Subgroups — C₃×C₅×#2719 #14275753

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic
12	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic
13	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic
15	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
16	C₅×#2719	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₅×#125	—	2	4	no	—
18	C₃×C₅×#125	—	2	4	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₃×C₅×#95	C₂²	1	1	yes	characteristic
39	C₃×C₅×#95	C₂²	1	1	yes	characteristic
40	C₃×C₅×#95	C₂²	1	1	yes	characteristic
41	C₃×C₅×#95	C₂²	1	1	yes	characteristic
42	C₃×C₅×#95	C₂²	1	1	yes	characteristic
43	C₃×C₅×#95	C₂²	1	1	yes	characteristic
44	C₃×C₅×#95	C₂²	1	1	yes	characteristic
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic
52	C₃×C₅×#95	C₂²	1	1	yes	characteristic
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic
54	C₃×#2719	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
56	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
57	C₅×#400	C₂×C₃	1	1	yes	characteristic
58	C₅×#400	C₂×C₃	1	1	yes	characteristic
59	C₅×#400	C₂×C₃	1	1	yes	characteristic
60	C₅×#398	C₂×C₃	1	1	yes	characteristic
61	C₅×#398	C₂×C₃	1	1	yes	characteristic
62	C₅×#398	C₂×C₃	1	1	yes	characteristic
63	C₅×#389	C₂×C₃	1	1	yes	characteristic
64	C₅×#389	C₂×C₃	1	1	yes	characteristic
65	C₅×#387	C₂×C₃	1	1	yes	characteristic
66	C₅×#387	C₂×C₃	1	1	yes	characteristic
67	C₅×#387	C₂×C₃	1	1	yes	characteristic
68	C₅×#387	C₂×C₃	1	1	yes	characteristic
69	C₅×#382	C₂×C₃	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₃×C₅×C₄⋊C₄	—	2	2	no	—
86	C₃×C₅×C₄⋊C₄	—	2	2	no	—
87	C₃×C₅×C₄⋊C₄	—	2	2	no	—
88	C₃×C₅×C₄⋊C₄	—	2	2	no	—
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	—	2	2	no	—
91	C₃×C₅×C₄⋊C₄	—	2	2	no	—
92	C₃×C₅×C₄⋊C₄	—	2	2	no	—
93	C₃×C₅×C₄⋊C₄	—	2	2	no	—
94	C₃×C₅×C₄⋊C₄	—	2	2	no	—
95	C₃×C₅×C₄⋊C₄	—	2	2	no	—
96	C₃×C₅×C₄⋊C₄	—	2	2	no	—
97	C₃×C₅×C₄⋊C₄	—	2	2	no	—
98	C₃×C₅×C₄⋊C₄	—	2	2	no	—
99	C₃×C₅×C₄⋊C₄	—	2	2	no	—
100	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
101	C₃×C₄²×C₅	—	2	2	no	—
102	C₃×C₄²×C₅	—	2	2	no	—
103	C₃×C₄²×C₅	—	2	2	no	—
104	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
105	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
106	C₃×#400	C₂×C₅	1	1	yes	characteristic
107	C₃×#400	C₂×C₅	1	1	yes	characteristic
108	C₃×#400	C₂×C₅	1	1	yes	characteristic
109	C₃×#398	C₂×C₅	1	1	yes	characteristic
110	C₃×#398	C₂×C₅	1	1	yes	characteristic
111	C₃×#398	C₂×C₅	1	1	yes	characteristic
112	C₃×#389	C₂×C₅	1	1	yes	characteristic
113	C₃×#389	C₂×C₅	1	1	yes	characteristic
114	C₃×#387	C₂×C₅	1	1	yes	characteristic
115	C₃×#387	C₂×C₅	1	1	yes	characteristic
116	C₃×#387	C₂×C₅	1	1	yes	characteristic
117	C₃×#387	C₂×C₅	1	1	yes	characteristic
118	C₃×#382	C₂×C₅	1	1	yes	characteristic
119	C₅×#125	—	2	4	no	—
120	C₅×#125	—	2	4	no	—
121	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
140	C₅×#95	C₂²×C₃	1	1	yes	characteristic
141	C₅×#95	C₂²×C₃	1	1	yes	characteristic
142	C₅×#95	C₂²×C₃	1	1	yes	characteristic
143	C₅×#95	C₂²×C₃	1	1	yes	characteristic
144	C₅×#95	C₂²×C₃	1	1	yes	characteristic
145	C₅×#95	C₂²×C₃	1	1	yes	characteristic
146	C₅×#95	C₂²×C₃	1	1	yes	characteristic
147	C₅×#95	C₂²×C₃	1	1	yes	characteristic
148	C₅×#95	C₂²×C₃	1	1	yes	characteristic
149	C₅×#95	C₂²×C₃	1	1	yes	characteristic
150	C₅×#95	C₂²×C₃	1	1	yes	characteristic
151	C₅×#95	C₂²×C₃	1	1	yes	characteristic
152	C₅×#95	C₂²×C₃	1	1	yes	characteristic
153	C₅×#95	C₂²×C₃	1	1	yes	characteristic
