Subgroups — C₃×#10615842 #14412717

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₃×#66161	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	3	yes	maximal, complemented
5	C₃×#65521	C₂	1	3	yes	maximal, complemented
6	C₃×#65514	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#3967	C₂	1	3	yes	maximal, complemented
8	#10615842	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
10	C₃×C₅×2₋¹⁺⁴	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×#41	—	2	3	no	—
12	C₂×C₃×C₅×#41	C₂²	1	3	yes	—
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	—	2	1	no	—
15	C₂²×C₃×C₅×Q₈	C₂²	1	3	yes	—
16	C₃×#4094	—	2	4	no	—
17	C₃×Q₈×Dic₅	—	2	1	no	—
18	C₃×D₄×Dic₅	—	2	3	no	—
19	C₃×#4072	C₂²	1	3	yes	—
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	3	yes	—
21	C₂×C₃×#681	C₂²	1	3	yes	—
22	C₂²×C₃×#168	C₂²	1	3	yes	—
23	C₃×#3967	C₂²	1	3	yes	—
24	C₃×#3967	C₂²	1	6	yes	—
25	C₃×#3967	C₂²	1	3	yes	—
26	C₃×#3964	C₂²	1	3	yes	—
27	C₃×#3964	C₂²	1	1	yes	characteristic
28	C₃×#2898	—	5	1	no	maximal, Hall
29	C₂×C₅×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic
30	#66161	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
32	#65522	C₂×C₃	1	3	yes	complemented
33	#65521	C₂×C₃	1	3	yes	complemented
34	#65514	C₂×C₃	1	3	yes	complemented
35	C₂×#3967	C₂×C₃	1	3	yes	complemented
36	C₃×C₅×#41	—	2	24	no	—
37	C₃×C₅×#41	—	2	6	no	—
38	C₃×C₅×#41	C₂×C₄	1	4	yes	—
39	C₃×C₅×#41	C₂×C₄	1	12	yes	complemented
40	C₃×C₅×#41	D₄	1	4	yes	—
41	C₂×C₃×C₅×Q₈	—	2	8	no	—
42	C₂×C₃×C₅×Q₈	—	2	3	no	—
43	C₂×C₃×C₅×Q₈	—	2	6	no	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	12	yes	complemented
45	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
46	C₂×C₃×C₅×Q₈	C₂³	1	3	yes	—
47	C₂×C₃×C₅×D₄	—	2	3	no	—
48	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
49	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	—	2	3	no	—
51	C₂²×C₃×C₄×C₅	—	2	3	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
53	C₂²×C₃×Dic₅	—	2	3	no	—
54	C₃×C₂²⋊Dic₅	—	2	3	no	—
55	C₃×C₄⋊Dic₅	—	2	3	no	—
56	C₃×C₄⋊Dic₅	C₂³	1	3	yes	—
57	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
58	C₃×C₄×Dic₅	—	2	3	no	—
59	C₃×#681	—	2	6	no	—
60	C₂×C₃×#168	—	2	6	no	—
61	C₂×C₃×#168	C₂³	1	1	yes	characteristic
62	C₂×C₃×#168	C₂³	1	3	yes	—
63	C₂×C₃×2₋¹⁺⁴	D₅	1	1	yes	characteristic
64	C₂×C₃×#131	—	5	1	no	—
65	C₃×#520	—	5	1	no	—
66	C₃×#419	—	5	3	no	—
67	C₃×#417	—	5	3	no	—
68	C₃×#416	—	5	3	no	—
69	C₂×C₃×#103	—	5	3	no	—
70	C₅×2₋¹⁺⁴	—	2	4	no	—
71	C₅×2₋¹⁺⁴	C₃×C₄	1	8	yes	complemented
72	C₂×C₅×#41	—	2	3	no	—
73	C₂×C₅×#41	C₂²×C₃	1	3	yes	—
74	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₅×Q₈	—	2	1	no	—
