Subgroups — C₅×#17417 #11940137

Order 1280.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#552	C₂	1	1	yes	maximal, characteristic
2	C₅×#2924	C₂	1	2	yes	maximal, complemented
3	C₅×#1473	C₂	1	2	yes	maximal, complemented
4	C₅×#1470	C₂	1	2	yes	maximal, complemented
5	C₅×#1468	C₂	1	2	yes	maximal
6	C₅×#1467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1458	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#552	—	2	2	no	—
13	C₅×#552	—	2	2	no	—
14	C₅×#552	—	2	2	no	—
15	C₅×#552	—	2	2	no	—
16	C₂×C₅×#126	C₄	1	1	yes	characteristic
17	C₂×C₅×#126	C₂²	1	1	yes	characteristic
18	C₂×C₅×#125	C₄	1	1	yes	characteristic
19	C₂×C₅×#125	C₄	1	1	yes	characteristic
20	C₂×C₅×#125	C₂²	1	1	yes	characteristic
21	C₂×C₅×#123	C₄	1	1	yes	characteristic
22	C₂×C₅×#123	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
25	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
27	C₂×C₅×#117	C₄	1	1	yes	characteristic
28	C₂×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂×C₅×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#433	—	2	2	no	—
32	C₅×#433	—	2	2	no	—
33	C₅×#432	C₂²	1	2	yes	—
34	C₅×#432	C₂²	1	2	yes	—
35	C₅×#431	C₂²	1	2	yes	—
36	C₅×#431	C₂²	1	2	yes	—
37	C₅×#424	—	2	2	no	—
38	C₅×#407	C₂²	1	2	yes	—
39	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
40	C₅×#405	—	2	2	no	—
41	C₅×#324	C₂²	1	1	yes	characteristic
42	C₅×#324	C₂²	1	1	yes	characteristic
43	C₅×#324	C₂²	1	2	yes	—
44	C₅×#324	C₂²	1	1	yes	characteristic
45	C₅×#324	C₂²	1	1	yes	characteristic
46	C₅×#324	C₂²	1	2	yes	—
47	C₅×#324	C₂²	1	2	yes	—
48	C₅×#324	C₂²	1	2	yes	—
49	C₅×#323	C₂²	1	2	yes	—
50	C₅×#323	C₂²	1	2	yes	—
51	#17417	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₅×#126	—	2	2	no	—
61	C₅×#126	—	2	2	no	—
62	C₅×#126	—	2	2	no	—
63	C₅×#126	—	2	2	no	—
64	C₅×#125	—	2	2	no	—
65	C₅×#125	—	2	2	no	—
66	C₅×#125	—	2	2	no	—
67	C₅×#125	—	2	2	no	—
68	C₅×#125	—	2	2	no	—
69	C₅×#125	—	2	2	no	—
70	C₅×#123	—	2	2	no	—
71	C₅×#123	—	2	2	no	—
72	C₅×#123	—	2	2	no	—
73	C₅×#123	—	2	2	no	—
74	C₅×C₂²⋊Q₈	—	2	2	no	—
75	C₅×C₂²⋊Q₈	—	2	2	no	—
76	C₅×C₂²⋊Q₈	—	2	2	no	—
77	C₅×C₂²⋊Q₈	—	2	2	no	—
78	C₄×C₅×Q₈	—	2	2	no	—
79	C₄×C₅×Q₈	—	2	2	no	—
80	C₄×C₅×D₄	—	2	1	no	—
81	C₄×C₅×D₄	—	2	1	no	—
82	C₄×C₅×D₄	—	2	1	no	—
83	C₄×C₅×D₄	—	2	1	no	—
84	C₅×#117	—	2	1	no	—
85	C₅×#117	—	2	1	no	—
86	C₅×#117	—	2	1	no	—
87	C₅×#117	—	2	1	no	—
88	C₅×#117	—	2	2	no	—
89	C₅×#117	—	2	2	no	—
90	C₅×#117	D₄	1	2	yes	—
91	C₅×#117	D₄	1	2	yes	—
92	C₅×#117	D₄	1	2	yes	—
93	C₅×#117	D₄	1	2	yes	—
94	C₂×C₅×C₄⋊C₄	—	2	2	no	—
95	C₂×C₅×C₄⋊C₄	—	2	2	no	—
96	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₅×C₄⋊C₈	—	2	2	no	—
126	C₅×C₄⋊C₈	—	2	2	no	—
127	C₅×C₄⋊C₈	—	2	2	no	—
128	C₅×C₄⋊C₈	—	2	2	no	—
129	C₅×C₂²⋊C₈	—	2	2	no	—
130	C₅×C₂²⋊C₈	—	2	2	no	—
131	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
132	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
133	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
134	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
135	C₅×#97	—	2	2	no	—
136	C₅×#97	—	2	2	no	—
137	C₄×C₅×C₈	—	2	2	no	—
138	C₄×C₅×C₈	—	2	2	no	—
139	C₂×#552	C₂×C₅	1	1	yes	characteristic
140	#2924	C₂×C₅	1	2	yes	complemented
141	#1473	C₂×C₅	1	2	yes	complemented
142	#1470	C₂×C₅	1	2	yes	complemented
143	#1468	C₂×C₅	1	2	yes	—
144	#1467	C₂×C₅	1	1	yes	characteristic, complemented
145	#1464	C₂×C₅	1	1	yes	characteristic, complemented
146	#1463	C₂×C₅	1	1	yes	characteristic, complemented
147	#1461	C₂×C₅	1	1	yes	characteristic, complemented
148	#1458	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂×#324	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×Q₈	—	2	2	no	—
153	C₂×C₅×Q₈	—	2	2	no	—
154	C₂×C₅×Q₈	—	4	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	4	2	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	—	2	2	no	—
166	C₂²×C₄×C₅	—	4	1	no	—
167	C₂²×C₄×C₅	—	4	1	no	—
168	C₂²×C₄×C₅	—	4	2	no	—
169	C₂²×C₄×C₅	—	4	2	no	—
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
185	C₅×M₁₆	—	4	4	no	—
186	C₂×C₅×C₈	—	2	2	no	—
187	C₂×C₅×C₈	—	2	2	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	—	4	4	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	—	2	2	no	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	—	2	2	no	—
