Subgroups — C₂×C₃×#65161 #14415986

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4039	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3941	C₂	1	2	yes	maximal, complemented
6	C₃×#65161	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65161	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
9	C₂²×C₃×C₄×D₅	—	2	2	no	—
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×#685	—	2	2	no	—
13	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄₀	C₄	1	8	yes	complemented
16	C₂×C₃×D₄₀	C₂²	1	4	yes	—
17	C₃×#4039	—	2	4	no	—
18	C₃×#4039	C₂²	1	8	yes	complemented
19	C₃×C₅×#107	C₂²	1	4	yes	complemented
20	C₃×C₈×Dic₅	C₂²	1	4	yes	complemented
21	C₃×#3941	C₂²	1	8	yes	complemented
22	C₂×C₃×C₄×D₈	—	5	1	no	maximal, Hall
23	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic
24	C₂×#4039	C₂×C₃	1	2	yes	complemented
25	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#3941	C₂×C₃	1	2	yes	complemented
28	#65161	C₂×C₃	1	8	yes	direct product factor
29	C₂³×C₃×D₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
32	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
34	C₂×C₃×D₂₀	—	2	2	no	—
35	C₂×C₃×D₂₀	—	2	4	no	—
36	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	complemented
37	C₂×C₃×D₂₀	C₂³	1	4	yes	—
38	C₂×C₃×C₄×D₅	—	2	8	no	—
39	C₂×C₃×C₄×D₅	—	4	8	no	—
40	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
41	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
44	C₃×#685	—	2	8	no	—
45	C₃×C₄×Dic₅	D₄	1	2	yes	—
46	C₃×C₄×Dic₅	C₂³	1	2	yes	—
47	C₂×C₃×#168	—	2	2	no	—
48	C₂×C₃×#168	C₂³	1	2	yes	—
49	C₃×D₄₀	C₂×C₄	1	16	yes	complemented
50	C₂²×C₃×D₈	—	5	1	no	—
51	C₂×C₃×C₄×D₄	—	5	2	no	—
52	C₃×C₄×D₈	—	5	8	no	—
53	C₂×C₃×#107	D₅	1	1	yes	characteristic, complemented
54	C₂×C₃×#102	—	5	2	no	—
55	C₂×C₃×C₄×C₈	—	5	1	no	—
56	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
57	C₂²×C₄×D₅	—	2	2	no	—
58	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
60	C₂×#685	—	2	2	no	—
61	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
62	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
63	C₂×D₄₀	C₃×C₄	1	8	yes	complemented
64	C₂×D₄₀	C₂²×C₃	1	4	yes	—
65	#4039	—	2	4	no	—
66	#4039	C₂²×C₃	1	8	yes	complemented
67	C₅×#107	C₂²×C₃	1	4	yes	complemented
68	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
69	#3941	C₂²×C₃	1	8	yes	complemented
70	C₂×C₄×D₈	—	5	1	no	Sylow
71	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₃×D₅	—	2	8	no	—
73	C₂²×C₃×D₅	—	2	4	no	—
74	C₂²×C₃×D₅	—	4	4	no	—
75	C₂²×C₃×D₅	—	4	4	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	—	4	4	no	—
78	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	#41	1	2	yes	—
81	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
82	C₂×C₃×Dic₅	—	2	2	no	—
83	C₂×C₃×Dic₅	D₈	1	4	yes	complemented
84	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
85	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
86	C₃×D₂₀	—	2	8	no	—
87	C₃×D₂₀	—	2	4	no	—
88	C₃×D₂₀	C₂²×C₄	1	8	yes	complemented
89	C₃×C₄×D₅	—	4	16	no	—
90	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
91	C₃×#168	—	2	2	no	—
92	C₂²×C₃×D₄	—	5	2	no	—
93	C₂³×C₃×C₄	—	10	2	no	—
94	C₂×C₃×D₈	—	5	8	no	—
95	C₂×C₃×D₈	—	5	4	no	—
96	C₂²×C₃×C₈	—	5	1	no	—
97	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
98	C₃×C₄×D₄	—	5	8	no	—
