Subgroups — C₃×C₅×#2513 #14275547

Order 1920.

880 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2513	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	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	1	yes	characteristic
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×C₂²⋊C₄	C₂²	1	2	yes	—
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×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic
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×#2513	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#397	C₂×C₃	1	2	yes	complemented
38	C₅×#397	C₂×C₃	1	2	yes	complemented
39	C₅×#390	C₂×C₃	1	1	yes	characteristic
40	C₅×#390	C₂×C₃	1	1	yes	characteristic
41	C₅×#390	C₂×C₃	1	1	yes	characteristic
42	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#388	C₂×C₃	1	2	yes	complemented
44	C₅×#388	C₂×C₃	1	2	yes	complemented
45	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
49	C₂×C₃×C₅×D₄	—	2	2	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
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	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	2	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×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
71	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
72	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
73	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
74	C₃×C₄²×C₅	—	2	2	no	—
75	C₃×C₄²×C₅	—	2	2	no	—
76	C₃×C₄²×C₅	—	2	2	no	—
77	C₃×C₄²×C₅	—	4	2	no	—
78	C₃×#397	C₂×C₅	1	2	yes	complemented
79	C₃×#397	C₂×C₅	1	2	yes	complemented
80	C₃×#390	C₂×C₅	1	1	yes	characteristic
81	C₃×#390	C₂×C₅	1	1	yes	characteristic
82	C₃×#390	C₂×C₅	1	1	yes	characteristic
83	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#388	C₂×C₅	1	2	yes	complemented
85	C₃×#388	C₂×C₅	1	2	yes	complemented
86	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
106	C₅×#95	C₂²×C₃	1	1	yes	characteristic
107	C₅×#95	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	2	yes	—
111	C₅×#95	C₂²×C₃	1	2	yes	—
112	#2513	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	C₂⁴	1	1	yes	characteristic
121	C₃×C₅×D₄	—	4	4	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	1	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	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	#41	1	2	yes	—
148	C₂×C₃×C₄×C₅	#41	1	2	yes	—
149	C₂×C₃×C₄×C₅	#41	1	2	yes	—
150	C₂×C₃×C₄×C₅	#41	1	2	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
165	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
169	C₃×#95	C₂²×C₅	1	1	yes	characteristic
170	C₃×#95	C₂²×C₅	1	1	yes	characteristic
171	C₃×#95	C₂²×C₅	1	2	yes	—
172	C₃×#95	C₂²×C₅	1	2	yes	—
173	C₃×#95	C₂²×C₅	1	2	yes	—
174	C₃×#95	C₂²×C₅	1	2	yes	—
175	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
176	C₂×C₅×D₄	—	2	2	no	—
177	C₂×C₅×D₄	—	2	2	no	—
178	C₂×C₅×D₄	—	2	2	no	—
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
185	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
186	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	4	2	no	—
195	C₅×C₂²⋊C₄	—	2	4	no	—
196	C₅×C₂²⋊C₄	—	2	4	no	—
197	C₅×C₂²⋊C₄	—	4	2	no	—
198	C₅×C₂²⋊C₄	—	4	2	no	—
199	C₅×C₂²⋊C₄	—	4	2	no	—
200	C₅×C₂²⋊C₄	—	4	2	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	—	2	2	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	4	2	no	—
205	#397	C₂×C₃×C₅	1	2	yes	complemented
206	#397	C₂×C₃×C₅	1	2	yes	complemented
207	#390	C₂×C₃×C₅	1	1	yes	characteristic
208	#390	C₂×C₃×C₅	1	1	yes	characteristic
209	#390	C₂×C₃×C₅	1	1	yes	characteristic
210	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
211	#388	C₂×C₃×C₅	1	2	yes	complemented
212	#388	C₂×C₃×C₅	1	2	yes	complemented
213	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	—	4	2	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
224	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
225	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
226	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
227	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
