Subgroups — C₂×C₃×C₅×#459 #14276063

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

Subgroups — C2×C3×C5×#459 #14276063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#459 #14276063