Subgroups — C₂×C₅×#4872 #14415985

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#893	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#809	C₂	1	2	yes	maximal, complemented
6	C₅×#4872	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄×C₅×D₈	—	3	1	no	maximal, Hall
8	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
9	C₂²×C₄×C₅×D₃	—	2	2	no	—
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₂₄	C₄	1	8	yes	complemented
16	C₂×C₅×D₂₄	C₂²	1	4	yes	—
17	C₅×#893	—	2	4	no	—
18	C₅×#893	C₂²	1	8	yes	complemented
19	C₃×C₅×#107	C₂²	1	4	yes	complemented
20	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
21	C₅×#809	C₂²	1	8	yes	complemented
22	C₂×#4872	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂²×C₅×D₈	—	3	1	no	—
24	C₂×C₄×C₅×D₄	—	3	2	no	—
25	C₄×C₅×D₈	—	3	8	no	—
26	C₂×C₅×#107	D₃	1	1	yes	characteristic, complemented
27	C₂×C₅×#102	—	3	2	no	—
28	C₂×C₄×C₅×C₈	—	3	1	no	—
29	C₂³×C₅×D₃	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
32	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
33	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
34	C₂×C₅×D₁₂	—	2	2	no	—
35	C₂×C₅×D₁₂	—	2	4	no	—
36	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
37	C₂×C₅×D₁₂	C₂³	1	4	yes	—
38	C₂×C₄×C₅×D₃	—	2	8	no	—
39	C₂×C₄×C₅×D₃	—	4	8	no	—
40	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
41	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
44	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
45	C₄×C₅×Dic₃	D₄	1	2	yes	—
46	C₄×C₅×Dic₃	C₂³	1	2	yes	—
47	C₂×C₅×C₃⋊C₈	—	2	2	no	—
48	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
49	C₅×D₂₄	C₂×C₄	1	16	yes	complemented
50	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic
51	C₂×#893	C₂×C₅	1	2	yes	complemented
52	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂×#809	C₂×C₅	1	2	yes	complemented
55	#4872	C₂×C₅	1	8	yes	direct product factor
56	C₂²×C₅×D₄	—	3	2	no	—
57	C₂³×C₄×C₅	—	6	2	no	—
58	C₂×C₅×D₈	—	3	8	no	—
59	C₂×C₅×D₈	—	3	4	no	—
60	C₂²×C₅×C₈	—	3	1	no	—
61	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
62	C₄×C₅×D₄	—	3	8	no	—
63	C₄×C₅×D₄	—	6	4	no	—
64	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
65	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
66	C₂×C₄²×C₅	—	3	1	no	—
67	C₅×#107	C₂×D₃	1	4	yes	complemented
68	C₅×#102	—	3	8	no	—
69	C₄×C₅×C₈	—	3	4	no	—
70	C₂×C₄×D₈	—	3	1	no	Sylow
71	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₅×D₃	—	2	8	no	—
73	C₂²×C₅×D₃	—	2	4	no	—
74	C₂²×C₅×D₃	—	4	4	no	—
75	C₂²×C₅×D₃	—	4	4	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	—	4	4	no	—
78	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	#41	1	2	yes	—
81	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
82	C₂×C₅×Dic₃	—	2	2	no	—
83	C₂×C₅×Dic₃	D₈	1	4	yes	complemented
84	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
85	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
86	C₅×D₁₂	—	2	8	no	—
87	C₅×D₁₂	—	2	4	no	—
88	C₅×D₁₂	C₂²×C₄	1	8	yes	complemented
89	C₄×C₅×D₃	—	4	16	no	—
90	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
91	C₅×C₃⋊C₈	—	2	2	no	—
92	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
93	C₂²×C₄×D₃	—	2	2	no	—
94	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
96	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
97	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
