Subgroups — #12106795

Order 1280.

842 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65411	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#10605211	C₂	1	1	yes	maximal, characteristic
4	C₅×#1753	C₂	1	1	yes	maximal, characteristic
5	#10602776	C₂	1	1	yes	maximal, characteristic
6	#10600743	C₂	1	1	yes	maximal, characteristic
7	#10600702	C₂	1	1	yes	maximal, characteristic
8	#10600626	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600603	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600576	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600242	C₂	1	1	yes	maximal, characteristic
12	#10599413	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599411	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599404	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599403	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×#4072	C₂²	1	1	yes	characteristic
18	C₂³×#168	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
26	#65411	—	2	4	no	—
27	C₂×#3947	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	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
37	#65238	C₄	1	1	yes	characteristic
38	#65237	C₄	1	1	yes	characteristic
39	#65237	C₄	1	1	yes	characteristic
40	#65236	C₄	1	1	yes	characteristic
41	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
42	C₄×#683	C₂²	1	1	yes	characteristic
43	C₄×#683	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
46	C₈×Dic₁₀	—	2	4	no	—
47	#64950	C₄	1	1	yes	characteristic
48	#64949	C₄	1	1	yes	characteristic
49	#64946	C₄	1	1	yes	characteristic
50	#64945	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	#64770	C₂²	1	1	yes	characteristic
58	#64770	C₂²	1	1	yes	characteristic
59	#64744	C₂²	1	1	yes	characteristic
60	#64744	C₂²	1	1	yes	characteristic
61	#21602	—	5	1	no	maximal, Sylow
62	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₀	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅×M₁₆	—	2	2	no	—
65	C₂×C₅×M₁₆	—	2	2	no	—
66	C₂×C₅×M₁₆	Q₈	1	4	yes	complemented
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	#4072	—	2	2	no	—
80	#4072	—	2	2	no	—
81	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
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×#683	C₂×C₄	1	1	yes	characteristic
87	C₂×#683	C₂×C₄	1	1	yes	characteristic
88	C₂×#683	C₂×C₄	1	1	yes	characteristic
89	C₂×#683	C₂×C₄	1	1	yes	characteristic
90	C₂×#683	C₂×C₄	1	1	yes	characteristic
91	C₂×#683	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	—	2	2	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	C₄×Dic₁₀	—	2	2	no	—
104	C₄×Dic₁₀	—	2	2	no	—
105	C₅×C₂²⋊C₈	—	2	2	no	—
106	C₅×#97	—	2	2	no	—
107	C₄×C₅×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	#3963	C₂×C₄	1	1	yes	characteristic
117	#3963	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#168	—	2	2	no	—
119	#3947	—	2	2	no	—
120	#3947	—	2	2	no	—
121	#3947	—	2	2	no	—
122	#3946	—	2	2	no	—
123	#3946	—	2	2	no	—
124	#3946	—	2	2	no	—
125	#3946	—	2	2	no	—
126	C₈×Dic₅	—	2	2	no	—
127	C₈×Dic₅	—	2	2	no	—
128	C₈×Dic₅	D₄	1	4	yes	—
129	C₄⋊#168	—	2	2	no	—
130	C₄⋊#168	—	2	2	no	—
131	C₂×C₈×Q₈	—	5	1	no	—
132	C₂×#405	—	5	1	no	—
133	#2396	—	5	1	no	—
134	#1985	—	5	1	no	—
135	#1940	—	5	1	no	—
136	#1916	—	5	1	no	—
137	#1916	—	5	1	no	—
138	#1850	—	5	1	no	—
139	#1850	—	5	1	no	—
140	#1798	—	5	1	no	—
141	#1771	—	5	1	no	—
142	#1771	—	5	1	no	—
143	#1770	—	5	1	no	—
144	#1753	—	5	1	no	—
145	#1753	D₅	1	1	yes	characteristic
