Subgroups — C₃×C₅×#2430 #14275464

Order 1920.

1828 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2430	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	—	2	8	no	—
14	C₂×C₃×C₅×#41	—	2	4	no	—
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
19	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
20	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
21	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
22	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#123	—	2	4	no	—
24	C₃×C₅×#121	—	2	8	no	—
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×C₅×#95	C₂²	1	1	yes	characteristic
37	C₃×C₅×#95	C₂²	1	1	yes	characteristic
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×C₅×#95	C₂²	1	2	yes	—
40	C₃×#2430	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂²×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
44	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#393	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#386	C₂×C₃	1	2	yes	complemented
49	C₅×#386	C₂×C₃	1	2	yes	complemented
50	C₅×#385	C₂×C₃	1	2	yes	complemented
51	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
53	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
54	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₅×#41	—	2	32	no	—
56	C₂×C₃×C₅×Q₈	—	2	4	no	—
57	C₂×C₃×C₅×Q₈	—	2	2	no	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	2	4	no	—
61	C₂×C₃×C₅×D₄	—	2	4	no	—
62	C₂×C₃×C₅×D₄	—	2	4	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	2	4	no	—
66	C₂×C₃×C₅×D₄	—	4	2	no	—
67	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	—	2	4	no	—
70	C₂²×C₃×C₄×C₅	—	2	4	no	—
71	C₂²×C₃×C₄×C₅	—	2	4	no	—
72	C₂²×C₃×C₄×C₅	—	2	4	no	—
73	C₂²×C₃×C₄×C₅	—	2	4	no	—
74	C₂²×C₃×C₄×C₅	—	4	2	no	—
75	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
84	C₃×C₅×C₄⋊C₄	—	2	4	no	—
85	C₃×C₅×C₄⋊C₄	—	2	2	no	—
86	C₃×C₅×C₄⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
93	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
94	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
97	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#393	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#386	C₂×C₅	1	2	yes	complemented
102	C₃×#386	C₂×C₅	1	2	yes	complemented
103	C₃×#385	C₂×C₅	1	2	yes	complemented
104	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₅×#41	—	2	8	no	—
106	C₂×C₅×#41	—	2	4	no	—
107	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
111	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
112	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
113	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
114	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
115	C₅×#123	—	2	4	no	—
116	C₅×#121	—	2	8	no	—
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
125	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
127	C₅×#95	C₂²×C₃	1	2	yes	—
128	C₅×#95	C₂²×C₃	1	1	yes	characteristic
129	C₅×#95	C₂²×C₃	1	1	yes	characteristic
130	C₅×#95	C₂²×C₃	1	2	yes	—
131	C₅×#95	C₂²×C₃	1	2	yes	—
132	#2430	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
133	C₂³×C₃×C₅	—	2	2	no	—
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	—	2	2	no	—
138	C₂³×C₃×C₅	—	2	2	no	—
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	2	1	no	—
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	1	no	—
147	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
148	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
149	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
150	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
151	C₃×C₅×Q₈	—	2	8	no	—
152	C₃×C₅×D₄	—	2	8	no	—
153	C₃×C₅×D₄	—	2	16	no	—
154	C₃×C₅×D₄	—	4	8	no	—
155	C₃×C₅×D₄	—	4	4	no	—
156	C₂×C₃×C₄×C₅	—	2	16	no	—
