Subgroups — C₃×#10610248 #14413910

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65415	C₂	1	2	yes	maximal
4	C₃×#65407	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64994	C₂	1	4	yes	maximal, complemented
7	C₃×#64974	C₂	1	4	yes	maximal, complemented
8	#10610248	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₄×D₅	C₄	1	2	yes	—
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	2	yes	—
16	C₃×C₄²×D₅	C₄	1	2	yes	—
17	C₃×C₄²×D₅	C₄	1	2	yes	—
18	C₃×C₄²×D₅	C₂²	1	2	yes	—
19	C₃×C₄²×D₅	C₂²	1	2	yes	—
20	C₃×C₅×#97	C₂²	1	2	yes	complemented
21	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
22	C₃×#3952	C₂²	1	8	yes	—
23	C₃×#3946	C₂²	1	8	yes	complemented
24	C₃×#3935	C₂²	1	2	yes	complemented
25	C₃×C₄×#168	C₂²	1	2	yes	complemented
26	C₃×#2920	—	5	1	no	maximal, Hall
27	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
28	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	#65415	C₂×C₃	1	2	yes	—
30	#65407	C₂×C₃	1	2	yes	complemented
31	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
32	#64994	C₂×C₃	1	4	yes	complemented
33	#64974	C₂×C₃	1	4	yes	complemented
34	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
38	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	—	2	4	no	—
40	C₂×C₃×C₄×D₅	—	2	8	no	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	4	no	—
48	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
49	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
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×C₄×Dic₅	C₂×C₄	1	2	yes	—
58	C₃×C₄×Dic₅	C₂³	1	2	yes	—
59	C₃×#681	—	2	4	no	—
60	C₂×C₃×#168	C₂³	1	4	yes	—
61	C₂²×C₃×C₄²	—	5	1	no	—
62	C₃×#432	—	5	4	no	—
63	C₃×#431	—	5	4	no	—
64	C₃×#423	—	5	2	no	—
65	C₃×#407	—	5	2	no	—
66	C₃×C₄×M₁₆	—	5	1	no	—
67	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
68	C₂²×C₄×D₅	C₃×C₄	1	2	yes	—
69	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
73	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×#681	C₂²×C₃	1	2	yes	—
75	C₄²×D₅	C₃×C₄	1	2	yes	—
76	C₄²×D₅	C₃×C₄	1	2	yes	—
77	C₄²×D₅	C₂²×C₃	1	2	yes	—
78	C₄²×D₅	C₂²×C₃	1	2	yes	—
79	C₅×#97	C₂²×C₃	1	2	yes	complemented
80	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
81	#3952	C₂²×C₃	1	8	yes	—
82	#3946	C₂²×C₃	1	8	yes	complemented
83	#3935	C₂²×C₃	1	2	yes	complemented
84	C₄×#168	C₂²×C₃	1	2	yes	complemented
85	#2920	—	5	1	no	Sylow
86	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₃×D₅	—	2	2	no	—
88	C₂²×C₃×D₅	—	2	4	no	—
89	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	4	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×Dic₅	—	2	2	no	—
97	C₂×C₃×Dic₅	—	2	4	no	—
98	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
101	C₃×C₄×D₅	—	2	4	no	—
102	C₃×C₄×D₅	—	2	4	no	—
103	C₃×C₄×D₅	—	2	4	no	—
104	C₃×C₄×D₅	—	2	4	no	—
105	C₃×C₄×D₅	—	2	4	no	—
106	C₃×C₄×D₅	M₁₆	1	8	yes	complemented
107	C₃×C₅×C₈	—	2	4	no	—
108	C₃×#168	—	2	4	no	—
109	C₂³×C₃×C₄	—	5	2	no	—
110	C₂³×C₃×C₄	—	5	1	no	—
