Subgroups — C₂×C₅×#1283 #11930651

Order 1280.

722 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#1283	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×M₁₆	C₄	1	2	yes	—
6	C₂³×C₅×C₈	C₄	1	2	yes	—
7	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₅×#431	—	2	1	no	—
9	C₅×#431	—	2	1	no	—
10	C₅×#431	C₄	1	2	yes	—
11	C₅×#431	C₂²	1	2	yes	—
12	C₂×C₅×C₄⋊C₈	—	2	1	no	—
13	C₂×C₅×C₄⋊C₈	—	2	1	no	—
14	C₂×C₅×C₄⋊C₈	—	2	1	no	—
15	C₂×C₅×C₄⋊C₈	—	2	1	no	—
16	C₂×C₅×C₄⋊C₈	—	2	1	no	—
17	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
20	C₄×C₅×M₁₆	—	2	1	no	—
21	C₄×C₅×M₁₆	—	2	1	no	—
22	C₄×C₅×M₁₆	C₄	1	2	yes	—
23	C₄×C₅×M₁₆	C₂²	1	2	yes	—
24	C₂×C₅×#97	—	2	1	no	—
25	C₂×C₄×C₅×C₈	—	2	1	no	—
26	C₂×C₄×C₅×C₈	—	2	1	no	—
27	C₂×#1283	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	4	no	—
33	C₂×C₅×M₁₆	C₈	1	8	yes	complemented
34	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
35	C₂²×C₅×C₈	—	2	2	no	—
36	C₂²×C₅×C₈	—	2	2	no	—
37	C₂²×C₅×C₈	—	2	2	no	—
38	C₂²×C₅×C₈	—	2	2	no	—
39	C₂²×C₅×C₈	—	4	4	no	—
40	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×C₄⋊C₈	—	2	2	no	—
54	C₅×C₄⋊C₈	—	2	2	no	—
55	C₅×C₄⋊C₈	—	2	2	no	—
56	C₅×C₄⋊C₈	—	2	2	no	—
57	C₅×C₄⋊C₈	—	2	2	no	—
58	C₅×C₄⋊C₈	—	2	2	no	—
59	C₅×C₂²⋊C₈	—	2	2	no	—
60	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₅×#97	—	2	2	no	—
62	C₅×#97	—	2	2	no	—
63	C₄×C₅×C₈	—	2	2	no	—
64	C₄×C₅×C₈	—	2	2	no	—
65	C₄×C₅×C₈	—	2	2	no	—
66	C₄×C₅×C₈	—	2	2	no	—
67	C₂×#431	C₂×C₅	1	1	yes	characteristic
68	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
69	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
70	#1283	C₂×C₅	1	4	yes	direct product factor
71	C₂⁴×C₅	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₅	—	2	2	no	—
73	C₂²×C₄×C₅	—	2	2	no	—
74	C₂²×C₄×C₅	—	4	2	no	—
75	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
91	C₂²×C₄×C₅	M₁₆	1	4	yes	—
92	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₅×M₁₆	—	2	8	no	—
96	C₅×M₁₆	—	2	4	no	—
97	C₅×M₁₆	C₂×C₈	1	8	yes	complemented
98	C₂×C₅×C₈	—	2	8	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₂×C₅×C₈	—	2	4	no	—
101	C₂×C₅×C₈	—	2	4	no	—
102	C₂×C₅×C₈	—	4	4	no	—
103	C₂×C₅×C₈	—	4	4	no	—
104	C₂×C₅×C₈	—	4	4	no	—
105	C₂×C₅×C₈	—	4	4	no	—
106	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₂²×M₁₆	C₄×C₅	1	2	yes	—
123	C₂³×C₈	C₄×C₅	1	2	yes	—
124	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
125	#431	—	2	1	no	—
126	#431	—	2	1	no	—
127	#431	C₄×C₅	1	2	yes	—
128	#431	C₂²×C₅	1	2	yes	—
129	C₂×C₄⋊C₈	—	2	1	no	—
130	C₂×C₄⋊C₈	—	2	1	no	—
131	C₂×C₄⋊C₈	—	2	1	no	—
132	C₂×C₄⋊C₈	—	2	1	no	—
133	C₂×C₄⋊C₈	—	2	1	no	—
134	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	—
135	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
136	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	—
137	C₄×M₁₆	—	2	1	no	—
138	C₄×M₁₆	—	2	1	no	—
139	C₄×M₁₆	C₄×C₅	1	2	yes	—
140	C₄×M₁₆	C₂²×C₅	1	2	yes	—
141	C₂×#97	—	2	1	no	—
142	C₂×C₄×C₈	—	2	1	no	—
143	C₂×C₄×C₈	—	2	1	no	—
144	C₂³×C₅	—	2	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	#95	1	1	yes	characteristic
147	C₂³×C₅	#95	1	1	yes	characteristic
148	C₂³×C₅	C₄×C₈	1	2	yes	—
149	C₂³×C₅	#97	1	2	yes	—
150	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	1	no	—
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	4	1	no	—
161	C₂×C₄×C₅	—	4	1	no	—
162	C₂×C₄×C₅	—	4	1	no	—
