Subgroups — C₃×C₅×#2408 #14275442

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#120	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#379	C₂	1	2	yes	maximal, complemented
10	C₅×#2408	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	—	2	8	no	—
13	C₂²×C₃×C₅×D₄	—	2	4	no	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#121	—	2	8	no	—
21	C₃×C₅×#120	—	2	8	no	—
22	C₃×C₄×C₅×D₄	—	2	4	no	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
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, complemented
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#95	C₂²	1	2	yes	complemented
33	C₃×#2408	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
36	C₂×C₅×#120	C₂×C₃	1	2	yes	complemented
37	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#394	C₂×C₃	1	2	yes	complemented
39	C₅×#392	C₂×C₃	1	2	yes	complemented
40	C₅×#390	C₂×C₃	1	2	yes	complemented
41	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#379	C₂×C₃	1	2	yes	complemented
43	C₂⁴×C₃×C₅	—	2	8	no	—
44	C₂⁴×C₃×C₅	—	2	4	no	—
45	C₂⁴×C₃×C₅	—	2	4	no	—
46	C₂⁴×C₃×C₅	—	2	4	no	—
47	C₂⁴×C₃×C₅	—	4	4	no	—
48	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
49	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
50	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₅×D₄	—	2	32	no	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	—	2	8	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	—	2	8	no	—
56	C₂×C₃×C₅×D₄	—	2	8	no	—
57	C₂×C₃×C₅×D₄	—	2	4	no	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	4	4	no	—
61	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
62	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
63	C₂²×C₃×C₄×C₅	—	2	4	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	4	no	—
66	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
80	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
81	C₃×C₄²×C₅	—	2	2	no	—
82	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
84	C₂×C₃×#120	C₂×C₅	1	2	yes	complemented
85	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#394	C₂×C₅	1	2	yes	complemented
87	C₃×#392	C₂×C₅	1	2	yes	complemented
88	C₃×#390	C₂×C₅	1	2	yes	complemented
89	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#379	C₂×C₅	1	2	yes	complemented
91	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
92	C₂²×C₅×D₄	—	2	8	no	—
93	C₂²×C₅×D₄	—	2	4	no	—
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
97	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
98	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₅×#121	—	2	8	no	—
101	C₅×#120	—	2	8	no	—
102	C₄×C₅×D₄	—	2	4	no	—
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
104	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
108	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
109	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
111	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₅×#95	C₂²×C₃	1	2	yes	complemented
113	#2408	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	16	no	—
117	C₂³×C₃×C₅	—	2	1	no	—
118	C₂³×C₃×C₅	—	2	4	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	4	no	—
121	C₂³×C₃×C₅	—	2	4	no	—
122	C₂³×C₃×C₅	—	2	1	no	—
123	C₂³×C₃×C₅	—	2	4	no	—
124	C₂³×C₃×C₅	—	2	4	no	—
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂³×C₃×C₅	—	2	4	no	—
127	C₂³×C₃×C₅	—	4	16	no	—
128	C₂³×C₃×C₅	—	4	16	no	—
129	C₂³×C₃×C₅	—	4	8	no	—
130	C₂³×C₃×C₅	—	4	8	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
134	C₂³×C₃×C₅	C₂×D₄	1	2	yes	complemented
135	C₂³×C₃×C₅	#41	1	2	yes	—
136	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
137	C₃×C₅×D₄	—	2	16	no	—
138	C₃×C₅×D₄	—	2	8	no	—
139	C₃×C₅×D₄	—	2	16	no	—
140	C₃×C₅×D₄	—	4	16	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	8	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	4	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	4	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	4	no	—
152	C₂×C₃×C₄×C₅	—	4	4	no	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	complemented
157	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
158	C₂²×C₃×D₄	—	2	8	no	—
159	C₂²×C₃×D₄	—	2	4	no	—
160	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
