Subgroups — C₃×#10603913 #14295160

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₂²⋊AGL(1,𝔽₅)	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	#10603913	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₄	1	2	yes	—
9	C₂²×C₃×#170	C₄	1	2	yes	complemented
10	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
11	C₂×C₃×D₅⋊C₈	—	2	4	no	—
12	C₂×C₃×D₅⋊C₈	C₄	1	2	yes	complemented
13	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
16	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₄	1	2	yes	—
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×C₈×C₂²⋊C₄	—	5	1	no	maximal, Hall
22	C₂²×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₄×C₂²⋊AGL(1,𝔽₅)	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)	C₂×C₄	1	4	yes	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₄×D₅	—	2	2	no	—
32	C₂×C₃×C₄×D₅	—	2	2	no	—
33	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
37	C₃×C₂²⋊AGL(1,𝔽₅)	C₈	1	8	yes	complemented
38	C₂×C₃×#170	—	2	4	no	—
39	C₂×C₃×#170	C₂×C₄	1	2	yes	—
40	C₂×C₃×#170	C₂×C₄	1	2	yes	—
41	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
42	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
43	C₃×D₅⋊C₈	—	2	2	no	—
44	C₃×D₅⋊C₈	—	2	4	no	—
45	C₃×D₅⋊C₈	D₄	1	4	yes	—
46	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
47	C₂×C₃×#168	C₂×C₄	1	2	yes	—
48	C₃×C₈×D₅	—	2	2	no	—
49	C₃×C₈×D₅	—	2	2	no	—
50	C₂³×C₃×C₈	—	5	1	no	—
51	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
52	C₂×C₃×C₄×C₈	—	5	2	no	—
53	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
54	C₃×#336	—	5	2	no	—
55	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₂²⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
57	C₂²×#170	C₃×C₄	1	2	yes	complemented
58	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
59	C₂×D₅⋊C₈	—	2	4	no	—
60	C₂×D₅⋊C₈	C₃×C₄	1	2	yes	complemented
61	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
62	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
64	(C₂×AGL(1,𝔽₅))⋊C₄	C₃×C₄	1	2	yes	—
65	C₈×AGL(1,𝔽₅)	—	2	4	no	—
66	C₅×C₂²⋊C₈	C₃×C₄	1	1	yes	characteristic, complemented
67	C₂²⋊#168	C₃×C₄	1	1	yes	characteristic, complemented
68	#3952	C₃×C₄	1	2	yes	complemented
69	C₈×C₂²⋊C₄	—	5	1	no	Sylow
70	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
71	C₂²×C₃×D₅	—	2	2	no	—
72	C₂²×C₃×D₅	—	2	2	no	—
73	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
74	C₂²×C₃×D₅	C₂×C₈	1	4	yes	—
75	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
77	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
78	C₂×C₃×AGL(1,𝔽₅)	C₂×C₈	1	8	yes	complemented
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₃×Dic₅	—	2	1	no	—
83	C₂×C₃×Dic₅	—	2	1	no	—
84	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
85	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
86	C₃×C₄×D₅	—	2	2	no	—
87	C₃×C₄×D₅	—	2	2	no	—
88	C₃×C₄×D₅	—	2	1	no	—
89	C₃×C₄×D₅	—	2	1	no	—
90	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
91	C₃×C₄×D₅	#41	1	2	yes	—
92	C₃×#170	—	2	2	no	—
93	C₃×#170	C₂²⋊C₄	1	4	yes	complemented
