Subgroups — C₃×C₅×#2446 #14275480

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	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×#391	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#387	C₂	1	2	yes	maximal
10	C₃×C₅×#387	C₂	1	2	yes	maximal
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2446	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
16	C₃×C₄×C₅×Q₈	—	2	4	no	—
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×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
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×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×#2446	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×C₄⋊Q₈	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×#391	C₂×C₃	1	1	yes	characteristic
46	C₅×#389	C₂×C₃	1	1	yes	characteristic
47	C₅×#387	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	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
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	1	yes	characteristic
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	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	4	no	—
68	C₃×C₅×C₄⋊C₄	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	4	no	—
70	C₃×C₅×C₄⋊C₄	—	2	4	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	4	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	complemented
75	C₃×C₄²×C₅	—	2	4	no	—
76	C₃×C₄²×C₅	—	2	2	no	—
77	C₃×C₄²×C₅	—	2	2	no	—
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
80	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
81	C₃×#400	C₂×C₅	1	2	yes	—
82	C₃×#398	C₂×C₅	1	2	yes	—
83	C₃×#391	C₂×C₅	1	1	yes	characteristic
84	C₃×#391	C₂×C₅	1	1	yes	characteristic
85	C₃×#391	C₂×C₅	1	1	yes	characteristic
86	C₃×#389	C₂×C₅	1	1	yes	characteristic
87	C₃×#387	C₂×C₅	1	2	yes	—
88	C₃×#387	C₂×C₅	1	2	yes	—
89	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
90	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₅×C₄⋊Q₈	—	2	4	no	—
93	C₄×C₅×Q₈	—	2	4	no	—
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
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	C₅×#95	C₂²×C₃	1	2	yes	—
115	#2446	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
116	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
117	C₃×C₅×Q₈	—	2	8	no	—
118	C₃×C₅×Q₈	—	4	4	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	1	no	—
124	C₂×C₃×C₄×C₅	—	2	2	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	1	no	—
129	C₂×C₃×C₄×C₅	—	2	2	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	1	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	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	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	—	2	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂×Q₈	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×Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₃×C₄⋊Q₈	—	2	4	no	—
155	C₃×C₄×Q₈	—	2	4	no	—
156	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
158	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	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	1	yes	characteristic
167	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
168	C₃×#95	C₂²×C₅	1	1	yes	characteristic
169	C₃×#95	C₂²×C₅	1	1	yes	characteristic
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	C₃×#95	C₂²×C₅	1	2	yes	—
176	C₃×#95	C₂²×C₅	1	2	yes	—
177	C₂×C₅×Q₈	—	2	2	no	—
178	C₂×C₅×Q₈	—	2	2	no	—
179	C₂×C₅×Q₈	—	2	2	no	—
180	C₂×C₅×Q₈	—	2	2	no	—
181	C₂×C₅×Q₈	—	2	2	no	—
182	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
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	1	yes	characteristic
186	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
187	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
188	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
189	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	4	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	4	no	—
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	complemented
202	C₄²×C₅	—	2	4	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	2	2	no	—
205	C₄²×C₅	—	2	2	no	—
206	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
208	#400	C₂×C₃×C₅	1	2	yes	—
209	#398	C₂×C₃×C₅	1	2	yes	—
210	#391	C₂×C₃×C₅	1	1	yes	characteristic
211	#391	C₂×C₃×C₅	1	1	yes	characteristic
212	#391	C₂×C₃×C₅	1	1	yes	characteristic
213	#389	C₂×C₃×C₅	1	1	yes	characteristic
214	#387	C₂×C₃×C₅	1	2	yes	—
215	#387	C₂×C₃×C₅	1	2	yes	—
216	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
217	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂²×C₃×C₅	C₂²×Q₈	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	2₋¹⁺⁴	1	1	yes	characteristic
223	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
224	C₃×C₄×C₅	—	2	4	no	—
225	C₃×C₄×C₅	—	2	2	no	—
226	C₃×C₄×C₅	—	2	2	no	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	2	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	—	4	2	no	—
234	C₃×C₄×C₅	#123	1	4	yes	—
235	C₂×C₃×Q₈	—	2	2	no	—
236	C₂×C₃×Q₈	—	2	2	no	—
237	C₂×C₃×Q₈	—	2	2	no	—
238	C₂×C₃×Q₈	—	2	2	no	—
239	C₂×C₃×Q₈	—	2	2	no	—
240	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
241	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
243	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
244	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
247	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₃×C₄⋊C₄	—	2	4	no	—
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	2	4	no	—
255	C₃×C₄⋊C₄	—	2	4	no	—
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	—	2	4	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	complemented
260	C₃×C₄²	—	2	4	no	—
261	C₃×C₄²	—	2	2	no	—
262	C₃×C₄²	—	2	2	no	—
263	C₃×C₄²	—	2	2	no	—
264	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
265	C₅×Q₈	—	2	8	no	—
266	C₅×Q₈	—	4	4	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	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	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	1	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	1	no	—
281	C₂×C₄×C₅	—	2	1	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	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
294	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
295	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
