Subgroups — C₃×C₅×#2392 #14275426

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 596 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	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#396	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic
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	C₅×#2392	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×D₄	—	2	8	no	—
18	C₃×C₄×C₅×D₄	—	2	4	no	—
19	C₃×C₅×#117	—	2	4	no	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	1	yes	characteristic
38	C₃×C₅×#95	C₂²	1	1	yes	characteristic
39	C₃×#2392	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
41	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#396	C₂×C₃	1	2	yes	complemented
46	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#394	C₂×C₃	1	2	yes	complemented
48	C₅×#392	C₂×C₃	1	1	yes	characteristic
49	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
50	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
51	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₄	—	2	4	no	—
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	4	no	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	—	2	4	no	—
61	C₂²×C₃×C₄×C₅	—	2	4	no	—
62	C₂²×C₃×C₄×C₅	—	2	4	no	—
63	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	4	no	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	—	2	4	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
85	C₃×C₄²×C₅	—	2	2	no	—
86	C₃×C₄²×C₅	—	2	4	no	—
87	C₃×C₄²×C₅	D₄	1	4	yes	complemented
88	C₂×C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
89	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#396	C₂×C₅	1	2	yes	complemented
94	C₃×#394	C₂×C₅	1	2	yes	complemented
95	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#392	C₂×C₅	1	1	yes	characteristic
97	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
99	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
101	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
102	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
103	C₄×C₅×D₄	—	2	8	no	—
104	C₄×C₅×D₄	—	2	4	no	—
105	C₅×#117	—	2	4	no	—
106	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
113	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
117	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
120	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
121	C₅×#95	C₂²×C₃	1	2	yes	—
122	C₅×#95	C₂²×C₃	1	2	yes	—
123	C₅×#95	C₂²×C₃	1	1	yes	characteristic
124	C₅×#95	C₂²×C₃	1	1	yes	characteristic
125	#2392	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₂³×C₃×C₅	—	2	2	no	—
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	—	2	2	no	—
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
137	C₂³×C₃×C₅	#41	1	4	yes	—
138	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
139	C₃×C₅×D₄	—	2	8	no	—
140	C₃×C₅×D₄	—	2	16	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	8	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	4	8	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
164	C₂×C₃×C₄×C₅	#41	1	4	yes	—
165	C₂×C₃×C₄×C₅	#41	1	2	yes	—
166	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
168	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
169	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄×D₄	—	2	8	no	—
171	C₃×C₄×D₄	—	2	4	no	—
172	C₃×#117	—	2	4	no	—
173	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
180	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
183	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
184	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
185	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
187	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
188	C₃×#95	C₂²×C₅	1	2	yes	—
189	C₃×#95	C₂²×C₅	1	2	yes	—
190	C₃×#95	C₂²×C₅	1	1	yes	characteristic
191	C₃×#95	C₂²×C₅	1	1	yes	characteristic
192	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
194	C₂×C₅×D₄	—	2	4	no	—
195	C₂×C₅×D₄	—	2	4	no	—
196	C₂×C₅×D₄	—	2	4	no	—
197	C₂×C₅×D₄	—	2	2	no	—
198	C₂×C₅×D₄	—	2	4	no	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	4	no	—
202	C₂²×C₄×C₅	—	2	4	no	—
203	C₂²×C₄×C₅	—	2	4	no	—
204	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
205	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
213	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₄⋊C₄	—	2	4	no	—
217	C₅×C₄⋊C₄	—	2	2	no	—
218	C₅×C₄⋊C₄	—	2	4	no	—
219	C₅×C₂²⋊C₄	—	2	4	no	—
220	C₅×C₂²⋊C₄	—	2	4	no	—
221	C₅×C₂²⋊C₄	—	2	2	no	—
222	C₅×C₂²⋊C₄	—	2	2	no	—
223	C₅×C₂²⋊C₄	—	2	4	no	—
224	C₅×C₂²⋊C₄	—	2	4	no	—
225	C₅×C₂²⋊C₄	—	2	4	no	—
226	C₄²×C₅	—	2	2	no	—
227	C₄²×C₅	—	2	4	no	—
228	C₄²×C₅	C₃×D₄	1	4	yes	complemented
229	C₂×C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
230	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	#396	C₂×C₃×C₅	1	2	yes	complemented
235	#394	C₂×C₃×C₅	1	2	yes	complemented
236	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	#392	C₂×C₃×C₅	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
239	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	4	no	—
242	C₂²×C₃×C₅	—	2	4	no	—
243	C₂²×C₃×C₅	—	2	4	no	—
244	C₂²×C₃×C₅	—	2	4	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	—	4	2	no	—
248	C₂²×C₃×C₅	—	4	2	no	—
249	C₂²×C₃×C₅	—	4	2	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	—	4	2	no	—
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
255	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
