Subgroups — C₃×C₅×#2668 #14275702

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 632 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	2	yes	maximal, complemented
2	C₂×C₃×C₅×#120	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2668	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
17	C₃×C₅×#121	—	2	8	no	—
18	C₃×C₅×#120	—	2	8	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₅×#95	C₂²	1	2	yes	complemented
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#95	C₂²	1	2	yes	complemented
33	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
34	C₃×#2668	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
36	C₂×C₅×#120	C₂×C₃	1	2	yes	complemented
37	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#397	C₂×C₃	1	2	yes	complemented
39	C₅×#394	C₂×C₃	1	2	yes	complemented
40	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#386	C₂×C₃	1	2	yes	complemented
42	C₅×#386	C₂×C₃	1	2	yes	complemented
43	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁴×C₃×C₅	—	2	4	no	—
45	C₂⁴×C₃×C₅	—	2	2	no	—
46	C₂⁴×C₃×C₅	—	4	1	no	—
47	C₂⁴×C₃×C₅	—	4	2	no	—
48	C₂⁴×C₃×C₅	—	4	1	no	—
49	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
50	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
51	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×D₄	—	2	4	no	—
53	C₂×C₃×C₅×D₄	—	2	4	no	—
54	C₂×C₃×C₅×D₄	—	2	4	no	—
55	C₂×C₃×C₅×D₄	—	2	4	no	—
56	C₂×C₃×C₅×D₄	—	2	4	no	—
57	C₂×C₃×C₅×D₄	—	4	2	no	—
58	C₂×C₃×C₅×D₄	—	4	2	no	—
59	C₂×C₃×C₅×D₄	—	4	2	no	—
60	C₂×C₃×C₅×D₄	—	4	2	no	—
61	C₂×C₃×C₅×D₄	—	4	1	no	—
62	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
63	C₂²×C₃×C₄×C₅	—	2	4	no	—
64	C₂²×C₃×C₄×C₅	—	4	2	no	—
65	C₂²×C₃×C₄×C₅	—	4	2	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	—	2	4	no	—
73	C₃×C₅×C₄⋊C₄	—	4	1	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
79	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
80	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
81	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
82	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
83	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
84	C₂×C₃×#120	C₂×C₅	1	2	yes	complemented
85	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#397	C₂×C₅	1	2	yes	complemented
87	C₃×#394	C₂×C₅	1	2	yes	complemented
88	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#386	C₂×C₅	1	2	yes	complemented
90	C₃×#386	C₂×C₅	1	2	yes	complemented
91	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
94	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
95	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
96	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	complemented
98	C₅×#121	—	2	8	no	—
99	C₅×#120	—	2	8	no	—
100	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
101	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
110	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
111	C₅×#95	C₂²×C₃	1	2	yes	complemented
112	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₅×#95	C₂²×C₃	1	2	yes	complemented
114	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
115	#2668	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	—	2	1	no	—
123	C₂³×C₃×C₅	—	2	1	no	—
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂³×C₃×C₅	—	2	2	no	—
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₂³×C₃×C₅	—	2	2	no	—
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	4	4	no	—
133	C₂³×C₃×C₅	—	4	8	no	—
134	C₂³×C₃×C₅	—	4	8	no	—
135	C₂³×C₃×C₅	—	4	4	no	—
136	C₂³×C₃×C₅	—	4	4	no	—
137	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
138	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
139	C₂³×C₃×C₅	#41	1	2	yes	—
140	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×C₅×D₄	—	4	8	no	—
142	C₃×C₅×D₄	—	4	4	no	—
