Subgroups — C₃×#10605492 #14323133

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65277	C₂	1	2	yes	maximal
4	C₃×#65262	C₂	1	2	yes	maximal, complemented
5	C₃×#65229	C₂	1	4	yes	maximal, complemented
6	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64956	C₂	1	2	yes	maximal, complemented
8	C₃×#64953	C₂	1	2	yes	maximal, complemented
9	#10605492	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#685	C₂²	1	4	yes	—
16	C₂×C₃×#685	C₂²	1	4	yes	—
17	C₂×C₃×#685	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#683	C₂²	1	4	yes	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
21	C₃×C₄×D₂₀	C₄	1	8	yes	complemented
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×#3963	C₂²	1	1	yes	characteristic
24	C₃×#3963	C₂²	1	4	yes	—
25	C₃×#3963	C₂²	1	1	yes	characteristic
26	C₃×#3963	C₂²	1	2	yes	—
27	C₃×#2319	—	5	1	no	maximal, Hall
28	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
29	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
30	#65277	C₂×C₃	1	2	yes	—
31	#65262	C₂×C₃	1	2	yes	complemented
32	#65229	C₂×C₃	1	4	yes	complemented
33	#65221	C₂×C₃	1	1	yes	characteristic, complemented
34	#64956	C₂×C₃	1	2	yes	complemented
35	#64953	C₂×C₃	1	2	yes	complemented
36	C₂³×C₃×D₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
43	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
44	C₂×C₃×D₂₀	—	2	4	no	—
45	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
46	C₂×C₃×C₄×D₅	—	4	4	no	—
47	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₄²×C₅	—	4	2	no	—
50	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
51	C₃×#685	—	4	4	no	—
52	C₃×#685	—	4	4	no	—
53	C₃×#685	C₂×C₄	1	8	yes	—
54	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
55	C₃×#683	—	4	4	no	—
56	C₃×C₄×Dic₅	—	2	4	no	—
57	C₂×C₃×C₄×D₄	—	5	1	no	—
58	C₃×#390	—	5	2	no	—
59	C₃×#389	—	5	2	no	—
60	C₃×#388	—	5	4	no	—
61	C₃×#381	—	5	2	no	—
62	C₃×#380	—	5	2	no	—
63	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
64	C₃×#376	—	5	1	no	—
65	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×#685	C₂²×C₃	1	4	yes	—
71	C₂×#685	C₂²×C₃	1	4	yes	—
72	C₂×#685	C₂²×C₃	1	2	yes	—
73	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×#683	C₂²×C₃	1	4	yes	—
75	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
76	C₄×D₂₀	C₃×C₄	1	8	yes	complemented
77	C₅×#95	C₂²×C₃	1	2	yes	—
78	#3963	C₂²×C₃	1	1	yes	characteristic
79	#3963	C₂²×C₃	1	4	yes	—
80	#3963	C₂²×C₃	1	1	yes	characteristic
81	#3963	C₂²×C₃	1	2	yes	—
82	#2319	—	5	1	no	Sylow
83	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
84	C₂²×C₃×D₅	—	2	4	no	—
85	C₂²×C₃×D₅	—	2	2	no	—
86	C₂²×C₃×D₅	—	2	4	no	—
87	C₂²×C₃×D₅	—	2	2	no	—
88	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	#41	1	4	yes	—
99	C₂×C₃×Dic₅	—	2	4	no	—
100	C₂×C₃×Dic₅	—	2	2	no	—
101	C₂×C₃×Dic₅	—	2	2	no	—
102	C₂×C₃×Dic₅	—	2	2	no	—
103	C₂×C₃×Dic₅	—	2	2	no	—
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₂×C₃×Dic₅	—	2	2	no	—
