Subgroups — C₃×C₄×C₅×#121 #14275334

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 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	C₂×C₃×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#121	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#121	C₄	1	8	yes	direct product factor
20	C₃×C₄×C₅×D₄	—	2	8	no	—
21	C₃×C₄×C₅×D₄	—	2	4	no	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	—	2	4	no	—
32	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
36	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×C₅×#95	C₂²	1	2	yes	—
40	C₃×C₄×#121	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
42	C₂×C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
43	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#388	C₂×C₃	1	2	yes	complemented
48	C₅×#386	C₂×C₃	1	2	yes	complemented
49	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
50	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
51	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
52	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
53	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₅×D₄	—	2	4	no	—
55	C₂×C₃×C₅×D₄	—	2	4	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	complemented
59	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
60	C₂²×C₃×C₄×C₅	—	2	2	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	—	2	2	no	—
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	—	2	4	no	—
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	—	2	4	no	—
70	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
71	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
72	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	—	2	4	no	—
82	C₃×C₅×C₄⋊C₄	—	2	2	no	—
83	C₃×C₅×C₄⋊C₄	—	2	2	no	—
84	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
85	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
89	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
90	C₃×C₄²×C₅	—	2	2	no	—
91	C₃×C₄²×C₅	—	2	2	no	—
92	C₃×C₄²×C₅	—	2	2	no	—
93	C₃×C₄²×C₅	—	2	4	no	—
94	C₃×C₄²×C₅	D₄	1	4	yes	complemented
95	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
96	C₂×C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
97	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#388	C₂×C₅	1	2	yes	complemented
102	C₃×#386	C₂×C₅	1	2	yes	complemented
103	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
106	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
107	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
108	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
109	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
110	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
111	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
112	C₅×#121	C₃×C₄	1	8	yes	direct product factor
113	C₄×C₅×D₄	—	2	8	no	—
114	C₄×C₅×D₄	—	2	4	no	—
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
124	C₂×C₄²×C₅	—	2	4	no	—
125	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
127	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
130	C₅×#95	C₂²×C₃	1	2	yes	—
131	C₅×#95	C₂²×C₃	1	2	yes	—
132	C₅×#95	C₂²×C₃	1	2	yes	—
133	C₄×#121	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	—	2	2	no	—
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	2	2	no	—
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
145	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
146	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
147	C₂³×C₃×C₅	#41	1	2	yes	—
148	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
149	C₃×C₅×D₄	—	2	16	no	—
150	C₃×C₅×D₄	—	2	8	no	—
151	C₂×C₃×C₄×C₅	—	2	8	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	—	2	2	no	—
162	C₂×C₃×C₄×C₅	—	2	8	no	—
163	C₂×C₃×C₄×C₅	—	2	8	no	—
164	C₂×C₃×C₄×C₅	—	2	2	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	4	8	no	—
171	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
172	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
174	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
175	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
177	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
178	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
179	C₂×C₃×C₄×C₅	#41	1	2	yes	—
180	C₂×C₃×C₄×C₅	#41	1	2	yes	—
181	C₂×C₃×C₄×C₅	#41	1	2	yes	—
182	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
183	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
184	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
185	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
186	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
