Subgroups — C₂×C₅×#5033 #14431398

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5033	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#807	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#480	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	—	2	1	no	—
12	C₃×C₅×#121	—	2	2	no	—
13	C₃×C₅×#121	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	—	2	2	no	—
17	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	complemented
20	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
21	C₅×#832	C₂²	1	8	yes	complemented
22	C₅×#830	C₂²	1	4	yes	complemented
23	C₅×#807	C₂²	1	8	yes	complemented
24	C₂×#5033	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×#121	D₃	1	1	yes	characteristic
26	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
27	C₅×#480	—	3	8	no	—
28	C₂×C₅×#107	—	3	2	no	—
29	C₂×C₅×#102	—	3	2	no	—
30	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
31	C₂⁴×C₃×C₅	—	2	1	no	—
32	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	4	4	no	—
37	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	2	no	—
45	C₂²×C₅×Dic₃	—	2	4	no	—
46	C₂²×C₅×Dic₃	—	4	4	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
49	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
50	C₅×C₄⋊Dic₃	—	2	2	no	—
51	C₅×C₄⋊Dic₃	—	2	4	no	—
52	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
53	C₂×C₅×C₃⋊C₈	—	2	4	no	—
54	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
55	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
56	C₂²×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×#832	C₂×C₅	1	2	yes	complemented
58	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
59	#5033	C₂×C₅	1	8	yes	direct product factor
60	C₂×#807	C₂×C₅	1	2	yes	complemented
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	6	1	no	—
64	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
65	C₂²×C₅×C₈	—	3	2	no	—
66	C₅×#121	—	2	2	no	—
67	C₅×#121	C₂×D₃	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	—	3	2	no	—
69	C₂×C₅×C₄⋊C₄	—	3	4	no	—
70	C₂×C₅×C₄⋊C₄	—	6	2	no	—
71	C₂×C₅×C₄⋊C₄	—	6	1	no	—
72	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
73	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₅×#107	—	3	8	no	—
75	C₅×#102	—	3	8	no	—
76	C₅×C₂²⋊C₈	—	3	4	no	—
77	C₂×#480	—	3	1	no	Sylow
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	2	2	no	—
81	C₂³×C₃×C₅	—	4	2	no	—
82	C₂³×C₃×C₅	—	4	2	no	—
83	C₂³×C₃×C₅	—	4	2	no	—
84	C₂³×C₃×C₅	D₈	1	4	yes	—
85	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
86	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
87	C₃×C₅×D₄	—	2	4	no	—
88	C₃×C₅×D₄	—	4	8	no	—
89	C₃×C₅×D₄	—	4	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
99	C₂×C₅×Dic₃	—	2	4	no	—
100	C₂×C₅×Dic₃	—	4	8	no	—
101	C₂×C₅×Dic₃	—	4	4	no	—
102	C₅×C₃⋊C₈	—	2	4	no	—
103	C₂²×C₃×D₄	—	2	1	no	—
104	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂³×Dic₃	—	2	1	no	—
107	C₃×#121	—	2	2	no	—
108	C₃×#121	C₂²×C₅	1	4	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₄⋊Dic₃	—	2	2	no	—
112	C₂×C₄⋊Dic₃	—	2	1	no	—
113	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
114	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	complemented
115	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
116	#832	C₂²×C₅	1	8	yes	complemented
117	#830	C₂²×C₅	1	4	yes	complemented
118	#807	C₂²×C₅	1	8	yes	complemented
119	C₂⁴×C₅	—	2	1	no	—
120	C₂⁴×C₅	#67	1	1	yes	characteristic
121	C₂×C₅×D₄	—	2	4	no	—
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	4	4	no	—
125	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	6	4	no	—
129	C₂²×C₄×C₅	—	6	2	no	—
130	C₂²×C₄×C₅	—	12	4	no	—
131	C₂²×C₄×C₅	#67	1	2	yes	—
132	C₂²×C₄×C₅	#67	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
134	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
