Subgroups — C₃×C₅×#2511 #14275545

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#400	C₂	1	2	yes	maximal
2	C₃×C₅×#400	C₂	1	2	yes	maximal
3	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#387	C₂	1	2	yes	maximal
8	C₃×C₅×#387	C₂	1	2	yes	maximal
9	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2511	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	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	2	yes	—
33	C₃×C₅×#95	C₂²	1	2	yes	—
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×#2511	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#400	C₂×C₃	1	2	yes	—
38	C₅×#400	C₂×C₃	1	2	yes	—
39	C₅×#391	C₂×C₃	1	1	yes	characteristic
40	C₅×#391	C₂×C₃	1	1	yes	characteristic
41	C₅×#391	C₂×C₃	1	1	yes	characteristic
42	C₅×#389	C₂×C₃	1	1	yes	characteristic
43	C₅×#387	C₂×C₃	1	2	yes	—
44	C₅×#387	C₂×C₃	1	2	yes	—
45	C₅×#384	C₂×C₃	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₂×C₃×C₅×Q₈	—	2	2	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	—	2	4	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₄⋊C₄	—	2	2	no	—
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	4	2	no	—
68	C₃×C₅×C₄⋊C₄	—	4	2	no	—
69	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	complemented
70	C₃×C₄²×C₅	—	2	2	no	—
71	C₃×C₄²×C₅	—	2	2	no	—
72	C₃×C₄²×C₅	—	2	2	no	—
73	C₃×C₄²×C₅	—	4	2	no	—
74	C₃×#400	C₂×C₅	1	2	yes	—
75	C₃×#400	C₂×C₅	1	2	yes	—
76	C₃×#391	C₂×C₅	1	1	yes	characteristic
77	C₃×#391	C₂×C₅	1	1	yes	characteristic
78	C₃×#391	C₂×C₅	1	1	yes	characteristic
79	C₃×#389	C₂×C₅	1	1	yes	characteristic
80	C₃×#387	C₂×C₅	1	2	yes	—
81	C₃×#387	C₂×C₅	1	2	yes	—
82	C₃×#384	C₂×C₅	1	1	yes	characteristic
83	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
84	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
85	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
94	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
98	C₅×#95	C₂²×C₃	1	1	yes	characteristic
99	C₅×#95	C₂²×C₃	1	2	yes	—
100	C₅×#95	C₂²×C₃	1	1	yes	characteristic
101	C₅×#95	C₂²×C₃	1	2	yes	—
102	C₅×#95	C₂²×C₃	1	2	yes	—
103	C₅×#95	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	2	yes	—
107	C₅×#95	C₂²×C₃	1	2	yes	—
108	#2511	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	4	4	no	—
111	C₂×C₃×C₄×C₅	—	2	1	no	—
112	C₂×C₃×C₄×C₅	—	2	1	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	1	no	—
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	1	no	—
120	C₂×C₃×C₄×C₅	—	2	1	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	2	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	1	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
140	C₂×C₃×C₄×C₅	#41	1	2	yes	—
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	#41	1	2	yes	—
143	C₂×C₃×C₄×C₅	#41	1	2	yes	—
144	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
157	C₃×#95	C₂²×C₅	1	1	yes	characteristic
158	C₃×#95	C₂²×C₅	1	2	yes	—
159	C₃×#95	C₂²×C₅	1	1	yes	characteristic
160	C₃×#95	C₂²×C₅	1	2	yes	—
161	C₃×#95	C₂²×C₅	1	2	yes	—
162	C₃×#95	C₂²×C₅	1	2	yes	—
163	C₃×#95	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	2	yes	—
167	C₂×C₅×Q₈	—	2	2	no	—
168	C₂×C₅×Q₈	—	2	2	no	—
169	C₂×C₅×Q₈	—	2	2	no	—
170	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	4	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	4	2	no	—
187	C₅×C₄⋊C₄	—	4	2	no	—
188	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	complemented
189	C₄²×C₅	—	2	2	no	—
190	C₄²×C₅	—	2	2	no	—
191	C₄²×C₅	—	2	2	no	—
192	C₄²×C₅	—	4	2	no	—
193	#400	C₂×C₃×C₅	1	2	yes	—
194	#400	C₂×C₃×C₅	1	2	yes	—
195	#391	C₂×C₃×C₅	1	1	yes	characteristic
