Subgroups — C₃×C₅×#2318 #14275352

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#386	C₂	1	2	yes	maximal
5	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#383	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2318	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×D₄	C₄	1	8	yes	complemented
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	1	yes	characteristic
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	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	1	yes	characteristic
33	C₃×C₅×#95	C₂²	1	2	yes	—
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×#2318	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
39	C₅×#388	C₂×C₃	1	2	yes	complemented
40	C₅×#387	C₂×C₃	1	2	yes	complemented
41	C₅×#386	C₂×C₃	1	2	yes	—
42	C₅×#385	C₂×C₃	1	2	yes	complemented
43	C₅×#383	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
50	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₅×D₄	—	2	4	no	—
52	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
53	C₂²×C₃×C₄×C₅	—	2	4	no	—
54	C₂²×C₃×C₄×C₅	—	4	2	no	—
55	C₂²×C₃×C₄×C₅	—	4	2	no	—
56	C₂²×C₃×C₄×C₅	—	4	2	no	—
57	C₂²×C₃×C₄×C₅	—	4	2	no	—
58	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
59	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	—	4	2	no	—
70	C₃×C₅×C₄⋊C₄	—	4	2	no	—
71	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
72	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
73	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
74	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
75	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
76	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
77	C₃×C₄²×C₅	—	4	2	no	—
78	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
79	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
80	C₃×#388	C₂×C₅	1	2	yes	complemented
81	C₃×#387	C₂×C₅	1	2	yes	complemented
82	C₃×#386	C₂×C₅	1	2	yes	—
83	C₃×#385	C₂×C₅	1	2	yes	complemented
84	C₃×#383	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
91	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
92	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₄×C₅×D₄	C₃×C₄	1	8	yes	complemented
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
104	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
105	C₅×#95	C₂²×C₃	1	1	yes	characteristic
106	C₅×#95	C₂²×C₃	1	1	yes	characteristic
107	C₅×#95	C₂²×C₃	1	2	yes	—
108	C₅×#95	C₂²×C₃	1	1	yes	characteristic
109	C₅×#95	C₂²×C₃	1	1	yes	characteristic
110	C₅×#95	C₂²×C₃	1	2	yes	—
111	C₅×#95	C₂²×C₃	1	2	yes	—
112	C₅×#95	C₂²×C₃	1	2	yes	—
113	C₅×#95	C₂²×C₃	1	2	yes	—
114	#2318	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	1	no	—
117	C₂³×C₃×C₅	—	2	1	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	2	1	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	1	no	—
122	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
123	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
124	C₂³×C₃×C₅	#41	1	4	yes	—
125	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
126	C₃×C₅×D₄	—	2	8	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	4	4	no	—
146	C₂×C₃×C₄×C₅	—	4	4	no	—
147	C₂×C₃×C₄×C₅	—	4	8	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
153	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
155	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
157	C₃×C₄×D₄	C₄×C₅	1	8	yes	complemented
158	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
167	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
168	C₃×#95	C₂²×C₅	1	1	yes	characteristic
169	C₃×#95	C₂²×C₅	1	1	yes	characteristic
170	C₃×#95	C₂²×C₅	1	2	yes	—
171	C₃×#95	C₂²×C₅	1	1	yes	characteristic
172	C₃×#95	C₂²×C₅	1	1	yes	characteristic
173	C₃×#95	C₂²×C₅	1	2	yes	—
174	C₃×#95	C₂²×C₅	1	2	yes	—
175	C₃×#95	C₂²×C₅	1	2	yes	—
176	C₃×#95	C₂²×C₅	1	2	yes	—
177	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₅×D₄	—	2	4	no	—
180	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
181	C₂²×C₄×C₅	—	2	4	no	—
182	C₂²×C₄×C₅	—	4	2	no	—
183	C₂²×C₄×C₅	—	4	2	no	—
184	C₂²×C₄×C₅	—	4	2	no	—
185	C₂²×C₄×C₅	—	4	2	no	—
186	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
187	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
188	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
189	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
190	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
191	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
192	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₅×C₄⋊C₄	—	4	2	no	—
198	C₅×C₄⋊C₄	—	4	2	no	—
199	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
200	C₅×C₂²⋊C₄	—	2	4	no	—
201	C₅×C₂²⋊C₄	—	4	2	no	—
202	C₅×C₂²⋊C₄	—	4	2	no	—
203	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
204	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
205	C₄²×C₅	—	4	2	no	—
206	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
207	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
208	#388	C₂×C₃×C₅	1	2	yes	complemented
209	#387	C₂×C₃×C₅	1	2	yes	complemented
210	#386	C₂×C₃×C₅	1	2	yes	—
211	#385	C₂×C₃×C₅	1	2	yes	complemented
212	#383	C₂×C₃×C₅	1	1	yes	characteristic, complemented
213	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	#381	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
216	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
217	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
218	C₂²×C₃×C₅	—	2	2	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	—	2	4	no	—
