Subgroups — C₃×#10601220 #14281919

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65813	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64704	C₂	1	2	yes	maximal, complemented
5	C₃×#64703	C₂	1	2	yes	maximal, complemented
6	#10601220	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₈	—	2	1	no	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₃×#4076	C₄	1	1	yes	characteristic
10	C₃×#4075	—	2	1	no	—
11	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
12	C₃×#4070	C₄	1	1	yes	characteristic
13	C₂×C₃×#681	—	2	1	no	—
14	C₃×#4022	—	2	1	no	—
15	C₃×#4021	C₄	1	1	yes	characteristic
16	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
17	C₃×#4018	—	2	1	no	—
18	C₃×#4016	C₄	1	1	yes	characteristic
19	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	—	2	1	no	—
21	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
22	C₃×#3935	—	2	1	no	—
23	C₃×C₄×#168	C₂²	1	2	yes	—
24	C₃×#1483	—	5	1	no	maximal, Hall
25	#65813	C₂×C₃	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
28	#64704	C₂×C₃	1	2	yes	complemented
29	#64703	C₂×C₃	1	2	yes	complemented
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
34	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	—	2	1	no	—
36	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₅×C₈	—	2	2	no	—
38	C₂×C₃×C₅×C₈	—	4	2	no	—
39	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₂²⋊Dic₅	—	2	1	no	—
44	C₃×#685	—	2	1	no	—
45	C₃×#685	—	2	1	no	—
46	C₃×#685	—	2	1	no	—
47	C₃×#685	—	2	1	no	—
48	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
50	C₃×#683	—	2	1	no	—
51	C₃×#683	—	2	1	no	—
52	C₃×#683	—	2	1	no	—
53	C₃×#683	—	2	1	no	—
54	C₃×C₄×Dic₅	—	2	1	no	—
55	C₃×#681	—	2	4	no	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₃×#529	—	5	1	no	—
58	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
59	C₃×C₄×M₁₆	—	5	1	no	—
60	C₃×Q₈⋊C₈	—	5	2	no	—
61	C₃×D₄⋊C₈	—	5	2	no	—
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
64	#4076	C₃×C₄	1	1	yes	characteristic
65	#4075	—	2	1	no	—
66	C₄×C₂²⋊D₅	—	2	1	no	—
67	#4070	C₃×C₄	1	1	yes	characteristic
68	C₂×#681	—	2	1	no	—
69	#4022	—	2	1	no	—
70	#4021	C₃×C₄	1	1	yes	characteristic
71	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
72	#4018	—	2	1	no	—
73	#4016	C₃×C₄	1	1	yes	characteristic
74	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	2	1	no	—
76	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
77	#3935	—	2	1	no	—
78	C₄×#168	C₂²×C₃	1	2	yes	—
79	#1483	—	5	1	no	Sylow
80	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₃×D₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₂²⋊D₅	—	4	2	no	—
93	C₂×C₃×Dic₅	—	2	1	no	—
94	C₂×C₃×Dic₅	—	2	1	no	—
95	C₂×C₃×Dic₅	—	2	1	no	—
96	C₃×D₂₀	—	2	2	no	—
97	C₃×C₄×D₅	—	4	1	no	—
98	C₃×C₄×D₅	—	4	1	no	—
99	C₃×Dic₁₀	—	2	2	no	—
100	C₃×C₅×C₈	—	4	2	no	—
101	C₃×#168	—	2	4	no	—
102	C₂×C₃×M₁₆	—	10	1	no	—
103	C₂²×C₃×C₈	—	2	1	no	—
104	C₃×#126	—	10	1	no	—
105	C₃×#125	—	5	1	no	—
106	C₃×#124	—	5	1	no	—
107	C₃×#123	—	10	1	no	—
108	C₃×C₂²⋊Q₈	—	5	1	no	—
109	C₃×#121	—	5	1	no	—
110	C₃×C₄×Q₈	—	5	1	no	—
111	C₃×C₄×D₄	—	5	1	no	—
112	C₃×C₄×D₄	—	10	1	no	—
113	C₃×#117	—	10	1	no	—
114	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
115	C₃×C₄⋊C₈	—	2	1	no	—
116	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
117	C₃×#97	—	10	1	no	—
118	C₃×C₄×C₈	—	5	2	no	—
119	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
122	C₂×C₂²⋊D₅	—	2	1	no	—
123	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂×C₄×D₅	—	2	1	no	—
125	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	4	2	no	—
128	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
129	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
130	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
