Subgroups — C₃×C₅×#2453 #14275487

Order 1920.

904 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	2	yes	maximal
4	C₃×C₅×#398	C₂	1	2	yes	maximal
5	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#389	C₂	1	2	yes	maximal
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#387	C₂	1	2	yes	maximal
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2453	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#125	—	2	4	no	—
15	C₃×C₄×C₅×Q₈	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
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×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×#2453	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
40	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
41	C₅×#400	C₂×C₃	1	2	yes	—
42	C₅×#398	C₂×C₃	1	2	yes	—
43	C₅×#391	C₂×C₃	1	1	yes	characteristic
44	C₅×#391	C₂×C₃	1	1	yes	characteristic
45	C₅×#389	C₂×C₃	1	1	yes	characteristic
46	C₅×#389	C₂×C₃	1	1	yes	characteristic
47	C₅×#389	C₂×C₃	1	2	yes	—
48	C₅×#387	C₂×C₃	1	2	yes	—
49	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂×C₃×C₅×Q₈	—	2	2	no	—
51	C₂×C₃×C₅×Q₈	—	2	2	no	—
52	C₂×C₃×C₅×Q₈	Q₈	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	—	2	4	no	—
65	C₃×C₅×C₄⋊C₄	—	2	4	no	—
66	C₃×C₅×C₄⋊C₄	—	2	4	no	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	4	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	4	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
74	C₃×C₄²×C₅	—	2	4	no	—
75	C₃×C₄²×C₅	—	2	2	no	—
76	C₃×C₄²×C₅	—	2	2	no	—
77	C₃×C₄²×C₅	—	2	2	no	—
78	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
79	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
80	C₃×#400	C₂×C₅	1	2	yes	—
81	C₃×#398	C₂×C₅	1	2	yes	—
82	C₃×#391	C₂×C₅	1	1	yes	characteristic
83	C₃×#391	C₂×C₅	1	1	yes	characteristic
84	C₃×#389	C₂×C₅	1	1	yes	characteristic
85	C₃×#389	C₂×C₅	1	2	yes	—
86	C₃×#389	C₂×C₅	1	1	yes	characteristic
87	C₃×#387	C₂×C₅	1	2	yes	—
88	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
89	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
90	C₅×#125	—	2	4	no	—
91	C₄×C₅×Q₈	—	2	4	no	—
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	2	yes	—
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	C₅×#95	C₂²×C₃	1	2	yes	—
113	C₅×#95	C₂²×C₃	1	2	yes	—
114	#2453	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
116	C₃×C₅×Q₈	—	2	8	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	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	2	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	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	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	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
146	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
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	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
151	C₃×#125	—	2	4	no	—
152	C₃×C₄×Q₈	—	2	4	no	—
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	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
167	C₃×#95	C₂²×C₅	1	1	yes	characteristic
168	C₃×#95	C₂²×C₅	1	1	yes	characteristic
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	C₃×#95	C₂²×C₅	1	2	yes	—
173	C₃×#95	C₂²×C₅	1	2	yes	—
174	C₃×#95	C₂²×C₅	1	2	yes	—
175	C₂×C₅×Q₈	—	2	2	no	—
176	C₂×C₅×Q₈	—	2	2	no	—
177	C₂×C₅×Q₈	C₃×Q₈	1	4	yes	—
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	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
183	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	4	no	—
190	C₅×C₄⋊C₄	—	2	4	no	—
191	C₅×C₄⋊C₄	—	2	4	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	4	no	—
195	C₅×C₄⋊C₄	—	2	2	no	—
196	C₅×C₄⋊C₄	—	2	4	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
199	C₄²×C₅	—	2	4	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	—	2	2	no	—
203	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
204	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
205	#400	C₂×C₃×C₅	1	2	yes	—
206	#398	C₂×C₃×C₅	1	2	yes	—
207	#391	C₂×C₃×C₅	1	1	yes	characteristic
208	#391	C₂×C₃×C₅	1	1	yes	characteristic
209	#389	C₂×C₃×C₅	1	1	yes	characteristic
210	#389	C₂×C₃×C₅	1	2	yes	—
211	#389	C₂×C₃×C₅	1	1	yes	characteristic
212	#387	C₂×C₃×C₅	1	2	yes	—
213	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
214	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
216	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
217	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
218	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
219	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
220	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
221	C₃×C₄×C₅	—	2	4	no	—
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	—	2	4	no	—
224	C₃×C₄×C₅	—	2	2	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	—	4	1	no	—
227	C₃×C₄×C₅	—	4	1	no	—
228	C₃×C₄×C₅	—	4	1	no	—
229	C₃×C₄×C₅	—	4	1	no	—
230	C₃×C₄×C₅	—	4	2	no	—
231	C₃×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
232	C₂×C₃×Q₈	—	2	2	no	—
233	C₂×C₃×Q₈	—	2	2	no	—
234	C₂×C₃×Q₈	C₅×Q₈	1	4	yes	—
235	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
237	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₃×C₄⋊C₄	—	2	4	no	—
247	C₃×C₄⋊C₄	—	2	4	no	—
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	4	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	—	2	4	no	—
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
256	C₃×C₄²	—	2	4	no	—
257	C₃×C₄²	—	2	2	no	—
258	C₃×C₄²	—	2	2	no	—
259	C₃×C₄²	—	2	2	no	—
260	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₅×Q₈	—	2	8	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	1	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	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	2	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	2	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	C₂×C₃×D₄	1	4	yes	—
289	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
290	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
291	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
292	C₂×C₄×C₅	C₃×#41	1	2	yes	—
293	C₂×C₄×C₅	C₃×#41	1	2	yes	—
294	C₂×C₄×C₅	C₃×#41	1	2	yes	—
295	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
296	#125	—	2	4	no	—
297	C₄×Q₈	—	2	4	no	—
298	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
