Subgroups — #12128024

Order 1280.

960 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#65421	C₂	1	1	yes	maximal, characteristic
3	C₂×#65421	C₂	1	1	yes	maximal, characteristic
4	C₂×#65421	C₂	1	1	yes	maximal, characteristic
5	C₂×#65414	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#65413	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64780	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601525	C₂	1	4	yes	maximal, complemented
9	#10601523	C₂	1	4	yes	maximal, complemented
10	C₂²×#709	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×#681	C₂²	1	1	yes	characteristic
15	C₂²×#681	C₂²	1	1	yes	characteristic
16	C₂²×#681	C₂²	1	1	yes	characteristic
17	C₅×#430	—	2	2	no	—
18	C₅×#430	C₂²	1	4	yes	—
19	C₂×C₅×#108	—	2	2	no	—
20	C₂×#3956	C₂²	1	2	yes	—
21	C₂×#3956	C₂²	1	2	yes	—
22	C₂×#3956	C₂²	1	2	yes	—
23	#65421	—	2	2	no	—
24	#65421	—	2	2	no	—
25	#65421	—	2	2	no	—
26	#65421	—	2	2	no	—
27	#65421	—	2	2	no	—
28	#65421	—	2	2	no	—
29	C₂×#3955	C₂²	1	2	yes	—
30	C₂×#3955	C₂²	1	2	yes	—
31	C₂×#3955	C₂²	1	2	yes	—
32	#65414	—	2	2	no	—
33	#65414	C₂²	1	4	yes	—
34	#65413	—	2	2	no	—
35	#65413	C₂²	1	4	yes	—
36	C₂×#3954	—	2	2	no	—
37	C₂×#3951	—	2	2	no	—
38	#64780	C₂²	1	4	yes	—
39	#23622	—	5	1	no	maximal, Sylow
40	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₂²⋊D₅	Q₈	1	2	yes	—
42	C₂×#709	—	2	1	no	—
43	C₂×#709	—	2	1	no	—
44	C₂×#709	—	2	1	no	—
45	C₂×#709	—	2	1	no	—
46	C₂×#709	—	2	1	no	—
47	C₂×#709	—	2	1	no	—
48	C₂×#709	—	2	1	no	—
49	C₂×#709	—	2	1	no	—
50	C₂×#709	—	2	1	no	—
51	C₂×#709	—	2	1	no	—
52	C₂×#709	—	2	1	no	—
53	C₂×#709	—	2	1	no	—
54	C₂²×D₂₀	C₂³	1	1	yes	characteristic
55	C₂²×C₄×D₅	Q₈	1	2	yes	—
56	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂×C₅×M₁₆	—	2	1	no	—
63	C₂×C₅×M₁₆	—	2	1	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₅×M₁₆	—	2	1	no	—
67	C₂×C₅×M₁₆	—	2	1	no	—
68	C₂×C₅×M₁₆	D₄	1	2	yes	—
69	C₂×C₅×M₁₆	D₄	1	2	yes	—
70	C₂×C₅×M₁₆	D₄	1	2	yes	—
71	C₂×C₅×M₁₆	D₄	1	2	yes	—
72	C₂×C₅×M₁₆	C₂³	1	2	yes	—
73	C₂×C₅×M₁₆	C₂³	1	2	yes	—
74	C₂×C₅×M₁₆	C₂³	1	2	yes	—
75	C₂²×C₅×C₈	—	2	1	no	—
76	C₂²×C₅×C₈	—	2	1	no	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₂×#681	—	2	1	no	—
79	C₂×#681	—	2	1	no	—
80	C₂×#681	—	2	1	no	—
81	C₂×#681	—	2	1	no	—
