Subgroups — C₂×C₃×C₅×#560 #14276559

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#560	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#126	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#123	C₂	1	3	yes	maximal, complemented
5	C₂×C₃×C₅×#121	C₂	1	6	yes	maximal, complemented
6	C₂×C₃×C₅×#120	C₂	1	3	yes	maximal, complemented
7	C₂×C₅×#560	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	6	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	complemented
12	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	complemented
13	C₃×C₅×#127	C₂²	1	8	yes	complemented
14	C₃×C₅×#126	C₂²	1	16	yes	complemented
15	C₃×C₅×#123	C₂²	1	24	yes	complemented
16	C₃×C₅×#121	C₂²	1	48	yes	complemented
17	C₃×C₅×#120	C₂²	1	24	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	6	yes	complemented
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	6	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×#560	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₅×#560	C₂×C₃	1	16	yes	direct product factor
25	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#126	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#123	C₂×C₃	1	3	yes	complemented
28	C₂×C₅×#121	C₂×C₃	1	6	yes	complemented
29	C₂×C₅×#120	C₂×C₃	1	3	yes	complemented
30	C₂⁴×C₃×C₅	—	4	6	no	—
31	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
34	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
35	C₂×C₃×C₅×D₄	—	4	12	no	—
36	C₂×C₃×C₅×D₄	—	4	6	no	—
37	C₂×C₃×C₅×D₄	—	4	6	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	24	yes	—
39	C₂×C₃×C₅×D₄	C₂³	1	12	yes	—
40	C₂×C₃×C₅×D₄	C₂³	1	12	yes	complemented
41	C₂²×C₃×C₄×C₅	—	4	6	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	12	yes	complemented
45	C₃×C₅×C₄⋊C₄	C₂³	1	24	yes	complemented
46	C₃×C₅×C₂²⋊C₄	C₂³	1	24	yes	—
47	C₃×C₅×C₂²⋊C₄	C₂³	1	12	yes	—
48	C₃×C₅×C₂²⋊C₄	C₂³	1	12	yes	complemented
49	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
50	C₃×#560	C₂×C₅	1	16	yes	direct product factor
51	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
52	C₂×C₃×#126	C₂×C₅	1	2	yes	complemented
53	C₂×C₃×#123	C₂×C₅	1	3	yes	complemented
54	C₂×C₃×#121	C₂×C₅	1	6	yes	complemented
55	C₂×C₃×#120	C₂×C₅	1	3	yes	complemented
56	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₅×D₄	C₂²×C₃	1	6	yes	—
58	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
59	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	complemented
60	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	complemented
61	C₅×#127	C₂²×C₃	1	8	yes	complemented
62	C₅×#126	C₂²×C₃	1	16	yes	complemented
63	C₅×#123	C₂²×C₃	1	24	yes	complemented
64	C₅×#121	C₂²×C₃	1	48	yes	complemented
65	C₅×#120	C₂²×C₃	1	24	yes	complemented
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	6	yes	complemented
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
71	C₂×#560	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³×C₃×C₅	—	2	6	no	—
73	C₂³×C₃×C₅	—	2	12	no	—
74	C₂³×C₃×C₅	—	2	12	no	—
75	C₂³×C₃×C₅	—	2	6	no	—
76	C₂³×C₃×C₅	—	4	12	no	—
77	C₂³×C₃×C₅	—	4	16	no	—
