Subgroups — C₃×C₅×#2336 #14275370

Order 1920.

856 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#389	C₂	1	2	yes	maximal
3	C₃×C₅×#387	C₂	1	2	yes	maximal
4	C₃×C₅×#387	C₂	1	2	yes	maximal
5	C₃×C₅×#387	C₂	1	2	yes	maximal
6	C₃×C₅×#387	C₂	1	2	yes	maximal
7	C₃×C₅×#383	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
9	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₅×#2336	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×#125	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×#2336	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic
35	C₅×#389	C₂×C₃	1	2	yes	—
36	C₅×#387	C₂×C₃	1	2	yes	—
37	C₅×#387	C₂×C₃	1	2	yes	—
38	C₅×#387	C₂×C₃	1	2	yes	—
39	C₅×#387	C₂×C₃	1	2	yes	—
40	C₅×#383	C₂×C₃	1	1	yes	characteristic
41	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
42	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₄⋊C₄	—	4	2	no	—
55	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
56	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
59	C₃×C₄²×C₅	—	2	4	no	—
60	C₃×C₄²×C₅	—	4	1	no	—
61	C₃×C₄²×C₅	—	4	2	no	—
62	C₃×C₄²×C₅	—	4	1	no	—
63	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
64	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic
65	C₃×#389	C₂×C₅	1	2	yes	—
66	C₃×#387	C₂×C₅	1	2	yes	—
67	C₃×#387	C₂×C₅	1	2	yes	—
68	C₃×#387	C₂×C₅	1	2	yes	—
69	C₃×#387	C₂×C₅	1	2	yes	—
70	C₃×#383	C₂×C₅	1	1	yes	characteristic
71	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
72	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
73	C₅×#125	C₃×C₄	1	8	yes	complemented
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
82	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
85	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
86	C₅×#95	C₂²×C₃	1	2	yes	—
87	C₅×#95	C₂²×C₃	1	2	yes	—
88	C₅×#95	C₂²×C₃	1	2	yes	—
89	C₅×#95	C₂²×C₃	1	2	yes	—
90	C₅×#95	C₂²×C₃	1	1	yes	characteristic
91	C₅×#95	C₂²×C₃	1	1	yes	characteristic
92	C₅×#95	C₂²×C₃	1	2	yes	—
93	C₅×#95	C₂²×C₃	1	2	yes	—
94	C₅×#95	C₂²×C₃	1	2	yes	—
95	#2336	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	1	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
121	C₂×C₃×C₄×C₅	#41	1	4	yes	—
122	C₃×#125	C₄×C₅	1	8	yes	complemented
123	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
135	C₃×#95	C₂²×C₅	1	2	yes	—
136	C₃×#95	C₂²×C₅	1	2	yes	—
137	C₃×#95	C₂²×C₅	1	2	yes	—
138	C₃×#95	C₂²×C₅	1	1	yes	characteristic
139	C₃×#95	C₂²×C₅	1	2	yes	—
140	C₃×#95	C₂²×C₅	1	1	yes	characteristic
141	C₃×#95	C₂²×C₅	1	2	yes	—
142	C₃×#95	C₂²×C₅	1	2	yes	—
143	C₃×#95	C₂²×C₅	1	2	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
145	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	4	2	no	—
156	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
157	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
158	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
159	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
160	C₄²×C₅	—	2	4	no	—
161	C₄²×C₅	—	4	1	no	—
162	C₄²×C₅	—	4	2	no	—
163	C₄²×C₅	—	4	1	no	—
164	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
165	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic
166	#389	C₂×C₃×C₅	1	2	yes	—
167	#387	C₂×C₃×C₅	1	2	yes	—
168	#387	C₂×C₃×C₅	1	2	yes	—
169	#387	C₂×C₃×C₅	1	2	yes	—
170	#387	C₂×C₃×C₅	1	2	yes	—
171	#383	C₂×C₃×C₅	1	1	yes	characteristic
172	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
173	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
175	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
176	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
178	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
179	C₃×C₄×C₅	—	2	4	no	—
180	C₃×C₄×C₅	—	2	2	no	—
181	C₃×C₄×C₅	—	2	2	no	—
182	C₃×C₄×C₅	—	2	2	no	—
183	C₃×C₄×C₅	—	2	4	no	—
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	—	4	2	no	—
187	C₃×C₄×C₅	—	4	2	no	—
188	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
189	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
190	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
194	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
197	C₃×C₄⋊C₄	—	2	4	no	—
198	C₃×C₄⋊C₄	—	2	4	no	—
199	C₃×C₄⋊C₄	—	4	2	no	—
200	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
201	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
202	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
203	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
204	C₃×C₄²	—	2	4	no	—
205	C₃×C₄²	—	4	1	no	—
206	C₃×C₄²	—	4	2	no	—
207	C₃×C₄²	—	4	1	no	—
208	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
209	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
230	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
231	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
232	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
233	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
234	C₂×C₄×C₅	C₃×#41	1	4	yes	—
235	#125	C₃×C₄×C₅	1	8	yes	complemented
236	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
