Subgroups — C₂×C₃×#65440 #14438767

Order 1920.

1520 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	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4086	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×#686	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65440	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65440	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₂²⋊D₅	—	2	4	no	—
10	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×#4086	—	2	4	no	—
15	C₃×#4086	C₂²	1	8	yes	complemented
16	C₂×C₃×#686	—	2	8	no	—
17	C₂×C₃×#686	C₂²	1	8	yes	complemented
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄₀	—	2	4	no	—
21	C₂×C₃×D₄₀	C₂²	1	4	yes	complemented
22	C₃×C₈×Dic₅	C₂²	1	4	yes	complemented
23	C₂×C₃×#493	—	5	1	no	maximal, Hall
24	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#4086	C₂×C₃	1	2	yes	complemented
26	C₂²×#686	C₂×C₃	1	2	yes	complemented
27	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
28	#65440	C₂×C₃	1	8	yes	direct product factor
29	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂³×C₃×D₅	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	2	4	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
38	C₂×C₃×C₂²⋊D₅	—	4	16	no	—
39	C₂²×C₃×Dic₅	D₄	1	2	yes	—
40	C₂×C₃×D₂₀	—	2	4	no	—
41	C₂×C₃×D₂₀	—	2	4	no	—
42	C₂×C₃×D₂₀	—	2	2	no	—
43	C₂×C₃×D₂₀	C₂³	1	4	yes	—
44	C₃×C₅×D₈	—	2	8	no	—
45	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
46	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
47	C₃×#686	—	2	16	no	—
48	C₃×C₄×Dic₅	D₄	1	2	yes	—
49	C₃×C₄×Dic₅	C₂³	1	2	yes	—
50	C₂×C₃×#168	D₄	1	4	yes	complemented
51	C₂×C₃×#168	C₂³	1	2	yes	—
52	C₃×D₄₀	—	2	8	no	—
53	C₂²×C₃×D₈	—	5	2	no	—
54	C₂²×C₃×D₈	—	5	1	no	—
55	C₂²×C₃×D₈	D₅	1	1	yes	characteristic, complemented
56	C₂×C₃×#127	—	5	2	no	—
57	C₃×#493	—	5	8	no	—
58	C₂×C₃×C₄×C₈	—	5	1	no	—
59	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
60	C₂²×C₂²⋊D₅	—	2	4	no	—
61	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
62	C₂×C₅×D₈	—	2	4	no	—
63	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
64	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
65	#4086	—	2	4	no	—
66	#4086	C₂²×C₃	1	8	yes	complemented
67	C₂×#686	—	2	8	no	—
68	C₂×#686	C₂²×C₃	1	8	yes	complemented
69	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
70	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
71	C₂×D₄₀	—	2	4	no	—
72	C₂×D₄₀	C₂²×C₃	1	4	yes	complemented
73	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
74	C₂×#493	—	5	1	no	Sylow
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	4	4	no	—
77	C₂³×C₃×C₅	—	4	8	no	—
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₃×D₅	—	2	4	no	—
80	C₂²×C₃×D₅	—	4	4	no	—
81	C₂²×C₃×D₅	—	4	8	no	—
82	C₃×C₅×D₄	—	2	4	no	—
83	C₃×C₅×D₄	—	2	4	no	—
84	C₃×C₅×D₄	—	4	4	no	—
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
89	C₃×C₂²⋊D₅	—	4	32	no	—
90	C₂×C₃×Dic₅	D₈	1	8	yes	complemented
91	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
92	C₃×D₂₀	—	2	4	no	—
93	C₃×D₂₀	—	2	4	no	—
94	C₃×D₂₀	—	4	4	no	—
95	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
96	C₃×#168	C₂×D₄	1	4	yes	complemented
97	C₂²×C₃×D₄	—	5	2	no	—