208	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
209	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
210	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
211	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₅×C₂²⋊C₄	—	2	1	no	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	2	1	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₅×C₂²⋊C₄	—	2	2	no	—
219	C₅×C₂²⋊C₄	—	2	2	no	—
220	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
221	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
222	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
224	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
225	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₄²×C₅	C₂×D₄	1	2	yes	—
233	C₄²×C₅	C₂×D₄	1	2	yes	—
234	C₄²×C₅	C₂×D₄	1	2	yes	—
235	C₄²×C₅	C₂×D₄	1	2	yes	—
236	#552	—	2	2	no	—
237	#552	—	2	2	no	—
238	#552	—	2	2	no	—
239	#552	—	2	2	no	—
240	C₂×#126	C₄×C₅	1	1	yes	characteristic
241	C₂×#126	C₂²×C₅	1	1	yes	characteristic
242	C₂×#125	C₄×C₅	1	1	yes	characteristic
243	C₂×#125	C₄×C₅	1	1	yes	characteristic
244	C₂×#125	C₂²×C₅	1	1	yes	characteristic
245	C₂×#123	C₄×C₅	1	1	yes	characteristic
246	C₂×#123	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
251	C₂×#117	C₄×C₅	1	1	yes	characteristic
252	C₂×#117	C₂²×C₅	1	1	yes	characteristic
253	C₂×#117	C₂²×C₅	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	#433	—	2	2	no	—
256	#433	—	2	2	no	—
257	#432	C₂²×C₅	1	2	yes	—
258	#432	C₂²×C₅	1	2	yes	—
259	#431	C₂²×C₅	1	2	yes	—
260	#431	C₂²×C₅	1	2	yes	—
261	#424	—	2	2	no	—
262	#407	C₂²×C₅	1	2	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
264	#405	—	2	2	no	—
265	#324	C₂²×C₅	1	1	yes	characteristic
266	#324	C₂²×C₅	1	1	yes	characteristic
267	#324	C₂²×C₅	1	2	yes	—
268	#324	C₂²×C₅	1	1	yes	characteristic
269	#324	C₂²×C₅	1	1	yes	characteristic
270	#324	C₂²×C₅	1	2	yes	—
271	#324	C₂²×C₅	1	2	yes	—
272	#324	C₂²×C₅	1	2	yes	—
273	#323	C₂²×C₅	1	2	yes	—
274	#323	C₂²×C₅	1	2	yes	—
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	—	4	1	no	—
284	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
287	C₅×Q₈	—	4	4	no	—
288	C₅×D₄	—	4	2	no	—
289	C₅×D₄	—	4	2	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	4	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	2	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	2	no	—
313	C₂×C₄×C₅	—	4	2	no	—
314	C₂×C₄×C₅	—	4	2	no	—
315	C₂×C₄×C₅	—	4	2	no	—
316	C₂×C₄×C₅	—	4	2	no	—
317	C₂×C₄×C₅	—	4	2	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
327	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂×C₄×C₅	#131	1	2	yes	—
330	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
331	C₅×C₈	—	4	2	no	—
332	C₅×C₈	—	4	2	no	—
333	C₅×C₈	—	4	2	no	—
334	C₅×C₈	—	4	2	no	—
335	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
336	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
338	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
341	C₂×M₁₆	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	#126	—	2	2	no	—
344	#126	—	2	2	no	—
345	#126	—	2	2	no	—
346	#126	—	2	2	no	—
347	#125	—	2	2	no	—
348	#125	—	2	2	no	—
349	#125	—	2	2	no	—
350	#125	—	2	2	no	—
351	#125	—	2	2	no	—
352	#125	—	2	2	no	—
353	#123	—	2	2	no	—
354	#123	—	2	2	no	—
355	#123	—	2	2	no	—
356	#123	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	C₅×D₄	1	2	yes	—
374	#117	C₅×D₄	1	2	yes	—
375	#117	C₅×D₄	1	2	yes	—
376	#117	C₅×D₄	1	2	yes	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
404	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
405	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
408	C₄⋊C₈	—	2	2	no	—
409	C₄⋊C₈	—	2	2	no	—
410	C₄⋊C₈	—	2	2	no	—
411	C₄⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
415	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
416	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
417	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
418	#97	—	2	2	no	—
419	#97	—	2	2	no	—
420	C₄×C₈	—	2	2	no	—
421	C₄×C₈	—	2	2	no	—
422	C₂²×C₅	—	2	1	no	—
423	C₂²×C₅	—	2	1	no	—
424	C₂²×C₅	—	2	1	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	—	2	1	no	—