76	C₂²×C₅×Q₈	C₂²×C₃	1	3	yes	—
77	#4094	—	2	4	no	—
78	Q₈×Dic₅	—	2	1	no	—
79	D₄×Dic₅	—	2	3	no	—
80	#4072	C₂²×C₃	1	3	yes	—
81	C₂×C₄⋊Dic₅	C₂²×C₃	1	3	yes	—
82	C₂×#681	C₂²×C₃	1	3	yes	—
83	C₂²×#168	C₂²×C₃	1	3	yes	—
84	#3967	C₂²×C₃	1	3	yes	—
85	#3967	C₂²×C₃	1	6	yes	—
86	#3967	C₂²×C₃	1	3	yes	—
87	#3964	C₂²×C₃	1	3	yes	—
88	#3964	C₂²×C₃	1	1	yes	characteristic
89	#2898	—	5	1	no	Sylow
90	C₂³×C₃×C₅	—	2	1	no	—
91	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
92	C₃×C₅×Q₈	—	2	12	no	—
93	C₃×C₅×Q₈	—	2	3	no	—
94	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
95	C₃×C₅×Q₈	C₂²×C₄	1	6	yes	—
96	C₃×C₅×D₄	—	2	12	no	—
97	C₃×C₅×D₄	—	2	1	no	—
98	C₃×C₅×D₄	C₂²⋊C₄	1	12	yes	—
99	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	—	2	12	no	—
101	C₂×C₃×C₄×C₅	—	2	3	no	—
102	C₂×C₃×C₄×C₅	—	2	12	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×Dic₅	—	2	1	no	—
108	C₂×C₃×Dic₅	—	2	3	no	—
109	C₂×C₃×Dic₅	—	8	3	no	—
110	C₃×#168	—	2	1	no	—
111	C₃×#168	—	2	3	no	—
112	C₃×2₋¹⁺⁴	—	2	4	no	—
113	C₃×2₋¹⁺⁴	Dic₅	1	8	yes	complemented
114	C₂×C₃×#41	—	2	3	no	—
115	C₂×C₃×#41	C₂×D₅	1	3	yes	—
116	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
117	C₂²×C₃×Q₈	—	2	1	no	—
118	C₂²×C₃×Q₈	C₂×D₅	1	3	yes	—
119	C₃×#131	—	10	4	no	—
120	C₂×C₃×M₁₆	—	5	3	no	—
121	C₂²×C₃×C₈	—	5	3	no	—
122	C₃×C₄×Q₈	—	10	1	no	—
123	C₃×C₄×D₄	—	10	3	no	—
124	C₃×#117	—	5	3	no	—
125	C₂×C₃×C₄⋊C₄	—	5	3	no	—
126	C₃×#103	—	5	3	no	—
127	C₃×#103	—	5	6	no	—
128	C₃×#103	—	5	3	no	—
129	C₃×#102	—	5	1	no	—
130	C₃×#102	—	5	3	no	—
131	C₅×#41	—	2	24	no	—
132	C₅×#41	—	2	6	no	—
133	C₅×#41	C₂×C₃×C₄	1	4	yes	—
134	C₅×#41	C₂×C₃×C₄	1	12	yes	complemented
135	C₅×#41	C₃×D₄	1	4	yes	—
136	C₂×C₅×Q₈	—	2	8	no	—
137	C₂×C₅×Q₈	—	2	3	no	—
138	C₂×C₅×Q₈	—	2	6	no	—
139	C₂×C₅×Q₈	C₂×C₃×C₄	1	12	yes	complemented
140	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
141	C₂×C₅×Q₈	C₂³×C₃	1	3	yes	—
142	C₂×C₅×D₄	—	2	3	no	—
143	C₂×C₅×D₄	C₃×D₄	1	3	yes	—
144	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	—	2	3	no	—
146	C₂²×C₄×C₅	—	2	3	no	—
147	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
148	C₂²×Dic₅	—	2	3	no	—
149	C₂²⋊Dic₅	—	2	3	no	—
150	C₄⋊Dic₅	—	2	3	no	—
151	C₄⋊Dic₅	C₂³×C₃	1	3	yes	—
152	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
153	C₄×Dic₅	—	2	3	no	—
154	#681	—	2	6	no	—
155	C₂×#168	—	2	6	no	—
156	C₂×#168	C₂³×C₃	1	1	yes	characteristic
157	C₂×#168	C₂³×C₃	1	3	yes	—
158	C₂×2₋¹⁺⁴	C₃×D₅	1	1	yes	characteristic
159	C₂×#131	—	5	1	no	—
160	#520	—	5	1	no	—
161	#419	—	5	3	no	—
162	#417	—	5	3	no	—
163	#416	—	5	3	no	—
164	C₂×#103	—	5	3	no	—
165	C₂²×C₃×C₅	—	2	3	no	—
166	C₂²×C₃×C₅	—	2	3	no	—
167	C₂²×C₃×C₅	—	2	2	no	—
