Subgroups — C₃×C₄×C₅×#120 #14275333

Order 1920.

2448 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	C₂⁴×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×D₄	C₂	1	3	yes	maximal, complemented
4	C₃×C₅×#386	C₂	1	3	yes	maximal, complemented
5	C₃×C₅×#385	C₂	1	3	yes	maximal, complemented
6	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
8	C₄×C₅×#120	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
11	C₂³×C₃×C₄×C₅	—	2	12	no	—
12	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
13	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#120	C₄	1	8	yes	direct product factor
16	C₃×C₄×C₅×D₄	—	2	12	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
22	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	complemented
23	C₃×C₅×#95	C₂²	1	6	yes	complemented
24	C₃×C₄×#120	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂⁴×C₄×C₅	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂×C₃	1	3	yes	complemented
28	C₅×#386	C₂×C₃	1	3	yes	complemented
29	C₅×#385	C₂×C₃	1	3	yes	complemented
30	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
31	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	3	yes	complemented
32	C₂⁴×C₃×C₅	—	2	6	no	—
33	C₂⁴×C₃×C₅	—	2	6	no	—
34	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
35	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
36	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
37	C₂×C₃×C₅×D₄	—	2	6	no	—
38	C₂×C₃×C₅×D₄	—	2	6	no	—
39	C₂×C₃×C₅×D₄	C₂×C₄	1	12	yes	complemented
40	C₂²×C₃×C₄×C₅	—	2	32	no	—
41	C₂²×C₃×C₄×C₅	—	2	6	no	—
42	C₂²×C₃×C₄×C₅	—	2	12	no	—
43	C₂²×C₃×C₄×C₅	—	2	12	no	—
44	C₂²×C₃×C₄×C₅	—	2	6	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	12	yes	complemented
46	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	—	2	6	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
55	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	12	yes	complemented
56	C₃×C₄²×C₅	—	2	6	no	—
57	C₂⁴×C₃×C₄	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×C₄×D₄	C₂×C₅	1	3	yes	complemented
60	C₃×#386	C₂×C₅	1	3	yes	complemented
61	C₃×#385	C₂×C₅	1	3	yes	complemented
62	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	3	yes	complemented
64	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
66	C₂³×C₄×C₅	—	2	12	no	—
67	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
68	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
69	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
70	C₅×#120	C₃×C₄	1	8	yes	direct product factor
71	C₄×C₅×D₄	—	2	12	no	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
73	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
75	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
76	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
77	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	complemented
78	C₅×#95	C₂²×C₃	1	6	yes	complemented
79	C₄×#120	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
80	C₂³×C₃×C₅	—	2	8	no	—
81	C₂³×C₃×C₅	—	2	24	no	—
82	C₂³×C₃×C₅	—	2	24	no	—
83	C₂³×C₃×C₅	—	2	6	no	—
84	C₂³×C₃×C₅	—	2	6	no	—
85	C₂³×C₃×C₅	—	2	3	no	—
86	C₂³×C₃×C₅	—	2	3	no	—
87	C₂³×C₃×C₅	C₂²×C₄	1	6	yes	—
88	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	complemented
89	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
90	C₂³×C₃×C₅	#41	1	6	yes	—
