Subgroups — C₃×C₅×#2372 #14275406

Order 1920.

1120 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	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#386	C₂	1	2	yes	maximal
5	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#376	C₂	1	2	yes	maximal, complemented
7	C₅×#2372	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
11	C₃×C₅×#124	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#95	C₂²	1	2	yes	—
20	C₃×C₅×#95	C₂²	1	4	yes	—
21	C₃×C₅×#95	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×#2372	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
25	C₅×#391	C₂×C₃	1	2	yes	complemented
26	C₅×#388	C₂×C₃	1	4	yes	complemented
27	C₅×#386	C₂×C₃	1	2	yes	—
28	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
29	C₅×#376	C₂×C₃	1	2	yes	complemented
30	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
31	C₂×C₃×C₅×Q₈	—	4	1	no	—
32	C₂×C₃×C₅×Q₈	—	4	1	no	—
33	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
34	C₂×C₃×C₅×D₄	—	4	1	no	—
35	C₂×C₃×C₅×D₄	—	4	1	no	—
36	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	—	2	8	no	—
38	C₂²×C₃×C₄×C₅	—	4	2	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	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	4	yes	—
44	C₃×C₅×C₄⋊C₄	—	4	2	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
46	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
47	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
48	C₃×C₄²×C₅	—	2	8	no	—
49	C₃×C₄²×C₅	—	4	2	no	—
50	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
51	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
52	C₃×#391	C₂×C₅	1	2	yes	complemented
53	C₃×#388	C₂×C₅	1	4	yes	complemented
54	C₃×#386	C₂×C₅	1	2	yes	—
55	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
56	C₃×#376	C₂×C₅	1	2	yes	complemented
57	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
59	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
60	C₅×#124	C₃×C₄	1	8	yes	complemented
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
65	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
66	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
67	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₅×#95	C₂²×C₃	1	2	yes	—
69	C₅×#95	C₂²×C₃	1	4	yes	—
70	C₅×#95	C₂²×C₃	1	2	yes	—
71	C₅×#95	C₂²×C₃	1	4	yes	—
72	#2372	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³×C₃×C₅	—	2	4	no	—
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
78	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
79	C₃×C₅×Q₈	—	4	4	no	—
80	C₃×C₅×D₄	—	4	4	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	4	8	no	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
95	C₂×C₃×C₄×C₅	#41	1	8	yes	—
96	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
97	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
98	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
99	C₃×#124	C₄×C₅	1	8	yes	complemented
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
102	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
104	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
105	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
106	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
107	C₃×#95	C₂²×C₅	1	2	yes	—
108	C₃×#95	C₂²×C₅	1	4	yes	—
109	C₃×#95	C₂²×C₅	1	2	yes	—
110	C₃×#95	C₂²×C₅	1	4	yes	—
111	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
112	C₂×C₅×Q₈	—	4	1	no	—
113	C₂×C₅×Q₈	—	4	1	no	—
114	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂×C₅×D₄	—	4	1	no	—
117	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
118	C₂²×C₄×C₅	—	2	8	no	—
119	C₂²×C₄×C₅	—	4	2	no	—
120	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
125	C₅×C₄⋊C₄	—	4	2	no	—
126	C₅×C₂²⋊C₄	—	2	8	no	—
127	C₅×C₂²⋊C₄	—	4	2	no	—
128	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
129	C₄²×C₅	—	2	8	no	—
130	C₄²×C₅	—	4	2	no	—
131	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
132	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
133	#391	C₂×C₃×C₅	1	2	yes	complemented
134	#388	C₂×C₃×C₅	1	4	yes	complemented
135	#386	C₂×C₃×C₅	1	2	yes	—
136	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	4	yes	complemented
137	#376	C₂×C₃×C₅	1	2	yes	complemented
138	C₂²×C₃×C₅	—	2	8	no	—
139	C₂²×C₃×C₅	—	2	4	no	—
140	C₂²×C₃×C₅	—	4	2	no	—
141	C₂²×C₃×C₅	—	4	2	no	—
142	C₂²×C₃×C₅	—	4	4	no	—
143	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
145	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
146	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
147	C₃×C₄×C₅	—	2	4	no	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	—	2	4	no	—
150	C₃×C₄×C₅	—	2	8	no	—
151	C₃×C₄×C₅	—	4	4	no	—
152	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
153	C₂×C₃×Q₈	—	4	1	no	—
154	C₂×C₃×Q₈	—	4	1	no	—
155	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
156	C₂×C₃×D₄	—	4	1	no	—
157	C₂×C₃×D₄	—	4	1	no	—
158	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
159	C₂²×C₃×C₄	—	2	8	no	—
160	C₂²×C₃×C₄	—	4	2	no	—
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	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
166	C₃×C₄⋊C₄	—	4	2	no	—
167	C₃×C₂²⋊C₄	—	2	8	no	—
168	C₃×C₂²⋊C₄	—	4	2	no	—
169	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
170	C₃×C₄²	—	2	8	no	—
171	C₃×C₄²	—	4	2	no	—
172	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
173	C₂³×C₅	—	2	4	no	—
174	C₂³×C₅	—	2	4	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
178	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
179	C₅×Q₈	—	4	4	no	—
180	C₅×D₄	—	4	4	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	2	4	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	4	8	no	—
192	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
193	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
194	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
195	C₂×C₄×C₅	C₃×#41	1	8	yes	—
196	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
197	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