143	C₃×C₅×D₄	—	4	8	no	—
144	C₃×C₅×D₄	—	4	8	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	4	8	no	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
162	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
164	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
165	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
166	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
167	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	complemented
168	C₃×#121	—	2	8	no	—
169	C₃×#120	—	2	8	no	—
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
171	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
180	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
181	C₃×#95	C₂²×C₅	1	2	yes	complemented
182	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₃×#95	C₂²×C₅	1	2	yes	complemented
184	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₂⁴×C₅	—	2	4	no	—
186	C₂⁴×C₅	—	2	2	no	—
187	C₂⁴×C₅	—	4	1	no	—
188	C₂⁴×C₅	—	4	2	no	—
189	C₂⁴×C₅	—	4	1	no	—
190	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
191	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
192	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×D₄	—	2	4	no	—
194	C₂×C₅×D₄	—	2	4	no	—
195	C₂×C₅×D₄	—	2	4	no	—
196	C₂×C₅×D₄	—	2	4	no	—
197	C₂×C₅×D₄	—	2	4	no	—
198	C₂×C₅×D₄	—	4	2	no	—
199	C₂×C₅×D₄	—	4	2	no	—
200	C₂×C₅×D₄	—	4	2	no	—
201	C₂×C₅×D₄	—	4	2	no	—
202	C₂×C₅×D₄	—	4	1	no	—
203	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
204	C₂²×C₄×C₅	—	2	4	no	—
205	C₂²×C₄×C₅	—	4	2	no	—
206	C₂²×C₄×C₅	—	4	2	no	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
211	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
212	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	4	no	—
214	C₅×C₄⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	—	2	4	no	—
216	C₅×C₂²⋊C₄	—	2	4	no	—
217	C₅×C₂²⋊C₄	—	2	4	no	—
218	C₅×C₂²⋊C₄	—	2	4	no	—
219	C₅×C₂²⋊C₄	—	2	4	no	—
220	C₅×C₂²⋊C₄	—	4	2	no	—
221	C₅×C₂²⋊C₄	—	4	1	no	—
222	C₅×C₂²⋊C₄	—	4	1	no	—
223	C₅×C₂²⋊C₄	—	4	2	no	—
224	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
225	C₂×#120	C₂×C₃×C₅	1	2	yes	complemented
226	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
227	#397	C₂×C₃×C₅	1	2	yes	complemented
228	#394	C₂×C₃×C₅	1	2	yes	complemented
229	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	#386	C₂×C₃×C₅	1	2	yes	complemented
231	#386	C₂×C₃×C₅	1	2	yes	complemented
232	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	C₂²×C₃×C₅	—	2	4	no	—
234	C₂²×C₃×C₅	—	2	4	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	2	4	no	—
237	C₂²×C₃×C₅	—	2	4	no	—
238	C₂²×C₃×C₅	—	2	4	no	—
239	C₂²×C₃×C₅	—	2	4	no	—
240	C₂²×C₃×C₅	—	2	4	no	—
241	C₂²×C₃×C₅	—	4	16	no	—
242	C₂²×C₃×C₅	—	4	2	no	—
243	C₂²×C₃×C₅	—	4	2	no	—
244	C₂²×C₃×C₅	—	4	2	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	—	4	2	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	—	4	2	no	—
249	C₂²×C₃×C₅	—	4	2	no	—
250	C₂²×C₃×C₅	—	4	2	no	—
251	C₂²×C₃×C₅	—	4	2	no	—
252	C₂²×C₃×C₅	—	4	1	no	—
253	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
254	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
255	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
257	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
258	C₃×C₄×C₅	—	2	4	no	—
259	C₃×C₄×C₅	—	4	2	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	—	4	1	no	—
262	C₃×C₄×C₅	—	4	2	no	—
263	C₃×C₄×C₅	—	4	1	no	—
264	C₂⁴×C₃	—	2	4	no	—
265	C₂⁴×C₃	—	2	2	no	—
266	C₂⁴×C₃	—	4	1	no	—
267	C₂⁴×C₃	—	4	2	no	—
268	C₂⁴×C₃	—	4	1	no	—
269	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
270	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
271	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃×D₄	—	2	4	no	—
273	C₂×C₃×D₄	—	2	4	no	—
274	C₂×C₃×D₄	—	2	4	no	—
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	2	4	no	—
