Subgroups — C₃×#10610350 #14413904

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic
3	C₃×#65496	C₂	1	1	yes	maximal, characteristic
4	C₃×#65407	C₂	1	2	yes	maximal, complemented
5	C₃×M₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
6	C₃×#65008	C₂	1	4	yes	maximal, complemented
7	C₃×#65007	C₂	1	4	yes	maximal, complemented
8	#10610350	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×Dic₅	C₄	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
13	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	—
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×#681	C₂²	1	2	yes	—
20	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
21	C₃×C₂²⋊#168	C₂²	1	4	yes	—
22	C₃×#3947	C₂²	1	4	yes	complemented
23	C₃×#3946	C₂²	1	8	yes	complemented
24	C₃×C₈×Dic₅	C₂²	1	4	yes	complemented
25	C₃×#2920	—	5	1	no	maximal, Hall
26	C₂²×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
27	C₅×#407	C₂×C₃	1	1	yes	characteristic
28	#65496	C₂×C₃	1	1	yes	characteristic
29	#65407	C₂×C₃	1	2	yes	complemented
30	M₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
31	#65008	C₂×C₃	1	4	yes	complemented
32	#65007	C₂×C₃	1	4	yes	complemented
33	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₅	—	2	8	no	—
40	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
41	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
44	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
45	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
46	C₃×C₅×M₁₆	—	2	4	no	—
47	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
48	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
49	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
51	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
52	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
53	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
54	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
56	C₃×C₄×Dic₅	C₂³	1	2	yes	—
57	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
58	C₃×#681	—	2	4	no	—
59	C₂×C₃×#168	C₂³	1	4	yes	—
60	C₂²×C₃×C₄²	—	5	1	no	—
61	C₃×#432	—	5	4	no	—
62	C₃×#431	—	5	4	no	—
63	C₃×#423	—	5	2	no	—
64	C₃×#407	—	5	1	no	—
65	C₃×#407	D₅	1	1	yes	characteristic
66	C₃×C₄×M₁₆	—	5	2	no	—
67	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₂³×Dic₅	C₃×C₄	1	2	yes	—
69	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
70	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
71	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
72	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	—
73	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
76	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
77	C₂×#681	C₂²×C₃	1	2	yes	—
78	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
79	C₂²⋊#168	C₂²×C₃	1	4	yes	—
80	#3947	C₂²×C₃	1	4	yes	complemented
81	#3946	C₂²×C₃	1	8	yes	complemented
82	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
83	#2920	—	5	1	no	Sylow
84	C₂³×C₃×C₅	—	2	2	no	—
85	C₂³×C₃×C₅	—	2	4	no	—
86	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
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	#41	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
95	C₂×C₃×Dic₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	4	no	—
97	C₂×C₃×Dic₅	—	2	4	no	—
98	C₂×C₃×Dic₅	—	2	4	no	—
99	C₂×C₃×Dic₅	—	2	4	no	—
100	C₂×C₃×Dic₅	M₁₆	1	8	yes	complemented
101	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
105	C₃×C₅×C₈	—	2	4	no	—
106	C₃×#168	—	2	4	no	—
107	C₂³×C₃×C₄	—	5	2	no	—
108	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
109	C₂×C₃×M₁₆	—	5	2	no	—
110	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
111	C₂×C₃×C₄²	—	5	2	no	—
112	C₂×C₃×C₄²	—	5	2	no	—
113	C₂×C₃×C₄²	—	5	2	no	—
114	C₂×C₃×C₄²	—	5	1	no	—
115	C₂×C₃×C₄²	—	5	1	no	—
116	C₂×C₃×C₄²	—	5	2	no	—
117	C₂×C₃×C₄²	—	5	2	no	—
118	C₃×C₄⋊C₈	—	5	8	no	—
119	C₃×C₂²⋊C₈	—	5	4	no	—
120	C₃×C₂²⋊C₈	C₂×D₅	1	4	yes	—
121	C₃×#97	—	5	4	no	—
122	C₃×C₄×C₈	—	5	4	no	—
123	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×Dic₅	—	2	8	no	—
130	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
131	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
132	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
133	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
134	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
135	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
136	C₅×M₁₆	—	2	4	no	—
137	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
138	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
139	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
140	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
141	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
142	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
143	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
144	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
145	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
146	C₄×Dic₅	C₂³×C₃	1	2	yes	—
147	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
148	#681	—	2	4	no	—
149	C₂×#168	C₂³×C₃	1	4	yes	—
150	C₂²×C₄²	—	5	1	no	—
151	#432	—	5	4	no	—
152	#431	—	5	4	no	—
153	#423	—	5	2	no	—
154	#407	—	5	1	no	—
155	#407	C₃×D₅	1	1	yes	characteristic
156	C₄×M₁₆	—	5	2	no	—
157	C₂²×C₃×C₅	—	2	8	no	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	#117	1	2	yes	—
162	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
163	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	#117	1	2	yes	—
166	C₃×C₄×C₅	C₂×#41	1	2	yes	—
167	C₃×Dic₅	—	2	2	no	—
168	C₃×Dic₅	—	2	2	no	—
169	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
170	C₃×Dic₅	C₂×M₁₆	1	4	yes	—
