Subgroups — C₃×C₄×#1220 #13088025

Order 1440.

430 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1220	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6719	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6712	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#1220	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×C₄×C₂²⋊D₅	—	3	1	no	maximal
10	C₂³×C₃²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×D₁₅	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄×C₅	—	2	2	no	—
13	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×#1220	C₄	1	4	yes	direct product factor
16	C₂×C₃×Dic₁₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×Dic₁₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×Dic₁₅	C₂²	1	1	yes	characteristic
19	C₃×C₄×D₁₅	—	2	2	no	—
20	C₃×C₄×#67	—	5	1	no	maximal, Hall
21	C₂²×C₃×C₄×C₅	—	2	1	no	—
22	C₂²×C₃×C₄×C₅	D₃	1	1	yes	characteristic, complemented
23	C₂²×C₃×C₄×C₅	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×#1220	C₂×C₃	1	1	yes	characteristic
25	C₂×C₄×D₁₅	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×C₂²⋊D₅	—	3	1	no	—
27	C₂×C₃×C₄×D₅	—	3	1	no	—
28	#6719	C₂×C₃	1	1	yes	characteristic, complemented
29	#6714	C₂×C₃	1	1	yes	characteristic, complemented
30	#6712	C₂×C₃	1	1	yes	characteristic, complemented
31	C₄×Dic₁₅	C₂×C₃	1	1	yes	characteristic, complemented
32	C₃×C₂²⋊Dic₅	—	3	1	no	—
33	C₃×#685	—	3	1	no	—
34	C₃×#683	—	3	1	no	—
35	C₃×C₄×Dic₅	—	3	1	no	—
36	C₂²×C₃²×C₅	—	2	1	no	—
37	C₂²×C₃²×C₅	—	2	1	no	—
38	C₂²×C₃²×C₅	C₂×C₄	1	2	yes	complemented
39	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×D₁₅	—	2	1	no	—
41	C₂×C₃×D₁₅	—	2	1	no	—
42	C₂×C₃×D₁₅	C₂×C₄	1	2	yes	complemented
43	C₃²×C₄×C₅	—	2	1	no	—
44	C₃²×C₄×C₅	D₄	1	2	yes	complemented
45	C₃×Dic₁₅	—	2	1	no	—
46	C₃×Dic₁₅	—	2	1	no	—
47	C₃×Dic₁₅	C₂×C₄	1	2	yes	complemented
48	C₄×C₂²⋊D₅	—	3	1	no	Hall
49	C₂²×C₃²×C₄	D₅	1	1	yes	characteristic, complemented
50	C₂×C₃×#67	—	5	1	no	—
51	C₂×C₃×C₄×D₃	—	5	1	no	—
52	C₃×#217	—	5	1	no	—
53	C₃×(C₂×D₃)⋊C₄	—	5	1	no	—
54	C₃×Dic₃⋊C₄	—	5	1	no	—
55	C₃×C₄×Dic₃	—	5	1	no	—
56	C₂³×C₃×C₅	—	2	1	no	—
57	C₂³×C₃×C₅	C₂×D₃	1	1	yes	characteristic
58	C₂³×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
59	C₂²×D₁₅	C₂²×C₃	1	1	yes	characteristic
60	C₂²×C₃×D₅	—	3	1	no	—
61	C₂×C₃×C₄×C₅	—	2	4	no	—
62	C₂×C₃×C₄×C₅	—	2	1	no	—
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	—	2	2	no	—
65	C₂×C₃×C₄×C₅	—	2	2	no	—
