Subgroups — C₃×C₅×#2312 #14275346

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#388	C₂	1	8	yes	maximal, complemented
3	C₃×C₅×#380	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#379	C₂	1	2	yes	maximal
5	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₅×#2312	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
11	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	complemented
17	C₃×C₅×#95	C₂²	1	4	yes	complemented
18	C₃×C₅×#95	C₂²	1	4	yes	complemented
19	C₃×#2312	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
21	C₅×#388	C₂×C₃	1	8	yes	complemented
22	C₅×#380	C₂×C₃	1	2	yes	complemented
23	C₅×#379	C₂×C₃	1	2	yes	—
24	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	—	2	4	no	—
26	C₂⁴×C₃×C₅	—	4	2	no	—
27	C₂⁴×C₃×C₅	—	4	2	no	—
28	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	—
29	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
30	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	—	4	2	no	—
32	C₂²×C₃×C₄×C₅	—	4	2	no	—
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₃×C₅×C₄⋊C₄	—	4	4	no	—
39	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
40	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
41	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
42	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	—
43	C₃×C₄²×C₅	—	4	4	no	—
44	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
45	C₃×#388	C₂×C₅	1	8	yes	complemented
46	C₃×#380	C₂×C₅	1	2	yes	complemented
47	C₃×#379	C₂×C₅	1	2	yes	—
48	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
49	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
51	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
53	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	8	yes	complemented
54	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
55	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
56	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
57	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
58	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	complemented
59	C₅×#95	C₂²×C₃	1	4	yes	complemented
60	C₅×#95	C₂²×C₃	1	4	yes	complemented
61	#2312	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
62	C₂³×C₃×C₅	—	2	2	no	—
63	C₂³×C₃×C₅	—	2	2	no	—
64	C₂³×C₃×C₅	—	2	8	no	—
65	C₂³×C₃×C₅	—	2	4	no	—
66	C₂³×C₃×C₅	—	2	4	no	—
67	C₂³×C₃×C₅	—	2	4	no	—
68	C₂³×C₃×C₅	—	4	4	no	—
69	C₂³×C₃×C₅	—	4	4	no	—
70	C₂³×C₃×C₅	—	4	16	no	—
71	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
72	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
73	C₂³×C₃×C₅	#41	1	4	yes	—
74	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	—	2	4	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	—	2	8	no	—
78	C₂×C₃×C₄×C₅	—	2	8	no	—
79	C₂×C₃×C₄×C₅	—	2	8	no	—
80	C₂×C₃×C₄×C₅	—	4	4	no	—
81	C₂×C₃×C₄×C₅	—	4	4	no	—
82	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
83	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
84	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
85	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
88	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	8	yes	complemented
89	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
93	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	complemented
94	C₃×#95	C₂²×C₅	1	4	yes	complemented
95	C₃×#95	C₂²×C₅	1	4	yes	complemented
96	C₂⁴×C₅	—	2	4	no	—
97	C₂⁴×C₅	—	4	2	no	—
98	C₂⁴×C₅	—	4	2	no	—
99	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	—
100	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
101	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
102	C₂²×C₄×C₅	—	4	2	no	—
103	C₂²×C₄×C₅	—	4	2	no	—
104	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
105	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
106	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
107	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
108	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
109	C₅×C₄⋊C₄	—	4	4	no	—
110	C₅×C₂²⋊C₄	—	2	8	no	—
111	C₅×C₂²⋊C₄	—	4	4	no	—
112	C₅×C₂²⋊C₄	—	4	4	no	—
113	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	—
114	C₄²×C₅	—	4	4	no	—
115	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
116	#388	C₂×C₃×C₅	1	8	yes	complemented
117	#380	C₂×C₃×C₅	1	2	yes	complemented
118	#379	C₂×C₃×C₅	1	2	yes	—
119	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
120	C₂²×C₃×C₅	—	2	2	no	—
