Subgroups — C₃×#10610720 #14418009

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66156	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65413	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65294	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65113	C₂	1	4	yes	maximal, complemented
9	C₃×#65112	C₂	1	4	yes	maximal, complemented
10	#10610720	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₃×#709	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×#4097	C₄	1	2	yes	complemented
16	C₃×#4096	C₂²	1	4	yes	—
17	C₃×#4095	C₄	1	2	yes	complemented
18	C₃×#4094	—	2	1	no	—
19	C₃×#4094	—	2	1	no	—
20	C₃×#4094	C₂²	1	2	yes	complemented
21	C₃×#4094	C₂²	1	2	yes	complemented
22	C₃×#4088	C₄	1	2	yes	complemented
23	C₃×#4078	C₄	1	2	yes	complemented
24	C₂×C₃×#681	—	2	1	no	—
25	C₂×C₃×#681	C₂²	1	1	yes	characteristic
26	C₂×C₃×#681	C₂²	1	1	yes	characteristic
27	C₂²×C₃×#168	—	2	1	no	—
28	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
29	C₃×#4053	—	2	1	no	—
30	C₃×#4053	—	2	1	no	—
31	C₃×#4053	C₂²	1	2	yes	complemented
32	C₃×#4053	C₂²	1	2	yes	complemented
33	C₂×C₃×#676	—	2	1	no	—
34	C₂×C₃×C₈×D₅	—	2	1	no	—
35	C₃×C₅×#104	C₂²	1	4	yes	complemented
36	C₃×#3954	C₂²	1	4	yes	complemented
37	C₃×#3937	C₂²	1	4	yes	complemented
38	C₃×#3935	C₂²	1	2	yes	complemented
39	C₃×C₄×#168	C₂²	1	2	yes	complemented
40	C₃×#2955	—	5	1	no	maximal, Hall
41	#66156	C₂×C₃	1	1	yes	characteristic
42	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#421	C₂×C₃	1	1	yes	characteristic, complemented
45	#65413	C₂×C₃	1	1	yes	characteristic, complemented
46	#65294	C₂×C₃	1	1	yes	characteristic, complemented
47	#65286	C₂×C₃	1	1	yes	characteristic, complemented
48	#65113	C₂×C₃	1	4	yes	complemented
49	#65112	C₂×C₃	1	4	yes	complemented
50	C₃×C₅×#41	—	2	1	no	—
51	C₃×C₅×#41	—	2	1	no	—
52	C₃×C₅×#41	C₂×C₄	1	2	yes	—
53	C₃×C₅×#41	C₂³	1	2	yes	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₃×#709	—	2	1	no	—
61	C₃×#709	—	2	1	no	—
62	C₃×#709	C₂×C₄	1	2	yes	—
63	C₃×#709	C₂³	1	2	yes	—
64	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	—	2	1	no	—
66	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
67	C₃×C₅×M₁₆	—	2	1	no	—
68	C₃×C₅×M₁₆	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₃×C₄²×C₅	C₂³	1	2	yes	—
73	C₃×#689	C₂×C₄	1	4	yes	—
74	C₃×#688	C₂×C₄	1	4	yes	—
75	C₃×#687	C₂×C₄	1	4	yes	—
76	C₃×#686	C₂×C₄	1	4	yes	—
77	C₃×#681	—	2	1	no	—
78	C₃×#681	—	2	2	no	—
79	C₃×#681	—	2	2	no	—
80	C₃×#681	C₂×C₄	1	2	yes	—
81	C₃×#681	C₂×C₄	1	2	yes	—
82	C₃×#681	C₂³	1	2	yes	—
83	C₂×C₃×#168	—	2	1	no	—
84	C₂×C₃×#168	—	2	2	no	—
85	C₂×C₃×#168	—	2	2	no	—
86	C₂×C₃×#168	D₄	1	1	yes	characteristic
87	C₂×C₃×#168	D₄	1	1	yes	characteristic
88	C₂×C₃×#168	D₄	1	1	yes	characteristic
89	C₂×C₃×#168	D₄	1	1	yes	characteristic
90	C₂×C₃×#168	C₂³	1	2	yes	—
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	1	yes	characteristic
93	C₃×#676	—	2	2	no	—
94	C₃×#676	—	2	2	no	—
95	C₃×C₈×D₅	—	2	2	no	—
96	C₃×C₈×D₅	—	2	2	no	—
97	C₃×#575	—	5	1	no	—
98	C₂×C₃×#131	—	5	1	no	—
99	C₂×C₃×#131	—	5	1	no	—
