Subgroups — C₅×#17480 #11940200

Order 1280.

1020 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1495	C₂	1	4	yes	maximal, complemented
5	C₅×#1494	C₂	1	4	yes	maximal, complemented
6	C₅×#1479	C₂	1	2	yes	maximal, complemented
7	C₅×#1478	C₂	1	2	yes	maximal, complemented
8	C₅×#529	—	2	1	no	—
9	C₅×#529	—	2	1	no	—
10	C₅×#529	—	2	1	no	—
11	C₅×#529	—	2	1	no	—
12	C₅×#529	C₄	1	2	yes	—
13	C₅×#529	C₄	1	2	yes	—
14	C₅×#529	C₂²	1	2	yes	—
15	C₅×#529	C₂²	1	2	yes	—
16	C₂×C₅×#126	—	2	1	no	—
17	C₂×C₅×#125	C₄	1	1	yes	characteristic
18	C₂×C₅×#124	C₄	1	1	yes	characteristic
19	C₂×C₅×#123	—	2	1	no	—
20	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
21	C₂×C₅×#121	C₄	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	—	2	1	no	—
24	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₅×#117	—	2	1	no	—
26	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₅×#432	—	2	1	no	—
28	C₅×#432	C₂²	1	2	yes	complemented
29	C₅×#431	—	2	1	no	—
30	C₅×#431	—	2	1	no	—
31	C₅×#431	—	2	1	no	—
32	C₅×#431	C₂²	1	2	yes	—
33	C₅×#431	C₂²	1	2	yes	—
34	C₅×#431	C₂²	1	2	yes	complemented
35	C₅×#423	C₂²	1	2	yes	complemented
36	C₂×C₅×C₄⋊C₈	—	2	1	no	—
37	C₅×#407	—	2	1	no	—
38	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
39	C₄×C₅×M₁₆	—	2	1	no	—
40	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
41	C₅×Q₈⋊C₈	C₂²	1	8	yes	complemented
42	C₅×D₄⋊C₈	C₂²	1	8	yes	complemented
43	#17480	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₅×#126	—	2	2	no	—
54	C₅×#126	—	2	2	no	—
55	C₅×#126	—	2	2	no	—
56	C₅×#126	—	2	2	no	—
57	C₅×#125	—	2	1	no	—
58	C₅×#125	—	2	1	no	—
59	C₅×#125	C₂×C₄	1	2	yes	—
60	C₅×#125	C₂×C₄	1	2	yes	—
61	C₅×#124	—	2	1	no	—
62	C₅×#124	—	2	1	no	—
63	C₅×#124	C₂×C₄	1	2	yes	—
64	C₅×#124	C₂×C₄	1	2	yes	—
65	C₅×#123	—	2	2	no	—
66	C₅×#123	—	2	2	no	—
67	C₅×#123	—	2	2	no	—
68	C₅×#123	—	2	2	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×C₂²⋊Q₈	—	2	1	no	—
71	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#121	C₂×C₄	1	2	yes	—
76	C₅×#121	C₂×C₄	1	2	yes	—
77	C₄×C₅×Q₈	—	2	1	no	—
78	C₄×C₅×Q₈	—	2	1	no	—
79	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
80	C₄×C₅×Q₈	C₂³	1	2	yes	—
81	C₄×C₅×D₄	—	2	2	no	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₄×C₅×D₄	—	2	2	no	—
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	—	2	1	no	—
86	C₄×C₅×D₄	—	2	1	no	—
87	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
88	C₄×C₅×D₄	C₂³	1	2	yes	—
89	C₅×#117	—	2	2	no	—
90	C₅×#117	—	2	2	no	—
91	C₅×#117	—	2	2	no	—
92	C₅×#117	—	2	2	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₄²×C₅	—	2	1	no	—
105	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₅×C₄⋊C₈	—	2	2	no	—
118	C₅×C₄⋊C₈	—	2	2	no	—
119	C₅×C₄⋊C₈	—	2	2	no	—
120	C₅×C₄⋊C₈	C₂³	1	4	yes	—
121	C₅×C₂²⋊C₈	—	2	2	no	—
122	C₅×C₂²⋊C₈	—	2	2	no	—
123	C₅×C₂²⋊C₈	—	2	2	no	—
124	C₅×C₂²⋊C₈	—	2	2	no	—
125	C₅×#97	—	2	2	no	—
126	C₄×C₅×C₈	—	2	2	no	—
127	C₄×C₅×C₈	—	2	2	no	—
128	C₄×C₅×C₈	C₂³	1	4	yes	—
129	C₂×#529	C₂×C₅	1	1	yes	characteristic
130	#2920	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
132	#1495	C₂×C₅	1	4	yes	complemented
133	#1494	C₂×C₅	1	4	yes	complemented
134	#1479	C₂×C₅	1	2	yes	complemented
135	#1478	C₂×C₅	1	2	yes	complemented
136	C₂⁴×C₅	—	2	1	no	—
137	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₅×Q₈	—	2	1	no	—
139	C₂×C₅×Q₈	—	2	4	no	—
140	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	—	2	4	no	—
145	C₂×C₅×D₄	—	4	4	no	—
146	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	—	2	2	no	—
153	C₂²×C₄×C₅	—	4	2	no	—
154	C₂²×C₄×C₅	—	4	2	no	—
155	C₂²×C₄×C₅	—	4	4	no	—
156	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₅×M₁₆	—	4	4	no	—
175	C₂×C₅×C₈	—	2	4	no	—
176	C₂×C₅×C₈	—	2	4	no	—
177	C₂×C₅×C₈	—	4	4	no	—
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	2	no	—
180	C₅×C₄⋊C₄	—	2	2	no	—
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
189	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
190	C₅×C₂²⋊C₄	—	2	2	no	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₅	C₂⁴	1	1	yes	characteristic