66	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
67	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
70	#1220	C₃×C₄	1	4	yes	direct product factor
71	C₂×Dic₁₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×Dic₁₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×Dic₁₅	C₂²×C₃	1	1	yes	characteristic
74	C₄×D₁₅	—	2	2	no	—
75	C₃×C₂²⋊D₅	—	3	4	no	—
76	C₂×C₃×Dic₅	—	3	1	no	—
77	C₂×C₃×Dic₅	—	3	1	no	—
78	C₂×C₃×Dic₅	—	3	1	no	—
79	C₃×C₄×D₅	—	6	2	no	—
80	C₃×C₄×D₄	—	15	1	no	—
81	C₄×#67	—	5	1	no	—
82	C₂×C₃²×C₅	—	2	2	no	—
83	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃²×C₅	#41	1	1	yes	characteristic
86	C₃×D₁₅	—	2	2	no	—
87	C₂²×C₄×C₅	C₃×D₃	1	1	yes	characteristic, complemented
88	C₂×C₂²⋊D₅	—	3	1	no	—
89	C₂×C₄×D₅	—	3	1	no	—
90	C₂²⋊Dic₅	—	3	1	no	—
91	#685	—	3	1	no	—
92	#683	—	3	1	no	—
93	C₄×Dic₅	—	3	1	no	—
94	C₂³×C₃²	C₂×D₅	1	1	yes	characteristic
95	C₂²×C₃×D₃	—	5	1	no	—
96	C₂×C₃²×C₄	—	2	2	no	—
97	C₂×C₃²×C₄	C₂×D₅	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂×D₅	1	1	yes	characteristic
99	C₃×#67	—	5	4	no	—
100	C₂×C₃×Dic₃	—	5	1	no	—
101	C₂×C₃×Dic₃	—	5	1	no	—
102	C₂×C₃×Dic₃	—	5	1	no	—
103	C₃×C₄×D₃	—	10	2	no	—
104	C₂²×C₃×C₅	—	2	2	no	—
105	C₂²×C₃×C₅	—	2	2	no	—
106	C₂²×C₃×C₅	—	2	1	no	—
107	C₂²×C₃×C₅	—	2	1	no	—
108	C₂²×C₃×C₅	—	2	1	no	—
109	C₂²×C₃×C₅	—	2	1	no	—
110	C₂²×C₃×C₅	—	2	2	no	—
111	C₂²×C₃×C₅	—	2	1	no	—
112	C₂²×C₃×C₅	C₄×D₃	1	2	yes	complemented
113	C₂²×C₃×C₅	C₂×C₃×C₄	1	2	yes	complemented
114	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
115	C₂²×C₃×C₅	C₂³×C₃	1	1	yes	characteristic
116	C₂×D₁₅	—	2	1	no	—
117	C₂×D₁₅	—	2	1	no	—
118	C₂×D₁₅	C₂×C₃×C₄	1	2	yes	complemented
119	C₂×C₃×D₅	—	3	2	no	—
120	C₂×C₃×D₅	—	6	1	no	—
121	C₂×C₃×D₅	—	6	1	no	—
122	C₃×C₄×C₅	—	2	2	no	—
123	C₃×C₄×C₅	—	2	1	no	—
124	C₃×C₄×C₅	—	2	1	no	—
125	C₃×C₄×C₅	—	2	2	no	—
126	C₃×C₄×C₅	#67	1	2	yes	complemented
127	C₃×C₄×C₅	C₃×D₄	1	2	yes	complemented
128	Dic₁₅	—	2	1	no	—
129	Dic₁₅	—	2	1	no	—
130	Dic₁₅	C₂×C₃×C₄	1	2	yes	complemented
131	C₃×Dic₅	—	3	2	no	—
132	C₃×Dic₅	—	6	1	no	—
133	C₃×Dic₅	—	6	1	no	—
134	C₂×C₃×D₄	—	15	1	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	15	1	no	—
137	C₂²×C₃×C₄	C₃×D₅	1	1	yes	characteristic, complemented
138	C₂²×C₃×C₄	D₁₅	1	1	yes	characteristic, complemented
139	C₂×#67	—	5	1	no	—
140	C₂×C₄×D₃	—	5	1	no	—
141	C₃×C₄⋊C₄	—	15	1	no	—
142	C₃×C₂²⋊C₄	—	15	1	no	—
143	C₃×C₂²⋊C₄	—	15	1	no	—
144	C₃×C₄²	—	15	1	no	—
145	#217	—	5	1	no	—
146	(C₂×D₃)⋊C₄	—	5	1	no	—