171	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	5	2	no	—
174	C₂²×C₃×C₄	—	5	2	no	—
175	C₂²×C₃×C₄	—	5	2	no	—
176	C₂²×C₃×C₄	—	5	2	no	—
177	C₂²×C₃×C₄	—	5	2	no	—
178	C₂²×C₃×C₄	—	5	2	no	—
179	C₂²×C₃×C₄	—	10	8	no	—
180	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
182	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
183	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
184	C₃×M₁₆	—	2	4	no	—
185	C₃×M₁₆	—	10	4	no	—
186	C₂×C₃×C₈	—	5	4	no	—
187	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
188	C₃×C₄²	—	5	2	no	—
189	C₃×C₄²	—	5	1	no	—
190	C₃×C₄²	—	5	2	no	—
191	C₃×C₄²	—	5	2	no	—
192	C₃×C₄²	—	5	2	no	—
193	C₃×C₄²	—	5	2	no	—
194	C₃×C₄²	—	5	1	no	—
195	C₃×C₄²	—	5	1	no	—
196	C₃×C₄²	—	5	1	no	—
197	C₃×C₄²	—	5	2	no	—
198	C₂³×C₅	—	2	2	no	—
199	C₂³×C₅	—	2	4	no	—
200	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
201	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₃×#41	1	4	yes	—
208	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
209	C₂×Dic₅	—	2	4	no	—
210	C₂×Dic₅	—	2	4	no	—
211	C₂×Dic₅	—	2	4	no	—
212	C₂×Dic₅	—	2	4	no	—
213	C₂×Dic₅	—	2	4	no	—
214	C₂×Dic₅	C₃×M₁₆	1	8	yes	complemented
215	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
216	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
217	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
218	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
219	C₅×C₈	—	2	4	no	—
220	#168	—	2	4	no	—
221	C₂³×C₄	—	5	2	no	—
222	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
223	C₂×M₁₆	—	5	2	no	—
224	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
225	C₂×C₄²	—	5	2	no	—
226	C₂×C₄²	—	5	2	no	—
227	C₂×C₄²	—	5	2	no	—
228	C₂×C₄²	—	5	1	no	—
229	C₂×C₄²	—	5	1	no	—
230	C₂×C₄²	—	5	2	no	—
231	C₂×C₄²	—	5	2	no	—
232	C₄⋊C₈	—	5	8	no	—
233	C₂²⋊C₈	—	5	4	no	—
234	C₂²⋊C₈	C₂×C₃×D₅	1	4	yes	—
235	#97	—	5	4	no	—
236	C₄×C₈	—	5	4	no	—
237	C₂×C₃×C₅	—	2	2	no	—
238	C₂×C₃×C₅	—	2	4	no	—
239	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
240	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
241	C₂³×C₃	—	2	2	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
244	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	5	2	no	—
249	C₂×C₃×C₄	—	5	2	no	—
250	C₂×C₃×C₄	—	5	8	no	—
251	C₂×C₃×C₄	—	5	2	no	—
252	C₂×C₃×C₄	—	5	2	no	—
253	C₂×C₃×C₄	—	10	4	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	4	no	—
258	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	#711	1	4	yes	—
261	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
262	C₃×C₈	—	2	4	no	—
263	C₃×C₈	—	10	4	no	—
264	C₂²×C₅	—	2	8	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	C₃×#117	1	2	yes	—
269	C₂²×C₅	C₂×C₃×M₁₆	1	4	yes	—
270	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
271	C₄×C₅	—	2	2	no	—
272	C₄×C₅	C₃×#117	1	2	yes	—
273	C₄×C₅	C₂×C₃×#41	1	2	yes	—
274	Dic₅	—	2	2	no	—
275	Dic₅	—	2	2	no	—
276	Dic₅	C₂×C₃×M₁₆	1	4	yes	—
277	Dic₅	C₂×C₃×M₁₆	1	4	yes	—
278	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	5	2	no	—
281	C₂²×C₄	—	5	2	no	—
282	C₂²×C₄	—	5	2	no	—
283	C₂²×C₄	—	5	2	no	—
284	C₂²×C₄	—	5	2	no	—
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	10	8	no	—
287	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
288	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
289	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
290	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
291	M₁₆	—	2	4	no	—
292	M₁₆	—	10	4	no	—
293	C₂×C₈	—	5	4	no	—
294	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
295	C₄²	—	5	2	no	—
296	C₄²	—	5	1	no	—
297	C₄²	—	5	2	no	—
298	C₄²	—	5	2	no	—
299	C₄²	—	5	2	no	—
300	C₄²	—	5	2	no	—
301	C₄²	—	5	1	no	—
302	C₄²	—	5	1	no	—
303	C₄²	—	5	1	no	—
304	C₄²	—	5	2	no	—
305	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
306	C₂²×C₃	—	2	8	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	#4023	1	2	yes	—
311	C₂²×C₃	D₅×M₁₆	1	4	yes	—
312	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	5	4	no	—
315	C₃×C₄	—	5	4	no	—
316	C₃×C₄	—	10	2	no	—
317	C₃×C₄	—	10	2	no	—
318	C₃×C₄	#4023	1	2	yes	—
319	C₃×C₄	C₂×#711	1	2	yes	—
320	C₂×C₅	—	2	2	no	—
321	C₂×C₅	—	2	4	no	—
322	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
323	C₂×C₅	C₂²×C₃×M₁₆	1	2	yes	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	4	no	—
326	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
327	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	5	2	no	—
332	C₂×C₄	—	5	2	no	—
333	C₂×C₄	—	5	8	no	—
334	C₂×C₄	—	5	2	no	—
335	C₂×C₄	—	5	2	no	—
336	C₂×C₄	—	10	4	no	—
337	C₂×C₄	—	10	4	no	—
338	C₂×C₄	—	10	4	no	—
339	C₂×C₄	—	10	4	no	—
340	C₂×C₄	—	10	4	no	—
341	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
342	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
343	C₂×C₄	C₃×#711	1	4	yes	—
344	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
345	C₈	—	2	4	no	—
346	C₈	—	10	4	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	C₂×#4023	1	1	yes	characteristic
350	C₂×C₃	C₂×D₅×M₁₆	1	2	yes	—
351	C₅	C₃×#2920	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	2	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	C₃×#4023	1	2	yes	—
357	C₂²	C₃×D₅×M₁₆	1	4	yes	—
358	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	5	4	no	—
361	C₄	—	5	4	no	—
362	C₄	—	10	2	no	—
363	C₄	—	10	2	no	—
364	C₄	C₃×#4023	1	2	yes	—
365	C₄	C₂×C₃×#711	1	2	yes	—
366	C₃	#10610350	1	1	yes	characteristic, direct product factor, Sylow
367	C₂	—	2	2	no	—
368	C₂	—	2	4	no	—
369	C₂	C₂×C₃×#4023	1	1	yes	characteristic
370	C₂	C₂×C₃×D₅×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#407	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#407	D₅
hypocenter	C₅	C₃×#2920
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#407

