Subgroups — C₅×#10602438 #72223413

Order 3200.

974 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#66156	C₂	1	1	yes	maximal, characteristic
3	C₅×#65525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#65295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#3937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#64753	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#64743	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅²×#41	C₂²	1	1	yes	characteristic
9	C₂×C₅×#709	C₂²	1	1	yes	characteristic
10	C₄×C₅²×Q₈	—	2	1	no	—
11	C₄×C₅²×D₄	—	2	1	no	—
12	C₄×C₅²×D₄	—	2	2	no	—
13	C₅²×#117	—	2	1	no	—
14	C₅²×#117	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₅²	—	2	1	no	—
16	C₂×C₄²×C₅²	C₂²	1	1	yes	characteristic
17	C₅×#4097	C₄	1	2	yes	complemented
18	C₅×#4096	—	2	2	no	—
19	C₅×#4095	C₄	1	2	yes	complemented
20	C₅×#4088	—	2	1	no	—
21	C₅×#4078	—	2	1	no	—
22	C₅×#4072	C₂²	1	1	yes	characteristic
23	C₂×C₅×#681	C₂²	1	1	yes	characteristic
24	C₂×C₅×#681	C₂²	1	1	yes	characteristic
25	C₅×#3969	—	2	2	no	—
26	C₅×#3938	—	2	2	no	—
27	C₅×#3937	—	2	1	no	—
28	C₅×#3937	—	2	1	no	—
29	C₅×#1906	—	5	1	no	maximal
30	#10602438	C₅	1	1	yes	maximal, characteristic, direct product factor
31	C₅²×#41	—	2	1	no	—
32	C₅²×#41	—	2	1	no	—
33	C₅²×#41	C₂×C₄	1	2	yes	—
34	C₅²×#41	D₄	1	2	yes	—
35	C₂×C₅²×Q₈	D₄	1	1	yes	characteristic
36	C₂×C₅²×D₄	—	2	1	no	—
37	C₂×C₅²×D₄	D₄	1	1	yes	characteristic
38	C₂²×C₄×C₅²	—	2	1	no	—
39	C₂²×C₄×C₅²	—	2	2	no	—
40	C₂²×C₄×C₅²	—	2	1	no	—
41	C₂²×C₄×C₅²	C₂³	1	1	yes	characteristic
42	C₂×C₅×C₂²⋊D₅	—	2	1	no	—
43	C₅×#709	—	2	1	no	—
44	C₅×#709	—	2	1	no	—
45	C₅×#709	—	2	1	no	—
46	C₅×#709	—	2	1	no	—
47	C₂×C₅×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×C₄×C₅×D₅	—	2	1	no	—
49	C₂×C₅×Dic₁₀	C₂×C₄	1	1	yes	characteristic, complemented
50	C₅²×C₄⋊C₄	—	2	2	no	—
51	C₅²×C₄⋊C₄	—	2	1	no	—
52	C₅²×C₂²⋊C₄	—	2	2	no	—
53	C₅²×C₂²⋊C₄	D₄	1	2	yes	—
54	C₄²×C₅²	—	2	2	no	—
55	C₄²×C₅²	—	2	1	no	—
56	C₄²×C₅²	—	2	1	no	—
57	C₄²×C₅²	D₄	1	1	yes	characteristic
58	C₄²×C₅²	D₄	1	1	yes	characteristic
59	C₅×C₂²⋊Dic₅	—	2	1	no	—
60	C₅×#689	—	2	2	no	—
61	C₅×#688	—	2	2	no	—
62	C₅×#687	—	2	2	no	—
63	C₅×#686	—	2	2	no	—
64	C₅×C₄⋊Dic₅	—	2	1	no	—
65	C₄×C₅×Dic₅	—	2	1	no	—
66	C₅×#681	—	2	1	no	—
67	C₅×#681	—	2	1	no	—
68	C₅×#681	—	2	1	no	—
69	C₅×#681	C₂×C₄	1	2	yes	complemented
70	C₂×C₅×#168	—	2	1	no	—
71	C₂×C₅×#168	—	2	1	no	—
72	C₅×#575	—	5	1	no	—
73	C₄×C₅×#41	—	2	2	no	—
74	C₄×C₅×#41	D₅	1	1	yes	characteristic, complemented
75	C₄×C₅×#41	C₂×C₅	1	1	yes	characteristic, complemented
