Subgroups — #12106233

Order 1280.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
2	#10615659	C₂	1	1	yes	maximal, characteristic
3	#10615523	C₂	1	2	yes	maximal, complemented
4	C₄×#4047	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602879	C₂	1	1	yes	maximal, characteristic, complemented
6	#10602804	C₂	1	2	yes	maximal, complemented
7	#10601512	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601499	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601184	C₂	1	2	yes	maximal, complemented
10	#10601171	C₂	1	2	yes	maximal, complemented
11	#10600572	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	#66156	C₂²	1	2	yes	—
15	C₂×#4047	C₂²	1	1	yes	characteristic
16	C₂×#4047	C₂²	1	1	yes	characteristic
17	C₄×#709	C₂²	1	1	yes	characteristic
18	C₅×#443	—	2	1	no	—
19	C₅×#443	—	2	1	no	—
20	C₅×#443	—	2	1	no	—
21	C₅×#443	—	2	1	no	—
22	C₂×C₅×#108	C₂²	1	1	yes	characteristic
23	C₂×C₅×#104	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	#65529	C₂²	1	2	yes	—
26	#65526	C₂²	1	2	yes	—
27	#65525	C₂²	1	2	yes	—
28	#65481	C₄	1	2	yes	complemented
29	#65466	C₄	1	4	yes	complemented
30	#65449	C₄	1	2	yes	complemented
31	#65434	—	2	4	no	—
32	#65433	—	2	4	no	—
33	#65428	C₂²	1	2	yes	—
34	#65413	C₂²	1	2	yes	—
35	C₂×#3951	C₂²	1	1	yes	characteristic
36	#65395	C₂²	1	1	yes	characteristic
37	#65390	C₂²	1	1	yes	characteristic
38	#65390	C₂²	1	1	yes	characteristic
39	#65390	C₂²	1	2	yes	—
40	C₄×#681	C₂²	1	1	yes	characteristic
41	#64978	—	2	1	no	—
42	#64978	—	2	1	no	—
43	C₄×#676	—	2	1	no	—
44	C₄×C₈×D₅	—	2	1	no	—
45	#64776	C₂²	1	2	yes	—
46	#64776	C₂²	1	2	yes	—
47	#64743	C₂²	1	2	yes	—
48	#21558	—	5	1	no	maximal, Sylow
49	C₂×C₅×#41	C₂³	1	2	yes	—
50	C₂×#709	C₂³	1	1	yes	characteristic
51	C₅×#135	—	2	1	no	—
52	C₅×#135	—	2	1	no	—
53	C₅×#135	—	2	1	no	—
54	C₅×#135	—	2	1	no	—
55	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
57	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
58	C₅×#131	—	2	2	no	—
59	C₅×#131	—	2	2	no	—
60	C₅×#131	—	2	2	no	—
61	C₅×#131	—	2	2	no	—
62	C₂×C₅×M₁₆	—	2	2	no	—
63	C₂×C₅×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	#4097	—	2	2	no	—
69	#4096	—	2	4	no	—
70	#4095	—	2	2	no	—
71	#4088	C₂×C₄	1	4	yes	—
72	#4078	C₂×C₄	1	4	yes	—
73	C₄×C₂²⋊D₅	—	2	2	no	—
74	#4072	C₂³	1	2	yes	—
75	#4072	C₂³	1	1	yes	characteristic
76	C₂×#681	C₂³	1	1	yes	characteristic
77	C₂×#681	C₂³	1	2	yes	—
78	C₂×#681	C₂³	1	1	yes	characteristic
79	#4047	—	2	1	no	—
80	#4047	—	2	1	no	—
81	#4047	—	2	1	no	—
82	#4047	—	2	1	no	—
