Subgroups — #12117753

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2906	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#65434	C₂	1	1	yes	maximal, characteristic
3	C₂×#65433	C₂	1	1	yes	maximal, characteristic
4	#10614237	C₂	1	1	yes	maximal, characteristic
5	#10610743	C₂	1	1	yes	maximal, characteristic, complemented
6	#10602810	C₂	1	1	yes	maximal, characteristic, complemented
7	#10602810	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602439	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601338	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601338	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601331	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601330	C₂	1	1	yes	maximal, characteristic, complemented
13	#10601322	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601312	C₂	1	1	yes	maximal, characteristic, complemented
15	#10601260	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#131	C₂²	1	1	yes	characteristic
17	C₂×C₅×#131	C₂²	1	1	yes	characteristic
18	C₄×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×#4096	C₂²	1	1	yes	characteristic
20	C₂×#4047	C₂²	1	1	yes	characteristic
21	C₂×#4047	C₂²	1	1	yes	characteristic
22	C₄×#709	C₂²	1	1	yes	characteristic
23	C₅×#424	—	2	1	no	—
24	C₅×#424	—	2	1	no	—
25	C₅×#424	C₂²	1	1	yes	characteristic
26	C₅×#424	C₂²	1	1	yes	characteristic
27	C₅×#423	—	2	1	no	—
28	C₅×#423	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	—	2	1	no	—
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×#3969	C₂²	1	1	yes	characteristic
32	C₂×#3969	C₂²	1	1	yes	characteristic
33	#65522	C₂²	1	1	yes	characteristic
34	#65434	—	2	4	no	—
35	#65433	—	2	4	no	—
36	C₂×#3957	C₂²	1	1	yes	characteristic
37	C₂×#3957	C₂²	1	1	yes	characteristic
38	C₂×#3954	C₂²	1	1	yes	characteristic
39	C₂×#3954	C₂²	1	1	yes	characteristic
40	C₂×#3954	C₂²	1	1	yes	characteristic
41	C₂×#3954	C₂²	1	1	yes	characteristic
42	#65391	C₂²	1	1	yes	characteristic
43	#65391	C₂²	1	1	yes	characteristic
44	C₂×#3947	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
46	#65319	C₄	1	1	yes	characteristic, complemented
47	#65319	C₄	1	1	yes	characteristic, complemented
48	#65315	C₄	1	1	yes	characteristic, complemented
49	#65315	C₄	1	1	yes	characteristic, complemented
50	#65307	C₄	1	1	yes	characteristic, complemented
51	#65307	C₄	1	1	yes	characteristic, complemented
52	#65303	C₄	1	1	yes	characteristic, complemented
53	#65303	C₄	1	1	yes	characteristic, complemented
54	#65291	C₂²	1	1	yes	characteristic
55	#65287	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
57	#65213	C₂²	1	1	yes	characteristic
58	C₂×#3935	C₂²	1	1	yes	characteristic
59	#65128	—	2	1	no	—
60	#65128	—	2	1	no	—
61	#65126	—	2	1	no	—
62	D₅×C₄⋊C₈	—	2	1	no	—
63	#64775	C₂²	1	1	yes	characteristic
64	#64775	C₂²	1	1	yes	characteristic
65	#64770	C₂²	1	1	yes	characteristic
66	#64770	C₂²	1	1	yes	characteristic
67	#64752	C₂²	1	1	yes	characteristic
68	#64752	C₂²	1	1	yes	characteristic
69	#22687	—	5	1	no	maximal, Sylow
