Subgroups — C₂×C₃×C₅×#484 #14276124

Order 1920.

920 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	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#484	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#107	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#484	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	—	2	1	no	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
13	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
21	C₃×C₅×#107	C₂²	1	8	yes	complemented
22	C₃×C₅×#103	C₂²	1	8	yes	complemented
23	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
24	C₂×C₃×#484	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₅×#484	C₂×C₃	1	8	yes	direct product factor
28	C₂×C₅×#107	C₂×C₃	1	2	yes	complemented
29	C₂×C₅×#103	C₂×C₃	1	2	yes	complemented
30	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
31	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×Q₈	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	4	no	—
34	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	4	4	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	—	2	4	no	—
46	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
53	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
54	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
55	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
56	C₃×#484	C₂×C₅	1	8	yes	direct product factor
57	C₂×C₃×#107	C₂×C₅	1	2	yes	complemented
58	C₂×C₃×#103	C₂×C₅	1	2	yes	complemented
59	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
60	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
61	C₂³×C₄×C₅	—	2	1	no	—
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
64	C₅×C₂²⋊Q₈	—	2	2	no	—
65	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₅×#107	C₂²×C₃	1	8	yes	complemented
74	C₅×#103	C₂²×C₃	1	8	yes	complemented
75	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
76	C₂×#484	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	Q₁₆	1	4	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	4	no	—
83	C₃×C₅×Q₈	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	4	8	no	—
91	C₂×C₃×C₄×C₅	—	4	2	no	—
92	C₂×C₃×C₄×C₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	4	4	no	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
98	C₃×C₅×C₈	—	2	4	no	—
99	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
100	C₂³×C₃×C₄	—	2	1	no	—
101	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
103	C₃×C₂²⋊Q₈	—	2	2	no	—
104	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
105	C₂×C₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
111	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
112	C₃×#107	C₂²×C₅	1	8	yes	complemented
113	C₃×#103	C₂²×C₅	1	8	yes	complemented
114	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
115	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	4	no	—
118	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
119	C₂²×C₄×C₅	—	2	4	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	4	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	4	4	no	—
125	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₅×C₈	—	2	4	no	—
130	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
136	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
137	C₅×C₂²⋊C₄	—	2	4	no	—
138	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
139	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
140	#484	C₂×C₃×C₅	1	8	yes	direct product factor
141	C₂×#107	C₂×C₃×C₅	1	2	yes	complemented
142	C₂×#103	C₂×C₃×C₅	1	2	yes	complemented
143	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
144	C₂²×C₃×C₅	—	2	2	no	—
145	C₂²×C₃×C₅	—	2	2	no	—
146	C₂²×C₃×C₅	—	2	8	no	—
147	C₂²×C₃×C₅	#123	1	2	yes	—
148	C₂²×C₃×C₅	C₂×Q₁₆	1	4	yes	—
149	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
150	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
151	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
152	C₃×C₄×C₅	—	2	2	no	—
153	C₃×C₄×C₅	—	4	2	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	—	4	4	no	—
156	C₃×C₄×C₅	#123	1	2	yes	—
157	C₃×C₄×C₅	C₂×#41	1	2	yes	—
158	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
159	C₂×C₃×Q₈	—	2	1	no	—
160	C₂×C₃×Q₈	—	2	4	no	—
161	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
162	C₂²×C₃×C₄	—	2	4	no	—
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	—	2	4	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	4	4	no	—
168	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₂×C₃×C₈	—	2	4	no	—
173	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
174	C₃×C₄⋊C₄	—	2	4	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	—	2	4	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
179	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
180	C₃×C₂²⋊C₄	—	2	4	no	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	C₃×Q₁₆	1	4	yes	—
184	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
185	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
186	C₅×Q₈	—	2	4	no	—
187	C₅×Q₈	—	4	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	4	8	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	4	no	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₃×#41	1	4	yes	—
201	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
202	C₅×C₈	—	2	4	no	—
203	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂³×C₄	—	2	1	no	—
205	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