94	C₃×C₅×C₈	—	2	2	no	—
95	C₃×#168	—	2	2	no	—
96	C₂³×C₃×C₄	—	5	1	no	—
97	C₂²×C₃×C₈	—	5	1	no	—
98	C₂²×C₃×C₈	—	5	2	no	—
99	C₂²×C₃×C₈	—	5	1	no	—
100	C₂²×C₃×C₈	—	5	2	no	—
101	C₂²×C₃×C₈	—	5	2	no	—
102	C₂²×C₃×C₈	—	10	4	no	—
103	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
104	C₂×C₃×C₄²	—	5	2	no	—
105	C₃×C₂²⋊C₈	—	5	1	no	—
106	C₃×C₂²⋊C₈	—	5	2	no	—
107	C₃×C₂²⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
108	C₃×C₄×C₈	—	10	4	no	—
109	C₃×#95	—	5	2	no	—
110	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
111	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
112	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
114	C₂×C₄×D₅	—	2	2	no	—
115	C₂×C₄×D₅	—	2	2	no	—
116	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
120	C₂²⋊AGL(1,𝔽₅)	C₃×C₈	1	8	yes	complemented
121	C₂×#170	—	2	4	no	—
122	C₂×#170	C₂×C₃×C₄	1	2	yes	—
123	C₂×#170	C₂×C₃×C₄	1	2	yes	—
124	C₄×AGL(1,𝔽₅)	—	2	2	no	—
125	C₄×AGL(1,𝔽₅)	—	2	2	no	—
126	D₅⋊C₈	—	2	2	no	—
127	D₅⋊C₈	—	2	4	no	—
128	D₅⋊C₈	C₃×D₄	1	4	yes	—
129	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
130	C₂×#168	C₂×C₃×C₄	1	2	yes	—
131	C₈×D₅	—	2	2	no	—
132	C₈×D₅	—	2	2	no	—
133	C₂³×C₈	—	5	1	no	—
134	C₂×C₂²⋊C₈	—	5	1	no	—
135	C₂×C₄×C₈	—	5	2	no	—
136	C₄×C₂²⋊C₄	—	5	1	no	—
137	#336	—	5	2	no	—
138	C₂²×C₃×C₅	—	2	1	no	—
139	C₂²×C₃×C₅	—	2	1	no	—
140	C₂²×C₃×C₅	C₄×C₈	1	2	yes	complemented
141	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₃×D₅	—	2	1	no	—
143	C₂×C₃×D₅	—	2	1	no	—
144	C₂×C₃×D₅	—	2	8	no	—
145	C₂×C₃×D₅	C₄×C₈	1	2	yes	complemented
146	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
147	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
148	C₂×C₃×D₅	#131	1	2	yes	—
149	C₃×AGL(1,𝔽₅)	—	2	8	no	—
150	C₃×C₄×C₅	—	2	1	no	—
151	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
152	C₃×Dic₅	—	2	1	no	—
153	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₃×Dic₅	#117	1	1	yes	characteristic
155	C₂⁴×C₃	—	5	1	no	—
156	C₂²×C₃×C₄	—	5	1	no	—
157	C₂²×C₃×C₄	—	5	4	no	—
158	C₂²×C₃×C₄	—	5	1	no	—
159	C₂²×C₃×C₄	—	5	1	no	—
160	C₂²×C₃×C₄	—	5	1	no	—
161	C₂²×C₃×C₄	—	5	1	no	—
162	C₂²×C₃×C₄	—	10	2	no	—
163	C₂²×C₃×C₄	—	10	2	no	—
164	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
165	C₂×C₃×C₈	—	5	4	no	—
166	C₂×C₃×C₈	—	5	2	no	—
167	C₂×C₃×C₈	—	5	2	no	—
168	C₂×C₃×C₈	—	5	2	no	—
169	C₂×C₃×C₈	—	10	2	no	—
170	C₂×C₃×C₈	—	10	2	no	—
171	C₂×C₃×C₈	—	10	4	no	—
172	C₂×C₃×C₈	—	10	4	no	—
173	C₂×C₃×C₈	—	10	2	no	—
174	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
175	C₃×C₂²⋊C₄	—	5	8	no	—
176	C₃×C₄²	—	10	2	no	—
177	C₃×C₄²	—	10	2	no	—
178	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
179	C₂²×D₅	—	2	2	no	—
180	C₂²×D₅	—	2	2	no	—
181	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
182	C₂²×D₅	C₂×C₃×C₈	1	4	yes	—
183	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
184	C₂×AGL(1,𝔽₅)	—	2	4	no	—
185	C₂×AGL(1,𝔽₅)	—	2	4	no	—
186	C₂×AGL(1,𝔽₅)	C₂×C₃×C₈	1	8	yes	complemented
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
190	C₂×Dic₅	—	2	1	no	—
191	C₂×Dic₅	—	2	1	no	—
