Subgroups — #12070739

Order 1280.

716 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611693	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	#10611271	C₂	1	1	yes	maximal, characteristic
4	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601746	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601692	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601657	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599322	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599309	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599029	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599009	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598965	C₂	1	1	yes	maximal, characteristic
13	#10598948	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#677	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₅×SD₁₆	C₄	1	1	yes	characteristic
17	C₂×D₅×M₁₆	—	2	1	no	—
18	C₄×Q₈×D₅	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₅×#446	C₂²	1	1	yes	characteristic, complemented
21	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₅×#436	C₂²	1	1	yes	characteristic
23	SD₁₆×Dic₅	C₄	1	1	yes	characteristic
24	#65416	—	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	#65126	—	2	1	no	—
32	#65126	C₂²	1	1	yes	characteristic
33	#65126	C₂²	1	1	yes	characteristic
34	#65123	C₂²	1	1	yes	characteristic
35	#65119	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	#65017	—	2	1	no	—
42	#65015	—	2	1	no	—
43	#64996	—	2	1	no	—
44	#64990	—	2	1	no	—
45	C₄×#677	C₂²	1	1	yes	characteristic
46	C₄×#676	C₂²	1	1	yes	characteristic
47	C₈×D₂₀	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₀	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	#64700	C₂²	1	1	yes	characteristic, complemented
60	#64700	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	#64675	C₂²	1	1	yes	characteristic, complemented
65	#64674	C₂²	1	1	yes	characteristic, complemented
66	C₈×#168	C₂²	1	1	yes	characteristic, complemented
67	M₁₆×SD₁₆	—	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	D₅×M₁₆	—	4	4	no	—
83	C₂×#677	C₂×C₄	1	1	yes	characteristic
84	C₂×#676	—	2	1	no	—
85	C₂×#676	—	2	1	no	—
86	C₂×#676	D₄	1	1	yes	characteristic
87	C₂×#676	D₄	1	1	yes	characteristic
88	C₂×C₈×D₅	—	2	1	no	—
89	C₂×C₈×D₅	—	2	1	no	—
90	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
91	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
92	#4039	C₂×C₄	1	1	yes	characteristic
93	D₅×C₄⋊C₄	—	2	1	no	—
94	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	#4033	—	2	1	no	—
97	#4033	C₂×C₄	1	1	yes	characteristic
98	#4027	—	2	1	no	—
99	D₅×C₂²⋊C₄	—	2	1	no	—
100	C₄×D₂₀	C₂³	1	1	yes	characteristic
101	C₄²×D₅	—	2	1	no	—
102	C₄²×D₅	C₂³	1	1	yes	characteristic
