Subgroups — C₂×C₃×#64776 #14294811

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic
4	C₃×#64776	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64776	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₅×M₁₆	—	2	1	no	—
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂×C₃×C₅×M₁₆	—	2	1	no	—
10	C₂×C₃×C₅×M₁₆	—	2	1	no	—
11	C₂×C₃×C₅×M₁₆	C₄	1	2	yes	complemented
12	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×C₈	C₄	1	2	yes	complemented
14	C₂×C₃×C₂²⋊Dic₅	C₄	1	2	yes	—
15	C₃×#4072	—	2	1	no	—
16	C₃×#4072	—	2	1	no	—
17	C₃×#4072	C₄	1	2	yes	—
18	C₃×#4072	C₂²	1	2	yes	—
19	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
20	C₂×C₃×C₄×Dic₅	—	2	1	no	—
21	C₂×C₃×#681	—	2	1	no	—
22	C₂×C₃×#681	—	2	1	no	—
23	C₂×C₃×#681	—	2	1	no	—
24	C₂×C₃×#681	C₄	1	2	yes	complemented
25	C₂×C₃×#681	C₄	1	2	yes	complemented
26	C₂×C₃×#681	C₂²	1	2	yes	—
27	C₂²×C₃×#168	—	2	1	no	—
28	C₂×C₃×#344	—	5	1	no	maximal, Hall
29	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
30	C₂×#4072	C₂×C₃	1	1	yes	characteristic
31	C₂²×#681	C₂×C₃	1	1	yes	characteristic
32	#64776	C₂×C₃	1	4	yes	direct product factor
33	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	Q₈	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	Q₈	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	—	2	2	no	—
49	C₃×C₅×M₁₆	—	2	2	no	—
50	C₃×C₅×M₁₆	—	2	2	no	—
51	C₃×C₅×M₁₆	—	2	2	no	—
52	C₃×C₅×M₁₆	—	2	2	no	—
53	C₂×C₃×C₅×C₈	—	2	2	no	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
56	C₃×C₂²⋊Dic₅	—	2	2	no	—
57	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
58	C₃×C₄⋊Dic₅	—	2	2	no	—
59	C₃×C₄⋊Dic₅	—	2	2	no	—
60	C₃×C₄×Dic₅	—	2	2	no	—
61	C₃×C₄×Dic₅	—	2	2	no	—
62	C₃×#681	—	2	2	no	—
63	C₃×#681	—	2	2	no	—
64	C₃×#681	—	2	2	no	—
65	C₃×#681	C₂×C₄	1	4	yes	complemented
66	C₂×C₃×#168	—	2	2	no	—
67	C₂×C₃×#168	—	2	2	no	—
68	C₂×C₃×#168	—	2	2	no	—
69	C₂²×C₃×M₁₆	—	5	1	no	—
70	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic
71	C₂×C₃×#117	—	5	1	no	—
72	C₃×#344	—	5	4	no	—
73	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	1	no	—
78	C₂×C₅×M₁₆	C₃×C₄	1	2	yes	complemented
79	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
80	C₂²×C₅×C₈	C₃×C₄	1	2	yes	complemented
81	C₂×C₂²⋊Dic₅	C₃×C₄	1	2	yes	—
82	#4072	—	2	1	no	—
83	#4072	—	2	1	no	—
84	#4072	C₃×C₄	1	2	yes	—
85	#4072	C₂²×C₃	1	2	yes	—
86	C₂×C₄⋊Dic₅	—	2	1	no	—
87	C₂×C₄×Dic₅	—	2	1	no	—
88	C₂×#681	—	2	1	no	—
89	C₂×#681	—	2	1	no	—
90	C₂×#681	—	2	1	no	—
91	C₂×#681	C₃×C₄	1	2	yes	complemented
92	C₂×#681	C₃×C₄	1	2	yes	complemented
93	C₂×#681	C₂²×C₃	1	2	yes	—
94	C₂²×#168	—	2	1	no	—
95	C₂×#344	—	5	1	no	Sylow
96	C₂³×C₃×C₅	—	4	2	no	—
97	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
98	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
99	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
102	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
103	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂²⋊C₄	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	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₄⋊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	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
132	C₂×C₃×Dic₅	—	2	4	no	—
133	C₂×C₃×Dic₅	—	4	4	no	—
134	C₃×C₅×C₈	—	2	4	no	—
135	C₃×#168	—	2	4	no	—
136	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
137	C₂×C₃×M₁₆	—	2	1	no	—