100	C₃×#444	—	5	4	no	—
101	C₃×#443	—	5	4	no	—
102	C₃×#430	—	5	1	no	—
103	C₃×#421	—	5	1	no	—
104	C₃×#421	D₅	1	1	yes	characteristic, complemented
105	C₃×#405	—	5	1	no	—
106	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
107	C₂×#709	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
109	C₅×#117	C₂²×C₃	1	1	yes	characteristic
110	#4097	C₃×C₄	1	2	yes	complemented
111	#4096	C₂²×C₃	1	4	yes	—
112	#4095	C₃×C₄	1	2	yes	complemented
113	#4094	—	2	1	no	—
114	#4094	—	2	1	no	—
115	#4094	C₂²×C₃	1	2	yes	complemented
116	#4094	C₂²×C₃	1	2	yes	complemented
117	#4088	C₃×C₄	1	2	yes	complemented
118	#4078	C₃×C₄	1	2	yes	complemented
119	C₂×#681	—	2	1	no	—
120	C₂×#681	C₂²×C₃	1	1	yes	characteristic
121	C₂×#681	C₂²×C₃	1	1	yes	characteristic
122	C₂²×#168	—	2	1	no	—
123	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
124	#4053	—	2	1	no	—
125	#4053	—	2	1	no	—
126	#4053	C₂²×C₃	1	2	yes	complemented
127	#4053	C₂²×C₃	1	2	yes	complemented
128	C₂×#676	—	2	1	no	—
129	C₂×C₈×D₅	—	2	1	no	—
130	C₅×#104	C₂²×C₃	1	4	yes	complemented
131	#3954	C₂²×C₃	1	4	yes	complemented
132	#3937	C₂²×C₃	1	4	yes	complemented
133	#3935	C₂²×C₃	1	2	yes	complemented
134	C₄×#168	C₂²×C₃	1	2	yes	complemented
135	#2955	—	5	1	no	Sylow
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	#41	1	1	yes	characteristic
138	C₂²×C₃×D₅	—	2	1	no	—
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₃×C₂²⋊D₅	—	2	2	no	—
156	C₃×C₂²⋊D₅	—	2	2	no	—
157	C₂×C₃×Dic₅	—	2	1	no	—
158	C₃×D₂₀	—	2	1	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×Dic₁₀	—	2	1	no	—
163	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×#168	—	2	2	no	—
166	C₃×#168	C₂²×C₄	1	4	yes	—
167	C₃×#168	C₂×D₄	1	1	yes	characteristic
168	C₃×#168	C₂×D₄	1	1	yes	characteristic
169	C₃×#168	C₂×D₄	1	1	yes	characteristic
170	C₃×#168	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×#41	—	5	1	no	—
172	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
173	C₃×#137	—	5	2	no	—
174	C₃×#137	—	5	2	no	—
175	C₃×AGL(1,ℤ/8)	—	5	2	no	—
176	C₃×AGL(1,ℤ/8)	—	5	2	no	—
177	C₃×#135	—	5	4	no	—
178	C₃×#131	—	5	2	no	—
179	C₃×#131	—	5	2	no	—
180	C₃×#131	—	5	2	no	—
181	C₃×#131	—	5	2	no	—
182	C₃×#131	—	10	1	no	—
183	C₃×#131	—	10	1	no	—
184	C₃×#131	—	10	1	no	—
185	C₃×#131	—	10	1	no	—
186	C₂×C₃×M₁₆	—	5	1	no	—
187	C₂×C₃×M₁₆	—	5	1	no	—
188	C₂×C₃×M₁₆	—	10	1	no	—
189	C₂×C₃×M₁₆	—	10	1	no	—
190	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
191	C₂²×C₃×C₈	—	5	1	no	—
192	C₂²×C₃×C₈	—	10	1	no	—
193	C₂²×C₃×C₈	—	10	1	no	—
194	C₃×#117	C₂×D₅	1	1	yes	characteristic
195	C₃×#108	—	5	4	no	—
196	C₃×#104	—	5	4	no	—
197	C₃×#104	C₂×D₅	1	4	yes	complemented
198	C₃×#97	—	5	2	no	—
199	C₃×C₄×C₈	—	5	2	no	—
200	C₅×#41	—	2	1	no	—
201	C₅×#41	—	2	1	no	—
202	C₅×#41	C₂×C₃×C₄	1	2	yes	—
203	C₅×#41	C₂³×C₃	1	2	yes	—
204	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	—	2	1	no	—
210	#709	—	2	1	no	—
211	#709	—	2	1	no	—
212	#709	C₂×C₃×C₄	1	2	yes	—
213	#709	C₂³×C₃	1	2	yes	—
214	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×D₅	—	2	1	no	—