161	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
162	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
164	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
166	C₃×#121	—	2	8	no	—
167	C₃×#120	—	2	8	no	—
168	C₃×C₄×D₄	—	2	4	no	—
169	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
174	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
175	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
177	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₃×#95	C₂²×C₅	1	2	yes	complemented
179	C₂⁴×C₅	—	2	8	no	—
180	C₂⁴×C₅	—	2	4	no	—
181	C₂⁴×C₅	—	2	4	no	—
182	C₂⁴×C₅	—	2	4	no	—
183	C₂⁴×C₅	—	4	4	no	—
184	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
185	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₅×D₄	—	2	32	no	—
188	C₂×C₅×D₄	—	2	2	no	—
189	C₂×C₅×D₄	—	2	8	no	—
190	C₂×C₅×D₄	—	2	2	no	—
191	C₂×C₅×D₄	—	2	8	no	—
192	C₂×C₅×D₄	—	2	8	no	—
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	—	4	4	no	—
197	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
198	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
199	C₂²×C₄×C₅	—	2	4	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	4	no	—
202	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
203	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₅×C₄⋊C₄	—	2	2	no	—
210	C₅×C₄⋊C₄	—	2	4	no	—
211	C₅×C₂²⋊C₄	—	2	2	no	—
212	C₅×C₂²⋊C₄	—	2	4	no	—
213	C₅×C₂²⋊C₄	—	2	8	no	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	2	8	no	—
216	C₅×C₂²⋊C₄	—	4	4	no	—
217	C₄²×C₅	—	2	2	no	—
218	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
219	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
220	C₂×#120	C₂×C₃×C₅	1	2	yes	complemented
221	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
222	#394	C₂×C₃×C₅	1	2	yes	complemented
223	#392	C₂×C₃×C₅	1	2	yes	complemented
224	#390	C₂×C₃×C₅	1	2	yes	complemented
225	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#379	C₂×C₃×C₅	1	2	yes	complemented
227	C₂²×C₃×C₅	—	2	2	no	—
228	C₂²×C₃×C₅	—	2	2	no	—
229	C₂²×C₃×C₅	—	2	4	no	—
230	C₂²×C₃×C₅	—	2	4	no	—
231	C₂²×C₃×C₅	—	2	8	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	4	no	—
234	C₂²×C₃×C₅	—	2	8	no	—
235	C₂²×C₃×C₅	—	2	8	no	—
236	C₂²×C₃×C₅	—	4	32	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	—	4	4	no	—
239	C₂²×C₃×C₅	—	4	1	no	—
240	C₂²×C₃×C₅	—	4	4	no	—
241	C₂²×C₃×C₅	—	4	4	no	—
242	C₂²×C₃×C₅	—	4	2	no	—
243	C₂²×C₃×C₅	—	4	4	no	—
244	C₂²×C₃×C₅	#121	1	4	yes	complemented
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
247	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
249	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	—	4	4	no	—
255	C₃×C₄×C₅	#120	1	4	yes	complemented
256	C₂⁴×C₃	—	2	8	no	—
257	C₂⁴×C₃	—	2	4	no	—
258	C₂⁴×C₃	—	2	4	no	—
259	C₂⁴×C₃	—	2	4	no	—
260	C₂⁴×C₃	—	4	4	no	—
261	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
262	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
263	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₃×D₄	—	2	32	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	8	no	—
267	C₂×C₃×D₄	—	2	2	no	—
268	C₂×C₃×D₄	—	2	8	no	—
269	C₂×C₃×D₄	—	2	8	no	—
270	C₂×C₃×D₄	—	2	4	no	—
271	C₂×C₃×D₄	—	2	4	no	—
272	C₂×C₃×D₄	—	2	4	no	—
273	C₂×C₃×D₄	—	4	4	no	—
274	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
275	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
276	C₂²×C₃×C₄	—	2	4	no	—
277	C₂²×C₃×C₄	—	2	2	no	—
278	C₂²×C₃×C₄	—	2	4	no	—
279	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
280	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
286	C₃×C₄⋊C₄	—	2	2	no	—
287	C₃×C₄⋊C₄	—	2	4	no	—
288	C₃×C₂²⋊C₄	—	2	2	no	—
289	C₃×C₂²⋊C₄	—	2	4	no	—
290	C₃×C₂²⋊C₄	—	2	8	no	—
291	C₃×C₂²⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	—	2	8	no	—
293	C₃×C₂²⋊C₄	—	4	4	no	—
294	C₃×C₄²	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	16	no	—
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	4	no	—
300	C₂³×C₅	—	2	2	no	—
301	C₂³×C₅	—	2	4	no	—
302	C₂³×C₅	—	2	4	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	2	4	no	—
305	C₂³×C₅	—	2	4	no	—
306	C₂³×C₅	—	2	2	no	—
307	C₂³×C₅	—	2	4	no	—
308	C₂³×C₅	—	4	16	no	—
309	C₂³×C₅	—	4	16	no	—
310	C₂³×C₅	—	4	8	no	—
311	C₂³×C₅	—	4	8	no	—
