Subgroups — C₂×C₅×#5151 #14438766

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#940	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×#213	C₂	1	2	yes	maximal, complemented
4	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5151	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#493	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂²×C₅×#67	—	2	4	no	—
10	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#940	—	2	4	no	—
15	C₅×#940	C₂²	1	8	yes	complemented
16	C₂×C₅×#213	—	2	8	no	—
17	C₂×C₅×#213	C₂²	1	8	yes	complemented
18	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₂₄	—	2	4	no	—
21	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
22	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
23	C₂×#5151	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	—	3	2	no	—
25	C₂²×C₅×D₈	—	3	1	no	—
26	C₂²×C₅×D₈	D₃	1	1	yes	characteristic, complemented
27	C₂×C₅×#127	—	3	2	no	—
28	C₅×#493	—	3	8	no	—
29	C₂×C₄×C₅×C₈	—	3	1	no	—
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂³×C₅×D₃	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	2	4	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×#67	—	2	16	no	—
38	C₂×C₅×#67	—	4	16	no	—
39	C₂²×C₅×Dic₃	D₄	1	2	yes	—
40	C₂×C₅×D₁₂	—	2	4	no	—
41	C₂×C₅×D₁₂	—	2	4	no	—
42	C₂×C₅×D₁₂	—	2	2	no	—
43	C₂×C₅×D₁₂	C₂³	1	4	yes	—
44	C₃×C₅×D₈	—	2	8	no	—
45	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
46	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
47	C₅×#213	—	2	16	no	—
48	C₄×C₅×Dic₃	D₄	1	2	yes	—
49	C₄×C₅×Dic₃	C₂³	1	2	yes	—
50	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
51	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
52	C₅×D₂₄	—	2	8	no	—
53	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂×#940	C₂×C₅	1	2	yes	complemented
55	C₂²×#213	C₂×C₅	1	2	yes	complemented
56	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
57	#5151	C₂×C₅	1	8	yes	direct product factor
58	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂²×C₅×D₄	—	3	2	no	—
60	C₂²×C₅×D₄	—	6	4	no	—
61	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
62	C₂×C₅×D₈	—	2	4	no	—
63	C₂×C₅×D₈	—	3	8	no	—
64	C₂×C₅×D₈	—	3	4	no	—
65	C₂×C₅×D₈	—	6	8	no	—
66	C₂×C₅×D₈	—	6	4	no	—
67	C₂×C₅×D₈	C₂×D₃	1	4	yes	complemented
68	C₂²×C₅×C₈	—	3	1	no	—
69	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
70	C₅×#127	—	3	8	no	—
71	C₅×#127	—	6	4	no	—
72	C₂×C₄²×C₅	—	3	1	no	—
73	C₄×C₅×C₈	—	3	4	no	—
74	C₂×#493	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	4	4	no	—
77	C₂³×C₃×C₅	—	4	8	no	—
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₅×D₃	—	2	4	no	—
80	C₂²×C₅×D₃	—	4	4	no	—
81	C₂²×C₅×D₃	—	4	8	no	—
82	C₃×C₅×D₄	—	2	4	no	—
83	C₃×C₅×D₄	—	2	4	no	—
84	C₃×C₅×D₄	—	4	4	no	—
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
89	C₅×#67	—	4	32	no	—
90	C₂×C₅×Dic₃	D₈	1	8	yes	complemented
91	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
92	C₅×D₁₂	—	2	4	no	—
93	C₅×D₁₂	—	2	4	no	—
94	C₅×D₁₂	—	4	4	no	—
95	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
96	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
97	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
98	C₂²×#67	—	2	4	no	—
