Subgroups — C₃×#10602546 #14282521

Order 1920.

432 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×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65213	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Q₈⋊#168	C₂	1	2	yes	maximal, complemented
5	C₃×D₄⋊#168	C₂	1	2	yes	maximal, complemented
6	#10602546	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×#126	—	2	1	no	—
8	C₃×C₅×#125	C₄	1	1	yes	characteristic
9	C₃×C₅×#124	C₄	1	1	yes	characteristic
10	C₃×C₅×#123	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
12	C₃×C₅×#121	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#681	—	2	1	no	—
19	C₃×C₂²⋊#168	—	2	1	no	—
20	C₃×C₄⋊#168	—	2	1	no	—
21	C₃×C₄⋊#168	—	2	1	no	—
22	C₃×C₄⋊#168	C₂²	1	2	yes	—
23	C₃×C₄×#168	C₂²	1	2	yes	—
24	C₃×#1495	—	5	1	no	maximal, Hall
25	C₅×#529	C₂×C₃	1	1	yes	characteristic
26	#65214	C₂×C₃	1	1	yes	characteristic, complemented
27	#65213	C₂×C₃	1	1	yes	characteristic, complemented
28	Q₈⋊#168	C₂×C₃	1	2	yes	complemented
29	D₄⋊#168	C₂×C₃	1	2	yes	complemented
30	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₄	—	2	1	no	—
38	C₃×C₅×C₄⋊C₄	—	2	1	no	—
39	C₃×C₅×C₄⋊C₄	—	2	1	no	—
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₃×#681	—	4	2	no	—
54	C₂×C₃×#168	—	2	2	no	—
55	C₂×C₃×#168	—	2	2	no	—
56	C₃×#529	D₅	1	1	yes	characteristic
57	C₃×#431	—	5	1	no	—
58	C₃×#423	—	5	1	no	—
59	C₃×Q₈⋊C₈	—	5	2	no	—
60	C₃×D₄⋊C₈	—	5	2	no	—
61	C₅×#126	—	2	1	no	—
62	C₅×#125	C₃×C₄	1	1	yes	characteristic
63	C₅×#124	C₃×C₄	1	1	yes	characteristic
64	C₅×#123	—	2	1	no	—
65	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
66	C₅×#121	C₃×C₄	1	1	yes	characteristic
67	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
70	C₅×#117	—	2	1	no	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×#681	—	2	1	no	—
73	C₂²⋊#168	—	2	1	no	—
74	C₄⋊#168	—	2	1	no	—
75	C₄⋊#168	—	2	1	no	—
76	C₄⋊#168	C₂²×C₃	1	2	yes	—
77	C₄×#168	C₂²×C₃	1	2	yes	—
78	#1495	—	5	1	no	Sylow
79	C₂³×C₃×C₅	—	2	1	no	—
80	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	2	2	no	—
82	C₃×C₅×D₄	—	2	2	no	—
83	C₃×C₅×D₄	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₃×#168	—	4	2	no	—
100	C₃×#168	—	4	2	no	—
101	C₂×C₃×M₁₆	—	10	1	no	—
102	C₃×#126	—	2	1	no	—
103	C₃×#125	Dic₅	1	1	yes	characteristic
104	C₃×#124	Dic₅	1	1	yes	characteristic
105	C₃×#123	—	2	1	no	—
106	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
107	C₃×#121	Dic₅	1	1	yes	characteristic
108	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
109	C₃×C₄×D₄	—	2	1	no	—
110	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
111	C₃×#117	—	2	1	no	—
112	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
113	C₃×C₄⋊C₈	—	5	2	no	—
114	C₃×C₄⋊C₈	—	10	1	no	—
115	C₃×C₄⋊C₈	—	10	1	no	—
116	C₃×C₂²⋊C₈	—	10	1	no	—
117	C₃×C₄×C₈	—	5	2	no	—
118	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
125	C₅×C₄⋊C₄	—	2	1	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
130	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
131	C₅×C₂²⋊C₄	—	2	1	no	—
132	C₅×C₂²⋊C₄	—	2	1	no	—
133	C₅×C₂²⋊C₄	—	2	1	no	—
134	C₅×C₂²⋊C₄	—	2	1	no	—
135	C₅×C₂²⋊C₄	—	2	1	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
138	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
139	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
140	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
141	#681	—	4	2	no	—
142	C₂×#168	—	2	2	no	—
143	C₂×#168	—	2	2	no	—
144	#529	C₃×D₅	1	1	yes	characteristic
145	#431	—	5	1	no	—
146	#423	—	5	1	no	—
147	Q₈⋊C₈	—	5	2	no	—
148	D₄⋊C₈	—	5	2	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	—	4	1	no	—
153	C₂²×C₃×C₅	—	4	1	no	—
154	C₂²×C₃×C₅	—	4	1	no	—
155	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
161	C₃×C₄×C₅	—	4	1	no	—
162	C₃×C₄×C₅	—	4	1	no	—
163	C₃×C₄×C₅	#131	1	2	yes	—
164	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₃×C₄×C₅	#137	1	1	yes	characteristic
166	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
173	C₃×M₁₆	—	20	2	no	—
174	C₂×C₃×C₈	—	10	2	no	—
175	C₂×C₃×C₈	—	10	2	no	—
176	C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	1	no	—
179	C₃×C₄⋊C₄	—	2	1	no	—
180	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
181	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
182	C₃×C₂²⋊C₄	—	2	1	no	—
183	C₃×C₂²⋊C₄	—	2	1	no	—
184	C₃×C₂²⋊C₄	—	2	1	no	—
185	C₃×C₂²⋊C₄	—	2	1	no	—
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₄²	—	2	1	no	—
188	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