103	C₄×Dic₁₀	—	2	1	no	—
104	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
105	C₅×#106	C₂×C₄	1	1	yes	characteristic
106	C₅×C₄⋊C₈	—	2	1	no	—
107	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
109	C₅×#103	C₂×C₄	1	1	yes	characteristic
110	C₅×#102	C₂×C₄	1	1	yes	characteristic
111	C₅×C₂²⋊C₈	—	2	1	no	—
112	C₅×#97	—	2	1	no	—
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
116	#3967	C₂×C₄	1	1	yes	characteristic
117	#3964	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#168	—	2	1	no	—
119	#3953	C₂×C₄	1	1	yes	characteristic
120	#3952	—	2	1	no	—
121	#3952	—	2	1	no	—
122	#3952	—	2	1	no	—
123	#3949	C₂×C₄	1	1	yes	characteristic
124	#3948	C₂×C₄	1	1	yes	characteristic
125	#3947	D₄	1	1	yes	characteristic
126	#3947	D₄	1	1	yes	characteristic
127	#3946	—	2	1	no	—
128	#3946	—	2	1	no	—
129	#3946	—	2	1	no	—
130	#3946	—	2	1	no	—
131	#3946	—	2	1	no	—
132	C₈×Dic₅	—	2	1	no	—
133	C₈×Dic₅	—	2	1	no	—
134	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
136	#3942	C₂×C₄	1	1	yes	characteristic
137	#3941	C₂×C₄	1	1	yes	characteristic
138	#3940	C₂×C₄	1	1	yes	characteristic
139	#3940	C₂×C₄	1	1	yes	characteristic
140	C₄⋊#168	—	2	1	no	—
141	C₄⋊#168	C₂³	1	1	yes	characteristic
142	C₄⋊#168	C₂³	1	1	yes	characteristic
143	#3935	—	2	1	no	—
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	Q₈×M₁₆	—	5	1	no	—
148	C₂×C₄×SD₁₆	—	5	1	no	—
149	D₄×M₁₆	—	5	1	no	—
150	#1590	—	5	1	no	—
151	#1590	D₅	1	1	yes	characteristic, complemented
152	#1583	—	5	1	no	—
153	#1583	—	5	1	no	—
154	#1582	—	5	1	no	—
155	#1582	—	5	1	no	—
156	C₈×SD₁₆	—	5	1	no	—
157	C₈×SD₁₆	—	5	1	no	—
158	#1566	—	5	1	no	—
159	#1487	—	5	1	no	—
160	#1486	—	5	1	no	—
161	C₈×M₁₆	—	5	1	no	—
162	C₂³×D₅	—	2	1	no	—
163	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂×C₂²⋊D₅	—	2	1	no	—
167	C₂²×Dic₅	—	2	1	no	—
168	Q₈×D₅	—	2	2	no	—
169	Q₈×D₅	—	4	1	no	—
170	D₄×D₅	—	2	2	no	—
171	D₄×D₅	—	4	1	no	—
172	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
178	C₂×C₄×D₅	—	4	2	no	—
179	C₂×C₄×D₅	—	4	2	no	—
180	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄×D₅	#41	1	1	yes	characteristic
183	C₂×Dic₁₀	—	2	1	no	—
184	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
185	C₅×SD₁₆	—	2	2	no	—
186	C₅×M₁₆	—	4	2	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₅×C₂²⋊C₄	—	2	1	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	C₂⁴	1	1	yes	characteristic
200	C₂²⋊Dic₅	—	2	1	no	—
201	#688	—	2	2	no	—
202	#687	—	2	2	no	—
203	#685	—	2	1	no	—
204	#685	—	2	1	no	—
205	C₄⋊Dic₅	—	2	1	no	—
206	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
208	#683	—	2	1	no	—
209	#683	—	2	1	no	—
210	#683	—	2	1	no	—
211	#683	—	2	1	no	—
212	C₄×Dic₅	—	2	1	no	—
213	C₄×Dic₅	—	2	1	no	—
214	C₄×Dic₅	—	2	1	no	—
