Subgroups — C₃×C₅×#2445 #14275479

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#123	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2445	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	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
18	C₃×C₅×#127	—	2	4	no	—
19	C₃×C₅×#123	—	2	8	no	—
20	C₃×C₄×C₅×D₄	—	2	4	no	—
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	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×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
36	C₃×C₅×#95	C₂²	1	1	yes	characteristic
37	C₃×C₅×#95	C₂²	1	1	yes	characteristic
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×#2445	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
41	C₂×C₅×#123	C₂×C₃	1	2	yes	complemented
42	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#394	C₂×C₃	1	2	yes	complemented
44	C₅×#394	C₂×C₃	1	2	yes	complemented
45	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#386	C₂×C₃	1	2	yes	complemented
50	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
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	2	no	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	4	2	no	—
63	C₂×C₃×C₅×D₄	—	4	2	no	—
64	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
65	C₂²×C₃×C₄×C₅	—	2	4	no	—
66	C₂²×C₃×C₄×C₅	—	2	4	no	—
67	C₂²×C₃×C₄×C₅	—	4	2	no	—
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	2	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	4	no	—
79	C₃×C₅×C₄⋊C₄	—	2	2	no	—
80	C₃×C₅×C₄⋊C₄	—	2	2	no	—
81	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
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×C₅×C₂²⋊C₄	—	2	4	no	—
86	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
88	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
89	C₃×C₄²×C₅	—	2	2	no	—
90	C₃×C₄²×C₅	—	2	2	no	—
91	C₃×C₄²×C₅	—	2	2	no	—
92	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
93	C₂×C₃×#123	C₂×C₅	1	2	yes	complemented
94	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#394	C₂×C₅	1	2	yes	complemented
96	C₃×#394	C₂×C₅	1	2	yes	complemented
97	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#390	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×#386	C₂×C₅	1	2	yes	complemented
102	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
105	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
106	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
107	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
108	C₅×#127	—	2	4	no	—
109	C₅×#123	—	2	8	no	—
110	C₄×C₅×D₄	—	2	4	no	—
111	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
117	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
126	C₅×#95	C₂²×C₃	1	1	yes	characteristic
127	C₅×#95	C₂²×C₃	1	1	yes	characteristic
128	C₅×#95	C₂²×C₃	1	2	yes	—
129	#2445	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³×C₃×C₅	—	2	2	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	—	2	2	no	—
137	C₂³×C₃×C₅	—	2	2	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	C₂×D₄	1	4	yes	—
144	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
145	C₃×C₅×D₄	—	2	8	no	—
146	C₃×C₅×D₄	—	4	8	no	—
147	C₃×C₅×D₄	—	4	8	no	—
148	C₃×C₅×D₄	—	4	4	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	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	1	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	2	1	no	—
162	C₂×C₃×C₄×C₅	—	2	1	no	—
163	C₂×C₃×C₄×C₅	—	2	2	no	—
164	C₂×C₃×C₄×C₅	—	2	1	no	—
165	C₂×C₃×C₄×C₅	—	2	1	no	—
166	C₂×C₃×C₄×C₅	—	2	1	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	4	8	no	—
170	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
