Subgroups — C₃×C₅×#1850 #14274884

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#336	C₂	1	2	yes	maximal, complemented
6	C₅×#1850	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	—	2	2	no	—
9	C₂²×C₃×C₅×C₈	—	2	4	no	—
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
14	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊C₈	—	2	4	no	—
17	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
18	C₃×C₅×#95	C₄	1	2	yes	—
19	C₃×#1850	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂³×C₅×C₈	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
22	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₅×#336	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₅×C₈	—	2	8	no	—
35	C₂×C₃×C₅×C₈	—	2	2	no	—
36	C₂×C₃×C₅×C₈	—	2	2	no	—
37	C₂×C₃×C₅×C₈	—	2	1	no	—
38	C₂×C₃×C₅×C₈	—	2	1	no	—
39	C₂×C₃×C₅×C₈	—	2	2	no	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
42	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
43	C₃×C₅×C₂²⋊C₄	C₈	1	4	yes	complemented
44	C₃×C₄²×C₅	—	2	2	no	—
45	C₃×C₄²×C₅	—	2	2	no	—
46	C₂³×C₃×C₈	C₂×C₅	1	1	yes	characteristic
47	C₂×C₃×C₄⋊C₈	C₂×C₅	1	2	yes	complemented
48	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
49	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
50	C₃×#336	C₂×C₅	1	2	yes	complemented
51	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	4	no	—
54	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
57	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
58	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
60	C₅×C₄⋊C₈	—	2	4	no	—
61	C₅×C₂²⋊C₈	—	2	2	no	—
62	C₅×#95	C₃×C₄	1	2	yes	—
63	#1850	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂³×C₃×C₅	—	2	2	no	—
65	C₂³×C₃×C₅	—	2	2	no	—
66	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
67	C₂³×C₃×C₅	C₂×C₈	1	2	yes	—
68	C₂³×C₃×C₅	M₁₆	1	2	yes	—
69	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	—	2	2	no	—
71	C₂×C₃×C₄×C₅	—	2	2	no	—
72	C₂×C₃×C₄×C₅	—	2	2	no	—
73	C₂×C₃×C₄×C₅	—	2	2	no	—
74	C₂×C₃×C₄×C₅	—	2	4	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
81	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	#41	1	2	yes	—
85	C₃×C₅×C₈	—	2	4	no	—
86	C₃×C₅×C₈	—	4	1	no	—
87	C₃×C₅×C₈	—	4	1	no	—
88	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
89	C₂²×C₃×C₈	—	2	2	no	—
90	C₂²×C₃×C₈	—	2	4	no	—
91	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
92	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
94	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
95	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
96	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
97	C₃×C₄⋊C₈	—	2	4	no	—
98	C₃×C₂²⋊C₈	—	2	2	no	—
99	C₃×#95	C₄×C₅	1	2	yes	—
100	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
106	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
107	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
108	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
109	C₂×C₅×C₈	—	2	8	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	—	2	1	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
117	C₅×C₂²⋊C₄	—	2	2	no	—
118	C₅×C₂²⋊C₄	C₃×C₈	1	4	yes	complemented
119	C₄²×C₅	—	2	2	no	—
120	C₄²×C₅	—	2	2	no	—
121	C₂³×C₈	C₂×C₃×C₅	1	1	yes	characteristic
122	C₂×C₄⋊C₈	C₂×C₃×C₅	1	2	yes	complemented
123	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
124	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
125	#336	C₂×C₃×C₅	1	2	yes	complemented
126	C₂²×C₃×C₅	—	2	2	no	—
127	C₂²×C₃×C₅	—	2	2	no	—
128	C₂²×C₃×C₅	—	2	4	no	—
129	C₂²×C₃×C₅	—	2	4	no	—
130	C₂²×C₃×C₅	C₄⋊C₈	1	4	yes	complemented
131	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
133	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