99	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
100	C₂×C₃×D₈	—	2	4	no	—
101	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
102	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
103	#940	—	2	4	no	—
104	#940	C₂²×C₅	1	8	yes	complemented
105	C₂×#213	—	2	8	no	—
106	C₂×#213	C₂²×C₅	1	8	yes	complemented
107	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
109	C₂×D₂₄	—	2	4	no	—
110	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
111	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
112	C₂⁴×C₅	—	2	2	no	—
113	C₂⁴×C₅	—	6	2	no	—
114	C₂×C₅×D₄	—	2	4	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	4	no	—
117	C₂×C₅×D₄	—	3	4	no	—
118	C₂×C₅×D₄	—	6	16	no	—
119	C₂×C₅×D₄	—	6	4	no	—
120	C₂×C₅×D₄	—	6	2	no	—
121	C₂×C₅×D₄	—	6	4	no	—
122	C₂×C₅×D₄	—	12	16	no	—
123	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
124	C₂²×C₄×C₅	—	3	2	no	—
125	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
126	C₅×D₈	—	2	8	no	—
127	C₅×D₈	—	6	16	no	—
128	C₅×D₈	—	6	8	no	—
129	C₂×C₅×C₈	—	3	4	no	—
130	C₂×C₅×C₈	—	3	2	no	—
131	C₂×C₅×C₈	#67	1	4	yes	complemented
132	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
133	C₄²×C₅	—	3	2	no	—
134	C₄²×C₅	—	3	2	no	—
135	C₂²×D₈	—	3	2	no	—
136	C₂²×D₈	—	3	1	no	—
137	C₂²×D₈	C₅×D₃	1	1	yes	characteristic, complemented
138	C₂×#127	—	3	2	no	—
139	#493	—	3	8	no	—
140	C₂×C₄×C₈	—	3	1	no	—
141	C₂²×C₃×C₅	—	4	4	no	—
142	C₂²×C₃×C₅	—	4	8	no	—
143	C₂²×C₃×C₅	—	8	8	no	—
144	C₂²×C₃×C₅	#127	1	2	yes	—
145	C₂²×C₃×C₅	C₂×D₈	1	4	yes	—
146	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₅×D₃	—	4	4	no	—
148	C₂×C₅×D₃	—	4	8	no	—
149	C₂×C₅×D₃	—	8	8	no	—
150	C₃×C₄×C₅	#127	1	2	yes	—
151	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
152	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
153	C₅×Dic₃	C₂×D₈	1	8	yes	complemented
154	C₂⁴×C₃	—	2	2	no	—
155	C₂³×D₃	—	2	2	no	—
156	C₂×C₃×D₄	—	2	4	no	—
157	C₂×C₃×D₄	—	2	4	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
160	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
161	C₂×#67	—	2	16	no	—
162	C₂×#67	—	4	16	no	—
163	C₂²×Dic₃	C₅×D₄	1	2	yes	—
164	C₂×D₁₂	—	2	4	no	—
165	C₂×D₁₂	—	2	4	no	—
166	C₂×D₁₂	—	2	2	no	—
167	C₂×D₁₂	C₂³×C₅	1	4	yes	—
168	C₃×D₈	—	2	8	no	—
169	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
170	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
171	#213	—	2	16	no	—
172	C₄×Dic₃	C₅×D₄	1	2	yes	—
173	C₄×Dic₃	C₂³×C₅	1	2	yes	—
174	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
175	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
176	D₂₄	—	2	8	no	—
177	C₂³×C₅	—	2	4	no	—
178	C₂³×C₅	—	4	8	no	—
179	C₂³×C₅	—	4	4	no	—
180	C₂³×C₅	—	6	4	no	—
181	C₂³×C₅	—	12	8	no	—
182	C₂³×C₅	—	12	4	no	—
183	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
184	C₅×D₄	—	2	4	no	—
185	C₅×D₄	—	2	4	no	—
186	C₅×D₄	—	4	4	no	—
187	C₅×D₄	—	6	4	no	—
188	C₅×D₄	—	6	4	no	—
189	C₅×D₄	—	12	32	no	—
190	C₅×D₄	—	12	4	no	—
191	C₂×C₄×C₅	—	3	8	no	—
192	C₂×C₄×C₅	—	3	4	no	—
193	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
195	C₂×C₄×C₅	C₂×#67	1	2	yes	—
196	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
197	C₅×C₈	—	3	4	no	—
198	C₅×C₈	C₂×#67	1	4	yes	complemented
