Subgroups — C₃×C₅×#2517 #14275551

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#397	C₂	1	2	yes	maximal
4	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#382	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
10	C₅×#2517	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic
32	C₃×#2517	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#399	C₂×C₃	1	1	yes	characteristic
34	C₅×#397	C₂×C₃	1	1	yes	characteristic
35	C₅×#397	C₂×C₃	1	2	yes	—
36	C₅×#387	C₂×C₃	1	2	yes	complemented
37	C₅×#387	C₂×C₃	1	2	yes	complemented
38	C₅×#387	C₂×C₃	1	2	yes	complemented
39	C₅×#385	C₂×C₃	1	1	yes	characteristic
40	C₅×#382	C₂×C₃	1	2	yes	complemented
41	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	—	4	1	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	4	1	no	—
57	C₃×C₅×C₄⋊C₄	—	4	1	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
62	C₃×C₄²×C₅	—	2	4	no	—
63	C₃×C₄²×C₅	—	4	2	no	—
64	C₃×#399	C₂×C₅	1	1	yes	characteristic
65	C₃×#397	C₂×C₅	1	1	yes	characteristic
66	C₃×#397	C₂×C₅	1	2	yes	—
67	C₃×#387	C₂×C₅	1	2	yes	complemented
68	C₃×#387	C₂×C₅	1	2	yes	complemented
69	C₃×#387	C₂×C₅	1	2	yes	complemented
70	C₃×#385	C₂×C₅	1	1	yes	characteristic
71	C₃×#382	C₂×C₅	1	2	yes	complemented
72	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
73	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
84	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	2	yes	—
86	C₅×#95	C₂²×C₃	1	2	yes	—
87	C₅×#95	C₂²×C₃	1	1	yes	characteristic
88	C₅×#95	C₂²×C₃	1	2	yes	—
89	C₅×#95	C₂²×C₃	1	2	yes	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	2	yes	—
92	C₅×#95	C₂²×C₃	1	2	yes	—
93	C₅×#95	C₂²×C₃	1	1	yes	characteristic
94	#2517	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	2	1	no	—
98	C₂³×C₃×C₅	—	2	1	no	—
99	C₂³×C₃×C₅	#41	1	2	yes	—
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	1	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	4	4	no	—
122	C₂×C₃×C₄×C₅	#41	1	4	yes	—
123	C₂×C₃×C₄×C₅	#41	1	4	yes	—
124	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
135	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
136	C₃×#95	C₂²×C₅	1	2	yes	—
137	C₃×#95	C₂²×C₅	1	2	yes	—
138	C₃×#95	C₂²×C₅	1	1	yes	characteristic
139	C₃×#95	C₂²×C₅	1	2	yes	—
140	C₃×#95	C₂²×C₅	1	2	yes	—
141	C₃×#95	C₂²×C₅	1	2	yes	—
142	C₃×#95	C₂²×C₅	1	2	yes	—
143	C₃×#95	C₂²×C₅	1	2	yes	—
144	C₃×#95	C₂²×C₅	1	1	yes	characteristic
145	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	4	1	no	—
148	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
156	C₅×C₄⋊C₄	—	2	4	no	—
157	C₅×C₄⋊C₄	—	2	4	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₄⋊C₄	—	4	1	no	—
160	C₅×C₄⋊C₄	—	4	1	no	—
161	C₅×C₂²⋊C₄	—	2	4	no	—
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	2	4	no	—
164	C₅×C₂²⋊C₄	—	4	1	no	—
165	C₄²×C₅	—	2	4	no	—
166	C₄²×C₅	—	4	2	no	—
167	#399	C₂×C₃×C₅	1	1	yes	characteristic
168	#397	C₂×C₃×C₅	1	1	yes	characteristic
169	#397	C₂×C₃×C₅	1	2	yes	—
170	#387	C₂×C₃×C₅	1	2	yes	complemented
171	#387	C₂×C₃×C₅	1	2	yes	complemented
172	#387	C₂×C₃×C₅	1	2	yes	complemented
173	#385	C₂×C₃×C₅	1	1	yes	characteristic
174	#382	C₂×C₃×C₅	1	2	yes	complemented
175	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
176	C₂²×C₃×C₅	—	2	4	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	4	1	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	4	1	no	—
181	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
183	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
184	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
186	C₃×C₄×C₅	—	2	4	no	—
187	C₃×C₄×C₅	—	2	4	no	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	1	no	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	—	4	1	no	—
194	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
195	C₂²×C₃×C₄	—	2	4	no	—
196	C₂²×C₃×C₄	—	4	1	no	—
197	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
198	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
199	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
200	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
201	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
205	C₃×C₄⋊C₄	—	2	4	no	—
206	C₃×C₄⋊C₄	—	2	4	no	—
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	4	1	no	—
209	C₃×C₄⋊C₄	—	4	1	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	2	2	no	—
212	C₃×C₂²⋊C₄	—	2	4	no	—
213	C₃×C₂²⋊C₄	—	4	1	no	—
214	C₃×C₄²	—	2	4	no	—
215	C₃×C₄²	—	4	2	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	C₃×#41	1	2	yes	—
221	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	4	4	no	—
243	C₂×C₄×C₅	C₃×#41	1	4	yes	—