91	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
92	C₃×C₅×D₄	—	2	24	no	—
93	C₂×C₃×C₄×C₅	—	2	24	no	—
94	C₂×C₃×C₄×C₅	—	2	3	no	—
95	C₂×C₃×C₄×C₅	—	2	6	no	—
96	C₂×C₃×C₄×C₅	—	2	3	no	—
97	C₂×C₃×C₄×C₅	—	2	24	no	—
98	C₂×C₃×C₄×C₅	—	2	3	no	—
99	C₂×C₃×C₄×C₅	—	2	3	no	—
100	C₂×C₃×C₄×C₅	—	2	6	no	—
101	C₂×C₃×C₄×C₅	—	4	4	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	complemented
103	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
105	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
106	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
107	C₂³×C₃×C₄	—	2	12	no	—
108	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	—
109	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	—
110	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
111	C₃×#120	C₄×C₅	1	8	yes	direct product factor
112	C₃×C₄×D₄	—	2	12	no	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	3	yes	complemented
114	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
118	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	complemented
119	C₃×#95	C₂²×C₅	1	6	yes	complemented
120	C₂⁴×C₅	—	2	6	no	—
121	C₂⁴×C₅	—	2	6	no	—
122	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	complemented
123	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
125	C₂×C₅×D₄	—	2	6	no	—
126	C₂×C₅×D₄	—	2	6	no	—
127	C₂×C₅×D₄	C₂×C₃×C₄	1	12	yes	complemented
128	C₂²×C₄×C₅	—	2	32	no	—
129	C₂²×C₄×C₅	—	2	6	no	—
130	C₂²×C₄×C₅	—	2	12	no	—
131	C₂²×C₄×C₅	—	2	12	no	—
132	C₂²×C₄×C₅	—	2	6	no	—
133	C₂²×C₄×C₅	C₃×D₄	1	12	yes	complemented
134	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₅×C₄⋊C₄	—	2	6	no	—
140	C₅×C₂²⋊C₄	—	2	6	no	—
141	C₅×C₂²⋊C₄	—	2	6	no	—
142	C₅×C₂²⋊C₄	—	2	6	no	—
143	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	12	yes	complemented
144	C₄²×C₅	—	2	6	no	—
145	C₂⁴×C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
147	C₂×C₄×D₄	C₂×C₃×C₅	1	3	yes	complemented
148	#386	C₂×C₃×C₅	1	3	yes	complemented
149	#385	C₂×C₃×C₅	1	3	yes	complemented
150	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	3	yes	complemented
152	C₂²×C₃×C₅	—	2	32	no	—
153	C₂²×C₃×C₅	—	2	12	no	—
154	C₂²×C₃×C₅	—	2	6	no	—
155	C₂²×C₃×C₅	—	2	6	no	—
156	C₂²×C₃×C₅	—	2	12	no	—
157	C₂²×C₃×C₅	—	2	6	no	—
158	C₂²×C₃×C₅	—	4	1	no	—
159	C₂²×C₃×C₅	—	4	3	no	—
160	C₂²×C₃×C₅	C₄×D₄	1	12	yes	complemented
161	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
163	C₂²×C₃×C₅	C₂×#41	1	3	yes	—
164	C₃×C₄×C₅	—	2	6	no	—
165	C₃×C₄×C₅	—	2	6	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	—	4	3	no	—
168	C₃×C₄×C₅	#120	1	4	yes	direct product factor
169	C₂⁴×C₃	—	2	6	no	—
170	C₂⁴×C₃	—	2	6	no	—
171	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	complemented
172	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
173	C₂⁴×C₃	C₂³×C₅	1	3	yes	—
174	C₂×C₃×D₄	—	2	6	no	—
175	C₂×C₃×D₄	—	2	6	no	—
176	C₂×C₃×D₄	C₂×C₄×C₅	1	12	yes	complemented
177	C₂²×C₃×C₄	—	2	32	no	—
178	C₂²×C₃×C₄	—	2	6	no	—
179	C₂²×C₃×C₄	—	2	12	no	—
180	C₂²×C₃×C₄	—	2	12	no	—
181	C₂²×C₃×C₄	—	2	6	no	—
182	C₂²×C₃×C₄	C₅×D₄	1	12	yes	complemented
183	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	2	6	no	—
189	C₃×C₂²⋊C₄	—	2	6	no	—
190	C₃×C₂²⋊C₄	—	2	6	no	—
191	C₃×C₂²⋊C₄	—	2	6	no	—
192	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	12	yes	complemented
193	C₃×C₄²	—	2	6	no	—
194	C₂³×C₅	—	2	8	no	—
195	C₂³×C₅	—	2	24	no	—
