Subgroups — C₅×#21441 #11944161

Order 1280.

1584 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#436	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#120	C₂	1	1	yes	maximal, characteristic
5	C₅×#1870	C₂	1	2	yes	maximal, complemented
6	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1851	C₂	1	2	yes	maximal, complemented
8	C₅×#1850	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1779	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1753	C₂	1	2	yes	maximal, complemented
11	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	—	2	8	no	—
14	C₂²×C₅×M₁₆	—	2	4	no	—
15	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
16	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#120	C₄	1	1	yes	characteristic
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
23	C₅×#436	—	2	8	no	—
24	C₅×#435	—	2	4	no	—
25	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
32	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
35	C₅×#386	C₄	1	1	yes	characteristic
36	C₅×#386	C₄	1	2	yes	—
37	C₅×#385	C₄	1	2	yes	—
38	C₅×#385	C₄	1	1	yes	characteristic
39	C₅×#379	C₄	1	1	yes	characteristic
40	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	complemented
43	C₅×#336	C₂²	1	2	yes	complemented
44	C₅×#336	C₂²	1	2	yes	complemented
45	#21441	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₅	—	2	4	no	—
50	C₂³×C₄×C₅	—	2	2	no	—
51	C₂³×C₄×C₅	—	2	4	no	—
52	C₂³×C₄×C₅	—	2	2	no	—
53	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₅×M₁₆	—	2	32	no	—
59	C₂×C₅×M₁₆	—	2	4	no	—
60	C₂×C₅×M₁₆	—	2	4	no	—
61	C₂×C₅×M₁₆	—	2	4	no	—
62	C₂×C₅×M₁₆	—	2	4	no	—
63	C₂×C₅×M₁₆	—	2	4	no	—
64	C₂×C₅×M₁₆	—	2	2	no	—
65	C₂×C₅×M₁₆	—	2	4	no	—
66	C₂×C₅×M₁₆	D₄	1	8	yes	complemented
67	C₂²×C₅×C₈	—	2	2	no	—
68	C₂²×C₅×C₈	—	2	4	no	—
69	C₂²×C₅×C₈	—	2	4	no	—
70	C₂²×C₅×C₈	D₄	1	4	yes	complemented
71	C₂²×C₅×C₈	C₂³	1	2	yes	—
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	2	yes	—
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₅×#120	—	2	4	no	—
78	C₄×C₅×D₄	—	2	2	no	—
79	C₄×C₅×D₄	—	2	4	no	—
80	C₄×C₅×D₄	—	2	2	no	—
81	C₄×C₅×D₄	—	2	4	no	—
82	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
86	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂³	1	2	yes	—
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₅×C₄⋊C₈	—	2	2	no	—
95	C₅×C₄⋊C₈	—	2	4	no	—
96	C₅×C₂²⋊C₈	—	2	2	no	—
97	C₅×C₂²⋊C₈	—	2	4	no	—
98	C₅×C₂²⋊C₈	—	2	2	no	—
99	C₅×C₂²⋊C₈	—	2	4	no	—
100	C₅×C₂²⋊C₈	—	2	2	no	—
101	C₅×C₂²⋊C₈	—	2	4	no	—
102	C₅×#97	—	2	2	no	—
103	C₄×C₅×C₈	—	2	4	no	—
104	C₅×#95	C₂×C₄	1	2	yes	—
105	C₅×#95	C₂×C₄	1	2	yes	—
106	C₅×#95	C₂×C₄	1	2	yes	—
107	C₂³×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#436	C₂×C₅	1	2	yes	complemented
109	C₂×#435	C₂×C₅	1	1	yes	characteristic, complemented
110	C₄×#120	C₂×C₅	1	1	yes	characteristic
111	#1870	C₂×C₅	1	2	yes	complemented
112	#1869	C₂×C₅	1	1	yes	characteristic, complemented
113	#1851	C₂×C₅	1	2	yes	complemented
114	#1850	C₂×C₅	1	1	yes	characteristic, complemented
115	#1779	C₂×C₅	1	1	yes	characteristic, complemented
116	#1753	C₂×C₅	1	2	yes	complemented
117	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂⁴×C₅	—	2	4	no	—
119	C₂⁴×C₅	—	2	2	no	—
120	C₂⁴×C₅	—	2	2	no	—
121	C₂⁴×C₅	—	2	2	no	—
122	C₂⁴×C₅	—	4	2	no	—
123	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
125	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₅×D₄	—	2	4	no	—
127	C₂×C₅×D₄	—	2	2	no	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	—	2	4	no	—
131	C₂×C₅×D₄	—	4	2	no	—
132	C₂²×C₄×C₅	—	2	8	no	—
133	C₂²×C₄×C₅	—	2	8	no	—
134	C₂²×C₄×C₅	—	2	16	no	—
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	—	2	4	no	—
138	C₂²×C₄×C₅	—	2	4	no	—
139	C₂²×C₄×C₅	—	2	4	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₅	#41	1	4	yes	—
160	C₂²×C₄×C₅	#41	1	2	yes	—