157	C₂×C₃×C₄×C₅	—	2	8	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	2	2	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	2	no	—
164	C₂×C₃×C₄×C₅	—	2	1	no	—
165	C₂×C₃×C₄×C₅	—	2	1	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	2	2	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	4	8	no	—
175	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
177	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
178	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
179	C₂×C₃×#41	—	2	8	no	—
180	C₂×C₃×#41	—	2	4	no	—
181	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
183	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
185	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
186	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
187	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
188	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
189	C₃×#123	—	2	4	no	—
190	C₃×#121	—	2	8	no	—
191	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
201	C₃×#95	C₂²×C₅	1	2	yes	—
202	C₃×#95	C₂²×C₅	1	1	yes	characteristic
203	C₃×#95	C₂²×C₅	1	1	yes	characteristic
204	C₃×#95	C₂²×C₅	1	2	yes	—
205	C₃×#95	C₂²×C₅	1	2	yes	—
206	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
208	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₅×#41	—	2	32	no	—
210	C₂×C₅×Q₈	—	2	4	no	—
211	C₂×C₅×Q₈	—	2	2	no	—
212	C₂×C₅×D₄	—	2	4	no	—
213	C₂×C₅×D₄	—	2	4	no	—
214	C₂×C₅×D₄	—	2	4	no	—
215	C₂×C₅×D₄	—	2	4	no	—
216	C₂×C₅×D₄	—	2	4	no	—
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	2	4	no	—
220	C₂×C₅×D₄	—	4	2	no	—
221	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
222	C₂²×C₄×C₅	—	2	4	no	—
223	C₂²×C₄×C₅	—	2	4	no	—
224	C₂²×C₄×C₅	—	2	4	no	—
225	C₂²×C₄×C₅	—	2	4	no	—
226	C₂²×C₄×C₅	—	2	4	no	—
227	C₂²×C₄×C₅	—	2	4	no	—
228	C₂²×C₄×C₅	—	4	2	no	—
229	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
230	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
233	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
236	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
237	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
238	C₅×C₄⋊C₄	—	2	4	no	—
239	C₅×C₄⋊C₄	—	2	2	no	—
240	C₅×C₄⋊C₄	—	2	2	no	—
241	C₅×C₂²⋊C₄	—	2	4	no	—
242	C₅×C₂²⋊C₄	—	2	2	no	—
243	C₅×C₂²⋊C₄	—	2	4	no	—
244	C₅×C₂²⋊C₄	—	2	2	no	—
245	C₅×C₂²⋊C₄	—	2	2	no	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	4	2	no	—
248	C₂²×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
251	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
252	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
253	#393	C₂×C₃×C₅	1	1	yes	characteristic, complemented
254	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	#386	C₂×C₃×C₅	1	2	yes	complemented
256	#386	C₂×C₃×C₅	1	2	yes	complemented
257	#385	C₂×C₃×C₅	1	2	yes	complemented
258	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
259	C₂²×C₃×C₅	—	2	2	no	—
260	C₂²×C₃×C₅	—	2	2	no	—
261	C₂²×C₃×C₅	—	2	4	no	—
262	C₂²×C₃×C₅	—	2	4	no	—
263	C₂²×C₃×C₅	—	2	4	no	—
264	C₂²×C₃×C₅	—	2	4	no	—
265	C₂²×C₃×C₅	—	2	4	no	—
266	C₂²×C₃×C₅	—	4	2	no	—
267	C₂²×C₃×C₅	—	4	2	no	—
268	C₂²×C₃×C₅	—	4	2	no	—
269	C₂²×C₃×C₅	—	4	2	no	—
270	C₂²×C₃×C₅	—	4	1	no	—
271	C₂²×C₃×C₅	—	4	1	no	—
272	C₂²×C₃×C₅	—	4	1	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	2	no	—
275	C₂²×C₃×C₅	#120	1	4	yes	—
276	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
278	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
279	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
281	C₃×C₄×C₅	—	2	2	no	—
282	C₃×C₄×C₅	—	2	4	no	—
283	C₃×C₄×C₅	—	2	2	no	—
284	C₃×C₄×C₅	—	2	4	no	—
285	C₃×C₄×C₅	—	4	1	no	—
286	C₃×C₄×C₅	—	4	1	no	—
287	C₃×C₄×C₅	—	4	1	no	—
288	C₃×C₄×C₅	—	4	2	no	—
289	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
290	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