168	C₂²×C₃×C₅	—	4	1	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₃×C₄×C₅	—	2	6	no	—
173	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	6	yes	—
174	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₃×Dic₅	—	4	3	no	—
177	C₃×Dic₅	—	4	1	no	—
178	C₃×#41	—	2	24	no	—
179	C₃×#41	—	2	6	no	—
180	C₃×#41	C₂×Dic₅	1	4	yes	—
181	C₃×#41	C₂×Dic₅	1	12	yes	complemented
182	C₃×#41	C₂²⋊D₅	1	4	yes	—
183	C₂×C₃×Q₈	—	2	8	no	—
184	C₂×C₃×Q₈	—	2	3	no	—
185	C₂×C₃×Q₈	—	2	6	no	—
186	C₂×C₃×Q₈	C₂×Dic₅	1	12	yes	complemented
187	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
188	C₂×C₃×Q₈	C₂²×D₅	1	3	yes	—
189	C₂×C₃×D₄	—	2	3	no	—
190	C₂×C₃×D₄	C₂²⋊D₅	1	3	yes	—
191	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	—	2	3	no	—
193	C₂²×C₃×C₄	—	2	3	no	—
194	C₂²×C₃×C₄	—	10	3	no	—
195	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
196	C₃×M₁₆	—	10	6	no	—
197	C₂×C₃×C₈	—	5	1	no	—
198	C₂×C₃×C₈	—	5	3	no	—
199	C₂×C₃×C₈	—	10	6	no	—
200	C₃×C₄⋊C₄	—	5	3	no	—
201	C₃×C₄⋊C₄	—	5	1	no	—
202	C₃×C₄⋊C₄	—	10	3	no	—
203	C₃×C₂²⋊C₄	—	10	3	no	—
204	C₃×C₄²	—	10	3	no	—
205	C₂³×C₅	—	2	1	no	—
206	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
207	C₅×Q₈	—	2	12	no	—
208	C₅×Q₈	—	2	3	no	—
209	C₅×Q₈	C₃×C₂²⋊C₄	1	4	yes	—
210	C₅×Q₈	C₂²×C₃×C₄	1	6	yes	—
211	C₅×D₄	—	2	12	no	—
212	C₅×D₄	—	2	1	no	—
213	C₅×D₄	C₃×C₂²⋊C₄	1	12	yes	—
214	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
215	C₂×C₄×C₅	—	2	12	no	—
216	C₂×C₄×C₅	—	2	3	no	—
217	C₂×C₄×C₅	—	2	12	no	—
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	6	yes	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
220	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
221	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
222	C₂×Dic₅	—	2	1	no	—
223	C₂×Dic₅	—	2	3	no	—
224	C₂×Dic₅	—	8	3	no	—
225	#168	—	2	1	no	—
226	#168	—	2	3	no	—
227	2₋¹⁺⁴	—	2	4	no	—
228	2₋¹⁺⁴	C₃×Dic₅	1	8	yes	complemented
229	C₂×#41	—	2	3	no	—
230	C₂×#41	C₂×C₃×D₅	1	3	yes	—
231	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	C₂×C₃×D₅	1	3	yes	—
234	#131	—	10	4	no	—
235	C₂×M₁₆	—	5	3	no	—
236	C₂²×C₈	—	5	3	no	—
237	C₄×Q₈	—	10	1	no	—
238	C₄×D₄	—	10	3	no	—
239	#117	—	5	3	no	—
240	C₂×C₄⋊C₄	—	5	3	no	—
241	#103	—	5	3	no	—
242	#103	—	5	6	no	—
243	#103	—	5	3	no	—
244	#102	—	5	1	no	—
245	#102	—	5	3	no	—
246	C₂×C₃×C₅	—	2	6	no	—
247	C₂×C₃×C₅	—	4	2	no	—
248	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₃×C₅	#577	1	1	yes	characteristic
250	C₂×C₃×C₅	#578	1	1	yes	characteristic
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	C₂×C₂²⋊D₅	1	3	yes	—
253	C₃×Q₈	—	2	12	no	—
254	C₃×Q₈	—	2	3	no	—
255	C₃×Q₈	C₂²⋊Dic₅	1	4	yes	—
256	C₃×Q₈	C₂²×Dic₅	1	6	yes	—
