Subgroups — C₅×#82049 #14413915

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#5207	C₂	1	2	yes	maximal
3	C₅×#4926	C₂	1	4	yes	maximal, complemented
4	C₅×#4925	C₂	1	4	yes	maximal, complemented
5	C₅×#4924	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#208	C₂	1	2	yes	maximal, complemented
7	C₅×#2920	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₄	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²×C₅	C₄	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₄	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₄	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₅×#208	C₂²	1	4	yes	—
18	C₅×#830	C₂²	1	8	yes	—
19	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	8	yes	complemented
20	C₅×#803	C₂²	1	4	yes	complemented
21	C₄×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
22	#82049	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂²×C₄²×C₅	D₃	1	1	yes	characteristic
24	C₅×#432	—	3	4	no	—
25	C₅×#431	—	3	4	no	—
26	C₅×#423	—	3	2	no	—
27	C₅×#407	—	3	2	no	—
28	C₄×C₅×M₁₆	—	3	2	no	—
29	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	—	2	8	no	—
31	C₂²×C₃×C₄×C₅	—	2	4	no	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
43	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
44	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
45	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
46	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₄²×C₅	C₂³	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₅×#208	—	2	8	no	—
53	C₂×C₅×C₃⋊C₈	C₂³	1	8	yes	—
54	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic
55	#5207	C₂×C₅	1	2	yes	—
56	#4926	C₂×C₅	1	4	yes	complemented
57	#4925	C₂×C₅	1	4	yes	complemented
58	#4924	C₂×C₅	1	2	yes	complemented
59	C₄×#208	C₂×C₅	1	2	yes	complemented
60	C₂³×C₄×C₅	Dic₃	1	2	yes	—
61	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
62	C₂×C₅×M₁₆	—	3	4	no	—
63	C₂×C₄²×C₅	Dic₃	1	2	yes	—
64	C₂×C₄²×C₅	Dic₃	1	2	yes	—
65	C₂×C₄²×C₅	Dic₃	1	2	yes	—
66	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
68	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
70	C₅×C₄⋊C₈	—	3	8	no	—
71	C₅×C₂²⋊C₈	—	3	8	no	—
72	C₅×#97	—	3	4	no	—
73	C₄×C₅×C₈	—	3	4	no	—
74	#2920	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	M₁₆	1	8	yes	complemented
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
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	C₅×C₃⋊C₈	—	2	8	no	—
97	C₂³×C₃×C₄	C₄×C₅	1	2	yes	—
98	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
99	C₂×C₃×C₄²	C₄×C₅	1	2	yes	—
100	C₂×C₃×C₄²	C₄×C₅	1	2	yes	—
101	C₂×C₃×C₄²	C₄×C₅	1	2	yes	—
102	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
103	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
106	C₂×#208	C₂²×C₅	1	4	yes	—
107	#830	C₂²×C₅	1	8	yes	—
108	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	8	yes	complemented
109	#803	C₂²×C₅	1	4	yes	complemented
110	C₄×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
111	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
112	C₂²×C₄×C₅	—	2	8	no	—
113	C₂²×C₄×C₅	—	2	4	no	—
114	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
116	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
117	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
118	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
119	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
120	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
121	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
122	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
123	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
124	C₅×M₁₆	—	6	8	no	—
125	C₂×C₅×C₈	—	3	8	no	—
126	C₄²×C₅	C₂×Dic₃	1	2	yes	—
127	C₄²×C₅	C₂×Dic₃	1	2	yes	—
128	C₄²×C₅	C₂×Dic₃	1	2	yes	—
129	C₄²×C₅	C₂×Dic₃	1	2	yes	—
130	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
131	C₄²×C₅	C₂×Dic₃	1	2	yes	—
132	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
133	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
134	C₄²×C₅	C₂²×D₃	1	2	yes	—
135	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
136	C₂²×C₄²	C₅×D₃	1	1	yes	characteristic
137	#432	—	3	4	no	—
138	#431	—	3	4	no	—
139	#423	—	3	2	no	—
140	#407	—	3	2	no	—
141	C₄×M₁₆	—	3	2	no	—
142	C₂²×C₃×C₅	—	2	8	no	—
143	C₂²×C₃×C₅	—	2	2	no	—
144	C₂²×C₃×C₅	—	2	2	no	—
145	C₂²×C₃×C₅	—	2	2	no	—
146	C₂²×C₃×C₅	#117	1	2	yes	—
147	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
148	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
149	C₃×C₄×C₅	—	2	2	no	—
150	C₃×C₄×C₅	—	2	2	no	—
151	C₃×C₄×C₅	—	2	2	no	—
152	C₃×C₄×C₅	#117	1	2	yes	—
153	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	—
154	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	—
155	C₃×C₄×C₅	C₂×#41	1	2	yes	—
156	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
157	C₂²×C₃×C₄	—	2	8	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
161	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
162	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
163	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
164	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
165	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
166	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
170	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
171	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
172	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
173	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
174	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
175	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
176	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
177	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
178	C₃×C₄²	C₂³×C₅	1	2	yes	—
179	#208	—	2	8	no	—
180	C₂×C₃⋊C₈	C₂³×C₅	1	8	yes	—
181	C₂³×C₅	—	2	4	no	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
184	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	#208	1	8	yes	complemented
