Subgroups — C₃×#10615661 #14417007

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 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
2	C₃×#66161	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66132	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3964	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65453	C₂	1	2	yes	maximal, complemented
7	C₃×SD₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
8	C₃×#65441	C₂	1	2	yes	maximal, complemented
9	C₃×D₈×Dic₅	C₂	1	2	yes	maximal, complemented
10	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65410	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615661	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	C₃×C₅×AGL(1,ℤ/8)	C₄	1	8	yes	complemented
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊Dic₅	—	2	2	no	—
20	C₃×Q₈×Dic₅	C₂²	1	2	yes	complemented
21	C₃×D₄×Dic₅	—	2	2	no	—
22	C₃×D₄×Dic₅	—	2	1	no	—
23	C₃×D₄×Dic₅	—	2	1	no	—
24	C₃×D₄×Dic₅	C₂²	1	2	yes	—
25	C₃×D₄×Dic₅	C₂²	1	2	yes	—
26	C₃×D₄×Dic₅	C₂²	1	2	yes	complemented
27	C₃×#4072	—	2	1	no	—
28	C₃×#4072	C₂²	1	1	yes	characteristic
29	C₃×#4072	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
31	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
32	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3964	C₂²	1	2	yes	—
36	C₃×#3964	C₂²	1	2	yes	—
37	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3950	C₂²	1	2	yes	complemented
40	C₃×#3949	C₂²	1	2	yes	complemented
41	C₃×#3947	C₂²	1	2	yes	complemented
42	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
43	C₃×#2946	—	5	1	no	maximal, Hall
44	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
45	#66161	C₂×C₃	1	1	yes	characteristic, complemented
46	#66132	C₂×C₃	1	1	yes	characteristic, complemented
47	#65522	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#3964	C₂×C₃	1	1	yes	characteristic, complemented
49	#65453	C₂×C₃	1	2	yes	complemented
50	SD₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
51	#65441	C₂×C₃	1	2	yes	complemented
52	D₈×Dic₅	C₂×C₃	1	2	yes	complemented
53	#65411	C₂×C₃	1	1	yes	characteristic, complemented
54	#65410	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂⁴×C₃×C₅	—	2	1	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×Dic₅	—	2	1	no	—
68	C₂²×C₃×Dic₅	—	2	2	no	—
69	C₂²×C₃×Dic₅	—	2	2	no	—
70	C₂²×C₃×Dic₅	—	2	2	no	—
71	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
72	C₃×C₅×D₈	C₂×C₄	1	8	yes	complemented
73	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₃×C₂²⋊Dic₅	—	2	1	no	—
76	C₃×C₂²⋊Dic₅	—	2	2	no	—
77	C₃×C₂²⋊Dic₅	—	2	2	no	—
78	C₃×C₂²⋊Dic₅	—	2	2	no	—
79	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
80	C₃×C₄⋊Dic₅	—	2	1	no	—
81	C₃×C₄⋊Dic₅	—	2	2	no	—
82	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
83	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
84	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
86	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
87	C₃×C₄×Dic₅	—	2	1	no	—
88	C₃×C₄×Dic₅	—	2	2	no	—
89	C₃×C₄×Dic₅	C₂³	1	2	yes	—
90	C₂×C₃×#168	—	2	2	no	—
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	1	yes	characteristic
93	C₂×C₃×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic
94	C₃×#520	—	5	1	no	—
