Subgroups — C₃×AGL(1,𝔽₅)×C₂²⋊C₈ #14295010

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 400 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	C₃×D₅⋊(C₂²⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
4	C₃×D₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	1	2	yes	maximal, complemented
6	AGL(1,𝔽₅)×C₂²⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
8	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
10	C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	1	2	yes	—
11	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
14	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
15	C₃×C₂²⋊#170	C₄	1	2	yes	complemented
16	C₃×#4003	C₄	1	2	yes	complemented
17	C₃×C₈×AGL(1,𝔽₅)	—	2	4	no	—
18	C₃×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic, complemented
19	C₃×C₂²⋊#168	C₄	1	1	yes	characteristic, complemented
20	C₃×#3952	C₄	1	2	yes	complemented
21	C₃×C₄×C₂²⋊C₈	—	5	1	no	maximal, Hall
22	C₂²×C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
23	D₅⋊(C₂²⋊C₈)	C₂×C₃	1	1	yes	characteristic
24	C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
25	D₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
26	(C₂×AGL(1,𝔽₅))⋊C₈	C₂×C₃	1	2	yes	complemented
27	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
29	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
30	C₂²×C₃×AGL(1,𝔽₅)	C₈	1	8	yes	complemented
31	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
32	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	2	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	—	2	2	no	—
36	C₂×C₃×C₄×D₅	—	2	2	no	—
37	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×#170	C₂×C₄	1	4	yes	complemented
42	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
43	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
44	C₃×C₄×AGL(1,𝔽₅)	D₄	1	4	yes	—
45	C₃×D₅⋊C₈	—	2	2	no	—
46	C₃×D₅⋊C₈	—	2	2	no	—
47	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
48	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
49	C₃×C₈×D₅	—	2	2	no	—
50	C₃×C₈×D₅	—	2	2	no	—
51	C₂²×C₃×C₄²	—	5	1	no	—
52	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
53	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
54	C₂×C₃×C₄×C₈	—	5	2	no	—
55	C₃×#336	—	5	2	no	—
56	C₂³×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
57	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₄×AGL(1,𝔽₅)	—	2	4	no	—
59	C₂×C₄×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
60	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
62	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
63	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
64	C₂²⋊#170	C₃×C₄	1	2	yes	complemented
65	#4003	C₃×C₄	1	2	yes	complemented
66	C₈×AGL(1,𝔽₅)	—	2	4	no	—
67	C₅×C₂²⋊C₈	C₃×C₄	1	1	yes	characteristic, complemented
68	C₂²⋊#168	C₃×C₄	1	1	yes	characteristic, complemented
69	#3952	C₃×C₄	1	2	yes	complemented
