Subgroups — C₃×C₅×#2640 #14275674

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#397	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#393	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	2	yes	maximal
7	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2640	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
13	C₃×C₅×#124	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×#95	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	8	yes	—
24	C₃×#2640	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
27	C₅×#397	C₂×C₃	1	4	yes	complemented
28	C₅×#393	C₂×C₃	1	4	yes	complemented
29	C₅×#391	C₂×C₃	1	2	yes	complemented
30	C₅×#390	C₂×C₃	1	2	yes	—
31	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	—	2	4	no	—
36	C₂×C₃×C₅×Q₈	—	4	4	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
49	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
50	C₃×C₄²×C₅	—	2	4	no	—
51	C₃×C₄²×C₅	D₄	1	4	yes	—
52	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
54	C₃×#397	C₂×C₅	1	4	yes	complemented
55	C₃×#393	C₂×C₅	1	4	yes	complemented
56	C₃×#391	C₂×C₅	1	2	yes	complemented
57	C₃×#390	C₂×C₅	1	2	yes	—
58	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
61	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	—	2	4	no	—
63	C₅×#124	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
69	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₅×#95	C₂²×C₃	1	2	yes	—
72	C₅×#95	C₂²×C₃	1	2	yes	—
73	C₅×#95	C₂²×C₃	1	8	yes	—
74	#2640	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₃×C₅×Q₈	—	4	8	no	—
81	C₃×C₅×Q₈	—	4	4	no	—
82	C₃×C₅×D₄	—	4	4	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	8	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	#41	1	4	yes	—
96	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
97	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
98	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
99	C₃×C₄⋊Q₈	—	2	4	no	—
100	C₃×#124	—	2	4	no	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
106	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₃×#95	C₂²×C₅	1	2	yes	—
109	C₃×#95	C₂²×C₅	1	2	yes	—
110	C₃×#95	C₂²×C₅	1	8	yes	—
111	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	4	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	4	4	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	4	no	—
118	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₅×C₄⋊C₄	—	2	4	no	—
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₂²⋊C₄	—	2	4	no	—
127	C₅×C₂²⋊C₄	—	2	4	no	—
128	C₅×C₂²⋊C₄	—	4	8	no	—
129	C₄²×C₅	—	2	4	no	—
130	C₄²×C₅	C₃×D₄	1	4	yes	—
131	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
132	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
133	#397	C₂×C₃×C₅	1	4	yes	complemented
134	#393	C₂×C₃×C₅	1	4	yes	complemented
135	#391	C₂×C₃×C₅	1	2	yes	complemented
136	#390	C₂×C₃×C₅	1	2	yes	—
137	#376	C₂×C₃×C₅	1	1	yes	characteristic, complemented
138	C₂²×C₃×C₅	—	4	2	no	—
139	C₂²×C₃×C₅	—	4	2	no	—
140	C₂²×C₃×C₅	—	4	2	no	—
141	C₂²×C₃×C₅	—	4	8	no	—
142	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
144	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
145	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
146	C₃×C₄×C₅	—	2	2	no	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	4	2	no	—
149	C₃×C₄×C₅	—	4	4	no	—
150	C₃×C₄×C₅	—	4	4	no	—
151	C₃×C₄×C₅	#124	1	4	yes	—
152	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
153	C₂×C₃×Q₈	—	2	2	no	—
154	C₂×C₃×Q₈	—	2	4	no	—
155	C₂×C₃×Q₈	—	2	4	no	—
156	C₂×C₃×Q₈	—	4	4	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	4	no	—
159	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
160	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
161	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
162	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	—	2	4	no	—
167	C₃×C₂²⋊C₄	—	2	4	no	—
168	C₃×C₂²⋊C₄	—	2	4	no	—
169	C₃×C₂²⋊C₄	—	4	8	no	—
170	C₃×C₄²	—	2	4	no	—
171	C₃×C₄²	C₅×D₄	1	4	yes	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	4	no	—
174	C₂³×C₅	—	2	4	no	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
177	C₅×Q₈	—	4	8	no	—
178	C₅×Q₈	—	4	4	no	—
179	C₅×D₄	—	4	4	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	8	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
190	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
192	C₂×C₄×C₅	C₃×#41	1	4	yes	—
193	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
194	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
195	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
196	C₄⋊Q₈	—	2	4	no	—
197	#124	—	2	4	no	—
198	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
199	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
202	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
203	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
204	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
205	#95	C₂²×C₃×C₅	1	2	yes	—