78	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
79	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	6	yes	—
81	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
82	C₃×C₅×D₄	—	4	24	no	—
83	C₃×C₅×D₄	—	4	12	no	—
84	C₃×C₅×D₄	—	4	12	no	—
85	C₂×C₃×C₄×C₅	—	2	12	no	—
86	C₂×C₃×C₄×C₅	—	2	6	no	—
87	C₂×C₃×C₄×C₅	—	4	12	no	—
88	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
89	C₂×C₃×C₄×C₅	C₂⁴	1	12	yes	—
90	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
91	C₂²×C₃×D₄	C₂²×C₅	1	6	yes	—
92	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
93	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	complemented
94	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	complemented
95	C₃×#127	C₂²×C₅	1	8	yes	complemented
96	C₃×#126	C₂²×C₅	1	16	yes	complemented
97	C₃×#123	C₂²×C₅	1	24	yes	complemented
98	C₃×#121	C₂²×C₅	1	48	yes	complemented
99	C₃×#120	C₂²×C₅	1	24	yes	complemented
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	6	yes	complemented
101	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	—
102	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
104	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	—	4	6	no	—
106	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
107	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
108	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
109	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
110	C₂×C₅×D₄	—	4	12	no	—
111	C₂×C₅×D₄	—	4	6	no	—
112	C₂×C₅×D₄	—	4	6	no	—
113	C₂×C₅×D₄	C₂³×C₃	1	24	yes	—
114	C₂×C₅×D₄	C₂³×C₃	1	12	yes	—
115	C₂×C₅×D₄	C₂³×C₃	1	12	yes	complemented
116	C₂²×C₄×C₅	—	4	6	no	—
117	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
118	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	12	yes	complemented
120	C₅×C₄⋊C₄	C₂³×C₃	1	24	yes	complemented
121	C₅×C₂²⋊C₄	C₂³×C₃	1	24	yes	—
122	C₅×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
123	C₅×C₂²⋊C₄	C₂³×C₃	1	12	yes	complemented
124	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
125	#560	C₂×C₃×C₅	1	16	yes	direct product factor
126	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
127	C₂×#126	C₂×C₃×C₅	1	2	yes	complemented
128	C₂×#123	C₂×C₃×C₅	1	3	yes	complemented
129	C₂×#121	C₂×C₃×C₅	1	6	yes	complemented
130	C₂×#120	C₂×C₃×C₅	1	3	yes	complemented
131	C₂²×C₃×C₅	—	2	6	no	—
132	C₂²×C₃×C₅	—	2	12	no	—
133	C₂²×C₃×C₅	—	2	12	no	—
134	C₂²×C₃×C₅	—	2	6	no	—
135	C₂²×C₃×C₅	—	4	16	no	—
136	C₂²×C₃×C₅	—	4	12	no	—
137	C₂²×C₃×C₅	—	4	8	no	—
138	C₂²×C₃×C₅	—	4	4	no	—
139	C₂²×C₃×C₅	H(5,𝔽₂)	1	6	yes	—
140	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
141	C₃×C₄×C₅	—	2	12	no	—
142	C₃×C₄×C₅	—	2	6	no	—
143	C₂⁴×C₃	—	4	6	no	—
144	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
145	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
146	C₂⁴×C₃	C₂³×C₅	1	3	yes	—
147	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
148	C₂×C₃×D₄	—	4	12	no	—
149	C₂×C₃×D₄	—	4	6	no	—
150	C₂×C₃×D₄	—	4	6	no	—
151	C₂×C₃×D₄	C₂³×C₅	1	24	yes	—
152	C₂×C₃×D₄	C₂³×C₅	1	12	yes	—
153	C₂×C₃×D₄	C₂³×C₅	1	12	yes	complemented