70	C₂×C₅×#41	C₂³	1	1	yes	characteristic
71	C₂×#709	C₂³	1	1	yes	characteristic
72	C₅×#131	—	2	2	no	—
73	C₅×#131	—	2	2	no	—
74	C₅×#131	—	4	1	no	—
75	C₅×#131	—	4	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	1	no	—
78	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	—	2	1	no	—
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
85	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×D₄	—	2	1	no	—
87	C₄×C₅×D₄	—	2	1	no	—
88	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
89	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
90	C₅×#117	—	2	1	no	—
91	C₅×#117	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅	—	2	1	no	—
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	#4096	D₄	1	4	yes	—
95	#4096	Q₈	1	4	yes	—
96	C₂×#689	C₂×C₄	1	1	yes	characteristic
97	C₂×#688	C₂×C₄	1	1	yes	characteristic
98	C₂×#687	C₂×C₄	1	1	yes	characteristic
99	C₂×#686	C₂×C₄	1	1	yes	characteristic
100	C₄×C₂²⋊D₅	—	2	1	no	—
101	C₄×C₂²⋊D₅	—	2	1	no	—
102	#4072	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊Dic₅	—	2	1	no	—
104	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
105	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
106	C₂×#681	C₂³	1	1	yes	characteristic
107	C₂×#681	C₂³	1	1	yes	characteristic
108	C₂²×#168	C₂³	1	1	yes	characteristic
109	C₂²×#168	C₂³	1	1	yes	characteristic
110	#4047	—	2	2	no	—
111	#4047	—	2	2	no	—
112	#4047	—	4	1	no	—
113	#4047	—	4	1	no	—
114	C₂×#676	—	2	1	no	—
115	C₂×#676	—	2	1	no	—
116	C₂×C₈×D₅	—	2	1	no	—
117	C₂×C₈×D₅	—	2	1	no	—
118	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
119	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
120	#4018	—	2	1	no	—
121	C₄²×D₅	—	2	1	no	—
122	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
123	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
124	C₅×C₄⋊C₈	—	2	1	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	—	2	1	no	—
127	C₅×C₄⋊C₈	—	2	1	no	—
128	C₅×C₄⋊C₈	—	2	1	no	—
129	C₅×C₄⋊C₈	—	2	1	no	—
130	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
131	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
132	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
133	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
134	#3969	—	2	2	no	—
135	#3969	—	2	2	no	—
136	#3967	C₂×C₄	1	1	yes	characteristic
137	#3967	C₂×C₄	1	1	yes	characteristic
138	#3964	C₂×C₄	1	1	yes	characteristic
139	#3964	C₂×C₄	1	1	yes	characteristic
140	#3963	—	2	1	no	—
141	#3957	—	2	2	no	—
142	#3957	—	2	2	no	—
143	#3954	—	2	2	no	—
144	#3954	—	2	2	no	—
145	#3954	—	4	1	no	—
146	#3954	—	4	1	no	—
147	#3947	—	2	2	no	—
148	#3946	—	2	1	no	—
149	#3946	—	2	1	no	—
150	#3946	—	2	1	no	—
151	#3946	—	2	1	no	—
152	C₈×Dic₅	—	2	2	no	—
153	#3942	C₂×C₄	1	1	yes	characteristic
154	#3942	C₂×C₄	1	1	yes	characteristic
155	#3941	C₂×C₄	1	1	yes	characteristic
156	#3941	C₂×C₄	1	1	yes	characteristic
157	#3940	C₂×C₄	1	1	yes	characteristic
158	#3940	C₂×C₄	1	1	yes	characteristic
159	#3939	C₂×C₄	1	1	yes	characteristic
160	#3939	C₂×C₄	1	1	yes	characteristic
161	C₄⋊#168	—	2	1	no	—
