Subgroups — C₃×#10610739 #14418658

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65804	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#65391	C₂	1	2	yes	maximal
4	C₃×#65390	C₂	1	2	yes	maximal
5	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic
6	C₃×#65120	C₂	1	2	yes	maximal, complemented
7	C₃×#65119	C₂	1	2	yes	maximal, complemented
8	C₃×#65117	C₂	1	4	yes	maximal, complemented
9	#10610739	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₃×#4072	C₂²	1	2	yes	—
13	C₃×#4070	C₄	1	2	yes	—
14	C₃×#4070	C₄	1	2	yes	—
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	C₂×C₃×#681	C₂²	1	1	yes	characteristic
17	C₃×#4016	C₄	1	2	yes	—
18	C₃×#4015	C₄	1	1	yes	characteristic
19	C₃×#4015	C₄	1	1	yes	characteristic
20	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
21	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
22	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
23	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₃×#3947	C₂²	1	4	yes	—
26	C₃×#3946	C₂²	1	4	yes	—
27	C₃×#3946	C₂²	1	4	yes	—
28	C₃×C₈×Dic₅	C₂²	1	4	yes	—
29	C₃×#3935	C₂²	1	2	yes	—
30	C₃×C₄×#168	C₂²	1	2	yes	—
31	C₃×#2962	—	5	1	no	maximal, Hall
32	#65804	C₂×C₃	1	1	yes	characteristic
33	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
34	#65391	C₂×C₃	1	2	yes	—
35	#65390	C₂×C₃	1	2	yes	—
36	C₄×#681	C₂×C₃	1	1	yes	characteristic
37	#65120	C₂×C₃	1	2	yes	complemented
38	#65119	C₂×C₃	1	2	yes	complemented
39	#65117	C₂×C₃	1	4	yes	complemented
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
44	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×C₈	—	2	4	no	—
46	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
53	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
54	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
56	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
57	C₃×#683	C₂×C₄	1	4	yes	—
58	C₃×#683	C₂×C₄	1	4	yes	—
59	C₃×C₄×Dic₅	C₂³	1	4	yes	—
60	C₃×#681	—	2	2	no	—
61	C₃×#681	Q₈	1	4	yes	complemented
62	C₂×C₃×#168	C₂³	1	2	yes	—
63	C₂×C₃×#168	C₂³	1	2	yes	—
64	C₃×#533	—	5	1	no	—
65	C₃×#446	—	5	4	no	—
66	C₃×#446	—	5	2	no	—
67	C₃×C₈×Q₈	—	5	2	no	—
68	C₃×#424	—	5	2	no	—
69	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic
70	C₃×#405	—	5	2	no	—
71	C₃×C₄×M₁₆	—	5	1	no	—
72	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	#4072	C₂²×C₃	1	2	yes	—
75	#4070	C₃×C₄	1	2	yes	—
76	#4070	C₃×C₄	1	2	yes	—
77	C₂×#681	C₂²×C₃	1	1	yes	characteristic
78	C₂×#681	C₂²×C₃	1	1	yes	characteristic
79	#4016	C₃×C₄	1	2	yes	—
80	#4015	C₃×C₄	1	1	yes	characteristic
81	#4015	C₃×C₄	1	1	yes	characteristic
82	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
83	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
84	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
85	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
87	#3947	C₂²×C₃	1	4	yes	—
88	#3946	C₂²×C₃	1	4	yes	—
89	#3946	C₂²×C₃	1	4	yes	—
90	C₈×Dic₅	C₂²×C₃	1	4	yes	—
91	#3935	C₂²×C₃	1	2	yes	—
92	C₄×#168	C₂²×C₃	1	2	yes	—
93	#2962	—	5	1	no	Sylow
94	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
105	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
106	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
107	C₃×Dic₁₀	—	2	4	no	—
108	C₃×Dic₁₀	—	4	2	no	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₃×C₅×C₈	—	2	2	no	—
111	C₃×#168	—	2	2	no	—
112	C₃×#168	C₂×Q₈	1	4	yes	—
113	C₂×C₃×M₁₆	—	5	1	no	—
114	C₂×C₃×M₁₆	—	5	1	no	—
115	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
116	C₃×C₄⋊Q₈	—	5	1	no	—
117	C₃×C₄⋊Q₈	—	5	1	no	—
118	C₃×#125	—	5	2	no	—
119	C₃×C₂²⋊Q₈	—	5	2	no	—
120	C₃×C₂²⋊Q₈	—	5	2	no	—
121	C₃×C₄×Q₈	—	5	2	no	—
122	C₃×C₄×Q₈	—	5	2	no	—
123	C₃×#117	—	5	2	no	—
124	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
125	C₃×C₄⋊C₈	—	5	4	no	—
126	C₃×C₄⋊C₈	—	5	4	no	—
127	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
128	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
129	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
130	C₃×#97	—	5	4	no	—
