Subgroups — #12117764

Order 1280.

870 conjugacy classes of subgroups.

The subgroup lattice has 576 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×#65433	C₂	1	2	yes	maximal
3	C₄×#4096	C₂	1	1	yes	maximal, characteristic
4	#10610743	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602810	C₂	1	2	yes	maximal, complemented
6	#10602439	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601338	C₂	1	2	yes	maximal, complemented
8	#10601330	C₂	1	2	yes	maximal, complemented
9	#10601322	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601311	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601258	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	C₂²	1	2	yes	—
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×#4096	C₂²	1	1	yes	characteristic
15	C₂×#4047	C₂²	1	2	yes	—
16	C₄×#709	C₂²	1	1	yes	characteristic
17	C₅×#424	—	2	2	no	—
18	C₅×#424	C₂²	1	2	yes	—
19	C₅×#423	—	2	1	no	—
20	C₅×#423	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	—	2	1	no	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×#3969	C₂²	1	2	yes	—
24	#65522	C₂²	1	1	yes	characteristic
25	#65433	—	2	8	no	—
26	C₂×#3957	C₂²	1	2	yes	—
27	C₂×#3954	C₂²	1	2	yes	—
28	C₂×#3954	C₂²	1	2	yes	—
29	#65391	C₂²	1	2	yes	—
30	C₂×C₈×Dic₅	C₂²	1	2	yes	—
31	C₄×#689	C₄	1	1	yes	characteristic, complemented
32	C₄×#689	C₄	1	1	yes	characteristic, complemented
33	C₄×#688	C₄	1	1	yes	characteristic, complemented
34	C₄×#688	C₄	1	1	yes	characteristic, complemented
35	C₄×#687	C₄	1	1	yes	characteristic, complemented
36	C₄×#687	C₄	1	1	yes	characteristic, complemented
37	C₄×#686	C₄	1	1	yes	characteristic, complemented
38	C₄×#686	C₄	1	1	yes	characteristic, complemented
39	#65291	C₂²	1	1	yes	characteristic
40	#65287	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
42	#65213	C₂²	1	1	yes	characteristic
43	C₂×C₄×#168	C₂²	1	1	yes	characteristic
44	#65128	—	2	2	no	—
45	#65126	—	2	1	no	—
46	D₅×C₄⋊C₈	—	2	1	no	—
47	#64775	C₂²	1	2	yes	—
48	#64770	C₂²	1	2	yes	—
49	#64752	C₂²	1	2	yes	—
50	#22688	—	5	1	no	maximal, Sylow
51	C₂×C₅×#41	C₂³	1	1	yes	characteristic
52	C₂×#709	C₂³	1	1	yes	characteristic
53	C₅×#131	—	2	4	no	—
54	C₅×#131	—	4	2	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	C₂³	1	2	yes	—
57	C₂²×C₅×C₈	—	2	2	no	—
58	C₂²×C₅×C₈	C₂³	1	2	yes	—
59	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
60	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×D₄	—	2	1	no	—
62	C₄×C₅×D₄	—	2	1	no	—
63	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
64	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
65	C₅×#117	—	2	1	no	—
66	C₅×#117	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	—	2	1	no	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	#4096	D₄	1	4	yes	—