188	C₃×#121	C₄×C₅	1	8	yes	direct product factor
189	C₃×C₄×D₄	—	2	8	no	—
190	C₃×C₄×D₄	—	2	4	no	—
191	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₃×C₄²	—	2	4	no	—
201	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
203	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
206	C₃×#95	C₂²×C₅	1	2	yes	—
207	C₃×#95	C₂²×C₅	1	2	yes	—
208	C₃×#95	C₂²×C₅	1	2	yes	—
209	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
210	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₅×D₄	—	2	4	no	—
212	C₂×C₅×D₄	—	2	4	no	—
213	C₂×C₅×D₄	—	2	2	no	—
214	C₂×C₅×D₄	—	2	2	no	—
215	C₂×C₅×D₄	C₂×C₃×C₄	1	8	yes	complemented
216	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
217	C₂²×C₄×C₅	—	2	2	no	—
218	C₂²×C₄×C₅	—	2	2	no	—
219	C₂²×C₄×C₅	—	2	2	no	—
220	C₂²×C₄×C₅	—	2	2	no	—
221	C₂²×C₄×C₅	—	2	2	no	—
222	C₂²×C₄×C₅	—	2	2	no	—
223	C₂²×C₄×C₅	—	2	2	no	—
224	C₂²×C₄×C₅	—	2	4	no	—
225	C₂²×C₄×C₅	—	2	4	no	—
226	C₂²×C₄×C₅	—	2	4	no	—
227	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
228	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
229	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
230	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
231	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
233	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
237	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
238	C₅×C₄⋊C₄	—	2	4	no	—
239	C₅×C₄⋊C₄	—	2	2	no	—
240	C₅×C₄⋊C₄	—	2	2	no	—
241	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
242	C₅×C₂²⋊C₄	—	2	4	no	—
243	C₅×C₂²⋊C₄	—	2	4	no	—
244	C₅×C₂²⋊C₄	—	2	4	no	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
247	C₄²×C₅	—	2	2	no	—
248	C₄²×C₅	—	2	2	no	—
249	C₄²×C₅	—	2	2	no	—
250	C₄²×C₅	—	2	4	no	—
251	C₄²×C₅	C₃×D₄	1	4	yes	complemented
252	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
254	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	C₂²×C₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
257	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	#388	C₂×C₃×C₅	1	2	yes	complemented
259	#386	C₂×C₃×C₅	1	2	yes	complemented
260	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
261	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
263	C₂²×C₃×C₅	—	2	2	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	2	4	no	—
270	C₂²×C₃×C₅	—	2	4	no	—
271	C₂²×C₃×C₅	—	2	4	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	2	no	—
275	C₂²×C₃×C₅	—	4	2	no	—
276	C₂²×C₃×C₅	C₄×D₄	1	4	yes	complemented
277	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
278	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
281	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
282	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
283	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
284	C₃×C₄×C₅	—	2	2	no	—
285	C₃×C₄×C₅	—	2	4	no	—
286	C₃×C₄×C₅	—	2	2	no	—
287	C₃×C₄×C₅	—	2	2	no	—
288	C₃×C₄×C₅	—	2	2	no	—
289	C₃×C₄×C₅	—	4	2	no	—
290	C₃×C₄×C₅	—	4	2	no	—
291	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
292	C₃×C₄×C₅	#121	1	4	yes	direct product factor
293	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
294	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	4	no	—
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
300	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
301	C₂²×C₃×C₄	—	2	2	no	—
302	C₂²×C₃×C₄	—	2	2	no	—
303	C₂²×C₃×C₄	—	2	2	no	—
304	C₂²×C₃×C₄	—	2	2	no	—
305	C₂²×C₃×C₄	—	2	2	no	—
306	C₂²×C₃×C₄	—	2	2	no	—
307	C₂²×C₃×C₄	—	2	2	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	2	4	no	—
310	C₂²×C₃×C₄	—	2	4	no	—
311	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
312	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
313	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
314	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
315	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
317	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
326	C₃×C₂²⋊C₄	—	2	4	no	—
327	C₃×C₂²⋊C₄	—	2	4	no	—
328	C₃×C₂²⋊C₄	—	2	4	no	—
329	C₃×C₂²⋊C₄	—	2	4	no	—
330	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
331	C₃×C₄²	—	2	2	no	—
332	C₃×C₄²	—	2	2	no	—
333	C₃×C₄²	—	2	2	no	—
334	C₃×C₄²	—	2	4	no	—
335	C₃×C₄²	C₅×D₄	1	4	yes	complemented
336	C₂³×C₅	—	2	1	no	—
337	C₂³×C₅	—	2	1	no	—
338	C₂³×C₅	—	2	1	no	—
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	2	2	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	2	2	no	—
345	C₂³×C₅	—	2	2	no	—
346	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
347	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
