Subgroups — C₃×D₄×#681 #14415685

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#681	C₂	1	2	yes	maximal, complemented
3	C₃×#65496	C₂	1	2	yes	maximal, complemented
4	C₃×#65301	C₂	1	2	yes	maximal, complemented
5	C₃×#65300	C₂	1	4	yes	maximal, complemented
6	C₃×D₄×#168	C₂	1	2	yes	maximal, complemented
7	C₃×#65213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×#681	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₄×C₅×D₄	C₄	1	2	yes	—
13	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×#681	—	2	8	no	—
22	C₂×C₃×#681	C₂²	1	2	yes	—
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic
24	C₂×C₃×#681	C₂²	1	1	yes	characteristic
25	C₂×C₃×#681	C₂²	1	4	yes	complemented
26	C₂²×C₃×#168	C₂²	1	4	yes	complemented
27	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
28	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
29	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
30	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
31	C₃×#3935	C₂²	1	2	yes	complemented
32	C₃×C₄×#168	C₂²	1	2	yes	complemented
33	C₃×D₄×M₁₆	—	5	1	no	maximal, Hall
34	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
35	C₂²×#681	C₂×C₃	1	2	yes	complemented
36	#65496	C₂×C₃	1	2	yes	complemented
37	#65301	C₂×C₃	1	2	yes	complemented
38	#65300	C₂×C₃	1	4	yes	complemented
39	D₄×#168	C₂×C₃	1	2	yes	complemented
40	#65213	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₃×#681	—	2	4	no	—
69	C₃×#681	—	2	2	no	—
70	C₃×#681	—	2	8	no	—
71	C₃×#681	D₄	1	4	yes	direct product factor
72	C₂×C₃×#168	—	2	8	no	—
73	C₂×C₃×#168	C₂³	1	2	yes	—
74	C₂×C₃×#168	C₂³	1	4	yes	—
75	C₂×C₃×#168	C₂³	1	2	yes	—
76	C₂²×C₃×M₁₆	—	5	2	no	—
77	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic
78	C₃×#436	—	5	2	no	—
79	C₃×#435	—	5	4	no	—
80	C₃×C₈×D₄	—	5	2	no	—
81	C₃×#423	—	5	1	no	—
82	C₃×#407	—	5	2	no	—
83	C₃×C₄×M₁₆	—	5	1	no	—
84	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
86	C₄×C₅×D₄	C₃×C₄	1	2	yes	—
87	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
88	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
89	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
91	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	2	yes	—
94	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
95	C₂×#681	—	2	8	no	—
96	C₂×#681	C₂²×C₃	1	2	yes	—
97	C₂×#681	C₂²×C₃	1	1	yes	characteristic
98	C₂×#681	C₂²×C₃	1	1	yes	characteristic
99	C₂×#681	C₂²×C₃	1	4	yes	complemented
100	C₂²×#168	C₂²×C₃	1	4	yes	complemented
101	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
102	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
103	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
104	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
105	#3935	C₂²×C₃	1	2	yes	complemented
106	C₄×#168	C₂²×C₃	1	2	yes	complemented
107	D₄×M₁₆	—	5	1	no	Sylow
108	C₂³×C₃×C₅	—	2	4	no	—
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	4	2	no	—
111	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
112	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₃×C₅×D₄	—	2	4	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	M₁₆	1	4	yes	complemented
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	4	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₃×#168	—	2	4	no	—
137	C₃×#168	—	2	2	no	—
138	C₃×#168	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×D₄	Dic₅	1	1	yes	characteristic
140	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
141	C₂×C₃×M₁₆	—	5	1	no	—
142	C₂×C₃×M₁₆	—	5	2	no	—
143	C₂×C₃×M₁₆	—	5	4	no	—
144	C₂×C₃×M₁₆	—	5	1	no	—
145	C₂×C₃×M₁₆	—	10	8	no	—
146	C₂²×C₃×C₈	—	5	4	no	—
147	C₃×C₄×D₄	Dic₅	1	2	yes	—
148	C₃×C₄×D₄	Dic₅	1	1	yes	characteristic
149	C₃×C₄×D₄	Dic₅	1	1	yes	characteristic
150	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
151	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
152	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	Dic₅	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	Dic₅	1	2	yes	—
155	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
156	C₃×C₄⋊C₈	—	5	2	no	—
157	C₃×C₄⋊C₈	—	5	2	no	—
158	C₃×C₂²⋊C₈	—	5	4	no	—
159	C₃×C₂²⋊C₈	—	5	4	no	—
160	C₃×#97	—	5	2	no	—
161	C₃×C₄×C₈	—	5	2	no	—
162	C₂⁴×C₅	C₂×C₃×C₄	1	2	yes	—
163	C₂×C₅×D₄	—	2	4	no	—
164	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
165	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
171	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
172	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
173	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
178	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
179	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
180	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
182	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
183	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
184	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
185	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
186	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
188	#681	—	2	4	no	—
189	#681	—	2	2	no	—
190	#681	—	2	8	no	—
191	#681	C₃×D₄	1	4	yes	direct product factor
192	C₂×#168	—	2	8	no	—
193	C₂×#168	C₂³×C₃	1	2	yes	—
194	C₂×#168	C₂³×C₃	1	4	yes	—
195	C₂×#168	C₂³×C₃	1	2	yes	—
196	C₂²×M₁₆	—	5	2	no	—
197	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic
198	#436	—	5	2	no	—
199	#435	—	5	4	no	—
200	C₈×D₄	—	5	2	no	—
201	#423	—	5	1	no	—
202	#407	—	5	2	no	—
203	C₄×M₁₆	—	5	1	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	—	2	1	no	—
207	C₂²×C₃×C₅	—	2	2	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	2	no	—
211	C₂²×C₃×C₅	—	4	8	no	—
212	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
213	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
214	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	2	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	—	2	1	no	—
219	C₃×C₄×C₅	—	2	1	no	—
220	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
221	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
222	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
224	C₂⁴×C₃	C₂×Dic₅	1	2	yes	—
225	C₂×C₃×D₄	—	2	4	no	—
226	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
227	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
228	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	—	2	4	no	—
230	C₂²×C₃×C₄	—	2	4	no	—
231	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
233	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
234	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
235	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
237	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
238	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
239	C₃×M₁₆	—	5	4	no	—
240	C₃×M₁₆	—	10	8	no	—
241	C₃×M₁₆	—	10	4	no	—
242	C₃×M₁₆	—	10	2	no	—
243	C₂×C₃×C₈	—	5	2	no	—
244	C₂×C₃×C₈	—	5	2	no	—
245	C₂×C₃×C₈	—	5	4	no	—
246	C₂×C₃×C₈	—	10	8	no	—
247	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
248	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
249	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
250	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
251	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
252	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
253	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
254	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
255	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
256	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
257	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
258	C₂³×C₅	—	2	4	no	—
259	C₂³×C₅	—	2	4	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
264	C₅×D₄	—	2	4	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	C₃×M₁₆	1	4	yes	complemented
267	C₂×C₄×C₅	—	2	4	no	—
268	C₂×C₄×C₅	—	2	4	no	—
269	C₂×C₄×C₅	—	2	4	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	4	1	no	—
276	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
280	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
281	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
284	C₂×C₄×C₅	C₃×#41	1	2	yes	—
285	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
286	#168	—	2	4	no	—
287	#168	—	2	2	no	—
288	#168	C₂×C₃×D₄	1	4	yes	complemented
289	C₂²×D₄	C₃×Dic₅	1	1	yes	characteristic
290	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
291	C₂×M₁₆	—	5	1	no	—
292	C₂×M₁₆	—	5	2	no	—
293	C₂×M₁₆	—	5	4	no	—
294	C₂×M₁₆	—	5	1	no	—
295	C₂×M₁₆	—	10	8	no	—
296	C₂²×C₈	—	5	4	no	—
297	C₄×D₄	C₃×Dic₅	1	2	yes	—
298	C₄×D₄	C₃×Dic₅	1	1	yes	characteristic
299	C₄×D₄	C₃×Dic₅	1	1	yes	characteristic
300	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
301	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
302	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₃×Dic₅	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₃×Dic₅	1	2	yes	—
305	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
306	C₄⋊C₈	—	5	2	no	—
307	C₄⋊C₈	—	5	2	no	—
308	C₂²⋊C₈	—	5	4	no	—
309	C₂²⋊C₈	—	5	4	no	—
310	#97	—	5	2	no	—
311	C₄×C₈	—	5	2	no	—
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	—	2	4	no	—
314	C₂×C₃×C₅	—	4	2	no	—
315	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
317	C₂×C₃×C₅	#568	1	1	yes	characteristic
318	C₂³×C₃	—	2	4	no	—
319	C₂³×C₃	—	2	4	no	—
320	C₂³×C₃	—	4	2	no	—
321	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
322	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
323	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
324	C₃×D₄	—	2	4	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	#681	1	4	yes	direct product factor
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	4	no	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	4	1	no	—
336	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
337	C₂×C₃×C₄	#711	1	2	yes	—
338	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
342	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
343	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
346	C₃×C₈	—	5	4	no	—
347	C₃×C₈	—	10	4	no	—
348	C₃×C₈	—	10	2	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	2	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	2	no	—
356	C₂²×C₅	—	4	8	no	—
357	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
358	C₂²×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
359	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
366	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	complemented
367	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
368	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