256	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	2	2	no	—
259	C₃×C₄×C₅	—	2	4	no	—
260	C₃×C₄×C₅	—	2	2	no	—
261	C₃×C₄×C₅	—	4	2	no	—
262	C₃×C₄×C₅	—	4	2	no	—
263	C₃×C₄×C₅	—	4	1	no	—
264	C₃×C₄×C₅	—	4	1	no	—
265	C₃×C₄×C₅	#121	1	4	yes	—
266	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
267	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
268	C₂×C₃×D₄	—	2	4	no	—
269	C₂×C₃×D₄	—	2	4	no	—
270	C₂×C₃×D₄	—	2	4	no	—
271	C₂×C₃×D₄	—	2	2	no	—
272	C₂×C₃×D₄	—	2	4	no	—
273	C₂²×C₃×C₄	—	2	2	no	—
274	C₂²×C₃×C₄	—	2	2	no	—
275	C₂²×C₃×C₄	—	2	4	no	—
276	C₂²×C₃×C₄	—	2	4	no	—
277	C₂²×C₃×C₄	—	2	4	no	—
278	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
279	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
283	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
286	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
287	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
288	C₃×C₄⋊C₄	—	2	2	no	—
289	C₃×C₄⋊C₄	—	2	2	no	—
290	C₃×C₄⋊C₄	—	2	4	no	—
291	C₃×C₄⋊C₄	—	2	2	no	—
292	C₃×C₄⋊C₄	—	2	4	no	—
293	C₃×C₂²⋊C₄	—	2	4	no	—
294	C₃×C₂²⋊C₄	—	2	4	no	—
295	C₃×C₂²⋊C₄	—	2	2	no	—
296	C₃×C₂²⋊C₄	—	2	2	no	—
297	C₃×C₂²⋊C₄	—	2	4	no	—
298	C₃×C₂²⋊C₄	—	2	4	no	—
299	C₃×C₂²⋊C₄	—	2	4	no	—
300	C₃×C₄²	—	2	2	no	—
301	C₃×C₄²	—	2	4	no	—
302	C₃×C₄²	C₅×D₄	1	4	yes	complemented
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	2	2	no	—
310	C₂³×C₅	—	2	2	no	—
311	C₂³×C₅	—	2	2	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
314	C₂³×C₅	C₃×#41	1	4	yes	—
315	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
316	C₅×D₄	—	2	8	no	—
317	C₅×D₄	—	2	16	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	8	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	4	8	no	—
336	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
337	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
338	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
339	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
340	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
341	C₂×C₄×C₅	C₃×#41	1	4	yes	—
342	C₂×C₄×C₅	C₃×#41	1	2	yes	—
343	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
345	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
346	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
347	C₄×D₄	—	2	8	no	—
348	C₄×D₄	—	2	4	no	—
349	#117	—	2	4	no	—
350	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
353	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
360	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
361	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
362	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
363	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
364	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
365	#95	C₂²×C₃×C₅	1	2	yes	—
366	#95	C₂²×C₃×C₅	1	2	yes	—
367	#95	C₂²×C₃×C₅	1	1	yes	characteristic
368	#95	C₂²×C₃×C₅	1	1	yes	characteristic
369	C₂×C₃×C₅	—	4	2	no	—
370	C₂×C₃×C₅	—	4	4	no	—
371	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
372	C₂×C₃×C₅	#525	1	1	yes	characteristic
373	C₂×C₃×C₅	#525	1	2	yes	—
374	C₂×C₃×C₅	#529	1	2	yes	—
375	C₂×C₃×C₅	#532	1	1	yes	characteristic
376	C₂³×C₃	—	2	1	no	—
377	C₂³×C₃	—	2	2	no	—
378	C₂³×C₃	—	2	2	no	—
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	—	2	2	no	—
382	C₂³×C₃	—	2	2	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	2	2	no	—
385	C₂³×C₃	—	2	2	no	—
386	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
387	C₂³×C₃	C₅×#41	1	4	yes	—
388	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
389	C₃×D₄	—	2	8	no	—
390	C₃×D₄	—	2	16	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	8	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	4	8	no	—
409	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
410	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
411	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
412	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
413	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
414	C₂×C₃×C₄	C₅×#41	1	4	yes	—
415	C₂×C₃×C₄	C₅×#41	1	2	yes	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	4	no	—
418	C₂²×C₅	—	2	4	no	—
419	C₂²×C₅	—	2	4	no	—
420	C₂²×C₅	—	2	4	no	—
421	C₂²×C₅	—	4	2	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	2	no	—
424	C₂²×C₅	—	4	2	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	2	no	—
428	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
429	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
430	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
431	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
432	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	2	no	—
435	C₄×C₅	—	2	4	no	—
436	C₄×C₅	—	2	2	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	C₃×#121	1	4	yes	—
442	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
443	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
455	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
456	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
457	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
458	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
459	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
460	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
461	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
462	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