106	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
107	C₃×D₂₀	—	2	8	no	—
108	C₃×C₄×D₅	—	4	8	no	—
109	C₂²×C₃×D₄	—	5	1	no	—
110	C₂³×C₃×C₄	—	5	2	no	—
111	C₃×C₄×D₄	—	5	8	no	—
112	C₂×C₃×C₄⋊C₄	—	5	1	no	—
113	C₂×C₃×C₄⋊C₄	—	5	4	no	—
114	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
115	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
116	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
117	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
118	C₂×C₃×C₄²	—	5	2	no	—
119	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
120	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
121	C₃×#95	—	5	1	no	—
122	C₃×#95	—	5	1	no	—
123	C₃×#95	—	5	2	no	—
124	C₃×#95	—	5	4	no	—
125	C₃×#95	C₂×D₅	1	2	yes	—
126	C₂³×D₅	C₂³×C₃	1	2	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
132	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
133	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
134	C₂×D₂₀	—	2	4	no	—
135	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
136	C₂×C₄×D₅	—	4	4	no	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₄²×C₅	—	4	2	no	—
140	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
141	#685	—	4	4	no	—
142	#685	—	4	4	no	—
143	#685	C₂×C₃×C₄	1	8	yes	—
144	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
145	#683	—	4	4	no	—
146	C₄×Dic₅	—	2	4	no	—
147	C₂×C₄×D₄	—	5	1	no	—
148	#390	—	5	2	no	—
149	#389	—	5	2	no	—
150	#388	—	5	4	no	—
151	#381	—	5	2	no	—
152	#380	—	5	2	no	—
153	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
154	#376	—	5	1	no	—
155	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
157	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
159	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×C₃×D₅	—	2	4	no	—
161	C₂×C₃×D₅	—	2	4	no	—
162	C₂×C₃×D₅	—	2	4	no	—
163	C₂×C₃×D₅	—	4	4	no	—
164	C₂×C₃×D₅	—	4	4	no	—
165	C₃×C₄×C₅	—	2	2	no	—
166	C₃×C₄×C₅	—	2	2	no	—
167	C₃×C₄×C₅	—	4	4	no	—
168	C₃×C₄×C₅	#117	1	4	yes	—
169	C₃×Dic₅	—	2	4	no	—
170	C₃×Dic₅	—	4	2	no	—
171	C₃×Dic₅	—	4	2	no	—
172	C₂⁴×C₃	—	5	2	no	—
173	C₂×C₃×D₄	—	5	4	no	—
174	C₂×C₃×D₄	—	10	4	no	—
175	C₂²×C₃×C₄	—	5	2	no	—
176	C₂²×C₃×C₄	—	5	8	no	—
177	C₂²×C₃×C₄	—	5	2	no	—
178	C₂²×C₃×C₄	—	5	2	no	—
179	C₂²×C₃×C₄	—	20	4	no	—
180	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
181	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	—	5	4	no	—
186	C₃×C₄⋊C₄	—	20	4	no	—
187	C₃×C₂²⋊C₄	—	5	8	no	—
188	C₃×C₂²⋊C₄	—	20	4	no	—
189	C₃×C₂²⋊C₄	—	20	4	no	—
190	C₃×C₄²	—	4	2	no	—
191	C₃×C₄²	—	10	4	no	—
192	C₃×C₄²	C₄×D₅	1	4	yes	—
193	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
194	C₂²×D₅	—	2	4	no	—
195	C₂²×D₅	—	2	2	no	—
196	C₂²×D₅	—	2	4	no	—
197	C₂²×D₅	—	2	2	no	—
198	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
207	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
208	C₂×C₄×C₅	C₃×#41	1	4	yes	—
209	C₂×Dic₅	—	2	4	no	—
210	C₂×Dic₅	—	2	2	no	—
211	C₂×Dic₅	—	2	2	no	—
212	C₂×Dic₅	—	2	2	no	—
