Subgroups — C₃×#10605125 #14330062

Order 1920.

896 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×#4016	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
3	C₃×#65222	C₂	1	2	yes	maximal
4	C₃×#65221	C₂	1	1	yes	maximal, characteristic
5	C₃×C₄×#683	C₂	1	2	yes	maximal
6	C₃×#64943	C₂	1	2	yes	maximal
7	C₃×#64942	C₂	1	2	yes	maximal
8	C₃×#64941	C₂	1	2	yes	maximal
9	C₃×#64938	C₂	1	2	yes	maximal
10	#10605125	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#683	C₂²	1	2	yes	—
16	C₂×C₃×#683	C₂²	1	2	yes	—
17	C₂×C₃×#683	C₂²	1	2	yes	—
18	C₂×C₃×#683	C₂²	1	2	yes	—
19	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
22	C₃×#4016	C₄	1	8	yes	complemented
23	C₃×C₅×#95	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	1	yes	characteristic
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×#3963	C₂²	1	2	yes	—
27	C₃×#3963	C₂²	1	2	yes	—
28	C₃×#3963	C₂²	1	2	yes	—
29	C₃×#3963	C₂²	1	2	yes	—
30	C₃×#3963	C₂²	1	2	yes	—
31	C₃×#3963	C₂²	1	1	yes	characteristic
32	C₃×#3963	C₂²	1	1	yes	characteristic
33	C₃×#2371	—	5	1	no	maximal, Hall
34	C₂×#4016	C₂×C₃	1	1	yes	characteristic
35	C₅×#376	C₂×C₃	1	1	yes	characteristic
36	#65222	C₂×C₃	1	2	yes	—
37	#65221	C₂×C₃	1	1	yes	characteristic
38	C₄×#683	C₂×C₃	1	2	yes	—
39	#64943	C₂×C₃	1	2	yes	—
40	#64942	C₂×C₃	1	2	yes	—
41	#64941	C₂×C₃	1	2	yes	—
42	#64938	C₂×C₃	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
52	C₃×C₄²×C₅	—	2	4	no	—
53	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
54	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
56	C₃×#683	—	2	4	no	—
57	C₃×#683	—	2	4	no	—
58	C₃×#683	C₂×C₄	1	8	yes	—
59	C₃×#683	C₂×C₄	1	8	yes	—
60	C₃×C₄×Dic₅	—	2	4	no	—
61	C₃×C₄×Dic₅	—	2	4	no	—
62	C₃×C₄×Dic₅	—	2	4	no	—
63	C₂×C₃×#125	—	5	1	no	—
64	C₃×#387	—	5	2	no	—
65	C₃×#387	—	5	2	no	—
66	C₃×#387	—	5	2	no	—
67	C₃×#387	—	5	2	no	—
68	C₃×C₄×C₄⋊C₄	—	5	2	no	—
69	C₃×C₄×C₄⋊C₄	—	5	2	no	—
70	C₃×#376	—	5	1	no	—
71	C₃×#376	D₅	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×#683	C₂²×C₃	1	2	yes	—
77	C₂×#683	C₂²×C₃	1	2	yes	—
78	C₂×#683	C₂²×C₃	1	2	yes	—
79	C₂×#683	C₂²×C₃	1	2	yes	—
80	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
82	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
83	#4016	C₃×C₄	1	8	yes	complemented
84	C₅×#95	C₂²×C₃	1	1	yes	characteristic
85	C₅×#95	C₂²×C₃	1	1	yes	characteristic
86	C₅×#95	C₂²×C₃	1	2	yes	—
87	#3963	C₂²×C₃	1	2	yes	—
88	#3963	C₂²×C₃	1	2	yes	—
89	#3963	C₂²×C₃	1	2	yes	—
90	#3963	C₂²×C₃	1	2	yes	—
91	#3963	C₂²×C₃	1	2	yes	—
92	#3963	C₂²×C₃	1	1	yes	characteristic
93	#3963	C₂²×C₃	1	1	yes	characteristic
94	#2371	—	5	1	no	Sylow
95	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	#41	1	4	yes	—
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
119	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
120	C₂×C₃×Dic₅	#41	1	4	yes	—
121	C₃×#125	—	5	8	no	—
122	C₂×C₃×C₄⋊C₄	—	5	2	no	—
123	C₂×C₃×C₄⋊C₄	—	5	2	no	—
124	C₂×C₃×C₄⋊C₄	—	5	1	no	—
125	C₂×C₃×C₄⋊C₄	—	5	1	no	—
126	C₂×C₃×C₄⋊C₄	—	5	2	no	—
127	C₂×C₃×C₄⋊C₄	—	5	2	no	—
128	C₂×C₃×C₄²	—	5	2	no	—
129	C₂×C₃×C₄²	—	5	2	no	—
130	C₂×C₃×C₄²	—	5	2	no	—
131	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
133	C₃×#95	—	5	1	no	—
134	C₃×#95	—	5	2	no	—
135	C₃×#95	—	5	1	no	—
136	C₃×#95	—	5	2	no	—
137	C₃×#95	—	5	2	no	—
138	C₃×#95	—	5	2	no	—
139	C₃×#95	—	5	2	no	—
140	C₃×#95	C₂×D₅	1	1	yes	characteristic
141	C₃×#95	C₂×D₅	1	1	yes	characteristic
142	C₃×#95	C₂×D₅	1	2	yes	—
143	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
148	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
