Subgroups — C₃×C₅×#3042 #14276076

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#463	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#461	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3042	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	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
15	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₃×C₅×#124	C₂²	1	2	yes	complemented
23	C₃×C₅×#123	—	2	2	no	—
24	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
25	C₃×C₄×C₅×D₄	—	2	2	no	—
26	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
27	C₃×C₅×#117	C₂²	1	1	yes	characteristic
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
31	C₃×C₅×#103	C₂²	1	2	yes	complemented
32	C₃×C₅×#103	C₂²	1	4	yes	complemented
33	C₃×C₅×#102	C₂²	1	2	yes	complemented
34	C₃×#3042	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
36	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#518	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#463	C₂×C₃	1	4	yes	complemented
40	C₅×#461	C₂×C₃	1	4	yes	complemented
41	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁴×C₃×C₅	—	2	1	no	—
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	—	2	1	no	—
48	C₂×C₃×C₅×Q₈	—	2	2	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×D₄	—	2	1	no	—
53	C₂×C₃×C₅×D₄	—	2	1	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	—	2	4	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₅×SD₁₆	—	2	8	no	—
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₃×C₅×D₈	—	2	4	no	—
65	C₃×C₅×M₁₆	—	2	2	no	—
66	C₂×C₃×C₅×C₈	—	2	2	no	—
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₃×C₅×C₄⋊C₄	—	2	4	no	—
70	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₃×C₄²×C₅	C₂³	1	2	yes	—
78	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic
79	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#463	C₂×C₅	1	4	yes	complemented
83	C₃×#461	C₂×C₅	1	4	yes	complemented
84	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₅×AGL(1,ℤ/8)	—	2	4	no	—
91	C₂×C₅×SD₁₆	—	2	4	no	—
92	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
93	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
94	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
95	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
96	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
98	C₅×#124	C₂²×C₃	1	2	yes	complemented
99	C₅×#123	—	2	2	no	—
100	C₅×C₂²⋊Q₈	—	2	2	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
103	C₅×#117	C₂²×C₃	1	1	yes	characteristic
104	C₅×#117	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
106	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
107	C₅×#103	C₂²×C₃	1	2	yes	complemented
108	C₅×#103	C₂²×C₃	1	4	yes	complemented
109	C₅×#102	C₂²×C₃	1	2	yes	complemented
110	#3042	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	4	no	—
113	C₂³×C₃×C₅	—	2	1	no	—
114	C₂³×C₃×C₅	—	8	2	no	—
115	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
116	C₃×C₅×Q₈	—	2	2	no	—
117	C₃×C₅×Q₈	—	2	1	no	—
118	C₃×C₅×Q₈	—	2	2	no	—
119	C₃×C₅×Q₈	—	2	1	no	—
120	C₃×C₅×Q₈	—	4	2	no	—
121	C₃×C₅×D₄	—	2	4	no	—
122	C₃×C₅×D₄	—	2	1	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₃×C₅×D₄	—	2	1	no	—
125	C₃×C₅×D₄	—	4	2	no	—
126	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	4	2	no	—
131	C₂×C₃×C₄×C₅	—	4	2	no	—
132	C₂×C₃×C₄×C₅	—	8	4	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	#41	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×C₅×C₈	—	2	2	no	—
139	C₃×C₅×C₈	—	2	2	no	—
140	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
141	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
142	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
143	C₃×AGL(1,ℤ/8)	—	2	4	no	—
144	C₂×C₃×SD₁₆	—	2	4	no	—
145	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
146	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