70	C₄×C₂²⋊C₈	—	5	1	no	Sylow
71	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
72	C₂²×C₃×D₅	—	2	1	no	—
73	C₂²×C₃×D₅	—	2	1	no	—
74	C₂²×C₃×D₅	—	2	2	no	—
75	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
76	C₂²×C₃×D₅	C₂×C₈	1	4	yes	—
77	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
79	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
80	C₂×C₃×AGL(1,𝔽₅)	—	2	16	no	—
81	C₂×C₃×AGL(1,𝔽₅)	C₂²⋊C₄	1	4	yes	—
82	C₂×C₃×AGL(1,𝔽₅)	C₂×C₈	1	4	yes	—
83	C₂×C₃×AGL(1,𝔽₅)	C₂×C₈	1	4	yes	—
84	C₂×C₃×AGL(1,𝔽₅)	M₁₆	1	4	yes	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×Dic₅	—	2	2	no	—
89	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
90	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
91	C₃×C₄×D₅	—	2	1	no	—
92	C₃×C₄×D₅	—	2	1	no	—
93	C₃×C₄×D₅	—	2	2	no	—
94	C₃×C₄×D₅	—	2	2	no	—
95	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
96	C₃×C₄×D₅	#41	1	2	yes	—
97	C₃×#170	—	2	4	no	—
98	C₃×C₅×C₈	—	2	2	no	—
99	C₃×#168	—	2	2	no	—
100	C₂³×C₃×C₄	—	5	2	no	—
101	C₂³×C₃×C₄	—	5	1	no	—
102	C₂²×C₃×C₈	—	5	2	no	—
103	C₂²×C₃×C₈	—	5	2	no	—
104	C₂×C₃×C₄²	—	5	1	no	—
105	C₂×C₃×C₄²	—	5	2	no	—
106	C₂×C₃×C₄²	—	5	1	no	—
107	C₂×C₃×C₄²	—	10	4	no	—
108	C₃×C₂²⋊C₈	—	5	2	no	—
109	C₃×C₂²⋊C₈	—	5	2	no	—
110	C₃×C₂²⋊C₈	—	5	1	no	—
111	C₃×C₂²⋊C₈	—	5	2	no	—
112	C₃×C₂²⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
113	C₃×C₄×C₈	—	10	4	no	—
114	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
115	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
116	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
117	C₂²×AGL(1,𝔽₅)	C₃×C₈	1	8	yes	complemented
118	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	2	yes	—
119	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂×C₄×D₅	—	2	2	no	—
123	C₂×C₄×D₅	—	2	2	no	—
124	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
125	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
128	C₂×#170	C₂×C₃×C₄	1	4	yes	complemented
129	C₄×AGL(1,𝔽₅)	—	2	4	no	—
130	C₄×AGL(1,𝔽₅)	—	2	2	no	—
131	C₄×AGL(1,𝔽₅)	C₃×D₄	1	4	yes	—
132	D₅⋊C₈	—	2	2	no	—
133	D₅⋊C₈	—	2	2	no	—
134	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	complemented
135	C₂×#168	C₂×C₃×C₄	1	2	yes	complemented
136	C₈×D₅	—	2	2	no	—
137	C₈×D₅	—	2	2	no	—
138	C₂²×C₄²	—	5	1	no	—
139	C₂×C₂²⋊C₈	—	5	1	no	—
140	C₂×C₂²⋊C₈	—	5	1	no	—
141	C₂×C₄×C₈	—	5	2	no	—
142	#336	—	5	2	no	—
143	C₂²×C₃×C₅	—	2	1	no	—
144	C₂²×C₃×C₅	—	2	1	no	—
145	C₂²×C₃×C₅	C₄×C₈	1	2	yes	complemented
146	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₃×D₅	—	2	1	no	—
148	C₂×C₃×D₅	—	2	1	no	—
149	C₂×C₃×D₅	—	2	4	no	—
150	C₂×C₃×D₅	—	2	4	no	—
151	C₂×C₃×D₅	C₄×C₈	1	2	yes	complemented
152	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₃×D₅	#117	1	1	yes	characteristic
154	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
155	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
156	C₃×AGL(1,𝔽₅)	—	2	4	no	—
