Subgroups — C₃×C₅×#2285 #14275319

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	2	yes	maximal
2	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#384	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#382	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#380	C₂	1	4	yes	maximal
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₅×#2285	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	—	2	8	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₄²×C₅	C₄	1	8	yes	complemented
15	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
19	C₃×C₅×#95	C₂²	1	8	yes	—
20	C₃×#2285	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₅×#117	C₂×C₃	1	2	yes	—
22	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
23	C₅×#384	C₂×C₃	1	2	yes	complemented
24	C₅×#382	C₂×C₃	1	2	yes	complemented
25	C₅×#380	C₂×C₃	1	4	yes	—
26	C₄×C₅×C₄⋊C₄	C₂×C₃	1	4	yes	complemented
27	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	—	2	8	no	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
31	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
32	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
33	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₄	—	2	8	no	—
39	C₃×C₅×C₄⋊C₄	—	2	16	no	—
40	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
41	C₃×C₄²×C₅	—	2	8	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
43	C₃×C₄²×C₅	C₂×C₄	1	8	yes	—
44	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
45	C₂×C₃×#117	C₂×C₅	1	2	yes	—
46	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic
47	C₃×#384	C₂×C₅	1	2	yes	complemented
48	C₃×#382	C₂×C₅	1	2	yes	complemented
49	C₃×#380	C₂×C₅	1	4	yes	—
50	C₃×C₄×C₄⋊C₄	C₂×C₅	1	4	yes	complemented
51	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
52	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
53	C₅×#117	—	2	8	no	—
54	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
55	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
56	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
57	C₂×C₄²×C₅	C₃×C₄	1	8	yes	complemented
58	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
59	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
60	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₅×#95	C₂²×C₃	1	8	yes	—
63	#2285	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂³×C₃×C₅	—	2	4	no	—
65	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
66	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
67	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
68	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	—	2	4	no	—
70	C₂×C₃×C₄×C₅	—	2	16	no	—
71	C₂×C₃×C₄×C₅	—	2	8	no	—
72	C₂×C₃×C₄×C₅	—	2	16	no	—
73	C₂×C₃×C₄×C₅	C₄⋊C₄	1	16	yes	complemented
74	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
75	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
76	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
78	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
81	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
82	C₂×C₃×C₄×C₅	#41	1	8	yes	—
83	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
84	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
85	C₃×#117	—	2	8	no	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
87	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
89	C₂×C₃×C₄²	C₄×C₅	1	8	yes	complemented
90	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
91	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
92	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
94	C₃×#95	C₂²×C₅	1	8	yes	—
95	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
96	C₂²×C₄×C₅	—	2	8	no	—
97	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
98	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
99	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
100	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
101	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
102	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
103	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
106	C₅×C₄⋊C₄	—	2	8	no	—
107	C₅×C₄⋊C₄	—	2	16	no	—
108	C₅×C₂²⋊C₄	—	2	8	no	—
109	C₄²×C₅	—	2	8	no	—
110	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
111	C₄²×C₅	C₂×C₃×C₄	1	8	yes	—
112	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
113	C₂×#117	C₂×C₃×C₅	1	2	yes	—
114	C₂²×C₄²	C₂×C₃×C₅	1	1	yes	characteristic
115	#384	C₂×C₃×C₅	1	2	yes	complemented
116	#382	C₂×C₃×C₅	1	2	yes	complemented
117	#380	C₂×C₃×C₅	1	4	yes	—
118	C₄×C₄⋊C₄	C₂×C₃×C₅	1	4	yes	complemented
119	C₂²×C₃×C₅	—	2	4	no	—
120	C₂²×C₃×C₅	—	2	4	no	—
121	C₂²×C₃×C₅	—	2	4	no	—
122	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
123	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
124	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
125	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
126	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
127	C₃×C₄×C₅	—	2	4	no	—
128	C₃×C₄×C₅	—	4	8	no	—
129	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
130	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
131	C₃×C₄×C₅	#117	1	8	yes	complemented
132	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
133	C₂²×C₃×C₄	—	2	8	no	—
134	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
135	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
136	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
137	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
138	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
139	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
140	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
143	C₃×C₄⋊C₄	—	2	8	no	—
144	C₃×C₄⋊C₄	—	2	16	no	—
145	C₃×C₂²⋊C₄	—	2	8	no	—
146	C₃×C₄²	—	2	8	no	—
147	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
148	C₃×C₄²	C₂×C₄×C₅	1	8	yes	—
149	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
150	C₂³×C₅	—	2	4	no	—
151	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
152	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
153	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
154	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
155	C₂×C₄×C₅	—	2	4	no	—
156	C₂×C₄×C₅	—	2	16	no	—
157	C₂×C₄×C₅	—	2	8	no	—
158	C₂×C₄×C₅	—	2	16	no	—
159	C₂×C₄×C₅	C₃×C₄⋊C₄	1	16	yes	complemented
160	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
161	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
162	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
163	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
164	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
165	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
166	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
167	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
168	C₂×C₄×C₅	C₃×#41	1	8	yes	—
169	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
170	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
171	#117	—	2	8	no	—
172	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