192	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
193	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
194	C₄×D₅	—	2	2	no	—
195	C₄×D₅	—	2	2	no	—
196	C₄×D₅	—	2	1	no	—
197	C₄×D₅	—	2	1	no	—
198	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
199	C₄×D₅	C₃×#41	1	2	yes	—
200	#170	—	2	2	no	—
201	#170	C₃×C₂²⋊C₄	1	4	yes	complemented
202	C₅×C₈	—	2	2	no	—
203	#168	—	2	2	no	—
204	C₂³×C₄	—	5	1	no	—
205	C₂²×C₈	—	5	1	no	—
206	C₂²×C₈	—	5	2	no	—
207	C₂²×C₈	—	5	1	no	—
208	C₂²×C₈	—	5	2	no	—
209	C₂²×C₈	—	5	2	no	—
210	C₂²×C₈	—	10	4	no	—
211	C₂×C₂²⋊C₄	—	5	2	no	—
212	C₂×C₄²	—	5	2	no	—
213	C₂²⋊C₈	—	5	1	no	—
214	C₂²⋊C₈	—	5	2	no	—
215	C₂²⋊C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
216	C₄×C₈	—	10	4	no	—
217	#95	—	5	2	no	—
218	C₂×C₃×C₅	—	2	2	no	—
219	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
221	C₂×C₃×C₅	#405	1	1	yes	characteristic
222	C₃×D₅	—	2	2	no	—
223	C₃×D₅	C₈×D₄	1	4	yes	—
224	C₂³×C₃	—	5	1	no	—
225	C₂³×C₃	—	5	1	no	—
226	C₂³×C₃	—	5	4	no	—
227	C₂³×C₃	—	10	2	no	—
228	C₂³×C₃	—	10	2	no	—
229	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	5	1	no	—
232	C₂×C₃×C₄	—	5	2	no	—
233	C₂×C₃×C₄	—	5	2	no	—
234	C₂×C₃×C₄	—	5	8	no	—
235	C₂×C₃×C₄	—	5	1	no	—
236	C₂×C₃×C₄	—	10	1	no	—
237	C₂×C₃×C₄	—	10	1	no	—
238	C₂×C₃×C₄	—	10	2	no	—
239	C₂×C₃×C₄	—	10	1	no	—
240	C₂×C₃×C₄	—	10	1	no	—
241	C₂×C₃×C₄	—	10	4	no	—
242	C₂×C₃×C₄	—	10	4	no	—
243	C₂×C₃×C₄	—	10	2	no	—
244	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
246	C₃×C₈	—	2	2	no	—
247	C₃×C₈	—	5	4	no	—
248	C₃×C₈	—	10	2	no	—
249	C₃×C₈	—	10	2	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	C₃×C₄×C₈	1	2	yes	complemented
253	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
254	C₂×D₅	—	2	1	no	—
255	C₂×D₅	—	2	1	no	—
256	C₂×D₅	—	2	8	no	—
257	C₂×D₅	C₃×C₄×C₈	1	2	yes	complemented
258	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
259	C₂×D₅	C₂²×C₃×C₈	1	2	yes	—
260	C₂×D₅	C₃×#131	1	2	yes	—
261	AGL(1,𝔽₅)	—	2	8	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
264	Dic₅	—	2	1	no	—
265	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
266	Dic₅	C₃×#117	1	1	yes	characteristic
267	C₂⁴	—	5	1	no	—
268	C₂²×C₄	—	5	1	no	—
269	C₂²×C₄	—	5	4	no	—
270	C₂²×C₄	—	5	1	no	—
271	C₂²×C₄	—	5	1	no	—
272	C₂²×C₄	—	5	1	no	—
273	C₂²×C₄	—	5	1	no	—
274	C₂²×C₄	—	10	2	no	—
275	C₂²×C₄	—	10	2	no	—
276	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
277	C₂×C₈	—	5	4	no	—
278	C₂×C₈	—	5	2	no	—
279	C₂×C₈	—	5	2	no	—
280	C₂×C₈	—	5	2	no	—
281	C₂×C₈	—	10	2	no	—
282	C₂×C₈	—	10	2	no	—
283	C₂×C₈	—	10	4	no	—
284	C₂×C₈	—	10	4	no	—
285	C₂×C₈	—	10	2	no	—
286	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
287	C₂²⋊C₄	—	5	8	no	—
288	C₄²	—	10	2	no	—
289	C₄²	—	10	2	no	—
290	C₃×C₅	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	5	2	no	—
294	C₂²×C₃	—	5	2	no	—
295	C₂²×C₃	—	5	2	no	—
296	C₂²×C₃	—	5	2	no	—
297	C₂²×C₃	—	10	8	no	—
298	C₂²×C₃	—	10	1	no	—
299	C₂²×C₃	—	10	1	no	—
300	C₂²×C₃	C₈×AGL(1,𝔽₅)	1	2	yes	complemented
301	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	5	1	no	—