76	#66156	C₂×C₅	1	1	yes	characteristic
77	C₅×#421	—	5	1	no	—
78	C₂×C₅×#104	—	5	1	no	—
79	C₅×#410	—	5	1	no	—
80	#65525	C₂×C₅	1	1	yes	characteristic, complemented
81	#65295	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×#3937	C₂×C₅	1	1	yes	characteristic, complemented
83	C₅×#344	—	5	1	no	—
84	C₅×#339	—	5	1	no	—
85	#64753	C₂×C₅	1	1	yes	characteristic, complemented
86	#64743	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂³×C₅²	—	2	1	no	—
88	C₂³×C₅²	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₅×D₅	—	2	1	no	—
90	C₅²×Q₈	—	2	1	no	—
91	C₅²×Q₈	C₂²⋊C₄	1	2	yes	—
92	C₅²×D₄	—	2	2	no	—
93	C₅²×D₄	—	2	2	no	—
94	C₅²×D₄	—	2	1	no	—
95	C₅²×D₄	C₂²⋊C₄	1	2	yes	—
96	C₂×C₄×C₅²	—	2	1	no	—
97	C₂×C₄×C₅²	—	2	1	no	—
98	C₂×C₄×C₅²	—	2	2	no	—
99	C₂×C₄×C₅²	—	2	2	no	—
100	C₂×C₄×C₅²	—	2	2	no	—
101	C₂×C₄×C₅²	—	2	1	no	—
102	C₂×C₄×C₅²	—	4	2	no	—
103	C₂×C₄×C₅²	—	4	4	no	—
104	C₂×C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×C₅²	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×C₅²	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×C₅²	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×C₅²	#41	1	1	yes	characteristic
109	C₂×C₄×C₅²	#41	1	1	yes	characteristic
110	C₅×C₂²⋊D₅	—	4	1	no	—
111	C₅×C₂²⋊D₅	—	4	1	no	—
112	C₂×C₅×Dic₅	—	2	1	no	—
113	C₂×C₅×Dic₅	—	4	1	no	—
114	C₅×D₂₀	—	2	1	no	—
115	C₅×D₂₀	—	2	1	no	—
116	C₄×C₅×D₅	—	4	1	no	—
117	C₄×C₅×D₅	—	4	1	no	—
118	C₅×Dic₁₀	—	2	1	no	—
119	C₅×Dic₁₀	—	2	1	no	—
120	C₅×#168	—	2	2	no	—
121	C₅×#168	—	4	1	no	—
122	C₂×C₅×#41	—	2	2	no	—
123	C₂×C₅×#41	—	5	1	no	—
124	C₂×C₅×#41	C₂×D₅	1	1	yes	characteristic
125	C₂×C₅×#41	C₂²×C₅	1	1	yes	characteristic
126	C₂×#709	C₂²×C₅	1	1	yes	characteristic
127	C₅×#137	—	5	2	no	—
128	C₅×#137	—	10	1	no	—
129	C₅×AGL(1,ℤ/8)	—	5	2	no	—
130	C₅×AGL(1,ℤ/8)	—	10	1	no	—
131	C₅×#135	—	10	2	no	—
132	C₂×C₅×M₁₆	—	5	1	no	—
133	C₂×C₅×M₁₆	—	5	1	no	—
134	C₄×C₅×Q₈	—	2	4	no	—
135	C₄×C₅×Q₈	—	2	1	no	—
136	C₄×C₅×Q₈	—	2	1	no	—
137	C₄×C₅×D₄	—	2	4	no	—
138	C₄×C₅×D₄	—	2	8	no	—
139	C₄×C₅×D₄	—	2	1	no	—
140	C₄×C₅×D₄	—	2	1	no	—
141	C₄×C₅×D₄	—	2	2	no	—
142	C₄×C₅×D₄	—	2	2	no	—
143	C₅×#117	—	2	4	no	—
144	C₅×#117	—	2	1	no	—
145	C₅×#117	—	2	1	no	—
146	C₅×#117	—	2	2	no	—
147	C₅×#117	—	5	1	no	—
148	C₅×#117	C₂×D₅	1	1	yes	characteristic
149	C₅×#117	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₄²×C₅	—	2	4	no	—
151	C₂×C₄²×C₅	—	2	1	no	—
152	C₂×C₄²×C₅	—	2	1	no	—
153	C₂×C₄²×C₅	—	2	2	no	—
154	C₂×C₄²×C₅	C₂×D₅	1	1	yes	characteristic
155	C₂×C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
