Subgroups — C₂×C₃×#65728 #14411317

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4130	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#65728	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3992	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
7	C₂×#65728	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₄	1	2	yes	—
10	C₂²×C₃×#170	C₄	1	2	yes	complemented
11	C₃×#4130	C₄	1	4	yes	—
12	C₃×#4130	C₂²	1	4	yes	—
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₄	1	2	yes	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
15	C₂×C₃×D₅⋊C₈	C₄	1	4	yes	complemented
16	C₂×C₃×D₅⋊C₈	C₄	1	2	yes	complemented
17	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₅⋊C₈	C₂²	1	4	yes	—
20	C₂×C₃×C₅×M₁₆	C₄	1	1	yes	characteristic, complemented
21	C₂×C₃×#681	C₄	1	1	yes	characteristic, complemented
22	C₃×D₅×M₁₆	C₄	1	4	yes	complemented
23	C₃×D₅×M₁₆	C₂²	1	4	yes	—
24	C₂×C₃×#676	C₄	1	2	yes	complemented
25	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
26	C₃×#3992	C₂²	1	8	yes	complemented
27	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
28	C₂×C₃×#405	—	5	1	no	maximal, Hall
29	C₂×#4130	C₂×C₃	1	1	yes	characteristic
30	C₂²×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic
31	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
32	#65728	C₂×C₃	1	8	yes	direct product factor
33	C₂×#3992	C₂×C₃	1	2	yes	complemented
34	C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
35	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
47	C₃×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	8	yes	—
48	C₂×C₃×#170	C₂×C₄	1	2	yes	—
49	C₂×C₃×#170	C₂×C₄	1	2	yes	—
50	C₂×C₃×#170	C₂×C₄	1	8	yes	complemented
51	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	8	yes	—
52	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
53	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	4	yes	—
54	C₃×D₅⋊C₈	C₂×C₄	1	2	yes	—
55	C₃×D₅⋊C₈	C₂×C₄	1	2	yes	—
56	C₃×D₅⋊C₈	C₂×C₄	1	8	yes	complemented
57	C₃×D₅⋊C₈	C₂³	1	2	yes	—
58	C₃×D₅⋊C₈	C₂³	1	2	yes	—
59	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
61	C₃×#681	C₂×C₄	1	4	yes	complemented
62	C₂×C₃×#168	C₂×C₄	1	2	yes	—
63	C₃×#676	C₂×C₄	1	8	yes	complemented
64	C₃×C₈×D₅	C₂×C₄	1	4	yes	—
65	C₃×C₈×D₅	C₂³	1	4	yes	—
66	C₂²×C₃×M₁₆	—	5	1	no	—
67	C₂³×C₃×C₈	—	5	1	no	—
68	C₂×C₃×#117	—	5	1	no	—
69	C₃×#405	—	5	8	no	—
70	C₂×C₃×#97	—	5	2	no	—
71	C₂×C₃×C₄×C₈	—	5	2	no	—
72	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₂²⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
74	C₂²×#170	C₃×C₄	1	2	yes	complemented
75	#4130	C₃×C₄	1	4	yes	—
76	#4130	C₂²×C₃	1	4	yes	—
77	C₂×C₄⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
78	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
79	C₂×D₅⋊C₈	C₃×C₄	1	4	yes	complemented
80	C₂×D₅⋊C₈	C₃×C₄	1	2	yes	complemented
81	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×D₅⋊C₈	C₂²×C₃	1	4	yes	—
84	C₂×C₅×M₁₆	C₃×C₄	1	1	yes	characteristic, complemented
85	C₂×#681	C₃×C₄	1	1	yes	characteristic, complemented
86	D₅×M₁₆	C₃×C₄	1	4	yes	complemented
87	D₅×M₁₆	C₂²×C₃	1	4	yes	—
88	C₂×#676	C₃×C₄	1	2	yes	complemented
89	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
90	#3992	C₂²×C₃	1	8	yes	complemented
91	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	complemented
92	C₂×#405	—	5	1	no	Sylow
