Subgroups — C₃×C₅×#2562 #14275596

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 420 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, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#394	C₂	1	2	yes	maximal
5	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#380	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#380	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2562	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×C₅×#125	—	2	4	no	—
13	C₃×C₄×C₅×D₄	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2562	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
31	C₅×#400	C₂×C₃	1	2	yes	complemented
32	C₅×#394	C₂×C₃	1	2	yes	—
33	C₅×#388	C₂×C₃	1	4	yes	complemented
34	C₅×#380	C₂×C₃	1	2	yes	complemented
35	C₅×#380	C₂×C₃	1	2	yes	complemented
36	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
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	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
59	C₃×C₄²×C₅	—	4	2	no	—
60	C₃×C₄²×C₅	D₄	1	4	yes	—
61	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
63	C₃×#400	C₂×C₅	1	2	yes	complemented
64	C₃×#394	C₂×C₅	1	2	yes	—
65	C₃×#388	C₂×C₅	1	4	yes	complemented
66	C₃×#380	C₂×C₅	1	2	yes	complemented
67	C₃×#380	C₂×C₅	1	2	yes	complemented
68	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
70	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
71	C₅×#125	—	2	4	no	—
72	C₄×C₅×D₄	—	2	4	no	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
82	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
83	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
84	C₅×#95	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	4	yes	—
86	C₅×#95	C₂²×C₃	1	4	yes	—
87	#2562	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	#41	1	4	yes	—
95	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
96	C₃×C₅×D₄	—	2	8	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	4	8	no	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	#41	1	4	yes	—
116	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
118	C₃×#125	—	2	4	no	—
119	C₃×C₄×D₄	—	2	4	no	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	1	yes	characteristic
126	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
127	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
129	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
131	C₃×#95	C₂²×C₅	1	2	yes	—
132	C₃×#95	C₂²×C₅	1	4	yes	—
133	C₃×#95	C₂²×C₅	1	4	yes	—
134	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂²×C₄×C₅	—	2	4	no	—
138	C₂²×C₄×C₅	—	2	4	no	—
139	C₂²×C₄×C₅	—	2	4	no	—
140	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
141	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
142	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
143	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	4	no	—
149	C₅×C₄⋊C₄	—	2	4	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	4	no	—
153	C₅×C₂²⋊C₄	—	2	8	no	—
154	C₅×C₂²⋊C₄	—	2	4	no	—
155	C₅×C₂²⋊C₄	—	4	4	no	—
156	C₄²×C₅	—	4	2	no	—
157	C₄²×C₅	C₃×D₄	1	4	yes	—
158	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
159	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
160	#400	C₂×C₃×C₅	1	2	yes	complemented
161	#394	C₂×C₃×C₅	1	2	yes	—
162	#388	C₂×C₃×C₅	1	4	yes	complemented
163	#380	C₂×C₃×C₅	1	2	yes	complemented
164	#380	C₂×C₃×C₅	1	2	yes	complemented
165	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₅	—	2	4	no	—
167	C₂²×C₃×C₅	—	2	4	no	—
168	C₂²×C₃×C₅	—	2	4	no	—
169	C₂²×C₃×C₅	—	4	2	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
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	1	yes	characteristic
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	2	no	—
180	C₃×C₄×C₅	—	4	2	no	—
181	C₃×C₄×C₅	—	4	2	no	—
182	C₃×C₄×C₅	—	4	2	no	—
183	C₃×C₄×C₅	—	4	4	no	—
184	C₃×C₄×C₅	#124	1	4	yes	—
185	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
186	C₂×C₃×D₄	—	2	4	no	—
187	C₂×C₃×D₄	—	2	2	no	—
188	C₂²×C₃×C₄	—	2	4	no	—
189	C₂²×C₃×C₄	—	2	4	no	—
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
192	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
193	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
194	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₃×C₄⋊C₄	—	2	2	no	—
199	C₃×C₄⋊C₄	—	2	4	no	—
200	C₃×C₄⋊C₄	—	2	4	no	—
201	C₃×C₄⋊C₄	—	2	2	no	—
202	C₃×C₄⋊C₄	—	2	2	no	—
203	C₃×C₄⋊C₄	—	2	4	no	—
204	C₃×C₂²⋊C₄	—	2	8	no	—
205	C₃×C₂²⋊C₄	—	2	4	no	—
206	C₃×C₂²⋊C₄	—	4	4	no	—
207	C₃×C₄²	—	4	2	no	—
208	C₃×C₄²	C₅×D₄	1	4	yes	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	—	2	2	no	—
212	C₂³×C₅	—	2	2	no	—
213	C₂³×C₅	—	2	2	no	—
214	C₂³×C₅	—	2	2	no	—
215	C₂³×C₅	C₃×#41	1	4	yes	—
216	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
217	C₅×D₄	—	2	8	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	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	4	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	4	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	4	8	no	—
233	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
234	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
235	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
236	C₂×C₄×C₅	C₃×#41	1	4	yes	—
237	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
238	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
239	#125	—	2	4	no	—
240	C₄×D₄	—	2	4	no	—
241	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