157	C₃×AGL(1,𝔽₅)	C₂²⋊C₈	1	8	yes	direct product factor
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
160	C₃×Dic₅	—	2	1	no	—
161	C₃×Dic₅	C₄×D₄	1	2	yes	—
162	C₂⁴×C₃	—	5	1	no	—
163	C₂²×C₃×C₄	—	5	2	no	—
164	C₂²×C₃×C₄	—	5	1	no	—
165	C₂²×C₃×C₄	—	5	8	no	—
166	C₂²×C₃×C₄	—	5	2	no	—
167	C₂²×C₃×C₄	—	5	1	no	—
168	C₂²×C₃×C₄	—	5	1	no	—
169	C₂²×C₃×C₄	—	5	1	no	—
170	C₂²×C₃×C₄	—	5	1	no	—
171	C₂²×C₃×C₄	—	10	2	no	—
172	C₂²×C₃×C₄	—	10	2	no	—
173	C₂²×C₃×C₄	—	10	4	no	—
174	C₂²×C₃×C₄	—	10	4	no	—
175	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
176	C₂×C₃×C₈	—	5	4	no	—
177	C₂×C₃×C₈	—	5	2	no	—
178	C₂×C₃×C₈	—	10	2	no	—
179	C₂×C₃×C₈	—	10	2	no	—
180	C₂×C₃×C₈	—	10	2	no	—
181	C₂×C₃×C₈	—	10	2	no	—
182	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
183	C₃×C₄²	—	5	4	no	—
184	C₃×C₄²	—	10	4	no	—
185	C₃×C₄²	—	10	2	no	—
186	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
187	C₂²×D₅	—	2	1	no	—
188	C₂²×D₅	—	2	1	no	—
189	C₂²×D₅	—	2	2	no	—
190	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
191	C₂²×D₅	C₂×C₃×C₈	1	4	yes	—
192	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
193	C₂×AGL(1,𝔽₅)	—	2	2	no	—
194	C₂×AGL(1,𝔽₅)	—	2	2	no	—
195	C₂×AGL(1,𝔽₅)	—	2	16	no	—
196	C₂×AGL(1,𝔽₅)	C₃×C₂²⋊C₄	1	4	yes	—
197	C₂×AGL(1,𝔽₅)	C₂×C₃×C₈	1	4	yes	—
198	C₂×AGL(1,𝔽₅)	C₂×C₃×C₈	1	4	yes	—
199	C₂×AGL(1,𝔽₅)	C₃×M₁₆	1	4	yes	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
203	C₂×Dic₅	—	2	2	no	—
204	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
205	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
206	C₄×D₅	—	2	1	no	—
207	C₄×D₅	—	2	1	no	—
208	C₄×D₅	—	2	2	no	—
209	C₄×D₅	—	2	2	no	—
210	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
211	C₄×D₅	C₃×#41	1	2	yes	—
212	#170	—	2	4	no	—
213	C₅×C₈	—	2	2	no	—
214	#168	—	2	2	no	—
215	C₂³×C₄	—	5	2	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂²×C₈	—	5	2	no	—
218	C₂²×C₈	—	5	2	no	—
219	C₂×C₄²	—	5	1	no	—
220	C₂×C₄²	—	5	2	no	—
221	C₂×C₄²	—	5	1	no	—
222	C₂×C₄²	—	10	4	no	—
223	C₂²⋊C₈	—	5	2	no	—
224	C₂²⋊C₈	—	5	2	no	—
225	C₂²⋊C₈	—	5	1	no	—
226	C₂²⋊C₈	—	5	2	no	—
227	C₂²⋊C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
228	C₄×C₈	—	10	4	no	—
229	C₂×C₃×C₅	—	2	2	no	—
230	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
232	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
233	C₃×D₅	—	2	2	no	—
234	C₃×D₅	C₂×C₂²⋊C₈	1	2	yes	—
235	C₃×D₅	#431	1	2	yes	—
236	C₂³×C₃	—	5	1	no	—
237	C₂³×C₃	—	5	1	no	—
238	C₂³×C₃	—	5	4	no	—
239	C₂³×C₃	—	10	1	no	—
240	C₂³×C₃	—	10	1	no	—
241	C₂³×C₃	—	10	2	no	—
242	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	5	4	no	—
245	C₂×C₃×C₄	—	5	4	no	—
246	C₂×C₃×C₄	—	5	4	no	—
247	C₂×C₃×C₄	—	5	1	no	—
248	C₂×C₃×C₄	—	5	2	no	—
249	C₂×C₃×C₄	—	5	2	no	—
250	C₂×C₃×C₄	—	5	4	no	—
251	C₂×C₃×C₄	—	5	1	no	—
252	C₂×C₃×C₄	—	10	2	no	—
253	C₂×C₃×C₄	—	10	1	no	—
254	C₂×C₃×C₄	—	10	1	no	—
255	C₂×C₃×C₄	—	10	2	no	—
