Subgroups — C₅×#8051 #11930771

Order 1280.

1090 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#407	C₂	1	1	yes	maximal, characteristic
2	C₅×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1297	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂²×C₅×M₁₆	C₄	1	2	yes	complemented
7	C₂×C₅×#117	—	2	1	no	—
8	C₂²×C₅×C₂²⋊C₄	—	2	1	no	—
9	C₂²×C₄²×C₅	—	2	1	no	—
10	C₅×#407	—	2	1	no	—
11	C₅×#407	—	2	1	no	—
12	C₅×#407	C₄	1	2	yes	complemented
13	C₅×#407	C₂²	1	2	yes	—
14	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
15	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
16	C₅×#381	C₄	1	2	yes	complemented
17	C₅×#380	—	2	1	no	—
18	C₅×#380	C₄	1	2	yes	complemented
19	C₅×#379	—	2	1	no	—
20	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
21	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
22	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
23	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	complemented
24	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×#95	C₄	1	2	yes	complemented
27	#8051	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂⁵×C₅	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	—	2	2	no	—
30	C₂³×C₄×C₅	—	4	4	no	—
31	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
43	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₅×M₁₆	—	2	2	no	—
46	C₂×C₅×M₁₆	—	4	4	no	—
47	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
48	C₂²×C₅×C₈	—	2	2	no	—
49	C₅×#117	—	4	4	no	—
50	C₂×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
52	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₄²×C₅	—	2	2	no	—
58	C₂×C₄²×C₅	—	2	2	no	—
59	C₂×C₄²×C₅	—	2	2	no	—
60	C₂×C₄²×C₅	—	4	4	no	—
61	C₅×C₂²⋊C₈	—	2	2	no	—
62	C₅×C₂²⋊C₈	—	2	2	no	—
63	C₅×C₂²⋊C₈	—	2	2	no	—
64	C₅×C₂²⋊C₈	—	2	2	no	—
65	C₅×#95	—	2	2	no	—
66	C₅×#95	—	2	2	no	—
67	C₅×#95	C₂×C₄	1	4	yes	—
68	C₅×#95	C₂×C₄	1	4	yes	complemented
69	C₂×#407	C₂×C₅	1	1	yes	characteristic
70	#2280	C₂×C₅	1	1	yes	characteristic
71	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
72	#1297	C₂×C₅	1	4	yes	complemented
73	C₂⁴×C₅	—	2	4	no	—
74	C₂⁴×C₅	—	4	2	no	—
75	C₂⁴×C₅	—	4	2	no	—
76	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
81	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
82	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	—	2	4	no	—
84	C₂²×C₄×C₅	—	2	4	no	—
85	C₂²×C₄×C₅	—	2	4	no	—
86	C₂²×C₄×C₅	—	2	8	no	—
87	C₂²×C₄×C₅	—	2	4	no	—
88	C₂²×C₄×C₅	—	2	4	no	—
89	C₂²×C₄×C₅	—	4	2	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	—	4	2	no	—
92	C₂²×C₄×C₅	—	4	2	no	—
93	C₂²×C₄×C₅	—	4	2	no	—
94	C₂²×C₄×C₅	—	4	2	no	—
95	C₂²×C₄×C₅	—	4	2	no	—
96	C₂²×C₄×C₅	—	4	2	no	—
97	C₂²×C₄×C₅	—	4	2	no	—
98	C₂²×C₄×C₅	—	4	2	no	—
99	C₂²×C₄×C₅	—	4	2	no	—
100	C₂²×C₄×C₅	—	4	4	no	—
101	C₂²×C₄×C₅	—	4	4	no	—
102	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
130	C₅×M₁₆	—	4	4	no	—
131	C₅×M₁₆	—	4	4	no	—
132	C₂×C₅×C₈	—	2	4	no	—
133	C₂×C₅×C₈	—	4	4	no	—
134	C₅×C₄⋊C₄	—	4	4	no	—
135	C₅×C₂²⋊C₄	—	2	8	no	—
136	C₅×C₂²⋊C₄	—	2	8	no	—
137	C₅×C₂²⋊C₄	—	4	4	no	—
138	C₅×C₂²⋊C₄	—	4	4	no	—
139	C₅×C₂²⋊C₄	—	4	4	no	—
140	C₄²×C₅	—	4	4	no	—
141	C₄²×C₅	—	4	4	no	—
142	C₄²×C₅	—	4	4	no	—
143	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂²×M₁₆	C₄×C₅	1	2	yes	complemented
145	C₂×#117	—	2	1	no	—
146	C₂²×C₂²⋊C₄	—	2	1	no	—
147	C₂²×C₄²	—	2	1	no	—
148	#407	—	2	1	no	—
149	#407	—	2	1	no	—
150	#407	C₄×C₅	1	2	yes	complemented
151	#407	C₂²×C₅	1	2	yes	—
152	C₂×C₂²⋊C₈	—	2	1	no	—
153	C₂×C₂²⋊C₈	—	2	1	no	—
154	#381	C₄×C₅	1	2	yes	complemented
155	#380	—	2	1	no	—
156	#380	C₄×C₅	1	2	yes	complemented
157	#379	—	2	1	no	—
158	C₄×C₂²⋊C₄	—	2	1	no	—
159	C₄×C₂²⋊C₄	—	2	1	no	—
160	C₄×C₂²⋊C₄	—	2	1	no	—
