Subgroups — C₃×#10615668 #14439127

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66166	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4078	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4054	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65465	C₂	1	2	yes	maximal, complemented
8	C₃×#65464	C₂	1	2	yes	maximal, complemented
9	C₃×#65443	C₂	1	2	yes	maximal, complemented
10	C₃×#65440	C₂	1	2	yes	maximal, complemented
11	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615668	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
16	C₂×C₃×#709	C₂²	1	1	yes	characteristic
17	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
18	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
19	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₃×#4095	—	2	4	no	—
23	C₃×#4093	C₂²	1	1	yes	characteristic, complemented
24	C₃×#4090	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#688	C₂²	1	2	yes	complemented
26	C₃×#4086	—	2	2	no	—
27	C₃×#4086	C₂²	1	2	yes	—
28	C₃×#4086	C₂²	1	2	yes	—
29	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4085	—	2	2	no	—
31	C₃×#4082	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#687	C₂²	1	2	yes	complemented
33	C₃×#4078	—	2	4	no	—
34	C₂×C₃×#686	C₂²	1	2	yes	complemented
35	C₂×C₃×#686	C₂²	1	2	yes	complemented
36	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
37	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×#681	C₂²	1	1	yes	characteristic
39	C₃×#4054	—	2	4	no	—
40	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
41	C₂×C₃×#677	C₂²	1	2	yes	complemented
42	C₃×#3947	C₂²	1	2	yes	complemented
43	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
44	C₃×#3151	—	5	1	no	maximal, Hall
45	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
46	#66166	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#4095	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#4086	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#4078	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4054	C₂×C₃	1	1	yes	characteristic, complemented
51	#65465	C₂×C₃	1	2	yes	complemented
52	#65464	C₂×C₃	1	2	yes	complemented
53	#65443	C₂×C₃	1	2	yes	complemented
54	#65440	C₂×C₃	1	2	yes	complemented
55	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₂³×C₃×D₅	—	2	1	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
70	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
71	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
72	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
73	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
74	C₂²×C₃×Dic₅	D₄	1	2	yes	—
75	C₃×#709	—	2	2	no	—
76	C₃×#709	—	2	2	no	—
77	C₂×C₃×D₂₀	—	2	2	no	—
78	C₂×C₃×D₂₀	—	2	2	no	—
79	C₂×C₃×D₂₀	—	2	1	no	—
80	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
81	C₂×C₃×D₂₀	C₂³	1	2	yes	—
82	C₂×C₃×C₄×D₅	—	2	1	no	—
83	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
84	C₃×C₅×SD₁₆	—	2	4	no	—
85	C₃×C₅×D₈	—	2	4	no	—
86	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
87	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
