Subgroups — C₂×C₅×#4908 #14478332

Order 1920.

800 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×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4908	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#800	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×D₄₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#509	—	3	1	no	maximal, Hall
8	C₂×C₅×#235	—	2	1	no	—
9	C₂²×C₅×D₁₂	—	2	1	no	—
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
12	C₅×#904	—	2	2	no	—
13	C₅×#904	C₂²	1	4	yes	complemented
14	C₂×C₅×D₂₄	—	2	2	no	—
15	C₂×C₅×D₂₄	—	2	1	no	—
16	C₂×C₅×D₂₄	C₂²	1	2	yes	—
17	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
18	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×#204	—	2	1	no	—
20	C₃×C₅×M₃₂	C₂²	1	4	yes	complemented
21	C₂×C₃×C₅×C₁₆	C₂²	1	2	yes	complemented
22	C₅×#800	C₂²	1	8	yes	complemented
23	C₅×D₄₈	C₂²	1	8	yes	complemented
24	C₂×#4908	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×#135	—	3	1	no	—
26	C₂²×C₅×D₈	—	3	1	no	—
27	C₅×#509	—	3	8	no	—
28	C₂×C₅×SD₃₂	—	3	2	no	—
29	C₂×C₅×D₁₆	—	3	2	no	—
30	C₂×C₅×M₃₂	D₃	1	1	yes	characteristic, complemented
31	C₂³×C₅×D₃	—	4	1	no	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×#67	—	4	1	no	—
34	C₅×#235	—	2	4	no	—
35	C₅×#235	—	4	2	no	—
36	C₂×C₅×D₁₂	—	2	1	no	—
37	C₂×C₅×D₁₂	—	2	2	no	—
38	C₂×C₅×D₁₂	—	2	4	no	—
39	C₂×C₅×D₁₂	—	4	1	no	—
40	C₂×C₅×D₁₂	—	4	2	no	—
41	C₂×C₄×C₅×D₃	—	4	1	no	—
42	C₂×C₅×Dic₆	—	2	1	no	—
43	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
45	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
47	C₅×Dic₁₂	—	2	1	no	—
48	C₅×Dic₁₂	C₂³	1	2	yes	complemented
49	C₅×D₂₄	—	2	2	no	—
50	C₅×D₂₄	—	2	4	no	—
51	C₅×D₂₄	—	2	1	no	—
52	C₅×D₂₄	C₂³	1	4	yes	—
53	C₅×D₂₄	C₂³	1	2	yes	complemented
54	C₅×#204	—	2	4	no	—
55	C₃×C₅×C₁₆	C₂³	1	4	yes	complemented
56	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₃×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
59	#4908	C₂×C₅	1	8	yes	direct product factor
60	C₂×#800	C₂×C₅	1	2	yes	complemented
61	C₂×D₄₈	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×#41	—	6	1	no	—
63	C₂²×C₅×D₄	—	6	1	no	—
64	C₅×#135	—	3	4	no	—
65	C₅×#135	—	6	2	no	—
66	C₂×C₅×Q₁₆	—	3	1	no	—
67	C₂×C₅×SD₁₆	—	6	1	no	—
68	C₂×C₅×D₈	—	3	2	no	—
69	C₂×C₅×D₈	—	3	1	no	—
70	C₂×C₅×D₈	—	3	4	no	—
71	C₂×C₅×D₈	—	6	1	no	—
72	C₂×C₅×D₈	—	6	2	no	—
73	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
74	C₅×SD₃₂	—	3	8	no	—
75	C₅×D₁₆	—	3	8	no	—
76	C₅×M₃₂	C₂×D₃	1	4	yes	complemented
77	C₂×C₅×C₁₆	C₂×D₃	1	2	yes	complemented
