Subgroups — #12106779

Order 1280.

886 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64990	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#676	C₂	1	1	yes	maximal, characteristic
3	C₄×#4042	C₂	1	1	yes	maximal, characteristic
4	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601271	C₂	1	1	yes	maximal, characteristic
6	#10601245	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600604	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600601	C₂	1	1	yes	maximal, characteristic
9	#10600601	C₂	1	1	yes	maximal, characteristic
10	C₈×#683	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600275	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599460	C₂	1	1	yes	maximal, characteristic
13	#10599455	C₂	1	1	yes	maximal, characteristic
14	#10599448	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599413	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#676	C₂²	1	1	yes	characteristic
17	C₂²×#676	C₂²	1	1	yes	characteristic
18	C₂×#4042	C₄	1	1	yes	characteristic
19	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×#97	C₂²	1	1	yes	characteristic
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×#3952	C₂²	1	1	yes	characteristic
27	C₂×#3952	C₂²	1	1	yes	characteristic
28	C₂×#3947	C₂²	1	1	yes	characteristic
29	C₂×#3947	C₂²	1	1	yes	characteristic
30	C₂×#3946	C₂²	1	1	yes	characteristic
31	C₂×#3946	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	1	yes	characteristic
37	#65270	C₄	1	1	yes	characteristic
38	#65261	C₄	1	1	yes	characteristic
39	C₄×#685	C₂²	1	1	yes	characteristic
40	C₄×#685	C₂²	1	1	yes	characteristic
41	C₄×#683	C₂²	1	1	yes	characteristic
42	C₄×#683	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
44	C₂×C₄×#168	C₂²	1	1	yes	characteristic
45	#64990	—	2	4	no	—
46	C₄×#676	—	2	4	no	—
47	#64957	C₄	1	1	yes	characteristic
48	#64956	C₄	1	1	yes	characteristic
49	#64941	C₄	1	1	yes	characteristic
50	#64935	C₄	1	1	yes	characteristic
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	#64744	C₂²	1	1	yes	characteristic
60	#64744	C₂²	1	1	yes	characteristic
61	#21600	—	5	1	no	maximal, Sylow
62	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₀	C₂×C₄	1	1	yes	characteristic
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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₄⋊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×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×#685	C₂×C₄	1	1	yes	characteristic
76	C₂×#685	C₂×C₄	1	1	yes	characteristic
77	C₂×#685	C₂×C₄	1	1	yes	characteristic
78	C₂×#685	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
80	C₂×#683	C₂×C₄	1	1	yes	characteristic
81	C₂×#683	C₂×C₄	1	1	yes	characteristic
82	C₂×#683	C₂×C₄	1	1	yes	characteristic