154	C₂²×C₃×C₄	—	4	6	no	—
155	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
156	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
157	C₂²×C₃×C₄	C₂³×C₅	1	12	yes	complemented
158	C₃×C₄⋊C₄	C₂³×C₅	1	24	yes	complemented
159	C₃×C₂²⋊C₄	C₂³×C₅	1	24	yes	—
160	C₃×C₂²⋊C₄	C₂³×C₅	1	12	yes	—
161	C₃×C₂²⋊C₄	C₂³×C₅	1	12	yes	complemented
162	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
163	C₂³×C₅	—	2	6	no	—
164	C₂³×C₅	—	2	12	no	—
165	C₂³×C₅	—	2	12	no	—
166	C₂³×C₅	—	2	6	no	—
167	C₂³×C₅	—	4	12	no	—
168	C₂³×C₅	—	4	16	no	—
169	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
170	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
171	C₂³×C₅	C₂⁴×C₃	1	6	yes	—
172	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
173	C₅×D₄	—	4	24	no	—
174	C₅×D₄	—	4	12	no	—
175	C₅×D₄	—	4	12	no	—
176	C₂×C₄×C₅	—	2	12	no	—
177	C₂×C₄×C₅	—	2	6	no	—
178	C₂×C₄×C₅	—	4	12	no	—
179	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
180	C₂×C₄×C₅	C₂⁴×C₃	1	12	yes	—
181	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
182	C₂²×D₄	C₂²×C₃×C₅	1	6	yes	—
183	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
184	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	complemented
185	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	complemented
186	#127	C₂²×C₃×C₅	1	8	yes	complemented
187	#126	C₂²×C₃×C₅	1	16	yes	complemented
188	#123	C₂²×C₃×C₅	1	24	yes	complemented
189	#121	C₂²×C₃×C₅	1	48	yes	complemented
190	#120	C₂²×C₃×C₅	1	24	yes	complemented
191	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	6	yes	complemented
192	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	6	yes	—
193	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	—
194	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
195	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
196	C₂×C₃×C₅	—	4	6	no	—
197	C₂×C₃×C₅	—	4	4	no	—
198	C₂×C₃×C₅	—	4	2	no	—
199	C₂×C₃×C₅	#560	1	4	yes	direct product factor
200	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	3	yes	—
201	C₂³×C₃	—	2	6	no	—
202	C₂³×C₃	—	2	12	no	—
203	C₂³×C₃	—	2	12	no	—
204	C₂³×C₃	—	2	6	no	—
205	C₂³×C₃	—	4	12	no	—
206	C₂³×C₃	—	4	16	no	—
207	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
208	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
209	C₂³×C₃	C₂⁴×C₅	1	6	yes	—
210	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
211	C₃×D₄	—	4	24	no	—
212	C₃×D₄	—	4	12	no	—
213	C₃×D₄	—	4	12	no	—
214	C₂×C₃×C₄	—	2	12	no	—
215	C₂×C₃×C₄	—	2	6	no	—
216	C₂×C₃×C₄	—	4	12	no	—
217	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
218	C₂×C₃×C₄	C₂⁴×C₅	1	12	yes	—
219	C₂²×C₅	—	2	6	no	—
220	C₂²×C₅	—	2	12	no	—
221	C₂²×C₅	—	2	12	no	—
222	C₂²×C₅	—	2	6	no	—
223	C₂²×C₅	—	4	16	no	—
224	C₂²×C₅	—	4	12	no	—
225	C₂²×C₅	—	4	8	no	—
226	C₂²×C₅	—	4	4	no	—
227	C₂²×C₅	C₃×H(5,𝔽₂)	1	6	yes	—
228	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
229	C₄×C₅	—	2	12	no	—
230	C₄×C₅	—	2	6	no	—
231	C₂⁴	—	4	6	no	—
232	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
233	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
