	—
132	C₄×#168	—	2	2	no	—
133	C₄×#168	—	2	2	no	—
134	C₂×#436	—	5	1	no	—
135	C₂×C₄×M₁₆	—	5	1	no	—
136	C₄×#123	D₅	1	1	yes	characteristic
137	#1924	—	5	1	no	—
138	#1923	—	5	1	no	—
139	#1917	—	5	1	no	—
140	#1916	—	5	1	no	—
141	#1870	—	5	1	no	—
142	#1851	—	5	1	no	—
143	#1817	—	5	1	no	—
144	#1771	—	5	1	no	—
145	C₈×C₄⋊C₄	—	5	1	no	—
146	#1753	—	5	1	no	—
147	#1753	—	5	1	no	—
148	#1753	—	5	1	no	—
149	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	4	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	2	2	no	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	—	2	2	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	4	1	no	—
169	C₂²×C₄×C₅	—	4	1	no	—
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₅	#41	1	2	yes	—
184	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	—	4	1	no	—
189	C₅×C₄⋊C₄	M₁₆	1	4	yes	complemented
190	C₅×C₂²⋊C₄	—	2	2	no	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	—	4	1	no	—
197	C₅×C₂²⋊C₄	—	4	1	no	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	—	2	1	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	#681	—	2	8	no	—
211	#681	—	2	8	no	—
212	#681	—	4	4	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	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	2	1	no	—
222	C₂×#168	—	2	1	no	—
223	C₂×#168	—	2	1	no	—
224	C₂×#168	—	2	1	no	—
225	C₂×#168	—	2	1	no	—
226	C₂×#168	—	2	1	no	—
227	C₂×#168	—	2	1	no	—
228	C₂×#168	—	2	1	no	—
229	C₂×#168	—	2	1	no	—
230	C₂×#168	—	2	1	no	—
231	C₂×#168	C₂×D₄	1	2	yes	—
232	C₂×#168	C₂×D₄	1	2	yes	—
233	C₂×#168	#41	1	2	yes	—
234	C₂×#168	#41	1	2	yes	—
235	C₂×#168	#41	1	2	yes	—
236	C₂×#168	#41	1	2	yes	—
237	C₂²×M₁₆	—	5	1	no	—
238	C₂²×M₁₆	—	5	1	no	—
239	C₂²×M₁₆	—	5	1	no	—
240	C₂×#123	Dic₅	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
242	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
243	#436	—	10	4	no	—
244	C₂×C₄⋊C₈	—	5	1	no	—
245	C₂×C₄⋊C₈	—	5	1	no	—
246	C₂×C₄⋊C₈	—	5	1	no	—
247	C₂×C₂²⋊C₈	—	5	1	no	—
248	C₂×C₂²⋊C₈	—	5	1	no	—
249	C₂×C₂²⋊C₈	—	5	1	no	—
250	C₂×C₂²⋊C₈	—	5	1	no	—
251	C₂×C₂²⋊C₈	—	5	1	no	—
252	C₄×M₁₆	—	10	4	no	—
253	C₂×#97	—	5	1	no	—
254	C₂×#97	—	5	1	no	—
255	C₂×#97	—	5	1	no	—
256	C₂×C₄×C₈	—	5	1	no	—
257	C₂×C₄×C₈	—	5	1	no	—
258	C₂×C₄×C₈	—	5	1	no	—
259	C₂×C₄×C₈	—	5	1	no	—
260	#388	Dic₅	1	1	yes	characteristic
261	#388	Dic₅	1	1	yes	characteristic
262	#387	Dic₅	1	1	yes	characteristic
263	#387	Dic₅	1	1	yes	characteristic
264	#386	Dic₅	1	1	yes	characteristic
265	#385	Dic₅	1	1	yes	characteristic
266	#381	Dic₅	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
269	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
270	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
271	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
272	#336	—	5	1	no	—
273	#336	—	5	1	no	—
274	#336	—	5	1	no	—
275	#336	—	5	1	no	—
276	#336	—	5	1	no	—
277	#336	—	5	1	no	—
278	#336	—	5	1	no	—
279	#336	—	5	1	no	—
280	#336	—	5	1	no	—
281	#336	—	5	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	2	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	C₄×D₄	1	2	yes	—
296	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
297	C₅×D₄	—	4	4	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	4	4	no	—
334	C₂×C₄×C₅	—	4	4	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
340	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
341	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
342	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
343	C₂×C₄×C₅	#131	1	2	yes	—
344	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	#168	—	2	2	no	—
351	#168	—	2	2	no	—
352	#168	—	2	2	no	—
353	#168	—	4	1	no	—
354	#168	—	4	1	no	—
355	#168	—	4	1	no	—
356	#168	—	4	1	no	—
357	#168	#123	1	4	yes	complemented