149	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
150	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
151	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
152	C₄²×C₅	—	2	4	no	—
153	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
154	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
155	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
156	#683	—	2	4	no	—
157	#683	—	2	4	no	—
158	#683	C₂×C₃×C₄	1	8	yes	—
159	#683	C₂×C₃×C₄	1	8	yes	—
160	C₄×Dic₅	—	2	4	no	—
161	C₄×Dic₅	—	2	4	no	—
162	C₄×Dic₅	—	2	4	no	—
163	C₂×#125	—	5	1	no	—
164	#387	—	5	2	no	—
165	#387	—	5	2	no	—
166	#387	—	5	2	no	—
167	#387	—	5	2	no	—
168	C₄×C₄⋊C₄	—	5	2	no	—
169	C₄×C₄⋊C₄	—	5	2	no	—
170	#376	—	5	1	no	—
171	#376	C₃×D₅	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
174	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
175	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
176	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	2	no	—
180	C₃×C₄×C₅	—	2	4	no	—
181	C₃×C₄×C₅	—	4	2	no	—
182	C₃×Dic₅	—	2	4	no	—
183	C₃×Dic₅	—	2	4	no	—
184	C₃×Dic₅	—	2	4	no	—
185	C₃×Dic₅	—	4	2	no	—
186	C₂²×C₃×C₄	—	5	2	no	—
187	C₂²×C₃×C₄	—	5	2	no	—
188	C₂²×C₃×C₄	—	5	2	no	—
189	C₂²×C₃×C₄	—	5	2	no	—
190	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
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	2	yes	—
195	C₃×C₄⋊C₄	—	5	8	no	—
196	C₃×C₄⋊C₄	—	5	8	no	—
197	C₃×C₄⋊C₄	—	5	4	no	—
198	C₃×C₄⋊C₄	—	5	4	no	—
199	C₃×C₄⋊C₄	—	10	4	no	—
200	C₃×C₄⋊C₄	—	10	4	no	—
201	C₃×C₄²	—	2	4	no	—
202	C₃×C₄²	—	10	4	no	—
203	C₃×C₄²	—	10	4	no	—
204	C₃×C₄²	—	10	4	no	—
205	C₃×C₄²	C₄×D₅	1	4	yes	—
206	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
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	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×C₄×C₅	C₃×#41	1	4	yes	—
220	C₂×Dic₅	—	2	2	no	—
221	C₂×Dic₅	—	2	2	no	—
222	C₂×Dic₅	—	2	2	no	—
223	C₂×Dic₅	—	2	2	no	—
224	C₂×Dic₅	—	2	2	no	—
225	C₂×Dic₅	—	2	2	no	—
226	C₂×Dic₅	—	2	2	no	—
227	C₂×Dic₅	—	2	2	no	—
228	C₂×Dic₅	—	2	2	no	—
229	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
230	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
231	C₂×Dic₅	C₃×#41	1	4	yes	—
232	#125	—	5	8	no	—
233	C₂×C₄⋊C₄	—	5	2	no	—
234	C₂×C₄⋊C₄	—	5	2	no	—
235	C₂×C₄⋊C₄	—	5	1	no	—
236	C₂×C₄⋊C₄	—	5	1	no	—
237	C₂×C₄⋊C₄	—	5	2	no	—
238	C₂×C₄⋊C₄	—	5	2	no	—
239	C₂×C₄²	—	5	2	no	—
240	C₂×C₄²	—	5	2	no	—
241	C₂×C₄²	—	5	2	no	—
242	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
243	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
244	#95	—	5	1	no	—
245	#95	—	5	2	no	—
246	#95	—	5	1	no	—
247	#95	—	5	2	no	—
248	#95	—	5	2	no	—
249	#95	—	5	2	no	—
250	#95	—	5	2	no	—
251	#95	C₂×C₃×D₅	1	1	yes	characteristic
252	#95	C₂×C₃×D₅	1	1	yes	characteristic
253	#95	C₂×C₃×D₅	1	2	yes	—
254	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
255	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
256	C₂×C₃×C₅	#519	1	1	yes	characteristic
257	C₂×C₃×C₅	#552	1	2	yes	—
258	C₂×C₃×C₅	#552	1	2	yes	—
259	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	5	4	no	—
270	C₂×C₃×C₄	—	5	4	no	—
271	C₂×C₃×C₄	—	5	4	no	—
272	C₂×C₃×C₄	—	10	2	no	—
273	C₂×C₃×C₄	—	10	2	no	—
274	C₂×C₃×C₄	—	10	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	—	10	2	no	—
278	C₂×C₃×C₄	—	10	2	no	—
279	C₂×C₃×C₄	—	10	2	no	—
280	C₂×C₃×C₄	—	10	2	no	—
281	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
283	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
284	C₂×C₃×C₄	#709	1	4	yes	—
285	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