98	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
99	C₂×D₂₄	C₄×C₅	1	8	yes	complemented
100	C₂×D₂₄	C₂²×C₅	1	4	yes	—
101	#893	—	2	4	no	—
102	#893	C₂²×C₅	1	8	yes	complemented
103	C₃×#107	C₂²×C₅	1	4	yes	complemented
104	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
105	#809	C₂²×C₅	1	8	yes	complemented
106	C₂⁴×C₅	—	6	2	no	—
107	C₂×C₅×D₄	—	3	8	no	—
108	C₂×C₅×D₄	—	3	4	no	—
109	C₂×C₅×D₄	—	6	2	no	—
110	C₂×C₅×D₄	—	6	4	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	3	1	no	—
113	C₂²×C₄×C₅	—	3	1	no	—
114	C₂²×C₄×C₅	—	6	8	no	—
115	C₂²×C₄×C₅	—	12	8	no	—
116	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₅×D₈	—	3	16	no	—
118	C₂×C₅×C₈	—	3	2	no	—
119	C₂×C₅×C₈	—	6	2	no	—
120	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
121	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
124	C₅×C₂²⋊C₄	—	6	8	no	—
125	C₄²×C₅	—	3	2	no	—
126	C₄²×C₅	—	3	2	no	—
127	C₂²×D₈	—	3	1	no	—
128	C₂×C₄×D₄	—	3	2	no	—
129	C₄×D₈	—	3	8	no	—
130	C₂×#107	C₅×D₃	1	1	yes	characteristic, complemented
131	C₂×#102	—	3	2	no	—
132	C₂×C₄×C₈	—	3	1	no	—
133	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
134	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
135	C₂²×C₃×C₅	#135	1	2	yes	—
136	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₅×D₃	—	2	8	no	—
138	C₂×C₅×D₃	—	4	4	no	—
139	C₂×C₅×D₃	—	4	4	no	—
140	C₂×C₅×D₃	—	4	16	no	—
141	C₃×C₄×C₅	—	4	4	no	—
142	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
143	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
144	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
145	C₅×Dic₃	—	2	2	no	—
146	C₅×Dic₃	C₂×D₈	1	4	yes	complemented
147	C₂³×D₃	—	2	2	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
150	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
151	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
152	C₂×D₁₂	—	2	2	no	—
153	C₂×D₁₂	—	2	4	no	—
154	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
155	C₂×D₁₂	C₂³×C₅	1	4	yes	—
156	C₂×C₄×D₃	—	2	8	no	—
157	C₂×C₄×D₃	—	4	8	no	—
158	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
159	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
160	C₃×C₄⋊C₄	—	2	2	no	—
161	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
162	(C₂×D₃)⋊C₄	—	2	8	no	—
163	C₄×Dic₃	C₅×D₄	1	2	yes	—
164	C₄×Dic₃	C₂³×C₅	1	2	yes	—
165	C₂×C₃⋊C₈	—	2	2	no	—
166	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
167	D₂₄	C₂×C₄×C₅	1	16	yes	complemented
168	C₂³×C₅	—	6	8	no	—
169	C₂³×C₅	—	6	4	no	—
170	C₂³×C₅	—	12	4	no	—
171	C₂³×C₅	—	12	4	no	—
172	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
173	C₅×D₄	—	3	8	no	—
174	C₅×D₄	—	6	8	no	—
175	C₅×D₄	—	6	4	no	—
176	C₂×C₄×C₅	—	2	4	no	—
177	C₂×C₄×C₅	—	3	4	no	—
178	C₂×C₄×C₅	—	3	2	no	—
179	C₂×C₄×C₅	—	3	2	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	—	6	2	no	—
182	C₂×C₄×C₅	—	12	16	no	—
183	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
184	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅	#239	1	2	yes	—
186	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
187	C₅×C₈	—	6	2	no	—
188	C₅×C₈	C₂×C₄×D₃	1	4	yes	complemented
189	C₂²×D₄	—	3	2	no	—
190	C₂³×C₄	—	6	2	no	—
191	C₂×D₈	—	3	8	no	—
192	C₂×D₈	—	3	4	no	—
193	C₂²×C₈	—	3	1	no	—
194	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
195	C₄×D₄	—	3	8	no	—
196	C₄×D₄	—	6	4	no	—