206	#95	C₂²×C₃×C₅	1	2	yes	—
207	#95	C₂²×C₃×C₅	1	8	yes	—
208	C₂×C₃×C₅	—	8	2	no	—
209	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
210	C₂×C₃×C₅	#535	1	1	yes	characteristic
211	C₂×C₃×C₅	#536	1	1	yes	characteristic
212	C₂×C₃×C₅	#542	1	4	yes	—
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	4	no	—
215	C₂³×C₃	—	2	4	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
218	C₃×Q₈	—	4	8	no	—
219	C₃×Q₈	—	4	4	no	—
220	C₃×D₄	—	4	4	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	2	4	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	8	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
232	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
233	C₂×C₃×C₄	C₅×#41	1	4	yes	—
234	C₂²×C₅	—	4	2	no	—
235	C₂²×C₅	—	4	2	no	—
236	C₂²×C₅	—	4	2	no	—
237	C₂²×C₅	—	4	8	no	—
238	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
239	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
240	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
241	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
242	C₄×C₅	—	2	2	no	—
243	C₄×C₅	—	2	2	no	—
244	C₄×C₅	—	4	2	no	—
245	C₄×C₅	—	4	4	no	—
246	C₄×C₅	—	4	4	no	—
247	C₄×C₅	C₃×#124	1	4	yes	—
248	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
249	C₂×Q₈	—	2	2	no	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
256	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
257	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
258	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
259	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
260	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	2	4	no	—
263	C₂²⋊C₄	—	2	4	no	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₂²⋊C₄	—	4	8	no	—
266	C₄²	—	2	4	no	—
267	C₄²	C₃×C₅×D₄	1	4	yes	—
268	C₃×C₅	#2640	1	1	yes	characteristic, direct product factor, Hall
269	C₂²×C₃	—	4	2	no	—
270	C₂²×C₃	—	4	2	no	—
271	C₂²×C₃	—	4	2	no	—
272	C₂²×C₃	—	4	8	no	—
273	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
274	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
275	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
276	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
277	C₃×C₄	—	2	2	no	—
278	C₃×C₄	—	2	2	no	—
279	C₃×C₄	—	4	2	no	—
280	C₃×C₄	—	4	4	no	—
281	C₃×C₄	—	4	4	no	—
282	C₃×C₄	C₅×#124	1	4	yes	—
283	C₂×C₅	—	8	2	no	—
284	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
285	C₂×C₅	C₃×#535	1	1	yes	characteristic
286	C₂×C₅	C₃×#536	1	1	yes	characteristic
287	C₂×C₅	C₃×#542	1	4	yes	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	2	4	no	—
292	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
293	Q₈	—	4	8	no	—
294	Q₈	—	4	4	no	—
295	D₄	—	4	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
306	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
307	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
308	C₂×C₄	C₃×C₅×#41	1	4	yes	—
309	C₂×C₃	—	8	2	no	—
310	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
311	C₂×C₃	C₅×#535	1	1	yes	characteristic
312	C₂×C₃	C₅×#536	1	1	yes	characteristic
313	C₂×C₃	C₅×#542	1	4	yes	—
314	C₅	C₃×#2640	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	8	no	—
319	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
320	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
321	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
322	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	4	2	no	—
326	C₄	—	4	4	no	—
327	C₄	—	4	4	no	—
328	C₄	C₃×C₅×#124	1	4	yes	—
329	C₃	C₅×#2640	1	1	yes	characteristic, direct product factor, Sylow
330	C₂	—	8	2	no	—
331	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
332	C₂	C₃×C₅×#535	1	1	yes	characteristic
333	C₂	C₃×C₅×#536	1	1	yes	characteristic
334	C₂	C₃×C₅×#542	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#393	C₂	semidirect
5. C₃×C₅×#391	C₂	semidirect
7. C₃×C₅×#376	C₂	semidirect
8. C₅×#2640	C₃	direct (N × H)
24. C₃×#2640	C₅	direct (N × H)
25. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
27. C₅×#397	C₂×C₃	semidirect
28. C₅×#393	C₂×C₃	semidirect
29. C₅×#391	C₂×C₃	semidirect
31. C₅×#376	C₂×C₃	semidirect
52. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
54. C₃×#397	C₂×C₅	semidirect
55. C₃×#393	C₂×C₅	semidirect
56. C₃×#391	C₂×C₅	semidirect
58. C₃×#376	C₂×C₅	semidirect
74. #2640	C₃×C₅	direct (N × H)
131. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
133. #397	C₂×C₃×C₅	semidirect
134. #393	C₂×C₃×C₅	semidirect
135. #391	C₂×C₃×C₅	semidirect
137. #376	C₂×C₃×C₅	semidirect
268. C₃×C₅	#2640	direct (N × H)
314. C₅	C₃×#2640	direct (N × H)
329. C₃	C₅×#2640	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×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×C₅×#124	2
C₃×C₅×#397	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#390	2
C₃×C₅×#376	2
C₅×#2640	3
C₃×#2640	5

Subgroups — C3×C5×#2640 #14275674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2640 #14275674