147	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
148	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
149	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
150	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
151	C₃×#124	C₂²×C₅	1	2	yes	complemented
152	C₃×#123	—	2	2	no	—
153	C₃×C₂²⋊Q₈	—	2	2	no	—
154	C₃×C₄×D₄	—	2	2	no	—
155	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
156	C₃×#117	C₂²×C₅	1	1	yes	characteristic
157	C₃×#117	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
159	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
160	C₃×#103	C₂²×C₅	1	2	yes	complemented
161	C₃×#103	C₂²×C₅	1	4	yes	complemented
162	C₃×#102	C₂²×C₅	1	2	yes	complemented
163	C₂⁴×C₅	—	2	1	no	—
164	C₅×#41	—	2	2	no	—
165	C₅×#41	—	2	2	no	—
166	C₂×C₅×Q₈	—	2	1	no	—
167	C₂×C₅×Q₈	—	2	2	no	—
168	C₂×C₅×Q₈	—	2	2	no	—
169	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
170	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
175	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	4	no	—
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₅×SD₁₆	—	2	8	no	—
182	C₅×SD₁₆	—	2	4	no	—
183	C₅×D₈	—	2	4	no	—
184	C₅×M₁₆	—	2	2	no	—
185	C₂×C₅×C₈	—	2	2	no	—
186	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
187	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
188	C₅×C₄⋊C₄	—	2	4	no	—
189	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
190	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
191	C₅×C₂²⋊C₄	—	2	1	no	—
192	C₅×C₂²⋊C₄	—	2	4	no	—
193	C₅×C₂²⋊C₄	—	2	4	no	—
194	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	C₂³×C₃	1	2	yes	—
197	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic
198	C₂²×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
199	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
200	#518	C₂×C₃×C₅	1	1	yes	characteristic, complemented
201	#463	C₂×C₃×C₅	1	4	yes	complemented
202	#461	C₂×C₃×C₅	1	4	yes	complemented
203	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
204	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
206	C₂²×C₃×C₅	—	2	2	no	—
207	C₂²×C₃×C₅	—	2	4	no	—
208	C₂²×C₃×C₅	—	4	4	no	—
209	C₂²×C₃×C₅	—	4	1	no	—
210	C₂²×C₃×C₅	—	4	2	no	—
211	C₂²×C₃×C₅	—	8	4	no	—
212	C₂²×C₃×C₅	#121	1	2	yes	—
213	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×C₄×C₅	—	2	4	no	—
215	C₃×C₄×C₅	—	4	1	no	—
216	C₃×C₄×C₅	—	4	2	no	—
217	C₃×C₄×C₅	—	4	2	no	—
218	C₃×C₄×C₅	#121	1	2	yes	—
219	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₂⁴×C₃	—	2	1	no	—
222	C₃×#41	—	2	2	no	—
223	C₃×#41	—	2	2	no	—
224	C₂×C₃×Q₈	—	2	1	no	—
225	C₂×C₃×Q₈	—	2	2	no	—
226	C₂×C₃×Q₈	—	2	2	no	—
227	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
228	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
229	C₂×C₃×D₄	—	2	1	no	—
230	C₂×C₃×D₄	—	2	1	no	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
233	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
234	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	—	2	4	no	—
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₃×SD₁₆	—	2	8	no	—
240	C₃×SD₁₆	—	2	4	no	—
241	C₃×D₈	—	2	4	no	—
242	C₃×M₁₆	—	2	2	no	—
243	C₂×C₃×C₈	—	2	2	no	—
244	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
245	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
246	C₃×C₄⋊C₄	—	2	4	no	—
247	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
248	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
249	C₃×C₂²⋊C₄	—	2	1	no	—
250	C₃×C₂²⋊C₄	—	2	4	no	—
251	C₃×C₂²⋊C₄	—	2	4	no	—
252	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
253	C₃×C₄²	—	2	1	no	—
254	C₃×C₄²	C₂³×C₅	1	2	yes	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	4	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	8	2	no	—
259	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
260	C₅×Q₈	—	2	2	no	—
261	C₅×Q₈	—	2	1	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₅×Q₈	—	2	1	no	—