70	#4096	Q₈	1	4	yes	—
71	C₂×#689	C₂×C₄	1	1	yes	characteristic
72	C₂×#688	C₂×C₄	1	1	yes	characteristic
73	C₂×#687	C₂×C₄	1	1	yes	characteristic
74	C₂×#686	C₂×C₄	1	1	yes	characteristic
75	C₄×C₂²⋊D₅	—	2	1	no	—
76	C₄×C₂²⋊D₅	—	2	1	no	—
77	#4072	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊Dic₅	—	2	1	no	—
79	C₂×C₄×Dic₅	C₂³	1	2	yes	—
80	C₂×#681	C₂³	1	2	yes	—
81	C₂²×#168	C₂³	1	1	yes	characteristic
82	C₂²×#168	C₂³	1	1	yes	characteristic
83	#4047	—	2	4	no	—
84	#4047	—	4	2	no	—
85	C₂×#676	—	2	2	no	—
86	C₂×C₈×D₅	—	2	2	no	—
87	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
88	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
89	#4018	—	2	1	no	—
90	C₄²×D₅	—	2	1	no	—
91	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×C₄⋊C₈	—	2	2	no	—
95	C₅×C₄⋊C₈	—	2	1	no	—
96	C₅×C₄⋊C₈	—	2	1	no	—
97	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
98	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
99	C₅×C₄⋊C₈	D₄	1	2	yes	—
100	#3969	—	2	4	no	—
101	#3967	C₂×C₄	1	1	yes	characteristic
102	#3967	C₂×C₄	1	1	yes	characteristic
103	#3964	C₂×C₄	1	1	yes	characteristic
104	#3964	C₂×C₄	1	1	yes	characteristic
105	#3963	—	2	1	no	—
106	#3957	—	2	4	no	—
107	#3954	—	2	4	no	—
108	#3954	—	4	2	no	—
109	#3946	—	2	2	no	—
110	#3946	—	2	2	no	—
111	C₈×Dic₅	—	2	4	no	—
112	#3942	C₂×C₄	1	1	yes	characteristic
113	#3942	C₂×C₄	1	1	yes	characteristic
114	#3941	C₂×C₄	1	1	yes	characteristic
115	#3941	C₂×C₄	1	1	yes	characteristic
116	#3940	C₂×C₄	1	1	yes	characteristic
117	#3940	C₂×C₄	1	1	yes	characteristic
118	#3939	C₂×C₄	1	1	yes	characteristic
119	#3939	C₂×C₄	1	1	yes	characteristic
120	C₄⋊#168	—	2	1	no	—
121	C₄⋊#168	—	2	1	no	—
122	C₄×#168	C₂×C₄	1	1	yes	characteristic
123	C₄×#168	C₂×C₄	1	1	yes	characteristic
124	C₄×#168	C₂×C₄	1	1	yes	characteristic
125	C₄×#168	C₂×C₄	1	1	yes	characteristic
126	C₂×#443	—	5	2	no	—
127	C₄×#135	—	5	1	no	—
128	#2906	—	5	1	no	—
129	#2906	D₅	1	1	yes	characteristic, complemented
130	#1945	—	5	2	no	—
131	#1866	—	5	2	no	—
132	#1866	—	5	2	no	—
133	#1848	—	5	1	no	—
134	#1806	—	5	1	no	—
135	#1806	—	5	1	no	—
136	C₈×C₄⋊C₄	—	5	1	no	—
137	C₅×#41	—	2	1	no	—
138	C₅×#41	—	2	1	no	—
139	C₅×#41	C₂×D₄	1	2	yes	—
140	C₅×#41	C₂×Q₈	1	2	yes	—
141	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	#41	1	1	yes	characteristic
148	C₂²×C₄×C₅	#41	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₂×C₂²⋊D₅	—	2	1	no	—
151	C₂²×Dic₅	—	2	2	no	—
152	#709	—	2	1	no	—
153	#709	—	2	1	no	—
154	#709	C₂×D₄	1	2	yes	—
155	#709	C₂×Q₈	1	2	yes	—
156	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₅	—	2	1	no	—
158	C₂×C₄×D₅	—	2	1	no	—
159	C₂×C₄×D₅	—	2	1	no	—
160	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
161	C₅×M₁₆	—	2	2	no	—
162	C₅×M₁₆	—	2	2	no	—
163	C₅×M₁₆	—	4	4	no	—
