Subgroups — #72242118

Order 2560.

940 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊#2171	C₂	1	2	yes	maximal, complemented
2	#13025285	C₂	1	1	yes	maximal, characteristic, complemented
3	#13025284	C₂	1	1	yes	maximal, characteristic, complemented
4	#13025283	C₂	1	2	yes	maximal, complemented
5	#13025282	C₂	1	2	yes	maximal, complemented
6	#13025281	C₂	1	1	yes	maximal, characteristic, complemented
7	#13025280	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅⋊#1369	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅⋊#1336	C₂	1	2	yes	maximal, complemented
10	#13022987	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#2179	C₂	1	1	yes	maximal, characteristic
12	D₅⋊#504	—	2	2	no	—
13	D₅×#508	C₄	1	1	yes	characteristic
14	D₅×#443	C₂²	1	2	yes	—
15	#10604862	C₂²	1	2	yes	complemented
16	#10604862	C₂²	1	2	yes	complemented
17	D₅⋊#350	—	2	2	no	—
18	#10604084	C₂²	1	2	yes	complemented
19	#10604084	C₂²	1	2	yes	complemented
20	#10604000	—	2	2	no	—
21	#10604000	—	2	2	no	—
22	D₅⋊#364	C₂²	1	2	yes	—
23	#10603823	C₂²	1	1	yes	characteristic
24	#10603807	C₂²	1	1	yes	characteristic
25	C₅×#2179	C₄	1	1	yes	characteristic
26	#10602305	C₂²	1	1	yes	characteristic
27	#10601715	C₄	1	2	yes	—
28	D₅×#368	C₄	1	1	yes	characteristic
29	#10600151	C₂²	1	1	yes	characteristic
30	D₅×#359	C₄	1	2	yes	—
31	#10600032	C₂²	1	2	yes	—
32	#10599878	C₄	1	1	yes	characteristic
33	D₅×#346	C₂²	1	1	yes	characteristic
34	#10598816	C₂²	1	2	yes	complemented
35	#10598816	C₂²	1	2	yes	complemented
36	#10598649	C₂²	1	2	yes	complemented
37	#10598648	C₂²	1	1	yes	characteristic, complemented
38	#10598648	C₂²	1	1	yes	characteristic, complemented
39	#10598639	C₂²	1	1	yes	characteristic, complemented
40	#10598639	C₂²	1	1	yes	characteristic, complemented
41	#10598638	C₂²	1	1	yes	characteristic, complemented
42	#10598638	C₂²	1	1	yes	characteristic, complemented
43	#10598624	C₂²	1	2	yes	complemented
44	#10598624	C₂²	1	2	yes	complemented
45	C₂×#12068	—	5	1	no	maximal, Sylow
46	D₅×#135	C₂×C₄	1	2	yes	—
47	D₅×#131	—	2	2	no	—
48	#65791	—	2	2	no	—
49	#65791	—	2	2	no	—
50	#65725	—	2	2	no	—
51	#65725	—	2	2	no	—
52	#65725	—	4	2	no	—
53	#65725	—	4	2	no	—
54	D₅⋊M₃₂	—	2	2	no	—
55	D₅⋊M₃₂	—	4	2	no	—
56	C₂×D₅⋊C₁₆	—	4	2	no	—
57	C₂×D₅⋊C₁₆	D₄	1	2	yes	—
58	C₄×D₅⋊C₈	—	2	1	no	—