83	C₂×#683	C₂×C₄	1	1	yes	characteristic
84	C₂×#683	C₂×C₄	1	1	yes	characteristic
85	C₂×#683	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	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
91	C₂²×#168	C₂³	1	1	yes	characteristic
92	C₂²×#168	C₂³	1	1	yes	characteristic
93	C₂²×#168	C₂³	1	1	yes	characteristic
94	C₂²×#168	C₂³	1	1	yes	characteristic
95	C₂×#676	—	2	2	no	—
96	C₂×#676	—	2	2	no	—
97	C₂×#676	—	2	2	no	—
98	C₂×#676	—	2	2	no	—
99	C₂×#676	—	2	2	no	—
100	C₂×#676	Q₈	1	4	yes	complemented
101	#4042	—	2	4	no	—
102	C₄²×D₅	—	2	2	no	—
103	C₄²×D₅	—	2	2	no	—
104	C₄×Dic₁₀	—	2	2	no	—
105	C₄×Dic₁₀	—	2	2	no	—
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×#97	—	2	2	no	—
108	C₅×#97	—	2	2	no	—
109	C₄×C₅×C₈	—	2	2	no	—
110	C₅×#95	C₂×C₄	1	1	yes	characteristic
111	C₅×#95	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	#3963	C₂×C₄	1	1	yes	characteristic
117	#3963	C₂×C₄	1	1	yes	characteristic
118	#3963	C₂×C₄	1	1	yes	characteristic
119	#3963	C₂×C₄	1	1	yes	characteristic
120	#3952	—	2	2	no	—
121	#3952	—	2	2	no	—
122	#3947	—	2	2	no	—
123	#3947	D₄	1	4	yes	—
124	#3946	—	2	2	no	—
125	#3946	—	2	2	no	—
126	#3946	—	2	2	no	—
127	#3946	—	2	2	no	—
128	C₈×Dic₅	—	2	2	no	—
129	C₈×Dic₅	—	2	2	no	—
130	C₄⋊#168	—	2	2	no	—
131	C₄×#168	—	2	2	no	—
132	C₂×#446	—	5	1	no	—
133	C₂×C₄×M₁₆	—	5	1	no	—
134	C₄×C₂²⋊Q₈	—	5	1	no	—
135	#1985	—	5	1	no	—
136	#1940	—	5	1	no	—
137	#1916	—	5	1	no	—
138	#1916	—	5	1	no	—
139	#1851	—	5	1	no	—
140	#1851	—	5	1	no	—
141	#1797	—	5	1	no	—
142	#1771	—	5	1	no	—
143	#1771	D₅	1	1	yes	characteristic, complemented
144	C₈×C₄⋊C₄	—	5	1	no	—
145	#1753	—	5	1	no	—
146	#1753	—	5	1	no	—
147	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
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	C₂×C₄×D₅	—	2	1	no	—
163	C₂×C₄×D₅	—	2	1	no	—
164	C₂×C₄×D₅	—	2	1	no	—
165	C₂×C₄×D₅	—	2	1	no	—
166	C₂×C₄×D₅	—	2	2	no	—
167	C₂×C₄×D₅	—	2	2	no	—
168	C₂×C₄×D₅	—	2	2	no	—
169	C₂×C₄×D₅	—	2	2	no	—
170	C₂×C₄×D₅	—	4	1	no	—
171	C₂×C₄×D₅	—	4	1	no	—
172	C₂×C₄×D₅	C₂×Q₈	1	2	yes	—
173	C₂×C₄×D₅	#41	1	2	yes	—
174	C₂×Dic₁₀	—	2	2	no	—
175	C₂×Dic₁₀	—	2	2	no	—
176	C₂×Dic₁₀	—	4	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
186	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
187	C₂×C₅×C₈	#41	1	2	yes	—
188	C₂×C₅×C₈	#41	1	2	yes	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₄²×C₅	—	2	1	no	—
192	C₄²×C₅	—	2	1	no	—
193	C₄²×C₅	—	2	1	no	—
194	C₄²×C₅	—	2	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	#685	—	2	2	no	—
198	#685	—	2	2	no	—
199	#685	—	4	1	no	—
200	#685	—	4	1	no	—
201	C₄⋊Dic₅	—	2	2	no	—
202	#683	—	2	2	no	—
203	#683	—	2	2	no	—
204	#683	—	2	2	no	—
205	#683	—	2	2	no	—
206	#683	—	4	1	no	—
207	#683	M₁₆	1	4	yes	complemented