164	C₂×C₅×C₈	—	2	2	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	4	4	no	—
168	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
169	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	1	no	—
172	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
173	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	2	1	no	—
176	C₅×C₂²⋊C₄	—	2	1	no	—
177	C₄²×C₅	—	2	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²⋊Dic₅	—	2	1	no	—
185	#689	C₄⋊C₄	1	4	yes	complemented
186	#688	C₄⋊C₄	1	4	yes	complemented
187	#687	C₄⋊C₄	1	4	yes	complemented
188	#686	C₄⋊C₄	1	4	yes	complemented
189	#685	—	2	1	no	—
190	#685	—	2	1	no	—
191	C₄⋊Dic₅	—	2	4	no	—
192	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
194	#683	—	2	1	no	—
195	#683	—	2	1	no	—
196	C₄×Dic₅	—	2	1	no	—
197	C₄×Dic₅	—	2	1	no	—
198	C₄×Dic₅	—	2	1	no	—
199	C₄×Dic₅	—	2	2	no	—
200	C₄×Dic₅	—	2	2	no	—
201	#681	—	2	2	no	—
202	#681	—	2	2	no	—
203	C₂×#168	—	2	1	no	—
204	C₂×#168	—	2	1	no	—
205	C₂×#168	—	2	2	no	—
206	C₂×#168	C₂²×C₄	1	1	yes	characteristic
207	C₂×#168	C₂²×C₄	1	1	yes	characteristic
208	C₂×#168	C₂²×C₄	1	1	yes	characteristic
209	C₂×#168	C₂²×C₄	1	1	yes	characteristic
210	C₂×#168	C₂×D₄	1	2	yes	—
211	C₂×#168	C₂×Q₈	1	2	yes	—
212	#676	—	4	4	no	—
213	C₈×D₅	—	4	4	no	—
214	C₂×#135	—	5	1	no	—
215	C₂×#131	—	5	2	no	—
216	C₂×#131	C₂×D₅	1	2	yes	—
217	C₄×#41	—	5	1	no	—
218	C₄×#41	C₂×D₅	1	1	yes	characteristic
219	#443	—	10	8	no	—
220	C₄×Q₁₆	—	5	1	no	—
221	C₄×Q₁₆	—	5	1	no	—
222	C₄×SD₁₆	—	5	1	no	—
223	C₄×SD₁₆	—	5	1	no	—
224	C₄×SD₁₆	—	5	1	no	—
225	C₄×SD₁₆	—	5	1	no	—
226	C₄×D₈	—	5	1	no	—
227	C₄×D₈	—	5	1	no	—
228	C₂×#108	—	5	2	no	—
229	C₂×#108	—	5	2	no	—
230	#427	—	5	1	no	—
231	#424	—	2	2	no	—
232	#424	—	5	2	no	—
233	#424	—	10	2	no	—
234	#424	C₂×D₅	1	2	yes	—
235	#423	—	2	1	no	—
236	#423	—	5	1	no	—
237	#423	—	10	1	no	—
238	#423	C₂×D₅	1	1	yes	characteristic
239	C₂×C₄⋊C₈	—	2	1	no	—
240	C₂×C₄⋊C₈	—	10	1	no	—
241	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
242	C₂×#104	—	5	2	no	—
243	C₂×#104	—	5	2	no	—
244	#416	—	5	1	no	—
245	#416	—	5	1	no	—
246	C₂×C₄×C₈	—	5	1	no	—
247	C₂×C₄×C₈	—	5	2	no	—
248	C₄×C₄⋊C₄	—	5	1	no	—
249	#339	—	5	2	no	—
250	#339	—	5	2	no	—
251	#336	—	5	2	no	—
252	C₂³×C₅	—	2	1	no	—
253	C₂³×C₅	C₂×#41	1	1	yes	characteristic
254	C₂²×D₅	—	2	1	no	—
255	C₅×Q₈	—	2	1	no	—
256	C₅×Q₈	C₂×C₄⋊C₄	1	2	yes	—
257	C₅×D₄	—	2	2	no	—
258	C₅×D₄	—	2	2	no	—
259	C₅×D₄	—	2	1	no	—
260	C₅×D₄	C₂×C₄⋊C₄	1	2	yes	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	4	1	no	—
268	C₂×C₄×C₅	—	4	2	no	—
269	C₂×C₄×C₅	—	8	1	no	—
270	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
278	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
280	C₂²⋊D₅	—	2	2	no	—
281	C₂²⋊D₅	—	2	2	no	—
282	C₂×Dic₅	—	2	1	no	—