154	C₅×#95	C₂²×C₃	1	1	yes	characteristic
155	C₅×#95	C₂²×C₃	1	1	yes	characteristic
156	#2719	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
157	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
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	1	no	—
162	C₂×C₃×C₄×C₅	—	2	1	no	—
163	C₂×C₃×C₄×C₅	—	2	1	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	1	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
199	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
200	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
201	C₂×C₃×C₄×C₅	#41	1	2	yes	—
202	C₂×C₃×C₄×C₅	#41	1	2	yes	—
203	C₃×#125	—	2	4	no	—
204	C₃×#125	—	2	4	no	—
205	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
224	C₃×#95	C₂²×C₅	1	1	yes	characteristic
225	C₃×#95	C₂²×C₅	1	1	yes	characteristic
226	C₃×#95	C₂²×C₅	1	1	yes	characteristic
227	C₃×#95	C₂²×C₅	1	1	yes	characteristic
228	C₃×#95	C₂²×C₅	1	1	yes	characteristic
229	C₃×#95	C₂²×C₅	1	1	yes	characteristic
230	C₃×#95	C₂²×C₅	1	1	yes	characteristic
231	C₃×#95	C₂²×C₅	1	1	yes	characteristic
232	C₃×#95	C₂²×C₅	1	1	yes	characteristic
233	C₃×#95	C₂²×C₅	1	1	yes	characteristic
234	C₃×#95	C₂²×C₅	1	1	yes	characteristic
235	C₃×#95	C₂²×C₅	1	1	yes	characteristic
236	C₃×#95	C₂²×C₅	1	1	yes	characteristic
237	C₃×#95	C₂²×C₅	1	1	yes	characteristic
238	C₃×#95	C₂²×C₅	1	1	yes	characteristic
239	C₃×#95	C₂²×C₅	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
247	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
248	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₅×C₄⋊C₄	—	2	2	no	—
256	C₅×C₄⋊C₄	—	2	2	no	—
257	C₅×C₄⋊C₄	—	2	2	no	—
258	C₅×C₄⋊C₄	—	2	2	no	—
259	C₅×C₄⋊C₄	—	2	2	no	—
260	C₅×C₄⋊C₄	—	2	2	no	—
261	C₅×C₄⋊C₄	—	2	2	no	—
262	C₅×C₄⋊C₄	—	2	2	no	—
263	C₅×C₄⋊C₄	—	2	2	no	—
264	C₅×C₄⋊C₄	—	2	2	no	—
265	C₅×C₄⋊C₄	—	2	2	no	—
266	C₅×C₄⋊C₄	—	2	2	no	—
267	C₅×C₄⋊C₄	—	2	2	no	—
268	C₅×C₄⋊C₄	—	2	2	no	—
269	C₅×C₄⋊C₄	—	2	2	no	—
270	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
271	C₄²×C₅	—	2	2	no	—
272	C₄²×C₅	—	2	2	no	—
273	C₄²×C₅	—	2	2	no	—
274	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
275	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
276	#400	C₂×C₃×C₅	1	1	yes	characteristic
277	#400	C₂×C₃×C₅	1	1	yes	characteristic
278	#400	C₂×C₃×C₅	1	1	yes	characteristic
279	#398	C₂×C₃×C₅	1	1	yes	characteristic
280	#398	C₂×C₃×C₅	1	1	yes	characteristic
281	#398	C₂×C₃×C₅	1	1	yes	characteristic
282	#389	C₂×C₃×C₅	1	1	yes	characteristic
283	#389	C₂×C₃×C₅	1	1	yes	characteristic
284	#387	C₂×C₃×C₅	1	1	yes	characteristic
285	#387	C₂×C₃×C₅	1	1	yes	characteristic
286	#387	C₂×C₃×C₅	1	1	yes	characteristic
287	#387	C₂×C₃×C₅	1	1	yes	characteristic
288	#382	C₂×C₃×C₅	1	1	yes	characteristic
289	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
290	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
291	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
292	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
293	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
294	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
295	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
296	C₃×C₄×C₅	—	2	2	no	—
297	C₃×C₄×C₅	—	2	2	no	—
298	C₃×C₄×C₅	—	2	2	no	—
299	C₃×C₄×C₅	—	2	2	no	—
300	C₃×C₄×C₅	—	2	2	no	—
301	C₃×C₄×C₅	—	4	1	no	—
302	C₃×C₄×C₅	—	4	1	no	—
303	C₃×C₄×C₅	—	4	1	no	—
304	C₃×C₄×C₅	—	4	1	no	—
305	C₃×C₄×C₅	—	4	1	no	—
306	C₃×C₄×C₅	—	4	1	no	—
307	C₃×C₄×C₅	—	4	1	no	—
308	C₃×C₄×C₅	—	4	1	no	—
309	C₃×C₄×C₅	—	4	1	no	—
310	C₃×C₄×C₅	—	4	1	no	—