196	#391	C₂×C₃×C₅	1	1	yes	characteristic
197	#391	C₂×C₃×C₅	1	1	yes	characteristic
198	#389	C₂×C₃×C₅	1	1	yes	characteristic
199	#387	C₂×C₃×C₅	1	2	yes	—
200	#387	C₂×C₃×C₅	1	2	yes	—
201	#384	C₂×C₃×C₅	1	1	yes	characteristic
202	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
203	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
206	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
207	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
208	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
209	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	2	no	—
214	C₃×C₄×C₅	—	2	2	no	—
215	C₃×C₄×C₅	—	4	2	no	—
216	C₃×C₄×C₅	—	4	1	no	—
217	C₃×C₄×C₅	—	4	2	no	—
218	C₃×C₄×C₅	—	4	1	no	—
219	C₃×C₄×C₅	—	4	2	no	—
220	C₃×C₄×C₅	—	4	2	no	—
221	C₃×C₄×C₅	#126	1	4	yes	—
222	C₂×C₃×Q₈	—	2	2	no	—
223	C₂×C₃×Q₈	—	2	2	no	—
224	C₂×C₃×Q₈	—	2	2	no	—
225	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
230	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
231	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	2	4	no	—
238	C₃×C₄⋊C₄	—	2	2	no	—
239	C₃×C₄⋊C₄	—	2	2	no	—
240	C₃×C₄⋊C₄	—	2	2	no	—
241	C₃×C₄⋊C₄	—	4	2	no	—
242	C₃×C₄⋊C₄	—	4	2	no	—
243	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	complemented
244	C₃×C₄²	—	2	2	no	—
245	C₃×C₄²	—	2	2	no	—
246	C₃×C₄²	—	2	2	no	—
247	C₃×C₄²	—	4	2	no	—
248	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
249	C₅×Q₈	—	4	4	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
277	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
278	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
279	C₂×C₄×C₅	C₃×#41	1	2	yes	—
280	C₂×C₄×C₅	C₃×#41	1	2	yes	—
281	C₂×C₄×C₅	C₃×#41	1	2	yes	—
282	C₂×C₄×C₅	C₃×#41	1	2	yes	—
283	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
288	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
290	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
291	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
292	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
294	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
296	#95	C₂²×C₃×C₅	1	1	yes	characteristic
297	#95	C₂²×C₃×C₅	1	2	yes	—
298	#95	C₂²×C₃×C₅	1	1	yes	characteristic
299	#95	C₂²×C₃×C₅	1	2	yes	—
300	#95	C₂²×C₃×C₅	1	2	yes	—
301	#95	C₂²×C₃×C₅	1	2	yes	—
302	#95	C₂²×C₃×C₅	1	2	yes	—
303	#95	C₂²×C₃×C₅	1	2	yes	—
304	#95	C₂²×C₃×C₅	1	2	yes	—
305	#95	C₂²×C₃×C₅	1	2	yes	—
306	C₂×C₃×C₅	C₂×#126	1	1	yes	characteristic
307	C₂×C₃×C₅	#533	1	1	yes	characteristic
308	C₂×C₃×C₅	#542	1	1	yes	characteristic
309	C₂×C₃×C₅	#552	1	1	yes	characteristic
310	C₂×C₃×C₅	#554	1	1	yes	characteristic
311	C₂×C₃×C₅	#557	1	1	yes	characteristic
312	C₂×C₃×C₅	#559	1	1	yes	characteristic
313	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
314	C₃×Q₈	—	4	4	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
342	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
344	C₂×C₃×C₄	C₅×#41	1	2	yes	—
345	C₂×C₃×C₄	C₅×#41	1	2	yes	—
346	C₂×C₃×C₄	C₅×#41	1	2	yes	—
347	C₂×C₃×C₄	C₅×#41	1	2	yes	—
348	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
349	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
350	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
351	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
352	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
353	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	—	2	2	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	—	4	2	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	—	4	1	no	—
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	—	4	1	no	—
