Subgroups — #12071055

Order 1280.

722 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611329	C₂	1	1	yes	maximal, characteristic
2	#10611272	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1581	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601672	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#686	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599352	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598961	C₂	1	1	yes	maximal, characteristic, complemented
11	#10598961	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598953	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598941	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598871	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598860	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4053	—	2	1	no	—
17	C₂×#4047	—	2	1	no	—
18	#65882	C₂²	1	1	yes	characteristic
19	#65882	C₂²	1	1	yes	characteristic
20	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₅×#436	C₂²	1	1	yes	characteristic
22	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
23	#65446	C₄	1	1	yes	characteristic
24	#65440	C₄	1	1	yes	characteristic
25	#65416	—	2	1	no	—
26	#65400	—	2	1	no	—
27	C₄×#686	C₂²	1	1	yes	characteristic
28	C₄×#686	C₂²	1	1	yes	characteristic
29	#65301	C₂²	1	1	yes	characteristic
30	D₄×#168	C₂²	1	1	yes	characteristic
31	#65172	C₄	1	1	yes	characteristic
32	#65163	C₄	1	1	yes	characteristic
33	#65127	C₂²	1	1	yes	characteristic
34	#65123	C₂²	1	1	yes	characteristic
35	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	#65064	C₄	1	1	yes	characteristic
38	#65064	C₄	1	1	yes	characteristic
39	#65049	C₄	1	1	yes	characteristic
40	#65049	C₄	1	1	yes	characteristic
41	#65019	—	2	1	no	—
42	#65017	—	2	1	no	—
43	#65016	—	2	1	no	—
44	#65016	—	2	1	no	—
45	C₄×D₄₀	C₂²	1	1	yes	characteristic
46	#64977	C₂²	1	1	yes	characteristic
47	C₄×#676	C₂²	1	1	yes	characteristic
48	C₈×D₂₀	C₂²	1	1	yes	characteristic
49	#64974	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic
52	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×#322	C₂²	1	1	yes	characteristic
55	D₄⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	#64703	C₂²	1	1	yes	characteristic
58	#64703	C₂²	1	1	yes	characteristic
59	#64699	C₂²	1	1	yes	characteristic
60	#64699	C₂²	1	1	yes	characteristic
61	#64679	C₂²	1	1	yes	characteristic
62	#64679	C₂²	1	1	yes	characteristic
63	#64678	C₂²	1	1	yes	characteristic
64	#64674	C₂²	1	1	yes	characteristic
65	C₈×#168	C₂²	1	1	yes	characteristic
66	C₈×#168	C₂²	1	1	yes	characteristic
67	#18066	—	5	1	no	maximal, Sylow
68	C₂×#709	—	2	1	no	—
69	C₂×#709	—	2	1	no	—
70	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×M₁₆	—	2	1	no	—
72	C₂²×C₅×C₈	—	2	1	no	—
73	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	#4086	C₂×C₄	1	1	yes	characteristic
76	#4086	C₂×C₄	1	1	yes	characteristic
77	#4084	C₂×C₄	1	1	yes	characteristic