245	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
246	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
247	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
248	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
249	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
250	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
251	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
252	#95	C₂²×C₃×C₅	1	2	yes	—
253	#95	C₂²×C₃×C₅	1	4	yes	—
254	#95	C₂²×C₃×C₅	1	4	yes	—
255	C₂×C₃×C₅	—	4	4	no	—
256	C₂×C₃×C₅	#525	1	1	yes	characteristic
257	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
258	C₂×C₃×C₅	#537	1	1	yes	characteristic
259	C₂×C₃×C₅	#552	1	2	yes	—
260	C₂×C₃×C₅	#553	1	2	yes	—
261	C₂³×C₃	—	2	2	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	—	2	2	no	—
265	C₂³×C₃	—	2	2	no	—
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	C₅×#41	1	4	yes	—
268	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
269	C₃×D₄	—	2	8	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	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	4	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	4	8	no	—
285	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
286	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
288	C₂×C₃×C₄	C₅×#41	1	4	yes	—
289	C₂²×C₅	—	2	4	no	—
290	C₂²×C₅	—	2	4	no	—
291	C₂²×C₅	—	2	4	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	4	2	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
298	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
299	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
300	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	4	4	no	—
307	C₄×C₅	C₃×#124	1	4	yes	—
308	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
315	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
316	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
317	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
318	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
319	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
320	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₄²	—	4	2	no	—
331	C₄²	C₃×C₅×D₄	1	4	yes	—
332	C₃×C₅	#2562	1	1	yes	characteristic, direct product factor, Hall
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	2	4	no	—
335	C₂²×C₃	—	2	4	no	—
336	C₂²×C₃	—	4	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
341	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
342	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
343	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	—	4	2	no	—
349	C₃×C₄	—	4	2	no	—
350	C₃×C₄	—	4	4	no	—
351	C₃×C₄	C₅×#124	1	4	yes	—
352	C₂×C₅	—	4	4	no	—
353	C₂×C₅	C₃×#525	1	1	yes	characteristic
354	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
355	C₂×C₅	C₃×#537	1	1	yes	characteristic
356	C₂×C₅	C₃×#552	1	2	yes	—
357	C₂×C₅	C₃×#553	1	2	yes	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	C₃×C₅×#41	1	4	yes	—
365	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
366	D₄	—	2	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
383	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
384	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
385	C₂×C₄	C₃×C₅×#41	1	4	yes	—
386	C₂×C₃	—	4	4	no	—
387	C₂×C₃	C₅×#525	1	1	yes	characteristic
388	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
389	C₂×C₃	C₅×#537	1	1	yes	characteristic
390	C₂×C₃	C₅×#552	1	2	yes	—
391	C₂×C₃	C₅×#553	1	2	yes	—
392	C₅	C₃×#2562	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²	—	2	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
401	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
402	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
403	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	4	no	—
411	C₄	C₃×C₅×#124	1	4	yes	—
412	C₃	C₅×#2562	1	1	yes	characteristic, direct product factor, Sylow
413	C₂	—	4	4	no	—
414	C₂	C₃×C₅×#525	1	1	yes	characteristic
415	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
416	C₂	C₃×C₅×#537	1	1	yes	characteristic
417	C₂	C₃×C₅×#552	1	2	yes	—
418	C₂	C₃×C₅×#553	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
5. C₃×C₅×#388	C₂	semidirect
6. C₃×C₅×#380	C₂	semidirect
7. C₃×C₅×#380	C₂	semidirect
8. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
9. C₅×#2562	C₃	direct (N × H)
28. C₃×#2562	C₅	direct (N × H)
29. C₂×C₅×#125	C₂×C₃	semidirect
31. C₅×#400	C₂×C₃	semidirect
33. C₅×#388	C₂×C₃	semidirect
34. C₅×#380	C₂×C₃	semidirect
35. C₅×#380	C₂×C₃	semidirect
36. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
61. C₂×C₃×#125	C₂×C₅	semidirect
63. C₃×#400	C₂×C₅	semidirect
65. C₃×#388	C₂×C₅	semidirect
66. C₃×#380	C₂×C₅	semidirect
67. C₃×#380	C₂×C₅	semidirect
68. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
87. #2562	C₃×C₅	direct (N × H)
158. C₂×#125	C₂×C₃×C₅	semidirect
160. #400	C₂×C₃×C₅	semidirect
162. #388	C₂×C₃×C₅	semidirect
163. #380	C₂×C₃×C₅	semidirect
164. #380	C₂×C₃×C₅	semidirect
165. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
332. C₃×C₅	#2562	direct (N × H)
392. C₅	C₃×#2562	direct (N × H)
412. C₃	C₅×#2562	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
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#400	2
C₃×C₅×#394	2
C₃×C₅×#388	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2562	3
C₃×#2562	5

Subgroups — C3×C5×#2562 #14275596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2562 #14275596