171	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
172	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
173	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
174	C₂×C₃×C₄×C₅	#41	1	2	yes	—
175	C₂×C₃×C₄×C₅	#41	1	2	yes	—
176	C₂×C₃×C₄×C₅	#41	1	2	yes	—
177	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
178	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
179	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
180	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
182	C₃×#127	—	2	4	no	—
183	C₃×#123	—	2	8	no	—
184	C₃×C₄×D₄	—	2	4	no	—
185	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
192	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
197	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
199	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
200	C₃×#95	C₂²×C₅	1	1	yes	characteristic
201	C₃×#95	C₂²×C₅	1	1	yes	characteristic
202	C₃×#95	C₂²×C₅	1	2	yes	—
203	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
204	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
205	C₂×C₅×D₄	—	2	4	no	—
206	C₂×C₅×D₄	—	2	4	no	—
207	C₂×C₅×D₄	—	2	4	no	—
208	C₂×C₅×D₄	—	2	2	no	—
209	C₂×C₅×D₄	—	2	2	no	—
210	C₂×C₅×D₄	—	2	2	no	—
211	C₂×C₅×D₄	—	2	4	no	—
212	C₂×C₅×D₄	—	2	2	no	—
213	C₂×C₅×D₄	—	2	2	no	—
214	C₂×C₅×D₄	—	4	2	no	—
215	C₂×C₅×D₄	—	4	2	no	—
216	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
217	C₂²×C₄×C₅	—	2	4	no	—
218	C₂²×C₄×C₅	—	2	4	no	—
219	C₂²×C₄×C₅	—	4	2	no	—
220	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
223	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
224	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
227	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
229	C₅×C₄⋊C₄	—	2	2	no	—
230	C₅×C₄⋊C₄	—	2	4	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
234	C₅×C₂²⋊C₄	—	2	4	no	—
235	C₅×C₂²⋊C₄	—	2	4	no	—
236	C₅×C₂²⋊C₄	—	2	4	no	—
237	C₅×C₂²⋊C₄	—	2	4	no	—
238	C₅×C₂²⋊C₄	—	4	2	no	—
239	C₅×C₂²⋊C₄	—	4	2	no	—
240	C₅×C₂²⋊C₄	—	4	2	no	—
241	C₄²×C₅	—	2	2	no	—
242	C₄²×C₅	—	2	2	no	—
243	C₄²×C₅	—	2	2	no	—
244	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
245	C₂×#123	C₂×C₃×C₅	1	2	yes	complemented
246	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
247	#394	C₂×C₃×C₅	1	2	yes	complemented
248	#394	C₂×C₃×C₅	1	2	yes	complemented
249	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
251	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
252	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
253	#386	C₂×C₃×C₅	1	2	yes	complemented
254	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	C₂²×C₃×C₅	—	2	4	no	—
256	C₂²×C₃×C₅	—	2	4	no	—
257	C₂²×C₃×C₅	—	2	4	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	—	4	2	no	—
260	C₂²×C₃×C₅	—	4	2	no	—
261	C₂²×C₃×C₅	—	4	2	no	—
262	C₂²×C₃×C₅	—	4	2	no	—
263	C₂²×C₃×C₅	—	4	2	no	—
264	C₂²×C₃×C₅	—	4	2	no	—
265	C₂²×C₃×C₅	—	4	2	no	—
266	C₂²×C₃×C₅	—	4	2	no	—
267	C₂²×C₃×C₅	—	4	2	no	—
268	C₂²×C₃×C₅	—	4	2	no	—
269	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
272	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
273	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
274	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
276	C₃×C₄×C₅	—	2	2	no	—
277	C₃×C₄×C₅	—	2	2	no	—
278	C₃×C₄×C₅	—	2	2	no	—
279	C₃×C₄×C₅	—	2	2	no	—
280	C₃×C₄×C₅	—	4	1	no	—
281	C₃×C₄×C₅	—	4	2	no	—
282	C₃×C₄×C₅	—	4	1	no	—
283	C₃×C₄×C₅	—	4	2	no	—
284	C₃×C₄×C₅	#123	1	4	yes	complemented
285	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
286	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
287	C₂×C₃×D₄	—	2	4	no	—
288	C₂×C₃×D₄	—	2	4	no	—
289	C₂×C₃×D₄	—	2	4	no	—
