Subgroups — C₃×C₅×#1954 #14274988

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1954	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
10	C₃×C₄×C₅×D₄	—	2	2	no	—
11	C₃×C₄×C₅×D₄	—	2	2	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊C₈	—	2	2	no	—
16	C₃×C₅×C₂²⋊C₈	—	2	8	no	—
17	C₃×C₄×C₅×C₈	—	2	2	no	—
18	C₃×#1954	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	4	yes	complemented
22	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
24	C₂×C₃×C₅×D₄	—	2	2	no	—
25	C₂×C₃×C₅×D₄	—	2	2	no	—
26	C₂×C₃×C₅×D₄	C₈	1	4	yes	complemented
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	—	2	4	no	—
30	C₂²×C₃×C₄×C₅	—	2	4	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₅×C₈	—	2	2	no	—
36	C₂×C₃×C₅×C₈	—	2	2	no	—
37	C₂×C₃×C₅×C₈	—	2	4	no	—
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
40	C₃×C₅×C₄⋊C₄	—	2	2	no	—
41	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
42	C₃×C₄²×C₅	D₄	1	2	yes	—
43	C₃×C₄²×C₅	D₄	1	2	yes	—
44	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
45	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
46	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	4	yes	complemented
47	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
48	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
50	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
51	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
52	C₄×C₅×D₄	—	2	2	no	—
53	C₄×C₅×D₄	—	2	2	no	—
54	C₂×C₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
55	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	2	yes	—
56	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
57	C₅×C₄⋊C₈	—	2	2	no	—
58	C₅×C₂²⋊C₈	—	2	8	no	—
59	C₄×C₅×C₈	—	2	2	no	—
60	#1954	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂³×C₃×C₅	—	2	2	no	—
62	C₂³×C₃×C₅	—	2	4	no	—
63	C₂³×C₃×C₅	—	2	2	no	—
64	C₂³×C₃×C₅	—	2	4	no	—
65	C₂³×C₃×C₅	C₂×C₈	1	4	yes	—
66	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
67	C₃×C₅×D₄	—	2	8	no	—
68	C₂×C₃×C₄×C₅	—	2	2	no	—
69	C₂×C₃×C₄×C₅	—	2	2	no	—
70	C₂×C₃×C₄×C₅	—	2	4	no	—
71	C₂×C₃×C₄×C₅	—	4	4	no	—
72	C₂×C₃×C₄×C₅	—	4	2	no	—
73	C₂×C₃×C₄×C₅	—	4	2	no	—
74	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
75	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
76	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
77	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
78	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	#41	1	2	yes	—
82	C₃×C₅×C₈	—	2	4	no	—
83	C₃×C₅×C₈	—	4	2	no	—
84	C₂²×C₃×D₄	C₄×C₅	1	1	yes	characteristic
85	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
86	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
87	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
88	C₃×C₄×D₄	—	2	2	no	—
89	C₃×C₄×D₄	—	2	2	no	—
90	C₂×C₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
92	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
93	C₃×C₄⋊C₈	—	2	2	no	—
94	C₃×C₂²⋊C₈	—	2	8	no	—
95	C₃×C₄×C₈	—	2	2	no	—
96	C₂⁴×C₅	C₂×C₃×C₄	1	2	yes	—
97	C₂×C₅×D₄	—	2	2	no	—
98	C₂×C₅×D₄	—	2	2	no	—
99	C₂×C₅×D₄	C₃×C₈	1	4	yes	complemented
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	4	no	—
103	C₂²×C₄×C₅	—	2	4	no	—
104	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
105	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	4	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
113	C₅×C₄⋊C₄	—	2	2	no	—
114	C₅×C₂²⋊C₄	—	2	4	no	—
115	C₄²×C₅	C₃×D₄	1	2	yes	—
116	C₄²×C₅	C₃×D₄	1	2	yes	—
117	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
118	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
119	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	4	yes	complemented
120	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
121	C₂²×C₃×C₅	—	2	4	no	—
122	C₂²×C₃×C₅	—	2	8	no	—
123	C₂²×C₃×C₅	—	4	2	no	—
124	C₂²×C₃×C₅	—	4	2	no	—
125	C₂²×C₃×C₅	—	4	4	no	—
126	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
128	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