365	C₄×C₅	C₃×#126	1	4	yes	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
370	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
371	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
372	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
373	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
374	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
375	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
376	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
378	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
379	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	4	2	no	—
392	C₃×C₅	#2511	1	1	yes	characteristic, direct product factor, Hall
393	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
394	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
395	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
396	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
397	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
398	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	4	2	no	—
405	C₃×C₄	—	4	1	no	—
406	C₃×C₄	—	4	2	no	—
407	C₃×C₄	—	4	1	no	—
408	C₃×C₄	—	4	2	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	C₅×#126	1	4	yes	—
411	C₂×C₅	C₂×C₃×#126	1	1	yes	characteristic
412	C₂×C₅	C₃×#533	1	1	yes	characteristic
413	C₂×C₅	C₃×#542	1	1	yes	characteristic
414	C₂×C₅	C₃×#552	1	1	yes	characteristic
415	C₂×C₅	C₃×#554	1	1	yes	characteristic
416	C₂×C₅	C₃×#557	1	1	yes	characteristic
417	C₂×C₅	C₃×#559	1	1	yes	characteristic
418	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
419	Q₈	—	4	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
447	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
448	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
449	C₂×C₄	C₃×C₅×#41	1	2	yes	—
450	C₂×C₄	C₃×C₅×#41	1	2	yes	—
451	C₂×C₄	C₃×C₅×#41	1	2	yes	—
452	C₂×C₄	C₃×C₅×#41	1	2	yes	—
453	C₂×C₃	C₂×C₅×#126	1	1	yes	characteristic
454	C₂×C₃	C₅×#533	1	1	yes	characteristic
455	C₂×C₃	C₅×#542	1	1	yes	characteristic
456	C₂×C₃	C₅×#552	1	1	yes	characteristic
457	C₂×C₃	C₅×#554	1	1	yes	characteristic
458	C₂×C₃	C₅×#557	1	1	yes	characteristic
459	C₂×C₃	C₅×#559	1	1	yes	characteristic
460	C₅	C₃×#2511	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
462	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
463	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
464	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
465	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
466	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	C₃×C₅×#126	1	4	yes	—
479	C₃	C₅×#2511	1	1	yes	characteristic, direct product factor, Sylow
480	C₂	C₂×C₃×C₅×#126	1	1	yes	characteristic
481	C₂	C₃×C₅×#533	1	1	yes	characteristic
482	C₂	C₃×C₅×#542	1	1	yes	characteristic
483	C₂	C₃×C₅×#552	1	1	yes	characteristic
484	C₂	C₃×C₅×#554	1	1	yes	characteristic
485	C₂	C₃×C₅×#557	1	1	yes	characteristic
486	C₂	C₃×C₅×#559	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
12. C₅×#2511	C₃	direct (N × H)
36. C₃×#2511	C₅	direct (N × H)
69. C₃×C₅×C₄⋊C₄	Q₈	semidirect
108. #2511	C₃×C₅	direct (N × H)
188. C₅×C₄⋊C₄	C₃×Q₈	semidirect
243. C₃×C₄⋊C₄	C₅×Q₈	semidirect
387. C₄⋊C₄	C₃×C₅×Q₈	semidirect
392. C₃×C₅	#2511	direct (N × H)
460. C₅	C₃×#2511	direct (N × H)
479. C₃	C₅×#2511	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×#400	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#384	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2511	3
C₃×#2511	5

Subgroups — C3×C5×#2511 #14275545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2511 #14275545