Subgroups — C₃×#10605989 #14320044

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 392 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×#383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64956	C₂	1	2	yes	maximal
5	C₃×#64955	C₂	1	2	yes	maximal
6	C₃×#64953	C₂	1	2	yes	maximal
7	C₃×#64939	C₂	1	2	yes	maximal, complemented
8	C₃×#64938	C₂	1	2	yes	maximal, complemented
9	C₃×#64937	C₂	1	2	yes	maximal, complemented
10	#10605989	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	1	yes	characteristic
15	C₂×C₃×#685	C₂²	1	4	yes	—
16	C₂×C₃×#683	C₂²	1	4	yes	—
17	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₃×C₄²×D₅	C₄	1	8	yes	complemented
22	C₃×C₅×#95	C₂²	1	2	yes	—
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	2	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×#383	C₂×C₃	1	1	yes	characteristic, complemented
32	#65226	C₂×C₃	1	1	yes	characteristic, complemented
33	#64956	C₂×C₃	1	2	yes	—
34	#64955	C₂×C₃	1	2	yes	—
35	#64953	C₂×C₃	1	2	yes	—
36	#64939	C₂×C₃	1	2	yes	complemented
37	#64938	C₂×C₃	1	2	yes	complemented
38	#64937	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	C₂×C₄	1	4	yes	—
55	C₃×#685	—	2	8	no	—
56	C₃×#683	—	2	8	no	—
57	C₃×C₄×Dic₅	—	2	8	no	—
58	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
59	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
60	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
61	C₂²×C₃×C₄²	—	5	1	no	—
62	C₃×#383	—	5	1	no	—
63	C₃×#383	D₅	1	1	yes	characteristic, complemented
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	2	no	—
70	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×#685	C₂²×C₃	1	4	yes	—
75	C₂×#683	C₂²×C₃	1	4	yes	—
76	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
77	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
80	C₄²×D₅	C₃×C₄	1	8	yes	complemented
81	C₅×#95	C₂²×C₃	1	2	yes	—
82	C₅×#95	C₂²×C₃	1	2	yes	—
83	C₅×#95	C₂²×C₃	1	2	yes	—
84	#3963	C₂²×C₃	1	4	yes	—
85	#3963	C₂²×C₃	1	2	yes	—
86	#3963	C₂²×C₃	1	2	yes	—
87	#3963	C₂²×C₃	1	2	yes	—
88	#2283	—	5	1	no	Sylow
89	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
90	C₂²×C₃×D₅	—	2	2	no	—
91	C₂²×C₃×D₅	—	2	2	no	—
92	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₃×D₅	#41	1	4	yes	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
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×Dic₅	—	2	2	no	—
104	C₂×C₃×Dic₅	—	2	4	no	—
105	C₂×C₃×Dic₅	—	2	4	no	—
106	C₂×C₃×Dic₅	—	2	4	no	—
107	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
108	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
109	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×Dic₅	#41	1	4	yes	—
111	C₂×C₃×Dic₅	#41	1	4	yes	—
112	C₃×C₄×D₅	—	2	8	no	—
113	C₃×C₄×D₅	—	2	8	no	—
114	C₃×C₄×D₅	—	2	8	no	—
115	C₂³×C₃×C₄	—	5	1	no	—
116	C₂³×C₃×C₄	—	5	1	no	—
117	C₂³×C₃×C₄	—	5	1	no	—
118	C₂×C₃×C₄⋊C₄	—	5	4	no	—
119	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
120	C₂×C₃×C₄²	—	5	1	no	—
121	C₂×C₃×C₄²	—	5	1	no	—
122	C₂×C₃×C₄²	—	5	1	no	—
123	C₂×C₃×C₄²	—	5	8	no	—
124	C₂×C₃×C₄²	—	5	4	no	—
125	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
126	C₃×#95	—	5	2	no	—
127	C₃×#95	—	5	4	no	—
128	C₃×#95	—	5	2	no	—
129	C₃×#95	—	5	2	no	—
130	C₃×#95	C₂×D₅	1	2	yes	—
131	C₃×#95	C₂×D₅	1	2	yes	—
132	C₃×#95	C₂×D₅	1	2	yes	—
133	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
139	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
141	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₄×D₅	—	2	4	no	—
143	C₂×C₄×D₅	—	2	4	no	—
144	C₂×C₄×D₅	—	2	4	no	—
145	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
146	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
147	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
