Subgroups — #12070405

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10614260	C₂	1	1	yes	maximal, characteristic
2	#10614250	C₂	1	1	yes	maximal, characteristic, complemented
3	#10610735	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1477	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601558	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601536	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601216	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599016	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599010	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599007	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599005	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598956	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598953	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598951	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598946	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×#4047	—	2	1	no	—
18	#65811	C₂²	1	1	yes	characteristic
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	#65527	C₄	1	1	yes	characteristic
22	#65527	C₄	1	1	yes	characteristic
23	#65399	—	2	1	no	—
24	#65316	C₄	1	1	yes	characteristic
25	C₄×#688	C₂²	1	1	yes	characteristic
26	C₄×#688	C₂²	1	1	yes	characteristic
27	Q₈×#168	C₂²	1	1	yes	characteristic
28	Q₈×#168	C₂²	1	1	yes	characteristic
29	#65310	C₄	1	1	yes	characteristic
30	#65304	C₄	1	1	yes	characteristic
31	C₄×#686	C₂²	1	1	yes	characteristic
32	C₄×#686	C₂²	1	1	yes	characteristic
33	#65301	—	2	1	no	—
34	#65301	—	2	1	no	—
35	#65301	C₂²	1	1	yes	characteristic
36	#65301	C₂²	1	1	yes	characteristic
37	#65297	C₄	1	1	yes	characteristic
38	#65292	C₄	1	1	yes	characteristic
39	#65292	C₄	1	1	yes	characteristic
40	#65215	—	2	1	no	—
41	#65215	C₂²	1	1	yes	characteristic
42	#65214	C₂²	1	1	yes	characteristic
43	C₄×#681	—	2	1	no	—
44	C₄×#681	C₂²	1	1	yes	characteristic
45	#65127	C₂²	1	1	yes	characteristic
46	#65127	C₂²	1	1	yes	characteristic
47	#65125	—	2	1	no	—
48	#65125	—	2	1	no	—
49	#65123	C₂²	1	1	yes	characteristic
50	#65123	C₂²	1	1	yes	characteristic
51	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
55	#64700	C₂²	1	1	yes	characteristic
56	#64700	C₂²	1	1	yes	characteristic
57	#64699	C₂²	1	1	yes	characteristic
58	#64699	C₂²	1	1	yes	characteristic
59	#64679	C₂²	1	1	yes	characteristic
60	#64679	C₂²	1	1	yes	characteristic
61	#64679	C₂²	1	1	yes	characteristic
62	#64679	C₂²	1	1	yes	characteristic
63	#64675	C₂²	1	1	yes	characteristic
64	#64674	C₂²	1	1	yes	characteristic
65	#64674	C₂²	1	1	yes	characteristic
66	C₈×#168	C₂²	1	1	yes	characteristic
67	#18011	—	5	1	no	maximal, Sylow
68	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
69	C₂×#709	—	2	1	no	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×D₄	—	2	1	no	—
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
77	C₅×#117	—	2	1	no	—
78	C₅×#117	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×#688	C₂×C₄	1	1	yes	characteristic
82	C₂×#688	C₂×C₄	1	1	yes	characteristic
83	C₂×#686	C₂×C₄	1	1	yes	characteristic
84	C₂×#686	C₂×C₄	1	1	yes	characteristic
85	#4076	—	2	1	no	—
86	#4076	C₂×C₄	1	1	yes	characteristic
87	#4076	C₂×C₄	1	1	yes	characteristic
88	C₂×#681	—	2	1	no	—
89	C₂×#681	—	2	1	no	—
90	C₂×#681	D₄	1	1	yes	characteristic
