Subgroups — C₅×#69478 #14296367

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₅×#4524	C₂	1	1	yes	maximal, characteristic
7	C₅×#4524	C₂	1	1	yes	maximal, characteristic
8	C₅×#1771	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#95	C₄	1	2	yes	—
18	C₅×C₄⋊(C₃⋊C₈)	C₄	1	4	yes	complemented
19	C₅×#803	—	2	2	no	—
20	C₅×#803	C₄	1	4	yes	complemented
21	C₄×C₅×C₃⋊C₈	—	2	2	no	—
22	#69478	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₅×C₄⋊C₈	—	3	1	no	—
24	C₂×C₅×#97	—	3	1	no	—
25	C₂×C₅×#97	—	3	1	no	—
26	C₂×C₄×C₅×C₈	—	3	1	no	—
27	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic
28	C₅×#336	—	3	1	no	—
29	C₅×#336	—	3	1	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₃×C₅×C₄⋊C₄	—	2	4	no	—
36	C₃×C₄²×C₅	—	2	1	no	—
37	C₃×C₄²×C₅	—	2	1	no	—
38	C₃×C₄²×C₅	—	2	1	no	—
39	C₃×C₄²×C₅	—	2	1	no	—
40	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
41	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
42	C₂×C₅×C₃⋊C₈	—	2	1	no	—
43	C₂×C₅×C₃⋊C₈	—	2	1	no	—
44	C₂×C₅×C₃⋊C₈	—	2	1	no	—
45	C₂×C₅×C₃⋊C₈	—	2	1	no	—
46	C₂×C₅×C₃⋊C₈	—	2	1	no	—
47	C₂×C₅×C₃⋊C₈	—	2	1	no	—
48	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
49	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
50	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
51	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
53	C₂×C₅×C₃⋊C₈	Q₈	1	2	yes	—
54	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
55	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic
56	C₂×#803	C₂×C₅	1	1	yes	characteristic
57	C₂×#803	C₂×C₅	1	1	yes	characteristic
58	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic
59	#4524	C₂×C₅	1	1	yes	characteristic
60	#4524	C₂×C₅	1	1	yes	characteristic
61	C₂²×C₅×C₈	—	3	1	no	—
62	C₂²×C₅×C₈	—	3	1	no	—
63	C₂²×C₅×C₈	—	3	1	no	—
64	C₂²×C₅×C₈	—	3	1	no	—
65	C₂×C₅×C₄⋊C₄	Dic₃	1	2	yes	—
66	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
69	C₅×C₄⋊C₈	—	3	4	no	—
70	C₅×#97	—	3	4	no	—
71	C₅×#97	—	6	2	no	—
72	C₄×C₅×C₈	—	6	2	no	—
73	C₅×#95	Dic₃	1	2	yes	—
74	#1771	—	3	1	no	Sylow
75	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
85	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
92	C₅×C₃⋊C₈	—	2	2	no	—
93	C₅×C₃⋊C₈	—	2	2	no	—
94	C₅×C₃⋊C₈	—	2	2	no	—
95	C₅×C₃⋊C₈	C₄⋊C₄	1	4	yes	complemented
96	C₂×C₃×C₄⋊C₄	C₄×C₅	1	2	yes	—
97	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
98	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
99	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
100	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
101	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
103	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
104	C₃×#95	C₄×C₅	1	2	yes	—
105	C₄⋊(C₃⋊C₈)	C₄×C₅	1	4	yes	complemented
106	#803	—	2	2	no	—
107	#803	C₄×C₅	1	4	yes	complemented
108	C₄×C₃⋊C₈	—	2	2	no	—
109	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
110	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
111	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
114	C₂×C₅×C₈	—	3	2	no	—
115	C₂×C₅×C₈	—	3	2	no	—
116	C₂×C₅×C₈	—	3	2	no	—
117	C₂×C₅×C₈	—	3	2	no	—
118	C₂×C₅×C₈	—	3	2	no	—
119	C₂×C₅×C₈	—	3	2	no	—
120	C₂×C₅×C₈	—	6	1	no	—
121	C₂×C₅×C₈	—	6	1	no	—
122	C₂×C₅×C₈	—	6	1	no	—
123	C₂×C₅×C₈	—	6	1	no	—
124	C₂×C₅×C₈	—	6	1	no	—
125	C₂×C₅×C₈	—	6	1	no	—
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₄²×C₅	—	2	1	no	—
128	C₄²×C₅	—	2	1	no	—
129	C₄²×C₅	—	2	1	no	—
130	C₄²×C₅	—	2	1	no	—
131	C₄²×C₅	C₄×D₃	1	2	yes	—
132	C₄²×C₅	C₄×D₃	1	2	yes	—
133	C₂×C₄⋊C₈	—	3	1	no	—
134	C₂×#97	—	3	1	no	—
135	C₂×#97	—	3	1	no	—
136	C₂×C₄×C₈	—	3	1	no	—