146	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
157	C₂²×C₄×C₅	#41	1	2	yes	—
158	C₂²×C₄×C₅	C₂⁴	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	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
167	C₂×Dic₁₀	—	2	2	no	—
168	C₂×Dic₁₀	—	2	2	no	—
169	C₂×Dic₁₀	—	2	2	no	—
170	C₅×M₁₆	—	2	8	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	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
180	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
181	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
182	C₂×C₅×C₈	#41	1	2	yes	—
183	C₅×C₂²⋊C₄	—	2	2	no	—
184	C₅×C₂²⋊C₄	—	4	1	no	—
185	C₄²×C₅	—	2	1	no	—
186	C₄²×C₅	—	2	1	no	—
187	C₄²×C₅	—	2	1	no	—
188	C₄²×C₅	—	2	1	no	—
189	C₂²⋊Dic₅	—	2	2	no	—
190	C₂²⋊Dic₅	—	2	2	no	—
191	C₂²⋊Dic₅	—	2	2	no	—
192	C₂²⋊Dic₅	—	4	1	no	—
193	C₄⋊Dic₅	—	2	2	no	—
194	C₄⋊Dic₅	—	2	2	no	—
195	C₄⋊Dic₅	—	2	2	no	—
196	C₄⋊Dic₅	—	2	2	no	—
197	C₄⋊Dic₅	—	4	1	no	—
198	#683	—	2	2	no	—
199	#683	—	2	2	no	—
200	#683	—	2	2	no	—
201	#683	—	4	1	no	—
202	#683	—	4	1	no	—
203	#683	—	4	1	no	—
204	C₄×Dic₅	—	2	1	no	—
205	C₄×Dic₅	—	2	1	no	—
206	C₄×Dic₅	—	2	1	no	—
207	C₄×Dic₅	—	2	1	no	—
208	C₄×Dic₅	—	2	1	no	—
209	C₄×Dic₅	—	2	1	no	—
210	C₄×Dic₅	C₂×D₄	1	2	yes	—
211	C₄×Dic₅	#41	1	2	yes	—
212	C₂×#168	—	2	8	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	C₂×D₄	1	2	yes	—
224	C₂×#168	#41	1	2	yes	—
225	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
226	C₂³×C₈	—	5	1	no	—
227	C₂×C₄×Q₈	—	5	1	no	—
228	C₂×#117	—	5	1	no	—
229	C₈×Q₈	—	10	4	no	—
230	C₂×C₄⋊C₈	—	5	1	no	—
231	C₂×C₄⋊C₈	—	5	1	no	—
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	C₂×C₂²⋊C₈	—	5	1	no	—
237	C₂×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
238	#405	—	10	4	no	—
239	C₂×#97	—	5	1	no	—
240	C₂×#97	—	5	1	no	—
241	C₂×#97	—	5	1	no	—
242	C₂×#97	C₂×D₅	1	1	yes	characteristic
243	C₂×C₄×C₈	—	5	1	no	—
244	C₂×C₄×C₈	—	5	1	no	—
245	C₂×C₄×C₈	—	5	1	no	—
246	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
247	#400	—	5	1	no	—
248	#399	—	5	1	no	—
249	#398	—	5	1	no	—
250	#398	—	5	1	no	—
251	#396	—	5	1	no	—
252	#396	—	5	1	no	—
253	#395	—	5	1	no	—
254	#393	—	5	1	no	—
255	C₄×C₄⋊C₄	—	5	1	no	—
256	C₄×C₄⋊C₄	—	5	1	no	—
257	C₄×C₄⋊C₄	—	5	1	no	—
258	C₄×C₂²⋊C₄	—	5	1	no	—
259	C₄×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
260	#336	—	5	1	no	—
261	#336	—	5	1	no	—
262	#336	—	5	1	no	—
263	#336	—	5	1	no	—
264	#336	—	5	1	no	—
265	#336	—	5	1	no	—
266	#336	—	5	1	no	—
267	#336	—	5	1	no	—
268	#336	C₂×D₅	1	1	yes	characteristic
269	#336	C₂×D₅	1	1	yes	characteristic
270	C₂³×C₅	—	2	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	C₄×Q₈	1	2	yes	—
277	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	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	C₄×Q₈	1	2	yes	—
296	C₂×C₄×C₅	#131	1	2	yes	—
297	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
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	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	—	2	1	no	—
324	C₂×Dic₅	C₄×D₄	1	2	yes	—
325	C₂×Dic₅	C₄×D₄	1	2	yes	—
326	C₂×Dic₅	#131	1	2	yes	—
327	Dic₁₀	—	2	8	no	—
328	C₅×C₈	—	2	2	no	—
329	C₅×C₈	—	4	1	no	—
330	C₅×C₈	—	4	1	no	—
331	C₅×C₈	C₂²⋊Q₈	1	4	yes	—
332	#168	—	2	2	no	—
333	#168	—	2	2	no	—
334	#168	—	4	1	no	—
335	#168	—	4	1	no	—
336	C₂²×Q₈	—	5	1	no	—
337	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	Dic₁₀	1	4	yes	complemented
341	C₂²×C₈	—	5	1	no	—
342	C₂²×C₈	—	5	1	no	—
343	C₂²×C₈	—	5	1	no	—
344	C₂²×C₈	—	5	1	no	—
345	C₂²×C₈	—	10	2	no	—
346	C₂²×C₈	—	10	2	no	—