277	C₂×C₃×D₄	—	4	2	no	—
278	C₂×C₃×D₄	—	4	2	no	—
279	C₂×C₃×D₄	—	4	2	no	—
280	C₂×C₃×D₄	—	4	2	no	—
281	C₂×C₃×D₄	—	4	1	no	—
282	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
283	C₂²×C₃×C₄	—	2	4	no	—
284	C₂²×C₃×C₄	—	4	2	no	—
285	C₂²×C₃×C₄	—	4	2	no	—
286	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
287	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
288	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
289	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
291	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
292	C₃×C₄⋊C₄	—	2	4	no	—
293	C₃×C₄⋊C₄	—	4	1	no	—
294	C₃×C₂²⋊C₄	—	2	4	no	—
295	C₃×C₂²⋊C₄	—	2	4	no	—
296	C₃×C₂²⋊C₄	—	2	4	no	—
297	C₃×C₂²⋊C₄	—	2	4	no	—
298	C₃×C₂²⋊C₄	—	2	4	no	—
299	C₃×C₂²⋊C₄	—	4	2	no	—
300	C₃×C₂²⋊C₄	—	4	1	no	—
301	C₃×C₂²⋊C₄	—	4	1	no	—
302	C₃×C₂²⋊C₄	—	4	2	no	—
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	—	2	2	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	2	2	no	—
312	C₂³×C₅	—	2	2	no	—
313	C₂³×C₅	—	2	2	no	—
314	C₂³×C₅	—	2	2	no	—
315	C₂³×C₅	—	2	2	no	—
316	C₂³×C₅	—	2	2	no	—
317	C₂³×C₅	—	2	2	no	—
318	C₂³×C₅	—	2	2	no	—
319	C₂³×C₅	—	4	4	no	—
320	C₂³×C₅	—	4	8	no	—
321	C₂³×C₅	—	4	8	no	—
322	C₂³×C₅	—	4	4	no	—
323	C₂³×C₅	—	4	4	no	—
324	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
325	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
326	C₂³×C₅	C₃×#41	1	2	yes	—
327	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
328	C₅×D₄	—	4	8	no	—
329	C₅×D₄	—	4	4	no	—
330	C₅×D₄	—	4	8	no	—
331	C₅×D₄	—	4	8	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	4	8	no	—
348	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
349	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
350	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
351	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
352	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
353	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
354	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	complemented
355	#121	—	2	8	no	—
356	#120	—	2	8	no	—
357	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
358	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
359	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
360	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
361	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
363	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
367	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
368	#95	C₂²×C₃×C₅	1	2	yes	complemented
369	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
370	#95	C₂²×C₃×C₅	1	2	yes	complemented
371	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
372	C₂×C₃×C₅	—	4	4	no	—
373	C₂×C₃×C₅	—	4	4	no	—
374	C₂×C₃×C₅	—	4	2	no	—
375	C₂×C₃×C₅	#534	1	2	yes	—
376	C₂×C₃×C₅	#538	1	1	yes	characteristic
377	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
378	C₂×C₃×C₅	#546	1	2	yes	—
379	C₂×C₃×C₅	#560	1	1	yes	characteristic
380	C₂³×C₃	—	2	2	no	—
381	C₂³×C₃	—	2	2	no	—
382	C₂³×C₃	—	2	2	no	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	2	2	no	—
385	C₂³×C₃	—	2	2	no	—
386	C₂³×C₃	—	2	1	no	—
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	—	2	2	no	—
389	C₂³×C₃	—	2	2	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	2	2	no	—
392	C₂³×C₃	—	2	2	no	—
393	C₂³×C₃	—	2	2	no	—
394	C₂³×C₃	—	2	2	no	—
395	C₂³×C₃	—	2	2	no	—
396	C₂³×C₃	—	4	4	no	—
397	C₂³×C₃	—	4	8	no	—
398	C₂³×C₃	—	4	8	no	—
399	C₂³×C₃	—	4	4	no	—
400	C₂³×C₃	—	4	4	no	—
401	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
402	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
403	C₂³×C₃	C₅×#41	1	2	yes	—
404	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
405	C₃×D₄	—	4	8	no	—
406	C₃×D₄	—	4	4	no	—
407	C₃×D₄	—	4	8	no	—
