Subgroups — C₃×#10604760 #14294782

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 560 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	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#64899	C₂	1	4	yes	maximal, complemented
5	#10604760	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₄	1	2	yes	—
8	C₂×C₃×#704	C₄	1	2	yes	complemented
9	C₃×#4130	—	2	1	no	—
10	C₃×#4130	—	2	1	no	—
11	C₃×#4130	—	2	1	no	—
12	C₃×#4130	—	2	1	no	—
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	1	2	yes	—
15	C₃×D₅⋊M₁₆	—	2	1	no	—
16	C₃×D₅⋊M₁₆	—	2	1	no	—
17	C₃×D₅⋊M₁₆	C₄	1	2	yes	complemented
18	C₃×D₅⋊M₁₆	C₂²	1	2	yes	—
19	C₂×C₃×#700	—	2	1	no	—
20	C₂×C₃×D₅⋊C₈	—	2	1	no	—
21	C₂×C₃×C₅×M₁₆	C₄	1	1	yes	characteristic, complemented
22	C₂×C₃×#681	C₄	1	1	yes	characteristic, complemented
23	C₃×D₅×M₁₆	—	2	1	no	—
24	C₃×D₅×M₁₆	—	2	1	no	—
25	C₃×D₅×M₁₆	C₄	1	2	yes	complemented
26	C₃×D₅×M₁₆	C₂²	1	2	yes	—
27	C₂×C₃×#676	—	2	1	no	—
28	C₂×C₃×C₈×D₅	—	2	1	no	—
29	C₃×#1742	—	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	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
33	#64899	C₂×C₃	1	4	yes	complemented
34	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	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	1	yes	characteristic
41	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
50	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
51	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
52	C₃×#704	—	2	2	no	—
53	C₃×#704	C₂×C₄	1	4	yes	—
54	C₂×C₃×#170	—	2	2	no	—
55	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
56	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
57	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
58	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
59	C₃×#700	—	2	2	no	—
60	C₃×#700	—	2	2	no	—
61	C₃×D₅⋊C₈	—	2	2	no	—
62	C₃×D₅⋊C₈	—	2	2	no	—
63	C₃×C₅×M₁₆	—	2	1	no	—
64	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
65	C₂×C₃×C₅×C₈	—	2	1	no	—
66	C₃×#681	—	2	1	no	—
67	C₃×#681	C₂×C₄	1	2	yes	—
68	C₂×C₃×#168	—	2	1	no	—
69	C₃×#676	—	2	2	no	—
70	C₃×#676	—	2	2	no	—
71	C₃×C₈×D₅	—	2	2	no	—
72	C₃×C₈×D₅	—	2	2	no	—
73	C₂²×C₃×M₁₆	—	5	1	no	—
74	C₂²×C₃×M₁₆	—	5	1	no	—
75	C₂×C₃×#117	—	5	1	no	—
76	C₃×#343	—	5	4	no	—
77	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₂²⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
79	C₂×#704	C₃×C₄	1	2	yes	complemented
80	#4130	—	2	1	no	—
81	#4130	—	2	1	no	—
82	#4130	—	2	1	no	—
83	#4130	—	2	1	no	—
84	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
85	C₂×C₄×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
86	D₅⋊M₁₆	—	2	1	no	—
87	D₅⋊M₁₆	—	2	1	no	—
88	D₅⋊M₁₆	C₃×C₄	1	2	yes	complemented
89	D₅⋊M₁₆	C₂²×C₃	1	2	yes	—
90	C₂×#700	—	2	1	no	—
91	C₂×D₅⋊C₈	—	2	1	no	—
92	C₂×C₅×M₁₆	C₃×C₄	1	1	yes	characteristic, complemented
93	C₂×#681	C₃×C₄	1	1	yes	characteristic, complemented
94	D₅×M₁₆	—	2	1	no	—
95	D₅×M₁₆	—	2	1	no	—
96	D₅×M₁₆	C₃×C₄	1	2	yes	complemented
97	D₅×M₁₆	C₂²×C₃	1	2	yes	—
