Subgroups — C₃×C₅×#2500 #14275534

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2500	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×#121	—	2	4	no	—
15	C₃×C₅×#117	—	2	4	no	—
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	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	4	yes	—
30	C₃×#2500	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
32	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#394	C₂×C₃	1	4	yes	complemented
34	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#388	C₂×C₃	1	4	yes	complemented
37	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
39	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	4	4	no	—
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	4	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
64	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
65	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
66	C₃×C₄²×C₅	—	2	4	no	—
67	C₃×C₄²×C₅	—	2	2	no	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
70	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#394	C₂×C₅	1	4	yes	complemented
72	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#388	C₂×C₅	1	4	yes	complemented
75	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
76	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
80	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₅×#121	—	2	4	no	—
82	C₅×#117	—	2	4	no	—
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
92	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
95	C₅×#95	C₂²×C₃	1	2	yes	—
96	C₅×#95	C₂²×C₃	1	4	yes	—
97	#2500	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	1	no	—
100	C₂³×C₃×C₅	—	2	1	no	—
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	4	no	—
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	4	no	—
107	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
108	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
109	C₃×C₅×D₄	—	4	8	no	—
110	C₃×C₅×D₄	—	4	4	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	1	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	8	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	4	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	4	no	—
124	C₂×C₃×C₄×C₅	—	2	4	no	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	#41	1	4	yes	—
128	C₂×C₃×C₄×C₅	#41	1	2	yes	—
129	C₂×C₃×C₄×C₅	#41	1	2	yes	—
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
132	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
133	C₃×#121	—	2	4	no	—
134	C₃×#117	—	2	4	no	—
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
144	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
147	C₃×#95	C₂²×C₅	1	2	yes	—
148	C₃×#95	C₂²×C₅	1	4	yes	—
149	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
150	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₅×D₄	—	2	4	no	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	—	4	4	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
165	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	4	4	no	—
170	C₅×C₂²⋊C₄	—	2	4	no	—
171	C₅×C₂²⋊C₄	—	2	4	no	—
172	C₅×C₂²⋊C₄	—	2	4	no	—
173	C₅×C₂²⋊C₄	—	2	8	no	—
174	C₅×C₂²⋊C₄	—	4	4	no	—
175	C₄²×C₅	—	2	4	no	—
176	C₄²×C₅	—	2	2	no	—
177	C₄²×C₅	—	2	2	no	—
178	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
179	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
180	#394	C₂×C₃×C₅	1	4	yes	complemented
181	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
182	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
183	#388	C₂×C₃×C₅	1	4	yes	complemented
184	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
187	C₂²×C₃×C₅	—	2	2	no	—
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	4	2	no	—
193	C₂²×C₃×C₅	—	4	2	no	—
194	C₂²×C₃×C₅	—	4	2	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	—	4	4	no	—
197	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
201	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
202	C₃×C₄×C₅	—	2	2	no	—
203	C₃×C₄×C₅	—	2	4	no	—
204	C₃×C₄×C₅	—	4	2	no	—
205	C₃×C₄×C₅	—	4	2	no	—
206	C₃×C₄×C₅	—	4	2	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	#123	1	4	yes	—
209	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
210	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
211	C₂×C₃×D₄	—	2	4	no	—
212	C₂×C₃×D₄	—	2	2	no	—
213	C₂×C₃×D₄	—	2	2	no	—
214	C₂×C₃×D₄	—	2	2	no	—
215	C₂×C₃×D₄	—	4	4	no	—
216	C₂²×C₃×C₄	—	2	2	no	—
217	C₂²×C₃×C₄	—	2	2	no	—
218	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
219	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₃×C₄⋊C₄	—	2	2	no	—
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	2	no	—
229	C₃×C₄⋊C₄	—	4	4	no	—
230	C₃×C₂²⋊C₄	—	2	4	no	—
231	C₃×C₂²⋊C₄	—	2	4	no	—
232	C₃×C₂²⋊C₄	—	2	4	no	—
233	C₃×C₂²⋊C₄	—	2	8	no	—
234	C₃×C₂²⋊C₄	—	4	4	no	—
235	C₃×C₄²	—	2	4	no	—
236	C₃×C₄²	—	2	2	no	—
237	C₃×C₄²	—	2	2	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	1	no	—
240	C₂³×C₅	—	2	1	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	—	2	4	no	—
244	C₂³×C₅	—	2	2	no	—
245	C₂³×C₅	—	2	2	no	—
246	C₂³×C₅	—	2	4	no	—
247	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
248	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
249	C₅×D₄	—	4	8	no	—
250	C₅×D₄	—	4	4	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	8	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	4	no	—
264	C₂×C₄×C₅	—	2	4	no	—
265	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
266	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₄×C₅	C₃×#41	1	4	yes	—
268	C₂×C₄×C₅	C₃×#41	1	2	yes	—
269	C₂×C₄×C₅	C₃×#41	1	2	yes	—
270	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
271	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
272	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
273	#121	—	2	4	no	—
274	#117	—	2	4	no	—
275	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
279	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
283	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
284	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
285	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
286	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