162	C₄⋊#168	—	2	1	no	—
163	#3935	C₂×C₄	1	1	yes	characteristic
164	#3935	C₂×C₄	1	1	yes	characteristic
165	#3935	C₂×C₄	1	1	yes	characteristic
166	#3935	C₂×C₄	1	1	yes	characteristic
167	C₂×#444	—	5	1	no	—
168	C₂×#443	—	5	1	no	—
169	#2943	—	5	1	no	—
170	#2906	—	5	1	no	—
171	#2906	D₅	1	1	yes	characteristic, complemented
172	#1946	—	5	1	no	—
173	#1945	—	5	1	no	—
174	#1866	—	5	1	no	—
175	#1866	—	5	1	no	—
176	#1866	—	5	1	no	—
177	#1866	—	5	1	no	—
178	#1849	—	5	1	no	—
179	#1806	—	5	1	no	—
180	#1806	—	5	1	no	—
181	#1771	—	5	1	no	—
182	C₅×#41	—	2	1	no	—
183	C₅×#41	—	2	1	no	—
184	C₅×#41	C₂×D₄	1	2	yes	—
185	C₅×#41	C₂×Q₈	1	2	yes	—
186	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×D₄	—	2	1	no	—
188	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	#41	1	1	yes	characteristic
193	C₂²×C₄×C₅	#41	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
195	C₂×C₂²⋊D₅	—	2	1	no	—
196	C₂²×Dic₅	—	2	1	no	—
197	C₂²×Dic₅	—	2	1	no	—
198	#709	—	2	1	no	—
199	#709	—	2	1	no	—
200	#709	C₂×D₄	1	2	yes	—
201	#709	C₂×Q₈	1	2	yes	—
202	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄×D₅	—	2	1	no	—
204	C₂×C₄×D₅	—	2	1	no	—
205	C₂×C₄×D₅	—	2	1	no	—
206	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
207	C₅×M₁₆	—	2	1	no	—
208	C₅×M₁₆	—	2	1	no	—
209	C₅×M₁₆	—	2	1	no	—
210	C₅×M₁₆	—	2	1	no	—
211	C₅×M₁₆	—	4	2	no	—
212	C₅×M₁₆	—	4	2	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	4	2	no	—
220	C₂×C₅×C₈	—	4	2	no	—
221	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
223	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
224	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
228	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
229	C₅×C₂²⋊C₄	—	2	1	no	—
230	C₅×C₂²⋊C₄	—	2	1	no	—
231	C₅×C₂²⋊C₄	—	2	1	no	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	—	2	1	no	—
234	C₄²×C₅	—	2	1	no	—
235	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
236	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
237	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
239	C₂²⋊Dic₅	—	2	1	no	—
240	#689	C₄⋊C₄	1	4	yes	complemented
241	#688	C₄⋊C₄	1	4	yes	complemented
242	#687	C₄⋊C₄	1	4	yes	complemented
243	#686	C₄⋊C₄	1	4	yes	complemented
244	#685	—	2	1	no	—
245	#685	—	2	1	no	—
246	C₄⋊Dic₅	—	4	2	no	—
247	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
248	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
249	#683	—	2	1	no	—
250	#683	—	2	1	no	—
251	C₄×Dic₅	—	2	1	no	—
252	C₄×Dic₅	—	2	1	no	—
253	C₄×Dic₅	—	2	1	no	—
254	C₄×Dic₅	—	2	1	no	—
255	C₄×Dic₅	—	2	1	no	—
256	C₄×Dic₅	—	2	1	no	—
257	C₄×Dic₅	—	2	1	no	—
258	#681	—	2	1	no	—
259	#681	—	2	1	no	—
260	#681	—	2	1	no	—
261	#681	—	2	1	no	—
262	C₂×#168	—	2	1	no	—
263	C₂×#168	—	2	1	no	—
264	C₂×#168	—	2	1	no	—
265	C₂×#168	—	2	1	no	—
266	C₂×#168	C₂²×C₄	1	1	yes	characteristic
267	C₂×#168	C₂²×C₄	1	1	yes	characteristic
268	C₂×#168	C₂²×C₄	1	1	yes	characteristic
269	C₂×#168	C₂²×C₄	1	1	yes	characteristic
270	C₂×#168	C₂×D₄	1	2	yes	—
271	C₂×#168	C₂×Q₈	1	2	yes	—
272	#676	—	4	2	no	—
273	#676	—	4	2	no	—