221	C₂²×C₃×C₅	—	2	4	no	—
222	C₂²×C₃×C₅	—	2	2	no	—
223	C₂²×C₃×C₅	—	2	2	no	—
224	C₂²×C₃×C₅	—	2	2	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	—	4	2	no	—
227	C₂²×C₃×C₅	#117	1	4	yes	—
228	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
229	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
230	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
231	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	2	no	—
235	C₃×C₄×C₅	—	2	2	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	4	2	no	—
239	C₃×C₄×C₅	—	4	2	no	—
240	C₃×C₄×C₅	—	4	2	no	—
241	C₃×C₄×C₅	—	4	2	no	—
242	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
243	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
244	C₂×C₃×D₄	—	2	4	no	—
245	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
246	C₂²×C₃×C₄	—	2	4	no	—
247	C₂²×C₃×C₄	—	4	2	no	—
248	C₂²×C₃×C₄	—	4	2	no	—
249	C₂²×C₃×C₄	—	4	2	no	—
250	C₂²×C₃×C₄	—	4	2	no	—
251	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
252	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
253	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
254	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
255	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
256	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
257	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₃×C₄⋊C₄	—	4	2	no	—
263	C₃×C₄⋊C₄	—	4	2	no	—
264	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
265	C₃×C₂²⋊C₄	—	2	4	no	—
266	C₃×C₂²⋊C₄	—	4	2	no	—
267	C₃×C₂²⋊C₄	—	4	2	no	—
268	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
269	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
270	C₃×C₄²	—	4	2	no	—
271	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
280	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
281	C₂³×C₅	C₃×#41	1	4	yes	—
282	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
283	C₅×D₄	—	2	8	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	4	4	no	—
303	C₂×C₄×C₅	—	4	4	no	—
304	C₂×C₄×C₅	—	4	8	no	—
305	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
306	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
307	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
308	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
309	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
310	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
311	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
312	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
313	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
314	C₄×D₄	C₃×C₄×C₅	1	8	yes	complemented
315	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
316	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
317	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
323	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
324	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
325	#95	C₂²×C₃×C₅	1	1	yes	characteristic
326	#95	C₂²×C₃×C₅	1	1	yes	characteristic
327	#95	C₂²×C₃×C₅	1	2	yes	—
328	#95	C₂²×C₃×C₅	1	1	yes	characteristic
329	#95	C₂²×C₃×C₅	1	1	yes	characteristic
330	#95	C₂²×C₃×C₅	1	2	yes	—
331	#95	C₂²×C₃×C₅	1	2	yes	—
332	#95	C₂²×C₃×C₅	1	2	yes	—
333	#95	C₂²×C₃×C₅	1	2	yes	—
334	C₂×C₃×C₅	—	2	4	no	—
335	C₂×C₃×C₅	—	4	2	no	—
336	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
337	C₂×C₃×C₅	#518	1	1	yes	characteristic
338	C₂×C₃×C₅	#520	1	1	yes	characteristic
339	C₂×C₃×C₅	#538	1	2	yes	—
340	C₂×C₃×C₅	#539	1	2	yes	—
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	2	2	no	—
345	C₂³×C₃	—	2	1	no	—
346	C₂³×C₃	—	2	2	no	—
347	C₂³×C₃	—	2	1	no	—
348	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
349	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
350	C₂³×C₃	C₅×#41	1	4	yes	—
351	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
352	C₃×D₄	—	2	8	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	4	4	no	—
372	C₂×C₃×C₄	—	4	4	no	—
373	C₂×C₃×C₄	—	4	8	no	—
374	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
375	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
376	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
377	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
378	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
379	C₂²×C₅	—	2	2	no	—
380	C₂²×C₅	—	2	2	no	—
381	C₂²×C₅	—	2	4	no	—
382	C₂²×C₅	—	2	4	no	—
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	—	2	2	no	—
385	C₂²×C₅	—	2	2	no	—
386	C₂²×C₅	—	4	2	no	—
387	C₂²×C₅	—	4	2	no	—
388	C₂²×C₅	C₃×#117	1	4	yes	—
389	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
390	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
391	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
392	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
394	C₄×C₅	—	2	2	no	—
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	—	2	2	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	2	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	—	4	2	no	—
403	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
413	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
414	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
415	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
416	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
417	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
418	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
419	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
