Subgroups — C₅×#78517 #14413909

Order 1920.

968 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	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5126	C₂	1	2	yes	maximal
4	C₅×#5118	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4705	C₂	1	4	yes	maximal, complemented
7	C₅×#4685	C₂	1	4	yes	maximal, complemented
8	C₅×#2920	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₄	1	2	yes	—
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	2	yes	—
16	C₄²×C₅×D₃	C₄	1	2	yes	—
17	C₄²×C₅×D₃	C₄	1	2	yes	—
18	C₄²×C₅×D₃	C₂²	1	2	yes	—
19	C₄²×C₅×D₃	C₂²	1	2	yes	—
20	C₃×C₅×#97	C₂²	1	2	yes	complemented
21	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
22	C₅×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
23	C₅×Dic₃⋊C₈	C₂²	1	8	yes	complemented
24	C₅×#803	C₂²	1	2	yes	complemented
25	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
26	#78517	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂²×C₄²×C₅	—	3	1	no	—
28	C₅×#432	—	3	4	no	—
29	C₅×#431	—	3	4	no	—
30	C₅×#423	—	3	2	no	—
31	C₅×#407	—	3	2	no	—
32	C₄×C₅×M₁₆	—	3	1	no	—
33	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
39	C₂×C₄×C₅×D₃	—	2	4	no	—
40	C₂×C₄×C₅×D₃	—	2	8	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
45	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
46	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	4	no	—
48	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
49	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
55	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
56	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
57	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
58	C₄×C₅×Dic₃	C₂³	1	2	yes	—
59	C₅×#208	—	2	4	no	—
60	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
61	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
62	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
63	#5126	C₂×C₅	1	2	yes	—
64	#5118	C₂×C₅	1	2	yes	complemented
65	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
66	#4705	C₂×C₅	1	4	yes	complemented
67	#4685	C₂×C₅	1	4	yes	complemented
68	C₂³×C₄×C₅	—	3	2	no	—
69	C₂³×C₄×C₅	—	3	1	no	—
70	C₂×C₅×M₁₆	—	3	2	no	—
71	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
72	C₂×C₄²×C₅	—	3	2	no	—
73	C₂×C₄²×C₅	—	3	1	no	—
74	C₂×C₄²×C₅	—	3	2	no	—
75	C₂×C₄²×C₅	—	3	2	no	—
76	C₂×C₄²×C₅	—	3	2	no	—
77	C₂×C₄²×C₅	—	3	2	no	—
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	—	3	8	no	—
80	C₅×C₂²⋊C₈	—	3	8	no	—
81	C₅×#97	—	3	2	no	—
82	C₅×#97	C₂×D₃	1	2	yes	complemented
83	C₄×C₅×C₈	—	3	2	no	—
84	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
85	#2920	—	3	1	no	Sylow
86	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₅×D₃	—	2	2	no	—
88	C₂²×C₅×D₃	—	2	4	no	—
89	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	4	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₅×Dic₃	—	2	2	no	—
97	C₂×C₅×Dic₃	—	2	4	no	—
98	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
99	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
100	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
101	C₄×C₅×D₃	—	2	4	no	—
102	C₄×C₅×D₃	—	2	4	no	—
103	C₄×C₅×D₃	—	2	4	no	—
104	C₄×C₅×D₃	—	2	4	no	—
