Subgroups — C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₈ #14294277

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	1	4	yes	maximal, direct product factor
5	C₂×(C₂×AGL(1,𝔽₅))⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×#170	C₄	1	2	yes	complemented
9	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
10	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
11	C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	1	2	yes	—
12	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
13	C₂×C₃×D₅⋊C₈	—	2	2	no	—
14	C₂×C₃×D₅⋊C₈	—	2	2	no	—
15	C₂×C₃×D₅⋊C₈	C₄	1	2	yes	complemented
16	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
17	C₂²×C₃×C₅×C₈	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₃×#168	C₄	1	1	yes	characteristic, complemented
19	C₂×C₃×C₈×D₅	—	2	2	no	—
20	C₂×C₃×C₈×D₅	—	2	2	no	—
21	C₂×C₃×C₈×D₅	C₄	1	2	yes	complemented
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	C₂×C₃×#336	—	5	1	no	maximal, Hall
24	C₂²×C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
25	C₂²×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
27	(C₂×AGL(1,𝔽₅))⋊C₈	C₂×C₃	1	4	yes	direct product factor
28	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
30	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
31	C₂²×C₃×AGL(1,𝔽₅)	C₈	1	8	yes	complemented
32	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
39	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
40	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
41	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
42	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×#170	—	2	4	no	—
44	C₂×C₃×#170	C₂×C₄	1	4	yes	complemented
45	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
46	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
47	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
48	C₃×D₅⋊C₈	—	2	4	no	—
49	C₃×D₅⋊C₈	—	2	2	no	—
50	C₃×D₅⋊C₈	—	2	2	no	—
51	C₂×C₃×C₅×C₈	—	2	2	no	—
52	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
53	C₂×C₃×#168	—	2	2	no	—
54	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
55	C₃×C₈×D₅	—	2	4	no	—
56	C₃×C₈×D₅	—	2	2	no	—
57	C₃×C₈×D₅	—	2	2	no	—
58	C₂³×C₃×C₈	—	5	1	no	—
59	C₂³×C₃×C₈	—	5	1	no	—
60	C₂²×C₃×C₄²	—	5	1	no	—
61	C₃×#336	—	5	4	no	—
62	C₂³×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
63	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
64	C₂²×#170	C₃×C₄	1	2	yes	complemented
65	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
66	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
67	C₂×C₄×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
68	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
69	C₂×D₅⋊C₈	—	2	2	no	—
70	C₂×D₅⋊C₈	—	2	2	no	—
71	C₂×D₅⋊C₈	C₃×C₄	1	2	yes	complemented
72	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
73	C₂²×C₅×C₈	C₃×C₄	1	1	yes	characteristic, complemented
74	C₂²×#168	C₃×C₄	1	1	yes	characteristic, complemented
75	C₂×C₈×D₅	—	2	2	no	—
76	C₂×C₈×D₅	—	2	2	no	—
77	C₂×C₈×D₅	C₃×C₄	1	2	yes	complemented
78	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
79	C₂×#336	—	5	1	no	Sylow
80	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
81	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
82	C₂²×C₃×D₅	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
84	C₂²×C₃×D₅	C₂×C₈	1	4	yes	—
85	C₂²×C₃×D₅	M₁₆	1	4	yes	—