88	C₃×C₂²⋊Dic₅	—	2	2	no	—
89	C₃×#688	—	2	4	no	—
90	C₃×#687	—	2	4	no	—
91	C₃×#686	—	2	4	no	—
92	C₃×#686	—	2	4	no	—
93	C₃×#685	—	2	2	no	—
94	C₃×#683	—	2	2	no	—
95	C₃×C₄×Dic₅	D₄	1	2	yes	—
96	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
97	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
98	C₃×#681	D₄	1	4	yes	complemented
99	C₂×C₃×#168	C₂³	1	2	yes	—
100	C₃×D₄₀	—	2	4	no	—
101	C₃×#677	—	2	4	no	—
102	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
103	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
104	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
105	C₂×C₃×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic, complemented
106	C₃×#532	—	5	1	no	—
107	C₂×C₃×#127	—	5	1	no	—
108	C₃×#496	—	5	2	no	—
109	C₃×#496	—	5	2	no	—
110	C₃×#493	—	5	2	no	—
111	C₃×#492	—	5	2	no	—
112	C₃×C₄×M₁₆	—	5	1	no	—
113	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₂²⋊D₅	—	2	2	no	—
116	C₂×#709	C₂²×C₃	1	1	yes	characteristic
117	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
118	C₅×AGL(1,ℤ/8)	—	2	4	no	—
119	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
120	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
121	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
122	#4095	—	2	4	no	—
123	#4093	C₂²×C₃	1	1	yes	characteristic, complemented
124	#4090	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×#688	C₂²×C₃	1	2	yes	complemented
126	#4086	—	2	2	no	—
127	#4086	C₂²×C₃	1	2	yes	—
128	#4086	C₂²×C₃	1	2	yes	—
129	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
130	#4085	—	2	2	no	—
131	#4082	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₂×#687	C₂²×C₃	1	2	yes	complemented
133	#4078	—	2	4	no	—
134	C₂×#686	C₂²×C₃	1	2	yes	complemented
135	C₂×#686	C₂²×C₃	1	2	yes	complemented
136	C₄×C₂²⋊D₅	—	2	2	no	—
137	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
138	C₂×#681	C₂²×C₃	1	1	yes	characteristic
139	#4054	—	2	4	no	—
140	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
141	C₂×#677	C₂²×C₃	1	2	yes	complemented
142	#3947	C₂²×C₃	1	2	yes	complemented
143	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
144	#3151	—	5	1	no	Sylow
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	4	4	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	C₂²×C₃×D₅	—	2	2	no	—
152	C₂²×C₃×D₅	—	4	4	no	—
153	C₂²×C₃×D₅	—	4	2	no	—
154	C₃×C₅×Q₈	—	2	1	no	—
155	C₃×C₅×Q₈	—	2	1	no	—
156	C₃×C₅×D₄	—	2	1	no	—
157	C₃×C₅×D₄	—	2	2	no	—
158	C₃×C₅×D₄	—	2	1	no	—
159	C₃×C₅×D₄	—	2	2	no	—
160	C₃×C₅×D₄	—	4	2	no	—
161	C₃×C₅×D₄	—	4	2	no	—
162	C₂×C₃×C₄×C₅	—	2	1	no	—
163	C₂×C₃×C₄×C₅	—	4	2	no	—
164	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₃×C₂²⋊D₅	—	4	8	no	—
169	C₃×C₂²⋊D₅	—	4	2	no	—
170	C₃×C₂²⋊D₅	—	4	4	no	—
171	C₃×C₂²⋊D₅	—	4	8	no	—
172	C₂×C₃×Dic₅	—	2	4	no	—
173	C₂×C₃×Dic₅	—	2	1	no	—
174	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
175	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
176	C₃×D₂₀	—	2	2	no	—
177	C₃×D₂₀	—	2	1	no	—
178	C₃×D₂₀	—	2	1	no	—
179	C₃×D₂₀	—	2	2	no	—
180	C₃×D₂₀	—	4	2	no	—
181	C₃×C₄×D₅	—	4	2	no	—
182	C₃×Dic₁₀	—	2	1	no	—