256	C₂×C₃×C₄	—	10	16	no	—
257	C₂×C₃×C₄	—	10	2	no	—
258	C₂×C₃×C₄	—	10	2	no	—
259	C₂×C₃×C₄	—	10	2	no	—
260	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	10	4	no	—
264	C₃×C₈	—	10	2	no	—
265	C₂²×C₅	—	2	1	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	C₃×C₄×C₈	1	2	yes	complemented
268	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
269	C₂×D₅	—	2	1	no	—
270	C₂×D₅	—	2	1	no	—
271	C₂×D₅	—	2	4	no	—
272	C₂×D₅	—	2	4	no	—
273	C₂×D₅	C₃×C₄×C₈	1	2	yes	complemented
274	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×D₅	C₃×#117	1	1	yes	characteristic
276	C₂×D₅	C₂²×C₃×C₈	1	2	yes	—
277	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	—
278	AGL(1,𝔽₅)	—	2	4	no	—
279	AGL(1,𝔽₅)	C₃×C₂²⋊C₈	1	8	yes	direct product factor
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
282	Dic₅	—	2	1	no	—
283	Dic₅	C₃×C₄×D₄	1	2	yes	—
284	C₂⁴	—	5	1	no	—
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	5	1	no	—
287	C₂²×C₄	—	5	2	no	—
288	C₂²×C₄	—	5	8	no	—
289	C₂²×C₄	—	5	1	no	—
290	C₂²×C₄	—	5	1	no	—
291	C₂²×C₄	—	5	1	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	10	2	no	—
294	C₂²×C₄	—	10	2	no	—
295	C₂²×C₄	—	10	4	no	—
296	C₂²×C₄	—	10	4	no	—
297	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₂×C₈	—	5	4	no	—
299	C₂×C₈	—	5	2	no	—
300	C₂×C₈	—	10	2	no	—
301	C₂×C₈	—	10	2	no	—
302	C₂×C₈	—	10	2	no	—
303	C₂×C₈	—	10	2	no	—
304	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
305	C₄²	—	5	4	no	—
306	C₄²	—	10	4	no	—
307	C₄²	—	10	2	no	—
308	C₃×C₅	C₄×C₂²⋊C₈	1	1	yes	characteristic, complemented, Hall
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	5	1	no	—
312	C₂²×C₃	—	5	1	no	—
313	C₂²×C₃	—	5	2	no	—
314	C₂²×C₃	—	5	2	no	—
315	C₂²×C₃	—	5	2	no	—
316	C₂²×C₃	—	10	4	no	—
317	C₂²×C₃	—	10	4	no	—
318	C₂²×C₃	—	10	1	no	—
319	C₂²×C₃	—	10	1	no	—
320	C₂²×C₃	C₈×AGL(1,𝔽₅)	1	2	yes	complemented
321	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	5	8	no	—
324	C₃×C₄	—	5	2	no	—
325	C₃×C₄	—	10	4	no	—
326	C₃×C₄	—	10	1	no	—
327	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
328	C₂×C₅	—	2	2	no	—
329	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
330	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
331	C₂×C₅	C₃×C₄×M₁₆	1	1	yes	characteristic
332	D₅	—	2	2	no	—
333	D₅	C₂×C₃×C₂²⋊C₈	1	2	yes	—
334	D₅	C₃×#431	1	2	yes	—
335	C₂³	—	5	1	no	—
336	C₂³	—	5	4	no	—
337	C₂³	—	5	1	no	—
338	C₂³	—	10	1	no	—
339	C₂³	—	10	1	no	—
340	C₂³	—	10	2	no	—
341	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	5	4	no	—
344	C₂×C₄	—	5	4	no	—
345	C₂×C₄	—	5	4	no	—
346	C₂×C₄	—	5	1	no	—
347	C₂×C₄	—	5	2	no	—
348	C₂×C₄	—	5	2	no	—
349	C₂×C₄	—	5	4	no	—
350	C₂×C₄	—	5	1	no	—
351	C₂×C₄	—	10	2	no	—
352	C₂×C₄	—	10	1	no	—
353	C₂×C₄	—	10	1	no	—
354	C₂×C₄	—	10	2	no	—
355	C₂×C₄	—	10	16	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	—	10	2	no	—
359	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	10	4	no	—