290	C₂×C₃×D₄	—	2	2	no	—
291	C₂×C₃×D₄	—	2	2	no	—
292	C₂×C₃×D₄	—	2	2	no	—
293	C₂×C₃×D₄	—	2	4	no	—
294	C₂×C₃×D₄	—	2	2	no	—
295	C₂×C₃×D₄	—	2	2	no	—
296	C₂×C₃×D₄	—	4	2	no	—
297	C₂×C₃×D₄	—	4	2	no	—
298	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
299	C₂²×C₃×C₄	—	2	4	no	—
300	C₂²×C₃×C₄	—	2	4	no	—
301	C₂²×C₃×C₄	—	4	2	no	—
302	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
303	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
305	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
306	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
311	C₃×C₄⋊C₄	—	2	2	no	—
312	C₃×C₄⋊C₄	—	2	4	no	—
313	C₃×C₄⋊C₄	—	2	2	no	—
314	C₃×C₄⋊C₄	—	2	2	no	—
315	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
316	C₃×C₂²⋊C₄	—	2	4	no	—
317	C₃×C₂²⋊C₄	—	2	4	no	—
318	C₃×C₂²⋊C₄	—	2	4	no	—
319	C₃×C₂²⋊C₄	—	2	4	no	—
320	C₃×C₂²⋊C₄	—	4	2	no	—
321	C₃×C₂²⋊C₄	—	4	2	no	—
322	C₃×C₂²⋊C₄	—	4	2	no	—
323	C₃×C₄²	—	2	2	no	—
324	C₃×C₄²	—	2	2	no	—
325	C₃×C₄²	—	2	2	no	—
326	C₂³×C₅	—	2	2	no	—
327	C₂³×C₅	—	2	2	no	—
328	C₂³×C₅	—	2	2	no	—
329	C₂³×C₅	—	2	2	no	—
330	C₂³×C₅	—	2	2	no	—
331	C₂³×C₅	—	2	2	no	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	2	2	no	—
334	C₂³×C₅	—	2	2	no	—
335	C₂³×C₅	—	2	2	no	—
336	C₂³×C₅	—	2	2	no	—
337	C₂³×C₅	—	2	2	no	—
338	C₂³×C₅	—	2	2	no	—
339	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
340	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
341	C₅×D₄	—	2	8	no	—
342	C₅×D₄	—	4	8	no	—
343	C₅×D₄	—	4	8	no	—
344	C₅×D₄	—	4	4	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	2	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	2	no	—
365	C₂×C₄×C₅	—	4	8	no	—
366	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
367	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
368	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
369	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
370	C₂×C₄×C₅	C₃×#41	1	2	yes	—
371	C₂×C₄×C₅	C₃×#41	1	2	yes	—
372	C₂×C₄×C₅	C₃×#41	1	2	yes	—
373	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
374	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
375	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
376	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
377	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
378	#127	—	2	4	no	—
379	#123	—	2	8	no	—
380	C₄×D₄	—	2	4	no	—
381	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
383	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
393	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
395	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
396	#95	C₂²×C₃×C₅	1	1	yes	characteristic
397	#95	C₂²×C₃×C₅	1	1	yes	characteristic
398	#95	C₂²×C₃×C₅	1	2	yes	—
399	C₂×C₃×C₅	—	4	4	no	—
400	C₂×C₃×C₅	—	8	2	no	—
401	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
402	C₂×C₃×C₅	#532	1	1	yes	characteristic
403	C₂×C₃×C₅	#540	1	1	yes	characteristic
404	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
405	C₂×C₃×C₅	#546	1	1	yes	characteristic
406	C₂×C₃×C₅	#550	1	1	yes	characteristic
407	C₂×C₃×C₅	#559	1	1	yes	characteristic
408	C₂³×C₃	—	2	2	no	—
409	C₂³×C₃	—	2	2	no	—
410	C₂³×C₃	—	2	2	no	—
411	C₂³×C₃	—	2	2	no	—
412	C₂³×C₃	—	2	2	no	—
413	C₂³×C₃	—	2	2	no	—
414	C₂³×C₃	—	2	2	no	—
415	C₂³×C₃	—	2	2	no	—
416	C₂³×C₃	—	2	2	no	—
417	C₂³×C₃	—	2	2	no	—
418	C₂³×C₃	—	2	2	no	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
422	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
423	C₃×D₄	—	2	8	no	—
424	C₃×D₄	—	4	8	no	—
425	C₃×D₄	—	4	8	no	—
426	C₃×D₄	—	4	4	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	2	1	no	—
429	C₂×C₃×C₄	—	2	1	no	—
