Subgroups — #12116671

Order 1280.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2896	C₂	1	1	yes	maximal, characteristic
2	#10615806	C₂	1	1	yes	maximal, characteristic
3	#10613941	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602931	C₂	1	1	yes	maximal, characteristic
5	#10602793	C₂	1	1	yes	maximal, characteristic, complemented
6	#10602776	C₂	1	1	yes	maximal, characteristic, complemented
7	#10602383	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601085	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601085	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601084	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601084	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601083	C₂	1	1	yes	maximal, characteristic, complemented
13	#10601082	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601081	C₂	1	1	yes	maximal, characteristic, complemented
15	#10601080	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×#4094	C₂²	1	1	yes	characteristic
20	C₂×#4094	C₂²	1	1	yes	characteristic
21	C₅×#419	C₄	1	1	yes	characteristic, complemented
22	C₅×#419	C₄	1	1	yes	characteristic, complemented
23	C₅×#418	C₄	1	1	yes	characteristic, complemented
24	C₅×#418	C₄	1	1	yes	characteristic, complemented
25	C₅×#417	C₄	1	1	yes	characteristic, complemented
26	C₅×#417	C₄	1	1	yes	characteristic, complemented
27	C₅×#417	C₄	1	1	yes	characteristic, complemented
28	C₅×#417	C₄	1	1	yes	characteristic, complemented
29	C₅×#416	C₂²	1	1	yes	characteristic
30	C₅×#416	C₂²	1	1	yes	characteristic
31	C₅×#416	C₂²	1	1	yes	characteristic
32	C₅×#416	C₂²	1	1	yes	characteristic
33	C₂×#3969	C₂²	1	1	yes	characteristic
34	C₂×#3969	C₂²	1	1	yes	characteristic
35	C₂×#3969	C₂²	1	1	yes	characteristic
36	C₂×#3969	C₂²	1	1	yes	characteristic
37	#65523	—	2	1	no	—
38	#65523	—	2	1	no	—
39	#65523	C₂²	1	1	yes	characteristic
40	#65523	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
42	#65496	—	2	1	no	—
43	#65496	C₂²	1	1	yes	characteristic
44	#65496	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊#168	—	2	1	no	—
46	C₂×C₂²⋊#168	C₂²	1	1	yes	characteristic
47	C₂×#3951	C₂²	1	1	yes	characteristic, complemented
48	C₂×#3951	C₂²	1	1	yes	characteristic, complemented
49	C₂×#3947	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
51	#65289	—	2	1	no	—
52	#65289	—	2	1	no	—
53	#65288	C₂²	1	1	yes	characteristic, complemented
54	#65288	C₂²	1	1	yes	characteristic, complemented
55	#65286	C₂²	1	1	yes	characteristic, complemented
56	#65286	C₂²	1	1	yes	characteristic, complemented
57	#65215	—	2	1	no	—
58	#65214	—	2	1	no	—
59	#64772	C₂²	1	1	yes	characteristic, complemented
60	#64772	C₂²	1	1	yes	characteristic, complemented
61	#64770	C₂²	1	1	yes	characteristic, complemented