208	C₄×Dic₅	—	2	1	no	—
209	C₄×Dic₅	—	2	1	no	—
210	C₄×Dic₅	—	2	1	no	—
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	—	2	2	no	—
213	C₄×Dic₅	—	2	2	no	—
214	C₄×Dic₅	C₂×D₄	1	2	yes	—
215	C₄×Dic₅	#41	1	2	yes	—
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	C₂×D₄	1	2	yes	—
227	C₂×#168	C₂×Q₈	1	2	yes	—
228	#676	—	2	8	no	—
229	#676	—	2	8	no	—
230	C₂²×M₁₆	—	5	1	no	—
231	C₂²×M₁₆	—	5	1	no	—
232	C₂×C₂²⋊Q₈	—	5	1	no	—
233	C₂×C₄×Q₈	—	5	1	no	—
234	C₂²×C₄²	—	5	1	no	—
235	#446	—	10	4	no	—
236	C₂×C₄⋊C₈	—	5	1	no	—
237	C₂×C₄⋊C₈	—	5	1	no	—
238	C₂×C₄⋊C₈	—	5	1	no	—
239	C₂×C₄⋊C₈	—	5	1	no	—
240	C₂×C₄⋊C₈	—	5	1	no	—
241	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	—	5	1	no	—
243	C₂×C₂²⋊C₈	—	5	1	no	—
244	C₄×M₁₆	—	10	4	no	—
245	C₂×#97	—	5	1	no	—
246	C₂×#97	—	5	1	no	—
247	C₂×#97	C₂×D₅	1	1	yes	characteristic
248	C₂×#97	C₂×D₅	1	1	yes	characteristic
249	C₂×C₄×C₈	—	5	1	no	—
250	C₂×C₄×C₈	—	5	1	no	—
251	C₂×C₄×C₈	—	5	1	no	—
252	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
253	#391	—	5	1	no	—
254	#389	—	5	1	no	—
255	#387	—	5	1	no	—
256	#387	—	5	1	no	—
257	#385	—	5	1	no	—
258	#385	—	5	1	no	—
259	#380	—	5	1	no	—
260	C₄×C₄⋊C₄	—	5	1	no	—
261	C₄×C₄⋊C₄	—	5	1	no	—
262	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	—	5	1	no	—
264	C₄×C₂²⋊C₄	—	5	1	no	—
265	#336	—	5	1	no	—
266	#336	—	5	1	no	—
267	#336	—	5	1	no	—
268	#336	—	5	1	no	—
269	#336	—	5	1	no	—
270	#336	—	5	1	no	—
271	#336	—	5	1	no	—
272	#336	—	5	1	no	—
273	#336	C₂×D₅	1	1	yes	characteristic
274	#336	C₂×D₅	1	1	yes	characteristic
275	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
276	C₂²×D₅	—	2	1	no	—
277	C₂²×D₅	—	2	1	no	—
278	C₂²×D₅	—	2	1	no	—
279	C₂²×D₅	—	2	1	no	—
280	C₂²×D₅	—	2	1	no	—
281	C₂²×D₅	—	2	1	no	—
282	C₂²×D₅	C₄×Q₈	1	2	yes	—
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	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
300	C₂×C₄×C₅	#131	1	2	yes	—
301	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
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	1	no	—
312	C₂×Dic₅	—	2	1	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	—	2	1	no	—
315	C₂×Dic₅	—	2	1	no	—
316	C₂×Dic₅	—	2	1	no	—
317	C₂×Dic₅	—	2	1	no	—
318	C₂×Dic₅	—	2	1	no	—
319	C₂×Dic₅	—	2	1	no	—
320	C₂×Dic₅	—	2	1	no	—
321	C₂×Dic₅	—	2	1	no	—
322	C₂×Dic₅	—	2	1	no	—
323	C₂×Dic₅	C₄×D₄	1	2	yes	—
324	C₂×Dic₅	C₄×D₄	1	2	yes	—
325	C₂×Dic₅	C₄×Q₈	1	2	yes	—
326	C₂×Dic₅	C₂×M₁₆	1	2	yes	—
327	C₂×Dic₅	C₂×M₁₆	1	2	yes	—
328	C₄×D₅	—	2	2	no	—
329	C₄×D₅	—	2	2	no	—
330	C₄×D₅	—	2	2	no	—
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	4	4	no	—
333	C₄×D₅	—	4	4	no	—
334	Dic₁₀	—	4	4	no	—
335	C₅×C₈	—	2	2	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	C₂²⋊Q₈	1	4	yes	complemented