257	C₃×D₄	—	2	12	no	—
258	C₃×D₄	—	2	1	no	—
259	C₃×D₄	C₂²⋊Dic₅	1	12	yes	—
260	C₃×D₄	C₂²×Dic₅	1	2	yes	—
261	C₂×C₃×C₄	—	2	12	no	—
262	C₂×C₃×C₄	—	2	3	no	—
263	C₂×C₃×C₄	—	2	12	no	—
264	C₂×C₃×C₄	—	10	1	no	—
265	C₂×C₃×C₄	—	10	3	no	—
266	C₂×C₃×C₄	—	40	3	no	—
267	C₂×C₃×C₄	C₂²×Dic₅	1	6	yes	—
268	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
269	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	6	yes	—
270	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
271	C₃×C₈	—	10	1	no	—
272	C₃×C₈	—	10	3	no	—
273	C₂²×C₅	—	2	3	no	—
274	C₂²×C₅	—	2	3	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
279	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
280	C₄×C₅	—	2	6	no	—
281	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
282	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
283	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
284	Dic₅	—	4	3	no	—
285	Dic₅	—	4	1	no	—
286	#41	—	2	24	no	—
287	#41	—	2	6	no	—
288	#41	C₂×C₃×Dic₅	1	4	yes	—
289	#41	C₂×C₃×Dic₅	1	12	yes	complemented
290	#41	C₃×C₂²⋊D₅	1	4	yes	—
291	C₂×Q₈	—	2	8	no	—
292	C₂×Q₈	—	2	3	no	—
293	C₂×Q₈	—	2	6	no	—
294	C₂×Q₈	C₂×C₃×Dic₅	1	12	yes	complemented
295	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
296	C₂×Q₈	C₂²×C₃×D₅	1	3	yes	—
297	C₂×D₄	—	2	3	no	—
298	C₂×D₄	C₃×C₂²⋊D₅	1	3	yes	—
299	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
300	C₂²×C₄	—	2	3	no	—
301	C₂²×C₄	—	2	3	no	—
302	C₂²×C₄	—	10	3	no	—
303	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
304	M₁₆	—	10	6	no	—
305	C₂×C₈	—	5	1	no	—
306	C₂×C₈	—	5	3	no	—
307	C₂×C₈	—	10	6	no	—
308	C₄⋊C₄	—	5	3	no	—
309	C₄⋊C₄	—	5	1	no	—
310	C₄⋊C₄	—	10	3	no	—
311	C₂²⋊C₄	—	10	3	no	—
312	C₄²	—	10	3	no	—
313	C₃×C₅	#2898	1	1	yes	characteristic, complemented, Hall
314	C₂²×C₃	—	2	3	no	—
315	C₂²×C₃	—	2	3	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	4	1	no	—
318	C₂²×C₃	—	4	1	no	—
319	C₂²×C₃	C₂×C₂²⋊Dic₅	1	6	yes	—
320	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
321	C₃×C₄	—	2	6	no	—
322	C₃×C₄	—	20	3	no	—
323	C₃×C₄	—	20	1	no	—
324	C₃×C₄	C₂×C₂²⋊Dic₅	1	6	yes	—
325	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
326	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
327	C₂×C₅	—	2	6	no	—
328	C₂×C₅	—	4	2	no	—
329	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
330	C₂×C₅	C₃×#577	1	1	yes	characteristic
331	C₂×C₅	C₃×#578	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	C₂³	C₂×C₃×C₂²⋊D₅	1	3	yes	—
334	Q₈	—	2	12	no	—
335	Q₈	—	2	3	no	—
336	Q₈	C₃×C₂²⋊Dic₅	1	4	yes	—
337	Q₈	C₂²×C₃×Dic₅	1	6	yes	—
338	D₄	—	2	12	no	—
339	D₄	—	2	1	no	—
340	D₄	C₃×C₂²⋊Dic₅	1	12	yes	—