82	C₂×#681	—	2	1	no	—
83	C₂×#681	—	2	1	no	—
84	C₂×#681	—	2	1	no	—
85	C₂×#681	—	2	1	no	—
86	C₂×#681	—	2	1	no	—
87	C₂×#681	—	2	1	no	—
88	C₂×#681	—	2	1	no	—
89	C₂×#681	—	2	1	no	—
90	C₂×#681	—	2	1	no	—
91	C₂×#681	D₄	1	2	yes	—
92	C₂×#681	D₄	1	2	yes	—
93	C₂×#681	C₂³	1	2	yes	—
94	C₂×#681	C₂³	1	2	yes	—
95	C₂×#681	C₂³	1	2	yes	—
96	C₂²×#168	—	2	1	no	—
97	C₂²×#168	—	2	1	no	—
98	C₂²×#168	—	2	1	no	—
99	C₅×#108	—	2	8	no	—
100	#3956	—	2	4	no	—
101	#3956	—	2	4	no	—
102	#3956	—	2	4	no	—
103	#3955	—	2	4	no	—
104	#3955	—	2	4	no	—
105	#3955	—	2	4	no	—
106	#3954	—	2	8	no	—
107	#3951	—	2	8	no	—
108	C₂×#430	—	5	1	no	—
109	C₂×#430	—	5	1	no	—
110	C₂×#430	D₅	1	1	yes	characteristic, complemented
111	C₂×#413	—	5	1	no	—
112	C₂×#413	—	5	1	no	—
113	C₂×#413	—	5	1	no	—
114	#2070	—	5	4	no	—
115	#2069	—	5	4	no	—
116	C₂×#338	—	5	1	no	—
117	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
118	C₂³×D₅	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₅	#41	1	1	yes	characteristic
127	C₂²×C₄×C₅	#41	1	1	yes	characteristic
128	C₂²×C₄×C₅	#41	1	1	yes	characteristic
129	C₂²×C₄×C₅	#41	1	1	yes	characteristic
130	C₂²×C₄×C₅	#41	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₅	—	2	2	no	—
134	C₂×C₂²⋊D₅	—	2	2	no	—
135	C₂×C₂²⋊D₅	—	2	2	no	—
136	C₂×C₂²⋊D₅	—	2	2	no	—
137	C₂×C₂²⋊D₅	—	2	2	no	—
138	C₂×C₂²⋊D₅	—	2	2	no	—
139	C₂²×Dic₅	C₂×Q₈	1	2	yes	—
140	#709	—	4	1	no	—
141	#709	—	4	1	no	—
142	#709	—	4	1	no	—
143	#709	—	4	1	no	—
144	#709	—	4	1	no	—
145	#709	—	4	1	no	—
146	#709	—	4	1	no	—
147	#709	—	4	1	no	—
148	#709	—	4	1	no	—
149	#709	—	4	1	no	—
150	#709	—	4	1	no	—
151	#709	—	4	1	no	—
152	#709	—	4	1	no	—
153	#709	—	4	1	no	—
154	#709	—	4	1	no	—
155	#709	—	4	1	no	—
156	C₂×D₂₀	—	2	1	no	—
157	C₂×D₂₀	—	2	1	no	—
158	C₂×D₂₀	—	2	1	no	—
159	C₂×D₂₀	—	2	1	no	—
160	C₂×D₂₀	—	2	1	no	—
161	C₂×D₂₀	—	2	1	no	—
162	C₂×C₄×D₅	—	2	2	no	—
163	C₂×C₄×D₅	—	2	2	no	—
164	C₂×C₄×D₅	—	2	2	no	—
165	C₂×C₄×D₅	—	2	2	no	—
166	C₂×C₄×D₅	—	2	2	no	—
167	C₂×C₄×D₅	—	2	2	no	—
168	C₂×Dic₁₀	—	2	1	no	—
169	C₂×Dic₁₀	—	2	1	no	—
170	C₂×Dic₁₀	—	2	1	no	—
171	C₂×Dic₁₀	—	2	1	no	—
172	C₂×Dic₁₀	—	2	1	no	—
173	C₂×Dic₁₀	—	2	1	no	—
174	C₅×M₁₆	—	2	2	no	—
175	C₅×M₁₆	—	2	2	no	—
176	C₅×M₁₆	—	2	2	no	—
177	C₅×M₁₆	—	2	2	no	—
178	C₅×M₁₆	—	2	2	no	—
