Subgroups — C₃×C₄×#4095 #14416650

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	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4095	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65521	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65315	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#688	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×#65290	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65284	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4095	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	—	2	1	no	—
16	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₄×C₅×D₄	—	2	1	no	—
19	C₃×C₄×C₅×D₄	—	2	1	no	—
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#117	—	2	1	no	—
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	—	2	1	no	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×#4095	C₄	1	8	yes	direct product factor
27	C₂×C₃×#688	C₂²	1	2	yes	—
28	C₂×C₃×#686	C₂²	1	2	yes	—
29	C₂×C₃×#685	—	2	1	no	—
30	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×#681	C₂²	1	1	yes	characteristic
32	C₂×C₃×#681	C₂²	1	1	yes	characteristic
33	C₃×C₄×D₂₀	—	2	1	no	—
34	C₃×C₄×D₂₀	—	2	1	no	—
35	C₃×C₄×D₂₀	C₂²	1	2	yes	—
36	C₃×C₄×D₂₀	C₂²	1	2	yes	—
37	C₃×#3967	C₂²	1	2	yes	complemented
38	C₃×#3964	C₂²	1	2	yes	complemented
39	C₃×#3941	C₂²	1	2	yes	—
40	C₃×#3941	C₂²	1	2	yes	—
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	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#4095	C₂×C₃	1	1	yes	characteristic
48	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
49	#65521	C₂×C₃	1	1	yes	characteristic, complemented
50	#65315	C₂×C₃	1	2	yes	complemented
51	C₄×#688	C₂×C₃	1	2	yes	complemented
52	#65303	C₂×C₃	1	2	yes	complemented
53	C₄×#686	C₂×C₃	1	2	yes	complemented
54	#65290	C₂×C₃	1	1	yes	characteristic, complemented
55	#65284	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂³×C₃×D₅	—	2	1	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	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	C₂²×C₃×Dic₅	—	2	1	no	—
70	C₂×C₃×D₂₀	—	2	1	no	—
71	C₂×C₃×D₂₀	—	2	2	no	—
72	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	complemented
73	C₂×C₃×D₂₀	C₂³	1	2	yes	—
74	C₂×C₃×C₄×D₅	—	2	2	no	—
75	C₂×C₃×C₄×D₅	—	2	2	no	—
76	C₂×C₃×C₄×D₅	—	4	4	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₄²×C₅	—	2	1	no	—
85	C₃×C₄²×C₅	—	2	1	no	—
86	C₃×C₄²×C₅	—	2	1	no	—
87	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
88	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
89	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₃×#688	C₂×C₄	1	8	yes	complemented
92	C₃×#686	C₂×C₄	1	8	yes	complemented
93	C₃×#685	—	2	2	no	—
94	C₃×#685	—	2	2	no	—
95	C₃×C₄⋊Dic₅	—	2	1	no	—
96	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
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	D₅	1	1	yes	characteristic, complemented
103	C₂×C₃×C₄×D₄	—	5	1	no	—
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	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₄×D₅	—	2	1	no	—
115	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₄×C₅×D₄	—	2	1	no	—
118	C₄×C₅×D₄	—	2	1	no	—
119	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₅×#117	—	2	1	no	—
122	C₅×#117	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄²×C₅	—	2	1	no	—
124	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
125	#4095	C₃×C₄	1	8	yes	direct product factor
126	C₂×#688	C₂²×C₃	1	2	yes	—
127	C₂×#686	C₂²×C₃	1	2	yes	—