99	C₃×C₄×D₄	—	10	4	no	—
100	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
102	C₂×C₃×C₄²	—	5	1	no	—
103	C₃×#107	C₂×D₅	1	4	yes	complemented
104	C₃×#102	—	5	8	no	—
105	C₃×C₄×C₈	—	5	4	no	—
106	C₂³×D₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
109	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
110	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
111	C₂×D₂₀	—	2	2	no	—
112	C₂×D₂₀	—	2	4	no	—
113	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	complemented
114	C₂×D₂₀	C₂³×C₃	1	4	yes	—
115	C₂×C₄×D₅	—	2	8	no	—
116	C₂×C₄×D₅	—	4	8	no	—
117	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
118	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
121	#685	—	2	8	no	—
122	C₄×Dic₅	C₃×D₄	1	2	yes	—
123	C₄×Dic₅	C₂³×C₃	1	2	yes	—
124	C₂×#168	—	2	2	no	—
125	C₂×#168	C₂³×C₃	1	2	yes	—
126	D₄₀	C₂×C₃×C₄	1	16	yes	complemented
127	C₂²×D₈	—	5	1	no	—
128	C₂×C₄×D₄	—	5	2	no	—
129	C₄×D₈	—	5	8	no	—
130	C₂×#107	C₃×D₅	1	1	yes	characteristic, complemented
131	C₂×#102	—	5	2	no	—
132	C₂×C₄×C₈	—	5	1	no	—
133	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
134	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
135	C₂²×C₃×C₅	#135	1	2	yes	—
136	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₃×D₅	—	2	8	no	—
138	C₂×C₃×D₅	—	4	4	no	—
139	C₂×C₃×D₅	—	4	4	no	—
140	C₂×C₃×D₅	—	4	16	no	—
141	C₃×C₄×C₅	—	4	4	no	—
142	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
143	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
144	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
145	C₃×Dic₅	—	2	2	no	—
146	C₃×Dic₅	C₂×D₈	1	4	yes	complemented
147	C₂⁴×C₃	—	10	2	no	—
148	C₂×C₃×D₄	—	5	8	no	—
149	C₂×C₃×D₄	—	5	4	no	—
150	C₂×C₃×D₄	—	10	2	no	—
151	C₂×C₃×D₄	—	10	4	no	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	5	1	no	—
154	C₂²×C₃×C₄	—	5	1	no	—
155	C₂²×C₃×C₄	—	10	8	no	—
156	C₂²×C₃×C₄	—	20	8	no	—
157	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
158	C₃×D₈	—	5	16	no	—
159	C₂×C₃×C₈	—	5	2	no	—
160	C₂×C₃×C₈	—	10	2	no	—
161	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
162	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
163	C₃×C₄⋊C₄	—	2	2	no	—
164	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
165	C₃×C₂²⋊C₄	—	10	8	no	—
166	C₃×C₄²	—	5	2	no	—
167	C₃×C₄²	—	5	2	no	—
168	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
169	C₂²×D₅	—	2	8	no	—
170	C₂²×D₅	—	2	4	no	—
171	C₂²×D₅	—	4	4	no	—
172	C₂²×D₅	—	4	4	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	4	4	no	—
175	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
176	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₃×#41	1	2	yes	—
178	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
179	C₂×Dic₅	—	2	2	no	—
180	C₂×Dic₅	C₃×D₈	1	4	yes	complemented
181	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
182	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
183	D₂₀	—	2	8	no	—
184	D₂₀	—	2	4	no	—
185	D₂₀	C₂²×C₃×C₄	1	8	yes	complemented
186	C₄×D₅	—	4	16	no	—
187	C₅×C₈	C₂²×C₃×C₄	1	4	yes	complemented
188	#168	—	2	2	no	—
189	C₂²×D₄	—	5	2	no	—
190	C₂³×C₄	—	10	2	no	—
191	C₂×D₈	—	5	8	no	—
192	C₂×D₈	—	5	4	no	—
193	C₂²×C₈	—	5	1	no	—
194	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
195	C₄×D₄	—	5	8	no	—
196	C₄×D₄	—	10	4	no	—
