Subgroups — C₃×C₅×#2388 #14275422

Order 1920.

1888 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	3	yes	maximal, complemented
3	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	3	yes	maximal, complemented
5	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#392	C₂	1	3	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
8	C₅×#2388	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	—	2	12	no	—
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
15	C₃×C₄×C₅×D₄	—	2	12	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	6	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
21	C₃×C₅×#95	C₂²	1	3	yes	—
22	C₃×C₅×#95	C₂²	1	3	yes	—
23	C₃×#2388	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×C₄×C₅×D₄	C₂×C₃	1	3	yes	complemented
26	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×#394	C₂×C₃	1	3	yes	complemented
28	C₅×#393	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#392	C₂×C₃	1	3	yes	complemented
30	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	3	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₃×C₅×#41	—	2	32	no	—
34	C₂×C₃×C₅×Q₈	—	2	6	no	—
35	C₂×C₃×C₅×D₄	—	2	6	no	—
36	C₂×C₃×C₅×D₄	—	2	12	no	—
37	C₂×C₃×C₅×D₄	—	2	6	no	—
38	C₂×C₃×C₅×D₄	—	2	6	no	—
39	C₂×C₃×C₅×D₄	—	2	6	no	—
40	C₂²×C₃×C₄×C₅	—	2	12	no	—
41	C₂²×C₃×C₄×C₅	—	2	6	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	12	yes	complemented
43	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	—	2	6	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	12	no	—
52	C₃×C₄²×C₅	—	2	6	no	—
53	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂×C₃×C₄×D₄	C₂×C₅	1	3	yes	complemented
55	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
56	C₃×#394	C₂×C₅	1	3	yes	complemented
57	C₃×#393	C₂×C₅	1	1	yes	characteristic, complemented
58	C₃×#392	C₂×C₅	1	3	yes	complemented
59	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	3	yes	complemented
60	C₂×C₅×#41	—	2	12	no	—
61	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
63	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
64	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
66	C₄×C₅×D₄	—	2	12	no	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	3	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
71	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	—
72	C₅×#95	C₂²×C₃	1	3	yes	—
73	C₅×#95	C₂²×C₃	1	3	yes	—
74	#2388	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
75	C₂³×C₃×C₅	—	2	3	no	—
76	C₂³×C₃×C₅	—	2	6	no	—
77	C₂³×C₃×C₅	—	2	6	no	—
78	C₂³×C₃×C₅	—	2	3	no	—
79	C₂³×C₃×C₅	—	2	3	no	—
80	C₂³×C₃×C₅	—	2	3	no	—
81	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
82	C₂³×C₃×C₅	#41	1	2	yes	complemented
83	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
84	C₃×C₅×Q₈	—	2	8	no	—
85	C₃×C₅×D₄	—	2	24	no	—
86	C₃×C₅×D₄	—	2	24	no	—
87	C₂×C₃×C₄×C₅	—	2	3	no	—
88	C₂×C₃×C₄×C₅	—	2	6	no	—
89	C₂×C₃×C₄×C₅	—	2	3	no	—
90	C₂×C₃×C₄×C₅	—	2	24	no	—
91	C₂×C₃×C₄×C₅	—	2	3	no	—
92	C₂×C₃×C₄×C₅	—	2	3	no	—
93	C₂×C₃×C₄×C₅	—	2	6	no	—
94	C₂×C₃×C₄×C₅	—	4	4	no	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
97	C₂×C₃×C₄×C₅	#41	1	6	yes	complemented
98	C₂×C₃×#41	—	2	12	no	—
99	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
