Subgroups — C₃×C₅×#2494 #14275528

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#401	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#397	C₂	1	2	yes	maximal
3	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#388	C₂	1	2	yes	maximal
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2494	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×C₄×C₅	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	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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×#2494	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#401	C₂×C₃	1	2	yes	complemented
38	C₅×#397	C₂×C₃	1	2	yes	—
39	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#388	C₂×C₃	1	2	yes	—
42	C₅×#387	C₂×C₃	1	2	yes	complemented
43	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#380	C₂×C₃	1	1	yes	characteristic
45	C₅×#380	C₂×C₃	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	—	2	2	no	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	—	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	2	yes	—
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	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	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	4	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
72	C₃×C₄²×C₅	—	2	2	no	—
73	C₃×C₄²×C₅	—	2	2	no	—
74	C₃×C₄²×C₅	—	4	2	no	—
75	C₃×#401	C₂×C₅	1	2	yes	complemented
76	C₃×#397	C₂×C₅	1	2	yes	—
77	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#388	C₂×C₅	1	2	yes	—
80	C₃×#387	C₂×C₅	1	2	yes	complemented
81	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#380	C₂×C₅	1	1	yes	characteristic
83	C₃×#380	C₂×C₅	1	1	yes	characteristic
84	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
86	C₂³×C₄×C₅	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	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
100	C₅×#95	C₂²×C₃	1	1	yes	characteristic
101	C₅×#95	C₂²×C₃	1	1	yes	characteristic
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	C₅×#95	C₂²×C₃	1	2	yes	—
109	#2494	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³×C₃×C₅	—	2	1	no	—
111	C₂³×C₃×C₅	—	2	1	no	—
112	C₂³×C₃×C₅	—	2	1	no	—
113	C₂³×C₃×C₅	—	2	1	no	—
114	C₂³×C₃×C₅	—	2	1	no	—
115	C₂³×C₃×C₅	—	2	1	no	—
116	C₂³×C₃×C₅	#41	1	2	yes	—
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
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	1	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	1	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	2	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	—	2	1	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	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	4	4	no	—
145	C₂×C₃×C₄×C₅	#41	1	2	yes	—
146	C₂×C₃×C₄×C₅	#41	1	2	yes	—
147	C₂×C₃×C₄×C₅	#41	1	2	yes	—
148	C₂×C₃×C₄×C₅	#41	1	2	yes	—
149	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	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	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
156	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
163	C₃×#95	C₂²×C₅	1	1	yes	characteristic
164	C₃×#95	C₂²×C₅	1	1	yes	characteristic
165	C₃×#95	C₂²×C₅	1	2	yes	—
166	C₃×#95	C₂²×C₅	1	2	yes	—
167	C₃×#95	C₂²×C₅	1	2	yes	—
168	C₃×#95	C₂²×C₅	1	2	yes	—
169	C₃×#95	C₂²×C₅	1	2	yes	—
170	C₃×#95	C₂²×C₅	1	2	yes	—
171	C₃×#95	C₂²×C₅	1	2	yes	—
172	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	—	2	2	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
182	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₅×C₄⋊C₄	—	2	4	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	4	2	no	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	4	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	4	2	no	—
196	C₄²×C₅	—	2	2	no	—
197	C₄²×C₅	—	2	2	no	—
198	C₄²×C₅	—	4	2	no	—
199	#401	C₂×C₃×C₅	1	2	yes	complemented
200	#397	C₂×C₃×C₅	1	2	yes	—
201	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#388	C₂×C₃×C₅	1	2	yes	—
204	#387	C₂×C₃×C₅	1	2	yes	complemented
205	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
206	#380	C₂×C₃×C₅	1	1	yes	characteristic
207	#380	C₂×C₃×C₅	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
