Subgroups — C₃×#10611628 #14418012

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66102	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅×#131	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65434	C₂	1	2	yes	maximal, complemented
6	C₃×#65184	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65182	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65113	C₂	1	2	yes	maximal, complemented
9	C₃×#65110	C₂	1	2	yes	maximal, complemented
10	C₃×#65006	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64997	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611628	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	C₂²	1	2	yes	—
14	C₃×C₅×#135	C₂²	1	1	yes	characteristic
15	C₃×C₅×#131	C₂²	1	2	yes	complemented
16	C₃×#4096	C₂²	1	2	yes	—
17	C₃×#4094	C₂²	1	2	yes	complemented
18	C₃×#4064	C₄	1	2	yes	complemented
19	C₃×#4061	C₄	1	2	yes	complemented
20	C₃×#4060	C₄	1	2	yes	complemented
21	C₃×#4057	C₄	1	2	yes	complemented
22	C₃×#4053	—	2	2	no	—
23	C₃×#4053	C₂²	1	2	yes	complemented
24	C₃×D₅×M₁₆	—	2	2	no	—
25	C₃×D₅×M₁₆	C₂²	1	2	yes	—
26	C₃×#4050	C₂²	1	1	yes	characteristic
27	C₃×#4047	—	2	2	no	—
28	C₃×#4047	C₂²	1	2	yes	complemented
29	C₂×C₃×#676	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₈×D₅	—	2	2	no	—
31	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
32	C₃×#4018	C₂²	1	1	yes	characteristic
33	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#104	C₂²	1	2	yes	complemented
35	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3969	C₂²	1	2	yes	complemented
37	C₃×#3957	C₂²	1	2	yes	complemented
38	C₃×#3954	C₂²	1	2	yes	complemented
39	C₃×#3951	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3937	C₂²	1	2	yes	complemented
43	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
44	C₃×#2955	—	5	1	no	maximal, Hall
45	#66102	C₂×C₃	1	1	yes	characteristic
46	D₅×#131	C₂×C₃	1	2	yes	complemented
47	C₅×#444	C₂×C₃	1	1	yes	characteristic, complemented
48	#65485	C₂×C₃	1	1	yes	characteristic, complemented
49	#65434	C₂×C₃	1	2	yes	complemented
50	#65184	C₂×C₃	1	1	yes	characteristic, complemented
51	#65182	C₂×C₃	1	1	yes	characteristic, complemented
52	#65113	C₂×C₃	1	2	yes	complemented
53	#65110	C₂×C₃	1	2	yes	complemented
54	#65006	C₂×C₃	1	1	yes	characteristic, complemented
55	#64997	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	C₂³	1	2	yes	—
57	C₃×#713	C₂×C₄	1	2	yes	—
58	C₃×Q₈×D₅	C₂×C₄	1	2	yes	—
59	C₃×#711	—	2	2	no	—
60	C₃×#711	C₂×C₄	1	2	yes	—
61	C₃×D₄×D₅	—	2	2	no	—
62	C₃×D₄×D₅	C₂×C₄	1	2	yes	—
63	C₃×#709	—	2	2	no	—
64	C₃×#709	C₂³	1	2	yes	—
65	C₂×C₃×C₄×D₅	—	2	2	no	—
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
68	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	—