228	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	—	4	1	no	—
236	C₃×C₄×C₅	—	4	1	no	—
237	C₃×C₄×C₅	—	4	2	no	—
238	C₃×C₄×C₅	—	4	2	no	—
239	C₃×C₄×C₅	#126	1	4	yes	—
240	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
241	C₂×C₃×D₄	—	2	2	no	—
242	C₂×C₃×D₄	—	2	2	no	—
243	C₂×C₃×D₄	—	2	2	no	—
244	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
248	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
249	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	—	4	2	no	—
260	C₃×C₂²⋊C₄	—	2	4	no	—
261	C₃×C₂²⋊C₄	—	2	4	no	—
262	C₃×C₂²⋊C₄	—	4	2	no	—
263	C₃×C₂²⋊C₄	—	4	2	no	—
264	C₃×C₂²⋊C₄	—	4	2	no	—
265	C₃×C₂²⋊C₄	—	4	2	no	—
266	C₃×C₄²	—	2	2	no	—
267	C₃×C₄²	—	2	2	no	—
268	C₃×C₄²	—	2	2	no	—
269	C₃×C₄²	—	4	2	no	—
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	2	2	no	—
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	—	2	2	no	—
274	C₂³×C₅	—	2	2	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	2	2	no	—
277	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
278	C₅×D₄	—	4	4	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	C₃×#41	1	2	yes	—
305	C₂×C₄×C₅	C₃×#41	1	2	yes	—
306	C₂×C₄×C₅	C₃×#41	1	2	yes	—
307	C₂×C₄×C₅	C₃×#41	1	2	yes	—
308	C₂×C₄×C₅	C₃×#41	1	2	yes	—
309	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
322	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
323	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
324	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
325	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
326	#95	C₂²×C₃×C₅	1	1	yes	characteristic
327	#95	C₂²×C₃×C₅	1	1	yes	characteristic
328	#95	C₂²×C₃×C₅	1	2	yes	—
329	#95	C₂²×C₃×C₅	1	2	yes	—
330	#95	C₂²×C₃×C₅	1	2	yes	—
331	#95	C₂²×C₃×C₅	1	2	yes	—
332	C₂×C₃×C₅	—	8	2	no	—
333	C₂×C₃×C₅	C₂×#126	1	1	yes	characteristic
334	C₂×C₃×C₅	#529	1	1	yes	characteristic
335	C₂×C₃×C₅	#540	1	1	yes	characteristic
336	C₂×C₃×C₅	#553	1	1	yes	characteristic
337	C₂×C₃×C₅	#555	1	1	yes	characteristic
338	C₂×C₃×C₅	#559	1	1	yes	characteristic
339	C₂×C₃×C₅	#559	1	1	yes	characteristic
340	C₂³×C₃	—	2	2	no	—
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	2	no	—
343	C₂³×C₃	—	2	2	no	—
344	C₂³×C₃	—	2	2	no	—
345	C₂³×C₃	—	2	2	no	—
346	C₂³×C₃	—	2	2	no	—
347	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
348	C₃×D₄	—	4	4	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	C₅×#41	1	2	yes	—
375	C₂×C₃×C₄	C₅×#41	1	2	yes	—
376	C₂×C₃×C₄	C₅×#41	1	2	yes	—
377	C₂×C₃×C₄	C₅×#41	1	2	yes	—
378	C₂×C₃×C₄	C₅×#41	1	2	yes	—
379	C₂²×C₅	—	4	2	no	—
380	C₂²×C₅	—	4	2	no	—
381	C₂²×C₅	—	4	2	no	—
382	C₂²×C₅	—	4	2	no	—
383	C₂²×C₅	—	4	2	no	—
384	C₂²×C₅	—	4	2	no	—
385	C₂²×C₅	—	4	2	no	—
386	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
387	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
388	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
389	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
390	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
391	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
393	C₄×C₅	—	2	2	no	—
394	C₄×C₅	—	2	2	no	—
395	C₄×C₅	—	4	2	no	—
396	C₄×C₅	—	4	2	no	—
397	C₄×C₅	—	4	1	no	—
398	C₄×C₅	—	4	2	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	C₃×#126	1	4	yes	—
403	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
408	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
409	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
410	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
411	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
412	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
413	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
414	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
415	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
416	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	4	2	no	—
433	C₃×C₅	#2513	1	1	yes	characteristic, direct product factor, Hall
434	C₂²×C₃	—	4	2	no	—
435	C₂²×C₃	—	4	2	no	—