78	#4084	C₂×C₄	1	1	yes	characteristic
79	C₂×#686	C₂×C₄	1	1	yes	characteristic
80	C₂×#686	C₂×C₄	1	1	yes	characteristic
81	C₄×C₂²⋊D₅	—	2	1	no	—
82	C₄×C₂²⋊D₅	—	2	1	no	—
83	C₂×#681	—	2	1	no	—
84	C₂²×#168	—	2	1	no	—
85	#4053	—	4	4	no	—
86	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
87	#4047	—	4	4	no	—
88	C₂×#676	—	2	1	no	—
89	C₂×#676	—	2	1	no	—
90	C₂×#676	D₄	1	1	yes	characteristic
91	C₂×#676	D₄	1	1	yes	characteristic
92	C₂×C₈×D₅	—	2	1	no	—
93	C₂×C₈×D₅	—	2	1	no	—
94	C₂×C₈×D₅	—	2	1	no	—
95	C₂×C₈×D₅	—	2	1	no	—
96	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
97	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
98	#4041	C₂×C₄	1	1	yes	characteristic
99	#4041	C₂×C₄	1	1	yes	characteristic
100	#4034	C₂×C₄	1	1	yes	characteristic
101	#4034	C₂×C₄	1	1	yes	characteristic
102	#4031	—	2	1	no	—
103	#4031	—	2	1	no	—
104	#4030	—	2	1	no	—
105	#4030	—	2	1	no	—
106	C₄×D₂₀	C₂³	1	1	yes	characteristic
107	C₄×D₂₀	C₂³	1	1	yes	characteristic
108	C₄²×D₅	C₂³	1	1	yes	characteristic
109	C₅×#107	C₂×C₄	1	1	yes	characteristic
110	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₅×#102	C₂×C₄	1	1	yes	characteristic
113	C₅×#102	C₂×C₄	1	1	yes	characteristic
114	C₅×C₂²⋊C₈	—	2	1	no	—
115	C₅×C₂²⋊C₈	—	2	1	no	—
116	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
117	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
118	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
119	#3964	C₂×C₄	1	1	yes	characteristic
120	#3964	C₂×C₄	1	1	yes	characteristic
121	C₂²⋊#168	—	2	1	no	—
122	C₂²⋊#168	—	2	1	no	—
123	#3953	C₂×C₄	1	1	yes	characteristic
124	#3953	C₂×C₄	1	1	yes	characteristic
125	#3952	—	2	1	no	—
126	#3952	—	2	1	no	—
127	#3952	—	2	1	no	—
128	#3952	—	2	1	no	—
129	#3952	—	2	1	no	—
130	#3950	C₂×C₄	1	1	yes	characteristic
131	#3947	D₄	1	1	yes	characteristic
132	#3947	D₄	1	1	yes	characteristic
133	#3946	—	2	1	no	—
134	#3946	—	2	1	no	—
135	#3946	—	2	1	no	—
136	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
137	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
138	#3941	C₂×C₄	1	1	yes	characteristic
139	#3941	C₂×C₄	1	1	yes	characteristic
140	#3939	C₂×C₄	1	1	yes	characteristic
141	#3939	C₂×C₄	1	1	yes	characteristic
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	C₄×#168	C₂³	1	1	yes	characteristic
147	#3169	—	5	1	no	—
148	#2935	—	5	1	no	—
149	#2935	—	5	1	no	—
150	#1589	—	5	1	no	—
151	#1589	—	5	1	no	—
152	#1581	—	5	1	no	—
153	#1581	—	5	1	no	—
154	#1581	—	5	1	no	—
155	#1581	D₅	1	1	yes	characteristic, complemented
156	C₈×D₈	—	5	1	no	—
157	C₈×D₈	—	5	1	no	—
158	C₂×#335	—	5	1	no	—
159	#1480	—	5	1	no	—
160	#1480	—	5	1	no	—
161	C₈×M₁₆	—	5	1	no	—
162	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂×C₂²⋊D₅	—	2	1	no	—
167	C₂×C₂²⋊D₅	—	2	1	no	—
168	C₂×C₂²⋊D₅	—	2	1	no	—
169	C₂×C₂²⋊D₅	—	2	1	no	—
170	C₂×C₂²⋊D₅	—	2	1	no	—
171	C₂×C₂²⋊D₅	—	2	1	no	—
172	#709	—	4	2	no	—