291	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
292	C₃×#41	—	2	32	no	—
293	C₂×C₃×Q₈	—	2	4	no	—
294	C₂×C₃×Q₈	—	2	2	no	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	4	no	—
297	C₂×C₃×D₄	—	2	4	no	—
298	C₂×C₃×D₄	—	2	4	no	—
299	C₂×C₃×D₄	—	2	4	no	—
300	C₂×C₃×D₄	—	2	2	no	—
301	C₂×C₃×D₄	—	2	2	no	—
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	—	4	2	no	—
304	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
305	C₂²×C₃×C₄	—	2	4	no	—
306	C₂²×C₃×C₄	—	2	4	no	—
307	C₂²×C₃×C₄	—	2	4	no	—
308	C₂²×C₃×C₄	—	2	4	no	—
309	C₂²×C₃×C₄	—	2	4	no	—
310	C₂²×C₃×C₄	—	2	4	no	—
311	C₂²×C₃×C₄	—	4	2	no	—
312	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
313	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
314	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
319	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	2	no	—
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₂²⋊C₄	—	2	4	no	—
325	C₃×C₂²⋊C₄	—	2	2	no	—
326	C₃×C₂²⋊C₄	—	2	4	no	—
327	C₃×C₂²⋊C₄	—	2	2	no	—
328	C₃×C₂²⋊C₄	—	2	2	no	—
329	C₃×C₂²⋊C₄	—	2	4	no	—
330	C₃×C₂²⋊C₄	—	4	2	no	—
331	C₂³×C₅	—	2	2	no	—
332	C₂³×C₅	—	2	1	no	—
333	C₂³×C₅	—	2	1	no	—
334	C₂³×C₅	—	2	2	no	—
335	C₂³×C₅	—	2	2	no	—
336	C₂³×C₅	—	2	2	no	—
337	C₂³×C₅	—	2	2	no	—
338	C₂³×C₅	—	2	2	no	—
339	C₂³×C₅	—	2	2	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	1	no	—
344	C₂³×C₅	—	2	1	no	—
345	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
346	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
347	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
348	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
349	C₅×Q₈	—	2	8	no	—
350	C₅×D₄	—	2	8	no	—
351	C₅×D₄	—	2	16	no	—
352	C₅×D₄	—	4	8	no	—
353	C₅×D₄	—	4	4	no	—
354	C₂×C₄×C₅	—	2	16	no	—
355	C₂×C₄×C₅	—	2	8	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	2	2	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	2	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	4	8	no	—
373	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
374	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
375	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
376	C₂×C₄×C₅	C₃×#41	1	4	yes	complemented
377	C₂×#41	—	2	8	no	—
378	C₂×#41	—	2	4	no	—
379	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
380	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
381	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
382	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
383	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
384	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
385	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
386	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
387	#123	—	2	4	no	—
388	#121	—	2	8	no	—
389	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
390	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
399	#95	C₂²×C₃×C₅	1	2	yes	—
400	#95	C₂²×C₃×C₅	1	1	yes	characteristic
401	#95	C₂²×C₃×C₅	1	1	yes	characteristic
402	#95	C₂²×C₃×C₅	1	2	yes	—
403	#95	C₂²×C₃×C₅	1	2	yes	—
404	C₂×C₃×C₅	—	2	4	no	—
405	C₂×C₃×C₅	—	4	4	no	—
406	C₂×C₃×C₅	—	8	1	no	—
407	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
408	C₂×C₃×C₅	#532	1	1	yes	characteristic
409	C₂×C₃×C₅	#537	1	1	yes	characteristic
410	C₂×C₃×C₅	#546	1	2	yes	—
411	C₂×C₃×C₅	#547	1	2	yes	—
412	C₂³×C₃	—	2	2	no	—
413	C₂³×C₃	—	2	1	no	—
414	C₂³×C₃	—	2	1	no	—
415	C₂³×C₃	—	2	2	no	—
416	C₂³×C₃	—	2	2	no	—
417	C₂³×C₃	—	2	2	no	—
418	C₂³×C₃	—	2	2	no	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	2	1	no	—
422	C₂³×C₃	—	2	2	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	—	2	1	no	—
425	C₂³×C₃	—	2	1	no	—
426	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
427	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
428	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