111	C₂×C₃×M₁₆	—	5	2	no	—
112	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
113	C₂×C₃×C₄²	—	5	2	no	—
114	C₂×C₃×C₄²	—	5	1	no	—
115	C₂×C₃×C₄²	—	5	2	no	—
116	C₂×C₃×C₄²	—	5	2	no	—
117	C₂×C₃×C₄²	—	5	2	no	—
118	C₂×C₃×C₄²	—	5	2	no	—
119	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
120	C₃×C₄⋊C₈	—	5	8	no	—
121	C₃×C₂²⋊C₈	—	5	8	no	—
122	C₃×#97	—	5	2	no	—
123	C₃×#97	C₂×D₅	1	2	yes	complemented
124	C₃×C₄×C₈	—	5	2	no	—
125	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
126	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
130	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂×C₄×D₅	—	2	4	no	—
132	C₂×C₄×D₅	—	2	8	no	—
133	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
134	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
136	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
139	C₅×M₁₆	—	2	4	no	—
140	C₂×C₅×C₈	C₂³×C₃	1	4	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	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
145	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
146	C₄×Dic₅	C₂×C₃×C₄	1	2	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	C₂³×C₃	1	2	yes	—
151	#681	—	2	4	no	—
152	C₂×#168	C₂³×C₃	1	4	yes	—
153	C₂²×C₄²	—	5	1	no	—
154	#432	—	5	4	no	—
155	#431	—	5	4	no	—
156	#423	—	5	2	no	—
157	#407	—	5	2	no	—
158	C₄×M₁₆	—	5	1	no	—
159	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	#117	1	2	yes	—
162	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₃×D₅	—	2	8	no	—
164	C₂×C₃×D₅	—	2	2	no	—
165	C₂×C₃×D₅	—	2	2	no	—
166	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	#117	1	2	yes	—
169	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	—
170	C₃×C₄×C₅	C₂×#41	1	2	yes	—
171	C₃×Dic₅	—	2	2	no	—
172	C₃×Dic₅	—	2	2	no	—
173	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
174	C₂⁴×C₃	—	5	1	no	—
175	C₂²×C₃×C₄	—	5	2	no	—
176	C₂²×C₃×C₄	—	5	2	no	—
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	2	no	—
179	C₂²×C₃×C₄	—	5	2	no	—
180	C₂²×C₃×C₄	—	5	2	no	—
181	C₂²×C₃×C₄	—	5	2	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	—	10	8	no	—
184	C₂²×C₃×C₄	—	10	4	no	—
185	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
187	C₃×M₁₆	—	2	4	no	—
188	C₃×M₁₆	—	10	4	no	—
189	C₂×C₃×C₈	—	5	4	no	—
190	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
191	C₃×C₄²	—	5	1	no	—
192	C₃×C₄²	—	5	2	no	—
193	C₃×C₄²	—	5	2	no	—
194	C₃×C₄²	—	5	2	no	—
195	C₃×C₄²	—	5	1	no	—
196	C₃×C₄²	—	5	2	no	—
197	C₃×C₄²	—	5	2	no	—
198	C₃×C₄²	C₄×D₅	1	2	yes	—
199	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
200	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
201	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₂²×D₅	—	2	2	no	—
203	C₂²×D₅	—	2	4	no	—
204	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
207	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
209	C₂×C₄×C₅	C₃×#41	1	4	yes	—
210	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