179	C₅×M₁₆	—	2	2	no	—
180	C₅×M₁₆	—	2	2	no	—
181	C₅×M₁₆	—	2	2	no	—
182	C₅×M₁₆	—	4	1	no	—
183	C₅×M₁₆	—	4	1	no	—
184	C₅×M₁₆	C₂×D₄	1	4	yes	—
185	C₅×M₁₆	C₂×D₄	1	4	yes	—
186	C₂×C₅×C₈	—	2	2	no	—
187	C₂×C₅×C₈	—	2	2	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	—	2	2	no	—
191	C₂×C₅×C₈	—	2	2	no	—
192	C₂×C₅×C₈	—	2	2	no	—
193	C₂×C₅×C₈	—	4	1	no	—
194	C₂×C₅×C₈	—	4	1	no	—
195	#681	—	2	2	no	—
196	#681	—	2	2	no	—
197	#681	—	2	2	no	—
198	#681	—	2	2	no	—
199	#681	—	2	2	no	—
200	#681	—	2	2	no	—
201	#681	—	2	2	no	—
202	#681	—	4	1	no	—
203	#681	—	4	1	no	—
204	#681	—	4	1	no	—
205	#681	—	4	1	no	—
206	#681	C₂×D₄	1	4	yes	—
207	C₂×#168	—	2	2	no	—
208	C₂×#168	—	2	2	no	—
209	C₂×#168	—	2	2	no	—
210	C₂×#168	—	2	2	no	—
211	C₂×#168	—	2	2	no	—
212	C₂×#168	—	4	1	no	—
213	C₂×#168	—	4	1	no	—
214	C₂×#168	—	4	1	no	—
215	C₂×#168	—	4	1	no	—
216	C₂²×#41	—	5	1	no	—
217	C₂²×M₁₆	—	5	1	no	—
218	C₂²×M₁₆	—	5	1	no	—
219	C₂²×M₁₆	—	5	1	no	—
220	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
221	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
222	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
223	#430	—	2	2	no	—
224	#430	—	5	4	no	—
225	#430	—	5	4	no	—
226	#430	—	10	2	no	—
227	#430	—	10	2	no	—
228	#430	C₂×D₅	1	4	yes	—
229	C₂×#108	—	2	2	no	—
230	C₂×#108	—	10	2	no	—
231	C₂×#108	—	10	2	no	—
232	#413	—	10	2	no	—
233	#413	—	10	2	no	—
234	#413	—	10	2	no	—
235	#413	—	10	2	no	—
236	#413	—	10	2	no	—
237	#413	—	10	2	no	—
238	C₂×#101	—	5	2	no	—
239	C₂×#101	—	5	2	no	—
240	C₂×#101	—	5	2	no	—
241	C₂×#100	—	5	2	no	—
242	C₂×#100	—	5	2	no	—
243	C₂×#100	—	5	2	no	—
244	#338	—	5	4	no	—
245	C₂³×C₅	—	8	1	no	—
246	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂³×C₅	C₂²×Q₈	1	1	yes	characteristic
253	C₂²×D₅	—	2	2	no	—
254	C₂²×D₅	—	2	2	no	—
255	C₂²×D₅	—	2	2	no	—
256	C₂²×D₅	—	8	2	no	—
257	C₂×C₄×C₅	#121	1	1	yes	characteristic
258	C₂×C₄×C₅	#121	1	1	yes	characteristic
259	C₂×C₄×C₅	#121	1	1	yes	characteristic
260	C₂×C₄×C₅	#121	1	1	yes	characteristic
261	C₂×C₄×C₅	#121	1	1	yes	characteristic
262	C₂×C₄×C₅	#121	1	1	yes	characteristic
263	C₂×C₄×C₅	#121	1	1	yes	characteristic
264	C₂×C₄×C₅	#121	1	1	yes	characteristic
265	C₂×C₄×C₅	#121	1	1	yes	characteristic
266	C₂×C₄×C₅	#121	1	1	yes	characteristic
