Subgroups — C₃×C₅×#2364 #14275398

Order 1920.

1432 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2364	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#121	C₄	1	8	yes	complemented
17	C₃×C₄×C₅×D₄	—	2	8	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
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×#2364	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
36	C₂×C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
37	C₅×#388	C₂×C₃	1	2	yes	complemented
38	C₅×#387	C₂×C₃	1	2	yes	complemented
39	C₅×#386	C₂×C₃	1	2	yes	complemented
40	C₅×#386	C₂×C₃	1	2	yes	complemented
41	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
42	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	4	2	no	—
49	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	complemented
50	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
51	C₂²×C₃×C₄×C₅	—	2	4	no	—
52	C₂²×C₃×C₄×C₅	—	2	4	no	—
53	C₂²×C₃×C₄×C₅	—	2	4	no	—
54	C₂²×C₃×C₄×C₅	—	2	4	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	complemented
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	—	2	4	no	—
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
71	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
72	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
73	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
74	C₃×C₄²×C₅	—	2	4	no	—
75	C₃×C₄²×C₅	—	4	2	no	—
76	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
77	C₂×C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
78	C₃×#388	C₂×C₅	1	2	yes	complemented
79	C₃×#387	C₂×C₅	1	2	yes	complemented
80	C₃×#386	C₂×C₅	1	2	yes	complemented
81	C₃×#386	C₂×C₅	1	2	yes	complemented
82	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
83	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
86	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
88	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
89	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
90	C₅×#121	C₃×C₄	1	8	yes	complemented
91	C₄×C₅×D₄	—	2	8	no	—
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
101	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
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	#2364	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	2	no	—
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
118	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
119	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
120	C₂³×C₃×C₅	#41	1	2	yes	—
121	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
122	C₃×C₅×D₄	—	2	16	no	—
123	C₃×C₅×D₄	—	4	4	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	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	4	no	—
139	C₂×C₃×C₄×C₅	—	4	8	no	—
140	C₂×C₃×C₄×C₅	—	4	8	no	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
145	C₂×C₃×C₄×C₅	#41	1	4	yes	—
146	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
147	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
148	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
149	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
150	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
151	C₃×#121	C₄×C₅	1	8	yes	complemented
152	C₃×C₄×D₄	—	2	8	no	—
153	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
157	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
162	C₂×C₃×C₄²	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	1	yes	characteristic
166	C₃×#95	C₂²×C₅	1	2	yes	—
167	C₃×#95	C₂²×C₅	1	2	yes	—
168	C₃×#95	C₂²×C₅	1	2	yes	—
169	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
170	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₅×D₄	—	2	4	no	—
172	C₂×C₅×D₄	—	2	4	no	—
173	C₂×C₅×D₄	—	4	2	no	—
174	C₂×C₅×D₄	C₂×C₃×C₄	1	8	yes	complemented
175	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
176	C₂²×C₄×C₅	—	2	4	no	—
177	C₂²×C₄×C₅	—	2	4	no	—
178	C₂²×C₄×C₅	—	2	4	no	—
179	C₂²×C₄×C₅	—	2	4	no	—
180	C₂²×C₄×C₅	—	4	2	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	4	2	no	—
183	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
184	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
185	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
186	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
190	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
191	C₅×C₄⋊C₄	—	2	4	no	—
192	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	4	no	—
195	C₅×C₂²⋊C₄	—	2	4	no	—
196	C₅×C₂²⋊C₄	—	4	2	no	—
197	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
198	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
199	C₄²×C₅	—	2	4	no	—
200	C₄²×C₅	—	4	2	no	—
201	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
203	#388	C₂×C₃×C₅	1	2	yes	complemented
204	#387	C₂×C₃×C₅	1	2	yes	complemented
205	#386	C₂×C₃×C₅	1	2	yes	complemented
206	#386	C₂×C₃×C₅	1	2	yes	complemented
207	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
208	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
210	C₂²×C₃×C₅	—	2	2	no	—
211	C₂²×C₃×C₅	—	2	2	no	—
212	C₂²×C₃×C₅	—	2	4	no	—
213	C₂²×C₃×C₅	—	2	4	no	—
214	C₂²×C₃×C₅	—	2	4	no	—
215	C₂²×C₃×C₅	—	2	4	no	—
216	C₂²×C₃×C₅	—	2	4	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	—	4	2	no	—
221	C₂²×C₃×C₅	C₄×D₄	1	4	yes	—
222	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
225	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
226	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
227	C₃×C₄×C₅	—	2	4	no	—
228	C₃×C₄×C₅	—	2	2	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	—	2	4	no	—
231	C₃×C₄×C₅	—	2	4	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
235	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
236	C₂×C₃×D₄	—	2	4	no	—
237	C₂×C₃×D₄	—	2	4	no	—
