Subgroups — #12097889

Order 1280.

998 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65434	C₂	1	1	yes	maximal, characteristic
2	#10615513	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#65112	C₂	1	1	yes	maximal, characteristic
4	#10610549	C₂	1	1	yes	maximal, characteristic
5	#10610281	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1764	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601147	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601082	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600683	C₂	1	1	yes	maximal, characteristic, complemented
10	#10600582	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600542	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599719	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599709	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599535	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599522	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#131	C₂²	1	1	yes	characteristic
17	#41×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×#4096	C₂²	1	1	yes	characteristic
19	C₂×#4094	C₂²	1	1	yes	characteristic
20	C₂×#4053	C₂²	1	1	yes	characteristic
21	C₂×#4047	C₂²	1	1	yes	characteristic
22	#65856	C₂²	1	1	yes	characteristic
23	C₂×C₅×#104	C₂²	1	1	yes	characteristic
24	C₅×#416	C₂²	1	1	yes	characteristic
25	C₅×#405	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₂×#3969	C₂²	1	1	yes	characteristic
28	#65434	C₄	1	8	yes	complemented
29	C₂×#3957	C₂²	1	1	yes	characteristic
30	C₂×#3954	C₂²	1	1	yes	characteristic
31	C₂×#3954	C₂²	1	1	yes	characteristic
32	#65411	—	2	1	no	—
33	#65411	C₂²	1	1	yes	characteristic
34	M₁₆×Dic₅	—	2	1	no	—
35	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
36	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
37	#65402	C₂²	1	1	yes	characteristic
38	#65390	—	2	1	no	—
39	#65390	C₂²	1	1	yes	characteristic
40	C₂×#3947	—	2	1	no	—
41	C₂×#3947	C₂²	1	1	yes	characteristic
42	C₂×#3947	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
45	#65287	C₂²	1	1	yes	characteristic
46	#65286	C₂²	1	1	yes	characteristic
47	#65221	C₂²	1	1	yes	characteristic
48	C₂×#3937	C₂²	1	1	yes	characteristic
49	C₂×#3935	C₂²	1	1	yes	characteristic
50	#65112	C₄	1	8	yes	complemented
51	#65079	C₄	1	2	yes	complemented
52	#65077	C₄	1	2	yes	complemented
53	#65047	C₄	1	2	yes	complemented
54	#65045	C₄	1	2	yes	complemented
55	#64997	—	2	1	no	—
56	D₅×#97	—	2	1	no	—
57	#64978	—	2	1	no	—
58	C₄×#676	—	2	1	no	—
59	C₅×#341	C₂²	1	1	yes	characteristic
60	C₅×#339	C₂²	1	1	yes	characteristic
