Subgroups — C₃×C₅×#3011 #14276045

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#452	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#451	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3011	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
12	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
13	C₂×C₃×C₅×#41	—	2	2	no	—
14	C₂×C₃×C₅×#41	—	2	1	no	—
15	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
16	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	—	2	1	no	—
19	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
20	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#137	—	2	4	no	—
23	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
24	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
25	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
26	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
27	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
30	C₃×C₅×#124	—	2	1	no	—
31	C₃×C₅×#123	—	2	2	no	—
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
33	C₃×C₅×#117	C₂²	1	1	yes	characteristic
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	4	yes	—
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
38	C₃×#3011	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic
40	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#452	C₂×C₃	1	4	yes	complemented
44	C₅×#451	C₂×C₃	1	4	yes	complemented
45	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃×C₅×#41	—	2	16	no	—
49	C₃×C₅×#41	—	2	8	no	—
50	C₃×C₅×#41	—	2	4	no	—
51	C₃×C₅×#41	—	2	4	no	—
52	C₃×C₅×#41	—	2	2	no	—
53	C₃×C₅×#41	—	2	2	no	—
54	C₃×C₅×#41	—	2	2	no	—
55	C₃×C₅×#41	D₄	1	4	yes	—
56	C₂×C₃×C₅×Q₈	—	2	8	no	—
57	C₂×C₃×C₅×Q₈	—	2	4	no	—
58	C₂×C₃×C₅×Q₈	—	2	4	no	—
59	C₂×C₃×C₅×Q₈	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	—	2	1	no	—
61	C₂×C₃×C₅×Q₈	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	—	2	1	no	—
63	C₂×C₃×C₅×Q₈	—	2	2	no	—
64	C₂×C₃×C₅×Q₈	—	2	2	no	—
65	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
66	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
67	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
68	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
70	C₂×C₃×C₅×D₄	—	2	2	no	—
71	C₂×C₃×C₅×D₄	—	2	1	no	—
72	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
73	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
74	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	—	2	2	no	—
76	C₂²×C₃×C₄×C₅	—	2	1	no	—
77	C₂²×C₃×C₄×C₅	—	2	2	no	—
78	C₂²×C₃×C₄×C₅	—	2	1	no	—
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₃×C₅×Q₁₆	—	2	8	no	—
83	C₃×C₅×Q₁₆	—	2	4	no	—
84	C₃×C₅×SD₁₆	—	2	4	no	—
85	C₃×C₅×M₁₆	—	2	2	no	—
86	C₂×C₃×C₅×C₈	—	2	2	no	—
87	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
88	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
89	C₃×C₅×C₄⋊C₄	—	2	4	no	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
91	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
93	C₃×C₄²×C₅	—	2	1	no	—
94	C₂×C₃×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic
95	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#452	C₂×C₅	1	4	yes	complemented
99	C₃×#451	C₂×C₅	1	4	yes	complemented
100	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
103	C₅×2₋¹⁺⁴	—	2	4	no	—
104	C₅×2₋¹⁺⁴	—	2	4	no	—
105	C₂×C₅×#41	—	2	2	no	—
106	C₂×C₅×#41	—	2	1	no	—
107	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
108	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₅×Q₈	—	2	1	no	—
111	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
112	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₅×#137	—	2	4	no	—
115	C₂×C₅×Q₁₆	—	2	4	no	—
116	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
117	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
118	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
119	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
120	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×C₄⋊Q₈	—	2	1	no	—
122	C₅×#124	—	2	1	no	—
123	C₅×#123	—	2	2	no	—
124	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
125	C₅×#117	C₂²×C₃	1	1	yes	characteristic
126	C₅×#103	C₂²×C₃	1	2	yes	—
127	C₅×#103	C₂²×C₃	1	4	yes	—
128	C₅×#102	C₂²×C₃	1	2	yes	—
129	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
130	#3011	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₅×Q₈	—	2	8	no	—
135	C₃×C₅×Q₈	—	2	4	no	—
136	C₃×C₅×Q₈	—	2	2	no	—
137	C₃×C₅×Q₈	—	2	1	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	4	2	no	—
142	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
