Subgroups — C₃×#10601581 #14282759

Order 1920.

476 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	C₃×#65813	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64690	C₂	1	2	yes	maximal
5	C₃×#64687	C₂	1	2	yes	maximal, complemented
6	#10601581	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₃×#4076	C₂²	1	1	yes	characteristic
9	C₃×#4075	—	2	1	no	—
10	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
11	C₃×#4070	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₅	—	2	1	no	—
13	C₃×#4022	—	2	1	no	—
14	C₃×#4021	C₄	1	1	yes	characteristic, complemented
15	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic, complemented
16	C₃×#4018	—	2	1	no	—
17	C₃×#4016	C₄	1	1	yes	characteristic, complemented
18	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic, complemented
19	C₃×C₅×C₄⋊C₈	—	2	1	no	—
20	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₃×C₄×C₅×C₈	—	2	1	no	—
22	C₃×#3963	—	2	1	no	—
23	C₃×#3963	C₂²	1	2	yes	—
24	C₃×#1500	—	5	1	no	maximal, Hall
25	#65813	C₂×C₃	1	1	yes	characteristic
26	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
27	#65221	C₂×C₃	1	1	yes	characteristic, complemented
28	#64690	C₂×C₃	1	2	yes	—
29	#64687	C₂×C₃	1	2	yes	complemented
30	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
34	C₂²×C₃×Dic₅	—	2	2	no	—
35	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	—	2	1	no	—
37	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₃×C₄²×C₅	D₄	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	4	no	—
55	C₃×C₄×Dic₅	—	2	1	no	—
56	C₃×#529	—	5	1	no	—
57	C₃×#431	D₅	1	1	yes	characteristic, complemented
58	C₃×#376	—	5	1	no	—
59	C₃×#328	—	5	2	no	—
60	C₃×#327	—	5	2	no	—
61	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
62	#4076	C₂²×C₃	1	1	yes	characteristic
63	#4075	—	2	1	no	—
64	C₄×C₂²⋊D₅	—	2	1	no	—
65	#4070	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₄×Dic₅	—	2	1	no	—
67	#4022	—	2	1	no	—
68	#4021	C₃×C₄	1	1	yes	characteristic, complemented
69	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
70	#4018	—	2	1	no	—
71	#4016	C₃×C₄	1	1	yes	characteristic, complemented
72	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic, complemented
73	C₅×C₄⋊C₈	—	2	1	no	—
74	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
75	C₄×C₅×C₈	—	2	1	no	—
76	#3963	—	2	1	no	—
77	#3963	C₂²×C₃	1	2	yes	—
78	#1500	—	5	1	no	Sylow
79	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₃×D₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	4	1	no	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
90	C₃×C₂²⋊D₅	—	4	2	no	—
91	C₂×C₃×Dic₅	—	2	4	no	—
92	C₂×C₃×Dic₅	—	2	1	no	—
93	C₂×C₃×Dic₅	—	2	1	no	—
94	C₂×C₃×Dic₅	—	2	1	no	—
95	C₂×C₃×Dic₅	—	4	2	no	—
96	C₂×C₃×Dic₅	—	4	2	no	—
97	C₃×D₂₀	—	4	1	no	—
98	C₃×C₄×D₅	—	4	2	no	—
99	C₃×Dic₁₀	—	4	1	no	—
100	C₃×C₅×C₈	—	4	2	no	—
101	C₃×#126	—	10	1	no	—
102	C₃×#125	—	5	1	no	—
103	C₃×#124	—	5	1	no	—
104	C₃×#123	—	10	1	no	—
105	C₃×C₂²⋊Q₈	—	5	1	no	—
106	C₃×#121	—	5	1	no	—
107	C₃×C₄×Q₈	—	5	1	no	—
108	C₃×C₄×D₄	—	5	1	no	—
109	C₃×C₄×D₄	—	10	1	no	—
110	C₃×#117	—	10	1	no	—
111	C₂×C₃×C₄²	—	10	1	no	—
112	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
113	C₃×C₄⋊C₈	—	2	1	no	—
114	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
115	C₃×C₄×C₈	—	2	1	no	—
116	C₃×#95	—	5	2	no	—
117	C₃×#95	—	10	1	no	—
118	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂×C₂²⋊D₅	—	2	1	no	—
122	C₂²×Dic₅	—	2	2	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	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
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	C₂²⋊Dic₅	—	2	1	no	—
132	#685	—	2	1	no	—
133	#685	—	2	1	no	—
