Subgroups — C₅×#21593 #11944313

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3091	C₂	1	1	yes	maximal, characteristic
2	C₅×#2929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1929	C₂	1	2	yes	maximal, complemented
5	C₅×#1922	C₂	1	2	yes	maximal, complemented
6	C₅×#1871	C₂	1	1	yes	maximal, characteristic
7	C₅×#1855	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1826	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1773	C₂	1	2	yes	maximal, complemented
10	C₅×#1765	C₂	1	2	yes	maximal, complemented
11	C₅×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#525	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₅×#485	C₄	1	2	yes	complemented
18	C₅×#484	C₄	1	1	yes	characteristic, complemented
19	C₅×#483	C₄	1	1	yes	characteristic, complemented
20	C₅×#482	C₄	1	2	yes	complemented
21	C₅×#481	C₄	1	1	yes	characteristic, complemented
22	C₅×#480	C₄	1	1	yes	characteristic, complemented
23	C₅×#435	—	2	1	no	—
24	C₅×#435	—	2	1	no	—
25	C₅×C₈×D₄	—	2	1	no	—
26	C₅×C₈×D₄	—	2	1	no	—
27	C₂×C₅×#108	C₂²	1	2	yes	—
28	C₅×#427	C₂²	1	2	yes	—
29	C₅×#424	C₂²	1	1	yes	characteristic
30	C₂×C₅×#104	C₂²	1	2	yes	—
31	C₅×#416	C₂²	1	2	yes	—
32	C₅×#408	C₂²	1	1	yes	characteristic
33	C₅×#407	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₅×#405	—	2	1	no	—
36	C₅×#405	—	2	1	no	—
37	C₅×#405	C₂²	1	2	yes	—
38	C₅×#405	C₂²	1	1	yes	characteristic
39	C₅×#405	C₂²	1	2	yes	—
40	C₂×C₅×#97	—	2	1	no	—
41	C₂×C₅×#97	C₂²	1	2	yes	—
42	C₂×C₄×C₅×C₈	—	2	1	no	—
43	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₅×#341	C₂²	1	2	yes	—
45	C₅×#339	C₂²	1	2	yes	—
46	C₅×#339	C₂²	1	2	yes	—
47	C₅×#339	C₂²	1	2	yes	—
48	C₅×#336	C₂²	1	2	yes	—
49	#21593	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₅×#131	—	2	4	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	4	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₅×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₂²×C₅×C₈	—	2	4	no	—
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
64	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
65	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	2	yes	—
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₅×#123	—	2	1	no	—
70	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
71	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
72	C₅×#121	C₂×C₄	1	1	yes	characteristic
73	C₅×#121	C₂×C₄	1	1	yes	characteristic
74	C₅×#120	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₅×#117	—	2	1	no	—
78	C₅×#117	—	2	1	no	—
79	C₅×#117	C₂×C₄	1	2	yes	—
80	C₅×#117	C₂³	1	2	yes	—
81	C₅×#117	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	C₂³	1	2	yes	—
88	C₅×#108	—	2	4	no	—
89	C₅×#107	C₂×C₄	1	2	yes	—
90	C₅×#107	C₂×C₄	1	2	yes	—
91	C₅×#106	C₂×C₄	1	2	yes	—
92	C₅×#106	C₂×C₄	1	2	yes	—
93	C₅×C₄⋊C₈	—	2	1	no	—
94	C₅×C₄⋊C₈	—	2	1	no	—
95	C₅×#104	—	2	4	no	—
96	C₅×#103	C₂×C₄	1	2	yes	—
97	C₅×#103	C₂×C₄	1	2	yes	—
98	C₅×#102	C₂×C₄	1	2	yes	—
99	C₅×#102	C₂×C₄	1	2	yes	—
100	C₅×C₂²⋊C₈	—	2	1	no	—
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
107	C₅×#97	—	2	2	no	—
108	C₅×#97	—	2	2	no	—
109	C₅×#97	—	2	1	no	—
110	C₅×#97	—	2	4	no	—
111	C₄×C₅×C₈	—	2	2	no	—
112	C₄×C₅×C₈	—	2	2	no	—
113	C₄×C₅×C₈	—	2	1	no	—
114	C₅×#95	—	2	1	no	—
115	#3091	C₂×C₅	1	1	yes	characteristic
116	#2929	C₂×C₅	1	1	yes	characteristic
117	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
118	#1929	C₂×C₅	1	2	yes	complemented
119	#1922	C₂×C₅	1	2	yes	complemented
120	#1871	C₂×C₅	1	1	yes	characteristic
121	#1855	C₂×C₅	1	1	yes	characteristic, complemented
122	#1826	C₂×C₅	1	1	yes	characteristic, complemented
123	#1773	C₂×C₅	1	2	yes	complemented
124	#1765	C₂×C₅	1	2	yes	complemented
125	#1752	C₂×C₅	1	1	yes	characteristic, complemented
126	C₂⁴×C₅	#41	1	1	yes	characteristic
127	C₅×#41	—	2	2	no	—
128	C₅×#41	—	2	2	no	—
129	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	—	2	2	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	#41	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₅×M₁₆	—	2	4	no	—
147	C₅×M₁₆	—	2	2	no	—
148	C₅×M₁₆	—	2	2	no	—
149	C₅×M₁₆	—	2	2	no	—