78	C₂×#509	—	3	1	no	Sylow
79	C₂³×C₃×C₅	D₈	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	4	1	no	—
81	C₂²×C₅×D₃	—	4	4	no	—
82	C₂²×C₅×D₃	—	4	2	no	—
83	C₂²×C₅×D₃	—	8	4	no	—
84	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₅×#67	—	4	4	no	—
89	C₂×C₅×Dic₃	—	4	1	no	—
90	C₅×D₁₂	—	2	2	no	—
91	C₅×D₁₂	—	2	4	no	—
92	C₅×D₁₂	—	4	2	no	—
93	C₅×D₁₂	—	4	4	no	—
94	C₅×D₁₂	—	4	1	no	—
95	C₄×C₅×D₃	—	4	4	no	—
96	C₅×Dic₆	—	2	2	no	—
97	C₅×Dic₆	—	4	1	no	—
98	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
99	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
100	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
101	C₂×#235	—	2	1	no	—
102	C₂²×D₁₂	—	2	1	no	—
103	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
104	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
105	#904	—	2	2	no	—
106	#904	C₂²×C₅	1	4	yes	complemented
107	C₂×D₂₄	—	2	2	no	—
108	C₂×D₂₄	—	2	1	no	—
109	C₂×D₂₄	C₂²×C₅	1	2	yes	—
110	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
111	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
112	C₂×#204	—	2	1	no	—
113	C₃×M₃₂	C₂²×C₅	1	4	yes	complemented
114	C₂×C₃×C₁₆	C₂²×C₅	1	2	yes	complemented
115	#800	C₂²×C₅	1	8	yes	complemented
116	D₄₈	C₂²×C₅	1	8	yes	complemented
117	C₂⁴×C₅	—	12	1	no	—
118	C₅×#41	—	6	4	no	—
119	C₅×#41	—	12	2	no	—
120	C₂×C₅×Q₈	—	6	1	no	—
121	C₂×C₅×D₄	—	6	4	no	—
122	C₂×C₅×D₄	—	6	2	no	—
123	C₂×C₅×D₄	—	6	1	no	—
124	C₂×C₅×D₄	—	12	1	no	—
125	C₂×C₅×D₄	—	12	2	no	—
126	C₂×C₅×D₄	—	12	1	no	—
127	C₂²×C₄×C₅	—	12	1	no	—
128	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
129	C₅×Q₁₆	—	3	2	no	—
130	C₅×Q₁₆	—	6	1	no	—
131	C₅×SD₁₆	—	6	4	no	—
132	C₅×D₈	—	3	4	no	—
133	C₅×D₈	—	3	2	no	—
134	C₅×D₈	—	6	2	no	—
135	C₅×D₈	—	6	4	no	—
136	C₅×D₈	—	6	1	no	—
137	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
138	C₂×C₅×C₈	D₁₂	1	2	yes	—
139	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
141	C₅×C₁₆	C₂²×D₃	1	4	yes	complemented
142	C₂×#135	—	3	1	no	—
143	C₂²×D₈	—	3	1	no	—
144	#509	—	3	8	no	—
145	C₂×SD₃₂	—	3	2	no	—
146	C₂×D₁₆	—	3	2	no	—
147	C₂×M₃₂	C₅×D₃	1	1	yes	characteristic, complemented
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
150	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
151	C₂×C₅×D₃	—	4	2	no	—
152	C₂×C₅×D₃	—	4	4	no	—
153	C₂×C₅×D₃	—	8	8	no	—
154	C₂×C₅×D₃	—	8	2	no	—
155	C₂×C₅×D₃	—	8	4	no	—
156	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
157	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
158	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
159	C₅×Dic₃	—	4	2	no	—