348	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
349	C₂³×C₅	C₃×#41	1	2	yes	—
350	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
351	C₅×D₄	—	2	16	no	—
352	C₅×D₄	—	2	8	no	—
353	C₂×C₄×C₅	—	2	8	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	2	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	1	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	8	no	—
365	C₂×C₄×C₅	—	2	8	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	2	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	4	8	no	—
373	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
374	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
375	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
376	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
377	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
378	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
379	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
380	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
381	C₂×C₄×C₅	C₃×#41	1	2	yes	—
382	C₂×C₄×C₅	C₃×#41	1	2	yes	—
383	C₂×C₄×C₅	C₃×#41	1	2	yes	—
384	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
385	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
386	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
387	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
388	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
389	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
390	#121	C₃×C₄×C₅	1	8	yes	direct product factor
391	C₄×D₄	—	2	8	no	—
392	C₄×D₄	—	2	4	no	—
393	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
395	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
402	C₂×C₄²	—	2	4	no	—
403	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
404	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
405	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
406	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
407	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
408	#95	C₂²×C₃×C₅	1	2	yes	—
409	#95	C₂²×C₃×C₅	1	2	yes	—
410	#95	C₂²×C₃×C₅	1	2	yes	—
411	C₂×C₃×C₅	—	2	4	no	—
412	C₂×C₃×C₅	—	4	4	no	—
413	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
414	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
415	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
416	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
417	C₂×C₃×C₅	#525	1	1	yes	characteristic
418	C₂×C₃×C₅	#529	1	1	yes	characteristic
419	C₂×C₃×C₅	#532	1	1	yes	characteristic
420	C₂³×C₃	—	2	1	no	—
421	C₂³×C₃	—	2	1	no	—
422	C₂³×C₃	—	2	1	no	—
423	C₂³×C₃	—	2	1	no	—
424	C₂³×C₃	—	2	2	no	—
425	C₂³×C₃	—	2	2	no	—
426	C₂³×C₃	—	2	2	no	—
427	C₂³×C₃	—	2	2	no	—
428	C₂³×C₃	—	2	2	no	—
429	C₂³×C₃	—	2	2	no	—
430	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
431	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
432	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
433	C₂³×C₃	C₅×#41	1	2	yes	—
434	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
435	C₃×D₄	—	2	16	no	—
436	C₃×D₄	—	2	8	no	—
437	C₂×C₃×C₄	—	2	8	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	2	8	no	—
449	C₂×C₃×C₄	—	2	8	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	2	2	no	—
455	C₂×C₃×C₄	—	2	2	no	—
456	C₂×C₃×C₄	—	4	8	no	—
457	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
458	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
459	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
460	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
461	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
462	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
463	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
464	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
465	C₂×C₃×C₄	C₅×#41	1	2	yes	—
466	C₂×C₃×C₄	C₅×#41	1	2	yes	—
467	C₂×C₃×C₄	C₅×#41	1	2	yes	—
468	C₂²×C₅	—	2	2	no	—
469	C₂²×C₅	—	2	2	no	—
470	C₂²×C₅	—	2	2	no	—
471	C₂²×C₅	—	2	2	no	—
472	C₂²×C₅	—	2	2	no	—
473	C₂²×C₅	—	2	2	no	—
474	C₂²×C₅	—	2	4	no	—
475	C₂²×C₅	—	2	4	no	—
476	C₂²×C₅	—	2	4	no	—
477	C₂²×C₅	—	4	2	no	—
478	C₂²×C₅	—	4	2	no	—
479	C₂²×C₅	—	4	2	no	—
480	C₂²×C₅	—	4	2	no	—
481	C₂²×C₅	C₃×C₄×D₄	1	4	yes	complemented
482	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
483	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
484	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
485	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
486	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
487	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
488	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
