Subgroups — C₂×C₃×#64899 #14294751

Order 1920.

864 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₃	(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	C₂²×C₃×C₅	#95
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₂×C₃×M₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#343
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ 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	direct (N × H)
5. C₂×#64899	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	direct (N × H)
54. C₃×#704	C₂×C₄	semidirect
65. C₃×C₅×M₁₆	C₂×C₄	semidirect
68. C₃×#681	C₂×C₄	semidirect
80. C₂×#704	C₃×C₄	semidirect
89. D₅⋊M₁₆	C₃×C₄	semidirect
93. C₂×C₅×M₁₆	C₃×C₄	semidirect
94. C₂×#681	C₃×C₄	semidirect
97. D₅×M₁₆	C₃×C₄	semidirect
160. C₂×C₃×M₁₆	AGL(1,𝔽₅)	semidirect
189. #704	C₂×C₃×C₄	semidirect
200. C₅×M₁₆	C₂×C₃×C₄	semidirect
203. #681	C₂×C₃×C₄	semidirect
267. C₃×M₁₆	C₂×AGL(1,𝔽₅)	semidirect
337. C₂×M₁₆	C₃×AGL(1,𝔽₅)	semidirect
348. C₂×C₃×C₅	#343	semidirect
352. C₃×D₅	#343	semidirect
453. M₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
465. C₃×C₅	C₂×#343	semidirect
494. C₂×C₅	C₃×#343	semidirect
498. D₅	C₃×#343	semidirect
552. C₂×C₃	#64899	direct (N × H)
554. C₅	C₂×C₃×#343	semidirect
581. C₃	C₂×#64899	direct (N × H)
589. C₂	C₃×#64899	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄⋊AGL(1,𝔽₅)	2
C₂×C₃×D₅⋊M₁₆	2
C₂×C₃×D₅×M₁₆	2
C₃×#64899	2
C₂×#64899	3
C₂×C₃×#343	5

Subgroups — C2×C3×#64899 #14294751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64899 #14294751