Subgroups — C₃×C₅×#2375 #14275409

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#390	C₂	1	3	yes	maximal, complemented
3	C₃×C₅×#388	C₂	1	6	yes	maximal, complemented
4	C₃×C₅×#386	C₂	1	3	yes	maximal, complemented
5	C₃×C₅×#379	C₂	1	2	yes	maximal, complemented
6	C₅×#2375	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
10	C₃×C₅×#120	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	complemented
12	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	6	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	6	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
16	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	complemented
17	C₃×C₅×#95	C₂²	1	6	yes	complemented
18	C₃×#2375	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic
20	C₅×#390	C₂×C₃	1	3	yes	complemented
21	C₅×#388	C₂×C₃	1	6	yes	complemented
22	C₅×#386	C₂×C₃	1	3	yes	complemented
23	C₅×#379	C₂×C₃	1	2	yes	complemented
24	C₂⁴×C₃×C₅	—	4	3	no	—
25	C₂⁴×C₃×C₅	—	4	3	no	—
26	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
27	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
28	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₃×C₅×D₄	—	4	3	no	—
30	C₂×C₃×C₅×D₄	—	4	3	no	—
31	C₂×C₃×C₅×D₄	C₂×C₄	1	12	yes	—
32	C₂²×C₃×C₄×C₅	—	4	3	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
36	C₃×C₅×C₄⋊C₄	—	4	3	no	—
37	C₃×C₅×C₂²⋊C₄	—	4	6	no	—
38	C₃×C₅×C₂²⋊C₄	—	4	6	no	—
39	C₃×C₅×C₂²⋊C₄	—	4	3	no	—
40	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	12	yes	complemented
41	C₃×C₄²×C₅	—	4	3	no	—
42	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
43	C₃×#390	C₂×C₅	1	3	yes	complemented
44	C₃×#388	C₂×C₅	1	6	yes	complemented
45	C₃×#386	C₂×C₅	1	3	yes	complemented
46	C₃×#379	C₂×C₅	1	2	yes	complemented
47	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
49	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
50	C₅×#120	C₃×C₄	1	8	yes	complemented
51	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
52	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
53	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
54	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
55	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
56	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	complemented
57	C₅×#95	C₂²×C₃	1	6	yes	complemented
58	#2375	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₂³×C₃×C₅	—	2	3	no	—
60	C₂³×C₃×C₅	—	2	6	no	—
61	C₂³×C₃×C₅	—	2	6	no	—
62	C₂³×C₃×C₅	—	2	3	no	—
63	C₂³×C₃×C₅	—	2	3	no	—
64	C₂³×C₃×C₅	—	2	3	no	—
65	C₂³×C₃×C₅	—	4	12	no	—
66	C₂³×C₃×C₅	—	4	12	no	—
67	C₂³×C₃×C₅	—	4	4	no	—
68	C₂³×C₃×C₅	C₂²×C₄	1	6	yes	—
69	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
70	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
71	C₃×C₅×D₄	—	4	12	no	—
72	C₂×C₃×C₄×C₅	—	2	3	no	—
73	C₂×C₃×C₄×C₅	—	2	3	no	—
74	C₂×C₃×C₄×C₅	—	2	6	no	—
75	C₂×C₃×C₄×C₅	—	2	6	no	—
76	C₂×C₃×C₄×C₅	—	2	6	no	—
77	C₂×C₃×C₄×C₅	—	2	6	no	—
78	C₂×C₃×C₄×C₅	—	4	4	no	—
79	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
80	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
81	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
82	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
83	C₃×#120	C₄×C₅	1	8	yes	complemented