358	C₂²×D₄	C₂×Dic₅	1	1	yes	characteristic
359	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
360	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
361	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
362	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
363	C₂×M₁₆	—	5	4	no	—
364	C₂×M₁₆	—	10	2	no	—
365	C₂×M₁₆	—	10	2	no	—
366	C₂×M₁₆	—	10	2	no	—
367	C₂×M₁₆	—	10	2	no	—
368	C₂×M₁₆	—	10	2	no	—
369	C₂×M₁₆	—	10	2	no	—
370	C₂×M₁₆	—	10	2	no	—
371	C₂×M₁₆	—	10	2	no	—
372	C₂²×C₈	—	5	1	no	—
373	C₂²×C₈	—	5	1	no	—
374	C₂²×C₈	—	5	1	no	—
375	C₂²×C₈	—	5	1	no	—
376	C₂²×C₈	—	5	1	no	—
377	C₂²×C₈	—	5	1	no	—
378	C₂²×C₈	—	5	1	no	—
379	C₂²×C₈	—	5	1	no	—
380	#123	—	2	4	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₂×Dic₅	1	1	yes	characteristic
396	C₂×C₄²	—	2	2	no	—
397	C₂×C₄²	—	2	2	no	—
398	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
399	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
400	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
401	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
402	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
403	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
404	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
405	C₄⋊C₈	—	10	2	no	—
406	C₄⋊C₈	—	10	2	no	—
407	C₄⋊C₈	—	10	2	no	—
408	C₂²⋊C₈	—	10	2	no	—
409	C₂²⋊C₈	—	10	2	no	—
410	C₂²⋊C₈	—	10	2	no	—
411	C₂²⋊C₈	—	10	2	no	—
412	C₂²⋊C₈	—	10	2	no	—
413	#97	—	10	2	no	—
414	#97	—	10	2	no	—
415	#97	—	10	2	no	—
416	C₄×C₈	—	10	2	no	—
417	C₄×C₈	—	10	2	no	—
418	C₄×C₈	—	10	2	no	—
419	C₄×C₈	—	10	2	no	—
420	#95	C₂×Dic₅	1	1	yes	characteristic
421	#95	C₂×Dic₅	1	1	yes	characteristic
422	#95	C₂×Dic₅	1	1	yes	characteristic
423	#95	C₂×Dic₅	1	1	yes	characteristic
424	#95	C₂×Dic₅	1	1	yes	characteristic
425	#95	C₂×Dic₅	1	1	yes	characteristic
426	#95	C₂×Dic₅	1	1	yes	characteristic
427	#95	C₂×Dic₅	1	1	yes	characteristic
428	#95	C₂×Dic₅	1	1	yes	characteristic
429	#95	C₂×Dic₅	1	1	yes	characteristic
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	4	1	no	—
437	C₂²×C₅	—	4	1	no	—
438	C₂²×C₅	—	4	1	no	—
439	C₂²×C₅	—	4	1	no	—
440	C₂²×C₅	—	4	1	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
445	C₂²×C₅	C₄×#41	1	1	yes	characteristic
446	C₂²×C₅	C₄×#41	1	1	yes	characteristic
447	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
448	C₂²×C₅	C₂×#131	1	1	yes	characteristic
449	C₂²×C₅	#568	1	1	yes	characteristic
450	C₂²×C₅	#568	1	1	yes	characteristic
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	2	2	no	—
455	C₄×C₅	—	2	2	no	—
456	C₄×C₅	—	4	1	no	—
457	C₄×C₅	—	4	1	no	—
458	C₄×C₅	—	4	1	no	—
459	C₄×C₅	—	4	1	no	—
460	C₄×C₅	—	4	1	no	—
461	C₄×C₅	—	4	1	no	—
462	C₄×C₅	—	4	1	no	—
463	C₄×C₅	C₂×#123	1	1	yes	characteristic
464	C₄×C₅	#525	1	1	yes	characteristic
465	C₄×C₅	#529	1	1	yes	characteristic
466	C₄×C₅	#529	1	1	yes	characteristic
467	C₂⁴	C₂²×Dic₅	1	1	yes	characteristic
468	C₂⁴	C₂²×Dic₅	1	1	yes	characteristic
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	D₄×D₅	1	2	yes	—
489	C₂²×C₄	#711	1	2	yes	—
490	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
493	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
494	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
495	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
496	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
497	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
498	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
499	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
500	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
501	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
502	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
503	M₁₆	—	10	8	no	—
