Subgroups — C₃×C₅×#2357 #14275391

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#390	C₂	1	2	yes	maximal
3	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#381	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₅×#2357	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₄×C₅×D₄	C₄	1	8	yes	complemented
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	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×#95	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	1	yes	characteristic
25	C₃×C₅×#95	C₂²	1	4	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×#2357	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
29	C₅×#390	C₂×C₃	1	2	yes	—
30	C₅×#388	C₂×C₃	1	4	yes	complemented
31	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#381	C₂×C₃	1	2	yes	complemented
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
35	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
36	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	—	4	4	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
53	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
54	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
55	C₃×C₄²×C₅	—	2	4	no	—
56	C₃×C₄²×C₅	—	4	4	no	—
57	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
58	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
59	C₃×#390	C₂×C₅	1	2	yes	—
60	C₃×#388	C₂×C₅	1	4	yes	complemented
61	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#381	C₂×C₅	1	2	yes	complemented
63	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
65	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
66	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
68	C₄×C₅×D₄	C₃×C₄	1	8	yes	complemented
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
73	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
76	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
78	C₅×#95	C₂²×C₃	1	1	yes	characteristic
79	C₅×#95	C₂²×C₃	1	2	yes	—
80	C₅×#95	C₂²×C₃	1	1	yes	characteristic
81	C₅×#95	C₂²×C₃	1	4	yes	—
82	C₅×#95	C₂²×C₃	1	2	yes	—
83	#2357	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³×C₃×C₅	—	2	4	no	—
85	C₂³×C₃×C₅	—	2	2	no	—
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	4	no	—
88	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
89	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
90	C₃×C₅×D₄	—	2	8	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	4	8	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	4	yes	—
108	C₂×C₃×C₄×C₅	#41	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	2	yes	—
110	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
111	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
112	C₃×C₄×D₄	C₄×C₅	1	8	yes	complemented
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
118	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
121	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
122	C₃×#95	C₂²×C₅	1	1	yes	characteristic
123	C₃×#95	C₂²×C₅	1	2	yes	—
124	C₃×#95	C₂²×C₅	1	1	yes	characteristic
125	C₃×#95	C₂²×C₅	1	4	yes	—
126	C₃×#95	C₂²×C₅	1	2	yes	—
127	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
131	C₂²×C₄×C₅	—	4	4	no	—
132	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
143	C₅×C₂²⋊C₄	—	2	8	no	—
144	C₅×C₂²⋊C₄	—	4	4	no	—
145	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
146	C₄²×C₅	—	2	4	no	—
147	C₄²×C₅	—	4	4	no	—
148	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
149	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
150	#390	C₂×C₃×C₅	1	2	yes	—
151	#388	C₂×C₃×C₅	1	4	yes	complemented
152	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
153	#381	C₂×C₃×C₅	1	2	yes	complemented
154	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
155	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
156	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
157	C₂²×C₃×C₅	—	2	4	no	—
158	C₂²×C₃×C₅	—	2	4	no	—
159	C₂²×C₃×C₅	—	2	4	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	—	4	4	no	—
162	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
166	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	2	4	no	—
170	C₃×C₄×C₅	—	2	4	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	4	no	—
173	C₃×C₄×C₅	#117	1	4	yes	—
174	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	2	2	no	—
177	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
178	C₂²×C₃×C₄	—	4	4	no	—
179	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
180	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
190	C₃×C₂²⋊C₄	—	2	8	no	—
191	C₃×C₂²⋊C₄	—	4	4	no	—
192	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
193	C₃×C₄²	—	2	4	no	—
194	C₃×C₄²	—	4	4	no	—
195	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	2	2	no	—
199	C₂³×C₅	—	2	4	no	—
200	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
201	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
202	C₅×D₄	—	2	8	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	8	no	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×C₄×C₅	C₃×#41	1	4	yes	—
220	C₂×C₄×C₅	C₃×#41	1	2	yes	—
221	C₂×C₄×C₅	C₃×#41	1	2	yes	—
222	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
224	C₄×D₄	C₃×C₄×C₅	1	8	yes	complemented
225	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
230	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
232	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
233	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
234	#95	C₂²×C₃×C₅	1	1	yes	characteristic
235	#95	C₂²×C₃×C₅	1	2	yes	—
236	#95	C₂²×C₃×C₅	1	1	yes	characteristic
237	#95	C₂²×C₃×C₅	1	4	yes	—
238	#95	C₂²×C₃×C₅	1	2	yes	—