430	C₂×C₃×C₄	—	2	1	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	2	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	2	no	—
446	C₂×C₃×C₄	—	2	2	no	—
447	C₂×C₃×C₄	—	4	8	no	—
448	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
449	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
450	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
451	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
452	C₂×C₃×C₄	C₅×#41	1	2	yes	—
453	C₂×C₃×C₄	C₅×#41	1	2	yes	—
454	C₂×C₃×C₄	C₅×#41	1	2	yes	—
455	C₂²×C₅	—	2	4	no	—
456	C₂²×C₅	—	2	4	no	—
457	C₂²×C₅	—	2	4	no	—
458	C₂²×C₅	—	4	2	no	—
459	C₂²×C₅	—	4	2	no	—
460	C₂²×C₅	—	4	2	no	—
461	C₂²×C₅	—	4	2	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	2	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	4	2	no	—
468	C₂²×C₅	—	4	2	no	—
469	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
470	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
471	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
472	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
473	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
474	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₄×C₅	—	2	2	no	—
477	C₄×C₅	—	2	2	no	—
478	C₄×C₅	—	2	2	no	—
479	C₄×C₅	—	2	2	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	4	2	no	—
482	C₄×C₅	—	4	1	no	—
483	C₄×C₅	—	4	2	no	—
484	C₄×C₅	C₃×#123	1	4	yes	complemented
485	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
486	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	4	2	no	—
497	C₂×D₄	—	4	2	no	—
498	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
503	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
504	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
505	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
506	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
507	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
508	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
509	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
510	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₃×C₅	#2445	1	1	yes	characteristic, direct product factor, Hall
527	C₂²×C₃	—	2	4	no	—
528	C₂²×C₃	—	2	4	no	—
529	C₂²×C₃	—	2	4	no	—
530	C₂²×C₃	—	4	2	no	—
531	C₂²×C₃	—	4	2	no	—
532	C₂²×C₃	—	4	2	no	—
533	C₂²×C₃	—	4	2	no	—
534	C₂²×C₃	—	4	2	no	—
535	C₂²×C₃	—	4	2	no	—
536	C₂²×C₃	—	4	2	no	—
537	C₂²×C₃	—	4	2	no	—
538	C₂²×C₃	—	4	2	no	—
539	C₂²×C₃	—	4	2	no	—
540	C₂²×C₃	—	4	2	no	—
541	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
542	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
543	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
544	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
545	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
546	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
548	C₃×C₄	—	2	2	no	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	4	1	no	—
553	C₃×C₄	—	4	2	no	—
554	C₃×C₄	—	4	1	no	—
555	C₃×C₄	—	4	2	no	—
556	C₃×C₄	C₅×#123	1	4	yes	complemented
557	C₂×C₅	—	4	4	no	—
558	C₂×C₅	—	8	2	no	—
559	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
560	C₂×C₅	C₃×#532	1	1	yes	characteristic
561	C₂×C₅	C₃×#540	1	1	yes	characteristic
562	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
563	C₂×C₅	C₃×#546	1	1	yes	characteristic
564	C₂×C₅	C₃×#550	1	1	yes	characteristic
565	C₂×C₅	C₃×#559	1	1	yes	characteristic
566	C₂³	—	2	2	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
580	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
581	D₄	—	2	8	no	—
582	D₄	—	4	8	no	—
583	D₄	—	4	8	no	—
584	D₄	—	4	4	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	4	8	no	—