183	C₃×Dic₁₀	—	2	1	no	—
184	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
185	C₃×#168	C₂×D₄	1	4	yes	complemented
186	C₂×C₃×#41	—	5	1	no	—
187	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
188	C₂²×C₃×D₄	—	5	1	no	—
189	C₂²×C₃×D₄	—	10	2	no	—
190	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
191	C₃×AGL(1,ℤ/8)	—	2	4	no	—
192	C₃×AGL(1,ℤ/8)	—	10	4	no	—
193	C₃×AGL(1,ℤ/8)	—	10	4	no	—
194	C₃×AGL(1,ℤ/8)	—	10	4	no	—
195	C₂×C₃×SD₁₆	—	5	2	no	—
196	C₂×C₃×SD₁₆	—	5	2	no	—
197	C₂×C₃×SD₁₆	—	5	2	no	—
198	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
199	C₂×C₃×D₈	—	5	2	no	—
200	C₂×C₃×D₈	—	5	2	no	—
201	C₂×C₃×D₈	—	5	2	no	—
202	C₂×C₃×D₈	C₂×D₅	1	2	yes	complemented
203	C₂×C₃×M₁₆	—	5	1	no	—
204	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
205	C₃×C₄⋊Q₈	—	5	1	no	—
206	C₃×#127	—	5	2	no	—
207	C₃×#127	—	5	2	no	—
208	C₃×#127	—	5	1	no	—
209	C₃×#127	—	10	2	no	—
210	C₃×#124	—	5	1	no	—
211	C₃×#124	—	5	1	no	—
212	C₃×#121	—	10	2	no	—
213	C₃×C₄×D₄	—	10	2	no	—
214	C₂×C₃×C₄²	—	5	1	no	—
215	C₃×#97	—	5	2	no	—
216	C₃×C₄×C₈	—	5	2	no	—
217	C₂⁴×C₅	—	2	1	no	—
218	C₂³×D₅	—	2	1	no	—
219	C₅×#41	—	2	2	no	—
220	C₅×#41	—	2	2	no	—
221	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₅×D₄	—	2	1	no	—
223	C₂×C₅×D₄	—	2	2	no	—
224	C₂×C₅×D₄	—	2	2	no	—
225	C₂×C₅×D₄	—	2	1	no	—
226	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₂²⋊D₅	—	2	1	no	—
231	C₂×C₂²⋊D₅	—	2	4	no	—
232	C₂×C₂²⋊D₅	—	2	4	no	—
233	C₂×C₂²⋊D₅	—	2	2	no	—
234	C₂×C₂²⋊D₅	—	4	8	no	—
235	C₂²×Dic₅	C₃×D₄	1	2	yes	—
236	#709	—	2	2	no	—
237	#709	—	2	2	no	—
238	C₂×D₂₀	—	2	2	no	—
239	C₂×D₂₀	—	2	2	no	—
240	C₂×D₂₀	—	2	1	no	—
241	C₂×D₂₀	C₂³×C₃	1	2	yes	—
242	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₄×D₅	—	2	1	no	—
244	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
245	C₅×SD₁₆	—	2	4	no	—
246	C₅×D₈	—	2	4	no	—
247	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
248	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
249	C₂²⋊Dic₅	—	2	2	no	—
250	#688	—	2	4	no	—
251	#687	—	2	4	no	—
252	#686	—	2	4	no	—
253	#686	—	2	4	no	—
254	#685	—	2	2	no	—
255	#683	—	2	2	no	—
256	C₄×Dic₅	C₃×D₄	1	2	yes	—
257	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
258	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
259	#681	C₃×D₄	1	4	yes	complemented
260	C₂×#168	C₂³×C₃	1	2	yes	—
261	D₄₀	—	2	4	no	—
262	#677	—	2	4	no	—
263	C₂×AGL(1,ℤ/8)	—	5	1	no	—
264	C₂×AGL(1,ℤ/8)	—	5	1	no	—
265	C₂×AGL(1,ℤ/8)	—	5	1	no	—
266	C₂×AGL(1,ℤ/8)	C₃×D₅	1	1	yes	characteristic, complemented
267	#532	—	5	1	no	—
268	C₂×#127	—	5	1	no	—
269	#496	—	5	2	no	—
270	#496	—	5	2	no	—
271	#493	—	5	2	no	—
272	#492	—	5	2	no	—
273	C₄×M₁₆	—	5	1	no	—
274	C₂²×C₃×C₅	—	2	2	no	—
275	C₂²×C₃×C₅	—	4	1	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	—	4	4	no	—
278	C₂²×C₃×C₅	—	4	2	no	—
279	C₂²×C₃×C₅	—	8	4	no	—
280	C₂²×C₃×C₅	#127	1	2	yes	—
281	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₃×D₅	—	4	1	no	—
283	C₂×C₃×D₅	—	4	2	no	—
284	C₂×C₃×D₅	—	4	4	no	—
285	C₂×C₃×D₅	—	4	2	no	—
286	C₂×C₃×D₅	—	8	4	no	—
287	C₃×C₄×C₅	—	4	1	no	—
288	C₃×C₄×C₅	#127	1	2	yes	—