436	C₂²×C₃	—	4	2	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	4	2	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	—	4	2	no	—
441	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
442	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
443	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
444	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
445	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
446	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
448	C₃×C₄	—	2	2	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	4	1	no	—
451	C₃×C₄	—	4	2	no	—
452	C₃×C₄	—	4	1	no	—
453	C₃×C₄	—	4	1	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	—	4	2	no	—
457	C₃×C₄	C₅×#126	1	4	yes	—
458	C₂×C₅	—	8	2	no	—
459	C₂×C₅	C₂×C₃×#126	1	1	yes	characteristic
460	C₂×C₅	C₃×#529	1	1	yes	characteristic
461	C₂×C₅	C₃×#540	1	1	yes	characteristic
462	C₂×C₅	C₃×#553	1	1	yes	characteristic
463	C₂×C₅	C₃×#555	1	1	yes	characteristic
464	C₂×C₅	C₃×#559	1	1	yes	characteristic
465	C₂×C₅	C₃×#559	1	1	yes	characteristic
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
474	D₄	—	4	4	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	C₃×C₅×#41	1	2	yes	—
501	C₂×C₄	C₃×C₅×#41	1	2	yes	—
502	C₂×C₄	C₃×C₅×#41	1	2	yes	—
503	C₂×C₄	C₃×C₅×#41	1	2	yes	—
504	C₂×C₄	C₃×C₅×#41	1	2	yes	—
505	C₂×C₃	—	8	2	no	—
506	C₂×C₃	C₂×C₅×#126	1	1	yes	characteristic
507	C₂×C₃	C₅×#529	1	1	yes	characteristic
508	C₂×C₃	C₅×#540	1	1	yes	characteristic
509	C₂×C₃	C₅×#553	1	1	yes	characteristic
510	C₂×C₃	C₅×#555	1	1	yes	characteristic
511	C₂×C₃	C₅×#559	1	1	yes	characteristic
512	C₂×C₃	C₅×#559	1	1	yes	characteristic
513	C₅	C₃×#2513	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
522	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
523	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
524	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
525	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
526	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	C₃×C₅×#126	1	4	yes	—
538	C₃	C₅×#2513	1	1	yes	characteristic, direct product factor, Sylow
539	C₂	—	8	2	no	—
540	C₂	C₂×C₃×C₅×#126	1	1	yes	characteristic
541	C₂	C₃×C₅×#529	1	1	yes	characteristic
542	C₂	C₃×C₅×#540	1	1	yes	characteristic
543	C₂	C₃×C₅×#553	1	1	yes	characteristic
544	C₂	C₃×C₅×#555	1	1	yes	characteristic
545	C₂	C₃×C₅×#559	1	1	yes	characteristic
546	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	C₂²×C₃×C₅×D₄	C₂²
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. C₃×C₅×#397	C₂	semidirect
2. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#388	C₂	semidirect
9. C₃×C₅×#382	C₂	semidirect
10. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
11. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#2513	C₃	direct (N × H)
36. C₃×#2513	C₅	direct (N × H)
37. C₅×#397	C₂×C₃	semidirect
38. C₅×#397	C₂×C₃	semidirect
42. C₅×#389	C₂×C₃	semidirect
43. C₅×#388	C₂×C₃	semidirect
44. C₅×#388	C₂×C₃	semidirect
45. C₅×#382	C₂×C₃	semidirect
46. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
47. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
78. C₃×#397	C₂×C₅	semidirect
79. C₃×#397	C₂×C₅	semidirect
83. C₃×#389	C₂×C₅	semidirect
84. C₃×#388	C₂×C₅	semidirect
85. C₃×#388	C₂×C₅	semidirect
86. C₃×#382	C₂×C₅	semidirect
87. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
88. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
112. #2513	C₃×C₅	direct (N × H)
205. #397	C₂×C₃×C₅	semidirect
206. #397	C₂×C₃×C₅	semidirect
210. #389	C₂×C₃×C₅	semidirect
211. #388	C₂×C₃×C₅	semidirect
212. #388	C₂×C₃×C₅	semidirect
213. #382	C₂×C₃×C₅	semidirect
214. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
215. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
433. C₃×C₅	#2513	direct (N × H)
513. C₅	C₃×#2513	direct (N × H)
538. C₃	C₅×#2513	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×#397	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2513	3
C₃×#2513	5

Subgroups — C3×C5×#2513 #14275547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2513 #14275547