Subgroups — C₃×C₅×#2680 #14275714

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2680	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₃×C₅×#123	—	2	8	no	—
15	C₃×C₅×C₂²⋊Q₈	—	2	8	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	1	yes	characteristic
33	C₃×C₅×#95	C₂²	1	1	yes	characteristic
34	C₃×#2680	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#123	C₂×C₃	1	2	yes	—
36	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
37	C₅×#398	C₂×C₃	1	2	yes	complemented
38	C₅×#397	C₂×C₃	1	2	yes	complemented
39	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#394	C₂×C₃	1	1	yes	characteristic
41	C₅×#388	C₂×C₃	1	2	yes	complemented
42	C₅×#385	C₂×C₃	1	2	yes	complemented
43	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂×C₃×C₅×Q₈	—	2	4	no	—
46	C₂×C₃×C₅×Q₈	—	4	1	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	4	1	no	—
49	C₂²×C₃×C₄×C₅	—	2	4	no	—
50	C₂²×C₃×C₄×C₅	—	2	4	no	—
51	C₂²×C₃×C₄×C₅	—	4	2	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	—	2	4	no	—
61	C₃×C₅×C₄⋊C₄	—	2	4	no	—
62	C₃×C₅×C₄⋊C₄	—	2	4	no	—
63	C₃×C₅×C₄⋊C₄	—	2	4	no	—
64	C₃×C₅×C₄⋊C₄	—	2	4	no	—
65	C₃×C₅×C₄⋊C₄	—	4	1	no	—
66	C₃×C₅×C₄⋊C₄	—	4	1	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
71	C₃×C₅×C₂²⋊C₄	D₄	1	8	yes	—
72	C₃×C₄²×C₅	—	2	2	no	—
73	C₂×C₃×#123	C₂×C₅	1	2	yes	—
74	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
75	C₃×#398	C₂×C₅	1	2	yes	complemented
76	C₃×#397	C₂×C₅	1	2	yes	complemented
77	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×#394	C₂×C₅	1	1	yes	characteristic
79	C₃×#388	C₂×C₅	1	2	yes	complemented
80	C₃×#385	C₂×C₅	1	2	yes	complemented
81	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
85	C₅×#123	—	2	8	no	—
86	C₅×C₂²⋊Q₈	—	2	8	no	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	C₅×#95	C₂²×C₃	1	2	yes	—
102	C₅×#95	C₂²×C₃	1	2	yes	—
103	C₅×#95	C₂²×C₃	1	1	yes	characteristic
104	C₅×#95	C₂²×C₃	1	1	yes	characteristic
105	#2680	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₃×C₅×Q₈	—	4	4	no	—
115	C₃×C₅×D₄	—	4	4	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	1	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	1	no	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	4	8	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
138	C₂×C₃×C₄×C₅	#41	1	2	yes	—
139	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
140	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
142	C₃×#123	—	2	8	no	—
143	C₃×C₂²⋊Q₈	—	2	8	no	—
144	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
152	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
155	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
156	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
157	C₃×#95	C₂²×C₅	1	2	yes	—
158	C₃×#95	C₂²×C₅	1	2	yes	—
159	C₃×#95	C₂²×C₅	1	2	yes	—
160	C₃×#95	C₂²×C₅	1	1	yes	characteristic
161	C₃×#95	C₂²×C₅	1	1	yes	characteristic
162	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
163	C₂×C₅×Q₈	—	2	4	no	—
164	C₂×C₅×Q₈	—	4	1	no	—
165	C₂×C₅×D₄	—	2	4	no	—
166	C₂×C₅×D₄	—	4	1	no	—
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	—	4	2	no	—
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
174	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
177	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₅×C₄⋊C₄	—	2	4	no	—
179	C₅×C₄⋊C₄	—	2	4	no	—
180	C₅×C₄⋊C₄	—	2	4	no	—
181	C₅×C₄⋊C₄	—	2	4	no	—
182	C₅×C₄⋊C₄	—	2	4	no	—
183	C₅×C₄⋊C₄	—	4	1	no	—
184	C₅×C₄⋊C₄	—	4	1	no	—
185	C₅×C₂²⋊C₄	—	2	4	no	—
186	C₅×C₂²⋊C₄	—	2	4	no	—
187	C₅×C₂²⋊C₄	—	2	4	no	—
188	C₅×C₂²⋊C₄	—	2	4	no	—
189	C₅×C₂²⋊C₄	C₃×D₄	1	8	yes	—
190	C₄²×C₅	—	2	2	no	—
191	C₂×#123	C₂×C₃×C₅	1	2	yes	—
192	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
193	#398	C₂×C₃×C₅	1	2	yes	complemented
194	#397	C₂×C₃×C₅	1	2	yes	complemented
195	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
196	#394	C₂×C₃×C₅	1	1	yes	characteristic
197	#388	C₂×C₃×C₅	1	2	yes	complemented
198	#385	C₂×C₃×C₅	1	2	yes	complemented