218	#529	—	2	1	no	—
219	#529	—	2	1	no	—
220	#529	—	2	1	no	—
221	#529	—	2	1	no	—
222	#529	C₄×C₅	1	2	yes	—
223	#529	C₄×C₅	1	2	yes	—
224	#529	C₂²×C₅	1	2	yes	—
225	#529	C₂²×C₅	1	2	yes	—
226	C₂×#126	—	2	1	no	—
227	C₂×#125	C₄×C₅	1	1	yes	characteristic
228	C₂×#124	C₄×C₅	1	1	yes	characteristic
229	C₂×#123	—	2	1	no	—
230	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
231	C₂×#121	C₄×C₅	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×#117	—	2	1	no	—
236	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
237	#432	—	2	1	no	—
238	#432	C₂²×C₅	1	2	yes	complemented
239	#431	—	2	1	no	—
240	#431	—	2	1	no	—
241	#431	—	2	1	no	—
242	#431	C₂²×C₅	1	2	yes	—
243	#431	C₂²×C₅	1	2	yes	—
244	#431	C₂²×C₅	1	2	yes	complemented
245	#423	C₂²×C₅	1	2	yes	complemented
246	C₂×C₄⋊C₈	—	2	1	no	—
247	#407	—	2	1	no	—
248	C₂×C₂²⋊C₈	—	2	1	no	—
249	C₄×M₁₆	—	2	1	no	—
250	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
251	Q₈⋊C₈	C₂²×C₅	1	8	yes	complemented
252	D₄⋊C₈	C₂²×C₅	1	8	yes	complemented
253	C₂³×C₅	—	2	2	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	4	1	no	—
257	C₂³×C₅	—	4	2	no	—
258	C₂³×C₅	—	4	2	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₅×Q₈	—	2	4	no	—
264	C₅×Q₈	—	4	2	no	—
265	C₅×D₄	—	2	4	no	—
266	C₅×D₄	—	4	4	no	—
267	C₅×D₄	—	4	4	no	—
268	C₅×D₄	—	4	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	4	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	4	2	no	—
292	C₂×C₄×C₅	—	4	2	no	—
293	C₂×C₄×C₅	—	4	4	no	—
294	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₅	#131	1	4	yes	—
304	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
307	C₅×C₈	—	4	4	no	—
308	C₅×C₈	—	4	4	no	—
309	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
315	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
316	C₂×M₁₆	—	2	2	no	—
317	C₂²×C₈	—	2	2	no	—
318	#126	—	2	2	no	—
319	#126	—	2	2	no	—
320	#126	—	2	2	no	—
321	#126	—	2	2	no	—
322	#125	—	2	1	no	—
323	#125	—	2	1	no	—
324	#125	C₂×C₄×C₅	1	2	yes	—
325	#125	C₂×C₄×C₅	1	2	yes	—
326	#124	—	2	1	no	—
327	#124	—	2	1	no	—
328	#124	C₂×C₄×C₅	1	2	yes	—
329	#124	C₂×C₄×C₅	1	2	yes	—
330	#123	—	2	2	no	—
331	#123	—	2	2	no	—
332	#123	—	2	2	no	—
333	#123	—	2	2	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
337	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	C₂×C₄×C₅	1	2	yes	—
341	#121	C₂×C₄×C₅	1	2	yes	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
345	C₄×Q₈	C₂³×C₅	1	2	yes	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
353	C₄×D₄	C₂³×C₅	1	2	yes	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	#117	—	2	2	no	—
357	#117	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
373	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
374	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
375	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
376	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
377	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
378	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
382	C₄⋊C₈	—	2	2	no	—
383	C₄⋊C₈	—	2	2	no	—
384	C₄⋊C₈	—	2	2	no	—
385	C₄⋊C₈	C₂³×C₅	1	4	yes	—
386	C₂²⋊C₈	—	2	2	no	—
387	C₂²⋊C₈	—	2	2	no	—
388	C₂²⋊C₈	—	2	2	no	—
389	C₂²⋊C₈	—	2	2	no	—
390	#97	—	2	2	no	—
391	C₄×C₈	—	2	2	no	—
392	C₄×C₈	—	2	2	no	—
393	C₄×C₈	C₂³×C₅	1	4	yes	—
394	C₂²×C₅	—	2	1	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	4	4	no	—
402	C₂²×C₅	—	4	2	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	8	4	no	—
406	C₂²×C₅	#408	1	2	yes	—
407	C₂²×C₅	#421	1	2	yes	—
408	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	4	2	no	—
419	C₄×C₅	—	4	2	no	—
420	C₄×C₅	—	4	2	no	—
421	C₄×C₅	#408	1	2	yes	—
422	C₄×C₅	C₂×#131	1	2	yes	—
423	C₄×C₅	#575	1	2	yes	—
424	C₂⁴	—	2	1	no	—
425	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
445	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
446	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
447	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