83	#4047	C₂×C₄	1	2	yes	—
84	#4047	C₂×C₄	1	2	yes	—
85	#4047	D₄	1	2	yes	—
86	#4047	D₄	1	2	yes	—
87	C₂×#676	—	2	1	no	—
88	C₂×#676	—	2	1	no	—
89	C₂×C₈×D₅	—	2	1	no	—
90	C₂×C₈×D₅	—	2	1	no	—
91	C₄×D₂₀	—	2	1	no	—
92	#4018	—	2	1	no	—
93	C₄²×D₅	—	2	1	no	—
94	C₄×Dic₁₀	—	2	1	no	—
95	C₅×#108	—	2	1	no	—
96	C₅×#108	—	2	1	no	—
97	C₅×#104	—	2	2	no	—
98	C₅×#104	—	2	2	no	—
99	C₄×C₅×C₈	D₄	1	1	yes	characteristic
100	C₄×C₅×C₈	D₄	1	1	yes	characteristic
101	C₄×C₅×C₈	D₄	1	1	yes	characteristic
102	C₄×C₅×C₈	D₄	1	1	yes	characteristic
103	#3969	—	2	4	no	—
104	#3968	C₂×C₄	1	4	yes	complemented
105	#3966	—	2	4	no	—
106	#3965	C₂×C₄	1	4	yes	complemented
107	#3957	—	2	4	no	—
108	#3954	—	2	4	no	—
109	#3951	C₂×C₄	1	2	yes	complemented
110	#3951	C₂×C₄	1	2	yes	complemented
111	#3950	—	2	1	no	—
112	#3949	—	2	1	no	—
113	#3947	—	2	2	no	—
114	#3947	—	2	1	no	—
115	#3947	—	2	1	no	—
116	C₈×Dic₅	—	2	2	no	—
117	C₈×Dic₅	—	2	1	no	—
118	C₈×Dic₅	—	2	1	no	—
119	#3935	—	2	1	no	—
120	C₄×#168	—	2	1	no	—
121	#3067	—	5	1	no	—
122	#2955	—	5	2	no	—
123	C₂×#443	D₅	1	1	yes	characteristic, complemented
124	C₄×#131	—	5	1	no	—
125	#1976	—	5	1	no	—
126	#1953	—	5	1	no	—
127	#1932	—	5	2	no	—
128	#1906	—	5	2	no	—
129	#1814	—	5	1	no	—
130	#1772	—	5	1	no	—
131	#1757	—	5	2	no	—
132	C₅×#41	—	2	2	no	—
133	C₅×#41	—	2	2	no	—
134	C₅×#41	—	2	2	no	—
135	C₅×#41	—	2	2	no	—
136	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
137	C₂×C₅×D₄	—	2	2	no	—
138	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂×C₂²⋊D₅	—	2	1	no	—
143	#709	—	2	1	no	—
144	#709	—	2	1	no	—
145	#709	C₂²×C₄	1	2	yes	—
146	#709	C₂×D₄	1	2	yes	—
147	C₂×D₂₀	#41	1	1	yes	characteristic
148	C₂×C₄×D₅	—	2	1	no	—
149	C₂×C₄×D₅	—	2	2	no	—
150	C₂×Dic₁₀	#41	1	1	yes	characteristic
151	C₅×Q₁₆	—	2	1	no	—
152	C₅×Q₁₆	—	2	1	no	—
153	C₅×SD₁₆	—	2	2	no	—
154	C₅×SD₁₆	—	2	2	no	—
155	C₅×D₈	—	2	1	no	—
156	C₅×D₈	—	2	1	no	—
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	—	2	2	no	—
159	C₅×M₁₆	—	4	2	no	—
160	C₅×M₁₆	—	4	2	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	4	2	no	—
163	C₂×C₅×C₈	—	4	2	no	—
164	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₅×C₈	#41	1	1	yes	characteristic
173	C₂×C₅×C₈	#41	1	1	yes	characteristic
174	C₂×C₅×C₈	#41	1	1	yes	characteristic
175	C₂×C₅×C₈	#41	1	1	yes	characteristic
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²⋊Dic₅	—	2	2	no	—
180	C₂²⋊Dic₅	#41	1	2	yes	—
181	#689	—	2	4	no	—
182	#688	—	2	4	no	—
183	#687	—	2	4	no	—
184	#686	—	2	4	no	—
185	#685	—	2	2	no	—