173	#709	—	4	2	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×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
184	C₂×C₄×D₅	#41	1	1	yes	characteristic
185	C₂×Dic₁₀	—	2	1	no	—
186	C₂×Dic₁₀	—	2	1	no	—
187	C₅×D₈	—	4	1	no	—
188	C₅×M₁₆	—	4	2	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	4	2	no	—
193	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
197	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
199	C₅×C₂²⋊C₄	—	2	1	no	—
200	C₅×C₂²⋊C₄	—	2	1	no	—
201	C₄²×C₅	C₂⁴	1	1	yes	characteristic
202	C₂²⋊Dic₅	—	2	1	no	—
203	C₂²⋊Dic₅	—	2	1	no	—
204	#686	—	2	2	no	—
205	#686	—	2	2	no	—
206	#685	—	2	1	no	—
207	#685	—	2	1	no	—
208	#685	—	2	1	no	—
209	#685	—	2	1	no	—
210	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
212	#683	—	2	1	no	—
213	#683	—	2	1	no	—
214	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
216	C₄×Dic₅	#41	1	1	yes	characteristic
217	#681	—	4	2	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	4	2	no	—
222	C₂×#168	C₂²×C₄	1	1	yes	characteristic
223	C₂×#168	C₂²×C₄	1	1	yes	characteristic
224	C₂×#168	C₂×D₄	1	1	yes	characteristic
225	C₂×#168	C₂×D₄	1	1	yes	characteristic
226	D₄₀	—	4	1	no	—
227	#676	—	2	2	no	—
228	#676	—	4	2	no	—
229	#676	—	4	2	no	—
230	#676	D₈	1	4	yes	complemented
231	C₈×D₅	—	2	2	no	—
232	C₈×D₅	—	4	1	no	—
233	C₈×D₅	—	4	2	no	—
234	C₈×D₅	—	4	2	no	—
235	C₈×D₅	—	4	2	no	—
236	C₈×D₅	—	4	2	no	—
237	C₂×#131	—	10	1	no	—
238	C₂×#131	—	10	1	no	—
239	#532	—	5	1	no	—
240	#532	—	5	1	no	—
241	#500	—	5	1	no	—
242	#493	—	5	1	no	—
243	#486	—	5	1	no	—
244	#486	—	5	1	no	—
245	#466	—	5	1	no	—
246	#466	—	5	1	no	—
247	#466	—	5	1	no	—
248	#466	—	5	1	no	—
249	C₄×D₈	—	5	1	no	—
250	C₄×D₈	—	5	1	no	—
251	C₄×D₈	—	5	1	no	—
252	C₄×D₈	C₂×D₅	1	1	yes	characteristic
253	#436	—	5	1	no	—
254	#436	—	5	1	no	—
255	#436	—	5	1	no	—
256	#436	C₂×D₅	1	1	yes	characteristic
257	#435	—	10	1	no	—
258	#435	—	10	1	no	—
259	#435	—	10	1	no	—
260	#435	—	10	1	no	—
261	C₈×D₄	—	5	1	no	—
262	C₈×D₄	—	5	1	no	—
263	C₈×D₄	—	5	1	no	—
264	C₈×D₄	C₂×D₅	1	1	yes	characteristic
265	#431	—	5	1	no	—
266	C₂×C₄⋊C₈	—	5	1	no	—
267	C₂×C₄⋊C₈	—	5	1	no	—
268	#408	—	10	1	no	—
269	#408	—	10	1	no	—
270	C₄×M₁₆	—	5	1	no	—
271	C₂×C₄×C₈	—	5	1	no	—
272	#335	—	5	1	no	—
273	#335	—	5	1	no	—
274	#335	—	5	1	no	—
275	#335	C₂×D₅	1	1	yes	characteristic
276	D₄⋊C₈	—	5	1	no	—
277	D₄⋊C₈	—	5	1	no	—
278	D₄⋊C₈	—	5	1	no	—
279	D₄⋊C₈	—	5	1	no	—
280	D₄⋊C₈	—	5	1	no	—
281	D₄⋊C₈	—	5	1	no	—
282	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
283	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
284	#322	—	5	1	no	—
285	#322	C₂×D₅	1	1	yes	characteristic
286	C₈²	—	5	1	no	—
287	C₈²	—	5	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂²×D₅	—	2	1	no	—
291	C₂²×D₅	—	2	1	no	—
292	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	2	1	no	—
296	C₅×D₄	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
306	C₂²⋊D₅	—	4	2	no	—