69	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic
70	C₃×C₅×M₁₆	—	2	2	no	—
71	C₃×C₅×M₁₆	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	—	2	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×#689	C₂×C₄	1	2	yes	—
77	C₃×#688	C₂×C₄	1	2	yes	—
78	C₃×#687	C₂×C₄	1	2	yes	—
79	C₃×#686	C₂×C₄	1	2	yes	—
80	C₃×#685	—	2	1	no	—
81	C₃×#683	—	2	1	no	—
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₃×#681	—	2	2	no	—
84	C₃×#681	C₂³	1	2	yes	—
85	C₂×C₃×#168	—	2	2	no	—
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₃×Dic₂₀	C₂×C₄	1	1	yes	characteristic
89	C₃×D₄₀	C₂×C₄	1	1	yes	characteristic
90	C₃×#677	C₂×C₄	1	2	yes	—
91	C₃×#676	—	2	2	no	—
92	C₃×#676	—	2	2	no	—
93	C₃×#676	—	2	2	no	—
94	C₃×#676	C₂×C₄	1	2	yes	—
95	C₃×#676	C₂×C₄	1	2	yes	—
96	C₃×C₈×D₅	—	2	2	no	—
97	C₃×C₈×D₅	—	2	2	no	—
98	C₃×C₈×D₅	—	2	2	no	—
99	C₃×C₈×D₅	D₄	1	2	yes	—
100	C₃×C₈×D₅	D₄	1	2	yes	—
101	C₃×#575	—	5	1	no	—
102	C₂×C₃×#131	—	5	2	no	—
103	C₃×#444	—	5	2	no	—
104	C₃×#444	—	5	1	no	—
105	C₃×#444	D₅	1	1	yes	characteristic, complemented
106	C₃×#443	—	5	1	no	—
107	C₃×#443	—	5	1	no	—
108	C₃×#443	—	5	2	no	—
109	C₃×#430	—	5	1	no	—
110	C₃×#421	—	5	2	no	—
111	C₃×#405	—	5	1	no	—
112	D₅×#41	C₂²×C₃	1	2	yes	—
113	C₅×#135	C₂²×C₃	1	1	yes	characteristic
114	C₅×#131	C₂²×C₃	1	2	yes	complemented
115	#4096	C₂²×C₃	1	2	yes	—
116	#4094	C₂²×C₃	1	2	yes	complemented
117	#4064	C₃×C₄	1	2	yes	complemented
118	#4061	C₃×C₄	1	2	yes	complemented
119	#4060	C₃×C₄	1	2	yes	complemented
120	#4057	C₃×C₄	1	2	yes	complemented
121	#4053	—	2	2	no	—
122	#4053	C₂²×C₃	1	2	yes	complemented
123	D₅×M₁₆	—	2	2	no	—
124	D₅×M₁₆	C₂²×C₃	1	2	yes	—
125	#4050	C₂²×C₃	1	1	yes	characteristic
126	#4047	—	2	2	no	—
127	#4047	C₂²×C₃	1	2	yes	complemented
128	C₂×#676	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₈×D₅	—	2	2	no	—
130	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
131	#4018	C₂²×C₃	1	1	yes	characteristic
132	C₅×#108	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₅×#104	C₂²×C₃	1	2	yes	complemented
134	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
135	#3969	C₂²×C₃	1	2	yes	complemented
136	#3957	C₂²×C₃	1	2	yes	complemented
137	#3954	C₂²×C₃	1	2	yes	complemented
138	#3951	C₂²×C₃	1	1	yes	characteristic, complemented
139	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
141	#3937	C₂²×C₃	1	2	yes	complemented
142	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
143	#2955	—	5	1	no	Sylow
144	C₂²×C₃×D₅	—	2	2	no	—
145	C₂²×C₃×D₅	#41	1	1	yes	characteristic
146	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₃×C₂²⋊D₅	—	2	2	no	—
153	C₃×C₂²⋊D₅	—	2	2	no	—
154	C₃×C₂²⋊D₅	—	2	2	no	—
155	C₂×C₃×Dic₅	—	2	2	no	—
156	C₂×C₃×Dic₅	—	2	1	no	—
157	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
158	C₃×D₂₀	—	2	2	no	—