138	C₂×C₃×M₁₆	—	2	1	no	—
139	C₂×C₃×M₁₆	—	2	1	no	—
140	C₂×C₃×M₁₆	—	2	1	no	—
141	C₂×C₃×M₁₆	—	5	2	no	—
142	C₂×C₃×M₁₆	—	5	2	no	—
143	C₂×C₃×M₁₆	—	5	2	no	—
144	C₂×C₃×M₁₆	—	10	1	no	—
145	C₂×C₃×M₁₆	—	10	1	no	—
146	C₂×C₃×M₁₆	—	10	1	no	—
147	C₂×C₃×M₁₆	Dic₅	1	2	yes	complemented
148	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
149	C₂²×C₃×C₈	—	10	1	no	—
150	C₂²×C₃×C₈	Dic₅	1	2	yes	complemented
151	C₃×#117	—	5	2	no	—
152	C₃×#117	—	5	2	no	—
153	C₃×#117	—	10	1	no	—
154	C₃×#117	—	10	1	no	—
155	C₂×C₃×C₄⋊C₄	—	10	1	no	—
156	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
157	C₂×C₃×C₄²	—	10	1	no	—
158	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₃×Q₈	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₃×Q₈	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
173	C₂²×Dic₅	—	2	2	no	—
174	C₅×M₁₆	—	2	2	no	—
175	C₅×M₁₆	—	2	2	no	—
176	C₅×M₁₆	—	2	2	no	—
177	C₅×M₁₆	—	2	2	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
181	C₂²⋊Dic₅	—	2	2	no	—
182	C₂²⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
183	C₄⋊Dic₅	—	2	2	no	—
184	C₄⋊Dic₅	—	2	2	no	—
185	C₄×Dic₅	—	2	2	no	—
186	C₄×Dic₅	—	2	2	no	—
187	#681	—	2	2	no	—
188	#681	—	2	2	no	—
189	#681	—	2	2	no	—
190	#681	C₂×C₃×C₄	1	4	yes	complemented
191	C₂×#168	—	2	2	no	—
192	C₂×#168	—	2	2	no	—
193	C₂×#168	—	2	2	no	—
194	C₂²×M₁₆	—	5	1	no	—
195	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic
196	C₂×#117	—	5	1	no	—
197	#344	—	5	4	no	—
198	C₂²×C₃×C₅	—	2	2	no	—
199	C₂²×C₃×C₅	—	2	2	no	—
200	C₂²×C₃×C₅	—	2	2	no	—
201	C₂²×C₃×C₅	—	4	1	no	—
202	C₂²×C₃×C₅	—	4	1	no	—
203	C₂²×C₃×C₅	—	4	1	no	—
204	C₂²×C₃×C₅	—	4	1	no	—
205	C₂²×C₃×C₅	#95	1	1	yes	characteristic
206	C₂²×C₃×C₅	#95	1	1	yes	characteristic
207	C₂²×C₃×C₅	#95	1	1	yes	characteristic
208	C₂²×C₃×C₅	#95	1	1	yes	characteristic
209	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
210	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₃×C₄×C₅	#95	1	1	yes	characteristic
213	C₃×C₄×C₅	#95	1	1	yes	characteristic
214	C₃×C₄×C₅	#95	1	1	yes	characteristic
215	C₃×C₄×C₅	#95	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₃×Dic₅	—	4	4	no	—
221	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	—	10	2	no	—
223	C₂²×C₃×C₄	Dic₁₀	1	1	yes	characteristic
224	C₂²×C₃×C₄	Dic₁₀	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
228	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
229	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
237	C₃×M₁₆	—	2	2	no	—
238	C₃×M₁₆	—	2	2	no	—
239	C₃×M₁₆	—	2	2	no	—
240	C₃×M₁₆	—	2	2	no	—
241	C₃×M₁₆	—	5	4	no	—
242	C₃×M₁₆	—	10	2	no	—
243	C₃×M₁₆	—	10	2	no	—
244	C₃×M₁₆	—	10	2	no	—
245	C₂×C₃×C₈	—	2	2	no	—
246	C₂×C₃×C₈	—	2	2	no	—
247	C₂×C₃×C₈	—	10	2	no	—
248	C₂×C₃×C₈	—	10	2	no	—
249	C₂×C₃×C₈	—	10	2	no	—
250	C₂×C₃×C₈	C₂×Dic₅	1	4	yes	complemented
251	C₃×C₄⋊C₄	—	10	2	no	—
252	C₃×C₄⋊C₄	—	10	2	no	—
253	C₃×C₂²⋊C₄	—	5	4	no	—
254	C₃×C₂²⋊C₄	—	10	2	no	—
255	C₃×C₄²	—	10	2	no	—
256	C₃×C₄²	—	10	2	no	—
257	C₂³×C₅	—	4	2	no	—
258	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
259	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
260	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
261	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
262	C₂³×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
263	C₂³×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