98	C₂²×C₃×D₄	—	10	4	no	—
99	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
100	C₂×C₃×D₈	—	2	4	no	—
101	C₂×C₃×D₈	—	5	8	no	—
102	C₂×C₃×D₈	—	5	4	no	—
103	C₂×C₃×D₈	—	10	8	no	—
104	C₂×C₃×D₈	—	10	4	no	—
105	C₂×C₃×D₈	C₂×D₅	1	4	yes	complemented
106	C₂²×C₃×C₈	—	5	1	no	—
107	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
108	C₃×#127	—	5	8	no	—
109	C₃×#127	—	10	4	no	—
110	C₂×C₃×C₄²	—	5	1	no	—
111	C₃×C₄×C₈	—	5	4	no	—
112	C₂⁴×C₅	—	2	2	no	—
113	C₂³×D₅	—	2	2	no	—
114	C₂×C₅×D₄	—	2	4	no	—
115	C₂×C₅×D₄	—	2	4	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
118	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
119	C₂×C₂²⋊D₅	—	2	16	no	—
120	C₂×C₂²⋊D₅	—	4	16	no	—
121	C₂²×Dic₅	C₃×D₄	1	2	yes	—
122	C₂×D₂₀	—	2	4	no	—
123	C₂×D₂₀	—	2	4	no	—
124	C₂×D₂₀	—	2	2	no	—
125	C₂×D₂₀	C₂³×C₃	1	4	yes	—
126	C₅×D₈	—	2	8	no	—
127	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
128	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
129	#686	—	2	16	no	—
130	C₄×Dic₅	C₃×D₄	1	2	yes	—
131	C₄×Dic₅	C₂³×C₃	1	2	yes	—
132	C₂×#168	C₃×D₄	1	4	yes	complemented
133	C₂×#168	C₂³×C₃	1	2	yes	—
134	D₄₀	—	2	8	no	—
135	C₂²×D₈	—	5	2	no	—
136	C₂²×D₈	—	5	1	no	—
137	C₂²×D₈	C₃×D₅	1	1	yes	characteristic, complemented
138	C₂×#127	—	5	2	no	—
139	#493	—	5	8	no	—
140	C₂×C₄×C₈	—	5	1	no	—
141	C₂²×C₃×C₅	—	4	4	no	—
142	C₂²×C₃×C₅	—	4	8	no	—
143	C₂²×C₃×C₅	—	8	8	no	—
144	C₂²×C₃×C₅	#127	1	2	yes	—
145	C₂²×C₃×C₅	C₂×D₈	1	4	yes	—
146	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₃×D₅	—	4	4	no	—
148	C₂×C₃×D₅	—	4	8	no	—
149	C₂×C₃×D₅	—	8	8	no	—
150	C₃×C₄×C₅	#127	1	2	yes	—
151	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
152	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
153	C₃×Dic₅	C₂×D₈	1	8	yes	complemented
154	C₂⁴×C₃	—	2	2	no	—
155	C₂⁴×C₃	—	10	2	no	—
156	C₂×C₃×D₄	—	2	4	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	4	no	—
159	C₂×C₃×D₄	—	5	4	no	—
160	C₂×C₃×D₄	—	10	16	no	—
161	C₂×C₃×D₄	—	10	4	no	—
162	C₂×C₃×D₄	—	10	2	no	—
163	C₂×C₃×D₄	—	10	4	no	—
164	C₂×C₃×D₄	—	20	16	no	—
165	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
166	C₂²×C₃×C₄	—	5	2	no	—
167	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
168	C₃×D₈	—	2	8	no	—
169	C₃×D₈	—	10	16	no	—
170	C₃×D₈	—	10	8	no	—
171	C₂×C₃×C₈	—	5	4	no	—
172	C₂×C₃×C₈	—	5	2	no	—
173	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
174	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
175	C₃×C₄²	—	5	2	no	—
176	C₃×C₄²	—	5	2	no	—
177	C₂³×C₅	—	2	4	no	—
178	C₂³×C₅	—	4	4	no	—
179	C₂³×C₅	—	4	8	no	—
180	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
181	C₂²×D₅	—	2	4	no	—
182	C₂²×D₅	—	4	4	no	—
183	C₂²×D₅	—	4	8	no	—
184	C₅×D₄	—	2	4	no	—
185	C₅×D₄	—	2	4	no	—
186	C₅×D₄	—	4	4	no	—
187	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
189	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
190	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
191	C₂²⋊D₅	—	4	32	no	—
192	C₂×Dic₅	C₃×D₈	1	8	yes	complemented
193	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
194	D₂₀	—	2	4	no	—
195	D₂₀	—	2	4	no	—
196	D₂₀	—	4	4	no	—
197	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
198	#168	C₂×C₃×D₄	1	4	yes	complemented
199	C₂²×D₄	—	5	2	no	—
