Subgroups — #12069131

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611694	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	#10611274	C₂	1	1	yes	maximal, characteristic
4	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601748	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601692	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601653	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599320	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599316	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599024	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599019	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598960	C₂	1	1	yes	maximal, characteristic
13	#10598955	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598848	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598840	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₅×SD₁₆	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₅	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
19	C₅×#446	C₂²	1	1	yes	characteristic, complemented
20	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₅×#436	C₂²	1	1	yes	characteristic
22	SD₁₆×Dic₅	C₄	1	1	yes	characteristic
23	#65417	—	2	1	no	—
24	#65415	—	2	1	no	—
25	C₄×#688	C₂²	1	1	yes	characteristic
26	#65313	C₂²	1	1	yes	characteristic, complemented
27	C₄×#687	C₂²	1	1	yes	characteristic
28	#65301	C₂²	1	1	yes	characteristic
29	D₅×#106	C₄	1	1	yes	characteristic
30	#65141	C₄	1	1	yes	characteristic
31	#65127	C₂²	1	1	yes	characteristic
32	#65124	—	2	1	no	—
33	#65122	C₂²	1	1	yes	characteristic
34	#65122	C₂²	1	1	yes	characteristic
35	#65120	C₂²	1	1	yes	characteristic, complemented
36	#65117	—	2	1	no	—
37	D₅×#103	C₄	1	1	yes	characteristic
38	#65077	C₄	1	1	yes	characteristic
39	D₅×#102	C₄	1	1	yes	characteristic
40	#65047	C₄	1	1	yes	characteristic
41	#65018	—	2	1	no	—
42	#65015	—	2	1	no	—
43	#64994	—	2	1	no	—
44	#64990	—	2	1	no	—
45	C₄×#677	C₂²	1	1	yes	characteristic
46	#64977	C₂²	1	1	yes	characteristic
47	#64974	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
50	#64968	C₂²	1	1	yes	characteristic, complemented
51	C₅×#334	C₂²	1	1	yes	characteristic, complemented
52	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
55	Q₈⋊#168	C₂²	1	1	yes	characteristic, complemented
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	#64704	C₂²	1	1	yes	characteristic, complemented
58	#64703	C₂²	1	1	yes	characteristic
59	#64699	C₂²	1	1	yes	characteristic, complemented
60	#64699	C₂²	1	1	yes	characteristic, complemented
61	#64679	C₂²	1	1	yes	characteristic
62	#64677	C₂²	1	1	yes	characteristic, complemented
63	#64676	C₂²	1	1	yes	characteristic, complemented
64	#64674	C₂²	1	1	yes	characteristic, complemented
65	#64674	C₂²	1	1	yes	characteristic, complemented
66	C₈×#168	C₂²	1	1	yes	characteristic, complemented
67	#17896	—	5	1	no	maximal, Sylow