95	C₃×#518	—	5	1	no	—
96	C₃×#442	—	5	2	no	—
97	C₃×#440	—	5	2	no	—
98	C₃×C₄×SD₁₆	—	5	2	no	—
99	C₃×C₄×D₈	—	5	2	no	—
100	C₃×#428	—	5	1	no	—
101	C₃×#416	—	5	1	no	—
102	C₂×C₃×#102	—	5	1	no	—
103	C₃×#405	—	5	1	no	—
104	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
105	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
106	C₅×AGL(1,ℤ/8)	C₃×C₄	1	8	yes	complemented
107	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
108	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
109	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₂²⋊Dic₅	—	2	2	no	—
111	Q₈×Dic₅	C₂²×C₃	1	2	yes	complemented
112	D₄×Dic₅	—	2	2	no	—
113	D₄×Dic₅	—	2	1	no	—
114	D₄×Dic₅	—	2	1	no	—
115	D₄×Dic₅	C₂²×C₃	1	2	yes	—
116	D₄×Dic₅	C₂²×C₃	1	2	yes	—
117	D₄×Dic₅	C₂²×C₃	1	2	yes	complemented
118	#4072	—	2	1	no	—
119	#4072	C₂²×C₃	1	1	yes	characteristic
120	#4072	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₄⋊Dic₅	—	2	1	no	—
122	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
123	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
124	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
126	#3964	C₂²×C₃	1	2	yes	—
127	#3964	C₂²×C₃	1	2	yes	—
128	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
129	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
130	#3950	C₂²×C₃	1	2	yes	complemented
131	#3949	C₂²×C₃	1	2	yes	complemented
132	#3947	C₂²×C₃	1	2	yes	complemented
133	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
134	#2946	—	5	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	—	2	4	no	—
138	C₂³×C₃×C₅	—	8	1	no	—
139	C₂³×C₃×C₅	—	8	1	no	—
140	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
141	C₃×C₅×Q₈	—	2	1	no	—
142	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×D₄	—	2	4	no	—
144	C₃×C₅×D₄	—	2	4	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
148	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	4	no	—
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	#41	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₂×C₃×Dic₅	—	2	2	no	—
156	C₂×C₃×Dic₅	—	2	1	no	—
157	C₂×C₃×Dic₅	—	2	1	no	—
158	C₂×C₃×Dic₅	—	8	2	no	—
159	C₂×C₃×Dic₅	—	8	2	no	—
160	C₂×C₃×Dic₅	—	8	2	no	—
161	C₂×C₃×Dic₅	—	8	1	no	—
162	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
163	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
164	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
165	C₃×#168	—	2	1	no	—
166	C₃×#168	—	2	1	no	—
167	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
168	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
169	C₃×AGL(1,ℤ/8)	Dic₅	1	8	yes	complemented
170	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
171	C₂×C₃×D₈	C₂×D₅	1	2	yes	—
172	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
173	C₂²×C₃×C₈	—	5	1	no	—
174	C₃×C₄×Q₈	—	5	2	no	—
175	C₃×C₄×D₄	—	5	2	no	—
176	C₃×C₄×D₄	—	5	2	no	—
177	C₃×C₄×D₄	—	5	2	no	—
178	C₃×C₄×D₄	—	10	2	no	—
179	C₃×C₄×D₄	—	10	1	no	—
180	C₃×C₄×D₄	—	10	1	no	—
181	C₃×#117	—	5	1	no	—
182	C₃×#117	—	5	1	no	—
183	C₃×#117	—	10	1	no	—
184	C₂×C₃×C₄⋊C₄	—	5	1	no	—
185	C₂×C₃×C₄⋊C₄	—	10	1	no	—
186	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
187	C₃×#107	—	5	2	no	—
188	C₃×#106	—	5	2	no	—
189	C₃×#103	—	5	1	no	—