186	C₄⋊Dic₅	—	2	1	no	—
187	C₄⋊Dic₅	—	2	2	no	—
188	#683	—	2	2	no	—
189	C₄×Dic₅	—	2	2	no	—
190	C₄×Dic₅	—	2	1	no	—
191	C₄×Dic₅	—	2	2	no	—
192	#681	—	2	2	no	—
193	#681	—	2	1	no	—
194	#681	—	2	1	no	—
195	#681	C₂²×C₄	1	4	yes	—
196	#681	C₂²×C₄	1	2	yes	—
197	#681	C₂×D₄	1	2	yes	—
198	C₂×#168	—	2	2	no	—
199	C₂×#168	—	2	1	no	—
200	C₂×#168	—	2	1	no	—
201	#676	—	2	2	no	—
202	#676	—	2	2	no	—
203	#676	—	2	2	no	—
204	#676	—	2	2	no	—
205	C₈×D₅	—	2	2	no	—
206	C₈×D₅	—	2	2	no	—
207	C₈×D₅	—	2	2	no	—
208	C₈×D₅	—	2	2	no	—
209	#575	—	5	2	no	—
210	C₂×#135	C₂×D₅	1	1	yes	characteristic
211	C₂×#131	—	5	1	no	—
212	C₂×#131	—	5	1	no	—
213	C₂×#131	C₂×D₅	1	2	yes	—
214	C₄×#41	—	5	1	no	—
215	#473	—	5	2	no	—
216	#472	—	5	2	no	—
217	#471	—	5	4	no	—
218	#444	—	10	4	no	—
219	#443	—	2	1	no	—
220	#443	—	2	1	no	—
221	#443	—	2	1	no	—
222	#443	—	2	1	no	—
223	#443	—	10	4	no	—
224	#430	—	5	2	no	—
225	C₂×#108	—	5	1	no	—
226	C₂×#108	C₂×D₅	1	1	yes	characteristic
227	#427	—	5	1	no	—
228	#421	—	5	2	no	—
229	#421	—	5	2	no	—
230	C₂×#104	C₂×D₅	1	2	yes	—
231	#413	—	5	2	no	—
232	#410	—	5	2	no	—
233	#405	—	5	1	no	—
234	#405	—	5	1	no	—
235	#405	—	5	2	no	—
236	#405	—	10	1	no	—
237	#405	—	10	1	no	—
238	C₄×M₁₆	—	5	1	no	—
239	C₄×M₁₆	—	10	1	no	—
240	C₂×C₄×C₈	—	10	1	no	—
241	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
242	#344	—	5	2	no	—
243	#344	—	5	2	no	—
244	#339	—	5	2	no	—
245	C₂³×C₅	—	2	2	no	—
246	C₂³×C₅	C₂×#41	1	1	yes	characteristic
247	C₂²×D₅	—	2	1	no	—
248	C₅×Q₈	—	2	2	no	—
249	C₅×Q₈	—	2	2	no	—
250	C₅×D₄	—	2	2	no	—
251	C₅×D₄	—	2	2	no	—
252	C₅×D₄	—	4	2	no	—
253	C₅×D₄	—	4	2	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	2	no	—
260	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₂²⋊D₅	—	2	2	no	—
267	C₂²⋊D₅	—	2	2	no	—
268	C₂×Dic₅	—	2	1	no	—
269	C₂×Dic₅	—	2	2	no	—
270	C₂×Dic₅	—	4	2	no	—
271	D₂₀	—	2	1	no	—
272	D₂₀	C₄×D₄	1	2	yes	—
273	C₄×D₅	—	2	2	no	—
274	C₄×D₅	—	2	2	no	—
275	C₄×D₅	—	4	4	no	—
276	Dic₁₀	—	2	1	no	—
277	Dic₁₀	C₄×D₄	1	2	yes	—
278	C₅×C₈	—	4	2	no	—
279	C₅×C₈	C₄×D₄	1	1	yes	characteristic
280	C₅×C₈	C₄×D₄	1	1	yes	characteristic
281	C₅×C₈	C₄×D₄	1	1	yes	characteristic
282	C₅×C₈	C₄×D₄	1	1	yes	characteristic
283	C₅×C₈	#121	1	1	yes	characteristic
284	C₅×C₈	#121	1	1	yes	characteristic
285	C₅×C₈	#121	1	1	yes	characteristic
286	C₅×C₈	#121	1	1	yes	characteristic
287	#168	—	2	2	no	—
288	#168	—	2	4	no	—
289	#168	—	2	2	no	—
290	C₂×#41	—	5	1	no	—
291	C₂×#41	C₂²×D₅	1	2	yes	—
292	#137	—	5	4	no	—
293	#137	—	10	2	no	—
294	AGL(1,ℤ/8)	—	5	4	no	—