150	C₅×M₁₆	—	4	2	no	—
151	C₅×M₁₆	#41	1	4	yes	—
152	C₂×C₅×C₈	—	2	4	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	4	2	no	—
164	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×C₈	#41	1	4	yes	—
171	C₅×C₄⋊C₄	—	2	1	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
176	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
177	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
179	C₅×C₂²⋊C₄	—	2	2	no	—
180	C₅×C₂²⋊C₄	—	2	1	no	—
181	C₅×C₂²⋊C₄	—	2	1	no	—
182	C₅×C₂²⋊C₄	—	2	2	no	—
183	C₅×C₂²⋊C₄	—	2	1	no	—
184	C₅×C₂²⋊C₄	—	2	1	no	—
185	C₅×C₂²⋊C₄	—	2	1	no	—
186	C₅×C₂²⋊C₄	—	4	2	no	—
187	C₄²×C₅	—	2	2	no	—
188	C₄²×C₅	—	2	2	no	—
189	C₄²×C₅	—	2	1	no	—
190	C₄²×C₅	—	2	2	no	—
191	C₄²×C₅	—	2	2	no	—
192	C₂×#131	C₂²×C₅	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
195	#525	C₂²×C₅	1	1	yes	characteristic
196	C₂×#117	C₂²×C₅	1	1	yes	characteristic
197	#485	C₄×C₅	1	2	yes	complemented
198	#484	C₄×C₅	1	1	yes	characteristic, complemented
199	#483	C₄×C₅	1	1	yes	characteristic, complemented
200	#482	C₄×C₅	1	2	yes	complemented
201	#481	C₄×C₅	1	1	yes	characteristic, complemented
202	#480	C₄×C₅	1	1	yes	characteristic, complemented
203	#435	—	2	1	no	—
204	#435	—	2	1	no	—
205	C₈×D₄	—	2	1	no	—
206	C₈×D₄	—	2	1	no	—
207	C₂×#108	C₂²×C₅	1	2	yes	—
208	#427	C₂²×C₅	1	2	yes	—
209	#424	C₂²×C₅	1	1	yes	characteristic
210	C₂×#104	C₂²×C₅	1	2	yes	—
211	#416	C₂²×C₅	1	2	yes	—
212	#408	C₂²×C₅	1	1	yes	characteristic
213	#407	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
215	#405	—	2	1	no	—
216	#405	—	2	1	no	—
217	#405	C₂²×C₅	1	2	yes	—
218	#405	C₂²×C₅	1	2	yes	—
219	#405	C₂²×C₅	1	1	yes	characteristic
220	C₂×#97	—	2	1	no	—
221	C₂×#97	C₂²×C₅	1	2	yes	—
222	C₂×C₄×C₈	—	2	1	no	—
223	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	#341	C₂²×C₅	1	2	yes	—
225	#339	C₂²×C₅	1	2	yes	—
226	#339	C₂²×C₅	1	2	yes	—
227	#339	C₂²×C₅	1	2	yes	—
228	#336	C₂²×C₅	1	2	yes	—
229	C₂³×C₅	—	2	2	no	—
230	C₂³×C₅	—	2	2	no	—
231	C₂³×C₅	—	2	1	no	—
232	C₂³×C₅	—	4	1	no	—
233	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
234	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂³×C₅	C₂×#41	1	1	yes	characteristic
236	C₅×Q₈	—	2	2	no	—
237	C₅×D₄	—	2	2	no	—
238	C₅×D₄	—	4	2	no	—
239	C₅×D₄	—	4	2	no	—
240	C₅×D₄	—	4	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	2	no	—
260	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×#41	1	2	yes	—
265	C₂×C₄×C₅	C₂×#41	1	2	yes	—
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	2	2	no	—
268	C₅×C₈	—	2	1	no	—
269	C₅×C₈	—	2	1	no	—
270	C₅×C₈	—	2	4	no	—
271	C₅×C₈	—	4	1	no	—
272	C₅×C₈	—	4	1	no	—
273	C₅×C₈	#123	1	2	yes	—
274	C₅×C₈	#123	1	2	yes	—
275	C₂×#41	C₂³×C₅	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
277	#131	—	2	4	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
282	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
283	C₂×M₁₆	C₂³×C₅	1	2	yes	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	4	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
288	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
289	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
290	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₅	1	2	yes	—
292	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
296	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
297	#121	C₂×C₄×C₅	1	1	yes	characteristic
298	#121	C₂×C₄×C₅	1	1	yes	characteristic
299	#120	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	1	no	—
304	#117	C₂×C₄×C₅	1	2	yes	—
305	#117	C₂³×C₅	1	2	yes	—
306	#117	C₂³×C₅	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₅	1	2	yes	—
313	#108	—	2	4	no	—
314	#107	C₂×C₄×C₅	1	2	yes	—
315	#107	C₂×C₄×C₅	1	2	yes	—
316	#106	C₂×C₄×C₅	1	2	yes	—
317	#106	C₂×C₄×C₅	1	2	yes	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	2	1	no	—
320	#104	—	2	4	no	—
321	#103	C₂×C₄×C₅	1	2	yes	—
322	#103	C₂×C₄×C₅	1	2	yes	—
323	#102	C₂×C₄×C₅	1	2	yes	—
324	#102	C₂×C₄×C₅	1	2	yes	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
330	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
