Subgroups — C₃×C₄×#4078 #14416656

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 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, complemented
2	C₂×C₃×#4078	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65504	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65307	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#687	C₂	1	2	yes	maximal, complemented
7	C₃×#65303	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#686	C₂	1	2	yes	maximal, complemented
9	C₃×#65255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65253	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4078	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	—	2	1	no	—
15	C₂×C₃×#709	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	—	2	1	no	—
17	C₃×C₄×C₅×D₄	—	2	1	no	—
18	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
19	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×#687	C₂²	1	2	yes	—
24	C₃×#4078	C₄	1	8	yes	direct product factor
25	C₂×C₃×#686	C₂²	1	2	yes	—
26	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
27	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
28	C₃×#4072	C₂²	1	1	yes	characteristic
29	C₂×C₃×#681	C₂²	1	1	yes	characteristic
30	C₂×C₃×#681	C₂²	1	1	yes	characteristic
31	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
33	C₃×#4018	—	2	1	no	—
34	C₃×C₄²×D₅	—	2	1	no	—
35	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3964	C₂²	1	2	yes	—
38	C₃×#3964	C₂²	1	2	yes	—
39	C₃×#3942	C₂²	1	2	yes	complemented
40	C₃×#3941	C₂²	1	2	yes	complemented
41	C₃×#3940	C₂²	1	2	yes	complemented
42	C₃×#3939	C₂²	1	2	yes	complemented
43	C₃×#3935	C₂²	1	2	yes	complemented
44	C₃×C₄×#168	C₂²	1	2	yes	complemented
45	C₃×C₄×AGL(1,ℤ/8)	—	5	1	no	maximal, Hall
46	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#4078	C₂×C₃	1	1	yes	characteristic
48	C₄×#709	C₂×C₃	1	1	yes	characteristic, complemented
49	#65504	C₂×C₃	1	1	yes	characteristic, complemented
50	#65307	C₂×C₃	1	2	yes	complemented
51	C₄×#687	C₂×C₃	1	2	yes	complemented
52	#65303	C₂×C₃	1	2	yes	complemented
53	C₄×#686	C₂×C₃	1	2	yes	complemented
54	#65255	C₂×C₃	1	1	yes	characteristic, complemented
55	#65253	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂⁴×C₃×C₅	—	2	1	no	—
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
61	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	4	4	no	—
66	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
70	C₃×#709	—	2	2	no	—
71	C₃×#709	C₂×C₄	1	4	yes	complemented
72	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×D₅	—	2	1	no	—
74	C₂×C₃×C₄×D₅	—	2	1	no	—
75	C₂×C₃×C₄×D₅	—	2	1	no	—
76	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
82	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₃×C₂²⋊Dic₅	—	2	1	no	—
86	C₃×#687	C₂×C₄	1	8	yes	complemented
87	C₃×#686	C₂×C₄	1	8	yes	complemented
88	C₃×#685	—	2	1	no	—
89	C₃×#685	—	2	1	no	—
90	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
91	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
92	C₃×#683	—	2	1	no	—
93	C₃×#683	—	2	1	no	—
94	C₃×C₄×Dic₅	—	2	1	no	—
95	C₃×C₄×Dic₅	—	2	1	no	—
96	C₃×C₄×Dic₅	—	2	1	no	—
97	C₃×#681	—	2	2	no	—
98	C₃×#681	C₂×C₄	1	4	yes	complemented
99	C₂×C₃×#168	C₂³	1	2	yes	—
100	C₂×C₃×#168	C₂³	1	2	yes	—
101	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
102	C₃×C₄×#41	—	5	1	no	—
103	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
104	C₃×#442	—	5	2	no	—