59	C₅×#508	C₂×C₄	1	1	yes	characteristic
60	C₅×#443	C₂×C₄	1	2	yes	—
61	#65485	C₂³	1	2	yes	—
62	#65483	C₂×C₄	1	2	yes	—
63	#65433	—	2	2	no	—
64	#65208	C₈	1	1	yes	characteristic, complemented
65	D₅×Q₃₂	C₈	1	1	yes	characteristic, complemented
66	#65205	C₈	1	2	yes	complemented
67	D₅×SD₃₂	C₈	1	2	yes	complemented
68	#65201	C₈	1	1	yes	characteristic, complemented
69	D₅×D₁₆	C₈	1	1	yes	characteristic, complemented
70	#65193	C₂×C₄	1	1	yes	characteristic
71	C₂×D₅×C₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×D₅×C₁₆	C₂×C₄	1	1	yes	characteristic
73	#65184	C₂³	1	2	yes	—
74	D₅×#108	C₂×C₄	1	2	yes	—
75	#65113	—	2	2	no	—
76	D₅×#104	—	2	2	no	—
77	#64989	C₂×C₄	1	2	yes	—
78	C₄×C₈×D₅	C₂³	1	1	yes	characteristic
79	#64932	—	2	2	no	—
80	#64932	—	2	2	no	—
81	#64898	—	2	2	no	—
82	#64898	—	2	2	no	—
83	#64889	C₂³	1	2	yes	—
84	#64889	C₂³	1	2	yes	—
85	#64886	C₂³	1	1	yes	characteristic
86	#64886	C₂³	1	1	yes	characteristic
87	#64879	—	2	1	no	—
88	#64879	C₂³	1	1	yes	characteristic
89	#64879	C₂³	1	1	yes	characteristic
90	#64861	—	2	2	no	—
91	#64859	D₄	1	2	yes	—
92	C₅×#368	C₂×C₄	1	1	yes	characteristic
93	C₅×#359	C₂×C₄	1	2	yes	—
94	C₅×#346	C₂×C₄	1	1	yes	characteristic
95	#64787	C₂×C₄	1	2	yes	—
96	#64730	C₂×C₄	1	2	yes	—
97	#64726	C₂×C₄	1	1	yes	characteristic
98	#64722	C₂³	1	1	yes	characteristic
99	#64722	C₂³	1	1	yes	characteristic
100	#64717	C₂×C₄	1	2	yes	—
101	#64713	C₂×C₄	1	2	yes	—
102	#64681	C₂×C₄	1	1	yes	characteristic
103	C₂×#2179	—	5	1	no	—
104	C₂×#2171	—	5	2	no	—
105	#12068	—	5	1	no	—
106	#12068	—	5	1	no	—
107	#12068	—	5	2	no	—
108	#12068	—	5	2	no	—
109	#12068	—	5	1	no	—
110	#12068	—	5	1	no	—
111	C₂×#1369	—	5	1	no	—
112	C₂×#1336	—	5	2	no	—
113	C₂×#1313	—	5	1	no	—
114	D₅×#41	—	2	2	no	—
115	C₂×D₅⋊C₈	—	4	1	no	—
116	C₅×#135	C₂²×C₄	1	2	yes	—
117	C₅×#131	—	2	2	no	—
118	#4096	—	2	2	no	—
119	#4094	—	2	2	no	—
120	#4065	C₂×C₈	1	2	yes	—
121	D₅×Q₁₆	C₂×C₈	1	2	yes	—
122	#4062	—	2	2	no	—
123	D₅×SD₁₆	—	2	2	no	—
124	#4058	C₂×C₈	1	2	yes	—
125	D₅×D₈	C₂×C₈	1	2	yes	—
126	#4053	—	2	2	no	—
127	#4053	—	4	2	no	—
128	D₅×M₁₆	—	2	2	no	—
129	D₅×M₁₆	—	4	2	no	—
130	#4050	C₂²×C₄	1	2	yes	—
131	#4047	—	2	2	no	—
132	#4047	—	4	2	no	—
133	C₂×C₈×D₅	—	4	2	no	—
134	C₂×C₈×D₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×D₅	C₂×D₄	1	1	yes	characteristic