148	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
149	#685	—	2	8	no	—
150	#683	—	2	8	no	—
151	C₄×Dic₅	—	2	8	no	—
152	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
153	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
154	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
155	C₂²×C₄²	—	5	1	no	—
156	#383	—	5	1	no	—
157	#383	C₃×D₅	1	1	yes	characteristic, complemented
158	#382	—	5	2	no	—
159	#381	—	5	2	no	—
160	#380	—	5	2	no	—
161	C₄×C₄⋊C₄	—	5	2	no	—
162	C₄×C₂²⋊C₄	—	5	2	no	—
163	#376	—	5	2	no	—
164	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
166	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
167	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
168	C₂×C₃×D₅	—	2	2	no	—
169	C₂×C₃×D₅	—	2	2	no	—
170	C₂×C₃×D₅	—	2	8	no	—
171	C₂×C₃×D₅	#117	1	4	yes	—
172	C₃×C₄×C₅	—	2	2	no	—
173	C₃×C₄×C₅	—	2	2	no	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	—	4	4	no	—
176	C₃×Dic₅	—	2	2	no	—
177	C₃×Dic₅	—	4	4	no	—
178	C₃×Dic₅	#117	1	4	yes	—
179	C₃×Dic₅	#117	1	4	yes	—
180	C₂⁴×C₃	—	5	1	no	—
181	C₂²×C₃×C₄	—	5	1	no	—
182	C₂²×C₃×C₄	—	5	1	no	—
183	C₂²×C₃×C₄	—	5	1	no	—
184	C₂²×C₃×C₄	—	5	4	no	—
185	C₂²×C₃×C₄	—	5	4	no	—
186	C₂²×C₃×C₄	—	5	4	no	—
187	C₂²×C₃×C₄	—	5	4	no	—
188	C₂²×C₃×C₄	—	10	4	no	—
189	C₂²×C₃×C₄	—	10	4	no	—
190	C₂²×C₃×C₄	—	10	4	no	—
191	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
192	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
195	C₃×C₄⋊C₄	—	10	8	no	—
196	C₃×C₂²⋊C₄	—	10	8	no	—
197	C₃×C₄²	—	5	4	no	—
198	C₃×C₄²	—	5	4	no	—
199	C₃×C₄²	—	5	4	no	—
200	C₃×C₄²	—	10	8	no	—
201	C₃×C₄²	C₄×D₅	1	4	yes	—
202	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
203	C₂²×D₅	—	2	2	no	—
204	C₂²×D₅	—	2	2	no	—
205	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
206	C₂²×D₅	C₃×#41	1	4	yes	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
216	C₂×Dic₅	—	2	2	no	—
217	C₂×Dic₅	—	2	4	no	—
218	C₂×Dic₅	—	2	4	no	—
219	C₂×Dic₅	—	2	4	no	—
220	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
221	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
222	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
223	C₂×Dic₅	C₃×#41	1	4	yes	—
224	C₂×Dic₅	C₃×#41	1	4	yes	—
225	C₄×D₅	—	2	8	no	—
226	C₄×D₅	—	2	8	no	—
227	C₄×D₅	—	2	8	no	—
228	C₂³×C₄	—	5	1	no	—
229	C₂³×C₄	—	5	1	no	—
230	C₂³×C₄	—	5	1	no	—
231	C₂×C₄⋊C₄	—	5	4	no	—
232	C₂×C₂²⋊C₄	—	5	4	no	—
233	C₂×C₄²	—	5	1	no	—
234	C₂×C₄²	—	5	1	no	—
235	C₂×C₄²	—	5	1	no	—
236	C₂×C₄²	—	5	8	no	—
237	C₂×C₄²	—	5	4	no	—
238	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
239	#95	—	5	2	no	—
240	#95	—	5	4	no	—
241	#95	—	5	2	no	—
242	#95	—	5	2	no	—
243	#95	C₂×C₃×D₅	1	2	yes	—
244	#95	C₂×C₃×D₅	1	2	yes	—
245	#95	C₂×C₃×D₅	1	2	yes	—
246	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
249	C₂×C₃×C₅	#529	1	4	yes	—
250	C₃×D₅	—	2	4	no	—
251	C₂³×C₃	—	5	2	no	—
252	C₂³×C₃	—	5	4	no	—
253	C₂³×C₃	—	10	2	no	—
254	C₂³×C₃	—	10	2	no	—
255	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	5	2	no	—
263	C₂×C₃×C₄	—	5	2	no	—
264	C₂×C₃×C₄	—	5	4	no	—
265	C₂×C₃×C₄	—	5	4	no	—
266	C₂×C₃×C₄	—	5	2	no	—
267	C₂×C₃×C₄	—	10	8	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	4	no	—
272	C₂×C₃×C₄	—	10	4	no	—
273	C₂×C₃×C₄	—	10	4	no	—
274	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
276	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
277	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
278	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
279	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
280	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
281	C₂×D₅	—	2	2	no	—
282	C₂×D₅	—	2	2	no	—
283	C₂×D₅	—	2	8	no	—
284	C₂×D₅	C₃×#117	1	4	yes	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	4	4	no	—
289	Dic₅	—	2	2	no	—