200	C₂²×D₄	—	10	4	no	—
201	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
202	C₂×D₈	—	2	4	no	—
203	C₂×D₈	—	5	8	no	—
204	C₂×D₈	—	5	4	no	—
205	C₂×D₈	—	10	8	no	—
206	C₂×D₈	—	10	4	no	—
207	C₂×D₈	C₂×C₃×D₅	1	4	yes	complemented
208	C₂²×C₈	—	5	1	no	—
209	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
210	#127	—	5	8	no	—
211	#127	—	10	4	no	—
212	C₂×C₄²	—	5	1	no	—
213	C₄×C₈	—	5	4	no	—
214	C₂×C₃×C₅	—	8	4	no	—
215	C₂×C₃×C₅	#493	1	4	yes	complemented
216	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
217	C₂×C₃×C₅	C₂²×D₈	1	2	yes	—
218	C₃×D₅	—	8	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	—	4	8	no	—
221	C₂³×C₃	—	4	4	no	—
222	C₂³×C₃	—	10	4	no	—
223	C₂³×C₃	—	20	8	no	—
224	C₂³×C₃	—	20	4	no	—
225	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
226	C₃×D₄	—	2	4	no	—
227	C₃×D₄	—	2	4	no	—
228	C₃×D₄	—	4	4	no	—
229	C₃×D₄	—	10	4	no	—
230	C₃×D₄	—	10	4	no	—
231	C₃×D₄	—	20	32	no	—
232	C₃×D₄	—	20	4	no	—
233	C₂×C₃×C₄	—	5	4	no	—
234	C₂×C₃×C₄	—	5	8	no	—
235	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
236	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
238	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
239	C₃×C₈	—	5	4	no	—
240	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
241	C₂²×C₅	—	4	8	no	—
242	C₂²×C₅	—	4	4	no	—
243	C₂²×C₅	—	8	8	no	—
244	C₂²×C₅	C₃×#127	1	2	yes	—
245	C₂²×C₅	C₂×C₃×D₈	1	4	yes	—
246	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
247	C₂×D₅	—	4	8	no	—
248	C₂×D₅	—	4	4	no	—
249	C₂×D₅	—	8	8	no	—
250	C₄×C₅	C₃×#127	1	2	yes	—
251	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
252	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
253	Dic₅	C₂×C₃×D₈	1	8	yes	complemented
254	C₂⁴	—	2	2	no	—
255	C₂⁴	—	10	2	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	5	4	no	—
260	C₂×D₄	—	10	16	no	—
261	C₂×D₄	—	10	4	no	—
262	C₂×D₄	—	10	2	no	—
263	C₂×D₄	—	10	4	no	—
264	C₂×D₄	—	20	16	no	—
265	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
266	C₂²×C₄	—	5	2	no	—
267	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
268	D₈	—	2	8	no	—
269	D₈	—	10	16	no	—
270	D₈	—	10	8	no	—
271	C₂×C₈	—	5	4	no	—
272	C₂×C₈	—	5	2	no	—
273	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
274	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
275	C₄²	—	5	2	no	—
276	C₄²	—	5	2	no	—
277	C₃×C₅	C₂×#493	1	1	yes	characteristic, complemented, Hall
278	C₂²×C₃	—	4	8	no	—
279	C₂²×C₃	—	4	4	no	—
280	C₂²×C₃	—	8	8	no	—
281	C₂²×C₃	—	20	8	no	—
282	C₂²×C₃	—	20	4	no	—
283	C₂²×C₃	—	40	8	no	—
284	C₂²×C₃	D₅×D₈	1	4	yes	—
285	C₂²×C₃	#4086	1	2	yes	—
286	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
287	C₃×C₄	—	5	8	no	—
288	C₃×C₄	#4086	1	2	yes	—
289	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
290	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
291	C₂×C₅	—	8	4	no	—
292	C₂×C₅	C₃×#493	1	4	yes	complemented
293	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
294	C₂×C₅	C₂²×C₃×D₈	1	2	yes	—
295	D₅	—	8	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	10	4	no	—
300	C₂³	—	20	4	no	—
301	C₂³	—	20	8	no	—
302	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
303	D₄	—	2	4	no	—
304	D₄	—	2	4	no	—
305	D₄	—	4	4	no	—