156	#4097	C₄×C₅	1	2	yes	complemented
157	#4096	—	2	2	no	—
158	#4095	C₄×C₅	1	2	yes	complemented
159	#4088	—	2	1	no	—
160	#4078	—	2	1	no	—
161	#4072	C₂²×C₅	1	1	yes	characteristic
162	C₂×#681	C₂²×C₅	1	1	yes	characteristic
163	C₂×#681	C₂²×C₅	1	1	yes	characteristic
164	C₅×#104	—	10	2	no	—
165	C₅×#104	—	10	1	no	—
166	C₅×#104	—	10	1	no	—
167	C₅×#99	—	10	2	no	—
168	#3969	—	2	2	no	—
169	#3938	—	2	2	no	—
170	#3937	—	2	1	no	—
171	#3937	—	2	1	no	—
172	#1906	—	5	1	no	Sylow
173	C₂²×C₅²	—	2	2	no	—
174	C₂²×C₅²	—	4	1	no	—
175	C₂²×C₅²	—	4	2	no	—
176	C₂²×C₅²	C₄×D₄	1	1	yes	characteristic
177	C₂²×C₅²	#120	1	1	yes	characteristic
178	C₂²×C₅²	#121	1	1	yes	characteristic
179	C₂×C₅×D₅	—	4	1	no	—
180	C₂×C₅×D₅	—	8	1	no	—
181	C₄×C₅²	—	2	2	no	—
182	C₄×C₅²	—	2	2	no	—
183	C₄×C₅²	—	4	2	no	—
184	C₄×C₅²	—	4	1	no	—
185	C₄×C₅²	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₄×C₅²	C₄×D₄	1	1	yes	characteristic
187	C₄×C₅²	#121	1	1	yes	characteristic
188	C₄×C₅²	#123	1	1	yes	characteristic
189	C₅×Dic₅	—	4	1	no	—
190	C₅×Dic₅	—	8	1	no	—
191	C₅×#41	—	2	4	no	—
192	C₅×#41	—	2	4	no	—
193	C₅×#41	—	2	1	no	—
194	C₅×#41	—	2	1	no	—
195	C₅×#41	—	2	1	no	—
196	C₅×#41	—	2	1	no	—
197	C₅×#41	—	2	4	no	—
198	C₅×#41	—	2	4	no	—
199	C₅×#41	—	10	1	no	—
200	C₅×#41	—	10	1	no	—
201	C₅×#41	—	10	1	no	—
202	C₅×#41	—	10	1	no	—
203	C₅×#41	C₄×D₅	1	2	yes	—
204	C₅×#41	D₂₀	1	2	yes	—
205	C₅×#41	C₂×C₄×C₅	1	2	yes	—
206	C₅×#41	C₅×D₄	1	2	yes	—
207	C₂×C₅×Q₈	—	2	2	no	—
208	C₂×C₅×Q₈	—	5	1	no	—
209	C₂×C₅×Q₈	C₂²⋊D₅	1	1	yes	characteristic
210	C₂×C₅×Q₈	C₅×D₄	1	1	yes	characteristic
211	C₂×C₅×D₄	—	2	4	no	—
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	—	2	1	no	—
214	C₂×C₅×D₄	—	2	2	no	—
215	C₂×C₅×D₄	—	5	1	no	—
216	C₂×C₅×D₄	—	10	1	no	—
217	C₂×C₅×D₄	C₂²⋊D₅	1	1	yes	characteristic
218	C₂×C₅×D₄	C₅×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅	—	2	4	no	—
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	8	no	—
223	C₂²×C₄×C₅	—	2	2	no	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	—	2	4	no	—
226	C₂²×C₄×C₅	—	2	1	no	—
227	C₂²×C₄×C₅	—	2	1	no	—
228	C₂²×C₄×C₅	—	2	2	no	—
229	C₂²×C₄×C₅	—	10	1	no	—
230	C₂²×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
232	C₂×C₂²⋊D₅	—	2	1	no	—
233	#709	—	2	1	no	—
234	#709	—	2	1	no	—
235	#709	—	2	1	no	—
236	#709	—	2	1	no	—
237	C₂×D₂₀	C₂×C₄×C₅	1	1	yes	characteristic, complemented
238	C₂×C₄×D₅	—	2	1	no	—
239	C₂×Dic₁₀	C₂×C₄×C₅	1	1	yes	characteristic, complemented
240	C₅×Q₁₆	—	10	2	no	—
241	C₅×SD₁₆	—	10	2	no	—
242	C₅×SD₁₆	—	10	2	no	—
243	C₅×D₈	—	10	2	no	—