234	C₂⁴	C₂³×C₃×C₅	1	3	yes	—
235	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
236	C₂×D₄	—	4	12	no	—
237	C₂×D₄	—	4	6	no	—
238	C₂×D₄	—	4	6	no	—
239	C₂×D₄	C₂³×C₃×C₅	1	24	yes	—
240	C₂×D₄	C₂³×C₃×C₅	1	12	yes	—
241	C₂×D₄	C₂³×C₃×C₅	1	12	yes	complemented
242	C₂²×C₄	—	4	6	no	—
243	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
244	C₂²×C₄	C₂³×C₃×C₅	1	6	yes	—
245	C₂²×C₄	C₂³×C₃×C₅	1	12	yes	complemented
246	C₄⋊C₄	C₂³×C₃×C₅	1	24	yes	complemented
247	C₂²⋊C₄	C₂³×C₃×C₅	1	24	yes	—
248	C₂²⋊C₄	C₂³×C₃×C₅	1	12	yes	—
249	C₂²⋊C₄	C₂³×C₃×C₅	1	12	yes	complemented
250	C₄²	C₂³×C₃×C₅	1	4	yes	complemented
251	C₃×C₅	C₂×#560	1	1	yes	characteristic, direct product factor, Hall
252	C₂²×C₃	—	2	6	no	—
253	C₂²×C₃	—	2	12	no	—
254	C₂²×C₃	—	2	12	no	—
255	C₂²×C₃	—	2	6	no	—
256	C₂²×C₃	—	4	16	no	—
257	C₂²×C₃	—	4	12	no	—
258	C₂²×C₃	—	4	8	no	—
259	C₂²×C₃	—	4	4	no	—
260	C₂²×C₃	C₅×H(5,𝔽₂)	1	6	yes	—
261	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
262	C₃×C₄	—	2	12	no	—
263	C₃×C₄	—	2	6	no	—
264	C₂×C₅	—	4	4	no	—
265	C₂×C₅	—	4	2	no	—
266	C₂×C₅	—	4	6	no	—
267	C₂×C₅	C₃×#560	1	4	yes	direct product factor
268	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
269	C₂³	—	2	6	no	—
270	C₂³	—	2	12	no	—
271	C₂³	—	2	12	no	—
272	C₂³	—	2	6	no	—
273	C₂³	—	4	12	no	—
274	C₂³	—	4	16	no	—
275	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
276	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
277	C₂³	C₂⁴×C₃×C₅	1	6	yes	—
278	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
279	D₄	—	4	24	no	—
280	D₄	—	4	12	no	—
281	D₄	—	4	12	no	—
282	C₂×C₄	—	2	12	no	—
283	C₂×C₄	—	2	6	no	—
284	C₂×C₄	—	4	12	no	—
285	C₂×C₄	C₂⁴×C₃×C₅	1	6	yes	—
286	C₂×C₄	C₂⁴×C₃×C₅	1	12	yes	—
287	C₂×C₃	—	4	4	no	—
288	C₂×C₃	—	4	2	no	—
289	C₂×C₃	—	4	6	no	—
290	C₂×C₃	C₅×#560	1	4	yes	direct product factor
291	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	3	yes	—
292	C₅	C₂×C₃×#560	1	1	yes	characteristic, direct product factor, Sylow
293	C₂²	—	2	6	no	—
294	C₂²	—	2	12	no	—
295	C₂²	—	2	12	no	—
296	C₂²	—	2	6	no	—
297	C₂²	—	4	16	no	—
298	C₂²	—	4	8	no	—
299	C₂²	—	4	4	no	—
300	C₂²	—	4	12	no	—
301	C₂²	C₃×C₅×H(5,𝔽₂)	1	6	yes	—
302	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
303	C₄	—	2	12	no	—
304	C₄	—	2	6	no	—
305	C₃	C₂×C₅×#560	1	1	yes	characteristic, direct product factor, Sylow
306	C₂	—	4	4	no	—
307	C₂	—	4	2	no	—
308	C₂	—	4	6	no	—
309	C₂	C₃×C₅×#560	1	4	yes	direct product factor
310	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#560	C₂	direct (N × H)
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₃×C₅×#126	C₂	semidirect
4. C₂×C₃×C₅×#123	C₂	semidirect
5. C₂×C₃×C₅×#121	C₂	semidirect
6. C₂×C₃×C₅×#120	C₂	semidirect
7. C₂×C₅×#560	C₃	direct (N × H)
11. C₂²×C₃×C₅×D₄	C₂²	semidirect
12. C₂³×C₃×C₄×C₅	C₂²	semidirect
13. C₃×C₅×#127	C₂²	semidirect
14. C₃×C₅×#126	C₂²	semidirect
15. C₃×C₅×#123	C₂²	semidirect
16. C₃×C₅×#121	C₂²	semidirect
17. C₃×C₅×#120	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
21. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
22. C₂×C₃×C₄²×C₅	C₂²	semidirect