159	C₃×D₂₀	C₂²×C₄	1	2	yes	—
160	C₃×C₄×D₅	—	2	2	no	—
161	C₃×C₄×D₅	—	2	2	no	—
162	C₃×C₄×D₅	—	2	2	no	—
163	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
164	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
165	C₃×Dic₁₀	—	2	2	no	—
166	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
167	C₃×C₅×C₈	—	2	2	no	—
168	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
171	C₃×#168	—	2	2	no	—
172	C₃×#168	C₂²×C₄	1	2	yes	—
173	C₃×#168	C₂×D₄	1	1	yes	characteristic
174	C₃×#168	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×#41	—	5	2	no	—
176	C₃×#137	—	5	2	no	—
177	C₃×#137	—	5	2	no	—
178	C₃×AGL(1,ℤ/8)	—	5	2	no	—
179	C₃×AGL(1,ℤ/8)	—	5	2	no	—
180	C₃×#135	—	5	2	no	—
181	C₃×#135	—	5	1	no	—
182	C₃×#135	C₂×D₅	1	1	yes	characteristic
183	C₃×#131	—	5	2	no	—
184	C₃×#131	—	5	2	no	—
185	C₃×#131	—	5	2	no	—
186	C₃×#131	—	10	2	no	—
187	C₃×#131	—	10	2	no	—
188	C₃×#131	C₂×D₅	1	2	yes	complemented
189	C₂×C₃×M₁₆	—	5	1	no	—
190	C₂×C₃×M₁₆	—	5	2	no	—
191	C₂×C₃×M₁₆	—	10	2	no	—
192	C₂²×C₃×C₈	—	5	1	no	—
193	C₂²×C₃×C₈	—	10	2	no	—
194	C₃×#117	—	5	1	no	—
195	C₃×#108	—	5	2	no	—
196	C₃×#108	—	5	1	no	—
197	C₃×#108	C₂×D₅	1	1	yes	characteristic, complemented
198	C₃×#104	—	5	2	no	—
199	C₃×#104	—	5	2	no	—
200	C₃×#104	—	5	2	no	—
201	C₃×#104	C₂×D₅	1	2	yes	complemented
202	C₃×#97	—	5	1	no	—
203	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
204	C₃×C₄×C₈	—	5	1	no	—
205	C₃×C₄×C₈	—	5	1	no	—
206	C₅×#41	C₂³×C₃	1	2	yes	—
207	#713	C₂×C₃×C₄	1	2	yes	—
208	Q₈×D₅	C₂×C₃×C₄	1	2	yes	—
209	#711	—	2	2	no	—
210	#711	C₂×C₃×C₄	1	2	yes	—
211	D₄×D₅	—	2	2	no	—
212	D₄×D₅	C₂×C₃×C₄	1	2	yes	—
213	#709	—	2	2	no	—
214	#709	C₂³×C₃	1	2	yes	—
215	C₂×C₄×D₅	—	2	2	no	—
216	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
217	C₅×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
218	C₅×SD₁₆	C₂×C₃×C₄	1	2	yes	—
219	C₅×D₈	C₂×C₃×C₄	1	1	yes	characteristic
220	C₅×M₁₆	—	2	2	no	—
221	C₅×M₁₆	C₂³×C₃	1	2	yes	—
222	C₂×C₅×C₈	—	2	2	no	—
223	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
225	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
226	#689	C₂×C₃×C₄	1	2	yes	—
227	#688	C₂×C₃×C₄	1	2	yes	—
228	#687	C₂×C₃×C₄	1	2	yes	—
229	#686	C₂×C₃×C₄	1	2	yes	—
230	#685	—	2	1	no	—
231	#683	—	2	1	no	—
232	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
233	#681	—	2	2	no	—
234	#681	C₂³×C₃	1	2	yes	—
235	C₂×#168	—	2	2	no	—
236	C₂×#168	C₂³×C₃	1	1	yes	characteristic
237	C₂×#168	C₂³×C₃	1	1	yes	characteristic
238	Dic₂₀	C₂×C₃×C₄	1	1	yes	characteristic
239	D₄₀	C₂×C₃×C₄	1	1	yes	characteristic
240	#677	C₂×C₃×C₄	1	2	yes	—
241	#676	—	2	2	no	—
242	#676	—	2	2	no	—
243	#676	—	2	2	no	—
244	#676	C₂×C₃×C₄	1	2	yes	—
245	#676	C₂×C₃×C₄	1	2	yes	—
246	C₈×D₅	—	2	2	no	—
247	C₈×D₅	—	2	2	no	—