131	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₂²⋊Dic₅	—	2	1	no	—
133	#685	—	2	1	no	—
134	#685	—	2	1	no	—
135	#685	—	2	1	no	—
136	#685	—	2	1	no	—
137	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
138	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
139	#683	—	2	1	no	—
140	#683	—	2	1	no	—
141	#683	—	2	1	no	—
142	#683	—	2	1	no	—
143	C₄×Dic₅	—	2	1	no	—
144	#681	—	2	4	no	—
145	C₂×#168	—	2	2	no	—
146	#529	—	5	1	no	—
147	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
148	C₄×M₁₆	—	5	1	no	—
149	Q₈⋊C₈	—	5	2	no	—
150	D₄⋊C₈	—	5	2	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	—	2	1	no	—
153	C₂²×C₃×C₅	#104	1	2	yes	—
154	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₃×D₅	—	4	1	no	—
156	C₂×C₃×D₅	—	4	1	no	—
157	C₂×C₃×D₅	—	4	1	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	#131	1	2	yes	—
163	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₃×C₄×C₅	#137	1	1	yes	characteristic
165	C₃×Dic₅	—	4	1	no	—
166	C₃×Dic₅	—	4	1	no	—
167	C₃×Dic₅	—	4	1	no	—
168	C₂×C₃×Q₈	—	5	1	no	—
169	C₂×C₃×D₄	—	5	1	no	—
170	C₂×C₃×D₄	—	10	1	no	—
171	C₂²×C₃×C₄	—	10	1	no	—
172	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
175	C₃×M₁₆	—	10	4	no	—
176	C₂×C₃×C₈	—	2	2	no	—
177	C₂×C₃×C₈	—	4	2	no	—
178	C₂×C₃×C₈	—	10	2	no	—
179	C₃×C₄⋊C₄	—	5	1	no	—
180	C₃×C₄⋊C₄	—	5	1	no	—
181	C₃×C₄⋊C₄	—	10	1	no	—
182	C₃×C₄⋊C₄	—	10	1	no	—
183	C₃×C₄⋊C₄	—	10	1	no	—
184	C₃×C₄⋊C₄	—	10	1	no	—
185	C₃×C₂²⋊C₄	—	10	1	no	—
186	C₃×C₂²⋊C₄	—	10	1	no	—
187	C₃×C₂²⋊C₄	—	10	1	no	—
188	C₃×C₂²⋊C₄	—	10	1	no	—
189	C₃×C₂²⋊C₄	—	10	1	no	—
190	C₃×C₄²	—	10	1	no	—
191	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
192	C₃×C₄²	D₂₀	1	1	yes	characteristic
193	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
194	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
195	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×D₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂²⋊D₅	—	4	2	no	—
208	C₂×Dic₅	—	2	1	no	—
209	C₂×Dic₅	—	2	1	no	—
210	C₂×Dic₅	—	2	1	no	—
211	D₂₀	—	2	2	no	—
212	C₄×D₅	—	4	1	no	—
213	C₄×D₅	—	4	1	no	—
214	Dic₁₀	—	2	2	no	—
215	C₅×C₈	—	4	2	no	—
216	#168	—	2	4	no	—
217	C₂×M₁₆	—	10	1	no	—
218	C₂²×C₈	—	2	1	no	—
219	#126	—	10	1	no	—
220	#125	—	5	1	no	—
221	#124	—	5	1	no	—
222	#123	—	10	1	no	—
223	C₂²⋊Q₈	—	5	1	no	—
224	#121	—	5	1	no	—
225	C₄×Q₈	—	5	1	no	—
226	C₄×D₄	—	5	1	no	—
227	C₄×D₄	—	10	1	no	—
228	#117	—	10	1	no	—
229	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
230	C₄⋊C₈	—	2	1	no	—
231	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
232	#97	—	10	1	no	—
233	C₄×C₈	—	5	2	no	—
234	C₂×C₃×C₅	—	2	2	no	—
235	C₂×C₃×C₅	#408	1	1	yes	characteristic
236	C₂×C₃×C₅	#417	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
238	C₃×D₅	—	8	1	no	—
239	C₂³×C₃	—	10	1	no	—
240	C₂³×C₃	#685	1	1	yes	characteristic
241	C₃×Q₈	—	10	2	no	—
242	C₃×D₄	—	10	2	no	—
243	C₃×D₄	—	20	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	10	1	no	—
249	C₂×C₃×C₄	—	10	1	no	—
250	C₂×C₃×C₄	—	10	1	no	—
251	C₂×C₃×C₄	—	20	1	no	—
252	C₂×C₃×C₄	—	20	1	no	—
253	C₂×C₃×C₄	#685	1	1	yes	characteristic
254	C₂×C₃×C₄	#685	1	1	yes	characteristic
255	C₂×C₃×C₄	#685	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
259	C₃×C₈	—	4	2	no	—
260	C₃×C₈	—	10	4	no	—
261	C₂²×C₅	—	2	1	no	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	C₃×#104	1	2	yes	—
264	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×D₅	—	4	1	no	—
266	C₂×D₅	—	4	1	no	—
267	C₂×D₅	—	4	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	C₃×#131	1	2	yes	—
273	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₄×C₅	C₃×#137	1	1	yes	characteristic
275	Dic₅	—	4	1	no	—
276	Dic₅	—	4	1	no	—
277	Dic₅	—	4	1	no	—
278	C₂×Q₈	—	5	1	no	—
279	C₂×D₄	—	5	1	no	—
280	C₂×D₄	—	10	1	no	—
281	C₂²×C₄	—	10	1	no	—