239	C₂×C₃×C₅	—	4	4	no	—
240	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
241	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
242	C₂×C₃×C₅	#518	1	1	yes	characteristic
243	C₂×C₃×C₅	#553	1	2	yes	—
244	C₂×C₃×C₅	#559	1	2	yes	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
250	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
251	C₃×D₄	—	2	8	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	4	8	no	—
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
266	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
268	C₂×C₃×C₄	C₅×#41	1	4	yes	—
269	C₂×C₃×C₄	C₅×#41	1	2	yes	—
270	C₂×C₃×C₄	C₅×#41	1	2	yes	—
271	C₂²×C₅	—	2	4	no	—
272	C₂²×C₅	—	2	4	no	—
273	C₂²×C₅	—	2	4	no	—
274	C₂²×C₅	—	4	4	no	—
275	C₂²×C₅	—	4	4	no	—
276	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
277	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
278	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
279	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
280	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
281	C₄×C₅	—	2	2	no	—
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	2	4	no	—
284	C₄×C₅	—	2	4	no	—
285	C₄×C₅	—	4	4	no	—
286	C₄×C₅	—	4	2	no	—
287	C₄×C₅	C₃×#117	1	4	yes	—
288	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	C₂×C₃×C₄×C₅	1	8	yes	—
294	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
295	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
296	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
298	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
300	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
304	C₂²⋊C₄	—	2	8	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
307	C₄²	—	2	4	no	—
308	C₄²	—	4	4	no	—
309	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
310	C₃×C₅	#2357	1	1	yes	characteristic, direct product factor, Hall
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	4	4	no	—
315	C₂²×C₃	—	4	4	no	—
316	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
317	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
319	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
320	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	4	2	no	—
326	C₃×C₄	—	4	4	no	—
327	C₃×C₄	C₅×#117	1	4	yes	—
328	C₂×C₅	—	4	4	no	—
329	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
330	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
331	C₂×C₅	C₃×#518	1	1	yes	characteristic
332	C₂×C₅	C₃×#553	1	2	yes	—
333	C₂×C₅	C₃×#559	1	2	yes	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
339	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
340	D₄	—	2	8	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
354	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
355	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
356	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
357	C₂×C₄	C₃×C₅×#41	1	4	yes	—
358	C₂×C₄	C₃×C₅×#41	1	2	yes	—
359	C₂×C₄	C₃×C₅×#41	1	2	yes	—
360	C₂×C₃	—	4	4	no	—
361	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
362	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
363	C₂×C₃	C₅×#518	1	1	yes	characteristic
364	C₂×C₃	C₅×#553	1	2	yes	—
365	C₂×C₃	C₅×#559	1	2	yes	—
366	C₅	C₃×#2357	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	2	4	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
373	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
374	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
375	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
376	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	4	no	—
380	C₄	—	2	4	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	4	no	—
383	C₄	C₃×C₅×#117	1	4	yes	—
384	C₃	C₅×#2357	1	1	yes	characteristic, direct product factor, Sylow
385	C₂	—	4	4	no	—
386	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
387	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
388	C₂	C₃×C₅×#518	1	1	yes	characteristic
389	C₂	C₃×C₅×#553	1	2	yes	—
390	C₂	C₃×C₅×#559	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
3. C₃×C₅×#388	C₂	semidirect
4. C₃×C₅×#382	C₂	semidirect
5. C₃×C₅×#381	C₂	semidirect
6. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
9. C₅×#2357	C₃	direct (N × H)
12. C₃×C₄×C₅×D₄	C₄	semidirect
27. C₃×#2357	C₅	direct (N × H)
30. C₅×#388	C₂×C₃	semidirect
31. C₅×#382	C₂×C₃	semidirect
32. C₅×#381	C₂×C₃	semidirect
33. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
34. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
35. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
60. C₃×#388	C₂×C₅	semidirect
61. C₃×#382	C₂×C₅	semidirect
62. C₃×#381	C₂×C₅	semidirect
63. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
64. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
65. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
68. C₄×C₅×D₄	C₃×C₄	semidirect
83. #2357	C₃×C₅	direct (N × H)
112. C₃×C₄×D₄	C₄×C₅	semidirect
151. #388	C₂×C₃×C₅	semidirect
152. #382	C₂×C₃×C₅	semidirect
153. #381	C₂×C₃×C₅	semidirect
154. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
155. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
156. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
224. C₄×D₄	C₃×C₄×C₅	semidirect
310. C₃×C₅	#2357	direct (N × H)
366. C₅	C₃×#2357	direct (N × H)
384. C₃	C₅×#2357	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×C₄×C₅×D₄	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#382	2
C₃×C₅×#381	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2357	3
C₃×#2357	5

Subgroups — C3×C5×#2357 #14275391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2357 #14275391