129	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
130	C₂²×C₃×C₅	#131	1	2	yes	—
131	C₃×C₄×C₅	—	2	2	no	—
132	C₃×C₄×C₅	—	4	2	no	—
133	C₃×C₄×C₅	C₂²⋊C₈	1	4	yes	complemented
134	C₃×C₄×C₅	#121	1	2	yes	—
135	C₃×C₄×C₅	#124	1	1	yes	characteristic
136	C₃×C₄×C₅	#127	1	1	yes	characteristic
137	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
138	C₂×C₃×D₄	—	2	2	no	—
139	C₂×C₃×D₄	—	2	2	no	—
140	C₂×C₃×D₄	C₅×C₈	1	4	yes	complemented
141	C₂²×C₃×C₄	—	2	4	no	—
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	4	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	1	yes	characteristic
148	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	4	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
154	C₃×C₄⋊C₄	—	2	2	no	—
155	C₃×C₂²⋊C₄	—	2	4	no	—
156	C₃×C₄²	C₅×D₄	1	2	yes	—
157	C₃×C₄²	C₅×D₄	1	2	yes	—
158	C₂³×C₅	—	2	2	no	—
159	C₂³×C₅	—	2	4	no	—
160	C₂³×C₅	—	2	2	no	—
161	C₂³×C₅	—	2	4	no	—
162	C₂³×C₅	C₂×C₃×C₈	1	4	yes	—
163	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
164	C₅×D₄	—	2	8	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	4	no	—
168	C₂×C₄×C₅	—	4	4	no	—
169	C₂×C₄×C₅	—	4	2	no	—
170	C₂×C₄×C₅	—	4	2	no	—
171	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
174	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
175	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
177	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₃×#41	1	2	yes	—
179	C₅×C₈	—	2	4	no	—
180	C₅×C₈	—	4	2	no	—
181	C₂²×D₄	C₃×C₄×C₅	1	1	yes	characteristic
182	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
183	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
184	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
185	C₄×D₄	—	2	2	no	—
186	C₄×D₄	—	2	2	no	—
187	C₂×C₄⋊C₄	C₃×C₄×C₅	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	C₃×C₄×C₅	1	2	yes	—
189	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
190	C₄⋊C₈	—	2	2	no	—
191	C₂²⋊C₈	—	2	8	no	—
192	C₄×C₈	—	2	2	no	—
193	C₂×C₃×C₅	—	4	4	no	—
194	C₂×C₃×C₅	#390	1	1	yes	characteristic
195	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
196	C₂×C₃×C₅	#408	1	1	yes	characteristic
197	C₂×C₃×C₅	C₈×D₄	1	2	yes	—
198	C₂×C₃×C₅	#436	1	2	yes	—
199	C₂³×C₃	—	2	2	no	—
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	—	2	2	no	—
202	C₂³×C₃	—	2	4	no	—
203	C₂³×C₃	C₂×C₅×C₈	1	4	yes	—
204	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
205	C₃×D₄	—	2	8	no	—
206	C₂×C₃×C₄	—	2	2	no	—
207	C₂×C₃×C₄	—	2	2	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	4	4	no	—
210	C₂×C₃×C₄	—	4	2	no	—
211	C₂×C₃×C₄	—	4	2	no	—
212	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
213	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
214	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
215	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
216	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
218	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄	C₅×#41	1	2	yes	—
220	C₃×C₈	—	2	4	no	—
221	C₃×C₈	—	4	2	no	—
222	C₂²×C₅	—	2	4	no	—
223	C₂²×C₅	—	2	8	no	—
224	C₂²×C₅	—	4	2	no	—
225	C₂²×C₅	—	4	2	no	—
226	C₂²×C₅	—	4	4	no	—
227	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
229	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
230	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
231	C₂²×C₅	C₃×#131	1	2	yes	—
232	C₄×C₅	—	2	2	no	—
233	C₄×C₅	—	4	2	no	—
234	C₄×C₅	C₃×C₂²⋊C₈	1	4	yes	complemented
235	C₄×C₅	C₃×#121	1	2	yes	—
236	C₄×C₅	C₃×#124	1	1	yes	characteristic
237	C₄×C₅	C₃×#127	1	1	yes	characteristic
238	C₂⁴	C₂×C₃×C₄×C₅	1	2	yes	—
239	C₂×D₄	—	2	2	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	C₃×C₅×C₈	1	4	yes	complemented
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
247	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
248	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
255	C₄⋊C₄	—	2	2	no	—
256	C₂²⋊C₄	—	2	4	no	—
257	C₄²	C₃×C₅×D₄	1	2	yes	—
258	C₄²	C₃×C₅×D₄	1	2	yes	—
259	C₃×C₅	#1954	1	1	yes	characteristic, direct product factor, Hall
260	C₂²×C₃	—	2	4	no	—
