Subgroups — C₃×C₅×#2343 #14275377

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#385	C₂	1	2	yes	maximal
5	C₃×C₅×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
10	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
12	C₅×#2343	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₄	1	8	yes	complemented
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	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×C₅×#95	C₂²	1	2	yes	—
34	C₃×C₅×#95	C₂²	1	1	yes	characteristic
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×#2343	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
39	C₅×#387	C₂×C₃	1	2	yes	complemented
40	C₅×#387	C₂×C₃	1	2	yes	complemented
41	C₅×#385	C₂×C₃	1	2	yes	—
42	C₅×#383	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#381	C₂×C₃	1	1	yes	characteristic
45	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
47	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
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	—	4	2	no	—
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	—	2	4	no	—
66	C₃×C₅×C₄⋊C₄	—	4	2	no	—
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
72	C₃×C₄²×C₅	—	2	4	no	—
73	C₃×C₄²×C₅	—	4	2	no	—
74	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
75	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
76	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
77	C₃×#387	C₂×C₅	1	2	yes	complemented
78	C₃×#387	C₂×C₅	1	2	yes	complemented
79	C₃×#385	C₂×C₅	1	2	yes	—
80	C₃×#383	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#381	C₂×C₅	1	1	yes	characteristic
83	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
85	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
88	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
89	C₅×#117	C₃×C₄	1	8	yes	complemented
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	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
98	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
101	C₅×#95	C₂²×C₃	1	1	yes	characteristic
102	C₅×#95	C₂²×C₃	1	1	yes	characteristic
103	C₅×#95	C₂²×C₃	1	2	yes	—
104	C₅×#95	C₂²×C₃	1	1	yes	characteristic
105	C₅×#95	C₂²×C₃	1	2	yes	—
106	C₅×#95	C₂²×C₃	1	2	yes	—
107	C₅×#95	C₂²×C₃	1	2	yes	—
108	C₅×#95	C₂²×C₃	1	1	yes	characteristic
109	C₅×#95	C₂²×C₃	1	2	yes	—
110	C₅×#95	C₂²×C₃	1	2	yes	—
111	#2343	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂³×C₃×C₅	—	2	1	no	—
114	C₂³×C₃×C₅	—	2	1	no	—
115	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
116	C₂³×C₃×C₅	#41	1	4	yes	—
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	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	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	4	8	no	—
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	#41	1	4	yes	—
146	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
147	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
148	C₃×#117	C₄×C₅	1	8	yes	complemented
149	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
157	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
158	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
160	C₃×#95	C₂²×C₅	1	1	yes	characteristic
161	C₃×#95	C₂²×C₅	1	1	yes	characteristic
162	C₃×#95	C₂²×C₅	1	2	yes	—
163	C₃×#95	C₂²×C₅	1	1	yes	characteristic
164	C₃×#95	C₂²×C₅	1	2	yes	—
165	C₃×#95	C₂²×C₅	1	2	yes	—
166	C₃×#95	C₂²×C₅	1	2	yes	—
167	C₃×#95	C₂²×C₅	1	1	yes	characteristic
168	C₃×#95	C₂²×C₅	1	2	yes	—
169	C₃×#95	C₂²×C₅	1	2	yes	—
170	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	—	2	4	no	—
172	C₂²×C₄×C₅	—	2	4	no	—
173	C₂²×C₄×C₅	—	2	4	no	—
174	C₂²×C₄×C₅	—	4	2	no	—
175	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
176	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
177	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
186	C₅×C₄⋊C₄	—	2	4	no	—
187	C₅×C₄⋊C₄	—	4	2	no	—
188	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
189	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
190	C₅×C₂²⋊C₄	—	2	4	no	—
191	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
192	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
193	C₄²×C₅	—	2	4	no	—
194	C₄²×C₅	—	4	2	no	—
195	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
196	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
197	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
198	#387	C₂×C₃×C₅	1	2	yes	complemented
199	#387	C₂×C₃×C₅	1	2	yes	complemented
200	#385	C₂×C₃×C₅	1	2	yes	—
201	#383	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#381	C₂×C₃×C₅	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
206	#376	C₂×C₃×C₅	1	1	yes	characteristic, complemented
207	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	—	2	4	no	—
212	C₂²×C₃×C₅	#117	1	4	yes	—
213	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
214	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
215	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
216	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	—	2	2	no	—