289	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
290	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
291	C₃×Dic₅	—	2	2	no	—
292	C₃×Dic₅	—	4	1	no	—
293	C₃×Dic₅	AGL(1,ℤ/8)	1	4	yes	complemented
294	C₂⁴×C₃	—	2	1	no	—
295	C₂⁴×C₃	—	10	1	no	—
296	C₃×#41	—	2	2	no	—
297	C₃×#41	—	2	2	no	—
298	C₃×#41	—	10	2	no	—
299	C₃×#41	—	10	2	no	—
300	C₂×C₃×Q₈	—	5	1	no	—
301	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
302	C₂×C₃×D₄	—	2	1	no	—
303	C₂×C₃×D₄	—	2	2	no	—
304	C₂×C₃×D₄	—	2	1	no	—
305	C₂×C₃×D₄	—	2	2	no	—
306	C₂×C₃×D₄	—	5	1	no	—
307	C₂×C₃×D₄	—	5	2	no	—
308	C₂×C₃×D₄	—	10	2	no	—
309	C₂×C₃×D₄	—	10	4	no	—
310	C₂×C₃×D₄	—	10	4	no	—
311	C₂×C₃×D₄	—	10	1	no	—
312	C₂×C₃×D₄	—	10	2	no	—
313	C₂×C₃×D₄	—	10	1	no	—
314	C₂×C₃×D₄	—	10	2	no	—
315	C₂×C₃×D₄	—	20	8	no	—
316	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
317	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
318	C₂²×C₃×C₄	—	2	1	no	—
319	C₂²×C₃×C₄	—	5	2	no	—
320	C₂²×C₃×C₄	—	10	1	no	—
321	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
322	C₃×SD₁₆	—	2	4	no	—
323	C₃×SD₁₆	—	10	4	no	—
324	C₃×SD₁₆	—	10	4	no	—
325	C₃×SD₁₆	—	10	4	no	—
326	C₃×D₈	—	2	4	no	—
327	C₃×D₈	—	10	4	no	—
328	C₃×D₈	—	10	4	no	—
329	C₃×D₈	—	10	4	no	—
330	C₃×M₁₆	—	5	4	no	—
331	C₃×M₁₆	C₂²⋊D₅	1	4	yes	complemented
332	C₂×C₃×C₈	—	5	2	no	—
333	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
334	C₃×C₄⋊C₄	—	10	2	no	—
335	C₃×C₂²⋊C₄	—	10	2	no	—
336	C₃×C₂²⋊C₄	—	10	2	no	—
337	C₃×C₄²	—	5	2	no	—
338	C₃×C₄²	—	5	1	no	—
339	C₃×C₄²	—	5	1	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	4	4	no	—
343	C₂³×C₅	—	4	2	no	—
344	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂²×D₅	—	2	1	no	—
346	C₂²×D₅	—	2	2	no	—
347	C₂²×D₅	—	4	4	no	—
348	C₂²×D₅	—	4	2	no	—
349	C₅×Q₈	—	2	1	no	—
350	C₅×Q₈	—	2	1	no	—
351	C₅×D₄	—	2	1	no	—
352	C₅×D₄	—	2	2	no	—
353	C₅×D₄	—	2	1	no	—
354	C₅×D₄	—	2	2	no	—
355	C₅×D₄	—	4	2	no	—
356	C₅×D₄	—	4	2	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	4	2	no	—
359	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
361	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
362	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
363	C₂²⋊D₅	—	4	8	no	—
364	C₂²⋊D₅	—	4	2	no	—
365	C₂²⋊D₅	—	4	4	no	—
366	C₂²⋊D₅	—	4	8	no	—
367	C₂×Dic₅	—	2	4	no	—
368	C₂×Dic₅	—	2	1	no	—
369	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
370	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
371	D₂₀	—	2	2	no	—
372	D₂₀	—	2	1	no	—
373	D₂₀	—	2	1	no	—
374	D₂₀	—	2	2	no	—
375	D₂₀	—	4	2	no	—
376	C₄×D₅	—	4	2	no	—
377	Dic₁₀	—	2	1	no	—
378	Dic₁₀	—	2	1	no	—
379	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
380	#168	C₂×C₃×D₄	1	4	yes	complemented
381	C₂×#41	—	5	1	no	—
382	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
383	C₂²×D₄	—	5	1	no	—
384	C₂²×D₄	—	10	2	no	—
385	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
386	AGL(1,ℤ/8)	—	2	4	no	—
387	AGL(1,ℤ/8)	—	10	4	no	—
388	AGL(1,ℤ/8)	—	10	4	no	—
389	AGL(1,ℤ/8)	—	10	4	no	—
390	C₂×SD₁₆	—	5	2	no	—
391	C₂×SD₁₆	—	5	2	no	—
392	C₂×SD₁₆	—	5	2	no	—