215	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
217	C₄×Dic₅	#41	1	1	yes	characteristic
218	#681	—	4	2	no	—
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	2	1	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	#677	M₁₆	1	4	yes	complemented
227	#676	—	2	2	no	—
228	#676	—	4	2	no	—
229	#676	—	4	2	no	—
230	#676	SD₁₆	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	C₂²×SD₁₆	—	5	1	no	—
236	C₂²×M₁₆	—	10	1	no	—
237	C₂×C₄×Q₈	—	5	1	no	—
238	C₂×C₄×D₄	—	5	1	no	—
239	#446	—	5	1	no	—
240	#446	—	10	1	no	—
241	#446	—	10	1	no	—
242	#446	C₂×D₅	1	1	yes	characteristic, complemented
243	C₈×Q₈	—	5	1	no	—
244	C₈×Q₈	—	5	1	no	—
245	C₄×SD₁₆	—	5	1	no	—
246	C₄×SD₁₆	—	5	1	no	—
247	C₄×SD₁₆	—	5	1	no	—
248	C₄×SD₁₆	—	5	1	no	—
249	C₄×SD₁₆	—	5	1	no	—
250	C₄×SD₁₆	—	5	1	no	—
251	C₄×SD₁₆	—	5	1	no	—
252	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
253	#436	—	5	1	no	—
254	#436	C₂×D₅	1	1	yes	characteristic
255	#435	—	10	1	no	—
256	#435	—	10	1	no	—
257	C₈×D₄	—	5	1	no	—
258	C₈×D₄	—	5	1	no	—
259	#431	—	5	1	no	—
260	C₂×#106	—	5	1	no	—
261	#423	—	5	1	no	—
262	#423	—	5	1	no	—
263	#423	—	10	1	no	—
264	C₂×#103	—	5	1	no	—
265	C₂×#102	—	5	1	no	—
266	#407	—	10	1	no	—
267	C₄×M₁₆	—	5	1	no	—
268	C₄×M₁₆	—	10	1	no	—
269	C₂×C₄×C₈	—	5	1	no	—
270	#334	—	5	1	no	—
271	#334	—	5	1	no	—
272	#334	—	5	1	no	—
273	#334	C₂×D₅	1	1	yes	characteristic, complemented
274	Q₈⋊C₈	—	5	1	no	—
275	Q₈⋊C₈	—	5	1	no	—
276	Q₈⋊C₈	—	5	1	no	—
277	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
278	D₄⋊C₈	—	5	1	no	—
279	D₄⋊C₈	—	5	1	no	—
280	D₄⋊C₈	—	5	1	no	—
281	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
282	#322	—	5	1	no	—
283	#322	—	5	1	no	—
284	C₈²	—	5	1	no	—
285	C₈²	C₂×D₅	1	1	yes	characteristic, complemented
286	C₂³×C₅	—	2	1	no	—
287	C₂²×D₅	—	2	1	no	—
288	C₂²×D₅	—	4	2	no	—
289	C₂²×D₅	—	4	2	no	—
290	C₂²×D₅	—	8	1	no	—
291	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
292	C₅×Q₈	—	2	1	no	—
293	C₅×Q₈	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	2	1	no	—
296	C₂×C₄×C₅	—	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	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
304	C₂²⋊D₅	—	4	2	no	—
305	C₂×Dic₅	—	2	1	no	—
306	C₂×Dic₅	—	2	1	no	—
307	C₂×Dic₅	—	2	1	no	—
308	C₂×Dic₅	—	4	2	no	—
309	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
310	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
311	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
312	D₂₀	—	2	1	no	—
313	D₂₀	C₂×M₁₆	1	2	yes	—
314	C₄×D₅	—	2	1	no	—
315	C₄×D₅	—	2	1	no	—
316	C₄×D₅	—	4	1	no	—
317	C₄×D₅	—	4	2	no	—
318	C₄×D₅	—	4	2	no	—
319	C₄×D₅	—	4	1	no	—
320	C₄×D₅	—	4	1	no	—
321	C₄×D₅	—	4	2	no	—
322	C₄×D₅	—	8	1	no	—
323	C₄×D₅	C₂×SD₁₆	1	2	yes	—
324	C₄×D₅	#135	1	2	yes	—
325	Dic₁₀	—	2	1	no	—
