Subgroups — C₃×C₅×#2374 #14275408

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 508 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	1	yes	maximal, characteristic
2	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#2374	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×#123	C₄	1	8	yes	complemented
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
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	2	yes	—
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	2	yes	—
33	C₃×#2374	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic
35	C₅×#390	C₂×C₃	1	1	yes	characteristic
36	C₅×#388	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	1	yes	characteristic
40	C₄×C₅×C₄⋊C₄	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	2	yes	complemented
43	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
44	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×D₄	—	4	1	no	—
46	C₂×C₃×C₅×D₄	—	4	1	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	—	4	1	no	—
50	C₂²×C₃×C₄×C₅	—	4	1	no	—
51	C₂²×C₃×C₄×C₅	—	4	1	no	—
52	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
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	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	4	no	—
61	C₃×C₅×C₄⋊C₄	—	4	1	no	—
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
63	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
64	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
66	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
67	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
68	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
69	C₃×C₄²×C₅	—	2	4	no	—
70	C₃×C₄²×C₅	—	4	1	no	—
71	C₃×C₄²×C₅	—	4	2	no	—
72	C₃×C₄²×C₅	—	4	2	no	—
73	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic
74	C₃×#390	C₂×C₅	1	1	yes	characteristic
75	C₃×#388	C₂×C₅	1	2	yes	complemented
76	C₃×#388	C₂×C₅	1	2	yes	complemented
77	C₃×#387	C₂×C₅	1	2	yes	complemented
78	C₃×#386	C₂×C₅	1	1	yes	characteristic
79	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
80	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
81	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
82	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
85	C₅×#123	C₃×C₄	1	8	yes	complemented
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
96	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
98	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₅×#95	C₂²×C₃	1	2	yes	—
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	2	yes	—
104	#2374	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
105	C₂³×C₃×C₅	—	2	2	no	—
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	1	no	—
110	C₂³×C₃×C₅	—	2	1	no	—
111	C₂³×C₃×C₅	—	2	1	no	—
112	C₂³×C₃×C₅	—	2	1	no	—
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
115	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
116	C₃×C₅×D₄	—	4	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	1	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	—	4	4	no	—
134	C₂×C₃×C₄×C₅	—	4	4	no	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	#41	1	4	yes	—
139	C₂×C₃×C₄×C₅	#41	1	4	yes	—
140	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
143	C₃×#123	C₄×C₅	1	8	yes	complemented
144	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×C₃×C₂²⋊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	1	yes	characteristic
153	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
155	C₂×C₃×C₄²	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	2	yes	—
161	C₃×#95	C₂²×C₅	1	2	yes	—
162	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₅×D₄	—	4	1	no	—
165	C₂×C₅×D₄	—	4	1	no	—
166	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	4	1	no	—
169	C₂²×C₄×C₅	—	4	1	no	—
170	C₂²×C₄×C₅	—	4	1	no	—
171	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
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	2	yes	—
175	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
179	C₅×C₄⋊C₄	—	2	4	no	—
180	C₅×C₄⋊C₄	—	4	1	no	—
181	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	2	4	no	—
184	C₅×C₂²⋊C₄	—	2	4	no	—
185	C₅×C₂²⋊C₄	—	4	1	no	—
186	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
187	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
188	C₄²×C₅	—	2	4	no	—
189	C₄²×C₅	—	4	1	no	—
190	C₄²×C₅	—	4	2	no	—
191	C₄²×C₅	—	4	2	no	—
192	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic
193	#390	C₂×C₃×C₅	1	1	yes	characteristic
194	#388	C₂×C₃×C₅	1	2	yes	complemented
195	#388	C₂×C₃×C₅	1	2	yes	complemented
196	#387	C₂×C₃×C₅	1	2	yes	complemented
197	#386	C₂×C₃×C₅	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
199	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
200	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
201	C₂²×C₃×C₅	—	2	4	no	—
202	C₂²×C₃×C₅	—	2	4	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	4	1	no	—