137	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic
138	#336	—	3	1	no	—
139	#336	—	3	1	no	—
140	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
141	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
142	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
144	C₂²×C₃×C₅	#131	1	2	yes	—
145	C₃×C₄×C₅	—	2	2	no	—
146	C₃×C₄×C₅	—	2	2	no	—
147	C₃×C₄×C₅	—	2	4	no	—
148	C₃×C₄×C₅	—	4	2	no	—
149	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₃×C₄×C₅	#117	1	1	yes	characteristic
151	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
152	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
154	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
157	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
158	C₃×C₄⋊C₄	—	2	4	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	—	2	1	no	—
161	C₃×C₄²	—	2	1	no	—
162	C₃×C₄²	—	2	1	no	—
163	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
164	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
165	C₂×C₃⋊C₈	—	2	1	no	—
166	C₂×C₃⋊C₈	—	2	1	no	—
167	C₂×C₃⋊C₈	—	2	1	no	—
168	C₂×C₃⋊C₈	—	2	1	no	—
169	C₂×C₃⋊C₈	—	2	1	no	—
170	C₂×C₃⋊C₈	—	2	1	no	—
171	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
172	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
173	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
174	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
175	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
176	C₂×C₃⋊C₈	C₅×Q₈	1	2	yes	—
177	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	#208	1	4	yes	—
186	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
187	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
188	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
190	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	#237	1	1	yes	characteristic
192	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₅	#239	1	1	yes	characteristic
194	C₅×C₈	—	3	4	no	—
195	C₅×C₈	—	6	2	no	—
196	C₅×C₈	—	6	2	no	—
197	C₅×C₈	—	6	2	no	—
198	C₂²×C₈	—	3	1	no	—
199	C₂²×C₈	—	3	1	no	—
200	C₂²×C₈	—	3	1	no	—
201	C₂²×C₈	—	3	1	no	—
202	C₂×C₄⋊C₄	C₅×Dic₃	1	2	yes	—
203	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
205	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
206	C₄⋊C₈	—	3	4	no	—
207	#97	—	3	4	no	—
208	#97	—	6	2	no	—
209	C₄×C₈	—	6	2	no	—
210	#95	C₅×Dic₃	1	2	yes	—
211	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
213	C₂×C₃×C₅	#405	1	1	yes	characteristic
214	C₂×C₃×C₅	#435	1	2	yes	—
215	C₂×C₃×C₅	#446	1	2	yes	—
216	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
225	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
226	C₂×C₃×C₄	C₅×M₁₆	1	4	yes	—
227	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
231	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
232	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
233	C₃⋊C₈	—	2	2	no	—
234	C₃⋊C₈	—	2	2	no	—
235	C₃⋊C₈	—	2	2	no	—
236	C₃⋊C₈	C₅×C₄⋊C₄	1	4	yes	complemented
237	C₂²×C₅	C₂×#208	1	2	yes	—
238	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
239	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
240	C₂²×C₅	Q₈×Dic₃	1	1	yes	characteristic
241	C₂²×C₅	#948	1	2	yes	—
242	C₄×C₅	—	2	2	no	—
243	C₄×C₅	—	2	2	no	—
244	C₄×C₅	—	2	4	no	—
245	C₄×C₅	—	4	2	no	—
246	C₄×C₅	#887	1	1	yes	characteristic
247	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
248	C₄×C₅	#892	1	1	yes	characteristic
249	C₄×C₅	#893	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
251	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
252	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
253	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