62	#64770	C₂²	1	1	yes	characteristic, complemented
63	#64752	C₂²	1	1	yes	characteristic, complemented
64	#64752	C₂²	1	1	yes	characteristic, complemented
65	#64752	C₂²	1	1	yes	characteristic, complemented
66	#64752	C₂²	1	1	yes	characteristic, complemented
67	#22588	—	5	1	no	maximal, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	—	2	1	no	—
70	C₂×C₅×#41	—	2	2	no	—
71	C₂×C₅×#41	—	2	2	no	—
72	C₂×C₅×#41	—	4	1	no	—
73	C₂×C₅×#41	—	4	1	no	—
74	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
75	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
76	C₂×C₅×#41	C₂³	1	1	yes	characteristic
77	C₂×C₅×#41	C₂³	1	1	yes	characteristic
78	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₅×D₄	—	2	1	no	—
80	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₅	—	2	1	no	—
82	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×M₁₆	—	4	1	no	—
84	C₂×C₅×M₁₆	—	4	1	no	—
85	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
88	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₅×#117	—	2	1	no	—
92	C₅×#117	—	2	1	no	—
93	C₅×#117	C₂×C₄	1	1	yes	characteristic
94	C₅×#117	C₂×C₄	1	1	yes	characteristic
95	C₅×#117	C₂³	1	1	yes	characteristic
96	C₅×#117	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₂²⋊Dic₅	—	2	1	no	—
102	#4094	—	2	2	no	—
103	#4094	—	2	2	no	—
104	#4094	—	4	1	no	—
105	#4094	—	4	1	no	—
106	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
107	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
108	C₂×#681	—	2	1	no	—
109	C₂×#681	—	2	1	no	—
110	C₂×#681	C₂³	1	1	yes	characteristic
111	C₂×#681	C₂³	1	1	yes	characteristic
112	C₂×#681	C₂³	1	1	yes	characteristic
113	C₂×#681	C₂³	1	1	yes	characteristic
114	C₂²×#168	—	2	1	no	—
115	C₂²×#168	—	2	1	no	—
116	C₂²×#168	C₂³	1	1	yes	characteristic
117	C₂²×#168	C₂³	1	1	yes	characteristic
118	C₅×#103	C₂×C₄	1	1	yes	characteristic
119	C₅×#103	C₂×C₄	1	1	yes	characteristic
120	C₅×#103	C₂×C₄	1	1	yes	characteristic
121	C₅×#103	C₂×C₄	1	1	yes	characteristic
122	C₅×#103	C₂×C₄	1	1	yes	characteristic
123	C₅×#103	C₂×C₄	1	1	yes	characteristic
124	C₅×#103	C₂×C₄	1	1	yes	characteristic
125	C₅×#103	C₂×C₄	1	1	yes	characteristic
126	C₅×#102	C₂×C₄	1	1	yes	characteristic
127	C₅×#102	C₂×C₄	1	1	yes	characteristic
128	C₅×#102	C₂×C₄	1	1	yes	characteristic
129	C₅×#102	C₂×C₄	1	1	yes	characteristic
130	C₅×#102	C₂×C₄	1	1	yes	characteristic
131	C₅×#102	C₂×C₄	1	1	yes	characteristic
132	C₅×#102	C₂×C₄	1	1	yes	characteristic
133	C₅×#102	C₂×C₄	1	1	yes	characteristic
134	#3969	—	2	2	no	—
135	#3969	—	2	2	no	—
136	#3969	—	4	1	no	—
137	#3969	—	4	1	no	—
138	#3963	—	2	1	no	—
139	C₂²⋊#168	—	2	1	no	—
140	C₂²⋊#168	—	2	1	no	—
141	C₂²⋊#168	—	2	1	no	—
142	C₂²⋊#168	—	2	1	no	—
143	C₂²⋊#168	—	2	1	no	—
144	C₂²⋊#168	—	2	1	no	—
145	C₂²⋊#168	—	2	1	no	—
146	C₂²⋊#168	—	2	1	no	—