68	C₂×Q₈×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×D₄×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄×D₅	—	2	1	no	—
71	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₂×#688	C₂×C₄	1	1	yes	characteristic
77	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₂×#687	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₅	—	2	1	no	—
80	C₂×#681	—	2	1	no	—
81	D₅×SD₁₆	—	2	4	no	—
82	C₂×#677	C₂×C₄	1	1	yes	characteristic
83	C₂×#676	—	2	1	no	—
84	C₂×#676	—	2	1	no	—
85	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
87	#4039	C₂×C₄	1	1	yes	characteristic
88	D₅×C₄⋊C₄	—	2	1	no	—
89	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	#4033	—	2	1	no	—
92	#4033	C₂×C₄	1	1	yes	characteristic
93	#4027	—	2	1	no	—
94	D₅×C₂²⋊C₄	—	2	1	no	—
95	C₄×D₂₀	C₂³	1	1	yes	characteristic
96	C₄²×D₅	—	2	1	no	—
97	C₄²×D₅	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₀	—	2	1	no	—
99	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
100	C₅×#106	C₂×C₄	1	1	yes	characteristic
101	C₅×C₄⋊C₈	—	2	1	no	—
102	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₅×#103	C₂×C₄	1	1	yes	characteristic
105	C₅×#102	C₂×C₄	1	1	yes	characteristic
106	C₅×C₂²⋊C₈	—	2	1	no	—
107	C₅×#97	—	2	1	no	—
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	#3967	C₂×C₄	1	1	yes	characteristic
112	#3964	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊#168	—	2	1	no	—
114	#3953	C₂×C₄	1	1	yes	characteristic
115	#3952	—	2	1	no	—
116	#3952	—	2	1	no	—
117	#3952	—	2	1	no	—
118	#3952	—	2	1	no	—
119	#3952	—	2	1	no	—
120	#3952	D₄	1	1	yes	characteristic
121	#3952	D₄	1	1	yes	characteristic
122	#3949	C₂×C₄	1	1	yes	characteristic
123	#3948	C₂×C₄	1	1	yes	characteristic
124	#3947	—	2	1	no	—
125	#3947	—	2	1	no	—
126	#3946	—	2	1	no	—
127	#3946	—	2	1	no	—
128	#3946	—	2	1	no	—
129	#3946	D₄	1	1	yes	characteristic
130	#3946	D₄	1	1	yes	characteristic
131	C₈×Dic₅	—	2	1	no	—
132	C₈×Dic₅	—	2	1	no	—
133	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
135	#3942	C₂×C₄	1	1	yes	characteristic
136	#3941	C₂×C₄	1	1	yes	characteristic
137	#3940	C₂×C₄	1	1	yes	characteristic
138	#3940	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#168	—	2	1	no	—
140	C₄⋊#168	C₂³	1	1	yes	characteristic
141	C₄⋊#168	C₂³	1	1	yes	characteristic
142	#3935	—	2	1	no	—
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	#2983	—	5	1	no	—
147	#2975	—	5	1	no	—
148	C₂×C₄×SD₁₆	—	5	1	no	—
149	#1592	—	5	1	no	—
150	#1592	—	5	1	no	—
151	#1592	—	5	1	no	—
152	#1592	—	5	1	no	—
153	#1590	—	5	1	no	—
154	#1590	—	5	1	no	—
155	#1590	—	5	1	no	—
156	#1590	D₅	1	1	yes	characteristic, complemented
157	#1564	—	5	1	no	—
158	#1479	—	5	1	no	—
159	#1478	—	5	1	no	—
160	#1450	—	5	1	no	—
161	C₂³×D₅	—	2	1	no	—
162	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂×C₂²⋊D₅	—	2	1	no	—
166	C₂²×Dic₅	—	2	1	no	—
167	Q₈×D₅	—	2	2	no	—
168	Q₈×D₅	—	2	2	no	—
169	D₄×D₅	—	2	2	no	—
170	D₄×D₅	—	2	2	no	—
171	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₅	—	2	1	no	—
173	C₂×C₄×D₅	—	2	1	no	—
