Subgroups — C₃×C₅×#2540 #14275574

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#399	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#390	C₂	1	4	yes	maximal, complemented
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2540	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₃×C₅×#124	—	2	4	no	—
16	C₃×C₅×C₂²⋊Q₈	—	2	8	no	—
17	C₃×C₅×#121	—	2	8	no	—
18	C₃×C₄×C₅×D₄	—	2	4	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₄⋊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×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×#2540	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
33	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
34	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#399	C₂×C₃	1	2	yes	complemented
36	C₅×#392	C₂×C₃	1	2	yes	complemented
37	C₅×#390	C₂×C₃	1	4	yes	complemented
38	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
40	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
41	C₂×C₃×C₅×Q₈	—	2	4	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	—	2	8	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	8	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	—	4	4	no	—
50	C₂²×C₃×C₄×C₅	—	2	4	no	—
51	C₂²×C₃×C₄×C₅	—	2	4	no	—
52	C₂²×C₃×C₄×C₅	—	2	4	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	8	no	—
61	C₃×C₅×C₄⋊C₄	D₄	1	8	yes	complemented
62	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
64	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
67	C₃×C₄²×C₅	—	4	2	no	—
68	C₃×C₄²×C₅	D₄	1	4	yes	complemented
69	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
71	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
72	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×#399	C₂×C₅	1	2	yes	complemented
74	C₃×#392	C₂×C₅	1	2	yes	complemented
75	C₃×#390	C₂×C₅	1	4	yes	complemented
76	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
81	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
82	C₅×#124	—	2	4	no	—
83	C₅×C₂²⋊Q₈	—	2	8	no	—
84	C₅×#121	—	2	8	no	—
85	C₄×C₅×D₄	—	2	4	no	—
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
95	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	#2540	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂³×C₃×C₅	—	2	4	no	—
106	C₂³×C₃×C₅	—	2	4	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	#41	1	4	yes	—
110	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
111	C₃×C₅×Q₈	—	4	4	no	—
112	C₃×C₅×D₄	—	2	8	no	—
113	C₃×C₅×D₄	—	4	16	no	—
114	C₃×C₅×D₄	—	4	4	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	2	1	no	—
120	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
125	C₂×C₃×C₄×C₅	—	4	8	no	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
131	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
132	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
133	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
135	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
136	C₃×#124	—	2	4	no	—
137	C₃×C₂²⋊Q₈	—	2	8	no	—
138	C₃×#121	—	2	8	no	—
139	C₃×C₄×D₄	—	2	4	no	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
141	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
150	C₃×#95	C₂²×C₅	1	2	yes	—
151	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
152	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
153	C₂×C₅×Q₈	—	2	4	no	—
154	C₂×C₅×Q₈	—	2	2	no	—
155	C₂×C₅×D₄	—	2	4	no	—
156	C₂×C₅×D₄	—	2	8	no	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	—	2	8	no	—
159	C₂×C₅×D₄	—	2	4	no	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	4	4	no	—
162	C₂²×C₄×C₅	—	2	4	no	—
163	C₂²×C₄×C₅	—	2	4	no	—
164	C₂²×C₄×C₅	—	2	4	no	—
165	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	8	no	—
173	C₅×C₄⋊C₄	C₃×D₄	1	8	yes	complemented
174	C₅×C₂²⋊C₄	—	2	4	no	—
175	C₅×C₂²⋊C₄	—	2	8	no	—
176	C₅×C₂²⋊C₄	—	2	8	no	—
177	C₅×C₂²⋊C₄	—	2	4	no	—
178	C₅×C₂²⋊C₄	—	2	4	no	—
179	C₄²×C₅	—	4	2	no	—
180	C₄²×C₅	C₃×D₄	1	4	yes	complemented
181	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
182	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
183	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
184	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	#399	C₂×C₃×C₅	1	2	yes	complemented
186	#392	C₂×C₃×C₅	1	2	yes	complemented
187	#390	C₂×C₃×C₅	1	4	yes	complemented
188	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
189	C₂²×C₃×C₅	—	2	4	no	—
190	C₂²×C₃×C₅	—	2	4	no	—
191	C₂²×C₃×C₅	—	2	4	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	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	4	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	4	no	—
200	C₂²×C₃×C₅	—	4	4	no	—
201	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