420	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
421	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
422	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
430	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
431	C₄²	—	4	2	no	—
432	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
433	C₃×C₅	#2318	1	1	yes	characteristic, direct product factor, Hall
434	C₂²×C₃	—	2	2	no	—
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	4	no	—
437	C₂²×C₃	—	2	4	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	2	2	no	—
440	C₂²×C₃	—	2	2	no	—
441	C₂²×C₃	—	4	2	no	—
442	C₂²×C₃	—	4	2	no	—
443	C₂²×C₃	C₅×#117	1	4	yes	—
444	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
445	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
446	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
447	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	4	2	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	—	4	2	no	—
457	C₃×C₄	—	4	2	no	—
458	C₂×C₅	—	2	4	no	—
459	C₂×C₅	—	4	2	no	—
460	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
461	C₂×C₅	C₃×#518	1	1	yes	characteristic
462	C₂×C₅	C₃×#520	1	1	yes	characteristic
463	C₂×C₅	C₃×#538	1	2	yes	—
464	C₂×C₅	C₃×#539	1	2	yes	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	1	no	—
472	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
473	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
474	C₂³	C₃×C₅×#41	1	4	yes	—
475	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
476	D₄	—	2	8	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
499	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
500	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
501	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
502	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
503	C₂×C₃	—	2	4	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
506	C₂×C₃	C₅×#518	1	1	yes	characteristic
507	C₂×C₃	C₅×#520	1	1	yes	characteristic
508	C₂×C₃	C₅×#538	1	2	yes	—
509	C₂×C₃	C₅×#539	1	2	yes	—
510	C₅	C₃×#2318	1	1	yes	characteristic, direct product factor, Sylow
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	C₃×C₅×#117	1	4	yes	—
521	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
522	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
523	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
524	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₃	C₅×#2318	1	1	yes	characteristic, direct product factor, Sylow
536	C₂	—	2	4	no	—
537	C₂	—	4	2	no	—
538	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
539	C₂	C₃×C₅×#518	1	1	yes	characteristic
540	C₂	C₃×C₅×#520	1	1	yes	characteristic
541	C₂	C₃×C₅×#538	1	2	yes	—
542	C₂	C₃×C₅×#539	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#388	C₂	semidirect
3. C₃×C₅×#387	C₂	semidirect
5. C₃×C₅×#385	C₂	semidirect
6. C₃×C₅×#383	C₂	semidirect
7. C₃×C₅×#382	C₂	semidirect
8. C₃×C₅×#381	C₂	semidirect
9. C₃×C₅×#380	C₂	semidirect
10. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
11. C₂×C₃×C₅×#95	C₂	semidirect
12. C₅×#2318	C₃	direct (N × H)
17. C₃×C₄×C₅×D₄	C₄	semidirect
37. C₃×#2318	C₅	direct (N × H)
39. C₅×#388	C₂×C₃	semidirect
40. C₅×#387	C₂×C₃	semidirect
42. C₅×#385	C₂×C₃	semidirect
43. C₅×#383	C₂×C₃	semidirect
44. C₅×#382	C₂×C₃	semidirect
45. C₅×#381	C₂×C₃	semidirect
46. C₅×#380	C₂×C₃	semidirect
47. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
48. C₂×C₅×#95	C₂×C₃	semidirect
59. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
71. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
76. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
78. C₃×C₄²×C₅	C₂×C₄	semidirect
80. C₃×#388	C₂×C₅	semidirect
81. C₃×#387	C₂×C₅	semidirect
83. C₃×#385	C₂×C₅	semidirect
84. C₃×#383	C₂×C₅	semidirect
85. C₃×#382	C₂×C₅	semidirect
86. C₃×#381	C₂×C₅	semidirect
87. C₃×#380	C₂×C₅	semidirect
88. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
89. C₂×C₃×#95	C₂×C₅	semidirect
94. C₄×C₅×D₄	C₃×C₄	semidirect
114. #2318	C₃×C₅	direct (N × H)
157. C₃×C₄×D₄	C₄×C₅	semidirect
187. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
199. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
204. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
206. C₄²×C₅	C₂×C₃×C₄	semidirect
208. #388	C₂×C₃×C₅	semidirect
209. #387	C₂×C₃×C₅	semidirect
211. #385	C₂×C₃×C₅	semidirect
212. #383	C₂×C₃×C₅	semidirect
213. #382	C₂×C₃×C₅	semidirect
214. #381	C₂×C₃×C₅	semidirect
215. #380	C₂×C₃×C₅	semidirect
216. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
217. C₂×#95	C₂×C₃×C₅	semidirect
252. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
264. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
269. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
271. C₃×C₄²	C₂×C₄×C₅	semidirect
314. C₄×D₄	C₃×C₄×C₅	semidirect
413. C₂²×C₄	C₂×C₃×C₄×C₅	semidirect
425. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
430. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
432. C₄²	C₂×C₃×C₄×C₅	semidirect
433. C₃×C₅	#2318	direct (N × H)
510. C₅	C₃×#2318	direct (N × H)
535. C₃	C₅×#2318	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×C₄×C₅×D₄	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#383	2
C₃×C₅×#382	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₃×C₅×#95	2
C₅×#2318	3
C₃×#2318	5

Subgroups — C3×C5×#2318 #14275352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2318 #14275352