Subgroups — C₃×#10605144 #14320029

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 396 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×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#685	C₂	1	2	yes	maximal
4	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#683	C₂	1	2	yes	maximal, complemented
6	C₃×#64956	C₂	1	2	yes	maximal
7	C₃×#64953	C₂	1	2	yes	maximal
8	C₃×#64940	C₂	1	2	yes	maximal, complemented
9	C₃×#64939	C₂	1	2	yes	maximal, complemented
10	#10605144	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#685	C₂²	1	4	yes	—
17	C₂×C₃×#683	C₂²	1	4	yes	—
18	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₄	1	8	yes	complemented
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×#3963	C₂²	1	4	yes	—
26	C₃×#3963	C₂²	1	2	yes	—
27	C₃×#3963	C₂²	1	4	yes	—
28	C₃×#3963	C₂²	1	2	yes	—
29	C₃×#2283	—	5	1	no	maximal, Hall
30	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
31	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
32	C₄×#685	C₂×C₃	1	2	yes	—
33	#65221	C₂×C₃	1	1	yes	characteristic, complemented
34	C₄×#683	C₂×C₃	1	2	yes	complemented
35	#64956	C₂×C₃	1	2	yes	—
36	#64953	C₂×C₃	1	2	yes	—
37	#64940	C₂×C₃	1	2	yes	complemented
38	#64939	C₂×C₃	1	2	yes	complemented
39	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
45	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	—	2	4	no	—
49	C₂×C₃×C₄×D₅	—	2	4	no	—
50	C₂×C₃×C₄×D₅	—	2	4	no	—
51	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
52	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
53	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
54	C₃×C₄²×C₅	—	2	4	no	—
55	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
56	C₃×#685	—	2	8	no	—
57	C₃×#683	—	2	8	no	—
58	C₃×C₄×Dic₅	—	2	4	no	—
59	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
60	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
61	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
62	C₂²×C₃×C₄²	—	5	1	no	—
63	C₃×#383	—	5	2	no	—
64	C₃×#382	—	5	2	no	—
65	C₃×#381	—	5	2	no	—
66	C₃×#380	—	5	2	no	—
67	C₃×C₄×C₄⋊C₄	—	5	2	no	—
68	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
69	C₃×#376	—	5	1	no	—
70	C₃×#376	D₅	1	1	yes	characteristic, complemented
71	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×#685	C₂²×C₃	1	4	yes	—
77	C₂×#683	C₂²×C₃	1	4	yes	—
78	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
79	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
82	C₄²×D₅	C₃×C₄	1	8	yes	complemented
83	C₅×#95	C₂²×C₃	1	2	yes	—
84	C₅×#95	C₂²×C₃	1	2	yes	—
85	#3963	C₂²×C₃	1	4	yes	—
86	#3963	C₂²×C₃	1	2	yes	—
87	#3963	C₂²×C₃	1	4	yes	—
88	#3963	C₂²×C₃	1	2	yes	—
89	#2283	—	5	1	no	Sylow
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₂²×C₃×D₅	—	2	2	no	—
92	C₂²×C₃×D₅	—	2	2	no	—
93	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₃×D₅	#41	1	4	yes	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	4	yes	—
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₂×C₃×Dic₅	—	2	2	no	—
106	C₂×C₃×Dic₅	—	2	4	no	—
