Subgroups — C₃×#10604033 #14296250

Order 1920.

592 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	1	2	yes	maximal
6	#10604033	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₄	1	2	yes	—
8	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
9	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
12	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
13	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₄	1	2	yes	—
14	C₃×C₄×#170	C₄	1	2	yes	complemented
15	C₃×C₄×#170	C₄	1	2	yes	complemented
16	C₃×C₈×AGL(1,𝔽₅)	—	2	4	no	—
17	C₃×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
18	C₃×#3946	C₄	1	2	yes	complemented
19	C₃×C₄⋊#168	C₄	1	1	yes	characteristic, complemented
20	C₃×C₈×C₄⋊C₄	—	5	1	no	maximal, Hall
21	C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
22	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
23	C₄×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic
24	D₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
25	(C₂×AGL(1,𝔽₅))⋊C₈	C₂×C₃	1	2	yes	—
26	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
27	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×#170	C₂×C₄	1	2	yes	—
31	C₂×C₃×#170	C₂×C₄	1	2	yes	—
32	C₃×C₄⋊AGL(1,𝔽₅)	C₈	1	8	yes	complemented
33	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
34	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
35	C₃×D₅⋊C₈	—	2	1	no	—
36	C₃×D₅⋊C₈	—	2	1	no	—
37	C₃×D₅⋊C₈	D₄	1	2	yes	—
38	C₃×D₅⋊C₈	Q₈	1	2	yes	—
39	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
40	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
42	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
43	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×#168	C₂×C₄	1	2	yes	—
45	C₃×C₈×D₅	—	2	2	no	—
46	C₃×C₈×D₅	—	2	2	no	—
47	C₂×C₃×C₄⋊C₈	—	5	1	no	—
48	C₂×C₃×C₄×C₈	—	5	1	no	—
49	C₂×C₃×C₄×C₈	—	5	2	no	—
50	C₃×C₄×C₄⋊C₄	—	5	1	no	—
51	C₃×#336	—	5	2	no	—
52	C₂×C₄⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
53	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
54	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
55	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
57	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
58	(C₂×AGL(1,𝔽₅))⋊C₄	C₃×C₄	1	2	yes	—
59	C₄×#170	C₃×C₄	1	2	yes	complemented
60	C₄×#170	C₃×C₄	1	2	yes	complemented
61	C₈×AGL(1,𝔽₅)	—	2	4	no	—
62	C₅×C₄⋊C₈	C₃×C₄	1	1	yes	characteristic, complemented
63	#3946	C₃×C₄	1	2	yes	complemented
64	C₄⋊#168	C₃×C₄	1	1	yes	characteristic, complemented
65	C₈×C₄⋊C₄	—	5	1	no	Sylow
66	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
68	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
69	C₂×C₃×AGL(1,𝔽₅)	C₂×C₈	1	8	yes	—
70	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
74	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
75	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
76	C₃×C₄×D₅	—	2	2	no	—
77	C₃×C₄×D₅	C₂×C₈	1	4	yes	—
78	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
79	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