160	C₂³×D₃	—	4	1	no	—
161	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
162	C₂×#67	—	4	1	no	—
163	#235	—	2	4	no	—
164	#235	—	4	2	no	—
165	C₂×D₁₂	—	2	1	no	—
166	C₂×D₁₂	—	2	2	no	—
167	C₂×D₁₂	—	2	4	no	—
168	C₂×D₁₂	—	4	1	no	—
169	C₂×D₁₂	—	4	2	no	—
170	C₂×C₄×D₃	—	4	1	no	—
171	C₂×Dic₆	—	2	1	no	—
172	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
173	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
174	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
176	Dic₁₂	—	2	1	no	—
177	Dic₁₂	C₂³×C₅	1	2	yes	complemented
178	D₂₄	—	2	2	no	—
179	D₂₄	—	2	4	no	—
180	D₂₄	—	2	1	no	—
181	D₂₄	C₂³×C₅	1	4	yes	—
182	D₂₄	C₂³×C₅	1	2	yes	complemented
183	#204	—	2	4	no	—
184	C₃×C₁₆	C₂³×C₅	1	4	yes	complemented
185	C₂³×C₅	—	12	4	no	—
186	C₂³×C₅	—	12	1	no	—
187	C₂³×C₅	—	12	2	no	—
188	C₂³×C₅	—	24	4	no	—
189	C₂³×C₅	D₂₄	1	1	yes	characteristic
190	C₅×Q₈	—	6	2	no	—
191	C₅×Q₈	—	12	1	no	—
192	C₅×D₄	—	6	4	no	—
193	C₅×D₄	—	6	2	no	—
194	C₅×D₄	—	12	4	no	—
195	C₅×D₄	—	12	4	no	—
196	C₅×D₄	—	12	2	no	—
197	C₅×D₄	—	12	1	no	—
198	C₂×C₄×C₅	—	12	1	no	—
199	C₂×C₄×C₅	—	12	4	no	—
200	C₂×C₄×C₅	D₂₄	1	2	yes	—
201	C₂×C₄×C₅	D₂₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
203	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
204	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
205	C₅×C₈	C₂×D₁₂	1	2	yes	—
206	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
207	C₂×#41	—	6	1	no	—
208	C₂²×D₄	—	6	1	no	—
209	#135	—	3	4	no	—
210	#135	—	6	2	no	—
211	C₂×Q₁₆	—	3	1	no	—
212	C₂×SD₁₆	—	6	1	no	—
213	C₂×D₈	—	3	2	no	—
214	C₂×D₈	—	3	4	no	—
215	C₂×D₈	—	3	1	no	—
216	C₂×D₈	—	6	1	no	—
217	C₂×D₈	—	6	2	no	—
218	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
219	SD₃₂	—	3	8	no	—
220	D₁₆	—	3	8	no	—
221	M₃₂	C₂×C₅×D₃	1	4	yes	complemented
222	C₂×C₁₆	C₂×C₅×D₃	1	2	yes	complemented
223	C₂×C₃×C₅	—	2	2	no	—
224	C₂×C₃×C₅	#509	1	2	yes	complemented
225	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
226	C₅×D₃	—	8	2	no	—
227	C₅×D₃	—	8	4	no	—
228	C₂³×C₃	C₅×D₈	1	1	yes	characteristic
229	C₂²×D₃	—	4	1	no	—
230	C₂²×D₃	—	4	4	no	—
231	C₂²×D₃	—	4	2	no	—
232	C₂²×D₃	—	8	4	no	—
233	C₂×C₃×C₄	C₅×D₈	1	1	yes	characteristic
234	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
237	#67	—	4	4	no	—
238	C₂×Dic₃	—	4	1	no	—
239	D₁₂	—	2	2	no	—
240	D₁₂	—	2	4	no	—
241	D₁₂	—	4	2	no	—
242	D₁₂	—	4	4	no	—
243	D₁₂	—	4	1	no	—
244	C₄×D₃	—	4	4	no	—
245	Dic₆	—	2	2	no	—
246	Dic₆	—	4	1	no	—
247	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
248	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