105	C₃×#440	—	5	2	no	—
106	C₃×C₄×SD₁₆	—	5	2	no	—
107	C₃×C₄×D₈	—	5	2	no	—
108	C₃×#428	—	5	1	no	—
109	C₃×#418	—	5	1	no	—
110	C₃×#417	—	5	1	no	—
111	C₃×C₄×M₁₆	—	5	1	no	—
112	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
113	C₂³×C₄×C₅	—	2	1	no	—
114	C₂×#709	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	—	2	1	no	—
116	C₄×C₅×D₄	—	2	1	no	—
117	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
118	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
122	C₂×#687	C₂²×C₃	1	2	yes	—
123	#4078	C₃×C₄	1	8	yes	direct product factor
124	C₂×#686	C₂²×C₃	1	2	yes	—
125	C₄×C₂²⋊D₅	—	2	1	no	—
126	C₄×C₂²⋊D₅	—	2	1	no	—
127	#4072	C₂²×C₃	1	1	yes	characteristic
128	C₂×#681	C₂²×C₃	1	1	yes	characteristic
129	C₂×#681	C₂²×C₃	1	1	yes	characteristic
130	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
132	#4018	—	2	1	no	—
133	C₄²×D₅	—	2	1	no	—
134	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
136	#3964	C₂²×C₃	1	2	yes	—
137	#3964	C₂²×C₃	1	2	yes	—
138	#3942	C₂²×C₃	1	2	yes	complemented
139	#3941	C₂²×C₃	1	2	yes	complemented
140	#3940	C₂²×C₃	1	2	yes	complemented
141	#3939	C₂²×C₃	1	2	yes	complemented
142	#3935	C₂²×C₃	1	2	yes	complemented
143	C₄×#168	C₂²×C₃	1	2	yes	complemented
144	C₄×AGL(1,ℤ/8)	—	5	1	no	Sylow
145	C₂³×C₃×C₅	—	2	4	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	4	2	no	—
148	C₂³×C₃×C₅	—	4	2	no	—
149	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₃×D₅	—	2	1	no	—
151	C₃×C₅×D₄	—	2	4	no	—
152	C₃×C₅×D₄	—	2	2	no	—
153	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	4	1	no	—
157	C₂×C₃×C₄×C₅	—	4	4	no	—
158	C₂×C₃×C₄×C₅	—	4	2	no	—
159	C₂×C₃×C₄×C₅	—	4	4	no	—
160	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	#41	1	2	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₃×C₂²⋊D₅	—	2	4	no	—
169	C₂×C₃×Dic₅	—	2	1	no	—
170	C₂×C₃×Dic₅	—	2	1	no	—
171	C₂×C₃×Dic₅	—	2	1	no	—
172	C₃×D₂₀	—	2	1	no	—
173	C₃×D₂₀	C₂²×C₄	1	2	yes	complemented
174	C₃×C₄×D₅	—	2	4	no	—
175	C₃×C₄×D₅	—	4	2	no	—
176	C₃×C₄×D₅	—	4	2	no	—
177	C₃×Dic₁₀	—	2	1	no	—
178	C₃×Dic₁₀	C₂²×C₄	1	2	yes	complemented
179	C₃×#168	—	2	2	no	—
180	C₃×#168	C₂²×C₄	1	4	yes	complemented
181	C₂×C₃×#41	—	5	1	no	—
182	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
183	C₂³×C₃×C₄	—	2	1	no	—
184	C₃×AGL(1,ℤ/8)	—	5	8	no	—
185	C₂×C₃×SD₁₆	—	5	2	no	—
186	C₂×C₃×D₈	—	5	2	no	—
187	C₂×C₃×M₁₆	—	5	1	no	—
188	C₂×C₃×M₁₆	—	5	1	no	—
189	C₃×C₄×Q₈	—	5	1	no	—
190	C₃×C₄×Q₈	—	5	1	no	—
191	C₃×C₄×D₄	—	2	1	no	—
192	C₃×C₄×D₄	—	2	1	no	—
193	C₃×C₄×D₄	—	5	1	no	—
194	C₃×C₄×D₄	—	5	1	no	—
195	C₃×C₄×D₄	—	10	1	no	—
196	C₃×C₄×D₄	—	10	1	no	—
197	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
198	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
199	C₃×#117	—	5	1	no	—
200	C₃×#117	—	10	1	no	—
201	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
203	C₂×C₃×C₄²	—	10	1	no	—
204	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
205	C₃×#107	—	5	2	no	—
206	C₃×#106	—	5	2	no	—
207	C₃×#103	—	5	2	no	—
208	C₃×#102	—	5	2	no	—
209	C₃×#102	—	5	2	no	—
210	C₃×#102	—	5	2	no	—
211	C₃×#97	—	5	2	no	—
212	C₃×C₄×C₈	—	5	2	no	—
213	C₂⁴×C₅	—	2	1	no	—
214	C₂×C₅×D₄	—	2	1	no	—
215	C₂×C₅×D₄	—	2	2	no	—
216	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
217	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	2	2	no	—
220	C₂²×C₄×C₅	—	2	2	no	—
221	C₂²×C₄×C₅	—	4	4	no	—
222	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₂²⋊D₅	—	2	1	no	—