197	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
198	C₂×C₂²⋊C₄	—	10	2	no	—
199	C₂×C₄²	—	5	1	no	—
200	#107	C₂×C₃×D₅	1	4	yes	complemented
201	#102	—	5	8	no	—
202	C₄×C₈	—	5	4	no	—
203	C₂×C₃×C₅	C₄×D₈	1	4	yes	complemented
204	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
206	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
207	C₃×D₅	—	4	8	no	—
208	C₂³×C₃	—	10	4	no	—
209	C₂³×C₃	—	10	8	no	—
210	C₂³×C₃	—	20	4	no	—
211	C₂³×C₃	—	20	4	no	—
212	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
213	C₃×D₄	—	5	8	no	—
214	C₃×D₄	—	10	4	no	—
215	C₃×D₄	—	10	8	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	4	4	no	—
218	C₂×C₃×C₄	—	5	2	no	—
219	C₂×C₃×C₄	—	5	4	no	—
220	C₂×C₃×C₄	—	5	2	no	—
221	C₂×C₃×C₄	—	10	2	no	—
222	C₂×C₃×C₄	—	20	16	no	—
223	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
224	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
225	C₂×C₃×C₄	#713	1	2	yes	—
226	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
227	C₃×C₈	—	10	2	no	—
228	C₃×C₈	C₂×C₄×D₅	1	4	yes	complemented
229	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
230	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
231	C₂²×C₅	C₃×#135	1	2	yes	—
232	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
233	C₂×D₅	—	2	8	no	—
234	C₂×D₅	—	4	4	no	—
235	C₂×D₅	—	4	4	no	—
236	C₂×D₅	—	4	16	no	—
237	C₄×C₅	—	4	4	no	—
238	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
239	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
240	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
241	Dic₅	—	2	2	no	—
242	Dic₅	C₂×C₃×D₈	1	4	yes	complemented
243	C₂⁴	—	10	2	no	—
244	C₂×D₄	—	5	8	no	—
245	C₂×D₄	—	5	4	no	—
246	C₂×D₄	—	10	2	no	—
247	C₂×D₄	—	10	4	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	5	1	no	—
250	C₂²×C₄	—	5	1	no	—
251	C₂²×C₄	—	10	8	no	—
252	C₂²×C₄	—	20	8	no	—
253	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
254	D₈	—	5	16	no	—
255	C₂×C₈	—	5	2	no	—
256	C₂×C₈	—	10	2	no	—
257	C₂×C₈	C₃×C₄×D₅	1	4	yes	complemented
258	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
261	C₂²⋊C₄	—	10	8	no	—
262	C₄²	—	5	2	no	—
263	C₄²	—	5	2	no	—
264	C₃×C₅	C₂×C₄×D₈	1	1	yes	characteristic, complemented, Hall
265	C₂²×C₃	—	10	8	no	—
266	C₂²×C₃	—	20	4	no	—
267	C₂²×C₃	—	20	4	no	—
268	C₂²×C₃	—	20	16	no	—
269	C₂²×C₃	#4039	1	2	yes	—
270	C₂²×C₃	D₅×D₈	1	2	yes	—
271	C₂²×C₃	#4065	1	2	yes	—
272	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
273	C₃×C₄	—	4	4	no	—
274	C₃×C₄	—	5	4	no	—
275	C₃×C₄	—	10	2	no	—
276	C₃×C₄	#4039	1	2	yes	—
277	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
278	C₃×C₄	C₂×#713	1	1	yes	characteristic
279	C₂×C₅	C₃×C₄×D₈	1	4	yes	complemented
280	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
281	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
282	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
283	D₅	—	4	8	no	—
284	C₂³	—	10	4	no	—
285	C₂³	—	10	8	no	—
286	C₂³	—	20	4	no	—
287	C₂³	—	20	4	no	—
288	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
289	D₄	—	5	8	no	—
290	D₄	—	10	4	no	—
291	D₄	—	10	8	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	5	2	no	—
295	C₂×C₄	—	5	4	no	—
296	C₂×C₄	—	5	2	no	—
297	C₂×C₄	—	10	2	no	—
298	C₂×C₄	—	20	16	no	—
299	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