100	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
101	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
102	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂²×C₅	1	3	yes	—
104	C₃×C₄×D₄	—	2	12	no	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	3	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
109	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	—
110	C₃×#95	C₂²×C₅	1	3	yes	—
111	C₃×#95	C₂²×C₅	1	3	yes	—
112	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
113	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
114	C₅×#41	—	2	32	no	—
115	C₂×C₅×Q₈	—	2	6	no	—
116	C₂×C₅×D₄	—	2	6	no	—
117	C₂×C₅×D₄	—	2	12	no	—
118	C₂×C₅×D₄	—	2	6	no	—
119	C₂×C₅×D₄	—	2	6	no	—
120	C₂×C₅×D₄	—	2	6	no	—
121	C₂²×C₄×C₅	—	2	12	no	—
122	C₂²×C₄×C₅	—	2	6	no	—
123	C₂²×C₄×C₅	C₃×D₄	1	12	yes	complemented
124	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₅×C₄⋊C₄	—	2	6	no	—
130	C₅×C₂²⋊C₄	—	2	6	no	—
131	C₅×C₂²⋊C₄	—	2	6	no	—
132	C₅×C₂²⋊C₄	—	2	12	no	—
133	C₄²×C₅	—	2	6	no	—
134	C₂²×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
135	C₂×C₄×D₄	C₂×C₃×C₅	1	3	yes	complemented
136	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
137	#394	C₂×C₃×C₅	1	3	yes	complemented
138	#393	C₂×C₃×C₅	1	1	yes	characteristic, complemented
139	#392	C₂×C₃×C₅	1	3	yes	complemented
140	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	3	yes	complemented
141	C₂²×C₃×C₅	—	2	6	no	—
142	C₂²×C₃×C₅	—	2	6	no	—
143	C₂²×C₃×C₅	—	2	6	no	—
144	C₂²×C₃×C₅	—	2	6	no	—
145	C₂²×C₃×C₅	—	4	1	no	—
146	C₂²×C₃×C₅	—	4	6	no	—
147	C₂²×C₃×C₅	—	4	3	no	—
148	C₂²×C₃×C₅	—	4	6	no	—
149	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
150	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×#41	1	3	yes	—
152	C₃×C₄×C₅	—	2	6	no	—
153	C₃×C₄×C₅	—	2	6	no	—
154	C₃×C₄×C₅	—	4	1	no	—
155	C₃×C₄×C₅	—	4	3	no	—
156	C₃×C₄×C₅	#120	1	4	yes	—
157	C₂⁴×C₃	C₂³×C₅	1	3	yes	—
158	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
159	C₃×#41	—	2	32	no	—
160	C₂×C₃×Q₈	—	2	6	no	—
161	C₂×C₃×D₄	—	2	6	no	—
162	C₂×C₃×D₄	—	2	12	no	—
163	C₂×C₃×D₄	—	2	6	no	—
164	C₂×C₃×D₄	—	2	6	no	—
165	C₂×C₃×D₄	—	2	6	no	—
166	C₂²×C₃×C₄	—	2	12	no	—
167	C₂²×C₃×C₄	—	2	6	no	—
168	C₂²×C₃×C₄	C₅×D₄	1	12	yes	complemented
169	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
172	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₃×C₄⋊C₄	—	2	6	no	—
175	C₃×C₂²⋊C₄	—	2	6	no	—
176	C₃×C₂²⋊C₄	—	2	6	no	—
177	C₃×C₂²⋊C₄	—	2	12	no	—
178	C₃×C₄²	—	2	6	no	—
179	C₂³×C₅	—	2	3	no	—
180	C₂³×C₅	—	2	6	no	—
181	C₂³×C₅	—	2	6	no	—
182	C₂³×C₅	—	2	3	no	—
183	C₂³×C₅	—	2	3	no	—
184	C₂³×C₅	—	2	3	no	—
185	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
186	C₂³×C₅	C₃×#41	1	2	yes	complemented
187	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
188	C₅×Q₈	—	2	8	no	—
189	C₅×D₄	—	2	24	no	—
190	C₅×D₄	—	2	24	no	—
191	C₂×C₄×C₅	—	2	3	no	—
192	C₂×C₄×C₅	—	2	6	no	—
193	C₂×C₄×C₅	—	2	3	no	—
194	C₂×C₄×C₅	—	2	24	no	—
195	C₂×C₄×C₅	—	2	3	no	—
196	C₂×C₄×C₅	—	2	3	no	—
197	C₂×C₄×C₅	—	2	6	no	—
198	C₂×C₄×C₅	—	4	4	no	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
200	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
201	C₂×C₄×C₅	C₃×#41	1	6	yes	complemented
202	C₂×#41	—	2	12	no	—
203	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