190	C₃×#103	—	5	1	no	—
191	C₃×#102	—	5	2	no	—
192	C₃×#102	—	5	2	no	—
193	C₃×#102	—	5	1	no	—
194	C₃×#102	—	5	1	no	—
195	C₃×#97	—	5	2	no	—
196	C₃×C₄×C₈	—	5	2	no	—
197	C₂⁴×C₅	—	2	1	no	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	C₂×C₃×C₄	1	4	yes	complemented
200	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	—	2	2	no	—
204	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
205	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂²×Dic₅	—	2	1	no	—
210	C₂²×Dic₅	—	2	2	no	—
211	C₂²×Dic₅	—	2	2	no	—
212	C₂²×Dic₅	—	2	2	no	—
213	C₅×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
214	C₅×D₈	C₂×C₃×C₄	1	8	yes	complemented
215	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
216	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
217	C₂²⋊Dic₅	—	2	1	no	—
218	C₂²⋊Dic₅	—	2	2	no	—
219	C₂²⋊Dic₅	—	2	2	no	—
220	C₂²⋊Dic₅	—	2	2	no	—
221	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
222	C₄⋊Dic₅	—	2	1	no	—
223	C₄⋊Dic₅	—	2	2	no	—
224	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
225	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
226	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
227	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
228	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
229	C₄×Dic₅	—	2	1	no	—
230	C₄×Dic₅	—	2	2	no	—
231	C₄×Dic₅	C₂³×C₃	1	2	yes	—
232	C₂×#168	—	2	2	no	—
233	C₂×#168	C₂³×C₃	1	1	yes	characteristic
234	C₂×#168	C₂³×C₃	1	1	yes	characteristic
235	C₂×AGL(1,ℤ/8)	C₃×D₅	1	1	yes	characteristic
236	#520	—	5	1	no	—
237	#518	—	5	1	no	—
238	#442	—	5	2	no	—
239	#440	—	5	2	no	—
240	C₄×SD₁₆	—	5	2	no	—
241	C₄×D₈	—	5	2	no	—
242	#428	—	5	1	no	—
243	#416	—	5	1	no	—
244	C₂×#102	—	5	1	no	—
245	#405	—	5	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	2	4	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	—	4	2	no	—
252	C₂²×C₃×C₅	—	4	2	no	—
253	C₂²×C₃×C₅	—	4	1	no	—
254	C₂²×C₃×C₅	—	8	4	no	—
255	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
256	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
259	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
260	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₃×Dic₅	—	2	2	no	—
262	C₃×Dic₅	—	2	2	no	—
263	C₃×Dic₅	—	4	2	no	—
264	C₃×Dic₅	—	4	1	no	—
265	C₃×Dic₅	—	4	1	no	—
266	C₂⁴×C₃	—	2	1	no	—
267	C₃×#41	—	2	2	no	—
268	C₃×#41	C₂×Dic₅	1	4	yes	complemented
269	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	complemented
274	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
276	C₂²×C₃×C₄	—	2	1	no	—
277	C₂²×C₃×C₄	—	10	2	no	—
278	C₂²×C₃×C₄	—	10	2	no	—
279	C₂²×C₃×C₄	—	10	2	no	—
280	C₂²×C₃×C₄	—	10	1	no	—
281	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
282	C₃×SD₁₆	C₂×Dic₅	1	8	yes	complemented
283	C₃×D₈	C₂×Dic₅	1	8	yes	complemented
284	C₃×M₁₆	C₂×Dic₅	1	4	yes	complemented
285	C₂×C₃×C₈	—	5	1	no	—
286	C₂×C₃×C₈	—	5	1	no	—
287	C₂×C₃×C₈	—	10	2	no	—
288	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
289	C₃×C₄⋊C₄	—	5	1	no	—
290	C₃×C₄⋊C₄	—	5	1	no	—
291	C₃×C₄⋊C₄	—	5	2	no	—
292	C₃×C₄⋊C₄	—	5	1	no	—
293	C₃×C₄⋊C₄	—	5	1	no	—
294	C₃×C₄⋊C₄	—	10	2	no	—
295	C₃×C₄⋊C₄	—	10	1	no	—
296	C₃×C₂²⋊C₄	—	5	2	no	—
297	C₃×C₂²⋊C₄	—	10	2	no	—
298	C₃×C₂²⋊C₄	—	10	2	no	—
299	C₃×C₂²⋊C₄	—	10	2	no	—