86	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×AGL(1,𝔽₅)	—	2	16	no	—
88	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
89	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
90	C₂×C₃×AGL(1,𝔽₅)	C₂×C₈	1	8	yes	complemented
91	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
96	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
97	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
98	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
99	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
100	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
101	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
102	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
103	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
104	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
105	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
106	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
107	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
108	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
109	C₃×#170	—	2	4	no	—
110	C₃×C₅×C₈	—	2	2	no	—
111	C₃×#168	—	2	2	no	—
112	C₂³×C₃×C₄	—	5	1	no	—
113	C₂³×C₃×C₄	—	5	2	no	—
114	C₂²×C₃×C₈	—	5	2	no	—
115	C₂²×C₃×C₈	—	5	2	no	—
116	C₂²×C₃×C₈	—	5	2	no	—
117	C₂²×C₃×C₈	—	5	1	no	—
118	C₂²×C₃×C₈	—	5	2	no	—
119	C₂²×C₃×C₈	—	5	2	no	—
120	C₂²×C₃×C₈	—	10	2	no	—
121	C₂²×C₃×C₈	—	10	2	no	—
122	C₂²×C₃×C₈	—	10	2	no	—
123	C₂²×C₃×C₈	—	10	2	no	—
124	C₂²×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
125	C₂×C₃×C₄²	—	5	2	no	—
126	C₂×C₃×C₄²	—	5	2	no	—
127	C₂×C₃×C₄²	—	10	2	no	—
128	C₂×C₃×C₄²	—	10	2	no	—
129	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
131	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
132	C₂²×AGL(1,𝔽₅)	C₃×C₈	1	8	yes	complemented
133	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
134	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
140	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
141	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
142	C₂×C₄×D₅	C₃×Q₈	1	2	yes	—
143	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
144	C₂×#170	—	2	4	no	—
145	C₂×#170	C₂×C₃×C₄	1	4	yes	complemented
146	C₄×AGL(1,𝔽₅)	—	2	4	no	—
147	C₄×AGL(1,𝔽₅)	—	2	2	no	—
148	C₄×AGL(1,𝔽₅)	—	2	2	no	—
149	D₅⋊C₈	—	2	4	no	—
150	D₅⋊C₈	—	2	2	no	—
151	D₅⋊C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	complemented
154	C₂×#168	—	2	2	no	—
155	C₂×#168	C₂×C₃×C₄	1	2	yes	complemented
156	C₈×D₅	—	2	4	no	—
157	C₈×D₅	—	2	2	no	—
158	C₈×D₅	—	2	2	no	—
159	C₂³×C₈	—	5	1	no	—
160	C₂³×C₈	—	5	1	no	—
161	C₂²×C₄²	—	5	1	no	—
162	#336	—	5	4	no	—
163	C₂²×C₃×C₅	#95	1	2	yes	—
164	C₂²×C₃×C₅	C₄×C₈	1	2	yes	—
165	C₂²×C₃×C₅	#97	1	2	yes	—
166	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₃×D₅	#95	1	2	yes	—
168	C₂×C₃×D₅	C₄×C₈	1	2	yes	—
169	C₂×C₃×D₅	#97	1	2	yes	—
170	C₂×C₃×D₅	C₂²⋊C₈	1	8	yes	—
171	C₂×C₃×D₅	C₄⋊C₈	1	8	yes	—
172	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
175	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
176	C₃×AGL(1,𝔽₅)	—	2	8	no	—
177	C₃×C₄×C₅	#95	1	2	yes	—
178	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₃×Dic₅	#95	1	2	yes	—
181	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂⁴×C₃	—	5	1	no	—
184	C₂²×C₃×C₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	2	no	—
188	C₂²×C₃×C₄	—	5	2	no	—
189	C₂²×C₃×C₄	—	5	2	no	—
190	C₂²×C₃×C₄	—	5	2	no	—
191	C₂²×C₃×C₄	—	5	1	no	—