196	C₂³×C₅	—	2	24	no	—
197	C₂³×C₅	—	2	6	no	—
198	C₂³×C₅	—	2	6	no	—
199	C₂³×C₅	—	2	3	no	—
200	C₂³×C₅	—	2	3	no	—
201	C₂³×C₅	C₂²×C₃×C₄	1	6	yes	—
202	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	complemented
203	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
204	C₂³×C₅	C₃×#41	1	6	yes	—
205	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
206	C₅×D₄	—	2	24	no	—
207	C₂×C₄×C₅	—	2	24	no	—
208	C₂×C₄×C₅	—	2	3	no	—
209	C₂×C₄×C₅	—	2	6	no	—
210	C₂×C₄×C₅	—	2	3	no	—
211	C₂×C₄×C₅	—	2	24	no	—
212	C₂×C₄×C₅	—	2	3	no	—
213	C₂×C₄×C₅	—	2	3	no	—
214	C₂×C₄×C₅	—	2	6	no	—
215	C₂×C₄×C₅	—	4	4	no	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	6	yes	complemented
217	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
218	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
219	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
221	C₂³×C₄	—	2	12	no	—
222	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	—
223	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	—
224	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
225	#120	C₃×C₄×C₅	1	8	yes	direct product factor
226	C₄×D₄	—	2	12	no	—
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
228	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	—
230	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	—
231	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
232	C₂×C₄²	C₂²×C₃×C₅	1	3	yes	complemented
233	#95	C₂²×C₃×C₅	1	6	yes	complemented
234	C₂×C₃×C₅	—	2	12	no	—
235	C₂×C₃×C₅	—	4	2	no	—
236	C₂×C₃×C₅	C₂×C₄×D₄	1	3	yes	—
237	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
238	C₂×C₃×C₅	#525	1	3	yes	—
239	C₂³×C₃	—	2	8	no	—
240	C₂³×C₃	—	2	24	no	—
241	C₂³×C₃	—	2	24	no	—
242	C₂³×C₃	—	2	6	no	—
243	C₂³×C₃	—	2	6	no	—
244	C₂³×C₃	—	2	3	no	—
245	C₂³×C₃	—	2	3	no	—
246	C₂³×C₃	C₂²×C₄×C₅	1	6	yes	—
247	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	complemented
248	C₂³×C₃	C₂×C₅×D₄	1	6	yes	—
249	C₂³×C₃	C₅×#41	1	6	yes	—
250	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
251	C₃×D₄	—	2	24	no	—
252	C₂×C₃×C₄	—	2	24	no	—
253	C₂×C₃×C₄	—	2	3	no	—
254	C₂×C₃×C₄	—	2	6	no	—
255	C₂×C₃×C₄	—	2	3	no	—
256	C₂×C₃×C₄	—	2	24	no	—
257	C₂×C₃×C₄	—	2	3	no	—
258	C₂×C₃×C₄	—	2	3	no	—
259	C₂×C₃×C₄	—	2	6	no	—
260	C₂×C₃×C₄	—	4	4	no	—
261	C₂×C₃×C₄	C₂²×C₄×C₅	1	6	yes	complemented
262	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
264	C₂²×C₅	—	2	32	no	—
265	C₂²×C₅	—	2	12	no	—
266	C₂²×C₅	—	2	6	no	—
267	C₂²×C₅	—	2	6	no	—
268	C₂²×C₅	—	2	12	no	—
269	C₂²×C₅	—	2	6	no	—
270	C₂²×C₅	—	4	1	no	—
271	C₂²×C₅	—	4	3	no	—
272	C₂²×C₅	C₃×C₄×D₄	1	12	yes	complemented
273	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
274	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
275	C₂²×C₅	C₂×C₃×#41	1	3	yes	—
276	C₄×C₅	—	2	6	no	—
277	C₄×C₅	—	2	6	no	—
278	C₄×C₅	—	4	1	no	—
279	C₄×C₅	—	4	3	no	—
280	C₄×C₅	C₃×#120	1	4	yes	direct product factor
281	C₂⁴	—	2	6	no	—
282	C₂⁴	—	2	6	no	—
283	C₂⁴	C₂×C₃×C₄×C₅	1	4	yes	complemented
284	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
285	C₂⁴	C₂³×C₃×C₅	1	3	yes	—
286	C₂×D₄	—	2	6	no	—
287	C₂×D₄	—	2	6	no	—
288	C₂×D₄	C₂×C₃×C₄×C₅	1	12	yes	complemented
289	C₂²×C₄	—	2	32	no	—
290	C₂²×C₄	—	2	6	no	—
291	C₂²×C₄	—	2	12	no	—
292	C₂²×C₄	—	2	12	no	—
293	C₂²×C₄	—	2	6	no	—
294	C₂²×C₄	C₃×C₅×D₄	1	12	yes	complemented
