Subgroups — C₃×C₅×#2455 #14275489

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2455	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₃×C₅×#123	—	2	8	no	—
16	C₃×C₄×C₅×D₄	—	2	8	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	1	yes	characteristic
33	C₃×C₅×#95	C₂²	1	1	yes	characteristic
34	C₃×#2455	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#123	C₂×C₃	1	2	yes	complemented
36	C₂×C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
37	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#394	C₂×C₃	1	2	yes	complemented
39	C₅×#392	C₂×C₃	1	1	yes	characteristic
40	C₅×#389	C₂×C₃	1	2	yes	complemented
41	C₅×#388	C₂×C₃	1	2	yes	complemented
42	C₅×#385	C₂×C₃	1	2	yes	complemented
43	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	—	4	1	no	—
51	C₂²×C₃×C₄×C₅	—	2	4	no	—
52	C₂²×C₃×C₄×C₅	—	2	4	no	—
53	C₂²×C₃×C₄×C₅	—	2	4	no	—
54	C₂²×C₃×C₄×C₅	—	4	1	no	—
55	C₂²×C₃×C₄×C₅	—	4	2	no	—
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	—	2	4	no	—
64	C₃×C₅×C₄⋊C₄	—	2	4	no	—
65	C₃×C₅×C₄⋊C₄	—	2	4	no	—
66	C₃×C₅×C₄⋊C₄	—	2	4	no	—
67	C₃×C₅×C₄⋊C₄	—	4	1	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
73	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
74	C₃×C₅×C₂²⋊C₄	D₄	1	8	yes	complemented
75	C₃×C₄²×C₅	—	2	4	no	—
76	C₂×C₃×#123	C₂×C₅	1	2	yes	complemented
77	C₂×C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
78	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#394	C₂×C₅	1	2	yes	complemented
80	C₃×#392	C₂×C₅	1	1	yes	characteristic
81	C₃×#389	C₂×C₅	1	2	yes	complemented
82	C₃×#388	C₂×C₅	1	2	yes	complemented
83	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#385	C₂×C₅	1	2	yes	complemented
85	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
86	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
89	C₅×#123	—	2	8	no	—
90	C₄×C₅×D₄	—	2	8	no	—
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
104	C₅×#95	C₂²×C₃	1	2	yes	—
105	C₅×#95	C₂²×C₃	1	2	yes	—
106	C₅×#95	C₂²×C₃	1	1	yes	characteristic
107	C₅×#95	C₂²×C₃	1	1	yes	characteristic
108	#2455	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	1	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	1	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
120	C₂³×C₃×C₅	#41	1	2	yes	—
121	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
122	C₃×C₅×D₄	—	2	16	no	—
123	C₃×C₅×D₄	—	4	4	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	4	4	no	—
141	C₂×C₃×C₄×C₅	—	4	8	no	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
144	C₂×C₃×C₄×C₅	#41	1	4	yes	—
145	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
146	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
147	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
148	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
149	C₃×#123	—	2	8	no	—
150	C₃×C₄×D₄	—	2	8	no	—
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
164	C₃×#95	C₂²×C₅	1	2	yes	—
165	C₃×#95	C₂²×C₅	1	2	yes	—
166	C₃×#95	C₂²×C₅	1	1	yes	characteristic
167	C₃×#95	C₂²×C₅	1	1	yes	characteristic
168	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
169	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₅×D₄	—	2	4	no	—
171	C₂×C₅×D₄	—	2	4	no	—
172	C₂×C₅×D₄	—	2	4	no	—
173	C₂×C₅×D₄	—	2	4	no	—
174	C₂×C₅×D₄	—	4	1	no	—
175	C₂²×C₄×C₅	—	2	4	no	—
176	C₂²×C₄×C₅	—	2	4	no	—
177	C₂²×C₄×C₅	—	2	4	no	—
178	C₂²×C₄×C₅	—	4	1	no	—
179	C₂²×C₄×C₅	—	4	2	no	—
180	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
185	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
186	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
187	C₅×C₄⋊C₄	—	2	4	no	—
188	C₅×C₄⋊C₄	—	2	4	no	—
189	C₅×C₄⋊C₄	—	2	4	no	—
190	C₅×C₄⋊C₄	—	2	4	no	—
191	C₅×C₄⋊C₄	—	4	1	no	—
192	C₅×C₂²⋊C₄	—	2	4	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	4	no	—
195	C₅×C₂²⋊C₄	—	2	4	no	—
196	C₅×C₂²⋊C₄	—	2	4	no	—
197	C₅×C₂²⋊C₄	—	4	1	no	—
198	C₅×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
199	C₄²×C₅	—	2	4	no	—
200	C₂×#123	C₂×C₃×C₅	1	2	yes	complemented
201	C₂×C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
202	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#394	C₂×C₃×C₅	1	2	yes	complemented
204	#392	C₂×C₃×C₅	1	1	yes	characteristic
205	#389	C₂×C₃×C₅	1	2	yes	complemented
206	#388	C₂×C₃×C₅	1	2	yes	complemented
207	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
208	#385	C₂×C₃×C₅	1	2	yes	complemented
209	C₂²×C₃×C₅	—	2	4	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	—	2	2	no	—
212	C₂²×C₃×C₅	—	2	4	no	—