161	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	complemented
162	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
163	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×#95	C₄×C₅	1	2	yes	complemented
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	—	2	2	no	—
170	C₂³×C₅	—	2	2	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	—	4	1	no	—
178	C₂³×C₅	—	4	1	no	—
179	C₂³×C₅	—	4	1	no	—
180	C₂³×C₅	—	4	1	no	—
181	C₂³×C₅	—	4	1	no	—
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	16	no	—
186	C₂³×C₅	#95	1	1	yes	characteristic
187	C₂³×C₅	#95	1	1	yes	characteristic
188	C₂³×C₅	#95	1	1	yes	characteristic
189	C₂³×C₅	#95	1	1	yes	characteristic
190	C₂³×C₅	#104	1	4	yes	—
191	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	8	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	4	no	—
223	C₂×C₄×C₅	—	4	16	no	—
224	C₂×C₄×C₅	—	4	4	no	—
225	C₂×C₄×C₅	—	4	4	no	—
226	C₂×C₄×C₅	—	4	4	no	—
227	C₂×C₄×C₅	—	4	4	no	—
228	C₂×C₄×C₅	#95	1	1	yes	characteristic
229	C₂×C₄×C₅	#95	1	1	yes	characteristic
230	C₂×C₄×C₅	#95	1	1	yes	characteristic
231	C₂×C₄×C₅	#95	1	1	yes	characteristic
232	C₂×C₄×C₅	#99	1	4	yes	—
233	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₅×C₈	—	4	4	no	—
238	C₂⁵	C₅×D₄	1	1	yes	characteristic
239	C₂³×C₄	—	2	2	no	—
240	C₂³×C₄	—	4	4	no	—
241	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
245	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
246	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
247	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
248	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
249	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
250	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
251	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
252	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
253	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	4	4	no	—
257	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
258	C₂²×C₈	—	2	2	no	—
259	#117	—	4	4	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	8	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	4	4	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	C₂×C₄×C₅	1	4	yes	—
278	#95	C₂×C₄×C₅	1	4	yes	complemented
279	C₂²×C₅	—	2	8	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	2	1	no	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	4	4	no	—
297	C₂²×C₅	—	4	4	no	—
298	C₂²×C₅	—	4	4	no	—
299	C₂²×C₅	—	4	4	no	—
300	C₂²×C₅	—	4	4	no	—
301	C₂²×C₅	—	4	4	no	—
302	C₂²×C₅	#339	1	2	yes	—
303	C₂²×C₅	#339	1	2	yes	—
304	C₂²×C₅	#342	1	2	yes	—
305	C₂²×C₅	C₂×#95	1	1	yes	characteristic
306	C₂²×C₅	C₂×#104	1	2	yes	—
307	C₂²×C₅	#421	1	2	yes	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	4	8	no	—
315	C₄×C₅	—	8	4	no	—
316	C₄×C₅	#342	1	2	yes	—
317	C₄×C₅	C₂×#99	1	2	yes	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	4	2	no	—
320	C₂⁴	—	4	2	no	—
321	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
322	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
323	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
324	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
325	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
326	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
327	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
348	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
349	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
350	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
351	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
352	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
353	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
356	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
