Subgroups — C₂×C₅×#5012 #14414822

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#208	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#830	C₂	1	2	yes	maximal, complemented
4	C₅×#5012	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#436	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₃×C₄×C₅×D₄	C₄	1	4	yes	—
11	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	—	2	8	no	—
16	C₂×C₅×#208	C₂²	1	8	yes	complemented
17	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₅×#830	C₂²	1	8	yes	complemented
21	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
22	C₄×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
23	C₂×#5012	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×M₁₆	—	3	2	no	—
25	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
26	C₅×#436	—	3	8	no	—
27	C₂×C₅×C₄⋊C₈	—	3	1	no	—
28	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
29	C₂×C₄×C₅×C₈	—	3	1	no	—
30	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
31	C₂×C₃×C₅×D₄	—	2	4	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
42	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
43	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
44	C₃×C₄²×C₅	C₂³	1	2	yes	—
45	C₅×#208	—	2	16	no	—
46	C₂×C₅×C₃⋊C₈	—	2	4	no	—
47	C₂×C₅×C₃⋊C₈	—	2	2	no	—
48	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
49	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
50	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
51	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
52	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
53	C₂²×#208	C₂×C₅	1	2	yes	complemented
54	C₂×#830	C₂×C₅	1	2	yes	complemented
55	#5012	C₂×C₅	1	8	yes	direct product factor
56	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂²×C₅×D₄	Dic₃	1	1	yes	characteristic
59	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
60	C₂×C₅×M₁₆	—	3	8	no	—
61	C₂×C₅×M₁₆	—	6	8	no	—
62	C₂²×C₅×C₈	—	3	1	no	—
63	C₂²×C₅×C₈	—	3	1	no	—
64	C₂²×C₅×C₈	—	3	2	no	—
65	C₄×C₅×D₄	Dic₃	1	4	yes	—
66	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
68	C₂×C₅×C₂²⋊C₄	Dic₃	1	2	yes	—
69	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
70	C₅×C₄⋊C₈	—	3	4	no	—
71	C₅×C₂²⋊C₈	—	3	8	no	—
72	C₄×C₅×C₈	—	3	4	no	—
73	C₂×#436	—	3	1	no	Sylow
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
78	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₃×C₅×D₄	—	2	8	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	8	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	#41	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₅×C₃⋊C₈	—	2	4	no	—
94	C₅×C₃⋊C₈	—	2	2	no	—
95	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
96	C₂²×C₃×D₄	C₄×C₅	1	1	yes	characteristic
97	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
98	C₃×C₄×D₄	C₄×C₅	1	4	yes	—
99	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
100	C₂×C₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
101	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
102	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
103	C₂×#208	—	2	8	no	—
104	C₂×#208	C₂²×C₅	1	8	yes	complemented
105	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
106	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
107	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
108	#830	C₂²×C₅	1	8	yes	complemented
109	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
110	C₄×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
111	C₂⁴×C₅	C₂×Dic₃	1	2	yes	—
112	C₂×C₅×D₄	—	2	4	no	—
113	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	4	no	—
116	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
118	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	—
119	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
121	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
122	C₅×M₁₆	—	6	16	no	—
123	C₂×C₅×C₈	—	3	4	no	—
124	C₂×C₅×C₈	—	3	2	no	—
125	C₂×C₅×C₈	—	3	4	no	—
126	C₂×C₅×C₈	—	3	2	no	—
127	C₂×C₅×C₈	—	6	4	no	—
128	C₂×C₅×C₈	—	6	2	no	—
129	C₅×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
130	C₅×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
131	C₄²×C₅	C₂×Dic₃	1	2	yes	—
132	C₄²×C₅	C₂²×D₃	1	2	yes	—
133	C₂²×M₁₆	—	3	2	no	—
134	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
135	#436	—	3	8	no	—
136	C₂×C₄⋊C₈	—	3	1	no	—
137	C₂×C₂²⋊C₈	—	3	2	no	—
138	C₂×C₄×C₈	—	3	1	no	—
139	C₂²×C₃×C₅	—	2	4	no	—