199	C₂²×D₄	—	3	2	no	—
200	C₂²×D₄	—	6	4	no	—
201	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
202	C₂×D₈	—	2	4	no	—
203	C₂×D₈	—	3	8	no	—
204	C₂×D₈	—	3	4	no	—
205	C₂×D₈	—	6	8	no	—
206	C₂×D₈	—	6	4	no	—
207	C₂×D₈	C₂×C₅×D₃	1	4	yes	complemented
208	C₂²×C₈	—	3	1	no	—
209	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
210	#127	—	3	8	no	—
211	#127	—	6	4	no	—
212	C₂×C₄²	—	3	1	no	—
213	C₄×C₈	—	3	4	no	—
214	C₂×C₃×C₅	—	8	4	no	—
215	C₂×C₃×C₅	#493	1	4	yes	complemented
216	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
217	C₂×C₃×C₅	C₂²×D₈	1	2	yes	—
218	C₅×D₃	—	8	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	—	4	4	no	—
221	C₂³×C₃	—	4	8	no	—
222	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
223	C₂²×D₃	—	2	4	no	—
224	C₂²×D₃	—	4	4	no	—
225	C₂²×D₃	—	4	8	no	—
226	C₃×D₄	—	2	4	no	—
227	C₃×D₄	—	2	4	no	—
228	C₃×D₄	—	4	4	no	—
229	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
232	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
233	#67	—	4	32	no	—
234	C₂×Dic₃	C₅×D₈	1	8	yes	complemented
235	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
236	D₁₂	—	2	4	no	—
237	D₁₂	—	2	4	no	—
238	D₁₂	—	4	4	no	—
239	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
240	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	complemented
241	C₂²×C₅	—	4	8	no	—
242	C₂²×C₅	—	4	4	no	—
243	C₂²×C₅	—	8	8	no	—
244	C₂²×C₅	—	12	8	no	—
245	C₂²×C₅	—	12	4	no	—
246	C₂²×C₅	—	24	8	no	—
247	C₂²×C₅	D₃×D₈	1	4	yes	—
248	C₂²×C₅	#940	1	2	yes	—
249	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
250	C₄×C₅	—	3	8	no	—
251	C₄×C₅	#940	1	2	yes	—
252	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
253	C₄×C₅	C₂²×#67	1	1	yes	characteristic
254	C₂⁴	—	2	2	no	—
255	C₂⁴	—	6	2	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	3	4	no	—
260	C₂×D₄	—	6	16	no	—
261	C₂×D₄	—	6	4	no	—
262	C₂×D₄	—	6	2	no	—
263	C₂×D₄	—	6	4	no	—
264	C₂×D₄	—	12	16	no	—
265	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
266	C₂²×C₄	—	3	2	no	—
267	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
268	D₈	—	2	8	no	—
269	D₈	—	6	16	no	—
270	D₈	—	6	8	no	—
271	C₂×C₈	—	3	4	no	—
272	C₂×C₈	—	3	2	no	—
273	C₂×C₈	C₅×#67	1	4	yes	complemented
274	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
275	C₄²	—	3	2	no	—
276	C₄²	—	3	2	no	—
277	C₃×C₅	C₂×#493	1	1	yes	characteristic, complemented, Hall
278	C₂²×C₃	—	4	4	no	—
279	C₂²×C₃	—	4	8	no	—
280	C₂²×C₃	—	8	8	no	—
281	C₂²×C₃	C₅×#127	1	2	yes	—
282	C₂²×C₃	C₂×C₅×D₈	1	4	yes	—
283	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
284	C₂×D₃	—	4	4	no	—
285	C₂×D₃	—	4	8	no	—
286	C₂×D₃	—	8	8	no	—
287	C₃×C₄	C₅×#127	1	2	yes	—
288	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
289	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
290	Dic₃	C₂×C₅×D₈	1	8	yes	complemented
291	C₂×C₅	—	8	4	no	—
292	C₂×C₅	—	24	4	no	—
293	C₂×C₅	#5151	1	4	yes	direct product factor
294	C₂×C₅	C₂×D₃×D₈	1	2	yes	—
295	C₂×C₅	C₂×#940	1	1	yes	characteristic
296	C₂³	—	2	4	no	—
297	C₂³	—	4	8	no	—
298	C₂³	—	4	4	no	—
299	C₂³	—	6	4	no	—
300	C₂³	—	12	8	no	—
301	C₂³	—	12	4	no	—
302	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
303	D₄	—	2	4	no	—