210	C₂²×C₃×C₅	—	2	2	no	—
211	C₂²×C₃×C₅	—	2	2	no	—
212	C₂²×C₃×C₅	—	2	2	no	—
213	C₂²×C₃×C₅	—	4	1	no	—
214	C₂²×C₃×C₅	—	4	1	no	—
215	C₂²×C₃×C₅	—	4	1	no	—
216	C₂²×C₃×C₅	—	4	1	no	—
217	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
218	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
219	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
220	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
221	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
222	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
224	C₃×C₄×C₅	—	2	2	no	—
225	C₃×C₄×C₅	—	4	1	no	—
226	C₃×C₄×C₅	—	4	2	no	—
227	C₃×C₄×C₅	—	4	2	no	—
228	C₃×C₄×C₅	—	4	1	no	—
229	C₃×C₄×C₅	—	4	2	no	—
230	C₃×C₄×C₅	—	4	1	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	#126	1	4	yes	—
234	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₃×C₄	—	2	2	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	2	no	—
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
242	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
243	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	—	2	4	no	—
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	2	no	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	—	4	2	no	—
254	C₃×C₂²⋊C₄	—	2	2	no	—
255	C₃×C₂²⋊C₄	—	2	4	no	—
256	C₃×C₂²⋊C₄	—	2	2	no	—
257	C₃×C₂²⋊C₄	—	4	2	no	—
258	C₃×C₄²	—	2	2	no	—
259	C₃×C₄²	—	2	2	no	—
260	C₃×C₄²	—	4	2	no	—
261	C₂³×C₅	—	2	1	no	—
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	—	2	1	no	—
264	C₂³×C₅	—	2	1	no	—
265	C₂³×C₅	—	2	1	no	—
266	C₂³×C₅	—	2	1	no	—
267	C₂³×C₅	C₃×#41	1	2	yes	—
268	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	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	1	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	4	4	no	—
296	C₂×C₄×C₅	C₃×#41	1	2	yes	—
297	C₂×C₄×C₅	C₃×#41	1	2	yes	—
298	C₂×C₄×C₅	C₃×#41	1	2	yes	—
299	C₂×C₄×C₅	C₃×#41	1	2	yes	—
300	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
306	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
311	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
313	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
314	#95	C₂²×C₃×C₅	1	1	yes	characteristic
315	#95	C₂²×C₃×C₅	1	1	yes	characteristic
316	#95	C₂²×C₃×C₅	1	2	yes	—
317	#95	C₂²×C₃×C₅	1	2	yes	—
318	#95	C₂²×C₃×C₅	1	2	yes	—
319	#95	C₂²×C₃×C₅	1	2	yes	—
320	#95	C₂²×C₃×C₅	1	2	yes	—
321	#95	C₂²×C₃×C₅	1	2	yes	—
322	#95	C₂²×C₃×C₅	1	2	yes	—
323	C₂×C₃×C₅	—	4	2	no	—
324	C₂×C₃×C₅	C₂×#126	1	1	yes	characteristic
325	C₂×C₃×C₅	#529	1	1	yes	characteristic
326	C₂×C₃×C₅	#542	1	1	yes	characteristic
327	C₂×C₃×C₅	#552	1	1	yes	characteristic
328	C₂×C₃×C₅	#553	1	1	yes	characteristic
329	C₂×C₃×C₅	#553	1	1	yes	characteristic
330	C₂×C₃×C₅	#556	1	1	yes	characteristic
331	C₂³×C₃	—	2	1	no	—
332	C₂³×C₃	—	2	1	no	—
333	C₂³×C₃	—	2	1	no	—
334	C₂³×C₃	—	2	1	no	—
335	C₂³×C₃	—	2	1	no	—
336	C₂³×C₃	—	2	1	no	—
337	C₂³×C₃	C₅×#41	1	2	yes	—
338	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	4	4	no	—
366	C₂×C₃×C₄	C₅×#41	1	2	yes	—
367	C₂×C₃×C₄	C₅×#41	1	2	yes	—
368	C₂×C₃×C₄	C₅×#41	1	2	yes	—
369	C₂×C₃×C₄	C₅×#41	1	2	yes	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	—	2	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	—	4	1	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
378	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
379	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
380	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
381	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
382	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
384	C₄×C₅	—	2	2	no	—
385	C₄×C₅	—	4	1	no	—
386	C₄×C₅	—	4	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	—	4	2	no	—
390	C₄×C₅	—	4	1	no	—
391	C₄×C₅	—	4	2	no	—
392	C₄×C₅	—	4	1	no	—
393	C₄×C₅	C₃×#126	1	4	yes	—
394	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
399	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
400	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
402	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
403	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