140	C₂²×C₃×C₅	—	2	4	no	—
141	C₂²×C₃×C₅	—	2	4	no	—
142	C₂²×C₃×C₅	—	4	8	no	—
143	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
144	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
145	C₂²×C₃×C₅	#131	1	2	yes	—
146	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
147	C₃×C₄×C₅	—	2	4	no	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
150	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
151	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
152	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
153	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
154	C₂×C₃×D₄	—	2	4	no	—
155	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	2	4	no	—
158	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
160	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
161	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
163	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
164	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
165	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
166	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
167	C₃×C₄²	C₂³×C₅	1	2	yes	—
168	#208	—	2	16	no	—
169	C₂×C₃⋊C₈	—	2	4	no	—
170	C₂×C₃⋊C₈	—	2	2	no	—
171	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
172	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
173	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
174	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	—	2	4	no	—
177	C₂³×C₅	—	2	4	no	—
178	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
179	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
180	C₅×D₄	—	2	8	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	8	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	#208	1	4	yes	complemented
187	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
188	C₂×C₄×C₅	#237	1	2	yes	—
189	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
190	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
191	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
192	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
194	C₅×C₈	—	3	4	no	—
195	C₅×C₈	—	6	4	no	—
196	C₅×C₈	—	6	2	no	—
197	C₂²×D₄	C₅×Dic₃	1	1	yes	characteristic
198	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
199	C₂×M₁₆	—	3	8	no	—
200	C₂×M₁₆	—	6	8	no	—
201	C₂²×C₈	—	3	1	no	—
202	C₂²×C₈	—	3	2	no	—
203	C₂²×C₈	—	3	1	no	—
204	C₄×D₄	C₅×Dic₃	1	4	yes	—
205	C₄×D₄	C₂×C₅×D₃	1	4	yes	—
206	C₂×C₄⋊C₄	C₅×Dic₃	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₅×Dic₃	1	2	yes	—
208	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
209	C₄⋊C₈	—	3	4	no	—
210	C₂²⋊C₈	—	3	8	no	—
211	C₄×C₈	—	3	4	no	—
212	C₂×C₃×C₅	—	4	4	no	—
213	C₂×C₃×C₅	#436	1	4	yes	complemented
214	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
216	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
221	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
222	C₃×D₄	—	2	8	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	8	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	C₅×M₁₆	1	4	yes	complemented
229	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
230	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
231	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
233	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
234	C₂×C₃×C₄	C₅×#41	1	2	yes	—
235	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
236	C₃⋊C₈	—	2	4	no	—
237	C₃⋊C₈	—	2	2	no	—
238	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
239	C₂²×C₅	—	2	4	no	—
240	C₂²×C₅	—	2	4	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	4	8	no	—
243	C₂²×C₅	C₂×#208	1	2	yes	—
244	C₂²×C₅	D₄×Dic₃	1	2	yes	—
245	C₂²×C₅	#948	1	2	yes	—
246	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
247	C₄×C₅	—	2	4	no	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	C₂×#208	1	4	yes	complemented
250	C₄×C₅	D₄×Dic₃	1	2	yes	—
251	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
252	C₄×C₅	C₂×#237	1	1	yes	characteristic
253	C₂⁴	C₂×C₅×Dic₃	1	2	yes	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
260	C₂²×C₄	C₂×C₅×Dic₃	1	4	yes	—
261	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
263	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
264	M₁₆	—	6	16	no	—
265	C₂×C₈	—	3	4	no	—
266	C₂×C₈	—	3	2	no	—
267	C₂×C₈	—	3	2	no	—
268	C₂×C₈	—	3	4	no	—
269	C₂×C₈	—	6	4	no	—
270	C₂×C₈	—	6	2	no	—