161	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₅×M₁₆	—	2	16	no	—
163	C₅×M₁₆	—	2	16	no	—
164	C₅×M₁₆	—	4	4	no	—
165	C₂×C₅×C₈	—	2	8	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	2	2	no	—
168	C₂×C₅×C₈	—	2	2	no	—
169	C₂×C₅×C₈	—	2	8	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	—	2	2	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	2	no	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	2	2	no	—
177	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
178	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
179	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
180	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
181	C₅×C₄⋊C₄	—	2	4	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₂²⋊C₄	—	2	4	no	—
184	C₅×C₂²⋊C₄	—	2	2	no	—
185	C₅×C₂²⋊C₄	—	2	2	no	—
186	C₅×C₂²⋊C₄	—	2	2	no	—
187	C₅×C₂²⋊C₄	—	2	4	no	—
188	C₅×C₂²⋊C₄	—	2	4	no	—
189	C₅×C₂²⋊C₄	—	4	2	no	—
190	C₅×C₂²⋊C₄	M₁₆	1	4	yes	complemented
191	C₄²×C₅	—	2	2	no	—
192	C₄²×C₅	—	2	1	no	—
193	C₄²×C₅	—	2	2	no	—
194	C₄²×C₅	—	2	1	no	—
195	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
196	C₂²×M₁₆	—	2	8	no	—
197	C₂²×M₁₆	—	2	4	no	—
198	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
199	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
200	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
201	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
202	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
203	C₂×#120	C₄×C₅	1	1	yes	characteristic
204	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
206	#436	—	2	8	no	—
207	#435	—	2	4	no	—
208	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
209	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
210	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
212	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
215	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
216	C₂×#97	C₂²×C₅	1	1	yes	characteristic, complemented
217	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
218	#386	C₄×C₅	1	1	yes	characteristic
219	#386	C₄×C₅	1	2	yes	—
220	#385	C₄×C₅	1	2	yes	—
221	#385	C₄×C₅	1	1	yes	characteristic
222	#379	C₄×C₅	1	1	yes	characteristic
223	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
225	#336	C₂²×C₅	1	2	yes	complemented
226	#336	C₂²×C₅	1	2	yes	complemented
227	#336	C₂²×C₅	1	2	yes	complemented
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	2	no	—
230	C₂³×C₅	—	2	8	no	—
231	C₂³×C₅	—	2	2	no	—
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	2	1	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	1	no	—
240	C₂³×C₅	—	2	1	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	4	8	no	—
243	C₂³×C₅	—	4	8	no	—
244	C₂³×C₅	—	4	4	no	—
245	C₂³×C₅	—	4	4	no	—
246	C₂³×C₅	C₄×D₄	1	4	yes	—
247	C₂³×C₅	C₄×D₄	1	2	yes	—
248	C₂³×C₅	C₂×M₁₆	1	2	yes	—
249	C₂³×C₅	#131	1	2	yes	—
250	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
251	C₅×D₄	—	4	8	no	—
252	C₅×D₄	—	4	4	no	—
253	C₂×C₄×C₅	—	2	8	no	—
254	C₂×C₄×C₅	—	2	16	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	4	no	—
264	C₂×C₄×C₅	—	2	4	no	—
265	C₂×C₄×C₅	—	2	4	no	—
266	C₂×C₄×C₅	—	2	4	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	4	1	no	—
278	C₂×C₄×C₅	—	4	1	no	—
279	C₂×C₄×C₅	—	4	2	no	—
280	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
281	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
282	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
283	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×#41	1	2	yes	—
287	C₅×C₈	—	2	4	no	—
288	C₅×C₈	—	2	2	no	—
289	C₅×C₈	—	4	1	no	—
290	C₅×C₈	—	4	2	no	—
291	C₅×C₈	—	4	1	no	—
292	C₅×C₈	#120	1	4	yes	complemented
293	C₂⁵	C₂×C₄×C₅	1	1	yes	characteristic
294	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
295	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
