Subgroups — C₃×C₅×#3057 #14276091

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#468	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#465	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3057	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₃×C₅×#131	—	2	4	no	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
22	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
23	C₃×C₅×#127	—	2	1	no	—
24	C₃×C₅×#124	—	2	1	no	—
25	C₃×C₅×#124	—	2	1	no	—
26	C₃×C₅×#123	—	2	2	no	—
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₃×C₅×#121	C₂²	1	4	yes	—
29	C₃×C₅×#120	—	2	2	no	—
30	C₃×C₅×#117	C₂²	1	1	yes	characteristic
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₃×C₅×#107	C₂²	1	2	yes	complemented
33	C₃×C₅×#106	C₂²	1	2	yes	complemented
34	C₃×C₅×#103	C₂²	1	4	yes	complemented
35	C₃×C₅×#102	C₂²	1	4	yes	—
36	C₃×#3057	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#535	C₂×C₃	1	1	yes	characteristic
41	C₅×#468	C₂×C₃	1	4	yes	complemented
42	C₅×#465	C₂×C₃	1	4	yes	complemented
43	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	—	2	1	no	—
47	C₃×C₅×#41	—	2	2	no	—
48	C₃×C₅×#41	—	2	2	no	—
49	C₂×C₃×C₅×Q₈	—	2	1	no	—
50	C₂×C₃×C₅×Q₈	—	2	2	no	—
51	C₂×C₃×C₅×Q₈	—	2	2	no	—
52	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×D₄	—	2	4	no	—
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
59	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×SD₁₆	—	2	4	no	—
65	C₃×C₅×SD₁₆	—	2	4	no	—
66	C₃×C₅×M₁₆	—	2	2	no	—
67	C₃×C₅×M₁₆	—	2	4	no	—
68	C₂×C₃×C₅×C₈	—	2	4	no	—
69	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	—	2	4	no	—
74	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
80	C₃×C₄²×C₅	—	2	1	no	—
81	C₃×C₄²×C₅	—	2	1	no	—
82	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#535	C₂×C₅	1	1	yes	characteristic
86	C₃×#468	C₂×C₅	1	4	yes	complemented
87	C₃×#465	C₂×C₅	1	4	yes	complemented
88	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×SD₁₆	—	2	4	no	—
95	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
96	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
97	C₅×#131	—	2	4	no	—
98	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
100	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
102	C₅×C₄⋊Q₈	—	2	1	no	—
103	C₅×#127	—	2	1	no	—
104	C₅×#124	—	2	1	no	—
105	C₅×#124	—	2	1	no	—
106	C₅×#123	—	2	2	no	—
107	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
108	C₅×#121	C₂²×C₃	1	4	yes	—
109	C₅×#120	—	2	2	no	—
110	C₅×#117	C₂²×C₃	1	1	yes	characteristic
111	C₅×#117	C₂²×C₃	1	1	yes	characteristic
112	C₅×#107	C₂²×C₃	1	2	yes	complemented
113	C₅×#106	C₂²×C₃	1	2	yes	complemented
114	C₅×#103	C₂²×C₃	1	4	yes	complemented
115	C₅×#102	C₂²×C₃	1	4	yes	—
116	#3057	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	4	2	no	—
119	C₂³×C₃×C₅	—	8	2	no	—
120	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
121	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
122	C₃×C₅×Q₈	—	2	2	no	—
123	C₃×C₅×Q₈	—	2	2	no	—
124	C₃×C₅×Q₈	—	2	2	no	—
125	C₃×C₅×Q₈	—	4	2	no	—
126	C₃×C₅×D₄	—	2	4	no	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	—	2	2	no	—
129	C₃×C₅×D₄	—	2	2	no	—
130	C₃×C₅×D₄	—	4	2	no	—
131	C₃×C₅×D₄	—	8	4	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	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	—	4	2	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₃×C₅×C₈	—	2	2	no	—
144	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
147	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
148	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×SD₁₆	—	2	4	no	—
150	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
151	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
152	C₃×#131	—	2	4	no	—
153	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
155	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
157	C₃×C₄⋊Q₈	—	2	1	no	—
158	C₃×#127	—	2	1	no	—
159	C₃×#124	—	2	1	no	—
160	C₃×#124	—	2	1	no	—
161	C₃×#123	—	2	2	no	—
162	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