197	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
198	C₂×C₂²⋊C₄	—	6	2	no	—
199	C₂×C₄²	—	3	1	no	—
200	#107	C₂×C₅×D₃	1	4	yes	complemented
201	#102	—	3	8	no	—
202	C₄×C₈	—	3	4	no	—
203	C₂×C₃×C₅	C₄×D₈	1	4	yes	complemented
204	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
206	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
207	C₅×D₃	—	4	8	no	—
208	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
209	C₂²×D₃	—	2	8	no	—
210	C₂²×D₃	—	2	4	no	—
211	C₂²×D₃	—	4	4	no	—
212	C₂²×D₃	—	4	4	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	4	4	no	—
215	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
216	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄	C₅×#41	1	2	yes	—
218	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
219	C₂×Dic₃	—	2	2	no	—
220	C₂×Dic₃	C₅×D₈	1	4	yes	complemented
221	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
222	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
223	D₁₂	—	2	8	no	—
224	D₁₂	—	2	4	no	—
225	D₁₂	C₂²×C₄×C₅	1	8	yes	complemented
226	C₄×D₃	—	4	16	no	—
227	C₃×C₈	C₂²×C₄×C₅	1	4	yes	complemented
228	C₃⋊C₈	—	2	2	no	—
229	C₂²×C₅	—	6	8	no	—
230	C₂²×C₅	—	12	16	no	—
231	C₂²×C₅	—	12	4	no	—
232	C₂²×C₅	—	12	4	no	—
233	C₂²×C₅	#893	1	2	yes	—
234	C₂²×C₅	D₃×D₈	1	2	yes	—
235	C₂²×C₅	#919	1	2	yes	—
236	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
237	C₄×C₅	—	3	4	no	—
238	C₄×C₅	—	4	4	no	—
239	C₄×C₅	—	6	2	no	—
240	C₄×C₅	#893	1	2	yes	—
241	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
242	C₄×C₅	C₂×#239	1	1	yes	characteristic
243	C₂⁴	—	6	2	no	—
244	C₂×D₄	—	3	8	no	—
245	C₂×D₄	—	3	4	no	—
246	C₂×D₄	—	6	2	no	—
247	C₂×D₄	—	6	4	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	3	1	no	—
250	C₂²×C₄	—	3	1	no	—
251	C₂²×C₄	—	6	8	no	—
252	C₂²×C₄	—	12	8	no	—
253	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
254	D₈	—	3	16	no	—
255	C₂×C₈	—	3	2	no	—
256	C₂×C₈	—	6	2	no	—
257	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
258	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
261	C₂²⋊C₄	—	6	8	no	—
262	C₄²	—	3	2	no	—
263	C₄²	—	3	2	no	—
264	C₃×C₅	C₂×C₄×D₈	1	1	yes	characteristic, complemented, Hall
265	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
266	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
267	C₂²×C₃	C₅×#135	1	2	yes	—
268	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
269	C₂×D₃	—	2	8	no	—
270	C₂×D₃	—	4	16	no	—
271	C₂×D₃	—	4	4	no	—
272	C₂×D₃	—	4	4	no	—
273	C₃×C₄	—	4	4	no	—
274	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
275	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
276	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
277	Dic₃	—	2	2	no	—
278	Dic₃	C₂×C₅×D₈	1	4	yes	complemented
279	C₂×C₅	—	12	8	no	—
280	C₂×C₅	#4872	1	4	yes	direct product factor
281	C₂×C₅	C₂×#893	1	1	yes	characteristic
282	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
283	C₂×C₅	C₂×#919	1	1	yes	characteristic
284	C₂³	—	6	8	no	—
285	C₂³	—	6	4	no	—
286	C₂³	—	12	4	no	—
287	C₂³	—	12	4	no	—
288	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
289	D₄	—	3	8	no	—
290	D₄	—	6	8	no	—
291	D₄	—	6	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	3	4	no	—
294	C₂×C₄	—	3	2	no	—
295	C₂×C₄	—	3	2	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	6	2	no	—
298	C₂×C₄	—	12	16	no	—
299	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