107	C₂×C₃×Dic₅	—	2	4	no	—
108	C₂×C₃×Dic₅	—	2	4	no	—
109	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×Dic₅	#41	1	4	yes	—
113	C₃×C₄×D₅	—	2	8	no	—
114	C₃×C₄×D₅	—	2	8	no	—
115	C₃×C₄×D₅	—	2	8	no	—
116	C₂³×C₃×C₄	—	5	1	no	—
117	C₂³×C₃×C₄	—	5	1	no	—
118	C₂³×C₃×C₄	—	5	1	no	—
119	C₂×C₃×C₄⋊C₄	—	5	4	no	—
120	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
121	C₂×C₃×C₄²	—	5	1	no	—
122	C₂×C₃×C₄²	—	5	1	no	—
123	C₂×C₃×C₄²	—	5	1	no	—
124	C₂×C₃×C₄²	—	5	8	no	—
125	C₂×C₃×C₄²	—	5	2	no	—
126	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	C₃×#95	—	5	2	no	—
129	C₃×#95	—	5	2	no	—
130	C₃×#95	—	5	4	no	—
131	C₃×#95	—	5	4	no	—
132	C₃×#95	C₂×D₅	1	2	yes	—
133	C₃×#95	C₂×D₅	1	2	yes	—
134	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
140	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
141	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
142	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₄×D₅	—	2	4	no	—
144	C₂×C₄×D₅	—	2	4	no	—
145	C₂×C₄×D₅	—	2	4	no	—
146	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
147	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
148	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
149	C₄²×C₅	—	2	4	no	—
150	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
151	#685	—	2	8	no	—
152	#683	—	2	8	no	—
153	C₄×Dic₅	—	2	4	no	—
154	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
155	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
156	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
157	C₂²×C₄²	—	5	1	no	—
158	#383	—	5	2	no	—
159	#382	—	5	2	no	—
160	#381	—	5	2	no	—
161	#380	—	5	2	no	—
162	C₄×C₄⋊C₄	—	5	2	no	—
163	C₄×C₂²⋊C₄	—	5	2	no	—
164	#376	—	5	1	no	—
165	#376	C₃×D₅	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
168	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
169	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
170	C₂×C₃×D₅	—	2	2	no	—
171	C₂×C₃×D₅	—	2	2	no	—
172	C₂×C₃×D₅	—	2	8	no	—
173	C₂×C₃×D₅	#117	1	4	yes	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	—	4	4	no	—
177	C₃×C₄×C₅	#117	1	4	yes	—
178	C₃×Dic₅	—	2	2	no	—
179	C₃×Dic₅	—	2	2	no	—
180	C₃×Dic₅	—	4	4	no	—
181	C₃×Dic₅	#117	1	4	yes	—
182	C₂⁴×C₃	—	5	1	no	—
183	C₂²×C₃×C₄	—	5	1	no	—
184	C₂²×C₃×C₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	4	no	—
187	C₂²×C₃×C₄	—	5	4	no	—
188	C₂²×C₃×C₄	—	5	4	no	—
189	C₂²×C₃×C₄	—	5	4	no	—
190	C₂²×C₃×C₄	—	10	4	no	—
191	C₂²×C₃×C₄	—	10	4	no	—
192	C₂²×C₃×C₄	—	10	4	no	—
193	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
194	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
197	C₃×C₄⋊C₄	—	10	8	no	—
198	C₃×C₂²⋊C₄	—	10	8	no	—
199	C₃×C₄²	—	2	4	no	—
200	C₃×C₄²	—	5	4	no	—
201	C₃×C₄²	—	5	4	no	—
202	C₃×C₄²	—	5	4	no	—
203	C₃×C₄²	—	10	4	no	—
204	C₃×C₄²	C₄×D₅	1	4	yes	—
205	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
206	C₂²×D₅	—	2	2	no	—
207	C₂²×D₅	—	2	2	no	—
208	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
209	C₂²×D₅	C₃×#41	1	4	yes	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