408	C₃×D₄	—	4	8	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	2	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	4	8	no	—
425	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
426	C₂²×C₅	—	2	4	no	—
427	C₂²×C₅	—	2	4	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	4	no	—
430	C₂²×C₅	—	2	4	no	—
431	C₂²×C₅	—	2	4	no	—
432	C₂²×C₅	—	2	4	no	—
433	C₂²×C₅	—	2	4	no	—
434	C₂²×C₅	—	4	16	no	—
435	C₂²×C₅	—	4	2	no	—
436	C₂²×C₅	—	4	2	no	—
437	C₂²×C₅	—	4	1	no	—
438	C₂²×C₅	—	4	2	no	—
439	C₂²×C₅	—	4	2	no	—
440	C₂²×C₅	—	4	2	no	—
441	C₂²×C₅	—	4	2	no	—
442	C₂²×C₅	—	4	2	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
447	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
448	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
451	C₄×C₅	—	2	4	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	2	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	2	no	—
459	C₂⁴	—	4	1	no	—
460	C₂⁴	—	4	2	no	—
461	C₂⁴	—	4	1	no	—
462	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
463	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
464	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	C₃×C₅×D₄	1	8	yes	complemented
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
480	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
481	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
482	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
483	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
484	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₃×C₅	#2668	1	1	yes	characteristic, direct product factor, Hall
497	C₂²×C₃	—	2	4	no	—
498	C₂²×C₃	—	2	4	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	4	no	—
501	C₂²×C₃	—	2	4	no	—
502	C₂²×C₃	—	2	4	no	—
503	C₂²×C₃	—	2	4	no	—
504	C₂²×C₃	—	2	4	no	—
505	C₂²×C₃	—	4	16	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	4	2	no	—
508	C₂²×C₃	—	4	2	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	—	4	2	no	—
511	C₂²×C₃	—	4	1	no	—
512	C₂²×C₃	—	4	2	no	—
513	C₂²×C₃	—	4	2	no	—
514	C₂²×C₃	—	4	2	no	—
515	C₂²×C₃	—	4	2	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
518	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
519	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
521	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
522	C₃×C₄	—	2	4	no	—
523	C₃×C₄	—	4	2	no	—
524	C₃×C₄	—	4	2	no	—
525	C₃×C₄	—	4	1	no	—
526	C₃×C₄	—	4	2	no	—
527	C₃×C₄	—	4	1	no	—
528	C₂×C₅	—	4	4	no	—
529	C₂×C₅	—	4	2	no	—
530	C₂×C₅	—	4	4	no	—
531	C₂×C₅	C₃×#534	1	2	yes	—
532	C₂×C₅	C₃×#538	1	1	yes	characteristic
533	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
534	C₂×C₅	C₃×#546	1	2	yes	—
535	C₂×C₅	C₃×#560	1	1	yes	characteristic
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	4	4	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	4	8	no	—
555	C₂³	—	4	4	no	—
556	C₂³	—	4	4	no	—
557	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
558	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
559	C₂³	C₃×C₅×#41	1	2	yes	—
560	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
561	D₄	—	4	8	no	—
562	D₄	—	4	4	no	—
563	D₄	—	4	8	no	—
564	D₄	—	4	8	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
582	C₂×C₃	—	4	4	no	—
583	C₂×C₃	—	4	2	no	—
584	C₂×C₃	—	4	4	no	—
585	C₂×C₃	C₅×#534	1	2	yes	—
586	C₂×C₃	C₅×#538	1	1	yes	characteristic
587	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
588	C₂×C₃	C₅×#546	1	2	yes	—
589	C₂×C₃	C₅×#560	1	1	yes	characteristic
590	C₅	C₃×#2668	1	1	yes	characteristic, direct product factor, Sylow
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	4	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	4	16	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
612	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
