Subgroups — C₅×#70757 #14281689

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4459	C₂	1	4	yes	maximal, complemented
5	C₅×#1478	—	3	1	no	maximal, Hall
6	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₅×D₃	—	2	1	no	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
10	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
11	C₄×C₅×D₁₂	—	2	1	no	—
12	C₄×C₅×D₁₂	—	2	1	no	—
13	C₄×C₅×D₁₂	C₄	1	2	yes	—
14	C₄×C₅×D₁₂	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊C₈	—	2	1	no	—
16	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
17	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
18	C₅×#830	—	2	1	no	—
19	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
20	C₄×C₅×C₃⋊C₈	—	2	1	no	—
21	#70757	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₄×C₅×D₄	—	3	1	no	—
23	C₅×#431	—	3	1	no	—
24	C₅×#431	D₃	1	1	yes	characteristic, complemented
25	C₅×D₄⋊C₈	—	3	4	no	—
26	C₂³×C₅×D₃	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂²×C₅×Dic₃	—	2	1	no	—
31	C₂×C₅×D₁₂	—	2	1	no	—
32	C₂×C₅×D₁₂	—	2	2	no	—
33	C₂×C₅×D₁₂	C₈	1	4	yes	complemented
34	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
35	C₂×C₄×C₅×D₃	—	2	2	no	—
36	C₂×C₄×C₅×D₃	—	2	2	no	—
37	C₂×C₄×C₅×D₃	—	4	4	no	—
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
44	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
45	C₅×C₄⋊Dic₃	—	2	1	no	—
46	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
47	C₂×C₅×C₃⋊C₈	—	2	2	no	—
48	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
49	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
50	#4925	C₂×C₅	1	1	yes	characteristic, complemented
51	#4459	C₂×C₅	1	4	yes	complemented
52	C₂²×C₅×D₄	—	3	1	no	—
53	C₂³×C₄×C₅	—	6	1	no	—
54	C₄×C₅×D₄	—	3	2	no	—
55	C₄×C₅×D₄	—	3	2	no	—
56	C₄×C₅×D₄	—	6	1	no	—
57	C₄×C₅×D₄	—	6	1	no	—
58	C₂×C₅×C₄⋊C₄	—	3	1	no	—
59	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
60	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
61	C₅×C₄⋊C₈	—	2	1	no	—
62	C₅×C₄⋊C₈	—	3	2	no	—
63	C₅×C₂²⋊C₈	—	2	1	no	—
64	C₅×C₂²⋊C₈	—	6	1	no	—
65	C₄×C₅×C₈	—	6	1	no	—
66	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
67	#1478	—	3	1	no	Sylow
68	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₅×D₃	—	2	4	no	—
70	C₂²×C₅×D₃	—	2	2	no	—
71	C₂²×C₅×D₃	—	4	2	no	—
72	C₂²×C₅×D₃	—	4	2	no	—
73	C₂×C₃×C₄×C₅	—	2	2	no	—
74	C₂×C₃×C₄×C₅	—	4	1	no	—
75	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
79	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₅×Dic₃	—	2	2	no	—
84	C₂×C₅×Dic₃	—	4	2	no	—
85	C₅×D₁₂	—	2	4	no	—
86	C₅×D₁₂	—	2	2	no	—
87	C₅×D₁₂	C₂×C₈	1	4	yes	—
88	C₄×C₅×D₃	—	4	4	no	—
89	C₄×C₅×D₃	—	4	4	no	—
90	C₃×C₅×C₈	—	4	2	no	—
91	C₅×C₃⋊C₈	—	4	2	no	—
92	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic
93	C₂²×C₄×D₃	—	2	1	no	—
94	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
95	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
96	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic
97	C₄×D₁₂	—	2	1	no	—
98	C₄×D₁₂	—	2	1	no	—
99	C₄×D₁₂	C₄×C₅	1	2	yes	—
100	C₄×D₁₂	C₂²×C₅	1	2	yes	—
101	C₃×C₄⋊C₈	—	2	1	no	—
102	C₃×C₂²⋊C₈	—	2	1	no	—
103	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
104	#830	—	2	1	no	—
105	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
106	C₄×C₃⋊C₈	—	2	1	no	—
107	C₂⁴×C₅	—	6	1	no	—
108	C₂×C₅×D₄	—	3	4	no	—
109	C₂×C₅×D₄	—	3	2	no	—
110	C₂×C₅×D₄	—	6	2	no	—
111	C₂×C₅×D₄	—	6	1	no	—
112	C₂²×C₄×C₅	—	6	1	no	—
113	C₂²×C₄×C₅	—	6	2	no	—
114	C₂²×C₄×C₅	—	6	2	no	—
115	C₂²×C₄×C₅	—	12	4	no	—
116	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
118	C₂²×C₄×C₅	#67	1	1	yes	characteristic
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	6	2	no	—
121	C₅×C₄⋊C₄	—	3	2	no	—
122	C₅×C₄⋊C₄	—	6	1	no	—
123	C₅×C₂²⋊C₄	—	6	2	no	—
124	C₅×C₂²⋊C₄	—	6	2	no	—
125	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
126	C₄²×C₅	D₁₂	1	1	yes	characteristic
127	C₄²×C₅	#67	1	1	yes	characteristic