135	C₂×C₅×C₈	—	3	4	no	—
136	C₂×C₅×C₈	—	6	4	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	3	4	no	—
139	C₅×C₄⋊C₄	—	6	4	no	—
140	C₅×C₄⋊C₄	—	6	2	no	—
141	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
142	C₅×C₂²⋊C₄	—	2	4	no	—
143	C₂×#121	C₅×D₃	1	1	yes	characteristic
144	C₂²×C₄⋊C₄	—	3	1	no	—
145	#480	—	3	8	no	—
146	C₂×#107	—	3	2	no	—
147	C₂×#102	—	3	2	no	—
148	C₂×C₂²⋊C₈	—	3	1	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	2	2	no	—
151	C₂²×C₃×C₅	—	2	8	no	—
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	8	4	no	—
156	C₂²×C₃×C₅	#123	1	2	yes	—
157	C₂²×C₃×C₅	C₂×D₈	1	4	yes	—
158	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
159	C₂²×C₃×C₅	#137	1	2	yes	—
160	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
161	C₃×C₄×C₅	—	2	2	no	—
162	C₃×C₄×C₅	—	4	2	no	—
163	C₃×C₄×C₅	#123	1	2	yes	—
164	C₃×C₄×C₅	C₂×#41	1	2	yes	—
165	C₅×Dic₃	—	4	4	no	—
166	C₂⁴×C₃	—	2	1	no	—
167	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
168	C₂×C₃×D₄	—	2	4	no	—
169	C₂×C₃×D₄	—	2	1	no	—
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	—	4	4	no	—
172	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂²×Dic₃	—	2	2	no	—
180	C₂²×Dic₃	—	2	4	no	—
181	C₂²×Dic₃	—	4	4	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
184	C₃×C₂²⋊C₄	—	2	4	no	—
185	C₄⋊Dic₃	—	2	2	no	—
186	C₄⋊Dic₃	—	2	4	no	—
187	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
188	C₂×C₃⋊C₈	—	2	4	no	—
189	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
190	C₂³×C₅	—	2	2	no	—
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	4	2	no	—
194	C₂³×C₅	—	4	2	no	—
195	C₂³×C₅	—	4	2	no	—
196	C₂³×C₅	#213	1	4	yes	—
197	C₂³×C₅	C₂×#67	1	2	yes	—
198	C₂³×C₅	C₂×#67	1	1	yes	characteristic
199	C₅×D₄	—	2	4	no	—
200	C₅×D₄	—	4	8	no	—
201	C₅×D₄	—	4	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	6	4	no	—
208	C₂×C₄×C₅	—	12	8	no	—
209	C₂×C₄×C₅	—	12	4	no	—
210	C₂×C₄×C₅	#237	1	4	yes	—
211	C₂×C₄×C₅	C₂×#67	1	2	yes	—
212	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
214	C₅×C₈	—	6	4	no	—
215	C₂²×D₄	—	2	1	no	—
216	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
217	C₂³×C₄	—	6	1	no	—
218	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
219	C₂²×C₈	—	3	2	no	—
220	#121	—	2	2	no	—
221	#121	C₂×C₅×D₃	1	4	yes	—
222	C₂×C₄⋊C₄	—	3	2	no	—
223	C₂×C₄⋊C₄	—	3	4	no	—
224	C₂×C₄⋊C₄	—	6	1	no	—
225	C₂×C₄⋊C₄	—	6	2	no	—
226	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	#107	—	3	8	no	—
229	#102	—	3	8	no	—
230	C₂²⋊C₈	—	3	4	no	—
231	C₂×C₃×C₅	—	2	4	no	—
232	C₂×C₃×C₅	—	8	2	no	—
233	C₂×C₃×C₅	#480	1	4	yes	complemented
234	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
235	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
236	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	2	2	no	—
240	C₂³×C₃	—	4	2	no	—
241	C₂³×C₃	—	4	2	no	—
242	C₂³×C₃	—	4	2	no	—
243	C₂³×C₃	C₅×D₈	1	4	yes	—
244	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
245	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
246	C₃×D₄	—	2	4	no	—
247	C₃×D₄	—	4	8	no	—
248	C₃×D₄	—	4	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	4	2	no	—
254	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₅×#41	1	4	yes	—
257	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
258	C₂×Dic₃	—	2	4	no	—
259	C₂×Dic₃	—	4	8	no	—
260	C₂×Dic₃	—	4	4	no	—
261	C₃⋊C₈	—	2	4	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	8	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	—	4	2	no	—
267	C₂²×C₅	—	4	2	no	—
268	C₂²×C₅	—	8	4	no	—
269	C₂²×C₅	C₂×#213	1	4	yes	—
270	C₂²×C₅	C₂×#213	1	2	yes	—
271	C₂²×C₅	#935	1	2	yes	—
272	C₂²×C₅	#951	1	2	yes	—
273	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	12	4	no	—
277	C₄×C₅	#935	1	2	yes	—
278	C₄×C₅	C₂×#237	1	2	yes	—
279	C₂⁴	—	2	1	no	—
280	C₂⁴	C₅×#67	1	1	yes	characteristic