363	C₈	—	10	2	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	5	2	no	—
366	C₂×C₃	—	5	2	no	—
367	C₂×C₃	—	10	2	no	—
368	C₂×C₃	C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₂×C₃	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₂×C₃	M₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₅	C₃×C₄×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	5	1	no	—
375	C₂²	—	5	1	no	—
376	C₂²	—	5	2	no	—
377	C₂²	—	5	2	no	—
378	C₂²	—	5	2	no	—
379	C₂²	—	10	4	no	—
380	C₂²	—	10	4	no	—
381	C₂²	—	10	1	no	—
382	C₂²	—	10	1	no	—
383	C₂²	C₃×C₈×AGL(1,𝔽₅)	1	2	yes	complemented
384	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	5	8	no	—
387	C₄	—	5	2	no	—
388	C₄	—	10	4	no	—
389	C₄	—	10	1	no	—
390	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
391	C₃	AGL(1,𝔽₅)×C₂²⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
392	C₂	—	2	2	no	—
393	C₂	—	5	2	no	—
394	C₂	—	5	2	no	—
395	C₂	—	10	2	no	—
396	C₂	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
397	C₂	C₂×C₃×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
398	C₂	C₃×M₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	semidirect
5. C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	semidirect
6. AGL(1,𝔽₅)×C₂²⋊C₈	C₃	direct (N × H)
15. C₃×C₂²⋊#170	C₄	semidirect
16. C₃×#4003	C₄	semidirect
18. C₃×C₅×C₂²⋊C₈	C₄	semidirect
19. C₃×C₂²⋊#168	C₄	semidirect
20. C₃×#3952	C₄	semidirect
24. C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	semidirect
26. (C₂×AGL(1,𝔽₅))⋊C₈	C₂×C₃	semidirect
30. C₂²×C₃×AGL(1,𝔽₅)	C₈	semidirect
41. C₂×C₃×#170	C₂×C₄	semidirect
47. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
48. C₂×C₃×#168	C₂×C₄	semidirect
64. C₂²⋊#170	C₃×C₄	semidirect
65. #4003	C₃×C₄	semidirect
67. C₅×C₂²⋊C₈	C₃×C₄	semidirect
68. C₂²⋊#168	C₃×C₄	semidirect
69. #3952	C₃×C₄	semidirect
112. C₃×C₂²⋊C₈	AGL(1,𝔽₅)	direct (N × H)
117. C₂²×AGL(1,𝔽₅)	C₃×C₈	semidirect
128. C₂×#170	C₂×C₃×C₄	semidirect
134. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
135. C₂×#168	C₂×C₃×C₄	semidirect
145. C₂²×C₃×C₅	C₄×C₈	semidirect
151. C₂×C₃×D₅	C₄×C₈	semidirect
157. C₃×AGL(1,𝔽₅)	C₂²⋊C₈	direct (N × H)
182. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
227. C₂²⋊C₈	C₃×AGL(1,𝔽₅)	direct (N × H)
267. C₂²×C₅	C₃×C₄×C₈	semidirect
273. C₂×D₅	C₃×C₄×C₈	semidirect
279. AGL(1,𝔽₅)	C₃×C₂²⋊C₈	direct (N × H)
304. C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
308. C₃×C₅	C₄×C₂²⋊C₈	semidirect
320. C₂²×C₃	C₈×AGL(1,𝔽₅)	semidirect
371. C₅	C₃×C₄×C₂²⋊C₈	semidirect
383. C₂²	C₃×C₈×AGL(1,𝔽₅)	semidirect
391. C₃	AGL(1,𝔽₅)×C₂²⋊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
C₃×D₅⋊(C₂²⋊C₈)	2
C₂×C₃×C₈×AGL(1,𝔽₅)	2
C₃×D₅×C₂²⋊C₈	2
C₃×(C₂×AGL(1,𝔽₅))⋊C₈	2
AGL(1,𝔽₅)×C₂²⋊C₈	3
C₃×C₄×C₂²⋊C₈	5

Subgroups — C3×AGL(1,𝔽5)×C22⋊C8 #14295010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×AGL(1,𝔽₅)×C₂²⋊C₈ #14295010