Subgroups — C₃×C₅×#2555 #14275589

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#2555	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
17	C₃×C₅×#124	—	2	8	no	—
18	C₃×C₅×#121	—	2	8	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
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×#2555	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
36	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
37	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#392	C₂×C₃	1	2	yes	complemented
40	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#388	C₂×C₃	1	2	yes	complemented
42	C₅×#386	C₂×C₃	1	2	yes	complemented
43	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	—	4	1	no	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	—	2	4	no	—
51	C₂×C₃×C₅×D₄	—	2	4	no	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	—	2	4	no	—
54	C₂×C₃×C₅×D₄	—	4	1	no	—
55	C₂×C₃×C₅×D₄	—	4	1	no	—
56	C₂×C₃×C₅×D₄	—	4	2	no	—
57	C₂×C₃×C₅×D₄	—	4	2	no	—
58	C₂×C₃×C₅×D₄	—	4	1	no	—
59	C₂²×C₃×C₄×C₅	—	2	4	no	—
60	C₂²×C₃×C₄×C₅	—	2	4	no	—
61	C₂²×C₃×C₄×C₅	—	4	2	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₃×C₅×C₄⋊C₄	—	2	4	no	—
70	C₃×C₅×C₄⋊C₄	—	4	1	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₅×C₂²⋊C₄	D₄	1	8	yes	complemented
78	C₃×C₄²×C₅	—	2	4	no	—
79	C₃×C₄²×C₅	—	4	1	no	—
80	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
81	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
82	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#392	C₂×C₅	1	2	yes	complemented
85	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#388	C₂×C₅	1	2	yes	complemented
87	C₃×#386	C₂×C₅	1	2	yes	complemented
88	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
89	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
91	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
92	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
95	C₅×#124	—	2	8	no	—
96	C₅×#121	—	2	8	no	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
102	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
107	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
108	C₅×#95	C₂²×C₃	1	2	yes	—
109	C₅×#95	C₂²×C₃	1	2	yes	—
110	C₅×#95	C₂²×C₃	1	1	yes	characteristic
111	C₅×#95	C₂²×C₃	1	1	yes	characteristic
112	#2555	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	—	2	2	no	—
123	C₂³×C₃×C₅	—	2	2	no	—
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
127	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	4	4	no	—
129	C₃×C₅×D₄	—	4	8	no	—
130	C₃×C₅×D₄	—	4	8	no	—
131	C₃×C₅×D₄	—	4	4	no	—
132	C₃×C₅×D₄	—	4	4	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	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	4	8	no	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	#41	1	4	yes	—
153	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
155	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
156	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
158	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
159	C₃×#124	—	2	8	no	—
160	C₃×#121	—	2	8	no	—
161	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
170	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
171	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
172	C₃×#95	C₂²×C₅	1	2	yes	—
173	C₃×#95	C₂²×C₅	1	2	yes	—
174	C₃×#95	C₂²×C₅	1	1	yes	characteristic
175	C₃×#95	C₂²×C₅	1	1	yes	characteristic
176	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
177	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
178	C₂×C₅×Q₈	—	2	4	no	—
179	C₂×C₅×Q₈	—	4	1	no	—
180	C₂×C₅×D₄	—	2	4	no	—
181	C₂×C₅×D₄	—	2	4	no	—
182	C₂×C₅×D₄	—	2	4	no	—
183	C₂×C₅×D₄	—	2	4	no	—
184	C₂×C₅×D₄	—	2	2	no	—