264	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
266	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
267	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₃×C₄⋊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	C₃×C₄⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
293	C₂×Dic₅	—	2	4	no	—
294	C₂×Dic₅	—	4	4	no	—
295	C₅×C₈	—	2	4	no	—
296	#168	—	2	4	no	—
297	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	5	2	no	—
303	C₂×M₁₆	—	5	2	no	—
304	C₂×M₁₆	—	5	2	no	—
305	C₂×M₁₆	—	10	1	no	—
306	C₂×M₁₆	—	10	1	no	—
307	C₂×M₁₆	—	10	1	no	—
308	C₂×M₁₆	C₃×Dic₅	1	2	yes	complemented
309	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
310	C₂²×C₈	—	10	1	no	—
311	C₂²×C₈	C₃×Dic₅	1	2	yes	complemented
312	#117	—	5	2	no	—
313	#117	—	5	2	no	—
314	#117	—	10	1	no	—
315	#117	—	10	1	no	—
316	C₂×C₄⋊C₄	—	10	1	no	—
317	C₂×C₂²⋊C₄	—	5	2	no	—
318	C₂×C₄²	—	10	1	no	—
319	C₂×C₃×C₅	—	2	1	no	—
320	C₂×C₃×C₅	—	2	1	no	—
321	C₂×C₃×C₅	—	2	1	no	—
322	C₂×C₃×C₅	—	2	1	no	—
323	C₂×C₃×C₅	—	2	1	no	—
324	C₂×C₃×C₅	—	2	1	no	—
325	C₂×C₃×C₅	#344	1	2	yes	complemented
326	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
327	C₂³×C₃	—	4	2	no	—
328	C₂³×C₃	C₄×Dic₅	1	1	yes	characteristic
329	C₂³×C₃	C₄×Dic₅	1	1	yes	characteristic
330	C₂³×C₃	#683	1	1	yes	characteristic
331	C₂³×C₃	#683	1	1	yes	characteristic
332	C₂³×C₃	#685	1	1	yes	characteristic
333	C₂³×C₃	#685	1	1	yes	characteristic
334	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
335	C₂×C₃×C₄	—	10	4	no	—
336	C₂×C₃×C₄	—	20	4	no	—
337	C₂×C₃×C₄	C₄×Dic₅	1	1	yes	characteristic
338	C₂×C₃×C₄	C₄×Dic₅	1	1	yes	characteristic
339	C₂×C₃×C₄	#683	1	1	yes	characteristic
340	C₂×C₃×C₄	#683	1	1	yes	characteristic
341	C₂×C₃×C₄	#683	1	1	yes	characteristic
342	C₂×C₃×C₄	#683	1	1	yes	characteristic
343	C₂×C₃×C₄	#683	1	1	yes	characteristic
344	C₂×C₃×C₄	#683	1	1	yes	characteristic
345	C₂×C₃×C₄	C₄⋊Dic₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₄⋊Dic₅	1	1	yes	characteristic
347	C₂×C₃×C₄	C₄⋊Dic₅	1	1	yes	characteristic
348	C₂×C₃×C₄	C₄⋊Dic₅	1	1	yes	characteristic
349	C₂×C₃×C₄	#685	1	1	yes	characteristic
350	C₂×C₃×C₄	#685	1	1	yes	characteristic
351	C₂×C₃×C₄	#685	1	1	yes	characteristic
352	C₂×C₃×C₄	#685	1	1	yes	characteristic
353	C₂×C₃×C₄	#685	1	1	yes	characteristic
354	C₂×C₃×C₄	#685	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
361	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
365	C₃×C₈	—	2	4	no	—
366	C₃×C₈	—	10	4	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	—	4	1	no	—
371	C₂²×C₅	—	4	1	no	—
372	C₂²×C₅	—	4	1	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	C₃×#95	1	1	yes	characteristic
375	C₂²×C₅	C₃×#95	1	1	yes	characteristic
376	C₂²×C₅	C₃×#95	1	1	yes	characteristic
377	C₂²×C₅	C₃×#95	1	1	yes	characteristic
378	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
379	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
381	C₄×C₅	C₃×#95	1	1	yes	characteristic
382	C₄×C₅	C₃×#95	1	1	yes	characteristic
383	C₄×C₅	C₃×#95	1	1	yes	characteristic
384	C₄×C₅	C₃×#95	1	1	yes	characteristic
385	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
386	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
387	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
388	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
389	Dic₅	—	4	4	no	—
390	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
