Subgroups — C₂×C₃×#65718 #14411309

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 464 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	C₂×C₃×D₅⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#65718	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×#65718	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	C₂×C₃×#704	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	C₃×D₅⋊M₁₆	C₄	1	4	yes	complemented
16	C₃×D₅⋊M₁₆	C₂²	1	4	yes	—
17	C₂×C₃×#700	C₄	1	2	yes	complemented
18	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
19	C₂²×C₃×C₅×C₈	C₄	1	1	yes	characteristic, complemented
20	C₂²×C₃×#168	C₄	1	1	yes	characteristic, complemented
21	C₂×C₃×C₈×D₅	C₄	1	4	yes	complemented
22	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
24	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₈×D₅	C₂²	1	4	yes	—
27	C₃×#3992	C₂²	1	8	yes	complemented
28	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
29	C₂×C₃×#405	—	5	1	no	maximal, Hall
30	C₂×#4130	C₂×C₃	1	1	yes	characteristic
31	C₂×D₅⋊M₁₆	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
33	#65718	C₂×C₃	1	8	yes	direct product factor
34	C₂×#3992	C₂×C₃	1	2	yes	complemented
35	C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
36	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
48	C₃×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	8	yes	—
49	C₃×#704	C₂×C₄	1	8	yes	complemented
50	C₂×C₃×#170	C₂×C₄	1	4	yes	—
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×#700	C₂×C₄	1	8	yes	complemented
55	C₃×D₅⋊C₈	C₂×C₄	1	4	yes	—
56	C₃×D₅⋊C₈	C₂³	1	4	yes	—
57	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
63	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
64	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
65	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
66	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
67	C₃×C₈×D₅	C₂³	1	2	yes	—
68	C₃×C₈×D₅	C₂³	1	2	yes	—
69	C₂²×C₃×M₁₆	—	5	1	no	—
70	C₂³×C₃×C₈	—	5	1	no	—
71	C₂×C₃×#117	—	5	1	no	—
72	C₃×#405	—	5	8	no	—
73	C₂×C₃×#97	—	5	2	no	—
74	C₂×C₃×C₄×C₈	—	5	2	no	—
75	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₂²⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
77	C₂×#704	C₃×C₄	1	2	yes	complemented
78	#4130	C₃×C₄	1	4	yes	—
79	#4130	C₂²×C₃	1	4	yes	—
80	C₂×C₄⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
81	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
82	D₅⋊M₁₆	C₃×C₄	1	4	yes	complemented
83	D₅⋊M₁₆	C₂²×C₃	1	4	yes	—
84	C₂×#700	C₃×C₄	1	2	yes	complemented
85	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
86	C₂²×C₅×C₈	C₃×C₄	1	1	yes	characteristic, complemented
87	C₂²×#168	C₃×C₄	1	1	yes	characteristic, complemented
88	C₂×C₈×D₅	C₃×C₄	1	4	yes	complemented
89	C₂×C₈×D₅	C₃×C₄	1	1	yes	characteristic, complemented
90	C₂×C₈×D₅	C₃×C₄	1	1	yes	characteristic, complemented
91	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₈×D₅	C₂²×C₃	1	4	yes	—
94	#3992	C₂²×C₃	1	8	yes	complemented
95	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	complemented
96	C₂×#405	—	5	1	no	Sylow
97	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
98	C₂²×C₃×D₅	—	2	4	no	—
99	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
100	C₂²×C₃×D₅	C₄²	1	2	yes	—
101	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
104	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	—
105	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂×C₃×Dic₅	C₄²	1	2	yes	—