306	D₄	—	10	4	no	—
307	D₄	—	10	4	no	—
308	D₄	—	20	32	no	—
309	D₄	—	20	4	no	—
310	C₂×C₄	—	5	4	no	—
311	C₂×C₄	—	5	8	no	—
312	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
313	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
314	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
315	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
316	C₈	—	5	4	no	—
317	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	complemented
318	C₂×C₃	—	8	4	no	—
319	C₂×C₃	—	40	4	no	—
320	C₂×C₃	#65440	1	4	yes	direct product factor
321	C₂×C₃	C₂×D₅×D₈	1	2	yes	—
322	C₂×C₃	C₂×#4086	1	1	yes	characteristic
323	C₅	C₂×C₃×#493	1	1	yes	characteristic, complemented, Sylow
324	C₂²	—	4	4	no	—
325	C₂²	—	4	8	no	—
326	C₂²	—	8	8	no	—
327	C₂²	—	20	4	no	—
328	C₂²	—	20	8	no	—
329	C₂²	—	40	8	no	—
330	C₂²	C₃×D₅×D₈	1	4	yes	—
331	C₂²	C₃×#4086	1	2	yes	—
332	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
333	C₄	—	5	8	no	—
334	C₄	C₃×#4086	1	2	yes	—
335	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
336	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
337	C₃	C₂×#65440	1	1	yes	characteristic, direct product factor, Sylow
338	C₂	—	8	4	no	—
339	C₂	—	40	4	no	—
340	C₂	C₃×#65440	1	4	yes	direct product factor
341	C₂	C₂×C₃×D₅×D₈	1	2	yes	—
342	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₃×D₈	D₅
hypocenter	C₅	C₂×C₃×#493
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₃×#4086	C₂	semidirect
3. C₂²×C₃×#686	C₂	semidirect
4. C₂²×C₃×D₄₀	C₂	semidirect
5. C₃×#65440	C₂	direct (N × H)
6. C₂×C₃×C₈×Dic₅	C₂	semidirect
7. C₂×#65440	C₃	direct (N × H)
12. C₂×C₃×C₅×D₈	C₂²	semidirect
15. C₃×#4086	C₂²	semidirect
17. C₂×C₃×#686	C₂²	semidirect
21. C₂×C₃×D₄₀	C₂²	semidirect
22. C₃×C₈×Dic₅	C₂²	semidirect
24. C₂²×C₅×D₈	C₂×C₃	semidirect
25. C₂×#4086	C₂×C₃	semidirect
26. C₂²×#686	C₂×C₃	semidirect
27. C₂²×D₄₀	C₂×C₃	semidirect
28. #65440	C₂×C₃	direct (N × H)
29. C₂×C₈×Dic₅	C₂×C₃	semidirect
45. C₂×C₃×C₅×C₈	D₄	semidirect
50. C₂×C₃×#168	D₄	semidirect
55. C₂²×C₃×D₈	D₅	semidirect
63. C₂×C₅×D₈	C₂²×C₃	semidirect
66. #4086	C₂²×C₃	semidirect
68. C₂×#686	C₂²×C₃	semidirect
72. C₂×D₄₀	C₂²×C₃	semidirect
73. C₈×Dic₅	C₂²×C₃	semidirect
90. C₂×C₃×Dic₅	D₈	semidirect
95. C₃×C₅×C₈	C₂×D₄	semidirect
96. C₃×#168	C₂×D₄	semidirect
105. C₂×C₃×D₈	C₂×D₅	semidirect
127. C₂×C₅×C₈	C₃×D₄	semidirect
132. C₂×#168	C₃×D₄	semidirect
137. C₂²×D₈	C₃×D₅	semidirect
153. C₃×Dic₅	C₂×D₈	semidirect
173. C₂×C₃×C₈	C₂²⋊D₅	semidirect
192. C₂×Dic₅	C₃×D₈	semidirect
197. C₅×C₈	C₂×C₃×D₄	semidirect
198. #168	C₂×C₃×D₄	semidirect
207. C₂×D₈	C₂×C₃×D₅	semidirect
215. C₂×C₃×C₅	#493	semidirect
240. C₃×C₈	C₂×C₂²⋊D₅	semidirect
253. Dic₅	C₂×C₃×D₈	semidirect
273. C₂×C₈	C₃×C₂²⋊D₅	semidirect
277. C₃×C₅	C₂×#493	semidirect
292. C₂×C₅	C₃×#493	semidirect
317. C₈	C₂×C₃×C₂²⋊D₅	semidirect
320. C₂×C₃	#65440	direct (N × H)
323. C₅	C₂×C₃×#493	semidirect
337. C₃	C₂×#65440	direct (N × H)
340. C₂	C₃×#65440	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×D₈	2
C₂×C₃×#4086	2
C₂²×C₃×#686	2
C₂²×C₃×D₄₀	2
C₃×#65440	2
C₂×C₃×C₈×Dic₅	2
C₂×#65440	3
C₂×C₃×#493	5

Subgroups — C2×C3×#65440 #14438767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65440 #14438767