136	C₄²×D₅	#41	1	1	yes	characteristic
137	C₄×#170	—	2	1	no	—
138	C₄×#170	—	2	1	no	—
139	C₄×#170	—	4	1	no	—
140	#3998	—	2	2	no	—
141	#3998	—	2	2	no	—
142	#3998	—	4	2	no	—
143	#3998	—	4	2	no	—
144	C₂×#674	—	4	2	no	—
145	C₂×#674	—	4	2	no	—
146	C₂×#674	C₂×D₄	1	2	yes	—
147	C₂×#674	C₂×D₄	1	2	yes	—
148	#3990	—	4	2	no	—
149	#3990	—	4	2	no	—
150	#3990	—	4	2	no	—
151	D₅⋊C₁₆	—	2	2	no	—
152	D₅⋊C₁₆	—	2	2	no	—
153	D₅⋊C₁₆	—	4	2	no	—
154	D₅⋊C₁₆	—	4	2	no	—
155	D₅⋊C₁₆	—	4	2	no	—
156	C₅×Q₃₂	C₂×C₈	1	1	yes	characteristic, complemented
157	C₅×SD₃₂	C₂×C₈	1	2	yes	complemented
158	C₅×D₁₆	C₂×C₈	1	1	yes	characteristic, complemented
159	C₂×C₅×C₁₆	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×C₁₆	C₂²×C₄	1	1	yes	characteristic
161	C₅×#108	C₂²×C₄	1	2	yes	—
162	C₅×#104	—	2	2	no	—
163	C₄×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
164	#3969	—	2	2	no	—
165	#3961	C₂×C₈	1	2	yes	complemented
166	#3960	C₂×C₈	1	2	yes	complemented
167	#3959	C₂×C₈	1	2	yes	complemented
168	#3958	C₂×C₈	1	2	yes	complemented
169	#3957	—	2	2	no	—
170	#3954	—	2	2	no	—
171	#3951	C₂²×C₄	1	2	yes	—
172	C₈×Dic₅	#41	1	1	yes	characteristic
173	C₈×Dic₅	C₂⁴	1	1	yes	characteristic
174	C₂×#672	C₂²×C₄	1	1	yes	characteristic
175	C₂×#672	C₂²×C₄	1	1	yes	characteristic
176	#3937	—	2	2	no	—
177	C₄×#168	C₂×D₄	1	1	yes	characteristic
178	Dic₄₀	C₂×C₈	1	1	yes	characteristic, complemented
179	#3932	C₂×C₈	1	2	yes	complemented
180	D₈₀	C₂×C₈	1	1	yes	characteristic, complemented
181	D₅×C₁₆	—	2	1	no	—
182	D₅×C₁₆	—	2	1	no	—
183	D₅×C₁₆	C₂×C₈	1	1	yes	characteristic
184	D₅×C₁₆	C₂×C₈	1	1	yes	characteristic
185	D₅×C₁₆	C₂×C₈	1	1	yes	characteristic
186	D₅×C₁₆	C₂×C₈	1	1	yes	characteristic
187	C₂×#508	—	5	1	no	—
188	C₂×#504	—	10	2	no	—
189	C₂×#443	—	5	2	no	—
190	#2179	—	5	1	no	—
191	#2179	—	5	2	no	—
192	#2179	—	5	1	no	—
193	#2179	—	5	2	no	—
194	#2179	—	5	1	no	—
195	#2179	AGL(1,𝔽₅)	1	1	yes	characteristic
196	#2171	—	5	2	no	—
197	#2171	—	5	2	no	—
198	#2171	—	5	2	no	—
199	#2171	—	5	2	no	—
200	#2171	—	10	2	no	—
201	#2171	—	10	2	no	—
202	C₂×#368	—	5	1	no	—
203	C₂×#364	—	5	2	no	—
204	C₂×#359	—	5	2	no	—
205	C₂×#350	—	10	2	no	—
206	C₂×#346	—	5	1	no	—
207	C₂×#346	—	5	1	no	—
208	C₂×#322	—	5	1	no	—
209	#1369	—	5	1	no	—
210	#1369	—	5	1	no	—
211	#1369	—	5	2	no	—
212	#1336	—	5	2	no	—