128	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₄×D₄	—	3	1	no	—
130	#431	—	3	1	no	—
131	#431	C₅×D₃	1	1	yes	characteristic, complemented
132	D₄⋊C₈	—	3	4	no	—
133	C₂²×C₃×C₅	—	2	1	no	—
134	C₂²×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
136	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₅×D₃	—	2	4	no	—
138	C₂×C₅×D₃	—	4	8	no	—
139	C₂×C₅×D₃	—	4	2	no	—
140	C₂×C₅×D₃	—	4	2	no	—
141	C₃×C₄×C₅	—	2	1	no	—
142	C₃×C₄×C₅	—	2	1	no	—
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
145	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
146	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
147	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
148	C₅×Dic₃	—	4	2	no	—
149	C₂³×D₃	—	2	1	no	—
150	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
153	C₂²×Dic₃	—	2	1	no	—
154	C₂×D₁₂	—	2	1	no	—
155	C₂×D₁₂	—	2	2	no	—
156	C₂×D₁₂	C₅×C₈	1	4	yes	complemented
157	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
158	C₂×C₄×D₃	—	2	2	no	—
159	C₂×C₄×D₃	—	2	2	no	—
160	C₂×C₄×D₃	—	4	4	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
163	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
164	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
165	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
166	(C₂×D₃)⋊C₄	—	2	2	no	—
167	(C₂×D₃)⋊C₄	—	2	2	no	—
168	C₄⋊Dic₃	—	2	1	no	—
169	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
170	C₂×C₃⋊C₈	—	2	2	no	—
171	C₂³×C₅	—	6	4	no	—
172	C₂³×C₅	—	6	2	no	—
173	C₂³×C₅	—	12	2	no	—
174	C₂³×C₅	—	12	2	no	—
175	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
176	C₅×D₄	—	3	4	no	—
177	C₅×D₄	—	6	4	no	—
178	C₅×D₄	—	6	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	6	2	no	—
182	C₂×C₄×C₅	—	12	4	no	—
183	C₂×C₄×C₅	—	12	2	no	—
184	C₂×C₄×C₅	—	12	4	no	—
185	C₂×C₄×C₅	D₃×C₈	1	2	yes	—
186	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
187	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
193	C₅×C₈	—	4	2	no	—
194	C₅×C₈	—	12	2	no	—
195	C₂²×D₄	—	3	1	no	—
196	C₂³×C₄	—	6	1	no	—
197	C₄×D₄	—	3	2	no	—
198	C₄×D₄	—	3	2	no	—
199	C₄×D₄	—	6	1	no	—
200	C₄×D₄	—	6	1	no	—
201	C₂×C₄⋊C₄	—	3	1	no	—
202	C₂×C₂²⋊C₄	—	6	1	no	—
203	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
204	C₄⋊C₈	—	2	1	no	—
205	C₄⋊C₈	—	3	2	no	—
206	C₂²⋊C₈	—	2	1	no	—
207	C₂²⋊C₈	—	6	1	no	—
208	C₄×C₈	—	6	1	no	—
209	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
210	C₂×C₃×C₅	—	2	2	no	—
211	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
212	C₂×C₃×C₅	#418	1	1	yes	characteristic
213	C₂×C₃×C₅	#421	1	1	yes	characteristic
214	C₅×D₃	—	4	4	no	—
215	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×D₃	—	2	2	no	—
217	C₂²×D₃	—	2	4	no	—
218	C₂²×D₃	—	4	2	no	—
219	C₂²×D₃	—	4	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	4	1	no	—
222	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
226	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
227	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
230	C₂×Dic₃	—	2	2	no	—
231	C₂×Dic₃	—	4	2	no	—
232	D₁₂	—	2	2	no	—
233	D₁₂	—	2	4	no	—
234	D₁₂	C₂×C₅×C₈	1	4	yes	—
235	C₄×D₃	—	4	4	no	—
236	C₄×D₃	—	4	4	no	—
237	C₃×C₈	—	4	2	no	—
238	C₃⋊C₈	—	4	2	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	6	4	no	—
242	C₂²×C₅	—	12	8	no	—
243	C₂²×C₅	—	12	2	no	—
244	C₂²×C₅	—	12	2	no	—
245	C₂²×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
246	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
247	C₄×C₅	—	2	1	no	—
248	C₄×C₅	—	2	1	no	—
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	12	2	no	—
251	C₄×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
252	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
253	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
254	C₄×C₅	#908	1	2	yes	—
255	C₂⁴	—	6	1	no	—
256	C₂×D₄	—	3	4	no	—
257	C₂×D₄	—	3	2	no	—
258	C₂×D₄	—	6	2	no	—
259	C₂×D₄	—	6	1	no	—
260	C₂²×C₄	—	6	1	no	—
261	C₂²×C₄	—	6	2	no	—
262	C₂²×C₄	—	6	2	no	—
263	C₂²×C₄	—	12	4	no	—