192	C₂²×C₃×C₄	—	5	1	no	—
193	C₂²×C₃×C₄	—	5	8	no	—
194	C₂²×C₃×C₄	—	5	4	no	—
195	C₂²×C₃×C₄	—	10	4	no	—
196	C₂²×C₃×C₄	—	10	4	no	—
197	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
198	C₂×C₃×C₈	—	2	2	no	—
199	C₂×C₃×C₈	—	5	4	no	—
200	C₂×C₃×C₈	—	5	2	no	—
201	C₂×C₃×C₈	—	10	4	no	—
202	C₂×C₃×C₈	—	10	2	no	—
203	C₂×C₃×C₈	—	10	2	no	—
204	C₂×C₃×C₈	—	10	2	no	—
205	C₂×C₃×C₈	—	10	2	no	—
206	C₂×C₃×C₈	—	10	4	no	—
207	C₂×C₃×C₈	—	10	4	no	—
208	C₂×C₃×C₈	—	10	2	no	—
209	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
210	C₃×C₄²	—	10	2	no	—
211	C₃×C₄²	—	10	2	no	—
212	C₃×C₄²	—	10	4	no	—
213	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
214	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
215	C₂²×D₅	C₃×C₂²⋊C₄	1	2	yes	—
216	C₂²×D₅	C₃×C₄⋊C₄	1	2	yes	—
217	C₂²×D₅	C₂×C₃×C₈	1	4	yes	—
218	C₂²×D₅	C₃×M₁₆	1	4	yes	—
219	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₂×AGL(1,𝔽₅)	—	2	16	no	—
221	C₂×AGL(1,𝔽₅)	—	2	4	no	—
222	C₂×AGL(1,𝔽₅)	—	2	4	no	—
223	C₂×AGL(1,𝔽₅)	C₂×C₃×C₈	1	8	yes	complemented
224	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
225	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
227	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
228	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
229	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
230	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
231	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
232	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
233	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
234	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
235	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
236	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
237	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
238	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
239	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
241	C₄×D₅	C₂×C₃×Q₈	1	1	yes	characteristic
242	#170	—	2	4	no	—
243	C₅×C₈	—	2	2	no	—
244	#168	—	2	2	no	—
245	C₂³×C₄	—	5	1	no	—
246	C₂³×C₄	—	5	2	no	—
247	C₂²×C₈	—	5	2	no	—
248	C₂²×C₈	—	5	2	no	—
249	C₂²×C₈	—	5	2	no	—
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	5	2	no	—
252	C₂²×C₈	—	5	2	no	—
253	C₂²×C₈	—	10	2	no	—
254	C₂²×C₈	—	10	2	no	—
255	C₂²×C₈	—	10	2	no	—
256	C₂²×C₈	—	10	2	no	—
257	C₂²×C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
258	C₂×C₄²	—	5	2	no	—
259	C₂×C₄²	—	5	2	no	—
260	C₂×C₄²	—	10	2	no	—
261	C₂×C₄²	—	10	2	no	—
262	C₂×C₃×C₅	#336	1	4	yes	complemented
263	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#97	1	1	yes	characteristic
266	C₃×D₅	#336	1	4	yes	complemented
267	C₃×D₅	C₂×C₂²⋊C₈	1	2	yes	—
268	C₃×D₅	C₂×C₄⋊C₈	1	2	yes	—
269	C₂³×C₃	—	5	1	no	—
270	C₂³×C₃	—	5	1	no	—
271	C₂³×C₃	—	5	4	no	—
272	C₂³×C₃	—	5	4	no	—
273	C₂³×C₃	—	5	2	no	—
274	C₂³×C₃	—	5	2	no	—
275	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
276	C₂×C₃×C₄	—	5	1	no	—
277	C₂×C₃×C₄	—	5	1	no	—
278	C₂×C₃×C₄	—	5	2	no	—
279	C₂×C₃×C₄	—	5	2	no	—
280	C₂×C₃×C₄	—	5	2	no	—
281	C₂×C₃×C₄	—	5	1	no	—
282	C₂×C₃×C₄	—	5	1	no	—
283	C₂×C₃×C₄	—	5	2	no	—
284	C₂×C₃×C₄	—	5	1	no	—
285	C₂×C₃×C₄	—	5	1	no	—
286	C₂×C₃×C₄	—	5	2	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	5	2	no	—
289	C₂×C₃×C₄	—	5	2	no	—
290	C₂×C₃×C₄	—	5	8	no	—
291	C₂×C₃×C₄	—	10	4	no	—
292	C₂×C₃×C₄	—	10	16	no	—
293	C₂×C₃×C₄	—	10	4	no	—
