Subgroups — C₂×C₃×C₅×#462 #14276067

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×Q₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#462	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal
7	C₂×C₅×#462	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×Q₁₆	—	2	8	no	—
11	C₂×C₃×C₅×Q₁₆	C₂²	1	8	yes	—
12	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
13	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
15	C₃×C₄×C₅×Q₈	—	2	2	no	—
16	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
18	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
19	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	—	2	1	no	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	—
24	C₃×C₅×#103	C₂²	1	8	yes	—
25	C₂×C₃×#462	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×Q₁₆	C₂×C₃	1	2	yes	—
27	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
29	C₅×#462	C₂×C₃	1	8	yes	direct product factor
30	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
31	C₂×C₅×#103	C₂×C₃	1	2	yes	—
32	C₂×C₃×C₅×Q₈	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	4	no	—
36	C₂×C₃×C₅×Q₈	—	2	4	no	—
37	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
38	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
39	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₃×C₅×Q₁₆	—	2	16	no	—
47	C₂×C₃×C₅×C₈	—	2	4	no	—
48	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
54	C₃×C₄²×C₅	—	2	4	no	—
55	C₃×C₄²×C₅	D₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×Q₁₆	C₂×C₅	1	2	yes	—
58	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
60	C₃×#462	C₂×C₅	1	8	yes	direct product factor
61	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
62	C₂×C₃×#103	C₂×C₅	1	2	yes	—
63	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
64	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₅×Q₁₆	—	2	8	no	—
66	C₂×C₅×Q₁₆	C₂²×C₃	1	8	yes	—
67	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
68	C₅×C₄⋊Q₈	—	2	2	no	—
69	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
70	C₄×C₅×Q₈	—	2	2	no	—
71	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	—	2	1	no	—
77	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
78	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	—
79	C₅×#103	C₂²×C₃	1	8	yes	—
80	C₂×#462	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	4	no	—
83	C₃×C₅×Q₈	—	2	2	no	—
84	C₃×C₅×Q₈	—	2	4	no	—
85	C₃×C₅×Q₈	—	2	4	no	—
86	C₃×C₅×Q₈	—	4	4	no	—
87	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	4	4	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	Q₁₆	1	4	yes	complemented
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	#41	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
102	C₃×C₅×C₈	—	2	4	no	—
103	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
104	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×Q₁₆	—	2	8	no	—
106	C₂×C₃×Q₁₆	C₂²×C₅	1	8	yes	—
107	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
108	C₃×C₄⋊Q₈	—	2	2	no	—
109	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
110	C₃×C₄×Q₈	—	2	2	no	—
111	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	—
112	C₂×C₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄²	—	2	1	no	—
117	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
118	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	—
119	C₃×#103	C₂²×C₅	1	8	yes	—
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂×C₅×Q₈	—	2	2	no	—
122	C₂×C₅×Q₈	—	2	2	no	—
123	C₂×C₅×Q₈	—	2	4	no	—
124	C₂×C₅×Q₈	—	2	4	no	—
125	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
126	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
127	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₅×Q₁₆	—	2	16	no	—
135	C₂×C₅×C₈	—	2	4	no	—
136	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	4	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
142	C₄²×C₅	—	2	4	no	—
143	C₄²×C₅	C₃×D₄	1	2	yes	—
144	C₄²×C₅	C₂³×C₃	1	2	yes	—
145	C₂²×Q₁₆	C₂×C₃×C₅	1	2	yes	—
146	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
147	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
148	#462	C₂×C₃×C₅	1	8	yes	direct product factor
149	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
150	C₂×#103	C₂×C₃×C₅	1	2	yes	—
151	C₂²×C₃×C₅	#121	1	2	yes	—
152	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
153	C₂²×C₃×C₅	#137	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₃×C₄×C₅	—	2	4	no	—
156	C₃×C₄×C₅	—	2	2	no	—
157	C₃×C₄×C₅	—	4	4	no	—
158	C₃×C₄×C₅	—	4	2	no	—
159	C₃×C₄×C₅	#121	1	2	yes	—
160	C₃×C₄×C₅	C₂×Q₁₆	1	4	yes	complemented
161	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
163	C₂×C₃×Q₈	—	2	1	no	—
164	C₂×C₃×Q₈	—	2	2	no	—
165	C₂×C₃×Q₈	—	2	2	no	—
166	C₂×C₃×Q₈	—	2	4	no	—
167	C₂×C₃×Q₈	—	2	4	no	—
168	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
169	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
170	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₃×Q₁₆	—	2	16	no	—
178	C₂×C₃×C₈	—	2	4	no	—
179	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
180	C₃×C₄⋊C₄	—	2	4	no	—
181	C₃×C₄⋊C₄	—	2	4	no	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
185	C₃×C₄²	—	2	4	no	—
186	C₃×C₄²	C₅×D₄	1	2	yes	—
187	C₃×C₄²	C₂³×C₅	1	2	yes	—
188	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
189	C₅×Q₈	—	2	4	no	—
190	C₅×Q₈	—	2	2	no	—
191	C₅×Q₈	—	2	4	no	—
192	C₅×Q₈	—	2	4	no	—
193	C₅×Q₈	—	4	4	no	—
194	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	4	4	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	C₃×Q₁₆	1	4	yes	complemented