326	Dic₁₀	—	4	2	no	—
327	Dic₁₀	C₂×M₁₆	1	2	yes	complemented
328	C₅×C₈	—	2	1	no	—
329	C₅×C₈	—	2	1	no	—
330	C₅×C₈	—	4	1	no	—
331	C₅×C₈	—	4	1	no	—
332	C₅×C₈	—	4	1	no	—
333	C₅×C₈	C₂×M₁₆	1	2	yes	complemented
334	C₅×C₈	C₂×SD₁₆	1	2	yes	complemented
335	#168	—	2	1	no	—
336	#168	—	2	1	no	—
337	#168	—	2	1	no	—
338	#168	—	4	1	no	—
339	#168	—	4	1	no	—
340	#168	—	4	1	no	—
341	#168	C₂×SD₁₆	1	2	yes	complemented
342	C₂²×Q₈	—	5	1	no	—
343	C₂²×D₄	—	5	1	no	—
344	C₂³×C₄	—	10	1	no	—
345	C₂×SD₁₆	—	5	1	no	—
346	C₂×SD₁₆	—	5	1	no	—
347	C₂×SD₁₆	—	5	1	no	—
348	C₂×SD₁₆	—	10	4	no	—
349	C₂×SD₁₆	C₄×D₅	1	1	yes	characteristic
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	5	1	no	—
352	C₂×M₁₆	—	5	1	no	—
353	C₂×M₁₆	—	10	1	no	—
354	C₂×M₁₆	—	10	1	no	—
355	C₂×M₁₆	—	10	1	no	—
356	C₂×M₁₆	—	20	4	no	—
357	C₂²×C₈	—	5	1	no	—
358	C₂²×C₈	—	5	1	no	—
359	C₂²×C₈	—	10	1	no	—
360	C₂²×C₈	—	10	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	10	1	no	—
365	C₄×Q₈	—	10	1	no	—
366	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
367	C₄×D₄	—	5	1	no	—
368	C₄×D₄	—	5	1	no	—
369	C₄×D₄	—	5	1	no	—
370	C₄×D₄	—	10	1	no	—
371	C₄×D₄	—	10	1	no	—
372	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
373	C₂×C₄⋊C₄	—	5	1	no	—
374	C₂×C₄⋊C₄	—	5	1	no	—
375	C₂×C₄⋊C₄	—	10	1	no	—
376	C₂×C₂²⋊C₄	—	10	1	no	—
377	C₂×C₄²	—	5	1	no	—
378	C₂×C₄²	—	10	1	no	—
379	#106	—	5	1	no	—
380	#106	—	5	1	no	—
381	#106	—	5	1	no	—
382	#106	C₄×D₅	1	1	yes	characteristic
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	5	1	no	—
385	C₄⋊C₈	—	5	1	no	—
386	C₄⋊C₈	—	10	1	no	—
387	C₄⋊C₈	—	10	1	no	—
388	C₄⋊C₈	—	10	1	no	—
389	C₄⋊C₈	—	10	1	no	—
390	C₄⋊C₈	—	10	1	no	—
391	C₄⋊C₈	—	10	1	no	—
392	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
394	#103	—	5	1	no	—
395	#103	—	5	1	no	—
396	#103	—	5	1	no	—
397	#103	C₄×D₅	1	1	yes	characteristic
398	#102	—	5	1	no	—
399	#102	—	5	1	no	—
400	#102	—	5	1	no	—
401	#102	C₄×D₅	1	1	yes	characteristic
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	10	1	no	—
404	C₂²⋊C₈	—	10	1	no	—
405	C₂²⋊C₈	—	10	1	no	—
406	C₂²⋊C₈	—	10	1	no	—
407	#97	—	2	1	no	—
408	#97	—	5	1	no	—
409	#97	—	5	1	no	—
410	#97	—	10	1	no	—
411	C₄×C₈	—	5	1	no	—
412	C₄×C₈	—	5	1	no	—
413	C₄×C₈	—	5	1	no	—
414	C₄×C₈	—	5	1	no	—
415	C₄×C₈	—	5	1	no	—
416	C₄×C₈	—	10	1	no	—
417	C₄×C₈	—	10	1	no	—
418	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
425	C₂×D₅	—	2	1	no	—
426	C₂×D₅	—	2	1	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	—	4	1	no	—
429	C₂×D₅	—	4	1	no	—
430	C₂×D₅	—	8	4	no	—
431	C₂×D₅	C₄×SD₁₆	1	2	yes	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
437	C₄×C₅	#568	1	1	yes	characteristic
438	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
439	C₄×C₅	C₂×#135	1	1	yes	characteristic