295	AGL(1,ℤ/8)	—	10	2	no	—
296	#135	—	2	1	no	—
297	#135	—	2	1	no	—
298	#135	—	2	1	no	—
299	#135	—	2	1	no	—
300	#135	—	10	4	no	—
301	C₂×Q₁₆	C₄×D₅	1	1	yes	characteristic, complemented
302	C₂×SD₁₆	C₄×D₅	1	2	yes	complemented
303	C₂×D₈	C₄×D₅	1	1	yes	characteristic, complemented
304	#131	—	2	2	no	—
305	#131	—	2	2	no	—
306	#131	—	2	2	no	—
307	#131	—	2	2	no	—
308	#131	—	5	2	no	—
309	#131	—	5	2	no	—
310	#131	—	5	2	no	—
311	#131	—	5	2	no	—
312	#131	—	10	1	no	—
313	#131	—	10	1	no	—
314	#131	—	10	1	no	—
315	#131	—	10	1	no	—
316	C₂×M₁₆	—	2	2	no	—
317	C₂×M₁₆	—	5	1	no	—
318	C₂×M₁₆	—	5	1	no	—
319	C₂×M₁₆	—	5	2	no	—
320	C₂×M₁₆	—	10	1	no	—
321	C₂×M₁₆	—	10	1	no	—
322	C₂×M₁₆	C₂²×D₅	1	2	yes	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	10	1	no	—
325	C₂²×C₈	—	10	1	no	—
326	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
328	C₄×Q₈	—	10	1	no	—
329	C₄×D₄	—	10	1	no	—
330	C₄×D₄	—	10	2	no	—
331	#117	—	5	1	no	—
332	#117	—	5	2	no	—
333	#117	—	10	1	no	—
334	C₂×C₄²	—	10	1	no	—
335	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
336	#108	—	2	1	no	—
337	#108	—	2	1	no	—
338	#108	—	5	2	no	—
339	#108	—	5	2	no	—
340	#108	—	10	4	no	—
341	#107	—	10	1	no	—
342	#106	—	10	1	no	—
343	#104	—	2	2	no	—
344	#104	—	2	2	no	—
345	#104	—	10	4	no	—
346	#104	—	10	4	no	—
347	#101	—	5	4	no	—
348	#100	—	5	4	no	—
349	#99	—	10	4	no	—
350	#97	—	10	2	no	—
351	#97	—	10	1	no	—
352	#97	—	10	1	no	—
353	#97	—	10	1	no	—
354	C₄×C₈	—	10	2	no	—
355	C₄×C₈	—	10	1	no	—
356	C₄×C₈	—	10	1	no	—
357	C₄×C₈	—	10	1	no	—
358	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
359	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
360	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
361	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
362	C₂²×C₅	—	4	1	no	—
363	C₂²×C₅	—	4	2	no	—
364	C₂²×C₅	—	8	2	no	—
365	C₂²×C₅	C₄×#41	1	1	yes	characteristic
366	C₂²×C₅	#525	1	1	yes	characteristic
367	C₂²×C₅	#532	1	1	yes	characteristic
368	C₂×D₅	—	2	2	no	—
369	C₂×D₅	—	4	2	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	4	1	no	—
372	C₄×C₅	—	4	2	no	—
373	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
374	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₄×C₅	C₂×#121	1	1	yes	characteristic
376	C₄×C₅	#529	1	1	yes	characteristic
377	Dic₅	—	2	2	no	—
378	Dic₅	—	4	2	no	—
379	Dic₅	—	8	2	no	—
380	#41	—	2	2	no	—
381	#41	—	2	2	no	—
382	#41	—	2	2	no	—
383	#41	—	2	2	no	—
384	#41	—	5	2	no	—
385	#41	—	5	2	no	—
386	#41	—	10	1	no	—
387	#41	—	10	1	no	—
388	C₂×Q₈	—	5	1	no	—