429	C₂²×C₅	—	4	2	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	8	1	no	—
435	C₂²×C₅	—	8	1	no	—
436	C₂²×C₅	#410	1	2	yes	—
437	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
438	C₂²×C₅	C₂×#131	1	1	yes	characteristic
439	C₂²×C₅	#568	1	1	yes	characteristic
440	C₄×C₅	—	2	2	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	1	no	—
443	C₄×C₅	—	2	2	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	1	no	—
447	C₄×C₅	—	2	1	no	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	—	4	1	no	—
451	C₄×C₅	—	4	1	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	4	1	no	—
454	C₄×C₅	—	4	1	no	—
455	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
456	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
483	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
484	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
485	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
486	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
488	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
490	M₁₆	—	4	4	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	4	4	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
514	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
515	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
516	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
526	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
527	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
528	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
529	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
530	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	C₂×C₅×D₄	1	2	yes	—
538	C₄²	C₂×C₅×D₄	1	2	yes	—
539	C₄²	C₂×C₅×D₄	1	2	yes	—
540	C₄²	C₂×C₅×D₄	1	2	yes	—
541	C₂×C₅	—	2	1	no	—
542	C₂×C₅	—	2	1	no	—
543	C₂×C₅	—	2	2	no	—
544	C₂×C₅	—	4	1	no	—
545	C₂×C₅	—	8	1	no	—
546	C₂×C₅	#2880	1	1	yes	characteristic
547	C₂×C₅	C₂×#410	1	1	yes	characteristic
548	C₂×C₅	#2889	1	1	yes	characteristic
549	C₂³	—	2	2	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
559	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
560	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
561	Q₈	—	4	4	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
597	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
598	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
599	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
600	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
601	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
602	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
603	C₂×C₄	C₅×#131	1	2	yes	—
604	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
605	C₈	—	4	2	no	—
606	C₈	—	4	2	no	—
607	C₈	—	4	2	no	—
608	C₈	—	4	2	no	—
609	C₅	#17417	1	1	yes	characteristic, direct product factor, Sylow
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	C₅×#410	1	2	yes	—
625	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
626	C₂²	C₂×C₅×#131	1	1	yes	characteristic
627	C₂²	C₅×#568	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₂	—	2	1	no	—
644	C₂	—	2	1	no	—
645	C₂	—	2	2	no	—
646	C₂	—	4	1	no	—
647	C₂	—	8	1	no	—
648	C₂	C₅×#2880	1	1	yes	characteristic
649	C₂	C₂×C₅×#410	1	1	yes	characteristic
650	C₂	C₅×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2924	C₂	semidirect
3. C₅×#1473	C₂	semidirect
4. C₅×#1470	C₂	semidirect
6. C₅×#1467	C₂	semidirect
7. C₅×#1464	C₂	semidirect
8. C₅×#1463	C₂	semidirect
9. C₅×#1461	C₂	semidirect
10. C₅×#1458	C₂	semidirect
11. C₂×C₅×#324	C₂	semidirect
51. #17417	C₅	direct (N × H)
140. #2924	C₂×C₅	semidirect
141. #1473	C₂×C₅	semidirect
142. #1470	C₂×C₅	semidirect
144. #1467	C₂×C₅	semidirect
145. #1464	C₂×C₅	semidirect
146. #1463	C₂×C₅	semidirect
147. #1461	C₂×C₅	semidirect
148. #1458	C₂×C₅	semidirect
149. C₂×#324	C₂×C₅	semidirect
609. C₅	#17417	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×#552	2
C₅×#2924	2
C₅×#1473	2
C₅×#1470	2
C₅×#1468	2
C₅×#1467	2
C₅×#1464	2
C₅×#1463	2
C₅×#1461	2
C₅×#1458	2
C₂×C₅×#324	2
#17417	5

Subgroups — C5×#17417 #11940137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17417 #11940137