261	C₂²×C₃	—	2	8	no	—
262	C₂²×C₃	—	4	2	no	—
263	C₂²×C₃	—	4	2	no	—
264	C₂²×C₃	—	4	4	no	—
265	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
267	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
268	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
269	C₂²×C₃	C₅×#131	1	2	yes	—
270	C₃×C₄	—	2	2	no	—
271	C₃×C₄	—	4	2	no	—
272	C₃×C₄	C₅×C₂²⋊C₈	1	4	yes	complemented
273	C₃×C₄	C₅×#121	1	2	yes	—
274	C₃×C₄	C₅×#124	1	1	yes	characteristic
275	C₃×C₄	C₅×#127	1	1	yes	characteristic
276	C₂×C₅	—	4	4	no	—
277	C₂×C₅	C₃×#390	1	1	yes	characteristic
278	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
279	C₂×C₅	C₃×#408	1	1	yes	characteristic
280	C₂×C₅	C₃×C₈×D₄	1	2	yes	—
281	C₂×C₅	C₃×#436	1	2	yes	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	4	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	4	no	—
286	C₂³	C₂×C₃×C₅×C₈	1	4	yes	—
287	C₂³	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
288	D₄	—	2	8	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
296	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
297	C₂×C₄	C₂×C₃×C₅×C₈	1	2	yes	—
298	C₂×C₄	C₃×C₅×M₁₆	1	2	yes	—
299	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
300	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
301	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
302	C₂×C₄	C₃×C₅×#41	1	2	yes	—
303	C₈	—	2	4	no	—
304	C₈	—	4	2	no	—
305	C₂×C₃	—	4	4	no	—
306	C₂×C₃	C₅×#390	1	1	yes	characteristic
307	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
308	C₂×C₃	C₅×#408	1	1	yes	characteristic
309	C₂×C₃	C₅×C₈×D₄	1	2	yes	—
310	C₂×C₃	C₅×#436	1	2	yes	—
311	C₅	C₃×#1954	1	1	yes	characteristic, direct product factor, Sylow
312	C₂²	—	2	4	no	—
313	C₂²	—	2	8	no	—
314	C₂²	—	4	2	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	4	no	—
317	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²	C₃×C₄×C₅×D₄	1	2	yes	—
319	C₂²	C₂²×C₃×C₅×C₈	1	1	yes	characteristic
320	C₂²	C₂×C₃×C₅×M₁₆	1	1	yes	characteristic
321	C₂²	C₃×C₅×#131	1	2	yes	—
322	C₄	—	2	2	no	—
323	C₄	—	4	2	no	—
324	C₄	C₃×C₅×C₂²⋊C₈	1	4	yes	complemented
325	C₄	C₃×C₅×#121	1	2	yes	—
326	C₄	C₃×C₅×#124	1	1	yes	characteristic
327	C₄	C₃×C₅×#127	1	1	yes	characteristic
328	C₃	C₅×#1954	1	1	yes	characteristic, direct product factor, Sylow
329	C₂	—	4	4	no	—
330	C₂	C₃×C₅×#390	1	1	yes	characteristic
331	C₂	C₂×C₃×C₅×C₂²⋊C₈	1	1	yes	characteristic
332	C₂	C₃×C₅×#408	1	1	yes	characteristic
333	C₂	C₃×C₅×C₈×D₄	1	2	yes	—
334	C₂	C₃×C₅×#436	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	C₂²×C₃×C₅×D₄	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
3. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
4. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
5. C₅×#1954	C₃	direct (N × H)
18. C₃×#1954	C₅	direct (N × H)
20. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
21. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
22. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
26. C₂×C₃×C₅×D₄	C₈	semidirect
39. C₂×C₃×C₅×C₈	D₄	semidirect
45. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
46. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
47. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
60. #1954	C₃×C₅	direct (N × H)
99. C₂×C₅×D₄	C₃×C₈	semidirect
112. C₂×C₅×C₈	C₃×D₄	semidirect
118. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
119. C₂×C₂²⋊C₈	C₂×C₃×C₅	semidirect
120. C₂×C₄×C₈	C₂×C₃×C₅	semidirect
133. C₃×C₄×C₅	C₂²⋊C₈	semidirect
140. C₂×C₃×D₄	C₅×C₈	semidirect
153. C₂×C₃×C₈	C₅×D₄	semidirect
234. C₄×C₅	C₃×C₂²⋊C₈	semidirect
241. C₂×D₄	C₃×C₅×C₈	semidirect
254. C₂×C₈	C₃×C₅×D₄	semidirect
259. C₃×C₅	#1954	direct (N × H)
272. C₃×C₄	C₅×C₂²⋊C₈	semidirect
311. C₅	C₃×#1954	direct (N × H)
324. C₄	C₃×C₅×C₂²⋊C₈	semidirect
328. C₃	C₅×#1954	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×C₃×C₄×C₅×D₄	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#1954	3
C₃×#1954	5

Subgroups — C3×C5×#1954 #14274988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1954 #14274988