98	C₂×#676	—	2	1	no	—
99	C₂×C₈×D₅	—	2	1	no	—
100	#1742	—	5	1	no	Sylow
101	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
102	C₂²×C₃×D₅	—	4	2	no	—
103	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
104	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
110	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
111	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
118	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
123	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
124	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
125	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
126	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
127	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
128	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
129	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
130	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
131	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
132	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
133	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
134	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
135	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
136	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
138	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
139	C₃×#170	—	2	4	no	—
140	C₃×C₅×C₈	—	2	2	no	—
141	C₃×#168	—	2	2	no	—
142	C₂³×C₃×C₄	—	5	1	no	—
143	C₂×C₃×M₁₆	—	5	2	no	—
144	C₂×C₃×M₁₆	—	5	2	no	—
145	C₂×C₃×M₁₆	—	5	2	no	—
146	C₂×C₃×M₁₆	—	5	1	no	—
147	C₂×C₃×M₁₆	—	5	2	no	—
148	C₂×C₃×M₁₆	—	5	2	no	—
149	C₂×C₃×M₁₆	—	10	1	no	—
150	C₂×C₃×M₁₆	—	10	1	no	—
151	C₂×C₃×M₁₆	—	10	1	no	—
152	C₂×C₃×M₁₆	—	10	1	no	—
153	C₂×C₃×M₁₆	—	10	1	no	—
154	C₂×C₃×M₁₆	—	10	1	no	—
155	C₂×C₃×M₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
156	C₂²×C₃×C₈	—	10	1	no	—
157	C₂²×C₃×C₈	—	10	1	no	—
158	C₃×#117	—	10	1	no	—
159	C₃×#117	—	10	1	no	—
160	C₃×#117	—	10	1	no	—
161	C₃×#117	—	10	1	no	—
162	C₂×C₃×C₄⋊C₄	—	5	2	no	—
163	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
164	C₂×C₃×C₄²	—	5	2	no	—
165	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
167	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
172	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
173	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
174	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
175	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
176	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
177	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
178	C₂×C₄×D₅	C₃×Q₈	1	1	yes	characteristic
179	C₂×C₄×D₅	C₃×Q₈	1	1	yes	characteristic
180	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
181	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
182	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
183	#704	—	2	2	no	—
184	#704	C₂×C₃×C₄	1	4	yes	—
185	C₂×#170	—	2	2	no	—
186	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