213	#1336	—	5	2	no	—
214	#1336	—	5	2	no	—
215	#1336	—	5	2	no	—
216	#1313	—	5	1	no	—
217	#1313	—	5	1	no	—
218	#1313	—	5	1	no	—
219	#1313	—	5	1	no	—
220	C₅×#41	—	2	2	no	—
221	#713	—	2	2	no	—
222	Q₈×D₅	—	2	2	no	—
223	#711	—	2	2	no	—
224	#711	—	4	2	no	—
225	D₄×D₅	—	2	2	no	—
226	D₄×D₅	—	4	2	no	—
227	#709	—	2	2	no	—
228	#709	—	4	2	no	—
229	C₂×C₄×D₅	—	2	1	no	—
230	C₂×C₄×D₅	—	4	2	no	—
231	C₂×C₄×D₅	C₄×D₄	1	1	yes	characteristic
232	C₂×#170	—	4	1	no	—
233	C₂×#170	—	4	1	no	—
234	D₅⋊C₈	—	8	2	no	—
235	C₅×Q₁₆	C₂²×C₈	1	2	yes	—
236	C₅×SD₁₆	—	2	2	no	—
237	C₅×D₈	C₂²×C₈	1	2	yes	—
238	C₅×M₁₆	—	2	2	no	—
239	C₅×M₁₆	—	4	2	no	—
240	C₂×C₅×C₈	—	4	2	no	—
241	C₂×C₅×C₈	C₄×D₄	1	1	yes	characteristic
242	C₂×C₅×C₈	C₂³×C₄	1	1	yes	characteristic
243	C₄²×C₅	C₄×D₄	1	1	yes	characteristic
244	#689	—	2	2	no	—
245	#688	—	2	2	no	—
246	#687	—	2	2	no	—
247	#686	—	2	2	no	—
248	C₄×Dic₅	—	2	1	no	—
249	C₄×Dic₅	C₂×#41	1	1	yes	characteristic
250	#681	—	2	2	no	—
251	#681	—	4	2	no	—
252	C₂×#168	—	4	2	no	—
253	C₂×#168	C₄×D₄	1	1	yes	characteristic
254	C₂×#168	C₂²×D₄	1	1	yes	characteristic
255	Dic₂₀	C₂²×C₈	1	2	yes	—
256	D₄₀	C₂²×C₈	1	2	yes	—
257	#677	—	2	2	no	—
258	#676	—	4	2	no	—
259	#676	—	4	2	no	—
260	#676	—	4	2	no	—
261	C₈×D₅	—	4	2	no	—
262	C₈×D₅	—	4	2	no	—
263	C₈×D₅	—	4	2	no	—
264	C₈×D₅	C₂²×C₈	1	1	yes	characteristic
265	C₈×D₅	C₂²×C₈	1	1	yes	characteristic
266	C₈×D₅	#131	1	1	yes	characteristic
267	C₈×D₅	#131	1	1	yes	characteristic
268	C₈×D₅	AGL(1,ℤ/8)	1	2	yes	—
269	C₈×D₅	AGL(1,ℤ/8)	1	2	yes	—
270	#674	—	2	2	no	—
271	#674	—	2	2	no	—
272	#674	—	4	2	no	—
273	#674	—	4	2	no	—
274	C₅×C₁₆	—	2	1	no	—
275	C₅×C₁₆	C₂²×C₈	1	1	yes	characteristic
276	C₅×C₁₆	C₂²×C₈	1	1	yes	characteristic
277	#672	—	2	1	no	—
278	#672	C₂²×C₈	1	1	yes	characteristic
279	#672	C₂²×C₈	1	1	yes	characteristic
280	C₂×#135	—	5	2	no	—
281	C₂×#131	—	10	2	no	—
282	#508	—	5	2	no	—
283	#508	—	5	1	no	—
284	#508	—	5	2	no	—
285	#508	—	5	1	no	—
286	#508	—	5	1	no	—
287	#508	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₂×Q₃₂	—	5	1	no	—
289	C₂×SD₃₂	—	5	2	no	—
290	C₂×D₁₆	—	5	1	no	—
291	#504	—	10	2	no	—
292	#504	—	10	2	no	—
293	#504	—	10	2	no	—
294	#504	—	10	2	no	—
295	#504	—	20	2	no	—
296	#504	—	20	2	no	—
297	C₂×M₃₂	—	10	2	no	—
298	C₂×M₃₂	—	20	2	no	—
299	C₂²×C₁₆	—	5	1	no	—
300	C₂²×C₁₆	—	5	2	no	—