267	C₂×C₄×C₅	#121	1	1	yes	characteristic
268	C₂×C₄×C₅	#121	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₅	#126	1	1	yes	characteristic
276	C₂×C₄×C₅	#126	1	1	yes	characteristic
277	C₂×C₄×C₅	#126	1	1	yes	characteristic
278	C₂×C₄×C₅	#126	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
285	C₂²⋊D₅	—	4	2	no	—
286	C₂²⋊D₅	—	4	2	no	—
287	C₂²⋊D₅	—	4	2	no	—
288	C₂²⋊D₅	—	4	2	no	—
289	C₂×Dic₅	—	2	2	no	—
290	C₂×Dic₅	—	2	2	no	—
291	C₂×Dic₅	—	2	2	no	—
292	D₂₀	—	4	1	no	—
293	D₂₀	—	4	1	no	—
294	D₂₀	—	4	1	no	—
295	D₂₀	—	4	1	no	—
296	C₄×D₅	—	4	2	no	—
297	C₄×D₅	—	4	2	no	—
298	C₄×D₅	—	4	2	no	—
299	C₄×D₅	—	4	2	no	—
300	Dic₁₀	—	4	1	no	—
301	Dic₁₀	—	4	1	no	—
302	Dic₁₀	—	4	1	no	—
303	Dic₁₀	—	4	1	no	—
304	C₅×C₈	—	2	4	no	—
305	C₅×C₈	—	2	4	no	—
306	C₅×C₈	—	4	2	no	—
307	#168	—	2	4	no	—
308	#168	—	4	2	no	—
309	#168	—	4	2	no	—
310	C₂×#41	—	10	1	no	—
311	C₂×#41	—	10	1	no	—
312	C₂×#41	—	10	1	no	—
313	C₂×#41	—	10	1	no	—
314	C₂×#41	—	10	1	no	—
315	C₂×#41	—	10	1	no	—
316	C₂×#41	—	10	1	no	—
317	C₂×#41	—	10	1	no	—
318	C₂×#41	—	10	1	no	—
319	C₂×#41	—	10	1	no	—
320	C₂×#41	—	10	1	no	—
321	C₂×#41	—	10	1	no	—
322	C₂²×Q₈	—	5	1	no	—
323	C₂²×D₄	—	5	2	no	—
324	C₂²×D₄	—	5	1	no	—
325	C₂³×C₄	—	5	2	no	—
326	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	5	2	no	—
339	C₂×M₁₆	—	5	2	no	—
340	C₂×M₁₆	—	5	2	no	—
341	C₂×M₁₆	—	5	2	no	—
342	C₂×M₁₆	—	5	2	no	—
343	C₂×M₁₆	—	10	1	no	—
344	C₂×M₁₆	—	10	1	no	—
345	C₂×M₁₆	—	10	1	no	—
346	C₂×M₁₆	—	10	1	no	—
347	C₂×M₁₆	—	10	1	no	—
348	C₂×M₁₆	—	10	1	no	—
349	C₂×M₁₆	—	10	1	no	—
350	C₂×M₁₆	—	10	1	no	—
351	C₂×M₁₆	—	10	1	no	—
352	C₂×M₁₆	—	10	1	no	—
353	C₂×M₁₆	—	10	1	no	—
354	C₂×M₁₆	—	10	1	no	—
355	C₂×M₁₆	—	10	1	no	—
356	C₂×M₁₆	D₂₀	1	2	yes	—
357	C₂×M₁₆	D₂₀	1	2	yes	—
358	C₂×M₁₆	C₂²⋊D₅	1	2	yes	—
359	C₂×M₁₆	C₂²⋊D₅	1	2	yes	—
360	C₂×M₁₆	C₂²×D₅	1	2	yes	—
361	C₂×M₁₆	C₂²×D₅	1	2	yes	—
362	C₂×M₁₆	C₂²×D₅	1	2	yes	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	10	1	no	—
367	C₂²×C₈	—	10	1	no	—
368	C₂²×C₈	—	10	1	no	—
369	#108	—	2	8	no	—
370	#108	—	10	8	no	—
371	#108	—	10	8	no	—
372	#101	—	10	4	no	—
373	#101	—	10	4	no	—
374	#101	—	10	4	no	—
375	#100	—	10	4	no	—
376	#100	—	10	4	no	—
377	#100	—	10	4	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	—	4	1	no	—