216	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
217	C₅×M₁₆	—	2	1	no	—
218	C₅×M₁₆	C₂³×C₃	1	2	yes	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₂²⋊C₄	—	2	1	no	—
222	C₄²×C₅	C₂³×C₃	1	2	yes	—
223	#689	C₂×C₃×C₄	1	4	yes	—
224	#688	C₂×C₃×C₄	1	4	yes	—
225	#687	C₂×C₃×C₄	1	4	yes	—
226	#686	C₂×C₃×C₄	1	4	yes	—
227	#681	—	2	1	no	—
228	#681	—	2	2	no	—
229	#681	—	2	2	no	—
230	#681	C₂×C₃×C₄	1	2	yes	—
231	#681	C₂×C₃×C₄	1	2	yes	—
232	#681	C₂³×C₃	1	2	yes	—
233	C₂×#168	—	2	1	no	—
234	C₂×#168	—	2	2	no	—
235	C₂×#168	—	2	2	no	—
236	C₂×#168	C₃×D₄	1	1	yes	characteristic
237	C₂×#168	C₃×D₄	1	1	yes	characteristic
238	C₂×#168	C₃×D₄	1	1	yes	characteristic
239	C₂×#168	C₃×D₄	1	1	yes	characteristic
240	C₂×#168	C₂³×C₃	1	2	yes	—
241	C₂×#168	C₂³×C₃	1	1	yes	characteristic
242	C₂×#168	C₂³×C₃	1	1	yes	characteristic
243	#676	—	2	2	no	—
244	#676	—	2	2	no	—
245	C₈×D₅	—	2	2	no	—
246	C₈×D₅	—	2	2	no	—
247	#575	—	5	1	no	—
248	C₂×#131	—	5	1	no	—
249	C₂×#131	—	5	1	no	—
250	#444	—	5	4	no	—
251	#443	—	5	4	no	—
252	#430	—	5	1	no	—
253	#421	—	5	1	no	—
254	#421	C₃×D₅	1	1	yes	characteristic, complemented
255	#405	—	5	1	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	—	4	1	no	—
258	C₂²×C₃×C₅	—	4	2	no	—
259	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
260	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
261	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₃×D₅	—	2	2	no	—
263	C₂×C₃×D₅	—	4	2	no	—
264	C₃×C₄×C₅	—	2	2	no	—
265	C₃×C₄×C₅	—	4	2	no	—
266	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
267	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
268	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
269	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₃×Dic₅	—	2	2	no	—
271	C₃×#41	—	2	1	no	—
272	C₃×#41	—	2	1	no	—
273	C₃×#41	—	5	2	no	—
274	C₃×#41	—	5	2	no	—
275	C₃×#41	—	10	1	no	—
276	C₃×#41	—	10	1	no	—
277	C₃×#41	C₄×D₅	1	2	yes	—
278	C₃×#41	C₂²×D₅	1	2	yes	—
279	C₂×C₃×Q₈	—	5	1	no	—
280	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
281	C₂×C₃×D₄	—	2	1	no	—
282	C₂×C₃×D₄	—	5	1	no	—
283	C₂×C₃×D₄	—	10	1	no	—
284	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
285	C₂²×C₃×C₄	—	2	1	no	—
286	C₂²×C₃×C₄	—	10	1	no	—
287	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
288	C₃×Q₁₆	—	5	4	no	—
289	C₃×SD₁₆	—	5	4	no	—
290	C₃×SD₁₆	—	5	4	no	—
291	C₃×D₈	—	5	4	no	—
292	C₃×M₁₆	—	2	1	no	—
293	C₃×M₁₆	—	5	2	no	—
294	C₃×M₁₆	—	5	2	no	—
295	C₃×M₁₆	—	5	2	no	—
296	C₃×M₁₆	—	10	2	no	—
297	C₃×M₁₆	—	10	2	no	—
298	C₃×M₁₆	—	10	2	no	—
299	C₃×M₁₆	—	10	2	no	—
300	C₃×M₁₆	—	10	1	no	—
301	C₃×M₁₆	C₂²×D₅	1	2	yes	—
302	C₂×C₃×C₈	—	2	1	no	—
303	C₂×C₃×C₈	—	5	1	no	—
304	C₂×C₃×C₈	—	5	1	no	—
305	C₂×C₃×C₈	—	5	1	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	1	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	—	10	1	no	—
315	C₃×C₄⋊C₄	—	2	1	no	—
316	C₃×C₂²⋊C₄	—	2	1	no	—
317	C₃×C₄²	C₂²×D₅	1	2	yes	—
318	C₂³×C₅	—	2	1	no	—
319	C₂³×C₅	C₃×#41	1	1	yes	characteristic
320	C₂²×D₅	—	2	1	no	—
321	C₅×Q₈	—	2	1	no	—
322	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	2	1	no	—