174	C₂×C₄×D₅	—	2	1	no	—
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	—	8	1	no	—
178	C₂×C₄×D₅	—	8	1	no	—
179	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄×D₅	#41	1	1	yes	characteristic
182	C₂×Dic₁₀	—	2	1	no	—
183	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
184	C₅×SD₁₆	—	2	2	no	—
185	C₅×M₁₆	—	8	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₅×C₂²⋊C₄	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	C₂⁴	1	1	yes	characteristic
199	C₂²⋊Dic₅	—	2	1	no	—
200	#688	—	2	2	no	—
201	#687	—	2	2	no	—
202	#685	—	2	1	no	—
203	#685	—	2	1	no	—
204	C₄⋊Dic₅	—	2	1	no	—
205	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
207	#683	—	2	1	no	—
208	#683	—	2	1	no	—
209	#683	—	2	1	no	—
210	#683	—	2	1	no	—
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	—	2	1	no	—
213	C₄×Dic₅	—	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	—	8	1	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
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	#677	—	2	2	no	—
226	#676	—	8	1	no	—
227	#676	—	8	1	no	—
228	C₈×D₅	—	2	2	no	—
229	C₈×D₅	M₁₆	1	4	yes	complemented
230	C₂²×SD₁₆	—	5	1	no	—
231	C₂×C₄×Q₈	—	5	1	no	—
232	C₂×C₄×D₄	—	5	1	no	—
233	#446	—	5	1	no	—
234	#446	—	5	1	no	—
235	#446	—	5	1	no	—
236	#446	—	10	1	no	—
237	#446	—	10	1	no	—
238	#446	C₂×D₅	1	1	yes	characteristic, complemented
239	C₄×SD₁₆	—	5	1	no	—
240	C₄×SD₁₆	—	5	1	no	—
241	C₄×SD₁₆	—	5	1	no	—
242	C₄×SD₁₆	—	5	1	no	—
243	C₄×SD₁₆	—	5	1	no	—
244	C₄×SD₁₆	—	5	1	no	—
245	C₄×SD₁₆	—	5	1	no	—
246	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
247	#436	—	5	1	no	—
248	#436	—	5	1	no	—
249	#436	—	5	1	no	—
250	#436	—	10	1	no	—
251	#436	—	10	1	no	—
252	#436	C₂×D₅	1	1	yes	characteristic
253	#432	—	10	1	no	—
254	#432	—	10	1	no	—
255	#431	—	5	1	no	—
256	#431	—	5	1	no	—
257	#431	—	5	1	no	—
258	#431	—	5	1	no	—
259	C₂×#106	—	5	1	no	—
260	C₂×#103	—	5	1	no	—
261	C₂×#102	—	5	1	no	—
262	#407	—	10	1	no	—
263	#407	—	10	1	no	—
264	C₂×C₄×C₈	—	5	1	no	—
265	#335	—	5	1	no	—
266	#335	—	5	1	no	—
267	#334	—	5	1	no	—
268	#334	C₂×D₅	1	1	yes	characteristic, complemented
269	Q₈⋊C₈	—	5	1	no	—
270	Q₈⋊C₈	—	5	1	no	—
271	Q₈⋊C₈	—	5	1	no	—
272	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
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	#322	—	5	1	no	—
278	#322	—	5	1	no	—
279	C₈²	—	5	1	no	—
280	C₈²	C₂×D₅	1	1	yes	characteristic, complemented
281	C₂³×C₅	—	2	1	no	—
282	C₂²×D₅	—	2	1	no	—
283	C₂²×D₅	—	4	2	no	—
284	C₂²×D₅	—	8	1	no	—
285	C₂²×D₅	—	8	1	no	—
286	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
287	C₅×Q₈	—	2	1	no	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	2	1	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	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
299	C₂²⋊D₅	—	4	2	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	1	no	—
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	—	8	1	no	—
304	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