244	C₅×M₁₆	—	5	2	no	—
245	C₅×M₁₆	—	10	1	no	—
246	C₅×M₁₆	—	10	1	no	—
247	C₅×M₁₆	—	10	1	no	—
248	C₂×C₅×C₈	—	10	1	no	—
249	C₂×C₅×C₈	—	10	1	no	—
250	C₅×C₄⋊C₄	—	2	8	no	—
251	C₅×C₄⋊C₄	—	2	2	no	—
252	C₅×C₄⋊C₄	—	2	2	no	—
253	C₅×C₄⋊C₄	—	2	4	no	—
254	C₅×C₄⋊C₄	—	2	1	no	—
255	C₅×C₄⋊C₄	—	2	1	no	—
256	C₅×C₄⋊C₄	—	10	1	no	—
257	C₅×C₂²⋊C₄	—	2	8	no	—
258	C₅×C₂²⋊C₄	—	2	2	no	—
259	C₅×C₂²⋊C₄	—	2	2	no	—
260	C₅×C₂²⋊C₄	—	2	4	no	—
261	C₅×C₂²⋊C₄	—	10	1	no	—
262	C₅×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
263	C₅×C₂²⋊C₄	C₅×D₄	1	2	yes	—
264	C₄²×C₅	—	2	4	no	—
265	C₄²×C₅	—	2	8	no	—
266	C₄²×C₅	—	2	2	no	—
267	C₄²×C₅	—	2	2	no	—
268	C₄²×C₅	—	2	4	no	—
269	C₄²×C₅	—	2	1	no	—
270	C₄²×C₅	—	2	1	no	—
271	C₄²×C₅	—	2	1	no	—
272	C₄²×C₅	—	2	1	no	—
273	C₄²×C₅	—	2	2	no	—
274	C₄²×C₅	—	2	2	no	—
275	C₄²×C₅	—	10	1	no	—
276	C₄²×C₅	C₂²⋊D₅	1	1	yes	characteristic
277	C₄²×C₅	C₂²⋊D₅	1	1	yes	characteristic
278	C₄²×C₅	C₅×D₄	1	1	yes	characteristic
279	C₄²×C₅	C₅×D₄	1	1	yes	characteristic
280	C₂²⋊Dic₅	—	2	1	no	—
281	#689	—	2	2	no	—
282	#688	—	2	2	no	—
283	#687	—	2	2	no	—
284	#686	—	2	2	no	—
285	C₄⋊Dic₅	—	2	1	no	—
286	C₄×Dic₅	—	2	1	no	—
287	#681	—	2	1	no	—
288	#681	—	2	1	no	—
289	#681	—	2	1	no	—
290	#681	C₂×C₄×C₅	1	2	yes	complemented
291	C₂×#168	—	2	1	no	—
292	C₂×#168	—	2	1	no	—
293	#575	—	5	1	no	—
294	C₄×#41	C₅×D₅	1	1	yes	characteristic, complemented
295	#421	—	5	1	no	—
296	C₂×#104	—	5	1	no	—
297	#410	—	5	1	no	—
298	#344	—	5	1	no	—
299	#339	—	5	1	no	—
300	C₂×C₅²	—	2	1	no	—
301	C₂×C₅²	—	2	1	no	—
302	C₂×C₅²	—	2	1	no	—
303	C₂×C₅²	—	4	2	no	—
304	C₂×C₅²	#386	1	1	yes	characteristic
305	C₅×D₅	—	8	1	no	—
306	C₂³×C₅	—	2	4	no	—
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	1	no	—
309	C₂³×C₅	—	2	2	no	—
310	C₂³×C₅	—	10	1	no	—
311	C₂³×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
312	C₂³×C₅	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×D₅	—	2	1	no	—
314	C₅×Q₈	—	2	4	no	—
315	C₅×Q₈	—	2	1	no	—
316	C₅×Q₈	—	2	1	no	—
317	C₅×Q₈	—	2	4	no	—
318	C₅×Q₈	—	10	1	no	—
319	C₅×Q₈	—	10	1	no	—
320	C₅×Q₈	#685	1	2	yes	—
321	C₅×Q₈	C₅×C₂²⋊C₄	1	2	yes	—
322	C₅×D₄	—	2	8	no	—
323	C₅×D₄	—	2	8	no	—
324	C₅×D₄	—	2	4	no	—
325	C₅×D₄	—	2	2	no	—
326	C₅×D₄	—	2	2	no	—
327	C₅×D₄	—	2	2	no	—
328	C₅×D₄	—	2	2	no	—
329	C₅×D₄	—	2	1	no	—
330	C₅×D₄	—	2	1	no	—
331	C₅×D₄	—	2	4	no	—
332	C₅×D₄	—	10	1	no	—
333	C₅×D₄	—	10	1	no	—
334	C₅×D₄	—	20	1	no	—
335	C₅×D₄	—	20	1	no	—
336	C₅×D₄	#685	1	2	yes	—
337	C₅×D₄	C₅×C₂²⋊C₄	1	2	yes	—
338	C₂×C₄×C₅	—	2	4	no	—
339	C₂×C₄×C₅	—	2	4	no	—
340	C₂×C₄×C₅	—	2	8	no	—