205	C₂²×D₄	C₂²×C₃×C₅	1	3	yes	—
206	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂³×C₄	C₂²×C₃×C₅	1	3	yes	—
208	C₄×D₄	—	2	12	no	—
209	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	3	yes	—
210	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	—
211	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	3	yes	—
212	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	6	yes	—
213	C₂×C₄²	C₂²×C₃×C₅	1	3	yes	—
214	#95	C₂²×C₃×C₅	1	3	yes	—
215	#95	C₂²×C₃×C₅	1	3	yes	—
216	C₂×C₃×C₅	—	4	6	no	—
217	C₂×C₃×C₅	—	4	2	no	—
218	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
219	C₂×C₃×C₅	#525	1	3	yes	—
220	C₂×C₃×C₅	#532	1	3	yes	—
221	C₂³×C₃	—	2	3	no	—
222	C₂³×C₃	—	2	6	no	—
223	C₂³×C₃	—	2	6	no	—
224	C₂³×C₃	—	2	3	no	—
225	C₂³×C₃	—	2	3	no	—
226	C₂³×C₃	—	2	3	no	—
227	C₂³×C₃	C₂×C₅×D₄	1	6	yes	—
228	C₂³×C₃	C₅×#41	1	2	yes	complemented
229	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
230	C₃×Q₈	—	2	8	no	—
231	C₃×D₄	—	2	24	no	—
232	C₃×D₄	—	2	24	no	—
233	C₂×C₃×C₄	—	2	3	no	—
234	C₂×C₃×C₄	—	2	6	no	—
235	C₂×C₃×C₄	—	2	3	no	—
236	C₂×C₃×C₄	—	2	24	no	—
237	C₂×C₃×C₄	—	2	3	no	—
238	C₂×C₃×C₄	—	2	3	no	—
239	C₂×C₃×C₄	—	2	6	no	—
240	C₂×C₃×C₄	—	4	4	no	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
243	C₂×C₃×C₄	C₅×#41	1	6	yes	complemented
244	C₂²×C₅	—	2	6	no	—
245	C₂²×C₅	—	2	6	no	—
246	C₂²×C₅	—	2	6	no	—
247	C₂²×C₅	—	2	6	no	—
248	C₂²×C₅	—	4	1	no	—
249	C₂²×C₅	—	4	6	no	—
250	C₂²×C₅	—	4	3	no	—
251	C₂²×C₅	—	4	6	no	—
252	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
253	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
254	C₂²×C₅	C₂×C₃×#41	1	3	yes	—
255	C₄×C₅	—	2	6	no	—
256	C₄×C₅	—	2	6	no	—
257	C₄×C₅	—	4	1	no	—
258	C₄×C₅	—	4	3	no	—
259	C₄×C₅	C₃×#120	1	4	yes	—
260	C₂⁴	C₂³×C₃×C₅	1	3	yes	—
261	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
262	#41	—	2	32	no	—
263	C₂×Q₈	—	2	6	no	—
264	C₂×D₄	—	2	6	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	6	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	2	6	no	—
269	C₂²×C₄	—	2	12	no	—
270	C₂²×C₄	—	2	6	no	—
271	C₂²×C₄	C₃×C₅×D₄	1	12	yes	complemented
272	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
273	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
275	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
276	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
277	C₄⋊C₄	—	2	6	no	—
278	C₂²⋊C₄	—	2	6	no	—
279	C₂²⋊C₄	—	2	6	no	—
280	C₂²⋊C₄	—	2	12	no	—
281	C₄²	—	2	6	no	—
282	C₃×C₅	#2388	1	1	yes	characteristic, direct product factor, Hall
283	C₂²×C₃	—	2	6	no	—
284	C₂²×C₃	—	2	6	no	—
285	C₂²×C₃	—	2	6	no	—
286	C₂²×C₃	—	2	6	no	—
287	C₂²×C₃	—	4	1	no	—
288	C₂²×C₃	—	4	6	no	—
289	C₂²×C₃	—	4	3	no	—
290	C₂²×C₃	—	4	6	no	—
291	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
292	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
293	C₂²×C₃	C₂×C₅×#41	1	3	yes	—
294	C₃×C₄	—	2	6	no	—
295	C₃×C₄	—	2	6	no	—
296	C₃×C₄	—	4	1	no	—
297	C₃×C₄	—	4	3	no	—
298	C₃×C₄	C₅×#120	1	4	yes	—
299	C₂×C₅	—	4	6	no	—
300	C₂×C₅	—	4	2	no	—
301	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
302	C₂×C₅	C₃×#525	1	3	yes	—
303	C₂×C₅	C₃×#532	1	3	yes	—
304	C₂³	—	2	3	no	—
305	C₂³	—	2	6	no	—
306	C₂³	—	2	6	no	—
307	C₂³	—	2	3	no	—
308	C₂³	—	2	3	no	—
309	C₂³	—	2	3	no	—