61	#64775	C₂²	1	1	yes	characteristic
62	#64772	C₂²	1	1	yes	characteristic
63	#64752	C₂²	1	1	yes	characteristic
64	#64743	C₂²	1	1	yes	characteristic
65	#20513	—	5	1	no	maximal, Sylow
66	C₂×C₅×#41	C₂³	1	1	yes	characteristic
67	C₂×#709	C₂³	1	1	yes	characteristic
68	C₅×#131	—	2	2	no	—
69	C₅×#131	C₂×C₄	1	4	yes	complemented
70	C₂×C₅×M₁₆	—	2	1	no	—
71	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	—	2	1	no	—
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₅×#117	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	#4096	C₂×C₄	1	4	yes	—
79	#4096	C₂×C₄	1	4	yes	—
80	#4094	—	2	2	no	—
81	#4094	C₂×C₄	1	4	yes	complemented
82	Q₈×Dic₅	C₂×C₄	1	2	yes	—
83	C₂×#689	C₂×C₄	1	1	yes	characteristic
84	C₂×#688	C₂×C₄	1	1	yes	characteristic
85	D₄×Dic₅	—	2	2	no	—
86	D₄×Dic₅	C₂×C₄	1	2	yes	—
87	C₂×#687	C₂×C₄	1	1	yes	characteristic
88	C₂×#686	C₂×C₄	1	1	yes	characteristic
89	#4072	—	2	1	no	—
90	#4072	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₅	—	2	1	no	—
92	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
93	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
94	C₂×#681	—	2	1	no	—
95	C₂×#681	C₂³	1	1	yes	characteristic
96	C₂×#681	C₂³	1	1	yes	characteristic
97	C₂²×#168	—	2	1	no	—
98	C₂²×#168	C₂³	1	1	yes	characteristic
99	C₂²×#168	C₂³	1	1	yes	characteristic
100	#4053	—	2	2	no	—
101	#4053	C₂×C₄	1	4	yes	complemented
102	#4047	—	2	2	no	—
103	#4047	C₂×C₄	1	4	yes	complemented
104	C₂×#676	—	2	1	no	—
105	C₂×#676	—	2	1	no	—
106	C₂×C₈×D₅	—	2	1	no	—
107	C₂×C₈×D₅	—	2	1	no	—
108	#4039	C₂×C₄	1	2	yes	—
109	#4033	C₂×C₄	1	2	yes	—
110	#4027	—	2	2	no	—
111	#4018	—	2	1	no	—
112	C₄²×D₅	—	2	1	no	—
113	C₅×#104	C₂×C₄	1	4	yes	complemented
114	C₅×#103	C₂×C₄	1	2	yes	—
115	C₅×#102	C₂×C₄	1	2	yes	—
116	C₅×#97	—	2	1	no	—
117	C₄×C₅×C₈	—	2	1	no	—
118	C₄×C₅×C₈	—	2	2	no	—
119	#3969	C₂×C₄	1	4	yes	complemented
120	#3963	—	2	2	no	—
121	#3957	C₂×C₄	1	4	yes	complemented
122	#3954	C₂×C₄	1	4	yes	complemented
123	#3954	C₂×C₄	1	4	yes	complemented
124	#3953	C₂×C₄	1	2	yes	—
125	#3948	C₂×C₄	1	2	yes	—
126	#3947	—	2	1	no	—
127	#3947	—	2	1	no	—
128	#3947	—	2	1	no	—
129	#3947	—	2	1	no	—
130	#3947	C₂×C₄	1	4	yes	complemented
131	#3947	D₄	1	1	yes	characteristic
132	#3947	D₄	1	1	yes	characteristic
133	#3947	D₄	1	1	yes	characteristic
134	#3947	D₄	1	1	yes	characteristic
135	C₈×Dic₅	—	2	1	no	—
136	C₈×Dic₅	—	2	1	no	—
137	C₈×Dic₅	—	2	1	no	—
138	C₈×Dic₅	—	2	1	no	—
139	C₈×Dic₅	—	2	2	no	—
140	C₈×Dic₅	C₂×C₄	1	2	yes	—
141	C₈×Dic₅	C₂×C₄	1	2	yes	—
142	#3940	C₂×C₄	1	2	yes	—
143	#3939	C₂×C₄	1	2	yes	—
144	#3937	C₂×C₄	1	4	yes	complemented