128	C₂×#685	—	2	1	no	—
129	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
130	C₂×#681	C₂²×C₃	1	1	yes	characteristic
131	C₂×#681	C₂²×C₃	1	1	yes	characteristic
132	C₄×D₂₀	—	2	1	no	—
133	C₄×D₂₀	—	2	1	no	—
134	C₄×D₂₀	C₂²×C₃	1	2	yes	—
135	C₄×D₂₀	C₂²×C₃	1	2	yes	—
136	#3967	C₂²×C₃	1	2	yes	complemented
137	#3964	C₂²×C₃	1	2	yes	complemented
138	#3941	C₂²×C₃	1	2	yes	—
139	#3941	C₂²×C₃	1	2	yes	—
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	1	no	—
146	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₃×D₅	—	2	4	no	—
148	C₂²×C₃×D₅	—	2	2	no	—
149	C₂²×C₃×D₅	—	4	2	no	—
150	C₂²×C₃×D₅	—	4	2	no	—
151	C₃×C₅×Q₈	—	2	1	no	—
152	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	complemented
153	C₃×C₅×D₄	—	2	4	no	—
154	C₃×C₅×D₄	—	2	1	no	—
155	C₃×C₅×D₄	C₂²×C₄	1	2	yes	complemented
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	4	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	—	4	1	no	—
162	C₂×C₃×C₄×C₅	—	4	2	no	—
163	C₂×C₃×C₄×C₅	—	4	2	no	—
164	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂×C₃×C₄×C₅	#41	1	2	yes	—
171	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₂×C₃×Dic₅	—	2	2	no	—
173	C₂×C₃×Dic₅	—	4	2	no	—
174	C₃×D₂₀	—	2	4	no	—
175	C₃×D₂₀	—	2	2	no	—
176	C₃×D₂₀	C₂²×C₄	1	4	yes	—
177	C₃×C₄×D₅	—	4	4	no	—
178	C₃×C₄×D₅	—	4	4	no	—
179	C₃×#168	—	2	2	no	—
180	C₃×#168	C₂²×C₄	1	4	yes	complemented
181	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
182	C₂²×C₃×D₄	—	5	1	no	—
183	C₂³×C₃×C₄	—	10	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	C₂×D₅	1	1	yes	characteristic, complemented
190	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
191	C₃×C₄×D₄	—	2	1	no	—
192	C₃×C₄×D₄	—	2	1	no	—
193	C₃×C₄×D₄	—	5	2	no	—
194	C₃×C₄×D₄	—	5	2	no	—
195	C₃×C₄×D₄	—	10	1	no	—
196	C₃×C₄×D₄	—	10	1	no	—
197	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
198	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
199	C₃×#117	—	2	1	no	—
200	C₃×#117	C₂×D₅	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	—	5	1	no	—
202	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
203	C₂×C₃×C₄²	—	2	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	C₂³×D₅	—	2	1	no	—
214	C₅×#41	—	2	2	no	—
215	C₅×#41	C₂×C₃×C₄	1	4	yes	complemented
216	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₅×D₄	—	2	1	no	—
218	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	—	2	1	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	C₂²×Dic₅	—	2	1	no	—
226	C₂×D₂₀	—	2	1	no	—
227	C₂×D₂₀	—	2	2	no	—
228	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
229	C₂×D₂₀	C₂³×C₃	1	2	yes	—
230	C₂×C₄×D₅	—	2	2	no	—
231	C₂×C₄×D₅	—	2	2	no	—
232	C₂×C₄×D₅	—	4	4	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
236	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
237	C₅×C₂²⋊C₄	—	2	1	no	—
238	C₅×C₂²⋊C₄	—	2	1	no	—
239	C₅×C₂²⋊C₄	—	2	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
244	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
245	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
246	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
247	#688	C₂×C₃×C₄	1	8	yes	complemented
248	#686	C₂×C₃×C₄	1	8	yes	complemented
249	#685	—	2	2	no	—
250	#685	—	2	2	no	—
251	C₄⋊Dic₅	—	2	1	no	—
252	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
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	C₃×D₅	1	1	yes	characteristic, complemented
259	C₂×C₄×D₄	—	5	1	no	—
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	2	no	—