312	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
313	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
314	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
315	C₂³×C₅	C₂×C₃×D₄	1	2	yes	complemented
316	C₂³×C₅	C₃×#41	1	2	yes	—
317	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
318	C₅×D₄	—	2	16	no	—
319	C₅×D₄	—	2	8	no	—
320	C₅×D₄	—	2	16	no	—
321	C₅×D₄	—	4	16	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	8	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	4	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	4	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	4	no	—
333	C₂×C₄×C₅	—	4	4	no	—
334	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
335	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
336	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
337	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	complemented
338	C₂⁵	C₂²×C₃×C₅	1	2	yes	—
339	C₂²×D₄	—	2	8	no	—
340	C₂²×D₄	—	2	4	no	—
341	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
342	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
344	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
345	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
347	#121	—	2	8	no	—
348	#120	—	2	8	no	—
349	C₄×D₄	—	2	4	no	—
350	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
351	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
352	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
355	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
356	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
357	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
358	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
359	#95	C₂²×C₃×C₅	1	2	yes	complemented
360	C₂×C₃×C₅	—	2	4	no	—
361	C₂×C₃×C₅	—	4	2	no	—
362	C₂×C₃×C₅	—	4	8	no	—
363	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
364	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
365	C₂×C₃×C₅	#535	1	1	yes	characteristic
366	C₂×C₃×C₅	D₄²	1	2	yes	—
367	C₂×C₃×C₅	#546	1	2	yes	—
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	2	2	no	—
370	C₂³×C₃	—	2	16	no	—
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	—	2	4	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	4	no	—
375	C₂³×C₃	—	2	4	no	—
376	C₂³×C₃	—	2	1	no	—
377	C₂³×C₃	—	2	4	no	—
378	C₂³×C₃	—	2	4	no	—
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	2	4	no	—
381	C₂³×C₃	—	4	16	no	—
382	C₂³×C₃	—	4	16	no	—
383	C₂³×C₃	—	4	8	no	—
384	C₂³×C₃	—	4	8	no	—
385	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
386	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
387	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
388	C₂³×C₃	C₂×C₅×D₄	1	2	yes	complemented
389	C₂³×C₃	C₅×#41	1	2	yes	—
390	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
391	C₃×D₄	—	2	16	no	—
392	C₃×D₄	—	2	8	no	—
393	C₃×D₄	—	2	16	no	—
394	C₃×D₄	—	4	16	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	8	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	4	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	4	no	—
406	C₂×C₃×C₄	—	4	4	no	—
407	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
408	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
409	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
410	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	complemented
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	4	no	—
414	C₂²×C₅	—	2	4	no	—
415	C₂²×C₅	—	2	8	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	4	no	—
418	C₂²×C₅	—	2	8	no	—
419	C₂²×C₅	—	2	8	no	—
420	C₂²×C₅	—	4	32	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	4	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	4	no	—
425	C₂²×C₅	—	4	4	no	—
426	C₂²×C₅	—	4	2	no	—
427	C₂²×C₅	—	4	4	no	—
428	C₂²×C₅	C₃×#121	1	4	yes	complemented
429	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
430	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
431	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
432	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
433	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
434	C₄×C₅	—	2	2	no	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	4	no	—
439	C₄×C₅	C₃×#120	1	4	yes	complemented