145	#3935	—	2	1	no	—
146	#3935	C₂×C₄	1	4	yes	complemented
147	C₄×#168	—	2	1	no	—
148	C₂×#444	—	5	1	no	—
149	C₂×#444	—	5	1	no	—
150	C₄×#135	—	5	1	no	—
151	#2875	—	5	1	no	—
152	#2875	—	5	1	no	—
153	C₄×#108	—	5	1	no	—
154	#1773	—	5	1	no	—
155	#1773	—	5	1	no	—
156	#1764	—	5	1	no	—
157	#1764	—	5	1	no	—
158	#1764	—	5	1	no	—
159	#1764	D₅	1	1	yes	characteristic, complemented
160	#1759	—	5	1	no	—
161	#1759	—	5	1	no	—
162	#1726	—	5	1	no	—
163	C₅×#41	—	2	1	no	—
164	C₅×#41	—	2	1	no	—
165	C₅×#41	C₂²×C₄	1	2	yes	—
166	C₅×#41	C₂²×C₄	1	2	yes	—
167	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₂×C₂²⋊D₅	—	2	1	no	—
174	C₂²×Dic₅	—	2	1	no	—
175	C₂²×Dic₅	—	2	2	no	—
176	C₂²×Dic₅	#41	1	2	yes	—
177	#709	—	2	1	no	—
178	#709	—	2	1	no	—
179	#709	C₂²×C₄	1	2	yes	—
180	#709	C₂²×C₄	1	2	yes	—
181	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄×D₅	—	2	1	no	—
183	C₂×C₄×D₅	—	2	2	no	—
184	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
185	C₅×M₁₆	—	2	1	no	—
186	C₅×M₁₆	—	2	1	no	—
187	C₅×M₁₆	—	2	4	no	—
188	C₅×M₁₆	C₂²×C₄	1	2	yes	—
189	C₅×M₁₆	C₂²×C₄	1	2	yes	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	4	no	—
195	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
196	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
197	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅×C₈	#41	1	2	yes	—
200	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
201	C₅×C₂²⋊C₄	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	—	2	1	no	—
204	C₄²×C₅	C₂²×C₄	1	2	yes	—
205	C₂²⋊Dic₅	—	2	1	no	—
206	C₂²⋊Dic₅	—	2	2	no	—
207	#689	C₄²	1	4	yes	—
208	#688	C₄²	1	4	yes	—
209	#687	C₄²	1	4	yes	—
210	#686	C₄²	1	4	yes	—
211	#685	—	2	2	no	—
212	C₄⋊Dic₅	—	2	2	no	—
213	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
214	#683	—	2	2	no	—
215	C₄×Dic₅	—	2	1	no	—
216	C₄×Dic₅	—	2	1	no	—
217	C₄×Dic₅	—	2	2	no	—
218	C₄×Dic₅	—	2	2	no	—
219	C₄×Dic₅	C₂²×C₄	1	2	yes	—
220	C₄×Dic₅	C₂²×C₄	1	2	yes	—
221	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
222	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
223	#681	—	2	1	no	—
224	#681	—	2	1	no	—
225	#681	—	2	4	no	—
226	#681	C₂²×C₄	1	2	yes	—
227	#681	C₂²×C₄	1	2	yes	—
228	C₂×#168	—	2	1	no	—
229	C₂×#168	—	2	1	no	—
230	C₂×#168	—	2	4	no	—
231	C₂×#168	C₂²×C₄	1	2	yes	—
232	C₂×#168	C₂²×C₄	1	2	yes	—
233	C₂×#168	C₂²×C₄	1	1	yes	characteristic
234	C₂×#168	C₂²×C₄	1	1	yes	characteristic
235	C₂×#168	C₂²×C₄	1	2	yes	—
236	C₂×#168	C₂×D₄	1	1	yes	characteristic
237	C₂×#168	C₂×D₄	1	1	yes	characteristic
238	C₂×#168	#41	1	2	yes	—
239	#676	—	2	4	no	—
240	#676	—	2	4	no	—
