Subgroups — C₃×C₅×#2724 #14275758

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	2	yes	maximal
2	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#397	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#385	C₂	1	4	yes	maximal, complemented
7	C₅×#2724	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₃×C₅×#123	—	2	8	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#95	C₂²	1	4	yes	—
21	C₃×C₅×#95	C₂²	1	4	yes	—
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×#2724	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#123	C₂×C₃	1	2	yes	—
25	C₅×#398	C₂×C₃	1	2	yes	complemented
26	C₅×#397	C₂×C₃	1	4	yes	complemented
27	C₅×#390	C₂×C₃	1	1	yes	characteristic
28	C₅×#389	C₂×C₃	1	2	yes	complemented
29	C₅×#385	C₂×C₃	1	4	yes	complemented
30	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
31	C₂×C₃×C₅×D₄	—	4	1	no	—
32	C₂×C₃×C₅×D₄	—	4	1	no	—
33	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	4	2	no	—
36	C₂²×C₃×C₄×C₅	—	4	2	no	—
37	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₃×C₅×C₄⋊C₄	—	2	8	no	—
43	C₃×C₅×C₄⋊C₄	—	2	4	no	—
44	C₃×C₅×C₄⋊C₄	—	4	2	no	—
45	C₃×C₅×C₄⋊C₄	—	4	1	no	—
46	C₃×C₅×C₄⋊C₄	—	4	2	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₃×C₄²×C₅	—	4	1	no	—
51	C₂×C₃×#123	C₂×C₅	1	2	yes	—
52	C₃×#398	C₂×C₅	1	2	yes	complemented
53	C₃×#397	C₂×C₅	1	4	yes	complemented
54	C₃×#390	C₂×C₅	1	1	yes	characteristic
55	C₃×#389	C₂×C₅	1	2	yes	complemented
56	C₃×#385	C₂×C₅	1	4	yes	complemented
57	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
58	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
59	C₅×#123	—	2	8	no	—
60	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
66	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₅×#95	C₂²×C₃	1	4	yes	—
70	C₅×#95	C₂²×C₃	1	4	yes	—
71	C₅×#95	C₂²×C₃	1	2	yes	—
72	#2724	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³×C₃×C₅	—	2	4	no	—
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
78	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
79	C₃×C₅×D₄	—	4	4	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	4	8	no	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	4	yes	—
95	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
96	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
97	C₃×#123	—	2	8	no	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
105	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
106	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
107	C₃×#95	C₂²×C₅	1	4	yes	—
108	C₃×#95	C₂²×C₅	1	4	yes	—
109	C₃×#95	C₂²×C₅	1	2	yes	—
110	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
118	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
122	C₅×C₄⋊C₄	—	2	8	no	—
123	C₅×C₄⋊C₄	—	2	4	no	—
124	C₅×C₄⋊C₄	—	4	2	no	—
125	C₅×C₄⋊C₄	—	4	1	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	2	4	no	—
128	C₅×C₂²⋊C₄	—	2	8	no	—
129	C₅×C₂²⋊C₄	—	2	8	no	—
130	C₄²×C₅	—	4	1	no	—
131	C₂×#123	C₂×C₃×C₅	1	2	yes	—
132	#398	C₂×C₃×C₅	1	2	yes	complemented
133	#397	C₂×C₃×C₅	1	4	yes	complemented
134	#390	C₂×C₃×C₅	1	1	yes	characteristic
135	#389	C₂×C₃×C₅	1	2	yes	complemented
136	#385	C₂×C₃×C₅	1	4	yes	complemented
137	C₂²×C₃×C₅	—	2	4	no	—
138	C₂²×C₃×C₅	—	2	8	no	—
139	C₂²×C₃×C₅	—	4	4	no	—
140	C₂²×C₃×C₅	—	4	2	no	—
141	C₂²×C₃×C₅	—	4	2	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	1	yes	characteristic
145	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
146	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	2	4	no	—
149	C₃×C₄×C₅	—	4	4	no	—
150	C₃×C₄×C₅	—	4	4	no	—
151	C₃×C₄×C₅	—	4	2	no	—
152	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
153	C₂×C₃×D₄	—	4	1	no	—
154	C₂×C₃×D₄	—	4	1	no	—
155	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	4	2	no	—
158	C₂²×C₃×C₄	—	4	2	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	2	yes	—
164	C₃×C₄⋊C₄	—	2	8	no	—
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	—	4	2	no	—
167	C₃×C₄⋊C₄	—	4	1	no	—
168	C₃×C₄⋊C₄	—	4	2	no	—
169	C₃×C₂²⋊C₄	—	2	4	no	—
170	C₃×C₂²⋊C₄	—	2	8	no	—
171	C₃×C₂²⋊C₄	—	2	8	no	—
172	C₃×C₄²	—	4	1	no	—
173	C₂³×C₅	—	2	4	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	—	2	4	no	—
177	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
178	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
179	C₅×D₄	—	4	4	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	2	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	4	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	4	8	no	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
194	C₂×C₄×C₅	C₃×#41	1	4	yes	—
195	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
196	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
197	#123	—	2	8	no	—
198	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