84	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	3	yes	complemented
85	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	—
87	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
89	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	complemented
90	C₃×#95	C₂²×C₅	1	6	yes	complemented
91	C₂⁴×C₅	—	4	3	no	—
92	C₂⁴×C₅	—	4	3	no	—
93	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	complemented
94	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
95	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
96	C₂×C₅×D₄	—	4	3	no	—
97	C₂×C₅×D₄	—	4	3	no	—
98	C₂×C₅×D₄	C₂×C₃×C₄	1	12	yes	—
99	C₂²×C₄×C₅	—	4	3	no	—
100	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
101	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
102	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
103	C₅×C₄⋊C₄	—	4	3	no	—
104	C₅×C₂²⋊C₄	—	4	6	no	—
105	C₅×C₂²⋊C₄	—	4	6	no	—
106	C₅×C₂²⋊C₄	—	4	3	no	—
107	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	12	yes	complemented
108	C₄²×C₅	—	4	3	no	—
109	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
110	#390	C₂×C₃×C₅	1	3	yes	complemented
111	#388	C₂×C₃×C₅	1	6	yes	complemented
112	#386	C₂×C₃×C₅	1	3	yes	complemented
113	#379	C₂×C₃×C₅	1	2	yes	complemented
114	C₂²×C₃×C₅	—	2	6	no	—
115	C₂²×C₃×C₅	—	2	6	no	—
116	C₂²×C₃×C₅	—	2	12	no	—
117	C₂²×C₃×C₅	—	4	16	no	—
118	C₂²×C₃×C₅	—	4	3	no	—
119	C₂²×C₃×C₅	—	4	3	no	—
120	C₂²×C₃×C₅	—	4	6	no	—
121	C₂²×C₃×C₅	—	4	1	no	—
122	C₂²×C₃×C₅	—	4	3	no	—
123	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
124	C₂²×C₃×C₅	H(5,𝔽₂)	1	3	yes	—
125	C₂²×C₃×C₅	H(5,𝔽₂)	1	3	yes	—
126	C₃×C₄×C₅	—	2	6	no	—
127	C₃×C₄×C₅	—	4	6	no	—
128	C₃×C₄×C₅	—	4	2	no	—
129	C₂⁴×C₃	—	4	3	no	—
130	C₂⁴×C₃	—	4	3	no	—
131	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	complemented
132	C₂⁴×C₃	C₂³×C₅	1	3	yes	—
133	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
134	C₂×C₃×D₄	—	4	3	no	—
135	C₂×C₃×D₄	—	4	3	no	—
136	C₂×C₃×D₄	C₂×C₄×C₅	1	12	yes	—
137	C₂²×C₃×C₄	—	4	3	no	—
138	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
139	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
140	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
141	C₃×C₄⋊C₄	—	4	3	no	—
142	C₃×C₂²⋊C₄	—	4	6	no	—
143	C₃×C₂²⋊C₄	—	4	6	no	—
144	C₃×C₂²⋊C₄	—	4	3	no	—
145	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	12	yes	complemented
146	C₃×C₄²	—	4	3	no	—
147	C₂³×C₅	—	2	3	no	—
148	C₂³×C₅	—	2	6	no	—
149	C₂³×C₅	—	2	6	no	—
150	C₂³×C₅	—	2	3	no	—
151	C₂³×C₅	—	2	3	no	—
152	C₂³×C₅	—	2	3	no	—
153	C₂³×C₅	—	4	12	no	—
154	C₂³×C₅	—	4	12	no	—
155	C₂³×C₅	—	4	4	no	—
156	C₂³×C₅	C₂²×C₃×C₄	1	6	yes	—
157	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
158	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
159	C₅×D₄	—	4	12	no	—
160	C₂×C₄×C₅	—	2	3	no	—
161	C₂×C₄×C₅	—	2	3	no	—
162	C₂×C₄×C₅	—	2	6	no	—
163	C₂×C₄×C₅	—	2	6	no	—
164	C₂×C₄×C₅	—	2	6	no	—
165	C₂×C₄×C₅	—	2	6	no	—
166	C₂×C₄×C₅	—	4	4	no	—
167	C₂×C₄×C₅	C₂²×C₃×C₄	1	6	yes	—
168	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
169	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
170	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
171	#120	C₃×C₄×C₅	1	8	yes	complemented
172	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