326	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
337	C₂²⋊D₅	—	2	2	no	—
338	C₂²⋊D₅	—	2	2	no	—
339	C₂×Dic₅	—	2	1	no	—
340	D₂₀	—	2	1	no	—
341	D₂₀	C₂²×C₃×C₄	1	2	yes	—
342	C₄×D₅	—	2	2	no	—
343	C₄×D₅	—	2	2	no	—
344	Dic₁₀	—	2	1	no	—
345	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
346	C₅×C₈	—	2	2	no	—
347	#168	—	2	2	no	—
348	#168	C₂²×C₃×C₄	1	4	yes	—
349	#168	C₂×C₃×D₄	1	1	yes	characteristic
350	#168	C₂×C₃×D₄	1	1	yes	characteristic
351	#168	C₂×C₃×D₄	1	1	yes	characteristic
352	#168	C₂×C₃×D₄	1	1	yes	characteristic
353	C₂×#41	—	5	1	no	—
354	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
355	#137	—	5	2	no	—
356	#137	—	5	2	no	—
357	AGL(1,ℤ/8)	—	5	2	no	—
358	AGL(1,ℤ/8)	—	5	2	no	—
359	#135	—	5	4	no	—
360	#131	—	5	2	no	—
361	#131	—	5	2	no	—
362	#131	—	5	2	no	—
363	#131	—	5	2	no	—
364	#131	—	10	1	no	—
365	#131	—	10	1	no	—
366	#131	—	10	1	no	—
367	#131	—	10	1	no	—
368	C₂×M₁₆	—	5	1	no	—
369	C₂×M₁₆	—	5	1	no	—
370	C₂×M₁₆	—	10	1	no	—
371	C₂×M₁₆	—	10	1	no	—
372	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
373	C₂²×C₈	—	5	1	no	—
374	C₂²×C₈	—	10	1	no	—
375	C₂²×C₈	—	10	1	no	—
376	#117	C₂×C₃×D₅	1	1	yes	characteristic
377	#108	—	5	4	no	—
378	#104	—	5	4	no	—
379	#104	C₂×C₃×D₅	1	4	yes	complemented
380	#97	—	5	2	no	—
381	C₄×C₈	—	5	2	no	—
382	C₂×C₃×C₅	—	2	1	no	—
383	C₂×C₃×C₅	—	2	1	no	—
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	—	4	2	no	—
386	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
387	C₃×D₅	—	4	2	no	—
388	C₂³×C₃	—	2	1	no	—
389	C₂³×C₃	—	10	1	no	—
390	C₂³×C₃	#711	1	1	yes	characteristic
391	C₃×Q₈	—	2	1	no	—
392	C₃×Q₈	—	5	2	no	—
393	C₃×Q₈	—	10	1	no	—
394	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
395	C₃×D₄	—	2	2	no	—
396	C₃×D₄	—	2	2	no	—
397	C₃×D₄	—	2	1	no	—
398	C₃×D₄	—	5	2	no	—
399	C₃×D₄	—	10	2	no	—
400	C₃×D₄	—	10	2	no	—
401	C₃×D₄	—	10	1	no	—
402	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	10	1	no	—
408	C₂×C₃×C₄	—	10	2	no	—
409	C₂×C₃×C₄	—	10	2	no	—
410	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
412	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
413	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
414	C₂×C₃×C₄	#711	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
416	C₃×C₈	—	2	2	no	—
417	C₃×C₈	—	5	4	no	—
418	C₃×C₈	—	5	1	no	—
419	C₃×C₈	—	5	1	no	—
420	C₃×C₈	—	5	1	no	—
421	C₃×C₈	—	5	1	no	—
422	C₃×C₈	—	10	2	no	—
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
427	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
428	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	4	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
434	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
435	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
436	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
437	Dic₅	—	2	2	no	—
438	#41	—	2	1	no	—
439	#41	—	2	1	no	—
440	#41	—	5	2	no	—
441	#41	—	5	2	no	—
442	#41	—	10	1	no	—
443	#41	—	10	1	no	—
444	#41	C₃×C₄×D₅	1	2	yes	—
445	#41	C₂²×C₃×D₅	1	2	yes	—
446	C₂×Q₈	—	5	1	no	—