147	Dic₃⋊C₄	—	5	1	no	—
148	C₄×Dic₃	—	5	1	no	—
149	C₃²×C₅	C₄×D₄	1	1	yes	characteristic, complemented, Hall
150	C₂³×C₅	C₂×C₃×D₃	1	1	yes	characteristic
151	C₂²×D₅	—	3	1	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	C₂×C₃×D₃	1	1	yes	characteristic
154	C₂×C₄×C₅	C₂×C₃×D₃	1	1	yes	characteristic
155	C₂²⋊D₅	—	3	4	no	—
156	C₂×Dic₅	—	3	1	no	—
157	C₂×Dic₅	—	3	1	no	—
158	C₂×Dic₅	—	3	1	no	—
159	C₄×D₅	—	6	2	no	—
160	C₂²×C₃²	—	2	1	no	—
161	C₂²×C₃²	—	2	1	no	—
162	C₂²×C₃²	C₄×D₅	1	2	yes	complemented
163	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
164	C₂×C₃×D₃	—	5	2	no	—
165	C₂×C₃×D₃	—	10	1	no	—
166	C₂×C₃×D₃	—	10	1	no	—
167	C₃²×C₄	—	2	1	no	—
168	C₃²×C₄	C₂²⋊D₅	1	2	yes	complemented
169	C₃×Dic₃	—	5	2	no	—
170	C₃×Dic₃	—	10	1	no	—
171	C₃×Dic₃	—	10	1	no	—
172	C₄×D₄	—	15	1	no	Sylow
173	C₂×C₃×C₅	—	2	4	no	—
174	C₂×C₃×C₅	—	2	2	no	—
175	C₂×C₃×C₅	—	2	2	no	—
176	C₂×C₃×C₅	—	2	1	no	—
177	C₂×C₃×C₅	—	2	1	no	—
178	C₂×C₃×C₅	—	2	1	no	—
179	C₂×C₃×C₅	C₂×C₄×D₃	1	1	yes	characteristic
180	C₂×C₃×C₅	#235	1	1	yes	characteristic
181	C₂×C₃×C₅	C₂×#67	1	1	yes	characteristic
182	C₂×C₃×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
183	C₂×C₃×C₅	C₂×C₃×D₄	1	1	yes	characteristic
184	C₂×C₃×C₅	C₃×#41	1	1	yes	characteristic
185	D₁₅	—	2	2	no	—
186	C₃×D₅	—	6	2	no	—
187	C₂³×C₃	—	2	1	no	—
188	C₂³×C₃	—	15	1	no	—
189	C₂³×C₃	C₂×C₃×D₅	1	1	yes	characteristic
190	C₂³×C₃	C₂×D₁₅	1	1	yes	characteristic
191	C₂²×D₃	—	5	1	no	—
192	C₃×D₄	—	15	4	no	—
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	15	1	no	—
199	C₂×C₃×C₄	—	15	1	no	—
200	C₂×C₃×C₄	—	15	1	no	—
201	C₂×C₃×C₄	—	30	2	no	—
202	C₂×C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂×C₃×D₅	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂×D₁₅	1	1	yes	characteristic
205	C₂×C₃×C₄	C₂×D₁₅	1	1	yes	characteristic
206	#67	—	5	4	no	—
207	C₂×Dic₃	—	5	1	no	—
208	C₂×Dic₃	—	5	1	no	—
209	C₂×Dic₃	—	5	1	no	—
210	C₄×D₃	—	10	2	no	—
211	C₂²×C₅	—	2	1	no	—
212	C₂²×C₅	—	2	1	no	—
213	C₂²×C₅	C₃×C₄×D₃	1	2	yes	complemented
214	C₂²×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
215	C₂×D₅	—	3	2	no	—
216	C₂×D₅	—	6	1	no	—
217	C₂×D₅	—	6	1	no	—
218	C₄×C₅	—	2	1	no	—
219	C₄×C₅	C₃×#67	1	2	yes	complemented
220	Dic₅	—	3	2	no	—
221	Dic₅	—	6	1	no	—
222	Dic₅	—	6	1	no	—
223	C₂×C₃²	—	2	2	no	—
224	C₂×C₃²	C₂×C₄×D₅	1	1	yes	characteristic
225	C₂×C₃²	#709	1	1	yes	characteristic
226	C₂×C₃²	C₂×C₂²⋊D₅	1	1	yes	characteristic
227	C₃×D₃	—	10	2	no	—
228	C₂×D₄	—	15	1	no	—