249	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	12	2	no	—
252	C₂²×C₅	—	12	4	no	—
253	C₂²×C₅	—	24	8	no	—
254	C₂²×C₅	—	24	2	no	—
255	C₂²×C₅	—	24	4	no	—
256	C₂²×C₅	C₂×D₂₄	1	2	yes	—
257	C₂²×C₅	C₂×D₂₄	1	1	yes	characteristic
258	C₄×C₅	—	12	2	no	—
259	C₄×C₅	C₂×D₂₄	1	2	yes	—
260	C₄×C₅	C₂×D₂₄	1	1	yes	characteristic
261	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
262	C₂⁴	—	12	1	no	—
263	#41	—	6	4	no	—
264	#41	—	12	2	no	—
265	C₂×Q₈	—	6	1	no	—
266	C₂×D₄	—	6	2	no	—
267	C₂×D₄	—	6	4	no	—
268	C₂×D₄	—	6	1	no	—
269	C₂×D₄	—	12	1	no	—
270	C₂×D₄	—	12	1	no	—
271	C₂×D₄	—	12	2	no	—
272	C₂²×C₄	—	12	1	no	—
273	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
274	Q₁₆	—	3	2	no	—
275	Q₁₆	—	6	1	no	—
276	SD₁₆	—	6	4	no	—
277	D₈	—	3	2	no	—
278	D₈	—	3	4	no	—
279	D₈	—	6	2	no	—
280	D₈	—	6	4	no	—
281	D₈	—	6	1	no	—
282	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
283	C₂×C₈	C₅×D₁₂	1	2	yes	—
284	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
286	C₁₆	C₂²×C₅×D₃	1	4	yes	complemented
287	C₃×C₅	C₂×#509	1	1	yes	characteristic, complemented, Hall
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
290	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
291	C₂×D₃	—	4	2	no	—
292	C₂×D₃	—	4	4	no	—
293	C₂×D₃	—	8	8	no	—
294	C₂×D₃	—	8	2	no	—
295	C₂×D₃	—	8	4	no	—
296	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
297	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
298	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
299	Dic₃	—	4	2	no	—
300	C₂×C₅	—	2	2	no	—
301	C₂×C₅	—	24	4	no	—
302	C₂×C₅	—	24	2	no	—
303	C₂×C₅	#4908	1	2	yes	direct product factor
304	C₂×C₅	C₂²×D₂₄	1	1	yes	characteristic
305	C₂³	—	12	1	no	—
306	C₂³	—	12	4	no	—
307	C₂³	—	12	2	no	—
308	C₂³	—	24	4	no	—
309	C₂³	C₅×D₂₄	1	1	yes	characteristic
310	Q₈	—	6	2	no	—
311	Q₈	—	12	1	no	—
312	D₄	—	6	4	no	—
313	D₄	—	6	2	no	—
314	D₄	—	12	4	no	—
315	D₄	—	12	4	no	—
316	D₄	—	12	2	no	—
317	D₄	—	12	1	no	—
318	C₂×C₄	—	12	1	no	—
319	C₂×C₄	—	12	4	no	—
320	C₂×C₄	C₅×D₂₄	1	1	yes	characteristic
321	C₂×C₄	C₅×D₂₄	1	2	yes	—
322	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
323	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
324	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
325	C₈	C₂×C₅×D₁₂	1	2	yes	—
326	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
327	C₂×C₃	—	2	2	no	—
328	C₂×C₃	C₅×#509	1	2	yes	complemented
329	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
330	D₃	—	8	4	no	—
331	D₃	—	8	2	no	—