206	C₂²×C₃×C₅	—	4	1	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	—	4	2	no	—
209	C₂²×C₃×C₅	—	4	1	no	—
210	C₂²×C₃×C₅	—	4	1	no	—
211	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
212	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
213	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
214	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
216	C₃×C₄×C₅	—	2	4	no	—
217	C₃×C₄×C₅	—	2	4	no	—
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	—	2	4	no	—
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
224	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₃×D₄	—	4	1	no	—
226	C₂×C₃×D₄	—	4	1	no	—
227	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
228	C₂²×C₃×C₄	—	2	4	no	—
229	C₂²×C₃×C₄	—	4	1	no	—
230	C₂²×C₃×C₄	—	4	1	no	—
231	C₂²×C₃×C₄	—	4	1	no	—
232	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
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	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	2	yes	—
239	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
240	C₃×C₄⋊C₄	—	2	4	no	—
241	C₃×C₄⋊C₄	—	4	1	no	—
242	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
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	—	4	1	no	—
247	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
248	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
249	C₃×C₄²	—	2	4	no	—
250	C₃×C₄²	—	4	1	no	—
251	C₃×C₄²	—	4	2	no	—
252	C₃×C₄²	—	4	2	no	—
253	C₂³×C₅	—	2	2	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	2	1	no	—
259	C₂³×C₅	—	2	1	no	—
260	C₂³×C₅	—	2	1	no	—
261	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
263	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
264	C₅×D₄	—	4	4	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	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	4	4	no	—
282	C₂×C₄×C₅	—	4	4	no	—
283	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
284	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
285	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
286	C₂×C₄×C₅	C₃×#41	1	4	yes	—
287	C₂×C₄×C₅	C₃×#41	1	4	yes	—
288	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
290	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
291	#123	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	1	yes	characteristic
294	C₂×C₄⋊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	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
301	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
302	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
303	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
304	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
305	#95	C₂²×C₃×C₅	1	2	yes	—
306	#95	C₂²×C₃×C₅	1	2	yes	—
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	C₂×C₃×C₅	—	4	2	no	—
311	C₂×C₃×C₅	—	4	2	no	—
312	C₂×C₃×C₅	C₄×#41	1	2	yes	—
313	C₂×C₃×C₅	#518	1	1	yes	characteristic
314	C₂×C₃×C₅	#551	1	1	yes	characteristic
315	C₂×C₃×C₅	#553	1	2	yes	—
316	C₂×C₃×C₅	#559	1	1	yes	characteristic
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	—	2	2	no	—
319	C₂³×C₃	—	2	2	no	—
320	C₂³×C₃	—	2	2	no	—
321	C₂³×C₃	—	2	1	no	—
322	C₂³×C₃	—	2	1	no	—
323	C₂³×C₃	—	2	1	no	—
324	C₂³×C₃	—	2	1	no	—
325	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
326	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
327	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
328	C₃×D₄	—	4	4	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	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	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	4	no	—
346	C₂×C₃×C₄	—	4	4	no	—
347	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
348	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
349	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
350	C₂×C₃×C₄	C₅×#41	1	4	yes	—
351	C₂×C₃×C₄	C₅×#41	1	4	yes	—
352	C₂²×C₅	—	2	4	no	—
353	C₂²×C₅	—	2	4	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	2	no	—
356	C₂²×C₅	—	4	1	no	—
357	C₂²×C₅	—	4	1	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
363	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
364	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
365	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
367	C₄×C₅	—	2	4	no	—
368	C₄×C₅	—	2	4	no	—
369	C₄×C₅	—	2	2	no	—
370	C₄×C₅	—	2	4	no	—
371	C₄×C₅	—	2	4	no	—
372	C₄×C₅	—	4	2	no	—
373	C₄×C₅	—	4	2	no	—
374	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
375	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
384	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
385	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
386	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
387	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
388	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