339	#168	—	2	2	no	—
340	#168	—	2	2	no	—
341	#168	—	4	1	no	—
342	#168	—	4	1	no	—
343	C₂²×Q₈	—	5	1	no	—
344	C₂³×C₄	—	5	1	no	—
345	C₂³×C₄	—	5	1	no	—
346	C₂³×C₄	—	5	1	no	—
347	C₂×M₁₆	—	5	4	no	—
348	C₂×M₁₆	—	10	2	no	—
349	C₂×M₁₆	—	10	2	no	—
350	C₂×M₁₆	—	10	2	no	—
351	C₂×M₁₆	—	10	2	no	—
352	C₂×M₁₆	—	10	2	no	—
353	C₂²×C₈	—	5	1	no	—
354	C₂²×C₈	—	5	1	no	—
355	C₂²×C₈	—	5	1	no	—
356	C₂²×C₈	—	5	1	no	—
357	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
358	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
359	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
360	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
361	C₂²⋊Q₈	—	10	4	no	—
362	C₄×Q₈	—	10	2	no	—
363	C₄×Q₈	—	10	2	no	—
364	C₂×C₄⋊C₄	—	5	1	no	—
365	C₂×C₄⋊C₄	—	5	1	no	—
366	C₂×C₄⋊C₄	—	5	1	no	—
367	C₂×C₄⋊C₄	—	5	1	no	—
368	C₂×C₄⋊C₄	—	5	1	no	—
369	C₂×C₄⋊C₄	—	5	1	no	—
370	C₂×C₄⋊C₄	—	5	1	no	—
371	C₂×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	5	1	no	—
374	C₂×C₂²⋊C₄	—	5	1	no	—
375	C₂×C₂²⋊C₄	—	5	1	no	—
376	C₂×C₂²⋊C₄	—	5	1	no	—
377	C₂×C₄²	—	5	1	no	—
378	C₂×C₄²	—	5	1	no	—
379	C₂×C₄²	—	5	1	no	—
380	C₂×C₄²	—	5	1	no	—
381	C₂×C₄²	—	5	1	no	—
382	C₂×C₄²	—	10	2	no	—
383	C₂×C₄²	—	10	2	no	—
384	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
385	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
386	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
387	C₄⋊C₈	—	2	2	no	—
388	C₄⋊C₈	—	10	2	no	—
389	C₄⋊C₈	—	10	2	no	—
390	C₄⋊C₈	—	10	2	no	—
391	C₄⋊C₈	—	10	2	no	—
392	C₄⋊C₈	—	10	2	no	—
393	C₂²⋊C₈	—	10	2	no	—
394	C₂²⋊C₈	—	10	2	no	—
395	#97	—	2	2	no	—
396	#97	—	2	2	no	—
397	#97	—	5	4	no	—
398	#97	—	10	2	no	—
399	C₄×C₈	—	2	2	no	—
400	C₄×C₈	—	10	2	no	—
401	C₄×C₈	—	10	2	no	—
402	C₄×C₈	—	10	2	no	—
403	#95	—	5	1	no	—
404	#95	—	5	1	no	—
405	#95	—	5	1	no	—
406	#95	—	5	1	no	—
407	#95	—	5	1	no	—
408	#95	—	5	1	no	—
409	#95	—	5	1	no	—
410	#95	—	5	1	no	—
411	#95	C₄×D₅	1	1	yes	characteristic
412	#95	C₄×D₅	1	1	yes	characteristic
413	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
414	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
415	C₂²×C₅	C₄×#41	1	1	yes	characteristic
416	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
417	C₂²×C₅	C₂×#131	1	1	yes	characteristic
418	C₂²×C₅	#568	1	1	yes	characteristic
419	C₂²×C₅	#568	1	1	yes	characteristic
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	2	2	no	—
422	C₂×D₅	—	2	2	no	—
423	C₂×D₅	—	4	1	no	—
424	C₂×D₅	—	4	1	no	—
425	C₂×D₅	—	4	1	no	—
426	C₂×D₅	—	4	1	no	—
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	4	1	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
434	C₄×C₅	#525	1	1	yes	characteristic
435	C₄×C₅	#529	1	1	yes	characteristic
436	C₄×C₅	#533	1	1	yes	characteristic