173	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	6	yes	—
174	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	6	yes	—
175	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	—
176	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	complemented
177	C₂×C₄²	C₂²×C₃×C₅	1	3	yes	complemented
178	#95	C₂²×C₃×C₅	1	6	yes	complemented
179	C₂×C₃×C₅	—	4	2	no	—
180	C₂×C₃×C₅	—	4	6	no	—
181	C₂×C₃×C₅	#518	1	3	yes	—
182	C₂×C₃×C₅	#560	1	3	yes	—
183	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
184	C₂³×C₃	—	2	3	no	—
185	C₂³×C₃	—	2	6	no	—
186	C₂³×C₃	—	2	6	no	—
187	C₂³×C₃	—	2	3	no	—
188	C₂³×C₃	—	2	3	no	—
189	C₂³×C₃	—	2	3	no	—
190	C₂³×C₃	—	4	12	no	—
191	C₂³×C₃	—	4	12	no	—
192	C₂³×C₃	—	4	4	no	—
193	C₂³×C₃	C₂²×C₄×C₅	1	6	yes	—
194	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
195	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
196	C₃×D₄	—	4	12	no	—
197	C₂×C₃×C₄	—	2	3	no	—
198	C₂×C₃×C₄	—	2	3	no	—
199	C₂×C₃×C₄	—	2	6	no	—
200	C₂×C₃×C₄	—	2	6	no	—
201	C₂×C₃×C₄	—	2	6	no	—
202	C₂×C₃×C₄	—	2	6	no	—
203	C₂×C₃×C₄	—	4	4	no	—
204	C₂×C₃×C₄	C₂²×C₄×C₅	1	6	yes	—
205	C₂²×C₅	—	2	6	no	—
206	C₂²×C₅	—	2	6	no	—
207	C₂²×C₅	—	2	12	no	—
208	C₂²×C₅	—	4	16	no	—
209	C₂²×C₅	—	4	3	no	—
210	C₂²×C₅	—	4	3	no	—
211	C₂²×C₅	—	4	6	no	—
212	C₂²×C₅	—	4	1	no	—
213	C₂²×C₅	—	4	3	no	—
214	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
215	C₂²×C₅	C₃×H(5,𝔽₂)	1	3	yes	—
216	C₂²×C₅	C₃×H(5,𝔽₂)	1	3	yes	—
217	C₄×C₅	—	2	6	no	—
218	C₄×C₅	—	4	6	no	—
219	C₄×C₅	—	4	2	no	—
220	C₂⁴	—	4	3	no	—
221	C₂⁴	—	4	3	no	—
222	C₂⁴	C₂×C₃×C₄×C₅	1	4	yes	complemented
223	C₂⁴	C₂³×C₃×C₅	1	3	yes	—
224	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
225	C₂×D₄	—	4	3	no	—
226	C₂×D₄	—	4	3	no	—
227	C₂×D₄	C₂×C₃×C₄×C₅	1	12	yes	—
228	C₂²×C₄	—	4	3	no	—
229	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
230	C₂²×C₄	C₂³×C₃×C₅	1	6	yes	—
231	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
232	C₄⋊C₄	—	4	3	no	—
233	C₂²⋊C₄	—	4	6	no	—
234	C₂²⋊C₄	—	4	6	no	—
235	C₂²⋊C₄	—	4	3	no	—
236	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	12	yes	complemented
237	C₄²	—	4	3	no	—
238	C₃×C₅	#2375	1	1	yes	characteristic, direct product factor, Hall
239	C₂²×C₃	—	2	6	no	—
240	C₂²×C₃	—	2	6	no	—
241	C₂²×C₃	—	2	12	no	—
242	C₂²×C₃	—	4	16	no	—
243	C₂²×C₃	—	4	3	no	—
244	C₂²×C₃	—	4	3	no	—
245	C₂²×C₃	—	4	6	no	—
246	C₂²×C₃	—	4	1	no	—
247	C₂²×C₃	—	4	3	no	—
248	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
249	C₂²×C₃	C₅×H(5,𝔽₂)	1	3	yes	—
250	C₂²×C₃	C₅×H(5,𝔽₂)	1	3	yes	—
251	C₃×C₄	—	2	6	no	—
252	C₃×C₄	—	4	6	no	—
253	C₃×C₄	—	4	2	no	—
254	C₂×C₅	—	4	6	no	—
255	C₂×C₅	—	4	2	no	—
256	C₂×C₅	C₃×#518	1	3	yes	—
257	C₂×C₅	C₃×#560	1	3	yes	—
258	C₂×C₅	C₃×H(3,𝔽₄)	1	1	yes	characteristic
259	C₂³	—	2	3	no	—
260	C₂³	—	2	6	no	—
261	C₂³	—	2	6	no	—
262	C₂³	—	2	3	no	—
263	C₂³	—	2	3	no	—
264	C₂³	—	2	3	no	—
265	C₂³	—	4	12	no	—
266	C₂³	—	4	12	no	—
267	C₂³	—	4	4	no	—
268	C₂³	C₂²×C₃×C₄×C₅	1	6	yes	—
269	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
270	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
271	D₄	—	4	12	no	—
272	C₂×C₄	—	2	3	no	—
273	C₂×C₄	—	2	3	no	—
274	C₂×C₄	—	2	6	no	—
275	C₂×C₄	—	2	6	no	—
276	C₂×C₄	—	2	6	no	—