229	C₂²×C₄	—	15	1	no	—
230	C₂²×C₄	C₃×D₁₅	1	1	yes	characteristic, complemented
231	C₄⋊C₄	—	15	1	no	—
232	C₂²⋊C₄	—	15	1	no	—
233	C₂²⋊C₄	—	15	1	no	—
234	C₄²	—	15	1	no	—
235	C₃×C₅	—	2	1	no	—
236	C₃×C₅	C₄×#67	1	1	yes	characteristic, complemented
237	C₃×C₅	C₃×C₄×D₄	1	1	yes	characteristic, complemented
238	C₂²×C₃	—	2	2	no	—
239	C₂²×C₃	—	2	2	no	—
240	C₂²×C₃	—	2	1	no	—
241	C₂²×C₃	—	2	1	no	—
242	C₂²×C₃	—	2	1	no	—
243	C₂²×C₃	—	2	1	no	—
244	C₂²×C₃	—	2	2	no	—
245	C₂²×C₃	—	2	1	no	—
246	C₂²×C₃	—	15	2	no	—
247	C₂²×C₃	—	30	1	no	—
248	C₂²×C₃	—	30	1	no	—
249	C₂²×C₃	C₃×C₄×D₅	1	2	yes	complemented
250	C₂²×C₃	C₄×D₁₅	1	2	yes	complemented
251	C₂²×C₃	C₂²×C₃×D₅	1	1	yes	characteristic
252	C₂²×C₃	C₂²×D₁₅	1	1	yes	characteristic
253	C₂×D₃	—	5	2	no	—
254	C₂×D₃	—	10	1	no	—
255	C₂×D₃	—	10	1	no	—
256	C₃×C₄	—	2	2	no	—
257	C₃×C₄	—	2	1	no	—
258	C₃×C₄	—	2	1	no	—
259	C₃×C₄	—	2	2	no	—
260	C₃×C₄	—	15	2	no	—
261	C₃×C₄	—	30	1	no	—
262	C₃×C₄	—	30	1	no	—
263	C₃×C₄	C₃×C₂²⋊D₅	1	2	yes	complemented
264	C₃×C₄	#1220	1	2	yes	direct product factor
265	Dic₃	—	5	2	no	—
266	Dic₃	—	10	1	no	—
267	Dic₃	—	10	1	no	—
268	C₂×C₅	—	2	2	no	—
269	C₂×C₅	C₂×C₃×C₄×D₃	1	1	yes	characteristic
270	C₂×C₅	C₃×#235	1	1	yes	characteristic
271	C₂×C₅	C₂×C₃×#67	1	1	yes	characteristic
272	D₅	—	6	2	no	—
273	C₃²	C₄×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
274	C₂³	—	15	1	no	—
275	C₂³	C₂×C₃×D₁₅	1	1	yes	characteristic
276	D₄	—	15	4	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	15	1	no	—
279	C₂×C₄	—	15	1	no	—
280	C₂×C₄	—	15	1	no	—
281	C₂×C₄	—	30	2	no	—
282	C₂×C₄	C₂×C₃×D₁₅	1	1	yes	characteristic
283	C₂×C₄	C₂×C₃×D₁₅	1	1	yes	characteristic
284	C₂×C₃	—	2	4	no	—
285	C₂×C₃	—	2	2	no	—
286	C₂×C₃	—	2	2	no	—
287	C₂×C₃	—	2	1	no	—
288	C₂×C₃	—	2	1	no	—
289	C₂×C₃	—	2	1	no	—
290	C₂×C₃	—	30	2	no	—
291	C₂×C₃	C₂×C₃×C₄×D₅	1	1	yes	characteristic
292	C₂×C₃	C₃×#709	1	1	yes	characteristic
293	C₂×C₃	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
294	C₂×C₃	C₂×C₄×D₁₅	1	1	yes	characteristic
295	C₂×C₃	#6817	1	1	yes	characteristic
296	C₂×C₃	C₂×#1220	1	1	yes	characteristic
297	D₃	—	10	2	no	—
298	C₅	C₃×C₄×#67	1	1	yes	characteristic, complemented, Sylow
299	C₂²	—	2	1	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	15	2	no	—
302	C₂²	—	30	1	no	—
303	C₂²	—	30	1	no	—
304	C₂²	C₃×C₄×D₁₅	1	2	yes	complemented
305	C₂²	C₂²×C₃×D₁₅	1	1	yes	characteristic
306	C₄	—	2	1	no	—
307	C₄	—	15	2	no	—
308	C₄	—	30	1	no	—
309	C₄	—	30	1	no	—