271	C₂²×C₃×C₅	—	4	1	no	—
272	C₂²×C₃×C₅	—	4	1	no	—
273	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
274	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₃×D₅	—	2	4	no	—
276	C₂×C₃×D₅	—	4	8	no	—
277	C₂×C₃×D₅	—	4	2	no	—
278	C₂×C₃×D₅	—	4	2	no	—
279	C₃×C₄×C₅	—	2	2	no	—
280	C₃×C₄×C₅	—	2	1	no	—
281	C₃×C₄×C₅	—	2	1	no	—
282	C₃×C₄×C₅	—	2	1	no	—
283	C₃×C₄×C₅	—	4	1	no	—
284	C₃×C₄×C₅	—	4	1	no	—
285	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
286	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
287	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
288	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
289	C₃×Dic₅	—	4	2	no	—
290	C₂⁴×C₃	—	10	1	no	—
291	C₃×#41	—	2	2	no	—
292	C₃×#41	C₄×D₅	1	4	yes	complemented
293	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
294	C₂×C₃×D₄	—	2	1	no	—
295	C₂×C₃×D₄	—	5	4	no	—
296	C₂×C₃×D₄	—	5	2	no	—
297	C₂×C₃×D₄	—	10	2	no	—
298	C₂×C₃×D₄	—	10	1	no	—
299	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
300	C₂²×C₃×C₄	—	2	1	no	—
301	C₂²×C₃×C₄	—	2	1	no	—
302	C₂²×C₃×C₄	—	2	1	no	—
303	C₂²×C₃×C₄	—	10	1	no	—
304	C₂²×C₃×C₄	—	10	2	no	—
305	C₂²×C₃×C₄	—	10	2	no	—
306	C₂²×C₃×C₄	—	20	4	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	—	2	1	no	—
318	C₃×C₄⋊C₄	—	5	2	no	—
319	C₃×C₄⋊C₄	—	10	1	no	—
320	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
321	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
322	C₃×C₂²⋊C₄	—	2	1	no	—
323	C₃×C₂²⋊C₄	—	2	1	no	—
324	C₃×C₂²⋊C₄	—	2	1	no	—
325	C₃×C₂²⋊C₄	—	10	2	no	—
326	C₃×C₂²⋊C₄	—	10	2	no	—
327	C₃×C₄²	—	2	1	no	—
328	C₃×C₄²	—	2	1	no	—
329	C₃×C₄²	—	2	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	1	no	—
335	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
336	C₂²×D₅	—	2	4	no	—
337	C₂²×D₅	—	2	2	no	—
338	C₂²×D₅	—	4	2	no	—
339	C₂²×D₅	—	4	2	no	—
340	C₅×Q₈	—	2	1	no	—
341	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	complemented
342	C₅×D₄	—	2	4	no	—
343	C₅×D₄	—	2	1	no	—
344	C₅×D₄	C₂²×C₃×C₄	1	2	yes	complemented
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	4	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	4	1	no	—
351	C₂×C₄×C₅	—	4	2	no	—
352	C₂×C₄×C₅	—	4	2	no	—
353	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
354	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
355	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
359	C₂×C₄×C₅	C₃×#41	1	2	yes	—
360	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
361	C₂×Dic₅	—	2	2	no	—
362	C₂×Dic₅	—	4	2	no	—
363	D₂₀	—	2	4	no	—
364	D₂₀	—	2	2	no	—
365	D₂₀	C₂²×C₃×C₄	1	4	yes	—
366	C₄×D₅	—	4	4	no	—
367	C₄×D₅	—	4	4	no	—
368	#168	—	2	2	no	—
369	#168	C₂²×C₃×C₄	1	4	yes	complemented
370	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
371	C₂²×D₄	—	5	1	no	—
372	C₂³×C₄	—	10	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	C₂×C₃×D₅	1	1	yes	characteristic, complemented
379	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	5	2	no	—
383	C₄×D₄	—	5	2	no	—
384	C₄×D₄	—	10	1	no	—
385	C₄×D₄	—	10	1	no	—
386	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
387	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
388	#117	—	2	1	no	—
389	#117	C₂×C₃×D₅	1	1	yes	characteristic
390	C₂×C₄⋊C₄	—	5	1	no	—
391	C₂×C₂²⋊C₄	—	10	1	no	—
392	C₂×C₄²	—	2	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	2	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	4	no	—
408	C₂³×C₃	—	2	1	no	—
409	C₂³×C₃	—	10	2	no	—
410	C₂³×C₃	—	10	4	no	—
411	C₂³×C₃	—	20	2	no	—