211	C₂×Dic₅	—	2	2	no	—
212	C₂×Dic₅	—	2	4	no	—
213	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
214	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
215	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
216	C₄×D₅	—	2	4	no	—
217	C₄×D₅	—	2	4	no	—
218	C₄×D₅	—	2	4	no	—
219	C₄×D₅	—	2	4	no	—
220	C₄×D₅	—	2	4	no	—
221	C₄×D₅	C₃×M₁₆	1	8	yes	complemented
222	C₅×C₈	—	2	4	no	—
223	#168	—	2	4	no	—
224	C₂³×C₄	—	5	2	no	—
225	C₂³×C₄	—	5	1	no	—
226	C₂×M₁₆	—	5	2	no	—
227	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
228	C₂×C₄²	—	5	2	no	—
229	C₂×C₄²	—	5	1	no	—
230	C₂×C₄²	—	5	2	no	—
231	C₂×C₄²	—	5	2	no	—
232	C₂×C₄²	—	5	2	no	—
233	C₂×C₄²	—	5	2	no	—
234	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
235	C₄⋊C₈	—	5	8	no	—
236	C₂²⋊C₈	—	5	8	no	—
237	#97	—	5	2	no	—
238	#97	C₂×C₃×D₅	1	2	yes	complemented
239	C₄×C₈	—	5	2	no	—
240	C₄×C₈	C₂×C₃×D₅	1	2	yes	complemented
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
244	C₃×D₅	—	2	4	no	—
245	C₂³×C₃	—	5	2	no	—
246	C₂³×C₃	—	10	4	no	—
247	C₂³×C₃	—	10	2	no	—
248	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	5	2	no	—
251	C₂×C₃×C₄	—	5	8	no	—
252	C₂×C₃×C₄	—	5	2	no	—
253	C₂×C₃×C₄	—	5	2	no	—
254	C₂×C₃×C₄	—	10	4	no	—
255	C₂×C₃×C₄	—	10	4	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	—	10	2	no	—
258	C₂×C₃×C₄	—	10	4	no	—
259	C₂×C₃×C₄	—	10	4	no	—
260	C₂×C₃×C₄	—	10	4	no	—
261	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
264	C₂×C₃×C₄	#709	1	4	yes	—
265	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
266	C₃×C₈	—	2	4	no	—
267	C₃×C₈	—	10	4	no	—
268	C₂²×C₅	—	2	2	no	—
269	C₂²×C₅	C₃×#117	1	2	yes	—
270	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
271	C₂×D₅	—	2	8	no	—
272	C₂×D₅	—	2	2	no	—
273	C₂×D₅	—	2	2	no	—
274	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	—
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	C₃×#117	1	2	yes	—
277	C₄×C₅	C₂×C₃×M₁₆	1	4	yes	—
278	C₄×C₅	C₂×C₃×#41	1	2	yes	—
279	Dic₅	—	2	2	no	—
280	Dic₅	—	2	2	no	—
281	Dic₅	C₂×C₃×M₁₆	1	4	yes	—
282	C₂⁴	—	5	1	no	—
283	C₂²×C₄	—	5	2	no	—
284	C₂²×C₄	—	5	2	no	—
285	C₂²×C₄	—	5	1	no	—
286	C₂²×C₄	—	5	2	no	—
287	C₂²×C₄	—	5	2	no	—
288	C₂²×C₄	—	5	2	no	—
289	C₂²×C₄	—	5	2	no	—
290	C₂²×C₄	—	5	2	no	—
291	C₂²×C₄	—	10	8	no	—
292	C₂²×C₄	—	10	4	no	—
293	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
294	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
295	M₁₆	—	2	4	no	—
296	M₁₆	—	10	4	no	—
297	C₂×C₈	—	5	4	no	—
298	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
299	C₄²	—	5	1	no	—
300	C₄²	—	5	2	no	—
301	C₄²	—	5	2	no	—
302	C₄²	—	5	2	no	—
303	C₄²	—	5	1	no	—
304	C₄²	—	5	2	no	—
305	C₄²	—	5	2	no	—
306	C₄²	C₃×C₄×D₅	1	2	yes	—
307	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
308	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
309	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	5	4	no	—
312	C₂²×C₃	—	10	8	no	—
313	C₂²×C₃	—	10	2	no	—
314	C₂²×C₃	—	10	2	no	—