187	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
188	C₄×AGL(1,𝔽₅)	—	2	2	no	—
189	C₄×AGL(1,𝔽₅)	—	2	2	no	—
190	#700	—	2	2	no	—
191	#700	—	2	2	no	—
192	D₅⋊C₈	—	2	2	no	—
193	D₅⋊C₈	—	2	2	no	—
194	C₅×M₁₆	—	2	1	no	—
195	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	—
196	C₂×C₅×C₈	—	2	1	no	—
197	#681	—	2	1	no	—
198	#681	C₂×C₃×C₄	1	2	yes	—
199	C₂×#168	—	2	1	no	—
200	#676	—	2	2	no	—
201	#676	—	2	2	no	—
202	C₈×D₅	—	2	2	no	—
203	C₈×D₅	—	2	2	no	—
204	C₂²×M₁₆	—	5	1	no	—
205	C₂²×M₁₆	—	5	1	no	—
206	C₂×#117	—	5	1	no	—
207	#343	—	5	4	no	—
208	C₂²×C₃×C₅	—	4	1	no	—
209	C₂²×C₃×C₅	#95	1	1	yes	characteristic
210	C₂²×C₃×C₅	#95	1	1	yes	characteristic
211	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
212	C₂×C₃×D₅	—	2	2	no	—
213	C₂×C₃×D₅	—	2	2	no	—
214	C₂×C₃×D₅	—	2	2	no	—
215	C₂×C₃×D₅	—	4	1	no	—
216	C₂×C₃×D₅	—	4	1	no	—
217	C₂×C₃×D₅	—	4	1	no	—
218	C₂×C₃×D₅	#95	1	1	yes	characteristic
219	C₂×C₃×D₅	#95	1	1	yes	characteristic
220	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₃×AGL(1,𝔽₅)	—	4	4	no	—
223	C₃×C₄×C₅	#95	1	1	yes	characteristic
224	C₃×C₄×C₅	#95	1	1	yes	characteristic
225	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₃×Dic₅	#95	1	1	yes	characteristic
228	C₃×Dic₅	#95	1	1	yes	characteristic
229	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂⁴×C₃	—	5	1	no	—
232	C₂²×C₃×C₄	—	5	1	no	—
233	C₂²×C₃×C₄	—	5	1	no	—
234	C₂²×C₃×C₄	—	5	1	no	—
235	C₂²×C₃×C₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	5	1	no	—
237	C₂²×C₃×C₄	—	5	1	no	—
238	C₂²×C₃×C₄	—	5	1	no	—
239	C₂²×C₃×C₄	—	5	1	no	—
240	C₂²×C₃×C₄	—	5	1	no	—
241	C₂²×C₃×C₄	—	5	1	no	—
242	C₂²×C₃×C₄	—	5	1	no	—
243	C₂²×C₃×C₄	—	5	1	no	—
244	C₂²×C₃×C₄	—	5	1	no	—
245	C₂²×C₃×C₄	—	5	4	no	—
246	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
247	C₃×M₁₆	—	2	1	no	—
248	C₃×M₁₆	—	5	4	no	—
249	C₃×M₁₆	—	5	2	no	—
250	C₃×M₁₆	—	10	2	no	—
251	C₃×M₁₆	—	10	2	no	—
252	C₃×M₁₆	—	10	2	no	—
253	C₃×M₁₆	—	10	2	no	—
254	C₃×M₁₆	—	10	2	no	—
255	C₃×M₁₆	—	10	1	no	—
256	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	—
257	C₂×C₃×C₈	—	2	1	no	—
258	C₂×C₃×C₈	—	10	2	no	—
259	C₂×C₃×C₈	—	10	2	no	—
260	C₂×C₃×C₈	—	10	2	no	—
261	C₂×C₃×C₈	—	10	2	no	—
262	C₂×C₃×C₈	—	10	2	no	—
263	C₂×C₃×C₈	—	10	1	no	—
264	C₃×C₄⋊C₄	—	10	2	no	—
265	C₃×C₄⋊C₄	—	10	2	no	—
266	C₃×C₂²⋊C₄	—	10	2	no	—
267	C₃×C₂²⋊C₄	—	10	2	no	—
268	C₃×C₄²	—	10	2	no	—
269	C₃×C₄²	—	10	2	no	—
270	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
271	C₂²×D₅	—	4	2	no	—
272	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
273	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
276	C₂²×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
277	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
278	C₂×AGL(1,𝔽₅)	—	2	4	no	—
279	C₂×AGL(1,𝔽₅)	—	4	4	no	—
280	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
281	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
286	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
287	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