218	C₂×C₄×C₅	C₃×#41	1	4	yes	—
219	C₂×Dic₅	—	2	2	no	—
220	C₂×Dic₅	—	2	2	no	—
221	C₂×Dic₅	—	2	4	no	—
222	C₂×Dic₅	—	2	4	no	—
223	C₂×Dic₅	—	2	4	no	—
224	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
225	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
226	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
227	C₂×Dic₅	C₃×#41	1	4	yes	—
228	C₄×D₅	—	2	8	no	—
229	C₄×D₅	—	2	8	no	—
230	C₄×D₅	—	2	8	no	—
231	C₂³×C₄	—	5	1	no	—
232	C₂³×C₄	—	5	1	no	—
233	C₂³×C₄	—	5	1	no	—
234	C₂×C₄⋊C₄	—	5	4	no	—
235	C₂×C₂²⋊C₄	—	5	4	no	—
236	C₂×C₄²	—	5	1	no	—
237	C₂×C₄²	—	5	1	no	—
238	C₂×C₄²	—	5	1	no	—
239	C₂×C₄²	—	5	8	no	—
240	C₂×C₄²	—	5	2	no	—
241	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
242	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
243	#95	—	5	2	no	—
244	#95	—	5	2	no	—
245	#95	—	5	4	no	—
246	#95	—	5	4	no	—
247	#95	C₂×C₃×D₅	1	2	yes	—
248	#95	C₂×C₃×D₅	1	2	yes	—
249	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
251	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
252	C₂×C₃×C₅	#529	1	4	yes	—
253	C₃×D₅	—	2	4	no	—
254	C₂³×C₃	—	5	2	no	—
255	C₂³×C₃	—	5	4	no	—
256	C₂³×C₃	—	10	2	no	—
257	C₂³×C₃	—	10	2	no	—
258	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	5	2	no	—
265	C₂×C₃×C₄	—	5	4	no	—
266	C₂×C₃×C₄	—	5	2	no	—
267	C₂×C₃×C₄	—	5	2	no	—
268	C₂×C₃×C₄	—	10	8	no	—
269	C₂×C₃×C₄	—	10	8	no	—
270	C₂×C₃×C₄	—	10	2	no	—
271	C₂×C₃×C₄	—	10	2	no	—
272	C₂×C₃×C₄	—	10	8	no	—
273	C₂×C₃×C₄	—	10	4	no	—
274	C₂×C₃×C₄	—	10	4	no	—
275	C₂×C₃×C₄	—	10	4	no	—
276	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
277	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
278	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
279	C₂×C₃×C₄	#709	1	4	yes	—
280	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
281	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
282	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
283	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
284	C₂×D₅	—	2	2	no	—
285	C₂×D₅	—	2	2	no	—
286	C₂×D₅	—	2	8	no	—
287	C₂×D₅	C₃×#117	1	4	yes	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	4	4	no	—
291	C₄×C₅	C₃×#117	1	4	yes	—
292	Dic₅	—	2	2	no	—
293	Dic₅	—	2	2	no	—
294	Dic₅	—	4	4	no	—
295	Dic₅	C₃×#117	1	4	yes	—
296	C₂⁴	—	5	1	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	4	no	—
301	C₂²×C₄	—	5	4	no	—
302	C₂²×C₄	—	5	4	no	—
303	C₂²×C₄	—	5	4	no	—
304	C₂²×C₄	—	10	4	no	—
305	C₂²×C₄	—	10	4	no	—
306	C₂²×C₄	—	10	4	no	—
307	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
308	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
311	C₄⋊C₄	—	10	8	no	—
312	C₂²⋊C₄	—	10	8	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	5	4	no	—
315	C₄²	—	5	4	no	—
316	C₄²	—	5	4	no	—
317	C₄²	—	10	4	no	—
318	C₄²	C₃×C₄×D₅	1	4	yes	—
319	C₃×C₅	#2283	1	1	yes	characteristic, complemented, Hall
320	C₂²×C₃	—	5	4	no	—
321	C₂²×C₃	—	10	2	no	—
322	C₂²×C₃	—	10	2	no	—
323	C₂²×C₃	—	10	8	no	—
324	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
325	C₂²×C₃	C₂×#709	1	2	yes	—