357	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
359	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
360	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
361	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
362	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
363	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
364	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
365	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
366	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
367	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
368	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
375	M₁₆	—	4	4	no	—
376	M₁₆	—	4	4	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	4	4	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₄²	—	4	4	no	—
386	C₄²	—	4	4	no	—
387	C₄²	—	4	4	no	—
388	C₂×C₅	—	2	2	no	—
389	C₂×C₅	—	2	2	no	—
390	C₂×C₅	—	2	2	no	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	—	2	2	no	—
393	C₂×C₅	—	4	1	no	—
394	C₂×C₅	—	4	1	no	—
395	C₂×C₅	C₂×#339	1	1	yes	characteristic
396	C₂×C₅	#1733	1	1	yes	characteristic
397	C₂×C₅	C₂×#342	1	1	yes	characteristic
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	16	no	—
419	C₂³	C₅×#95	1	1	yes	characteristic
420	C₂³	C₅×#95	1	1	yes	characteristic
421	C₂³	C₅×#95	1	1	yes	characteristic
422	C₂³	C₅×#95	1	1	yes	characteristic
423	C₂³	C₅×#104	1	4	yes	—
424	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
425	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
426	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	16	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	C₅×#95	1	1	yes	characteristic
462	C₂×C₄	C₅×#95	1	1	yes	characteristic
463	C₂×C₄	C₅×#95	1	1	yes	characteristic
464	C₂×C₄	C₅×#95	1	1	yes	characteristic
465	C₂×C₄	C₅×#99	1	4	yes	—
466	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
467	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
468	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
469	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
470	C₈	—	4	4	no	—
471	C₅	#8051	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²	—	2	8	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	C₅×#339	1	2	yes	—
496	C₂²	C₅×#339	1	2	yes	—
497	C₂²	C₅×#342	1	2	yes	—
498	C₂²	C₂×C₅×#95	1	1	yes	characteristic
499	C₂²	C₂×C₅×#104	1	2	yes	—
500	C₂²	C₅×#421	1	2	yes	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	4	8	no	—
508	C₄	—	8	4	no	—
509	C₄	C₅×#342	1	2	yes	—
510	C₄	C₂×C₅×#99	1	2	yes	—
511	C₂	—	2	2	no	—
512	C₂	—	2	2	no	—
513	C₂	—	2	2	no	—
514	C₂	—	2	2	no	—
515	C₂	—	2	2	no	—
516	C₂	—	4	1	no	—
517	C₂	—	4	1	no	—
518	C₂	C₂×C₅×#339	1	1	yes	characteristic
519	C₂	C₅×#1733	1	1	yes	characteristic
520	C₂	C₂×C₅×#342	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂²×C₅	C₂×#95
prime radical	C₂⁵×C₅	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂⁴×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1297	C₂	semidirect
6. C₂²×C₅×M₁₆	C₄	semidirect
12. C₅×#407	C₄	semidirect
16. C₅×#381	C₄	semidirect
18. C₅×#380	C₄	semidirect
23. C₄×C₅×C₂²⋊C₄	C₄	semidirect
26. C₂×C₅×#95	C₄	semidirect
27. #8051	C₅	direct (N × H)
47. C₂×C₅×M₁₆	C₂×C₄	semidirect
68. C₅×#95	C₂×C₄	semidirect
72. #1297	C₂×C₅	semidirect
144. C₂²×M₁₆	C₄×C₅	semidirect
150. #407	C₄×C₅	semidirect
154. #381	C₄×C₅	semidirect
156. #380	C₄×C₅	semidirect
161. C₄×C₂²⋊C₄	C₄×C₅	semidirect
164. C₂×#95	C₄×C₅	semidirect
257. C₂×M₁₆	C₂×C₄×C₅	semidirect
278. #95	C₂×C₄×C₅	semidirect
471. C₅	#8051	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×#407	2
C₅×#2280	2
C₂×C₄×C₅×C₂²⋊C₄	2
C₅×#1297	2
#8051	5

Subgroups — C5×#8051 #11930771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8051 #11930771