105	C₄×C₅×D₃	—	2	4	no	—
106	C₄×C₅×D₃	M₁₆	1	8	yes	complemented
107	C₃×C₅×C₈	—	2	4	no	—
108	C₅×C₃⋊C₈	—	2	4	no	—
109	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
110	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
113	C₂×C₄×Dic₃	C₄×C₅	1	2	yes	—
114	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
115	C₂×#208	C₂²×C₅	1	2	yes	—
116	C₄²×D₃	C₄×C₅	1	2	yes	—
117	C₄²×D₃	C₄×C₅	1	2	yes	—
118	C₄²×D₃	C₂²×C₅	1	2	yes	—
119	C₄²×D₃	C₂²×C₅	1	2	yes	—
120	C₃×#97	C₂²×C₅	1	2	yes	complemented
121	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
122	(C₂×D₃)⋊C₈	C₂²×C₅	1	8	yes	—
123	Dic₃⋊C₈	C₂²×C₅	1	8	yes	complemented
124	#803	C₂²×C₅	1	2	yes	complemented
125	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
126	C₂⁴×C₅	—	3	1	no	—
127	C₂²×C₄×C₅	—	3	2	no	—
128	C₂²×C₄×C₅	—	3	2	no	—
129	C₂²×C₄×C₅	—	3	1	no	—
130	C₂²×C₄×C₅	—	3	2	no	—
131	C₂²×C₄×C₅	—	3	2	no	—
132	C₂²×C₄×C₅	—	3	2	no	—
133	C₂²×C₄×C₅	—	3	2	no	—
134	C₂²×C₄×C₅	—	3	2	no	—
135	C₂²×C₄×C₅	—	6	8	no	—
136	C₂²×C₄×C₅	—	6	4	no	—
137	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₅×M₁₆	—	2	4	no	—
140	C₅×M₁₆	—	6	4	no	—
141	C₂×C₅×C₈	—	3	4	no	—
142	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
143	C₄²×C₅	—	3	1	no	—
144	C₄²×C₅	—	3	2	no	—
145	C₄²×C₅	—	3	2	no	—
146	C₄²×C₅	—	3	2	no	—
147	C₄²×C₅	—	3	1	no	—
148	C₄²×C₅	—	3	2	no	—
149	C₄²×C₅	—	3	2	no	—
150	C₄²×C₅	C₄×D₃	1	2	yes	—
151	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₂²×C₄²	—	3	1	no	—
154	#432	—	3	4	no	—
155	#431	—	3	4	no	—
156	#423	—	3	2	no	—
157	#407	—	3	2	no	—
158	C₄×M₁₆	—	3	1	no	—
159	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	#117	1	2	yes	—
162	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₅×D₃	—	2	8	no	—
164	C₂×C₅×D₃	—	2	2	no	—
165	C₂×C₅×D₃	—	2	2	no	—
166	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	#117	1	2	yes	—
169	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	—
170	C₃×C₄×C₅	C₂×#41	1	2	yes	—
171	C₅×Dic₃	—	2	2	no	—
172	C₅×Dic₃	—	2	2	no	—
173	C₅×Dic₃	C₂×M₁₆	1	4	yes	—
174	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
178	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
179	C₂×C₄×D₃	—	2	4	no	—
180	C₂×C₄×D₃	—	2	8	no	—
181	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
182	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
183	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
184	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
185	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
186	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
187	C₃×M₁₆	—	2	4	no	—
188	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
189	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
190	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
191	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
192	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
193	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
194	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
195	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
196	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
197	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