248	C₈×D₅	—	2	2	no	—
249	C₈×D₅	C₃×D₄	1	2	yes	—
250	C₈×D₅	C₃×D₄	1	2	yes	—
251	#575	—	5	1	no	—
252	C₂×#131	—	5	2	no	—
253	#444	—	5	2	no	—
254	#444	—	5	1	no	—
255	#444	C₃×D₅	1	1	yes	characteristic, complemented
256	#443	—	5	1	no	—
257	#443	—	5	1	no	—
258	#443	—	5	2	no	—
259	#430	—	5	1	no	—
260	#421	—	5	2	no	—
261	#405	—	5	1	no	—
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
264	C₂×C₃×D₅	—	2	2	no	—
265	C₂×C₃×D₅	—	4	1	no	—
266	C₂×C₃×D₅	—	4	4	no	—
267	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
268	C₃×C₄×C₅	—	2	2	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
271	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₃×Dic₅	—	2	2	no	—
273	C₃×Dic₅	—	4	1	no	—
274	C₃×Dic₅	C₄×D₄	1	2	yes	—
275	C₃×#41	—	5	2	no	—
276	C₃×#41	—	5	2	no	—
277	C₃×#41	—	5	2	no	—
278	C₃×#41	—	10	2	no	—
279	C₃×#41	—	10	2	no	—
280	C₃×#41	C₂²×D₅	1	2	yes	—
281	C₂×C₃×Q₈	—	5	2	no	—
282	C₂×C₃×D₄	—	5	2	no	—
283	C₂×C₃×D₄	—	10	2	no	—
284	C₂²×C₃×C₄	—	5	1	no	—
285	C₂²×C₃×C₄	—	10	2	no	—
286	C₃×Q₁₆	—	5	2	no	—
287	C₃×Q₁₆	—	5	1	no	—
288	C₃×Q₁₆	C₄×D₅	1	1	yes	characteristic
289	C₃×SD₁₆	—	5	2	no	—
290	C₃×SD₁₆	—	5	2	no	—
291	C₃×SD₁₆	—	5	2	no	—
292	C₃×SD₁₆	C₄×D₅	1	2	yes	—
293	C₃×D₈	—	5	2	no	—
294	C₃×D₈	—	5	1	no	—
295	C₃×D₈	C₄×D₅	1	1	yes	characteristic
296	C₃×M₁₆	—	2	2	no	—
297	C₃×M₁₆	—	5	2	no	—
298	C₃×M₁₆	—	5	2	no	—
299	C₃×M₁₆	—	5	2	no	—
300	C₃×M₁₆	—	10	2	no	—
301	C₃×M₁₆	—	10	2	no	—
302	C₃×M₁₆	—	10	2	no	—
303	C₃×M₁₆	—	10	2	no	—
304	C₃×M₁₆	C₂²×D₅	1	2	yes	—
305	C₂×C₃×C₈	—	2	2	no	—
306	C₂×C₃×C₈	—	5	1	no	—
307	C₂×C₃×C₈	—	5	1	no	—
308	C₂×C₃×C₈	—	5	2	no	—
309	C₂×C₃×C₈	—	5	2	no	—
310	C₂×C₃×C₈	—	10	2	no	—
311	C₂×C₃×C₈	—	10	2	no	—
312	C₂×C₃×C₈	—	10	2	no	—
313	C₂×C₃×C₈	—	10	2	no	—
314	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
315	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
316	C₃×C₄⋊C₄	—	10	1	no	—
317	C₃×C₂²⋊C₄	—	10	1	no	—
318	C₃×C₄²	—	5	1	no	—
319	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
320	C₂²×D₅	—	2	2	no	—
321	C₂²×D₅	C₃×#41	1	1	yes	characteristic
322	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
328	C₂²⋊D₅	—	2	2	no	—
329	C₂²⋊D₅	—	2	2	no	—
330	C₂²⋊D₅	—	2	2	no	—
331	C₂×Dic₅	—	2	2	no	—
332	C₂×Dic₅	—	2	1	no	—
333	C₂×Dic₅	C₃×#41	1	1	yes	characteristic
334	D₂₀	—	2	2	no	—
335	D₂₀	C₂²×C₃×C₄	1	2	yes	—
336	C₄×D₅	—	2	2	no	—
337	C₄×D₅	—	2	2	no	—
338	C₄×D₅	—	2	2	no	—
339	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
340	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
341	Dic₁₀	—	2	2	no	—
342	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
343	C₅×C₈	—	2	2	no	—
344	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
345	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
346	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