307	C₂²⋊D₅	—	4	2	no	—
308	C₂²⋊D₅	—	4	2	no	—
309	C₂²⋊D₅	—	4	2	no	—
310	C₂²⋊D₅	—	8	1	no	—
311	C₂²⋊D₅	—	8	1	no	—
312	C₂×Dic₅	—	2	1	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
315	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
316	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
317	D₂₀	—	2	1	no	—
318	D₂₀	—	2	1	no	—
319	D₂₀	—	2	1	no	—
320	D₂₀	—	2	1	no	—
321	D₂₀	—	4	2	no	—
322	D₂₀	—	4	2	no	—
323	C₄×D₅	—	2	1	no	—
324	C₄×D₅	—	2	1	no	—
325	C₄×D₅	—	4	1	no	—
326	C₄×D₅	—	4	1	no	—
327	C₄×D₅	—	4	1	no	—
328	C₄×D₅	—	4	1	no	—
329	C₄×D₅	—	4	1	no	—
330	C₄×D₅	C₂×D₈	1	2	yes	—
331	C₄×D₅	#135	1	2	yes	—
332	Dic₁₀	—	4	2	no	—
333	Dic₁₀	—	4	2	no	—
334	C₅×C₈	—	2	1	no	—
335	C₅×C₈	—	2	1	no	—
336	C₅×C₈	—	2	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	—	4	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	C₂×D₈	1	2	yes	—
341	#168	—	2	1	no	—
342	#168	—	2	1	no	—
343	#168	—	4	1	no	—
344	#168	—	4	1	no	—
345	#168	—	4	1	no	—
346	#168	#131	1	2	yes	complemented
347	#168	C₂×D₈	1	2	yes	—
348	C₂×#41	—	10	1	no	—
349	C₂×#41	—	10	1	no	—
350	C₂×D₈	—	5	1	no	—
351	C₂×D₈	—	5	1	no	—
352	C₂×D₈	—	5	1	no	—
353	C₂×D₈	C₄×D₅	1	1	yes	characteristic
354	#131	—	20	4	no	—
355	#131	—	20	4	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	5	1	no	—
358	C₂×M₁₆	—	5	1	no	—
359	C₂×M₁₆	—	10	1	no	—
360	C₂×M₁₆	—	10	1	no	—
361	C₂×M₁₆	—	10	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	5	1	no	—
364	C₂²×C₈	—	5	1	no	—
365	C₂²×C₈	—	10	1	no	—
366	C₂²×C₈	—	10	1	no	—
367	C₂²×C₈	—	10	1	no	—
368	C₂²×C₈	—	10	1	no	—
369	C₂²×C₈	—	10	1	no	—
370	C₄⋊Q₈	—	5	1	no	—
371	C₄⋊Q₈	—	5	1	no	—
372	#127	—	5	1	no	—
373	#127	—	5	1	no	—
374	#124	—	10	1	no	—
375	#124	—	10	1	no	—
376	#121	—	5	1	no	—
377	#121	—	5	1	no	—
378	#121	—	5	1	no	—
379	#121	—	5	1	no	—
380	#121	—	10	1	no	—
381	#121	—	10	1	no	—
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	1	no	—
384	C₄×D₄	—	10	1	no	—
385	C₄×D₄	—	10	1	no	—
386	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
387	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
388	C₂×C₄²	—	5	1	no	—
389	#107	—	5	1	no	—
390	#107	—	5	1	no	—
391	#107	—	5	1	no	—
392	#107	C₄×D₅	1	1	yes	characteristic
393	C₄⋊C₈	—	5	1	no	—
394	C₄⋊C₈	—	5	1	no	—
395	C₄⋊C₈	—	10	1	no	—
396	C₄⋊C₈	—	10	1	no	—
397	C₄⋊C₈	—	10	1	no	—
398	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
399	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
400	#102	—	5	1	no	—
401	#102	—	5	1	no	—
402	#102	—	5	1	no	—
403	#102	—	5	1	no	—
404	#102	—	5	1	no	—
405	#102	—	5	1	no	—
406	#102	C₄×D₅	1	1	yes	characteristic
407	#102	C₄×D₅	1	1	yes	characteristic
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	2	1	no	—
410	C₂²⋊C₈	—	10	1	no	—
411	C₂²⋊C₈	—	10	1	no	—
412	C₂²⋊C₈	—	10	1	no	—
413	C₂²⋊C₈	—	10	1	no	—
414	C₂²⋊C₈	—	10	1	no	—
415	C₂²⋊C₈	—	10	1	no	—
416	C₂²⋊C₈	—	10	1	no	—
417	#97	—	5	1	no	—
418	#97	—	5	1	no	—