301	C₂²×C₁₆	—	5	1	no	—
302	C₂²×C₁₆	—	20	2	no	—
303	#443	—	5	2	no	—
304	#443	—	5	2	no	—
305	#443	—	5	2	no	—
306	#443	—	10	2	no	—
307	#443	—	10	2	no	—
308	#443	C₂×AGL(1,𝔽₅)	1	2	yes	—
309	C₂×#108	—	5	2	no	—
310	C₂×#104	—	10	2	no	—
311	C₂×C₄×C₈	—	5	1	no	—
312	C₂×C₄×C₈	—	10	1	no	—
313	#368	—	5	1	no	—
314	#368	—	5	2	no	—
315	#368	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
316	#364	—	5	2	no	—
317	#364	—	5	2	no	—
318	#364	—	10	2	no	—
319	#359	—	5	2	no	—
320	#359	—	5	2	no	—
321	#359	—	5	2	no	—
322	#359	C₂×AGL(1,𝔽₅)	1	2	yes	—
323	#350	—	10	2	no	—
324	#350	—	10	2	no	—
325	#350	—	10	2	no	—
326	#350	—	10	2	no	—
327	#346	—	5	1	no	—
328	#346	—	5	1	no	—
329	#346	—	5	2	no	—
330	#346	—	5	1	no	—
331	#346	—	5	1	no	—
332	#346	—	5	1	no	—
333	#346	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
334	#322	—	5	1	no	—
335	#322	—	5	1	no	—
336	#322	—	10	1	no	—
337	C₂²×D₅	—	4	2	no	—
338	C₂²×D₅	#444	1	1	yes	characteristic
339	C₅×Q₈	—	2	2	no	—
340	C₅×D₄	—	2	2	no	—
341	C₅×D₄	—	4	2	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	4	2	no	—
344	C₂×C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
345	C₂²⋊D₅	—	4	2	no	—
346	C₂²⋊D₅	—	4	2	no	—
347	C₂²⋊D₅	—	4	2	no	—
348	C₂×Dic₅	—	2	1	no	—
349	C₂×Dic₅	—	4	2	no	—
350	C₂×Dic₅	#444	1	1	yes	characteristic
351	D₂₀	—	2	2	no	—
352	D₂₀	—	4	2	no	—
353	C₄×D₅	—	4	2	no	—
354	C₄×D₅	—	4	2	no	—
355	C₄×D₅	—	4	2	no	—
356	C₄×D₅	—	4	2	no	—
357	C₄×D₅	C₈×D₄	1	1	yes	characteristic
358	C₄×D₅	C₈×D₄	1	1	yes	characteristic
359	C₄×D₅	#442	1	1	yes	characteristic
360	C₄×D₅	#442	1	1	yes	characteristic
361	Dic₁₀	—	2	2	no	—
362	Dic₁₀	—	4	2	no	—
363	#170	—	8	1	no	—
364	#170	—	8	1	no	—
365	C₅×C₈	—	4	2	no	—
366	C₅×C₈	#442	1	2	yes	—
367	C₅×C₈	C₂³×C₈	1	1	yes	characteristic
368	C₅×C₈	C₂×#131	1	1	yes	characteristic
369	#168	—	4	2	no	—
370	#168	C₈×D₄	1	1	yes	characteristic
371	#168	C₈×D₄	1	1	yes	characteristic
372	#168	C₂×AGL(1,ℤ/8)	1	2	yes	—
373	C₂×#41	—	10	2	no	—
374	#135	—	5	2	no	—
375	#135	—	5	2	no	—
376	#135	—	5	2	no	—
377	#135	—	10	2	no	—
378	#135	—	10	2	no	—
379	#135	C₂²×AGL(1,𝔽₅)	1	2	yes	—
380	C₂×Q₁₆	—	5	2	no	—
381	C₂×SD₁₆	—	10	2	no	—
382	C₂×D₈	—	5	2	no	—
383	#131	—	2	2	no	—
384	#131	—	10	2	no	—
385	#131	—	10	2	no	—
386	#131	—	10	2	no	—
387	#131	—	20	2	no	—
388	#131	—	20	2	no	—
389	C₂×M₁₆	—	10	2	no	—