143	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
144	C₃×C₅×D₄	—	2	8	no	—
145	C₃×C₅×D₄	—	2	4	no	—
146	C₃×C₅×D₄	—	2	4	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	2	1	no	—
149	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	—	2	8	no	—
151	C₂×C₃×C₄×C₅	—	2	8	no	—
152	C₂×C₃×C₄×C₅	—	2	4	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	4	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	4	2	no	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
166	C₃×C₅×C₈	—	2	2	no	—
167	C₃×C₅×C₈	—	2	2	no	—
168	C₃×2₋¹⁺⁴	—	2	4	no	—
169	C₃×2₋¹⁺⁴	—	2	4	no	—
170	C₂×C₃×#41	—	2	2	no	—
171	C₂×C₃×#41	—	2	1	no	—
172	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
173	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
175	C₂²×C₃×Q₈	—	2	1	no	—
176	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
178	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₃×#137	—	2	4	no	—
180	C₂×C₃×Q₁₆	—	2	4	no	—
181	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
182	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
183	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
184	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
186	C₃×C₄⋊Q₈	—	2	1	no	—
187	C₃×#124	—	2	1	no	—
188	C₃×#123	—	2	2	no	—
189	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
190	C₃×#117	C₂²×C₅	1	1	yes	characteristic
191	C₃×#103	C₂²×C₅	1	2	yes	—
192	C₃×#103	C₂²×C₅	1	4	yes	—
193	C₃×#102	C₂²×C₅	1	2	yes	—
194	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
195	C₅×#41	—	2	16	no	—
196	C₅×#41	—	2	8	no	—
197	C₅×#41	—	2	4	no	—
198	C₅×#41	—	2	4	no	—
199	C₅×#41	—	2	2	no	—
200	C₅×#41	—	2	2	no	—
201	C₅×#41	—	2	2	no	—
202	C₅×#41	C₃×D₄	1	4	yes	—
203	C₂×C₅×Q₈	—	2	8	no	—
204	C₂×C₅×Q₈	—	2	4	no	—
205	C₂×C₅×Q₈	—	2	4	no	—
206	C₂×C₅×Q₈	—	2	2	no	—
207	C₂×C₅×Q₈	—	2	1	no	—
208	C₂×C₅×Q₈	—	2	2	no	—
209	C₂×C₅×Q₈	—	2	1	no	—
210	C₂×C₅×Q₈	—	2	2	no	—
211	C₂×C₅×Q₈	—	2	2	no	—
212	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
213	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
214	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
215	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
220	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
221	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₄×C₅	—	2	2	no	—
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	—	2	1	no	—
226	C₂²×C₄×C₅	—	2	1	no	—
227	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
228	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
229	C₅×Q₁₆	—	2	8	no	—
230	C₅×Q₁₆	—	2	4	no	—
231	C₅×SD₁₆	—	2	4	no	—
232	C₅×M₁₆	—	2	2	no	—
233	C₂×C₅×C₈	—	2	2	no	—
234	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
235	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
236	C₅×C₄⋊C₄	—	2	4	no	—
237	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
238	C₅×C₂²⋊C₄	—	2	1	no	—
239	C₅×C₂²⋊C₄	—	2	4	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₂×2₋¹⁺⁴	C₂×C₃×C₅	1	1	yes	characteristic
242	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
245	#452	C₂×C₃×C₅	1	4	yes	complemented
246	#451	C₂×C₃×C₅	1	4	yes	complemented
247	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
248	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	2	4	no	—
254	C₂²×C₃×C₅	—	4	2	no	—
255	C₂²×C₃×C₅	#120	1	2	yes	—
256	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₃×C₄×C₅	—	2	4	no	—
258	C₃×C₄×C₅	—	2	2	no	—
259	C₃×C₄×C₅	—	2	2	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	—	4	2	no	—
262	C₃×C₄×C₅	#120	1	2	yes	—
263	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×#41	—	2	16	no	—
266	C₃×#41	—	2	8	no	—
267	C₃×#41	—	2	4	no	—
268	C₃×#41	—	2	4	no	—
269	C₃×#41	—	2	2	no	—
270	C₃×#41	—	2	2	no	—
271	C₃×#41	—	2	2	no	—
272	C₃×#41	C₅×D₄	1	4	yes	—
273	C₂×C₃×Q₈	—	2	8	no	—
274	C₂×C₃×Q₈	—	2	4	no	—
275	C₂×C₃×Q₈	—	2	4	no	—
276	C₂×C₃×Q₈	—	2	2	no	—
277	C₂×C₃×Q₈	—	2	1	no	—
278	C₂×C₃×Q₈	—	2	2	no	—
279	C₂×C₃×Q₈	—	2	1	no	—
280	C₂×C₃×Q₈	—	2	2	no	—
281	C₂×C₃×Q₈	—	2	2	no	—
282	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
283	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
285	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
286	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
287	C₂×C₃×D₄	—	2	2	no	—
288	C₂×C₃×D₄	—	2	1	no	—
289	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
290	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
292	C₂²×C₃×C₄	—	2	2	no	—
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	—	2	2	no	—