310	C₂³	C₂×C₃×C₅×D₄	1	6	yes	—
311	C₂³	C₃×C₅×#41	1	2	yes	complemented
312	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
313	Q₈	—	2	8	no	—
314	D₄	—	2	24	no	—
315	D₄	—	2	24	no	—
316	C₂×C₄	—	2	3	no	—
317	C₂×C₄	—	2	6	no	—
318	C₂×C₄	—	2	3	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	3	no	—
321	C₂×C₄	—	2	3	no	—
322	C₂×C₄	—	2	6	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	—
325	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	—
326	C₂×C₄	C₃×C₅×#41	1	6	yes	complemented
327	C₂×C₃	—	4	6	no	—
328	C₂×C₃	—	4	2	no	—
329	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
330	C₂×C₃	C₅×#525	1	3	yes	—
331	C₂×C₃	C₅×#532	1	3	yes	—
332	C₅	C₃×#2388	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²	—	2	6	no	—
334	C₂²	—	2	6	no	—
335	C₂²	—	2	6	no	—
336	C₂²	—	2	6	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	6	no	—
339	C₂²	—	4	3	no	—
340	C₂²	—	4	6	no	—
341	C₂²	C₂²×C₃×C₅×D₄	1	3	yes	—
342	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
343	C₂²	C₂×C₃×C₅×#41	1	3	yes	—
344	C₄	—	2	6	no	—
345	C₄	—	2	6	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	3	no	—
348	C₄	C₃×C₅×#120	1	4	yes	—
349	C₃	C₅×#2388	1	1	yes	characteristic, direct product factor, Sylow
350	C₂	—	4	6	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
353	C₂	C₃×C₅×#525	1	3	yes	—
354	C₂	C₃×C₅×#532	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₅×#395	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#393	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₅×#2388	C₃	direct (N × H)
23. C₃×#2388	C₅	direct (N × H)
24. C₂²×C₅×#41	C₂×C₃	semidirect
25. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
26. C₅×#395	C₂×C₃	semidirect
27. C₅×#394	C₂×C₃	semidirect
28. C₅×#393	C₂×C₃	semidirect
29. C₅×#392	C₂×C₃	semidirect
30. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
42. C₂²×C₃×C₄×C₅	D₄	semidirect
53. C₂²×C₃×#41	C₂×C₅	semidirect
54. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
55. C₃×#395	C₂×C₅	semidirect
56. C₃×#394	C₂×C₅	semidirect
57. C₃×#393	C₂×C₅	semidirect
58. C₃×#392	C₂×C₅	semidirect
59. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
74. #2388	C₃×C₅	direct (N × H)
82. C₂³×C₃×C₅	#41	semidirect
97. C₂×C₃×C₄×C₅	#41	semidirect
123. C₂²×C₄×C₅	C₃×D₄	semidirect
134. C₂²×#41	C₂×C₃×C₅	semidirect
135. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
136. #395	C₂×C₃×C₅	semidirect
137. #394	C₂×C₃×C₅	semidirect
138. #393	C₂×C₃×C₅	semidirect
139. #392	C₂×C₃×C₅	semidirect
140. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
168. C₂²×C₃×C₄	C₅×D₄	semidirect
186. C₂³×C₅	C₃×#41	semidirect
201. C₂×C₄×C₅	C₃×#41	semidirect
228. C₂³×C₃	C₅×#41	semidirect
243. C₂×C₃×C₄	C₅×#41	semidirect
271. C₂²×C₄	C₃×C₅×D₄	semidirect
282. C₃×C₅	#2388	direct (N × H)
311. C₂³	C₃×C₅×#41	semidirect
326. C₂×C₄	C₃×C₅×#41	semidirect
332. C₅	C₃×#2388	direct (N × H)
349. C₃	C₅×#2388	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×#41	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#395	2
C₃×C₅×#394	2
C₃×C₅×#393	2
C₃×C₅×#392	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2388	3
C₃×#2388	5

Subgroups — C3×C5×#2388 #14275422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2388 #14275422