110	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
111	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
113	C₃×C₄×D₅	C₄²	1	2	yes	—
114	C₃×C₄×D₅	C₄²	1	2	yes	—
115	C₃×C₄×D₅	C₄²	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	C₂²×C₄	1	1	yes	characteristic
119	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
120	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
121	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
122	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
123	C₃×#170	C₂²×C₄	1	8	yes	—
124	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
125	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₃×#168	C₂²×C₄	1	2	yes	—
127	C₃×#168	C₂²×C₄	1	2	yes	—
128	C₂³×C₃×C₄	—	5	1	no	—
129	C₂×C₃×M₁₆	—	5	2	no	—
130	C₂×C₃×M₁₆	—	5	4	no	—
131	C₂×C₃×M₁₆	—	5	4	no	—
132	C₂×C₃×M₁₆	—	5	2	no	—
133	C₂²×C₃×C₈	—	5	2	no	—
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₂²×C₃×C₈	—	5	1	no	—
136	C₂²×C₃×C₈	—	5	1	no	—
137	C₂²×C₃×C₈	—	5	1	no	—
138	C₂²×C₃×C₈	—	5	1	no	—
139	C₂²×C₃×C₈	—	5	4	no	—
140	C₂²×C₃×C₈	—	5	4	no	—
141	C₂²×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
142	C₃×#117	—	5	4	no	—
143	C₃×#117	—	5	4	no	—
144	C₂×C₃×C₄⋊C₄	—	5	2	no	—
145	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
146	C₂×C₃×C₄²	—	5	2	no	—
147	C₃×#97	—	5	8	no	—
148	C₃×C₄×C₈	—	5	8	no	—
149	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
151	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
155	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
156	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
159	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
161	C₂²⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	—
162	#704	C₂×C₃×C₄	1	8	yes	complemented
163	C₂×#170	C₂×C₃×C₄	1	4	yes	—
164	C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	—
165	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
166	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
167	#700	C₂×C₃×C₄	1	8	yes	complemented
168	D₅⋊C₈	C₂×C₃×C₄	1	4	yes	—
169	D₅⋊C₈	C₂³×C₃	1	4	yes	—
170	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
172	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
173	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
174	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
175	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
176	C₈×D₅	C₂×C₃×C₄	1	2	yes	—
177	C₈×D₅	C₂×C₃×C₄	1	2	yes	—
178	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
179	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
180	C₈×D₅	C₂³×C₃	1	2	yes	—
181	C₈×D₅	C₂³×C₃	1	2	yes	—
182	C₂²×M₁₆	—	5	1	no	—
183	C₂³×C₈	—	5	1	no	—
184	C₂×#117	—	5	1	no	—
185	#405	—	5	8	no	—
186	C₂×#97	—	5	2	no	—
187	C₂×C₄×C₈	—	5	2	no	—
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
190	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₃×D₅	—	2	2	no	—
192	C₂×C₃×D₅	—	2	4	no	—
193	C₂×C₃×D₅	—	2	4	no	—
194	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
195	C₂×C₃×D₅	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₃×D₅	#131	1	4	yes	—
197	C₂×C₃×D₅	C₂³×C₄	1	1	yes	characteristic
198	C₃×AGL(1,𝔽₅)	—	2	8	no	—
199	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
201	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
202	C₃×Dic₅	C₂×C₄²	1	1	yes	characteristic
203	C₃×Dic₅	C₂×C₄²	1	2	yes	—
204	C₃×Dic₅	C₂³×C₄	1	1	yes	characteristic