91	C₂×#681	D₄	1	1	yes	characteristic
92	#4047	—	4	4	no	—
93	C₂×#676	—	2	1	no	—
94	C₂×#676	—	2	1	no	—
95	C₂×C₈×D₅	—	2	1	no	—
96	C₂×C₈×D₅	—	2	1	no	—
97	#4021	—	2	1	no	—
98	#4020	C₂×C₄	1	1	yes	characteristic
99	C₄×D₂₀	—	2	1	no	—
100	C₄×D₂₀	C₂³	1	1	yes	characteristic
101	C₄×D₂₀	C₂³	1	1	yes	characteristic
102	#4015	C₂×C₄	1	1	yes	characteristic
103	C₅×C₄⋊C₈	—	2	1	no	—
104	C₅×C₄⋊C₈	—	2	1	no	—
105	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₅×C₂²⋊C₈	—	2	1	no	—
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	#3967	C₂×C₄	1	1	yes	characteristic
111	#3967	C₂×C₄	1	1	yes	characteristic
112	#3964	C₂×C₄	1	1	yes	characteristic
113	#3964	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊#168	—	2	1	no	—
115	C₂²⋊#168	—	2	1	no	—
116	C₂²⋊#168	—	2	1	no	—
117	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
119	#3952	—	2	1	no	—
120	#3952	—	2	1	no	—
121	#3952	—	2	1	no	—
122	#3952	—	2	1	no	—
123	#3941	C₂×C₄	1	1	yes	characteristic
124	#3941	C₂×C₄	1	1	yes	characteristic
125	#3941	C₂×C₄	1	1	yes	characteristic
126	#3941	C₂×C₄	1	1	yes	characteristic
127	#3940	C₂×C₄	1	1	yes	characteristic
128	#3940	C₂×C₄	1	1	yes	characteristic
129	#3939	C₂×C₄	1	1	yes	characteristic
130	#3939	C₂×C₄	1	1	yes	characteristic
131	C₄⋊#168	—	2	1	no	—
132	C₄⋊#168	—	2	1	no	—
133	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
134	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#168	C₂³	1	1	yes	characteristic
136	C₄⋊#168	C₂³	1	1	yes	characteristic
137	#3935	—	2	1	no	—
138	#3935	D₄	1	1	yes	characteristic
139	#3935	D₄	1	1	yes	characteristic
140	C₄×#168	—	2	1	no	—
141	C₄×#168	—	2	1	no	—
142	C₄×#168	C₂³	1	1	yes	characteristic
143	C₄×#168	C₂³	1	1	yes	characteristic
144	C₄×#168	C₂³	1	1	yes	characteristic
145	C₄×#168	C₂³	1	1	yes	characteristic
146	#3106	—	5	1	no	—
147	#2971	—	5	1	no	—
148	#2935	—	5	1	no	—
149	#1594	—	5	1	no	—
150	#1589	—	5	1	no	—
151	#1588	—	5	1	no	—
152	#1586	—	5	1	no	—
153	#1583	—	5	1	no	—
154	#1581	—	5	1	no	—
155	SD₁₆⋊C₈	—	5	1	no	—
156	C₈×SD₁₆	—	5	1	no	—
157	#1573	—	5	1	no	—
158	#1496	—	5	1	no	—
159	#1477	D₅	1	1	yes	characteristic, complemented
160	#1453	—	5	1	no	—
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	4	1	no	—
163	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	#41	1	1	yes	characteristic
172	C₂×C₂²⋊D₅	—	2	1	no	—
173	C₂×C₂²⋊D₅	—	2	1	no	—
174	#709	—	4	2	no	—
175	#709	—	4	2	no	—
176	C₂×D₂₀	—	2	1	no	—
177	C₂×D₂₀	—	2	1	no	—
178	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
179	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×D₅	—	2	1	no	—
181	C₂×C₄×D₅	—	2	1	no	—
182	C₂×Dic₁₀	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	4	2	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
191	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
192	C₅×C₂²⋊C₄	—	2	1	no	—
193	C₅×C₂²⋊C₄	—	2	1	no	—
194	C₅×C₂²⋊C₄	—	2	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
199	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₅	#41	1	1	yes	characteristic
201	C₄²×C₅	C₂⁴	1	1	yes	characteristic
202	#688	—	2	2	no	—
203	#688	—	2	2	no	—
204	#686	—	4	1	no	—
205	#686	—	4	1	no	—
206	#685	—	2	1	no	—
207	#685	—	2	1	no	—
208	#685	—	2	1	no	—
209	#685	—	2	1	no	—
210	C₄⋊Dic₅	—	2	1	no	—
211	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