203	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
204	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
206	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
207	C₂×C₄×C₅	C₃×#41	1	2	yes	—
208	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
209	C₅×C₈	—	2	4	no	—
210	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
211	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
212	C₂×Q₁₆	—	2	8	no	—
213	C₂×Q₁₆	C₂²×C₃×C₅	1	8	yes	—
214	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
215	C₄⋊Q₈	—	2	2	no	—
216	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	—
219	C₂×C₄⋊C₄	—	2	1	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	—
226	#103	C₂²×C₃×C₅	1	8	yes	—
227	C₂×C₃×C₅	#462	1	4	yes	direct product factor
228	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
229	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
230	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
231	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
232	C₃×Q₈	—	2	4	no	—
233	C₃×Q₈	—	2	2	no	—
234	C₃×Q₈	—	2	4	no	—
235	C₃×Q₈	—	2	4	no	—
236	C₃×Q₈	—	4	4	no	—
237	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	4	4	no	—
244	C₂×C₃×C₄	—	4	2	no	—
245	C₂×C₃×C₄	C₅×Q₁₆	1	4	yes	complemented
246	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
250	C₂×C₃×C₄	C₅×#41	1	2	yes	—
251	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
252	C₃×C₈	—	2	4	no	—
253	C₂²×C₅	C₃×#121	1	2	yes	—
254	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
255	C₂²×C₅	C₃×#137	1	2	yes	—
256	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	4	2	no	—
260	C₄×C₅	—	4	4	no	—
261	C₄×C₅	C₃×#121	1	2	yes	—
262	C₄×C₅	C₂×C₃×Q₁₆	1	4	yes	complemented
263	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
264	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
265	C₂×Q₈	—	2	1	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
271	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
272	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
277	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
279	Q₁₆	—	2	16	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
287	C₄²	—	2	4	no	—
288	C₄²	C₃×C₅×D₄	1	2	yes	—
289	C₄²	C₂³×C₃×C₅	1	2	yes	—
290	C₃×C₅	C₂×#462	1	1	yes	characteristic, direct product factor, Hall
291	C₂²×C₃	C₅×#121	1	2	yes	—
292	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
293	C₂²×C₃	C₅×#137	1	2	yes	—
294	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	4	4	no	—
298	C₃×C₄	—	4	2	no	—
299	C₃×C₄	C₅×#121	1	2	yes	—
300	C₃×C₄	C₂×C₅×Q₁₆	1	4	yes	complemented
301	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
302	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
303	C₂×C₅	C₃×#462	1	4	yes	direct product factor
304	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
305	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
306	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
307	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
308	Q₈	—	2	4	no	—
309	Q₈	—	2	2	no	—
310	Q₈	—	2	4	no	—
311	Q₈	—	2	4	no	—
312	Q₈	—	4	4	no	—
313	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	C₃×C₅×Q₁₆	1	4	yes	complemented
322	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
323	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
324	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
326	C₂×C₄	C₃×C₅×#41	1	2	yes	—
327	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
328	C₈	—	2	4	no	—
329	C₂×C₃	C₅×#462	1	4	yes	direct product factor
330	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
331	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
332	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
333	C₅	C₂×C₃×#462	1	1	yes	characteristic, direct product factor, Sylow
334	C₂²	C₃×C₅×#121	1	2	yes	—
335	C₂²	C₂×C₃×C₅×Q₁₆	1	2	yes	—
336	C₂²	C₃×C₅×#137	1	2	yes	—
337	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
338	C₄	—	2	4	no	—
339	C₄	—	2	2	no	—
340	C₄	—	4	4	no	—
341	C₄	—	4	2	no	—
342	C₄	C₃×C₅×#121	1	2	yes	—
343	C₄	C₂×C₃×C₅×Q₁₆	1	4	yes	complemented
344	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
345	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
346	C₃	C₂×C₅×#462	1	1	yes	characteristic, direct product factor, Sylow
347	C₂	C₃×C₅×#462	1	4	yes	direct product factor
348	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
349	C₂	C₂²×C₃×C₅×Q₁₆	1	1	yes	characteristic
350	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#462	C₂	direct (N × H)
7. C₂×C₅×#462	C₃	direct (N × H)
25. C₂×C₃×#462	C₅	direct (N × H)
29. C₅×#462	C₂×C₃	direct (N × H)
60. C₃×#462	C₂×C₅	direct (N × H)
80. C₂×#462	C₃×C₅	direct (N × H)
95. C₂×C₃×C₄×C₅	Q₁₆	semidirect
148. #462	C₂×C₃×C₅	direct (N × H)
160. C₃×C₄×C₅	C₂×Q₁₆	semidirect
202. C₂×C₄×C₅	C₃×Q₁₆	semidirect
227. C₂×C₃×C₅	#462	direct (N × H)
245. C₂×C₃×C₄	C₅×Q₁₆	semidirect
262. C₄×C₅	C₂×C₃×Q₁₆	semidirect
290. C₃×C₅	C₂×#462	direct (N × H)
300. C₃×C₄	C₂×C₅×Q₁₆	semidirect
303. C₂×C₅	C₃×#462	direct (N × H)
321. C₂×C₄	C₃×C₅×Q₁₆	semidirect
329. C₂×C₃	C₅×#462	direct (N × H)
333. C₅	C₂×C₃×#462	direct (N × H)
343. C₄	C₂×C₃×C₅×Q₁₆	semidirect
346. C₃	C₂×C₅×#462	direct (N × H)
347. C₂	C₃×C₅×#462	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×Q₁₆	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#462	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×#103	2
C₂×C₅×#462	3
C₂×C₃×#462	5

Subgroups — C2×C3×C5×#462 #14276067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#462 #14276067