121	C₂²×C₃×C₅	—	2	2	no	—
122	C₂²×C₃×C₅	—	2	8	no	—
123	C₂²×C₃×C₅	—	2	4	no	—
124	C₂²×C₃×C₅	—	2	4	no	—
125	C₂²×C₃×C₅	—	2	4	no	—
126	C₂²×C₃×C₅	—	4	16	no	—
127	C₂²×C₃×C₅	—	4	8	no	—
128	C₂²×C₃×C₅	#117	1	4	yes	—
129	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
130	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
131	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
132	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
133	C₃×C₄×C₅	—	2	4	no	—
134	C₃×C₄×C₅	—	2	4	no	—
135	C₃×C₄×C₅	—	4	8	no	—
136	C₂⁴×C₃	—	2	4	no	—
137	C₂⁴×C₃	—	4	2	no	—
138	C₂⁴×C₃	—	4	2	no	—
139	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	—
140	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
141	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
142	C₂²×C₃×C₄	—	4	2	no	—
143	C₂²×C₃×C₄	—	4	2	no	—
144	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
145	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
146	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
147	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
148	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
149	C₃×C₄⋊C₄	—	4	4	no	—
150	C₃×C₂²⋊C₄	—	2	8	no	—
151	C₃×C₂²⋊C₄	—	4	4	no	—
152	C₃×C₂²⋊C₄	—	4	4	no	—
153	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	—
154	C₃×C₄²	—	4	4	no	—
155	C₂³×C₅	—	2	2	no	—
156	C₂³×C₅	—	2	2	no	—
157	C₂³×C₅	—	2	8	no	—
158	C₂³×C₅	—	2	4	no	—
159	C₂³×C₅	—	2	4	no	—
160	C₂³×C₅	—	2	4	no	—
161	C₂³×C₅	—	4	4	no	—
162	C₂³×C₅	—	4	4	no	—
163	C₂³×C₅	—	4	16	no	—
164	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
165	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
166	C₂³×C₅	C₃×#41	1	4	yes	—
167	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	4	no	—
170	C₂×C₄×C₅	—	2	8	no	—
171	C₂×C₄×C₅	—	2	8	no	—
172	C₂×C₄×C₅	—	2	8	no	—
173	C₂×C₄×C₅	—	4	4	no	—
174	C₂×C₄×C₅	—	4	4	no	—
175	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
176	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
177	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
178	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
179	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
180	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
181	C₂×C₂²⋊C₄	C₃×C₄×C₅	1	8	yes	complemented
182	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
183	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
184	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
185	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
186	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	complemented
187	#95	C₂²×C₃×C₅	1	4	yes	complemented
188	#95	C₂²×C₃×C₅	1	4	yes	complemented
189	C₂×C₃×C₅	—	2	4	no	—
190	C₂×C₃×C₅	—	4	4	no	—
191	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
192	C₂×C₃×C₅	#518	1	1	yes	characteristic
193	C₂×C₃×C₅	#518	1	1	yes	characteristic
194	C₂×C₃×C₅	#538	1	4	yes	—
195	C₂³×C₃	—	2	2	no	—
196	C₂³×C₃	—	2	2	no	—
197	C₂³×C₃	—	2	8	no	—
198	C₂³×C₃	—	2	4	no	—
199	C₂³×C₃	—	2	4	no	—
200	C₂³×C₃	—	2	4	no	—
201	C₂³×C₃	—	4	4	no	—
202	C₂³×C₃	—	4	4	no	—
203	C₂³×C₃	—	4	16	no	—
204	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
205	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
206	C₂³×C₃	C₅×#41	1	4	yes	—
207	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	4	no	—
210	C₂×C₃×C₄	—	2	8	no	—
211	C₂×C₃×C₄	—	2	8	no	—
212	C₂×C₃×C₄	—	2	8	no	—
213	C₂×C₃×C₄	—	4	4	no	—
214	C₂×C₃×C₄	—	4	4	no	—
215	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
216	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
217	C₂²×C₅	—	2	2	no	—
218	C₂²×C₅	—	2	2	no	—
219	C₂²×C₅	—	2	8	no	—
220	C₂²×C₅	—	2	4	no	—
221	C₂²×C₅	—	2	4	no	—
222	C₂²×C₅	—	2	4	no	—
223	C₂²×C₅	—	4	16	no	—
224	C₂²×C₅	—	4	8	no	—
225	C₂²×C₅	C₃×#117	1	4	yes	—
226	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
227	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
228	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
229	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
230	C₄×C₅	—	2	4	no	—
231	C₄×C₅	—	2	4	no	—
232	C₄×C₅	—	4	8	no	—
233	C₂⁴	—	2	4	no	—
234	C₂⁴	—	4	2	no	—
235	C₂⁴	—	4	2	no	—
236	C₂⁴	C₂×C₃×C₄×C₅	1	4	yes	—
237	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
238	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
242	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
243	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