163	C₃×#121	C₂²×C₅	1	4	yes	—
164	C₃×#120	—	2	2	no	—
165	C₃×#117	C₂²×C₅	1	1	yes	characteristic
166	C₃×#117	C₂²×C₅	1	1	yes	characteristic
167	C₃×#107	C₂²×C₅	1	2	yes	complemented
168	C₃×#106	C₂²×C₅	1	2	yes	complemented
169	C₃×#103	C₂²×C₅	1	4	yes	complemented
170	C₃×#102	C₂²×C₅	1	4	yes	—
171	C₂⁴×C₅	—	2	1	no	—
172	C₅×#41	—	2	2	no	—
173	C₅×#41	—	2	2	no	—
174	C₂×C₅×Q₈	—	2	1	no	—
175	C₂×C₅×Q₈	—	2	2	no	—
176	C₂×C₅×Q₈	—	2	2	no	—
177	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
178	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
179	C₂×C₅×D₄	—	2	4	no	—
180	C₂×C₅×D₄	—	2	2	no	—
181	C₂×C₅×D₄	—	2	1	no	—
182	C₂×C₅×D₄	—	2	2	no	—
183	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
184	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
185	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₅×SD₁₆	—	2	4	no	—
190	C₅×SD₁₆	—	2	4	no	—
191	C₅×M₁₆	—	2	2	no	—
192	C₅×M₁₆	—	2	4	no	—
193	C₂×C₅×C₈	—	2	4	no	—
194	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
195	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
196	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₅×C₄⋊C₄	—	2	4	no	—
199	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
200	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
201	C₅×C₂²⋊C₄	—	2	1	no	—
202	C₅×C₂²⋊C₄	—	2	1	no	—
203	C₅×C₂²⋊C₄	—	2	4	no	—
204	C₅×C₂²⋊C₄	—	2	4	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₂²×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
208	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
210	#535	C₂×C₃×C₅	1	1	yes	characteristic
211	#468	C₂×C₃×C₅	1	4	yes	complemented
212	#465	C₂×C₃×C₅	1	4	yes	complemented
213	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	#418	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	C₂²×C₃×C₅	—	2	2	no	—
217	C₂²×C₃×C₅	—	2	2	no	—
218	C₂²×C₃×C₅	—	2	4	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	—	4	4	no	—
221	C₂²×C₃×C₅	—	8	4	no	—
222	C₂²×C₃×C₅	#121	1	2	yes	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₃×C₄×C₅	—	2	2	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	—	4	2	no	—
227	C₃×C₄×C₅	—	4	2	no	—
228	C₃×C₄×C₅	#121	1	2	yes	—
229	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₂⁴×C₃	—	2	1	no	—
232	C₃×#41	—	2	2	no	—
233	C₃×#41	—	2	2	no	—
234	C₂×C₃×Q₈	—	2	1	no	—
235	C₂×C₃×Q₈	—	2	2	no	—
236	C₂×C₃×Q₈	—	2	2	no	—
237	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
238	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
239	C₂×C₃×D₄	—	2	4	no	—
240	C₂×C₃×D₄	—	2	2	no	—
241	C₂×C₃×D₄	—	2	1	no	—
242	C₂×C₃×D₄	—	2	2	no	—
243	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
244	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
245	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₃×SD₁₆	—	2	4	no	—
250	C₃×SD₁₆	—	2	4	no	—
251	C₃×M₁₆	—	2	2	no	—
252	C₃×M₁₆	—	2	4	no	—
253	C₂×C₃×C₈	—	2	4	no	—
254	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
255	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
256	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
258	C₃×C₄⋊C₄	—	2	4	no	—
259	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
260	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
261	C₃×C₂²⋊C₄	—	2	1	no	—
262	C₃×C₂²⋊C₄	—	2	1	no	—
263	C₃×C₂²⋊C₄	—	2	4	no	—
264	C₃×C₂²⋊C₄	—	2	4	no	—
265	C₃×C₄²	—	2	1	no	—
266	C₃×C₄²	—	2	1	no	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	4	2	no	—
269	C₂³×C₅	—	8	2	no	—
270	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
271	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
272	C₅×Q₈	—	2	2	no	—
273	C₅×Q₈	—	2	2	no	—
274	C₅×Q₈	—	2	2	no	—
275	C₅×Q₈	—	4	2	no	—
276	C₅×D₄	—	2	4	no	—
277	C₅×D₄	—	2	2	no	—
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	4	2	no	—
281	C₅×D₄	—	8	4	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	—	4	2	no	—
288	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
289	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
291	C₂×C₄×C₅	C₃×#41	1	2	yes	—
292	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