405	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
406	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	4	2	no	—
421	C₃×C₅	#2494	1	1	yes	characteristic, direct product factor, Hall
422	C₂²×C₃	—	2	2	no	—
423	C₂²×C₃	—	2	2	no	—
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	4	1	no	—
426	C₂²×C₃	—	4	1	no	—
427	C₂²×C₃	—	4	1	no	—
428	C₂²×C₃	—	4	1	no	—
429	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
430	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
431	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
432	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
433	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
434	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
436	C₃×C₄	—	2	2	no	—
437	C₃×C₄	—	4	1	no	—
438	C₃×C₄	—	4	2	no	—
439	C₃×C₄	—	4	2	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	4	2	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	—	4	2	no	—
444	C₃×C₄	—	4	1	no	—
445	C₃×C₄	C₅×#126	1	4	yes	—
446	C₂×C₅	—	4	2	no	—
447	C₂×C₅	C₂×C₃×#126	1	1	yes	characteristic
448	C₂×C₅	C₃×#529	1	1	yes	characteristic
449	C₂×C₅	C₃×#542	1	1	yes	characteristic
450	C₂×C₅	C₃×#552	1	1	yes	characteristic
451	C₂×C₅	C₃×#553	1	1	yes	characteristic
452	C₂×C₅	C₃×#553	1	1	yes	characteristic
453	C₂×C₅	C₃×#556	1	1	yes	characteristic
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	C₃×C₅×#41	1	2	yes	—
461	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	C₃×C₅×#41	1	2	yes	—
490	C₂×C₄	C₃×C₅×#41	1	2	yes	—
491	C₂×C₄	C₃×C₅×#41	1	2	yes	—
492	C₂×C₄	C₃×C₅×#41	1	2	yes	—
493	C₂×C₃	—	4	2	no	—
494	C₂×C₃	C₂×C₅×#126	1	1	yes	characteristic
495	C₂×C₃	C₅×#529	1	1	yes	characteristic
496	C₂×C₃	C₅×#542	1	1	yes	characteristic
497	C₂×C₃	C₅×#552	1	1	yes	characteristic
498	C₂×C₃	C₅×#553	1	1	yes	characteristic
499	C₂×C₃	C₅×#553	1	1	yes	characteristic
500	C₂×C₃	C₅×#556	1	1	yes	characteristic
501	C₅	C₃×#2494	1	1	yes	characteristic, direct product factor, Sylow
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
510	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
511	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
512	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
513	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
514	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	1	no	—
525	C₄	C₃×C₅×#126	1	4	yes	—
526	C₃	C₅×#2494	1	1	yes	characteristic, direct product factor, Sylow
527	C₂	—	4	2	no	—
528	C₂	C₂×C₃×C₅×#126	1	1	yes	characteristic
529	C₂	C₃×C₅×#529	1	1	yes	characteristic
530	C₂	C₃×C₅×#542	1	1	yes	characteristic
531	C₂	C₃×C₅×#552	1	1	yes	characteristic
532	C₂	C₃×C₅×#553	1	1	yes	characteristic
533	C₂	C₃×C₅×#553	1	1	yes	characteristic
534	C₂	C₃×C₅×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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×#401	C₂	semidirect
3. C₃×C₅×#389	C₂	semidirect
4. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
7. C₃×C₅×#382	C₂	semidirect
10. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#2494	C₃	direct (N × H)
36. C₃×#2494	C₅	direct (N × H)
37. C₅×#401	C₂×C₃	semidirect
39. C₅×#389	C₂×C₃	semidirect
40. C₅×#389	C₂×C₃	semidirect
42. C₅×#387	C₂×C₃	semidirect
43. C₅×#382	C₂×C₃	semidirect
46. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
75. C₃×#401	C₂×C₅	semidirect
77. C₃×#389	C₂×C₅	semidirect
78. C₃×#389	C₂×C₅	semidirect
80. C₃×#387	C₂×C₅	semidirect
81. C₃×#382	C₂×C₅	semidirect
84. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
109. #2494	C₃×C₅	direct (N × H)
199. #401	C₂×C₃×C₅	semidirect
201. #389	C₂×C₃×C₅	semidirect
202. #389	C₂×C₃×C₅	semidirect
204. #387	C₂×C₃×C₅	semidirect
205. #382	C₂×C₃×C₅	semidirect
208. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
421. C₃×C₅	#2494	direct (N × H)
501. C₅	C₃×#2494	direct (N × H)
526. C₃	C₅×#2494	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×#401	2
C₃×C₅×#397	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#382	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2494	3
C₃×#2494	5

Subgroups — C3×C5×#2494 #14275528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2494 #14275528