241	C₈×D₅	—	2	4	no	—
242	C₈×D₅	—	2	4	no	—
243	C₂×#135	—	5	1	no	—
244	C₂×#131	—	5	1	no	—
245	C₂×#131	—	5	1	no	—
246	C₂×#131	—	5	1	no	—
247	C₂×#131	C₂×D₅	1	1	yes	characteristic
248	C₄×#41	—	5	1	no	—
249	C₄×#41	—	5	1	no	—
250	#444	—	5	8	no	—
251	#444	—	5	8	no	—
252	C₄×Q₁₆	—	5	2	no	—
253	C₄×SD₁₆	—	5	2	no	—
254	C₄×SD₁₆	—	5	2	no	—
255	C₄×D₈	—	5	2	no	—
256	C₂×#108	—	5	1	no	—
257	C₂×#108	—	5	1	no	—
258	#427	—	5	1	no	—
259	C₂×#104	—	5	1	no	—
260	C₂×#104	—	5	1	no	—
261	C₂×#104	—	5	1	no	—
262	C₂×#104	C₂×D₅	1	1	yes	characteristic
263	#416	—	5	1	no	—
264	#416	C₂×D₅	1	1	yes	characteristic
265	#405	—	5	1	no	—
266	#405	—	5	1	no	—
267	#405	—	5	1	no	—
268	#405	—	10	1	no	—
269	#405	—	10	1	no	—
270	#405	—	10	1	no	—
271	#405	—	10	1	no	—
272	#405	C₂×D₅	1	1	yes	characteristic
273	C₄×M₁₆	—	5	1	no	—
274	C₄×M₁₆	—	5	1	no	—
275	C₄×M₁₆	—	10	1	no	—
276	C₄×M₁₆	—	10	1	no	—
277	C₂×#97	—	5	1	no	—
278	C₂×#97	—	5	1	no	—
279	C₂×#97	—	5	1	no	—
280	C₂×#97	—	10	1	no	—
281	C₂×#97	—	10	1	no	—
282	C₂×C₄×C₈	—	5	1	no	—
283	C₂×C₄×C₈	—	5	1	no	—
284	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
285	#376	—	5	1	no	—
286	#341	—	5	1	no	—
287	#341	C₂×D₅	1	1	yes	characteristic
288	#339	—	5	1	no	—
289	#339	—	5	1	no	—
290	#339	—	5	1	no	—
291	#339	C₂×D₅	1	1	yes	characteristic
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	C₂×#41	1	1	yes	characteristic
294	C₂²×D₅	—	2	1	no	—
295	C₅×Q₈	—	2	1	no	—
296	C₅×Q₈	C₂×C₄²	1	2	yes	—
297	C₅×D₄	—	2	2	no	—
298	C₅×D₄	—	2	2	no	—
299	C₅×D₄	—	2	1	no	—
300	C₅×D₄	C₂×C₄²	1	2	yes	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	4	2	no	—
307	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
313	C₂²⋊D₅	—	2	2	no	—
314	C₂²⋊D₅	—	2	2	no	—
315	C₂×Dic₅	—	2	1	no	—
316	C₂×Dic₅	—	2	2	no	—
317	C₂×Dic₅	—	2	2	no	—
318	C₂×Dic₅	—	4	2	no	—
319	C₂×Dic₅	—	4	2	no	—
320	C₂×Dic₅	—	8	2	no	—
321	C₂×Dic₅	C₄×D₄	1	2	yes	—
322	C₂×Dic₅	C₄×D₄	1	2	yes	—
323	D₂₀	—	2	1	no	—
324	D₂₀	C₂×C₄²	1	2	yes	—
325	C₄×D₅	—	2	2	no	—
326	C₄×D₅	—	2	2	no	—
327	C₄×D₅	—	8	2	no	—
328	Dic₁₀	—	2	1	no	—
329	Dic₁₀	C₂×C₄²	1	2	yes	—
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	2	2	no	—
332	C₅×C₈	—	2	2	no	—
333	C₅×C₈	C₄×D₄	1	2	yes	—
334	C₅×C₈	C₄×D₄	1	2	yes	—
335	#168	—	2	2	no	—
336	#168	—	2	2	no	—
337	#168	C₂×C₄²	1	2	yes	—
338	#168	C₂×C₄²	1	2	yes	—
339	#168	C₄×D₄	1	2	yes	—
340	#168	C₄×D₄	1	2	yes	—
341	C₂×#41	—	5	1	no	—
342	C₂×#41	C₂²×D₅	1	1	yes	characteristic
343	#135	—	5	4	no	—
344	#135	—	5	4	no	—
345	C₂×Q₁₆	—	5	1	no	—
346	C₂×SD₁₆	—	5	1	no	—
347	C₂×SD₁₆	—	5	1	no	—
348	C₂×D₈	—	5	1	no	—
349	#131	—	2	2	no	—
350	#131	—	5	4	no	—