198	C₄×Dic₃	C₂³×C₅	1	2	yes	—
199	#208	—	2	4	no	—
200	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
201	C₂³×C₅	—	3	2	no	—
202	C₂³×C₅	—	6	4	no	—
203	C₂³×C₅	—	6	2	no	—
204	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	3	2	no	—
207	C₂×C₄×C₅	—	3	8	no	—
208	C₂×C₄×C₅	—	3	2	no	—
209	C₂×C₄×C₅	—	3	2	no	—
210	C₂×C₄×C₅	—	6	4	no	—
211	C₂×C₄×C₅	—	6	4	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	—	6	2	no	—
214	C₂×C₄×C₅	—	6	4	no	—
215	C₂×C₄×C₅	—	6	4	no	—
216	C₂×C₄×C₅	—	6	4	no	—
217	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
218	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
220	C₂×C₄×C₅	#235	1	4	yes	—
221	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
222	C₅×C₈	—	2	4	no	—
223	C₅×C₈	—	6	4	no	—
224	C₂³×C₄	—	3	2	no	—
225	C₂³×C₄	—	3	1	no	—
226	C₂×M₁₆	—	3	2	no	—
227	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
228	C₂×C₄²	—	3	2	no	—
229	C₂×C₄²	—	3	1	no	—
230	C₂×C₄²	—	3	2	no	—
231	C₂×C₄²	—	3	2	no	—
232	C₂×C₄²	—	3	2	no	—
233	C₂×C₄²	—	3	2	no	—
234	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄⋊C₈	—	3	8	no	—
236	C₂²⋊C₈	—	3	8	no	—
237	#97	—	3	2	no	—
238	#97	C₂×C₅×D₃	1	2	yes	complemented
239	C₄×C₈	—	3	2	no	—
240	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
244	C₅×D₃	—	2	4	no	—
245	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
246	C₂²×D₃	—	2	2	no	—
247	C₂²×D₃	—	2	4	no	—
248	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
251	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
253	C₂×C₃×C₄	C₅×#41	1	4	yes	—
254	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
255	C₂×Dic₃	—	2	2	no	—
256	C₂×Dic₃	—	2	4	no	—
257	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
258	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
259	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
260	C₄×D₃	—	2	4	no	—
261	C₄×D₃	—	2	4	no	—
262	C₄×D₃	—	2	4	no	—
263	C₄×D₃	—	2	4	no	—
264	C₄×D₃	—	2	4	no	—
265	C₄×D₃	C₅×M₁₆	1	8	yes	complemented
266	C₃×C₈	—	2	4	no	—
267	C₃⋊C₈	—	2	4	no	—
268	C₂²×C₅	—	2	2	no	—
269	C₂²×C₅	—	3	4	no	—
270	C₂²×C₅	—	6	8	no	—
271	C₂²×C₅	—	6	2	no	—
272	C₂²×C₅	—	6	2	no	—
273	C₂²×C₅	#872	1	2	yes	—
274	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
275	C₄×C₅	—	2	2	no	—
276	C₄×C₅	—	3	4	no	—
277	C₄×C₅	—	6	2	no	—
278	C₄×C₅	—	6	2	no	—
279	C₄×C₅	#872	1	2	yes	—
280	C₄×C₅	D₃×M₁₆	1	4	yes	—
281	C₄×C₅	C₂×#235	1	2	yes	—
282	C₂⁴	—	3	1	no	—
283	C₂²×C₄	—	3	2	no	—
284	C₂²×C₄	—	3	2	no	—
285	C₂²×C₄	—	3	1	no	—
286	C₂²×C₄	—	3	2	no	—
287	C₂²×C₄	—	3	2	no	—
288	C₂²×C₄	—	3	2	no	—
289	C₂²×C₄	—	3	2	no	—
290	C₂²×C₄	—	3	2	no	—
291	C₂²×C₄	—	6	8	no	—
292	C₂²×C₄	—	6	4	no	—
293	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
294	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
295	M₁₆	—	2	4	no	—
296	M₁₆	—	6	4	no	—
297	C₂×C₈	—	3	4	no	—
298	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
299	C₄²	—	3	1	no	—
300	C₄²	—	3	2	no	—
301	C₄²	—	3	2	no	—
302	C₄²	—	3	2	no	—
303	C₄²	—	3	1	no	—
304	C₄²	—	3	2	no	—
305	C₄²	—	3	2	no	—
306	C₄²	C₄×C₅×D₃	1	2	yes	—
307	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
308	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
