Subgroups — C₅×#17537 #11940257

Order 1280.

1116 conjugacy classes of subgroups.

The subgroup lattice has 624 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	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1509	C₂	1	4	yes	maximal, complemented
5	C₅×#1508	C₂	1	2	yes	maximal, complemented
6	C₅×#1507	C₂	1	2	yes	maximal
7	C₅×#1500	C₂	1	4	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	complemented
13	C₅×#529	C₄	1	2	yes	complemented
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, complemented
18	C₂×C₅×#124	C₄	1	1	yes	characteristic, complemented
19	C₂×C₅×#123	—	2	1	no	—
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#121	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×C₅×D₄	—	2	1	no	—
24	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
25	C₂×C₅×#117	—	2	1	no	—
26	C₂×C₅×#117	—	2	1	no	—
27	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₅×#432	—	2	1	no	—
29	C₅×#432	C₂²	1	2	yes	complemented
30	C₅×#431	—	2	1	no	—
31	C₅×#431	C₂²	1	2	yes	complemented
32	C₅×#423	—	2	1	no	—
33	C₅×#407	C₂²	1	2	yes	—
34	C₄×C₅×M₁₆	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
37	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
38	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₅×#376	C₂²	1	2	yes	complemented
40	C₄³×C₅	—	2	1	no	—
41	C₅×#328	C₂²	1	8	yes	complemented
42	C₅×#327	C₂²	1	8	yes	—
43	#17537	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	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₅×#126	—	2	2	no	—
53	C₅×#126	—	2	2	no	—
54	C₅×#126	—	2	2	no	—
55	C₅×#126	—	2	2	no	—
56	C₅×#125	—	2	1	no	—
57	C₅×#125	—	2	1	no	—
58	C₅×#125	C₂×C₄	1	2	yes	—
59	C₅×#125	C₂×C₄	1	2	yes	—
60	C₅×#124	—	2	1	no	—
61	C₅×#124	—	2	1	no	—
62	C₅×#124	C₂×C₄	1	2	yes	—
63	C₅×#124	C₂×C₄	1	2	yes	—
64	C₅×#123	—	2	2	no	—
65	C₅×#123	—	2	2	no	—
66	C₅×#123	—	2	2	no	—
67	C₅×#123	—	2	2	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
72	C₅×#121	—	2	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	C₂×C₄	1	2	yes	—
75	C₅×#121	C₂³	1	2	yes	—
76	C₄×C₅×Q₈	—	2	1	no	—
77	C₄×C₅×Q₈	—	2	1	no	—
78	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
79	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
80	C₄×C₅×D₄	—	2	2	no	—
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	1	no	—
85	C₄×C₅×D₄	—	2	1	no	—
86	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
87	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
88	C₅×#117	—	2	8	no	—
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	2	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	2	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×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²×C₅	—	2	1	no	—
107	C₂×C₄²×C₅	—	2	2	no	—
108	C₂×C₄²×C₅	—	2	2	no	—
109	C₂×C₄²×C₅	—	2	2	no	—
110	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	—	2	2	no	—
123	C₅×C₄⋊C₈	—	2	2	no	—
124	C₅×C₂²⋊C₈	—	2	2	no	—
125	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
126	C₅×#97	—	2	2	no	—
127	C₄×C₅×C₈	—	2	2	no	—
128	C₅×#95	—	2	2	no	—
129	C₅×#95	C₂³	1	4	yes	—
130	C₂×#529	C₂×C₅	1	1	yes	characteristic
131	#2920	C₂×C₅	1	1	yes	characteristic, complemented
132	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
133	#1509	C₂×C₅	1	4	yes	complemented
134	#1508	C₂×C₅	1	2	yes	complemented
135	#1507	C₂×C₅	1	2	yes	—
136	#1500	C₂×C₅	1	4	yes	complemented
137	C₂⁴×C₅	—	2	1	no	—
138	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×Q₈	—	2	1	no	—
140	C₂×C₅×Q₈	—	4	2	no	—
141	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	4	2	no	—
146	C₂×C₅×D₄	—	4	4	no	—
147	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	4	no	—
153	C₂²×C₄×C₅	—	2	2	no	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	4	2	no	—
156	C₂²×C₄×C₅	—	4	2	no	—
157	C₂²×C₄×C₅	—	4	4	no	—
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	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
176	C₅×M₁₆	—	4	4	no	—
177	C₂×C₅×C₈	—	2	4	no	—
178	C₅×C₄⋊C₄	—	2	8	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	2	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
190	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
191	C₅×C₂²⋊C₄	—	2	8	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	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₄²×C₅	—	2	8	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	2	2	no	—
205	C₄²×C₅	—	4	4	no	—
206	C₄²×C₅	—	4	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
214	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
215	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
217	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