300	C₃×C₂²⋊C₄	—	10	1	no	—
301	C₃×C₄²	—	5	2	no	—
302	C₃×C₄²	—	10	2	no	—
303	C₃×C₄²	—	10	1	no	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	2	4	no	—
307	C₂³×C₅	—	8	1	no	—
308	C₂³×C₅	—	8	1	no	—
309	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₅×Q₈	—	2	1	no	—
311	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
312	C₅×D₄	—	2	4	no	—
313	C₅×D₄	—	2	4	no	—
314	C₅×D₄	—	2	2	no	—
315	C₅×D₄	—	2	1	no	—
316	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
317	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	4	no	—
320	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
321	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₃×#41	1	2	yes	—
323	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
324	C₂×Dic₅	—	2	2	no	—
325	C₂×Dic₅	—	2	1	no	—
326	C₂×Dic₅	—	2	1	no	—
327	C₂×Dic₅	—	8	2	no	—
328	C₂×Dic₅	—	8	2	no	—
329	C₂×Dic₅	—	8	2	no	—
330	C₂×Dic₅	—	8	1	no	—
331	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
332	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
333	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
334	#168	—	2	1	no	—
335	#168	—	2	1	no	—
336	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
337	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
338	AGL(1,ℤ/8)	C₃×Dic₅	1	8	yes	complemented
339	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
340	C₂×D₈	C₂×C₃×D₅	1	2	yes	—
341	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
342	C₂²×C₈	—	5	1	no	—
343	C₄×Q₈	—	5	2	no	—
344	C₄×D₄	—	5	2	no	—
345	C₄×D₄	—	5	2	no	—
346	C₄×D₄	—	5	2	no	—
347	C₄×D₄	—	10	2	no	—
348	C₄×D₄	—	10	1	no	—
349	C₄×D₄	—	10	1	no	—
350	#117	—	5	1	no	—
351	#117	—	5	1	no	—
352	#117	—	10	1	no	—
353	C₂×C₄⋊C₄	—	5	1	no	—
354	C₂×C₄⋊C₄	—	10	1	no	—
355	C₂×C₂²⋊C₄	—	10	2	no	—
356	#107	—	5	2	no	—
357	#106	—	5	2	no	—
358	#103	—	5	1	no	—
359	#103	—	5	1	no	—
360	#102	—	5	2	no	—
361	#102	—	5	2	no	—
362	#102	—	5	1	no	—
363	#102	—	5	1	no	—
364	#97	—	5	2	no	—
365	C₄×C₈	—	5	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	—	4	4	no	—
369	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
370	C₂×C₃×C₅	#576	1	1	yes	characteristic
371	C₂×C₃×C₅	#577	1	1	yes	characteristic
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	4	no	—
375	C₂³×C₃	—	8	1	no	—
376	C₂³×C₃	—	8	1	no	—
377	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
378	C₃×Q₈	—	2	1	no	—
379	C₃×Q₈	C₂²×Dic₅	1	2	yes	—
380	C₃×D₄	—	2	4	no	—
381	C₃×D₄	—	2	2	no	—
382	C₃×D₄	—	2	1	no	—
383	C₃×D₄	—	2	4	no	—
384	C₃×D₄	C₂²×Dic₅	1	2	yes	—
385	C₃×D₄	C₂²×Dic₅	1	4	yes	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	4	no	—
388	C₂×C₃×C₄	—	5	2	no	—
389	C₂×C₃×C₄	—	5	2	no	—
390	C₂×C₃×C₄	—	10	1	no	—
391	C₂×C₃×C₄	—	10	1	no	—
392	C₂×C₃×C₄	—	10	2	no	—
393	C₂×C₃×C₄	—	40	2	no	—
394	C₂×C₃×C₄	—	40	2	no	—
395	C₂×C₃×C₄	—	40	2	no	—
396	C₂×C₃×C₄	—	40	1	no	—
397	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
398	C₂×C₃×C₄	#711	1	2	yes	—
399	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
400	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
401	C₃×C₈	—	10	1	no	—
402	C₃×C₈	—	10	1	no	—
403	C₃×C₈	C₂²×Dic₅	1	4	yes	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	4	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	2	no	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	—	8	4	no	—