134	#685	—	2	1	no	—
135	#685	—	2	1	no	—
136	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
137	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
138	#683	—	2	1	no	—
139	#683	—	2	1	no	—
140	#683	—	2	1	no	—
141	#683	—	2	1	no	—
142	C₄×Dic₅	—	2	4	no	—
143	C₄×Dic₅	—	2	1	no	—
144	#529	—	5	1	no	—
145	#431	C₃×D₅	1	1	yes	characteristic, complemented
146	#376	—	5	1	no	—
147	#328	—	5	2	no	—
148	#327	—	5	2	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₃×C₅	#135	1	2	yes	—
153	C₂×C₃×D₅	—	4	1	no	—
154	C₂×C₃×D₅	—	4	1	no	—
155	C₂×C₃×D₅	—	4	1	no	—
156	C₃×C₄×C₅	—	2	1	no	—
157	C₃×C₄×C₅	—	2	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	#104	1	2	yes	—
162	C₃×Dic₅	—	4	4	no	—
163	C₃×Dic₅	—	4	1	no	—
164	C₃×Dic₅	—	4	1	no	—
165	C₃×Dic₅	—	4	1	no	—
166	C₂×C₃×Q₈	—	5	1	no	—
167	C₂×C₃×D₄	—	5	1	no	—
168	C₂×C₃×D₄	—	10	1	no	—
169	C₂²×C₃×C₄	—	10	2	no	—
170	C₂²×C₃×C₄	—	10	1	no	—
171	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
172	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
174	C₂×C₃×C₈	—	2	2	no	—
175	C₃×C₄⋊C₄	—	5	1	no	—
176	C₃×C₄⋊C₄	—	5	1	no	—
177	C₃×C₄⋊C₄	—	10	1	no	—
178	C₃×C₄⋊C₄	—	10	1	no	—
179	C₃×C₄⋊C₄	—	10	1	no	—
180	C₃×C₄⋊C₄	—	10	1	no	—
181	C₃×C₂²⋊C₄	—	10	1	no	—
182	C₃×C₂²⋊C₄	—	10	1	no	—
183	C₃×C₂²⋊C₄	—	10	1	no	—
184	C₃×C₂²⋊C₄	—	10	1	no	—
185	C₃×C₂²⋊C₄	—	10	1	no	—
186	C₃×C₄²	—	10	4	no	—
187	C₃×C₄²	—	10	1	no	—
188	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
189	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
190	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
191	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
192	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₂²×D₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₂²⋊D₅	—	4	2	no	—
204	C₂×Dic₅	—	2	4	no	—
205	C₂×Dic₅	—	2	1	no	—
206	C₂×Dic₅	—	2	1	no	—
207	C₂×Dic₅	—	2	1	no	—
208	C₂×Dic₅	—	4	2	no	—
209	C₂×Dic₅	—	4	2	no	—
210	D₂₀	—	4	1	no	—
211	C₄×D₅	—	4	2	no	—
212	Dic₁₀	—	4	1	no	—
213	C₅×C₈	—	4	2	no	—
214	#126	—	10	1	no	—
215	#125	—	5	1	no	—
216	#124	—	5	1	no	—
217	#123	—	10	1	no	—
218	C₂²⋊Q₈	—	5	1	no	—
219	#121	—	5	1	no	—
220	C₄×Q₈	—	5	1	no	—
221	C₄×D₄	—	5	1	no	—
222	C₄×D₄	—	10	1	no	—
223	#117	—	10	1	no	—
224	C₂×C₄²	—	10	1	no	—
225	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
226	C₄⋊C₈	—	2	1	no	—
227	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	—
228	C₄×C₈	—	2	1	no	—
229	#95	—	5	2	no	—
230	#95	—	10	1	no	—
231	C₂×C₃×C₅	—	2	2	no	—
232	C₂×C₃×C₅	#410	1	1	yes	characteristic
233	C₂×C₃×C₅	#416	1	1	yes	characteristic
234	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
235	C₃×D₅	—	8	1	no	—
236	C₂³×C₃	—	10	1	no	—
237	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
238	C₃×Q₈	—	20	1	no	—
239	C₃×D₄	—	20	1	no	—
240	C₃×D₄	—	20	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	4	1	no	—
244	C₂×C₃×C₄	—	10	4	no	—
245	C₂×C₃×C₄	—	10	1	no	—
246	C₂×C₃×C₄	—	10	1	no	—
247	C₂×C₃×C₄	—	10	1	no	—
248	C₂×C₃×C₄	—	20	2	no	—
249	C₂×C₃×C₄	—	20	2	no	—
250	C₂×C₃×C₄	—	20	2	no	—
251	C₂×C₃×C₄	#685	1	1	yes	characteristic
252	C₂×C₃×C₄	#685	1	1	yes	characteristic
253	C₂×C₃×C₄	#685	1	1	yes	characteristic
254	C₂×C₃×C₄	#685	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
257	C₃×C₈	—	4	2	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₅	C₃×#135	1	2	yes	—
262	C₂×D₅	—	4	1	no	—
263	C₂×D₅	—	4	1	no	—
264	C₂×D₅	—	4	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	C₃×#104	1	2	yes	—
271	Dic₅	—	4	4	no	—
272	Dic₅	—	4	1	no	—
273	Dic₅	—	4	1	no	—
274	Dic₅	—	4	1	no	—
275	C₂×Q₈	—	5	1	no	—
276	C₂×D₄	—	5	1	no	—
277	C₂×D₄	—	10	1	no	—
278	C₂²×C₄	—	10	2	no	—
279	C₂²×C₄	—	10	1	no	—