274	C₈×D₅	—	4	2	no	—
275	C₈×D₅	—	4	2	no	—
276	C₂×#135	—	5	1	no	—
277	C₂×#131	—	5	1	no	—
278	C₂×#131	—	5	1	no	—
279	C₂×#131	C₂×D₅	1	1	yes	characteristic
280	C₂×#131	C₂×D₅	1	1	yes	characteristic
281	C₄×#41	—	5	1	no	—
282	C₄×#41	C₂×D₅	1	1	yes	characteristic
283	#444	—	10	4	no	—
284	#443	—	10	4	no	—
285	#442	—	5	1	no	—
286	#442	—	5	1	no	—
287	#441	—	5	1	no	—
288	#441	—	5	1	no	—
289	#440	—	5	1	no	—
290	#440	—	5	1	no	—
291	#440	—	5	1	no	—
292	#440	—	5	1	no	—
293	C₂×#108	—	5	1	no	—
294	C₂×#108	—	5	1	no	—
295	C₂×#108	—	5	1	no	—
296	C₂×#108	—	5	1	no	—
297	#427	—	5	1	no	—
298	#424	—	2	1	no	—
299	#424	—	2	1	no	—
300	#424	—	5	1	no	—
301	#424	—	5	1	no	—
302	#424	—	10	1	no	—
303	#424	—	10	1	no	—
304	#424	C₂×D₅	1	1	yes	characteristic
305	#424	C₂×D₅	1	1	yes	characteristic
306	#423	—	2	1	no	—
307	#423	—	5	1	no	—
308	#423	—	10	1	no	—
309	#423	C₂×D₅	1	1	yes	characteristic
310	C₂×C₄⋊C₈	—	2	1	no	—
311	C₂×C₄⋊C₈	—	10	1	no	—
312	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
313	C₂×#104	—	5	1	no	—
314	C₂×#104	—	5	1	no	—
315	C₂×#104	—	5	1	no	—
316	C₂×#104	—	5	1	no	—
317	#416	—	5	1	no	—
318	#416	—	5	1	no	—
319	C₂×#97	—	5	1	no	—
320	C₂×#97	—	5	1	no	—
321	C₂×C₄×C₈	—	5	1	no	—
322	C₄×C₄⋊C₄	—	5	1	no	—
323	#339	—	5	1	no	—
324	#339	—	5	1	no	—
325	#339	—	5	1	no	—
326	#339	—	5	1	no	—
327	#336	—	5	1	no	—
328	#336	—	5	1	no	—
329	C₂³×C₅	—	2	1	no	—
330	C₂³×C₅	C₂×#41	1	1	yes	characteristic
331	C₂²×D₅	—	2	1	no	—
332	C₅×Q₈	—	2	1	no	—
333	C₅×Q₈	C₂×C₄⋊C₄	1	2	yes	—
334	C₅×D₄	—	2	2	no	—
335	C₅×D₄	—	2	2	no	—
336	C₅×D₄	—	2	1	no	—
337	C₅×D₄	C₂×C₄⋊C₄	1	2	yes	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	2	no	—
346	C₂×C₄×C₅	—	8	1	no	—
347	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
348	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
349	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
350	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
355	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
356	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
357	C₂²⋊D₅	—	2	2	no	—
358	C₂²⋊D₅	—	2	2	no	—
359	C₂×Dic₅	—	2	1	no	—
360	C₂×Dic₅	—	2	2	no	—
361	C₂×Dic₅	—	2	1	no	—
362	C₂×Dic₅	—	2	1	no	—
363	C₂×Dic₅	—	4	1	no	—
364	C₂×Dic₅	—	4	1	no	—
365	C₂×Dic₅	—	4	1	no	—
366	C₂×Dic₅	—	4	1	no	—
367	C₂×Dic₅	—	4	1	no	—
368	D₂₀	—	2	1	no	—
369	D₂₀	C₂×C₄⋊C₄	1	2	yes	—
370	C₄×D₅	—	2	2	no	—
371	C₄×D₅	—	2	2	no	—
372	C₄×D₅	—	4	2	no	—
373	C₄×D₅	—	8	1	no	—
374	Dic₁₀	—	2	1	no	—
375	Dic₁₀	C₂×C₄⋊C₄	1	2	yes	—
376	C₅×C₈	—	2	1	no	—
377	C₅×C₈	—	2	1	no	—
378	C₅×C₈	—	2	1	no	—
379	C₅×C₈	—	2	1	no	—
380	C₅×C₈	—	4	1	no	—
381	C₅×C₈	—	4	1	no	—
382	#168	—	2	1	no	—
383	#168	—	2	1	no	—
384	#168	—	4	1	no	—
385	#168	—	4	1	no	—
386	#168	C₂×C₄⋊C₄	1	2	yes	—
387	#168	C₂×C₄⋊C₄	1	2	yes	—
388	C₂×#41	—	5	1	no	—
389	C₂×#41	C₂²×D₅	1	1	yes	characteristic
390	#135	—	5	4	no	—
391	#135	—	5	4	no	—
392	C₂×Q₁₆	—	5	1	no	—
393	C₂×SD₁₆	—	5	1	no	—
394	C₂×SD₁₆	—	5	1	no	—
395	C₂×D₈	—	5	1	no	—
396	#131	—	2	2	no	—
397	#131	—	2	2	no	—
398	#131	—	4	1	no	—
399	#131	—	4	1	no	—