293	C₅×C₈	—	2	2	no	—
294	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
295	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
296	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
297	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
298	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂×SD₁₆	—	2	4	no	—
300	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
301	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
302	#131	—	2	4	no	—
303	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
304	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
305	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
306	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
307	C₄⋊Q₈	—	2	1	no	—
308	#127	—	2	1	no	—
309	#124	—	2	1	no	—
310	#124	—	2	1	no	—
311	#123	—	2	2	no	—
312	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
313	#121	C₂²×C₃×C₅	1	4	yes	—
314	#120	—	2	2	no	—
315	#117	C₂²×C₃×C₅	1	1	yes	characteristic
316	#117	C₂²×C₃×C₅	1	1	yes	characteristic
317	#107	C₂²×C₃×C₅	1	2	yes	complemented
318	#106	C₂²×C₃×C₅	1	2	yes	complemented
319	#103	C₂²×C₃×C₅	1	4	yes	complemented
320	#102	C₂²×C₃×C₅	1	4	yes	—
321	C₂×C₃×C₅	—	2	2	no	—
322	C₂×C₃×C₅	—	4	2	no	—
323	C₂×C₃×C₅	—	8	2	no	—
324	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
325	C₂×C₃×C₅	#577	1	2	yes	—
326	C₂³×C₃	—	2	2	no	—
327	C₂³×C₃	—	4	2	no	—
328	C₂³×C₃	—	8	2	no	—
329	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
330	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
331	C₃×Q₈	—	2	2	no	—
332	C₃×Q₈	—	2	2	no	—
333	C₃×Q₈	—	2	2	no	—
334	C₃×Q₈	—	4	2	no	—
335	C₃×D₄	—	2	4	no	—
336	C₃×D₄	—	2	2	no	—
337	C₃×D₄	—	2	2	no	—
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	—	4	2	no	—
340	C₃×D₄	—	8	4	no	—
341	C₂×C₃×C₄	—	2	2	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	2	no	—
346	C₂×C₃×C₄	—	4	2	no	—
347	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
348	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
350	C₂×C₃×C₄	C₅×#41	1	2	yes	—
351	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
352	C₃×C₈	—	2	2	no	—
353	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
354	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
355	C₂²×C₅	—	2	2	no	—
356	C₂²×C₅	—	2	4	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	4	4	no	—
359	C₂²×C₅	—	4	2	no	—
360	C₂²×C₅	—	8	4	no	—
361	C₂²×C₅	C₃×#121	1	2	yes	—
362	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	4	2	no	—
366	C₄×C₅	—	4	2	no	—
367	C₄×C₅	C₃×#121	1	2	yes	—
368	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
369	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
370	C₂⁴	—	2	1	no	—
371	#41	—	2	2	no	—
372	#41	—	2	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
377	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
383	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
384	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
387	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
388	SD₁₆	—	2	4	no	—
389	SD₁₆	—	2	4	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	4	no	—
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
394	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
395	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
396	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
399	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₃×C₅	#3057	1	1	yes	characteristic, direct product factor, Hall
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	4	2	no	—
411	C₂²×C₃	—	4	4	no	—
412	C₂²×C₃	—	8	4	no	—
413	C₂²×C₃	C₅×#121	1	2	yes	—
414	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	4	2	no	—
417	C₃×C₄	—	4	2	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	C₅×#121	1	2	yes	—
420	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
421	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
422	C₂×C₅	—	2	2	no	—
423	C₂×C₅	—	4	2	no	—
424	C₂×C₅	—	8	2	no	—
425	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
