Subgroups — C₃×C₅×#2011 #14275045

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2011	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	—	2	2	no	—
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×D₈	—	2	4	no	—
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	—	2	4	no	—
13	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
14	C₃×C₅×#127	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#102	—	2	4	no	—
19	C₃×#2011	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×D₈	C₂×C₃	1	2	yes	complemented
21	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
23	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
24	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂⁴×C₃×C₅	—	2	1	no	—
26	C₂⁴×C₃×C₅	—	2	2	no	—
27	C₂×C₃×C₅×D₄	—	2	8	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	—	2	2	no	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	4	4	no	—
37	C₂×C₃×C₅×D₄	—	4	4	no	—
38	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
39	C₂×C₃×C₅×D₄	D₄	1	2	yes	complemented
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×D₈	—	2	16	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
49	C₃×C₄²×C₅	—	2	2	no	—
50	C₂²×C₃×D₈	C₂×C₅	1	2	yes	complemented
51	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
52	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
53	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂²×C₅×D₄	—	2	2	no	—
56	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
57	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₅×D₈	—	2	4	no	—
59	C₂×C₅×D₈	—	2	4	no	—
60	C₂×C₅×D₈	—	2	4	no	—
61	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
62	C₅×#127	—	2	4	no	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
66	C₅×#102	—	2	4	no	—
67	#2011	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₂³×C₃×C₅	—	2	4	no	—
69	C₂³×C₃×C₅	—	2	2	no	—
70	C₂³×C₃×C₅	—	4	1	no	—
71	C₂³×C₃×C₅	—	4	2	no	—
72	C₂³×C₃×C₅	—	4	1	no	—
73	C₂³×C₃×C₅	—	4	2	no	—
74	C₂³×C₃×C₅	—	4	2	no	—
75	C₂³×C₃×C₅	—	4	4	no	—
76	C₂³×C₃×C₅	—	4	4	no	—
77	C₂³×C₃×C₅	—	4	2	no	—
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₃×C₅×D₄	—	2	4	no	—
80	C₃×C₅×D₄	—	2	4	no	—
81	C₃×C₅×D₄	—	2	4	no	—
82	C₃×C₅×D₄	—	4	16	no	—
83	C₃×C₅×D₄	—	4	2	no	—
84	C₃×C₅×D₄	—	4	2	no	—
85	C₃×C₅×D₄	—	4	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	2	no	—
90	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₃×C₅×C₈	—	2	4	no	—
96	C₂²×C₃×D₄	—	2	2	no	—
97	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
98	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
99	C₂×C₃×D₈	—	2	4	no	—
100	C₂×C₃×D₈	—	2	4	no	—
101	C₂×C₃×D₈	—	2	4	no	—
102	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
103	C₃×#127	—	2	4	no	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
107	C₃×#102	—	2	4	no	—
108	C₂⁴×C₅	—	2	1	no	—
109	C₂⁴×C₅	—	2	2	no	—
110	C₂×C₅×D₄	—	2	8	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	4	4	no	—
120	C₂×C₅×D₄	—	4	4	no	—
121	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
122	C₂×C₅×D₄	C₃×D₄	1	2	yes	complemented
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₅×D₈	—	2	16	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₂²⋊C₄	—	4	4	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₂²×D₈	C₂×C₃×C₅	1	2	yes	complemented
134	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
135	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
136	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
137	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
138	C₂²×C₃×C₅	—	4	4	no	—
139	C₂²×C₃×C₅	—	4	2	no	—
140	C₂²×C₃×C₅	—	4	8	no	—
141	C₂²×C₃×C₅	—	4	4	no	—
142	C₂²×C₃×C₅	—	8	2	no	—
143	C₂²×C₃×C₅	—	8	4	no	—
144	C₂²×C₃×C₅	—	8	1	no	—
145	C₂²×C₃×C₅	—	8	2	no	—
146	C₂²×C₃×C₅	—	8	2	no	—
147	C₂²×C₃×C₅	—	8	1	no	—