209	C₂×C₄⋊C₄	—	2	1	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	1	no	—
212	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
213	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
214	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	—	2	1	no	—
216	#107	C₂²×C₃×C₅	1	8	yes	complemented
217	#103	C₂²×C₃×C₅	1	8	yes	complemented
218	C₂²⋊C₈	C₂²×C₃×C₅	1	4	yes	—
219	C₂×C₃×C₅	—	2	4	no	—
220	C₂×C₃×C₅	#484	1	4	yes	direct product factor
221	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
222	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
223	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	C₅×Q₁₆	1	4	yes	—
227	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
228	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
229	C₃×Q₈	—	2	4	no	—
230	C₃×Q₈	—	4	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	4	8	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	—	4	4	no	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₅×#41	1	4	yes	—
244	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
245	C₃×C₈	—	2	4	no	—
246	C₂²×C₅	—	2	2	no	—
247	C₂²×C₅	—	2	2	no	—
248	C₂²×C₅	—	2	8	no	—
249	C₂²×C₅	C₃×#123	1	2	yes	—
250	C₂²×C₅	C₂×C₃×Q₁₆	1	4	yes	—
251	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
252	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
253	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
254	C₄×C₅	—	2	2	no	—
255	C₄×C₅	—	4	2	no	—
256	C₄×C₅	—	4	4	no	—
257	C₄×C₅	—	4	2	no	—
258	C₄×C₅	C₃×#123	1	2	yes	—
259	C₄×C₅	C₂×C₃×#41	1	2	yes	—
260	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
271	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
272	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
273	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
281	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
282	C₂²⋊C₄	—	2	4	no	—
283	C₃×C₅	C₂×#484	1	1	yes	characteristic, direct product factor, Hall
284	C₂²×C₃	—	2	8	no	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	C₅×#123	1	2	yes	—
288	C₂²×C₃	C₂×C₅×Q₁₆	1	4	yes	—
289	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
290	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
291	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	—	4	2	no	—
294	C₃×C₄	—	4	2	no	—
295	C₃×C₄	—	4	4	no	—
296	C₃×C₄	C₅×#123	1	2	yes	—
297	C₃×C₄	C₂×C₅×#41	1	2	yes	—
298	C₂×C₅	—	2	4	no	—
299	C₂×C₅	C₃×#484	1	4	yes	direct product factor
300	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
301	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
302	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	C₃×C₅×Q₁₆	1	4	yes	—
306	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
307	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
308	Q₈	—	2	4	no	—
309	Q₈	—	4	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
321	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
322	C₂×C₄	C₃×C₅×#41	1	4	yes	—
323	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
324	C₈	—	2	4	no	—
325	C₂×C₃	—	2	4	no	—
326	C₂×C₃	C₅×#484	1	4	yes	direct product factor
327	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
328	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
329	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
330	C₅	C₂×C₃×#484	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²	—	2	8	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	C₃×C₅×#123	1	2	yes	—
335	C₂²	C₂×C₃×C₅×Q₁₆	1	4	yes	—
336	C₂²	C₂×C₃×C₅×Q₁₆	1	2	yes	—
337	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
338	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
339	C₄	—	2	2	no	—
340	C₄	—	4	2	no	—
341	C₄	—	4	4	no	—
342	C₄	—	4	2	no	—
343	C₄	C₃×C₅×#123	1	2	yes	—
344	C₄	C₂×C₃×C₅×#41	1	2	yes	—
345	C₃	C₂×C₅×#484	1	1	yes	characteristic, direct product factor, Sylow
346	C₂	—	2	4	no	—
347	C₂	C₃×C₅×#484	1	4	yes	direct product factor
348	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
349	C₂	C₂²×C₃×C₅×Q₁₆	1	1	yes	characteristic
350	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#484	C₂	direct (N × H)
4. C₂×C₃×C₅×#107	C₂	semidirect
5. C₂×C₃×C₅×#103	C₂	semidirect
7. C₂×C₅×#484	C₃	direct (N × H)
21. C₃×C₅×#107	C₂²	semidirect
22. C₃×C₅×#103	C₂²	semidirect
24. C₂×C₃×#484	C₅	direct (N × H)
27. C₅×#484	C₂×C₃	direct (N × H)
28. C₂×C₅×#107	C₂×C₃	semidirect
29. C₂×C₅×#103	C₂×C₃	semidirect
56. C₃×#484	C₂×C₅	direct (N × H)
57. C₂×C₃×#107	C₂×C₅	semidirect
58. C₂×C₃×#103	C₂×C₅	semidirect
73. C₅×#107	C₂²×C₃	semidirect
74. C₅×#103	C₂²×C₃	semidirect
76. C₂×#484	C₃×C₅	direct (N × H)
112. C₃×#107	C₂²×C₅	semidirect
113. C₃×#103	C₂²×C₅	semidirect
140. #484	C₂×C₃×C₅	direct (N × H)
141. C₂×#107	C₂×C₃×C₅	semidirect
142. C₂×#103	C₂×C₃×C₅	semidirect
216. #107	C₂²×C₃×C₅	semidirect
217. #103	C₂²×C₃×C₅	semidirect
220. C₂×C₃×C₅	#484	direct (N × H)
283. C₃×C₅	C₂×#484	direct (N × H)
299. C₂×C₅	C₃×#484	direct (N × H)
326. C₂×C₃	C₅×#484	direct (N × H)
330. C₅	C₂×C₃×#484	direct (N × H)
345. C₃	C₂×C₅×#484	direct (N × H)
347. C₂	C₃×C₅×#484	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×C₂²⋊Q₈	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#484	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×#103	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#484	3
C₂×C₃×#484	5

Subgroups — C2×C3×C5×#484 #14276124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#484 #14276124