309	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	C₅×#117	1	2	yes	—
312	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₂×D₃	—	2	8	no	—
314	C₂×D₃	—	2	2	no	—
315	C₂×D₃	—	2	2	no	—
316	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	C₅×#117	1	2	yes	—
319	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	—
320	C₃×C₄	C₂×C₅×#41	1	2	yes	—
321	Dic₃	—	2	2	no	—
322	Dic₃	—	2	2	no	—
323	Dic₃	C₂×C₅×M₁₆	1	4	yes	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	6	4	no	—
326	C₂×C₅	C₂×#872	1	1	yes	characteristic
327	C₂×C₅	C₂×D₃×M₁₆	1	2	yes	—
328	C₂³	—	3	2	no	—
329	C₂³	—	6	4	no	—
330	C₂³	—	6	2	no	—
331	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	3	2	no	—
334	C₂×C₄	—	3	8	no	—
335	C₂×C₄	—	3	2	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	6	4	no	—
338	C₂×C₄	—	6	4	no	—
339	C₂×C₄	—	6	4	no	—
340	C₂×C₄	—	6	2	no	—
341	C₂×C₄	—	6	4	no	—
342	C₂×C₄	—	6	4	no	—
343	C₂×C₄	—	6	4	no	—
344	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
345	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
347	C₂×C₄	C₅×#235	1	4	yes	—
348	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₈	—	6	4	no	—
351	C₂×C₃	—	2	2	no	—
352	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
353	C₂×C₃	C₂²×C₅×M₁₆	1	2	yes	—
354	D₃	—	2	4	no	—
355	C₅	#78517	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²	—	2	2	no	—
357	C₂²	—	3	4	no	—
358	C₂²	—	6	8	no	—
359	C₂²	—	6	2	no	—
360	C₂²	—	6	2	no	—
361	C₂²	C₅×#872	1	2	yes	—
362	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	3	4	no	—
365	C₄	—	6	2	no	—
366	C₄	—	6	2	no	—
367	C₄	C₅×#872	1	2	yes	—
368	C₄	C₅×D₃×M₁₆	1	4	yes	—
369	C₄	C₂×C₅×#235	1	2	yes	—
370	C₃	C₅×#2920	1	1	yes	characteristic, complemented, Sylow
371	C₂	—	2	2	no	—
372	C₂	—	6	4	no	—
373	C₂	C₂×C₅×#872	1	1	yes	characteristic
374	C₂	C₂×C₅×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₄²×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#2920
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₅×#5118	C₂	semidirect
5. C₄×C₅×#208	C₂	semidirect
6. C₅×#4705	C₂	semidirect
7. C₅×#4685	C₂	semidirect
20. C₃×C₅×#97	C₂²	semidirect
21. C₃×C₄×C₅×C₈	C₂²	semidirect
23. C₅×Dic₃⋊C₈	C₂²	semidirect
24. C₅×#803	C₂²	semidirect
25. C₄×C₅×C₃⋊C₈	C₂²	semidirect
26. #78517	C₅	direct (N × H)
33. C₄×C₅×M₁₆	D₃	semidirect
62. C₃×C₄×M₁₆	C₂×C₅	semidirect
64. #5118	C₂×C₅	semidirect
65. C₄×#208	C₂×C₅	semidirect
66. #4705	C₂×C₅	semidirect
67. #4685	C₂×C₅	semidirect
82. C₅×#97	C₂×D₃	semidirect
84. C₄×C₅×C₈	C₂×D₃	semidirect
106. C₄×C₅×D₃	M₁₆	semidirect
120. C₃×#97	C₂²×C₅	semidirect
121. C₃×C₄×C₈	C₂²×C₅	semidirect
123. Dic₃⋊C₈	C₂²×C₅	semidirect
124. #803	C₂²×C₅	semidirect
125. C₄×C₃⋊C₈	C₂²×C₅	semidirect
159. C₄×M₁₆	C₅×D₃	semidirect
238. #97	C₂×C₅×D₃	semidirect
240. C₄×C₈	C₂×C₅×D₃	semidirect
265. C₄×D₃	C₅×M₁₆	semidirect
309. C₃×C₅	#2920	semidirect
355. C₅	#78517	direct (N × H)
370. C₃	C₅×#2920	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄²×C₅×D₃	2
C₃×C₄×C₅×M₁₆	2
C₅×#5126	2
C₅×#5118	2
C₄×C₅×#208	2
C₅×#4705	2
C₅×#4685	2
C₅×#2920	3
#78517	5

Subgroups — C5×#78517 #14413909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78517 #14413909