264	C₅×Q₈	—	4	2	no	—
265	C₅×D₄	—	2	4	no	—
266	C₅×D₄	—	2	1	no	—
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	2	1	no	—
269	C₅×D₄	—	4	2	no	—
270	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	4	2	no	—
275	C₂×C₄×C₅	—	4	2	no	—
276	C₂×C₄×C₅	—	8	4	no	—
277	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
278	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
280	C₂×C₄×C₅	C₃×#41	1	2	yes	—
281	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
282	C₅×C₈	—	2	2	no	—
283	C₅×C₈	—	2	2	no	—
284	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
285	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
286	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
287	AGL(1,ℤ/8)	—	2	4	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
290	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
291	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
292	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
294	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
295	#124	C₂²×C₃×C₅	1	2	yes	complemented
296	#123	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
300	#117	C₂²×C₃×C₅	1	1	yes	characteristic
301	#117	C₂²×C₃×C₅	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
304	#103	C₂²×C₃×C₅	1	2	yes	complemented
305	#103	C₂²×C₃×C₅	1	4	yes	complemented
306	#102	C₂²×C₃×C₅	1	2	yes	complemented
307	C₂×C₃×C₅	—	2	2	no	—
308	C₂×C₃×C₅	—	4	4	no	—
309	C₂×C₃×C₅	—	8	1	no	—
310	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
311	C₂×C₃×C₅	#577	1	2	yes	—
312	C₂³×C₃	—	2	2	no	—
313	C₂³×C₃	—	2	4	no	—
314	C₂³×C₃	—	2	1	no	—
315	C₂³×C₃	—	8	2	no	—
316	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
317	C₃×Q₈	—	2	2	no	—
318	C₃×Q₈	—	2	1	no	—
319	C₃×Q₈	—	2	2	no	—
320	C₃×Q₈	—	2	1	no	—
321	C₃×Q₈	—	4	2	no	—
322	C₃×D₄	—	2	4	no	—
323	C₃×D₄	—	2	1	no	—
324	C₃×D₄	—	2	2	no	—
325	C₃×D₄	—	2	1	no	—
326	C₃×D₄	—	4	2	no	—
327	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	4	2	no	—
332	C₂×C₃×C₄	—	4	2	no	—
333	C₂×C₃×C₄	—	8	4	no	—
334	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
335	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
337	C₂×C₃×C₄	C₅×#41	1	2	yes	—
338	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
339	C₃×C₈	—	2	2	no	—
340	C₃×C₈	—	2	2	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	2	4	no	—
343	C₂²×C₅	—	4	4	no	—
344	C₂²×C₅	—	4	2	no	—
345	C₂²×C₅	—	4	1	no	—
346	C₂²×C₅	—	8	4	no	—
347	C₂²×C₅	C₃×#121	1	2	yes	—
348	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
349	C₄×C₅	—	2	4	no	—
350	C₄×C₅	—	4	2	no	—
351	C₄×C₅	—	4	1	no	—
352	C₄×C₅	—	4	2	no	—
353	C₄×C₅	C₃×#121	1	2	yes	—
354	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
356	C₂⁴	—	2	1	no	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
363	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
368	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
369	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
374	SD₁₆	—	2	8	no	—
375	SD₁₆	—	2	4	no	—
376	D₈	—	2	4	no	—
377	M₁₆	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
380	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
383	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
388	C₄²	—	2	1	no	—
389	C₄²	C₂³×C₃×C₅	1	2	yes	—
390	C₃×C₅	#3042	1	1	yes	characteristic, direct product factor, Hall
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	4	4	no	—
394	C₂²×C₃	—	4	1	no	—
395	C₂²×C₃	—	4	2	no	—
396	C₂²×C₃	—	8	4	no	—
397	C₂²×C₃	C₅×#121	1	2	yes	—
398	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
399	C₃×C₄	—	2	4	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	C₅×#121	1	2	yes	—
404	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
405	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
406	C₂×C₅	—	2	2	no	—
407	C₂×C₅	—	4	4	no	—
408	C₂×C₅	—	8	1	no	—
409	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