198	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
199	#124	C₃×C₄×C₅	1	8	yes	complemented
200	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
202	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
203	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
204	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
205	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
206	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
207	#95	C₂²×C₃×C₅	1	2	yes	—
208	#95	C₂²×C₃×C₅	1	4	yes	—
209	#95	C₂²×C₃×C₅	1	2	yes	—
210	#95	C₂²×C₃×C₅	1	4	yes	—
211	C₂×C₃×C₅	—	4	4	no	—
212	C₂×C₃×C₅	C₄×#41	1	2	yes	—
213	C₂×C₃×C₅	#518	1	1	yes	characteristic
214	C₂×C₃×C₅	#551	1	2	yes	—
215	C₂×C₃×C₅	#555	1	2	yes	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	2	2	no	—
219	C₂³×C₃	—	2	2	no	—
220	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
221	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
222	C₃×Q₈	—	4	4	no	—
223	C₃×D₄	—	4	4	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	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	4	8	no	—
235	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
236	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
237	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
238	C₂×C₃×C₄	C₅×#41	1	8	yes	—
239	C₂²×C₅	—	2	8	no	—
240	C₂²×C₅	—	2	4	no	—
241	C₂²×C₅	—	4	2	no	—
242	C₂²×C₅	—	4	2	no	—
243	C₂²×C₅	—	4	4	no	—
244	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
245	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
246	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
247	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
248	C₄×C₅	—	2	4	no	—
249	C₄×C₅	—	2	2	no	—
250	C₄×C₅	—	2	4	no	—
251	C₄×C₅	—	2	8	no	—
252	C₄×C₅	—	4	4	no	—
253	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
254	C₂×Q₈	—	4	1	no	—
255	C₂×Q₈	—	4	1	no	—
256	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
257	C₂×D₄	—	4	1	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	4	2	no	—
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	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
266	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
267	C₄⋊C₄	—	4	2	no	—
268	C₂²⋊C₄	—	2	8	no	—
269	C₂²⋊C₄	—	4	2	no	—
270	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	16	yes	complemented
271	C₄²	—	2	8	no	—
272	C₄²	—	4	2	no	—
273	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
274	C₃×C₅	#2372	1	1	yes	characteristic, direct product factor, Hall
275	C₂²×C₃	—	2	8	no	—
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	4	2	no	—
278	C₂²×C₃	—	4	2	no	—
279	C₂²×C₃	—	4	4	no	—
280	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
282	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
283	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
284	C₃×C₄	—	2	4	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	2	4	no	—
287	C₃×C₄	—	2	8	no	—
288	C₃×C₄	—	4	4	no	—
289	C₂×C₅	—	4	4	no	—
290	C₂×C₅	C₃×C₄×#41	1	2	yes	—
291	C₂×C₅	C₃×#518	1	1	yes	characteristic
292	C₂×C₅	C₃×#551	1	2	yes	—
293	C₂×C₅	C₃×#555	1	2	yes	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
299	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
300	Q₈	—	4	4	no	—
301	D₄	—	4	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
314	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
315	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
316	C₂×C₄	C₃×C₅×#41	1	8	yes	—
317	C₂×C₃	—	4	4	no	—
318	C₂×C₃	C₄×C₅×#41	1	2	yes	—
319	C₂×C₃	C₅×#518	1	1	yes	characteristic
320	C₂×C₃	C₅×#551	1	2	yes	—
321	C₂×C₃	C₅×#555	1	2	yes	—
322	C₅	C₃×#2372	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	8	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	4	no	—
328	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
329	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
330	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	4	no	—
335	C₄	—	2	8	no	—
336	C₄	—	4	4	no	—
337	C₃	C₅×#2372	1	1	yes	characteristic, direct product factor, Sylow
338	C₂	—	4	4	no	—
339	C₂	C₃×C₄×C₅×#41	1	2	yes	—
340	C₂	C₃×C₅×#518	1	1	yes	characteristic
341	C₂	C₃×C₅×#551	1	2	yes	—
342	C₂	C₃×C₅×#555	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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×#391	C₂	semidirect
3. C₃×C₅×#388	C₂	semidirect
5. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
6. C₃×C₅×#376	C₂	semidirect
7. C₅×#2372	C₃	direct (N × H)
11. C₃×C₅×#124	C₄	semidirect
23. C₃×#2372	C₅	direct (N × H)
25. C₅×#391	C₂×C₃	semidirect
26. C₅×#388	C₂×C₃	semidirect
28. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
29. C₅×#376	C₂×C₃	semidirect
33. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
47. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
50. C₃×C₄²×C₅	C₂×C₄	semidirect
52. C₃×#391	C₂×C₅	semidirect
53. C₃×#388	C₂×C₅	semidirect
55. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
56. C₃×#376	C₂×C₅	semidirect
60. C₅×#124	C₃×C₄	semidirect
72. #2372	C₃×C₅	direct (N × H)
99. C₃×#124	C₄×C₅	semidirect
114. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
128. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
131. C₄²×C₅	C₂×C₃×C₄	semidirect
133. #391	C₂×C₃×C₅	semidirect
134. #388	C₂×C₃×C₅	semidirect
136. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
137. #376	C₂×C₃×C₅	semidirect
155. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
169. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
172. C₃×C₄²	C₂×C₄×C₅	semidirect
199. #124	C₃×C₄×C₅	semidirect
256. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
270. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
273. C₄²	C₂×C₃×C₄×C₅	semidirect
274. C₃×C₅	#2372	direct (N × H)
322. C₅	C₃×#2372	direct (N × H)
337. C₃	C₅×#2372	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×#124	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#376	2
C₅×#2372	3
C₃×#2372	5

Subgroups — C3×C5×#2372 #14275406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2372 #14275406