290	Dic₅	—	4	4	no	—
291	Dic₅	C₃×#117	1	4	yes	—
292	Dic₅	C₃×#117	1	4	yes	—
293	C₂⁴	—	5	1	no	—
294	C₂²×C₄	—	5	1	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	4	no	—
298	C₂²×C₄	—	5	4	no	—
299	C₂²×C₄	—	5	4	no	—
300	C₂²×C₄	—	5	4	no	—
301	C₂²×C₄	—	10	4	no	—
302	C₂²×C₄	—	10	4	no	—
303	C₂²×C₄	—	10	4	no	—
304	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
305	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
308	C₄⋊C₄	—	10	8	no	—
309	C₂²⋊C₄	—	10	8	no	—
310	C₄²	—	5	4	no	—
311	C₄²	—	5	4	no	—
312	C₄²	—	5	4	no	—
313	C₄²	—	10	8	no	—
314	C₄²	C₃×C₄×D₅	1	4	yes	—
315	C₃×C₅	#2283	1	1	yes	characteristic, complemented, Hall
316	C₂²×C₃	—	5	4	no	—
317	C₂²×C₃	—	10	2	no	—
318	C₂²×C₃	—	10	2	no	—
319	C₂²×C₃	—	10	8	no	—
320	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
321	C₂²×C₃	D₅×#41	1	2	yes	—
322	C₂²×C₃	D₅×#41	1	2	yes	—
323	C₂²×C₃	D₅×#41	1	2	yes	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	4	4	no	—
328	C₃×C₄	—	5	4	no	—
329	C₃×C₄	—	5	4	no	—
330	C₃×C₄	—	10	2	no	—
331	C₃×C₄	—	20	4	no	—
332	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
333	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
334	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
335	C₂×C₅	C₃×#529	1	4	yes	—
336	D₅	—	2	4	no	—
337	C₂³	—	5	2	no	—
338	C₂³	—	5	4	no	—
339	C₂³	—	10	2	no	—
340	C₂³	—	10	2	no	—
341	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	5	2	no	—
349	C₂×C₄	—	5	2	no	—
350	C₂×C₄	—	5	4	no	—
351	C₂×C₄	—	5	4	no	—
352	C₂×C₄	—	5	2	no	—
353	C₂×C₄	—	10	8	no	—
354	C₂×C₄	—	10	8	no	—
355	C₂×C₄	—	10	8	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	4	no	—
358	C₂×C₄	—	10	4	no	—
359	C₂×C₄	—	10	4	no	—
360	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
361	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
362	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
363	C₂×C₃	—	10	4	no	—
364	C₂×C₃	D₅×#117	1	1	yes	characteristic
365	C₂×C₃	D₅×#117	1	1	yes	characteristic
366	C₂×C₃	D₅×#117	1	1	yes	characteristic
367	C₂×C₃	#66040	1	4	yes	—
368	C₅	C₃×#2283	1	1	yes	characteristic, complemented, Sylow
369	C₂²	—	5	4	no	—
370	C₂²	—	10	2	no	—
371	C₂²	—	10	2	no	—
372	C₂²	—	10	8	no	—
373	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
374	C₂²	C₃×D₅×#41	1	2	yes	—
375	C₂²	C₃×D₅×#41	1	2	yes	—
376	C₂²	C₃×D₅×#41	1	2	yes	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	4	no	—
381	C₄	—	5	4	no	—
382	C₄	—	5	4	no	—
383	C₄	—	10	2	no	—
384	C₄	—	20	4	no	—
385	C₃	#10605989	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	10	4	no	—
387	C₂	C₃×D₅×#117	1	1	yes	characteristic
388	C₂	C₃×D₅×#117	1	1	yes	characteristic
389	C₂	C₃×D₅×#117	1	1	yes	characteristic
390	C₂	C₃×#66040	1	4	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#383	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#383	D₅
hypocenter	C₅	C₃×#2283
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#383

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#383	C₂	semidirect
3. C₃×#65226	C₂	semidirect
7. C₃×#64939	C₂	semidirect
8. C₃×#64938	C₂	semidirect
9. C₃×#64937	C₂	semidirect
10. #10605989	C₃	direct (N × H)
21. C₃×C₄²×D₅	C₄	semidirect
31. C₅×#383	C₂×C₃	semidirect
32. #65226	C₂×C₃	semidirect
36. #64939	C₂×C₃	semidirect
37. #64938	C₂×C₃	semidirect
38. #64937	C₂×C₃	semidirect
63. C₃×#383	D₅	semidirect
80. C₄²×D₅	C₃×C₄	semidirect
157. #383	C₃×D₅	semidirect
315. C₃×C₅	#2283	semidirect
368. C₅	C₃×#2283	semidirect
385. C₃	#10605989	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×#383	2
C₃×#65226	2
C₃×#64956	2
C₃×#64955	2
C₃×#64953	2
C₃×#64939	2
C₃×#64938	2
C₃×#64937	2
#10605989	3
C₃×#2283	5

Subgroups — C3×#10605989 #14320044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605989 #14320044