244	C₂×C₄×C₅	C₃×#41	1	4	yes	—
245	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
248	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
249	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
256	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
257	#95	C₂²×C₃×C₅	1	2	yes	—
258	#95	C₂²×C₃×C₅	1	2	yes	—
259	#95	C₂²×C₃×C₅	1	1	yes	characteristic
260	#95	C₂²×C₃×C₅	1	2	yes	—
261	#95	C₂²×C₃×C₅	1	2	yes	—
262	#95	C₂²×C₃×C₅	1	2	yes	—
263	#95	C₂²×C₃×C₅	1	2	yes	—
264	#95	C₂²×C₃×C₅	1	2	yes	—
265	#95	C₂²×C₃×C₅	1	1	yes	characteristic
266	C₂×C₃×C₅	—	4	2	no	—
267	C₂×C₃×C₅	#529	1	2	yes	—
268	C₂×C₃×C₅	#539	1	1	yes	characteristic
269	C₂×C₃×C₅	#551	1	1	yes	characteristic
270	C₂×C₃×C₅	#552	1	2	yes	—
271	C₂×C₃×C₅	#559	1	1	yes	characteristic
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	1	no	—
275	C₂³×C₃	—	2	1	no	—
276	C₂³×C₃	C₅×#41	1	2	yes	—
277	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	4	4	no	—
299	C₂×C₃×C₄	C₅×#41	1	4	yes	—
300	C₂×C₃×C₄	C₅×#41	1	4	yes	—
301	C₂²×C₅	—	2	4	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	—	4	1	no	—
305	C₂²×C₅	—	4	2	no	—
306	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
307	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
308	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
309	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
311	C₄×C₅	—	2	4	no	—
312	C₄×C₅	—	2	4	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	1	no	—
319	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
323	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
324	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
325	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
326	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
327	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
329	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	4	2	no	—
341	C₃×C₅	#2517	1	1	yes	characteristic, direct product factor, Hall
342	C₂²×C₃	—	2	4	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	—	4	2	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
348	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
349	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
350	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	2	4	no	—
354	C₃×C₄	—	4	2	no	—
355	C₃×C₄	—	4	2	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	—	4	1	no	—
358	C₃×C₄	—	4	2	no	—
359	C₃×C₄	—	4	1	no	—
360	C₂×C₅	—	4	2	no	—
361	C₂×C₅	C₃×#529	1	2	yes	—
362	C₂×C₅	C₃×#539	1	1	yes	characteristic
363	C₂×C₅	C₃×#551	1	1	yes	characteristic
364	C₂×C₅	C₃×#552	1	2	yes	—
365	C₂×C₅	C₃×#559	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	C₃×C₅×#41	1	2	yes	—
371	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	C₃×C₅×#41	1	4	yes	—
394	C₂×C₄	C₃×C₅×#41	1	4	yes	—
395	C₂×C₃	—	4	2	no	—
396	C₂×C₃	C₅×#529	1	2	yes	—
397	C₂×C₃	C₅×#539	1	1	yes	characteristic
398	C₂×C₃	C₅×#551	1	1	yes	characteristic
399	C₂×C₃	C₅×#552	1	2	yes	—
400	C₂×C₃	C₅×#559	1	1	yes	characteristic
401	C₅	C₃×#2517	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	4	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
408	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
409	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
410	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	1	no	—
420	C₃	C₅×#2517	1	1	yes	characteristic, direct product factor, Sylow
421	C₂	—	4	2	no	—
422	C₂	C₃×C₅×#529	1	2	yes	—
423	C₂	C₃×C₅×#539	1	1	yes	characteristic
424	C₂	C₃×C₅×#551	1	1	yes	characteristic
425	C₂	C₃×C₅×#552	1	2	yes	—
426	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	C₂⁴×C₃×C₅	C₂³
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
4. C₃×C₅×#387	C₂	semidirect
5. C₃×C₅×#387	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
8. C₃×C₅×#382	C₂	semidirect
10. C₅×#2517	C₃	direct (N × H)
32. C₃×#2517	C₅	direct (N × H)
36. C₅×#387	C₂×C₃	semidirect
37. C₅×#387	C₂×C₃	semidirect
38. C₅×#387	C₂×C₃	semidirect
40. C₅×#382	C₂×C₃	semidirect
67. C₃×#387	C₂×C₅	semidirect
68. C₃×#387	C₂×C₅	semidirect
69. C₃×#387	C₂×C₅	semidirect
71. C₃×#382	C₂×C₅	semidirect
94. #2517	C₃×C₅	direct (N × H)
170. #387	C₂×C₃×C₅	semidirect
171. #387	C₂×C₃×C₅	semidirect
172. #387	C₂×C₃×C₅	semidirect
174. #382	C₂×C₃×C₅	semidirect
341. C₃×C₅	#2517	direct (N × H)
401. C₅	C₃×#2517	direct (N × H)
420. C₃	C₅×#2517	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#399	2
C₃×C₅×#397	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2517	3
C₃×#2517	5

Subgroups — C3×C5×#2517 #14275551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2517 #14275551