504	M₁₆	—	10	8	no	—
505	M₁₆	—	20	4	no	—
506	C₂×C₈	—	5	2	no	—
507	C₂×C₈	—	5	2	no	—
508	C₂×C₈	—	5	2	no	—
509	C₂×C₈	—	5	2	no	—
510	C₂×C₈	—	5	2	no	—
511	C₂×C₈	—	5	2	no	—
512	C₂×C₈	—	10	1	no	—
513	C₂×C₈	—	10	1	no	—
514	C₂×C₈	—	10	1	no	—
515	C₂×C₈	—	10	1	no	—
516	C₂×C₈	—	10	1	no	—
517	C₂×C₈	—	10	1	no	—
518	C₂×C₈	—	10	1	no	—
519	C₂×C₈	—	10	1	no	—
520	C₂×C₈	—	10	1	no	—
521	C₂×C₈	—	10	1	no	—
522	C₂×C₈	—	10	1	no	—
523	C₂×C₈	—	10	1	no	—
524	C₂×C₈	—	10	1	no	—
525	C₂×C₈	—	10	1	no	—
526	C₂×C₈	—	10	1	no	—
527	C₂×C₈	—	10	1	no	—
528	C₂×C₈	—	10	1	no	—
529	C₂×C₈	—	10	1	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	#681	1	4	yes	complemented
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	4	1	no	—
542	C₂²⋊C₄	—	4	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₂×C₅	—	4	2	no	—
556	C₂×C₅	—	8	1	no	—
557	C₂×C₅	C₄×#123	1	1	yes	characteristic
558	C₂×C₅	#2933	1	1	yes	characteristic
559	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
560	C₂×C₅	#2965	1	1	yes	characteristic
561	C₂×C₅	#2967	1	1	yes	characteristic
562	C₂×C₅	#2969	1	1	yes	characteristic
563	C₂×C₅	#2971	1	1	yes	characteristic
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	D₄×Dic₅	1	2	yes	—
578	C₂³	C₂³×Dic₅	1	1	yes	characteristic
579	D₄	—	4	4	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	C₂×#681	1	2	yes	—
622	C₂×C₄	C₂×#681	1	2	yes	—
623	C₂×C₄	C₂×#681	1	2	yes	—
624	C₂×C₄	D₄×Dic₅	1	2	yes	—
625	C₂×C₄	#4094	1	2	yes	—
626	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
627	C₂×C₄	C₂×#711	1	1	yes	characteristic
628	C₂×C₄	D₅×#41	1	1	yes	characteristic
629	C₂×C₄	D₅×#41	1	1	yes	characteristic
630	C₂×C₄	D₅×#41	1	1	yes	characteristic
631	C₂×C₄	D₅×#41	1	1	yes	characteristic
632	C₈	—	5	4	no	—
633	C₈	—	10	2	no	—
634	C₈	—	10	2	no	—
635	C₈	—	10	2	no	—
636	C₈	—	20	1	no	—
637	C₈	—	20	1	no	—
638	C₈	—	20	1	no	—
639	C₈	—	20	1	no	—
640	C₅	#21565	1	1	yes	characteristic, complemented, Sylow
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	C₂²×#681	1	1	yes	characteristic
656	C₂²	C₂×D₄×Dic₅	1	1	yes	characteristic
657	C₂²	C₂×#4094	1	1	yes	characteristic
658	C₂²	#66153	1	1	yes	characteristic
659	C₂²	#66153	1	1	yes	characteristic
660	C₂²	#41×Dic₅	1	1	yes	characteristic
661	C₂²	#41×Dic₅	1	1	yes	characteristic
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	#65983	1	1	yes	characteristic
675	C₄	#65983	1	1	yes	characteristic
676	C₄	D₅×#123	1	1	yes	characteristic
677	C₄	#65990	1	1	yes	characteristic
678	C₂	—	4	2	no	—
679	C₂	—	8	1	no	—
680	C₂	D₄×#681	1	1	yes	characteristic
681	C₂	#10614248	1	1	yes	characteristic
682	C₂	#10614250	1	1	yes	characteristic
683	C₂	Dic₅×#123	1	1	yes	characteristic
684	C₂	#10614649	1	1	yes	characteristic
685	C₂	#10614858	1	1	yes	characteristic
686	C₂	#10614860	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₄×C₅×#123	C₂
prime radical	C₂²×C₅×D₄	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₄×#123	D₅
hypocenter	C₅	#21565
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#123

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×#681	C₂	semidirect
5. #10602324	C₂	semidirect
6. #10600276	C₂	semidirect
7. #10600275	C₂	semidirect
8. #10600271	C₂	semidirect
9. C₄⋊C₄×#168	C₂	semidirect
10. #10600245	C₂	semidirect
11. #10600244	C₂	semidirect
12. #10600243	C₂	semidirect
13. #10600241	C₂	semidirect
14. #10600241	C₂	semidirect
15. #10600241	C₂	semidirect
189. C₅×C₄⋊C₄	M₁₆	semidirect
357. #168	#123	semidirect
534. C₄⋊C₄	#681	semidirect
640. C₅	#21565	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#123	2
C₂×#65301	2
C₂×C₄×#681	2
#10602404	2
#10602324	2
#10600276	2
#10600275	2
#10600271	2
C₄⋊C₄×#168	2
#10600245	2
#10600244	2
#10600243	2
#10600241	2
#21565	5