341	C₂×C₄×C₅	—	2	8	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	8	no	—
351	C₂×C₄×C₅	—	2	4	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	2	2	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	4	2	no	—
363	C₂×C₄×C₅	—	4	2	no	—
364	C₂×C₄×C₅	—	4	8	no	—
365	C₂×C₄×C₅	—	4	16	no	—
366	C₂×C₄×C₅	—	4	4	no	—
367	C₂×C₄×C₅	—	4	4	no	—
368	C₂×C₄×C₅	—	10	1	no	—
369	C₂×C₄×C₅	—	20	1	no	—
370	C₂×C₄×C₅	—	20	1	no	—
371	C₂×C₄×C₅	—	20	1	no	—
372	C₂×C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
373	C₂×C₄×C₅	C₂×D₂₀	1	1	yes	characteristic
374	C₂×C₄×C₅	#709	1	1	yes	characteristic
375	C₂×C₄×C₅	#709	1	1	yes	characteristic
376	C₂×C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
377	C₂×C₄×C₅	C₂×C₂²⋊D₅	1	1	yes	characteristic
378	C₂×C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₂×C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂×C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂×C₄×C₅	C₅×#41	1	1	yes	characteristic
383	C₂×C₄×C₅	C₅×#41	1	1	yes	characteristic
384	C₂²⋊D₅	—	4	1	no	—
385	C₂²⋊D₅	—	4	1	no	—
386	C₂×Dic₅	—	2	1	no	—
387	C₂×Dic₅	—	4	1	no	—
388	D₂₀	—	2	1	no	—
389	D₂₀	—	2	1	no	—
390	C₄×D₅	—	4	1	no	—
391	C₄×D₅	—	4	1	no	—
392	Dic₁₀	—	2	1	no	—
393	Dic₁₀	—	2	1	no	—
394	C₅×C₈	—	10	2	no	—
395	C₅×C₈	—	20	1	no	—
396	#168	—	2	2	no	—
397	#168	—	4	1	no	—
398	C₂×#41	—	5	1	no	—
399	C₂×#41	C₂×C₅×D₅	1	1	yes	characteristic
400	#137	—	5	2	no	—
401	#137	—	10	1	no	—
402	AGL(1,ℤ/8)	—	5	2	no	—
403	AGL(1,ℤ/8)	—	10	1	no	—
404	#135	—	10	2	no	—
405	C₂×M₁₆	—	5	1	no	—
406	C₂×M₁₆	—	5	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	2	no	—
410	#117	—	2	1	no	—
411	#117	—	5	1	no	—
412	#117	C₂×C₅×D₅	1	1	yes	characteristic
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂×C₅×D₅	1	1	yes	characteristic
415	#104	—	10	2	no	—
416	#104	—	10	1	no	—
417	#104	—	10	1	no	—
418	#99	—	10	2	no	—
419	C₅²	#1906	1	1	yes	characteristic, complemented, Sylow
420	C₂²×C₅	—	2	8	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	4	no	—
429	C₂²×C₅	—	4	8	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	—	4	2	no	—
432	C₂²×C₅	—	20	1	no	—
433	C₂²×C₅	—	40	1	no	—
434	C₂²×C₅	C₄×C₂²⋊D₅	1	1	yes	characteristic
435	C₂²×C₅	#4076	1	1	yes	characteristic
436	C₂²×C₅	#4099	1	1	yes	characteristic
437	C₂²×C₅	C₄×C₅×D₄	1	1	yes	characteristic
438	C₂²×C₅	C₅×#120	1	1	yes	characteristic
439	C₂²×C₅	C₅×#121	1	1	yes	characteristic
440	C₂×D₅	—	4	1	no	—
441	C₂×D₅	—	8	1	no	—
442	C₄×C₅	—	2	8	no	—