199	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
200	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
201	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
202	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
204	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
206	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
207	#95	C₂²×C₃×C₅	1	4	yes	—
208	#95	C₂²×C₃×C₅	1	4	yes	—
209	#95	C₂²×C₃×C₅	1	2	yes	—
210	C₂×C₃×C₅	—	4	4	no	—
211	C₂×C₃×C₅	#534	1	1	yes	characteristic
212	C₂×C₃×C₅	#539	1	2	yes	—
213	C₂×C₃×C₅	#547	1	2	yes	—
214	C₂×C₃×C₅	#559	1	1	yes	characteristic
215	C₂×C₃×C₅	#563	1	1	yes	characteristic
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	2	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
221	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
222	C₃×D₄	—	4	4	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	4	8	no	—
236	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
237	C₂×C₃×C₄	C₅×#41	1	4	yes	—
238	C₂²×C₅	—	2	4	no	—
239	C₂²×C₅	—	2	8	no	—
240	C₂²×C₅	—	4	2	no	—
241	C₂²×C₅	—	4	2	no	—
242	C₂²×C₅	—	4	4	no	—
243	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
244	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
245	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
247	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	4	no	—
250	C₄×C₅	—	4	2	no	—
251	C₄×C₅	—	4	4	no	—
252	C₄×C₅	—	4	4	no	—
253	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	—	4	1	no	—
256	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
261	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
262	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
263	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
265	C₄⋊C₄	—	2	8	no	—
266	C₄⋊C₄	—	2	4	no	—
267	C₄⋊C₄	—	4	2	no	—
268	C₄⋊C₄	—	4	1	no	—
269	C₄⋊C₄	—	4	2	no	—
270	C₂²⋊C₄	—	2	4	no	—
271	C₂²⋊C₄	—	2	8	no	—
272	C₂²⋊C₄	—	2	8	no	—
273	C₄²	—	4	1	no	—
274	C₃×C₅	#2724	1	1	yes	characteristic, direct product factor, Hall
275	C₂²×C₃	—	2	4	no	—
276	C₂²×C₃	—	2	8	no	—
277	C₂²×C₃	—	4	4	no	—
278	C₂²×C₃	—	4	2	no	—
279	C₂²×C₃	—	4	2	no	—
280	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
282	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
283	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
284	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	2	4	no	—
287	C₃×C₄	—	4	4	no	—
288	C₃×C₄	—	4	4	no	—
289	C₃×C₄	—	4	2	no	—
290	C₂×C₅	—	4	4	no	—
291	C₂×C₅	C₃×#534	1	1	yes	characteristic
292	C₂×C₅	C₃×#539	1	2	yes	—
293	C₂×C₅	C₃×#547	1	2	yes	—
294	C₂×C₅	C₃×#559	1	1	yes	characteristic
295	C₂×C₅	C₃×#563	1	1	yes	characteristic
296	C₂³	—	2	4	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
301	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
302	D₄	—	4	4	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
317	C₂×C₄	C₃×C₅×#41	1	4	yes	—
318	C₂×C₃	—	4	4	no	—
319	C₂×C₃	C₅×#534	1	1	yes	characteristic
320	C₂×C₃	C₅×#539	1	2	yes	—
321	C₂×C₃	C₅×#547	1	2	yes	—
322	C₂×C₃	C₅×#559	1	1	yes	characteristic
323	C₂×C₃	C₅×#563	1	1	yes	characteristic
324	C₅	C₃×#2724	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	4	4	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	2	no	—
330	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
331	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
332	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
335	C₄	—	2	2	no	—
336	C₄	—	2	4	no	—
337	C₄	—	4	4	no	—
338	C₄	—	4	4	no	—
339	C₄	—	4	2	no	—
340	C₃	C₅×#2724	1	1	yes	characteristic, direct product factor, Sylow
341	C₂	—	4	4	no	—
342	C₂	C₃×C₅×#534	1	1	yes	characteristic
343	C₂	C₃×C₅×#539	1	2	yes	—
344	C₂	C₃×C₅×#547	1	2	yes	—
345	C₂	C₃×C₅×#559	1	1	yes	characteristic
346	C₂	C₃×C₅×#563	1	1	yes	characteristic

	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
2. C₃×C₅×#398	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#385	C₂	semidirect
7. C₅×#2724	C₃	direct (N × H)
23. C₃×#2724	C₅	direct (N × H)
25. C₅×#398	C₂×C₃	semidirect
26. C₅×#397	C₂×C₃	semidirect
28. C₅×#389	C₂×C₃	semidirect
29. C₅×#385	C₂×C₃	semidirect
52. C₃×#398	C₂×C₅	semidirect
53. C₃×#397	C₂×C₅	semidirect
55. C₃×#389	C₂×C₅	semidirect
56. C₃×#385	C₂×C₅	semidirect
72. #2724	C₃×C₅	direct (N × H)
132. #398	C₂×C₃×C₅	semidirect
133. #397	C₂×C₃×C₅	semidirect
135. #389	C₂×C₃×C₅	semidirect
136. #385	C₂×C₃×C₅	semidirect
274. C₃×C₅	#2724	direct (N × H)
324. C₅	C₃×#2724	direct (N × H)
340. C₃	C₅×#2724	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×#123	2
C₃×C₅×#398	2
C₃×C₅×#397	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#385	2
C₅×#2724	3
C₃×#2724	5

Subgroups — C3×C5×#2724 #14275758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2724 #14275758