305	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
306	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
307	D₂₀	—	2	1	no	—
308	D₂₀	—	2	1	no	—
309	C₄×D₅	—	2	1	no	—
310	C₄×D₅	—	2	1	no	—
311	C₄×D₅	—	4	1	no	—
312	C₄×D₅	—	4	2	no	—
313	C₄×D₅	—	4	1	no	—
314	C₄×D₅	—	4	1	no	—
315	C₄×D₅	—	8	1	no	—
316	C₄×D₅	—	8	1	no	—
317	C₄×D₅	—	8	1	no	—
318	C₄×D₅	C₂×M₁₆	1	2	yes	—
319	C₄×D₅	#131	1	2	yes	—
320	Dic₁₀	—	2	1	no	—
321	Dic₁₀	—	2	1	no	—
322	Dic₁₀	—	4	2	no	—
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	4	1	no	—
327	C₅×C₈	—	4	1	no	—
328	C₅×C₈	—	4	1	no	—
329	C₅×C₈	C₂×M₁₆	1	2	yes	—
330	#168	—	2	1	no	—
331	#168	—	2	1	no	—
332	#168	—	2	1	no	—
333	#168	—	4	1	no	—
334	#168	—	4	1	no	—
335	#168	—	4	1	no	—
336	#168	C₂×M₁₆	1	2	yes	—
337	C₂²×Q₈	—	5	1	no	—
338	C₂²×D₄	—	5	1	no	—
339	C₂³×C₄	—	10	1	no	—
340	C₂×SD₁₆	—	5	1	no	—
341	C₂×SD₁₆	—	5	1	no	—
342	C₂×SD₁₆	—	5	1	no	—
343	C₂×SD₁₆	—	10	4	no	—
344	C₂×SD₁₆	C₄×D₅	1	1	yes	characteristic
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	10	1	no	—
347	C₂×M₁₆	—	10	1	no	—
348	C₂×M₁₆	—	10	1	no	—
349	C₂²×C₈	—	5	1	no	—
350	C₂²×C₈	—	5	1	no	—
351	C₄×Q₈	—	5	1	no	—
352	C₄×Q₈	—	5	1	no	—
353	C₄×Q₈	—	5	1	no	—
354	C₄×Q₈	—	10	1	no	—
355	C₄×Q₈	—	10	1	no	—
356	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
357	C₄×D₄	—	5	1	no	—
358	C₄×D₄	—	5	1	no	—
359	C₄×D₄	—	5	1	no	—
360	C₄×D₄	—	10	1	no	—
361	C₄×D₄	—	10	1	no	—
362	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	—	5	1	no	—
364	C₂×C₄⋊C₄	—	5	1	no	—
365	C₂×C₄⋊C₄	—	10	1	no	—
366	C₂×C₂²⋊C₄	—	10	1	no	—
367	C₂×C₄²	—	5	1	no	—
368	C₂×C₄²	—	10	1	no	—
369	#106	—	5	1	no	—
370	#106	—	5	1	no	—
371	#106	—	5	1	no	—
372	#106	C₄×D₅	1	1	yes	characteristic
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	5	1	no	—
375	C₄⋊C₈	—	5	1	no	—
376	C₄⋊C₈	—	5	1	no	—
377	C₄⋊C₈	—	5	1	no	—
378	C₄⋊C₈	—	10	1	no	—
379	C₄⋊C₈	—	10	1	no	—
380	C₄⋊C₈	—	10	1	no	—
381	C₄⋊C₈	—	10	1	no	—
382	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
383	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
384	#103	—	5	1	no	—
385	#103	—	5	1	no	—
386	#103	—	5	1	no	—
387	#103	C₄×D₅	1	1	yes	characteristic
388	#102	—	5	1	no	—
389	#102	—	5	1	no	—
390	#102	—	5	1	no	—
391	#102	C₄×D₅	1	1	yes	characteristic
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	—	5	1	no	—
394	C₂²⋊C₈	—	5	1	no	—
395	C₂²⋊C₈	—	10	1	no	—
396	C₂²⋊C₈	—	10	1	no	—
397	C₂²⋊C₈	—	10	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₂²⋊C₈	—	10	1	no	—
400	C₂²⋊C₈	—	10	1	no	—
401	#97	—	2	1	no	—
402	#97	—	10	1	no	—
403	#97	—	10	1	no	—
404	#97	—	10	1	no	—
405	C₄×C₈	—	5	1	no	—
406	C₄×C₈	—	5	1	no	—
407	C₄×C₈	—	5	1	no	—
408	C₄×C₈	—	5	1	no	—
409	C₄×C₈	—	5	1	no	—
410	C₄×C₈	—	10	1	no	—
411	C₄×C₈	—	10	1	no	—
412	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
413	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
414	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
415	C₂²×C₅	—	4	1	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