147	C₂²⋊#168	D₄	1	1	yes	characteristic
148	C₂²⋊#168	D₄	1	1	yes	characteristic
149	C₂²⋊#168	D₄	1	1	yes	characteristic
150	C₂²⋊#168	D₄	1	1	yes	characteristic
151	#3951	—	4	1	no	—
152	#3951	—	4	1	no	—
153	#3947	—	4	1	no	—
154	C₈×Dic₅	—	4	1	no	—
155	C₄⋊#168	—	2	1	no	—
156	C₄⋊#168	—	2	1	no	—
157	C₄⋊#168	—	2	1	no	—
158	C₄⋊#168	—	2	1	no	—
159	#3935	—	2	1	no	—
160	#3935	—	2	1	no	—
161	C₄×#168	—	2	1	no	—
162	C₄×#168	—	2	1	no	—
163	#2924	—	5	1	no	—
164	#2896	D₅	1	1	yes	characteristic
165	#2880	—	5	1	no	—
166	#1938	—	5	1	no	—
167	#1937	—	5	1	no	—
168	#1929	—	5	1	no	—
169	#1929	—	5	1	no	—
170	#1866	—	5	1	no	—
171	#1866	—	5	1	no	—
172	#1826	—	5	1	no	—
173	#1811	—	5	1	no	—
174	#1789	—	5	1	no	—
175	#1765	—	5	1	no	—
176	#1764	—	5	1	no	—
177	#1753	—	5	1	no	—
178	C₂⁴×C₅	—	2	1	no	—
179	C₂⁴×C₅	#41	1	1	yes	characteristic
180	C₅×#41	—	2	1	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	—	2	2	no	—
183	C₅×#41	—	2	2	no	—
184	C₅×#41	—	2	1	no	—
185	C₅×#41	—	2	1	no	—
186	C₅×#41	—	2	1	no	—
187	C₅×#41	—	2	1	no	—
188	C₅×#41	—	4	2	no	—
189	C₅×#41	—	4	2	no	—
190	C₅×#41	—	4	1	no	—
191	C₅×#41	—	4	1	no	—
192	C₅×#41	—	4	2	no	—
193	C₅×#41	—	4	2	no	—
194	C₅×#41	#41	1	2	yes	—
195	C₅×#41	#41	1	2	yes	—
196	C₂×C₅×Q₈	—	2	1	no	—
197	C₂×C₅×Q₈	—	2	2	no	—
198	C₂×C₅×Q₈	—	4	1	no	—
199	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	—	2	1	no	—
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	—	2	1	no	—
207	C₂×C₅×D₄	—	4	1	no	—
208	C₂×C₅×D₄	—	4	2	no	—
209	C₂×C₅×D₄	—	4	2	no	—
210	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	2	1	no	—
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	1	no	—
223	C₂²×C₄×C₅	—	4	2	no	—
224	C₂²×C₄×C₅	—	4	2	no	—
225	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₅	#41	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
231	C₂²×Dic₅	—	2	1	no	—
232	C₂²×Dic₅	—	2	1	no	—
233	C₅×M₁₆	—	4	1	no	—
234	C₅×M₁₆	—	4	1	no	—
235	C₅×M₁₆	—	4	1	no	—
236	C₅×M₁₆	—	4	1	no	—
237	C₂×C₅×C₈	—	2	1	no	—
238	C₂×C₅×C₈	—	2	1	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	1	no	—
241	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
242	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
245	C₅×C₄⋊C₄	—	2	1	no	—
246	C₅×C₄⋊C₄	—	2	1	no	—
247	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
248	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
249	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
250	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
251	C₅×C₂²⋊C₄	—	2	1	no	—
252	C₅×C₂²⋊C₄	—	2	1	no	—
253	C₅×C₂²⋊C₄	—	2	1	no	—
254	C₅×C₂²⋊C₄	—	2	1	no	—
255	C₄²×C₅	—	2	1	no	—
256	C₄²×C₅	—	2	1	no	—
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	—	2	1	no	—
259	C₂²⋊Dic₅	—	4	2	no	—
260	C₄×Dic₅	—	2	1	no	—
261	C₄×Dic₅	—	2	1	no	—
262	C₄×Dic₅	—	2	1	no	—