296	C₂×C₄×C₅	C₂×C₃×Q₈	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	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
301	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
302	C₄⋊Q₈	—	2	4	no	—
303	C₄×Q₈	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
308	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
310	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
311	C₂×C₄⋊C₄	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	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
315	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
316	#95	C₂²×C₃×C₅	1	1	yes	characteristic
317	#95	C₂²×C₃×C₅	1	1	yes	characteristic
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	#95	C₂²×C₃×C₅	1	2	yes	—
324	#95	C₂²×C₃×C₅	1	2	yes	—
325	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
326	C₂×C₃×C₅	#533	1	1	yes	characteristic
327	C₂×C₃×C₅	#541	1	1	yes	characteristic
328	C₂×C₃×C₅	#548	1	1	yes	characteristic
329	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
330	C₂×C₃×C₅	#556	1	1	yes	characteristic
331	C₂×C₃×C₅	#557	1	1	yes	characteristic
332	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
333	C₃×Q₈	—	2	8	no	—
334	C₃×Q₈	—	4	4	no	—
335	C₂×C₃×C₄	—	2	1	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	2	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	2	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	1	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	C₂×C₅×D₄	1	4	yes	—
361	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
362	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
363	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
365	C₂×C₃×C₄	C₅×#41	1	2	yes	—
366	C₂×C₃×C₄	C₅×#41	1	2	yes	—
367	C₂×C₃×C₄	C₅×#41	1	2	yes	—
368	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
369	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
370	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
371	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
372	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
373	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
375	C₄×C₅	—	2	4	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	2	2	no	—
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	4	2	no	—
383	C₄×C₅	—	4	1	no	—
384	C₄×C₅	—	4	2	no	—
385	C₄×C₅	C₃×#123	1	4	yes	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
392	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
393	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
394	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
395	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
396	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
397	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
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	1	yes	characteristic
402	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₃×C₅	#2446	1	1	yes	characteristic, direct product factor, Hall
416	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
417	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
418	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
419	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
420	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
421	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
423	C₃×C₄	—	2	4	no	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	4	2	no	—
429	C₃×C₄	—	4	1	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	—	4	1	no	—
432	C₃×C₄	—	4	2	no	—
433	C₃×C₄	C₅×#123	1	4	yes	—
434	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
435	C₂×C₅	C₃×#533	1	1	yes	characteristic
436	C₂×C₅	C₃×#541	1	1	yes	characteristic
437	C₂×C₅	C₃×#548	1	1	yes	characteristic
438	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
439	C₂×C₅	C₃×#556	1	1	yes	characteristic
440	C₂×C₅	C₃×#557	1	1	yes	characteristic
441	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
442	Q₈	—	2	8	no	—
443	Q₈	—	4	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	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	2	no	—
469	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
470	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
471	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
472	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
473	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
474	C₂×C₄	C₃×C₅×#41	1	2	yes	—
475	C₂×C₄	C₃×C₅×#41	1	2	yes	—
476	C₂×C₄	C₃×C₅×#41	1	2	yes	—
477	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
478	C₂×C₃	C₅×#533	1	1	yes	characteristic
479	C₂×C₃	C₅×#541	1	1	yes	characteristic
480	C₂×C₃	C₅×#548	1	1	yes	characteristic
481	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
482	C₂×C₃	C₅×#556	1	1	yes	characteristic
483	C₂×C₃	C₅×#557	1	1	yes	characteristic
484	C₅	C₃×#2446	1	1	yes	characteristic, direct product factor, Sylow
485	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
486	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
487	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
488	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
489	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
490	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
491	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
492	C₄	—	2	4	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	2	no	—
502	C₄	C₃×C₅×#123	1	4	yes	—
503	C₃	C₅×#2446	1	1	yes	characteristic, direct product factor, Sylow
504	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
505	C₂	C₃×C₅×#533	1	1	yes	characteristic
506	C₂	C₃×C₅×#541	1	1	yes	characteristic
507	C₂	C₃×C₅×#548	1	1	yes	characteristic
508	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
509	C₂	C₃×C₅×#556	1	1	yes	characteristic
510	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×#2446	C₃	direct (N × H)
38. C₃×#2446	C₅	direct (N × H)
74. C₃×C₅×C₄⋊C₄	Q₈	semidirect
115. #2446	C₃×C₅	direct (N × H)
201. C₅×C₄⋊C₄	C₃×Q₈	semidirect
259. C₃×C₄⋊C₄	C₅×Q₈	semidirect
410. C₄⋊C₄	C₃×C₅×Q₈	semidirect
415. C₃×C₅	#2446	direct (N × H)
484. C₅	C₃×#2446	direct (N × H)
503. C₃	C₅×#2446	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×C₄⋊Q₈	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×#2446	3
C₃×#2446	5

Subgroups — C3×C5×#2446 #14275480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2446 #14275480