199	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
200	C₂²×C₃×C₅	—	2	4	no	—
201	C₂²×C₃×C₅	—	2	4	no	—
202	C₂²×C₃×C₅	—	2	4	no	—
203	C₂²×C₃×C₅	—	4	2	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	—	4	2	no	—
206	C₂²×C₃×C₅	—	4	2	no	—
207	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
208	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
209	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
211	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	4	no	—
214	C₃×C₄×C₅	—	2	4	no	—
215	C₃×C₄×C₅	—	4	2	no	—
216	C₃×C₄×C₅	—	4	2	no	—
217	C₃×C₄×C₅	—	4	1	no	—
218	C₃×C₄×C₅	—	4	1	no	—
219	C₃×C₄×C₅	—	4	2	no	—
220	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
221	C₂×C₃×Q₈	—	2	4	no	—
222	C₂×C₃×Q₈	—	4	1	no	—
223	C₂×C₃×D₄	—	2	4	no	—
224	C₂×C₃×D₄	—	4	1	no	—
225	C₂²×C₃×C₄	—	2	4	no	—
226	C₂²×C₃×C₄	—	2	4	no	—
227	C₂²×C₃×C₄	—	4	2	no	—
228	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
232	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
234	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
235	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
236	C₃×C₄⋊C₄	—	2	4	no	—
237	C₃×C₄⋊C₄	—	2	4	no	—
238	C₃×C₄⋊C₄	—	2	4	no	—
239	C₃×C₄⋊C₄	—	2	4	no	—
240	C₃×C₄⋊C₄	—	2	4	no	—
241	C₃×C₄⋊C₄	—	4	1	no	—
242	C₃×C₄⋊C₄	—	4	1	no	—
243	C₃×C₂²⋊C₄	—	2	4	no	—
244	C₃×C₂²⋊C₄	—	2	4	no	—
245	C₃×C₂²⋊C₄	—	2	4	no	—
246	C₃×C₂²⋊C₄	—	2	4	no	—
247	C₃×C₂²⋊C₄	C₅×D₄	1	8	yes	—
248	C₃×C₄²	—	2	2	no	—
249	C₂³×C₅	—	2	2	no	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	2	2	no	—
252	C₂³×C₅	—	2	2	no	—
253	C₂³×C₅	—	2	2	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
256	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
257	C₅×Q₈	—	4	4	no	—
258	C₅×D₄	—	4	4	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	2	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	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	4	8	no	—
279	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
280	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
281	C₂×C₄×C₅	C₃×#41	1	2	yes	—
282	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
283	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
284	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
285	#123	—	2	8	no	—
286	C₂²⋊Q₈	—	2	8	no	—
287	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
288	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
289	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
290	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
291	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
292	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
299	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
300	#95	C₂²×C₃×C₅	1	2	yes	—
301	#95	C₂²×C₃×C₅	1	2	yes	—
302	#95	C₂²×C₃×C₅	1	2	yes	—
303	#95	C₂²×C₃×C₅	1	1	yes	characteristic
304	#95	C₂²×C₃×C₅	1	1	yes	characteristic
305	C₂×C₃×C₅	—	4	4	no	—
306	C₂×C₃×C₅	#536	1	2	yes	—
307	C₂×C₃×C₅	#539	1	1	yes	characteristic
308	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
309	C₂×C₃×C₅	#547	1	2	yes	—
310	C₂×C₃×C₅	#563	1	1	yes	characteristic
311	C₂³×C₃	—	2	2	no	—
312	C₂³×C₃	—	2	2	no	—
313	C₂³×C₃	—	2	2	no	—
314	C₂³×C₃	—	2	2	no	—
315	C₂³×C₃	—	2	2	no	—
316	C₂³×C₃	—	2	2	no	—
317	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
318	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
319	C₃×Q₈	—	4	4	no	—
320	C₃×D₄	—	4	4	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	4	8	no	—
341	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
342	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
343	C₂×C₃×C₄	C₅×#41	1	2	yes	—
344	C₂²×C₅	—	2	4	no	—
345	C₂²×C₅	—	2	4	no	—
346	C₂²×C₅	—	2	4	no	—
347	C₂²×C₅	—	4	2	no	—
348	C₂²×C₅	—	4	2	no	—
349	C₂²×C₅	—	4	2	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
352	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
353	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
355	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	4	no	—
