Subgroups — C₂×C₃×#65320 #14426074

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 352 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×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#689	C₂	1	2	yes	maximal
3	C₂×C₃×#4015	C₂	1	1	yes	maximal, characteristic
4	C₃×#65320	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3942	C₂	1	2	yes	maximal
6	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
7	C₂×#65320	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
10	C₃×C₄×C₅×Q₈	—	2	2	no	—
11	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	—	2	1	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#689	—	2	8	no	—
17	C₂×C₃×#689	C₂²	1	8	yes	—
18	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
19	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
20	C₂²×C₃×#168	C₂²	1	2	yes	—
21	C₃×#4015	—	2	2	no	—
22	C₃×#4015	C₂²	1	4	yes	—
23	C₃×#3942	C₂²	1	8	yes	—
24	C₃×C₄⋊#168	C₂²	1	4	yes	—
25	C₂×C₃×#462	—	5	1	no	maximal, Hall
26	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
27	C₂²×#689	C₂×C₃	1	2	yes	—
28	C₂×#4015	C₂×C₃	1	1	yes	characteristic
29	#65320	C₂×C₃	1	8	yes	direct product factor
30	C₂×#3942	C₂×C₃	1	2	yes	—
31	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×C₅×Q₈	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
35	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	—	2	2	no	—
42	C₂×C₃×Dic₁₀	—	2	4	no	—
43	C₂×C₃×Dic₁₀	—	2	4	no	—
44	C₂×C₃×Dic₁₀	—	2	2	no	—
45	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
49	C₃×C₄²×C₅	—	2	4	no	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₃×#689	—	2	16	no	—
53	C₃×C₄⋊Dic₅	—	2	4	no	—
54	C₃×C₄⋊Dic₅	—	2	4	no	—
55	C₂×C₃×#168	—	2	4	no	—
56	C₂×C₃×#168	C₂³	1	4	yes	—
57	C₂²×C₃×Q₁₆	—	5	2	no	—
58	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
59	C₂×C₃×C₄×Q₈	D₅	1	1	yes	characteristic
60	C₃×#462	—	5	8	no	—
61	C₂×C₃×C₄⋊C₈	—	5	1	no	—
62	C₂×C₃×#103	—	5	2	no	—
63	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
64	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
65	C₄×C₅×Q₈	—	2	2	no	—
66	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₂×#689	—	2	8	no	—
72	C₂×#689	C₂²×C₃	1	8	yes	—
73	C₂×C₄⋊Dic₅	—	2	1	no	—
74	C₂×C₄⋊Dic₅	—	2	1	no	—
75	C₂²×#168	C₂²×C₃	1	2	yes	—
76	#4015	—	2	2	no	—
77	#4015	C₂²×C₃	1	4	yes	—
78	#3942	C₂²×C₃	1	8	yes	—
79	C₄⋊#168	C₂²×C₃	1	4	yes	—
80	C₂×#462	—	5	1	no	Sylow
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	4	no	—
83	C₃×C₅×Q₈	—	2	2	no	—
84	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	4	2	no	—
90	C₂×C₃×C₄×C₅	Q₁₆	1	4	yes	complemented
91	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	#41	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
97	C₂×C₃×Dic₅	—	2	4	no	—
98	C₂×C₃×Dic₅	—	4	4	no	—
99	C₃×Dic₁₀	—	2	4	no	—
100	C₃×Dic₁₀	—	2	4	no	—
101	C₃×Dic₁₀	—	4	4	no	—
102	C₃×#168	—	2	4	no	—
103	C₂²×C₃×Q₈	—	5	2	no	—
104	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
105	C₂×C₃×Q₁₆	—	5	8	no	—
106	C₂×C₃×Q₁₆	—	10	8	no	—
107	C₂²×C₃×C₈	—	5	2	no	—
108	C₃×C₄⋊Q₈	—	5	4	no	—
109	C₃×C₄⋊Q₈	—	10	2	no	—
110	C₃×C₄×Q₈	—	2	2	no	—
111	C₃×C₄×Q₈	C₂×D₅	1	4	yes	—
112	C₂×C₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₃×C₄⋊C₄	—	10	1	no	—
114	C₂×C₃×C₄⋊C₄	—	10	1	no	—
115	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
116	C₂×C₃×C₄²	—	2	1	no	—
117	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
118	C₃×C₄⋊C₈	—	5	4	no	—
119	C₃×#103	—	5	8	no	—
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂×C₅×Q₈	—	2	2	no	—
122	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
123	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×Dic₅	—	2	2	no	—
130	C₂×Dic₁₀	—	2	4	no	—
131	C₂×Dic₁₀	—	2	4	no	—
132	C₂×Dic₁₀	—	2	2	no	—