219	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
223	#529	—	2	1	no	—
224	#529	—	2	1	no	—
225	#529	—	2	1	no	—
226	#529	—	2	1	no	—
227	#529	C₄×C₅	1	2	yes	complemented
228	#529	C₄×C₅	1	2	yes	complemented
229	#529	C₂²×C₅	1	2	yes	—
230	#529	C₂²×C₅	1	2	yes	—
231	C₂×#126	—	2	1	no	—
232	C₂×#125	C₄×C₅	1	1	yes	characteristic, complemented
233	C₂×#124	C₄×C₅	1	1	yes	characteristic, complemented
234	C₂×#123	—	2	1	no	—
235	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×#121	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
238	C₂×C₄×D₄	—	2	1	no	—
239	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic, complemented
240	C₂×#117	—	2	1	no	—
241	C₂×#117	—	2	1	no	—
242	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
243	#432	—	2	1	no	—
244	#432	C₂²×C₅	1	2	yes	complemented
245	#431	—	2	1	no	—
246	#431	C₂²×C₅	1	2	yes	complemented
247	#423	—	2	1	no	—
248	#407	C₂²×C₅	1	2	yes	—
249	C₄×M₁₆	—	2	1	no	—
250	C₄×C₄⋊C₄	—	2	1	no	—
251	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
252	C₄×C₂²⋊C₄	—	2	1	no	—
253	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
254	#376	C₂²×C₅	1	2	yes	complemented
255	C₄³	—	2	1	no	—
256	#328	C₂²×C₅	1	8	yes	complemented
257	#327	C₂²×C₅	1	8	yes	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	4	1	no	—
262	C₂³×C₅	—	4	2	no	—
263	C₂³×C₅	—	4	2	no	—
264	C₂³×C₅	—	4	2	no	—
265	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₅×Q₈	—	4	2	no	—
269	C₅×Q₈	—	4	2	no	—
270	C₅×D₄	—	4	2	no	—
271	C₅×D₄	—	4	4	no	—
272	C₅×D₄	—	4	4	no	—
273	C₅×D₄	—	4	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	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	8	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	4	no	—
296	C₂×C₄×C₅	—	4	2	no	—
297	C₂×C₄×C₅	—	4	2	no	—
298	C₂×C₄×C₅	—	4	4	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	4	4	no	—
301	C₂×C₄×C₅	—	4	4	no	—
302	C₂×C₄×C₅	#104	1	4	yes	—
303	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
315	C₅×C₈	—	4	4	no	—
316	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
321	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
323	C₂×M₁₆	—	2	2	no	—
324	#126	—	2	2	no	—
325	#126	—	2	2	no	—
326	#126	—	2	2	no	—
327	#126	—	2	2	no	—
328	#125	—	2	1	no	—
329	#125	—	2	1	no	—
330	#125	C₂×C₄×C₅	1	2	yes	—
331	#125	C₂×C₄×C₅	1	2	yes	—
332	#124	—	2	1	no	—
333	#124	—	2	1	no	—
334	#124	C₂×C₄×C₅	1	2	yes	—
335	#124	C₂×C₄×C₅	1	2	yes	—
336	#123	—	2	2	no	—
337	#123	—	2	2	no	—
338	#123	—	2	2	no	—
339	#123	—	2	2	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
343	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	#121	C₂×C₄×C₅	1	2	yes	—
347	#121	C₂³×C₅	1	2	yes	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
351	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
359	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
360	#117	—	2	8	no	—
361	#117	—	2	2	no	—
362	#117	—	2	2	no	—
363	#117	—	2	2	no	—
364	#117	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	—	2	2	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
384	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
385	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
386	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
387	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
388	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
389	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
390	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
391	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	2	2	no	—
396	C₂²⋊C₈	—	2	2	no	—
397	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
398	#97	—	2	2	no	—
399	C₄×C₈	—	2	2	no	—
400	#95	—	2	2	no	—
401	#95	C₂³×C₅	1	4	yes	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	2	1	no	—
408	C₂²×C₅	—	2	1	no	—
409	C₂²×C₅	—	4	4	no	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	—	4	2	no	—
412	C₂²×C₅	—	4	2	no	—
413	C₂²×C₅	—	8	4	no	—
414	C₂²×C₅	C₂×#104	1	2	yes	—
415	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
416	C₂²×C₅	#575	1	2	yes	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	4	8	no	—
427	C₄×C₅	—	4	2	no	—
428	C₄×C₅	—	4	2	no	—
429	C₄×C₅	—	4	2	no	—
430	C₄×C₅	#410	1	2	yes	—
431	C₄×C₅	C₂×#104	1	2	yes	—
432	C₄×C₅	C₂×#104	1	2	yes	—
433	C₂⁴	—	2	1	no	—
434	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	4	2	no	—
437	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
455	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
456	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
459	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