410	C₂×C₅	C₃×#577	1	2	yes	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	8	2	no	—
415	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
416	Q₈	—	2	2	no	—
417	Q₈	—	2	1	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	1	no	—
420	Q₈	—	4	2	no	—
421	D₄	—	2	1	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	4	2	no	—
426	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	8	4	no	—
433	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
434	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
435	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
436	C₂×C₄	C₃×C₅×#41	1	2	yes	—
437	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₂×C₃	—	2	2	no	—
441	C₂×C₃	—	4	4	no	—
442	C₂×C₃	—	8	1	no	—
443	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
444	C₂×C₃	C₅×#577	1	2	yes	—
445	C₅	C₃×#3042	1	1	yes	characteristic, direct product factor, Sylow
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	8	4	no	—
452	C₂²	C₃×C₅×#121	1	2	yes	—
453	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	C₃×C₅×#121	1	2	yes	—
459	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
460	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
461	C₃	C₅×#3042	1	1	yes	characteristic, direct product factor, Sylow
462	C₂	—	2	2	no	—
463	C₂	—	4	4	no	—
464	C₂	—	8	1	no	—
465	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
466	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	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
4. C₃×C₅×#518	C₂	semidirect
5. C₃×C₅×#463	C₂	semidirect
6. C₃×C₅×#461	C₂	semidirect
7. C₃×C₅×#424	C₂	semidirect
8. C₃×C₅×#419	C₂	semidirect
9. C₃×C₅×#416	C₂	semidirect
10. C₅×#3042	C₃	direct (N × H)
21. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₃×C₅×#124	C₂²	semidirect
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×C₅×#103	C₂²	semidirect
32. C₃×C₅×#103	C₂²	semidirect
33. C₃×C₅×#102	C₂²	semidirect
34. C₃×#3042	C₅	direct (N × H)
36. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
37. C₅×#536	C₂×C₃	semidirect
38. C₅×#518	C₂×C₃	semidirect
39. C₅×#463	C₂×C₃	semidirect
40. C₅×#461	C₂×C₃	semidirect
41. C₅×#424	C₂×C₃	semidirect
42. C₅×#419	C₂×C₃	semidirect
43. C₅×#416	C₂×C₃	semidirect
79. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
80. C₃×#536	C₂×C₅	semidirect
81. C₃×#518	C₂×C₅	semidirect
82. C₃×#463	C₂×C₅	semidirect
83. C₃×#461	C₂×C₅	semidirect
84. C₃×#424	C₂×C₅	semidirect
85. C₃×#419	C₂×C₅	semidirect
86. C₃×#416	C₂×C₅	semidirect
97. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
98. C₅×#124	C₂²×C₃	semidirect
106. C₅×C₄⋊C₈	C₂²×C₃	semidirect
107. C₅×#103	C₂²×C₃	semidirect
108. C₅×#103	C₂²×C₃	semidirect
109. C₅×#102	C₂²×C₃	semidirect
110. #3042	C₃×C₅	direct (N × H)
150. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
151. C₃×#124	C₂²×C₅	semidirect
159. C₃×C₄⋊C₈	C₂²×C₅	semidirect
160. C₃×#103	C₂²×C₅	semidirect
161. C₃×#103	C₂²×C₅	semidirect
162. C₃×#102	C₂²×C₅	semidirect
198. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
199. #536	C₂×C₃×C₅	semidirect
200. #518	C₂×C₃×C₅	semidirect
201. #463	C₂×C₃×C₅	semidirect
202. #461	C₂×C₃×C₅	semidirect
203. #424	C₂×C₃×C₅	semidirect
204. #419	C₂×C₃×C₅	semidirect
205. #416	C₂×C₃×C₅	semidirect
294. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
295. #124	C₂²×C₃×C₅	semidirect
303. C₄⋊C₈	C₂²×C₃×C₅	semidirect
304. #103	C₂²×C₃×C₅	semidirect
305. #103	C₂²×C₃×C₅	semidirect
306. #102	C₂²×C₃×C₅	semidirect
390. C₃×C₅	#3042	direct (N × H)
445. C₅	C₃×#3042	direct (N × H)
461. C₃	C₅×#3042	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×AGL(1,ℤ/8)	2
C₂²×C₃×C₅×SD₁₆	2
C₃×C₅×#536	2
C₃×C₅×#518	2
C₃×C₅×#463	2
C₃×C₅×#461	2
C₃×C₅×#424	2
C₃×C₅×#419	2
C₃×C₅×#416	2
C₅×#3042	3
C₃×#3042	5

Subgroups — C3×C5×#3042 #14276076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3042 #14276076