295	C₂²×C₃×C₄	—	2	1	no	—
296	C₂²×C₃×C₄	—	2	1	no	—
297	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₃×Q₁₆	—	2	8	no	—
300	C₃×Q₁₆	—	2	4	no	—
301	C₃×SD₁₆	—	2	4	no	—
302	C₃×M₁₆	—	2	2	no	—
303	C₂×C₃×C₈	—	2	2	no	—
304	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
305	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
306	C₃×C₄⋊C₄	—	2	4	no	—
307	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
308	C₃×C₂²⋊C₄	—	2	1	no	—
309	C₃×C₂²⋊C₄	—	2	4	no	—
310	C₃×C₄²	—	2	1	no	—
311	C₂³×C₅	—	2	1	no	—
312	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
313	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₅×Q₈	—	2	8	no	—
315	C₅×Q₈	—	2	4	no	—
316	C₅×Q₈	—	2	2	no	—
317	C₅×Q₈	—	2	1	no	—
318	C₅×Q₈	—	2	2	no	—
319	C₅×Q₈	—	2	2	no	—
320	C₅×Q₈	—	2	2	no	—
321	C₅×Q₈	—	4	2	no	—
322	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
323	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
324	C₅×D₄	—	2	8	no	—
325	C₅×D₄	—	2	4	no	—
326	C₅×D₄	—	2	4	no	—
327	C₅×D₄	—	2	2	no	—
328	C₅×D₄	—	2	1	no	—
329	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
330	C₂×C₄×C₅	—	2	8	no	—
331	C₂×C₄×C₅	—	2	8	no	—
332	C₂×C₄×C₅	—	2	4	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	4	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	4	2	no	—
341	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
342	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
344	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
345	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
346	C₅×C₈	—	2	2	no	—
347	C₅×C₈	—	2	2	no	—
348	2₋¹⁺⁴	—	2	4	no	—
349	2₋¹⁺⁴	—	2	4	no	—
350	C₂×#41	—	2	2	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
353	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
354	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₂²×Q₈	—	2	1	no	—
356	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
357	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
358	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
359	#137	—	2	4	no	—
360	C₂×Q₁₆	—	2	4	no	—
361	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
362	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
363	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
364	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
365	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
366	C₄⋊Q₈	—	2	1	no	—
367	#124	—	2	1	no	—
368	#123	—	2	2	no	—
369	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
370	#117	C₂²×C₃×C₅	1	1	yes	characteristic
371	#103	C₂²×C₃×C₅	1	2	yes	—
372	#103	C₂²×C₃×C₅	1	4	yes	—
373	#102	C₂²×C₃×C₅	1	2	yes	—
374	C₂²⋊C₈	C₂²×C₃×C₅	1	4	yes	—
375	C₂×C₃×C₅	—	2	2	no	—
376	C₂×C₃×C₅	—	4	2	no	—
377	C₂×C₃×C₅	—	4	2	no	—
378	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
379	C₂×C₃×C₅	#578	1	2	yes	—
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
382	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
383	C₃×Q₈	—	2	8	no	—
384	C₃×Q₈	—	2	4	no	—
385	C₃×Q₈	—	2	2	no	—
386	C₃×Q₈	—	2	1	no	—
387	C₃×Q₈	—	2	2	no	—
388	C₃×Q₈	—	2	2	no	—
389	C₃×Q₈	—	2	2	no	—
390	C₃×Q₈	—	4	2	no	—
391	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
392	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
393	C₃×D₄	—	2	8	no	—
394	C₃×D₄	—	2	4	no	—
395	C₃×D₄	—	2	4	no	—
396	C₃×D₄	—	2	2	no	—
397	C₃×D₄	—	2	1	no	—
398	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
399	C₂×C₃×C₄	—	2	8	no	—
400	C₂×C₃×C₄	—	2	8	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	4	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	4	2	no	—
410	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
411	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
413	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
414	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
415	C₃×C₈	—	2	2	no	—
416	C₃×C₈	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	4	no	—
419	C₂²×C₅	—	2	2	no	—
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	4	2	no	—
422	C₂²×C₅	C₃×#120	1	2	yes	—
423	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
424	C₄×C₅	—	2	4	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	—	2	2	no	—
427	C₄×C₅	—	4	2	no	—
428	C₄×C₅	—	4	2	no	—
429	C₄×C₅	C₃×#120	1	2	yes	—
430	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
431	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
432	#41	—	2	16	no	—
433	#41	—	2	8	no	—
434	#41	—	2	4	no	—
435	#41	—	2	4	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	2	2	no	—
439	#41	C₃×C₅×D₄	1	4	yes	—