460	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
461	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
462	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
463	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
472	M₁₆	—	4	4	no	—
473	C₂×C₈	—	2	4	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
486	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₄²	—	2	8	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	4	4	no	—
502	C₄²	—	4	4	no	—
503	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
504	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
505	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
506	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
507	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
508	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
509	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
510	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
511	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
512	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
513	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
514	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
515	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
516	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
517	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
518	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂×C₅	—	2	2	no	—
520	C₂×C₅	—	2	2	no	—
521	C₂×C₅	—	4	1	no	—
522	C₂×C₅	—	8	2	no	—
523	C₂×C₅	C₂×#410	1	1	yes	characteristic
524	C₂×C₅	#2896	1	1	yes	characteristic
525	C₂×C₅	C₂²×#104	1	1	yes	characteristic
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	2	no	—
533	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
534	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
535	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
536	Q₈	—	4	2	no	—
537	Q₈	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	C₅×#104	1	4	yes	—
571	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
573	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
574	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
575	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
576	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
577	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
578	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
579	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
580	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
581	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
582	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
583	C₈	—	4	4	no	—
584	C₅	#17537	1	1	yes	characteristic, direct product factor, Sylow
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	8	4	no	—
597	C₂²	C₂×C₅×#104	1	2	yes	—
598	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
599	C₂²	C₅×#575	1	2	yes	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	4	8	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	C₅×#410	1	2	yes	—
614	C₄	C₂×C₅×#104	1	2	yes	—
615	C₄	C₂×C₅×#104	1	2	yes	—
616	C₂	—	2	2	no	—
617	C₂	—	2	2	no	—
618	C₂	—	4	1	no	—
619	C₂	—	8	2	no	—
620	C₂	C₂×C₅×#410	1	1	yes	characteristic
621	C₂	C₅×#2896	1	1	yes	characteristic
622	C₂	C₂²×C₅×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₅×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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. C₄×C₅×#117	C₂	semidirect
4. C₅×#1509	C₂	semidirect
5. C₅×#1508	C₂	semidirect
7. C₅×#1500	C₂	semidirect
12. C₅×#529	C₄	semidirect
13. C₅×#529	C₄	semidirect
17. C₂×C₅×#125	C₄	semidirect
18. C₂×C₅×#124	C₄	semidirect
22. C₂×C₄×C₅×Q₈	C₄	semidirect
24. C₂×C₄×C₅×D₄	C₄	semidirect
29. C₅×#432	C₂²	semidirect
31. C₅×#431	C₂²	semidirect
36. C₄×C₅×C₄⋊C₄	C₂²	semidirect
39. C₅×#376	C₂²	semidirect
41. C₅×#328	C₂²	semidirect
43. #17537	C₅	direct (N × H)
131. #2920	C₂×C₅	semidirect
132. C₄×#117	C₂×C₅	semidirect
133. #1509	C₂×C₅	semidirect
134. #1508	C₂×C₅	semidirect
136. #1500	C₂×C₅	semidirect
227. #529	C₄×C₅	semidirect
228. #529	C₄×C₅	semidirect
232. C₂×#125	C₄×C₅	semidirect
233. C₂×#124	C₄×C₅	semidirect
237. C₂×C₄×Q₈	C₄×C₅	semidirect
239. C₂×C₄×D₄	C₄×C₅	semidirect
244. #432	C₂²×C₅	semidirect
246. #431	C₂²×C₅	semidirect
251. C₄×C₄⋊C₄	C₂²×C₅	semidirect
254. #376	C₂²×C₅	semidirect
256. #328	C₂²×C₅	semidirect
584. C₅	#17537	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
C₄×C₅×#117	2
C₅×#1509	2
C₅×#1508	2
C₅×#1507	2
C₅×#1500	2
#17537	5

Subgroups — C5×#17537 #11940257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17537 #11940257