304	D₄	—	2	4	no	—
305	D₄	—	4	4	no	—
306	D₄	—	6	4	no	—
307	D₄	—	6	4	no	—
308	D₄	—	12	32	no	—
309	D₄	—	12	4	no	—
310	C₂×C₄	—	3	8	no	—
311	C₂×C₄	—	3	4	no	—
312	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
313	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
314	C₂×C₄	C₂×C₅×#67	1	2	yes	—
315	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
316	C₈	—	3	4	no	—
317	C₈	C₂×C₅×#67	1	4	yes	complemented
318	C₂×C₃	—	8	4	no	—
319	C₂×C₃	C₅×#493	1	4	yes	complemented
320	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
321	C₂×C₃	C₂²×C₅×D₈	1	2	yes	—
322	D₃	—	8	4	no	—
323	C₅	C₂×#5151	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²	—	4	8	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	8	8	no	—
327	C₂²	—	12	8	no	—
328	C₂²	—	12	4	no	—
329	C₂²	—	24	8	no	—
330	C₂²	C₅×D₃×D₈	1	4	yes	—
331	C₂²	C₅×#940	1	2	yes	—
332	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
333	C₄	—	3	8	no	—
334	C₄	C₅×#940	1	2	yes	—
335	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
336	C₄	C₂²×C₅×#67	1	1	yes	characteristic
337	C₃	C₂×C₅×#493	1	1	yes	characteristic, complemented, Sylow
338	C₂	—	8	4	no	—
339	C₂	—	24	4	no	—
340	C₂	C₅×#5151	1	4	yes	direct product factor
341	C₂	C₂×C₅×D₃×D₈	1	2	yes	—
342	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₅×D₈	D₃
hypocenter	C₃	C₂×C₅×#493
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₅×#940	C₂	semidirect
3. C₂²×C₅×#213	C₂	semidirect
4. C₂²×C₅×D₂₄	C₂	semidirect
5. C₅×#5151	C₂	direct (N × H)
6. C₂×C₅×C₈×Dic₃	C₂	semidirect
12. C₂×C₃×C₅×D₈	C₂²	semidirect
15. C₅×#940	C₂²	semidirect
17. C₂×C₅×#213	C₂²	semidirect
21. C₂×C₅×D₂₄	C₂²	semidirect
22. C₅×C₈×Dic₃	C₂²	semidirect
23. C₂×#5151	C₅	direct (N × H)
26. C₂²×C₅×D₈	D₃	semidirect
45. C₂×C₃×C₅×C₈	D₄	semidirect
50. C₂×C₅×C₃⋊C₈	D₄	semidirect
53. C₂²×C₃×D₈	C₂×C₅	semidirect
54. C₂×#940	C₂×C₅	semidirect
55. C₂²×#213	C₂×C₅	semidirect
56. C₂²×D₂₄	C₂×C₅	semidirect
57. #5151	C₂×C₅	direct (N × H)
58. C₂×C₈×Dic₃	C₂×C₅	semidirect
67. C₂×C₅×D₈	C₂×D₃	semidirect
90. C₂×C₅×Dic₃	D₈	semidirect
95. C₃×C₅×C₈	C₂×D₄	semidirect
96. C₅×C₃⋊C₈	C₂×D₄	semidirect
101. C₂×C₃×D₈	C₂²×C₅	semidirect
104. #940	C₂²×C₅	semidirect
106. C₂×#213	C₂²×C₅	semidirect
110. C₂×D₂₄	C₂²×C₅	semidirect
111. C₈×Dic₃	C₂²×C₅	semidirect
131. C₂×C₅×C₈	#67	semidirect
137. C₂²×D₈	C₅×D₃	semidirect
153. C₅×Dic₃	C₂×D₈	semidirect
169. C₂×C₃×C₈	C₅×D₄	semidirect
174. C₂×C₃⋊C₈	C₅×D₄	semidirect
198. C₅×C₈	C₂×#67	semidirect
207. C₂×D₈	C₂×C₅×D₃	semidirect
215. C₂×C₃×C₅	#493	semidirect
234. C₂×Dic₃	C₅×D₈	semidirect
239. C₃×C₈	C₂×C₅×D₄	semidirect
240. C₃⋊C₈	C₂×C₅×D₄	semidirect
273. C₂×C₈	C₅×#67	semidirect
277. C₃×C₅	C₂×#493	semidirect
290. Dic₃	C₂×C₅×D₈	semidirect
293. C₂×C₅	#5151	direct (N × H)
317. C₈	C₂×C₅×#67	semidirect
319. C₂×C₃	C₅×#493	semidirect
323. C₅	C₂×#5151	direct (N × H)
337. C₃	C₂×C₅×#493	semidirect
340. C₂	C₅×#5151	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×C₃×C₅×D₈	2
C₂×C₅×#940	2
C₂²×C₅×#213	2
C₂²×C₅×D₂₄	2
C₅×#5151	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#493	3
C₂×#5151	5

Subgroups — C2×C5×#5151 #14438766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5151 #14438766