213	#681	—	2	2	no	—
214	#681	—	4	1	no	—
215	#681	—	4	2	no	—
216	#681	—	4	2	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	C₂²×C₄	1	1	yes	characteristic
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂²×C₄	1	1	yes	characteristic
222	C₂×#168	C₂²×C₄	1	1	yes	characteristic
223	C₂×#168	C₂×D₄	1	1	yes	characteristic
224	C₂×#168	C₂×D₄	1	1	yes	characteristic
225	C₂×#168	C₂×D₄	1	1	yes	characteristic
226	C₂×#168	C₂×D₄	1	1	yes	characteristic
227	#676	—	4	2	no	—
228	#676	—	4	2	no	—
229	C₈×D₅	—	4	2	no	—
230	C₈×D₅	—	4	2	no	—
231	C₂×#131	—	10	1	no	—
232	#532	—	5	1	no	—
233	C₄×#41	C₂×D₅	1	1	yes	characteristic
234	#482	—	5	1	no	—
235	#482	—	5	1	no	—
236	#477	—	5	1	no	—
237	#476	—	5	1	no	—
238	#460	—	5	1	no	—
239	#459	—	5	1	no	—
240	#449	—	5	1	no	—
241	#449	—	5	1	no	—
242	C₈×Q₈	—	5	1	no	—
243	C₈×Q₈	—	5	1	no	—
244	C₄×SD₁₆	—	5	1	no	—
245	C₄×SD₁₆	—	5	1	no	—
246	C₄×D₈	—	5	1	no	—
247	C₄×D₈	—	5	1	no	—
248	#436	—	5	1	no	—
249	#436	—	5	1	no	—
250	#436	—	5	1	no	—
251	#436	—	5	1	no	—
252	#436	—	10	1	no	—
253	#436	—	10	1	no	—
254	#435	—	10	1	no	—
255	#435	—	10	1	no	—
256	C₈×D₄	—	5	1	no	—
257	C₈×D₄	—	5	1	no	—
258	#432	—	5	1	no	—
259	#432	—	10	1	no	—
260	#431	—	5	1	no	—
261	#431	C₂×D₅	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
263	#408	—	10	1	no	—
264	C₄×M₁₆	—	5	1	no	—
265	C₄×M₁₆	—	10	1	no	—
266	#335	—	5	1	no	—
267	#335	—	5	1	no	—
268	#334	—	5	1	no	—
269	#334	—	5	1	no	—
270	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
271	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
272	D₄⋊C₈	—	5	1	no	—
273	D₄⋊C₈	—	5	1	no	—
274	D₄⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
277	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
278	#322	—	5	1	no	—
279	#322	—	5	1	no	—
280	#322	—	5	1	no	—
281	C₈²	—	5	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
284	C₂²×D₅	—	2	1	no	—
285	C₂²×D₅	—	2	1	no	—
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	#131	1	2	yes	complemented
288	C₅×D₄	—	2	1	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	4	2	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	—	4	1	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	8	1	no	—
303	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
309	C₂²⋊D₅	—	4	2	no	—
310	C₂²⋊D₅	—	4	2	no	—
311	C₂×Dic₅	—	2	1	no	—
312	C₂×Dic₅	—	2	1	no	—
313	D₂₀	—	2	1	no	—
314	D₂₀	—	2	1	no	—
315	D₂₀	—	2	1	no	—
316	D₂₀	—	2	1	no	—
317	D₂₀	—	4	2	no	—
318	D₂₀	—	8	1	no	—
319	C₄×D₅	—	4	1	no	—
320	C₄×D₅	—	4	1	no	—
321	C₄×D₅	—	4	1	no	—
322	C₄×D₅	—	4	1	no	—
323	Dic₁₀	—	4	2	no	—
324	C₅×C₈	—	4	1	no	—
325	C₅×C₈	—	4	1	no	—
326	C₅×C₈	—	4	1	no	—
327	C₅×C₈	—	4	1	no	—
328	#168	—	2	1	no	—
329	#168	—	2	1	no	—
330	#168	—	2	1	no	—
331	#168	—	2	1	no	—
332	#168	—	2	1	no	—
333	#168	—	2	1	no	—
334	#168	—	2	1	no	—
335	#168	—	4	1	no	—
336	#168	—	4	1	no	—
337	#168	AGL(1,ℤ/8)	1	2	yes	—
338	C₂×#41	—	10	1	no	—
339	C₂×#41	C₄×D₅	1	1	yes	characteristic
340	C₂×SD₁₆	—	5	1	no	—
341	C₂×SD₁₆	—	5	1	no	—
342	C₂×D₈	—	5	1	no	—
343	C₂×D₈	—	5	1	no	—
344	#131	—	20	4	no	—
345	C₂×M₁₆	—	5	1	no	—
346	C₂×M₁₆	—	5	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	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	10	1	no	—
353	C₂²×C₈	—	10	1	no	—
354	C₄⋊Q₈	—	5	1	no	—
355	#127	—	5	1	no	—
356	#124	—	10	1	no	—
357	#121	—	5	1	no	—