347	#168	—	2	2	no	—
348	#168	C₂²×C₃×C₄	1	2	yes	—
349	#168	C₂×C₃×D₄	1	1	yes	characteristic
350	#168	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂×#41	—	5	2	no	—
352	#137	—	5	2	no	—
353	#137	—	5	2	no	—
354	AGL(1,ℤ/8)	—	5	2	no	—
355	AGL(1,ℤ/8)	—	5	2	no	—
356	#135	—	5	2	no	—
357	#135	—	5	1	no	—
358	#135	C₂×C₃×D₅	1	1	yes	characteristic
359	#131	—	5	2	no	—
360	#131	—	5	2	no	—
361	#131	—	5	2	no	—
362	#131	—	10	2	no	—
363	#131	—	10	2	no	—
364	#131	C₂×C₃×D₅	1	2	yes	complemented
365	C₂×M₁₆	—	5	1	no	—
366	C₂×M₁₆	—	5	2	no	—
367	C₂×M₁₆	—	10	2	no	—
368	C₂²×C₈	—	5	1	no	—
369	C₂²×C₈	—	10	2	no	—
370	#117	—	5	1	no	—
371	#108	—	5	2	no	—
372	#108	—	5	1	no	—
373	#108	C₂×C₃×D₅	1	1	yes	characteristic, complemented
374	#104	—	5	2	no	—
375	#104	—	5	2	no	—
376	#104	—	5	2	no	—
377	#104	C₂×C₃×D₅	1	2	yes	complemented
378	#97	—	5	1	no	—
379	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
380	C₄×C₈	—	5	1	no	—
381	C₄×C₈	—	5	1	no	—
382	C₂×C₃×C₅	—	2	1	no	—
383	C₂×C₃×C₅	—	4	2	no	—
384	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
385	C₃×D₅	—	2	2	no	—
386	C₃×D₅	—	4	2	no	—
387	C₂³×C₃	—	5	1	no	—
388	C₂³×C₃	—	10	2	no	—
389	C₃×Q₈	—	5	2	no	—
390	C₃×Q₈	—	10	2	no	—
391	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
392	C₃×D₄	—	2	2	no	—
393	C₃×D₄	—	5	2	no	—
394	C₃×D₄	—	10	2	no	—
395	C₃×D₄	—	10	2	no	—
396	C₃×D₄	—	10	2	no	—
397	C₃×D₄	—	10	2	no	—
398	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	5	1	no	—
402	C₂×C₃×C₄	—	5	2	no	—
403	C₂×C₃×C₄	—	5	2	no	—
404	C₂×C₃×C₄	—	10	2	no	—
405	C₂×C₃×C₄	—	10	2	no	—
406	C₂×C₃×C₄	—	10	2	no	—
407	C₂×C₃×C₄	—	10	2	no	—
408	C₂×C₃×C₄	—	10	1	no	—
409	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
410	C₃×C₈	—	2	2	no	—
411	C₃×C₈	—	5	2	no	—
412	C₃×C₈	—	5	1	no	—
413	C₃×C₈	—	5	1	no	—
414	C₃×C₈	—	10	2	no	—
415	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
416	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
417	C₃×C₈	D₄×D₅	1	2	yes	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	4	1	no	—
422	C₂×D₅	—	4	4	no	—
423	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
427	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
428	Dic₅	—	2	2	no	—
429	Dic₅	—	4	1	no	—
430	Dic₅	C₃×C₄×D₄	1	2	yes	—
431	#41	—	5	2	no	—
432	#41	—	5	2	no	—
433	#41	—	5	2	no	—
434	#41	—	10	2	no	—
435	#41	—	10	2	no	—
436	#41	C₂²×C₃×D₅	1	2	yes	—
437	C₂×Q₈	—	5	2	no	—
438	C₂×D₄	—	5	2	no	—
439	C₂×D₄	—	10	2	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	10	2	no	—
442	Q₁₆	—	5	2	no	—
443	Q₁₆	—	5	1	no	—
444	Q₁₆	C₃×C₄×D₅	1	1	yes	characteristic
445	SD₁₆	—	5	2	no	—
446	SD₁₆	—	5	2	no	—
447	SD₁₆	—	5	2	no	—
448	SD₁₆	C₃×C₄×D₅	1	2	yes	—
449	D₈	—	5	2	no	—
450	D₈	—	5	1	no	—