382	C₂²×C₅	—	4	1	no	—
383	C₂²×C₅	—	4	1	no	—
384	C₂²×C₅	—	4	1	no	—
385	C₂²×C₅	#396	1	1	yes	characteristic
386	C₂²×C₅	#396	1	1	yes	characteristic
387	C₂²×C₅	#396	1	1	yes	characteristic
388	C₂²×C₅	#396	1	1	yes	characteristic
389	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
391	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
392	C₂×D₅	—	4	2	no	—
393	C₂×D₅	—	8	2	no	—
394	C₂×D₅	—	8	2	no	—
395	C₂×D₅	—	8	2	no	—
396	C₄×C₅	#396	1	1	yes	characteristic
397	C₄×C₅	#396	1	1	yes	characteristic
398	C₄×C₅	#396	1	1	yes	characteristic
399	C₄×C₅	#396	1	1	yes	characteristic
400	C₄×C₅	C₂×#121	1	1	yes	characteristic
401	C₄×C₅	C₂×#121	1	1	yes	characteristic
402	C₄×C₅	C₂×#121	1	1	yes	characteristic
403	C₄×C₅	C₂×#126	1	1	yes	characteristic
404	Dic₅	—	4	2	no	—
405	C₂⁴	—	5	2	no	—
406	C₂⁴	Q₈×D₅	1	1	yes	characteristic
407	#41	—	20	1	no	—
408	#41	—	20	1	no	—
409	#41	—	20	1	no	—
410	#41	—	20	1	no	—
411	#41	—	20	1	no	—
412	#41	—	20	1	no	—
413	#41	—	20	1	no	—
414	#41	—	20	1	no	—
415	#41	—	20	1	no	—
416	#41	—	20	1	no	—
417	#41	—	20	1	no	—
418	#41	—	20	1	no	—
419	#41	—	20	1	no	—
420	#41	—	20	1	no	—
421	#41	—	20	1	no	—
422	#41	—	20	1	no	—
423	C₂×Q₈	—	10	1	no	—
424	C₂×Q₈	—	10	1	no	—
425	C₂×Q₈	—	10	1	no	—
426	C₂×Q₈	—	10	1	no	—
427	C₂×Q₈	—	10	1	no	—
428	C₂×Q₈	—	10	1	no	—
429	C₂×D₄	—	10	2	no	—
430	C₂×D₄	—	10	2	no	—
431	C₂×D₄	—	10	2	no	—
432	C₂×D₄	—	10	2	no	—
433	C₂×D₄	—	10	2	no	—
434	C₂×D₄	—	10	2	no	—
435	C₂×D₄	—	10	1	no	—
436	C₂×D₄	—	10	1	no	—
437	C₂×D₄	—	10	1	no	—
438	C₂×D₄	—	10	1	no	—
439	C₂×D₄	—	10	1	no	—
440	C₂×D₄	—	10	1	no	—
441	C₂²×C₄	—	5	2	no	—
442	C₂²×C₄	—	10	2	no	—
443	C₂²×C₄	—	10	2	no	—
444	C₂²×C₄	—	10	2	no	—
445	C₂²×C₄	—	10	2	no	—
446	C₂²×C₄	—	10	2	no	—
447	C₂²×C₄	—	10	2	no	—
448	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
450	C₂²×C₄	#709	1	1	yes	characteristic
451	C₂²×C₄	#709	1	1	yes	characteristic
452	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
453	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
454	C₂²×C₄	#711	1	1	yes	characteristic
455	C₂²×C₄	#711	1	1	yes	characteristic
456	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
457	C₂²×C₄	#713	1	1	yes	characteristic