163	C₂×C₄×C₅	—	4	1	no	—
164	C₂×C₄×C₅	#95	1	1	yes	characteristic
165	C₂×C₄×C₅	#95	1	1	yes	characteristic
166	C₂×C₄×C₅	#95	1	1	yes	characteristic
167	C₂×C₄×C₅	#95	1	1	yes	characteristic
168	C₂×C₄×C₅	#95	1	1	yes	characteristic
169	C₂×C₄×C₅	#95	1	1	yes	characteristic
170	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
171	C₂×C₄×C₅	#97	1	2	yes	—
172	C₂×C₄×C₅	C₂²⋊C₈	1	4	yes	—
173	C₂×C₄×C₅	C₂²⋊C₈	1	4	yes	—
174	C₂×C₄×C₅	#100	1	2	yes	—
175	C₂×C₄×C₅	#101	1	2	yes	—
176	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
177	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
178	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
185	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
186	C₅×C₈	—	2	8	no	—
187	C₅×C₈	—	4	4	no	—
188	C₅×C₈	—	4	4	no	—
189	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	4	no	—
194	C₂×M₁₆	C₅×C₈	1	8	yes	complemented
195	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
196	C₂²×C₈	—	2	2	no	—
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	—	2	2	no	—
199	C₂²×C₈	—	2	2	no	—
200	C₂²×C₈	—	4	4	no	—
201	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
202	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
206	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
207	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
208	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
209	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
210	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
211	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
212	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	2	2	no	—
217	C₄⋊C₈	—	2	2	no	—
218	C₄⋊C₈	—	2	2	no	—
219	C₄⋊C₈	—	2	2	no	—
220	C₂²⋊C₈	—	2	2	no	—
221	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
222	#97	—	2	2	no	—
223	#97	—	2	2	no	—
224	C₄×C₈	—	2	2	no	—
225	C₄×C₈	—	2	2	no	—
226	C₄×C₈	—	2	2	no	—
227	C₄×C₈	—	2	2	no	—
228	C₂²×C₅	—	2	4	no	—
229	C₂²×C₅	—	2	4	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	#336	1	2	yes	—
235	C₂²×C₅	#336	1	2	yes	—
236	C₂²×C₅	#343	1	2	yes	—
237	C₂²×C₅	#344	1	2	yes	—
238	C₂²×C₅	C₂×#95	1	1	yes	characteristic
239	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
240	C₂²×C₅	C₂×#97	1	1	yes	characteristic
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	2	1	no	—
245	C₄×C₅	—	2	1	no	—
246	C₄×C₅	—	2	1	no	—
247	C₄×C₅	#336	1	2	yes	—
248	C₄×C₅	#336	1	2	yes	—
249	C₄×C₅	#343	1	2	yes	—
250	C₄×C₅	C₂×C₂²⋊C₈	1	2	yes	—
251	C₄×C₅	C₂×#100	1	1	yes	characteristic
252	C₄×C₅	C₂×#101	1	1	yes	characteristic
253	C₄×C₅	C₂×C₄⋊C₈	1	2	yes	—
254	C₂⁴	C₄²×C₅	1	1	yes	characteristic
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
259	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
260	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
261	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₅×C₈	1	4	yes	—
274	C₂²×C₄	C₅×M₁₆	1	4	yes	—
275	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
278	M₁₆	—	2	4	no	—
279	M₁₆	—	2	8	no	—
280	M₁₆	C₂×C₅×C₈	1	8	yes	complemented
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	—	4	4	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	—	4	4	no	—
289	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
290	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
291	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