286	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
287	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
288	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
289	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	4	no	—
294	C₄×C₅	—	4	2	no	—
295	Dic₅	—	2	4	no	—
296	Dic₅	—	2	4	no	—
297	Dic₅	—	2	4	no	—
298	Dic₅	—	4	2	no	—
299	C₂²×C₄	—	5	2	no	—
300	C₂²×C₄	—	5	2	no	—
301	C₂²×C₄	—	5	2	no	—
302	C₂²×C₄	—	5	2	no	—
303	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
304	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
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	2	yes	—
308	C₄⋊C₄	—	5	8	no	—
309	C₄⋊C₄	—	5	8	no	—
310	C₄⋊C₄	—	5	4	no	—
311	C₄⋊C₄	—	5	4	no	—
312	C₄⋊C₄	—	10	4	no	—
313	C₄⋊C₄	—	10	4	no	—
314	C₄²	—	2	4	no	—
315	C₄²	—	10	4	no	—
316	C₄²	—	10	4	no	—
317	C₄²	—	10	4	no	—
318	C₄²	C₃×C₄×D₅	1	4	yes	—
319	C₃×C₅	#2371	1	1	yes	characteristic, complemented, Hall
320	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
321	C₂²×C₃	C₂×#709	1	2	yes	—
322	C₂²×C₃	D₅×#41	1	2	yes	—
323	C₂²×C₃	#4150	1	1	yes	characteristic
324	C₂²×C₃	#4150	1	1	yes	characteristic
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	2	4	no	—
329	C₃×C₄	—	4	2	no	—
330	C₃×C₄	—	10	4	no	—
331	C₃×C₄	—	10	4	no	—
332	C₃×C₄	—	10	4	no	—
333	C₃×C₄	—	20	2	no	—
334	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
335	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
336	C₂×C₅	C₃×#519	1	1	yes	characteristic
337	C₂×C₅	C₃×#552	1	2	yes	—
338	C₂×C₅	C₃×#552	1	2	yes	—
339	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	5	4	no	—
350	C₂×C₄	—	5	4	no	—
351	C₂×C₄	—	5	4	no	—
352	C₂×C₄	—	10	2	no	—
353	C₂×C₄	—	10	2	no	—
354	C₂×C₄	—	10	2	no	—
355	C₂×C₄	—	10	2	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	—	10	2	no	—
359	C₂×C₄	—	10	2	no	—
360	C₂×C₄	—	10	2	no	—
361	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
362	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
363	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
364	C₂×C₄	C₃×#709	1	4	yes	—
365	C₂×C₃	C₄×#709	1	1	yes	characteristic
366	C₂×C₃	#65850	1	1	yes	characteristic
367	C₂×C₃	#65856	1	1	yes	characteristic
368	C₂×C₃	#65863	1	2	yes	—
369	C₂×C₃	#65865	1	2	yes	—
370	C₅	C₃×#2371	1	1	yes	characteristic, complemented, Sylow
371	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
372	C₂²	C₂×C₃×#709	1	2	yes	—
373	C₂²	C₃×D₅×#41	1	2	yes	—
374	C₂²	C₃×#4150	1	1	yes	characteristic
375	C₂²	C₃×#4150	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	10	4	no	—
382	C₄	—	10	4	no	—
383	C₄	—	10	4	no	—
384	C₄	—	20	2	no	—
385	C₃	#10605125	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	C₃×C₄×#709	1	1	yes	characteristic
387	C₂	C₃×#65850	1	1	yes	characteristic
388	C₂	C₃×#65856	1	1	yes	characteristic
389	C₂	C₃×#65863	1	2	yes	—
390	C₂	C₃×#65865	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#376	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#376	D₅
hypocenter	C₅	C₃×#2371
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#376

Complements

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

N	H ≅ G/N	type
10. #10605125	C₃	direct (N × H)
22. C₃×#4016	C₄	semidirect
83. #4016	C₃×C₄	semidirect
319. C₃×C₅	#2371	semidirect
370. C₅	C₃×#2371	semidirect
385. C₃	#10605125	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×#4016	2
C₃×C₅×#376	2
C₃×#65222	2
C₃×#65221	2
C₃×C₄×#683	2
C₃×#64943	2
C₃×#64942	2
C₃×#64941	2
C₃×#64938	2
#10605125	3
C₃×#2371	5

Subgroups — C3×#10605125 #14330062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605125 #14330062