358	C₄×C₅	—	2	4	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	—	4	2	no	—
361	C₄×C₅	—	4	1	no	—
362	C₄×C₅	—	4	1	no	—
363	C₄×C₅	—	4	2	no	—
364	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	4	1	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	4	2	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	2	yes	—
376	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
378	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
379	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	C₃×C₅×D₄	1	8	yes	—
392	C₄²	—	2	2	no	—
393	C₃×C₅	#2680	1	1	yes	characteristic, direct product factor, Hall
394	C₂²×C₃	—	2	4	no	—
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	2	4	no	—
397	C₂²×C₃	—	4	2	no	—
398	C₂²×C₃	—	4	2	no	—
399	C₂²×C₃	—	4	2	no	—
400	C₂²×C₃	—	4	2	no	—
401	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
402	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
403	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	2	4	no	—
408	C₃×C₄	—	2	4	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	—	4	1	no	—
412	C₃×C₄	—	4	1	no	—
413	C₃×C₄	—	4	2	no	—
414	C₂×C₅	—	4	4	no	—
415	C₂×C₅	C₃×#536	1	2	yes	—
416	C₂×C₅	C₃×#539	1	1	yes	characteristic
417	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
418	C₂×C₅	C₃×#547	1	2	yes	—
419	C₂×C₅	C₃×#563	1	1	yes	characteristic
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	C₂×C₃×C₅×D₄	1	4	yes	—
427	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
428	Q₈	—	4	4	no	—
429	D₄	—	4	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
451	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
452	C₂×C₄	C₃×C₅×#41	1	2	yes	—
453	C₂×C₃	—	4	4	no	—
454	C₂×C₃	C₅×#536	1	2	yes	—
455	C₂×C₃	C₅×#539	1	1	yes	characteristic
456	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
457	C₂×C₃	C₅×#547	1	2	yes	—
458	C₂×C₃	C₅×#563	1	1	yes	characteristic
459	C₅	C₃×#2680	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	C₂²×C₃×C₅×D₄	1	2	yes	—
468	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
469	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
472	C₄	—	2	2	no	—
473	C₄	—	2	4	no	—
474	C₄	—	2	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	2	no	—
480	C₃	C₅×#2680	1	1	yes	characteristic, direct product factor, Sylow
481	C₂	—	4	4	no	—
482	C₂	C₃×C₅×#536	1	2	yes	—
483	C₂	C₃×C₅×#539	1	1	yes	characteristic
484	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
485	C₂	C₃×C₅×#547	1	2	yes	—
486	C₂	C₃×C₅×#563	1	1	yes	characteristic

	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
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₃×C₅×#398	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#395	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#385	C₂	semidirect
9. C₃×C₅×#384	C₂	semidirect
10. C₅×#2680	C₃	direct (N × H)
34. C₃×#2680	C₅	direct (N × H)
36. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
37. C₅×#398	C₂×C₃	semidirect
38. C₅×#397	C₂×C₃	semidirect
39. C₅×#395	C₂×C₃	semidirect
41. C₅×#388	C₂×C₃	semidirect
42. C₅×#385	C₂×C₃	semidirect
43. C₅×#384	C₂×C₃	semidirect
74. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
75. C₃×#398	C₂×C₅	semidirect
76. C₃×#397	C₂×C₅	semidirect
77. C₃×#395	C₂×C₅	semidirect
79. C₃×#388	C₂×C₅	semidirect
80. C₃×#385	C₂×C₅	semidirect
81. C₃×#384	C₂×C₅	semidirect
105. #2680	C₃×C₅	direct (N × H)
192. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
193. #398	C₂×C₃×C₅	semidirect
194. #397	C₂×C₃×C₅	semidirect
195. #395	C₂×C₃×C₅	semidirect
197. #388	C₂×C₃×C₅	semidirect
198. #385	C₂×C₃×C₅	semidirect
199. #384	C₂×C₃×C₅	semidirect
393. C₃×C₅	#2680	direct (N × H)
459. C₅	C₃×#2680	direct (N × H)
480. C₃	C₅×#2680	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×#123	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#398	2
C₃×C₅×#397	2
C₃×C₅×#395	2
C₃×C₅×#394	2
C₃×C₅×#388	2
C₃×C₅×#385	2
C₃×C₅×#384	2
C₅×#2680	3
C₃×#2680	5

Subgroups — C3×C5×#2680 #14275714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2680 #14275714