133	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
134	C₅×C₄⋊C₄	—	2	4	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
137	C₄²×C₅	—	2	4	no	—
138	C₄²×C₅	C₃×D₄	1	2	yes	—
139	C₄²×C₅	C₂³×C₃	1	2	yes	—
140	#689	—	2	16	no	—
141	C₄⋊Dic₅	—	2	4	no	—
142	C₄⋊Dic₅	—	2	4	no	—
143	C₂×#168	—	2	4	no	—
144	C₂×#168	C₂³×C₃	1	4	yes	—
145	C₂²×Q₁₆	—	5	2	no	—
146	C₂×C₄⋊Q₈	—	5	1	no	—
147	C₂×C₄×Q₈	C₃×D₅	1	1	yes	characteristic
148	#462	—	5	8	no	—
149	C₂×C₄⋊C₈	—	5	1	no	—
150	C₂×#103	—	5	2	no	—
151	C₂²×C₃×C₅	#121	1	2	yes	—
152	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
153	C₂²×C₃×C₅	#137	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₃×C₄×C₅	—	2	4	no	—
156	C₃×C₄×C₅	—	2	2	no	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	#121	1	2	yes	—
159	C₃×C₄×C₅	C₂×Q₁₆	1	4	yes	complemented
160	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
162	C₃×Dic₅	—	4	4	no	—
163	C₂×C₃×Q₈	—	2	2	no	—
164	C₂×C₃×Q₈	—	2	1	no	—
165	C₂×C₃×Q₈	—	5	4	no	—
166	C₂×C₃×Q₈	—	10	2	no	—
167	C₂×C₃×Q₈	—	10	4	no	—
168	C₂×C₃×Q₈	—	10	4	no	—
169	C₂×C₃×Q₈	D₂₀	1	4	yes	—
170	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	10	2	no	—
174	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
177	C₃×Q₁₆	—	10	16	no	—
178	C₂×C₃×C₈	—	5	4	no	—
179	C₂×C₃×C₈	—	10	4	no	—
180	C₃×C₄⋊C₄	—	2	4	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	10	4	no	—
183	C₃×C₄⋊C₄	—	10	4	no	—
184	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
185	C₃×C₄²	—	2	4	no	—
186	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
187	C₃×C₄²	C₂²×D₅	1	2	yes	—
188	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
189	C₅×Q₈	—	2	4	no	—
190	C₅×Q₈	—	2	2	no	—
191	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	C₃×Q₁₆	1	4	yes	complemented
198	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
202	C₂×C₄×C₅	C₃×#41	1	2	yes	—
203	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
204	C₂×Dic₅	—	2	4	no	—
205	C₂×Dic₅	—	4	4	no	—
206	Dic₁₀	—	2	4	no	—
207	Dic₁₀	—	2	4	no	—
208	Dic₁₀	—	4	4	no	—
209	#168	—	2	4	no	—
210	C₂²×Q₈	—	5	2	no	—
211	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
212	C₂×Q₁₆	—	5	8	no	—
213	C₂×Q₁₆	—	10	8	no	—
214	C₂²×C₈	—	5	2	no	—
215	C₄⋊Q₈	—	5	4	no	—
216	C₄⋊Q₈	—	10	2	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	C₂×C₃×D₅	1	4	yes	—
219	C₂×C₄⋊C₄	—	2	1	no	—
220	C₂×C₄⋊C₄	—	10	1	no	—
221	C₂×C₄⋊C₄	—	10	1	no	—
222	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
225	C₄⋊C₈	—	5	4	no	—
226	#103	—	5	8	no	—
227	C₂×C₃×C₅	#462	1	4	yes	complemented
228	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
229	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
230	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
231	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
232	C₃×Q₈	—	2	2	no	—
233	C₃×Q₈	—	2	4	no	—
234	C₃×Q₈	—	10	4	no	—
235	C₃×Q₈	—	10	4	no	—
236	C₃×Q₈	—	20	4	no	—
237	C₃×Q₈	C₂×D₂₀	1	4	yes	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	10	4	no	—
244	C₂×C₃×C₄	—	20	4	no	—
245	C₂×C₃×C₄	#689	1	4	yes	complemented
246	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
247	C₂×C₃×C₄	#709	1	2	yes	—
248	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
251	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
252	C₃×C₈	—	10	4	no	—
253	C₂²×C₅	C₃×#121	1	2	yes	—
254	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
255	C₂²×C₅	C₃×#137	1	2	yes	—
256	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	4	2	no	—
260	C₄×C₅	C₃×#121	1	2	yes	—
261	C₄×C₅	C₂×C₃×Q₁₆	1	4	yes	complemented
262	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
263	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
264	Dic₅	—	4	4	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	5	4	no	—
268	C₂×Q₈	—	10	2	no	—