93	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
94	C₂²×C₃×D₅	—	2	4	no	—
95	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
96	C₂²×C₃×D₅	C₄²	1	2	yes	—
97	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
98	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
100	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	—
101	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×Dic₅	C₄²	1	2	yes	—
106	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
107	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
109	C₃×C₄×D₅	C₄²	1	2	yes	—
110	C₃×C₄×D₅	C₄²	1	2	yes	—
111	C₃×C₄×D₅	C₄²	1	2	yes	—
112	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
113	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
114	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
115	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
116	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
117	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
118	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
119	C₃×#170	C₂²×C₄	1	4	yes	—
120	C₃×#170	C₂²×C₄	1	4	yes	—
121	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
122	C₃×#168	C₂²×C₄	1	4	yes	—
123	C₂³×C₃×C₄	—	5	1	no	—
124	C₂×C₃×M₁₆	—	5	1	no	—
125	C₂×C₃×M₁₆	—	5	4	no	—
126	C₂×C₃×M₁₆	—	5	4	no	—
127	C₂×C₃×M₁₆	—	5	2	no	—
128	C₂×C₃×M₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
129	C₂²×C₃×C₈	—	5	4	no	—
130	C₂²×C₃×C₈	—	5	2	no	—
131	C₂²×C₃×C₈	—	5	1	no	—
132	C₂²×C₃×C₈	—	5	1	no	—
133	C₂²×C₃×C₈	—	5	4	no	—
134	C₂²×C₃×C₈	—	5	2	no	—
135	C₂²×C₃×C₈	—	5	2	no	—
136	C₃×#117	—	5	4	no	—
137	C₃×#117	—	5	4	no	—
138	C₂×C₃×C₄⋊C₄	—	5	2	no	—
139	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
140	C₂×C₃×C₄²	—	5	2	no	—
141	C₃×#97	—	5	8	no	—
142	C₃×C₄×C₈	—	5	8	no	—
143	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
145	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
149	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
151	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
155	C₂²⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	—
156	C₂×#170	C₂×C₃×C₄	1	2	yes	—
157	C₂×#170	C₂×C₃×C₄	1	2	yes	—
158	C₂×#170	C₂×C₃×C₄	1	8	yes	complemented
159	C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	—
160	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
161	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
162	D₅⋊C₈	C₂×C₃×C₄	1	2	yes	—
163	D₅⋊C₈	C₂×C₃×C₄	1	2	yes	—
164	D₅⋊C₈	C₂×C₃×C₄	1	8	yes	complemented
165	D₅⋊C₈	C₂³×C₃	1	2	yes	—
166	D₅⋊C₈	C₂³×C₃	1	2	yes	—
167	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
168	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
169	#681	C₂×C₃×C₄	1	4	yes	complemented
170	C₂×#168	C₂×C₃×C₄	1	2	yes	—
171	#676	C₂×C₃×C₄	1	8	yes	complemented
172	C₈×D₅	C₂×C₃×C₄	1	4	yes	—
173	C₈×D₅	C₂³×C₃	1	4	yes	—
174	C₂²×M₁₆	—	5	1	no	—
175	C₂³×C₈	—	5	1	no	—
176	C₂×#117	—	5	1	no	—
177	#405	—	5	8	no	—
178	C₂×#97	—	5	2	no	—
179	C₂×C₄×C₈	—	5	2	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
182	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₃×D₅	—	2	2	no	—
184	C₂×C₃×D₅	—	2	4	no	—
185	C₂×C₃×D₅	—	2	4	no	—
186	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
187	C₂×C₃×D₅	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₃×D₅	#131	1	4	yes	—
189	C₂×C₃×D₅	C₂³×C₄	1	1	yes	characteristic
190	C₃×AGL(1,𝔽₅)	—	2	8	no	—