393	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
394	C₂×D₈	—	5	2	no	—
395	C₂×D₈	—	5	2	no	—
396	C₂×D₈	—	5	2	no	—
397	C₂×D₈	C₂×C₃×D₅	1	2	yes	complemented
398	C₂×M₁₆	—	5	1	no	—
399	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
400	C₄⋊Q₈	—	5	1	no	—
401	#127	—	5	2	no	—
402	#127	—	5	2	no	—
403	#127	—	5	1	no	—
404	#127	—	10	2	no	—
405	#124	—	5	1	no	—
406	#124	—	5	1	no	—
407	#121	—	10	2	no	—
408	C₄×D₄	—	10	2	no	—
409	C₂×C₄²	—	5	1	no	—
410	#97	—	5	2	no	—
411	C₄×C₈	—	5	2	no	—
412	C₂×C₃×C₅	—	2	2	no	—
413	C₂×C₃×C₅	—	8	1	no	—
414	C₂×C₃×C₅	—	8	2	no	—
415	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
416	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
417	C₃×D₅	—	8	1	no	—
418	C₃×D₅	—	8	2	no	—
419	C₂³×C₃	—	2	1	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	4	4	no	—
422	C₂³×C₃	—	4	2	no	—
423	C₂³×C₃	—	10	1	no	—
424	C₂³×C₃	—	10	2	no	—
425	C₂³×C₃	—	20	4	no	—
426	C₂³×C₃	—	20	2	no	—
427	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
428	C₃×Q₈	—	2	1	no	—
429	C₃×Q₈	—	2	1	no	—
430	C₃×Q₈	—	10	1	no	—
431	C₃×Q₈	—	10	1	no	—
432	C₃×D₄	—	2	1	no	—
433	C₃×D₄	—	2	2	no	—
434	C₃×D₄	—	2	1	no	—
435	C₃×D₄	—	2	2	no	—
436	C₃×D₄	—	4	2	no	—
437	C₃×D₄	—	4	2	no	—
438	C₃×D₄	—	10	1	no	—
439	C₃×D₄	—	10	2	no	—
440	C₃×D₄	—	10	1	no	—
441	C₃×D₄	—	10	2	no	—
442	C₃×D₄	—	20	4	no	—
443	C₃×D₄	—	20	8	no	—
444	C₃×D₄	—	20	8	no	—
445	C₃×D₄	—	20	2	no	—
446	C₃×D₄	—	20	2	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	4	2	no	—
449	C₂×C₃×C₄	—	5	2	no	—
450	C₂×C₃×C₄	—	5	2	no	—
451	C₂×C₃×C₄	—	10	4	no	—
452	C₂×C₃×C₄	—	10	1	no	—
453	C₂×C₃×C₄	—	20	2	no	—
454	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
455	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
456	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
457	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
458	C₃×C₈	—	5	4	no	—
459	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
460	C₂²×C₅	—	2	2	no	—
461	C₂²×C₅	—	4	4	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	1	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	8	4	no	—
466	C₂²×C₅	C₃×#127	1	2	yes	—
467	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
468	C₂×D₅	—	4	4	no	—
469	C₂×D₅	—	4	2	no	—
470	C₂×D₅	—	4	1	no	—
471	C₂×D₅	—	4	2	no	—
472	C₂×D₅	—	8	4	no	—
473	C₄×C₅	—	4	1	no	—
474	C₄×C₅	C₃×#127	1	2	yes	—
475	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
476	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
477	Dic₅	—	2	2	no	—
478	Dic₅	—	4	1	no	—
479	Dic₅	C₃×AGL(1,ℤ/8)	1	4	yes	complemented
480	C₂⁴	—	2	1	no	—
481	C₂⁴	—	10	1	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	—	10	2	no	—
485	#41	—	10	2	no	—
486	C₂×Q₈	—	5	1	no	—
487	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	5	1	no	—
493	C₂×D₄	—	5	2	no	—
494	C₂×D₄	—	10	2	no	—
495	C₂×D₄	—	10	4	no	—
496	C₂×D₄	—	10	4	no	—
497	C₂×D₄	—	10	1	no	—
498	C₂×D₄	—	10	2	no	—
499	C₂×D₄	—	10	1	no	—
500	C₂×D₄	—	10	2	no	—
501	C₂×D₄	—	20	8	no	—
502	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
503	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	5	2	no	—