290	C₂×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
291	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
292	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
294	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
295	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
296	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
298	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
299	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
300	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
301	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
302	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
303	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
304	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
306	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
307	C₄×D₅	C₂×C₃×Q₈	1	1	yes	characteristic
308	#170	—	2	4	no	—
309	C₅×C₈	—	2	2	no	—
310	#168	—	2	2	no	—
311	C₂³×C₄	—	5	1	no	—
312	C₂×M₁₆	—	5	2	no	—
313	C₂×M₁₆	—	5	2	no	—
314	C₂×M₁₆	—	5	2	no	—
315	C₂×M₁₆	—	5	1	no	—
316	C₂×M₁₆	—	5	2	no	—
317	C₂×M₁₆	—	5	2	no	—
318	C₂×M₁₆	—	10	1	no	—
319	C₂×M₁₆	—	10	1	no	—
320	C₂×M₁₆	—	10	1	no	—
321	C₂×M₁₆	—	10	1	no	—
322	C₂×M₁₆	—	10	1	no	—
323	C₂×M₁₆	—	10	1	no	—
324	C₂×M₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
325	C₂²×C₈	—	10	1	no	—
326	C₂²×C₈	—	10	1	no	—
327	#117	—	10	1	no	—
328	#117	—	10	1	no	—
329	#117	—	10	1	no	—
330	#117	—	10	1	no	—
331	C₂×C₄⋊C₄	—	5	2	no	—
332	C₂×C₂²⋊C₄	—	5	2	no	—
333	C₂×C₄²	—	5	2	no	—
334	C₂×C₃×C₅	—	2	1	no	—
335	C₂×C₃×C₅	—	2	1	no	—
336	C₂×C₃×C₅	—	2	1	no	—
337	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
338	C₃×D₅	—	2	1	no	—
339	C₃×D₅	—	2	1	no	—
340	C₃×D₅	—	2	1	no	—
341	C₃×D₅	#413	1	2	yes	—
342	C₂³×C₃	—	5	1	no	—
343	C₂³×C₃	—	5	1	no	—
344	C₂³×C₃	—	5	1	no	—
345	C₂³×C₃	—	5	1	no	—
346	C₂³×C₃	—	5	1	no	—
347	C₂³×C₃	—	5	1	no	—
348	C₂³×C₃	—	20	2	no	—
349	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₂×C₃×C₄	—	5	1	no	—
351	C₂×C₃×C₄	—	5	1	no	—
352	C₂×C₃×C₄	—	5	1	no	—
353	C₂×C₃×C₄	—	5	1	no	—
354	C₂×C₃×C₄	—	5	1	no	—
355	C₂×C₃×C₄	—	5	1	no	—
356	C₂×C₃×C₄	—	5	1	no	—
357	C₂×C₃×C₄	—	5	1	no	—
358	C₂×C₃×C₄	—	5	1	no	—
359	C₂×C₃×C₄	—	5	1	no	—
360	C₂×C₃×C₄	—	5	1	no	—
361	C₂×C₃×C₄	—	5	1	no	—
362	C₂×C₃×C₄	—	5	1	no	—
363	C₂×C₃×C₄	—	5	1	no	—
364	C₂×C₃×C₄	—	5	1	no	—
365	C₂×C₃×C₄	—	5	1	no	—
366	C₂×C₃×C₄	—	5	1	no	—
367	C₂×C₃×C₄	—	5	1	no	—
368	C₂×C₃×C₄	—	5	1	no	—
369	C₂×C₃×C₄	—	5	1	no	—
370	C₂×C₃×C₄	—	5	1	no	—
371	C₂×C₃×C₄	—	5	1	no	—
372	C₂×C₃×C₄	—	10	4	no	—
373	C₂×C₃×C₄	—	20	4	no	—
374	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
376	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
380	C₃×C₈	—	2	2	no	—
381	C₃×C₈	—	10	4	no	—
382	C₃×C₈	—	10	2	no	—
383	C₂²×C₅	—	4	1	no	—
384	C₂²×C₅	C₃×#95	1	1	yes	characteristic
385	C₂²×C₅	C₃×#95	1	1	yes	characteristic
386	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
387	C₂×D₅	—	2	2	no	—
388	C₂×D₅	—	2	2	no	—
389	C₂×D₅	—	2	2	no	—