296	C₂³×C₄	—	2	4	no	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	4	no	—
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
301	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₅	1	2	yes	—
305	C₂×M₁₆	—	2	32	no	—
306	C₂×M₁₆	—	2	4	no	—
307	C₂×M₁₆	—	2	4	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	—	2	4	no	—
310	C₂×M₁₆	—	2	4	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	4	no	—
313	C₂×M₁₆	C₅×D₄	1	8	yes	complemented
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	—	2	4	no	—
316	C₂²×C₈	—	2	4	no	—
317	C₂²×C₈	C₅×D₄	1	4	yes	complemented
318	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₅	1	2	yes	—
320	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₅	1	2	yes	—
322	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
324	#120	—	2	4	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	4	no	—
329	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
332	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
338	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₅	1	2	yes	—
340	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
341	C₄⋊C₈	—	2	2	no	—
342	C₄⋊C₈	—	2	4	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	—	2	4	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	4	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	2	4	no	—
349	#97	—	2	2	no	—
350	C₄×C₈	—	2	4	no	—
351	#95	C₂×C₄×C₅	1	2	yes	—
352	#95	C₂×C₄×C₅	1	2	yes	—
353	#95	C₂×C₄×C₅	1	2	yes	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	4	no	—
356	C₂²×C₅	—	2	4	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	2	4	no	—
359	C₂²×C₅	—	2	4	no	—
360	C₂²×C₅	—	2	4	no	—
361	C₂²×C₅	—	4	16	no	—
362	C₂²×C₅	—	4	2	no	—
363	C₂²×C₅	—	4	2	no	—
364	C₂²×C₅	—	4	2	no	—
365	C₂²×C₅	—	4	2	no	—
366	C₂²×C₅	—	4	1	no	—
367	C₂²×C₅	—	4	1	no	—
368	C₂²×C₅	—	4	2	no	—
369	C₂²×C₅	—	4	2	no	—
370	C₂²×C₅	—	4	1	no	—
371	C₂²×C₅	#436	1	4	yes	complemented
372	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
373	C₂²×C₅	C₂×C₄×D₄	1	2	yes	—
374	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
375	C₂²×C₅	C₂×#131	1	1	yes	characteristic
376	C₂²×C₅	#568	1	2	yes	—
377	C₄×C₅	—	2	4	no	—
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	2	4	no	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	4	2	no	—
383	C₄×C₅	—	4	1	no	—
384	C₄×C₅	C₂×#120	1	1	yes	characteristic
385	C₄×C₅	#525	1	2	yes	—
386	C₄×C₅	#525	1	1	yes	characteristic
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	4	2	no	—
392	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
393	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
394	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	16	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
420	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
421	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
425	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
426	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
427	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
428	C₂²×C₄	C₅×#41	1	4	yes	—
429	C₂²×C₄	C₅×#41	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
431	M₁₆	—	2	16	no	—
432	M₁₆	—	2	16	no	—
433	M₁₆	—	4	4	no	—
434	C₂×C₈	—	2	8	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	8	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
447	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
448	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
449	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	C₅×M₁₆	1	4	yes	complemented
460	C₄²	—	2	2	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	1	no	—
464	C₂×C₅	—	2	4	no	—
465	C₂×C₅	—	4	4	no	—
466	C₂×C₅	—	8	1	no	—
467	C₂×C₅	C₄×#120	1	1	yes	characteristic
468	C₂×C₅	C₂×#436	1	1	yes	characteristic
469	C₂×C₅	#2930	1	1	yes	characteristic
470	C₂×C₅	#2933	1	2	yes	—