263	C₄×Dic₅	—	2	1	no	—
264	#681	—	2	1	no	—
265	#681	—	2	1	no	—
266	#681	—	2	1	no	—
267	#681	—	2	1	no	—
268	#681	—	2	1	no	—
269	#681	—	2	1	no	—
270	#681	—	2	1	no	—
271	#681	—	2	1	no	—
272	#681	—	4	2	no	—
273	#681	—	4	2	no	—
274	C₂×#168	—	2	1	no	—
275	C₂×#168	—	2	1	no	—
276	C₂×#168	—	2	1	no	—
277	C₂×#168	—	2	1	no	—
278	C₂×#168	—	2	1	no	—
279	C₂×#168	—	2	1	no	—
280	C₂×#168	—	2	1	no	—
281	C₂×#168	—	2	1	no	—
282	C₂×#168	—	4	2	no	—
283	C₂×#168	—	4	2	no	—
284	C₂×#168	C₂×D₄	1	1	yes	characteristic
285	C₂×#168	C₂×D₄	1	1	yes	characteristic
286	C₂×#168	C₂×D₄	1	1	yes	characteristic
287	C₂×#168	C₂×D₄	1	1	yes	characteristic
288	C₂²×#41	C₂×D₅	1	1	yes	characteristic
289	C₂×#131	—	5	1	no	—
290	C₂×#131	—	5	1	no	—
291	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
292	C₂×#117	C₂×D₅	1	1	yes	characteristic
293	#433	—	10	1	no	—
294	#433	—	10	1	no	—
295	#432	—	10	1	no	—
296	#431	—	10	1	no	—
297	C₂×#108	—	5	1	no	—
298	C₂×#108	—	5	1	no	—
299	#424	—	5	1	no	—
300	#424	—	5	1	no	—
301	C₂×#104	—	5	1	no	—
302	C₂×#104	—	5	1	no	—
303	C₂×#104	—	5	1	no	—
304	C₂×#104	—	5	1	no	—
305	#419	Dic₅	1	1	yes	characteristic, complemented
306	#419	Dic₅	1	1	yes	characteristic, complemented
307	#418	Dic₅	1	1	yes	characteristic, complemented
308	#418	Dic₅	1	1	yes	characteristic, complemented
309	#417	Dic₅	1	1	yes	characteristic, complemented
310	#417	Dic₅	1	1	yes	characteristic, complemented
311	#417	Dic₅	1	1	yes	characteristic, complemented
312	#417	Dic₅	1	1	yes	characteristic, complemented
313	#416	C₂×D₅	1	1	yes	characteristic
314	#416	C₂×D₅	1	1	yes	characteristic
315	#416	C₂×D₅	1	1	yes	characteristic
316	#416	C₂×D₅	1	1	yes	characteristic
317	#408	—	5	1	no	—
318	#408	—	5	1	no	—
319	#408	—	10	1	no	—
320	#408	—	10	1	no	—
321	#407	—	5	1	no	—
322	#407	—	5	1	no	—
323	#407	—	10	1	no	—
324	C₂×C₂²⋊C₈	—	5	1	no	—
325	C₂×C₂²⋊C₈	—	10	1	no	—
326	#405	—	5	1	no	—
327	#405	—	5	1	no	—
328	C₂×#97	—	5	1	no	—
329	C₂×C₄×C₈	—	5	1	no	—
330	C₄×C₂²⋊C₄	—	5	1	no	—
331	#341	—	5	1	no	—
332	#341	—	5	1	no	—
333	#339	—	5	1	no	—
334	#339	—	5	1	no	—
335	#339	—	5	1	no	—
336	#339	—	5	1	no	—
337	#336	—	5	1	no	—
338	#336	—	5	1	no	—
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	—	2	1	no	—
342	C₂³×C₅	—	2	1	no	—
343	C₂³×C₅	—	4	1	no	—
344	C₂³×C₅	—	4	1	no	—
345	C₂³×C₅	—	4	2	no	—
346	C₂³×C₅	—	4	2	no	—
347	C₂³×C₅	—	8	1	no	—
348	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
349	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
350	C₂³×C₅	C₂×#41	1	1	yes	characteristic
351	C₅×Q₈	—	2	1	no	—
352	C₅×Q₈	—	2	1	no	—
353	C₅×Q₈	—	2	1	no	—
354	C₅×Q₈	—	4	2	no	—
355	C₅×Q₈	#117	1	2	yes	—
356	C₅×D₄	—	2	2	no	—
357	C₅×D₄	—	2	2	no	—
358	C₅×D₄	—	2	1	no	—
359	C₅×D₄	—	2	1	no	—
360	C₅×D₄	—	2	1	no	—
361	C₅×D₄	—	4	2	no	—
362	C₅×D₄	—	4	2	no	—