331	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
332	#97	—	2	2	no	—
333	#97	—	2	2	no	—
334	#97	—	2	1	no	—
335	#97	—	2	4	no	—
336	C₄×C₈	—	2	2	no	—
337	C₄×C₈	—	2	2	no	—
338	C₄×C₈	—	2	1	no	—
339	#95	—	2	1	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	1	no	—
342	C₂²×C₅	—	2	1	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	—	2	1	no	—
346	C₂²×C₅	—	2	1	no	—
347	C₂²×C₅	—	4	4	no	—
348	C₂²×C₅	—	4	1	no	—
349	C₂²×C₅	—	4	1	no	—
350	C₂²×C₅	—	4	1	no	—
351	C₂²×C₅	#444	1	2	yes	—
352	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂²×C₅	#529	1	2	yes	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	—	4	1	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	—	4	1	no	—
360	C₄×C₅	—	4	1	no	—
361	C₄×C₅	—	8	2	no	—
362	C₄×C₅	C₄×#41	1	2	yes	—
363	C₄×C₅	C₂×#123	1	1	yes	characteristic
364	C₄×C₅	#525	1	1	yes	characteristic
365	C₂⁴	C₅×#41	1	1	yes	characteristic
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₅×#41	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
385	M₁₆	—	2	4	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	4	2	no	—
390	M₁₆	C₅×#41	1	4	yes	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	4	2	no	—
403	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
404	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
405	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
408	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂×C₈	C₅×#41	1	4	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
415	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
416	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
417	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	—	2	2	no	—
433	C₂×C₅	—	4	1	no	—
434	C₂×C₅	—	8	1	no	—
435	C₂×C₅	C₄×#123	1	1	yes	characteristic
436	C₂×C₅	C₂×#444	1	1	yes	characteristic
437	C₂×C₅	#2955	1	1	yes	characteristic
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
443	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
444	C₂³	C₂×C₅×#41	1	1	yes	characteristic
445	Q₈	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
470	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
473	C₂×C₄	C₂×C₅×#41	1	2	yes	—
474	C₂×C₄	C₂×C₅×#41	1	2	yes	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	1	no	—
478	C₈	—	2	1	no	—
479	C₈	—	2	4	no	—
480	C₈	—	4	1	no	—
481	C₈	—	4	1	no	—
482	C₈	C₅×#123	1	2	yes	—
483	C₈	C₅×#123	1	2	yes	—
484	C₅	#21593	1	1	yes	characteristic, direct product factor, Sylow
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	C₅×#444	1	2	yes	—
497	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
498	C₂²	C₅×#529	1	2	yes	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	8	2	no	—
507	C₄	C₄×C₅×#41	1	2	yes	—
508	C₄	C₂×C₅×#123	1	1	yes	characteristic
509	C₄	C₅×#525	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	8	1	no	—
514	C₂	C₄×C₅×#123	1	1	yes	characteristic
515	C₂	C₂×C₅×#444	1	1	yes	characteristic
516	C₂	C₅×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#405	C₂	semidirect
4. C₅×#1929	C₂	semidirect
5. C₅×#1922	C₂	semidirect
7. C₅×#1855	C₂	semidirect
8. C₅×#1826	C₂	semidirect
9. C₅×#1773	C₂	semidirect
10. C₅×#1765	C₂	semidirect
11. C₅×#1752	C₂	semidirect
17. C₅×#485	C₄	semidirect
18. C₅×#484	C₄	semidirect
19. C₅×#483	C₄	semidirect
20. C₅×#482	C₄	semidirect
21. C₅×#481	C₄	semidirect
22. C₅×#480	C₄	semidirect
49. #21593	C₅	direct (N × H)
117. C₂×#405	C₂×C₅	semidirect
118. #1929	C₂×C₅	semidirect
119. #1922	C₂×C₅	semidirect
121. #1855	C₂×C₅	semidirect
122. #1826	C₂×C₅	semidirect
123. #1773	C₂×C₅	semidirect
124. #1765	C₂×C₅	semidirect
125. #1752	C₂×C₅	semidirect
197. #485	C₄×C₅	semidirect
198. #484	C₄×C₅	semidirect
199. #483	C₄×C₅	semidirect
200. #482	C₄×C₅	semidirect
201. #481	C₄×C₅	semidirect
202. #480	C₄×C₅	semidirect
484. C₅	#21593	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3091	2
C₅×#2929	2
C₂×C₅×#405	2
C₅×#1929	2
C₅×#1922	2
C₅×#1871	2
C₅×#1855	2
C₅×#1826	2
C₅×#1773	2
C₅×#1765	2
C₅×#1752	2
#21593	5

Subgroups — C5×#21593 #11944313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21593 #11944313