400	#131	—	10	2	no	—
401	#131	—	10	2	no	—
402	#131	—	20	1	no	—
403	#131	—	20	1	no	—
404	C₂×M₁₆	—	2	1	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂×M₁₆	—	5	1	no	—
407	C₂×M₁₆	—	5	1	no	—
408	C₂×M₁₆	—	10	1	no	—
409	C₂×M₁₆	—	10	1	no	—
410	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
411	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
412	C₂²×C₈	—	2	1	no	—
413	C₂²×C₈	—	2	1	no	—
414	C₂²×C₈	—	5	1	no	—
415	C₂²×C₈	—	5	1	no	—
416	C₂²×C₈	—	10	1	no	—
417	C₂²×C₈	—	10	1	no	—
418	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
419	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
420	C₄×Q₈	—	5	1	no	—
421	C₄×Q₈	—	5	1	no	—
422	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
423	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	5	1	no	—
427	C₄×D₄	—	5	1	no	—
428	C₄×D₄	—	10	1	no	—
429	C₄×D₄	—	10	1	no	—
430	C₄×D₄	C₄×D₅	1	1	yes	characteristic
431	C₄×D₄	C₄×D₅	1	1	yes	characteristic
432	#117	—	2	1	no	—
433	#117	—	5	1	no	—
434	#117	—	10	1	no	—
435	#117	C₂²×D₅	1	1	yes	characteristic
436	C₂×C₄⋊C₄	—	10	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	5	1	no	—
439	C₂×C₄²	—	5	1	no	—
440	C₂×C₄²	—	10	1	no	—
441	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
442	#108	—	10	2	no	—
443	#108	—	10	2	no	—
444	#108	—	20	1	no	—
445	#108	—	20	1	no	—
446	#107	—	5	1	no	—
447	#107	—	5	1	no	—
448	#106	—	5	1	no	—
449	#106	—	5	1	no	—
450	C₄⋊C₈	—	2	1	no	—
451	C₄⋊C₈	—	2	1	no	—
452	C₄⋊C₈	—	2	1	no	—
453	C₄⋊C₈	—	2	1	no	—
454	C₄⋊C₈	—	2	1	no	—
455	C₄⋊C₈	—	2	1	no	—
456	C₄⋊C₈	—	10	1	no	—
457	C₄⋊C₈	—	10	1	no	—
458	C₄⋊C₈	—	10	1	no	—
459	C₄⋊C₈	—	10	1	no	—
460	C₄⋊C₈	—	10	1	no	—
461	C₄⋊C₈	—	10	1	no	—
462	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
463	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
464	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
465	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
466	#104	—	10	2	no	—
467	#104	—	10	2	no	—
468	#104	—	10	2	no	—
469	#104	—	10	2	no	—
470	#103	—	5	1	no	—
471	#103	—	5	1	no	—
472	#103	—	5	1	no	—
473	#103	—	5	1	no	—
474	#102	—	5	1	no	—
475	#102	—	5	1	no	—
476	#102	—	5	1	no	—
477	#102	—	5	1	no	—
478	#97	—	5	1	no	—
479	#97	—	5	1	no	—
480	#97	—	5	1	no	—
481	#97	—	5	1	no	—
482	#97	—	10	2	no	—
483	C₄×C₈	—	10	2	no	—
484	#95	—	10	1	no	—
485	C₂²×C₅	—	2	1	no	—
486	C₂²×C₅	—	2	1	no	—
487	C₂²×C₅	—	2	2	no	—
488	C₂²×C₅	—	4	1	no	—
489	C₂²×C₅	—	4	1	no	—
490	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
491	C₂²×C₅	#547	1	1	yes	characteristic
492	C₂²×C₅	#554	1	1	yes	characteristic
493	C₂×D₅	—	2	2	no	—
494	C₂×D₅	—	4	1	no	—
495	C₂×D₅	—	4	1	no	—
496	C₄×C₅	—	2	2	no	—
497	C₄×C₅	—	2	1	no	—
498	C₄×C₅	—	2	1	no	—
499	C₄×C₅	—	2	1	no	—
500	C₄×C₅	—	2	1	no	—
501	C₄×C₅	—	4	1	no	—
502	C₄×C₅	—	4	1	no	—
503	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
504	C₄×C₅	#520	1	1	yes	characteristic
505	C₄×C₅	D₄²	1	1	yes	characteristic
506	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
507	Dic₅	—	2	2	no	—
508	Dic₅	—	4	2	no	—
509	Dic₅	—	4	1	no	—
510	Dic₅	—	4	1	no	—