440	Dic₅	—	2	2	no	—
441	Dic₅	—	2	1	no	—
442	Dic₅	—	2	1	no	—
443	Dic₅	—	4	1	no	—
444	Dic₅	—	4	1	no	—
445	Dic₅	C₄×SD₁₆	1	2	yes	—
446	C₂⁴	—	10	1	no	—
447	C₂×Q₈	—	5	1	no	—
448	C₂×Q₈	—	10	1	no	—
449	C₂×Q₈	—	10	2	no	—
450	C₂×Q₈	—	20	1	no	—
451	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
452	C₂×D₄	—	5	1	no	—
453	C₂×D₄	—	10	1	no	—
454	C₂×D₄	—	10	2	no	—
455	C₂×D₄	—	20	1	no	—
456	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	1	no	—
460	C₂²×C₄	—	5	1	no	—
461	C₂²×C₄	—	10	1	no	—
462	C₂²×C₄	—	10	1	no	—
463	C₂²×C₄	—	10	1	no	—
464	C₂²×C₄	—	10	1	no	—
465	C₂²×C₄	—	10	1	no	—
466	C₂²×C₄	—	10	1	no	—
467	C₂²×C₄	—	20	2	no	—
468	C₂²×C₄	—	20	2	no	—
469	SD₁₆	—	2	2	no	—
470	SD₁₆	—	5	4	no	—
471	SD₁₆	—	10	2	no	—
472	SD₁₆	—	10	2	no	—
473	M₁₆	—	4	2	no	—
474	M₁₆	—	5	4	no	—
475	M₁₆	—	10	2	no	—
476	M₁₆	—	20	2	no	—
477	M₁₆	—	20	2	no	—
478	M₁₆	—	20	2	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	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	—	10	2	no	—
487	C₂×C₈	—	10	1	no	—
488	C₂×C₈	—	10	1	no	—
489	C₂×C₈	—	10	1	no	—
490	C₂×C₈	—	20	1	no	—
491	C₂×C₈	—	20	2	no	—
492	C₂×C₈	—	20	2	no	—
493	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
494	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
495	C₂×C₈	D₄×D₅	1	1	yes	characteristic
496	C₂×C₈	D₄×D₅	1	1	yes	characteristic
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	5	1	no	—
499	C₄⋊C₄	—	5	1	no	—
500	C₄⋊C₄	—	10	1	no	—
501	C₄⋊C₄	—	10	1	no	—
502	C₄⋊C₄	—	10	1	no	—
503	C₄⋊C₄	—	10	1	no	—
504	C₄⋊C₄	—	10	1	no	—
505	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
506	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	10	1	no	—
509	C₂²⋊C₄	—	10	1	no	—
510	C₂²⋊C₄	—	10	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	5	1	no	—
513	C₄²	—	5	1	no	—
514	C₄²	—	5	1	no	—
515	C₄²	—	10	1	no	—
516	C₄²	—	10	1	no	—
517	C₄²	—	10	1	no	—
518	C₄²	C₂³×D₅	1	1	yes	characteristic
519	C₂×C₅	—	8	1	no	—
520	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
521	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
522	C₂×C₅	#2957	1	1	yes	characteristic
523	D₅	—	2	2	no	—
524	D₅	—	4	2	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	5	1	no	—
527	C₂³	—	10	1	no	—
528	C₂³	—	20	2	no	—
529	C₂³	—	20	2	no	—
530	C₂³	—	40	1	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	5	2	no	—
534	Q₈	—	10	1	no	—
535	Q₈	—	20	2	no	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	5	2	no	—
539	D₄	—	10	1	no	—
540	D₄	—	20	2	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	1	no	—
546	C₂×C₄	—	5	1	no	—
547	C₂×C₄	—	5	2	no	—
548	C₂×C₄	—	5	2	no	—
549	C₂×C₄	—	5	1	no	—
550	C₂×C₄	—	5	1	no	—
551	C₂×C₄	—	10	1	no	—
552	C₂×C₄	—	10	1	no	—
553	C₂×C₄	—	10	1	no	—
554	C₂×C₄	—	10	1	no	—
555	C₂×C₄	—	10	1	no	—