300	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
301	C₂×C₄	C₃×#713	1	2	yes	—
302	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
303	C₈	—	10	2	no	—
304	C₈	C₂×C₃×C₄×D₅	1	4	yes	complemented
305	C₂×C₃	—	20	8	no	—
306	C₂×C₃	#65161	1	4	yes	direct product factor
307	C₂×C₃	C₂×#4039	1	1	yes	characteristic
308	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
309	C₂×C₃	C₂×#4065	1	1	yes	characteristic
310	C₅	C₂×C₃×C₄×D₈	1	1	yes	characteristic, complemented, Sylow
311	C₂²	—	10	8	no	—
312	C₂²	—	20	4	no	—
313	C₂²	—	20	16	no	—
314	C₂²	—	20	4	no	—
315	C₂²	C₃×#4039	1	2	yes	—
316	C₂²	C₃×D₅×D₈	1	2	yes	—
317	C₂²	C₃×#4065	1	2	yes	—
318	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
319	C₄	—	4	4	no	—
320	C₄	—	5	4	no	—
321	C₄	—	10	2	no	—
322	C₄	C₃×#4039	1	2	yes	—
323	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
324	C₄	C₂×C₃×#713	1	1	yes	characteristic
325	C₃	C₂×#65161	1	1	yes	characteristic, direct product factor, Sylow
326	C₂	—	20	8	no	—
327	C₂	C₃×#65161	1	4	yes	direct product factor
328	C₂	C₂×C₃×#4039	1	1	yes	characteristic
329	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic
330	C₂	C₂×C₃×#4065	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₄₀	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#107	D₅
hypocenter	C₅	C₂×C₃×C₄×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#107

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4039	C₂	semidirect
3. C₂×C₃×C₅×#107	C₂	semidirect
4. C₂×C₃×C₈×Dic₅	C₂	semidirect
5. C₂×C₃×#3941	C₂	semidirect
6. C₃×#65161	C₂	direct (N × H)
7. C₂×#65161	C₃	direct (N × H)
15. C₂×C₃×D₄₀	C₄	semidirect
18. C₃×#4039	C₂²	semidirect
19. C₃×C₅×#107	C₂²	semidirect
20. C₃×C₈×Dic₅	C₂²	semidirect
21. C₃×#3941	C₂²	semidirect
24. C₂×#4039	C₂×C₃	semidirect
25. C₂×C₅×#107	C₂×C₃	semidirect
26. C₂×C₈×Dic₅	C₂×C₃	semidirect
27. C₂×#3941	C₂×C₃	semidirect
28. #65161	C₂×C₃	direct (N × H)
36. C₂×C₃×D₂₀	C₂×C₄	semidirect
40. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
49. C₃×D₄₀	C₂×C₄	semidirect
53. C₂×C₃×#107	D₅	semidirect
63. C₂×D₄₀	C₃×C₄	semidirect
66. #4039	C₂²×C₃	semidirect
67. C₅×#107	C₂²×C₃	semidirect
68. C₈×Dic₅	C₂²×C₃	semidirect
69. #3941	C₂²×C₃	semidirect
83. C₂×C₃×Dic₅	D₈	semidirect
88. C₃×D₂₀	C₂²×C₄	semidirect
90. C₃×C₅×C₈	C₂²×C₄	semidirect
103. C₃×#107	C₂×D₅	semidirect
113. C₂×D₂₀	C₂×C₃×C₄	semidirect
117. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
126. D₄₀	C₂×C₃×C₄	semidirect
130. C₂×#107	C₃×D₅	semidirect
146. C₃×Dic₅	C₂×D₈	semidirect
161. C₂×C₃×C₈	C₄×D₅	semidirect
180. C₂×Dic₅	C₃×D₈	semidirect
185. D₂₀	C₂²×C₃×C₄	semidirect
187. C₅×C₈	C₂²×C₃×C₄	semidirect
200. #107	C₂×C₃×D₅	semidirect
203. C₂×C₃×C₅	C₄×D₈	semidirect
228. C₃×C₈	C₂×C₄×D₅	semidirect
242. Dic₅	C₂×C₃×D₈	semidirect
257. C₂×C₈	C₃×C₄×D₅	semidirect
264. C₃×C₅	C₂×C₄×D₈	semidirect
279. C₂×C₅	C₃×C₄×D₈	semidirect
304. C₈	C₂×C₃×C₄×D₅	semidirect
306. C₂×C₃	#65161	direct (N × H)
310. C₅	C₂×C₃×C₄×D₈	semidirect
325. C₃	C₂×#65161	direct (N × H)
327. C₂	C₃×#65161	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×D₄₀	2
C₂×C₃×#4039	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₈×Dic₅	2
C₂×C₃×#3941	2
C₃×#65161	2
C₂×#65161	3
C₂×C₃×C₄×D₈	5

Subgroups — C2×C3×#65161 #14415986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65161 #14415986