Complements

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

N	H ≅ G/N	type
4. C₃×#65407	C₂	semidirect
5. C₃×M₁₆×Dic₅	C₂	semidirect
6. C₃×#65008	C₂	semidirect
7. C₃×#65007	C₂	semidirect
8. #10610350	C₃	direct (N × H)
22. C₃×#3947	C₂²	semidirect
23. C₃×#3946	C₂²	semidirect
24. C₃×C₈×Dic₅	C₂²	semidirect
29. #65407	C₂×C₃	semidirect
30. M₁₆×Dic₅	C₂×C₃	semidirect
31. #65008	C₂×C₃	semidirect
32. #65007	C₂×C₃	semidirect
80. #3947	C₂²×C₃	semidirect
81. #3946	C₂²×C₃	semidirect
82. C₈×Dic₅	C₂²×C₃	semidirect
100. C₂×C₃×Dic₅	M₁₆	semidirect
214. C₂×Dic₅	C₃×M₁₆	semidirect
305. C₃×C₅	#2920	semidirect
351. C₅	C₃×#2920	semidirect
366. C₃	#10610350	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×C₄×Dic₅	2
C₃×C₅×#407	2
C₃×#65496	2
C₃×#65407	2
C₃×M₁₆×Dic₅	2
C₃×#65008	2
C₃×#65007	2
#10610350	3
C₃×#2920	5

Subgroups — C3×#10610350 #14413904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610350 #14413904