280	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
281	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
283	C₂×C₈	—	2	2	no	—
284	C₄⋊C₄	—	5	1	no	—
285	C₄⋊C₄	—	5	1	no	—
286	C₄⋊C₄	—	10	1	no	—
287	C₄⋊C₄	—	10	1	no	—
288	C₄⋊C₄	—	10	1	no	—
289	C₄⋊C₄	—	10	1	no	—
290	C₂²⋊C₄	—	10	1	no	—
291	C₂²⋊C₄	—	10	1	no	—
292	C₂²⋊C₄	—	10	1	no	—
293	C₂²⋊C₄	—	10	1	no	—
294	C₂²⋊C₄	—	10	1	no	—
295	C₄²	—	10	4	no	—
296	C₄²	—	10	1	no	—
297	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
298	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
299	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
300	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
301	C₃×C₅	#1500	1	1	yes	characteristic, complemented, Hall
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	20	1	no	—
305	C₂²×C₃	—	20	1	no	—
306	C₂²×C₃	—	20	1	no	—
307	C₂²×C₃	#4050	1	2	yes	—
308	C₂²×C₃	C₂×#685	1	1	yes	characteristic
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	20	4	no	—
315	C₃×C₄	—	20	1	no	—
316	C₃×C₄	—	20	1	no	—
317	C₃×C₄	—	20	1	no	—
318	C₃×C₄	#3957	1	2	yes	—
319	C₂×C₅	—	2	2	no	—
320	C₂×C₅	C₃×#410	1	1	yes	characteristic
321	C₂×C₅	C₃×#416	1	1	yes	characteristic
322	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
323	D₅	—	8	1	no	—
324	C₂³	—	10	1	no	—
325	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
326	Q₈	—	20	1	no	—
327	D₄	—	20	1	no	—
328	D₄	—	20	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	10	4	no	—
333	C₂×C₄	—	10	1	no	—
334	C₂×C₄	—	10	1	no	—
335	C₂×C₄	—	10	1	no	—
336	C₂×C₄	—	20	2	no	—
337	C₂×C₄	—	20	2	no	—
338	C₂×C₄	—	20	2	no	—
339	C₂×C₄	C₃×#685	1	1	yes	characteristic
340	C₂×C₄	C₃×#685	1	1	yes	characteristic
341	C₂×C₄	C₃×#685	1	1	yes	characteristic
342	C₂×C₄	C₃×#685	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
344	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
345	C₈	—	4	2	no	—
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	40	1	no	—
348	C₂×C₃	#65295	1	1	yes	characteristic
349	C₂×C₃	#65402	1	1	yes	characteristic
350	C₂×C₃	C₂×#3957	1	1	yes	characteristic
351	C₅	C₃×#1500	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	20	1	no	—
355	C₂²	—	20	1	no	—
356	C₂²	—	20	1	no	—
357	C₂²	C₃×#4050	1	2	yes	—
358	C₂²	C₂×C₃×#685	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	20	4	no	—
365	C₄	—	20	1	no	—
366	C₄	—	20	1	no	—
367	C₄	—	20	1	no	—
368	C₄	C₃×#3957	1	2	yes	—
369	C₃	#10601581	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	2	no	—
371	C₂	—	40	1	no	—
372	C₂	C₃×#65295	1	1	yes	characteristic
373	C₂	C₃×#65402	1	1	yes	characteristic
374	C₂	C₂×C₃×#3957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	#685
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×#4076	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#431	D₅
hypocenter	C₅	C₃×#1500
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₃×#65221	C₂	semidirect
5. C₃×#64687	C₂	semidirect
6. #10601581	C₃	direct (N × H)
14. C₃×#4021	C₄	semidirect
15. C₃×C₄×D₂₀	C₄	semidirect
17. C₃×#4016	C₄	semidirect
18. C₃×C₄×Dic₁₀	C₄	semidirect
26. C₅×#431	C₂×C₃	semidirect
27. #65221	C₂×C₃	semidirect
29. #64687	C₂×C₃	semidirect
57. C₃×#431	D₅	semidirect
68. #4021	C₃×C₄	semidirect
69. C₄×D₂₀	C₃×C₄	semidirect
71. #4016	C₃×C₄	semidirect
72. C₄×Dic₁₀	C₃×C₄	semidirect
145. #431	C₃×D₅	semidirect
301. C₃×C₅	#1500	semidirect
351. C₅	C₃×#1500	semidirect
369. C₃	#10601581	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
C₃×C₅×#431	2
C₃×#65221	2
C₃×#64690	2
C₃×#64687	2
#10601581	3
C₃×#1500	5

Subgroups — C3×#10601581 #14282759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601581 #14282759