347	C₂²×C₈	—	10	2	no	—
348	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
349	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
350	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
352	C₄×Q₈	—	10	2	no	—
353	C₄×Q₈	—	10	2	no	—
354	#117	—	10	2	no	—
355	#117	—	10	2	no	—
356	C₂×C₄⋊C₄	—	5	1	no	—
357	C₂×C₄⋊C₄	—	5	1	no	—
358	C₂×C₄⋊C₄	—	5	1	no	—
359	C₂×C₄⋊C₄	—	5	1	no	—
360	C₂×C₄⋊C₄	—	5	1	no	—
361	C₂×C₄⋊C₄	—	5	1	no	—
362	C₂×C₄⋊C₄	—	5	1	no	—
363	C₂×C₄⋊C₄	—	5	1	no	—
364	C₂×C₄⋊C₄	—	5	1	no	—
365	C₂×C₄⋊C₄	—	5	1	no	—
366	C₂×C₄⋊C₄	—	5	1	no	—
367	C₂×C₂²⋊C₄	—	5	1	no	—
368	C₂×C₂²⋊C₄	—	5	1	no	—
369	C₂×C₂²⋊C₄	—	5	1	no	—
370	C₂×C₂²⋊C₄	—	5	1	no	—
371	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
373	C₂×C₄²	—	5	1	no	—
374	C₂×C₄²	—	5	1	no	—
375	C₂×C₄²	—	5	1	no	—
376	C₂×C₄²	—	5	1	no	—
377	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
379	C₄⋊C₈	—	10	2	no	—
380	C₄⋊C₈	—	10	2	no	—
381	C₄⋊C₈	—	10	2	no	—
382	C₄⋊C₈	—	10	2	no	—
383	C₄⋊C₈	—	10	2	no	—
384	C₄⋊C₈	—	10	2	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	C₂²⋊C₈	—	10	2	no	—
387	#97	—	2	2	no	—
388	#97	—	10	2	no	—
389	#97	—	10	2	no	—
390	#97	—	10	2	no	—
391	C₄×C₈	—	2	2	no	—
392	C₄×C₈	—	5	4	no	—
393	C₄×C₈	—	10	2	no	—
394	C₄×C₈	—	10	2	no	—
395	#95	—	5	1	no	—
396	#95	—	5	1	no	—
397	#95	—	5	1	no	—
398	#95	—	5	1	no	—
399	#95	—	5	1	no	—
400	#95	—	5	1	no	—
401	#95	—	5	1	no	—
402	#95	—	5	1	no	—
403	#95	C₄×D₅	1	1	yes	characteristic
404	#95	C₄×D₅	1	1	yes	characteristic
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	2	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	—	4	1	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
413	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
414	C₂²×C₅	C₄×#41	1	1	yes	characteristic
415	C₂²×C₅	C₂×#131	1	1	yes	characteristic
416	C₂²×C₅	C₂×#131	1	1	yes	characteristic
417	C₂²×C₅	#568	1	1	yes	characteristic
418	C₂²×C₅	#568	1	1	yes	characteristic
419	C₄×C₅	—	2	2	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	4	1	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
425	C₄×C₅	#525	1	1	yes	characteristic
426	C₄×C₅	#529	1	1	yes	characteristic
427	C₄×C₅	#533	1	1	yes	characteristic
428	Dic₅	—	2	2	no	—
429	Dic₅	—	2	2	no	—
430	Dic₅	—	2	2	no	—
431	Dic₅	—	4	1	no	—
432	Dic₅	—	4	1	no	—
433	Dic₅	—	4	1	no	—
434	Dic₅	—	4	1	no	—
435	Dic₅	—	4	1	no	—
436	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
437	C₂×Q₈	—	10	2	no	—
438	C₂×Q₈	—	10	2	no	—
439	C₂×Q₈	—	10	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	5	1	no	—
445	C₂²×C₄	—	5	1	no	—
446	C₂²×C₄	—	5	1	no	—
447	C₂²×C₄	—	5	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	C₂×Dic₁₀	1	2	yes	—
453	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
458	C₂²×C₄	#709	1	2	yes	—
459	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
460	M₁₆	—	2	8	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	5	2	no	—
470	C₂×C₈	—	5	2	no	—
471	C₂×C₈	—	10	8	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	—	10	1	no	—
477	C₂×C₈	—	10	1	no	—
478	C₂×C₈	—	10	1	no	—
479	C₂×C₈	—	10	1	no	—
480	C₂×C₈	—	10	1	no	—
481	C₂×C₈	—	10	1	no	—
482	C₂×C₈	C₂×Dic₁₀	1	2	yes	—
483	C₂×C₈	C₂×Dic₁₀	1	2	yes	—
484	C₂×C₈	D₄×D₅	1	2	yes	—
485	C₂×C₈	#711	1	2	yes	—
486	C₄⋊C₄	—	10	2	no	—
487	C₄⋊C₄	—	10	2	no	—
488	C₄⋊C₄	—	10	2	no	—
489	C₄⋊C₄	—	10	2	no	—
490	C₄⋊C₄	—	10	2	no	—
491	C₄⋊C₄	—	10	2	no	—
492	C₄⋊C₄	—	10	2	no	—
493	C₄⋊C₄	—	20	1	no	—
494	C₄⋊C₄	—	20	1	no	—
495	C₄⋊C₄	—	20	1	no	—