226	#709	—	2	2	no	—
227	#709	C₂×C₃×C₄	1	4	yes	complemented
228	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
229	C₂×C₄×D₅	—	2	1	no	—
230	C₂×C₄×D₅	—	2	1	no	—
231	C₂×C₄×D₅	—	2	1	no	—
232	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
235	C₅×C₂²⋊C₄	—	2	2	no	—
236	C₅×C₂²⋊C₄	—	2	2	no	—
237	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
238	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
239	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
240	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
241	C₂²⋊Dic₅	—	2	1	no	—
242	#687	C₂×C₃×C₄	1	8	yes	complemented
243	#686	C₂×C₃×C₄	1	8	yes	complemented
244	#685	—	2	1	no	—
245	#685	—	2	1	no	—
246	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
247	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
248	#683	—	2	1	no	—
249	#683	—	2	1	no	—
250	C₄×Dic₅	—	2	1	no	—
251	C₄×Dic₅	—	2	1	no	—
252	C₄×Dic₅	—	2	1	no	—
253	#681	—	2	2	no	—
254	#681	C₂×C₃×C₄	1	4	yes	complemented
255	C₂×#168	C₂³×C₃	1	2	yes	—
256	C₂×#168	C₂³×C₃	1	2	yes	—
257	C₂×AGL(1,ℤ/8)	—	5	1	no	—
258	C₄×#41	—	5	1	no	—
259	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic, complemented
260	#442	—	5	2	no	—
261	#440	—	5	2	no	—
262	C₄×SD₁₆	—	5	2	no	—
263	C₄×D₈	—	5	2	no	—
264	#428	—	5	1	no	—
265	#418	—	5	1	no	—
266	#417	—	5	1	no	—
267	C₄×M₁₆	—	5	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	—	2	1	no	—
270	C₂²×C₃×C₅	—	2	4	no	—
271	C₂²×C₃×C₅	—	4	8	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
275	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₃×D₅	—	2	2	no	—
277	C₂×C₃×D₅	—	4	1	no	—
278	C₂×C₃×D₅	—	4	1	no	—
279	C₃×C₄×C₅	—	2	1	no	—
280	C₃×C₄×C₅	—	2	1	no	—
281	C₃×C₄×C₅	—	2	1	no	—
282	C₃×C₄×C₅	—	4	2	no	—
283	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
284	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
285	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
286	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
287	C₃×Dic₅	—	2	2	no	—
288	C₃×Dic₅	—	4	1	no	—
289	C₃×Dic₅	—	4	1	no	—
290	C₂⁴×C₃	—	2	1	no	—
291	C₃×#41	—	5	4	no	—
292	C₃×#41	—	10	2	no	—
293	C₂×C₃×Q₈	—	5	1	no	—
294	C₂×C₃×D₄	—	2	2	no	—
295	C₂×C₃×D₄	—	2	1	no	—
296	C₂×C₃×D₄	—	5	1	no	—
297	C₂×C₃×D₄	—	10	1	no	—
298	C₂×C₃×D₄	C₄×D₅	1	4	yes	complemented
299	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
300	C₂²×C₃×C₄	—	2	1	no	—
301	C₂²×C₃×C₄	—	2	2	no	—
302	C₂²×C₃×C₄	—	2	2	no	—
303	C₂²×C₃×C₄	—	4	4	no	—
304	C₂²×C₃×C₄	—	10	1	no	—
305	C₂²×C₃×C₄	—	10	1	no	—
306	C₂²×C₃×C₄	—	10	1	no	—
307	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
310	C₃×SD₁₆	—	5	8	no	—
311	C₃×D₈	—	5	8	no	—
312	C₃×M₁₆	—	5	4	no	—
313	C₃×M₁₆	—	10	2	no	—
314	C₂×C₃×C₈	—	5	2	no	—
315	C₂×C₃×C₈	—	5	2	no	—
316	C₃×C₄⋊C₄	—	2	1	no	—
317	C₃×C₄⋊C₄	—	5	1	no	—
318	C₃×C₄⋊C₄	—	5	1	no	—
319	C₃×C₄⋊C₄	—	10	1	no	—
320	C₃×C₄⋊C₄	—	10	1	no	—
321	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
322	C₃×C₂²⋊C₄	—	2	2	no	—
323	C₃×C₂²⋊C₄	—	2	2	no	—
324	C₃×C₂²⋊C₄	—	10	1	no	—
325	C₃×C₂²⋊C₄	—	10	1	no	—
326	C₃×C₂²⋊C₄	—	10	1	no	—
327	C₃×C₄²	—	10	1	no	—
328	C₃×C₄²	—	10	1	no	—
329	C₃×C₄²	—	10	1	no	—
330	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
331	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
332	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
333	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
334	C₂³×C₅	—	2	4	no	—
335	C₂³×C₅	—	2	2	no	—
336	C₂³×C₅	—	4	2	no	—