390	C₂×M₁₆	—	20	2	no	—
391	C₂²×C₈	—	5	1	no	—
392	C₂²×C₈	—	5	1	no	—
393	C₂²×C₈	—	20	2	no	—
394	C₂²×C₈	—	20	1	no	—
395	C₂×C₄²	—	5	1	no	—
396	Q₃₂	—	5	2	no	—
397	Q₃₂	—	5	1	no	—
398	Q₃₂	D₅⋊C₈	1	1	yes	characteristic, complemented
399	SD₃₂	—	5	2	no	—
400	SD₃₂	—	5	2	no	—
401	SD₃₂	—	5	2	no	—
402	SD₃₂	D₅⋊C₈	1	2	yes	complemented
403	D₁₆	—	5	2	no	—
404	D₁₆	—	5	1	no	—
405	D₁₆	D₅⋊C₈	1	1	yes	characteristic, complemented
406	M₃₂	—	10	2	no	—
407	M₃₂	—	10	2	no	—
408	M₃₂	—	20	2	no	—
409	M₃₂	—	20	2	no	—
410	M₃₂	—	20	2	no	—
411	M₃₂	—	20	2	no	—
412	M₃₂	—	20	2	no	—
413	C₂×C₁₆	—	5	1	no	—
414	C₂×C₁₆	—	5	1	no	—
415	C₂×C₁₆	—	5	1	no	—
416	C₂×C₁₆	—	5	1	no	—
417	C₂×C₁₆	—	5	1	no	—
418	C₂×C₁₆	—	5	2	no	—
419	C₂×C₁₆	—	5	2	no	—
420	C₂×C₁₆	—	5	1	no	—
421	C₂×C₁₆	—	10	1	no	—
422	C₂×C₁₆	—	10	1	no	—
423	C₂×C₁₆	—	10	2	no	—
424	C₂×C₁₆	—	10	2	no	—
425	C₂×C₁₆	—	20	2	no	—
426	C₂×C₁₆	—	20	2	no	—
427	C₂×C₁₆	—	20	2	no	—
428	C₂×C₁₆	—	20	2	no	—
429	C₂×C₁₆	—	20	2	no	—
430	C₂×C₁₆	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
431	C₂×C₁₆	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
432	#108	—	5	2	no	—
433	#108	—	10	2	no	—
434	#108	C₂²×AGL(1,𝔽₅)	1	2	yes	—
435	#104	—	2	2	no	—
436	#104	—	10	2	no	—
437	#104	—	10	2	no	—
438	#104	—	10	2	no	—
439	C₄×C₈	—	5	1	no	—
440	C₄×C₈	—	5	1	no	—
441	C₄×C₈	—	5	1	no	—
442	C₄×C₈	—	10	1	no	—
443	C₄×C₈	—	10	1	no	—
444	C₄×C₈	—	20	1	no	—
445	C₄×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	C₂×#444	1	1	yes	characteristic
448	C₂×D₅	—	2	2	no	—
449	C₂×D₅	—	4	2	no	—
450	C₂×D₅	—	8	4	no	—
451	C₂×D₅	#1580	1	1	yes	characteristic
452	C₂×D₅	#1580	1	1	yes	characteristic
453	C₄×C₅	—	4	1	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	C₂×C₈×D₄	1	1	yes	characteristic
456	C₄×C₅	C₂×#442	1	1	yes	characteristic
457	Dic₅	—	4	1	no	—
458	Dic₅	—	4	2	no	—
459	Dic₅	#1580	1	1	yes	characteristic
460	Dic₅	#1580	1	1	yes	characteristic
461	#41	—	2	2	no	—
462	#41	—	10	2	no	—
463	#41	—	10	2	no	—
464	#41	—	10	2	no	—
465	#41	—	20	2	no	—
466	#41	—	20	2	no	—
467	C₂×Q₈	—	10	2	no	—
468	C₂×D₄	—	10	2	no	—
469	C₂×D₄	—	20	2	no	—
470	C₂²×C₄	—	5	1	no	—
471	C₂²×C₄	—	10	1	no	—
472	C₂²×C₄	—	20	2	no	—
473	Q₁₆	—	5	2	no	—
474	Q₁₆	—	10	2	no	—
475	Q₁₆	C₂×D₅⋊C₈	1	2	yes	—
476	SD₁₆	—	2	2	no	—
477	SD₁₆	—	10	2	no	—
478	SD₁₆	—	10	2	no	—
479	SD₁₆	—	10	2	no	—