332	C₅	C₂×#4908	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²	—	2	2	no	—
334	C₂²	—	12	2	no	—
335	C₂²	—	12	4	no	—
336	C₂²	—	24	8	no	—
337	C₂²	—	24	4	no	—
338	C₂²	—	24	2	no	—
339	C₂²	C₂×C₅×D₂₄	1	2	yes	—
340	C₂²	C₂×C₅×D₂₄	1	1	yes	characteristic
341	C₄	—	12	2	no	—
342	C₄	C₂×C₅×D₂₄	1	2	yes	—
343	C₄	C₂×C₅×D₂₄	1	1	yes	characteristic
344	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
345	C₃	C₂×C₅×#509	1	1	yes	characteristic, complemented, Sylow
346	C₂	—	2	2	no	—
347	C₂	—	24	4	no	—
348	C₂	—	24	2	no	—
349	C₂	C₅×#4908	1	2	yes	direct product factor
350	C₂	C₂²×C₅×D₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₂₄
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
hypercenter	C₂×C₅×M₃₂	D₃
hypocenter	C₃	C₂×C₅×#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#904	C₂	semidirect
2. C₂²×C₅×D₂₄	C₂	semidirect
3. C₂×C₃×C₅×M₃₂	C₂	semidirect
4. C₅×#4908	C₂	direct (N × H)
5. C₂×C₅×#800	C₂	semidirect
6. C₂×C₅×D₄₈	C₂	semidirect
11. C₂×C₅×Dic₁₂	C₂²	semidirect
13. C₅×#904	C₂²	semidirect
17. C₂×C₅×D₂₄	C₂²	semidirect
18. C₂×C₅×D₂₄	C₂²	semidirect
20. C₃×C₅×M₃₂	C₂²	semidirect
21. C₂×C₃×C₅×C₁₆	C₂²	semidirect
22. C₅×#800	C₂²	semidirect
23. C₅×D₄₈	C₂²	semidirect
24. C₂×#4908	C₅	direct (N × H)
30. C₂×C₅×M₃₂	D₃	semidirect
48. C₅×Dic₁₂	C₂³	semidirect
53. C₅×D₂₄	C₂³	semidirect
55. C₃×C₅×C₁₆	C₂³	semidirect
56. C₂×#904	C₂×C₅	semidirect
57. C₂²×D₂₄	C₂×C₅	semidirect
58. C₂×C₃×M₃₂	C₂×C₅	semidirect
59. #4908	C₂×C₅	direct (N × H)
60. C₂×#800	C₂×C₅	semidirect
61. C₂×D₄₈	C₂×C₅	semidirect
76. C₅×M₃₂	C₂×D₃	semidirect
77. C₂×C₅×C₁₆	C₂×D₃	semidirect
104. C₂×Dic₁₂	C₂²×C₅	semidirect
106. #904	C₂²×C₅	semidirect
110. C₂×D₂₄	C₂²×C₅	semidirect
111. C₂×D₂₄	C₂²×C₅	semidirect
113. C₃×M₃₂	C₂²×C₅	semidirect
114. C₂×C₃×C₁₆	C₂²×C₅	semidirect
115. #800	C₂²×C₅	semidirect
116. D₄₈	C₂²×C₅	semidirect
141. C₅×C₁₆	C₂²×D₃	semidirect
147. C₂×M₃₂	C₅×D₃	semidirect
177. Dic₁₂	C₂³×C₅	semidirect
182. D₂₄	C₂³×C₅	semidirect
184. C₃×C₁₆	C₂³×C₅	semidirect
221. M₃₂	C₂×C₅×D₃	semidirect
222. C₂×C₁₆	C₂×C₅×D₃	semidirect
224. C₂×C₃×C₅	#509	semidirect
286. C₁₆	C₂²×C₅×D₃	semidirect
287. C₃×C₅	C₂×#509	semidirect
303. C₂×C₅	#4908	direct (N × H)
328. C₂×C₃	C₅×#509	semidirect
332. C₅	C₂×#4908	direct (N × H)
345. C₃	C₂×C₅×#509	semidirect
349. C₂	C₅×#4908	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×C₅×#904	2
C₂²×C₅×D₂₄	2
C₂×C₃×C₅×M₃₂	2
C₅×#4908	2
C₂×C₅×#800	2
C₂×C₅×D₄₈	2
C₂×C₅×#509	3
C₂×#4908	5

Subgroups — C2×C5×#4908 #14478332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4908 #14478332