194	C₂×C₄×C₅	#235	1	4	yes	—
195	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
196	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
197	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
198	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
199	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
200	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
202	C₅×C₈	—	6	8	no	—
203	C₂³×C₄	C₅×Dic₃	1	2	yes	—
204	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
205	C₂×M₁₆	—	3	4	no	—
206	C₂×C₄²	C₅×Dic₃	1	2	yes	—
207	C₂×C₄²	C₅×Dic₃	1	2	yes	—
208	C₂×C₄²	C₅×Dic₃	1	2	yes	—
209	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
212	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
213	C₄⋊C₈	—	3	8	no	—
214	C₂²⋊C₈	—	3	8	no	—
215	#97	—	3	4	no	—
216	C₄×C₈	—	3	4	no	—
217	C₂×C₃×C₅	—	2	2	no	—
218	C₂×C₃×C₅	—	2	4	no	—
219	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
220	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
221	C₂³×C₃	—	2	2	no	—
222	C₂³×C₃	—	2	4	no	—
223	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
224	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	C₅×M₁₆	1	8	yes	complemented
234	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
235	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
236	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
237	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
239	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
240	C₂×C₃×C₄	C₅×#41	1	4	yes	—
241	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
242	C₃⋊C₈	—	2	8	no	—
243	C₂²×C₅	—	2	8	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	2	2	no	—
247	C₂²×C₅	C₂×#208	1	4	yes	—
248	C₂²×C₅	#926	1	2	yes	—
249	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	2	2	no	—
252	C₄×C₅	—	2	2	no	—
253	C₄×C₅	C₂×#208	1	4	yes	—
254	C₄×C₅	C₂×#208	1	4	yes	—
255	C₄×C₅	#926	1	2	yes	—
256	C₄×C₅	C₂×#235	1	2	yes	—
257	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
262	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
263	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
264	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
265	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
266	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
267	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
268	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
269	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
270	M₁₆	—	6	8	no	—
271	C₂×C₈	—	3	8	no	—
272	C₄²	C₂×C₅×Dic₃	1	2	yes	—
273	C₄²	C₂×C₅×Dic₃	1	2	yes	—
274	C₄²	C₂×C₅×Dic₃	1	2	yes	—
275	C₄²	C₂×C₅×Dic₃	1	2	yes	—
276	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
277	C₄²	C₂×C₅×Dic₃	1	2	yes	—
278	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
279	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
280	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
281	C₄²	C₂²×C₅×D₃	1	2	yes	—
282	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
283	C₂²×C₃	—	2	8	no	—
284	C₂²×C₃	—	2	2	no	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	C₅×#117	1	2	yes	—
288	C₂²×C₃	C₂×C₅×M₁₆	1	4	yes	—
289	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	2	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	C₅×#117	1	2	yes	—
294	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	—
295	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	—
296	C₃×C₄	C₂×C₅×#41	1	2	yes	—
297	C₂×C₅	—	2	4	no	—
298	C₂×C₅	—	2	2	no	—
299	C₂×C₅	C₂²×#208	1	2	yes	—
300	C₂×C₅	C₂×#926	1	1	yes	characteristic
301	C₂³	—	2	4	no	—
302	C₂³	—	2	2	no	—
303	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
304	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	C₅×#208	1	8	yes	complemented
314	C₂×C₄	C₅×#235	1	4	yes	—
315	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
316	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
317	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
318	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
319	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
320	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
321	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
322	C₈	—	6	8	no	—
323	C₂×C₃	—	2	2	no	—
324	C₂×C₃	—	2	4	no	—
325	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
326	C₂×C₃	C₂²×C₅×M₁₆	1	2	yes	—
327	C₅	#82049	1	1	yes	characteristic, direct product factor, Sylow
328	C₂²	—	2	8	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	C₂×C₅×#208	1	4	yes	—
333	C₂²	C₅×#926	1	2	yes	—
334	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
335	C₄	—	2	2	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	C₂×C₅×#208	1	4	yes	—
339	C₄	C₂×C₅×#208	1	4	yes	—
340	C₄	C₅×#926	1	2	yes	—
341	C₄	C₂×C₅×#235	1	2	yes	—
342	C₃	C₅×#2920	1	1	yes	characteristic, complemented, Sylow
343	C₂	—	2	4	no	—
344	C₂	—	2	2	no	—
345	C₂	C₂²×C₅×#208	1	2	yes	—
346	C₂	C₂×C₅×#926	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₅×#4926	C₂	semidirect
4. C₅×#4925	C₂	semidirect
5. C₅×#4924	C₂	semidirect
6. C₄×C₅×#208	C₂	semidirect
19. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
20. C₅×#803	C₂²	semidirect
21. C₄×C₅×C₃⋊C₈	C₂²	semidirect
22. #82049	C₅	direct (N × H)
56. #4926	C₂×C₅	semidirect
57. #4925	C₂×C₅	semidirect
58. #4924	C₂×C₅	semidirect
59. C₄×#208	C₂×C₅	semidirect
87. C₂×C₃×C₄×C₅	M₁₆	semidirect
108. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
109. #803	C₂²×C₅	semidirect
110. C₄×C₃⋊C₈	C₂²×C₅	semidirect
193. C₂×C₄×C₅	#208	semidirect
233. C₂×C₃×C₄	C₅×M₁₆	semidirect
282. C₃×C₅	#2920	semidirect
313. C₂×C₄	C₅×#208	semidirect
327. C₅	#82049	direct (N × H)
342. 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
C₂²×C₃×C₄²×C₅	2
C₅×#5207	2
C₅×#4926	2
C₅×#4925	2
C₅×#4924	2
C₄×C₅×#208	2
C₅×#2920	3
#82049	5

Subgroups — C5×#82049 #14413915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82049 #14413915