443	C₄×C₅	—	2	8	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	2	no	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	2	2	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	4	8	no	—
453	C₄×C₅	—	4	4	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	2	no	—
457	C₄×C₅	—	4	1	no	—
458	C₄×C₅	—	20	1	no	—
459	C₄×C₅	—	40	1	no	—
460	C₄×C₅	C₂×#685	1	1	yes	characteristic
461	C₄×C₅	C₄×C₂²⋊D₅	1	1	yes	characteristic
462	C₄×C₅	#4075	1	1	yes	characteristic
463	C₄×C₅	#4076	1	1	yes	characteristic
464	C₄×C₅	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
465	C₄×C₅	C₄×C₅×D₄	1	1	yes	characteristic
466	C₄×C₅	C₅×#121	1	1	yes	characteristic
467	C₄×C₅	C₅×#123	1	1	yes	characteristic
468	Dic₅	—	4	1	no	—
469	Dic₅	—	8	1	no	—
470	#41	—	2	1	no	—
471	#41	—	2	1	no	—
472	#41	—	10	1	no	—
473	#41	—	10	1	no	—
474	#41	—	10	1	no	—
475	#41	—	10	1	no	—
476	#41	C₄×C₅×D₅	1	2	yes	—
477	#41	C₅×D₂₀	1	2	yes	—
478	C₂×Q₈	—	5	1	no	—
479	C₂×Q₈	C₅×C₂²⋊D₅	1	1	yes	characteristic
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	5	1	no	—
482	C₂×D₄	—	10	1	no	—
483	C₂×D₄	C₅×C₂²⋊D₅	1	1	yes	characteristic
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	10	1	no	—
488	C₂²×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
489	Q₁₆	—	10	2	no	—
490	SD₁₆	—	10	2	no	—
491	SD₁₆	—	10	2	no	—
492	D₈	—	10	2	no	—
493	M₁₆	—	5	2	no	—
494	M₁₆	—	10	1	no	—
495	M₁₆	—	10	1	no	—
496	M₁₆	—	10	1	no	—
497	C₂×C₈	—	10	1	no	—
498	C₂×C₈	—	10	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	10	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	10	1	no	—
504	C₂²⋊C₄	C₅×C₂²⋊D₅	1	2	yes	—
505	C₄²	—	2	2	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	10	1	no	—
509	C₄²	C₅×C₂²⋊D₅	1	1	yes	characteristic
510	C₄²	C₅×C₂²⋊D₅	1	1	yes	characteristic
511	C₂×C₅	—	2	4	no	—
512	C₂×C₅	—	2	1	no	—
513	C₂×C₅	—	2	1	no	—
514	C₂×C₅	—	2	1	no	—
515	C₂×C₅	—	2	1	no	—
516	C₂×C₅	—	2	1	no	—
517	C₂×C₅	—	2	1	no	—
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	—	4	2	no	—
520	C₂×C₅	—	4	2	no	—
521	C₂×C₅	—	4	8	no	—
522	C₂×C₅	—	4	2	no	—
523	C₂×C₅	—	4	2	no	—
524	C₂×C₅	—	40	1	no	—
525	C₂×C₅	#65502	1	1	yes	characteristic
526	C₂×C₅	C₅×#386	1	1	yes	characteristic
527	D₅	—	8	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	10	1	no	—
530	C₂³	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
531	Q₈	—	2	1	no	—
532	Q₈	—	10	1	no	—
533	Q₈	—	10	1	no	—
534	Q₈	C₅×#685	1	2	yes	—
535	D₄	—	2	2	no	—
536	D₄	—	2	2	no	—
537	D₄	—	2	1	no	—
538	D₄	—	10	1	no	—
539	D₄	—	10	1	no	—
540	D₄	—	20	1	no	—
541	D₄	—	20	1	no	—
542	D₄	C₅×#685	1	2	yes	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	10	1	no	—