496	C₄⋊C₄	—	20	1	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	10	2	no	—
500	C₂²⋊C₄	—	10	2	no	—
501	C₂²⋊C₄	—	10	2	no	—
502	C₂²⋊C₄	—	20	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	5	2	no	—
508	C₄²	—	5	2	no	—
509	C₄²	—	10	1	no	—
510	C₄²	—	10	1	no	—
511	C₄²	—	10	1	no	—
512	C₄²	—	10	1	no	—
513	C₄²	—	10	1	no	—
514	C₄²	—	10	1	no	—
515	C₂×C₅	—	4	2	no	—
516	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
517	C₂×C₅	#2929	1	1	yes	characteristic
518	C₂×C₅	#2932	1	1	yes	characteristic
519	C₂×C₅	#2962	1	1	yes	characteristic
520	C₂×C₅	#2962	1	1	yes	characteristic
521	C₂×C₅	#2969	1	1	yes	characteristic
522	C₂×C₅	#2969	1	1	yes	characteristic
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	C₄×Dic₁₀	1	2	yes	—
530	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
531	Q₈	—	10	8	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	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	—	5	2	no	—
550	C₂×C₄	—	5	2	no	—
551	C₂×C₄	—	5	2	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	1	no	—
562	C₂×C₄	—	10	1	no	—
563	C₂×C₄	—	10	1	no	—
564	C₂×C₄	—	10	1	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	C₄×Dic₁₀	1	2	yes	—
574	C₂×C₄	#4053	1	2	yes	—
575	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
576	C₂×C₄	C₂×#709	1	1	yes	characteristic
577	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
578	C₂×C₄	C₂×#711	1	1	yes	characteristic
579	C₂×C₄	D₅×#41	1	1	yes	characteristic
580	C₂×C₄	D₅×#41	1	1	yes	characteristic
581	C₈	—	2	2	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	10	2	no	—
585	C₈	—	10	2	no	—
586	C₈	—	20	1	no	—
587	C₈	—	20	1	no	—
588	C₈	#4024	1	4	yes	—
589	C₅	#21602	1	1	yes	characteristic, complemented, Sylow
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	C₂×C₄×Dic₁₀	1	1	yes	characteristic
598	C₂²	C₄×#711	1	1	yes	characteristic
599	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
600	C₂²	C₂×#4053	1	1	yes	characteristic
601	C₂²	#66079	1	1	yes	characteristic
602	C₂²	D₅×#131	1	1	yes	characteristic
603	C₂²	#66084	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	10	2	no	—
610	C₄	—	10	2	no	—
611	C₄	—	10	2	no	—
612	C₄	—	20	1	no	—
613	C₄	—	20	1	no	—
614	C₄	—	20	1	no	—
615	C₄	—	20	1	no	—
616	C₄	—	20	1	no	—
617	C₄	C₂×#4024	1	1	yes	characteristic
618	C₄	#65851	1	1	yes	characteristic
619	C₄	#65872	1	1	yes	characteristic
620	C₄	#65881	1	1	yes	characteristic
621	C₂	—	4	2	no	—
622	C₂	C₄×#4024	1	1	yes	characteristic
623	C₂	#10610239	1	1	yes	characteristic
624	C₂	#10610275	1	1	yes	characteristic
625	C₂	#10611209	1	1	yes	characteristic
626	C₂	#10611211	1	1	yes	characteristic
627	C₂	#10611251	1	1	yes	characteristic
628	C₂	#10611252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₅×#1753	C₂
prime radical	C₂⁴×C₅	C₂²×C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1753	D₅
hypocenter	C₅	#21602
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #1753

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Dic₁₀	C₂	semidirect
8. #10600626	C₂	semidirect
9. #10600603	C₂	semidirect
10. #10600576	C₂	semidirect
12. #10599413	C₂	semidirect
13. #10599411	C₂	semidirect
14. #10599404	C₂	semidirect
15. #10599403	C₂	semidirect
66. C₂×C₅×M₁₆	Q₈	semidirect
340. C₂×M₁₆	Dic₁₀	semidirect
589. C₅	#21602	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65411	2
C₂×C₈×Dic₁₀	2
#10605211	2
C₅×#1753	2
#10602776	2
#10600743	2
#10600702	2
#10600626	2
#10600603	2
#10600576	2
#10600242	2
#10599413	2
#10599411	2
#10599404	2
#10599403	2
#21602	5