Subgroups — C₃×C₄×#4047 #14411445

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4047	C₂	1	2	yes	maximal
2	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65390	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64978	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×#676	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₈×D₅	C₂	1	2	yes	maximal, complemented
9	C₄×#4047	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₂²⋊D₅	C₄	1	4	yes	—
14	C₃×#4072	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	2	yes	—
16	C₃×#4047	C₄	1	16	yes	direct product factor
17	C₂×C₃×#676	C₂²	1	4	yes	—
18	C₂×C₃×C₈×D₅	C₂²	1	4	yes	—
19	C₃×C₄×D₂₀	C₄	1	2	yes	—
20	C₃×#4018	C₂²	1	2	yes	—
21	C₃×C₄²×D₅	C₂²	1	2	yes	—
22	C₃×C₄×Dic₁₀	C₄	1	2	yes	—
23	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×#3947	C₂²	1	4	yes	—
27	C₃×C₈×Dic₅	C₂²	1	4	yes	—
28	C₃×#3935	C₂²	1	2	yes	—
29	C₃×C₄×#168	C₂²	1	2	yes	—
30	C₃×C₄×#131	—	5	1	no	maximal, Hall
31	C₂×#4047	C₂×C₃	1	2	yes	—
32	C₄×#709	C₂×C₃	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	#65390	C₂×C₃	1	2	yes	complemented
35	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
36	#64978	C₂×C₃	1	4	yes	complemented
37	C₄×#676	C₂×C₃	1	2	yes	complemented
38	C₄×C₈×D₅	C₂×C₃	1	2	yes	complemented
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
42	C₃×#709	C₂×C₄	1	8	yes	—
43	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
45	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
46	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	C₂×C₄	1	8	yes	complemented
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
54	C₃×#685	C₂×C₄	1	4	yes	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
56	C₃×#683	C₂×C₄	1	4	yes	—
57	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
58	C₃×C₄×Dic₅	C₂³	1	2	yes	—
59	C₃×#681	C₂×C₄	1	8	yes	complemented
60	C₂×C₃×#168	C₂³	1	4	yes	—
61	C₃×#676	C₂×C₄	1	16	yes	complemented
62	C₃×C₈×D₅	C₂×C₄	1	16	yes	complemented
63	C₂×C₃×#131	—	5	2	no	—
64	C₃×C₄×#41	—	5	1	no	—
65	C₃×#405	—	5	2	no	—
66	C₃×#405	—	5	4	no	—
67	C₃×C₄×M₁₆	—	5	1	no	—
68	C₃×C₄×M₁₆	—	5	2	no	—
69	C₂×C₃×C₄×C₈	—	5	2	no	—
70	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic, complemented
71	C₂×#709	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₄×C₂²⋊D₅	C₃×C₄	1	4	yes	—
75	#4072	C₂²×C₃	1	1	yes	characteristic
76	C₂×#681	C₂²×C₃	1	2	yes	—
77	#4047	C₃×C₄	1	16	yes	direct product factor
78	C₂×#676	C₂²×C₃	1	4	yes	—
79	C₂×C₈×D₅	C₂²×C₃	1	4	yes	—
80	C₄×D₂₀	C₃×C₄	1	2	yes	—
81	#4018	C₂²×C₃	1	2	yes	—
82	C₄²×D₅	C₂²×C₃	1	2	yes	—
83	C₄×Dic₁₀	C₃×C₄	1	2	yes	—
84	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
85	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
86	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
87	#3947	C₂²×C₃	1	4	yes	—
88	C₈×Dic₅	C₂²×C₃	1	4	yes	—
89	#3935	C₂²×C₃	1	2	yes	—
90	C₄×#168	C₂²×C₃	1	2	yes	—
91	C₄×#131	—	5	1	no	Sylow
92	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₂²⋊D₅	C₄²	1	8	yes	—
101	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
102	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
103	C₃×D₂₀	C₄²	1	4	yes	—
104	C₃×C₄×D₅	—	2	8	no	—
105	C₃×C₄×D₅	C₂²×C₄	1	8	yes	—
106	C₃×Dic₁₀	C₄²	1	4	yes	—
107	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
108	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
109	C₃×#168	C₂²×C₄	1	8	yes	—
110	C₂×C₃×#41	—	5	1	no	—
111	C₃×#131	—	5	16	no	—
112	C₂×C₃×M₁₆	—	5	2	no	—
113	C₂×C₃×M₁₆	—	5	4	no	—
114	C₂²×C₃×C₈	—	5	4	no	—
115	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
116	C₃×C₄×Q₈	—	5	2	no	—
117	C₃×C₄×D₄	—	5	4	no	—
118	C₃×C₄×D₄	—	5	2	no	—
119	C₃×#117	—	5	1	no	—
120	C₃×#117	—	5	2	no	—
121	C₂×C₃×C₄²	—	5	2	no	—
122	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
123	C₃×#97	—	5	4	no	—
124	C₃×#97	—	5	2	no	—
125	C₃×C₄×C₈	—	5	4	no	—
126	C₃×C₄×C₈	—	5	2	no	—
127	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
128	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
129	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
133	#709	C₂×C₃×C₄	1	8	yes	—
134	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
136	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
137	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂×C₃×C₄	1	8	yes	complemented