390	C₂×D₅	—	4	1	no	—
391	C₂×D₅	—	4	1	no	—
392	C₂×D₅	—	4	1	no	—
393	C₂×D₅	C₃×#95	1	1	yes	characteristic
394	C₂×D₅	C₃×#95	1	1	yes	characteristic
395	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×D₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
397	AGL(1,𝔽₅)	—	4	4	no	—
398	C₄×C₅	C₃×#95	1	1	yes	characteristic
399	C₄×C₅	C₃×#95	1	1	yes	characteristic
400	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
401	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
402	Dic₅	C₃×#95	1	1	yes	characteristic
403	Dic₅	C₃×#95	1	1	yes	characteristic
404	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
405	Dic₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
406	C₂⁴	—	5	1	no	—
407	C₂²×C₄	—	5	1	no	—
408	C₂²×C₄	—	5	1	no	—
409	C₂²×C₄	—	5	1	no	—
410	C₂²×C₄	—	5	1	no	—
411	C₂²×C₄	—	5	1	no	—
412	C₂²×C₄	—	5	1	no	—
413	C₂²×C₄	—	5	1	no	—
414	C₂²×C₄	—	5	1	no	—
415	C₂²×C₄	—	5	1	no	—
416	C₂²×C₄	—	5	1	no	—
417	C₂²×C₄	—	5	1	no	—
418	C₂²×C₄	—	5	1	no	—
419	C₂²×C₄	—	5	1	no	—
420	C₂²×C₄	—	5	4	no	—
421	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
422	M₁₆	—	2	1	no	—
423	M₁₆	—	5	4	no	—
424	M₁₆	—	5	2	no	—
425	M₁₆	—	10	2	no	—
426	M₁₆	—	10	2	no	—
427	M₁₆	—	10	2	no	—
428	M₁₆	—	10	2	no	—
429	M₁₆	—	10	2	no	—
430	M₁₆	—	10	1	no	—
431	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	10	2	no	—
434	C₂×C₈	—	10	2	no	—
435	C₂×C₈	—	10	2	no	—
436	C₂×C₈	—	10	2	no	—
437	C₂×C₈	—	10	2	no	—
438	C₂×C₈	—	10	1	no	—
439	C₄⋊C₄	—	10	2	no	—
440	C₄⋊C₄	—	10	2	no	—
441	C₂²⋊C₄	—	10	2	no	—
442	C₂²⋊C₄	—	10	2	no	—
443	C₄²	—	10	2	no	—
444	C₄²	—	10	2	no	—
445	C₃×C₅	#1742	1	1	yes	characteristic, complemented, Hall
446	C₂²×C₃	—	4	1	no	—
447	C₂²×C₃	—	5	1	no	—
448	C₂²×C₃	—	5	1	no	—
449	C₂²×C₃	—	5	1	no	—
450	C₂²×C₃	—	5	1	no	—
451	C₂²×C₃	—	10	2	no	—
452	C₂²×C₃	—	10	2	no	—
453	C₂²×C₃	—	10	2	no	—
454	C₂²×C₃	—	20	1	no	—
455	C₂²×C₃	—	20	1	no	—
456	C₂²×C₃	—	20	1	no	—
457	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
458	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
459	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
460	C₃×C₄	—	5	1	no	—
461	C₃×C₄	—	5	1	no	—
462	C₃×C₄	—	5	1	no	—
463	C₃×C₄	—	5	1	no	—
464	C₃×C₄	—	20	4	no	—
465	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
466	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
467	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
468	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
469	C₂×C₅	—	2	1	no	—
470	C₂×C₅	—	2	1	no	—
471	C₂×C₅	—	2	1	no	—
472	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
473	D₅	—	2	1	no	—
474	D₅	—	2	1	no	—
475	D₅	—	2	1	no	—
476	D₅	C₃×#413	1	2	yes	—
477	C₂³	—	5	1	no	—
478	C₂³	—	5	1	no	—
479	C₂³	—	5	1	no	—
480	C₂³	—	5	1	no	—
481	C₂³	—	5	1	no	—
482	C₂³	—	5	1	no	—
483	C₂³	—	20	2	no	—
484	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
485	C₂×C₄	—	5	1	no	—
486	C₂×C₄	—	5	1	no	—
487	C₂×C₄	—	5	1	no	—
488	C₂×C₄	—	5	1	no	—
489	C₂×C₄	—	5	1	no	—
490	C₂×C₄	—	5	1	no	—