463	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	4	no	—
478	C₄²	C₃×C₅×D₄	1	4	yes	complemented
479	C₃×C₅	#2392	1	1	yes	characteristic, direct product factor, Hall
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	4	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	2	4	no	—
484	C₂²×C₃	—	2	4	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	—	4	1	no	—
487	C₂²×C₃	—	4	2	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	4	2	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	2	no	—
492	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
493	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
494	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
495	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
496	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
497	C₃×C₄	—	2	2	no	—
498	C₃×C₄	—	2	2	no	—
499	C₃×C₄	—	2	4	no	—
500	C₃×C₄	—	2	2	no	—
501	C₃×C₄	—	4	2	no	—
502	C₃×C₄	—	4	2	no	—
503	C₃×C₄	—	4	1	no	—
504	C₃×C₄	—	4	1	no	—
505	C₃×C₄	C₅×#121	1	4	yes	—
506	C₂×C₅	—	4	2	no	—
507	C₂×C₅	—	4	4	no	—
508	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
509	C₂×C₅	C₃×#525	1	1	yes	characteristic
510	C₂×C₅	C₃×#525	1	2	yes	—
511	C₂×C₅	C₃×#529	1	2	yes	—
512	C₂×C₅	C₃×#532	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
524	C₂³	C₃×C₅×#41	1	4	yes	—
525	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
526	D₄	—	2	8	no	—
527	D₄	—	2	16	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
547	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
548	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
549	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
550	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
551	C₂×C₄	C₃×C₅×#41	1	4	yes	—
552	C₂×C₄	C₃×C₅×#41	1	2	yes	—
553	C₂×C₃	—	4	2	no	—
554	C₂×C₃	—	4	4	no	—
555	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
556	C₂×C₃	C₅×#525	1	1	yes	characteristic
557	C₂×C₃	C₅×#525	1	2	yes	—
558	C₂×C₃	C₅×#529	1	2	yes	—
559	C₂×C₃	C₅×#532	1	1	yes	characteristic
560	C₅	C₃×#2392	1	1	yes	characteristic, direct product factor, Sylow
561	C₂²	—	2	2	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	2	4	no	—
564	C₂²	—	2	4	no	—
565	C₂²	—	2	4	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	2	no	—
573	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
574	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
575	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
576	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
577	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	4	no	—
581	C₄	—	2	2	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	C₃×C₅×#121	1	4	yes	—
587	C₃	C₅×#2392	1	1	yes	characteristic, direct product factor, Sylow
588	C₂	—	4	2	no	—
589	C₂	—	4	4	no	—
590	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
591	C₂	C₃×C₅×#525	1	1	yes	characteristic
592	C₂	C₃×C₅×#525	1	2	yes	—
593	C₂	C₃×C₅×#529	1	2	yes	—
594	C₂	C₃×C₅×#532	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₃×C₅×#392	C₂
LCS	G ▷ C₂³ ▷ 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. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂×C₃×C₅×#117	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#396	C₂	semidirect
7. C₃×C₅×#394	C₂	semidirect
8. C₃×C₅×#394	C₂	semidirect
10. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
11. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
12. C₅×#2392	C₃	direct (N × H)
39. C₃×#2392	C₅	direct (N × H)
40. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
41. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
42. C₂×C₅×#117	C₂×C₃	semidirect
43. C₅×#398	C₂×C₃	semidirect
44. C₅×#397	C₂×C₃	semidirect
45. C₅×#396	C₂×C₃	semidirect
46. C₅×#394	C₂×C₃	semidirect
47. C₅×#394	C₂×C₃	semidirect
49. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
50. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
63. C₂²×C₃×C₄×C₅	D₄	semidirect
87. C₃×C₄²×C₅	D₄	semidirect
88. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
89. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
90. C₂×C₃×#117	C₂×C₅	semidirect
91. C₃×#398	C₂×C₅	semidirect
92. C₃×#397	C₂×C₅	semidirect
93. C₃×#396	C₂×C₅	semidirect
94. C₃×#394	C₂×C₅	semidirect
95. C₃×#394	C₂×C₅	semidirect
97. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
98. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
125. #2392	C₃×C₅	direct (N × H)
204. C₂²×C₄×C₅	C₃×D₄	semidirect
228. C₄²×C₅	C₃×D₄	semidirect
229. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
230. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
231. C₂×#117	C₂×C₃×C₅	semidirect
232. #398	C₂×C₃×C₅	semidirect
233. #397	C₂×C₃×C₅	semidirect
234. #396	C₂×C₃×C₅	semidirect
235. #394	C₂×C₃×C₅	semidirect
236. #394	C₂×C₃×C₅	semidirect
238. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
239. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
278. C₂²×C₃×C₄	C₅×D₄	semidirect
302. C₃×C₄²	C₅×D₄	semidirect
454. C₂²×C₄	C₃×C₅×D₄	semidirect
478. C₄²	C₃×C₅×D₄	semidirect
479. C₃×C₅	#2392	direct (N × H)
560. C₅	C₃×#2392	direct (N × H)
587. C₃	C₅×#2392	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
C₂×C₃×C₅×#117	2
C₃×C₅×#398	2
C₃×C₅×#397	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2392	3
C₃×#2392	5

Subgroups — C3×C5×#2392 #14275426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2392 #14275426