300	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
301	C₂×C₄	C₅×#239	1	2	yes	—
302	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
303	C₈	—	6	2	no	—
304	C₈	C₂×C₄×C₅×D₃	1	4	yes	complemented
305	C₂×C₃	C₄×C₅×D₈	1	4	yes	complemented
306	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
307	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
308	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
309	D₃	—	4	8	no	—
310	C₅	C₂×#4872	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²	—	6	8	no	—
312	C₂²	—	12	4	no	—
313	C₂²	—	12	4	no	—
314	C₂²	—	12	16	no	—
315	C₂²	C₅×#893	1	2	yes	—
316	C₂²	C₅×D₃×D₈	1	2	yes	—
317	C₂²	C₅×#919	1	2	yes	—
318	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
319	C₄	—	3	4	no	—
320	C₄	—	4	4	no	—
321	C₄	—	6	2	no	—
322	C₄	C₅×#893	1	2	yes	—
323	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
324	C₄	C₂×C₅×#239	1	1	yes	characteristic
325	C₃	C₂×C₄×C₅×D₈	1	1	yes	characteristic, complemented, Sylow
326	C₂	—	12	8	no	—
327	C₂	C₅×#4872	1	4	yes	direct product factor
328	C₂	C₂×C₅×#893	1	1	yes	characteristic
329	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
330	C₂	C₂×C₅×#919	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₂₄	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#107	D₃
hypocenter	C₃	C₂×C₄×C₅×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#107

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#893	C₂	semidirect
3. C₂×C₃×C₅×#107	C₂	semidirect
4. C₂×C₅×C₈×Dic₃	C₂	semidirect
5. C₂×C₅×#809	C₂	semidirect
6. C₅×#4872	C₂	direct (N × H)
15. C₂×C₅×D₂₄	C₄	semidirect
18. C₅×#893	C₂²	semidirect
19. C₃×C₅×#107	C₂²	semidirect
20. C₅×C₈×Dic₃	C₂²	semidirect
21. C₅×#809	C₂²	semidirect
22. C₂×#4872	C₅	direct (N × H)
26. C₂×C₅×#107	D₃	semidirect
36. C₂×C₅×D₁₂	C₂×C₄	semidirect
40. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
49. C₅×D₂₄	C₂×C₄	semidirect
51. C₂×#893	C₂×C₅	semidirect
52. C₂×C₃×#107	C₂×C₅	semidirect
53. C₂×C₈×Dic₃	C₂×C₅	semidirect
54. C₂×#809	C₂×C₅	semidirect
55. #4872	C₂×C₅	direct (N × H)
67. C₅×#107	C₂×D₃	semidirect
83. C₂×C₅×Dic₃	D₈	semidirect
88. C₅×D₁₂	C₂²×C₄	semidirect
90. C₃×C₅×C₈	C₂²×C₄	semidirect
99. C₂×D₂₄	C₄×C₅	semidirect
102. #893	C₂²×C₅	semidirect
103. C₃×#107	C₂²×C₅	semidirect
104. C₈×Dic₃	C₂²×C₅	semidirect
105. #809	C₂²×C₅	semidirect
120. C₂×C₅×C₈	C₄×D₃	semidirect
130. C₂×#107	C₅×D₃	semidirect
146. C₅×Dic₃	C₂×D₈	semidirect
154. C₂×D₁₂	C₂×C₄×C₅	semidirect
158. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
167. D₂₄	C₂×C₄×C₅	semidirect
188. C₅×C₈	C₂×C₄×D₃	semidirect
200. #107	C₂×C₅×D₃	semidirect
203. C₂×C₃×C₅	C₄×D₈	semidirect
220. C₂×Dic₃	C₅×D₈	semidirect
225. D₁₂	C₂²×C₄×C₅	semidirect
227. C₃×C₈	C₂²×C₄×C₅	semidirect
257. C₂×C₈	C₄×C₅×D₃	semidirect
264. C₃×C₅	C₂×C₄×D₈	semidirect
278. Dic₃	C₂×C₅×D₈	semidirect
280. C₂×C₅	#4872	direct (N × H)
304. C₈	C₂×C₄×C₅×D₃	semidirect
305. C₂×C₃	C₄×C₅×D₈	semidirect
310. C₅	C₂×#4872	direct (N × H)
325. C₃	C₂×C₄×C₅×D₈	semidirect
327. C₂	C₅×#4872	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×C₅×D₂₄	2
C₂×C₅×#893	2
C₂×C₃×C₅×#107	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#809	2
C₅×#4872	2
C₂×C₄×C₅×D₈	3
C₂×#4872	5

Subgroups — C2×C5×#4872 #14415985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4872 #14415985