213	C₂×Dic₅	—	2	2	no	—
214	C₂×Dic₅	—	2	2	no	—
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
217	D₂₀	—	2	8	no	—
218	C₄×D₅	—	4	8	no	—
219	C₂²×D₄	—	5	1	no	—
220	C₂³×C₄	—	5	2	no	—
221	C₄×D₄	—	5	8	no	—
222	C₂×C₄⋊C₄	—	5	1	no	—
223	C₂×C₄⋊C₄	—	5	4	no	—
224	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
225	C₂×C₂²⋊C₄	—	5	2	no	—
226	C₂×C₂²⋊C₄	—	5	4	no	—
227	C₂×C₂²⋊C₄	—	5	4	no	—
228	C₂×C₄²	—	5	2	no	—
229	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
230	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
231	#95	—	5	1	no	—
232	#95	—	5	1	no	—
233	#95	—	5	2	no	—
234	#95	—	5	4	no	—
235	#95	C₂×C₃×D₅	1	2	yes	—
236	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
237	C₂×C₃×C₅	#518	1	1	yes	characteristic
238	C₂×C₃×C₅	#520	1	1	yes	characteristic
239	C₂×C₃×C₅	#540	1	2	yes	—
240	C₂×C₃×C₅	#542	1	2	yes	—
241	C₃×D₅	—	4	4	no	—
242	C₂³×C₃	—	5	4	no	—
243	C₂³×C₃	—	10	4	no	—
244	C₂³×C₃	—	10	2	no	—
245	C₂³×C₃	—	10	2	no	—
246	C₂³×C₃	—	10	4	no	—
247	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
248	C₃×D₄	—	10	8	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	5	4	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	—	10	2	no	—
258	C₂×C₃×C₄	—	10	2	no	—
259	C₂×C₃×C₄	—	10	2	no	—
260	C₂×C₃×C₄	—	10	2	no	—
261	C₂×C₃×C₄	—	10	2	no	—
262	C₂×C₃×C₄	—	10	2	no	—
263	C₂×C₃×C₄	—	20	8	no	—
264	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
265	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
267	C₂×C₃×C₄	#709	1	4	yes	—
268	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
269	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
270	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
271	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
272	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
273	C₂×D₅	—	2	4	no	—
274	C₂×D₅	—	2	4	no	—
275	C₂×D₅	—	2	4	no	—
276	C₂×D₅	—	4	4	no	—
277	C₂×D₅	—	4	4	no	—
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	4	4	no	—
281	C₄×C₅	C₃×#117	1	4	yes	—
282	Dic₅	—	2	4	no	—
283	Dic₅	—	4	2	no	—
284	Dic₅	—	4	2	no	—
285	C₂⁴	—	5	2	no	—
286	C₂×D₄	—	5	4	no	—
287	C₂×D₄	—	10	4	no	—
288	C₂²×C₄	—	5	2	no	—
289	C₂²×C₄	—	5	8	no	—
290	C₂²×C₄	—	5	2	no	—
291	C₂²×C₄	—	5	2	no	—
292	C₂²×C₄	—	20	4	no	—
293	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
294	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	5	4	no	—
299	C₄⋊C₄	—	20	4	no	—
300	C₂²⋊C₄	—	5	8	no	—
301	C₂²⋊C₄	—	20	4	no	—
302	C₂²⋊C₄	—	20	4	no	—
303	C₄²	—	4	2	no	—
304	C₄²	—	10	4	no	—
305	C₄²	C₃×C₄×D₅	1	4	yes	—
306	C₃×C₅	#2319	1	1	yes	characteristic, complemented, Hall
307	C₂²×C₃	—	10	4	no	—
308	C₂²×C₃	—	10	4	no	—
309	C₂²×C₃	—	10	4	no	—
310	C₂²×C₃	—	20	4	no	—
311	C₂²×C₃	—	20	4	no	—
312	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
313	C₂²×C₃	C₂×#709	1	2	yes	—
314	C₂²×C₃	#4144	1	1	yes	characteristic
315	C₂²×C₃	#4147	1	1	yes	characteristic
316	C₂²×C₃	#4149	1	2	yes	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	4	4	no	—