191	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
192	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₃×Dic₅	C₂×C₄²	1	1	yes	characteristic
195	C₃×Dic₅	C₂×C₄²	1	2	yes	—
196	C₃×Dic₅	C₂³×C₄	1	1	yes	characteristic
197	C₂⁴×C₃	—	5	1	no	—
198	C₂²×C₃×C₄	—	5	1	no	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	5	2	no	—
201	C₂²×C₃×C₄	—	5	2	no	—
202	C₂²×C₃×C₄	—	5	1	no	—
203	C₂²×C₃×C₄	—	5	2	no	—
204	C₂²×C₃×C₄	—	5	2	no	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	4	no	—
208	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
209	C₃×M₁₆	—	5	4	no	—
210	C₃×M₁₆	—	5	8	no	—
211	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
212	C₂×C₃×C₈	—	5	2	no	—
213	C₂×C₃×C₈	—	5	2	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₂×C₃×C₈	—	5	2	no	—
216	C₂×C₃×C₈	—	5	8	no	—
217	C₂×C₃×C₈	—	5	2	no	—
218	C₂×C₃×C₈	—	5	2	no	—
219	C₂×C₃×C₈	—	5	8	no	—
220	C₂×C₃×C₈	—	5	2	no	—
221	C₂×C₃×C₈	—	5	4	no	—
222	C₂×C₃×C₈	—	5	4	no	—
223	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
224	C₃×C₄⋊C₄	—	5	8	no	—
225	C₃×C₂²⋊C₄	—	5	8	no	—
226	C₃×C₄²	—	5	4	no	—
227	C₃×C₄²	—	5	4	no	—
228	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
229	C₂²×D₅	—	2	4	no	—
230	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
231	C₂²×D₅	C₃×C₄²	1	2	yes	—
232	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
233	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×AGL(1,𝔽₅)	—	2	8	no	—
235	C₂×AGL(1,𝔽₅)	C₂²×C₃×C₄	1	8	yes	—
236	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
237	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
240	C₂×Dic₅	C₃×C₄²	1	2	yes	—
241	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
242	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
244	C₄×D₅	C₃×C₄²	1	2	yes	—
245	C₄×D₅	C₃×C₄²	1	2	yes	—
246	C₄×D₅	C₃×C₄²	1	2	yes	—
247	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
248	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
249	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
250	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
251	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
253	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
254	#170	C₂²×C₃×C₄	1	4	yes	—
255	#170	C₂²×C₃×C₄	1	4	yes	—
256	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
257	#168	C₂²×C₃×C₄	1	4	yes	—
258	C₂³×C₄	—	5	1	no	—
259	C₂×M₁₆	—	5	1	no	—
260	C₂×M₁₆	—	5	4	no	—
261	C₂×M₁₆	—	5	4	no	—
262	C₂×M₁₆	—	5	2	no	—
263	C₂×M₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
264	C₂²×C₈	—	5	4	no	—
265	C₂²×C₈	—	5	2	no	—
266	C₂²×C₈	—	5	1	no	—
267	C₂²×C₈	—	5	1	no	—
268	C₂²×C₈	—	5	4	no	—
269	C₂²×C₈	—	5	2	no	—
270	C₂²×C₈	—	5	2	no	—
271	#117	—	5	4	no	—
272	#117	—	5	4	no	—
273	C₂×C₄⋊C₄	—	5	2	no	—
274	C₂×C₂²⋊C₄	—	5	2	no	—
275	C₂×C₄²	—	5	2	no	—
276	#97	—	5	8	no	—
277	C₄×C₈	—	5	8	no	—
278	C₂×C₃×C₅	—	2	2	no	—
279	C₂×C₃×C₅	#405	1	2	yes	complemented
280	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
281	C₃×D₅	—	2	2	no	—
282	C₃×D₅	#405	1	2	yes	complemented
283	C₃×D₅	C₂×#131	1	2	yes	—
284	C₂³×C₃	—	5	1	no	—
285	C₂³×C₃	—	5	2	no	—
286	C₂³×C₃	—	5	1	no	—
287	C₂³×C₃	—	5	2	no	—
288	C₂³×C₃	—	10	4	no	—
289	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₂×C₃×C₄	—	5	2	no	—
291	C₂×C₃×C₄	—	5	1	no	—
292	C₂×C₃×C₄	—	5	2	no	—
293	C₂×C₃×C₄	—	5	1	no	—
294	C₂×C₃×C₄	—	5	2	no	—
295	C₂×C₃×C₄	—	5	2	no	—