173	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
174	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
175	C₂×C₄²	C₃×C₄×C₅	1	8	yes	complemented
176	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
177	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
178	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
179	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
180	#95	C₂²×C₃×C₅	1	8	yes	—
181	C₂×C₃×C₅	—	2	4	no	—
182	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₃×C₅	C₂×#117	1	2	yes	—
184	C₂×C₃×C₅	#532	1	2	yes	—
185	C₂×C₃×C₅	#533	1	2	yes	—
186	C₂³×C₃	—	2	4	no	—
187	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
188	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
189	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
190	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
191	C₂×C₃×C₄	—	2	4	no	—
192	C₂×C₃×C₄	—	2	16	no	—
193	C₂×C₃×C₄	—	2	8	no	—
194	C₂×C₃×C₄	—	2	16	no	—
195	C₂×C₃×C₄	C₅×C₄⋊C₄	1	16	yes	complemented
196	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
197	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
198	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
199	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
200	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
201	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
202	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
203	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
204	C₂×C₃×C₄	C₅×#41	1	8	yes	—
205	C₂²×C₅	—	2	4	no	—
206	C₂²×C₅	—	2	4	no	—
207	C₂²×C₅	—	2	4	no	—
208	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
209	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
210	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
211	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
212	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
213	C₄×C₅	—	2	4	no	—
214	C₄×C₅	—	4	8	no	—
215	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
216	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
217	C₄×C₅	C₃×#117	1	8	yes	complemented
218	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
219	C₂²×C₄	—	2	8	no	—
220	C₂²×C₄	C₂×C₃×C₄×C₅	1	8	yes	—
221	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
222	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
223	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	—
224	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
225	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
226	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
227	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
228	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
229	C₄⋊C₄	—	2	8	no	—
230	C₄⋊C₄	—	2	16	no	—
231	C₂²⋊C₄	—	2	8	no	—
232	C₄²	—	2	8	no	—
233	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
234	C₄²	C₂×C₃×C₄×C₅	1	8	yes	—
235	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
236	C₃×C₅	#2285	1	1	yes	characteristic, direct product factor, Hall
237	C₂²×C₃	—	2	4	no	—
238	C₂²×C₃	—	2	4	no	—
239	C₂²×C₃	—	2	4	no	—
240	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
241	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
242	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
243	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
244	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
245	C₃×C₄	—	2	4	no	—
246	C₃×C₄	—	4	8	no	—
247	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
248	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
249	C₃×C₄	C₅×#117	1	8	yes	complemented
250	C₂×C₅	—	2	4	no	—
251	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₅	C₂×C₃×#117	1	2	yes	—
253	C₂×C₅	C₃×#532	1	2	yes	—
254	C₂×C₅	C₃×#533	1	2	yes	—
255	C₂³	—	2	4	no	—
256	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
257	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
258	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
259	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
260	C₂×C₄	—	2	4	no	—
261	C₂×C₄	—	2	16	no	—
262	C₂×C₄	—	2	8	no	—
263	C₂×C₄	—	2	16	no	—
264	C₂×C₄	C₃×C₅×C₄⋊C₄	1	16	yes	complemented
265	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
266	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
267	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
268	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
269	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
270	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
271	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
272	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
273	C₂×C₄	C₃×C₅×#41	1	8	yes	—
274	C₂×C₃	—	2	4	no	—
275	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₃	C₂×C₅×#117	1	2	yes	—
277	C₂×C₃	C₅×#532	1	2	yes	—
278	C₂×C₃	C₅×#533	1	2	yes	—
279	C₅	C₃×#2285	1	1	yes	characteristic, direct product factor, Sylow
280	C₂²	—	2	4	no	—
281	C₂²	—	2	4	no	—
282	C₂²	—	2	4	no	—
283	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	4	yes	—
284	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
285	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
286	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
287	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
288	C₄	—	2	4	no	—
289	C₄	—	4	8	no	—
290	C₄	C₂×C₃×C₅×C₄⋊C₄	1	4	yes	—
291	C₄	C₂×C₃×C₅×C₄⋊C₄	1	4	yes	—
292	C₄	C₃×C₅×#117	1	8	yes	complemented
293	C₃	C₅×#2285	1	1	yes	characteristic, direct product factor, Sylow
294	C₂	—	2	4	no	—
295	C₂	C₂²×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
296	C₂	C₂×C₃×C₅×#117	1	2	yes	—
297	C₂	C₃×C₅×#532	1	2	yes	—
298	C₂	C₃×C₅×#533	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#384	C₂	semidirect
4. C₃×C₅×#382	C₂	semidirect
6. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
7. C₅×#2285	C₃	direct (N × H)
14. C₂×C₃×C₄²×C₅	C₄	semidirect
20. C₃×#2285	C₅	direct (N × H)
23. C₅×#384	C₂×C₃	semidirect
24. C₅×#382	C₂×C₃	semidirect
26. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
47. C₃×#384	C₂×C₅	semidirect
48. C₃×#382	C₂×C₅	semidirect
50. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
57. C₂×C₄²×C₅	C₃×C₄	semidirect
63. #2285	C₃×C₅	direct (N × H)
73. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
89. C₂×C₃×C₄²	C₄×C₅	semidirect
115. #384	C₂×C₃×C₅	semidirect
116. #382	C₂×C₃×C₅	semidirect
118. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
131. C₃×C₄×C₅	#117	semidirect
159. C₂×C₄×C₅	C₃×C₄⋊C₄	semidirect
175. C₂×C₄²	C₃×C₄×C₅	semidirect
195. C₂×C₃×C₄	C₅×C₄⋊C₄	semidirect
217. C₄×C₅	C₃×#117	semidirect
236. C₃×C₅	#2285	direct (N × H)
249. C₃×C₄	C₅×#117	semidirect
264. C₂×C₄	C₃×C₅×C₄⋊C₄	semidirect
279. C₅	C₃×#2285	direct (N × H)
292. C₄	C₃×C₅×#117	semidirect
293. C₃	C₅×#2285	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×#117	2
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#384	2
C₃×C₅×#382	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2285	3
C₃×#2285	5

Subgroups — C3×C5×#2285 #14275319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2285 #14275319