203	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
204	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
206	C₃×C₄×C₅	—	2	2	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	2	8	no	—
209	C₃×C₄×C₅	—	4	2	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	#127	1	4	yes	—
212	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
213	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
214	C₂×C₃×Q₈	—	2	4	no	—
215	C₂×C₃×Q₈	—	2	2	no	—
216	C₂×C₃×D₄	—	2	4	no	—
217	C₂×C₃×D₄	—	2	8	no	—
218	C₂×C₃×D₄	—	2	2	no	—
219	C₂×C₃×D₄	—	2	8	no	—
220	C₂×C₃×D₄	—	2	4	no	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	—	4	4	no	—
223	C₂²×C₃×C₄	—	2	4	no	—
224	C₂²×C₃×C₄	—	2	4	no	—
225	C₂²×C₃×C₄	—	2	4	no	—
226	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₃×C₄⋊C₄	—	2	2	no	—
233	C₃×C₄⋊C₄	—	2	8	no	—
234	C₃×C₄⋊C₄	C₅×D₄	1	8	yes	complemented
235	C₃×C₂²⋊C₄	—	2	4	no	—
236	C₃×C₂²⋊C₄	—	2	8	no	—
237	C₃×C₂²⋊C₄	—	2	8	no	—
238	C₃×C₂²⋊C₄	—	2	4	no	—
239	C₃×C₂²⋊C₄	—	2	4	no	—
240	C₃×C₄²	—	4	2	no	—
241	C₃×C₄²	C₅×D₄	1	4	yes	complemented
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	—	2	2	no	—
244	C₂³×C₅	—	2	2	no	—
245	C₂³×C₅	—	2	2	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	2	2	no	—
249	C₂³×C₅	—	2	4	no	—
250	C₂³×C₅	—	2	4	no	—
251	C₂³×C₅	—	2	2	no	—
252	C₂³×C₅	—	2	2	no	—
253	C₂³×C₅	C₃×#41	1	4	yes	—
254	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
255	C₅×Q₈	—	4	4	no	—
256	C₅×D₄	—	2	8	no	—
257	C₅×D₄	—	4	16	no	—
258	C₅×D₄	—	4	4	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	4	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	4	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	4	8	no	—
270	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
271	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
272	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	—
273	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
274	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
275	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
276	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
277	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
279	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
280	#124	—	2	4	no	—
281	C₂²⋊Q₈	—	2	8	no	—
282	#121	—	2	8	no	—
283	C₄×D₄	—	2	4	no	—
284	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
286	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
290	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
291	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
292	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
293	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
294	#95	C₂²×C₃×C₅	1	2	yes	—
295	C₂×C₃×C₅	—	4	4	no	—
296	C₂×C₃×C₅	—	8	2	no	—
297	C₂×C₃×C₅	#525	1	1	yes	characteristic
298	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
299	C₂×C₃×C₅	#537	1	1	yes	characteristic
300	C₂×C₃×C₅	#546	1	2	yes	—
301	C₂×C₃×C₅	#548	1	2	yes	—
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	—	2	2	no	—
308	C₂³×C₃	—	2	2	no	—
309	C₂³×C₃	—	2	4	no	—
310	C₂³×C₃	—	2	4	no	—
311	C₂³×C₃	—	2	2	no	—
312	C₂³×C₃	—	2	2	no	—
313	C₂³×C₃	C₅×#41	1	4	yes	—
314	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
315	C₃×Q₈	—	4	4	no	—
316	C₃×D₄	—	2	8	no	—
317	C₃×D₄	—	4	16	no	—
318	C₃×D₄	—	4	4	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	4	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	4	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	4	8	no	—
330	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
331	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
332	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
333	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
334	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
335	C₂²×C₅	—	2	4	no	—
336	C₂²×C₅	—	2	4	no	—
337	C₂²×C₅	—	2	4	no	—
338	C₂²×C₅	—	4	2	no	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	—	4	2	no	—
341	C₂²×C₅	—	4	2	no	—
342	C₂²×C₅	—	4	2	no	—
343	C₂²×C₅	—	4	2	no	—
344	C₂²×C₅	—	4	2	no	—
345	C₂²×C₅	—	4	4	no	—
346	C₂²×C₅	—	4	4	no	—
347	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
348	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
349	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
350	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	2	2	no	—
354	C₄×C₅	—	2	8	no	—
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	—	4	2	no	—
357	C₄×C₅	C₃×#127	1	4	yes	—
358	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
359	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
373	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
374	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