296	C₂×C₃×C₄	—	5	2	no	—
297	C₂×C₃×C₄	—	5	1	no	—
298	C₂×C₃×C₄	—	5	2	no	—
299	C₂×C₃×C₄	—	5	2	no	—
300	C₂×C₃×C₄	—	5	1	no	—
301	C₂×C₃×C₄	—	5	1	no	—
302	C₂×C₃×C₄	—	5	2	no	—
303	C₂×C₃×C₄	—	5	1	no	—
304	C₂×C₃×C₄	—	5	8	no	—
305	C₂×C₃×C₄	—	10	8	no	—
306	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
308	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
309	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
310	C₃×C₈	—	5	4	no	—
311	C₃×C₈	—	5	4	no	—
312	C₃×C₈	—	5	4	no	—
313	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	4	yes	—
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
316	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
317	C₂×D₅	—	2	2	no	—
318	C₂×D₅	—	2	4	no	—
319	C₂×D₅	—	2	4	no	—
320	C₂×D₅	C₂×C₃×C₄²	1	2	yes	—
321	C₂×D₅	C₂×C₃×C₄²	1	1	yes	characteristic
322	C₂×D₅	C₃×#131	1	4	yes	—
323	C₂×D₅	C₂³×C₃×C₄	1	1	yes	characteristic
324	AGL(1,𝔽₅)	—	2	8	no	—
325	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
326	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
327	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
328	Dic₅	C₂×C₃×C₄²	1	1	yes	characteristic
329	Dic₅	C₂×C₃×C₄²	1	2	yes	—
330	Dic₅	C₂³×C₃×C₄	1	1	yes	characteristic
331	C₂⁴	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	5	1	no	—
334	C₂²×C₄	—	5	2	no	—
335	C₂²×C₄	—	5	2	no	—
336	C₂²×C₄	—	5	1	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	2	no	—
339	C₂²×C₄	—	5	2	no	—
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	5	4	no	—
342	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
343	M₁₆	—	5	4	no	—
344	M₁₆	—	5	8	no	—
345	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
346	C₂×C₈	—	5	2	no	—
347	C₂×C₈	—	5	2	no	—
348	C₂×C₈	—	5	2	no	—
349	C₂×C₈	—	5	2	no	—
350	C₂×C₈	—	5	8	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	5	8	no	—
354	C₂×C₈	—	5	2	no	—
355	C₂×C₈	—	5	4	no	—
356	C₂×C₈	—	5	4	no	—
357	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
358	C₄⋊C₄	—	5	8	no	—
359	C₂²⋊C₄	—	5	8	no	—
360	C₄²	—	5	4	no	—
361	C₄²	—	5	4	no	—
362	C₃×C₅	C₂×#405	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	5	4	no	—
365	C₂²×C₃	—	5	1	no	—
366	C₂²×C₃	—	5	1	no	—
367	C₂²×C₃	—	5	2	no	—
368	C₂²×C₃	—	10	4	no	—
369	C₂²×C₃	—	10	4	no	—
370	C₂²×C₃	—	10	2	no	—
371	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
372	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₃×C₄	—	5	1	no	—
374	C₃×C₄	—	5	2	no	—
375	C₃×C₄	—	5	1	no	—
376	C₃×C₄	—	10	8	no	—
377	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
378	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
380	C₂×C₅	—	2	2	no	—
381	C₂×C₅	C₃×#405	1	2	yes	complemented
382	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
383	D₅	—	2	2	no	—
384	D₅	C₃×#405	1	2	yes	complemented
385	D₅	C₂×C₃×#131	1	2	yes	—
386	C₂³	—	5	1	no	—
387	C₂³	—	5	2	no	—
388	C₂³	—	5	2	no	—
389	C₂³	—	5	1	no	—
390	C₂³	—	10	4	no	—
391	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₂×C₄	—	5	2	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	2	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	2	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	2	no	—
400	C₂×C₄	—	5	2	no	—
401	C₂×C₄	—	5	2	no	—
402	C₂×C₄	—	5	2	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	2	no	—
406	C₂×C₄	—	5	8	no	—
407	C₂×C₄	—	10	8	no	—
408	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