139	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
140	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
141	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
142	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
145	#685	C₂×C₃×C₄	1	4	yes	—
146	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
147	#683	C₂×C₃×C₄	1	4	yes	—
148	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
149	C₄×Dic₅	C₂³×C₃	1	2	yes	—
150	#681	C₂×C₃×C₄	1	8	yes	complemented
151	C₂×#168	C₂³×C₃	1	4	yes	—
152	#676	C₂×C₃×C₄	1	16	yes	complemented
153	C₈×D₅	C₂×C₃×C₄	1	16	yes	complemented
154	C₂×#131	—	5	2	no	—
155	C₄×#41	—	5	1	no	—
156	#405	—	5	2	no	—
157	#405	—	5	4	no	—
158	C₄×M₁₆	—	5	1	no	—
159	C₄×M₁₆	—	5	2	no	—
160	C₂×C₄×C₈	—	5	2	no	—
161	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic, complemented
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
164	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₃×D₅	—	2	4	no	—
166	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
169	C₃×C₄×C₅	#131	1	4	yes	complemented
170	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
171	C₃×Dic₅	—	2	4	no	—
172	C₃×Dic₅	C₂×C₄²	1	4	yes	—
173	C₃×#41	—	5	8	no	—
174	C₂×C₃×Q₈	—	5	1	no	—
175	C₂×C₃×D₄	—	5	2	no	—
176	C₂×C₃×D₄	—	5	1	no	—
177	C₂²×C₃×C₄	—	5	2	no	—
178	C₂²×C₃×C₄	—	5	4	no	—
179	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
180	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
181	C₃×M₁₆	—	5	8	no	—
182	C₃×M₁₆	—	5	16	no	—
183	C₂×C₃×C₈	—	5	4	no	—
184	C₂×C₃×C₈	—	5	16	no	—
185	C₂×C₃×C₈	C₄×D₅	1	8	yes	complemented
186	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
187	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
188	C₃×C₄⋊C₄	—	5	4	no	—
189	C₃×C₄⋊C₄	—	5	2	no	—
190	C₃×C₂²⋊C₄	—	5	2	no	—
191	C₃×C₂²⋊C₄	—	5	4	no	—
192	C₃×C₄²	—	5	4	no	—
193	C₃×C₄²	—	5	2	no	—
194	C₃×C₄²	C₄×D₅	1	2	yes	—
195	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
196	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
197	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
198	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
203	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
204	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
205	C₂²⋊D₅	C₃×C₄²	1	8	yes	—
206	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
207	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
208	D₂₀	C₃×C₄²	1	4	yes	—
209	C₄×D₅	—	2	8	no	—
210	C₄×D₅	C₂²×C₃×C₄	1	8	yes	—
211	Dic₁₀	C₃×C₄²	1	4	yes	—
212	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
213	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
214	#168	C₂²×C₃×C₄	1	8	yes	—
215	C₂×#41	—	5	1	no	—
216	#131	—	5	16	no	—
217	C₂×M₁₆	—	5	2	no	—
218	C₂×M₁₆	—	5	4	no	—
219	C₂²×C₈	—	5	4	no	—
220	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
221	C₄×Q₈	—	5	2	no	—
222	C₄×D₄	—	5	4	no	—
223	C₄×D₄	—	5	2	no	—
224	#117	—	5	1	no	—
225	#117	—	5	2	no	—
226	C₂×C₄²	—	5	2	no	—
227	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
228	#97	—	5	4	no	—
229	#97	—	5	2	no	—
230	C₄×C₈	—	5	4	no	—
231	C₄×C₈	—	5	2	no	—
232	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
233	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
234	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
235	C₂×C₃×C₅	—	2	2	no	—
236	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂×#131	1	2	yes	—
238	C₃×D₅	—	2	4	no	—
239	C₂³×C₃	—	5	2	no	—
240	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
241	C₃×Q₈	—	5	4	no	—
242	C₃×D₄	—	5	8	no	—
243	C₃×D₄	—	5	4	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	5	2	no	—
246	C₂×C₃×C₄	—	5	8	no	—
247	C₂×C₃×C₄	—	5	4	no	—
248	C₂×C₃×C₄	—	10	8	no	—
249	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
251	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
253	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
254	C₃×C₈	—	5	8	no	—
255	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
256	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
259	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
260	C₂×D₅	—	2	4	no	—
261	C₂×D₅	C₂×C₃×C₄²	1	4	yes	—
262	C₄×C₅	—	2	2	no	—
263	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
264	C₄×C₅	C₃×#131	1	4	yes	complemented
265	C₄×C₅	C₂³×C₃×C₄	1	2	yes	—