295	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
298	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
299	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
300	C₄⋊C₄	—	2	6	no	—
301	C₂²⋊C₄	—	2	6	no	—
302	C₂²⋊C₄	—	2	6	no	—
303	C₂²⋊C₄	—	2	6	no	—
304	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	12	yes	complemented
305	C₄²	—	2	6	no	—
306	C₃×C₅	C₄×#120	1	1	yes	characteristic, direct product factor, Hall
307	C₂²×C₃	—	2	32	no	—
308	C₂²×C₃	—	2	12	no	—
309	C₂²×C₃	—	2	6	no	—
310	C₂²×C₃	—	2	6	no	—
311	C₂²×C₃	—	2	12	no	—
312	C₂²×C₃	—	2	6	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	—	4	3	no	—
315	C₂²×C₃	C₄×C₅×D₄	1	12	yes	complemented
316	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
317	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
318	C₂²×C₃	C₂×C₅×#41	1	3	yes	—
319	C₃×C₄	—	2	6	no	—
320	C₃×C₄	—	2	6	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	—	4	3	no	—
323	C₃×C₄	C₅×#120	1	4	yes	direct product factor
324	C₂×C₅	—	2	12	no	—
325	C₂×C₅	—	4	2	no	—
326	C₂×C₅	C₂×C₃×C₄×D₄	1	3	yes	—
327	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
328	C₂×C₅	C₃×#525	1	3	yes	—
329	C₂³	—	2	8	no	—
330	C₂³	—	2	24	no	—
331	C₂³	—	2	24	no	—
332	C₂³	—	2	6	no	—
333	C₂³	—	2	6	no	—
334	C₂³	—	2	3	no	—
335	C₂³	—	2	3	no	—
336	C₂³	C₂²×C₃×C₄×C₅	1	6	yes	—
337	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	complemented
338	C₂³	C₂×C₃×C₅×D₄	1	6	yes	—
339	C₂³	C₃×C₅×#41	1	6	yes	—
340	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
341	D₄	—	2	24	no	—
342	C₂×C₄	—	2	24	no	—
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	2	6	no	—
345	C₂×C₄	—	2	3	no	—
346	C₂×C₄	—	2	24	no	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	2	3	no	—
349	C₂×C₄	—	2	6	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	C₂²×C₃×C₄×C₅	1	6	yes	complemented
352	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	—
353	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	—
354	C₂×C₃	—	2	12	no	—
355	C₂×C₃	—	4	2	no	—
356	C₂×C₃	C₂×C₄×C₅×D₄	1	3	yes	—
357	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
358	C₂×C₃	C₅×#525	1	3	yes	—
359	C₅	C₃×C₄×#120	1	1	yes	characteristic, direct product factor, Sylow
360	C₂²	—	2	32	no	—
361	C₂²	—	2	12	no	—
362	C₂²	—	2	6	no	—
363	C₂²	—	2	6	no	—
364	C₂²	—	2	12	no	—
365	C₂²	—	2	6	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	3	no	—
368	C₂²	C₃×C₄×C₅×D₄	1	12	yes	complemented
369	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
370	C₂²	C₂²×C₃×C₅×D₄	1	3	yes	—
371	C₂²	C₂×C₃×C₅×#41	1	3	yes	—
372	C₄	—	2	6	no	—
373	C₄	—	2	6	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	3	no	—
376	C₄	C₃×C₅×#120	1	4	yes	direct product factor
377	C₃	C₄×C₅×#120	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	2	12	no	—
379	C₂	—	4	2	no	—
380	C₂	C₂×C₃×C₄×C₅×D₄	1	3	yes	—
381	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
382	C₂	C₃×C₅×#525	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₃×C₅×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₄×C₅	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₃×C₅×#386	C₂	semidirect
5. C₃×C₅×#385	C₂	semidirect
6. C₃×C₅×#379	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₄×C₅×#120	C₃	direct (N × H)
14. C₂³×C₃×C₄×C₅	C₂²	semidirect
15. C₃×C₅×#120	C₄	direct (N × H)
17. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
21. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
22. C₂×C₃×C₄²×C₅	C₂²	semidirect
23. C₃×C₅×#95	C₂²	semidirect
24. C₃×C₄×#120	C₅	direct (N × H)
25. C₂⁴×C₄×C₅	C₂×C₃	semidirect
27. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
28. C₅×#386	C₂×C₃	semidirect
29. C₅×#385	C₂×C₃	semidirect
30. C₅×#379	C₂×C₃	semidirect
31. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
34. C₂⁴×C₃×C₅	C₂×C₄	semidirect
39. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
45. C₂²×C₃×C₄×C₅	D₄	semidirect
55. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
57. C₂⁴×C₃×C₄	C₂×C₅	semidirect
59. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
60. C₃×#386	C₂×C₅	semidirect
61. C₃×#385	C₂×C₅	semidirect
62. C₃×#379	C₂×C₅	semidirect
63. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
69. C₂³×C₄×C₅	C₂²×C₃	semidirect
70. C₅×#120	C₃×C₄	direct (N × H)
72. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
76. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
77. C₂×C₄²×C₅	C₂²×C₃	semidirect
78. C₅×#95	C₂²×C₃	semidirect
79. C₄×#120	C₃×C₅	direct (N × H)
88. C₂³×C₃×C₅	C₂²×C₄	semidirect
102. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
110. C₂³×C₃×C₄	C₂²×C₅	semidirect
111. C₃×#120	C₄×C₅	direct (N × H)
113. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
117. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
118. C₂×C₃×C₄²	C₂²×C₅	semidirect
119. C₃×#95	C₂²×C₅	semidirect
122. C₂⁴×C₅	C₂×C₃×C₄	semidirect
127. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
133. C₂²×C₄×C₅	C₃×D₄	semidirect
143. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
145. C₂⁴×C₄	C₂×C₃×C₅	semidirect
147. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
148. #386	C₂×C₃×C₅	semidirect
149. #385	C₂×C₃×C₅	semidirect
150. #379	C₂×C₃×C₅	semidirect
151. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
160. C₂²×C₃×C₅	C₄×D₄	semidirect
168. C₃×C₄×C₅	#120	direct (N × H)
171. C₂⁴×C₃	C₂×C₄×C₅	semidirect
176. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
182. C₂²×C₃×C₄	C₅×D₄	semidirect
192. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
202. C₂³×C₅	C₂²×C₃×C₄	semidirect
216. C₂×C₄×C₅	C₂²×C₃×C₄	semidirect
224. C₂³×C₄	C₂²×C₃×C₅	semidirect
225. #120	C₃×C₄×C₅	direct (N × H)
227. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
231. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
232. C₂×C₄²	C₂²×C₃×C₅	semidirect
233. #95	C₂²×C₃×C₅	semidirect
247. C₂³×C₃	C₂²×C₄×C₅	semidirect
261. C₂×C₃×C₄	C₂²×C₄×C₅	semidirect
272. C₂²×C₅	C₃×C₄×D₄	semidirect
280. C₄×C₅	C₃×#120	direct (N × H)
283. C₂⁴	C₂×C₃×C₄×C₅	semidirect
288. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
294. C₂²×C₄	C₃×C₅×D₄	semidirect
304. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
306. C₃×C₅	C₄×#120	direct (N × H)
315. C₂²×C₃	C₄×C₅×D₄	semidirect
323. C₃×C₄	C₅×#120	direct (N × H)
337. C₂³	C₂²×C₃×C₄×C₅	semidirect
351. C₂×C₄	C₂²×C₃×C₄×C₅	semidirect
359. C₅	C₃×C₄×#120	direct (N × H)
368. C₂²	C₃×C₄×C₅×D₄	semidirect
376. C₄	C₃×C₅×#120	direct (N × H)
377. C₃	C₄×C₅×#120	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₄×C₅	2
C₂×C₃×C₅×#120	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₄×C₅×#120	3
C₃×C₄×#120	5

Subgroups — C3×C4×C5×#120 #14275333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×#120 #14275333