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	6	4	no	—
289	C₂²×C₄	—	6	2	no	—
290	C₂²×C₄	—	12	4	no	—
291	C₂²×C₄	C₅×#67	1	1	yes	characteristic
292	C₂²×C₄	C₅×#67	1	2	yes	—
293	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
294	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
295	C₂×C₈	—	3	4	no	—
296	C₂×C₈	—	6	4	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	3	4	no	—
299	C₄⋊C₄	—	6	4	no	—
300	C₄⋊C₄	—	6	2	no	—
301	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₃×C₅	C₂×#480	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	2	8	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	4	2	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	4	2	no	—
310	C₂²×C₃	—	8	4	no	—
311	C₂²×C₃	C₅×#123	1	2	yes	—
312	C₂²×C₃	C₂×C₅×D₈	1	4	yes	—
313	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
314	C₂²×C₃	C₅×#137	1	2	yes	—
315	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	C₅×#123	1	2	yes	—
319	C₃×C₄	C₂×C₅×#41	1	2	yes	—
320	Dic₃	—	4	4	no	—
321	C₂×C₅	—	2	4	no	—
322	C₂×C₅	—	8	2	no	—
323	C₂×C₅	#5033	1	4	yes	direct product factor
324	C₂×C₅	C₂²×#213	1	1	yes	characteristic
325	C₂×C₅	C₂×#935	1	1	yes	characteristic
326	C₂×C₅	C₂×#951	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	C₅×#213	1	4	yes	—
334	C₂³	C₂×C₅×#67	1	2	yes	—
335	C₂³	C₂×C₅×#67	1	1	yes	characteristic
336	D₄	—	2	4	no	—
337	D₄	—	4	8	no	—
338	D₄	—	4	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	6	4	no	—
345	C₂×C₄	—	12	8	no	—
346	C₂×C₄	—	12	4	no	—
347	C₂×C₄	C₅×#237	1	4	yes	—
348	C₂×C₄	C₂×C₅×#67	1	2	yes	—
349	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
350	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
351	C₈	—	6	4	no	—
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	—	8	2	no	—
354	C₂×C₃	C₅×#480	1	4	yes	complemented
355	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
356	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
357	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
358	C₅	C₂×#5033	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	8	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	8	4	no	—
366	C₂²	C₂×C₅×#213	1	4	yes	—
367	C₂²	C₂×C₅×#213	1	2	yes	—
368	C₂²	C₅×#935	1	2	yes	—
369	C₂²	C₅×#951	1	2	yes	—
370	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	12	4	no	—
374	C₄	C₅×#935	1	2	yes	—
375	C₄	C₂×C₅×#237	1	2	yes	—
376	C₃	C₂×C₅×#480	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	8	2	no	—
379	C₂	C₅×#5033	1	4	yes	direct product factor
380	C₂	C₂²×C₅×#213	1	1	yes	characteristic
381	C₂	C₂×C₅×#935	1	1	yes	characteristic
382	C₂	C₂×C₅×#951	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#480
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×C₄⋊Dic₃	C₂	semidirect
3. C₂×C₅×#832	C₂	semidirect
4. C₂×C₅×#830	C₂	semidirect
5. C₅×#5033	C₂	direct (N × H)
6. C₂×C₅×#807	C₂	semidirect
19. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
21. C₅×#832	C₂²	semidirect
22. C₅×#830	C₂²	semidirect
23. C₅×#807	C₂²	semidirect
24. C₂×#5033	C₅	direct (N × H)
56. C₂²×C₄⋊Dic₃	C₂×C₅	semidirect
57. C₂×#832	C₂×C₅	semidirect
58. C₂×#830	C₂×C₅	semidirect
59. #5033	C₂×C₅	direct (N × H)
60. C₂×#807	C₂×C₅	semidirect
114. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
116. #832	C₂²×C₅	semidirect
117. #830	C₂²×C₅	semidirect
118. #807	C₂²×C₅	semidirect
233. C₂×C₃×C₅	#480	semidirect
303. C₃×C₅	C₂×#480	semidirect
323. C₂×C₅	#5033	direct (N × H)
354. C₂×C₃	C₅×#480	semidirect
358. C₅	C₂×#5033	direct (N × H)
376. C₃	C₂×C₅×#480	semidirect
379. C₂	C₅×#5033	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×#121	2
C₂²×C₅×C₄⋊Dic₃	2
C₂×C₅×#832	2
C₂×C₅×#830	2
C₅×#5033	2
C₂×C₅×#807	2
C₂×C₅×#480	3
C₂×#5033	5

Subgroups — C2×C5×#5033 #14431398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5033 #14431398