185	C₂×C₅×D₄	—	2	4	no	—
186	C₂×C₅×D₄	—	4	1	no	—
187	C₂×C₅×D₄	—	4	1	no	—
188	C₂×C₅×D₄	—	4	2	no	—
189	C₂×C₅×D₄	—	4	2	no	—
190	C₂×C₅×D₄	—	4	1	no	—
191	C₂²×C₄×C₅	—	2	4	no	—
192	C₂²×C₄×C₅	—	2	4	no	—
193	C₂²×C₄×C₅	—	4	2	no	—
194	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
195	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
198	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
199	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
201	C₅×C₄⋊C₄	—	2	4	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₂²⋊C₄	—	2	4	no	—
204	C₅×C₂²⋊C₄	—	2	4	no	—
205	C₅×C₂²⋊C₄	—	2	4	no	—
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₅×C₂²⋊C₄	—	2	4	no	—
208	C₅×C₂²⋊C₄	—	2	4	no	—
209	C₅×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
210	C₄²×C₅	—	2	4	no	—
211	C₄²×C₅	—	4	1	no	—
212	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
213	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
214	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	#392	C₂×C₃×C₅	1	2	yes	complemented
217	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
218	#388	C₂×C₃×C₅	1	2	yes	complemented
219	#386	C₂×C₃×C₅	1	2	yes	complemented
220	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
221	C₂²×C₃×C₅	—	2	4	no	—
222	C₂²×C₃×C₅	—	2	4	no	—
223	C₂²×C₃×C₅	—	2	4	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	—	4	2	no	—
227	C₂²×C₃×C₅	—	4	2	no	—
228	C₂²×C₃×C₅	—	4	2	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	—	4	2	no	—
234	C₂²×C₃×C₅	—	4	2	no	—
235	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
236	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
237	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
238	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	—	2	4	no	—
242	C₃×C₄×C₅	—	2	4	no	—
243	C₃×C₄×C₅	—	2	4	no	—
244	C₃×C₄×C₅	—	4	2	no	—
245	C₃×C₄×C₅	—	4	1	no	—
246	C₃×C₄×C₅	—	4	1	no	—
247	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
248	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
249	C₂×C₃×Q₈	—	2	4	no	—
250	C₂×C₃×Q₈	—	4	1	no	—
251	C₂×C₃×D₄	—	2	4	no	—
252	C₂×C₃×D₄	—	2	4	no	—
253	C₂×C₃×D₄	—	2	4	no	—
254	C₂×C₃×D₄	—	2	4	no	—
255	C₂×C₃×D₄	—	2	2	no	—
256	C₂×C₃×D₄	—	2	4	no	—
257	C₂×C₃×D₄	—	4	1	no	—
258	C₂×C₃×D₄	—	4	1	no	—
259	C₂×C₃×D₄	—	4	2	no	—
260	C₂×C₃×D₄	—	4	2	no	—
261	C₂×C₃×D₄	—	4	1	no	—
262	C₂²×C₃×C₄	—	2	4	no	—
263	C₂²×C₃×C₄	—	2	4	no	—
264	C₂²×C₃×C₄	—	4	2	no	—
265	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
266	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
270	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
271	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
272	C₃×C₄⋊C₄	—	2	4	no	—
273	C₃×C₄⋊C₄	—	4	1	no	—
274	C₃×C₂²⋊C₄	—	2	4	no	—
275	C₃×C₂²⋊C₄	—	2	4	no	—
276	C₃×C₂²⋊C₄	—	2	4	no	—
277	C₃×C₂²⋊C₄	—	2	4	no	—
278	C₃×C₂²⋊C₄	—	2	4	no	—
279	C₃×C₂²⋊C₄	—	2	4	no	—
280	C₃×C₂²⋊C₄	C₅×D₄	1	8	yes	complemented
281	C₃×C₄²	—	2	4	no	—
282	C₃×C₄²	—	4	1	no	—
283	C₂³×C₅	—	2	2	no	—
284	C₂³×C₅	—	2	2	no	—
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	—	2	2	no	—
287	C₂³×C₅	—	2	2	no	—
288	C₂³×C₅	—	2	2	no	—
289	C₂³×C₅	—	2	2	no	—
290	C₂³×C₅	—	2	2	no	—
291	C₂³×C₅	—	2	2	no	—
292	C₂³×C₅	—	2	2	no	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
297	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
298	C₅×Q₈	—	4	4	no	—
299	C₅×D₄	—	4	8	no	—
300	C₅×D₄	—	4	8	no	—
301	C₅×D₄	—	4	4	no	—
302	C₅×D₄	—	4	4	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	4	8	no	—
319	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
320	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
321	C₂×C₄×C₅	C₃×#41	1	2	yes	—
322	C₂×C₄×C₅	C₃×#41	1	4	yes	—
323	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