429	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
430	C₃×Q₈	—	2	8	no	—
431	C₃×D₄	—	2	8	no	—
432	C₃×D₄	—	2	16	no	—
433	C₃×D₄	—	4	8	no	—
434	C₃×D₄	—	4	4	no	—
435	C₂×C₃×C₄	—	2	16	no	—
436	C₂×C₃×C₄	—	2	8	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	2	no	—
439	C₂×C₃×C₄	—	2	2	no	—
440	C₂×C₃×C₄	—	2	2	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	2	2	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	2	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	4	8	no	—
454	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
455	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
456	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
457	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
458	C₂²×C₅	—	2	2	no	—
459	C₂²×C₅	—	2	2	no	—
460	C₂²×C₅	—	2	4	no	—
461	C₂²×C₅	—	2	4	no	—
462	C₂²×C₅	—	2	4	no	—
463	C₂²×C₅	—	2	4	no	—
464	C₂²×C₅	—	2	4	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	4	2	no	—
468	C₂²×C₅	—	4	2	no	—
469	C₂²×C₅	—	4	1	no	—
470	C₂²×C₅	—	4	1	no	—
471	C₂²×C₅	—	4	1	no	—
472	C₂²×C₅	—	4	2	no	—
473	C₂²×C₅	—	4	2	no	—
474	C₂²×C₅	C₃×#120	1	4	yes	—
475	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
476	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
477	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
478	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
480	C₄×C₅	—	2	2	no	—
481	C₄×C₅	—	2	4	no	—
482	C₄×C₅	—	2	2	no	—
483	C₄×C₅	—	2	4	no	—
484	C₄×C₅	—	4	1	no	—
485	C₄×C₅	—	4	1	no	—
486	C₄×C₅	—	4	1	no	—
487	C₄×C₅	—	4	2	no	—
488	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
489	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
490	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
491	#41	—	2	32	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	C₃×C₅×D₄	1	8	yes	complemented
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
512	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
513	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
514	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
515	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
516	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
517	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
518	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
519	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₃×C₅	#2430	1	1	yes	characteristic, direct product factor, Hall
531	C₂²×C₃	—	2	2	no	—
532	C₂²×C₃	—	2	2	no	—
533	C₂²×C₃	—	2	4	no	—
534	C₂²×C₃	—	2	4	no	—
535	C₂²×C₃	—	2	4	no	—
536	C₂²×C₃	—	2	4	no	—
537	C₂²×C₃	—	2	4	no	—
538	C₂²×C₃	—	4	2	no	—
539	C₂²×C₃	—	4	2	no	—
540	C₂²×C₃	—	4	2	no	—
541	C₂²×C₃	—	4	2	no	—
542	C₂²×C₃	—	4	1	no	—
543	C₂²×C₃	—	4	1	no	—
544	C₂²×C₃	—	4	1	no	—
545	C₂²×C₃	—	4	2	no	—
546	C₂²×C₃	—	4	2	no	—
547	C₂²×C₃	C₅×#120	1	4	yes	—
548	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
549	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
550	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
551	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
553	C₃×C₄	—	2	2	no	—
554	C₃×C₄	—	2	4	no	—
555	C₃×C₄	—	2	2	no	—
556	C₃×C₄	—	2	4	no	—
557	C₃×C₄	—	4	1	no	—
558	C₃×C₄	—	4	1	no	—
559	C₃×C₄	—	4	1	no	—
560	C₃×C₄	—	4	2	no	—
561	C₂×C₅	—	2	4	no	—
562	C₂×C₅	—	4	4	no	—
563	C₂×C₅	—	8	1	no	—
564	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
565	C₂×C₅	C₃×#532	1	1	yes	characteristic
566	C₂×C₅	C₃×#537	1	1	yes	characteristic
567	C₂×C₅	C₃×#546	1	2	yes	—
568	C₂×C₅	C₃×#547	1	2	yes	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
584	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
585	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
586	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
587	Q₈	—	2	8	no	—
588	D₄	—	2	8	no	—
589	D₄	—	2	16	no	—