437	Dic₅	—	2	2	no	—
438	Dic₅	—	2	2	no	—
439	Dic₅	—	2	2	no	—
440	Dic₅	—	2	2	no	—
441	Dic₅	—	2	2	no	—
442	Dic₅	—	4	1	no	—
443	Dic₅	—	4	1	no	—
444	C₂⁴	—	5	1	no	—
445	C₂×Q₈	—	10	2	no	—
446	C₂×Q₈	—	10	2	no	—
447	C₂×Q₈	—	20	1	no	—
448	C₂²×C₄	—	5	1	no	—
449	C₂²×C₄	—	5	1	no	—
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	1	no	—
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	2	no	—
454	C₂²×C₄	—	5	2	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	10	2	no	—
458	C₂²×C₄	—	10	2	no	—
459	C₂²×C₄	—	10	1	no	—
460	C₂²×C₄	—	10	1	no	—
461	C₂²×C₄	—	10	1	no	—
462	C₂²×C₄	—	10	1	no	—
463	C₂²×C₄	—	10	2	no	—
464	C₂²×C₄	—	10	2	no	—
465	C₂²×C₄	—	20	1	no	—
466	C₂²×C₄	—	20	1	no	—
467	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
473	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
474	M₁₆	—	10	8	no	—
475	M₁₆	—	10	8	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	5	2	no	—
485	C₂×C₈	—	5	2	no	—
486	C₂×C₈	—	10	1	no	—
487	C₂×C₈	—	10	1	no	—
488	C₂×C₈	—	10	1	no	—
489	C₂×C₈	—	10	1	no	—
490	C₂×C₈	—	10	1	no	—
491	C₂×C₈	—	10	1	no	—
492	C₂×C₈	—	10	1	no	—
493	C₂×C₈	—	10	1	no	—
494	C₂×C₈	—	10	1	no	—
495	C₂×C₈	—	10	1	no	—
496	C₂×C₈	#709	1	2	yes	—
497	C₂×C₈	#709	1	2	yes	—
498	C₂×C₈	D₄×D₅	1	2	yes	—
499	C₂×C₈	Q₈×D₅	1	2	yes	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	5	4	no	—
503	C₄⋊C₄	—	10	2	no	—
504	C₄⋊C₄	—	10	2	no	—
505	C₄⋊C₄	—	10	2	no	—
506	C₄⋊C₄	—	10	2	no	—
507	C₄⋊C₄	—	10	2	no	—
508	C₄⋊C₄	—	20	1	no	—
509	C₂²⋊C₄	—	10	2	no	—
510	C₂²⋊C₄	—	10	2	no	—
511	C₂²⋊C₄	—	20	1	no	—
512	C₂²⋊C₄	—	20	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	5	2	no	—
520	C₄²	—	5	2	no	—
521	C₄²	—	10	2	no	—
522	C₄²	—	10	2	no	—
523	C₄²	—	10	1	no	—
524	C₄²	—	10	1	no	—
525	C₄²	—	10	1	no	—
526	C₄²	—	10	1	no	—
527	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
528	C₂×C₅	#2933	1	1	yes	characteristic
529	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
530	C₂×C₅	#2962	1	1	yes	characteristic
531	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
532	C₂×C₅	#2965	1	1	yes	characteristic
533	C₂×C₅	#2967	1	1	yes	characteristic
534	D₅	—	4	2	no	—
535	C₂³	—	5	2	no	—
536	C₂³	—	10	1	no	—
537	C₂³	—	10	1	no	—
538	C₂³	—	10	1	no	—
539	C₂³	—	10	1	no	—
540	C₂³	—	10	1	no	—
541	C₂³	—	10	1	no	—
542	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
543	Q₈	—	20	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	5	2	no	—
561	C₂×C₄	—	5	2	no	—
562	C₂×C₄	—	5	2	no	—
563	C₂×C₄	—	5	2	no	—
564	C₂×C₄	—	5	2	no	—
565	C₂×C₄	—	10	1	no	—
566	C₂×C₄	—	10	1	no	—
567	C₂×C₄	—	10	1	no	—
568	C₂×C₄	—	10	1	no	—
569	C₂×C₄	—	10	1	no	—
570	C₂×C₄	—	10	1	no	—
571	C₂×C₄	—	10	1	no	—
572	C₂×C₄	—	10	1	no	—
573	C₂×C₄	—	10	1	no	—
574	C₂×C₄	—	10	1	no	—