294	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
296	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
297	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₃×C₈	—	2	2	no	—
299	C₃×C₈	—	10	4	no	—
300	C₃×C₈	—	10	2	no	—
301	C₂²×C₅	C₃×#95	1	2	yes	—
302	C₂²×C₅	C₃×C₄×C₈	1	2	yes	—
303	C₂²×C₅	C₃×#97	1	2	yes	—
304	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
305	C₂×D₅	C₃×#95	1	2	yes	—
306	C₂×D₅	C₃×C₄×C₈	1	2	yes	—
307	C₂×D₅	C₃×#97	1	2	yes	—
308	C₂×D₅	C₃×C₂²⋊C₈	1	8	yes	—
309	C₂×D₅	C₃×C₄⋊C₈	1	8	yes	—
310	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×D₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
312	C₂×D₅	C₂²×C₃×C₈	1	2	yes	—
313	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	—
314	AGL(1,𝔽₅)	—	2	8	no	—
315	C₄×C₅	C₃×#95	1	2	yes	—
316	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
317	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
318	Dic₅	C₃×#95	1	2	yes	—
319	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
320	Dic₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
321	C₂⁴	—	5	1	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	1	no	—
325	C₂²×C₄	—	5	2	no	—
326	C₂²×C₄	—	5	2	no	—
327	C₂²×C₄	—	5	2	no	—
328	C₂²×C₄	—	5	2	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	4	no	—
332	C₂²×C₄	—	5	8	no	—
333	C₂²×C₄	—	10	4	no	—
334	C₂²×C₄	—	10	4	no	—
335	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	5	4	no	—
338	C₂×C₈	—	5	2	no	—
339	C₂×C₈	—	10	2	no	—
340	C₂×C₈	—	10	2	no	—
341	C₂×C₈	—	10	4	no	—
342	C₂×C₈	—	10	2	no	—
343	C₂×C₈	—	10	4	no	—
344	C₂×C₈	—	10	2	no	—
345	C₂×C₈	—	10	4	no	—
346	C₂×C₈	—	10	2	no	—
347	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
348	C₄²	—	10	2	no	—
349	C₄²	—	10	4	no	—
350	C₄²	—	10	2	no	—
351	C₃×C₅	C₂×#336	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	5	8	no	—
353	C₂²×C₃	—	5	8	no	—
354	C₂²×C₃	—	5	2	no	—
355	C₂²×C₃	—	5	2	no	—
356	C₂²×C₃	—	5	2	no	—
357	C₂²×C₃	—	5	2	no	—
358	C₂²×C₃	—	5	2	no	—
359	C₂²×C₃	—	5	1	no	—
360	C₂²×C₃	—	5	1	no	—
361	C₂²×C₃	C₈×AGL(1,𝔽₅)	1	2	yes	—
362	C₂²×C₃	#3992	1	2	yes	—
363	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
364	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
365	C₃×C₄	—	5	2	no	—
366	C₃×C₄	—	5	1	no	—
367	C₃×C₄	—	5	1	no	—
368	C₃×C₄	—	10	8	no	—
369	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
370	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
372	C₂×C₅	C₃×#336	1	4	yes	complemented
373	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
374	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
375	C₂×C₅	C₂×C₃×#97	1	1	yes	characteristic
376	D₅	C₃×#336	1	4	yes	complemented
377	D₅	C₂×C₃×C₂²⋊C₈	1	2	yes	—
378	D₅	C₂×C₃×C₄⋊C₈	1	2	yes	—
379	C₂³	—	5	4	no	—
380	C₂³	—	5	4	no	—
381	C₂³	—	5	1	no	—
382	C₂³	—	5	1	no	—
383	C₂³	—	5	2	no	—
384	C₂³	—	5	2	no	—
385	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	2	no	—
389	C₂×C₄	—	5	2	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	2	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	2	no	—
394	C₂×C₄	—	5	2	no	—
395	C₂×C₄	—	5	2	no	—
396	C₂×C₄	—	5	2	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	2	no	—
400	C₂×C₄	—	5	8	no	—
401	C₂×C₄	—	10	4	no	—
402	C₂×C₄	—	10	4	no	—
403	C₂×C₄	—	10	16	no	—
404	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
405	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
406	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