506	C₂²×C₄	—	10	1	no	—
507	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
508	SD₁₆	—	2	4	no	—
509	SD₁₆	—	10	4	no	—
510	SD₁₆	—	10	4	no	—
511	SD₁₆	—	10	4	no	—
512	D₈	—	2	4	no	—
513	D₈	—	10	4	no	—
514	D₈	—	10	4	no	—
515	D₈	—	10	4	no	—
516	M₁₆	—	5	4	no	—
517	M₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
518	C₂×C₈	—	5	2	no	—
519	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
520	C₄⋊C₄	—	10	2	no	—
521	C₂²⋊C₄	—	10	2	no	—
522	C₂²⋊C₄	—	10	2	no	—
523	C₄²	—	5	2	no	—
524	C₄²	—	5	1	no	—
525	C₄²	—	5	1	no	—
526	C₃×C₅	#3151	1	1	yes	characteristic, complemented, Hall
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	4	4	no	—
529	C₂²×C₃	—	4	2	no	—
530	C₂²×C₃	—	4	1	no	—
531	C₂²×C₃	—	4	2	no	—
532	C₂²×C₃	—	8	4	no	—
533	C₂²×C₃	—	20	4	no	—
534	C₂²×C₃	—	20	2	no	—
535	C₂²×C₃	—	20	1	no	—
536	C₂²×C₃	—	20	2	no	—
537	C₂²×C₃	—	40	4	no	—
538	C₂²×C₃	#4086	1	2	yes	—
539	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
540	C₃×C₄	—	4	1	no	—
541	C₃×C₄	—	5	4	no	—
542	C₃×C₄	—	10	2	no	—
543	C₃×C₄	—	20	1	no	—
544	C₃×C₄	#4086	1	2	yes	—
545	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
546	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
547	C₂×C₅	—	2	2	no	—
548	C₂×C₅	—	8	2	no	—
549	C₂×C₅	—	8	1	no	—
550	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
551	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
552	D₅	—	8	2	no	—
553	D₅	—	8	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	4	4	no	—
557	C₂³	—	4	2	no	—
558	C₂³	—	10	1	no	—
559	C₂³	—	10	2	no	—
560	C₂³	—	20	4	no	—
561	C₂³	—	20	2	no	—
562	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
563	Q₈	—	2	1	no	—
564	Q₈	—	2	1	no	—
565	Q₈	—	10	1	no	—
566	Q₈	—	10	1	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	2	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	10	1	no	—
574	D₄	—	10	2	no	—
575	D₄	—	10	1	no	—
576	D₄	—	10	2	no	—
577	D₄	—	20	8	no	—
578	D₄	—	20	4	no	—
579	D₄	—	20	8	no	—
580	D₄	—	20	2	no	—
581	D₄	—	20	2	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	5	2	no	—
585	C₂×C₄	—	5	2	no	—
586	C₂×C₄	—	10	4	no	—
587	C₂×C₄	—	10	1	no	—
588	C₂×C₄	—	20	2	no	—
589	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
590	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
591	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
592	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
593	C₈	—	5	4	no	—
594	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	complemented
595	C₂×C₃	—	2	2	no	—
596	C₂×C₃	—	8	2	no	—
597	C₂×C₃	—	8	1	no	—
598	C₂×C₃	—	40	2	no	—
599	C₂×C₃	—	40	1	no	—
600	C₂×C₃	D₅×AGL(1,ℤ/8)	1	2	yes	—
601	C₂×C₃	C₂×#4086	1	1	yes	characteristic
602	C₅	C₃×#3151	1	1	yes	characteristic, complemented, Sylow
603	C₂²	—	2	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	8	4	no	—
609	C₂²	—	20	4	no	—
610	C₂²	—	20	2	no	—
611	C₂²	—	20	1	no	—
612	C₂²	—	20	2	no	—
613	C₂²	—	40	4	no	—
614	C₂²	C₃×#4086	1	2	yes	—
615	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
616	C₄	—	4	1	no	—
617	C₄	—	5	4	no	—
618	C₄	—	10	2	no	—
619	C₄	—	20	1	no	—
620	C₄	C₃×#4086	1	2	yes	—