292	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
293	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
294	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
295	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
296	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
297	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
298	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
299	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
300	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
301	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
302	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
303	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
304	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
305	C₂×C₅	—	2	2	no	—
306	C₂×C₅	—	2	1	no	—
307	C₂×C₅	—	2	1	no	—
308	C₂×C₅	#1283	1	4	yes	direct product factor
309	C₂×C₅	C₂×#336	1	1	yes	characteristic
310	C₂×C₅	C₂×#343	1	1	yes	characteristic
311	C₂×C₅	C₂×#344	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	C₅×#95	1	1	yes	characteristic
315	C₂³	C₅×#95	1	1	yes	characteristic
316	C₂³	C₄×C₅×C₈	1	2	yes	—
317	C₂³	C₅×#97	1	2	yes	—
318	C₂³	C₂×C₄²×C₅	1	1	yes	characteristic
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	C₅×#95	1	1	yes	characteristic
333	C₂×C₄	C₅×#95	1	1	yes	characteristic
334	C₂×C₄	C₅×#95	1	1	yes	characteristic
335	C₂×C₄	C₅×#95	1	1	yes	characteristic
336	C₂×C₄	C₅×#95	1	1	yes	characteristic
337	C₂×C₄	C₅×#95	1	1	yes	characteristic
338	C₂×C₄	C₄×C₅×C₈	1	2	yes	—
339	C₂×C₄	C₅×#97	1	2	yes	—
340	C₂×C₄	C₅×C₂²⋊C₈	1	4	yes	—
341	C₂×C₄	C₅×C₂²⋊C₈	1	4	yes	—
342	C₂×C₄	C₅×#100	1	2	yes	—
343	C₂×C₄	C₅×#101	1	2	yes	—
344	C₂×C₄	C₅×C₄⋊C₈	1	4	yes	—
345	C₂×C₄	C₅×C₄⋊C₈	1	4	yes	—
346	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
353	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
354	C₈	—	2	8	no	—
355	C₈	—	4	4	no	—
356	C₈	—	4	4	no	—
357	C₅	C₂×#1283	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	C₅×#336	1	2	yes	—
365	C₂²	C₅×#336	1	2	yes	—
366	C₂²	C₅×#343	1	2	yes	—
367	C₂²	C₅×#344	1	2	yes	—
368	C₂²	C₂×C₅×#95	1	1	yes	characteristic
369	C₂²	C₂×C₄×C₅×C₈	1	1	yes	characteristic
370	C₂²	C₂×C₅×#97	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	C₅×#336	1	2	yes	—
378	C₄	C₅×#336	1	2	yes	—
379	C₄	C₅×#343	1	2	yes	—
380	C₄	C₂×C₅×C₂²⋊C₈	1	2	yes	—
381	C₄	C₂×C₅×#100	1	1	yes	characteristic
382	C₄	C₂×C₅×#101	1	1	yes	characteristic
383	C₄	C₂×C₅×C₄⋊C₈	1	2	yes	—
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	2	2	no	—
387	C₂	C₅×#1283	1	4	yes	direct product factor
388	C₂	C₂×C₅×#336	1	1	yes	characteristic
389	C₂	C₂×C₅×#343	1	1	yes	characteristic
390	C₂	C₂×C₅×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂³×C₅	#95
prime radical	C₂⁴×C₅	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1283	C₂	direct (N × H)
27. C₂×#1283	C₅	direct (N × H)
33. C₂×C₅×M₁₆	C₈	semidirect
70. #1283	C₂×C₅	direct (N × H)
97. C₅×M₁₆	C₂×C₈	semidirect
194. C₂×M₁₆	C₅×C₈	semidirect
280. M₁₆	C₂×C₅×C₈	semidirect
308. C₂×C₅	#1283	direct (N × H)
357. C₅	C₂×#1283	direct (N × H)
387. C₂	C₅×#1283	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×#431	2
C₂²×C₅×C₄⋊C₈	2
C₂×C₄×C₅×M₁₆	2
C₅×#1283	2
C₂×#1283	5

Subgroups — C2×C5×#1283 #11930651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1283 #11930651