23. C₂×C₃×#560	C₅	direct (N × H)
24. C₅×#560	C₂×C₃	direct (N × H)
25. C₂×C₅×#127	C₂×C₃	semidirect
26. C₂×C₅×#126	C₂×C₃	semidirect
27. C₂×C₅×#123	C₂×C₃	semidirect
28. C₂×C₅×#121	C₂×C₃	semidirect
29. C₂×C₅×#120	C₂×C₃	semidirect
40. C₂×C₃×C₅×D₄	C₂³	semidirect
44. C₂²×C₃×C₄×C₅	C₂³	semidirect
45. C₃×C₅×C₄⋊C₄	C₂³	semidirect
48. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
49. C₃×C₄²×C₅	C₂³	semidirect
50. C₃×#560	C₂×C₅	direct (N × H)
51. C₂×C₃×#127	C₂×C₅	semidirect
52. C₂×C₃×#126	C₂×C₅	semidirect
53. C₂×C₃×#123	C₂×C₅	semidirect
54. C₂×C₃×#121	C₂×C₅	semidirect
55. C₂×C₃×#120	C₂×C₅	semidirect
59. C₂²×C₅×D₄	C₂²×C₃	semidirect
60. C₂³×C₄×C₅	C₂²×C₃	semidirect
61. C₅×#127	C₂²×C₃	semidirect
62. C₅×#126	C₂²×C₃	semidirect
63. C₅×#123	C₂²×C₃	semidirect
64. C₅×#121	C₂²×C₃	semidirect
65. C₅×#120	C₂²×C₃	semidirect
66. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
69. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
70. C₂×C₄²×C₅	C₂²×C₃	semidirect
71. C₂×#560	C₃×C₅	direct (N × H)
93. C₂²×C₃×D₄	C₂²×C₅	semidirect
94. C₂³×C₃×C₄	C₂²×C₅	semidirect
95. C₃×#127	C₂²×C₅	semidirect
96. C₃×#126	C₂²×C₅	semidirect
97. C₃×#123	C₂²×C₅	semidirect
98. C₃×#121	C₂²×C₅	semidirect
99. C₃×#120	C₂²×C₅	semidirect
100. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
103. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
104. C₂×C₃×C₄²	C₂²×C₅	semidirect
115. C₂×C₅×D₄	C₂³×C₃	semidirect
119. C₂²×C₄×C₅	C₂³×C₃	semidirect
120. C₅×C₄⋊C₄	C₂³×C₃	semidirect
123. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
124. C₄²×C₅	C₂³×C₃	semidirect
125. #560	C₂×C₃×C₅	direct (N × H)
126. C₂×#127	C₂×C₃×C₅	semidirect
127. C₂×#126	C₂×C₃×C₅	semidirect
128. C₂×#123	C₂×C₃×C₅	semidirect
129. C₂×#121	C₂×C₃×C₅	semidirect
130. C₂×#120	C₂×C₃×C₅	semidirect
153. C₂×C₃×D₄	C₂³×C₅	semidirect
157. C₂²×C₃×C₄	C₂³×C₅	semidirect
158. C₃×C₄⋊C₄	C₂³×C₅	semidirect
161. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
162. C₃×C₄²	C₂³×C₅	semidirect
184. C₂²×D₄	C₂²×C₃×C₅	semidirect
185. C₂³×C₄	C₂²×C₃×C₅	semidirect
186. #127	C₂²×C₃×C₅	semidirect
187. #126	C₂²×C₃×C₅	semidirect
188. #123	C₂²×C₃×C₅	semidirect
189. #121	C₂²×C₃×C₅	semidirect
190. #120	C₂²×C₃×C₅	semidirect
191. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
194. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
195. C₂×C₄²	C₂²×C₃×C₅	semidirect
199. C₂×C₃×C₅	#560	direct (N × H)
241. C₂×D₄	C₂³×C₃×C₅	semidirect
245. C₂²×C₄	C₂³×C₃×C₅	semidirect
246. C₄⋊C₄	C₂³×C₃×C₅	semidirect
249. C₂²⋊C₄	C₂³×C₃×C₅	semidirect
250. C₄²	C₂³×C₃×C₅	semidirect
251. C₃×C₅	C₂×#560	direct (N × H)
267. C₂×C₅	C₃×#560	direct (N × H)
290. C₂×C₃	C₅×#560	direct (N × H)
292. C₅	C₂×C₃×#560	direct (N × H)
305. C₃	C₂×C₅×#560	direct (N × H)
309. C₂	C₃×C₅×#560	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#560	2
C₂×C₃×C₅×#127	2
C₂×C₃×C₅×#126	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#120	2
C₂×C₅×#560	3
C₂×C₃×#560	5

Subgroups — C2×C3×C5×#560 #14276559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#560 #14276559