606	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
607	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
608	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
609	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
610	C₂×C₄	C₃×C₅×#41	1	2	yes	—
611	C₂×C₄	C₃×C₅×#41	1	2	yes	—
612	C₂×C₄	C₃×C₅×#41	1	2	yes	—
613	C₂×C₃	—	4	4	no	—
614	C₂×C₃	—	8	2	no	—
615	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
616	C₂×C₃	C₅×#532	1	1	yes	characteristic
617	C₂×C₃	C₅×#540	1	1	yes	characteristic
618	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
619	C₂×C₃	C₅×#546	1	1	yes	characteristic
620	C₂×C₃	C₅×#550	1	1	yes	characteristic
621	C₂×C₃	C₅×#559	1	1	yes	characteristic
622	C₅	C₃×#2445	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
638	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
639	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
640	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
641	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
642	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	2	no	—
652	C₄	C₃×C₅×#123	1	4	yes	complemented
653	C₃	C₅×#2445	1	1	yes	characteristic, direct product factor, Sylow
654	C₂	—	4	4	no	—
655	C₂	—	8	2	no	—
656	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
657	C₂	C₃×C₅×#532	1	1	yes	characteristic
658	C₂	C₃×C₅×#540	1	1	yes	characteristic
659	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
660	C₂	C₃×C₅×#546	1	1	yes	characteristic
661	C₂	C₃×C₅×#550	1	1	yes	characteristic
662	C₂	C₃×C₅×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#123	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₅×#390	C₂	semidirect
8. C₃×C₅×#390	C₂	semidirect
9. C₃×C₅×#389	C₂	semidirect
10. C₃×C₅×#386	C₂	semidirect
11. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#2445	C₃	direct (N × H)
39. C₃×#2445	C₅	direct (N × H)
41. C₂×C₅×#123	C₂×C₃	semidirect
42. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
43. C₅×#394	C₂×C₃	semidirect
44. C₅×#394	C₂×C₃	semidirect
45. C₅×#390	C₂×C₃	semidirect
46. C₅×#390	C₂×C₃	semidirect
47. C₅×#390	C₂×C₃	semidirect
48. C₅×#389	C₂×C₃	semidirect
49. C₅×#386	C₂×C₃	semidirect
50. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
81. C₃×C₅×C₄⋊C₄	D₄	semidirect
93. C₂×C₃×#123	C₂×C₅	semidirect
94. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
95. C₃×#394	C₂×C₅	semidirect
96. C₃×#394	C₂×C₅	semidirect
97. C₃×#390	C₂×C₅	semidirect
98. C₃×#390	C₂×C₅	semidirect
99. C₃×#390	C₂×C₅	semidirect
100. C₃×#389	C₂×C₅	semidirect
101. C₃×#386	C₂×C₅	semidirect
102. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
129. #2445	C₃×C₅	direct (N × H)
233. C₅×C₄⋊C₄	C₃×D₄	semidirect
245. C₂×#123	C₂×C₃×C₅	semidirect
246. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
247. #394	C₂×C₃×C₅	semidirect
248. #394	C₂×C₃×C₅	semidirect
249. #390	C₂×C₃×C₅	semidirect
250. #390	C₂×C₃×C₅	semidirect
251. #390	C₂×C₃×C₅	semidirect
252. #389	C₂×C₃×C₅	semidirect
253. #386	C₂×C₃×C₅	semidirect
254. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
284. C₃×C₄×C₅	#123	semidirect
315. C₃×C₄⋊C₄	C₅×D₄	semidirect
484. C₄×C₅	C₃×#123	semidirect
515. C₄⋊C₄	C₃×C₅×D₄	semidirect
526. C₃×C₅	#2445	direct (N × H)
556. C₃×C₄	C₅×#123	semidirect
622. C₅	C₃×#2445	direct (N × H)
652. C₄	C₃×C₅×#123	semidirect
653. C₃	C₅×#2445	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×#127	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2445	3
C₃×#2445	5

Subgroups — C3×C5×#2445 #14275479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2445 #14275479