458	C₂²×C₄	#713	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
461	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	5	4	no	—
473	M₁₆	—	10	2	no	—
474	M₁₆	—	10	2	no	—
475	M₁₆	—	10	2	no	—
476	M₁₆	—	10	2	no	—
477	M₁₆	—	10	2	no	—
478	M₁₆	—	10	2	no	—
479	M₁₆	—	10	2	no	—
480	M₁₆	—	20	1	no	—
481	M₁₆	—	20	1	no	—
482	M₁₆	—	20	1	no	—
483	M₁₆	—	20	1	no	—
484	M₁₆	C₂×D₂₀	1	4	yes	—
485	M₁₆	C₂×C₂²⋊D₅	1	4	yes	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	4	1	no	—
494	C₂×C₈	—	4	1	no	—
495	C₂×C₈	—	10	2	no	—
496	C₂×C₈	—	10	2	no	—
497	C₂×C₈	—	10	2	no	—
498	C₂×C₈	—	10	2	no	—
499	C₂×C₈	—	10	2	no	—
500	C₂×C₈	—	20	1	no	—
501	C₂×C₈	—	20	1	no	—
502	C₂×C₈	—	20	1	no	—
503	C₂×C₈	—	20	1	no	—
504	C₂×C₅	—	2	1	no	—
505	C₂×C₅	—	2	1	no	—
506	C₂×C₅	—	2	1	no	—
507	C₂×C₅	—	2	1	no	—
508	C₂×C₅	—	2	1	no	—
509	C₂×C₅	—	2	1	no	—
510	C₂×C₅	—	2	1	no	—
511	C₂×C₅	C₂×#396	1	1	yes	characteristic
512	D₅	—	8	2	no	—
513	C₂³	—	8	1	no	—
514	C₂³	—	10	2	no	—
515	C₂³	—	10	2	no	—
516	C₂³	—	10	2	no	—
517	C₂³	—	40	2	no	—
518	C₂³	#4042	1	1	yes	characteristic
519	C₂³	#4042	1	1	yes	characteristic
520	C₂³	#4043	1	1	yes	characteristic
521	C₂³	#4043	1	1	yes	characteristic
522	C₂³	#4092	1	1	yes	characteristic
523	C₂³	#4092	1	1	yes	characteristic
524	C₂³	C₂×Q₈×D₅	1	1	yes	characteristic
525	Q₈	—	20	1	no	—
526	Q₈	—	20	1	no	—
527	Q₈	—	20	1	no	—
528	Q₈	—	20	1	no	—
529	D₄	—	20	2	no	—
530	D₄	—	20	2	no	—
531	D₄	—	20	2	no	—
532	D₄	—	20	2	no	—
533	D₄	—	20	1	no	—
534	D₄	—	20	1	no	—
535	D₄	—	20	1	no	—
536	D₄	—	20	1	no	—
537	C₂×C₄	—	10	2	no	—
538	C₂×C₄	—	10	2	no	—
539	C₂×C₄	—	10	2	no	—
540	C₂×C₄	—	20	2	no	—
541	C₂×C₄	—	20	2	no	—
542	C₂×C₄	—	20	2	no	—
543	C₂×C₄	—	20	2	no	—
544	C₂×C₄	#4041	1	1	yes	characteristic
545	C₂×C₄	#4041	1	1	yes	characteristic
546	C₂×C₄	#4041	1	1	yes	characteristic
547	C₂×C₄	#4041	1	1	yes	characteristic
548	C₂×C₄	#4042	1	1	yes	characteristic
549	C₂×C₄	#4042	1	1	yes	characteristic
550	C₂×C₄	#4043	1	1	yes	characteristic
551	C₂×C₄	#4043	1	1	yes	characteristic
552	C₂×C₄	#4044	1	1	yes	characteristic
553	C₂×C₄	#4044	1	1	yes	characteristic
554	C₂×C₄	#4044	1	1	yes	characteristic
555	C₂×C₄	#4044	1	1	yes	characteristic
556	C₂×C₄	#4076	1	1	yes	characteristic
557	C₂×C₄	#4076	1	1	yes	characteristic
