Subgroups — C₃×C₅×#2509 #14275543

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 480 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×#389	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#389	C₂	1	2	yes	maximal
8	C₃×C₅×#387	C₂	1	2	yes	maximal
9	C₃×C₅×#382	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×#2509	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₄⋊C₄	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	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	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	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	1	yes	characteristic
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×#2509	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×#389	C₂×C₃	1	1	yes	characteristic
40	C₅×#389	C₂×C₃	1	1	yes	characteristic
41	C₅×#389	C₂×C₃	1	1	yes	characteristic
42	C₅×#389	C₂×C₃	1	1	yes	characteristic
43	C₅×#389	C₂×C₃	1	2	yes	—
44	C₅×#387	C₂×C₃	1	2	yes	—
45	C₅×#382	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	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	1	yes	characteristic
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	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	4	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	4	no	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₄⋊C₄	—	2	2	no	—
66	C₃×C₅×C₄⋊C₄	—	4	2	no	—
67	C₃×C₅×C₄⋊C₄	—	4	2	no	—
68	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	—	2	2	no	—
71	C₃×C₄²×C₅	—	2	2	no	—
72	C₃×C₄²×C₅	—	4	2	no	—
73	C₃×#400	C₂×C₅	1	2	yes	—
74	C₃×#400	C₂×C₅	1	2	yes	—
75	C₃×#389	C₂×C₅	1	2	yes	—
76	C₃×#389	C₂×C₅	1	1	yes	characteristic
77	C₃×#389	C₂×C₅	1	1	yes	characteristic
78	C₃×#389	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×#382	C₂×C₅	1	1	yes	characteristic
82	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
83	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	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	2	yes	—
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
100	C₅×#95	C₂²×C₃	1	2	yes	—
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	#2509	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
108	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	—	2	1	no	—
110	C₂×C₃×C₄×C₅	—	2	1	no	—
111	C₂×C₃×C₄×C₅	—	2	1	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	1	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	1	no	—
136	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
137	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
138	C₂×C₃×C₄×C₅	#41	1	2	yes	—
139	C₂×C₃×C₄×C₅	#41	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⋊C₄	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	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	2	yes	—
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	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×C₄²	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	2	yes	—
156	C₃×#95	C₂²×C₅	1	1	yes	characteristic
157	C₃×#95	C₂²×C₅	1	1	yes	characteristic
158	C₃×#95	C₂²×C₅	1	2	yes	—
159	C₃×#95	C₂²×C₅	1	2	yes	—
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	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
175	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	—	2	4	no	—
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	4	no	—
180	C₅×C₄⋊C₄	—	2	2	no	—
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	—	4	2	no	—
184	C₅×C₄⋊C₄	—	4	2	no	—
185	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	—
186	C₄²×C₅	—	2	2	no	—
187	C₄²×C₅	—	2	2	no	—
188	C₄²×C₅	—	2	2	no	—
189	C₄²×C₅	—	4	2	no	—
190	#400	C₂×C₃×C₅	1	2	yes	—
191	#400	C₂×C₃×C₅	1	2	yes	—
192	#389	C₂×C₃×C₅	1	2	yes	—
193	#389	C₂×C₃×C₅	1	1	yes	characteristic
194	#389	C₂×C₃×C₅	1	1	yes	characteristic
195	#389	C₂×C₃×C₅	1	1	yes	characteristic
196	#389	C₂×C₃×C₅	1	1	yes	characteristic
197	#387	C₂×C₃×C₅	1	2	yes	—
198	#382	C₂×C₃×C₅	1	1	yes	characteristic
199	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
200	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
202	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
203	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
204	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
206	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
208	C₃×C₄×C₅	—	2	2	no	—
209	C₃×C₄×C₅	—	2	2	no	—
210	C₃×C₄×C₅	—	2	4	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	—	4	1	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	—	4	1	no	—
215	C₃×C₄×C₅	—	4	2	no	—
216	C₃×C₄×C₅	—	4	1	no	—
217	C₃×C₄×C₅	—	4	1	no	—
218	C₃×C₄×C₅	#125	1	4	yes	—
219	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
226	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
230	C₃×C₄⋊C₄	—	2	2	no	—
231	C₃×C₄⋊C₄	—	2	4	no	—
232	C₃×C₄⋊C₄	—	2	2	no	—
233	C₃×C₄⋊C₄	—	2	4	no	—
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	2	2	no	—
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	4	2	no	—
238	C₃×C₄⋊C₄	—	4	2	no	—
239	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	—
240	C₃×C₄²	—	2	2	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	2	2	no	—
243	C₃×C₄²	—	4	2	no	—
244	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	2	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	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
273	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
274	C₂×C₄×C₅	C₃×#41	1	2	yes	—
275	C₂×C₄×C₅	C₃×#41	1	2	yes	—
276	C₂×C₄×C₅	C₃×#41	1	2	yes	—