480	D₈	—	5	2	no	—
481	D₈	—	10	2	no	—
482	D₈	C₂×D₅⋊C₈	1	2	yes	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	4	2	no	—
485	M₁₆	—	10	2	no	—
486	M₁₆	—	20	2	no	—
487	M₁₆	—	20	2	no	—
488	M₁₆	—	20	2	no	—
489	M₁₆	—	20	2	no	—
490	C₂×C₈	—	4	2	no	—
491	C₂×C₈	—	5	1	no	—
492	C₂×C₈	—	5	1	no	—
493	C₂×C₈	—	5	2	no	—
494	C₂×C₈	—	5	2	no	—
495	C₂×C₈	—	5	1	no	—
496	C₂×C₈	—	5	1	no	—
497	C₂×C₈	—	5	1	no	—
498	C₂×C₈	—	5	1	no	—
499	C₂×C₈	—	20	2	no	—
500	C₂×C₈	—	20	2	no	—
501	C₂×C₈	—	20	2	no	—
502	C₂×C₈	—	20	2	no	—
503	C₂×C₈	—	20	1	no	—
504	C₂×C₈	—	20	1	no	—
505	C₂×C₈	—	40	2	no	—
506	C₂×C₈	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₂×C₈	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
508	C₄²	—	5	1	no	—
509	C₄²	—	10	1	no	—
510	C₄²	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
511	C₁₆	—	2	1	no	—
512	C₁₆	—	5	1	no	—
513	C₁₆	—	5	1	no	—
514	C₁₆	—	10	2	no	—
515	C₁₆	—	10	2	no	—
516	C₁₆	—	10	1	no	—
517	C₁₆	—	20	2	no	—
518	C₁₆	—	20	2	no	—
519	C₁₆	C₂×D₅⋊C₈	1	1	yes	characteristic
520	C₁₆	C₂×D₅⋊C₈	1	1	yes	characteristic
521	C₂×C₅	—	2	1	no	—
522	C₂×C₅	—	8	2	no	—
523	C₂×C₅	C₂×#1580	1	1	yes	characteristic
524	D₅	—	2	1	no	—
525	D₅	—	8	2	no	—
526	D₅	#12068	1	2	yes	complemented
527	C₂³	—	5	1	no	—
528	C₂³	—	20	2	no	—
529	Q₈	—	2	2	no	—
530	Q₈	—	10	2	no	—
531	Q₈	—	20	2	no	—
532	D₄	—	2	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	10	2	no	—
535	D₄	—	20	2	no	—
536	D₄	—	20	2	no	—
537	D₄	—	20	2	no	—
538	D₄	—	20	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	5	1	no	—
542	C₂×C₄	—	5	1	no	—
543	C₂×C₄	—	5	1	no	—
544	C₂×C₄	—	5	1	no	—
545	C₂×C₄	—	5	1	no	—
546	C₂×C₄	—	10	1	no	—
547	C₂×C₄	—	20	2	no	—
548	C₂×C₄	—	20	2	no	—
549	C₂×C₄	—	20	2	no	—
550	C₂×C₄	—	20	2	no	—
551	C₂×C₄	—	20	2	no	—
552	C₂×C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
553	C₈	—	4	2	no	—
554	C₈	—	5	1	no	—
555	C₈	—	5	1	no	—
556	C₈	—	5	2	no	—
557	C₈	—	20	2	no	—
558	C₈	—	40	1	no	—
559	C₈	—	40	1	no	—
560	C₈	#65731	1	2	yes	—
561	C₈	C₂²×D₅⋊C₈	1	1	yes	characteristic
562	C₈	D₅⋊#131	1	1	yes	characteristic
563	C₅	C₂×#12068	1	1	yes	characteristic, complemented, Sylow
564	C₂²	—	4	2	no	—
565	C₂²	—	5	1	no	—
566	C₂²	—	5	1	no	—
567	C₂²	—	10	2	no	—
568	C₂²	—	20	2	no	—
569	C₂²	—	40	4	no	—
570	C₂²	D₅⋊#444	1	1	yes	characteristic