419	C₂×D₅	—	2	1	no	—
420	C₂×D₅	—	2	1	no	—
421	C₂×D₅	—	4	1	no	—
422	C₂×D₅	—	4	1	no	—
423	C₂×D₅	—	4	1	no	—
424	C₂×D₅	—	8	4	no	—
425	C₂×D₅	#436	1	2	yes	—
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	4	1	no	—
428	C₄×C₅	—	4	1	no	—
429	C₄×C₅	—	4	1	no	—
430	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
431	C₄×C₅	C₂×#131	1	1	yes	characteristic
432	C₄×C₅	#577	1	1	yes	characteristic
433	C₄×C₅	#577	1	1	yes	characteristic
434	Dic₅	—	2	1	no	—
435	Dic₅	—	2	1	no	—
436	Dic₅	—	4	1	no	—
437	Dic₅	—	4	1	no	—
438	Dic₅	—	4	1	no	—
439	Dic₅	#436	1	2	yes	—
440	C₂⁴	—	10	1	no	—
441	C₂×Q₈	—	5	1	no	—
442	C₂×Q₈	—	10	1	no	—
443	C₂×Q₈	—	10	2	no	—
444	C₂×Q₈	—	10	2	no	—
445	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
446	C₂×D₄	—	5	1	no	—
447	C₂×D₄	—	10	2	no	—
448	C₂×D₄	—	10	2	no	—
449	C₂×D₄	—	10	1	no	—
450	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	1	no	—
455	C₂²×C₄	—	10	1	no	—
456	C₂²×C₄	—	10	1	no	—
457	C₂²×C₄	—	10	1	no	—
458	C₂²×C₄	—	10	1	no	—
459	C₂²×C₄	—	10	1	no	—
460	C₂²×C₄	—	10	1	no	—
461	C₂²×C₄	—	40	1	no	—
462	C₂²×C₄	—	40	1	no	—
463	SD₁₆	—	2	2	no	—
464	SD₁₆	—	10	2	no	—
465	SD₁₆	—	10	2	no	—
466	SD₁₆	—	10	2	no	—
467	M₁₆	—	8	1	no	—
468	M₁₆	—	40	1	no	—
469	M₁₆	—	40	1	no	—
470	M₁₆	—	40	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	5	1	no	—
475	C₂×C₈	—	5	4	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	5	1	no	—
479	C₂×C₈	—	10	2	no	—
480	C₂×C₈	—	10	1	no	—
481	C₂×C₈	—	10	1	no	—
482	C₂×C₈	—	10	1	no	—
483	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
484	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
485	C₂×C₈	D₄×D₅	1	1	yes	characteristic
486	C₂×C₈	D₄×D₅	1	1	yes	characteristic
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	5	1	no	—
490	C₄⋊C₄	—	10	1	no	—
491	C₄⋊C₄	—	10	1	no	—
492	C₄⋊C₄	—	10	1	no	—
493	C₄⋊C₄	—	10	1	no	—
494	C₄⋊C₄	—	10	1	no	—
495	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
496	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	10	1	no	—
499	C₂²⋊C₄	—	10	1	no	—
500	C₂²⋊C₄	—	10	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	5	1	no	—
503	C₄²	—	5	1	no	—
504	C₄²	—	5	1	no	—
505	C₄²	—	10	1	no	—
506	C₄²	—	10	1	no	—
507	C₄²	—	10	1	no	—
508	C₄²	C₂³×D₅	1	1	yes	characteristic
509	C₂×C₅	—	8	1	no	—
510	C₂×C₅	C₂×#436	1	1	yes	characteristic
511	C₂×C₅	#2949	1	1	yes	characteristic
512	C₂×C₅	#2957	1	1	yes	characteristic
513	D₅	—	2	2	no	—
514	D₅	—	8	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	5	1	no	—
517	C₂³	—	10	1	no	—
518	C₂³	—	20	2	no	—
519	C₂³	—	40	1	no	—
520	C₂³	—	40	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	10	1	no	—
524	Q₈	—	10	1	no	—
525	Q₈	—	20	2	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	10	1	no	—
529	D₄	—	10	1	no	—
530	D₄	—	20	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	5	1	no	—
537	C₂×C₄	—	5	2	no	—
538	C₂×C₄	—	5	2	no	—
539	C₂×C₄	—	5	1	no	—
540	C₂×C₄	—	5	1	no	—
541	C₂×C₄	—	10	1	no	—