320	C₃×C₄	—	10	4	no	—
321	C₃×C₄	—	20	2	no	—
322	C₃×C₄	—	20	2	no	—
323	C₃×C₄	#4018	1	4	yes	—
324	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
325	C₂×C₅	C₃×#518	1	1	yes	characteristic
326	C₂×C₅	C₃×#520	1	1	yes	characteristic
327	C₂×C₅	C₃×#540	1	2	yes	—
328	C₂×C₅	C₃×#542	1	2	yes	—
329	D₅	—	4	4	no	—
330	C₂³	—	5	4	no	—
331	C₂³	—	10	4	no	—
332	C₂³	—	10	2	no	—
333	C₂³	—	10	2	no	—
334	C₂³	—	10	4	no	—
335	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
336	D₄	—	10	8	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	5	4	no	—
344	C₂×C₄	—	10	4	no	—
345	C₂×C₄	—	10	2	no	—
346	C₂×C₄	—	10	2	no	—
347	C₂×C₄	—	10	2	no	—
348	C₂×C₄	—	10	2	no	—
349	C₂×C₄	—	10	2	no	—
350	C₂×C₄	—	10	2	no	—
351	C₂×C₄	—	20	8	no	—
352	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
353	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
354	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
355	C₂×C₄	C₃×#709	1	4	yes	—
356	C₂×C₃	—	20	4	no	—
357	C₂×C₃	C₂×#4018	1	1	yes	characteristic
358	C₂×C₃	#65838	1	1	yes	characteristic
359	C₂×C₃	#65855	1	1	yes	characteristic
360	C₂×C₃	#65896	1	2	yes	—
361	C₂×C₃	#65916	1	2	yes	—
362	C₅	C₃×#2319	1	1	yes	characteristic, complemented, Sylow
363	C₂²	—	10	4	no	—
364	C₂²	—	10	4	no	—
365	C₂²	—	10	4	no	—
366	C₂²	—	20	4	no	—
367	C₂²	—	20	4	no	—
368	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
369	C₂²	C₂×C₃×#709	1	2	yes	—
370	C₂²	C₃×#4144	1	1	yes	characteristic
371	C₂²	C₃×#4147	1	1	yes	characteristic
372	C₂²	C₃×#4149	1	2	yes	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	4	4	no	—
376	C₄	—	10	4	no	—
377	C₄	—	20	2	no	—
378	C₄	—	20	2	no	—
379	C₄	C₃×#4018	1	4	yes	—
380	C₃	#10605492	1	1	yes	characteristic, direct product factor, Sylow
381	C₂	—	20	4	no	—
382	C₂	C₂×C₃×#4018	1	1	yes	characteristic
383	C₂	C₃×#65838	1	1	yes	characteristic
384	C₂	C₃×#65855	1	1	yes	characteristic
385	C₂	C₃×#65896	1	2	yes	—
386	C₂	C₃×#65916	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#2319
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₃×#65262	C₂	semidirect
5. C₃×#65229	C₂	semidirect
6. C₃×#65221	C₂	semidirect
7. C₃×#64956	C₂	semidirect
8. C₃×#64953	C₂	semidirect
9. #10605492	C₃	direct (N × H)
21. C₃×C₄×D₂₀	C₄	semidirect
29. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
31. #65262	C₂×C₃	semidirect
32. #65229	C₂×C₃	semidirect
33. #65221	C₂×C₃	semidirect
34. #64956	C₂×C₃	semidirect
35. #64953	C₂×C₃	semidirect
63. C₃×C₄×C₄⋊C₄	D₅	semidirect
76. C₄×D₂₀	C₃×C₄	semidirect
153. C₄×C₄⋊C₄	C₃×D₅	semidirect
306. C₃×C₅	#2319	semidirect
362. C₅	C₃×#2319	semidirect
380. C₃	#10605492	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×C₄×D₂₀	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×#65277	2
C₃×#65262	2
C₃×#65229	2
C₃×#65221	2
C₃×#64956	2
C₃×#64953	2
#10605492	3
C₃×#2319	5

Subgroups — C3×#10605492 #14323133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605492 #14323133