389	C₂×Q₈	C₂×C₄×D₅	1	2	yes	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	5	1	no	—
392	C₂×D₄	—	10	1	no	—
393	C₂×D₄	C₂×C₄×D₅	1	2	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	10	2	no	—
397	C₂²×C₄	—	10	1	no	—
398	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
399	Q₁₆	—	2	1	no	—
400	Q₁₆	—	2	1	no	—
401	Q₁₆	—	10	4	no	—
402	SD₁₆	—	2	2	no	—
403	SD₁₆	—	2	2	no	—
404	SD₁₆	—	10	4	no	—
405	SD₁₆	—	10	4	no	—
406	D₈	—	2	1	no	—
407	D₈	—	2	1	no	—
408	D₈	—	10	4	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	4	2	no	—
412	M₁₆	—	4	2	no	—
413	M₁₆	—	5	2	no	—
414	M₁₆	—	5	4	no	—
415	M₁₆	—	5	2	no	—
416	M₁₆	—	10	1	no	—
417	M₁₆	—	10	1	no	—
418	M₁₆	—	10	2	no	—
419	M₁₆	—	10	2	no	—
420	M₁₆	—	10	2	no	—
421	M₁₆	—	10	2	no	—
422	M₁₆	—	10	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	4	2	no	—
425	C₂×C₈	—	4	2	no	—
426	C₂×C₈	—	10	2	no	—
427	C₂×C₈	—	10	1	no	—
428	C₂×C₈	—	10	1	no	—
429	C₂×C₈	—	10	2	no	—
430	C₂×C₈	—	10	2	no	—
431	C₂×C₈	—	10	2	no	—
432	C₂×C₈	—	10	2	no	—
433	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
434	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
435	C₂×C₈	#709	1	1	yes	characteristic
436	C₂×C₈	#709	1	1	yes	characteristic
437	C₂×C₈	D₄×D₅	1	1	yes	characteristic
438	C₂×C₈	D₄×D₅	1	1	yes	characteristic
439	C₂×C₈	#711	1	1	yes	characteristic
440	C₂×C₈	#711	1	1	yes	characteristic
441	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
442	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
443	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
444	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
445	C₄⋊C₄	—	10	2	no	—
446	C₄⋊C₄	—	10	1	no	—
447	C₄⋊C₄	—	10	2	no	—
448	C₂²⋊C₄	—	5	2	no	—
449	C₂²⋊C₄	—	10	2	no	—
450	C₂²⋊C₄	—	10	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	10	2	no	—
453	C₄²	—	10	1	no	—
454	C₄²	—	10	2	no	—
455	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
456	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
457	C₂×C₅	—	2	1	no	—
458	C₂×C₅	—	2	1	no	—
459	C₂×C₅	—	2	1	no	—
460	C₂×C₅	—	8	2	no	—
461	C₂×C₅	C₄×#121	1	1	yes	characteristic
462	D₅	—	4	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	10	1	no	—
465	C₂³	D₅×#41	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	5	2	no	—
469	Q₈	—	10	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	5	2	no	—
475	D₄	—	10	2	no	—
476	D₄	—	10	2	no	—
477	D₄	—	10	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	10	1	no	—
485	C₂×C₄	—	10	2	no	—