489	C₄×C₅	—	2	2	no	—
490	C₄×C₅	—	2	4	no	—
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	—	2	2	no	—
493	C₄×C₅	—	2	2	no	—
494	C₄×C₅	—	4	2	no	—
495	C₄×C₅	—	4	2	no	—
496	C₄×C₅	C₃×C₄×D₄	1	4	yes	complemented
497	C₄×C₅	C₃×#121	1	4	yes	direct product factor
498	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
499	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
505	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
517	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
518	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
519	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
520	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
521	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
522	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
523	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
524	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
525	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
526	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	4	no	—
540	C₄²	C₃×C₅×D₄	1	4	yes	complemented
541	C₃×C₅	C₄×#121	1	1	yes	characteristic, direct product factor, Hall
542	C₂²×C₃	—	2	2	no	—
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	2	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	4	no	—
549	C₂²×C₃	—	2	4	no	—
550	C₂²×C₃	—	2	4	no	—
551	C₂²×C₃	—	4	2	no	—
552	C₂²×C₃	—	4	2	no	—
553	C₂²×C₃	—	4	2	no	—
554	C₂²×C₃	—	4	2	no	—
555	C₂²×C₃	C₄×C₅×D₄	1	4	yes	complemented
556	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
557	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
558	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
559	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
560	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
561	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
562	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
563	C₃×C₄	—	2	2	no	—
564	C₃×C₄	—	2	4	no	—
565	C₃×C₄	—	2	2	no	—
566	C₃×C₄	—	2	2	no	—
567	C₃×C₄	—	2	2	no	—
568	C₃×C₄	—	4	2	no	—
569	C₃×C₄	—	4	2	no	—
570	C₃×C₄	C₄×C₅×D₄	1	4	yes	complemented
571	C₃×C₄	C₅×#121	1	4	yes	direct product factor
572	C₂×C₅	—	2	4	no	—
573	C₂×C₅	—	4	4	no	—
574	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
575	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
576	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
577	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
578	C₂×C₅	C₃×#525	1	1	yes	characteristic
579	C₂×C₅	C₃×#529	1	1	yes	characteristic
580	C₂×C₅	C₃×#532	1	1	yes	characteristic
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
592	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
593	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
594	C₂³	C₃×C₅×#41	1	2	yes	—
595	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
596	D₄	—	2	16	no	—
597	D₄	—	2	8	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	8	no	—
610	C₂×C₄	—	2	8	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
619	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
620	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
621	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
622	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
623	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
624	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
625	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
626	C₂×C₄	C₃×C₅×#41	1	2	yes	—
627	C₂×C₄	C₃×C₅×#41	1	2	yes	—
628	C₂×C₄	C₃×C₅×#41	1	2	yes	—
629	C₂×C₃	—	2	4	no	—
630	C₂×C₃	—	4	4	no	—
631	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
632	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
633	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
634	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
635	C₂×C₃	C₅×#525	1	1	yes	characteristic
636	C₂×C₃	C₅×#529	1	1	yes	characteristic
637	C₂×C₃	C₅×#532	1	1	yes	characteristic
638	C₅	C₃×C₄×#121	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	C₃×C₄×C₅×D₄	1	4	yes	complemented
653	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
654	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
655	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
656	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
657	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
658	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
659	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
660	C₄	—	2	2	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	C₃×C₄×C₅×D₄	1	4	yes	complemented