511	Dic₅	—	8	1	no	—
512	#41	—	2	1	no	—
513	#41	—	2	1	no	—
514	#41	—	5	2	no	—
515	#41	—	5	2	no	—
516	#41	—	10	1	no	—
517	#41	—	10	1	no	—
518	#41	D₄×D₅	1	2	yes	—
519	#41	Q₈×D₅	1	2	yes	—
520	C₂×Q₈	—	5	1	no	—
521	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	5	1	no	—
524	C₂×D₄	—	10	1	no	—
525	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	10	1	no	—
530	C₂²×C₄	—	10	1	no	—
531	C₂²×C₄	—	10	1	no	—
532	C₂²×C₄	—	10	1	no	—
533	C₂²×C₄	—	10	1	no	—
534	C₂²×C₄	#709	1	1	yes	characteristic
535	C₂²×C₄	#709	1	1	yes	characteristic
536	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
537	Q₁₆	—	5	4	no	—
538	SD₁₆	—	5	4	no	—
539	SD₁₆	—	5	4	no	—
540	D₈	—	5	4	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	—	2	1	no	—
543	M₁₆	—	2	1	no	—
544	M₁₆	—	2	1	no	—
545	M₁₆	—	4	2	no	—
546	M₁₆	—	4	2	no	—
547	M₁₆	—	10	1	no	—
548	M₁₆	—	10	1	no	—
549	M₁₆	—	10	1	no	—
550	M₁₆	—	10	1	no	—
551	M₁₆	—	20	2	no	—
552	M₁₆	—	20	2	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	4	2	no	—
560	C₂×C₈	—	4	2	no	—
561	C₂×C₈	—	5	1	no	—
562	C₂×C₈	—	5	1	no	—
563	C₂×C₈	—	5	2	no	—
564	C₂×C₈	—	5	2	no	—
565	C₂×C₈	—	5	1	no	—
566	C₂×C₈	—	5	1	no	—
567	C₂×C₈	—	10	1	no	—
568	C₂×C₈	—	10	1	no	—
569	C₂×C₈	—	10	1	no	—
570	C₂×C₈	—	10	1	no	—
571	C₂×C₈	—	20	2	no	—
572	C₂×C₈	—	20	2	no	—
573	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
574	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
575	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
576	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	5	1	no	—
580	C₄⋊C₄	—	5	1	no	—
581	C₄⋊C₄	—	10	1	no	—
582	C₄⋊C₄	—	10	1	no	—
583	C₄⋊C₄	—	20	2	no	—
584	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
585	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
586	C₂²⋊C₄	—	2	1	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	10	1	no	—
590	C₂²⋊C₄	—	10	1	no	—
591	C₂²⋊C₄	—	10	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	10	1	no	—
596	C₄²	—	10	1	no	—
597	C₄²	—	10	1	no	—
598	C₄²	—	10	1	no	—
599	C₄²	—	10	1	no	—
600	C₄²	—	10	1	no	—
601	C₄²	—	10	1	no	—
602	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
603	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
604	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
605	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
606	C₂×C₅	—	2	1	no	—
607	C₂×C₅	—	2	1	no	—
608	C₂×C₅	—	4	2	no	—
609	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
610	C₂×C₅	#2955	1	1	yes	characteristic
611	C₂×C₅	#2956	1	1	yes	characteristic
612	D₅	—	4	2	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	10	1	no	—
615	C₂³	C₂×#709	1	1	yes	characteristic
616	Q₈	—	2	1	no	—
617	Q₈	—	5	2	no	—
618	Q₈	—	10	1	no	—
619	Q₈	D₅×C₄⋊C₄	1	2	yes	—
620	D₄	—	2	2	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	1	no	—
623	D₄	—	5	2	no	—
624	D₄	—	10	2	no	—
625	D₄	—	10	2	no	—
626	D₄	—	10	1	no	—
627	D₄	D₅×C₄⋊C₄	1	2	yes	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	8	1	no	—
637	C₂×C₄	—	10	1	no	—
638	C₂×C₄	—	10	2	no	—
639	C₂×C₄	—	10	2	no	—