310	C₄	C₃×#1220	1	2	yes	direct product factor
311	C₃	—	2	1	no	—
312	C₃	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic, complemented
313	C₃	C₄×#1220	1	1	yes	characteristic, direct product factor
314	C₂	—	2	2	no	—
315	C₂	—	30	2	no	—
316	C₂	C₂×C₃×C₄×D₁₅	1	1	yes	characteristic
317	C₂	C₃×#6817	1	1	yes	characteristic
318	C₂	C₂×C₃×#1220	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₅
commutator	C₂×C₃×C₅	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₁₅
Fitting	C₂²×C₃²×C₄×C₅	C₂
socle	C₂²×C₃²×C₅	C₂³
prime radical	C₂×C₃×#1220	C₂
cosocle	C₂²×C₃×C₅	C₂³×C₃
hypercenter	C₂²×C₃×C₄	D₁₅
hypocenter	C₃×C₅	C₃×C₄×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×C₄×C₅	C₂	semidirect
3. C₂×C₃×C₄×D₁₅	C₂	semidirect
4. C₃×#6719	C₂	semidirect
5. C₃×#6714	C₂	semidirect
6. C₃×#6712	C₂	semidirect
7. C₃×C₄×Dic₁₅	C₂	semidirect
8. C₄×#1220	C₃	direct (N × H)
15. C₃×#1220	C₄	direct (N × H)
22. C₂²×C₃×C₄×C₅	D₃	semidirect
23. C₂²×C₃×C₄×C₅	C₂×C₃	semidirect
25. C₂×C₄×D₁₅	C₂×C₃	semidirect
28. #6719	C₂×C₃	semidirect
29. #6714	C₂×C₃	semidirect
30. #6712	C₂×C₃	semidirect
31. C₄×Dic₁₅	C₂×C₃	semidirect
38. C₂²×C₃²×C₅	C₂×C₄	semidirect
42. C₂×C₃×D₁₅	C₂×C₄	semidirect
44. C₃²×C₄×C₅	D₄	semidirect
47. C₃×Dic₁₅	C₂×C₄	semidirect
49. C₂²×C₃²×C₄	D₅	semidirect
70. #1220	C₃×C₄	direct (N × H)
87. C₂²×C₄×C₅	C₃×D₃	semidirect
112. C₂²×C₃×C₅	C₄×D₃	semidirect
113. C₂²×C₃×C₅	C₂×C₃×C₄	semidirect
118. C₂×D₁₅	C₂×C₃×C₄	semidirect
126. C₃×C₄×C₅	#67	semidirect
127. C₃×C₄×C₅	C₃×D₄	semidirect
130. Dic₁₅	C₂×C₃×C₄	semidirect
137. C₂²×C₃×C₄	C₃×D₅	semidirect
138. C₂²×C₃×C₄	D₁₅	semidirect
149. C₃²×C₅	C₄×D₄	semidirect
162. C₂²×C₃²	C₄×D₅	semidirect
168. C₃²×C₄	C₂²⋊D₅	semidirect
213. C₂²×C₅	C₃×C₄×D₃	semidirect
219. C₄×C₅	C₃×#67	semidirect
230. C₂²×C₄	C₃×D₁₅	semidirect
236. C₃×C₅	C₄×#67	semidirect
237. C₃×C₅	C₃×C₄×D₄	semidirect
249. C₂²×C₃	C₃×C₄×D₅	semidirect
250. C₂²×C₃	C₄×D₁₅	semidirect
263. C₃×C₄	C₃×C₂²⋊D₅	semidirect
264. C₃×C₄	#1220	direct (N × H)
273. C₃²	C₄×C₂²⋊D₅	semidirect
298. C₅	C₃×C₄×#67	semidirect
304. C₂²	C₃×C₄×D₁₅	semidirect
310. C₄	C₃×#1220	direct (N × H)
312. C₃	C₃×C₄×C₂²⋊D₅	semidirect
313. C₃	C₄×#1220	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×C₃²×C₄×C₅	2
C₂×C₃×#1220	2
C₂×C₃×C₄×D₁₅	2
C₃×#6719	2
C₃×#6714	2
C₃×#6712	2
C₃×C₄×Dic₁₅	2
C₄×#1220	3
C₃×C₄×C₂²⋊D₅	3
C₃×C₄×#67	5

Subgroups — C3×C4×#1220 #13088025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#1220 #13088025