542	C₂×C₄	—	10	1	no	—
543	C₂×C₄	—	10	1	no	—
544	C₂×C₄	—	10	1	no	—
545	C₂×C₄	—	10	1	no	—
546	C₂×C₄	—	20	1	no	—
547	C₂×C₄	—	20	2	no	—
548	C₂×C₄	—	20	1	no	—
549	C₂×C₄	—	20	1	no	—
550	C₂×C₄	—	40	1	no	—
551	C₂×C₄	—	40	1	no	—
552	C₂×C₄	—	40	1	no	—
553	C₂×C₄	—	40	1	no	—
554	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
555	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
556	C₂×C₄	D₅×#41	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	5	2	no	—
564	C₈	—	10	1	no	—
565	C₈	—	10	1	no	—
566	C₈	—	10	1	no	—
567	C₈	—	20	1	no	—
568	C₈	—	20	1	no	—
569	C₈	—	20	1	no	—
570	C₈	D₅×M₁₆	1	2	yes	—
571	C₅	#17896	1	1	yes	characteristic, complemented, Sylow
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	5	2	no	—
576	C₂²	—	10	1	no	—
577	C₂²	—	10	1	no	—
578	C₂²	—	20	1	no	—
579	C₂²	—	20	1	no	—
580	C₂²	—	20	1	no	—
581	C₂²	—	40	4	no	—
582	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	5	2	no	—
588	C₄	—	10	1	no	—
589	C₄	—	10	1	no	—
590	C₄	—	20	1	no	—
591	C₄	—	20	1	no	—
592	C₄	—	20	1	no	—
593	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
594	C₄	D₅×#131	1	1	yes	characteristic
595	C₄	#66096	1	1	yes	characteristic
596	C₄	#66104	1	1	yes	characteristic
597	C₂	—	8	1	no	—
598	C₂	—	10	2	no	—
599	C₂	—	40	1	no	—
600	C₂	D₅×#436	1	1	yes	characteristic
601	C₂	#10611380	1	1	yes	characteristic
602	C₂	#10611621	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×#1590	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×D₄×D₅	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1590	D₅
hypocenter	C₅	#17896
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1590

Complements

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

N	H ≅ G/N	type
1. #10611694	C₂	semidirect
4. C₅×#1590	C₂	semidirect
5. #10601748	C₂	semidirect
6. #10601692	C₂	semidirect
7. #10601653	C₂	semidirect
8. #10599320	C₂	semidirect
9. #10599316	C₂	semidirect
10. #10599024	C₂	semidirect
11. #10599019	C₂	semidirect
13. #10598955	C₂	semidirect
14. #10598848	C₂	semidirect
15. #10598840	C₂	semidirect
19. C₅×#446	C₂²	semidirect
26. #65313	C₂²	semidirect
35. #65120	C₂²	semidirect
50. #64968	C₂²	semidirect
51. C₅×#334	C₂²	semidirect
52. C₅×Q₈⋊C₈	C₂²	semidirect
54. C₅×C₈²	C₂²	semidirect
55. Q₈⋊#168	C₂²	semidirect
57. #64704	C₂²	semidirect
59. #64699	C₂²	semidirect
60. #64699	C₂²	semidirect
62. #64677	C₂²	semidirect
63. #64676	C₂²	semidirect
64. #64674	C₂²	semidirect
65. #64674	C₂²	semidirect
66. C₈×#168	C₂²	semidirect
156. #1590	D₅	semidirect
229. C₈×D₅	M₁₆	semidirect
238. #446	C₂×D₅	semidirect
268. #334	C₂×D₅	semidirect
272. Q₈⋊C₈	C₂×D₅	semidirect
280. C₈²	C₂×D₅	semidirect
571. C₅	#17896	semidirect

Maximal subgroups

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

subgroup	index
#10611694	2
C₄×D₅×SD₁₆	2
#10611274	2
C₅×#1590	2
#10601748	2
#10601692	2
#10601653	2
#10599320	2
#10599316	2
#10599024	2
#10599019	2
#10598960	2
#10598955	2
#10598848	2
#10598840	2
#17896	5