412	C₂³×C₃	—	20	2	no	—
413	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
414	C₃×Q₈	—	2	1	no	—
415	C₃×Q₈	C₂×C₄×D₅	1	2	yes	complemented
416	C₃×D₄	—	2	4	no	—
417	C₃×D₄	—	2	1	no	—
418	C₃×D₄	—	5	4	no	—
419	C₃×D₄	—	10	2	no	—
420	C₃×D₄	—	10	4	no	—
421	C₃×D₄	C₂×C₄×D₅	1	2	yes	complemented
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	4	no	—
424	C₂×C₃×C₄	—	2	2	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	4	1	no	—
428	C₂×C₃×C₄	—	4	2	no	—
429	C₂×C₃×C₄	—	4	2	no	—
430	C₂×C₃×C₄	—	10	2	no	—
431	C₂×C₃×C₄	—	20	4	no	—
432	C₂×C₃×C₄	—	20	2	no	—
433	C₂×C₃×C₄	—	20	4	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	2	no	—
447	C₂²×C₅	—	4	1	no	—
448	C₂²×C₅	—	4	1	no	—
449	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
450	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
451	C₂×D₅	—	2	4	no	—
452	C₂×D₅	—	4	8	no	—
453	C₂×D₅	—	4	2	no	—
454	C₂×D₅	—	4	2	no	—
455	C₄×C₅	—	2	1	no	—
456	C₄×C₅	—	2	1	no	—
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	—	2	2	no	—
459	C₄×C₅	—	4	1	no	—
460	C₄×C₅	—	4	1	no	—
461	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
462	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
463	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
464	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
465	Dic₅	—	4	2	no	—
466	C₂⁴	—	10	1	no	—
467	#41	—	2	2	no	—
468	#41	C₃×C₄×D₅	1	4	yes	complemented
469	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	5	4	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	10	2	no	—
474	C₂×D₄	—	10	1	no	—
475	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	10	1	no	—
480	C₂²×C₄	—	10	2	no	—
481	C₂²×C₄	—	10	2	no	—
482	C₂²×C₄	—	20	4	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	—	2	1	no	—
494	C₄⋊C₄	—	5	2	no	—
495	C₄⋊C₄	—	10	1	no	—
496	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	10	2	no	—
502	C₂²⋊C₄	—	10	2	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	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	2	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	10	4	no	—
517	C₂²×C₃	—	20	8	no	—
518	C₂²×C₃	—	20	2	no	—
519	C₂²×C₃	—	20	2	no	—
520	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
521	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	1	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	4	1	no	—
527	C₃×C₄	—	4	1	no	—
528	C₃×C₄	—	20	2	no	—
529	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
530	C₃×C₄	#4095	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	2	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	4	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	10	2	no	—
541	C₂³	—	10	4	no	—
542	C₂³	—	20	2	no	—
543	C₂³	—	20	2	no	—
544	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
545	Q₈	—	2	1	no	—
546	Q₈	C₂×C₃×C₄×D₅	1	2	yes	complemented
547	D₄	—	2	4	no	—
548	D₄	—	2	1	no	—
549	D₄	—	5	4	no	—
550	D₄	—	10	2	no	—
551	D₄	—	10	4	no	—
552	D₄	C₂×C₃×C₄×D₅	1	2	yes	complemented
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	10	2	no	—
562	C₂×C₄	—	20	4	no	—
563	C₂×C₄	—	20	2	no	—
564	C₂×C₄	—	20	4	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	2	no	—
577	C₂×C₃	—	20	4	no	—
578	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
579	C₂×C₃	C₂×#4095	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	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	10	4	no	—
588	C₂²	—	20	8	no	—
589	C₂²	—	20	2	no	—
590	C₂²	—	20	2	no	—
591	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