277	C₂×C₄	—	2	6	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	C₂²×C₃×C₄×C₅	1	6	yes	—
280	C₂×C₃	—	4	6	no	—
281	C₂×C₃	—	4	2	no	—
282	C₂×C₃	C₅×#518	1	3	yes	—
283	C₂×C₃	C₅×#560	1	3	yes	—
284	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
285	C₅	C₃×#2375	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²	—	2	6	no	—
287	C₂²	—	2	6	no	—
288	C₂²	—	2	12	no	—
289	C₂²	—	4	16	no	—
290	C₂²	—	4	3	no	—
291	C₂²	—	4	6	no	—
292	C₂²	—	4	3	no	—
293	C₂²	—	4	1	no	—
294	C₂²	—	4	3	no	—
295	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
296	C₂²	C₃×C₅×H(5,𝔽₂)	1	3	yes	—
297	C₂²	C₃×C₅×H(5,𝔽₂)	1	3	yes	—
298	C₄	—	2	6	no	—
299	C₄	—	4	6	no	—
300	C₄	—	4	2	no	—
301	C₃	C₅×#2375	1	1	yes	characteristic, direct product factor, Sylow
302	C₂	—	4	6	no	—
303	C₂	—	4	2	no	—
304	C₂	C₃×C₅×#518	1	3	yes	—
305	C₂	C₃×C₅×#560	1	3	yes	—
306	C₂	C₃×C₅×H(3,𝔽₄)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#120	C₂
LCS	G ▷ C₂² ▷ 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×#390	C₂	semidirect
3. C₃×C₅×#388	C₂	semidirect
4. C₃×C₅×#386	C₂	semidirect
5. C₃×C₅×#379	C₂	semidirect
6. C₅×#2375	C₃	direct (N × H)
9. C₂³×C₃×C₄×C₅	C₂²	semidirect
10. C₃×C₅×#120	C₄	semidirect
11. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
15. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
16. C₂×C₃×C₄²×C₅	C₂²	semidirect
17. C₃×C₅×#95	C₂²	semidirect
18. C₃×#2375	C₅	direct (N × H)
20. C₅×#390	C₂×C₃	semidirect
21. C₅×#388	C₂×C₃	semidirect
22. C₅×#386	C₂×C₃	semidirect
23. C₅×#379	C₂×C₃	semidirect
26. C₂⁴×C₃×C₅	C₂×C₄	semidirect
40. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
43. C₃×#390	C₂×C₅	semidirect
44. C₃×#388	C₂×C₅	semidirect
45. C₃×#386	C₂×C₅	semidirect
46. C₃×#379	C₂×C₅	semidirect
49. C₂³×C₄×C₅	C₂²×C₃	semidirect
50. C₅×#120	C₃×C₄	semidirect
51. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
55. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
56. C₂×C₄²×C₅	C₂²×C₃	semidirect
57. C₅×#95	C₂²×C₃	semidirect
58. #2375	C₃×C₅	direct (N × H)
82. C₂³×C₃×C₄	C₂²×C₅	semidirect
83. C₃×#120	C₄×C₅	semidirect
84. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
88. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
89. C₂×C₃×C₄²	C₂²×C₅	semidirect
90. C₃×#95	C₂²×C₅	semidirect
93. C₂⁴×C₅	C₂×C₃×C₄	semidirect
107. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
110. #390	C₂×C₃×C₅	semidirect
111. #388	C₂×C₃×C₅	semidirect
112. #386	C₂×C₃×C₅	semidirect
113. #379	C₂×C₃×C₅	semidirect
131. C₂⁴×C₃	C₂×C₄×C₅	semidirect
145. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
170. C₂³×C₄	C₂²×C₃×C₅	semidirect
171. #120	C₃×C₄×C₅	semidirect
172. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
176. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
177. C₂×C₄²	C₂²×C₃×C₅	semidirect
178. #95	C₂²×C₃×C₅	semidirect
222. C₂⁴	C₂×C₃×C₄×C₅	semidirect
236. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
238. C₃×C₅	#2375	direct (N × H)
285. C₅	C₃×#2375	direct (N × H)
301. C₃	C₅×#2375	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×#120	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#379	2
C₅×#2375	3
C₃×#2375	5

Subgroups — C3×C5×#2375 #14275409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2375 #14275409