277	C₂×C₄×C₅	C₃×#41	1	2	yes	—
278	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
283	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
285	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
286	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
287	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
288	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
290	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
291	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
292	#95	C₂²×C₃×C₅	1	1	yes	characteristic
293	#95	C₂²×C₃×C₅	1	1	yes	characteristic
294	#95	C₂²×C₃×C₅	1	2	yes	—
295	#95	C₂²×C₃×C₅	1	2	yes	—
296	#95	C₂²×C₃×C₅	1	2	yes	—
297	#95	C₂²×C₃×C₅	1	2	yes	—
298	#95	C₂²×C₃×C₅	1	2	yes	—
299	#95	C₂²×C₃×C₅	1	2	yes	—
300	#95	C₂²×C₃×C₅	1	2	yes	—
301	C₂×C₃×C₅	C₂×#125	1	1	yes	characteristic
302	C₂×C₃×C₅	#529	1	1	yes	characteristic
303	C₂×C₃×C₅	#542	1	1	yes	characteristic
304	C₂×C₃×C₅	#553	1	1	yes	characteristic
305	C₂×C₃×C₅	#554	1	1	yes	characteristic
306	C₂×C₃×C₅	#556	1	1	yes	characteristic
307	C₂×C₃×C₅	#557	1	1	yes	characteristic
308	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	1	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	2	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	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	2	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	1	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
337	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
338	C₂×C₃×C₄	C₅×#41	1	2	yes	—
339	C₂×C₃×C₄	C₅×#41	1	2	yes	—
340	C₂×C₃×C₄	C₅×#41	1	2	yes	—
341	C₂×C₃×C₄	C₅×#41	1	2	yes	—
342	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
343	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
344	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
345	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
346	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
347	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	4	no	—
352	C₄×C₅	—	4	2	no	—
353	C₄×C₅	—	4	1	no	—
354	C₄×C₅	—	4	2	no	—
355	C₄×C₅	—	4	1	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	—	4	1	no	—
358	C₄×C₅	—	4	1	no	—
359	C₄×C₅	C₃×#125	1	4	yes	—
360	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
361	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
362	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
364	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
365	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
366	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
367	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
368	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
369	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
370	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	2	no	—
385	C₃×C₅	#2509	1	1	yes	characteristic, direct product factor, Hall
386	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
387	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
388	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
389	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
390	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
391	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	4	no	—
396	C₃×C₄	—	4	2	no	—
397	C₃×C₄	—	4	1	no	—
398	C₃×C₄	—	4	2	no	—
399	C₃×C₄	—	4	1	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	C₅×#125	1	4	yes	—
404	C₂×C₅	C₂×C₃×#125	1	1	yes	characteristic
405	C₂×C₅	C₃×#529	1	1	yes	characteristic
406	C₂×C₅	C₃×#542	1	1	yes	characteristic
407	C₂×C₅	C₃×#553	1	1	yes	characteristic
408	C₂×C₅	C₃×#554	1	1	yes	characteristic
409	C₂×C₅	C₃×#556	1	1	yes	characteristic
410	C₂×C₅	C₃×#557	1	1	yes	characteristic
411	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
440	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
441	C₂×C₄	C₃×C₅×#41	1	2	yes	—
442	C₂×C₄	C₃×C₅×#41	1	2	yes	—
443	C₂×C₄	C₃×C₅×#41	1	2	yes	—
444	C₂×C₄	C₃×C₅×#41	1	2	yes	—
445	C₂×C₃	C₂×C₅×#125	1	1	yes	characteristic
446	C₂×C₃	C₅×#529	1	1	yes	characteristic
447	C₂×C₃	C₅×#542	1	1	yes	characteristic
448	C₂×C₃	C₅×#553	1	1	yes	characteristic
449	C₂×C₃	C₅×#554	1	1	yes	characteristic
450	C₂×C₃	C₅×#556	1	1	yes	characteristic
451	C₂×C₃	C₅×#557	1	1	yes	characteristic
452	C₅	C₃×#2509	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
454	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
455	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
456	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
457	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
458	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	4	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	C₃×C₅×#125	1	4	yes	—
471	C₃	C₅×#2509	1	1	yes	characteristic, direct product factor, Sylow
472	C₂	C₂×C₃×C₅×#125	1	1	yes	characteristic
473	C₂	C₃×C₅×#529	1	1	yes	characteristic
474	C₂	C₃×C₅×#542	1	1	yes	characteristic
475	C₂	C₃×C₅×#553	1	1	yes	characteristic
476	C₂	C₃×C₅×#554	1	1	yes	characteristic
477	C₂	C₃×C₅×#556	1	1	yes	characteristic
478	C₂	C₃×C₅×#557	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×#2509	C₃	direct (N × H)
36. C₃×#2509	C₅	direct (N × H)
107. #2509	C₃×C₅	direct (N × H)
385. C₃×C₅	#2509	direct (N × H)
452. C₅	C₃×#2509	direct (N × H)
471. C₃	C₅×#2509	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×#389	2
C₃×C₅×#387	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2509	3
C₃×#2509	5

Subgroups — C3×C5×#2509 #14275543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2509 #14275543