148	C₂²×C₃×C₅	#120	1	1	yes	characteristic
149	C₂²×C₃×C₅	#121	1	1	yes	characteristic
150	C₂²×C₃×C₅	#127	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
152	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
153	C₃×C₄×C₅	—	2	4	no	—
154	C₃×C₄×C₅	—	8	1	no	—
155	C₃×C₄×C₅	#120	1	2	yes	—
156	C₃×C₄×C₅	#121	1	2	yes	—
157	C₂⁴×C₃	—	2	1	no	—
158	C₂⁴×C₃	—	2	2	no	—
159	C₂×C₃×D₄	—	2	8	no	—
160	C₂×C₃×D₄	—	2	2	no	—
161	C₂×C₃×D₄	—	2	2	no	—
162	C₂×C₃×D₄	—	2	2	no	—
163	C₂×C₃×D₄	—	2	2	no	—
164	C₂×C₃×D₄	—	2	2	no	—
165	C₂×C₃×D₄	—	2	2	no	—
166	C₂×C₃×D₄	—	2	2	no	—
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	—	4	4	no	—
169	C₂×C₃×D₄	—	4	4	no	—
170	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
171	C₂×C₃×D₄	C₅×D₄	1	2	yes	complemented
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
175	C₃×D₈	—	2	16	no	—
176	C₂×C₃×C₈	—	2	2	no	—
177	C₂×C₃×C₈	—	2	2	no	—
178	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₂²⋊C₄	—	4	4	no	—
181	C₃×C₄²	—	2	2	no	—
182	C₂³×C₅	—	2	4	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	2	no	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	—	4	2	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	4	4	no	—
190	C₂³×C₅	—	4	4	no	—
191	C₂³×C₅	—	4	2	no	—
192	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	4	16	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	2	no	—
199	C₅×D₄	—	4	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	C₃×D₈	1	4	yes	complemented
205	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
207	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
209	C₅×C₈	—	2	4	no	—
210	C₂²×D₄	—	2	2	no	—
211	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
212	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
213	C₂×D₈	—	2	4	no	—
214	C₂×D₈	—	2	4	no	—
215	C₂×D₈	—	2	4	no	—
216	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
217	#127	—	2	4	no	—
218	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
221	#102	—	2	4	no	—
222	C₂×C₃×C₅	—	8	4	no	—
223	C₂×C₃×C₅	—	8	2	no	—
224	C₂×C₃×C₅	#392	1	1	yes	characteristic
225	C₂×C₃×C₅	#447	1	2	yes	—
226	C₂×C₃×C₅	#459	1	2	yes	—
227	C₂×C₃×C₅	#493	1	1	yes	characteristic
228	C₂×C₃×C₅	#496	1	1	yes	characteristic
229	C₂³×C₃	—	2	4	no	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	4	1	no	—
232	C₂³×C₃	—	4	2	no	—
233	C₂³×C₃	—	4	2	no	—
234	C₂³×C₃	—	4	1	no	—
235	C₂³×C₃	—	4	2	no	—
236	C₂³×C₃	—	4	4	no	—
237	C₂³×C₃	—	4	4	no	—
238	C₂³×C₃	—	4	2	no	—
239	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
240	C₃×D₄	—	2	4	no	—
241	C₃×D₄	—	2	4	no	—
242	C₃×D₄	—	2	4	no	—
243	C₃×D₄	—	4	16	no	—
244	C₃×D₄	—	4	2	no	—
245	C₃×D₄	—	4	2	no	—
246	C₃×D₄	—	4	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	—	4	2	no	—
251	C₂×C₃×C₄	C₅×D₈	1	4	yes	complemented
252	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
256	C₃×C₈	—	2	4	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	4	2	no	—
259	C₂²×C₅	—	4	8	no	—
260	C₂²×C₅	—	4	4	no	—
261	C₂²×C₅	—	8	2	no	—
262	C₂²×C₅	—	8	4	no	—
263	C₂²×C₅	—	8	1	no	—
264	C₂²×C₅	—	8	2	no	—
265	C₂²×C₅	—	8	2	no	—
266	C₂²×C₅	—	8	1	no	—
267	C₂²×C₅	C₃×#120	1	1	yes	characteristic
268	C₂²×C₅	C₃×#121	1	1	yes	characteristic
269	C₂²×C₅	C₃×#127	1	1	yes	characteristic
270	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
271	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
272	C₄×C₅	—	2	4	no	—
273	C₄×C₅	—	8	1	no	—
274	C₄×C₅	C₃×#120	1	2	yes	—
275	C₄×C₅	C₃×#121	1	2	yes	—
276	C₂⁴	—	2	1	no	—
277	C₂⁴	—	2	2	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
290	C₂×D₄	C₃×C₅×D₄	1	2	yes	complemented
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
293	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
294	D₈	—	2	16	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