556	C₂×C₄	—	20	1	no	—
557	C₂×C₄	—	20	2	no	—
558	C₂×C₄	—	20	2	no	—
559	C₂×C₄	—	20	2	no	—
560	C₂×C₄	—	20	2	no	—
561	C₂×C₄	—	20	1	no	—
562	C₂×C₄	—	20	1	no	—
563	C₂×C₄	—	40	1	no	—
564	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
565	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
566	C₂×C₄	D₅×#41	1	1	yes	characteristic
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	5	2	no	—
573	C₈	—	10	1	no	—
574	C₈	—	10	1	no	—
575	C₈	—	10	1	no	—
576	C₈	—	20	1	no	—
577	C₈	—	20	1	no	—
578	C₈	—	20	1	no	—
579	C₈	D₅×M₁₆	1	2	yes	complemented
580	C₈	D₅×SD₁₆	1	2	yes	complemented
581	C₅	M₁₆×SD₁₆	1	1	yes	characteristic, complemented, Sylow
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	5	2	no	—
586	C₂²	—	10	1	no	—
587	C₂²	—	10	1	no	—
588	C₂²	—	10	2	no	—
589	C₂²	—	20	1	no	—
590	C₂²	—	20	1	no	—
591	C₂²	—	40	4	no	—
592	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	5	2	no	—
598	C₄	—	10	1	no	—
599	C₄	—	10	2	no	—
600	C₄	—	10	1	no	—
601	C₄	—	20	1	no	—
602	C₄	—	20	1	no	—
603	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
604	C₄	#66084	1	1	yes	characteristic
605	C₄	C₂×D₅×SD₁₆	1	1	yes	characteristic
606	C₄	D₅×#135	1	1	yes	characteristic
607	C₂	—	8	1	no	—
608	C₂	—	10	2	no	—
609	C₂	—	20	2	no	—
610	C₂	#10611271	1	1	yes	characteristic
611	C₂	C₄×D₅×SD₁₆	1	1	yes	characteristic
612	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	M₁₆×SD₁₆
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. #10611693	C₂	semidirect
4. C₅×#1590	C₂	semidirect
5. #10601746	C₂	semidirect
6. #10601692	C₂	semidirect
7. #10601657	C₂	semidirect
8. #10599322	C₂	semidirect
9. #10599309	C₂	semidirect
10. #10599029	C₂	semidirect
11. #10599009	C₂	semidirect
13. #10598948	C₂	semidirect
14. C₈×#677	C₂	semidirect
15. C₈×#676	C₂	semidirect
20. C₅×#446	C₂²	semidirect
26. #65313	C₂²	semidirect
35. #65119	C₂²	semidirect
50. C₈×Dic₁₀	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. #64700	C₂²	semidirect
60. #64700	C₂²	semidirect
62. #64677	C₂²	semidirect
63. #64676	C₂²	semidirect
64. #64675	C₂²	semidirect
65. #64674	C₂²	semidirect
66. C₈×#168	C₂²	semidirect
151. #1590	D₅	semidirect
226. #677	M₁₆	semidirect
230. #676	SD₁₆	semidirect
242. #446	C₂×D₅	semidirect
273. #334	C₂×D₅	semidirect
277. Q₈⋊C₈	C₂×D₅	semidirect
285. C₈²	C₂×D₅	semidirect
327. Dic₁₀	C₂×M₁₆	semidirect
333. C₅×C₈	C₂×M₁₆	semidirect
334. C₅×C₈	C₂×SD₁₆	semidirect
341. #168	C₂×SD₁₆	semidirect
579. C₈	D₅×M₁₆	semidirect
580. C₈	D₅×SD₁₆	semidirect
581. C₅	M₁₆×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
#10611693	2
C₄×D₅×SD₁₆	2
#10611271	2
C₅×#1590	2
#10601746	2
#10601692	2
#10601657	2
#10599322	2
#10599309	2
#10599029	2
#10599009	2
#10598965	2
#10598948	2
C₈×#677	2
C₈×#676	2
M₁₆×SD₁₆	5