558	C₂×C₄	#4076	1	1	yes	characteristic
559	C₂×C₄	#4076	1	1	yes	characteristic
560	C₂×C₄	#4085	1	1	yes	characteristic
561	C₂×C₄	#4085	1	1	yes	characteristic
562	C₂×C₄	#4085	1	1	yes	characteristic
563	C₂×C₄	#4085	1	1	yes	characteristic
564	C₂×C₄	#4092	1	1	yes	characteristic
565	C₂×C₄	#4092	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
567	C₂×C₄	C₂×#709	1	1	yes	characteristic
568	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
569	C₂×C₄	C₂×#711	1	1	yes	characteristic
570	C₂×C₄	C₂×#713	1	1	yes	characteristic
571	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
572	C₈	—	2	4	no	—
573	C₈	—	2	4	no	—
574	C₈	—	4	2	no	—
575	C₈	—	10	4	no	—
576	C₈	—	20	2	no	—
577	C₈	—	20	2	no	—
578	C₅	#23622	1	1	yes	characteristic, complemented, Sylow
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	20	2	no	—
587	C₂²	—	40	2	no	—
588	C₂²	—	40	2	no	—
589	C₂²	—	40	2	no	—
590	C₂²	#65283	1	1	yes	characteristic
591	C₂²	#65283	1	1	yes	characteristic
592	C₂²	#65283	1	1	yes	characteristic
593	C₂²	#65283	1	1	yes	characteristic
594	C₂²	C₂×#4042	1	1	yes	characteristic
595	C₂²	C₂×#4043	1	1	yes	characteristic
596	C₂²	C₂×#4092	1	1	yes	characteristic
597	C₄	—	20	2	no	—
598	C₄	#65283	1	1	yes	characteristic
599	C₄	#65283	1	1	yes	characteristic
600	C₄	#65283	1	1	yes	characteristic
601	C₄	#65283	1	1	yes	characteristic
602	C₄	C₂×#4041	1	1	yes	characteristic
603	C₄	C₂×#4044	1	1	yes	characteristic
604	C₄	C₂×#4076	1	1	yes	characteristic
605	C₄	C₂×#4085	1	1	yes	characteristic
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	40	2	no	—
614	C₂	C₂×#65283	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#65283
commutator, cosocle	C₂²×C₄×C₅	C₂⁴
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₂×C₅×#430	C₂
socle	C₂×C₅	C₂×#396
prime radical	C₂²×#709	C₂²
hypercenter	C₂×#430	D₅
hypocenter	C₅	#23622
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#430	C₂	semidirect
5. C₂×#65414	C₂	semidirect
6. C₂×#65413	C₂	semidirect
7. C₂×#64780	C₂	semidirect
8. #10601525	C₂	semidirect
9. #10601523	C₂	semidirect
110. C₂×#430	D₅	semidirect
578. C₅	#23622	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#430	2
C₂×#65421	2
C₂×#65414	2
C₂×#65413	2
C₂×#64780	2
#10601525	2
#10601523	2
#23622	5