407	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	10	4	no	—
410	C₈	—	10	2	no	—
411	C₂×C₃	—	5	2	no	—
412	C₂×C₃	—	5	4	no	—
413	C₂×C₃	—	5	2	no	—
414	C₂×C₃	(C₂×AGL(1,𝔽₅))⋊C₈	1	4	yes	direct product factor
415	C₂×C₃	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
416	C₂×C₃	C₂×#3992	1	1	yes	characteristic
417	C₂×C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
418	C₅	C₂×C₃×#336	1	1	yes	characteristic, complemented, Sylow
419	C₂²	—	5	2	no	—
420	C₂²	—	5	2	no	—
421	C₂²	—	5	2	no	—
422	C₂²	—	5	2	no	—
423	C₂²	—	5	1	no	—
424	C₂²	—	5	2	no	—
425	C₂²	—	5	1	no	—
426	C₂²	—	5	8	no	—
427	C₂²	—	5	8	no	—
428	C₂²	C₃×C₈×AGL(1,𝔽₅)	1	2	yes	—
429	C₂²	C₃×#3992	1	2	yes	—
430	C₂²	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
431	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
432	C₄	—	5	1	no	—
433	C₄	—	5	2	no	—
434	C₄	—	5	1	no	—
435	C₄	—	10	8	no	—
436	C₄	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
437	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
438	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
439	C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
440	C₂	—	5	2	no	—
441	C₂	—	5	2	no	—
442	C₂	—	5	4	no	—
443	C₂	C₃×(C₂×AGL(1,𝔽₅))⋊C₈	1	4	yes	direct product factor
444	C₂	C₂×C₃×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
445	C₂	C₂×C₃×#3992	1	1	yes	characteristic
446	C₂	C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂×C₃×C₄×C₈
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₅×C₈	C₄
socle	C₂³×C₃×C₅	C₄²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₂²×C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#336
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
4. C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	direct (N × H)
5. C₂×(C₂×AGL(1,𝔽₅))⋊C₈	C₃	direct (N × H)
8. C₂²×C₃×#170	C₄	semidirect
15. C₂×C₃×D₅⋊C₈	C₄	semidirect
17. C₂²×C₃×C₅×C₈	C₄	semidirect
18. C₂²×C₃×#168	C₄	semidirect
21. C₂×C₃×C₈×D₅	C₄	semidirect
27. (C₂×AGL(1,𝔽₅))⋊C₈	C₂×C₃	direct (N × H)
31. C₂²×C₃×AGL(1,𝔽₅)	C₈	semidirect
44. C₂×C₃×#170	C₂×C₄	semidirect
52. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
54. C₂×C₃×#168	C₂×C₄	semidirect
64. C₂²×#170	C₃×C₄	semidirect
71. C₂×D₅⋊C₈	C₃×C₄	semidirect
73. C₂²×C₅×C₈	C₃×C₄	semidirect
74. C₂²×#168	C₃×C₄	semidirect
77. C₂×C₈×D₅	C₃×C₄	semidirect
90. C₂×C₃×AGL(1,𝔽₅)	C₂×C₈	semidirect
124. C₂²×C₃×C₈	AGL(1,𝔽₅)	semidirect
132. C₂²×AGL(1,𝔽₅)	C₃×C₈	semidirect
145. C₂×#170	C₂×C₃×C₄	semidirect
153. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
155. C₂×#168	C₂×C₃×C₄	semidirect
209. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
223. C₂×AGL(1,𝔽₅)	C₂×C₃×C₈	semidirect
257. C₂²×C₈	C₃×AGL(1,𝔽₅)	semidirect
262. C₂×C₃×C₅	#336	semidirect
266. C₃×D₅	#336	semidirect
347. C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
351. C₃×C₅	C₂×#336	semidirect
372. C₂×C₅	C₃×#336	semidirect
376. D₅	C₃×#336	semidirect
414. C₂×C₃	(C₂×AGL(1,𝔽₅))⋊C₈	direct (N × H)
418. C₅	C₂×C₃×#336	semidirect
439. C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₈	direct (N × H)
443. C₂	C₃×(C₂×AGL(1,𝔽₅))⋊C₈	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×C₄×AGL(1,𝔽₅)	2
C₂²×C₃×D₅⋊C₈	2
C₂²×C₃×C₈×D₅	2
C₃×(C₂×AGL(1,𝔽₅))⋊C₈	2
C₂×(C₂×AGL(1,𝔽₅))⋊C₈	3
C₂×C₃×#336	5

Subgroups — C2×C3×(C2×AGL(1,𝔽5))⋊C8 #14294277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₈ #14294277