552	C₂×C₄	—	20	1	no	—
553	C₂×C₄	—	20	1	no	—
554	C₂×C₄	—	20	1	no	—
555	C₂×C₄	C₂×C₄×C₅×D₅	1	1	yes	characteristic
556	C₂×C₄	C₂×C₅×D₂₀	1	1	yes	characteristic
557	C₂×C₄	C₅×#709	1	1	yes	characteristic
558	C₂×C₄	C₅×#709	1	1	yes	characteristic
559	C₂×C₄	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
560	C₂×C₄	C₂×C₅×C₂²⋊D₅	1	1	yes	characteristic
561	C₈	—	10	2	no	—
562	C₈	—	20	1	no	—
563	C₅	—	2	2	no	—
564	C₅	#10602438	1	1	yes	characteristic, direct product factor
565	C₅	C₅×#1906	1	1	yes	characteristic, complemented
566	C₂²	—	2	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	20	1	no	—
570	C₂²	—	40	1	no	—
571	C₂²	C₄×C₅×C₂²⋊D₅	1	1	yes	characteristic
572	C₂²	C₅×#4076	1	1	yes	characteristic
573	C₂²	C₅×#4099	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	20	1	no	—
579	C₄	—	40	1	no	—
580	C₄	C₂×C₅×#685	1	1	yes	characteristic
581	C₄	C₄×C₅×C₂²⋊D₅	1	1	yes	characteristic
582	C₄	C₅×#4075	1	1	yes	characteristic
583	C₄	C₅×#4076	1	1	yes	characteristic
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	4	2	no	—
588	C₂	—	40	1	no	—
589	C₂	C₅×#65502	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#4076
commutator	C₂×C₄×C₅	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₅
Fitting	C₄×C₅²×#41	C₂
socle	C₂×C₅²	#386
prime radical	C₅×#66156	C₂
cosocle	C₂²×C₄×C₅	C₂³×C₅
hypercenter	C₄×C₅×#41	D₅
hypocenter	C₅	C₅×#1906
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₄×C₅²×#41	C₂	semidirect
3. C₅×#65525	C₂	semidirect
4. C₅×#65295	C₂	semidirect
5. C₂×C₅×#3937	C₂	semidirect
6. C₅×#64753	C₂	semidirect
7. C₅×#64743	C₂	semidirect
17. C₅×#4097	C₄	semidirect
19. C₅×#4095	C₄	semidirect
30. #10602438	C₅	direct (N × H)
47. C₂×C₅×D₂₀	C₂×C₄	semidirect
49. C₂×C₅×Dic₁₀	C₂×C₄	semidirect
69. C₅×#681	C₂×C₄	semidirect
74. C₄×C₅×#41	D₅	semidirect
75. C₄×C₅×#41	C₂×C₅	semidirect
80. #65525	C₂×C₅	semidirect
81. #65295	C₂×C₅	semidirect
82. C₂×#3937	C₂×C₅	semidirect
85. #64753	C₂×C₅	semidirect
86. #64743	C₂×C₅	semidirect
156. #4097	C₄×C₅	semidirect
158. #4095	C₄×C₅	semidirect
237. C₂×D₂₀	C₂×C₄×C₅	semidirect
239. C₂×Dic₁₀	C₂×C₄×C₅	semidirect
290. #681	C₂×C₄×C₅	semidirect
294. C₄×#41	C₅×D₅	semidirect
419. C₅²	#1906	semidirect
564. C₅	#10602438	direct (N × H)
565. C₅	C₅×#1906	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅²×#41	2
C₅×#66156	2
C₅×#65525	2
C₅×#65295	2
C₂×C₅×#3937	2
C₅×#64753	2
C₅×#64743	2
C₅×#1906	5
#10602438	5

Subgroups — C5×#10602438 #72223413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10602438 #72223413