238	C₂×C₃×D₄	—	4	2	no	—
239	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
240	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
241	C₂²×C₃×C₄	—	2	4	no	—
242	C₂²×C₃×C₄	—	2	4	no	—
243	C₂²×C₃×C₄	—	2	4	no	—
244	C₂²×C₃×C₄	—	2	4	no	—
245	C₂²×C₃×C₄	—	4	2	no	—
246	C₂²×C₃×C₄	—	4	2	no	—
247	C₂²×C₃×C₄	—	4	2	no	—
248	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
249	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
250	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	C₃×C₄⋊C₄	—	2	4	no	—
257	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	2	4	no	—
260	C₃×C₂²⋊C₄	—	2	4	no	—
261	C₃×C₂²⋊C₄	—	4	2	no	—
262	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
263	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
264	C₃×C₄²	—	2	4	no	—
265	C₃×C₄²	—	4	2	no	—
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	2	2	no	—
269	C₂³×C₅	—	2	2	no	—
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	2	2	no	—
272	C₂³×C₅	—	2	2	no	—
273	C₂³×C₅	—	2	2	no	—
274	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
275	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
276	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
277	C₂³×C₅	C₃×#41	1	2	yes	—
278	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
279	C₅×D₄	—	2	16	no	—
280	C₅×D₄	—	4	4	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	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	—	4	4	no	—
296	C₂×C₄×C₅	—	4	8	no	—
297	C₂×C₄×C₅	—	4	8	no	—
298	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
299	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
300	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
301	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
302	C₂×C₄×C₅	C₃×#41	1	4	yes	—
303	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
304	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
305	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
306	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
307	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
308	#121	C₃×C₄×C₅	1	8	yes	complemented
309	C₄×D₄	—	2	8	no	—
310	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
311	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
319	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
320	#95	C₂²×C₃×C₅	1	1	yes	characteristic
321	#95	C₂²×C₃×C₅	1	2	yes	—
322	#95	C₂²×C₃×C₅	1	1	yes	characteristic
323	#95	C₂²×C₃×C₅	1	2	yes	—
324	#95	C₂²×C₃×C₅	1	2	yes	—
325	#95	C₂²×C₃×C₅	1	2	yes	—
326	C₂×C₃×C₅	—	2	4	no	—
327	C₂×C₃×C₅	—	4	4	no	—
328	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
329	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
330	C₂×C₃×C₅	#518	1	1	yes	characteristic
331	C₂×C₃×C₅	#546	1	2	yes	—
332	C₂×C₃×C₅	#553	1	2	yes	—
333	C₂³×C₃	—	2	2	no	—
334	C₂³×C₃	—	2	2	no	—
335	C₂³×C₃	—	2	2	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	2	2	no	—
338	C₂³×C₃	—	2	2	no	—
339	C₂³×C₃	—	2	2	no	—
340	C₂³×C₃	—	2	2	no	—
341	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
342	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
343	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
344	C₂³×C₃	C₅×#41	1	2	yes	—
345	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
346	C₃×D₄	—	2	16	no	—
347	C₃×D₄	—	4	4	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	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	—	4	4	no	—
363	C₂×C₃×C₄	—	4	8	no	—
364	C₂×C₃×C₄	—	4	8	no	—
365	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
366	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
367	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
368	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
369	C₂×C₃×C₄	C₅×#41	1	4	yes	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	—	2	2	no	—
372	C₂²×C₅	—	2	4	no	—
373	C₂²×C₅	—	2	4	no	—
374	C₂²×C₅	—	2	4	no	—
375	C₂²×C₅	—	2	4	no	—
376	C₂²×C₅	—	2	4	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	2	no	—
379	C₂²×C₅	—	4	2	no	—
380	C₂²×C₅	—	4	2	no	—
381	C₂²×C₅	C₃×C₄×D₄	1	4	yes	—
382	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
383	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
384	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
385	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
386	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
387	C₄×C₅	—	2	4	no	—
388	C₄×C₅	—	2	2	no	—
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	2	4	no	—
391	C₄×C₅	—	2	4	no	—
392	C₄×C₅	—	4	2	no	—
393	C₄×C₅	—	4	2	no	—
394	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
395	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
400	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
409	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
410	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
411	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
412	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
413	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
414	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
415	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
423	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
424	C₄²	—	2	4	no	—
425	C₄²	—	4	2	no	—
426	C₃×C₅	#2364	1	1	yes	characteristic, direct product factor, Hall
427	C₂²×C₃	—	2	2	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	2	4	no	—
430	C₂²×C₃	—	2	4	no	—
431	C₂²×C₃	—	2	4	no	—
432	C₂²×C₃	—	2	4	no	—
433	C₂²×C₃	—	2	4	no	—
434	C₂²×C₃	—	4	2	no	—
435	C₂²×C₃	—	4	2	no	—
436	C₂²×C₃	—	4	2	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	C₄×C₅×D₄	1	4	yes	—
439	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
440	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