311	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
326	C₃×C₄⋊C₄	—	2	2	no	—
327	C₃×C₄⋊C₄	—	2	2	no	—
328	C₃×C₄⋊C₄	—	2	2	no	—
329	C₃×C₄⋊C₄	—	2	2	no	—
330	C₃×C₄⋊C₄	—	2	2	no	—
331	C₃×C₄⋊C₄	—	2	2	no	—
332	C₃×C₄⋊C₄	—	2	2	no	—
333	C₃×C₄⋊C₄	—	2	2	no	—
334	C₃×C₄⋊C₄	—	2	2	no	—
335	C₃×C₄⋊C₄	—	2	2	no	—
336	C₃×C₄⋊C₄	—	2	2	no	—
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	—	2	2	no	—
341	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
342	C₃×C₄²	—	2	2	no	—
343	C₃×C₄²	—	2	2	no	—
344	C₃×C₄²	—	2	2	no	—
345	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
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	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	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	1	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
387	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
388	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
389	C₂×C₄×C₅	C₃×#41	1	2	yes	—
390	C₂×C₄×C₅	C₃×#41	1	2	yes	—
391	#125	—	2	4	no	—
392	#125	—	2	4	no	—
393	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
409	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
410	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
411	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
412	#95	C₂²×C₃×C₅	1	1	yes	characteristic
413	#95	C₂²×C₃×C₅	1	1	yes	characteristic
414	#95	C₂²×C₃×C₅	1	1	yes	characteristic
415	#95	C₂²×C₃×C₅	1	1	yes	characteristic
416	#95	C₂²×C₃×C₅	1	1	yes	characteristic
417	#95	C₂²×C₃×C₅	1	1	yes	characteristic
418	#95	C₂²×C₃×C₅	1	1	yes	characteristic
419	#95	C₂²×C₃×C₅	1	1	yes	characteristic
420	#95	C₂²×C₃×C₅	1	1	yes	characteristic
421	#95	C₂²×C₃×C₅	1	1	yes	characteristic
422	#95	C₂²×C₃×C₅	1	1	yes	characteristic
423	#95	C₂²×C₃×C₅	1	1	yes	characteristic
424	#95	C₂²×C₃×C₅	1	1	yes	characteristic
425	#95	C₂²×C₃×C₅	1	1	yes	characteristic
426	#95	C₂²×C₃×C₅	1	1	yes	characteristic
427	#95	C₂²×C₃×C₅	1	1	yes	characteristic
428	C₂×C₃×C₅	#536	1	1	yes	characteristic
429	C₂×C₃×C₅	#541	1	1	yes	characteristic
430	C₂×C₃×C₅	#541	1	1	yes	characteristic
431	C₂×C₃×C₅	#547	1	1	yes	characteristic
432	C₂×C₃×C₅	#548	1	1	yes	characteristic
433	C₂×C₃×C₅	#552	1	1	yes	characteristic
434	C₂×C₃×C₅	#564	1	1	yes	characteristic
435	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	1	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	1	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	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
477	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
478	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
479	C₂×C₃×C₄	C₅×#41	1	2	yes	—
480	C₂×C₃×C₄	C₅×#41	1	2	yes	—
481	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
482	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
483	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
484	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
486	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
487	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
488	C₄×C₅	—	2	2	no	—
489	C₄×C₅	—	2	2	no	—
490	C₄×C₅	—	2	2	no	—
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	—	2	2	no	—
493	C₄×C₅	—	4	1	no	—
494	C₄×C₅	—	4	1	no	—
495	C₄×C₅	—	4	1	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	4	1	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	4	1	no	—
500	C₄×C₅	—	4	1	no	—
501	C₄×C₅	—	4	1	no	—
502	C₄×C₅	—	4	1	no	—
503	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
504	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