205	C₂⁴×C₃	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	2	no	—
209	C₂²×C₃×C₄	—	5	1	no	—
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	—	5	1	no	—
212	C₂²×C₃×C₄	—	5	2	no	—
213	C₂²×C₃×C₄	—	5	1	no	—
214	C₂²×C₃×C₄	—	5	2	no	—
215	C₂²×C₃×C₄	—	5	4	no	—
216	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
217	C₃×M₁₆	—	5	8	no	—
218	C₃×M₁₆	—	5	8	no	—
219	C₂×C₃×C₈	—	5	4	no	—
220	C₂×C₃×C₈	—	5	4	no	—
221	C₂×C₃×C₈	—	5	4	no	—
222	C₂×C₃×C₈	—	5	1	no	—
223	C₂×C₃×C₈	—	5	1	no	—
224	C₂×C₃×C₈	—	5	4	no	—
225	C₂×C₃×C₈	—	5	2	no	—
226	C₂×C₃×C₈	—	5	2	no	—
227	C₂×C₃×C₈	—	5	4	no	—
228	C₂×C₃×C₈	—	5	4	no	—
229	C₂×C₃×C₈	—	5	2	no	—
230	C₂×C₃×C₈	—	5	2	no	—
231	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
232	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
233	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
234	C₃×C₄⋊C₄	—	5	8	no	—
235	C₃×C₂²⋊C₄	—	5	8	no	—
236	C₃×C₄²	—	5	4	no	—
237	C₃×C₄²	—	5	4	no	—
238	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
239	C₂²×D₅	—	2	4	no	—
240	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
241	C₂²×D₅	C₃×C₄²	1	2	yes	—
242	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
243	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₂×AGL(1,𝔽₅)	—	2	8	no	—
245	C₂×AGL(1,𝔽₅)	C₂²×C₃×C₄	1	8	yes	—
246	C₂×C₄×C₅	C₃×C₄²	1	2	yes	—
247	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
250	C₂×Dic₅	C₃×C₄²	1	2	yes	—
251	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
252	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
253	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
254	C₄×D₅	C₃×C₄²	1	2	yes	—
255	C₄×D₅	C₃×C₄²	1	2	yes	—
256	C₄×D₅	C₃×C₄²	1	2	yes	—
257	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
259	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
260	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
261	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
262	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
263	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
264	#170	C₂²×C₃×C₄	1	8	yes	—
265	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
266	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
267	#168	C₂²×C₃×C₄	1	2	yes	—
268	#168	C₂²×C₃×C₄	1	2	yes	—
269	C₂³×C₄	—	5	1	no	—
270	C₂×M₁₆	—	5	2	no	—
271	C₂×M₁₆	—	5	4	no	—
272	C₂×M₁₆	—	5	4	no	—
273	C₂×M₁₆	—	5	2	no	—
274	C₂²×C₈	—	5	2	no	—
275	C₂²×C₈	—	5	1	no	—
276	C₂²×C₈	—	5	1	no	—
277	C₂²×C₈	—	5	1	no	—
278	C₂²×C₈	—	5	1	no	—
279	C₂²×C₈	—	5	1	no	—
280	C₂²×C₈	—	5	4	no	—
281	C₂²×C₈	—	5	4	no	—
282	C₂²×C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
283	#117	—	5	4	no	—
284	#117	—	5	4	no	—
285	C₂×C₄⋊C₄	—	5	2	no	—
286	C₂×C₂²⋊C₄	—	5	2	no	—
287	C₂×C₄²	—	5	2	no	—
288	#97	—	5	8	no	—
289	C₄×C₈	—	5	8	no	—
290	C₂×C₃×C₅	—	2	2	no	—
291	C₂×C₃×C₅	#405	1	2	yes	complemented
292	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
293	C₃×D₅	—	2	2	no	—
294	C₃×D₅	#405	1	2	yes	complemented
295	C₃×D₅	C₂×#131	1	2	yes	—
296	C₂³×C₃	—	5	1	no	—
297	C₂³×C₃	—	5	2	no	—
298	C₂³×C₃	—	5	1	no	—
299	C₂³×C₃	—	5	2	no	—
300	C₂³×C₃	—	10	4	no	—
301	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
302	C₂×C₃×C₄	—	5	2	no	—
303	C₂×C₃×C₄	—	5	1	no	—
304	C₂×C₃×C₄	—	5	1	no	—
305	C₂×C₃×C₄	—	5	2	no	—
306	C₂×C₃×C₄	—	5	2	no	—
307	C₂×C₃×C₄	—	5	2	no	—
308	C₂×C₃×C₄	—	5	2	no	—
309	C₂×C₃×C₄	—	5	1	no	—
310	C₂×C₃×C₄	—	5	2	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	2	no	—