441	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
442	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
443	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
444	C₃×C₄	—	2	4	no	—
445	C₃×C₄	—	2	2	no	—
446	C₃×C₄	—	2	2	no	—
447	C₃×C₄	—	2	4	no	—
448	C₃×C₄	—	2	4	no	—
449	C₃×C₄	—	4	2	no	—
450	C₃×C₄	—	4	2	no	—
451	C₂×C₅	—	2	4	no	—
452	C₂×C₅	—	4	4	no	—
453	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
454	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
455	C₂×C₅	C₃×#518	1	1	yes	characteristic
456	C₂×C₅	C₃×#546	1	2	yes	—
457	C₂×C₅	C₃×#553	1	2	yes	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
467	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
468	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
469	C₂³	C₃×C₅×#41	1	2	yes	—
470	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
471	D₄	—	2	16	no	—
472	D₄	—	4	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	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	—	4	4	no	—
488	C₂×C₄	—	4	8	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
491	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
492	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
493	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
494	C₂×C₄	C₃×C₅×#41	1	4	yes	—
495	C₂×C₃	—	2	4	no	—
496	C₂×C₃	—	4	4	no	—
497	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
498	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
499	C₂×C₃	C₅×#518	1	1	yes	characteristic
500	C₂×C₃	C₅×#546	1	2	yes	—
501	C₂×C₃	C₅×#553	1	2	yes	—
502	C₅	C₃×#2364	1	1	yes	characteristic, direct product factor, Sylow
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	C₃×C₄×C₅×D₄	1	4	yes	—
515	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
516	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
517	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
518	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
519	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
520	C₄	—	2	4	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	4	no	—
524	C₄	—	2	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₃	C₅×#2364	1	1	yes	characteristic, direct product factor, Sylow
528	C₂	—	2	4	no	—
529	C₂	—	4	4	no	—
530	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
531	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
532	C₂	C₃×C₅×#518	1	1	yes	characteristic
533	C₂	C₃×C₅×#546	1	2	yes	—
534	C₂	C₃×C₅×#553	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	C₂×C₃×C₅×#121	C₂
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. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₅×#388	C₂	semidirect
4. C₃×C₅×#387	C₂	semidirect
5. C₃×C₅×#386	C₂	semidirect
6. C₃×C₅×#386	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
9. C₂×C₃×C₅×#95	C₂	semidirect
10. C₅×#2364	C₃	direct (N × H)
16. C₃×C₅×#121	C₄	semidirect
34. C₃×#2364	C₅	direct (N × H)
36. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
37. C₅×#388	C₂×C₃	semidirect
38. C₅×#387	C₂×C₃	semidirect
39. C₅×#386	C₂×C₃	semidirect
40. C₅×#386	C₂×C₃	semidirect
41. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
42. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
43. C₂×C₅×#95	C₂×C₃	semidirect
49. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
50. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
58. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
67. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
72. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
73. C₃×C₅×C₂²⋊C₄	D₄	semidirect
77. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
78. C₃×#388	C₂×C₅	semidirect
79. C₃×#387	C₂×C₅	semidirect
80. C₃×#386	C₂×C₅	semidirect
81. C₃×#386	C₂×C₅	semidirect
82. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
83. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
84. C₂×C₃×#95	C₂×C₅	semidirect
90. C₅×#121	C₃×C₄	semidirect
108. #2364	C₃×C₅	direct (N × H)
151. C₃×#121	C₄×C₅	semidirect
174. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
175. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
183. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
192. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
197. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
198. C₅×C₂²⋊C₄	C₃×D₄	semidirect
202. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
203. #388	C₂×C₃×C₅	semidirect
204. #387	C₂×C₃×C₅	semidirect
205. #386	C₂×C₃×C₅	semidirect
206. #386	C₂×C₃×C₅	semidirect
207. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
208. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
209. C₂×#95	C₂×C₃×C₅	semidirect
239. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
240. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
248. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
257. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
262. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
263. C₃×C₂²⋊C₄	C₅×D₄	semidirect
308. #121	C₃×C₄×C₅	semidirect
399. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
400. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
408. C₂²×C₄	C₂×C₃×C₄×C₅	semidirect
417. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
422. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
423. C₂²⋊C₄	C₃×C₅×D₄	semidirect
426. C₃×C₅	#2364	direct (N × H)
502. C₅	C₃×#2364	direct (N × H)
527. C₃	C₅×#2364	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×#121	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₃×C₅×#95	2
C₅×#2364	3
C₃×#2364	5

Subgroups — C3×C5×#2364 #14275398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2364 #14275398