213	C₂²×C₃×C₅	—	2	4	no	—
214	C₂²×C₃×C₅	—	4	2	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	—	4	1	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	—	4	1	no	—
221	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
222	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
223	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
224	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
226	C₃×C₄×C₅	—	2	4	no	—
227	C₃×C₄×C₅	—	2	4	no	—
228	C₃×C₄×C₅	—	2	4	no	—
229	C₃×C₄×C₅	—	4	2	no	—
230	C₃×C₄×C₅	—	4	2	no	—
231	C₃×C₄×C₅	—	4	1	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
234	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
235	C₂×C₃×D₄	—	2	4	no	—
236	C₂×C₃×D₄	—	2	4	no	—
237	C₂×C₃×D₄	—	2	4	no	—
238	C₂×C₃×D₄	—	2	4	no	—
239	C₂×C₃×D₄	—	4	1	no	—
240	C₂²×C₃×C₄	—	2	4	no	—
241	C₂²×C₃×C₄	—	2	4	no	—
242	C₂²×C₃×C₄	—	2	4	no	—
243	C₂²×C₃×C₄	—	4	1	no	—
244	C₂²×C₃×C₄	—	4	2	no	—
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
247	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
250	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
251	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
252	C₃×C₄⋊C₄	—	2	4	no	—
253	C₃×C₄⋊C₄	—	2	4	no	—
254	C₃×C₄⋊C₄	—	2	4	no	—
255	C₃×C₄⋊C₄	—	2	4	no	—
256	C₃×C₄⋊C₄	—	4	1	no	—
257	C₃×C₂²⋊C₄	—	2	4	no	—
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	2	4	no	—
260	C₃×C₂²⋊C₄	—	2	4	no	—
261	C₃×C₂²⋊C₄	—	2	4	no	—
262	C₃×C₂²⋊C₄	—	4	1	no	—
263	C₃×C₂²⋊C₄	C₅×D₄	1	8	yes	complemented
264	C₃×C₄²	—	2	4	no	—
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	2	2	no	—
269	C₂³×C₅	—	2	2	no	—
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	2	no	—
275	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
276	C₂³×C₅	C₃×#41	1	2	yes	—
277	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
278	C₅×D₄	—	2	16	no	—
279	C₅×D₄	—	4	4	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	4	4	no	—
297	C₂×C₄×C₅	—	4	8	no	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
299	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
300	C₂×C₄×C₅	C₃×#41	1	4	yes	—
301	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
302	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
303	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
304	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
305	#123	—	2	8	no	—
306	C₄×D₄	—	2	8	no	—
307	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
308	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
309	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
310	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
311	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
314	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
319	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
320	#95	C₂²×C₃×C₅	1	2	yes	—
321	#95	C₂²×C₃×C₅	1	2	yes	—
322	#95	C₂²×C₃×C₅	1	1	yes	characteristic
323	#95	C₂²×C₃×C₅	1	1	yes	characteristic
324	C₂×C₃×C₅	—	4	4	no	—
325	C₂×C₃×C₅	—	4	2	no	—
326	C₂×C₃×C₅	#525	1	2	yes	—
327	C₂×C₃×C₅	#539	1	1	yes	characteristic
328	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
329	C₂×C₃×C₅	#547	1	2	yes	—
330	C₂×C₃×C₅	#559	1	1	yes	characteristic
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	—	2	2	no	—
333	C₂³×C₃	—	2	2	no	—
334	C₂³×C₃	—	2	2	no	—
335	C₂³×C₃	—	2	2	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	2	1	no	—
338	C₂³×C₃	—	2	2	no	—
339	C₂³×C₃	—	2	1	no	—
340	C₂³×C₃	—	2	2	no	—
341	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
342	C₂³×C₃	C₅×#41	1	2	yes	—
343	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
344	C₃×D₄	—	2	16	no	—
345	C₃×D₄	—	4	4	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	4	4	no	—
363	C₂×C₃×C₄	—	4	8	no	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
365	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
366	C₂×C₃×C₄	C₅×#41	1	4	yes	—
367	C₂²×C₅	—	2	4	no	—
368	C₂²×C₅	—	2	4	no	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	—	2	4	no	—
371	C₂²×C₅	—	2	4	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	—	4	2	no	—
375	C₂²×C₅	—	4	2	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	2	no	—
379	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
380	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
381	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
382	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
384	C₄×C₅	—	2	4	no	—
385	C₄×C₅	—	2	4	no	—
386	C₄×C₅	—	2	4	no	—