351	#131	—	5	4	no	—
352	#131	—	5	4	no	—
353	#131	—	10	2	no	—
354	#131	—	10	2	no	—
355	#131	—	10	2	no	—
356	#131	C₄×D₅	1	4	yes	complemented
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	5	1	no	—
359	C₂×M₁₆	—	5	1	no	—
360	C₂×M₁₆	—	10	1	no	—
361	C₂×M₁₆	—	10	1	no	—
362	C₂×M₁₆	—	10	1	no	—
363	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
364	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	5	1	no	—
367	C₂²×C₈	—	5	1	no	—
368	C₂²×C₈	—	10	1	no	—
369	C₂²×C₈	—	10	1	no	—
370	C₂²×C₈	—	10	1	no	—
371	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
372	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
373	C₄×Q₈	—	5	2	no	—
374	C₄×Q₈	—	5	2	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	—	5	2	no	—
377	C₄×D₄	—	10	2	no	—
378	C₄×D₄	—	10	2	no	—
379	#117	—	5	1	no	—
380	#117	—	10	1	no	—
381	#117	—	10	1	no	—
382	#117	C₂²×D₅	1	1	yes	characteristic
383	C₂×C₄²	—	5	1	no	—
384	C₂×C₄²	—	5	1	no	—
385	C₂×C₄²	—	10	1	no	—
386	C₂×C₄²	—	10	1	no	—
387	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
388	#108	—	5	4	no	—
389	#108	—	5	4	no	—
390	#107	—	5	2	no	—
391	#106	—	5	2	no	—
392	#104	—	5	4	no	—
393	#104	—	5	4	no	—
394	#104	—	5	4	no	—
395	#104	C₄×D₅	1	4	yes	complemented
396	#103	—	5	2	no	—
397	#103	C₄×D₅	1	2	yes	—
398	#102	—	5	2	no	—
399	#102	C₄×D₅	1	2	yes	—
400	#97	—	2	1	no	—
401	#97	—	5	4	no	—
402	#97	—	5	1	no	—
403	#97	—	5	1	no	—
404	#97	—	5	1	no	—
405	#97	—	5	1	no	—
406	#97	—	5	4	no	—
407	#97	—	10	1	no	—
408	#97	—	10	1	no	—
409	#97	—	10	1	no	—
410	#97	—	10	1	no	—
411	#97	—	10	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	—	2	2	no	—
414	C₄×C₈	—	5	2	no	—
415	C₄×C₈	—	5	2	no	—
416	C₄×C₈	—	10	1	no	—
417	C₄×C₈	—	10	1	no	—
418	C₄×C₈	—	10	1	no	—
419	C₄×C₈	—	10	2	no	—
420	C₄×C₈	—	10	1	no	—
421	C₄×C₈	—	10	1	no	—
422	#95	—	10	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
427	C₂²×C₅	C₄×#41	1	1	yes	characteristic
428	C₂²×C₅	C₄×#41	1	1	yes	characteristic
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	4	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
435	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
436	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
437	C₄×C₅	C₄×#41	1	1	yes	characteristic
438	Dic₅	—	2	2	no	—
439	Dic₅	—	2	2	no	—
440	Dic₅	—	2	2	no	—
441	Dic₅	—	4	2	no	—
442	Dic₅	—	4	2	no	—
443	#41	—	2	1	no	—
444	#41	—	2	1	no	—
445	#41	—	5	2	no	—
446	#41	—	5	2	no	—
447	#41	—	10	1	no	—
448	#41	—	10	1	no	—
449	#41	C₂×C₄×D₅	1	2	yes	—
450	#41	C₂×C₄×D₅	1	2	yes	—
451	C₂×Q₈	—	5	1	no	—
452	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	5	1	no	—