419	C₄×C₈	—	5	1	no	—
420	C₄×C₈	—	5	1	no	—
421	C₄×C₈	—	5	1	no	—
422	C₄×C₈	—	5	1	no	—
423	C₄×C₈	—	5	1	no	—
424	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
434	C₂×D₅	—	2	1	no	—
435	C₂×D₅	—	2	1	no	—
436	C₂×D₅	—	4	1	no	—
437	C₂×D₅	—	4	1	no	—
438	C₂×D₅	—	4	1	no	—
439	C₂×D₅	—	4	1	no	—
440	C₂×D₅	—	4	1	no	—
441	C₂×D₅	—	4	1	no	—
442	C₂×D₅	C₄×D₈	1	2	yes	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	4	1	no	—
445	C₄×C₅	—	4	1	no	—
446	C₄×C₅	C₂×#131	1	1	yes	characteristic
447	C₄×C₅	#568	1	1	yes	characteristic
448	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
449	C₄×C₅	C₂×#135	1	1	yes	characteristic
450	Dic₅	—	2	1	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	—	4	1	no	—
453	Dic₅	—	4	1	no	—
454	Dic₅	C₄×D₈	1	2	yes	—
455	#41	—	20	2	no	—
456	#41	—	20	2	no	—
457	#41	—	20	2	no	—
458	#41	—	20	2	no	—
459	C₂×Q₈	—	10	1	no	—
460	C₂×Q₈	—	10	1	no	—
461	C₂×D₄	—	5	1	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	—	10	1	no	—
464	C₂×D₄	—	10	1	no	—
465	C₂×D₄	—	10	1	no	—
466	C₂×D₄	—	10	1	no	—
467	C₂×D₄	—	10	1	no	—
468	C₂×D₄	—	10	1	no	—
469	C₂×D₄	—	10	1	no	—
470	C₂×D₄	—	10	1	no	—
471	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
472	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	5	1	no	—
476	C₂²×C₄	—	5	1	no	—
477	C₂²×C₄	—	5	1	no	—
478	C₂²×C₄	—	10	1	no	—
479	C₂²×C₄	—	10	1	no	—
480	D₈	—	4	1	no	—
481	D₈	—	10	2	no	—
482	D₈	—	10	2	no	—
483	D₈	—	20	1	no	—
484	M₁₆	—	4	2	no	—
485	M₁₆	—	5	4	no	—
486	M₁₆	—	10	2	no	—
487	M₁₆	—	20	2	no	—
488	M₁₆	—	20	2	no	—
489	M₁₆	—	20	2	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	4	2	no	—
494	C₂×C₈	—	5	1	no	—
495	C₂×C₈	—	5	1	no	—
496	C₂×C₈	—	5	1	no	—
497	C₂×C₈	—	5	1	no	—
498	C₂×C₈	—	10	2	no	—
499	C₂×C₈	—	10	1	no	—
500	C₂×C₈	—	10	1	no	—
501	C₂×C₈	—	10	1	no	—
502	C₂×C₈	—	20	1	no	—
503	C₂×C₈	—	20	2	no	—
504	C₂×C₈	—	20	2	no	—
505	C₂×C₈	—	20	2	no	—
506	C₂×C₈	—	20	2	no	—
507	C₂×C₈	—	20	2	no	—
508	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
509	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
510	C₂×C₈	D₄×D₅	1	1	yes	characteristic
511	C₂×C₈	D₄×D₅	1	1	yes	characteristic
512	C₄⋊C₄	—	5	1	no	—
513	C₄⋊C₄	—	5	1	no	—
514	C₄⋊C₄	—	10	1	no	—
515	C₄⋊C₄	—	10	1	no	—
516	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
517	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	10	1	no	—
521	C₂²⋊C₄	—	10	1	no	—
522	C₂²⋊C₄	—	10	1	no	—
523	C₂²⋊C₄	—	10	1	no	—
524	C₂²⋊C₄	—	10	1	no	—
525	C₂²⋊C₄	—	10	1	no	—
526	C₄²	—	5	1	no	—
527	C₄²	—	5	1	no	—
528	C₄²	—	5	1	no	—
529	C₄²	C₂³×D₅	1	1	yes	characteristic
530	C₂×C₅	—	8	1	no	—
531	C₂×C₅	—	8	1	no	—
532	C₂×C₅	#2935	1	1	yes	characteristic
533	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
534	C₂×C₅	#2957	1	1	yes	characteristic
535	D₅	—	2	2	no	—
536	D₅	—	8	1	no	—
537	D₅	—	8	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	5	1	no	—
541	C₂³	—	10	1	no	—
542	C₂³	—	10	1	no	—