358	#121	—	5	1	no	—
359	#121	—	10	1	no	—
360	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
361	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	5	1	no	—
365	C₄×D₄	—	5	1	no	—
366	C₄×D₄	—	10	1	no	—
367	C₄×D₄	C₄×D₅	1	1	yes	characteristic
368	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	C₄×D₅	1	1	yes	characteristic
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
373	#107	—	5	1	no	—
374	#107	—	5	1	no	—
375	#106	—	5	1	no	—
376	#106	—	5	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	5	1	no	—
380	C₄⋊C₈	—	5	1	no	—
381	C₄⋊C₈	—	5	1	no	—
382	C₄⋊C₈	—	5	1	no	—
383	C₄⋊C₈	—	10	1	no	—
384	C₄⋊C₈	—	10	1	no	—
385	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
386	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
387	#103	—	5	1	no	—
388	#103	—	5	1	no	—
389	#102	—	5	1	no	—
390	#102	—	5	1	no	—
391	#102	—	5	1	no	—
392	#102	—	5	1	no	—
393	#102	—	5	1	no	—
394	#102	—	5	1	no	—
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	5	1	no	—
397	C₂²⋊C₈	—	5	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₂²⋊C₈	—	10	1	no	—
400	C₂²⋊C₈	—	10	1	no	—
401	C₂²⋊C₈	—	10	1	no	—
402	C₂²⋊C₈	—	10	1	no	—
403	C₂²⋊C₈	—	10	1	no	—
404	C₂²⋊C₈	—	10	1	no	—
405	#97	—	5	1	no	—
406	#97	—	5	1	no	—
407	#97	—	10	1	no	—
408	C₄×C₈	—	5	1	no	—
409	C₄×C₈	—	5	1	no	—
410	C₄×C₈	—	5	1	no	—
411	C₄×C₈	—	5	1	no	—
412	C₄×C₈	—	10	1	no	—
413	C₄×C₈	—	10	1	no	—
414	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
415	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
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	C₂×D₅	—	4	1	no	—
428	C₂×D₅	—	4	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	C₂×#131	1	1	yes	characteristic
437	C₄×C₅	#568	1	1	yes	characteristic
438	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
439	C₄×C₅	#575	1	1	yes	characteristic
440	Dic₅	—	4	1	no	—
441	Dic₅	—	4	1	no	—
442	#41	—	2	2	no	—
443	#41	—	4	1	no	—
444	#41	—	20	2	no	—
445	#41	—	20	2	no	—
446	C₂×Q₈	—	10	1	no	—
447	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	—	10	1	no	—
452	C₂×D₄	—	10	1	no	—
453	C₂×D₄	—	10	1	no	—
454	C₂×D₄	—	10	1	no	—
455	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	10	1	no	—
460	C₂²×C₄	—	10	1	no	—
461	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
462	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
463	C₂²×C₄	#711	1	1	yes	characteristic
464	SD₁₆	—	10	2	no	—
465	SD₁₆	—	10	2	no	—
466	D₈	—	20	1	no	—
467	D₈	—	20	1	no	—
468	M₁₆	—	10	2	no	—
469	M₁₆	—	20	2	no	—
470	M₁₆	—	20	2	no	—
471	M₁₆	—	20	2	no	—
472	M₁₆	—	20	1	no	—
473	M₁₆	—	20	2	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	4	2	no	—
479	C₂×C₈	—	5	1	no	—
480	C₂×C₈	—	5	1	no	—
481	C₂×C₈	—	5	1	no	—
482	C₂×C₈	—	5	1	no	—
483	C₂×C₈	—	5	1	no	—
484	C₂×C₈	—	5	1	no	—
485	C₂×C₈	—	5	1	no	—
486	C₂×C₈	—	5	1	no	—
487	C₂×C₈	—	10	1	no	—
488	C₂×C₈	—	10	1	no	—
489	C₂×C₈	—	20	2	no	—
490	C₂×C₈	—	20	2	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	10	1	no	—
496	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
497	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	10	1	no	—
502	C₂²⋊C₄	—	10	1	no	—
503	C₂²⋊C₄	—	10	1	no	—
504	C₂²⋊C₄	—	10	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
509	C₄²	D₄×D₅	1	1	yes	characteristic
510	C₄²	#711	1	1	yes	characteristic