440	C₂⁴	—	2	8	no	—
441	C₂⁴	—	2	4	no	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	4	no	—
444	C₂⁴	—	4	4	no	—
445	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
446	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
447	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
448	C₂×D₄	—	2	32	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	8	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	C₃×C₅×D₄	1	8	yes	complemented
459	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
464	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
465	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
466	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
467	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
469	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	4	4	no	—
478	C₄²	—	2	2	no	—
479	C₃×C₅	#2408	1	1	yes	characteristic, direct product factor, Hall
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	4	no	—
483	C₂²×C₃	—	2	4	no	—
484	C₂²×C₃	—	2	8	no	—
485	C₂²×C₃	—	2	2	no	—
486	C₂²×C₃	—	2	4	no	—
487	C₂²×C₃	—	2	8	no	—
488	C₂²×C₃	—	2	8	no	—
489	C₂²×C₃	—	4	32	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	4	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	4	no	—
494	C₂²×C₃	—	4	4	no	—
495	C₂²×C₃	—	4	2	no	—
496	C₂²×C₃	—	4	4	no	—
497	C₂²×C₃	C₅×#121	1	4	yes	complemented
498	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
499	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
500	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
501	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
502	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
503	C₃×C₄	—	2	2	no	—
504	C₃×C₄	—	2	2	no	—
505	C₃×C₄	—	4	1	no	—
506	C₃×C₄	—	4	1	no	—
507	C₃×C₄	—	4	4	no	—
508	C₃×C₄	C₅×#120	1	4	yes	complemented
509	C₂×C₅	—	2	4	no	—
510	C₂×C₅	—	4	8	no	—
511	C₂×C₅	—	4	2	no	—
512	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
513	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
514	C₂×C₅	C₃×#535	1	1	yes	characteristic
515	C₂×C₅	C₃×D₄²	1	2	yes	—
516	C₂×C₅	C₃×#546	1	2	yes	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	16	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	4	16	no	—
531	C₂³	—	4	16	no	—
532	C₂³	—	4	8	no	—
533	C₂³	—	4	8	no	—
534	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
535	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
536	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
537	C₂³	C₂×C₃×C₅×D₄	1	2	yes	complemented
538	C₂³	C₃×C₅×#41	1	2	yes	—
539	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
540	D₄	—	2	16	no	—
541	D₄	—	2	8	no	—
542	D₄	—	2	16	no	—
543	D₄	—	4	16	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
557	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
558	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
559	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	complemented
560	C₂×C₃	—	2	4	no	—
561	C₂×C₃	—	4	8	no	—
562	C₂×C₃	—	4	2	no	—
563	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
564	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
565	C₂×C₃	C₅×#535	1	1	yes	characteristic
566	C₂×C₃	C₅×D₄²	1	2	yes	—
567	C₂×C₃	C₅×#546	1	2	yes	—
568	C₅	C₃×#2408	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	4	32	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	C₃×C₅×#121	1	4	yes	complemented
587	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
588	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
589	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
590	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
591	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	4	no	—
597	C₄	C₃×C₅×#120	1	4	yes	complemented
598	C₃	C₅×#2408	1	1	yes	characteristic, direct product factor, Sylow
599	C₂	—	2	4	no	—
600	C₂	—	4	8	no	—
601	C₂	—	4	2	no	—
602	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
603	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
604	C₂	C₃×C₅×#535	1	1	yes	characteristic
605	C₂	C₃×C₅×D₄²	1	2	yes	—
606	C₂	C₃×C₅×#546	1	2	yes	—

	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. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₅×#390	C₂	semidirect