363	C₅×D₄	—	4	2	no	—
364	C₅×D₄	—	4	1	no	—
365	C₅×D₄	—	4	1	no	—
366	C₅×D₄	#117	1	2	yes	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	2	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	4	2	no	—
386	C₂×C₄×C₅	—	4	2	no	—
387	C₂×C₄×C₅	—	4	2	no	—
388	C₂×C₄×C₅	—	4	2	no	—
389	C₂×C₄×C₅	—	4	1	no	—
390	C₂×C₄×C₅	—	4	1	no	—
391	C₂×C₄×C₅	—	8	1	no	—
392	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
393	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
394	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
395	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
397	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
398	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
400	C₂×Dic₅	—	2	2	no	—
401	C₂×Dic₅	—	4	1	no	—
402	C₂×Dic₅	—	4	1	no	—
403	C₂×Dic₅	—	4	1	no	—
404	C₂×Dic₅	—	4	1	no	—
405	C₂×Dic₅	—	4	1	no	—
406	C₅×C₈	—	2	1	no	—
407	C₅×C₈	—	2	1	no	—
408	C₅×C₈	—	2	1	no	—
409	C₅×C₈	—	2	1	no	—
410	#168	—	2	1	no	—
411	#168	—	2	1	no	—
412	#168	—	2	1	no	—
413	#168	—	2	1	no	—
414	#168	—	4	1	no	—
415	#168	—	4	1	no	—
416	#168	—	4	1	no	—
417	#168	—	4	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	4	1	no	—
423	C₂×#41	—	4	1	no	—
424	C₂×#41	C₂×Dic₅	1	1	yes	characteristic
425	C₂×#41	C₂×Dic₅	1	1	yes	characteristic
426	C₂×#41	C₂²×D₅	1	1	yes	characteristic
427	C₂×#41	C₂²×D₅	1	1	yes	characteristic
428	C₂²×Q₈	C₂×Dic₅	1	1	yes	characteristic
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	C₂×Dic₅	1	1	yes	characteristic
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
433	#131	—	10	2	no	—
434	#131	—	10	2	no	—
435	#131	—	20	1	no	—
436	#131	—	20	1	no	—
437	C₂×M₁₆	—	4	1	no	—
438	C₂×M₁₆	—	4	1	no	—
439	C₂×M₁₆	—	5	1	no	—
440	C₂×M₁₆	—	5	1	no	—
441	C₂×M₁₆	—	5	1	no	—
442	C₂×M₁₆	—	5	1	no	—
443	C₂×M₁₆	—	10	1	no	—
444	C₂×M₁₆	—	10	1	no	—
445	C₂×M₁₆	C₂×Dic₅	1	1	yes	characteristic
446	C₂×M₁₆	C₂×Dic₅	1	1	yes	characteristic
447	C₂×M₁₆	C₂×Dic₅	1	1	yes	characteristic
448	C₂×M₁₆	C₂×Dic₅	1	1	yes	characteristic
449	C₂²×C₈	—	5	1	no	—
450	C₂²×C₈	—	5	1	no	—
451	C₂²×C₈	—	10	1	no	—
452	C₂²×C₈	—	10	1	no	—
453	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
454	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
455	#117	—	2	1	no	—
456	#117	—	2	1	no	—
457	#117	C₂×Dic₅	1	1	yes	characteristic
458	#117	C₂×Dic₅	1	1	yes	characteristic
459	#117	C₂²×D₅	1	1	yes	characteristic
460	#117	C₂²×D₅	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	10	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	5	1	no	—
467	C₂×C₄²	—	5	1	no	—
468	#108	—	20	1	no	—
469	#108	—	20	1	no	—
470	C₄⋊C₈	—	10	1	no	—
471	C₄⋊C₈	—	10	1	no	—
472	C₄⋊C₈	—	10	1	no	—
473	C₄⋊C₈	—	10	1	no	—
474	#104	—	10	2	no	—
475	#104	—	10	2	no	—
476	#104	—	20	1	no	—
477	#104	—	20	1	no	—