189	C₃×C₄²	C₂²⋊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	—	2	1	no	—
193	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
194	C₅×Q₈	—	2	2	no	—
195	C₅×D₄	—	2	2	no	—
196	C₅×D₄	—	4	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
212	#168	—	4	2	no	—
213	#168	—	4	2	no	—
214	C₂×M₁₆	—	10	1	no	—
215	#126	—	2	1	no	—
216	#125	C₃×Dic₅	1	1	yes	characteristic
217	#124	C₃×Dic₅	1	1	yes	characteristic
218	#123	—	2	1	no	—
219	C₂²⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
220	#121	C₃×Dic₅	1	1	yes	characteristic
221	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
224	#117	—	2	1	no	—
225	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
226	C₄⋊C₈	—	5	2	no	—
227	C₄⋊C₈	—	10	1	no	—
228	C₄⋊C₈	—	10	1	no	—
229	C₂²⋊C₈	—	10	1	no	—
230	C₄×C₈	—	5	2	no	—
231	C₂×C₃×C₅	—	4	1	no	—
232	C₂×C₃×C₅	—	8	1	no	—
233	C₂×C₃×C₅	#408	1	1	yes	characteristic
234	C₂×C₃×C₅	#417	1	1	yes	characteristic
235	C₂×C₃×C₅	#421	1	1	yes	characteristic
236	C₂³×C₃	—	2	1	no	—
237	C₂³×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
238	C₃×Q₈	—	2	2	no	—
239	C₃×D₄	—	2	2	no	—
240	C₃×D₄	—	4	2	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	4	1	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
256	C₃×C₈	—	20	2	no	—
257	C₃×C₈	—	20	2	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	—	4	1	no	—
263	C₂²×C₅	—	4	1	no	—
264	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
270	C₄×C₅	—	4	1	no	—
271	C₄×C₅	—	4	1	no	—
272	C₄×C₅	C₃×#131	1	2	yes	—
273	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₄×C₅	C₃×#137	1	1	yes	characteristic
275	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
280	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
281	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
282	M₁₆	—	20	2	no	—
283	C₂×C₈	—	10	2	no	—
284	C₂×C₈	—	10	2	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
290	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
298	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
299	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
300	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
301	C₃×C₅	#1495	1	1	yes	characteristic, complemented, Hall
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	4	1	no	—
307	C₂²×C₃	—	4	1	no	—
308	C₂²×C₃	C₂×C₂²⋊Dic₅	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	—	4	1	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	#4094	1	2	yes	—
317	C₃×C₄	#4095	1	1	yes	characteristic
318	C₃×C₄	#4097	1	1	yes	characteristic
319	C₂×C₅	—	4	1	no	—
320	C₂×C₅	—	8	1	no	—
321	C₂×C₅	C₃×#408	1	1	yes	characteristic
322	C₂×C₅	C₃×#417	1	1	yes	characteristic
323	C₂×C₅	C₃×#421	1	1	yes	characteristic
324	C₂³	—	2	1	no	—
325	C₂³	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
339	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
340	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
341	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
342	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
344	C₈	—	20	2	no	—
345	C₈	—	20	2	no	—
346	C₂×C₃	—	4	1	no	—
347	C₂×C₃	—	8	1	no	—
348	C₂×C₃	#65521	1	1	yes	characteristic
349	C₂×C₃	#65523	1	1	yes	characteristic
350	C₂×C₃	#65525	1	1	yes	characteristic
351	C₅	C₃×#1495	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	C₂×C₃×C₂²⋊Dic₅	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	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	C₃×#4094	1	2	yes	—
367	C₄	C₃×#4095	1	1	yes	characteristic
368	C₄	C₃×#4097	1	1	yes	characteristic
369	C₃	#10602546	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	4	1	no	—
371	C₂	—	8	1	no	—
372	C₂	C₃×#65521	1	1	yes	characteristic
373	C₂	C₃×#65523	1	1	yes	characteristic
374	C₂	C₃×#65525	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×#529	D₅
hypocenter	C₅	C₃×#1495
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
2. C₃×#65214	C₂	semidirect
3. C₃×#65213	C₂	semidirect
4. C₃×Q₈⋊#168	C₂	semidirect
5. C₃×D₄⋊#168	C₂	semidirect
6. #10602546	C₃	direct (N × H)
26. #65214	C₂×C₃	semidirect
27. #65213	C₂×C₃	semidirect
28. Q₈⋊#168	C₂×C₃	semidirect
29. D₄⋊#168	C₂×C₃	semidirect
301. C₃×C₅	#1495	semidirect
351. C₅	C₃×#1495	semidirect
369. C₃	#10602546	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×C₅×#529	2
C₃×#65214	2
C₃×#65213	2
C₃×Q₈⋊#168	2
C₃×D₄⋊#168	2
#10602546	3
C₃×#1495	5

Subgroups — C3×#10602546 #14282521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602546 #14282521