244	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
245	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
246	C₄⋊C₄	—	4	4	no	—
247	C₂²⋊C₄	—	2	8	no	—
248	C₂²⋊C₄	—	4	4	no	—
249	C₂²⋊C₄	—	4	4	no	—
250	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	16	yes	—
251	C₄²	—	4	4	no	—
252	C₃×C₅	#2312	1	1	yes	characteristic, direct product factor, Hall
253	C₂²×C₃	—	2	2	no	—
254	C₂²×C₃	—	2	2	no	—
255	C₂²×C₃	—	2	8	no	—
256	C₂²×C₃	—	2	4	no	—
257	C₂²×C₃	—	2	4	no	—
258	C₂²×C₃	—	2	4	no	—
259	C₂²×C₃	—	4	16	no	—
260	C₂²×C₃	—	4	8	no	—
261	C₂²×C₃	C₅×#117	1	4	yes	—
262	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
263	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
264	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
265	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
266	C₃×C₄	—	2	4	no	—
267	C₃×C₄	—	2	4	no	—
268	C₃×C₄	—	4	8	no	—
269	C₂×C₅	—	2	4	no	—
270	C₂×C₅	—	4	4	no	—
271	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
272	C₂×C₅	C₃×#518	1	1	yes	characteristic
273	C₂×C₅	C₃×#518	1	1	yes	characteristic
274	C₂×C₅	C₃×#538	1	4	yes	—
275	C₂³	—	2	2	no	—
276	C₂³	—	2	2	no	—
277	C₂³	—	2	8	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	4	4	no	—
282	C₂³	—	4	4	no	—
283	C₂³	—	4	16	no	—
284	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
285	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
286	C₂³	C₃×C₅×#41	1	4	yes	—
287	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
296	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
297	C₂×C₃	—	2	4	no	—
298	C₂×C₃	—	4	4	no	—
299	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
300	C₂×C₃	C₅×#518	1	1	yes	characteristic
301	C₂×C₃	C₅×#518	1	1	yes	characteristic
302	C₂×C₃	C₅×#538	1	4	yes	—
303	C₅	C₃×#2312	1	1	yes	characteristic, direct product factor, Sylow
304	C₂²	—	2	2	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	8	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	4	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	4	16	no	—
311	C₂²	—	4	8	no	—
312	C₂²	C₃×C₅×#117	1	4	yes	—
313	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
314	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
315	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
316	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
317	C₄	—	2	4	no	—
318	C₄	—	2	4	no	—
319	C₄	—	4	8	no	—
320	C₃	C₅×#2312	1	1	yes	characteristic, direct product factor, Sylow
321	C₂	—	2	4	no	—
322	C₂	—	4	4	no	—
323	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
324	C₂	C₃×C₅×#518	1	1	yes	characteristic
325	C₂	C₃×C₅×#518	1	1	yes	characteristic
326	C₂	C₃×C₅×#538	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁵×C₃×C₅	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×#388	C₂	semidirect
3. C₃×C₅×#380	C₂	semidirect
5. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
6. C₅×#2312	C₃	direct (N × H)
10. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
11. C₂×C₃×C₅×C₂²⋊C₄	C₄	semidirect
16. C₂×C₃×C₄²×C₅	C₂²	semidirect
17. C₃×C₅×#95	C₂²	semidirect
18. C₃×C₅×#95	C₂²	semidirect
19. C₃×#2312	C₅	direct (N × H)
21. C₅×#388	C₂×C₃	semidirect
22. C₅×#380	C₂×C₃	semidirect
24. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
45. C₃×#388	C₂×C₅	semidirect
46. C₃×#380	C₂×C₅	semidirect
48. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
52. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
53. C₂×C₅×C₂²⋊C₄	C₃×C₄	semidirect
58. C₂×C₄²×C₅	C₂²×C₃	semidirect
59. C₅×#95	C₂²×C₃	semidirect
60. C₅×#95	C₂²×C₃	semidirect
61. #2312	C₃×C₅	direct (N × H)
87. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
88. C₂×C₃×C₂²⋊C₄	C₄×C₅	semidirect
93. C₂×C₃×C₄²	C₂²×C₅	semidirect
94. C₃×#95	C₂²×C₅	semidirect
95. C₃×#95	C₂²×C₅	semidirect
116. #388	C₂×C₃×C₅	semidirect
117. #380	C₂×C₃×C₅	semidirect
119. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
180. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
181. C₂×C₂²⋊C₄	C₃×C₄×C₅	semidirect
186. C₂×C₄²	C₂²×C₃×C₅	semidirect
187. #95	C₂²×C₃×C₅	semidirect
188. #95	C₂²×C₃×C₅	semidirect
252. C₃×C₅	#2312	direct (N × H)
303. C₅	C₃×#2312	direct (N × H)
320. C₃	C₅×#2312	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#388	2
C₃×C₅×#380	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2312	3
C₃×#2312	5

Subgroups — C3×C5×#2312 #14275346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2312 #14275346