391	C₂²×C₄	—	10	2	no	—
392	C₂²×C₄	C₃×Dic₁₀	1	1	yes	characteristic
393	C₂²×C₄	C₃×Dic₁₀	1	1	yes	characteristic
394	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
395	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
396	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
397	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
398	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
400	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
401	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
402	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
403	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
404	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	5	4	no	—
411	M₁₆	—	10	2	no	—
412	M₁₆	—	10	2	no	—
413	M₁₆	—	10	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	10	2	no	—
417	C₂×C₈	—	10	2	no	—
418	C₂×C₈	—	10	2	no	—
419	C₂×C₈	C₂×C₃×Dic₅	1	4	yes	complemented
420	C₄⋊C₄	—	10	2	no	—
421	C₄⋊C₄	—	10	2	no	—
422	C₂²⋊C₄	—	5	4	no	—
423	C₂²⋊C₄	—	10	2	no	—
424	C₄²	—	10	2	no	—
425	C₄²	—	10	2	no	—
426	C₃×C₅	C₂×#344	1	1	yes	characteristic, complemented, Hall
427	C₂²×C₃	—	2	2	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	2	2	no	—
430	C₂²×C₃	—	4	1	no	—
431	C₂²×C₃	—	4	1	no	—
432	C₂²×C₃	—	4	1	no	—
433	C₂²×C₃	—	4	1	no	—
434	C₂²×C₃	#3963	1	1	yes	characteristic
435	C₂²×C₃	#3963	1	1	yes	characteristic
436	C₂²×C₃	#3963	1	1	yes	characteristic
437	C₂²×C₃	#3963	1	1	yes	characteristic
438	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
439	C₂²×C₃	C₂×#683	1	1	yes	characteristic
440	C₂²×C₃	C₂×#685	1	1	yes	characteristic
441	C₃×C₄	—	20	4	no	—
442	C₃×C₄	#3963	1	1	yes	characteristic
443	C₃×C₄	#3963	1	1	yes	characteristic
444	C₃×C₄	#3963	1	1	yes	characteristic
445	C₃×C₄	#3963	1	1	yes	characteristic
446	C₃×C₄	C₂×#683	1	1	yes	characteristic
447	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
448	C₃×C₄	C₂×#685	1	1	yes	characteristic
449	C₃×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
450	C₂×C₅	—	2	1	no	—
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	2	1	no	—
454	C₂×C₅	—	2	1	no	—
455	C₂×C₅	—	2	1	no	—
456	C₂×C₅	C₃×#344	1	2	yes	complemented
457	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
458	C₂³	—	4	2	no	—
459	C₂³	C₃×C₄×Dic₅	1	1	yes	characteristic
460	C₂³	C₃×C₄×Dic₅	1	1	yes	characteristic
461	C₂³	C₃×#683	1	1	yes	characteristic
462	C₂³	C₃×#683	1	1	yes	characteristic
463	C₂³	C₃×#685	1	1	yes	characteristic
464	C₂³	C₃×#685	1	1	yes	characteristic
465	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
466	C₂×C₄	—	10	4	no	—
467	C₂×C₄	—	20	4	no	—
468	C₂×C₄	C₃×C₄×Dic₅	1	1	yes	characteristic
469	C₂×C₄	C₃×C₄×Dic₅	1	1	yes	characteristic
470	C₂×C₄	C₃×#683	1	1	yes	characteristic
471	C₂×C₄	C₃×#683	1	1	yes	characteristic
472	C₂×C₄	C₃×#683	1	1	yes	characteristic
473	C₂×C₄	C₃×#683	1	1	yes	characteristic
474	C₂×C₄	C₃×#683	1	1	yes	characteristic
475	C₂×C₄	C₃×#683	1	1	yes	characteristic
476	C₂×C₄	C₃×C₄⋊Dic₅	1	1	yes	characteristic
477	C₂×C₄	C₃×C₄⋊Dic₅	1	1	yes	characteristic
478	C₂×C₄	C₃×C₄⋊Dic₅	1	1	yes	characteristic
479	C₂×C₄	C₃×C₄⋊Dic₅	1	1	yes	characteristic
480	C₂×C₄	C₃×#685	1	1	yes	characteristic
481	C₂×C₄	C₃×#685	1	1	yes	characteristic
482	C₂×C₄	C₃×#685	1	1	yes	characteristic
483	C₂×C₄	C₃×#685	1	1	yes	characteristic
484	C₂×C₄	C₃×#685	1	1	yes	characteristic