341	D₄	C₂²×C₃×Dic₅	1	2	yes	—
342	C₂×C₄	—	2	12	no	—
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	2	12	no	—
345	C₂×C₄	—	10	1	no	—
346	C₂×C₄	—	10	3	no	—
347	C₂×C₄	—	40	3	no	—
348	C₂×C₄	C₂²×C₃×Dic₅	1	6	yes	—
349	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
350	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	6	yes	—
351	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
352	C₈	—	10	1	no	—
353	C₈	—	10	3	no	—
354	C₂×C₃	—	2	6	no	—
355	C₂×C₃	—	4	2	no	—
356	C₂×C₃	#66171	1	1	yes	characteristic
357	C₂×C₃	#66172	1	1	yes	characteristic
358	C₂×C₃	C₂²×C₂²⋊Dic₅	1	1	yes	characteristic
359	C₅	C₃×#2898	1	1	yes	characteristic, complemented, Sylow
360	C₂²	—	2	3	no	—
361	C₂²	—	2	3	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	C₂×C₃×C₂²⋊Dic₅	1	6	yes	—
366	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
367	C₄	—	2	6	no	—
368	C₄	—	20	3	no	—
369	C₄	—	20	1	no	—
370	C₄	C₂×C₃×C₂²⋊Dic₅	1	6	yes	—
371	C₄	C₂³×C₃×Dic₅	1	1	yes	characteristic
372	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
373	C₃	#10615842	1	1	yes	characteristic, direct product factor, Sylow
374	C₂	—	2	6	no	—
375	C₂	—	4	2	no	—
376	C₂	C₃×#66171	1	1	yes	characteristic
377	C₂	C₃×#66172	1	1	yes	characteristic
378	C₂	C₂²×C₃×C₂²⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×2₋¹⁺⁴	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×2₋¹⁺⁴	D₅
hypocenter	C₅	C₃×#2898
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
2. C₃×#66161	C₂	semidirect
3. C₂×C₃×#4094	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₃×#65521	C₂	semidirect
6. C₃×#65514	C₂	semidirect
7. C₂×C₃×#3967	C₂	semidirect
8. #10615842	C₃	direct (N × H)
10. C₃×C₅×2₋¹⁺⁴	C₄	semidirect
30. #66161	C₂×C₃	semidirect
31. C₂×#4094	C₂×C₃	semidirect
32. #65522	C₂×C₃	semidirect
33. #65521	C₂×C₃	semidirect
34. #65514	C₂×C₃	semidirect
35. C₂×#3967	C₂×C₃	semidirect
39. C₃×C₅×#41	C₂×C₄	semidirect
44. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
71. C₅×2₋¹⁺⁴	C₃×C₄	semidirect
113. C₃×2₋¹⁺⁴	Dic₅	semidirect
134. C₅×#41	C₂×C₃×C₄	semidirect
139. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
181. C₃×#41	C₂×Dic₅	semidirect
186. C₂×C₃×Q₈	C₂×Dic₅	semidirect
228. 2₋¹⁺⁴	C₃×Dic₅	semidirect
289. #41	C₂×C₃×Dic₅	semidirect
294. C₂×Q₈	C₂×C₃×Dic₅	semidirect
313. C₃×C₅	#2898	semidirect
359. C₅	C₃×#2898	semidirect
373. C₃	#10615842	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×C₅×2₋¹⁺⁴	2
C₃×#66161	2
C₂×C₃×#4094	2
C₃×#65522	2
C₃×#65521	2
C₃×#65514	2
C₂×C₃×#3967	2
#10615842	3
C₃×#2898	5

Subgroups — C3×#10615842 #14412717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615842 #14412717