266	Dic₅	—	2	4	no	—
267	Dic₅	C₂×C₃×C₄²	1	4	yes	—
268	#41	—	5	8	no	—
269	C₂×Q₈	—	5	1	no	—
270	C₂×D₄	—	5	2	no	—
271	C₂×D₄	—	5	1	no	—
272	C₂²×C₄	—	5	2	no	—
273	C₂²×C₄	—	5	4	no	—
274	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
275	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
276	M₁₆	—	5	8	no	—
277	M₁₆	—	5	16	no	—
278	C₂×C₈	—	5	4	no	—
279	C₂×C₈	—	5	16	no	—
280	C₂×C₈	C₃×C₄×D₅	1	8	yes	complemented
281	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
282	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
283	C₄⋊C₄	—	5	4	no	—
284	C₄⋊C₄	—	5	2	no	—
285	C₂²⋊C₄	—	5	2	no	—
286	C₂²⋊C₄	—	5	4	no	—
287	C₄²	—	5	4	no	—
288	C₄²	—	5	2	no	—
289	C₄²	C₃×C₄×D₅	1	2	yes	—
290	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
291	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
292	C₃×C₅	C₄×#131	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	5	4	no	—
295	C₂²×C₃	—	10	4	no	—
296	C₂²×C₃	C₄²×D₅	1	2	yes	—
297	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	5	4	no	—
300	C₃×C₄	—	10	4	no	—
301	C₃×C₄	C₄²×D₅	1	2	yes	—
302	C₃×C₄	#4047	1	4	yes	direct product factor
303	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
304	C₂×C₅	—	2	2	no	—
305	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
306	C₂×C₅	C₂×C₃×#131	1	2	yes	—
307	D₅	—	2	4	no	—
308	C₂³	—	5	2	no	—
309	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
310	Q₈	—	5	4	no	—
311	D₄	—	5	8	no	—
312	D₄	—	5	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	5	2	no	—
315	C₂×C₄	—	5	8	no	—
316	C₂×C₄	—	5	4	no	—
317	C₂×C₄	—	10	8	no	—
318	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
319	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
320	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
321	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
322	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
323	C₈	—	5	8	no	—
324	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
325	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
326	C₂×C₃	—	2	2	no	—
327	C₂×C₃	—	10	4	no	—
328	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
329	C₂×C₃	C₂×#4047	1	2	yes	—
330	C₅	C₃×C₄×#131	1	1	yes	characteristic, complemented, Sylow
331	C₂²	—	2	2	no	—
332	C₂²	—	5	4	no	—
333	C₂²	—	10	4	no	—
334	C₂²	C₃×C₄²×D₅	1	2	yes	—
335	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	5	4	no	—
338	C₄	—	10	4	no	—
339	C₄	C₃×C₄²×D₅	1	2	yes	—
340	C₄	C₃×#4047	1	4	yes	direct product factor
341	C₄	C₂²×C₃×C₄×D₅	1	2	yes	—
342	C₃	C₄×#4047	1	1	yes	characteristic, direct product factor, Sylow
343	C₂	—	2	2	no	—
344	C₂	—	10	4	no	—
345	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
346	C₂	C₂×C₃×#4047	1	2	yes	—

	subgroup	G/H
center	C₃×C₄×C₈	C₂×D₅
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×C₄×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄×C₈ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₃×#65390	C₂	semidirect
5. C₃×C₄×#681	C₂	semidirect
6. C₃×#64978	C₂	semidirect
7. C₃×C₄×#676	C₂	semidirect
8. C₃×C₄×C₈×D₅	C₂	semidirect
9. C₄×#4047	C₃	direct (N × H)
16. C₃×#4047	C₄	direct (N × H)
33. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
34. #65390	C₂×C₃	semidirect
35. C₄×#681	C₂×C₃	semidirect
36. #64978	C₂×C₃	semidirect
37. C₄×#676	C₂×C₃	semidirect
38. C₄×C₈×D₅	C₂×C₃	semidirect
47. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
59. C₃×#681	C₂×C₄	semidirect
61. C₃×#676	C₂×C₄	semidirect
62. C₃×C₈×D₅	C₂×C₄	semidirect
70. C₂×C₃×C₄×C₈	D₅	semidirect
77. #4047	C₃×C₄	direct (N × H)
138. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
150. #681	C₂×C₃×C₄	semidirect
152. #676	C₂×C₃×C₄	semidirect
153. C₈×D₅	C₂×C₃×C₄	semidirect
161. C₂×C₄×C₈	C₃×D₅	semidirect
169. C₃×C₄×C₅	#131	semidirect
185. C₂×C₃×C₈	C₄×D₅	semidirect
264. C₄×C₅	C₃×#131	semidirect
280. C₂×C₈	C₃×C₄×D₅	semidirect
292. C₃×C₅	C₄×#131	semidirect
302. C₃×C₄	#4047	direct (N × H)
330. C₅	C₃×C₄×#131	semidirect
340. C₄	C₃×#4047	direct (N × H)
342. C₃	C₄×#4047	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×#4047	2
C₃×C₄×#709	2
C₂×C₃×C₄×C₅×C₈	2
C₃×#65390	2
C₃×C₄×#681	2
C₃×#64978	2
C₃×C₄×#676	2
C₃×C₄×C₈×D₅	2
C₄×#4047	3
C₃×C₄×#131	5

Subgroups — C3×C4×#4047 #14411445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4047 #14411445