Subgroups — C₅×#21564 #11944284

Order 1280.

936 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#123	C₂	1	1	yes	maximal, characteristic
4	C₅×#1924	C₂	1	2	yes	maximal, complemented
5	C₅×#1917	C₂	1	2	yes	maximal, complemented
6	C₅×#1869	C₂	1	1	yes	maximal, characteristic
7	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1770	C₂	1	2	yes	maximal, complemented
10	C₅×#1753	C₂	1	2	yes	maximal, complemented
11	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#123	C₄	1	1	yes	characteristic
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#435	—	2	4	no	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#97	—	2	4	no	—
26	C₂×C₅×#97	C₂²	1	1	yes	characteristic
27	C₂×C₅×#97	C₂²	1	2	yes	—
28	C₂×C₅×#97	C₂²	1	2	yes	—
29	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₅×#388	C₄	1	2	yes	—
31	C₅×#387	C₄	1	2	yes	—
32	C₅×#386	C₄	1	1	yes	characteristic
33	C₅×#385	C₄	1	1	yes	characteristic
34	C₅×#381	C₄	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	#21564	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	4	no	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	4	no	—
53	C₂²×C₅×C₈	—	2	4	no	—
54	C₂²×C₅×C₈	D₄	1	4	yes	—
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	2	yes	—
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₅×#123	—	2	4	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₅	C₂³	1	2	yes	—
77	C₂×C₄²×C₅	C₂³	1	2	yes	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	4	no	—
81	C₅×C₂²⋊C₈	—	2	2	no	—
82	C₅×C₂²⋊C₈	—	2	2	no	—
83	C₅×C₂²⋊C₈	—	2	2	no	—
84	C₅×C₂²⋊C₈	—	2	4	no	—
85	C₅×#97	—	2	4	no	—
86	C₅×#97	—	2	4	no	—
87	C₅×#97	—	2	2	no	—
88	C₄×C₅×C₈	—	2	4	no	—
89	C₅×#95	C₂×C₄	1	2	yes	—
90	C₅×#95	C₂×C₄	1	2	yes	—
91	C₅×#95	C₂×C₄	1	2	yes	—
92	C₅×#95	C₂×C₄	1	2	yes	—
93	C₅×#95	C₂×C₄	1	2	yes	—
94	C₂×#435	C₂×C₅	1	1	yes	characteristic
95	C₂²×#97	C₂×C₅	1	1	yes	characteristic, complemented
96	C₄×#123	C₂×C₅	1	1	yes	characteristic
97	#1924	C₂×C₅	1	2	yes	complemented
98	#1917	C₂×C₅	1	2	yes	complemented
99	#1869	C₂×C₅	1	1	yes	characteristic
100	#1850	C₂×C₅	1	1	yes	characteristic, complemented
101	#1817	C₂×C₅	1	1	yes	characteristic, complemented
102	#1770	C₂×C₅	1	2	yes	complemented
103	#1753	C₂×C₅	1	2	yes	complemented
104	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	4	2	no	—
121	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₅	#41	1	2	yes	—
131	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₅×M₁₆	—	4	4	no	—
133	C₂×C₅×C₈	—	2	8	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	8	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₅×C₈	#41	1	4	yes	—
148	C₂×C₅×C₈	#41	1	4	yes	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	4	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₂²⋊C₄	—	2	2	no	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₅×C₂²⋊C₄	—	2	2	no	—
155	C₅×C₂²⋊C₄	—	2	4	no	—
156	C₅×C₂²⋊C₄	—	4	2	no	—
157	C₅×C₂²⋊C₄	M₁₆	1	4	yes	complemented
158	C₄²×C₅	—	2	4	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
166	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
168	C₂×#123	C₄×C₅	1	1	yes	characteristic
169	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
170	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
171	#435	—	2	4	no	—
172	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
173	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
178	C₂×#97	—	2	4	no	—
179	C₂×#97	C₂²×C₅	1	2	yes	—
180	C₂×#97	C₂²×C₅	1	2	yes	—
181	C₂×#97	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
183	#388	C₄×C₅	1	2	yes	—
184	#387	C₄×C₅	1	2	yes	—
185	#386	C₄×C₅	1	1	yes	characteristic
186	#385	C₄×C₅	1	1	yes	characteristic
187	#381	C₄×C₅	1	1	yes	characteristic
188	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
189	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
191	#336	C₂²×C₅	1	2	yes	—
192	#336	C₂²×C₅	1	2	yes	—
193	#336	C₂²×C₅	1	2	yes	—
194	#336	C₂²×C₅	1	2	yes	—
195	#336	C₂²×C₅	1	2	yes	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	2	2	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	2	no	—
203	C₂³×C₅	C₄×D₄	1	2	yes	—
204	C₂³×C₅	C₂×M₁₆	1	2	yes	—
205	C₂³×C₅	#131	1	2	yes	—
206	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
207	C₅×D₄	—	4	4	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	4	4	no	—
231	C₂×C₄×C₅	—	4	4	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
236	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
237	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#41	1	2	yes	—
239	C₂×C₄×C₅	C₂×#41	1	2	yes	—
240	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	2	4	no	—
243	C₅×C₈	—	4	1	no	—
244	C₅×C₈	—	4	1	no	—
245	C₅×C₈	—	4	2	no	—
246	C₅×C₈	#123	1	4	yes	complemented
247	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	—	2	4	no	—