389	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
390	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
399	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
400	C₄²	—	2	4	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	4	2	no	—
403	C₄²	—	4	2	no	—
404	C₃×C₅	#2374	1	1	yes	characteristic, direct product factor, Hall
405	C₂²×C₃	—	2	4	no	—
406	C₂²×C₃	—	2	4	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	—	4	1	no	—
411	C₂²×C₃	—	4	2	no	—
412	C₂²×C₃	—	4	2	no	—
413	C₂²×C₃	—	4	1	no	—
414	C₂²×C₃	—	4	1	no	—
415	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
416	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
417	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
418	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
420	C₃×C₄	—	2	4	no	—
421	C₃×C₄	—	2	4	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	2	4	no	—
424	C₃×C₄	—	2	4	no	—
425	C₃×C₄	—	4	2	no	—
426	C₃×C₄	—	4	2	no	—
427	C₂×C₅	—	4	2	no	—
428	C₂×C₅	—	4	2	no	—
429	C₂×C₅	C₃×C₄×#41	1	2	yes	—
430	C₂×C₅	C₃×#518	1	1	yes	characteristic
431	C₂×C₅	C₃×#551	1	1	yes	characteristic
432	C₂×C₅	C₃×#553	1	2	yes	—
433	C₂×C₅	C₃×#559	1	1	yes	characteristic
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
443	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
444	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
445	D₄	—	4	4	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	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
465	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
466	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
467	C₂×C₄	C₃×C₅×#41	1	4	yes	—
468	C₂×C₄	C₃×C₅×#41	1	4	yes	—
469	C₂×C₃	—	4	2	no	—
470	C₂×C₃	—	4	2	no	—
471	C₂×C₃	C₄×C₅×#41	1	2	yes	—
472	C₂×C₃	C₅×#518	1	1	yes	characteristic
473	C₂×C₃	C₅×#551	1	1	yes	characteristic
474	C₂×C₃	C₅×#553	1	2	yes	—
475	C₂×C₃	C₅×#559	1	1	yes	characteristic
476	C₅	C₃×#2374	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
488	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
489	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
490	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
492	C₄	—	2	4	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	4	no	—
496	C₄	—	2	4	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₃	C₅×#2374	1	1	yes	characteristic, direct product factor, Sylow
500	C₂	—	4	2	no	—
501	C₂	—	4	2	no	—
502	C₂	C₃×C₄×C₅×#41	1	2	yes	—
503	C₂	C₃×C₅×#518	1	1	yes	characteristic
504	C₂	C₃×C₅×#551	1	1	yes	characteristic
505	C₂	C₃×C₅×#553	1	2	yes	—
506	C₂	C₃×C₅×#559	1	1	yes	characteristic

	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
3. C₃×C₅×#388	C₂	semidirect
4. C₃×C₅×#388	C₂	semidirect
5. C₃×C₅×#387	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
9. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
10. C₅×#2374	C₃	direct (N × H)
14. C₃×C₅×#123	C₄	semidirect
33. C₃×#2374	C₅	direct (N × H)
36. C₅×#388	C₂×C₃	semidirect
37. C₅×#388	C₂×C₃	semidirect
38. C₅×#387	C₂×C₃	semidirect
40. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
41. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
42. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
52. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
62. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
68. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
75. C₃×#388	C₂×C₅	semidirect
76. C₃×#388	C₂×C₅	semidirect
77. C₃×#387	C₂×C₅	semidirect
79. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
80. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
81. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
85. C₅×#123	C₃×C₄	semidirect
104. #2374	C₃×C₅	direct (N × H)
143. C₃×#123	C₄×C₅	semidirect
171. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
181. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
187. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
194. #388	C₂×C₃×C₅	semidirect
195. #388	C₂×C₃×C₅	semidirect
196. #387	C₂×C₃×C₅	semidirect
198. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
199. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
200. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
232. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
242. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
248. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
291. #123	C₃×C₄×C₅	semidirect
383. C₂²×C₄	C₂×C₃×C₄×C₅	semidirect
393. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
399. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
404. C₃×C₅	#2374	direct (N × H)
476. C₅	C₃×#2374	direct (N × H)
499. C₃	C₅×#2374	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
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2374	3
C₃×#2374	5

Subgroups — C3×C5×#2374 #14275408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2374 #14275408