511	C₄²	C₂³×D₅	1	1	yes	characteristic
512	C₂×C₅	—	4	1	no	—
513	C₂×C₅	—	8	1	no	—
514	C₂×C₅	#2933	1	1	yes	characteristic
515	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
516	C₂×C₅	#2957	1	1	yes	characteristic
517	D₅	—	8	1	no	—
518	D₅	—	8	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	10	1	no	—
521	C₂³	—	10	1	no	—
522	C₂³	#4027	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	20	2	no	—
525	Q₈	#4047	1	2	yes	complemented
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	4	2	no	—
529	D₄	—	10	1	no	—
530	D₄	—	10	1	no	—
531	D₄	—	10	1	no	—
532	D₄	—	10	1	no	—
533	D₄	—	20	2	no	—
534	D₄	—	20	2	no	—
535	D₄	—	20	2	no	—
536	D₄	—	40	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	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	—	4	1	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	—	10	1	no	—
550	C₂×C₄	—	10	1	no	—
551	C₂×C₄	—	20	1	no	—
552	C₂×C₄	—	20	1	no	—
553	C₂×C₄	—	20	1	no	—
554	C₂×C₄	—	20	1	no	—
555	C₂×C₄	#4027	1	1	yes	characteristic
556	C₂×C₄	#4027	1	1	yes	characteristic
557	C₂×C₄	#4027	1	1	yes	characteristic
558	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
559	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
560	C₂×C₄	C₂×#711	1	1	yes	characteristic
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	5	2	no	—
566	C₈	—	10	1	no	—
567	C₈	—	10	1	no	—
568	C₈	—	10	1	no	—
569	C₈	—	10	1	no	—
570	C₈	—	10	1	no	—
571	C₈	—	10	1	no	—
572	C₈	—	10	1	no	—
573	C₈	—	20	1	no	—
574	C₈	—	20	1	no	—
575	C₅	#18011	1	1	yes	characteristic, complemented, Sylow
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	20	1	no	—
583	C₂²	—	20	1	no	—
584	C₂²	—	20	1	no	—
585	C₂²	—	20	1	no	—
586	C₂²	—	20	1	no	—
587	C₂²	—	20	1	no	—
588	C₂²	C₂×#4027	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	20	1	no	—
597	C₄	—	20	1	no	—
598	C₄	C₂×#4047	1	1	yes	characteristic
599	C₄	#66079	1	1	yes	characteristic
600	C₄	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
601	C₄	#66111	1	1	yes	characteristic
602	C₂	—	4	1	no	—
603	C₂	—	8	1	no	—
604	C₂	—	40	1	no	—
605	C₂	—	40	1	no	—
606	C₂	#10610327	1	1	yes	characteristic
607	C₂	#10610597	1	1	yes	characteristic
608	C₂	#10610721	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1477	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#10614260	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1477	D₅
hypocenter	C₅	#18011
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1477

Complements

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

N	H ≅ G/N	type
2. #10614250	C₂	semidirect
3. #10610735	C₂	semidirect
4. C₅×#1477	C₂	semidirect
5. #10601558	C₂	semidirect
6. #10601536	C₂	semidirect
7. #10601216	C₂	semidirect
8. #10599016	C₂	semidirect
9. #10599010	C₂	semidirect
10. #10599007	C₂	semidirect
11. #10599005	C₂	semidirect
12. #10598956	C₂	semidirect
13. #10598953	C₂	semidirect
14. #10598951	C₂	semidirect
15. #10598946	C₂	semidirect
159. #1477	D₅	semidirect
287. C₅×Q₈	#131	semidirect
525. Q₈	#4047	semidirect
575. C₅	#18011	semidirect

Maximal subgroups

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

subgroup	index
#10614260	2
#10614250	2
#10610735	2
C₅×#1477	2
#10601558	2
#10601536	2
#10601216	2
#10599016	2
#10599010	2
#10599007	2
#10599005	2
#10598956	2
#10598953	2
#10598951	2
#10598946	2
#18011	5