375	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
376	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₄²	—	4	2	no	—
387	C₄²	C₃×C₅×D₄	1	4	yes	complemented
388	C₃×C₅	#2540	1	1	yes	characteristic, direct product factor, Hall
389	C₂²×C₃	—	2	4	no	—
390	C₂²×C₃	—	2	4	no	—
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	4	2	no	—
393	C₂²×C₃	—	4	2	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	4	2	no	—
396	C₂²×C₃	—	4	2	no	—
397	C₂²×C₃	—	4	2	no	—
398	C₂²×C₃	—	4	2	no	—
399	C₂²×C₃	—	4	4	no	—
400	C₂²×C₃	—	4	4	no	—
401	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
402	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
403	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
404	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	2	8	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	C₅×#127	1	4	yes	—
412	C₂×C₅	—	4	4	no	—
413	C₂×C₅	—	8	2	no	—
414	C₂×C₅	C₃×#525	1	1	yes	characteristic
415	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
416	C₂×C₅	C₃×#537	1	1	yes	characteristic
417	C₂×C₅	C₃×#546	1	2	yes	—
418	C₂×C₅	C₃×#548	1	2	yes	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	C₃×C₅×#41	1	4	yes	—
431	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
432	Q₈	—	4	4	no	—
433	D₄	—	2	8	no	—
434	D₄	—	4	16	no	—
435	D₄	—	4	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	8	no	—
447	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
448	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
449	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	—
450	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
451	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
452	C₂×C₃	—	4	4	no	—
453	C₂×C₃	—	8	2	no	—
454	C₂×C₃	C₅×#525	1	1	yes	characteristic
455	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
456	C₂×C₃	C₅×#537	1	1	yes	characteristic
457	C₂×C₃	C₅×#546	1	2	yes	—
458	C₂×C₃	C₅×#548	1	2	yes	—
459	C₅	C₃×#2540	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	2	4	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
473	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
474	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
475	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	8	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	C₃×C₅×#127	1	4	yes	—
483	C₃	C₅×#2540	1	1	yes	characteristic, direct product factor, Sylow
484	C₂	—	4	4	no	—
485	C₂	—	8	2	no	—
486	C₂	C₃×C₅×#525	1	1	yes	characteristic
487	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
488	C₂	C₃×C₅×#537	1	1	yes	characteristic
489	C₂	C₃×C₅×#546	1	2	yes	—
490	C₂	C₃×C₅×#548	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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×#124	C₂	semidirect
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
5. C₃×C₅×#399	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₅×#390	C₂	semidirect
8. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
9. C₅×#2540	C₃	direct (N × H)
30. C₃×#2540	C₅	direct (N × H)
31. C₂×C₅×#124	C₂×C₃	semidirect
32. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
33. C₂×C₅×#121	C₂×C₃	semidirect
34. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
35. C₅×#399	C₂×C₃	semidirect
36. C₅×#392	C₂×C₃	semidirect
37. C₅×#390	C₂×C₃	semidirect
38. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
61. C₃×C₅×C₄⋊C₄	D₄	semidirect
68. C₃×C₄²×C₅	D₄	semidirect
69. C₂×C₃×#124	C₂×C₅	semidirect
70. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
71. C₂×C₃×#121	C₂×C₅	semidirect
72. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
73. C₃×#399	C₂×C₅	semidirect
74. C₃×#392	C₂×C₅	semidirect
75. C₃×#390	C₂×C₅	semidirect
76. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
97. #2540	C₃×C₅	direct (N × H)
173. C₅×C₄⋊C₄	C₃×D₄	semidirect
180. C₄²×C₅	C₃×D₄	semidirect
181. C₂×#124	C₂×C₃×C₅	semidirect
182. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
183. C₂×#121	C₂×C₃×C₅	semidirect
184. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
185. #399	C₂×C₃×C₅	semidirect
186. #392	C₂×C₃×C₅	semidirect
187. #390	C₂×C₃×C₅	semidirect
188. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
234. C₃×C₄⋊C₄	C₅×D₄	semidirect
241. C₃×C₄²	C₅×D₄	semidirect
380. C₄⋊C₄	C₃×C₅×D₄	semidirect
387. C₄²	C₃×C₅×D₄	semidirect
388. C₃×C₅	#2540	direct (N × H)
459. C₅	C₃×#2540	direct (N × H)
483. C₃	C₅×#2540	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×#124	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#399	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2540	3
C₃×#2540	5

Subgroups — C3×C5×#2540 #14275574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2540 #14275574