440	C₂×Q₈	—	2	8	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
450	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
451	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
452	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
453	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
457	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
458	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
465	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
466	Q₁₆	—	2	8	no	—
467	Q₁₆	—	2	4	no	—
468	SD₁₆	—	2	4	no	—
469	M₁₆	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
472	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₄²	—	2	1	no	—
478	C₃×C₅	#3011	1	1	yes	characteristic, direct product factor, Hall
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	C₅×#120	1	2	yes	—
485	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
486	C₃×C₄	—	2	4	no	—
487	C₃×C₄	—	2	2	no	—
488	C₃×C₄	—	2	2	no	—
489	C₃×C₄	—	4	2	no	—
490	C₃×C₄	—	4	2	no	—
491	C₃×C₄	C₅×#120	1	2	yes	—
492	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
493	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
494	C₂×C₅	—	2	2	no	—
495	C₂×C₅	—	4	2	no	—
496	C₂×C₅	—	4	2	no	—
497	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
498	C₂×C₅	C₃×#578	1	2	yes	—
499	C₂³	—	2	1	no	—
500	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
501	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
502	Q₈	—	2	8	no	—
503	Q₈	—	2	4	no	—
504	Q₈	—	2	2	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	2	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
511	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
512	D₄	—	2	8	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	1	no	—
517	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	8	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
530	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
531	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
532	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
533	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₂×C₃	—	2	2	no	—
537	C₂×C₃	—	4	2	no	—
538	C₂×C₃	—	4	2	no	—
539	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
540	C₂×C₃	C₅×#578	1	2	yes	—
541	C₅	C₃×#3011	1	1	yes	characteristic, direct product factor, Sylow
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	4	2	no	—
547	C₂²	C₃×C₅×#120	1	2	yes	—
548	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
549	C₄	—	2	4	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	C₃×C₅×#120	1	2	yes	—
555	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
556	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
557	C₃	C₅×#3011	1	1	yes	characteristic, direct product factor, Sylow
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	4	2	no	—
561	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
562	C₂	C₃×C₅×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×2₋¹⁺⁴	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₃×C₅×#536	C₂	semidirect
5. C₃×C₅×#452	C₂	semidirect
6. C₃×C₅×#451	C₂	semidirect
7. C₃×C₅×#419	C₂	semidirect
8. C₃×C₅×#416	C₂	semidirect
9. C₃×C₅×#408	C₂	semidirect
10. C₅×#3011	C₃	direct (N × H)
38. C₃×#3011	C₅	direct (N × H)
40. C₂×C₅×#137	C₂×C₃	semidirect
41. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
42. C₅×#536	C₂×C₃	semidirect
43. C₅×#452	C₂×C₃	semidirect
44. C₅×#451	C₂×C₃	semidirect
45. C₅×#419	C₂×C₃	semidirect
46. C₅×#416	C₂×C₃	semidirect
47. C₅×#408	C₂×C₃	semidirect
95. C₂×C₃×#137	C₂×C₅	semidirect
96. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
97. C₃×#536	C₂×C₅	semidirect
98. C₃×#452	C₂×C₅	semidirect
99. C₃×#451	C₂×C₅	semidirect
100. C₃×#419	C₂×C₅	semidirect
101. C₃×#416	C₂×C₅	semidirect
102. C₃×#408	C₂×C₅	semidirect
130. #3011	C₃×C₅	direct (N × H)
242. C₂×#137	C₂×C₃×C₅	semidirect
243. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
244. #536	C₂×C₃×C₅	semidirect
245. #452	C₂×C₃×C₅	semidirect
246. #451	C₂×C₃×C₅	semidirect
247. #419	C₂×C₃×C₅	semidirect
248. #416	C₂×C₃×C₅	semidirect
249. #408	C₂×C₃×C₅	semidirect
478. C₃×C₅	#3011	direct (N × H)
541. C₅	C₃×#3011	direct (N × H)
557. C₃	C₅×#3011	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×C₅×2₋¹⁺⁴	2
C₂×C₃×C₅×#137	2
C₂²×C₃×C₅×Q₁₆	2
C₃×C₅×#536	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#419	2
C₃×C₅×#416	2
C₃×C₅×#408	2
C₅×#3011	3
C₃×#3011	5

Subgroups — C3×C5×#3011 #14276045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3011 #14276045