134	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
135	C₂²×C₃×C₅	#131	1	2	yes	—
136	C₃×C₄×C₅	—	2	2	no	—
137	C₃×C₄×C₅	—	2	4	no	—
138	C₃×C₄×C₅	—	4	2	no	—
139	C₃×C₄×C₅	#120	1	1	yes	characteristic
140	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
141	C₃×C₄×C₅	#123	1	1	yes	characteristic
142	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
146	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
148	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
149	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
150	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
151	C₂×C₃×C₈	—	2	8	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	—	2	2	no	—
157	C₂×C₃×C₈	—	2	2	no	—
158	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
159	C₃×C₂²⋊C₄	—	2	2	no	—
160	C₃×C₂²⋊C₄	C₅×C₈	1	4	yes	complemented
161	C₃×C₄²	—	2	2	no	—
162	C₃×C₄²	—	2	2	no	—
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	2	2	no	—
165	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
166	C₂³×C₅	C₂×C₃×C₈	1	2	yes	—
167	C₂³×C₅	C₃×M₁₆	1	2	yes	—
168	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₅	C₂×C₃×C₈	1	4	yes	complemented
180	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
181	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₅	C₃×#41	1	2	yes	—
184	C₅×C₈	—	2	4	no	—
185	C₅×C₈	—	4	1	no	—
186	C₅×C₈	—	4	1	no	—
187	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	—	2	4	no	—
190	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
191	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
192	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
193	C₂×C₂²⋊C₄	C₃×C₄×C₅	1	1	yes	characteristic
194	C₂×C₂²⋊C₄	C₃×C₄×C₅	1	1	yes	characteristic
195	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
196	C₄⋊C₈	—	2	4	no	—
197	C₂²⋊C₈	—	2	2	no	—
198	#95	C₃×C₄×C₅	1	2	yes	—
199	C₂×C₃×C₅	—	2	4	no	—
200	C₂×C₃×C₅	#385	1	1	yes	characteristic
201	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
202	C₂×C₃×C₅	#424	1	1	yes	characteristic
203	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
204	C₂×C₃×C₅	#435	1	2	yes	—
205	C₂³×C₃	—	2	2	no	—
206	C₂³×C₃	—	2	2	no	—
207	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
208	C₂³×C₃	C₂×C₅×C₈	1	2	yes	—
209	C₂³×C₃	C₅×M₁₆	1	2	yes	—
210	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
221	C₂×C₃×C₄	C₂×C₅×C₈	1	4	yes	complemented
222	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
223	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
225	C₂×C₃×C₄	C₅×#41	1	2	yes	—
226	C₃×C₈	—	2	4	no	—
227	C₃×C₈	—	4	1	no	—
228	C₃×C₈	—	4	1	no	—
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	4	no	—
232	C₂²×C₅	—	2	4	no	—
233	C₂²×C₅	C₃×C₄⋊C₈	1	4	yes	complemented
234	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
236	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
237	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
238	C₂²×C₅	C₃×#131	1	2	yes	—
239	C₄×C₅	—	2	2	no	—
240	C₄×C₅	—	2	4	no	—
241	C₄×C₅	—	4	2	no	—
242	C₄×C₅	C₃×#120	1	1	yes	characteristic
243	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
244	C₄×C₅	C₃×#123	1	1	yes	characteristic
245	C₂⁴	C₂×C₃×C₄×C₅	1	1	yes	characteristic
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
249	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
251	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
252	C₂²×C₄	C₃×C₅×Q₈	1	2	yes	—
253	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
254	C₂×C₈	—	2	8	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
262	C₂²⋊C₄	—	2	2	no	—
263	C₂²⋊C₄	C₃×C₅×C₈	1	4	yes	complemented
264	C₄²	—	2	2	no	—
265	C₄²	—	2	2	no	—