478	#103	C₂×Dic₅	1	1	yes	characteristic
479	#103	C₂×Dic₅	1	1	yes	characteristic
480	#103	C₂×Dic₅	1	1	yes	characteristic
481	#103	C₂×Dic₅	1	1	yes	characteristic
482	#103	C₂×Dic₅	1	1	yes	characteristic
483	#103	C₂×Dic₅	1	1	yes	characteristic
484	#103	C₂×Dic₅	1	1	yes	characteristic
485	#103	C₂×Dic₅	1	1	yes	characteristic
486	#102	C₂×Dic₅	1	1	yes	characteristic
487	#102	C₂×Dic₅	1	1	yes	characteristic
488	#102	C₂×Dic₅	1	1	yes	characteristic
489	#102	C₂×Dic₅	1	1	yes	characteristic
490	#102	C₂×Dic₅	1	1	yes	characteristic
491	#102	C₂×Dic₅	1	1	yes	characteristic
492	#102	C₂×Dic₅	1	1	yes	characteristic
493	#102	C₂×Dic₅	1	1	yes	characteristic
494	C₂²⋊C₈	—	5	1	no	—
495	C₂²⋊C₈	—	5	1	no	—
496	C₂²⋊C₈	—	5	1	no	—
497	C₂²⋊C₈	—	5	1	no	—
498	C₂²⋊C₈	—	10	1	no	—
499	C₂²⋊C₈	—	10	1	no	—
500	C₂²⋊C₈	—	10	1	no	—
501	C₂²⋊C₈	—	10	1	no	—
502	C₂²⋊C₈	—	10	1	no	—
503	C₂²⋊C₈	—	10	1	no	—
504	C₂²⋊C₈	—	10	1	no	—
505	C₂²⋊C₈	—	10	1	no	—
506	#97	—	10	1	no	—
507	#97	—	10	1	no	—
508	#97	—	20	1	no	—
509	C₄×C₈	—	10	1	no	—
510	C₄×C₈	—	10	1	no	—
511	C₄×C₈	—	20	1	no	—
512	#95	—	10	1	no	—
513	C₂²×C₅	—	2	1	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	1	no	—
516	C₂²×C₅	—	2	1	no	—
517	C₂²×C₅	—	2	2	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	1	no	—
521	C₂²×C₅	—	2	1	no	—
522	C₂²×C₅	—	4	1	no	—
523	C₂²×C₅	—	4	1	no	—
524	C₂²×C₅	—	4	1	no	—
525	C₂²×C₅	—	4	1	no	—
526	C₂²×C₅	—	4	1	no	—
527	C₂²×C₅	—	8	1	no	—
528	C₂²×C₅	—	8	1	no	—
529	C₂²×C₅	—	8	4	no	—
530	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
531	C₂²×C₅	#551	1	1	yes	characteristic
532	C₂²×C₅	#551	1	1	yes	characteristic
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	—	2	1	no	—
535	C₄×C₅	—	2	2	no	—
536	C₄×C₅	—	4	1	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	4	1	no	—
539	C₄×C₅	—	4	1	no	—
540	C₄×C₅	—	4	1	no	—
541	C₄×C₅	C₂×#117	1	1	yes	characteristic
542	C₄×C₅	#518	1	1	yes	characteristic
543	C₄×C₅	#546	1	1	yes	characteristic
544	C₄×C₅	#546	1	1	yes	characteristic
545	Dic₅	—	4	2	no	—
546	Dic₅	—	8	1	no	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	#711	1	1	yes	characteristic
549	#41	—	2	1	no	—
550	#41	—	2	1	no	—
551	#41	—	2	2	no	—
552	#41	—	2	2	no	—
553	#41	—	2	1	no	—
554	#41	—	2	1	no	—
555	#41	—	2	1	no	—
556	#41	—	2	1	no	—
557	#41	—	4	2	no	—
558	#41	—	4	2	no	—
559	#41	—	4	1	no	—
560	#41	—	4	1	no	—
561	#41	—	4	2	no	—
562	#41	—	4	2	no	—
563	#41	#709	1	2	yes	—
564	#41	#709	1	2	yes	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	4	1	no	—
568	C₂×Q₈	C₂²×Dic₅	1	1	yes	characteristic
569	C₂×Q₈	C₂²×Dic₅	1	1	yes	characteristic
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
580	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	10	1	no	—
595	C₂²×C₄	—	10	1	no	—
596	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