324	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
325	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
326	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
327	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
328	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
329	#124	—	2	8	no	—
330	#121	—	2	8	no	—
331	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
332	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
334	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
337	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
338	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
340	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
341	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
342	#95	C₂²×C₃×C₅	1	2	yes	—
343	#95	C₂²×C₃×C₅	1	2	yes	—
344	#95	C₂²×C₃×C₅	1	1	yes	characteristic
345	#95	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂×C₃×C₅	—	4	4	no	—
347	C₂×C₃×C₅	—	8	2	no	—
348	C₂×C₃×C₅	#532	1	2	yes	—
349	C₂×C₃×C₅	#538	1	1	yes	characteristic
350	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
351	C₂×C₃×C₅	#546	1	2	yes	—
352	C₂×C₃×C₅	#555	1	1	yes	characteristic
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	2	2	no	—
356	C₂³×C₃	—	2	2	no	—
357	C₂³×C₃	—	2	2	no	—
358	C₂³×C₃	—	2	2	no	—
359	C₂³×C₃	—	2	2	no	—
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	—	2	2	no	—
362	C₂³×C₃	—	2	2	no	—
363	C₂³×C₃	—	2	2	no	—
364	C₂³×C₃	—	2	2	no	—
365	C₂³×C₃	—	2	2	no	—
366	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
367	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
368	C₃×Q₈	—	4	4	no	—
369	C₃×D₄	—	4	8	no	—
370	C₃×D₄	—	4	8	no	—
371	C₃×D₄	—	4	4	no	—
372	C₃×D₄	—	4	4	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	4	8	no	—
389	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
390	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
391	C₂×C₃×C₄	C₅×#41	1	2	yes	—
392	C₂×C₃×C₄	C₅×#41	1	4	yes	—
393	C₂²×C₅	—	2	4	no	—
394	C₂²×C₅	—	2	4	no	—
395	C₂²×C₅	—	2	4	no	—
396	C₂²×C₅	—	4	2	no	—
397	C₂²×C₅	—	4	2	no	—
398	C₂²×C₅	—	4	2	no	—
399	C₂²×C₅	—	4	2	no	—
400	C₂²×C₅	—	4	2	no	—
401	C₂²×C₅	—	4	2	no	—
402	C₂²×C₅	—	4	2	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	4	2	no	—
406	C₂²×C₅	—	4	2	no	—
407	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
408	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
409	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
410	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
412	C₄×C₅	—	2	2	no	—
413	C₄×C₅	—	2	4	no	—
414	C₄×C₅	—	2	4	no	—
415	C₄×C₅	—	2	4	no	—
416	C₄×C₅	—	4	2	no	—
417	C₄×C₅	—	4	1	no	—
418	C₄×C₅	—	4	1	no	—
419	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
420	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	4	1	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
438	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
439	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
440	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
441	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
442	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
443	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
453	C₄²	—	2	4	no	—
454	C₄²	—	4	1	no	—
455	C₃×C₅	#2555	1	1	yes	characteristic, direct product factor, Hall
456	C₂²×C₃	—	2	4	no	—
457	C₂²×C₃	—	2	4	no	—
458	C₂²×C₃	—	2	4	no	—
459	C₂²×C₃	—	4	2	no	—
460	C₂²×C₃	—	4	2	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	—	4	2	no	—
463	C₂²×C₃	—	4	2	no	—
464	C₂²×C₃	—	4	2	no	—
465	C₂²×C₃	—	4	2	no	—
466	C₂²×C₃	—	4	2	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	—	4	2	no	—
469	C₂²×C₃	—	4	2	no	—