590	D₄	—	4	8	no	—
591	D₄	—	4	4	no	—
592	C₂×C₄	—	2	16	no	—
593	C₂×C₄	—	2	8	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
612	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
613	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
614	C₂×C₄	C₃×C₅×#41	1	4	yes	complemented
615	C₂×C₃	—	2	4	no	—
616	C₂×C₃	—	4	4	no	—
617	C₂×C₃	—	8	1	no	—
618	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
619	C₂×C₃	C₅×#532	1	1	yes	characteristic
620	C₂×C₃	C₅×#537	1	1	yes	characteristic
621	C₂×C₃	C₅×#546	1	2	yes	—
622	C₂×C₃	C₅×#547	1	2	yes	—
623	C₅	C₃×#2430	1	1	yes	characteristic, direct product factor, Sylow
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	C₃×C₅×#120	1	4	yes	—
641	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
642	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
643	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
644	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	4	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	4	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	2	no	—
654	C₃	C₅×#2430	1	1	yes	characteristic, direct product factor, Sylow
655	C₂	—	2	4	no	—
656	C₂	—	4	4	no	—
657	C₂	—	8	1	no	—
658	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
659	C₂	C₃×C₅×#532	1	1	yes	characteristic
660	C₂	C₃×C₅×#537	1	1	yes	characteristic
661	C₂	C₃×C₅×#546	1	2	yes	—
662	C₂	C₃×C₅×#547	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. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂×C₃×C₅×#123	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₃×C₅×#395	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#393	C₂	semidirect
7. C₃×C₅×#392	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#386	C₂	semidirect
10. C₃×C₅×#385	C₂	semidirect
11. C₂×C₃×C₅×#95	C₂	semidirect
12. C₅×#2430	C₃	direct (N × H)
40. C₃×#2430	C₅	direct (N × H)
41. C₂²×C₅×#41	C₂×C₃	semidirect
42. C₂×C₅×#123	C₂×C₃	semidirect
43. C₂×C₅×#121	C₂×C₃	semidirect
44. C₅×#395	C₂×C₃	semidirect
45. C₅×#394	C₂×C₃	semidirect
46. C₅×#393	C₂×C₃	semidirect
47. C₅×#392	C₂×C₃	semidirect
48. C₅×#386	C₂×C₃	semidirect
49. C₅×#386	C₂×C₃	semidirect
50. C₅×#385	C₂×C₃	semidirect
51. C₂×C₅×#95	C₂×C₃	semidirect
67. C₂×C₃×C₅×D₄	D₄	semidirect
75. C₂²×C₃×C₄×C₅	D₄	semidirect
94. C₂²×C₃×#41	C₂×C₅	semidirect
95. C₂×C₃×#123	C₂×C₅	semidirect
96. C₂×C₃×#121	C₂×C₅	semidirect
97. C₃×#395	C₂×C₅	semidirect
98. C₃×#394	C₂×C₅	semidirect
99. C₃×#393	C₂×C₅	semidirect
100. C₃×#392	C₂×C₅	semidirect
101. C₃×#386	C₂×C₅	semidirect
102. C₃×#386	C₂×C₅	semidirect
103. C₃×#385	C₂×C₅	semidirect
104. C₂×C₃×#95	C₂×C₅	semidirect
132. #2430	C₃×C₅	direct (N × H)
178. C₂×C₃×C₄×C₅	#41	semidirect
221. C₂×C₅×D₄	C₃×D₄	semidirect
229. C₂²×C₄×C₅	C₃×D₄	semidirect
248. C₂²×#41	C₂×C₃×C₅	semidirect
249. C₂×#123	C₂×C₃×C₅	semidirect
250. C₂×#121	C₂×C₃×C₅	semidirect
251. #395	C₂×C₃×C₅	semidirect
252. #394	C₂×C₃×C₅	semidirect
253. #393	C₂×C₃×C₅	semidirect
254. #392	C₂×C₃×C₅	semidirect
255. #386	C₂×C₃×C₅	semidirect
256. #386	C₂×C₃×C₅	semidirect
257. #385	C₂×C₃×C₅	semidirect
258. C₂×#95	C₂×C₃×C₅	semidirect
304. C₂×C₃×D₄	C₅×D₄	semidirect
312. C₂²×C₃×C₄	C₅×D₄	semidirect
376. C₂×C₄×C₅	C₃×#41	semidirect
457. C₂×C₃×C₄	C₅×#41	semidirect
503. C₂×D₄	C₃×C₅×D₄	semidirect
511. C₂²×C₄	C₃×C₅×D₄	semidirect
530. C₃×C₅	#2430	direct (N × H)
614. C₂×C₄	C₃×C₅×#41	semidirect
623. C₅	C₃×#2430	direct (N × H)
654. C₃	C₅×#2430	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×#41	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×#121	2
C₃×C₅×#395	2
C₃×C₅×#394	2
C₃×C₅×#393	2
C₃×C₅×#392	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₂×C₃×C₅×#95	2
C₅×#2430	3
C₃×#2430	5

Subgroups — C3×C5×#2430 #14275464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2430 #14275464