283	C₂×Dic₅	—	2	4	no	—
284	C₂×Dic₅	—	2	1	no	—
285	C₂×Dic₅	—	2	1	no	—
286	C₂×Dic₅	—	4	2	no	—
287	C₂×Dic₅	—	4	2	no	—
288	D₂₀	—	2	1	no	—
289	D₂₀	C₂×C₄⋊C₄	1	2	yes	—
290	C₄×D₅	—	2	2	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	4	2	no	—
293	C₄×D₅	—	8	1	no	—
294	Dic₁₀	—	2	1	no	—
295	Dic₁₀	C₂×C₄⋊C₄	1	2	yes	—
296	C₅×C₈	—	2	2	no	—
297	C₅×C₈	—	2	2	no	—
298	C₅×C₈	—	4	2	no	—
299	#168	—	2	1	no	—
300	#168	—	2	1	no	—
301	#168	—	4	2	no	—
302	#168	C₂×C₄⋊C₄	1	2	yes	—
303	#168	C₂×C₄⋊C₄	1	2	yes	—
304	C₂×#41	—	5	1	no	—
305	C₂×#41	C₂²×D₅	1	1	yes	characteristic
306	#135	—	5	4	no	—
307	#135	—	5	4	no	—
308	C₂×Q₁₆	—	5	1	no	—
309	C₂×SD₁₆	—	5	1	no	—
310	C₂×SD₁₆	—	5	1	no	—
311	C₂×D₈	—	5	1	no	—
312	#131	—	2	4	no	—
313	#131	—	4	2	no	—
314	#131	—	10	4	no	—
315	#131	—	20	2	no	—
316	C₂×M₁₆	—	2	2	no	—
317	C₂×M₁₆	—	5	2	no	—
318	C₂×M₁₆	—	10	2	no	—
319	C₂×M₁₆	C₂²×D₅	1	2	yes	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	5	1	no	—
322	C₂²×C₈	—	5	1	no	—
323	C₂²×C₈	—	10	2	no	—
324	C₂²×C₈	C₂²×D₅	1	2	yes	—
325	C₄×Q₈	—	5	1	no	—
326	C₄×Q₈	—	5	1	no	—
327	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
328	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	5	1	no	—
332	C₄×D₄	—	5	1	no	—
333	C₄×D₄	—	10	1	no	—
334	C₄×D₄	—	10	1	no	—
335	C₄×D₄	C₄×D₅	1	1	yes	characteristic
336	C₄×D₄	C₄×D₅	1	1	yes	characteristic
337	#117	—	2	1	no	—
338	#117	—	5	1	no	—
339	#117	—	10	1	no	—
340	#117	C₂²×D₅	1	1	yes	characteristic
341	C₂×C₄⋊C₄	—	10	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	—	5	2	no	—
344	C₂×C₄²	—	10	1	no	—
345	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
346	#108	—	10	4	no	—
347	#108	—	20	2	no	—
348	#107	—	5	1	no	—
349	#107	—	5	1	no	—
350	#106	—	5	1	no	—
351	#106	—	5	1	no	—
352	C₄⋊C₈	—	2	2	no	—
353	C₄⋊C₈	—	2	2	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	1	no	—
356	C₄⋊C₈	—	10	2	no	—
357	C₄⋊C₈	—	10	2	no	—
358	C₄⋊C₈	—	10	1	no	—
359	C₄⋊C₈	—	10	1	no	—
360	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
361	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
362	C₄⋊C₈	C₂²⋊D₅	1	2	yes	—
363	#104	—	10	4	no	—
364	#104	—	10	4	no	—
365	#103	—	5	1	no	—
366	#103	—	5	1	no	—
367	#103	—	5	1	no	—
368	#103	—	5	1	no	—
369	#102	—	5	1	no	—
370	#102	—	5	1	no	—
371	#102	—	5	1	no	—
372	#102	—	5	1	no	—
373	C₄×C₈	—	5	1	no	—
374	C₄×C₈	—	5	1	no	—
375	C₄×C₈	—	5	1	no	—
376	C₄×C₈	—	5	1	no	—
377	C₄×C₈	—	10	4	no	—
378	#95	—	10	1	no	—
379	C₂²×C₅	—	2	1	no	—
380	C₂²×C₅	—	2	1	no	—
381	C₂²×C₅	—	2	2	no	—
382	C₂²×C₅	—	4	1	no	—
383	C₂²×C₅	—	4	1	no	—
384	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
385	C₂²×C₅	#547	1	1	yes	characteristic
386	C₂²×C₅	#554	1	1	yes	characteristic
387	C₂×D₅	—	2	2	no	—
388	C₂×D₅	—	4	1	no	—
389	C₂×D₅	—	4	1	no	—
390	C₄×C₅	—	2	2	no	—