282	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
283	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
284	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
285	M₁₆	—	10	4	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	—	10	2	no	—
289	C₄⋊C₄	—	5	1	no	—
290	C₄⋊C₄	—	5	1	no	—
291	C₄⋊C₄	—	10	1	no	—
292	C₄⋊C₄	—	10	1	no	—
293	C₄⋊C₄	—	10	1	no	—
294	C₄⋊C₄	—	10	1	no	—
295	C₂²⋊C₄	—	10	1	no	—
296	C₂²⋊C₄	—	10	1	no	—
297	C₂²⋊C₄	—	10	1	no	—
298	C₂²⋊C₄	—	10	1	no	—
299	C₂²⋊C₄	—	10	1	no	—
300	C₄²	—	10	1	no	—
301	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
302	C₄²	C₃×D₂₀	1	1	yes	characteristic
303	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
304	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
305	C₃×C₅	#1483	1	1	yes	characteristic, complemented, Hall
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	20	1	no	—
309	C₂²×C₃	—	20	1	no	—
310	C₂²×C₃	—	20	1	no	—
311	C₂²×C₃	#3957	1	2	yes	—
312	C₂²×C₃	C₂×#685	1	1	yes	characteristic
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	20	1	no	—
318	C₃×C₄	—	20	1	no	—
319	C₃×C₄	—	20	1	no	—
320	C₃×C₄	#4047	1	2	yes	—
321	C₃×C₄	#4078	1	1	yes	characteristic
322	C₃×C₄	#4088	1	1	yes	characteristic
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	C₃×#408	1	1	yes	characteristic
325	C₂×C₅	C₃×#417	1	1	yes	characteristic
326	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
327	D₅	—	8	1	no	—
328	C₂³	—	10	1	no	—
329	C₂³	C₃×#685	1	1	yes	characteristic
330	Q₈	—	10	2	no	—
331	D₄	—	10	2	no	—
332	D₄	—	20	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	10	1	no	—
338	C₂×C₄	—	10	1	no	—
339	C₂×C₄	—	10	1	no	—
340	C₂×C₄	—	20	1	no	—
341	C₂×C₄	—	20	1	no	—
342	C₂×C₄	C₃×#685	1	1	yes	characteristic
343	C₂×C₄	C₃×#685	1	1	yes	characteristic
344	C₂×C₄	C₃×#685	1	1	yes	characteristic
345	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
346	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
347	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
348	C₈	—	4	2	no	—
349	C₈	—	10	4	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	40	1	no	—
352	C₂×C₃	#65255	1	1	yes	characteristic
353	C₂×C₃	#65399	1	1	yes	characteristic
354	C₂×C₃	C₂×#3957	1	1	yes	characteristic
355	C₅	C₃×#1483	1	1	yes	characteristic, complemented, Sylow
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	20	1	no	—
359	C₂²	—	20	1	no	—
360	C₂²	—	20	1	no	—
361	C₂²	C₃×#3957	1	2	yes	—
362	C₂²	C₂×C₃×#685	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	20	1	no	—
368	C₄	—	20	1	no	—
369	C₄	—	20	1	no	—
370	C₄	C₃×#4047	1	2	yes	—
371	C₄	C₃×#4078	1	1	yes	characteristic
372	C₄	C₃×#4088	1	1	yes	characteristic
373	C₃	#10601220	1	1	yes	characteristic, direct product factor, Sylow
374	C₂	—	2	2	no	—
375	C₂	—	40	1	no	—
376	C₂	C₃×#65255	1	1	yes	characteristic
377	C₂	C₃×#65399	1	1	yes	characteristic
378	C₂	C₂×C₃×#3957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×#4076	C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#1483
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

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. C₃×C₄×#681	C₂	semidirect
4. C₃×#64704	C₂	semidirect
5. C₃×#64703	C₂	semidirect
6. #10601220	C₃	direct (N × H)
26. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
27. C₄×#681	C₂×C₃	semidirect
28. #64704	C₂×C₃	semidirect
29. #64703	C₂×C₃	semidirect
58. C₂×C₃×C₄⋊C₈	D₅	semidirect
147. C₂×C₄⋊C₈	C₃×D₅	semidirect
305. C₃×C₅	#1483	semidirect
355. C₅	C₃×#1483	semidirect
373. C₃	#10601220	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#65813	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×C₄×#681	2
C₃×#64704	2
C₃×#64703	2
#10601220	3
C₃×#1483	5

Subgroups — C3×#10601220 #14281919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601220 #14281919