491	C₂×C₄	—	5	1	no	—
492	C₂×C₄	—	5	1	no	—
493	C₂×C₄	—	5	1	no	—
494	C₂×C₄	—	5	1	no	—
495	C₂×C₄	—	5	1	no	—
496	C₂×C₄	—	5	1	no	—
497	C₂×C₄	—	5	1	no	—
498	C₂×C₄	—	5	1	no	—
499	C₂×C₄	—	5	1	no	—
500	C₂×C₄	—	5	1	no	—
501	C₂×C₄	—	5	1	no	—
502	C₂×C₄	—	5	1	no	—
503	C₂×C₄	—	5	1	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	1	no	—
506	C₂×C₄	—	5	1	no	—
507	C₂×C₄	—	10	4	no	—
508	C₂×C₄	—	20	4	no	—
509	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
510	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
511	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
512	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
513	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	10	4	no	—
517	C₈	—	10	2	no	—
518	C₂×C₃	—	2	1	no	—
519	C₂×C₃	—	2	1	no	—
520	C₂×C₃	—	2	1	no	—
521	C₂×C₃	—	5	2	no	—
522	C₂×C₃	—	10	1	no	—
523	C₂×C₃	—	10	1	no	—
524	C₂×C₃	—	10	1	no	—
525	C₂×C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
526	C₅	C₃×#1742	1	1	yes	characteristic, complemented, Sylow
527	C₂²	—	4	1	no	—
528	C₂²	—	5	1	no	—
529	C₂²	—	5	1	no	—
530	C₂²	—	5	1	no	—
531	C₂²	—	5	1	no	—
532	C₂²	—	10	2	no	—
533	C₂²	—	10	2	no	—
534	C₂²	—	10	2	no	—
535	C₂²	—	20	1	no	—
536	C₂²	—	20	1	no	—
537	C₂²	—	20	1	no	—
538	C₂²	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
539	C₂²	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
540	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
541	C₄	—	5	1	no	—
542	C₄	—	5	1	no	—
543	C₄	—	5	1	no	—
544	C₄	—	5	1	no	—
545	C₄	—	20	4	no	—
546	C₄	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
547	C₄	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
548	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
549	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
550	C₃	#10604760	1	1	yes	characteristic, direct product factor, Sylow
551	C₂	—	2	1	no	—
552	C₂	—	2	1	no	—
553	C₂	—	2	1	no	—
554	C₂	—	5	2	no	—
555	C₂	—	10	1	no	—
556	C₂	—	10	1	no	—
557	C₂	—	10	1	no	—
558	C₂	C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×M₁₆	C₄
socle	C₂×C₃×C₅	C₂×#95
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₂×C₃×M₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1742
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₃×#64899	C₂	semidirect
5. #10604760	C₃	direct (N × H)
8. C₂×C₃×#704	C₄	semidirect
17. C₃×D₅⋊M₁₆	C₄	semidirect
21. C₂×C₃×C₅×M₁₆	C₄	semidirect
22. C₂×C₃×#681	C₄	semidirect
25. C₃×D₅×M₁₆	C₄	semidirect
33. #64899	C₂×C₃	semidirect
79. C₂×#704	C₃×C₄	semidirect
88. D₅⋊M₁₆	C₃×C₄	semidirect
92. C₂×C₅×M₁₆	C₃×C₄	semidirect
93. C₂×#681	C₃×C₄	semidirect
96. D₅×M₁₆	C₃×C₄	semidirect
155. C₂×C₃×M₁₆	AGL(1,𝔽₅)	semidirect
324. C₂×M₁₆	C₃×AGL(1,𝔽₅)	semidirect
445. C₃×C₅	#1742	semidirect
526. C₅	C₃×#1742	semidirect
550. C₃	#10604760	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
C₂×C₃×D₅×M₁₆	2
C₃×#64899	2
#10604760	3
C₃×#1742	5

Subgroups — C3×#10604760 #14294782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604760 #14294782