471	C₂×C₅	D₄×M₁₆	1	2	yes	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	8	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	4	no	—
490	C₂³	C₄×C₅×D₄	1	4	yes	—
491	C₂³	C₄×C₅×D₄	1	2	yes	—
492	C₂³	C₂×C₅×M₁₆	1	2	yes	—
493	C₂³	C₅×#131	1	2	yes	—
494	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
495	D₄	—	4	8	no	—
496	D₄	—	4	4	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	16	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
525	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
526	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	complemented
527	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
529	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
530	C₂×C₄	C₂×C₅×#41	1	2	yes	—
531	C₈	—	2	4	no	—
532	C₈	—	2	2	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	2	no	—
535	C₈	—	4	1	no	—
536	C₈	C₅×#120	1	4	yes	complemented
537	C₅	#21441	1	1	yes	characteristic, direct product factor, Sylow
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	4	16	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	C₅×#436	1	4	yes	complemented
556	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
557	C₂²	C₂×C₄×C₅×D₄	1	2	yes	—
558	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
559	C₂²	C₂×C₅×#131	1	1	yes	characteristic
560	C₂²	C₅×#568	1	2	yes	—
561	C₄	—	2	2	no	—
562	C₄	—	2	4	no	—
563	C₄	—	2	4	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	C₂×C₅×#120	1	1	yes	characteristic
569	C₄	C₅×#525	1	2	yes	—
570	C₄	C₅×#525	1	1	yes	characteristic
571	C₂	—	2	4	no	—
572	C₂	—	4	4	no	—
573	C₂	—	8	1	no	—
574	C₂	C₄×C₅×#120	1	1	yes	characteristic
575	C₂	C₂×C₅×#436	1	1	yes	characteristic
576	C₂	C₅×#2930	1	1	yes	characteristic
577	C₂	C₅×#2933	1	2	yes	—
578	C₂	C₅×D₄×M₁₆	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	C₂×C₅×#120	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
1. C₂³×C₅×M₁₆	C₂	semidirect
2. C₂×C₅×#436	C₂	semidirect
3. C₂×C₅×#435	C₂	semidirect
5. C₅×#1870	C₂	semidirect
6. C₅×#1869	C₂	semidirect
7. C₅×#1851	C₂	semidirect
8. C₅×#1850	C₂	semidirect
9. C₅×#1779	C₂	semidirect
10. C₅×#1753	C₂	semidirect
11. C₅×C₈×C₂²⋊C₄	C₂	semidirect
17. C₂²×C₅×M₁₆	C₂²	semidirect
25. C₂×C₅×C₄⋊C₈	C₂²	semidirect
26. C₂×C₅×C₄⋊C₈	C₂²	semidirect
31. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
32. C₂×C₅×C₂²⋊C₈	C₂²	semidirect
33. C₂×C₅×#97	C₂²	semidirect
34. C₂×C₄×C₅×C₈	C₂²	semidirect
42. C₅×#336	C₂²	semidirect
43. C₅×#336	C₂²	semidirect
44. C₅×#336	C₂²	semidirect
45. #21441	C₅	direct (N × H)
66. C₂×C₅×M₁₆	D₄	semidirect
70. C₂²×C₅×C₈	D₄	semidirect
107. C₂³×M₁₆	C₂×C₅	semidirect
108. C₂×#436	C₂×C₅	semidirect
109. C₂×#435	C₂×C₅	semidirect
111. #1870	C₂×C₅	semidirect
112. #1869	C₂×C₅	semidirect
113. #1851	C₂×C₅	semidirect
114. #1850	C₂×C₅	semidirect
115. #1779	C₂×C₅	semidirect
116. #1753	C₂×C₅	semidirect
117. C₈×C₂²⋊C₄	C₂×C₅	semidirect
190. C₅×C₂²⋊C₄	M₁₆	semidirect
200. C₂²×M₁₆	C₂²×C₅	semidirect
208. C₂×C₄⋊C₈	C₂²×C₅	semidirect
209. C₂×C₄⋊C₈	C₂²×C₅	semidirect
214. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
215. C₂×C₂²⋊C₈	C₂²×C₅	semidirect
216. C₂×#97	C₂²×C₅	semidirect
217. C₂×C₄×C₈	C₂²×C₅	semidirect
225. #336	C₂²×C₅	semidirect
226. #336	C₂²×C₅	semidirect
227. #336	C₂²×C₅	semidirect
282. C₂×C₄×C₅	C₂×M₁₆	semidirect
292. C₅×C₈	#120	semidirect
313. C₂×M₁₆	C₅×D₄	semidirect
317. C₂²×C₈	C₅×D₄	semidirect
371. C₂²×C₅	#436	semidirect
459. C₂²⋊C₄	C₅×M₁₆	semidirect
526. C₂×C₄	C₂×C₅×M₁₆	semidirect
536. C₈	C₅×#120	semidirect
537. C₅	#21441	direct (N × H)
555. C₂²	C₅×#436	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×M₁₆	2
C₂×C₅×#436	2
C₂×C₅×#435	2
C₄×C₅×#120	2
C₅×#1870	2
C₅×#1869	2
C₅×#1851	2
C₅×#1850	2
C₅×#1779	2
C₅×#1753	2
C₅×C₈×C₂²⋊C₄	2
#21441	5

Subgroups — C5×#21441 #11944161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21441 #11944161