264	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
265	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
266	C₂²×C₄	C₅×#67	1	1	yes	characteristic
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	6	2	no	—
269	C₄⋊C₄	—	3	2	no	—
270	C₄⋊C₄	—	6	1	no	—
271	C₂²⋊C₄	—	6	2	no	—
272	C₂²⋊C₄	—	6	2	no	—
273	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
274	C₄²	C₅×D₁₂	1	1	yes	characteristic
275	C₄²	C₅×#67	1	1	yes	characteristic
276	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
277	C₃×C₅	#1478	1	1	yes	characteristic, complemented, Hall
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	C₅×C₂²⋊C₈	1	2	yes	—
281	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×D₃	—	2	4	no	—
283	C₂×D₃	—	4	8	no	—
284	C₂×D₃	—	4	2	no	—
285	C₂×D₃	—	4	2	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	C₅×C₂²⋊C₈	1	2	yes	—
290	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
291	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
292	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
293	Dic₃	—	4	2	no	—
294	C₂×C₅	—	2	2	no	—
295	C₂×C₅	—	12	4	no	—
296	C₂×C₅	#5005	1	1	yes	characteristic
297	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
298	C₂×C₅	#5131	1	1	yes	characteristic
299	C₂³	—	6	2	no	—
300	C₂³	—	6	4	no	—
301	C₂³	—	12	2	no	—
302	C₂³	—	12	2	no	—
303	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
304	D₄	—	3	4	no	—
305	D₄	—	6	2	no	—
306	D₄	—	6	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	6	2	no	—
310	C₂×C₄	—	12	4	no	—
311	C₂×C₄	—	12	2	no	—
312	C₂×C₄	—	12	4	no	—
313	C₂×C₄	C₅×D₃×C₈	1	2	yes	—
314	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
315	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
316	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
317	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
318	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
319	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
320	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
321	C₈	—	4	2	no	—
322	C₈	—	12	2	no	—
323	C₂×C₃	—	2	2	no	—
324	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
325	C₂×C₃	C₅×#418	1	1	yes	characteristic
326	C₂×C₃	C₅×#421	1	1	yes	characteristic
327	D₃	—	4	4	no	—
328	C₅	#70757	1	1	yes	characteristic, direct product factor, Sylow
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	6	4	no	—
332	C₂²	—	12	8	no	—
333	C₂²	—	12	2	no	—
334	C₂²	—	12	2	no	—
335	C₂²	C₅×(C₂×D₃)⋊C₈	1	2	yes	—
336	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	12	2	no	—
341	C₄	C₅×(C₂×D₃)⋊C₈	1	2	yes	—
342	C₄	C₂×C₅×D₃×C₈	1	1	yes	characteristic
343	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
344	C₄	C₅×#908	1	2	yes	—
345	C₃	C₅×#1478	1	1	yes	characteristic, complemented, Sylow
346	C₂	—	2	2	no	—
347	C₂	—	12	4	no	—
348	C₂	C₅×#5005	1	1	yes	characteristic
349	C₂	C₂×C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
350	C₂	C₅×#5131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×D₁₂	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#431	D₃
hypocenter	C₃	C₅×#1478
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₅×#4925	C₂	semidirect
4. C₅×#4459	C₂	semidirect
17. C₃×C₄×C₅×C₈	C₂²	semidirect
19. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
21. #70757	C₅	direct (N × H)
24. C₅×#431	D₃	semidirect
33. C₂×C₅×D₁₂	C₈	semidirect
49. C₃×#431	C₂×C₅	semidirect
50. #4925	C₂×C₅	semidirect
51. #4459	C₂×C₅	semidirect
66. C₄×C₅×C₈	C₂×D₃	semidirect
103. C₃×C₄×C₈	C₂²×C₅	semidirect
105. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
131. #431	C₅×D₃	semidirect
156. C₂×D₁₂	C₅×C₈	semidirect
209. C₄×C₈	C₂×C₅×D₃	semidirect
277. C₃×C₅	#1478	semidirect
328. C₅	#70757	direct (N × H)
345. C₃	C₅×#1478	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
C₃×C₅×#431	2
C₅×#4925	2
C₅×#4459	2
C₅×#1478	3
#70757	5

Subgroups — C5×#70757 #14281689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70757 #14281689