80	C₃×C₄×D₅	#41	1	1	yes	characteristic
81	C₃×C₄×D₅	#41	1	1	yes	characteristic
82	C₃×#170	—	2	2	no	—
83	C₃×#170	C₄⋊C₄	1	4	yes	complemented
84	C₃×C₅×C₈	—	2	2	no	—
85	C₃×#168	—	2	2	no	—
86	C₂²×C₃×C₈	—	5	1	no	—
87	C₂²×C₃×C₈	—	5	1	no	—
88	C₂²×C₃×C₈	—	5	2	no	—
89	C₂×C₃×C₄⋊C₄	—	5	2	no	—
90	C₂×C₃×C₄²	—	5	1	no	—
91	C₂×C₃×C₄²	—	5	2	no	—
92	C₃×C₄⋊C₈	—	5	2	no	—
93	C₃×C₄⋊C₈	—	5	1	no	—
94	C₃×C₄⋊C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
95	C₃×C₄×C₈	—	5	2	no	—
96	C₃×C₄×C₈	—	5	2	no	—
97	C₃×C₄×C₈	—	10	4	no	—
98	C₃×#95	—	5	2	no	—
99	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
100	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
102	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
103	C₂×#170	C₂×C₃×C₄	1	2	yes	—
104	C₂×#170	C₂×C₃×C₄	1	2	yes	—
105	C₄⋊AGL(1,𝔽₅)	C₃×C₈	1	8	yes	complemented
106	C₄×AGL(1,𝔽₅)	—	2	2	no	—
107	C₄×AGL(1,𝔽₅)	—	2	2	no	—
108	D₅⋊C₈	—	2	1	no	—
109	D₅⋊C₈	—	2	1	no	—
110	D₅⋊C₈	C₃×D₄	1	2	yes	—
111	D₅⋊C₈	C₃×Q₈	1	2	yes	—
112	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
113	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
114	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
115	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
116	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂×#168	C₂×C₃×C₄	1	2	yes	—
118	C₈×D₅	—	2	2	no	—
119	C₈×D₅	—	2	2	no	—
120	C₂×C₄⋊C₈	—	5	1	no	—
121	C₂×C₄×C₈	—	5	1	no	—
122	C₂×C₄×C₈	—	5	2	no	—
123	C₄×C₄⋊C₄	—	5	1	no	—
124	#336	—	5	2	no	—
125	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
126	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
127	C₂×C₃×D₅	C₄×Q₈	1	1	yes	characteristic
128	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
129	C₂×C₃×D₅	#131	1	2	yes	—
130	C₃×AGL(1,𝔽₅)	—	2	8	no	—
131	C₃×C₄×C₅	—	2	1	no	—
132	C₃×C₄×C₅	C₄×C₈	1	2	yes	complemented
133	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
134	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
135	C₃×Dic₅	—	2	1	no	—
136	C₃×Dic₅	C₄×C₈	1	2	yes	complemented
137	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₃×Dic₅	#117	1	1	yes	characteristic
139	C₂²×C₃×C₄	—	5	1	no	—
140	C₂²×C₃×C₄	—	5	1	no	—
141	C₂²×C₃×C₄	—	5	4	no	—
142	C₂²×C₃×C₄	—	5	1	no	—
143	C₂×C₃×C₈	—	5	2	no	—
144	C₂×C₃×C₈	—	5	2	no	—
145	C₂×C₃×C₈	—	5	2	no	—
146	C₂×C₃×C₈	—	5	2	no	—
147	C₂×C₃×C₈	—	5	2	no	—
148	C₂×C₃×C₈	—	10	2	no	—
149	C₂×C₃×C₈	—	10	2	no	—
150	C₂×C₃×C₈	—	10	1	no	—
151	C₂×C₃×C₈	—	10	1	no	—
152	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
153	C₃×C₄⋊C₄	—	5	8	no	—
154	C₃×C₄²	—	5	1	no	—
155	C₃×C₄²	—	5	1	no	—
156	C₃×C₄²	—	5	1	no	—
157	C₃×C₄²	—	10	2	no	—
158	C₃×C₄²	—	10	2	no	—
159	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
160	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
161	C₂×AGL(1,𝔽₅)	—	2	4	no	—
162	C₂×AGL(1,𝔽₅)	—	2	4	no	—
163	C₂×AGL(1,𝔽₅)	C₂×C₃×C₈	1	8	yes	—
164	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
167	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