271	C₄⋊C₄	C₂×C₅×Dic₃	1	4	yes	—
272	C₂²⋊C₄	C₂×C₅×Dic₃	1	8	yes	—
273	C₄²	C₂×C₅×Dic₃	1	2	yes	—
274	C₄²	C₂²×C₅×D₃	1	2	yes	—
275	C₃×C₅	C₂×#436	1	1	yes	characteristic, complemented, Hall
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	2	4	no	—
278	C₂²×C₃	—	2	4	no	—
279	C₂²×C₃	—	4	8	no	—
280	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
281	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
282	C₂²×C₃	C₅×#131	1	2	yes	—
283	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
284	C₃×C₄	—	2	4	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
287	C₃×C₄	C₂×C₅×M₁₆	1	4	yes	complemented
288	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
289	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
290	C₂×C₅	—	4	4	no	—
291	C₂×C₅	#5012	1	4	yes	direct product factor
292	C₂×C₅	C₂²×#208	1	1	yes	characteristic
293	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
294	C₂×C₅	C₂×#948	1	1	yes	characteristic
295	C₂³	—	2	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	C₂²×C₅×Dic₃	1	4	yes	—
299	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
300	D₄	—	2	8	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	C₅×#208	1	4	yes	complemented
307	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
308	C₂×C₄	C₅×#237	1	2	yes	—
309	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
310	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
311	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
312	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
313	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
314	C₈	—	3	4	no	—
315	C₈	—	6	4	no	—
316	C₈	—	6	2	no	—
317	C₂×C₃	—	4	4	no	—
318	C₂×C₃	C₅×#436	1	4	yes	complemented
319	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
320	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
321	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
322	C₅	C₂×#5012	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	4	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	4	8	no	—
327	C₂²	C₂×C₅×#208	1	2	yes	—
328	C₂²	C₅×D₄×Dic₃	1	2	yes	—
329	C₂²	C₅×#948	1	2	yes	—
330	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
331	C₄	—	2	4	no	—
332	C₄	—	2	2	no	—
333	C₄	C₂×C₅×#208	1	4	yes	complemented
334	C₄	C₅×D₄×Dic₃	1	2	yes	—
335	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
336	C₄	C₂×C₅×#237	1	1	yes	characteristic
337	C₃	C₂×C₅×#436	1	1	yes	characteristic, complemented, Sylow
338	C₂	—	4	4	no	—
339	C₂	C₅×#5012	1	4	yes	direct product factor
340	C₂	C₂²×C₅×#208	1	1	yes	characteristic
341	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic
342	C₂	C₂×C₅×#948	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₃×C₅×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#436
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#208	C₂	semidirect
3. C₂×C₅×#830	C₂	semidirect
4. C₅×#5012	C₂	direct (N × H)
5. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
16. C₂×C₅×#208	C₂²	semidirect
20. C₅×#830	C₂²	semidirect
21. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
22. C₄×C₅×C₃⋊C₈	C₂²	semidirect
23. C₂×#5012	C₅	direct (N × H)
48. C₂×C₅×C₃⋊C₈	D₄	semidirect
53. C₂²×#208	C₂×C₅	semidirect
54. C₂×#830	C₂×C₅	semidirect
55. #5012	C₂×C₅	direct (N × H)
56. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
57. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
85. C₂×C₃×C₄×C₅	M₁₆	semidirect
95. C₅×C₃⋊C₈	C₂×D₄	semidirect
104. C₂×#208	C₂²×C₅	semidirect
108. #830	C₂²×C₅	semidirect
109. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
110. C₄×C₃⋊C₈	C₂²×C₅	semidirect
150. C₃×C₄×C₅	C₂×M₁₆	semidirect
171. C₂×C₃⋊C₈	C₅×D₄	semidirect
186. C₂×C₄×C₅	#208	semidirect
213. C₂×C₃×C₅	#436	semidirect
228. C₂×C₃×C₄	C₅×M₁₆	semidirect
238. C₃⋊C₈	C₂×C₅×D₄	semidirect
249. C₄×C₅	C₂×#208	semidirect
275. C₃×C₅	C₂×#436	semidirect
287. C₃×C₄	C₂×C₅×M₁₆	semidirect
291. C₂×C₅	#5012	direct (N × H)
306. C₂×C₄	C₅×#208	semidirect
318. C₂×C₃	C₅×#436	semidirect
322. C₅	C₂×#5012	direct (N × H)
333. C₄	C₂×C₅×#208	semidirect
337. C₃	C₂×C₅×#436	semidirect
339. C₂	C₅×#5012	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×C₅×D₄	2
C₂²×C₅×#208	2
C₂×C₅×#830	2
C₅×#5012	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₄×C₅×C₃⋊C₈	2
C₂×C₅×#436	3
C₂×#5012	5

Subgroups — C2×C5×#5012 #14414822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5012 #14414822