287	#95	C₂²×C₃×C₅	1	2	yes	—
288	#95	C₂²×C₃×C₅	1	4	yes	—
289	C₂×C₃×C₅	—	4	2	no	—
290	C₂×C₃×C₅	—	8	2	no	—
291	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
292	C₂×C₃×C₅	#532	1	1	yes	characteristic
293	C₂×C₃×C₅	#535	1	1	yes	characteristic
294	C₂×C₃×C₅	#553	1	2	yes	—
295	C₂×C₃×C₅	#555	1	2	yes	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	2	1	no	—
298	C₂³×C₃	—	2	1	no	—
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	—	2	2	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	4	no	—
305	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
306	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
307	C₃×D₄	—	4	8	no	—
308	C₃×D₄	—	4	4	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	1	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	8	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	4	no	—
322	C₂×C₃×C₄	—	2	4	no	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
325	C₂×C₃×C₄	C₅×#41	1	4	yes	—
326	C₂×C₃×C₄	C₅×#41	1	2	yes	—
327	C₂×C₃×C₄	C₅×#41	1	2	yes	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	4	2	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	4	no	—
337	C₂²×C₅	—	4	4	no	—
338	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
339	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
340	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
341	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
342	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	2	4	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	—	4	2	no	—
349	C₄×C₅	C₃×#123	1	4	yes	—
350	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
351	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
360	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
361	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
362	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
363	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
364	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
365	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
366	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₄²	—	2	4	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₃×C₅	#2500	1	1	yes	characteristic, direct product factor, Hall
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	4	2	no	—
384	C₂²×C₃	—	4	2	no	—
385	C₂²×C₃	—	4	2	no	—
386	C₂²×C₃	—	4	2	no	—
387	C₂²×C₃	—	4	2	no	—
388	C₂²×C₃	—	4	4	no	—
389	C₂²×C₃	—	4	4	no	—
390	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
391	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
392	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
393	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
394	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	4	no	—
397	C₃×C₄	—	4	2	no	—
398	C₃×C₄	—	4	2	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	C₅×#123	1	4	yes	—
402	C₂×C₅	—	4	2	no	—
403	C₂×C₅	—	8	2	no	—
404	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
405	C₂×C₅	C₃×#532	1	1	yes	characteristic
406	C₂×C₅	C₃×#535	1	1	yes	characteristic
407	C₂×C₅	C₃×#553	1	2	yes	—
408	C₂×C₅	C₃×#555	1	2	yes	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
419	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
420	D₄	—	4	8	no	—
421	D₄	—	4	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
437	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
438	C₂×C₄	C₃×C₅×#41	1	4	yes	—
439	C₂×C₄	C₃×C₅×#41	1	2	yes	—
440	C₂×C₄	C₃×C₅×#41	1	2	yes	—
441	C₂×C₃	—	4	2	no	—
442	C₂×C₃	—	8	2	no	—
443	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
444	C₂×C₃	C₅×#532	1	1	yes	characteristic
445	C₂×C₃	C₅×#535	1	1	yes	characteristic
446	C₂×C₃	C₅×#553	1	2	yes	—
447	C₂×C₃	C₅×#555	1	2	yes	—
448	C₅	C₃×#2500	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
460	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
461	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
462	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
463	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
464	C₄	—	2	2	no	—
465	C₄	—	2	4	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	C₃×C₅×#123	1	4	yes	—
471	C₃	C₅×#2500	1	1	yes	characteristic, direct product factor, Sylow
472	C₂	—	4	2	no	—
473	C₂	—	8	2	no	—
474	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
475	C₂	C₃×C₅×#532	1	1	yes	characteristic
476	C₂	C₃×C₅×#535	1	1	yes	characteristic
477	C₂	C₃×C₅×#553	1	2	yes	—
478	C₂	C₃×C₅×#555	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#121	C₂
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
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₃×C₅×#394	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₃×C₅×#384	C₂	semidirect
8. C₃×C₅×#382	C₂	semidirect
9. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
10. C₅×#2500	C₃	direct (N × H)
30. C₃×#2500	C₅	direct (N × H)
32. C₂×C₅×#117	C₂×C₃	semidirect
33. C₅×#394	C₂×C₃	semidirect
34. C₅×#390	C₂×C₃	semidirect
35. C₅×#390	C₂×C₃	semidirect
36. C₅×#388	C₂×C₃	semidirect
37. C₅×#384	C₂×C₃	semidirect
38. C₅×#382	C₂×C₃	semidirect
39. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
70. C₂×C₃×#117	C₂×C₅	semidirect
71. C₃×#394	C₂×C₅	semidirect
72. C₃×#390	C₂×C₅	semidirect
73. C₃×#390	C₂×C₅	semidirect
74. C₃×#388	C₂×C₅	semidirect
75. C₃×#384	C₂×C₅	semidirect
76. C₃×#382	C₂×C₅	semidirect
77. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
97. #2500	C₃×C₅	direct (N × H)
179. C₂×#117	C₂×C₃×C₅	semidirect
180. #394	C₂×C₃×C₅	semidirect
181. #390	C₂×C₃×C₅	semidirect
182. #390	C₂×C₃×C₅	semidirect
183. #388	C₂×C₃×C₅	semidirect
184. #384	C₂×C₃×C₅	semidirect
185. #382	C₂×C₃×C₅	semidirect
186. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
379. C₃×C₅	#2500	direct (N × H)
448. C₅	C₃×#2500	direct (N × H)
471. C₃	C₅×#2500	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×#121	2
C₂×C₃×C₅×#117	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#384	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2500	3
C₃×#2500	5

Subgroups — C3×C5×#2500 #14275534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2500 #14275534