543	Q₈	—	20	2	no	—
544	Q₈	—	20	2	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	10	1	no	—
550	D₄	—	10	1	no	—
551	D₄	—	10	1	no	—
552	D₄	—	10	1	no	—
553	D₄	—	20	2	no	—
554	D₄	—	20	2	no	—
555	D₄	—	20	2	no	—
556	D₄	—	20	2	no	—
557	D₄	—	20	2	no	—
558	D₄	—	20	2	no	—
559	D₄	—	40	1	no	—
560	D₄	—	40	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	5	1	no	—
568	C₂×C₄	—	5	2	no	—
569	C₂×C₄	—	5	2	no	—
570	C₂×C₄	—	5	1	no	—
571	C₂×C₄	—	5	1	no	—
572	C₂×C₄	—	10	1	no	—
573	C₂×C₄	—	10	1	no	—
574	C₂×C₄	—	10	1	no	—
575	C₂×C₄	—	10	1	no	—
576	C₂×C₄	—	20	1	no	—
577	C₂×C₄	—	20	1	no	—
578	C₂×C₄	—	20	1	no	—
579	C₂×C₄	—	20	1	no	—
580	C₂×C₄	—	20	1	no	—
581	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
582	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
583	C₂×C₄	D₅×#41	1	1	yes	characteristic
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	2	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	5	2	no	—
591	C₈	—	5	2	no	—
592	C₈	—	10	1	no	—
593	C₈	—	10	1	no	—
594	C₈	—	20	1	no	—
595	C₈	—	20	1	no	—
596	C₈	—	20	1	no	—
597	C₈	D₅×D₈	1	2	yes	—
598	C₅	#18066	1	1	yes	characteristic, complemented, Sylow
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	5	2	no	—
606	C₂²	—	10	1	no	—
607	C₂²	—	10	1	no	—
608	C₂²	—	20	1	no	—
609	C₂²	—	20	1	no	—
610	C₂²	—	20	1	no	—
611	C₂²	—	20	1	no	—
612	C₂²	—	20	1	no	—
613	C₂²	—	20	1	no	—
614	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	5	2	no	—
619	C₄	—	10	1	no	—
620	C₄	—	10	1	no	—
621	C₄	—	20	1	no	—
622	C₄	—	20	1	no	—
623	C₄	#66079	1	1	yes	characteristic
624	C₄	D₅×#131	1	1	yes	characteristic
625	C₄	C₂×D₅×D₈	1	1	yes	characteristic
626	C₄	D₅×#135	1	1	yes	characteristic
627	C₂	—	8	1	no	—
628	C₂	—	8	1	no	—
629	C₂	—	10	2	no	—
630	C₂	—	40	1	no	—
631	C₂	—	40	1	no	—
632	C₂	#10611215	1	1	yes	characteristic
633	C₂	C₄×D₅×D₈	1	1	yes	characteristic
634	C₂	#10611630	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×#1581	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#10611329	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1581	D₅
hypocenter	C₅	#18066
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #10611272	C₂	semidirect
3. #10611156	C₂	semidirect
4. C₅×#1581	C₂	semidirect
5. #10601672	C₂	semidirect
6. #10601652	C₂	semidirect
7. C₈×#686	C₂	semidirect
8. D₅×#335	C₂	semidirect
9. #10599352	C₂	semidirect
10. #10598961	C₂	semidirect
11. #10598961	C₂	semidirect
12. #10598953	C₂	semidirect
13. #10598941	C₂	semidirect
14. #10598871	C₂	semidirect
15. #10598860	C₂	semidirect
155. #1581	D₅	semidirect
230. #676	D₈	semidirect
346. #168	#131	semidirect
598. C₅	#18066	semidirect

Maximal subgroups

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

subgroup	index
#10611329	2
#10611272	2
#10611156	2
C₅×#1581	2
#10601672	2
#10601652	2
C₈×#686	2
D₅×#335	2
#10599352	2
#10598961	2
#10598953	2
#10598941	2
#10598871	2
#10598860	2
#18066	5