8. C₃×C₅×#380	C₂	semidirect
9. C₃×C₅×#379	C₂	semidirect
10. C₅×#2408	C₃	direct (N × H)
17. C₂²×C₃×C₅×D₄	C₂²	semidirect
19. C₂³×C₃×C₄×C₅	C₂²	semidirect
23. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
27. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
30. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
31. C₂×C₃×C₄²×C₅	C₂²	semidirect
32. C₃×C₅×#95	C₂²	semidirect
33. C₃×#2408	C₅	direct (N × H)
34. C₂³×C₅×D₄	C₂×C₃	semidirect
35. C₂×C₅×#121	C₂×C₃	semidirect
36. C₂×C₅×#120	C₂×C₃	semidirect
37. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
38. C₅×#394	C₂×C₃	semidirect
39. C₅×#392	C₂×C₃	semidirect
40. C₅×#390	C₂×C₃	semidirect
41. C₅×#380	C₂×C₃	semidirect
42. C₅×#379	C₂×C₃	semidirect
61. C₂×C₃×C₅×D₄	D₄	semidirect
62. C₂×C₃×C₅×D₄	D₄	semidirect
66. C₂²×C₃×C₄×C₅	D₄	semidirect
82. C₂³×C₃×D₄	C₂×C₅	semidirect
83. C₂×C₃×#121	C₂×C₅	semidirect
84. C₂×C₃×#120	C₂×C₅	semidirect
85. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
86. C₃×#394	C₂×C₅	semidirect
87. C₃×#392	C₂×C₅	semidirect
88. C₃×#390	C₂×C₅	semidirect
89. C₃×#380	C₂×C₅	semidirect
90. C₃×#379	C₂×C₅	semidirect
97. C₂²×C₅×D₄	C₂²×C₃	semidirect
99. C₂³×C₄×C₅	C₂²×C₃	semidirect
103. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
104. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
107. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
108. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
109. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
110. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
111. C₂×C₄²×C₅	C₂²×C₃	semidirect
112. C₅×#95	C₂²×C₃	semidirect
113. #2408	C₃×C₅	direct (N × H)
134. C₂³×C₃×C₅	C₂×D₄	semidirect
156. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
163. C₂²×C₃×D₄	C₂²×C₅	semidirect
165. C₂³×C₃×C₄	C₂²×C₅	semidirect
169. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
170. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
173. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
174. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
175. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
176. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
177. C₂×C₃×C₄²	C₂²×C₅	semidirect
178. C₃×#95	C₂²×C₅	semidirect
197. C₂×C₅×D₄	C₃×D₄	semidirect
198. C₂×C₅×D₄	C₃×D₄	semidirect
202. C₂²×C₄×C₅	C₃×D₄	semidirect
218. C₂³×D₄	C₂×C₃×C₅	semidirect
219. C₂×#121	C₂×C₃×C₅	semidirect
220. C₂×#120	C₂×C₃×C₅	semidirect
221. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
222. #394	C₂×C₃×C₅	semidirect
223. #392	C₂×C₃×C₅	semidirect
224. #390	C₂×C₃×C₅	semidirect
225. #380	C₂×C₃×C₅	semidirect
226. #379	C₂×C₃×C₅	semidirect
244. C₂²×C₃×C₅	#121	semidirect
255. C₃×C₄×C₅	#120	semidirect
274. C₂×C₃×D₄	C₅×D₄	semidirect
275. C₂×C₃×D₄	C₅×D₄	semidirect
279. C₂²×C₃×C₄	C₅×D₄	semidirect
315. C₂³×C₅	C₂×C₃×D₄	semidirect
337. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
344. C₂²×D₄	C₂²×C₃×C₅	semidirect
346. C₂³×C₄	C₂²×C₃×C₅	semidirect
350. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
351. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
354. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
355. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
356. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
357. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
358. C₂×C₄²	C₂²×C₃×C₅	semidirect
359. #95	C₂²×C₃×C₅	semidirect
388. C₂³×C₃	C₂×C₅×D₄	semidirect
410. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
428. C₂²×C₅	C₃×#121	semidirect
439. C₄×C₅	C₃×#120	semidirect
458. C₂×D₄	C₃×C₅×D₄	semidirect
459. C₂×D₄	C₃×C₅×D₄	semidirect
463. C₂²×C₄	C₃×C₅×D₄	semidirect
479. C₃×C₅	#2408	direct (N × H)
497. C₂²×C₃	C₅×#121	semidirect
508. C₃×C₄	C₅×#120	semidirect
537. C₂³	C₂×C₃×C₅×D₄	semidirect
559. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
568. C₅	C₃×#2408	direct (N × H)
586. C₂²	C₃×C₅×#121	semidirect
597. C₄	C₃×C₅×#120	semidirect
598. C₃	C₅×#2408	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#120	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#380	2
C₃×C₅×#379	2
C₅×#2408	3
C₃×#2408	5

Subgroups — C3×C5×#2408 #14275442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2408 #14275442