337	C₂³×C₅	—	4	2	no	—
338	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂²×D₅	—	2	1	no	—
340	C₅×D₄	—	2	4	no	—
341	C₅×D₄	—	2	2	no	—
342	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	4	no	—
347	C₂×C₄×C₅	—	4	2	no	—
348	C₂×C₄×C₅	—	4	4	no	—
349	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
350	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
355	C₂×C₄×C₅	C₃×#41	1	2	yes	—
356	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
357	C₂²⋊D₅	—	2	4	no	—
358	C₂×Dic₅	—	2	1	no	—
359	C₂×Dic₅	—	2	1	no	—
360	C₂×Dic₅	—	2	1	no	—
361	D₂₀	—	2	1	no	—
362	D₂₀	C₂²×C₃×C₄	1	2	yes	complemented
363	C₄×D₅	—	2	4	no	—
364	C₄×D₅	—	4	2	no	—
365	C₄×D₅	—	4	2	no	—
366	Dic₁₀	—	2	1	no	—
367	Dic₁₀	C₂²×C₃×C₄	1	2	yes	complemented
368	#168	—	2	2	no	—
369	#168	C₂²×C₃×C₄	1	4	yes	complemented
370	C₂×#41	—	5	1	no	—
371	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
372	C₂³×C₄	—	2	1	no	—
373	AGL(1,ℤ/8)	—	5	8	no	—
374	C₂×SD₁₆	—	5	2	no	—
375	C₂×D₈	—	5	2	no	—
376	C₂×M₁₆	—	5	1	no	—
377	C₂×M₁₆	—	5	1	no	—
378	C₄×Q₈	—	5	1	no	—
379	C₄×Q₈	—	5	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	5	1	no	—
383	C₄×D₄	—	5	1	no	—
384	C₄×D₄	—	10	1	no	—
385	C₄×D₄	—	10	1	no	—
386	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
387	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
388	#117	—	5	1	no	—
389	#117	—	10	1	no	—
390	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	—	10	1	no	—
393	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
394	#107	—	5	2	no	—
395	#106	—	5	2	no	—
396	#103	—	5	2	no	—
397	#102	—	5	2	no	—
398	#102	—	5	2	no	—
399	#102	—	5	2	no	—
400	#97	—	5	2	no	—
401	C₄×C₈	—	5	2	no	—
402	C₂×C₃×C₅	—	2	2	no	—
403	C₂×C₃×C₅	—	4	4	no	—
404	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
405	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
406	C₂×C₃×C₅	#575	1	1	yes	characteristic
407	C₃×D₅	—	4	2	no	—
408	C₂³×C₃	—	2	2	no	—
409	C₂³×C₃	—	2	4	no	—
410	C₂³×C₃	—	4	2	no	—
411	C₂³×C₃	—	4	2	no	—
412	C₂³×C₃	—	10	1	no	—
413	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
414	C₃×Q₈	—	5	2	no	—
415	C₃×Q₈	—	10	1	no	—
416	C₃×D₄	—	2	2	no	—
417	C₃×D₄	—	2	4	no	—
418	C₃×D₄	—	5	2	no	—
419	C₃×D₄	—	10	4	no	—
420	C₃×D₄	—	10	1	no	—
421	C₃×D₄	C₂×C₄×D₅	1	4	yes	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	2	no	—
424	C₂×C₃×C₄	—	4	1	no	—
425	C₂×C₃×C₄	—	4	4	no	—
426	C₂×C₃×C₄	—	4	2	no	—
427	C₂×C₃×C₄	—	4	4	no	—
428	C₂×C₃×C₄	—	10	1	no	—
429	C₂×C₃×C₄	—	10	4	no	—
430	C₂×C₃×C₄	—	10	1	no	—
431	C₂×C₃×C₄	—	10	1	no	—
432	C₂×C₃×C₄	—	20	2	no	—
433	C₂×C₃×C₄	—	20	2	no	—
434	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
435	C₂×C₃×C₄	#709	1	2	yes	—
436	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
437	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
442	C₃×C₈	—	5	4	no	—
443	C₃×C₈	—	10	2	no	—
444	C₂²×C₅	—	2	1	no	—
445	C₂²×C₅	—	2	1	no	—
446	C₂²×C₅	—	2	4	no	—
447	C₂²×C₅	—	4	8	no	—
448	C₂²×C₅	—	4	2	no	—
449	C₂²×C₅	—	4	2	no	—
450	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
451	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
452	C₂×D₅	—	2	2	no	—
453	C₂×D₅	—	4	1	no	—
454	C₂×D₅	—	4	1	no	—
455	C₄×C₅	—	2	1	no	—
456	C₄×C₅	—	2	1	no	—
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	—	4	2	no	—
459	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
460	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
461	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