315	C₂²×C₃	#4018	1	2	yes	—
316	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	5	4	no	—
319	C₃×C₄	—	10	2	no	—
320	C₃×C₄	—	10	2	no	—
321	C₃×C₄	#4018	1	2	yes	—
322	C₃×C₄	D₅×M₁₆	1	4	yes	—
323	C₃×C₄	C₂×#709	1	2	yes	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
326	C₂×C₅	C₂²×C₃×M₁₆	1	2	yes	—
327	D₅	—	2	4	no	—
328	C₂³	—	5	2	no	—
329	C₂³	—	10	4	no	—
330	C₂³	—	10	2	no	—
331	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	5	2	no	—
334	C₂×C₄	—	5	8	no	—
335	C₂×C₄	—	5	2	no	—
336	C₂×C₄	—	5	2	no	—
337	C₂×C₄	—	10	4	no	—
338	C₂×C₄	—	10	4	no	—
339	C₂×C₄	—	10	4	no	—
340	C₂×C₄	—	10	2	no	—
341	C₂×C₄	—	10	4	no	—
342	C₂×C₄	—	10	4	no	—
343	C₂×C₄	—	10	4	no	—
344	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
345	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
346	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
347	C₂×C₄	C₃×#709	1	4	yes	—
348	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₈	—	10	4	no	—
351	C₂×C₃	—	2	2	no	—
352	C₂×C₃	—	10	4	no	—
353	C₂×C₃	C₂×#4018	1	1	yes	characteristic
354	C₂×C₃	C₂×D₅×M₁₆	1	2	yes	—
355	C₅	C₃×#2920	1	1	yes	characteristic, complemented, Sylow
356	C₂²	—	2	2	no	—
357	C₂²	—	5	4	no	—
358	C₂²	—	10	8	no	—
359	C₂²	—	10	2	no	—
360	C₂²	—	10	2	no	—
361	C₂²	C₃×#4018	1	2	yes	—
362	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	5	4	no	—
365	C₄	—	10	2	no	—
366	C₄	—	10	2	no	—
367	C₄	C₃×#4018	1	2	yes	—
368	C₄	C₃×D₅×M₁₆	1	4	yes	—
369	C₄	C₂×C₃×#709	1	2	yes	—
370	C₃	#10610248	1	1	yes	characteristic, direct product factor, Sylow
371	C₂	—	2	2	no	—
372	C₂	—	10	4	no	—
373	C₂	C₂×C₃×#4018	1	1	yes	characteristic
374	C₂	C₂×C₃×D₅×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×#2920
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₃×#65407	C₂	semidirect
5. C₃×C₄×#681	C₂	semidirect
6. C₃×#64994	C₂	semidirect
7. C₃×#64974	C₂	semidirect
8. #10610248	C₃	direct (N × H)
20. C₃×C₅×#97	C₂²	semidirect
21. C₃×C₄×C₅×C₈	C₂²	semidirect
23. C₃×#3946	C₂²	semidirect
24. C₃×#3935	C₂²	semidirect
25. C₃×C₄×#168	C₂²	semidirect
28. C₄×C₅×M₁₆	C₂×C₃	semidirect
30. #65407	C₂×C₃	semidirect
31. C₄×#681	C₂×C₃	semidirect
32. #64994	C₂×C₃	semidirect
33. #64974	C₂×C₃	semidirect
67. C₃×C₄×M₁₆	D₅	semidirect
79. C₅×#97	C₂²×C₃	semidirect
80. C₄×C₅×C₈	C₂²×C₃	semidirect
82. #3946	C₂²×C₃	semidirect
83. #3935	C₂²×C₃	semidirect
84. C₄×#168	C₂²×C₃	semidirect
106. C₃×C₄×D₅	M₁₆	semidirect
123. C₃×#97	C₂×D₅	semidirect
125. C₃×C₄×C₈	C₂×D₅	semidirect
159. C₄×M₁₆	C₃×D₅	semidirect
221. C₄×D₅	C₃×M₁₆	semidirect
238. #97	C₂×C₃×D₅	semidirect
240. C₄×C₈	C₂×C₃×D₅	semidirect
309. C₃×C₅	#2920	semidirect
355. C₅	C₃×#2920	semidirect
370. C₃	#10610248	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×C₄²×D₅	2
C₃×C₄×C₅×M₁₆	2
C₃×#65415	2
C₃×#65407	2
C₃×C₄×#681	2
C₃×#64994	2
C₃×#64974	2
#10610248	3
C₃×#2920	5

Subgroups — C3×#10610248 #14413910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610248 #14413910