470	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
471	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
472	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
473	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	4	no	—
477	C₃×C₄	—	2	4	no	—
478	C₃×C₄	—	2	4	no	—
479	C₃×C₄	—	4	2	no	—
480	C₃×C₄	—	4	1	no	—
481	C₃×C₄	—	4	1	no	—
482	C₂×C₅	—	4	4	no	—
483	C₂×C₅	—	8	2	no	—
484	C₂×C₅	C₃×#532	1	2	yes	—
485	C₂×C₅	C₃×#538	1	1	yes	characteristic
486	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
487	C₂×C₅	C₃×#546	1	2	yes	—
488	C₂×C₅	C₃×#555	1	1	yes	characteristic
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
503	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
504	Q₈	—	4	4	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
526	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
527	C₂×C₄	C₃×C₅×#41	1	2	yes	—
528	C₂×C₄	C₃×C₅×#41	1	4	yes	—
529	C₂×C₃	—	4	4	no	—
530	C₂×C₃	—	8	2	no	—
531	C₂×C₃	C₅×#532	1	2	yes	—
532	C₂×C₃	C₅×#538	1	1	yes	characteristic
533	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
534	C₂×C₃	C₅×#546	1	2	yes	—
535	C₂×C₃	C₅×#555	1	1	yes	characteristic
536	C₅	C₃×#2555	1	1	yes	characteristic, direct product factor, Sylow
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
552	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
553	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
554	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
555	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	4	no	—
558	C₄	—	2	4	no	—
559	C₄	—	2	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₃	C₅×#2555	1	1	yes	characteristic, direct product factor, Sylow
564	C₂	—	4	4	no	—
565	C₂	—	8	2	no	—
566	C₂	C₃×C₅×#532	1	2	yes	—
567	C₂	C₃×C₅×#538	1	1	yes	characteristic
568	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
569	C₂	C₃×C₅×#546	1	2	yes	—
570	C₂	C₃×C₅×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	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
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₃×C₅×#395	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#392	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
10. C₅×#2555	C₃	direct (N × H)
34. C₃×#2555	C₅	direct (N × H)
35. C₂×C₅×#124	C₂×C₃	semidirect
36. C₂×C₅×#121	C₂×C₃	semidirect
37. C₅×#395	C₂×C₃	semidirect
38. C₅×#394	C₂×C₃	semidirect
39. C₅×#392	C₂×C₃	semidirect
40. C₅×#390	C₂×C₃	semidirect
41. C₅×#388	C₂×C₃	semidirect
42. C₅×#386	C₂×C₃	semidirect
43. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
77. C₃×C₅×C₂²⋊C₄	D₄	semidirect
80. C₂×C₃×#124	C₂×C₅	semidirect
81. C₂×C₃×#121	C₂×C₅	semidirect
82. C₃×#395	C₂×C₅	semidirect
83. C₃×#394	C₂×C₅	semidirect
84. C₃×#392	C₂×C₅	semidirect
85. C₃×#390	C₂×C₅	semidirect
86. C₃×#388	C₂×C₅	semidirect
87. C₃×#386	C₂×C₅	semidirect
88. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
112. #2555	C₃×C₅	direct (N × H)
209. C₅×C₂²⋊C₄	C₃×D₄	semidirect
212. C₂×#124	C₂×C₃×C₅	semidirect
213. C₂×#121	C₂×C₃×C₅	semidirect
214. #395	C₂×C₃×C₅	semidirect
215. #394	C₂×C₃×C₅	semidirect
216. #392	C₂×C₃×C₅	semidirect
217. #390	C₂×C₃×C₅	semidirect
218. #388	C₂×C₃×C₅	semidirect
219. #386	C₂×C₃×C₅	semidirect
220. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
280. C₃×C₂²⋊C₄	C₅×D₄	semidirect
452. C₂²⋊C₄	C₃×C₅×D₄	semidirect
455. C₃×C₅	#2555	direct (N × H)
536. C₅	C₃×#2555	direct (N × H)
563. C₃	C₅×#2555	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×#124	2
C₂×C₃×C₅×#121	2
C₃×C₅×#395	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2555	3
C₃×#2555	5

Subgroups — C3×C5×#2555 #14275589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2555 #14275589