269	C₂×Q₈	—	10	4	no	—
270	C₂×Q₈	—	10	4	no	—
271	C₂×Q₈	C₃×D₂₀	1	4	yes	—
272	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	10	2	no	—
276	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
277	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
279	Q₁₆	—	10	16	no	—
280	C₂×C₈	—	5	4	no	—
281	C₂×C₈	—	10	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	1	no	—
284	C₄⋊C₄	—	10	4	no	—
285	C₄⋊C₄	—	10	4	no	—
286	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
287	C₄²	—	2	4	no	—
288	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
289	C₄²	C₂²×C₃×D₅	1	2	yes	—
290	C₃×C₅	C₂×#462	1	1	yes	characteristic, complemented, Hall
291	C₂²×C₃	#4076	1	2	yes	—
292	C₂²×C₃	C₂×#689	1	2	yes	—
293	C₂²×C₃	#4097	1	2	yes	—
294	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	4	2	no	—
298	C₃×C₄	—	20	4	no	—
299	C₃×C₄	#4076	1	2	yes	—
300	C₃×C₄	C₂×#689	1	4	yes	complemented
301	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
302	C₃×C₄	C₂×#709	1	1	yes	characteristic
303	C₂×C₅	C₃×#462	1	4	yes	complemented
304	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
305	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
306	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
307	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
308	Q₈	—	2	2	no	—
309	Q₈	—	2	4	no	—
310	Q₈	—	10	4	no	—
311	Q₈	—	10	4	no	—
312	Q₈	—	20	4	no	—
313	Q₈	C₂×C₃×D₂₀	1	4	yes	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	10	4	no	—
320	C₂×C₄	—	20	4	no	—
321	C₂×C₄	C₃×#689	1	4	yes	complemented
322	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
323	C₂×C₄	C₃×#709	1	2	yes	—
324	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
325	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
326	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
327	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
328	C₈	—	10	4	no	—
329	C₂×C₃	#65320	1	4	yes	direct product factor
330	C₂×C₃	C₂×#4076	1	1	yes	characteristic
331	C₂×C₃	C₂²×#689	1	1	yes	characteristic
332	C₂×C₃	C₂×#4097	1	1	yes	characteristic
333	C₅	C₂×C₃×#462	1	1	yes	characteristic, complemented, Sylow
334	C₂²	C₃×#4076	1	2	yes	—
335	C₂²	C₂×C₃×#689	1	2	yes	—
336	C₂²	C₃×#4097	1	2	yes	—
337	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
338	C₄	—	2	4	no	—
339	C₄	—	2	2	no	—
340	C₄	—	4	2	no	—
341	C₄	—	20	4	no	—
342	C₄	C₃×#4076	1	2	yes	—
343	C₄	C₂×C₃×#689	1	4	yes	complemented
344	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
345	C₄	C₂×C₃×#709	1	1	yes	characteristic
346	C₃	C₂×#65320	1	1	yes	characteristic, direct product factor, Sylow
347	C₂	C₃×#65320	1	4	yes	direct product factor
348	C₂	C₂×C₃×#4076	1	1	yes	characteristic
349	C₂	C₂²×C₃×#689	1	1	yes	characteristic
350	C₂	C₂×C₃×#4097	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×C₄×Q₈	D₅
hypocenter	C₅	C₂×C₃×#462
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
4. C₃×#65320	C₂	direct (N × H)
7. C₂×#65320	C₃	direct (N × H)
29. #65320	C₂×C₃	direct (N × H)
90. C₂×C₃×C₄×C₅	Q₁₆	semidirect
159. C₃×C₄×C₅	C₂×Q₁₆	semidirect
197. C₂×C₄×C₅	C₃×Q₁₆	semidirect
227. C₂×C₃×C₅	#462	semidirect
245. C₂×C₃×C₄	#689	semidirect
261. C₄×C₅	C₂×C₃×Q₁₆	semidirect
290. C₃×C₅	C₂×#462	semidirect
300. C₃×C₄	C₂×#689	semidirect
303. C₂×C₅	C₃×#462	semidirect
321. C₂×C₄	C₃×#689	semidirect
329. C₂×C₃	#65320	direct (N × H)
333. C₅	C₂×C₃×#462	semidirect
343. C₄	C₂×C₃×#689	semidirect
346. C₃	C₂×#65320	direct (N × H)
347. C₂	C₃×#65320	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×Q₈	2
C₂²×C₃×#689	2
C₂×C₃×#4015	2
C₃×#65320	2
C₂×C₃×#3942	2
C₂×C₃×C₄⋊#168	2
C₂×#65320	3
C₂×C₃×#462	5

Subgroups — C2×C3×#65320 #14426074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65320 #14426074