299	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
300	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
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	2	yes	—
305	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
307	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
308	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
310	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
311	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
312	#95	C₂²×C₃×C₅	1	1	yes	characteristic
313	#95	C₂²×C₃×C₅	1	1	yes	characteristic
314	#95	C₂²×C₃×C₅	1	2	yes	—
315	#95	C₂²×C₃×C₅	1	2	yes	—
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	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
321	C₂×C₃×C₅	#529	1	1	yes	characteristic
322	C₂×C₃×C₅	#541	1	1	yes	characteristic
323	C₂×C₃×C₅	#547	1	1	yes	characteristic
324	C₂×C₃×C₅	#548	1	1	yes	characteristic
325	C₂×C₃×C₅	#557	1	1	yes	characteristic
326	C₂×C₃×C₅	#557	1	1	yes	characteristic
327	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
328	C₃×Q₈	—	2	8	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	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	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	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	1	no	—
348	C₂×C₃×C₄	—	2	2	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	2	no	—
355	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
356	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
357	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
358	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
359	C₂×C₃×C₄	C₅×#41	1	2	yes	—
360	C₂×C₃×C₄	C₅×#41	1	2	yes	—
361	C₂×C₃×C₄	C₅×#41	1	2	yes	—
362	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
363	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
364	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
365	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
366	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
367	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
369	C₄×C₅	—	2	4	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	2	4	no	—
372	C₄×C₅	—	2	2	no	—
373	C₄×C₅	—	4	2	no	—
374	C₄×C₅	—	4	1	no	—
375	C₄×C₅	—	4	1	no	—
376	C₄×C₅	—	4	1	no	—
377	C₄×C₅	—	4	1	no	—
378	C₄×C₅	—	4	2	no	—
379	C₄×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	C₃×C₅×Q₈	1	4	yes	—
383	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
384	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
385	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
386	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
387	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
388	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
389	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
390	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
391	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
392	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
393	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₃×C₅	#2453	1	1	yes	characteristic, direct product factor, Hall
409	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
410	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
411	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
412	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
413	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
414	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
415	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
416	C₃×C₄	—	2	4	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	4	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	4	2	no	—
421	C₃×C₄	—	4	1	no	—
422	C₃×C₄	—	4	1	no	—
423	C₃×C₄	—	4	1	no	—
424	C₃×C₄	—	4	1	no	—
425	C₃×C₄	—	4	2	no	—
426	C₃×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
427	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
428	C₂×C₅	C₃×#529	1	1	yes	characteristic
429	C₂×C₅	C₃×#541	1	1	yes	characteristic
430	C₂×C₅	C₃×#547	1	1	yes	characteristic
431	C₂×C₅	C₃×#548	1	1	yes	characteristic
432	C₂×C₅	C₃×#557	1	1	yes	characteristic
433	C₂×C₅	C₃×#557	1	1	yes	characteristic
434	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
435	Q₈	—	2	8	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
463	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
464	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
465	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
466	C₂×C₄	C₃×C₅×#41	1	2	yes	—
467	C₂×C₄	C₃×C₅×#41	1	2	yes	—
468	C₂×C₄	C₃×C₅×#41	1	2	yes	—
469	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
470	C₂×C₃	C₅×#529	1	1	yes	characteristic
471	C₂×C₃	C₅×#541	1	1	yes	characteristic
472	C₂×C₃	C₅×#547	1	1	yes	characteristic
473	C₂×C₃	C₅×#548	1	1	yes	characteristic
474	C₂×C₃	C₅×#557	1	1	yes	characteristic
475	C₂×C₃	C₅×#557	1	1	yes	characteristic
476	C₅	C₃×#2453	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
478	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
479	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
480	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
481	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
482	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
484	C₄	—	2	4	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	4	no	—
487	C₄	—	2	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	2	no	—
494	C₄	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
495	C₃	C₅×#2453	1	1	yes	characteristic, direct product factor, Sylow
496	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
497	C₂	C₃×C₅×#529	1	1	yes	characteristic
498	C₂	C₃×C₅×#541	1	1	yes	characteristic
499	C₂	C₃×C₅×#547	1	1	yes	characteristic
500	C₂	C₃×C₅×#548	1	1	yes	characteristic
501	C₂	C₃×C₅×#557	1	1	yes	characteristic
502	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×#2453	C₃	direct (N × H)
38. C₃×#2453	C₅	direct (N × H)
114. #2453	C₃×C₅	direct (N × H)
408. C₃×C₅	#2453	direct (N × H)
476. C₅	C₃×#2453	direct (N × H)
495. C₃	C₅×#2453	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×#125	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2453	3
C₃×#2453	5

Subgroups — C3×C5×#2453 #14275487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2453 #14275487