131	C₃×#97	—	5	2	no	—
132	C₃×C₄×C₈	—	5	4	no	—
133	C₃×C₄×C₈	—	5	2	no	—
134	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
138	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
139	C₂×C₅×C₈	—	2	4	no	—
140	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
141	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
142	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
143	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
144	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
147	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
148	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
149	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
150	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
151	#683	C₂×C₃×C₄	1	4	yes	—
152	#683	C₂×C₃×C₄	1	4	yes	—
153	C₄×Dic₅	C₂³×C₃	1	4	yes	—
154	#681	—	2	2	no	—
155	#681	C₃×Q₈	1	4	yes	complemented
156	C₂×#168	C₂³×C₃	1	2	yes	—
157	C₂×#168	C₂³×C₃	1	2	yes	—
158	#533	—	5	1	no	—
159	#446	—	5	4	no	—
160	#446	—	5	2	no	—
161	C₈×Q₈	—	5	2	no	—
162	#424	—	5	2	no	—
163	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic
164	#405	—	5	2	no	—
165	C₄×M₁₆	—	5	1	no	—
166	C₂²×C₃×C₅	—	2	1	no	—
167	C₂²×C₃×C₅	—	2	1	no	—
168	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
169	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	2	1	no	—
172	C₃×C₄×C₅	—	2	1	no	—
173	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
174	C₃×C₄×C₅	#131	1	2	yes	—
175	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
176	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
177	C₃×Dic₅	—	2	4	no	—
178	C₃×Dic₅	—	2	4	no	—
179	C₂×C₃×Q₈	—	5	2	no	—
180	C₂×C₃×Q₈	—	5	2	no	—
181	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
184	C₃×M₁₆	—	5	4	no	—
185	C₃×M₁₆	—	10	2	no	—
186	C₂×C₃×C₈	—	2	4	no	—
187	C₂×C₃×C₈	—	5	2	no	—
188	C₂×C₃×C₈	—	5	2	no	—
189	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
190	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
191	C₃×C₄⋊C₄	—	5	4	no	—
192	C₃×C₄⋊C₄	—	5	4	no	—
193	C₃×C₄⋊C₄	—	5	2	no	—
194	C₃×C₄⋊C₄	—	5	2	no	—
195	C₃×C₄⋊C₄	—	5	2	no	—
196	C₃×C₄⋊C₄	—	5	2	no	—
197	C₃×C₂²⋊C₄	—	5	4	no	—
198	C₃×C₄²	—	5	4	no	—
199	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
200	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
201	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
202	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
203	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
212	C₂×C₄×C₅	C₃×#41	1	2	yes	—
213	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
214	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
215	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
216	Dic₁₀	—	2	4	no	—
217	Dic₁₀	—	4	2	no	—
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	2	2	no	—
220	#168	—	2	2	no	—
221	#168	C₂×C₃×Q₈	1	4	yes	—
222	C₂×M₁₆	—	5	1	no	—
223	C₂×M₁₆	—	5	1	no	—
224	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
225	C₄⋊Q₈	—	5	1	no	—
226	C₄⋊Q₈	—	5	1	no	—
227	#125	—	5	2	no	—
228	C₂²⋊Q₈	—	5	2	no	—
229	C₂²⋊Q₈	—	5	2	no	—
230	C₄×Q₈	—	5	2	no	—
231	C₄×Q₈	—	5	2	no	—
232	#117	—	5	2	no	—
233	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
234	C₄⋊C₈	—	5	4	no	—
235	C₄⋊C₈	—	5	4	no	—
236	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
237	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
238	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
239	#97	—	5	4	no	—
240	#97	—	5	2	no	—
241	C₄×C₈	—	5	4	no	—
242	C₄×C₈	—	5	2	no	—
243	C₂×C₃×C₅	—	2	2	no	—
244	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
245	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
246	C₂×C₃×C₅	#568	1	1	yes	characteristic
247	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
248	C₃×Q₈	—	10	4	no	—
249	C₃×Q₈	—	20	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	4	1	no	—
252	C₂×C₃×C₄	—	5	4	no	—
253	C₂×C₃×C₄	—	5	4	no	—
254	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
259	C₂×C₃×C₄	#711	1	2	yes	—