621	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
622	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
623	C₃	#10615668	1	1	yes	characteristic, direct product factor, Sylow
624	C₂	—	2	2	no	—
625	C₂	—	8	2	no	—
626	C₂	—	8	1	no	—
627	C₂	—	40	2	no	—
628	C₂	—	40	1	no	—
629	C₂	C₃×D₅×AGL(1,ℤ/8)	1	2	yes	—
630	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₃×#3151
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₃×#66166	C₂	semidirect
3. C₂×C₃×#4095	C₂	semidirect
4. C₂×C₃×#4086	C₂	semidirect
5. C₂×C₃×#4078	C₂	semidirect
6. C₂×C₃×#4054	C₂	semidirect
7. C₃×#65465	C₂	semidirect
8. C₃×#65464	C₂	semidirect
9. C₃×#65443	C₂	semidirect
10. C₃×#65440	C₂	semidirect
11. C₃×M₁₆×Dic₅	C₂	semidirect
12. #10615668	C₃	direct (N × H)
19. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
20. C₂×C₃×C₅×D₈	C₂²	semidirect
23. C₃×#4093	C₂²	semidirect
24. C₃×#4090	C₂²	semidirect
25. C₂×C₃×#688	C₂²	semidirect
29. C₃×#4086	C₂²	semidirect
31. C₃×#4082	C₂²	semidirect
32. C₂×C₃×#687	C₂²	semidirect
34. C₂×C₃×#686	C₂²	semidirect
35. C₂×C₃×#686	C₂²	semidirect
40. C₂×C₃×D₄₀	C₂²	semidirect
41. C₂×C₃×#677	C₂²	semidirect
42. C₃×#3947	C₂²	semidirect
43. C₃×C₈×Dic₅	C₂²	semidirect
45. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
46. #66166	C₂×C₃	semidirect
47. C₂×#4095	C₂×C₃	semidirect
48. C₂×#4086	C₂×C₃	semidirect
49. C₂×#4078	C₂×C₃	semidirect
50. C₂×#4054	C₂×C₃	semidirect
51. #65465	C₂×C₃	semidirect
52. #65464	C₂×C₃	semidirect
53. #65443	C₂×C₃	semidirect
54. #65440	C₂×C₃	semidirect
55. M₁₆×Dic₅	C₂×C₃	semidirect
86. C₃×C₅×M₁₆	D₄	semidirect
98. C₃×#681	D₄	semidirect
105. C₂×C₃×AGL(1,ℤ/8)	D₅	semidirect
119. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
120. C₂×C₅×D₈	C₂²×C₃	semidirect
123. #4093	C₂²×C₃	semidirect
124. #4090	C₂²×C₃	semidirect
125. C₂×#688	C₂²×C₃	semidirect
129. #4086	C₂²×C₃	semidirect
131. #4082	C₂²×C₃	semidirect
132. C₂×#687	C₂²×C₃	semidirect
134. C₂×#686	C₂²×C₃	semidirect
135. C₂×#686	C₂²×C₃	semidirect
140. C₂×D₄₀	C₂²×C₃	semidirect
141. C₂×#677	C₂²×C₃	semidirect
142. #3947	C₂²×C₃	semidirect
143. C₈×Dic₅	C₂²×C₃	semidirect
184. C₃×C₅×C₈	C₂×D₄	semidirect
185. C₃×#168	C₂×D₄	semidirect
198. C₂×C₃×SD₁₆	C₂×D₅	semidirect
202. C₂×C₃×D₈	C₂×D₅	semidirect
247. C₅×M₁₆	C₃×D₄	semidirect
259. #681	C₃×D₄	semidirect
266. C₂×AGL(1,ℤ/8)	C₃×D₅	semidirect
293. C₃×Dic₅	AGL(1,ℤ/8)	semidirect
331. C₃×M₁₆	C₂²⋊D₅	semidirect
379. C₅×C₈	C₂×C₃×D₄	semidirect
380. #168	C₂×C₃×D₄	semidirect
393. C₂×SD₁₆	C₂×C₃×D₅	semidirect
397. C₂×D₈	C₂×C₃×D₅	semidirect
459. C₃×C₈	C₂×C₂²⋊D₅	semidirect
479. Dic₅	C₃×AGL(1,ℤ/8)	semidirect
517. M₁₆	C₃×C₂²⋊D₅	semidirect
526. C₃×C₅	#3151	semidirect
594. C₈	C₂×C₃×C₂²⋊D₅	semidirect
602. C₅	C₃×#3151	semidirect
623. C₃	#10615668	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×C₅×AGL(1,ℤ/8)	2
C₃×#66166	2
C₂×C₃×#4095	2
C₂×C₃×#4086	2
C₂×C₃×#4078	2
C₂×C₃×#4054	2
C₃×#65465	2
C₃×#65464	2
C₃×#65443	2
C₃×#65440	2
C₃×M₁₆×Dic₅	2
#10615668	3
C₃×#3151	5

Subgroups — C3×#10615668 #14439127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615668 #14439127