255	C₂×C₈	—	3	2	no	—
256	C₂×C₈	—	3	2	no	—
257	C₂×C₈	—	3	2	no	—
258	C₂×C₈	—	3	2	no	—
259	C₂×C₈	—	3	2	no	—
260	C₂×C₈	—	3	2	no	—
261	C₂×C₈	—	6	1	no	—
262	C₂×C₈	—	6	1	no	—
263	C₂×C₈	—	6	1	no	—
264	C₂×C₈	—	6	1	no	—
265	C₂×C₈	—	6	1	no	—
266	C₂×C₈	—	6	1	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄²	—	2	1	no	—
269	C₄²	—	2	1	no	—
270	C₄²	—	2	1	no	—
271	C₄²	—	2	1	no	—
272	C₄²	C₄×C₅×D₃	1	2	yes	—
273	C₄²	C₄×C₅×D₃	1	2	yes	—
274	C₃×C₅	#1771	1	1	yes	characteristic, complemented, Hall
275	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
276	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
277	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
278	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
279	C₂²×C₃	C₅×#131	1	2	yes	—
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	—	2	2	no	—
282	C₃×C₄	—	2	4	no	—
283	C₃×C₄	—	4	2	no	—
284	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
285	C₃×C₄	C₅×#117	1	1	yes	characteristic
286	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
287	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
288	C₂×C₅	C₄×#208	1	1	yes	characteristic
289	C₂×C₅	Dic₃×C₄⋊C₄	1	1	yes	characteristic
290	C₂×C₅	#4997	1	1	yes	characteristic
291	C₂×C₅	#5011	1	2	yes	—
292	C₂×C₅	#5024	1	2	yes	—
293	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	C₅×#208	1	4	yes	—
302	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
303	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
304	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
305	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
306	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
307	C₂×C₄	C₅×#237	1	1	yes	characteristic
308	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
309	C₂×C₄	C₅×#239	1	1	yes	characteristic
310	C₈	—	3	4	no	—
311	C₈	—	6	2	no	—
312	C₈	—	6	2	no	—
313	C₈	—	6	2	no	—
314	C₂×C₃	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
315	C₂×C₃	C₄×C₅×M₁₆	1	1	yes	characteristic
316	C₂×C₃	C₅×#405	1	1	yes	characteristic
317	C₂×C₃	C₅×#435	1	2	yes	—
318	C₂×C₃	C₅×#446	1	2	yes	—
319	C₅	#69478	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²	C₂×C₅×#208	1	2	yes	—
321	C₂²	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
322	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
323	C₂²	C₅×Q₈×Dic₃	1	1	yes	characteristic
324	C₂²	C₅×#948	1	2	yes	—
325	C₄	—	2	2	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	4	no	—
328	C₄	—	4	2	no	—
329	C₄	C₅×#887	1	1	yes	characteristic
330	C₄	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
331	C₄	C₅×#892	1	1	yes	characteristic
332	C₄	C₅×#893	1	1	yes	characteristic
333	C₃	C₅×#1771	1	1	yes	characteristic, complemented, Sylow
334	C₂	C₄×C₅×#208	1	1	yes	characteristic
335	C₂	C₅×Dic₃×C₄⋊C₄	1	1	yes	characteristic
336	C₂	C₅×#4997	1	1	yes	characteristic
337	C₂	C₅×#5011	1	2	yes	—
338	C₂	C₅×#5024	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#1771
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
18. C₅×C₄⋊(C₃⋊C₈)	C₄	semidirect
20. C₅×#803	C₄	semidirect
22. #69478	C₅	direct (N × H)
95. C₅×C₃⋊C₈	C₄⋊C₄	semidirect
105. C₄⋊(C₃⋊C₈)	C₄×C₅	semidirect
107. #803	C₄×C₅	semidirect
236. C₃⋊C₈	C₅×C₄⋊C₄	semidirect
274. C₃×C₅	#1771	semidirect
319. C₅	#69478	direct (N × H)
333. C₃	C₅×#1771	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄×C₅×C₄⋊C₄	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#803	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#4524	2
C₅×#1771	3
#69478	5

Subgroups — C5×#69478 #14296367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69478 #14296367