260	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
261	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	2	2	no	—
264	C₃×C₈	—	5	4	no	—
265	C₃×C₈	—	10	2	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	C₃×C₄×Q₈	1	2	yes	—
269	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
274	C₄×C₅	C₃×#131	1	2	yes	—
275	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
276	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
277	Dic₅	—	2	4	no	—
278	Dic₅	—	2	4	no	—
279	C₂×Q₈	—	5	2	no	—
280	C₂×Q₈	—	5	2	no	—
281	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
282	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
284	M₁₆	—	5	4	no	—
285	M₁₆	—	10	2	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	5	2	no	—
288	C₂×C₈	—	5	2	no	—
289	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
290	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
291	C₄⋊C₄	—	5	2	no	—
292	C₄⋊C₄	—	5	2	no	—
293	C₄⋊C₄	—	5	4	no	—
294	C₄⋊C₄	—	5	4	no	—
295	C₄⋊C₄	—	5	2	no	—
296	C₄⋊C₄	—	5	2	no	—
297	C₂²⋊C₄	—	5	4	no	—
298	C₄²	—	5	4	no	—
299	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
300	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
301	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
302	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
303	C₃×C₅	#2962	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	#4033	1	2	yes	—
307	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	10	4	no	—
312	C₃×C₄	—	10	4	no	—
313	C₃×C₄	#4033	1	2	yes	—
314	C₃×C₄	#4047	1	2	yes	—
315	C₃×C₄	C₂×#711	1	1	yes	characteristic
316	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
317	C₂×C₅	—	2	2	no	—
318	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
319	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
320	C₂×C₅	C₃×#568	1	1	yes	characteristic
321	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
322	Q₈	—	10	4	no	—
323	Q₈	—	20	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	5	4	no	—
327	C₂×C₄	—	5	4	no	—
328	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
329	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
330	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
331	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
332	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
333	C₂×C₄	C₃×#711	1	2	yes	—
334	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
335	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	—	5	4	no	—
339	C₈	—	10	2	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	C₂×#4033	1	1	yes	characteristic
342	C₂×C₃	C₂×#4047	1	1	yes	characteristic
343	C₂×C₃	#66079	1	1	yes	characteristic
344	C₅	C₃×#2962	1	1	yes	characteristic, complemented, Sylow
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	C₃×#4033	1	2	yes	—
348	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	10	4	no	—
353	C₄	—	10	4	no	—
354	C₄	C₃×#4033	1	2	yes	—
355	C₄	C₃×#4047	1	2	yes	—
356	C₄	C₂×C₃×#711	1	1	yes	characteristic
357	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
358	C₃	#10610739	1	1	yes	characteristic, direct product factor, Sylow
359	C₂	—	2	2	no	—
360	C₂	C₂×C₃×#4033	1	1	yes	characteristic
361	C₂	C₂×C₃×#4047	1	1	yes	characteristic
362	C₂	C₃×#66079	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#2962
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
6. C₃×#65120	C₂	semidirect
7. C₃×#65119	C₂	semidirect
8. C₃×#65117	C₂	semidirect
9. #10610739	C₃	direct (N × H)
37. #65120	C₂×C₃	semidirect
38. #65119	C₂×C₃	semidirect
39. #65117	C₂×C₃	semidirect
61. C₃×#681	Q₈	semidirect
155. #681	C₃×Q₈	semidirect
303. C₃×C₅	#2962	semidirect
344. C₅	C₃×#2962	semidirect
358. C₃	#10610739	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×#65804	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×#65391	2
C₃×#65390	2
C₃×C₄×#681	2
C₃×#65120	2
C₃×#65119	2
C₃×#65117	2
#10610739	3
C₃×#2962	5

Subgroups — C3×#10610739 #14418658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610739 #14418658