391	C₄×C₅	—	2	1	no	—
392	C₄×C₅	—	2	1	no	—
393	C₄×C₅	—	2	1	no	—
394	C₄×C₅	—	4	1	no	—
395	C₄×C₅	—	4	1	no	—
396	C₄×C₅	#443	1	2	yes	complemented
397	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
398	C₄×C₅	#520	1	1	yes	characteristic
399	C₄×C₅	D₄²	1	1	yes	characteristic
400	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
401	Dic₅	—	2	2	no	—
402	Dic₅	—	4	4	no	—
403	Dic₅	—	4	1	no	—
404	Dic₅	—	4	1	no	—
405	#41	—	2	1	no	—
406	#41	—	2	1	no	—
407	#41	—	5	2	no	—
408	#41	—	5	2	no	—
409	#41	—	10	1	no	—
410	#41	—	10	1	no	—
411	#41	D₄×D₅	1	2	yes	—
412	#41	Q₈×D₅	1	2	yes	—
413	C₂×Q₈	—	5	1	no	—
414	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	5	1	no	—
417	C₂×D₄	—	10	1	no	—
418	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	10	1	no	—
423	C₂²×C₄	—	10	2	no	—
424	C₂²×C₄	—	10	1	no	—
425	C₂²×C₄	—	10	1	no	—
426	C₂²×C₄	#709	1	1	yes	characteristic
427	C₂²×C₄	#709	1	1	yes	characteristic
428	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
429	Q₁₆	—	5	4	no	—
430	SD₁₆	—	5	4	no	—
431	SD₁₆	—	5	4	no	—
432	D₈	—	5	4	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	4	4	no	—
436	M₁₆	—	10	2	no	—
437	M₁₆	—	10	2	no	—
438	M₁₆	—	20	4	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	4	4	no	—
443	C₂×C₈	—	5	1	no	—
444	C₂×C₈	—	5	1	no	—
445	C₂×C₈	—	5	2	no	—
446	C₂×C₈	—	5	2	no	—
447	C₂×C₈	—	5	1	no	—
448	C₂×C₈	—	5	1	no	—
449	C₂×C₈	—	10	1	no	—
450	C₂×C₈	—	10	1	no	—
451	C₂×C₈	—	10	2	no	—
452	C₂×C₈	—	20	4	no	—
453	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
454	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	5	1	no	—
458	C₄⋊C₄	—	5	1	no	—
459	C₄⋊C₄	—	10	4	no	—
460	C₄⋊C₄	—	10	1	no	—
461	C₄⋊C₄	—	10	1	no	—
462	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
463	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	10	1	no	—
468	C₂²⋊C₄	—	10	1	no	—
469	C₂²⋊C₄	—	10	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	10	1	no	—
474	C₄²	—	10	1	no	—
475	C₄²	—	10	1	no	—
476	C₄²	—	10	2	no	—
477	C₄²	—	10	2	no	—
478	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
479	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
480	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
481	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
482	C₂×C₅	—	2	1	no	—
483	C₂×C₅	—	2	1	no	—
484	C₂×C₅	—	4	2	no	—
485	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
486	C₂×C₅	C₂×#443	1	1	yes	characteristic
487	C₂×C₅	#2957	1	1	yes	characteristic
488	D₅	—	4	2	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	10	1	no	—
491	C₂³	C₂×#709	1	1	yes	characteristic
492	Q₈	—	2	1	no	—
493	Q₈	—	5	2	no	—
494	Q₈	—	10	1	no	—
495	Q₈	D₅×C₄⋊C₄	1	2	yes	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	1	no	—
499	D₄	—	5	2	no	—
500	D₄	—	10	2	no	—