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	5	1	no	—
574	C₄	—	5	1	no	—
575	C₄	—	20	1	no	—
576	C₄	—	20	2	no	—
577	C₄	D₄×D₅⋊C₈	1	1	yes	characteristic
578	C₄	C₂×#65731	1	1	yes	characteristic
579	C₂	—	2	1	no	—
580	C₂	—	5	2	no	—
581	C₂	—	8	2	no	—
582	C₂	—	10	1	no	—
583	C₂	—	40	2	no	—
584	C₂	D₅⋊#1580	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#65731
commutator	C₅×C₈	C₂³×C₈
Frattini	C₂×C₈	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#2179	C₄
socle	C₂×C₅	C₂×#1580
prime radical	D₅×#508	C₄
cosocle	C₈×Dic₅	C₂⁴
hypercenter	#2179	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#12068
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2179

Complements

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

N	H ≅ G/N	type
1. D₅⋊#2171	C₂	semidirect
2. #13025285	C₂	semidirect
3. #13025284	C₂	semidirect
4. #13025283	C₂	semidirect
5. #13025282	C₂	semidirect
6. #13025281	C₂	semidirect
7. #13025280	C₂	semidirect
8. D₅⋊#1369	C₂	semidirect
9. D₅⋊#1336	C₂	semidirect
10. #13022987	C₂	semidirect
15. #10604862	C₂²	semidirect
16. #10604862	C₂²	semidirect
18. #10604084	C₂²	semidirect
19. #10604084	C₂²	semidirect
34. #10598816	C₂²	semidirect
35. #10598816	C₂²	semidirect
36. #10598649	C₂²	semidirect
37. #10598648	C₂²	semidirect
38. #10598648	C₂²	semidirect
39. #10598639	C₂²	semidirect
40. #10598639	C₂²	semidirect
41. #10598638	C₂²	semidirect
42. #10598638	C₂²	semidirect
43. #10598624	C₂²	semidirect
44. #10598624	C₂²	semidirect
64. #65208	C₈	semidirect
65. D₅×Q₃₂	C₈	semidirect
66. #65205	C₈	semidirect
67. D₅×SD₃₂	C₈	semidirect
68. #65201	C₈	semidirect
69. D₅×D₁₆	C₈	semidirect
156. C₅×Q₃₂	C₂×C₈	semidirect
157. C₅×SD₃₂	C₂×C₈	semidirect
158. C₅×D₁₆	C₂×C₈	semidirect
165. #3961	C₂×C₈	semidirect
166. #3960	C₂×C₈	semidirect
167. #3959	C₂×C₈	semidirect
168. #3958	C₂×C₈	semidirect
178. Dic₄₀	C₂×C₈	semidirect
179. #3932	C₂×C₈	semidirect
180. D₈₀	C₂×C₈	semidirect
398. Q₃₂	D₅⋊C₈	semidirect
402. SD₃₂	D₅⋊C₈	semidirect
405. D₁₆	D₅⋊C₈	semidirect
526. D₅	#12068	semidirect
563. C₅	C₂×#12068	semidirect

Maximal subgroups

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

subgroup	index
D₅⋊#2171	2
#13025285	2
#13025284	2
#13025283	2
#13025282	2
#13025281	2
#13025280	2
D₅⋊#1369	2
D₅⋊#1336	2
#13022987	2
D₅×#2179	2
C₂×#12068	5