168	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
169	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
170	C₄×D₅	—	2	2	no	—
171	C₄×D₅	C₂×C₃×C₈	1	4	yes	—
172	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
173	C₄×D₅	C₂×C₃×Q₈	1	1	yes	characteristic
174	C₄×D₅	C₃×#41	1	1	yes	characteristic
175	C₄×D₅	C₃×#41	1	1	yes	characteristic
176	#170	—	2	2	no	—
177	#170	C₃×C₄⋊C₄	1	4	yes	complemented
178	C₅×C₈	—	2	2	no	—
179	#168	—	2	2	no	—
180	C₂²×C₈	—	5	1	no	—
181	C₂²×C₈	—	5	1	no	—
182	C₂²×C₈	—	5	2	no	—
183	C₂×C₄⋊C₄	—	5	2	no	—
184	C₂×C₄²	—	5	1	no	—
185	C₂×C₄²	—	5	2	no	—
186	C₄⋊C₈	—	5	2	no	—
187	C₄⋊C₈	—	5	1	no	—
188	C₄⋊C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
189	C₄×C₈	—	5	2	no	—
190	C₄×C₈	—	5	2	no	—
191	C₄×C₈	—	10	4	no	—
192	#95	—	5	2	no	—
193	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
195	C₂×C₃×C₅	#405	1	1	yes	characteristic
196	C₃×D₅	C₈×D₄	1	2	yes	—
197	C₃×D₅	C₈×Q₈	1	2	yes	—
198	C₂³×C₃	—	5	1	no	—
199	C₂×C₃×C₄	—	5	1	no	—
200	C₂×C₃×C₄	—	5	1	no	—
201	C₂×C₃×C₄	—	5	1	no	—
202	C₂×C₃×C₄	—	5	1	no	—
203	C₂×C₃×C₄	—	5	1	no	—
204	C₂×C₃×C₄	—	5	1	no	—
205	C₂×C₃×C₄	—	5	4	no	—
206	C₂×C₃×C₄	—	5	8	no	—
207	C₂×C₃×C₄	—	5	1	no	—
208	C₂×C₃×C₄	—	10	2	no	—
209	C₂×C₃×C₄	—	10	4	no	—
210	C₂×C₃×C₄	—	10	4	no	—
211	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
212	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
214	C₃×C₈	—	2	2	no	—
215	C₃×C₈	—	5	4	no	—
216	C₃×C₈	—	10	2	no	—
217	C₃×C₈	—	10	2	no	—
218	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
219	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
220	C₂×D₅	C₃×C₄×Q₈	1	1	yes	characteristic
221	C₂×D₅	C₂²×C₃×C₈	1	2	yes	—
222	C₂×D₅	C₃×#131	1	2	yes	—
223	AGL(1,𝔽₅)	—	2	8	no	—
224	C₄×C₅	—	2	1	no	—
225	C₄×C₅	C₃×C₄×C₈	1	2	yes	complemented
226	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
227	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
228	Dic₅	—	2	1	no	—
229	Dic₅	C₃×C₄×C₈	1	2	yes	complemented
230	Dic₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
231	Dic₅	C₃×#117	1	1	yes	characteristic
232	C₂²×C₄	—	5	1	no	—
233	C₂²×C₄	—	5	1	no	—
234	C₂²×C₄	—	5	4	no	—
235	C₂²×C₄	—	5	1	no	—
236	C₂×C₈	—	5	2	no	—
237	C₂×C₈	—	5	2	no	—
238	C₂×C₈	—	5	2	no	—
239	C₂×C₈	—	5	2	no	—
240	C₂×C₈	—	5	2	no	—
241	C₂×C₈	—	10	2	no	—
242	C₂×C₈	—	10	2	no	—
243	C₂×C₈	—	10	1	no	—
244	C₂×C₈	—	10	1	no	—
245	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
246	C₄⋊C₄	—	5	8	no	—
247	C₄²	—	5	1	no	—
248	C₄²	—	5	1	no	—
249	C₄²	—	5	1	no	—
250	C₄²	—	10	2	no	—
251	C₄²	—	10	2	no	—
252	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
253	C₃×C₅	C₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
254	C₂²×C₃	—	5	1	no	—
255	C₂²×C₃	—	5	1	no	—
256	C₂²×C₃	—	5	2	no	—
257	C₂²×C₃	—	5	2	no	—
258	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
259	C₃×C₄	—	2	1	no	—
260	C₃×C₄	—	5	1	no	—
261	C₃×C₄	—	5	1	no	—
262	C₃×C₄	—	5	2	no	—
263	C₃×C₄	—	10	8	no	—
264	C₃×C₄	—	10	1	no	—
265	C₃×C₄	C₈×AGL(1,𝔽₅)	1	2	yes	complemented