575	C₂×C₄	—	10	2	no	—
576	C₂×C₄	—	10	2	no	—
577	C₂×C₄	—	10	2	no	—
578	C₂×C₄	—	10	2	no	—
579	C₂×C₄	—	10	1	no	—
580	C₂×C₄	—	10	1	no	—
581	C₂×C₄	—	10	1	no	—
582	C₂×C₄	—	10	1	no	—
583	C₂×C₄	—	10	1	no	—
584	C₂×C₄	—	10	1	no	—
585	C₂×C₄	—	20	4	no	—
586	C₂×C₄	—	20	4	no	—
587	C₂×C₄	D₅×M₁₆	1	2	yes	—
588	C₂×C₄	#4053	1	2	yes	—
589	C₂×C₄	C₂×#709	1	1	yes	characteristic
590	C₂×C₄	C₂×#709	1	1	yes	characteristic
591	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
592	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
593	C₂×C₄	D₅×#41	1	1	yes	characteristic
594	C₂×C₄	D₅×#41	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	10	2	no	—
599	C₈	—	10	2	no	—
600	C₈	—	20	1	no	—
601	C₈	—	20	1	no	—
602	C₈	#4042	1	4	yes	complemented
603	C₅	#21600	1	1	yes	characteristic, complemented, Sylow
604	C₂²	—	10	2	no	—
605	C₂²	—	10	2	no	—
606	C₂²	—	10	2	no	—
607	C₂²	—	20	1	no	—
608	C₂²	—	20	1	no	—
609	C₂²	—	20	1	no	—
610	C₂²	—	20	1	no	—
611	C₂²	C₄×#709	1	1	yes	characteristic
612	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
613	C₂²	C₄×Q₈×D₅	1	1	yes	characteristic
614	C₂²	C₂×D₅×M₁₆	1	1	yes	characteristic
615	C₂²	C₂×#4053	1	1	yes	characteristic
616	C₂²	#66084	1	1	yes	characteristic
617	C₂²	#66084	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	10	2	no	—
625	C₄	—	10	2	no	—
626	C₄	—	10	2	no	—
627	C₄	—	10	2	no	—
628	C₄	—	10	2	no	—
629	C₄	—	20	1	no	—
630	C₄	—	20	1	no	—
631	C₄	C₂×#4042	1	1	yes	characteristic
632	C₄	#65862	1	1	yes	characteristic
633	C₄	#65881	1	1	yes	characteristic
634	C₄	#65912	1	1	yes	characteristic
635	C₂	—	20	2	no	—
636	C₂	C₄×#4042	1	1	yes	characteristic
637	C₂	#10610254	1	1	yes	characteristic
638	C₂	#10610288	1	1	yes	characteristic
639	C₂	#10611212	1	1	yes	characteristic
640	C₂	#10611214	1	1	yes	characteristic
641	C₂	#10611691	1	1	yes	characteristic
642	C₂	#10611693	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₅×#1771	C₂
prime radical	C₂³×D₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1771	D₅
hypocenter	C₅	#21600
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
1. C₂×#64990	C₂	semidirect
4. C₅×#1771	C₂	semidirect
6. #10601245	C₂	semidirect
7. #10600604	C₂	semidirect
10. C₈×#683	C₂	semidirect
11. #10600275	C₂	semidirect
14. #10599448	C₂	semidirect
15. #10599413	C₂	semidirect
100. C₂×#676	Q₈	semidirect
143. #1771	D₅	semidirect
207. #683	M₁₆	semidirect
338. C₅×C₈	C₂²⋊Q₈	semidirect
602. C₈	#4042	semidirect
603. C₅	#21600	semidirect

Maximal subgroups

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

subgroup	index
C₂×#64990	2
C₂×C₄×#676	2
C₄×#4042	2
C₅×#1771	2
#10601271	2
#10601245	2
#10600604	2
#10600601	2
C₈×#683	2
#10600275	2
#10599460	2
#10599455	2
#10599448	2
#10599413	2
#21600	5