592	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	20	2	no	—
600	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
601	C₄	C₃×#4095	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×#4095	1	1	yes	characteristic, direct product factor, Sylow
605	C₂	—	2	2	no	—
606	C₂	—	4	2	no	—
607	C₂	—	20	4	no	—
608	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
609	C₂	C₂×C₃×#4095	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	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4095	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
3. C₂×C₃×C₄×D₂₀	C₂	semidirect
4. C₃×#65521	C₂	semidirect
5. C₃×#65315	C₂	semidirect
6. C₃×C₄×#688	C₂	semidirect
7. C₃×#65303	C₂	semidirect
8. C₃×C₄×#686	C₂	semidirect
9. C₃×#65290	C₂	semidirect
10. C₃×#65284	C₂	semidirect
11. C₃×C₄×#681	C₂	semidirect
12. C₄×#4095	C₃	direct (N × H)
16. C₃×C₄×C₅×Q₈	C₂²	semidirect
17. C₃×C₄×C₅×Q₈	C₂²	semidirect
20. C₃×C₄×C₅×D₄	C₂²	semidirect
21. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₃×#4095	C₄	direct (N × H)
37. C₃×#3967	C₂²	semidirect
38. C₃×#3964	C₂²	semidirect
41. C₃×#3940	C₂²	semidirect
42. C₃×#3939	C₂²	semidirect
43. C₃×#3935	C₂²	semidirect
44. C₃×C₄×#168	C₂²	semidirect
46. C₄×C₅×#41	C₂×C₃	semidirect
48. C₂×C₄×D₂₀	C₂×C₃	semidirect
49. #65521	C₂×C₃	semidirect
50. #65315	C₂×C₃	semidirect
51. C₄×#688	C₂×C₃	semidirect
52. #65303	C₂×C₃	semidirect
53. C₄×#686	C₂×C₃	semidirect
54. #65290	C₂×C₃	semidirect
55. #65284	C₂×C₃	semidirect
56. C₄×#681	C₂×C₃	semidirect
59. C₃×C₅×#41	C₂×C₄	semidirect
72. C₂×C₃×D₂₀	C₂×C₄	semidirect
91. C₃×#688	C₂×C₄	semidirect
92. C₃×#686	C₂×C₄	semidirect
98. C₃×#681	C₂×C₄	semidirect
102. C₃×C₄×#41	D₅	semidirect
115. C₄×C₅×Q₈	C₂²×C₃	semidirect
116. C₄×C₅×Q₈	C₂²×C₃	semidirect
119. C₄×C₅×D₄	C₂²×C₃	semidirect
120. C₄×C₅×D₄	C₂²×C₃	semidirect
125. #4095	C₃×C₄	direct (N × H)
136. #3967	C₂²×C₃	semidirect
137. #3964	C₂²×C₃	semidirect
140. #3940	C₂²×C₃	semidirect
141. #3939	C₂²×C₃	semidirect
142. #3935	C₂²×C₃	semidirect
143. C₄×#168	C₂²×C₃	semidirect
152. C₃×C₅×Q₈	C₂²×C₄	semidirect
155. C₃×C₅×D₄	C₂²×C₄	semidirect
180. C₃×#168	C₂²×C₄	semidirect
189. C₃×C₄×Q₈	C₂×D₅	semidirect
190. C₃×C₄×Q₈	C₂×D₅	semidirect
197. C₃×C₄×D₄	C₂×D₅	semidirect
198. C₃×C₄×D₄	C₂×D₅	semidirect
215. C₅×#41	C₂×C₃×C₄	semidirect
228. C₂×D₂₀	C₂×C₃×C₄	semidirect
247. #688	C₂×C₃×C₄	semidirect
248. #686	C₂×C₃×C₄	semidirect
254. #681	C₂×C₃×C₄	semidirect
258. C₄×#41	C₃×D₅	semidirect
286. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
292. C₃×#41	C₄×D₅	semidirect
341. C₅×Q₈	C₂²×C₃×C₄	semidirect
344. C₅×D₄	C₂²×C₃×C₄	semidirect
369. #168	C₂²×C₃×C₄	semidirect
378. C₄×Q₈	C₂×C₃×D₅	semidirect
379. C₄×Q₈	C₂×C₃×D₅	semidirect
386. C₄×D₄	C₂×C₃×D₅	semidirect
387. C₄×D₄	C₂×C₃×D₅	semidirect
415. C₃×Q₈	C₂×C₄×D₅	semidirect
421. C₃×D₄	C₂×C₄×D₅	semidirect
462. C₄×C₅	C₃×AGL(1,ℤ/8)	semidirect
468. #41	C₃×C₄×D₅	semidirect
510. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
530. C₃×C₄	#4095	direct (N × H)
546. Q₈	C₂×C₃×C₄×D₅	semidirect
552. D₄	C₂×C₃×C₄×D₅	semidirect
581. C₅	C₃×C₄×AGL(1,ℤ/8)	semidirect
601. C₄	C₃×#4095	direct (N × H)
604. C₃	C₄×#4095	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₂×C₃×#4095	2
C₂×C₃×C₄×D₂₀	2
C₃×#65521	2
C₃×#65315	2
C₃×C₄×#688	2
C₃×#65303	2
C₃×C₄×#686	2
C₃×#65290	2
C₃×#65284	2
C₃×C₄×#681	2
C₄×#4095	3
C₃×C₄×AGL(1,ℤ/8)	5

Subgroups — C3×C4×#4095 #14416650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4095 #14416650