266	C₃×C₅	#1850	1	1	yes	characteristic, direct product factor, Hall
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	2	4	no	—
270	C₂²×C₃	—	2	4	no	—
271	C₂²×C₃	C₅×C₄⋊C₈	1	4	yes	complemented
272	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
273	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
274	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
275	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
276	C₂²×C₃	C₅×#131	1	2	yes	—
277	C₃×C₄	—	2	2	no	—
278	C₃×C₄	—	2	4	no	—
279	C₃×C₄	—	4	2	no	—
280	C₃×C₄	C₅×#120	1	1	yes	characteristic
281	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
282	C₃×C₄	C₅×#123	1	1	yes	characteristic
283	C₂×C₅	—	2	4	no	—
284	C₂×C₅	C₃×#385	1	1	yes	characteristic
285	C₂×C₅	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
286	C₂×C₅	C₃×#424	1	1	yes	characteristic
287	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
288	C₂×C₅	C₃×#435	1	2	yes	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	C₃×C₅×C₄⋊C₄	1	2	yes	—
292	C₂³	C₂×C₃×C₅×C₈	1	2	yes	—
293	C₂³	C₃×C₅×M₁₆	1	2	yes	—
294	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
305	C₂×C₄	C₂×C₃×C₅×C₈	1	4	yes	complemented
306	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
307	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
308	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
309	C₂×C₄	C₃×C₅×#41	1	2	yes	—
310	C₈	—	2	4	no	—
311	C₈	—	4	1	no	—
312	C₈	—	4	1	no	—
313	C₂×C₃	—	2	4	no	—
314	C₂×C₃	C₅×#385	1	1	yes	characteristic
315	C₂×C₃	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
316	C₂×C₃	C₅×#424	1	1	yes	characteristic
317	C₂×C₃	C₅×C₈×D₄	1	2	yes	—
318	C₂×C₃	C₅×#435	1	2	yes	—
319	C₅	C₃×#1850	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	C₃×C₅×C₄⋊C₈	1	4	yes	complemented
325	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
326	C₂²	C₃×C₄×C₅×D₄	1	2	yes	—
327	C₂²	C₂²×C₃×C₅×C₈	1	1	yes	characteristic
328	C₂²	C₂×C₃×C₅×M₁₆	1	1	yes	characteristic
329	C₂²	C₃×C₅×#131	1	2	yes	—
330	C₄	—	2	2	no	—
331	C₄	—	2	4	no	—
332	C₄	—	4	2	no	—
333	C₄	C₃×C₅×#120	1	1	yes	characteristic
334	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
335	C₄	C₃×C₅×#123	1	1	yes	characteristic
336	C₃	C₅×#1850	1	1	yes	characteristic, direct product factor, Sylow
337	C₂	—	2	4	no	—
338	C₂	C₃×C₅×#385	1	1	yes	characteristic
339	C₂	C₂×C₃×C₅×C₄⋊C₈	1	1	yes	characteristic
340	C₂	C₃×C₅×#424	1	1	yes	characteristic
341	C₂	C₃×C₅×C₈×D₄	1	2	yes	—
342	C₂	C₃×C₅×#435	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂²×C₃×C₅×C₈
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#1850	C₃	direct (N × H)
19. C₃×#1850	C₅	direct (N × H)
21. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
24. C₅×#336	C₂×C₃	semidirect
43. C₃×C₅×C₂²⋊C₄	C₈	semidirect
47. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
50. C₃×#336	C₂×C₅	semidirect
63. #1850	C₃×C₅	direct (N × H)
80. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
118. C₅×C₂²⋊C₄	C₃×C₈	semidirect
122. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
125. #336	C₂×C₃×C₅	semidirect
130. C₂²×C₃×C₅	C₄⋊C₈	semidirect
160. C₃×C₂²⋊C₄	C₅×C₈	semidirect
179. C₂×C₄×C₅	C₂×C₃×C₈	semidirect
221. C₂×C₃×C₄	C₂×C₅×C₈	semidirect
233. C₂²×C₅	C₃×C₄⋊C₈	semidirect
263. C₂²⋊C₄	C₃×C₅×C₈	semidirect
266. C₃×C₅	#1850	direct (N × H)
271. C₂²×C₃	C₅×C₄⋊C₈	semidirect
305. C₂×C₄	C₂×C₃×C₅×C₈	semidirect
319. C₅	C₃×#1850	direct (N × H)
324. C₂²	C₃×C₅×C₄⋊C₈	semidirect
336. C₃	C₅×#1850	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×C₈	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#336	2
C₅×#1850	3
C₃×#1850	5

Subgroups — C3×C5×#1850 #14274884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1850 #14274884