451	D₈	C₃×C₄×D₅	1	1	yes	characteristic
452	M₁₆	—	2	2	no	—
453	M₁₆	—	5	2	no	—
454	M₁₆	—	5	2	no	—
455	M₁₆	—	5	2	no	—
456	M₁₆	—	10	2	no	—
457	M₁₆	—	10	2	no	—
458	M₁₆	—	10	2	no	—
459	M₁₆	—	10	2	no	—
460	M₁₆	C₂²×C₃×D₅	1	2	yes	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	5	1	no	—
463	C₂×C₈	—	5	1	no	—
464	C₂×C₈	—	5	2	no	—
465	C₂×C₈	—	5	2	no	—
466	C₂×C₈	—	10	2	no	—
467	C₂×C₈	—	10	2	no	—
468	C₂×C₈	—	10	2	no	—
469	C₂×C₈	—	10	2	no	—
470	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
471	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
472	C₄⋊C₄	—	10	1	no	—
473	C₂²⋊C₄	—	10	1	no	—
474	C₄²	—	5	1	no	—
475	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
476	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	5	2	no	—
479	C₂²×C₃	—	10	2	no	—
480	C₂²×C₃	—	20	1	no	—
481	C₂²×C₃	—	20	4	no	—
482	C₂²×C₃	D₅×#41	1	1	yes	characteristic
483	C₃×C₄	—	2	2	no	—
484	C₃×C₄	—	4	1	no	—
485	C₃×C₄	—	5	2	no	—
486	C₃×C₄	—	10	2	no	—
487	C₃×C₄	—	20	1	no	—
488	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
489	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
490	C₂×C₅	—	2	1	no	—
491	C₂×C₅	—	4	2	no	—
492	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
493	D₅	—	2	2	no	—
494	D₅	—	4	2	no	—
495	C₂³	—	5	1	no	—
496	C₂³	—	10	2	no	—
497	Q₈	—	5	2	no	—
498	Q₈	—	10	2	no	—
499	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
500	D₄	—	2	2	no	—
501	D₄	—	5	2	no	—
502	D₄	—	10	2	no	—
503	D₄	—	10	2	no	—
504	D₄	—	10	2	no	—
505	D₄	—	10	2	no	—
506	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	2	no	—
511	C₂×C₄	—	5	2	no	—
512	C₂×C₄	—	10	2	no	—
513	C₂×C₄	—	10	2	no	—
514	C₂×C₄	—	10	2	no	—
515	C₂×C₄	—	10	2	no	—
516	C₂×C₄	—	10	1	no	—
517	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
518	C₈	—	2	2	no	—
519	C₈	—	5	2	no	—
520	C₈	—	5	1	no	—
521	C₈	—	5	1	no	—
522	C₈	—	10	2	no	—
523	C₈	C₂×C₃×C₄×D₅	1	1	yes	characteristic
524	C₈	C₂×C₃×C₄×D₅	1	1	yes	characteristic
525	C₈	C₃×D₄×D₅	1	2	yes	—
526	C₂×C₃	—	2	1	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	—	10	2	no	—
529	C₂×C₃	—	20	2	no	—
530	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
531	C₅	C₃×#2955	1	1	yes	characteristic, complemented, Sylow
532	C₂²	—	2	2	no	—
533	C₂²	—	5	2	no	—
534	C₂²	—	10	2	no	—
535	C₂²	—	20	1	no	—
536	C₂²	—	20	4	no	—
537	C₂²	C₃×D₅×#41	1	1	yes	characteristic
538	C₄	—	2	2	no	—
539	C₄	—	4	1	no	—
540	C₄	—	5	2	no	—
541	C₄	—	10	2	no	—
542	C₄	—	20	1	no	—
543	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
544	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
545	C₃	#10611628	1	1	yes	characteristic, direct product factor, Sylow
546	C₂	—	2	1	no	—
547	C₂	—	4	2	no	—
548	C₂	—	10	2	no	—
549	C₂	—	20	2	no	—