462	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
463	Dic₅	—	2	2	no	—
464	Dic₅	—	4	1	no	—
465	Dic₅	—	4	1	no	—
466	C₂⁴	—	2	1	no	—
467	#41	—	5	4	no	—
468	#41	—	10	2	no	—
469	C₂×Q₈	—	5	1	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	5	1	no	—
473	C₂×D₄	—	10	1	no	—
474	C₂×D₄	C₃×C₄×D₅	1	4	yes	complemented
475	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	10	1	no	—
481	C₂²×C₄	—	10	1	no	—
482	C₂²×C₄	—	10	1	no	—
483	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
484	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
485	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
486	SD₁₆	—	5	8	no	—
487	D₈	—	5	8	no	—
488	M₁₆	—	5	4	no	—
489	M₁₆	—	10	2	no	—
490	C₂×C₈	—	5	2	no	—
491	C₂×C₈	—	5	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	10	1	no	—
496	C₄⋊C₄	—	10	1	no	—
497	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	10	1	no	—
501	C₂²⋊C₄	—	10	1	no	—
502	C₂²⋊C₄	—	10	1	no	—
503	C₄²	—	10	1	no	—
504	C₄²	—	10	1	no	—
505	C₄²	—	10	1	no	—
506	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
507	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
508	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
509	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
510	C₃×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	4	no	—
514	C₂²×C₃	—	4	8	no	—
515	C₂²×C₃	—	4	2	no	—
516	C₂²×C₃	—	4	2	no	—
517	C₂²×C₃	—	10	2	no	—
518	C₂²×C₃	—	20	1	no	—
519	C₂²×C₃	—	20	1	no	—
520	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
521	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	4	2	no	—
526	C₃×C₄	—	10	2	no	—
527	C₃×C₄	—	20	1	no	—
528	C₃×C₄	—	20	1	no	—
529	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
530	C₃×C₄	#4078	1	2	yes	direct product factor
531	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
532	C₃×C₄	C₂×#709	1	1	yes	characteristic
533	C₂×C₅	—	2	2	no	—
534	C₂×C₅	—	4	4	no	—
535	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
536	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
537	C₂×C₅	C₃×#575	1	1	yes	characteristic
538	D₅	—	4	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	10	1	no	—
544	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
545	Q₈	—	5	2	no	—
546	Q₈	—	10	1	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	4	no	—
549	D₄	—	5	2	no	—
550	D₄	—	10	4	no	—
551	D₄	—	10	1	no	—
552	D₄	C₂×C₃×C₄×D₅	1	4	yes	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	10	1	no	—
560	C₂×C₄	—	10	4	no	—
561	C₂×C₄	—	10	1	no	—
562	C₂×C₄	—	10	1	no	—
563	C₂×C₄	—	20	2	no	—
564	C₂×C₄	—	20	2	no	—
565	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
566	C₂×C₄	C₃×#709	1	2	yes	—
567	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
568	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
569	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
570	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
571	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
572	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
573	C₈	—	5	4	no	—
574	C₈	—	10	2	no	—
575	C₂×C₃	—	2	2	no	—
576	C₂×C₃	—	4	4	no	—
577	C₂×C₃	—	20	2	no	—
578	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
579	C₂×C₃	C₂×#4078	1	1	yes	characteristic
580	C₂×C₃	#66156	1	1	yes	characteristic
581	C₅	C₃×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	4	8	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	10	2	no	—