387	C₄×C₅	—	4	1	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	—	4	2	no	—
390	C₄×C₅	—	4	1	no	—
391	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
392	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
405	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
406	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
408	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
409	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
422	C₄²	—	2	4	no	—
423	C₃×C₅	#2455	1	1	yes	characteristic, direct product factor, Hall
424	C₂²×C₃	—	2	4	no	—
425	C₂²×C₃	—	2	4	no	—
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	2	4	no	—
428	C₂²×C₃	—	2	4	no	—
429	C₂²×C₃	—	4	2	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	4	1	no	—
432	C₂²×C₃	—	4	2	no	—
433	C₂²×C₃	—	4	2	no	—
434	C₂²×C₃	—	4	2	no	—
435	C₂²×C₃	—	4	1	no	—
436	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
437	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
438	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
439	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
441	C₃×C₄	—	2	4	no	—
442	C₃×C₄	—	2	4	no	—
443	C₃×C₄	—	2	4	no	—
444	C₃×C₄	—	4	2	no	—
445	C₃×C₄	—	4	2	no	—
446	C₃×C₄	—	4	1	no	—
447	C₃×C₄	—	4	1	no	—
448	C₂×C₅	—	4	4	no	—
449	C₂×C₅	—	4	2	no	—
450	C₂×C₅	C₃×#525	1	2	yes	—
451	C₂×C₅	C₃×#539	1	1	yes	characteristic
452	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
453	C₂×C₅	C₃×#547	1	2	yes	—
454	C₂×C₅	C₃×#559	1	1	yes	characteristic
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	2	no	—
465	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
466	C₂³	C₃×C₅×#41	1	2	yes	—
467	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
468	D₄	—	2	16	no	—
469	D₄	—	4	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
489	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
490	C₂×C₄	C₃×C₅×#41	1	4	yes	—
491	C₂×C₃	—	4	4	no	—
492	C₂×C₃	—	4	2	no	—
493	C₂×C₃	C₅×#525	1	2	yes	—
494	C₂×C₃	C₅×#539	1	1	yes	characteristic
495	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
496	C₂×C₃	C₅×#547	1	2	yes	—
497	C₂×C₃	C₅×#559	1	1	yes	characteristic
498	C₅	C₃×#2455	1	1	yes	characteristic, direct product factor, Sylow
499	C₂²	—	2	4	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
512	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
513	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
514	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	2	4	no	—
518	C₄	—	2	4	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₃	C₅×#2455	1	1	yes	characteristic, direct product factor, Sylow
524	C₂	—	4	4	no	—
525	C₂	—	4	2	no	—
526	C₂	C₃×C₅×#525	1	2	yes	—
527	C₂	C₃×C₅×#539	1	1	yes	characteristic
528	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
529	C₂	C₃×C₅×#547	1	2	yes	—
530	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	C₃×C₅×#392	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
1. C₂×C₃×C₅×#123	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#385	C₂	semidirect
9. C₃×C₅×#385	C₂	semidirect
10. C₅×#2455	C₃	direct (N × H)
34. C₃×#2455	C₅	direct (N × H)
35. C₂×C₅×#123	C₂×C₃	semidirect
36. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
37. C₅×#399	C₂×C₃	semidirect
38. C₅×#394	C₂×C₃	semidirect
40. C₅×#389	C₂×C₃	semidirect
41. C₅×#388	C₂×C₃	semidirect
42. C₅×#385	C₂×C₃	semidirect
43. C₅×#385	C₂×C₃	semidirect
74. C₃×C₅×C₂²⋊C₄	D₄	semidirect
76. C₂×C₃×#123	C₂×C₅	semidirect
77. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
78. C₃×#399	C₂×C₅	semidirect
79. C₃×#394	C₂×C₅	semidirect
81. C₃×#389	C₂×C₅	semidirect
82. C₃×#388	C₂×C₅	semidirect
83. C₃×#385	C₂×C₅	semidirect
84. C₃×#385	C₂×C₅	semidirect
108. #2455	C₃×C₅	direct (N × H)
198. C₅×C₂²⋊C₄	C₃×D₄	semidirect
200. C₂×#123	C₂×C₃×C₅	semidirect
201. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
202. #399	C₂×C₃×C₅	semidirect
203. #394	C₂×C₃×C₅	semidirect
205. #389	C₂×C₃×C₅	semidirect
206. #388	C₂×C₃×C₅	semidirect
207. #385	C₂×C₃×C₅	semidirect
208. #385	C₂×C₃×C₅	semidirect
263. C₃×C₂²⋊C₄	C₅×D₄	semidirect
421. C₂²⋊C₄	C₃×C₅×D₄	semidirect
423. C₃×C₅	#2455	direct (N × H)
498. C₅	C₃×#2455	direct (N × H)
523. C₃	C₅×#2455	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×#123	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#399	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#385	2
C₅×#2455	3
C₃×#2455	5

Subgroups — C3×C5×#2455 #14275489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2455 #14275489