326	C₂²×C₃	D₅×#41	1	2	yes	—
327	C₂²×C₃	D₅×#41	1	2	yes	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	4	4	no	—
331	C₃×C₄	—	5	4	no	—
332	C₃×C₄	—	10	2	no	—
333	C₃×C₄	—	10	2	no	—
334	C₃×C₄	—	20	4	no	—
335	C₃×C₄	#4018	1	4	yes	—
336	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
337	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
338	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
339	C₂×C₅	C₃×#529	1	4	yes	—
340	D₅	—	2	4	no	—
341	C₂³	—	5	2	no	—
342	C₂³	—	5	4	no	—
343	C₂³	—	10	2	no	—
344	C₂³	—	10	2	no	—
345	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	5	2	no	—
352	C₂×C₄	—	5	4	no	—
353	C₂×C₄	—	5	2	no	—
354	C₂×C₄	—	5	2	no	—
355	C₂×C₄	—	10	8	no	—
356	C₂×C₄	—	10	8	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	—	10	2	no	—
359	C₂×C₄	—	10	8	no	—
360	C₂×C₄	—	10	4	no	—
361	C₂×C₄	—	10	4	no	—
362	C₂×C₄	—	10	4	no	—
363	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
364	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
365	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
366	C₂×C₄	C₃×#709	1	4	yes	—
367	C₂×C₃	—	10	4	no	—
368	C₂×C₃	C₂×#4018	1	1	yes	characteristic
369	C₂×C₃	D₅×#117	1	1	yes	characteristic
370	C₂×C₃	D₅×#117	1	1	yes	characteristic
371	C₂×C₃	#65862	1	4	yes	—
372	C₅	C₃×#2283	1	1	yes	characteristic, complemented, Sylow
373	C₂²	—	5	4	no	—
374	C₂²	—	10	2	no	—
375	C₂²	—	10	8	no	—
376	C₂²	—	10	2	no	—
377	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
378	C₂²	C₂×C₃×#709	1	2	yes	—
379	C₂²	C₃×D₅×#41	1	2	yes	—
380	C₂²	C₃×D₅×#41	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	4	4	no	—
384	C₄	—	5	4	no	—
385	C₄	—	10	2	no	—
386	C₄	—	10	2	no	—
387	C₄	—	20	4	no	—
388	C₄	C₃×#4018	1	4	yes	—
389	C₃	#10605144	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	—	10	4	no	—
391	C₂	C₂×C₃×#4018	1	1	yes	characteristic
392	C₂	C₃×D₅×#117	1	1	yes	characteristic
393	C₂	C₃×D₅×#117	1	1	yes	characteristic
394	C₂	C₃×#65862	1	4	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#376	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#376	D₅
hypocenter	C₅	C₃×#2283
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×#376

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#376	C₂	semidirect
4. C₃×#65221	C₂	semidirect
5. C₃×C₄×#683	C₂	semidirect
8. C₃×#64940	C₂	semidirect
9. C₃×#64939	C₂	semidirect
10. #10605144	C₃	direct (N × H)
22. C₃×C₄²×D₅	C₄	semidirect
31. C₅×#376	C₂×C₃	semidirect
33. #65221	C₂×C₃	semidirect
34. C₄×#683	C₂×C₃	semidirect
37. #64940	C₂×C₃	semidirect
38. #64939	C₂×C₃	semidirect
70. C₃×#376	D₅	semidirect
82. C₄²×D₅	C₃×C₄	semidirect
165. #376	C₃×D₅	semidirect
319. C₃×C₅	#2283	semidirect
372. C₅	C₃×#2283	semidirect
389. C₃	#10605144	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×C₅×#376	2
C₃×C₄×#685	2
C₃×#65221	2
C₃×C₄×#683	2
C₃×#64956	2
C₃×#64953	2
C₃×#64940	2
C₃×#64939	2
#10605144	3
C₃×#2283	5

Subgroups — C3×#10605144 #14320029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605144 #14320029