589	C₂²	—	20	1	no	—
590	C₂²	—	20	1	no	—
591	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
592	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	4	2	no	—
597	C₄	—	10	2	no	—
598	C₄	—	20	1	no	—
599	C₄	—	20	1	no	—
600	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
601	C₄	C₃×#4078	1	2	yes	direct product factor
602	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
603	C₄	C₂×C₃×#709	1	1	yes	characteristic
604	C₃	C₄×#4078	1	1	yes	characteristic, direct product factor, Sylow
605	C₂	—	2	2	no	—
606	C₂	—	4	4	no	—
607	C₂	—	20	2	no	—
608	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
609	C₂	C₂×C₃×#4078	1	1	yes	characteristic
610	C₂	C₃×#66156	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4078	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₃×C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₄×#709	C₂	semidirect
4. C₃×#65504	C₂	semidirect
5. C₃×#65307	C₂	semidirect
6. C₃×C₄×#687	C₂	semidirect
7. C₃×#65303	C₂	semidirect
8. C₃×C₄×#686	C₂	semidirect
9. C₃×#65255	C₂	semidirect
10. C₃×#65253	C₂	semidirect
11. C₃×C₄×#681	C₂	semidirect
12. C₄×#4078	C₃	direct (N × H)
24. C₃×#4078	C₄	direct (N × H)
31. C₃×C₄×D₂₀	C₂²	semidirect
32. C₃×C₄×D₂₀	C₂²	semidirect
35. C₃×C₄×Dic₁₀	C₂²	semidirect
36. C₃×C₄×Dic₁₀	C₂²	semidirect
39. C₃×#3942	C₂²	semidirect
40. C₃×#3941	C₂²	semidirect
41. C₃×#3940	C₂²	semidirect
42. C₃×#3939	C₂²	semidirect
43. C₃×#3935	C₂²	semidirect
44. C₃×C₄×#168	C₂²	semidirect
46. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
48. C₄×#709	C₂×C₃	semidirect
49. #65504	C₂×C₃	semidirect
50. #65307	C₂×C₃	semidirect
51. C₄×#687	C₂×C₃	semidirect
52. #65303	C₂×C₃	semidirect
53. C₄×#686	C₂×C₃	semidirect
54. #65255	C₂×C₃	semidirect
55. #65253	C₂×C₃	semidirect
56. C₄×#681	C₂×C₃	semidirect
60. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
71. C₃×#709	C₂×C₄	semidirect
86. C₃×#687	C₂×C₄	semidirect
87. C₃×#686	C₂×C₄	semidirect
98. C₃×#681	C₂×C₄	semidirect
103. C₂×C₃×C₄×D₄	D₅	semidirect
123. #4078	C₃×C₄	direct (N × H)
130. C₄×D₂₀	C₂²×C₃	semidirect
131. C₄×D₂₀	C₂²×C₃	semidirect
134. C₄×Dic₁₀	C₂²×C₃	semidirect
135. C₄×Dic₁₀	C₂²×C₃	semidirect
138. #3942	C₂²×C₃	semidirect
139. #3941	C₂²×C₃	semidirect
140. #3940	C₂²×C₃	semidirect
141. #3939	C₂²×C₃	semidirect
142. #3935	C₂²×C₃	semidirect
143. C₄×#168	C₂²×C₃	semidirect
173. C₃×D₂₀	C₂²×C₄	semidirect
178. C₃×Dic₁₀	C₂²×C₄	semidirect
180. C₃×#168	C₂²×C₄	semidirect
216. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
227. #709	C₂×C₃×C₄	semidirect
242. #687	C₂×C₃×C₄	semidirect
243. #686	C₂×C₃×C₄	semidirect
254. #681	C₂×C₃×C₄	semidirect
259. C₂×C₄×D₄	C₃×D₅	semidirect
284. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
298. C₂×C₃×D₄	C₄×D₅	semidirect
362. D₂₀	C₂²×C₃×C₄	semidirect
367. Dic₁₀	C₂²×C₃×C₄	semidirect
369. #168	C₂²×C₃×C₄	semidirect
460. C₄×C₅	C₃×AGL(1,ℤ/8)	semidirect
474. C₂×D₄	C₃×C₄×D₅	semidirect
510. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
530. C₃×C₄	#4078	direct (N × H)
581. C₅	C₃×C₄×AGL(1,ℤ/8)	semidirect
601. C₄	C₃×#4078	direct (N × H)
604. C₃	C₄×#4078	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
C₂×C₃×#4078	2
C₃×C₄×#709	2
C₃×#65504	2
C₃×#65307	2
C₃×C₄×#687	2
C₃×#65303	2
C₃×C₄×#686	2
C₃×#65255	2
C₃×#65253	2
C₃×C₄×#681	2
C₄×#4078	3
C₃×C₄×AGL(1,ℤ/8)	5

Subgroups — C3×C4×#4078 #14416656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4078 #14416656