597	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
598	C₂²×C₄	#711	1	1	yes	characteristic
599	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
600	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
601	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
602	M₁₆	—	4	1	no	—
603	M₁₆	—	4	1	no	—
604	M₁₆	—	4	1	no	—
605	M₁₆	—	4	1	no	—
606	M₁₆	—	10	1	no	—
607	M₁₆	—	10	1	no	—
608	M₁₆	—	10	1	no	—
609	M₁₆	—	10	1	no	—
610	M₁₆	—	10	1	no	—
611	M₁₆	—	10	1	no	—
612	M₁₆	—	10	1	no	—
613	M₁₆	—	10	1	no	—
614	M₁₆	—	20	2	no	—
615	M₁₆	—	20	2	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	5	1	no	—
621	C₂×C₈	—	5	1	no	—
622	C₂×C₈	—	5	1	no	—
623	C₂×C₈	—	5	1	no	—
624	C₂×C₈	—	10	1	no	—
625	C₂×C₈	—	10	1	no	—
626	C₂×C₈	—	10	1	no	—
627	C₂×C₈	—	10	1	no	—
628	C₂×C₈	—	10	1	no	—
629	C₂×C₈	—	10	1	no	—
630	C₂×C₈	—	10	1	no	—
631	C₂×C₈	—	10	1	no	—
632	C₂×C₈	—	20	2	no	—
633	C₂×C₈	—	20	2	no	—
634	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
635	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
636	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
637	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
641	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
642	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
643	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	20	2	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	10	1	no	—
654	C₄²	—	10	1	no	—
655	C₄²	—	10	1	no	—
656	C₄²	—	10	1	no	—
657	C₂×C₅	—	2	1	no	—
658	C₂×C₅	—	2	1	no	—
659	C₂×C₅	—	4	1	no	—
660	C₂×C₅	—	4	1	no	—
661	C₂×C₅	—	4	2	no	—
662	C₂×C₅	—	8	1	no	—
663	C₂×C₅	#2342	1	1	yes	characteristic
664	C₂×C₅	#2955	1	1	yes	characteristic
665	C₂×C₅	#2956	1	1	yes	characteristic
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	8	1	no	—
675	C₂³	D₄×Dic₅	1	1	yes	characteristic
676	C₂³	D₄×Dic₅	1	1	yes	characteristic
677	C₂³	C₂×#711	1	1	yes	characteristic
678	Q₈	—	2	1	no	—
679	Q₈	—	2	1	no	—
680	Q₈	—	2	1	no	—
681	Q₈	—	4	2	no	—
682	Q₈	#4072	1	2	yes	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	2	1	no	—
686	D₄	—	2	1	no	—
687	D₄	—	2	1	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	1	no	—
692	D₄	—	4	1	no	—
693	D₄	#4072	1	2	yes	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	8	1	no	—
719	C₂×C₄	—	10	2	no	—
720	C₂×C₄	—	20	1	no	—
721	C₂×C₄	—	20	1	no	—
722	C₂×C₄	—	20	1	no	—
723	C₂×C₄	—	20	1	no	—
724	C₂×C₄	—	20	1	no	—
725	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
726	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
727	C₂×C₄	C₂×#709	1	1	yes	characteristic
728	C₂×C₄	C₂×#709	1	1	yes	characteristic
729	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
730	C₂×C₄	#4144	1	1	yes	characteristic
731	C₂×C₄	#4144	1	1	yes	characteristic
732	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