409	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
412	C₈	—	5	4	no	—
413	C₈	—	5	4	no	—
414	C₈	—	5	4	no	—
415	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
416	C₂×C₃	—	2	2	no	—
417	C₂×C₃	—	5	2	no	—
418	C₂×C₃	—	5	2	no	—
419	C₂×C₃	—	10	2	no	—
420	C₂×C₃	#65728	1	2	yes	direct product factor
421	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
422	C₅	C₂×C₃×#405	1	1	yes	characteristic, complemented, Sylow
423	C₂²	—	2	2	no	—
424	C₂²	—	5	4	no	—
425	C₂²	—	5	1	no	—
426	C₂²	—	5	1	no	—
427	C₂²	—	5	2	no	—
428	C₂²	—	10	4	no	—
429	C₂²	—	10	4	no	—
430	C₂²	—	10	2	no	—
431	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
432	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
433	C₄	—	5	1	no	—
434	C₄	—	5	1	no	—
435	C₄	—	5	2	no	—
436	C₄	—	10	8	no	—
437	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
438	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
439	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₃	C₂×#65728	1	1	yes	characteristic, direct product factor, Sylow
441	C₂	—	2	2	no	—
442	C₂	—	5	2	no	—
443	C₂	—	5	2	no	—
444	C₂	—	10	2	no	—
445	C₂	C₃×#65728	1	2	yes	direct product factor
446	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×M₁₆	C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×M₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#405
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₃×#65728	C₂	direct (N × H)
5. C₂×C₃×#3992	C₂	semidirect
6. C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	semidirect
7. C₂×#65728	C₃	direct (N × H)
10. C₂²×C₃×#170	C₄	semidirect
15. C₂×C₃×D₅⋊C₈	C₄	semidirect
16. C₂×C₃×D₅⋊C₈	C₄	semidirect
20. C₂×C₃×C₅×M₁₆	C₄	semidirect
21. C₂×C₃×#681	C₄	semidirect
22. C₃×D₅×M₁₆	C₄	semidirect
24. C₂×C₃×#676	C₄	semidirect
26. C₃×#3992	C₂²	semidirect
27. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
32. #65728	C₂×C₃	direct (N × H)
33. C₂×#3992	C₂×C₃	semidirect
34. C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	semidirect
50. C₂×C₃×#170	C₂×C₄	semidirect
56. C₃×D₅⋊C₈	C₂×C₄	semidirect
59. C₃×C₅×M₁₆	C₂×C₄	semidirect
61. C₃×#681	C₂×C₄	semidirect
63. C₃×#676	C₂×C₄	semidirect
74. C₂²×#170	C₃×C₄	semidirect
79. C₂×D₅⋊C₈	C₃×C₄	semidirect
80. C₂×D₅⋊C₈	C₃×C₄	semidirect
84. C₂×C₅×M₁₆	C₃×C₄	semidirect
85. C₂×#681	C₃×C₄	semidirect
86. D₅×M₁₆	C₃×C₄	semidirect
88. C₂×#676	C₃×C₄	semidirect
90. #3992	C₂²×C₃	semidirect
91. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
128. C₂×C₃×M₁₆	AGL(1,𝔽₅)	semidirect
158. C₂×#170	C₂×C₃×C₄	semidirect
164. D₅⋊C₈	C₂×C₃×C₄	semidirect
167. C₅×M₁₆	C₂×C₃×C₄	semidirect
169. #681	C₂×C₃×C₄	semidirect
171. #676	C₂×C₃×C₄	semidirect
211. C₃×M₁₆	C₂×AGL(1,𝔽₅)	semidirect
263. C₂×M₁₆	C₃×AGL(1,𝔽₅)	semidirect
279. C₂×C₃×C₅	#405	semidirect
282. C₃×D₅	#405	semidirect
345. M₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
362. C₃×C₅	C₂×#405	semidirect
381. C₂×C₅	C₃×#405	semidirect
384. D₅	C₃×#405	semidirect
420. C₂×C₃	#65728	direct (N × H)
422. C₅	C₂×C₃×#405	semidirect
440. C₃	C₂×#65728	direct (N × H)
445. C₂	C₃×#65728	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×#4130	2
C₂²×C₃×D₅⋊C₈	2
C₂×C₃×D₅×M₁₆	2
C₃×#65728	2
C₂×C₃×#3992	2
C₂×C₃×C₈×AGL(1,𝔽₅)	2
C₂×#65728	3
C₂×C₃×#405	5

Subgroups — C2×C3×#65728 #14411317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65728 #14411317