220	C₃×C₄×C₅	—	2	2	no	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	—	2	2	no	—
224	C₃×C₄×C₅	—	2	4	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	—	4	2	no	—
227	C₃×C₄×C₅	—	4	2	no	—
228	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	—	2	4	no	—
230	C₂²×C₃×C₄	—	2	4	no	—
231	C₂²×C₃×C₄	—	2	4	no	—
232	C₂²×C₃×C₄	—	4	2	no	—
233	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
234	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
235	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
236	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
237	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
244	C₃×C₄⋊C₄	—	2	4	no	—
245	C₃×C₄⋊C₄	—	4	2	no	—
246	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
247	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
248	C₃×C₂²⋊C₄	—	2	4	no	—
249	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
250	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
251	C₃×C₄²	—	2	4	no	—
252	C₃×C₄²	—	4	2	no	—
253	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
254	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	1	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
259	C₂³×C₅	C₃×#41	1	4	yes	—
260	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₂×C₄×C₅	—	2	8	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	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	1	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	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	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	4	8	no	—
282	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
283	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
284	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
285	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
286	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
287	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
288	C₂×C₄×C₅	C₃×#41	1	4	yes	—
289	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
290	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
291	#117	C₃×C₄×C₅	1	8	yes	complemented
292	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
293	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
294	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
300	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
301	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
302	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
303	#95	C₂²×C₃×C₅	1	1	yes	characteristic
304	#95	C₂²×C₃×C₅	1	1	yes	characteristic
305	#95	C₂²×C₃×C₅	1	2	yes	—
306	#95	C₂²×C₃×C₅	1	1	yes	characteristic
307	#95	C₂²×C₃×C₅	1	2	yes	—
308	#95	C₂²×C₃×C₅	1	2	yes	—
309	#95	C₂²×C₃×C₅	1	2	yes	—
310	#95	C₂²×C₃×C₅	1	1	yes	characteristic
311	#95	C₂²×C₃×C₅	1	2	yes	—
312	#95	C₂²×C₃×C₅	1	2	yes	—
313	C₂×C₃×C₅	—	2	4	no	—
314	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
315	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
316	C₂×C₃×C₅	#520	1	1	yes	characteristic
317	C₂×C₃×C₅	#551	1	2	yes	—
318	C₂×C₃×C₅	#552	1	2	yes	—
319	C₂³×C₃	—	2	2	no	—
320	C₂³×C₃	—	2	1	no	—
321	C₂³×C₃	—	2	1	no	—
322	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
323	C₂³×C₃	C₅×#41	1	4	yes	—
324	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
325	C₂×C₃×C₄	—	2	8	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	1	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	2	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	—	2	2	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	4	8	no	—
346	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
347	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
348	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
349	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
350	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
351	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
352	C₂×C₃×C₄	C₅×#41	1	4	yes	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	4	no	—
356	C₂²×C₅	—	2	4	no	—
357	C₂²×C₅	C₃×#117	1	4	yes	—
358	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
359	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
360	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
361	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	2	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	—	2	2	no	—
368	C₄×C₅	—	2	2	no	—
369	C₄×C₅	—	2	4	no	—
370	C₄×C₅	—	4	2	no	—
371	C₄×C₅	—	4	2	no	—
372	C₄×C₅	—	4	2	no	—
373	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
379	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
380	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
381	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
382	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
383	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
384	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
385	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
386	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