733	C₈	—	2	1	no	—
734	C₈	—	2	1	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	1	no	—
737	C₈	—	10	1	no	—
738	C₈	—	10	1	no	—
739	C₈	—	10	1	no	—
740	C₈	—	10	1	no	—
741	C₈	—	20	1	no	—
742	C₈	—	20	1	no	—
743	C₈	—	20	1	no	—
744	C₈	—	20	1	no	—
745	C₅	#22588	1	1	yes	characteristic, complemented, Sylow
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	4	no	—
763	C₂²	#65829	1	1	yes	characteristic
764	C₂²	#65829	1	1	yes	characteristic
765	C₂²	C₂×D₄×Dic₅	1	1	yes	characteristic
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	20	2	no	—
775	C₄	—	40	1	no	—
776	C₄	#65824	1	1	yes	characteristic
777	C₄	#65824	1	1	yes	characteristic
778	C₄	C₂×#4072	1	1	yes	characteristic
779	C₄	#66132	1	1	yes	characteristic
780	C₂	—	2	1	no	—
781	C₂	—	2	1	no	—
782	C₂	—	4	1	no	—
783	C₂	—	4	1	no	—
784	C₂	—	4	2	no	—
785	C₂	—	8	1	no	—
786	C₂	#10613828	1	1	yes	characteristic
787	C₂	#10615730	1	1	yes	characteristic
788	C₂	#10615731	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#2896	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂²×C₅×#41	C₂²
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#2896	D₅
hypocenter	C₅	#22588
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2896

Complements

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

N	H ≅ G/N	type
3. #10613941	C₂	semidirect
5. #10602793	C₂	semidirect
6. #10602776	C₂	semidirect
7. #10602383	C₂	semidirect
8. #10601085	C₂	semidirect
9. #10601085	C₂	semidirect
10. #10601084	C₂	semidirect
11. #10601084	C₂	semidirect
12. #10601083	C₂	semidirect
13. #10601082	C₂	semidirect
14. #10601081	C₂	semidirect
15. #10601080	C₂	semidirect
21. C₅×#419	C₄	semidirect
22. C₅×#419	C₄	semidirect
23. C₅×#418	C₄	semidirect
24. C₅×#418	C₄	semidirect
25. C₅×#417	C₄	semidirect
26. C₅×#417	C₄	semidirect
27. C₅×#417	C₄	semidirect
28. C₅×#417	C₄	semidirect
47. C₂×#3951	C₂²	semidirect
48. C₂×#3951	C₂²	semidirect
49. C₂×#3947	C₂²	semidirect
50. C₂×C₈×Dic₅	C₂²	semidirect
53. #65288	C₂²	semidirect
54. #65288	C₂²	semidirect
55. #65286	C₂²	semidirect
56. #65286	C₂²	semidirect
59. #64772	C₂²	semidirect
60. #64772	C₂²	semidirect
61. #64770	C₂²	semidirect
62. #64770	C₂²	semidirect
63. #64752	C₂²	semidirect
64. #64752	C₂²	semidirect
65. #64752	C₂²	semidirect
66. #64752	C₂²	semidirect
305. #419	Dic₅	semidirect
306. #419	Dic₅	semidirect
307. #418	Dic₅	semidirect
308. #418	Dic₅	semidirect
309. #417	Dic₅	semidirect
310. #417	Dic₅	semidirect
311. #417	Dic₅	semidirect
312. #417	Dic₅	semidirect
745. C₅	#22588	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2896	2
#10615806	2
#10613941	2
#10602931	2
#10602793	2
#10602776	2
#10602383	2
#10601085	2
#10601084	2
#10601083	2
#10601082	2
#10601081	2
#10601080	2
#22588	5