313	C₂×C₃×C₄	—	5	1	no	—
314	C₂×C₃×C₄	—	5	2	no	—
315	C₂×C₃×C₄	—	5	1	no	—
316	C₂×C₃×C₄	—	5	8	no	—
317	C₂×C₃×C₄	—	10	8	no	—
318	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
319	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
322	C₃×C₈	—	5	8	no	—
323	C₃×C₈	—	5	2	no	—
324	C₃×C₈	—	5	2	no	—
325	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
326	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
327	C₂²×C₅	—	2	2	no	—
328	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
329	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
330	C₂×D₅	—	2	2	no	—
331	C₂×D₅	—	2	4	no	—
332	C₂×D₅	—	2	4	no	—
333	C₂×D₅	C₂×C₃×C₄²	1	2	yes	—
334	C₂×D₅	C₂×C₃×C₄²	1	1	yes	characteristic
335	C₂×D₅	C₃×#131	1	4	yes	—
336	C₂×D₅	C₂³×C₃×C₄	1	1	yes	characteristic
337	AGL(1,𝔽₅)	—	2	8	no	—
338	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
339	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
340	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
341	Dic₅	C₂×C₃×C₄²	1	1	yes	characteristic
342	Dic₅	C₂×C₃×C₄²	1	2	yes	—
343	Dic₅	C₂³×C₃×C₄	1	1	yes	characteristic
344	C₂⁴	—	5	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	—	5	1	no	—
347	C₂²×C₄	—	5	2	no	—
348	C₂²×C₄	—	5	1	no	—
349	C₂²×C₄	—	5	2	no	—
350	C₂²×C₄	—	5	1	no	—
351	C₂²×C₄	—	5	2	no	—
352	C₂²×C₄	—	5	1	no	—
353	C₂²×C₄	—	5	2	no	—
354	C₂²×C₄	—	5	4	no	—
355	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
356	M₁₆	—	5	8	no	—
357	M₁₆	—	5	8	no	—
358	C₂×C₈	—	5	4	no	—
359	C₂×C₈	—	5	4	no	—
360	C₂×C₈	—	5	4	no	—
361	C₂×C₈	—	5	1	no	—
362	C₂×C₈	—	5	1	no	—
363	C₂×C₈	—	5	4	no	—
364	C₂×C₈	—	5	2	no	—
365	C₂×C₈	—	5	2	no	—
366	C₂×C₈	—	5	2	no	—
367	C₂×C₈	—	5	2	no	—
368	C₂×C₈	—	5	4	no	—
369	C₂×C₈	—	5	4	no	—
370	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
372	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
373	C₄⋊C₄	—	5	8	no	—
374	C₂²⋊C₄	—	5	8	no	—
375	C₄²	—	5	4	no	—
376	C₄²	—	5	4	no	—
377	C₃×C₅	C₂×#405	1	1	yes	characteristic, complemented, Hall
378	C₂²×C₃	—	2	2	no	—
379	C₂²×C₃	—	5	4	no	—
380	C₂²×C₃	—	5	1	no	—
381	C₂²×C₃	—	5	1	no	—
382	C₂²×C₃	—	5	2	no	—
383	C₂²×C₃	—	10	4	no	—
384	C₂²×C₃	—	10	4	no	—
385	C₂²×C₃	—	10	2	no	—
386	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
387	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
388	C₃×C₄	—	5	1	no	—
389	C₃×C₄	—	5	2	no	—
390	C₃×C₄	—	5	1	no	—
391	C₃×C₄	—	10	8	no	—
392	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
394	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
395	C₂×C₅	—	2	2	no	—
396	C₂×C₅	C₃×#405	1	2	yes	complemented
397	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
398	D₅	—	2	2	no	—
399	D₅	C₃×#405	1	2	yes	complemented
400	D₅	C₂×C₃×#131	1	2	yes	—
401	C₂³	—	5	1	no	—
402	C₂³	—	5	2	no	—
403	C₂³	—	5	2	no	—
404	C₂³	—	5	1	no	—
405	C₂³	—	10	4	no	—
406	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	2	no	—
409	C₂×C₄	—	5	2	no	—
410	C₂×C₄	—	5	1	no	—
411	C₂×C₄	—	5	1	no	—
412	C₂×C₄	—	5	2	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	5	2	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	5	2	no	—
417	C₂×C₄	—	5	2	no	—
418	C₂×C₄	—	5	1	no	—
419	C₂×C₄	—	5	1	no	—
420	C₂×C₄	—	5	2	no	—
421	C₂×C₄	—	5	8	no	—
422	C₂×C₄	—	10	8	no	—
423	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
424	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
427	C₈	—	5	8	no	—
428	C₈	—	5	2	no	—
429	C₈	—	5	2	no	—
430	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