501	D₄	—	10	2	no	—
502	D₄	—	10	1	no	—
503	D₄	D₅×C₄⋊C₄	1	2	yes	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	—	10	1	no	—
514	C₂×C₄	—	10	2	no	—
515	C₂×C₄	—	10	2	no	—
516	C₂×C₄	—	10	4	no	—
517	C₂×C₄	—	10	1	no	—
518	C₂×C₄	—	10	1	no	—
519	C₂×C₄	—	20	2	no	—
520	C₂×C₄	—	20	2	no	—
521	C₂×C₄	—	20	2	no	—
522	C₂×C₄	—	40	1	no	—
523	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
524	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
525	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
526	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
527	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
528	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
529	C₂×C₄	#4144	1	1	yes	characteristic
530	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
531	C₂×C₄	#4147	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₈	—	4	2	no	—
536	C₈	—	5	2	no	—
537	C₈	—	5	2	no	—
538	C₈	—	10	1	no	—
539	C₈	—	10	1	no	—
540	C₈	—	20	2	no	—
541	C₅	#22688	1	1	yes	characteristic, complemented, Sylow
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	10	2	no	—
548	C₂²	—	20	1	no	—
549	C₂²	—	20	1	no	—
550	C₂²	#65841	1	1	yes	characteristic
551	C₂²	#65845	1	1	yes	characteristic
552	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
553	C₄	—	2	2	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	10	2	no	—
560	C₄	—	20	4	no	—
561	C₄	—	20	1	no	—
562	C₄	—	20	1	no	—
563	C₄	#65433	1	2	yes	complemented
564	C₄	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
565	C₄	#65838	1	1	yes	characteristic
566	C₄	D₄×C₂²⋊D₅	1	1	yes	characteristic
567	C₄	Q₈×C₂²⋊D₅	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	2	no	—
571	C₂	—	20	2	no	—
572	C₂	C₄⋊C₄×C₂²⋊D₅	1	1	yes	characteristic
573	C₂	C₂×#65433	1	1	yes	characteristic
574	C₂	#10615543	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	#22688
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
4. #10610743	C₂	semidirect
5. #10602810	C₂	semidirect
6. #10602439	C₂	semidirect
7. #10601338	C₂	semidirect
8. #10601330	C₂	semidirect
9. #10601322	C₂	semidirect
10. #10601311	C₂	semidirect
11. #10601258	C₂	semidirect
31. C₄×#689	C₄	semidirect
32. C₄×#689	C₄	semidirect
33. C₄×#688	C₄	semidirect
34. C₄×#688	C₄	semidirect
35. C₄×#687	C₄	semidirect
36. C₄×#687	C₄	semidirect
37. C₄×#686	C₄	semidirect
38. C₄×#686	C₄	semidirect
129. #2906	D₅	semidirect
185. #689	C₄⋊C₄	semidirect
186. #688	C₄⋊C₄	semidirect
187. #687	C₄⋊C₄	semidirect
188. #686	C₄⋊C₄	semidirect
396. C₄×C₅	#443	semidirect
541. C₅	#22688	semidirect
563. C₄	#65433	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×#65433	2
C₄×#4096	2
#10610743	2
#10602810	2
#10602439	2
#10601338	2
#10601330	2
#10601322	2
#10601311	2
#10601258	2
#22688	5