304	C₃×C₄	—	5	1	no	—
305	C₃×C₄	—	10	8	no	—
306	C₃×C₄	—	10	1	no	—
307	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
308	C₂×C₅	—	2	2	no	—
309	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
311	C₂×C₅	C₃×#405	1	1	yes	characteristic
312	D₅	—	2	2	no	—
313	D₅	C₃×C₈×D₄	1	4	yes	—
314	C₂³	—	5	1	no	—
315	C₂³	—	5	4	no	—
316	C₂³	—	5	1	no	—
317	C₂³	—	10	2	no	—
318	C₂³	—	10	2	no	—
319	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	5	1	no	—
322	C₂×C₄	—	5	2	no	—
323	C₂×C₄	—	5	2	no	—
324	C₂×C₄	—	5	8	no	—
325	C₂×C₄	—	5	1	no	—
326	C₂×C₄	—	10	1	no	—
327	C₂×C₄	—	10	1	no	—
328	C₂×C₄	—	10	2	no	—
329	C₂×C₄	—	10	1	no	—
330	C₂×C₄	—	10	1	no	—
331	C₂×C₄	—	10	4	no	—
332	C₂×C₄	—	10	4	no	—
333	C₂×C₄	—	10	2	no	—
334	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	5	4	no	—
338	C₈	—	10	2	no	—
339	C₈	—	10	2	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	5	4	no	—
342	C₂×C₃	—	10	2	no	—
343	C₂×C₃	C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
344	C₂×C₃	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₂×C₃	#65728	1	1	yes	characteristic
346	C₅	C₃×C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	5	2	no	—
350	C₂²	—	5	2	no	—
351	C₂²	—	5	2	no	—
352	C₂²	—	5	2	no	—
353	C₂²	—	10	8	no	—
354	C₂²	—	10	1	no	—
355	C₂²	—	10	1	no	—
356	C₂²	C₃×C₈×AGL(1,𝔽₅)	1	2	yes	complemented
357	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	5	1	no	—
360	C₄	—	5	1	no	—
361	C₄	—	10	8	no	—
362	C₄	—	10	1	no	—
363	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
364	C₃	#10603913	1	1	yes	characteristic, direct product factor, Sylow
365	C₂	—	2	2	no	—
366	C₂	—	5	4	no	—
367	C₂	—	10	2	no	—
368	C₂	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₂	C₂×C₃×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₂	C₃×#65728	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×C₈×C₂²⋊C₄
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. #10603913	C₃	direct (N × H)
9. C₂²×C₃×#170	C₄	semidirect
12. C₂×C₃×D₅⋊C₈	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
37. C₃×C₂²⋊AGL(1,𝔽₅)	C₈	semidirect
57. C₂²×#170	C₃×C₄	semidirect
60. C₂×D₅⋊C₈	C₃×C₄	semidirect
66. C₅×C₂²⋊C₈	C₃×C₄	semidirect
67. C₂²⋊#168	C₃×C₄	semidirect
68. #3952	C₃×C₄	semidirect
78. C₂×C₃×AGL(1,𝔽₅)	C₂×C₈	semidirect
93. C₃×#170	C₂²⋊C₄	semidirect
107. C₃×C₂²⋊C₈	AGL(1,𝔽₅)	semidirect
120. C₂²⋊AGL(1,𝔽₅)	C₃×C₈	semidirect
140. C₂²×C₃×C₅	C₄×C₈	semidirect
145. C₂×C₃×D₅	C₄×C₈	semidirect
186. C₂×AGL(1,𝔽₅)	C₂×C₃×C₈	semidirect
201. #170	C₃×C₂²⋊C₄	semidirect
215. C₂²⋊C₈	C₃×AGL(1,𝔽₅)	semidirect
252. C₂²×C₅	C₃×C₄×C₈	semidirect
257. C₂×D₅	C₃×C₄×C₈	semidirect
290. C₃×C₅	C₈×C₂²⋊C₄	semidirect
300. C₂²×C₃	C₈×AGL(1,𝔽₅)	semidirect
346. C₅	C₃×C₈×C₂²⋊C₄	semidirect
356. C₂²	C₃×C₈×AGL(1,𝔽₅)	semidirect
364. C₃	#10603913	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×D₅⋊C₈	2
C₃×C₄×C₂²⋊AGL(1,𝔽₅)	2
C₂×C₃×C₈×AGL(1,𝔽₅)	2
C₃×D₅×C₂²⋊C₈	2
C₃×(C₂×AGL(1,𝔽₅))⋊C₈	2
#10603913	3
C₃×C₈×C₂²⋊C₄	5

Subgroups — C3×#10603913 #14295160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10603913 #14295160