387	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
388	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
392	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
395	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
396	C₄²	—	2	4	no	—
397	C₄²	—	4	2	no	—
398	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
399	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
400	C₃×C₅	#2343	1	1	yes	characteristic, direct product factor, Hall
401	C₂²×C₃	—	2	2	no	—
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	2	4	no	—
404	C₂²×C₃	—	2	4	no	—
405	C₂²×C₃	C₅×#117	1	4	yes	—
406	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
407	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
408	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
409	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	4	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	—	4	2	no	—
420	C₃×C₄	—	4	2	no	—
421	C₂×C₅	—	2	4	no	—
422	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
423	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
424	C₂×C₅	C₃×#520	1	1	yes	characteristic
425	C₂×C₅	C₃×#551	1	2	yes	—
426	C₂×C₅	C₃×#552	1	2	yes	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
431	C₂³	C₃×C₅×#41	1	4	yes	—
432	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	2	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	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
455	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
456	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
457	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
458	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
459	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
460	C₂×C₄	C₃×C₅×#41	1	4	yes	—
461	C₂×C₃	—	2	4	no	—
462	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
463	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
464	C₂×C₃	C₅×#520	1	1	yes	characteristic
465	C₂×C₃	C₅×#551	1	2	yes	—
466	C₂×C₃	C₅×#552	1	2	yes	—
467	C₅	C₃×#2343	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	C₃×C₅×#117	1	4	yes	—
473	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
474	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
475	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
476	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	4	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₃	C₅×#2343	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	2	4	no	—
490	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
491	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
492	C₂	C₃×C₅×#520	1	1	yes	characteristic
493	C₂	C₃×C₅×#551	1	2	yes	—
494	C₂	C₃×C₅×#552	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	C₂⁴×C₃×C₅	C₂³
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×#387	C₂	semidirect
3. C₃×C₅×#387	C₂	semidirect
5. C₃×C₅×#383	C₂	semidirect
6. C₃×C₅×#382	C₂	semidirect
8. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
10. C₃×C₅×#376	C₂	semidirect
12. C₅×#2343	C₃	direct (N × H)
15. C₃×C₅×#117	C₄	semidirect
37. C₃×#2343	C₅	direct (N × H)
39. C₅×#387	C₂×C₃	semidirect
40. C₅×#387	C₂×C₃	semidirect
42. C₅×#383	C₂×C₃	semidirect
43. C₅×#382	C₂×C₃	semidirect
45. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
47. C₅×#376	C₂×C₃	semidirect
67. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
68. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
74. C₃×C₄²×C₅	C₂×C₄	semidirect
75. C₃×C₄²×C₅	C₂×C₄	semidirect
77. C₃×#387	C₂×C₅	semidirect
78. C₃×#387	C₂×C₅	semidirect
80. C₃×#383	C₂×C₅	semidirect
81. C₃×#382	C₂×C₅	semidirect
83. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
85. C₃×#376	C₂×C₅	semidirect
89. C₅×#117	C₃×C₄	semidirect
111. #2343	C₃×C₅	direct (N × H)
148. C₃×#117	C₄×C₅	semidirect
188. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
189. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
195. C₄²×C₅	C₂×C₃×C₄	semidirect
196. C₄²×C₅	C₂×C₃×C₄	semidirect
198. #387	C₂×C₃×C₅	semidirect
199. #387	C₂×C₃×C₅	semidirect
201. #383	C₂×C₃×C₅	semidirect
202. #382	C₂×C₃×C₅	semidirect
204. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
206. #376	C₂×C₃×C₅	semidirect
246. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
247. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
253. C₃×C₄²	C₂×C₄×C₅	semidirect
254. C₃×C₄²	C₂×C₄×C₅	semidirect
291. #117	C₃×C₄×C₅	semidirect
391. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
392. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
398. C₄²	C₂×C₃×C₄×C₅	semidirect
399. C₄²	C₂×C₃×C₄×C₅	semidirect
400. C₃×C₅	#2343	direct (N × H)
467. C₅	C₃×#2343	direct (N × H)
488. C₃	C₅×#2343	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×#117	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#383	2
C₃×C₅×#382	2
C₃×C₅×#381	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#376	2
C₂×C₃×C₅×#95	2
C₅×#2343	3
C₃×#2343	5

Subgroups — C3×C5×#2343 #14275377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2343 #14275377