613	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
615	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
616	C₄	—	2	4	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₃	C₅×#2668	1	1	yes	characteristic, direct product factor, Sylow
623	C₂	—	4	4	no	—
624	C₂	—	4	2	no	—
625	C₂	—	4	4	no	—
626	C₂	C₃×C₅×#534	1	2	yes	—
627	C₂	C₃×C₅×#538	1	1	yes	characteristic
628	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
629	C₂	C₃×C₅×#546	1	2	yes	—
630	C₂	C₃×C₅×#560	1	1	yes	characteristic

	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. C₂×C₃×C₅×#121	C₂	semidirect
2. C₂×C₃×C₅×#120	C₂	semidirect
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₅×#386	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#379	C₂	semidirect
10. C₅×#2668	C₃	direct (N × H)
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂³×C₃×C₄×C₅	C₂²	semidirect
19. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
20. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
30. C₃×C₅×#95	C₂²	semidirect
31. C₃×C₅×#95	C₂²	semidirect
32. C₃×C₅×#95	C₂²	semidirect
33. C₃×C₅×#95	C₂²	semidirect
34. C₃×#2668	C₅	direct (N × H)
35. C₂×C₅×#121	C₂×C₃	semidirect
36. C₂×C₅×#120	C₂×C₃	semidirect
37. C₅×#399	C₂×C₃	semidirect
38. C₅×#397	C₂×C₃	semidirect
39. C₅×#394	C₂×C₃	semidirect
40. C₅×#392	C₂×C₃	semidirect
41. C₅×#386	C₂×C₃	semidirect
42. C₅×#386	C₂×C₃	semidirect
43. C₅×#379	C₂×C₃	semidirect
62. C₂×C₃×C₅×D₄	D₄	semidirect
83. C₂×C₃×#121	C₂×C₅	semidirect
84. C₂×C₃×#120	C₂×C₅	semidirect
85. C₃×#399	C₂×C₅	semidirect
86. C₃×#397	C₂×C₅	semidirect
87. C₃×#394	C₂×C₅	semidirect
88. C₃×#392	C₂×C₅	semidirect
89. C₃×#386	C₂×C₅	semidirect
90. C₃×#386	C₂×C₅	semidirect
91. C₃×#379	C₂×C₅	semidirect
96. C₂²×C₅×D₄	C₂²×C₃	semidirect
97. C₂³×C₄×C₅	C₂²×C₃	semidirect
100. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
101. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
109. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
110. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
111. C₅×#95	C₂²×C₃	semidirect
112. C₅×#95	C₂²×C₃	semidirect
113. C₅×#95	C₂²×C₃	semidirect
114. C₅×#95	C₂²×C₃	semidirect
115. #2668	C₃×C₅	direct (N × H)
166. C₂²×C₃×D₄	C₂²×C₅	semidirect
167. C₂³×C₃×C₄	C₂²×C₅	semidirect
170. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
171. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
179. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
180. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
181. C₃×#95	C₂²×C₅	semidirect
182. C₃×#95	C₂²×C₅	semidirect
183. C₃×#95	C₂²×C₅	semidirect
184. C₃×#95	C₂²×C₅	semidirect
203. C₂×C₅×D₄	C₃×D₄	semidirect
224. C₂×#121	C₂×C₃×C₅	semidirect
225. C₂×#120	C₂×C₃×C₅	semidirect
226. #399	C₂×C₃×C₅	semidirect
227. #397	C₂×C₃×C₅	semidirect
228. #394	C₂×C₃×C₅	semidirect
229. #392	C₂×C₃×C₅	semidirect
230. #386	C₂×C₃×C₅	semidirect
231. #386	C₂×C₃×C₅	semidirect
232. #379	C₂×C₃×C₅	semidirect
282. C₂×C₃×D₄	C₅×D₄	semidirect
353. C₂²×D₄	C₂²×C₃×C₅	semidirect
354. C₂³×C₄	C₂²×C₃×C₅	semidirect
357. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
358. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
366. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
367. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
368. #95	C₂²×C₃×C₅	semidirect
369. #95	C₂²×C₃×C₅	semidirect
370. #95	C₂²×C₃×C₅	semidirect
371. #95	C₂²×C₃×C₅	semidirect
475. C₂×D₄	C₃×C₅×D₄	semidirect
496. C₃×C₅	#2668	direct (N × H)
590. C₅	C₃×#2668	direct (N × H)
622. C₃	C₅×#2668	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×C₅×#120	2
C₃×C₅×#399	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#386	2
C₃×C₅×#379	2
C₅×#2668	3
C₃×#2668	5

Subgroups — C3×C5×#2668 #14275702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2668 #14275702