668	C₄	C₃×C₅×#121	1	4	yes	direct product factor
669	C₃	C₄×C₅×#121	1	1	yes	characteristic, direct product factor, Sylow
670	C₂	—	2	4	no	—
671	C₂	—	4	4	no	—
672	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
673	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
674	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
675	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
676	C₂	C₃×C₅×#525	1	1	yes	characteristic
677	C₂	C₃×C₅×#529	1	1	yes	characteristic
678	C₂	C₃×C₅×#532	1	1	yes	characteristic

	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×#121	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
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₂²×C₃×C₄²×C₅	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#380	C₂	semidirect
10. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
11. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
12. C₄×C₅×#121	C₃	direct (N × H)
19. C₃×C₅×#121	C₄	direct (N × H)
40. C₃×C₄×#121	C₅	direct (N × H)
42. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
43. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
44. C₂²×C₄²×C₅	C₂×C₃	semidirect
45. C₅×#390	C₂×C₃	semidirect
46. C₅×#389	C₂×C₃	semidirect
47. C₅×#388	C₂×C₃	semidirect
48. C₅×#386	C₂×C₃	semidirect
49. C₅×#380	C₂×C₃	semidirect
50. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
51. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
58. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
59. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
70. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
71. C₂²×C₃×C₄×C₅	D₄	semidirect
84. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
89. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
94. C₃×C₄²×C₅	D₄	semidirect
96. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
97. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
98. C₂²×C₃×C₄²	C₂×C₅	semidirect
99. C₃×#390	C₂×C₅	semidirect
100. C₃×#389	C₂×C₅	semidirect
101. C₃×#388	C₂×C₅	semidirect
102. C₃×#386	C₂×C₅	semidirect
103. C₃×#380	C₂×C₅	semidirect
104. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
105. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
112. C₅×#121	C₃×C₄	direct (N × H)
133. C₄×#121	C₃×C₅	direct (N × H)
188. C₃×#121	C₄×C₅	direct (N × H)
215. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
216. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
227. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
228. C₂²×C₄×C₅	C₃×D₄	semidirect
241. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
246. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
251. C₄²×C₅	C₃×D₄	semidirect
253. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
254. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
255. C₂²×C₄²	C₂×C₃×C₅	semidirect
256. #390	C₂×C₃×C₅	semidirect
257. #389	C₂×C₃×C₅	semidirect
258. #388	C₂×C₃×C₅	semidirect
259. #386	C₂×C₃×C₅	semidirect
260. #380	C₂×C₃×C₅	semidirect
261. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
262. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
276. C₂²×C₃×C₅	C₄×D₄	semidirect
291. C₃×C₄×C₅	C₄×D₄	semidirect
292. C₃×C₄×C₅	#121	direct (N × H)
299. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
300. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
311. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
312. C₂²×C₃×C₄	C₅×D₄	semidirect
325. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
330. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
335. C₃×C₄²	C₅×D₄	semidirect
390. #121	C₃×C₄×C₅	direct (N × H)
481. C₂²×C₅	C₃×C₄×D₄	semidirect
496. C₄×C₅	C₃×C₄×D₄	semidirect
497. C₄×C₅	C₃×#121	direct (N × H)
504. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
505. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
516. C₂²×C₄	C₂×C₃×C₄×C₅	semidirect
517. C₂²×C₄	C₃×C₅×D₄	semidirect
530. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
535. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
540. C₄²	C₃×C₅×D₄	semidirect
541. C₃×C₅	C₄×#121	direct (N × H)
555. C₂²×C₃	C₄×C₅×D₄	semidirect
570. C₃×C₄	C₄×C₅×D₄	semidirect
571. C₃×C₄	C₅×#121	direct (N × H)
638. C₅	C₃×C₄×#121	direct (N × H)
652. C₂²	C₃×C₄×C₅×D₄	semidirect
667. C₄	C₃×C₄×C₅×D₄	semidirect
668. C₄	C₃×C₅×#121	direct (N × H)
669. C₃	C₄×C₅×#121	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
C₂×C₃×C₄×C₅×D₄	2
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₄×C₅×#121	3
C₃×C₄×#121	5

Subgroups — C3×C4×C5×#121 #14275334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×#121 #14275334