455	C₂×D₄	—	10	1	no	—
456	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	5	2	no	—
460	C₂²×C₄	—	10	2	no	—
461	C₂²×C₄	—	10	2	no	—
462	C₂²×C₄	—	10	1	no	—
463	C₂²×C₄	—	10	1	no	—
464	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
465	Q₁₆	—	5	4	no	—
466	SD₁₆	—	5	4	no	—
467	SD₁₆	—	5	4	no	—
468	D₈	—	5	4	no	—
469	M₁₆	—	2	1	no	—
470	M₁₆	—	2	1	no	—
471	M₁₆	—	2	4	no	—
472	M₁₆	—	5	2	no	—
473	M₁₆	—	5	2	no	—
474	M₁₆	—	10	4	no	—
475	M₁₆	—	10	4	no	—
476	M₁₆	—	10	1	no	—
477	M₁₆	—	10	1	no	—
478	M₁₆	—	10	4	no	—
479	M₁₆	C₂×C₄×D₅	1	2	yes	—
480	M₁₆	C₂×C₄×D₅	1	2	yes	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	4	no	—
486	C₂×C₈	—	5	1	no	—
487	C₂×C₈	—	5	1	no	—
488	C₂×C₈	—	5	2	no	—
489	C₂×C₈	—	5	2	no	—
490	C₂×C₈	—	5	2	no	—
491	C₂×C₈	—	5	1	no	—
492	C₂×C₈	—	5	1	no	—
493	C₂×C₈	—	5	2	no	—
494	C₂×C₈	—	10	4	no	—
495	C₂×C₈	—	10	4	no	—
496	C₂×C₈	—	10	1	no	—
497	C₂×C₈	—	10	1	no	—
498	C₂×C₈	—	10	4	no	—
499	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
500	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
501	C₂×C₈	D₄×D₅	1	1	yes	characteristic
502	C₂×C₈	D₄×D₅	1	1	yes	characteristic
503	C₂×C₈	#711	1	2	yes	—
504	C₄⋊C₄	—	5	2	no	—
505	C₄⋊C₄	—	10	2	no	—
506	C₄⋊C₄	—	10	2	no	—
507	C₄⋊C₄	C₂×C₄×D₅	1	2	yes	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	10	2	no	—
510	C₂²⋊C₄	—	10	2	no	—
511	C₂²⋊C₄	—	10	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	5	2	no	—
515	C₄²	—	5	1	no	—
516	C₄²	—	5	1	no	—
517	C₄²	—	5	2	no	—
518	C₄²	—	10	2	no	—
519	C₄²	—	10	2	no	—
520	C₄²	—	10	1	no	—
521	C₄²	—	10	1	no	—
522	C₄²	C₂×C₄×D₅	1	2	yes	—
523	C₂×C₅	—	2	1	no	—
524	C₂×C₅	—	2	1	no	—
525	C₂×C₅	—	4	2	no	—
526	C₂×C₅	C₄²×D₄	1	1	yes	characteristic
527	C₂×C₅	#2957	1	2	yes	—
528	D₅	—	4	2	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	10	1	no	—
531	C₂³	D₅×#41	1	1	yes	characteristic
532	Q₈	—	2	1	no	—
533	Q₈	—	5	2	no	—
534	Q₈	—	10	1	no	—
535	Q₈	C₄²×D₅	1	2	yes	—
536	D₄	—	2	2	no	—
537	D₄	—	2	2	no	—
538	D₄	—	2	1	no	—
539	D₄	—	5	2	no	—
540	D₄	—	10	2	no	—
541	D₄	—	10	2	no	—
542	D₄	—	10	1	no	—
543	D₄	C₄²×D₅	1	2	yes	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	5	2	no	—
551	C₂×C₄	—	5	2	no	—
552	C₂×C₄	—	10	1	no	—
553	C₂×C₄	—	10	2	no	—
554	C₂×C₄	—	10	2	no	—
555	C₂×C₄	—	10	2	no	—
556	C₂×C₄	—	10	2	no	—
557	C₂×C₄	—	20	2	no	—
558	C₂×C₄	—	20	2	no	—
559	C₂×C₄	—	40	2	no	—
560	C₂×C₄	—	40	2	no	—
561	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
562	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
564	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