413	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
414	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
417	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
418	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
419	Dic₅	—	2	2	no	—
420	Dic₅	—	2	2	no	—
421	Dic₅	—	4	2	no	—
422	Dic₅	—	4	1	no	—
423	Dic₅	—	4	1	no	—
424	C₂⁴	—	2	1	no	—
425	#41	—	2	2	no	—
426	#41	C₂×C₃×Dic₅	1	4	yes	complemented
427	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	complemented
432	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
433	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	10	2	no	—
436	C₂²×C₄	—	10	2	no	—
437	C₂²×C₄	—	10	2	no	—
438	C₂²×C₄	—	10	1	no	—
439	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
440	SD₁₆	C₂×C₃×Dic₅	1	8	yes	complemented
441	D₈	C₂×C₃×Dic₅	1	8	yes	complemented
442	M₁₆	C₂×C₃×Dic₅	1	4	yes	complemented
443	C₂×C₈	—	5	1	no	—
444	C₂×C₈	—	5	1	no	—
445	C₂×C₈	—	10	2	no	—
446	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
447	C₄⋊C₄	—	5	1	no	—
448	C₄⋊C₄	—	5	1	no	—
449	C₄⋊C₄	—	5	2	no	—
450	C₄⋊C₄	—	5	1	no	—
451	C₄⋊C₄	—	5	1	no	—
452	C₄⋊C₄	—	10	2	no	—
453	C₄⋊C₄	—	10	1	no	—
454	C₂²⋊C₄	—	5	2	no	—
455	C₂²⋊C₄	—	10	2	no	—
456	C₂²⋊C₄	—	10	2	no	—
457	C₂²⋊C₄	—	10	2	no	—
458	C₂²⋊C₄	—	10	1	no	—
459	C₄²	—	5	2	no	—
460	C₄²	—	10	2	no	—
461	C₄²	—	10	1	no	—
462	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	4	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	—	4	2	no	—
469	C₂²×C₃	—	4	2	no	—
470	C₂²×C₃	—	4	1	no	—
471	C₂²×C₃	—	8	4	no	—
472	C₂²×C₃	D₄×Dic₅	1	2	yes	—
473	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	10	2	no	—
476	C₃×C₄	—	10	2	no	—
477	C₃×C₄	—	20	1	no	—
478	C₃×C₄	—	20	2	no	—
479	C₃×C₄	—	20	1	no	—
480	C₃×C₄	D₄×Dic₅	1	2	yes	—
481	C₃×C₄	C₂×#711	1	1	yes	characteristic
482	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
483	C₂×C₅	—	2	2	no	—
484	C₂×C₅	—	4	4	no	—
485	C₂×C₅	—	4	2	no	—
486	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
487	C₂×C₅	C₃×#576	1	1	yes	characteristic
488	C₂×C₅	C₃×#577	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	8	1	no	—
493	C₂³	—	8	1	no	—
494	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
495	Q₈	—	2	1	no	—
496	Q₈	C₂²×C₃×Dic₅	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	2	no	—
500	D₄	—	2	1	no	—
501	D₄	C₂²×C₃×Dic₅	1	2	yes	—
502	D₄	C₂²×C₃×Dic₅	1	4	yes	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	5	2	no	—
506	C₂×C₄	—	5	2	no	—
507	C₂×C₄	—	10	1	no	—
508	C₂×C₄	—	10	1	no	—
509	C₂×C₄	—	10	2	no	—
510	C₂×C₄	—	40	2	no	—
511	C₂×C₄	—	40	2	no	—
512	C₂×C₄	—	40	2	no	—
513	C₂×C₄	—	40	1	no	—
514	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
515	C₂×C₄	C₃×#711	1	2	yes	—
516	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
517	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
518	C₈	—	10	1	no	—
519	C₈	—	10	1	no	—
520	C₈	C₂²×C₃×Dic₅	1	4	yes	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	4	4	no	—
523	C₂×C₃	—	4	2	no	—
524	C₂×C₃	#66108	1	1	yes	characteristic
525	C₂×C₃	#66109	1	1	yes	characteristic
526	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