550	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#444	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×#66102	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#444	D₅
hypocenter	C₅	C₃×#2955
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#444

Complements

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

N	H ≅ G/N	type
2. C₃×D₅×#131	C₂	semidirect
3. C₃×C₅×#444	C₂	semidirect
4. C₃×#65485	C₂	semidirect
5. C₃×#65434	C₂	semidirect
6. C₃×#65184	C₂	semidirect
7. C₃×#65182	C₂	semidirect
8. C₃×#65113	C₂	semidirect
9. C₃×#65110	C₂	semidirect
10. C₃×#65006	C₂	semidirect
11. C₃×#64997	C₂	semidirect
12. #10611628	C₃	direct (N × H)
15. C₃×C₅×#131	C₂²	semidirect
17. C₃×#4094	C₂²	semidirect
18. C₃×#4064	C₄	semidirect
19. C₃×#4061	C₄	semidirect
20. C₃×#4060	C₄	semidirect
21. C₃×#4057	C₄	semidirect
23. C₃×#4053	C₂²	semidirect
28. C₃×#4047	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. C₃×C₅×#104	C₂²	semidirect
35. C₃×C₅×#97	C₂²	semidirect
36. C₃×#3969	C₂²	semidirect
37. C₃×#3957	C₂²	semidirect
38. C₃×#3954	C₂²	semidirect
39. C₃×#3951	C₂²	semidirect
40. C₃×#3947	C₂²	semidirect
41. C₃×C₈×Dic₅	C₂²	semidirect
42. C₃×#3937	C₂²	semidirect
43. C₃×C₄×#168	C₂²	semidirect
46. D₅×#131	C₂×C₃	semidirect
47. C₅×#444	C₂×C₃	semidirect
48. #65485	C₂×C₃	semidirect
49. #65434	C₂×C₃	semidirect
50. #65184	C₂×C₃	semidirect
51. #65182	C₂×C₃	semidirect
52. #65113	C₂×C₃	semidirect
53. #65110	C₂×C₃	semidirect
54. #65006	C₂×C₃	semidirect
55. #64997	C₂×C₃	semidirect
105. C₃×#444	D₅	semidirect
114. C₅×#131	C₂²×C₃	semidirect
116. #4094	C₂²×C₃	semidirect
117. #4064	C₃×C₄	semidirect
118. #4061	C₃×C₄	semidirect
119. #4060	C₃×C₄	semidirect
120. #4057	C₃×C₄	semidirect
122. #4053	C₂²×C₃	semidirect
127. #4047	C₂²×C₃	semidirect
132. C₅×#108	C₂²×C₃	semidirect
133. C₅×#104	C₂²×C₃	semidirect
134. C₅×#97	C₂²×C₃	semidirect
135. #3969	C₂²×C₃	semidirect
136. #3957	C₂²×C₃	semidirect
137. #3954	C₂²×C₃	semidirect
138. #3951	C₂²×C₃	semidirect
139. #3947	C₂²×C₃	semidirect
140. C₈×Dic₅	C₂²×C₃	semidirect
141. #3937	C₂²×C₃	semidirect
142. C₄×#168	C₂²×C₃	semidirect
188. C₃×#131	C₂×D₅	semidirect
197. C₃×#108	C₂×D₅	semidirect
201. C₃×#104	C₂×D₅	semidirect
203. C₃×#97	C₂×D₅	semidirect
255. #444	C₃×D₅	semidirect
364. #131	C₂×C₃×D₅	semidirect
373. #108	C₂×C₃×D₅	semidirect
377. #104	C₂×C₃×D₅	semidirect
379. #97	C₂×C₃×D₅	semidirect
476. C₃×C₅	#2955	semidirect
531. C₅	C₃×#2955	semidirect
545. C₃	#10611628	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×#66102	2
C₃×D₅×#131	2
C₃×C₅×#444	2
C₃×#65485	2
C₃×#65434	2
C₃×#65184	2
C₃×#65182	2
C₃×#65113	2
C₃×#65110	2
C₃×#65006	2
C₃×#64997	2
#10611628	3
C₃×#2955	5

Subgroups — C3×#10611628 #14418012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611628 #14418012