431	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
432	C₂×C₃	—	2	2	no	—
433	C₂×C₃	—	5	2	no	—
434	C₂×C₃	—	5	2	no	—
435	C₂×C₃	—	10	2	no	—
436	C₂×C₃	#65718	1	2	yes	direct product factor
437	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
438	C₅	C₂×C₃×#405	1	1	yes	characteristic, complemented, Sylow
439	C₂²	—	2	2	no	—
440	C₂²	—	5	4	no	—
441	C₂²	—	5	1	no	—
442	C₂²	—	5	1	no	—
443	C₂²	—	5	2	no	—
444	C₂²	—	10	4	no	—
445	C₂²	—	10	4	no	—
446	C₂²	—	10	2	no	—
447	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
448	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
449	C₄	—	5	1	no	—
450	C₄	—	5	1	no	—
451	C₄	—	5	2	no	—
452	C₄	—	10	8	no	—
453	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
454	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
455	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
456	C₃	C₂×#65718	1	1	yes	characteristic, direct product factor, Sylow
457	C₂	—	2	2	no	—
458	C₂	—	5	2	no	—
459	C₂	—	5	2	no	—
460	C₂	—	10	2	no	—
461	C₂	C₃×#65718	1	2	yes	direct product factor
462	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₅×C₈	C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂²×C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#405
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
4. C₃×#65718	C₂	direct (N × H)
5. C₂×C₃×#3992	C₂	semidirect
6. C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	semidirect
7. C₂×#65718	C₃	direct (N × H)
10. C₂×C₃×#704	C₄	semidirect
15. C₃×D₅⋊M₁₆	C₄	semidirect
17. C₂×C₃×#700	C₄	semidirect
19. C₂²×C₃×C₅×C₈	C₄	semidirect
20. C₂²×C₃×#168	C₄	semidirect
21. C₂×C₃×C₈×D₅	C₄	semidirect
22. C₂×C₃×C₈×D₅	C₄	semidirect
23. C₂×C₃×C₈×D₅	C₄	semidirect
27. C₃×#3992	C₂²	semidirect
28. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
33. #65718	C₂×C₃	direct (N × H)
34. C₂×#3992	C₂×C₃	semidirect
35. C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	semidirect
49. C₃×#704	C₂×C₄	semidirect
54. C₃×#700	C₂×C₄	semidirect
59. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. C₂×C₃×#168	C₂×C₄	semidirect
65. C₃×C₈×D₅	C₂×C₄	semidirect
66. C₃×C₈×D₅	C₂×C₄	semidirect
77. C₂×#704	C₃×C₄	semidirect
82. D₅⋊M₁₆	C₃×C₄	semidirect
84. C₂×#700	C₃×C₄	semidirect
86. C₂²×C₅×C₈	C₃×C₄	semidirect
87. C₂²×#168	C₃×C₄	semidirect
88. C₂×C₈×D₅	C₃×C₄	semidirect
89. C₂×C₈×D₅	C₃×C₄	semidirect
90. C₂×C₈×D₅	C₃×C₄	semidirect
94. #3992	C₂²×C₃	semidirect
95. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
141. C₂²×C₃×C₈	AGL(1,𝔽₅)	semidirect
162. #704	C₂×C₃×C₄	semidirect
167. #700	C₂×C₃×C₄	semidirect
172. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
175. C₂×#168	C₂×C₃×C₄	semidirect
178. C₈×D₅	C₂×C₃×C₄	semidirect
179. C₈×D₅	C₂×C₃×C₄	semidirect
233. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
282. C₂²×C₈	C₃×AGL(1,𝔽₅)	semidirect
291. C₂×C₃×C₅	#405	semidirect
294. C₃×D₅	#405	semidirect
372. C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
377. C₃×C₅	C₂×#405	semidirect
396. C₂×C₅	C₃×#405	semidirect
399. D₅	C₃×#405	semidirect
436. C₂×C₃	#65718	direct (N × H)
438. C₅	C₂×C₃×#405	semidirect
456. C₃	C₂×#65718	direct (N × H)
461. C₂	C₃×#65718	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
C₂×C₃×D₅⋊M₁₆	2
C₂²×C₃×C₈×D₅	2
C₃×#65718	2
C₂×C₃×#3992	2
C₂×C₃×C₈×AGL(1,𝔽₅)	2
C₂×#65718	3
C₂×C₃×#405	5

Subgroups — C2×C3×#65718 #14411309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65718 #14411309