527	C₅	C₃×#2946	1	1	yes	characteristic, complemented, Sylow
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	8	4	no	—
537	C₂²	C₃×D₄×Dic₅	1	2	yes	—
538	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	10	2	no	—
541	C₄	—	10	2	no	—
542	C₄	—	20	1	no	—
543	C₄	—	20	2	no	—
544	C₄	—	20	1	no	—
545	C₄	C₃×D₄×Dic₅	1	2	yes	—
546	C₄	C₂×C₃×#711	1	1	yes	characteristic
547	C₄	C₂³×C₃×Dic₅	1	1	yes	characteristic
548	C₃	#10615661	1	1	yes	characteristic, direct product factor, Sylow
549	C₂	—	2	2	no	—
550	C₂	—	4	4	no	—
551	C₂	—	4	2	no	—
552	C₂	C₃×#66108	1	1	yes	characteristic
553	C₂	C₃×#66109	1	1	yes	characteristic
554	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₃×#2946
LCS	G ▷ 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
2. C₃×#66161	C₂	semidirect
3. C₃×#66132	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₂×C₃×#3964	C₂	semidirect
6. C₃×#65453	C₂	semidirect
7. C₃×SD₁₆×Dic₅	C₂	semidirect
8. C₃×#65441	C₂	semidirect
9. C₃×D₈×Dic₅	C₂	semidirect
10. C₃×#65411	C₂	semidirect
11. C₃×#65410	C₂	semidirect
12. #10615661	C₃	direct (N × H)
15. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
20. C₃×Q₈×Dic₅	C₂²	semidirect
26. C₃×D₄×Dic₅	C₂²	semidirect
33. C₃×#3967	C₂²	semidirect
34. C₃×#3967	C₂²	semidirect
37. C₃×#3964	C₂²	semidirect
38. C₃×#3964	C₂²	semidirect
39. C₃×#3950	C₂²	semidirect
40. C₃×#3949	C₂²	semidirect
41. C₃×#3947	C₂²	semidirect
42. C₃×C₈×Dic₅	C₂²	semidirect
45. #66161	C₂×C₃	semidirect
46. #66132	C₂×C₃	semidirect
47. #65522	C₂×C₃	semidirect
48. C₂×#3964	C₂×C₃	semidirect
49. #65453	C₂×C₃	semidirect
50. SD₁₆×Dic₅	C₂×C₃	semidirect
51. #65441	C₂×C₃	semidirect
52. D₈×Dic₅	C₂×C₃	semidirect
53. #65411	C₂×C₃	semidirect
54. #65410	C₂×C₃	semidirect
57. C₃×C₅×#41	C₂×C₄	semidirect
62. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
71. C₃×C₅×SD₁₆	C₂×C₄	semidirect
72. C₃×C₅×D₈	C₂×C₄	semidirect
73. C₃×C₅×M₁₆	C₂×C₄	semidirect
106. C₅×AGL(1,ℤ/8)	C₃×C₄	semidirect
111. Q₈×Dic₅	C₂²×C₃	semidirect
117. D₄×Dic₅	C₂²×C₃	semidirect
124. #3967	C₂²×C₃	semidirect
125. #3967	C₂²×C₃	semidirect
128. #3964	C₂²×C₃	semidirect
129. #3964	C₂²×C₃	semidirect
130. #3950	C₂²×C₃	semidirect
131. #3949	C₂²×C₃	semidirect
132. #3947	C₂²×C₃	semidirect
133. C₈×Dic₅	C₂²×C₃	semidirect
169. C₃×AGL(1,ℤ/8)	Dic₅	semidirect
199. C₅×#41	C₂×C₃×C₄	semidirect
204. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
213. C₅×SD₁₆	C₂×C₃×C₄	semidirect
214. C₅×D₈	C₂×C₃×C₄	semidirect
215. C₅×M₁₆	C₂×C₃×C₄	semidirect
268. C₃×#41	C₂×Dic₅	semidirect
273. C₂×C₃×D₄	C₂×Dic₅	semidirect
282. C₃×SD₁₆	C₂×Dic₅	semidirect
283. C₃×D₈	C₂×Dic₅	semidirect
284. C₃×M₁₆	C₂×Dic₅	semidirect
338. AGL(1,ℤ/8)	C₃×Dic₅	semidirect
426. #41	C₂×C₃×Dic₅	semidirect
431. C₂×D₄	C₂×C₃×Dic₅	semidirect
440. SD₁₆	C₂×C₃×Dic₅	semidirect
441. D₈	C₂×C₃×Dic₅	semidirect
442. M₁₆	C₂×C₃×Dic₅	semidirect
462. C₃×C₅	#2946	semidirect
527. C₅	C₃×#2946	semidirect
548. C₃	#10615661	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×#66161	2
C₃×#66132	2
C₃×#65522	2
C₂×C₃×#3964	2
C₃×#65453	2
C₃×SD₁₆×Dic₅	2
C₃×#65441	2
C₃×D₈×Dic₅	2
C₃×#65411	2
C₃×#65410	2
#10615661	3
C₃×#2946	5

Subgroups — C3×#10615661 #14417007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615661 #14417007