298	C₄⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₄²	—	2	2	no	—
301	C₃×C₅	#2011	1	1	yes	characteristic, direct product factor, Hall
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	—	4	2	no	—
304	C₂²×C₃	—	4	8	no	—
305	C₂²×C₃	—	4	4	no	—
306	C₂²×C₃	—	8	2	no	—
307	C₂²×C₃	—	8	4	no	—
308	C₂²×C₃	—	8	1	no	—
309	C₂²×C₃	—	8	2	no	—
310	C₂²×C₃	—	8	2	no	—
311	C₂²×C₃	—	8	1	no	—
312	C₂²×C₃	C₅×#120	1	1	yes	characteristic
313	C₂²×C₃	C₅×#121	1	1	yes	characteristic
314	C₂²×C₃	C₅×#127	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
316	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
317	C₃×C₄	—	2	4	no	—
318	C₃×C₄	—	8	1	no	—
319	C₃×C₄	C₅×#120	1	2	yes	—
320	C₃×C₄	C₅×#121	1	2	yes	—
321	C₂×C₅	—	8	4	no	—
322	C₂×C₅	—	8	2	no	—
323	C₂×C₅	C₃×#392	1	1	yes	characteristic
324	C₂×C₅	C₃×#447	1	2	yes	—
325	C₂×C₅	C₃×#459	1	2	yes	—
326	C₂×C₅	C₃×#493	1	1	yes	characteristic
327	C₂×C₅	C₃×#496	1	1	yes	characteristic
328	C₂³	—	2	4	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
339	D₄	—	2	4	no	—
340	D₄	—	2	4	no	—
341	D₄	—	2	4	no	—
342	D₄	—	4	16	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	C₃×C₅×D₈	1	4	yes	complemented
351	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
352	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
353	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
354	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
355	C₈	—	2	4	no	—
356	C₂×C₃	—	8	4	no	—
357	C₂×C₃	—	8	2	no	—
358	C₂×C₃	C₅×#392	1	1	yes	characteristic
359	C₂×C₃	C₅×#447	1	2	yes	—
360	C₂×C₃	C₅×#459	1	2	yes	—
361	C₂×C₃	C₅×#493	1	1	yes	characteristic
362	C₂×C₃	C₅×#496	1	1	yes	characteristic
363	C₅	C₃×#2011	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	8	no	—
368	C₂²	—	8	4	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	C₃×C₅×#120	1	1	yes	characteristic
375	C₂²	C₃×C₅×#121	1	1	yes	characteristic
376	C₂²	C₃×C₅×#127	1	1	yes	characteristic
377	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
378	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
379	C₄	—	2	4	no	—
380	C₄	—	8	1	no	—
381	C₄	C₃×C₅×#120	1	2	yes	—
382	C₄	C₃×C₅×#121	1	2	yes	—
383	C₃	C₅×#2011	1	1	yes	characteristic, direct product factor, Sylow
384	C₂	—	8	2	no	—
385	C₂	—	8	4	no	—
386	C₂	C₃×C₅×#392	1	1	yes	characteristic
387	C₂	C₃×C₅×#447	1	2	yes	—
388	C₂	C₃×C₅×#459	1	2	yes	—
389	C₂	C₃×C₅×#493	1	1	yes	characteristic
390	C₂	C₃×C₅×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₃×C₅×#102	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#2011	C₃	direct (N × H)
19. C₃×#2011	C₅	direct (N × H)
20. C₂²×C₅×D₈	C₂×C₃	semidirect
21. C₂×C₅×#127	C₂×C₃	semidirect
22. C₂×C₅×#102	C₂×C₃	semidirect
23. C₅×#390	C₂×C₃	semidirect
24. C₅×#336	C₂×C₃	semidirect
39. C₂×C₃×C₅×D₄	D₄	semidirect
46. C₂×C₃×C₅×C₈	D₄	semidirect
50. C₂²×C₃×D₈	C₂×C₅	semidirect
51. C₂×C₃×#127	C₂×C₅	semidirect
52. C₂×C₃×#102	C₂×C₅	semidirect
53. C₃×#390	C₂×C₅	semidirect
54. C₃×#336	C₂×C₅	semidirect
67. #2011	C₃×C₅	direct (N × H)
90. C₂×C₃×C₄×C₅	D₈	semidirect
122. C₂×C₅×D₄	C₃×D₄	semidirect
129. C₂×C₅×C₈	C₃×D₄	semidirect
133. C₂²×D₈	C₂×C₃×C₅	semidirect
134. C₂×#127	C₂×C₃×C₅	semidirect
135. C₂×#102	C₂×C₃×C₅	semidirect
136. #390	C₂×C₃×C₅	semidirect
137. #336	C₂×C₃×C₅	semidirect
171. C₂×C₃×D₄	C₅×D₄	semidirect
178. C₂×C₃×C₈	C₅×D₄	semidirect
204. C₂×C₄×C₅	C₃×D₈	semidirect
251. C₂×C₃×C₄	C₅×D₈	semidirect
290. C₂×D₄	C₃×C₅×D₄	semidirect
297. C₂×C₈	C₃×C₅×D₄	semidirect
301. C₃×C₅	#2011	direct (N × H)
350. C₂×C₄	C₃×C₅×D₈	semidirect
363. C₅	C₃×#2011	direct (N × H)
383. C₃	C₅×#2011	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×D₈	2
C₂×C₃×C₅×#127	2
C₂×C₃×C₅×#102	2
C₃×C₅×#390	2
C₃×C₅×#336	2
C₅×#2011	3
C₃×#2011	5

Subgroups — C3×C5×#2011 #14275045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2011 #14275045