369	C₂⁴	C₂×C₃×Dic₅	1	2	yes	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
372	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
373	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
378	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
379	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
380	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
382	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
383	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
384	M₁₆	—	5	4	no	—
385	M₁₆	—	10	8	no	—
386	M₁₆	—	10	4	no	—
387	M₁₆	—	10	2	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	5	4	no	—
391	C₂×C₈	—	10	8	no	—
392	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
393	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
394	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
395	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
396	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
397	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
398	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
399	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
400	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
401	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
402	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	2	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	4	8	no	—
412	C₂²×C₃	C₂×#681	1	4	yes	complemented
413	C₂²×C₃	D₄×Dic₅	1	2	yes	—
414	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	2	1	no	—
420	C₃×C₄	C₂×#681	1	2	yes	complemented
421	C₃×C₄	D₄×Dic₅	1	2	yes	—
422	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
423	C₃×C₄	C₂×#711	1	1	yes	characteristic
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	2	4	no	—
426	C₂×C₅	—	4	2	no	—
427	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
428	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
429	C₂×C₅	C₃×#568	1	1	yes	characteristic
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
434	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
435	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	C₃×#681	1	4	yes	direct product factor
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
449	C₂×C₄	C₃×#711	1	2	yes	—
450	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
454	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
455	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
456	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
458	C₈	—	5	4	no	—
459	C₈	—	10	4	no	—
460	C₈	—	10	2	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	2	4	no	—
463	C₂×C₃	—	4	2	no	—
464	C₂×C₃	C₂²×#681	1	1	yes	characteristic
465	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
466	C₂×C₃	#66153	1	1	yes	characteristic
467	C₅	C₃×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	8	no	—
476	C₂²	C₂×C₃×#681	1	4	yes	complemented
477	C₂²	C₃×D₄×Dic₅	1	2	yes	—
478	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	C₂×C₃×#681	1	2	yes	complemented
485	C₄	C₃×D₄×Dic₅	1	2	yes	—
486	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
487	C₄	C₂×C₃×#711	1	1	yes	characteristic
488	C₃	D₄×#681	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	2	4	no	—
491	C₂	—	4	2	no	—
492	C₂	C₂²×C₃×#681	1	1	yes	characteristic
493	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic
494	C₂	C₃×#66153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×C₅×D₄	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₃×D₄×M₁₆
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#681	C₂	semidirect
3. C₃×#65496	C₂	semidirect
4. C₃×#65301	C₂	semidirect
5. C₃×#65300	C₂	semidirect
6. C₃×D₄×#168	C₂	semidirect
7. C₃×#65213	C₂	semidirect
8. C₃×C₄×#681	C₂	semidirect
9. D₄×#681	C₃	direct (N × H)
25. C₂×C₃×#681	C₂²	semidirect
26. C₂²×C₃×#168	C₂²	semidirect
27. C₃×C₂²⋊#168	C₂²	semidirect
28. C₃×C₂²⋊#168	C₂²	semidirect
29. C₃×C₄⋊#168	C₂²	semidirect
30. C₃×C₄⋊#168	C₂²	semidirect
31. C₃×#3935	C₂²	semidirect
32. C₃×C₄×#168	C₂²	semidirect
35. C₂²×#681	C₂×C₃	semidirect
36. #65496	C₂×C₃	semidirect
37. #65301	C₂×C₃	semidirect
38. #65300	C₂×C₃	semidirect
39. D₄×#168	C₂×C₃	semidirect
40. #65213	C₂×C₃	semidirect
41. C₄×#681	C₂×C₃	semidirect
71. C₃×#681	D₄	direct (N × H)
99. C₂×#681	C₂²×C₃	semidirect
100. C₂²×#168	C₂²×C₃	semidirect
101. C₂²⋊#168	C₂²×C₃	semidirect
102. C₂²⋊#168	C₂²×C₃	semidirect
103. C₄⋊#168	C₂²×C₃	semidirect
104. C₄⋊#168	C₂²×C₃	semidirect
105. #3935	C₂²×C₃	semidirect
106. C₄×#168	C₂²×C₃	semidirect
116. C₃×C₅×D₄	M₁₆	semidirect
138. C₃×#168	C₂×D₄	semidirect
191. #681	C₃×D₄	direct (N × H)
213. C₂²×C₃×C₅	C₂×M₁₆	semidirect
221. C₃×C₄×C₅	C₂×M₁₆	semidirect
266. C₅×D₄	C₃×M₁₆	semidirect
288. #168	C₂×C₃×D₄	semidirect
326. C₃×D₄	#681	direct (N × H)
358. C₂²×C₅	C₂×C₃×M₁₆	semidirect
366. C₄×C₅	C₂×C₃×M₁₆	semidirect
403. C₃×C₅	D₄×M₁₆	semidirect
412. C₂²×C₃	C₂×#681	semidirect
420. C₃×C₄	C₂×#681	semidirect
438. D₄	C₃×#681	direct (N × H)
467. C₅	C₃×D₄×M₁₆	semidirect
476. C₂²	C₂×C₃×#681	semidirect
484. C₄	C₂×C₃×#681	semidirect
488. C₃	D₄×#681	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×C₄×C₅×D₄	2
C₂²×C₃×#681	2
C₃×#65496	2
C₃×#65301	2
C₃×#65300	2
C₃×D₄×#168	2
C₃×#65213	2
C₃×C₄×#681	2
D₄×#681	3
C₃×D₄×M₁₆	5

Subgroups — C3×D4×#681 #14415685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#681 #14415685