426	C₂×C₅	C₃×#577	1	2	yes	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	2	no	—
430	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
431	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	2	no	—
435	Q₈	—	4	2	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	4	2	no	—
441	D₄	—	8	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
449	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
450	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
451	C₂×C₄	C₃×C₅×#41	1	2	yes	—
452	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
455	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
456	C₂×C₃	—	2	2	no	—
457	C₂×C₃	—	4	2	no	—
458	C₂×C₃	—	8	2	no	—
459	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
460	C₂×C₃	C₅×#577	1	2	yes	—
461	C₅	C₃×#3057	1	1	yes	characteristic, direct product factor, Sylow
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	C₃×C₅×#121	1	2	yes	—
469	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	C₃×C₅×#121	1	2	yes	—
475	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
476	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
477	C₃	C₅×#3057	1	1	yes	characteristic, direct product factor, Sylow
478	C₂	—	2	2	no	—
479	C₂	—	4	2	no	—
480	C₂	—	8	2	no	—
481	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
482	C₂	C₃×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#535	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
1. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
2. C₂×C₃×C₅×#131	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
5. C₃×C₅×#468	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#427	C₂	semidirect
8. C₃×C₅×#419	C₂	semidirect
9. C₃×C₅×#418	C₂	semidirect
10. C₅×#3057	C₃	direct (N × H)
19. C₂×C₃×C₅×M₁₆	C₂²	semidirect
21. C₂²×C₃×C₅×C₈	C₂²	semidirect
27. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
32. C₃×C₅×#107	C₂²	semidirect
33. C₃×C₅×#106	C₂²	semidirect
34. C₃×C₅×#103	C₂²	semidirect
36. C₃×#3057	C₅	direct (N × H)
37. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
38. C₂×C₅×#131	C₂×C₃	semidirect
39. C₅×#536	C₂×C₃	semidirect
41. C₅×#468	C₂×C₃	semidirect
42. C₅×#465	C₂×C₃	semidirect
43. C₅×#427	C₂×C₃	semidirect
44. C₅×#419	C₂×C₃	semidirect
45. C₅×#418	C₂×C₃	semidirect
69. C₂×C₃×C₅×C₈	D₄	semidirect
82. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
83. C₂×C₃×#131	C₂×C₅	semidirect
84. C₃×#536	C₂×C₅	semidirect
86. C₃×#468	C₂×C₅	semidirect
87. C₃×#465	C₂×C₅	semidirect
88. C₃×#427	C₂×C₅	semidirect
89. C₃×#419	C₂×C₅	semidirect
90. C₃×#418	C₂×C₅	semidirect
99. C₂×C₅×M₁₆	C₂²×C₃	semidirect
101. C₂²×C₅×C₈	C₂²×C₃	semidirect
107. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
112. C₅×#107	C₂²×C₃	semidirect
113. C₅×#106	C₂²×C₃	semidirect
114. C₅×#103	C₂²×C₃	semidirect
116. #3057	C₃×C₅	direct (N × H)
154. C₂×C₃×M₁₆	C₂²×C₅	semidirect
156. C₂²×C₃×C₈	C₂²×C₅	semidirect
162. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
167. C₃×#107	C₂²×C₅	semidirect
168. C₃×#106	C₂²×C₅	semidirect
169. C₃×#103	C₂²×C₅	semidirect
194. C₂×C₅×C₈	C₃×D₄	semidirect
207. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
208. C₂×#131	C₂×C₃×C₅	semidirect
209. #536	C₂×C₃×C₅	semidirect
211. #468	C₂×C₃×C₅	semidirect
212. #465	C₂×C₃×C₅	semidirect
213. #427	C₂×C₃×C₅	semidirect
214. #419	C₂×C₃×C₅	semidirect
215. #418	C₂×C₃×C₅	semidirect
254. C₂×C₃×C₈	C₅×D₄	semidirect
304. C₂×M₁₆	C₂²×C₃×C₅	semidirect
306. C₂²×C₈	C₂²×C₃×C₅	semidirect
312. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
317. #107	C₂²×C₃×C₅	semidirect
318. #106	C₂²×C₃×C₅	semidirect
319. #103	C₂²×C₃×C₅	semidirect
393. C₂×C₈	C₃×C₅×D₄	semidirect
406. C₃×C₅	#3057	direct (N × H)
461. C₅	C₃×#3057	direct (N × H)
477. C₃	C₅×#3057	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×SD₁₆	2
C₂×C₃×C₅×#131	2
C₃×C₅×#536	2
C₃×C₅×#535	2
C₃×C₅×#468	2
C₃×C₅×#465	2
C₃×C₅×#427	2
C₃×C₅×#419	2
C₃×C₅×#418	2
C₅×#3057	3
C₃×#3057	5

Subgroups — C3×C5×#3057 #14276091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3057 #14276091