257	C₂²×C₈	C₅×D₄	1	4	yes	—
258	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₅	1	2	yes	—
260	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₅	1	2	yes	—
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	#123	—	2	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
275	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
279	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₅	1	2	yes	—
281	C₂×C₄²	C₂³×C₅	1	2	yes	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	4	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	#97	—	2	4	no	—
289	#97	—	2	4	no	—
290	#97	—	2	2	no	—
291	C₄×C₈	—	2	4	no	—
292	#95	C₂×C₄×C₅	1	2	yes	—
293	#95	C₂×C₄×C₅	1	2	yes	—
294	#95	C₂×C₄×C₅	1	2	yes	—
295	#95	C₂×C₄×C₅	1	2	yes	—
296	#95	C₂×C₄×C₅	1	2	yes	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	2	4	no	—
299	C₂²×C₅	—	2	4	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	4	1	no	—
302	C₂²×C₅	—	4	1	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	4	1	no	—
306	C₂²×C₅	#436	1	4	yes	—
307	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
308	C₂²×C₅	C₄×#41	1	2	yes	—
309	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
310	C₂²×C₅	C₂×#131	1	1	yes	characteristic
311	C₂²×C₅	#568	1	2	yes	—
312	C₄×C₅	—	2	4	no	—
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	1	no	—
316	C₄×C₅	—	4	1	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	C₂×#123	1	1	yes	characteristic
321	C₄×C₅	#525	1	1	yes	characteristic
322	C₄×C₅	#529	1	2	yes	—
323	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
324	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
342	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
347	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
348	C₂²×C₄	C₅×#41	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
350	M₁₆	—	4	4	no	—
351	C₂×C₈	—	2	8	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	8	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
364	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
365	C₂×C₈	C₅×#41	1	4	yes	—
366	C₂×C₈	C₅×#41	1	4	yes	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	C₅×M₁₆	1	4	yes	complemented
376	C₄²	—	2	4	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	1	no	—
383	C₂×C₅	—	2	4	no	—
384	C₂×C₅	—	8	1	no	—
385	C₂×C₅	C₄×#123	1	1	yes	characteristic
386	C₂×C₅	C₂×#436	1	1	yes	characteristic
387	C₂×C₅	#2930	1	1	yes	characteristic
388	C₂×C₅	#2968	1	2	yes	—
389	C₂×C₅	#2970	1	2	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	C₄×C₅×D₄	1	2	yes	—
398	C₂³	C₂×C₅×M₁₆	1	2	yes	—
399	C₂³	C₅×#131	1	2	yes	—
400	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
401	D₄	—	4	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
430	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
431	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂×C₅×#41	1	2	yes	—
433	C₂×C₄	C₂×C₅×#41	1	2	yes	—
434	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	2	4	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	2	no	—
440	C₈	C₅×#123	1	4	yes	complemented
441	C₅	#21564	1	1	yes	characteristic, direct product factor, Sylow
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₅×#436	1	4	yes	—
452	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
453	C₂²	C₄×C₅×#41	1	2	yes	—
454	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
455	C₂²	C₂×C₅×#131	1	1	yes	characteristic
456	C₂²	C₅×#568	1	2	yes	—
457	C₄	—	2	2	no	—
458	C₄	—	2	4	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	C₂×C₅×#123	1	1	yes	characteristic
466	C₄	C₅×#525	1	1	yes	characteristic
467	C₄	C₅×#529	1	2	yes	—
468	C₂	—	2	4	no	—
469	C₂	—	8	1	no	—
470	C₂	C₄×C₅×#123	1	1	yes	characteristic
471	C₂	C₂×C₅×#436	1	1	yes	characteristic
472	C₂	C₅×#2930	1	1	yes	characteristic
473	C₂	C₅×#2968	1	2	yes	—
474	C₂	C₅×#2970	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#97	C₂	semidirect
4. C₅×#1924	C₂	semidirect
5. C₅×#1917	C₂	semidirect
7. C₅×#1850	C₂	semidirect
8. C₅×#1817	C₂	semidirect
9. C₅×#1770	C₂	semidirect
10. C₅×#1753	C₂	semidirect
11. C₅×C₈×C₂²⋊C₄	C₂	semidirect
43. #21564	C₅	direct (N × H)
95. C₂²×#97	C₂×C₅	semidirect
97. #1924	C₂×C₅	semidirect
98. #1917	C₂×C₅	semidirect
100. #1850	C₂×C₅	semidirect
101. #1817	C₂×C₅	semidirect
102. #1770	C₂×C₅	semidirect
103. #1753	C₂×C₅	semidirect
104. C₈×C₂²⋊C₄	C₂×C₅	semidirect
157. C₅×C₂²⋊C₄	M₁₆	semidirect
246. C₅×C₈	#123	semidirect
375. C₂²⋊C₄	C₅×M₁₆	semidirect
440. C₈	C₅×#123	semidirect
441. C₅	#21564	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×#435	2
C₂²×C₅×#97	2
C₄×C₅×#123	2
C₅×#1924	2
C₅×#1917	2
C₅×#1869	2
C₅×#1850	2
C₅×#1817	2
C₅×#1770	2
C₅×#1753	2
C₅×C₈×C₂²⋊C₄	2
#21564	5

Subgroups — C5×#21564 #11944284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21564 #11944284