640	C₂×C₄	—	10	2	no	—
641	C₂×C₄	—	10	1	no	—
642	C₂×C₄	—	10	1	no	—
643	C₂×C₄	—	20	2	no	—
644	C₂×C₄	—	20	1	no	—
645	C₂×C₄	—	20	1	no	—
646	C₂×C₄	—	20	1	no	—
647	C₂×C₄	—	20	1	no	—
648	C₂×C₄	—	20	1	no	—
649	C₂×C₄	—	40	1	no	—
650	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
651	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
652	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
653	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
654	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
655	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
656	C₂×C₄	#4144	1	1	yes	characteristic
657	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
658	C₂×C₄	#4147	1	1	yes	characteristic
659	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
660	C₈	—	2	1	no	—
661	C₈	—	2	1	no	—
662	C₈	—	2	1	no	—
663	C₈	—	2	1	no	—
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₈	—	5	2	no	—
667	C₈	—	5	2	no	—
668	C₈	—	10	1	no	—
669	C₈	—	10	1	no	—
670	C₈	—	20	1	no	—
671	C₈	—	20	1	no	—
672	C₅	#22687	1	1	yes	characteristic, complemented, Sylow
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	10	2	no	—
679	C₂²	—	20	1	no	—
680	C₂²	—	20	1	no	—
681	C₂²	#65841	1	1	yes	characteristic
682	C₂²	#65845	1	1	yes	characteristic
683	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	10	2	no	—
692	C₄	—	20	2	no	—
693	C₄	—	20	1	no	—
694	C₄	—	20	1	no	—
695	C₄	—	40	1	no	—
696	C₄	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
697	C₄	#65838	1	1	yes	characteristic
698	C₄	D₄×C₂²⋊D₅	1	1	yes	characteristic
699	C₄	Q₈×C₂²⋊D₅	1	1	yes	characteristic
700	C₂	—	2	1	no	—
701	C₂	—	2	1	no	—
702	C₂	—	4	2	no	—
703	C₂	—	20	2	no	—
704	C₂	C₄⋊C₄×C₂²⋊D₅	1	1	yes	characteristic
705	C₂	#10615523	1	1	yes	characteristic
706	C₂	#10615542	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#2906	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4096	C₂²
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#2906	D₅
hypocenter	C₅	#22687
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2906

Complements

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

N	H ≅ G/N	type
1. C₅×#2906	C₂	semidirect
5. #10610743	C₂	semidirect
6. #10602810	C₂	semidirect
7. #10602810	C₂	semidirect
8. #10602439	C₂	semidirect
9. #10601338	C₂	semidirect
10. #10601338	C₂	semidirect
11. #10601331	C₂	semidirect
12. #10601330	C₂	semidirect
13. #10601322	C₂	semidirect
14. #10601312	C₂	semidirect
15. #10601260	C₂	semidirect
46. #65319	C₄	semidirect
47. #65319	C₄	semidirect
48. #65315	C₄	semidirect
49. #65315	C₄	semidirect
50. #65307	C₄	semidirect
51. #65307	C₄	semidirect
52. #65303	C₄	semidirect
53. #65303	C₄	semidirect
171. #2906	D₅	semidirect
240. #689	C₄⋊C₄	semidirect
241. #688	C₄⋊C₄	semidirect
242. #687	C₄⋊C₄	semidirect
243. #686	C₄⋊C₄	semidirect
672. C₅	#22687	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2906	2
C₂×#65434	2
C₂×#65433	2
#10614237	2
#10610743	2
#10602810	2
#10602439	2
#10601338	2
#10601331	2
#10601330	2
#10601322	2
#10601312	2
#10601260	2
#22687	5