448	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
449	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
450	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
451	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
452	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
455	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
462	M₁₆	—	4	4	no	—
463	C₂×C₈	—	2	4	no	—
464	C₂×C₈	—	2	4	no	—
465	C₂×C₈	—	4	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
477	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
491	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
492	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
493	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
494	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
495	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
496	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
497	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
498	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
499	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
500	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
501	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
502	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
503	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
504	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
505	C₄²	C₂⁴×C₅	1	1	yes	characteristic
506	C₂×C₅	—	2	2	no	—
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	—	4	1	no	—
509	C₂×C₅	—	8	2	no	—
510	C₂×C₅	C₂×#408	1	1	yes	characteristic
511	C₂×C₅	#2896	1	1	yes	characteristic
512	C₂×C₅	C₂×#421	1	1	yes	characteristic
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
521	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
522	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
523	Q₈	—	2	4	no	—
524	Q₈	—	4	2	no	—
525	D₄	—	2	4	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
555	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
556	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
557	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
558	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
560	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
561	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₅×#131	1	4	yes	—
564	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
567	C₈	—	4	4	no	—
568	C₈	—	4	4	no	—
569	C₅	#17480	1	1	yes	characteristic, direct product factor, Sylow
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	8	4	no	—
582	C₂²	C₅×#408	1	2	yes	—
583	C₂²	C₅×#421	1	2	yes	—
584	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	C₅×#408	1	2	yes	—
598	C₄	C₂×C₅×#131	1	2	yes	—
599	C₄	C₅×#575	1	2	yes	—
600	C₂	—	2	2	no	—
601	C₂	—	2	2	no	—
602	C₂	—	4	1	no	—
603	C₂	—	8	2	no	—
604	C₂	C₂×C₅×#408	1	1	yes	characteristic
605	C₂	C₅×#2896	1	1	yes	characteristic
606	C₂	C₂×C₅×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₅×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2920	C₂	semidirect
3. C₂×C₅×#431	C₂	semidirect
4. C₅×#1495	C₂	semidirect
5. C₅×#1494	C₂	semidirect
6. C₅×#1479	C₂	semidirect
7. C₅×#1478	C₂	semidirect
28. C₅×#432	C₂²	semidirect
34. C₅×#431	C₂²	semidirect
35. C₅×#423	C₂²	semidirect
40. C₂×C₄×C₅×C₈	C₂²	semidirect
41. C₅×Q₈⋊C₈	C₂²	semidirect
42. C₅×D₄⋊C₈	C₂²	semidirect
43. #17480	C₅	direct (N × H)
130. #2920	C₂×C₅	semidirect
131. C₂×#431	C₂×C₅	semidirect
132. #1495	C₂×C₅	semidirect
133. #1494	C₂×C₅	semidirect
134. #1479	C₂×C₅	semidirect
135. #1478	C₂×C₅	semidirect
238. #432	C₂²×C₅	semidirect
244. #431	C₂²×C₅	semidirect
245. #423	C₂²×C₅	semidirect
250. C₂×C₄×C₈	C₂²×C₅	semidirect
251. Q₈⋊C₈	C₂²×C₅	semidirect
252. D₄⋊C₈	C₂²×C₅	semidirect
569. C₅	#17480	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#529	2
C₅×#2920	2
C₂×C₅×#431	2
C₅×#1495	2
C₅×#1494	2
C₅×#1479	2
C₅×#1478	2
#17480	5

Subgroups — C5×#17480 #11940200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17480 #11940200