486	C₂×C₄	—	10	2	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	20	4	no	—
489	C₂×C₄	—	20	2	no	—
490	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
491	C₂×C₄	C₂×#709	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
493	C₂×C₄	C₂×#711	1	1	yes	characteristic
494	C₂×C₄	D₅×#41	1	1	yes	characteristic
495	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
496	C₈	—	4	2	no	—
497	C₈	—	10	2	no	—
498	C₈	—	10	4	no	—
499	C₈	—	10	2	no	—
500	C₈	C₄×C₂²⋊D₅	1	1	yes	characteristic
501	C₈	C₄×C₂²⋊D₅	1	1	yes	characteristic
502	C₈	C₄×C₂²⋊D₅	1	1	yes	characteristic
503	C₈	C₄×C₂²⋊D₅	1	1	yes	characteristic
504	C₈	#4084	1	1	yes	characteristic
505	C₈	#4084	1	1	yes	characteristic
506	C₈	#4084	1	1	yes	characteristic
507	C₈	#4084	1	1	yes	characteristic
508	C₅	#21558	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	10	2	no	—
513	C₂²	—	20	2	no	—
514	C₂²	C₄×#711	1	1	yes	characteristic
515	C₂²	#65882	1	1	yes	characteristic
516	C₂²	#66162	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	10	2	no	—
521	C₄	—	20	2	no	—
522	C₄	—	40	2	no	—
523	C₄	C₄×D₄×D₅	1	1	yes	characteristic
524	C₄	#65891	1	1	yes	characteristic
525	C₄	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
526	C₄	C₂×#4084	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	8	2	no	—
531	C₂	—	20	2	no	—
532	C₂	C₄×#4084	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#4084
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₂×C₅×#443	C₂
socle	C₂×C₅	C₄×#121
prime radical	#10615659	C₂
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₂×#443	D₅
hypocenter	C₅	#21558
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#443	C₂	semidirect
3. #10615523	C₂	semidirect
4. C₄×#4047	C₂	semidirect
5. #10602879	C₂	semidirect
6. #10602804	C₂	semidirect
7. #10601512	C₂	semidirect
8. #10601499	C₂	semidirect
9. #10601184	C₂	semidirect
10. #10601171	C₂	semidirect
11. #10600572	C₂	semidirect
28. #65481	C₄	semidirect
29. #65466	C₄	semidirect
30. #65449	C₄	semidirect
55. C₂×C₅×Q₁₆	C₂×C₄	semidirect
56. C₂×C₅×SD₁₆	C₂×C₄	semidirect
57. C₂×C₅×D₈	C₂×C₄	semidirect
104. #3968	C₂×C₄	semidirect
106. #3965	C₂×C₄	semidirect
109. #3951	C₂×C₄	semidirect
110. #3951	C₂×C₄	semidirect
123. C₂×#443	D₅	semidirect
301. C₂×Q₁₆	C₄×D₅	semidirect
302. C₂×SD₁₆	C₄×D₅	semidirect
303. C₂×D₈	C₄×D₅	semidirect
508. C₅	#21558	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#443	2
#10615659	2
#10615523	2
C₄×#4047	2
#10602879	2
#10602804	2
#10601512	2
#10601499	2
#10601184	2
#10601171	2
#10600572	2
#21558	5