505	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
512	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
513	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
514	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
515	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
516	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
517	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₃×C₅	#2719	1	1	yes	characteristic, direct product factor, Hall
538	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
539	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
540	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
541	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
543	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
544	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	—	2	2	no	—
548	C₃×C₄	—	2	2	no	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	4	1	no	—
551	C₃×C₄	—	4	1	no	—
552	C₃×C₄	—	4	1	no	—
553	C₃×C₄	—	4	1	no	—
554	C₃×C₄	—	4	1	no	—
555	C₃×C₄	—	4	1	no	—
556	C₃×C₄	—	4	1	no	—
557	C₃×C₄	—	4	1	no	—
558	C₃×C₄	—	4	1	no	—
559	C₃×C₄	—	4	1	no	—
560	C₂×C₅	C₃×#536	1	1	yes	characteristic
561	C₂×C₅	C₃×#541	1	1	yes	characteristic
562	C₂×C₅	C₃×#541	1	1	yes	characteristic
563	C₂×C₅	C₃×#547	1	1	yes	characteristic
564	C₂×C₅	C₃×#548	1	1	yes	characteristic
565	C₂×C₅	C₃×#552	1	1	yes	characteristic
566	C₂×C₅	C₃×#564	1	1	yes	characteristic
567	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	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	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	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	C₂×C₃×C₅×D₄	1	2	yes	—
609	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
610	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
611	C₂×C₄	C₃×C₅×#41	1	2	yes	—
612	C₂×C₄	C₃×C₅×#41	1	2	yes	—
613	C₂×C₃	C₅×#536	1	1	yes	characteristic
614	C₂×C₃	C₅×#541	1	1	yes	characteristic
615	C₂×C₃	C₅×#541	1	1	yes	characteristic
616	C₂×C₃	C₅×#547	1	1	yes	characteristic
617	C₂×C₃	C₅×#548	1	1	yes	characteristic
618	C₂×C₃	C₅×#552	1	1	yes	characteristic
619	C₂×C₃	C₅×#564	1	1	yes	characteristic
620	C₅	C₃×#2719	1	1	yes	characteristic, direct product factor, Sylow
621	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
622	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
623	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
624	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
625	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
626	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
627	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₃	C₅×#2719	1	1	yes	characteristic, direct product factor, Sylow
644	C₂	C₃×C₅×#536	1	1	yes	characteristic
645	C₂	C₃×C₅×#541	1	1	yes	characteristic
646	C₂	C₃×C₅×#541	1	1	yes	characteristic
647	C₂	C₃×C₅×#547	1	1	yes	characteristic
648	C₂	C₃×C₅×#548	1	1	yes	characteristic
649	C₂	C₃×C₅×#552	1	1	yes	characteristic
650	C₂	C₃×C₅×#564	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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
16. C₅×#2719	C₃	direct (N × H)
54. C₃×#2719	C₅	direct (N × H)
156. #2719	C₃×C₅	direct (N × H)
537. C₃×C₅	#2719	direct (N × H)
620. C₅	C₃×#2719	direct (N × H)
643. C₃	C₅×#2719	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×#125	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#382	2
C₅×#2719	3
C₃×#2719	5

Subgroups — C3×C5×#2719 #14275753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2719 #14275753