237	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
238	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
239	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
240	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
243	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
244	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
245	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
246	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
247	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
248	#95	C₂²×C₃×C₅	1	2	yes	—
249	#95	C₂²×C₃×C₅	1	2	yes	—
250	#95	C₂²×C₃×C₅	1	2	yes	—
251	#95	C₂²×C₃×C₅	1	1	yes	characteristic
252	#95	C₂²×C₃×C₅	1	2	yes	—
253	#95	C₂²×C₃×C₅	1	1	yes	characteristic
254	#95	C₂²×C₃×C₅	1	2	yes	—
255	#95	C₂²×C₃×C₅	1	2	yes	—
256	#95	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
258	C₂×C₃×C₅	#519	1	1	yes	characteristic
259	C₂×C₃×C₅	#520	1	1	yes	characteristic
260	C₂×C₃×C₅	#539	1	2	yes	—
261	C₂×C₃×C₅	#541	1	2	yes	—
262	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
283	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
284	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
285	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
286	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
287	C₂×C₃×C₄	C₅×#41	1	4	yes	—
288	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
289	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
290	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
292	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
293	C₄×C₅	—	2	4	no	—
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	2	4	no	—
298	C₄×C₅	—	2	4	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	4	2	no	—
302	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
303	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
304	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
305	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
306	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
308	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
309	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
310	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
315	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
316	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
317	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
318	C₄²	—	2	4	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	—	4	1	no	—
322	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
323	C₃×C₅	#2336	1	1	yes	characteristic, direct product factor, Hall
324	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
325	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
326	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
328	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
329	C₃×C₄	—	2	4	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	—	4	2	no	—
337	C₃×C₄	—	4	2	no	—
338	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
339	C₂×C₅	C₃×#519	1	1	yes	characteristic
340	C₂×C₅	C₃×#520	1	1	yes	characteristic
341	C₂×C₅	C₃×#539	1	2	yes	—
342	C₂×C₅	C₃×#541	1	2	yes	—
343	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
364	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
365	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
366	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
367	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
368	C₂×C₄	C₃×C₅×#41	1	4	yes	—
369	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
370	C₂×C₃	C₅×#519	1	1	yes	characteristic
371	C₂×C₃	C₅×#520	1	1	yes	characteristic
372	C₂×C₃	C₅×#539	1	2	yes	—
373	C₂×C₃	C₅×#541	1	2	yes	—
374	C₅	C₃×#2336	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
376	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
377	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
379	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
380	C₄	—	2	4	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	4	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₃	C₅×#2336	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
391	C₂	C₃×C₅×#519	1	1	yes	characteristic
392	C₂	C₃×C₅×#520	1	1	yes	characteristic
393	C₂	C₃×C₅×#539	1	2	yes	—
394	C₂	C₃×C₅×#541	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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
10. C₅×#2336	C₃	direct (N × H)
11. C₃×C₅×#125	C₄	semidirect
33. C₃×#2336	C₅	direct (N × H)
73. C₅×#125	C₃×C₄	semidirect
95. #2336	C₃×C₅	direct (N × H)
122. C₃×#125	C₄×C₅	semidirect
235. #125	C₃×C₄×C₅	semidirect
323. C₃×C₅	#2336	direct (N × H)
374. C₅	C₃×#2336	direct (N × H)
389. C₃	C₅×#2336	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×#125	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#383	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2336	3
C₃×#2336	5

Subgroups — C3×C5×#2336 #14275370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2336 #14275370