266	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
268	C₂×C₅	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
269	C₂×C₅	C₂×C₃×C₄×C₈	1	1	yes	characteristic
270	C₂×C₅	C₃×#405	1	1	yes	characteristic
271	D₅	C₃×C₈×D₄	1	2	yes	—
272	D₅	C₃×C₈×Q₈	1	2	yes	—
273	C₂³	—	5	1	no	—
274	C₂×C₄	—	5	1	no	—
275	C₂×C₄	—	5	1	no	—
276	C₂×C₄	—	5	4	no	—
277	C₂×C₄	—	5	1	no	—
278	C₂×C₄	—	5	1	no	—
279	C₂×C₄	—	5	1	no	—
280	C₂×C₄	—	5	1	no	—
281	C₂×C₄	—	5	8	no	—
282	C₂×C₄	—	5	1	no	—
283	C₂×C₄	—	10	2	no	—
284	C₂×C₄	—	10	4	no	—
285	C₂×C₄	—	10	4	no	—
286	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
287	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
289	C₈	—	2	2	no	—
290	C₈	—	5	4	no	—
291	C₈	—	10	2	no	—
292	C₈	—	10	2	no	—
293	C₂×C₃	—	5	2	no	—
294	C₂×C₃	—	5	2	no	—
295	C₂×C₃	C₄⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
296	C₂×C₃	C₂×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
297	C₂×C₃	#65728	1	1	yes	characteristic
298	C₅	C₃×C₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
299	C₂²	—	5	1	no	—
300	C₂²	—	5	1	no	—
301	C₂²	—	5	2	no	—
302	C₂²	—	5	2	no	—
303	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	5	1	no	—
306	C₄	—	5	1	no	—
307	C₄	—	5	2	no	—
308	C₄	—	10	8	no	—
309	C₄	—	10	1	no	—
310	C₄	C₃×C₈×AGL(1,𝔽₅)	1	2	yes	complemented
311	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
312	C₄	C₃×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₃	#10604033	1	1	yes	characteristic, direct product factor, Sylow
314	C₂	—	5	2	no	—
315	C₂	—	5	2	no	—
316	C₂	C₃×C₄⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂	C₂×C₃×C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
318	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×C₄⋊C₈	C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₃×C₄⋊C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₈×C₄⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
6. #10604033	C₃	direct (N × H)
14. C₃×C₄×#170	C₄	semidirect
15. C₃×C₄×#170	C₄	semidirect
17. C₃×C₅×C₄⋊C₈	C₄	semidirect
18. C₃×#3946	C₄	semidirect
19. C₃×C₄⋊#168	C₄	semidirect
32. C₃×C₄⋊AGL(1,𝔽₅)	C₈	semidirect
59. C₄×#170	C₃×C₄	semidirect
60. C₄×#170	C₃×C₄	semidirect
62. C₅×C₄⋊C₈	C₃×C₄	semidirect
63. #3946	C₃×C₄	semidirect
64. C₄⋊#168	C₃×C₄	semidirect
83. C₃×#170	C₄⋊C₄	semidirect
94. C₃×C₄⋊C₈	AGL(1,𝔽₅)	semidirect
105. C₄⋊AGL(1,𝔽₅)	C₃×C₈	semidirect
132. C₃×C₄×C₅	C₄×C₈	semidirect
136. C₃×Dic₅	C₄×C₈	semidirect
177. #170	C₃×C₄⋊C₄	semidirect
188. C₄⋊C₈	C₃×AGL(1,𝔽₅)	semidirect
225. C₄×C₅	C₃×C₄×C₈	semidirect
229. Dic₅	C₃×C₄×C₈	semidirect
253. C₃×C₅	C₈×C₄⋊C₄	semidirect
265. C₃×C₄	C₈×AGL(1,𝔽₅)	semidirect
298. C₅	C₃×C₈×C₄⋊C₄	semidirect
310. C₄	C₃×C₈×AGL(1,𝔽₅)	semidirect
313. C₃	#10604033	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×C₈×AGL(1,𝔽₅)	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×C₄×D₅⋊C₈	2
C₃×D₅×C₄⋊C₈	2
C₃×(C₂×AGL(1,𝔽₅))⋊C₈	2
#10604033	3
C₃×C₈×C₄⋊C₄	5

Subgroups — C3×#10604033 #14296250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604033 #14296250