565	C₂×C₄	C₂×#711	1	1	yes	characteristic
566	C₂×C₄	D₅×#41	1	1	yes	characteristic
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	5	2	no	—
571	C₈	—	5	2	no	—
572	C₈	—	5	2	no	—
573	C₈	—	5	2	no	—
574	C₈	—	10	2	no	—
575	C₈	—	10	2	no	—
576	C₈	#4027	1	2	yes	—
577	C₈	#4027	1	2	yes	—
578	C₅	#20513	1	1	yes	characteristic, complemented, Sylow
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	10	2	no	—
583	C₂²	—	20	2	no	—
584	C₂²	#65856	1	1	yes	characteristic
585	C₂²	C₄×#711	1	1	yes	characteristic
586	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
587	C₄	—	2	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	2	no	—
590	C₄	—	10	2	no	—
591	C₄	—	10	2	no	—
592	C₄	—	10	2	no	—
593	C₄	—	20	2	no	—
594	C₄	—	20	2	no	—
595	C₄	C₂×C₄²×D₅	1	1	yes	characteristic
596	C₄	C₂×#4027	1	1	yes	characteristic
597	C₄	C₄×#711	1	1	yes	characteristic
598	C₄	C₄×D₄×D₅	1	1	yes	characteristic
599	C₂	—	2	1	no	—
600	C₂	—	2	1	no	—
601	C₂	—	4	2	no	—
602	C₂	—	20	2	no	—
603	C₂	C₄×#4027	1	1	yes	characteristic
604	C₂	#10611621	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1764	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4096	C₂²
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1764	D₅
hypocenter	C₅	#20513
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1764

Complements

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

N	H ≅ G/N	type
2. #10615513	C₂	semidirect
5. #10610281	C₂	semidirect
6. C₅×#1764	C₂	semidirect
7. #10601147	C₂	semidirect
8. #10601082	C₂	semidirect
9. #10600683	C₂	semidirect
10. #10600582	C₂	semidirect
11. #10600542	C₂	semidirect
12. #10599719	C₂	semidirect
13. #10599709	C₂	semidirect
14. #10599535	C₂	semidirect
15. #10599522	C₂	semidirect
28. #65434	C₄	semidirect
50. #65112	C₄	semidirect
51. #65079	C₄	semidirect
52. #65077	C₄	semidirect
53. #65047	C₄	semidirect
54. #65045	C₄	semidirect
69. C₅×#131	C₂×C₄	semidirect
81. #4094	C₂×C₄	semidirect
101. #4053	C₂×C₄	semidirect
103. #4047	C₂×C₄	semidirect
113. C₅×#104	C₂×C₄	semidirect
119. #3969	C₂×C₄	semidirect
121. #3957	C₂×C₄	semidirect
122. #3954	C₂×C₄	semidirect
123. #3954	C₂×C₄	semidirect
130. #3947	C₂×C₄	semidirect
144. #3937	C₂×C₄	semidirect
146. #3935	C₂×C₄	semidirect
159. #1764	D₅	semidirect
356. #131	C₄×D₅	semidirect
395. #104	C₄×D₅	semidirect
578. C₅	#20513	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65434	2
#10615513	2
C₂×#65112	2
#10610549	2
#10610281	2
C₅×#1764	2
#10601147	2
#10601082	2
#10600683	2
#10600582	2
#10600542	2
#10599719	2
#10599709	2
#10599535	2
#10599522	2
#20513	5