485	C₂×C₄	C₃×#685	1	1	yes	characteristic
486	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
487	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
488	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
489	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
490	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
491	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
492	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
493	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
494	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
495	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
496	C₈	—	2	4	no	—
497	C₈	—	10	4	no	—
498	C₂×C₃	—	2	1	no	—
499	C₂×C₃	—	2	1	no	—
500	C₂×C₃	—	2	1	no	—
501	C₂×C₃	—	2	1	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	#64776	1	2	yes	direct product factor
505	C₂×C₃	C₂×#3963	1	1	yes	characteristic
506	C₅	C₂×C₃×#344	1	1	yes	characteristic, complemented, Sylow
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	C₃×#3963	1	1	yes	characteristic
515	C₂²	C₃×#3963	1	1	yes	characteristic
516	C₂²	C₃×#3963	1	1	yes	characteristic
517	C₂²	C₃×#3963	1	1	yes	characteristic
518	C₂²	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
519	C₂²	C₂×C₃×#683	1	1	yes	characteristic
520	C₂²	C₂×C₃×#685	1	1	yes	characteristic
521	C₄	—	20	4	no	—
522	C₄	C₃×#3963	1	1	yes	characteristic
523	C₄	C₃×#3963	1	1	yes	characteristic
524	C₄	C₃×#3963	1	1	yes	characteristic
525	C₄	C₃×#3963	1	1	yes	characteristic
526	C₄	C₂×C₃×#683	1	1	yes	characteristic
527	C₄	C₂×C₃×C₄⋊Dic₅	1	1	yes	characteristic
528	C₄	C₂×C₃×#685	1	1	yes	characteristic
529	C₄	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
530	C₃	C₂×#64776	1	1	yes	characteristic, direct product factor, Sylow
531	C₂	—	2	1	no	—
532	C₂	—	2	1	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	1	no	—
535	C₂	—	2	1	no	—
536	C₂	—	2	1	no	—
537	C₂	C₃×#64776	1	2	yes	direct product factor
538	C₂	C₂×C₃×#3963	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²⋊Dic₅
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	#95
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₂×C₃×#344
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₃×#64776	C₂	direct (N × H)
5. C₂×#64776	C₃	direct (N × H)
11. C₂×C₃×C₅×M₁₆	C₄	semidirect
13. C₂²×C₃×C₅×C₈	C₄	semidirect
24. C₂×C₃×#681	C₄	semidirect
25. C₂×C₃×#681	C₄	semidirect
32. #64776	C₂×C₃	direct (N × H)
55. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
65. C₃×#681	C₂×C₄	semidirect
78. C₂×C₅×M₁₆	C₃×C₄	semidirect
80. C₂²×C₅×C₈	C₃×C₄	semidirect
91. C₂×#681	C₃×C₄	semidirect
92. C₂×#681	C₃×C₄	semidirect
147. C₂×C₃×M₁₆	Dic₅	semidirect
150. C₂²×C₃×C₈	Dic₅	semidirect
180. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
190. #681	C₂×C₃×C₄	semidirect
250. C₂×C₃×C₈	C₂×Dic₅	semidirect
308. C₂×M₁₆	C₃×Dic₅	semidirect
311. C₂²×C₈	C₃×Dic₅	semidirect
325. C₂×C₃×C₅	#344	semidirect
419. C₂×C₈	C₂×C₃×Dic₅	semidirect
426. C₃×C₅	C₂×#344	semidirect
456. C₂×C₅	C₃×#344	semidirect
504. C₂×C₃	#64776	direct (N × H)
506. C₅	C₂×C₃×#344	semidirect
530. C₃	C₂×#64776	direct (N × H)
537. C₂	C₃×#64776	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×C₅×M₁₆	2
C₂×C₃×#4072	2
C₂²×C₃×#681	2
C₃×#64776	2
C₂×#64776	3
C₂×C₃×#344	5

Subgroups — C2×C3×#64776 #14294811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64776 #14294811