447	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	10	1	no	—
451	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	10	1	no	—
454	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
455	Q₁₆	—	5	4	no	—
456	SD₁₆	—	5	4	no	—
457	SD₁₆	—	5	4	no	—
458	D₈	—	5	4	no	—
459	M₁₆	—	2	1	no	—
460	M₁₆	—	5	2	no	—
461	M₁₆	—	5	2	no	—
462	M₁₆	—	5	2	no	—
463	M₁₆	—	10	2	no	—
464	M₁₆	—	10	2	no	—
465	M₁₆	—	10	2	no	—
466	M₁₆	—	10	2	no	—
467	M₁₆	—	10	1	no	—
468	M₁₆	C₂²×C₃×D₅	1	2	yes	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	5	1	no	—
471	C₂×C₈	—	5	1	no	—
472	C₂×C₈	—	5	1	no	—
473	C₂×C₈	—	5	1	no	—
474	C₂×C₈	—	5	1	no	—
475	C₂×C₈	—	5	2	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	10	2	no	—
478	C₂×C₈	—	10	2	no	—
479	C₂×C₈	—	10	2	no	—
480	C₂×C₈	—	10	2	no	—
481	C₂×C₈	—	10	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₄²	C₂²×C₃×D₅	1	2	yes	—
485	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
486	C₂²×C₃	—	2	2	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	10	2	no	—
490	C₂²×C₃	—	20	2	no	—
491	C₂²×C₃	#4027	1	1	yes	characteristic
492	C₂²×C₃	#4027	1	1	yes	characteristic
493	C₂²×C₃	C₂×#711	1	1	yes	characteristic
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	4	2	no	—
496	C₃×C₄	—	10	2	no	—
497	C₃×C₄	#4027	1	1	yes	characteristic
498	C₃×C₄	#4027	1	1	yes	characteristic
499	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
500	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
501	C₂×C₅	—	2	1	no	—
502	C₂×C₅	—	2	1	no	—
503	C₂×C₅	—	2	1	no	—
504	C₂×C₅	—	4	2	no	—
505	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
506	D₅	—	4	2	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	10	1	no	—
509	C₂³	C₃×#711	1	1	yes	characteristic
510	Q₈	—	2	1	no	—
511	Q₈	—	5	2	no	—
512	Q₈	—	10	1	no	—
513	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	1	no	—
517	D₄	—	5	2	no	—
518	D₄	—	10	2	no	—
519	D₄	—	10	2	no	—
520	D₄	—	10	1	no	—
521	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	10	1	no	—
527	C₂×C₄	—	10	2	no	—
528	C₂×C₄	—	10	2	no	—
529	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
530	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
531	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
532	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
533	C₂×C₄	C₃×#711	1	1	yes	characteristic
534	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
535	C₈	—	2	2	no	—
536	C₈	—	5	4	no	—
537	C₈	—	5	1	no	—
538	C₈	—	5	1	no	—
539	C₈	—	5	1	no	—
540	C₈	—	5	1	no	—
541	C₈	—	10	2	no	—
542	C₂×C₃	—	2	1	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	4	2	no	—
546	C₂×C₃	—	20	2	no	—
547	C₂×C₃	C₂×#4027	1	1	yes	characteristic
548	C₅	C₃×#2955	1	1	yes	characteristic, complemented, Sylow
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	10	2	no	—
553	C₂²	—	20	2	no	—
554	C₂²	C₃×#4027	1	1	yes	characteristic
555	C₂²	C₃×#4027	1	1	yes	characteristic
556	C₂²	C₂×C₃×#711	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	10	2	no	—
560	C₄	C₃×#4027	1	1	yes	characteristic
561	C₄	C₃×#4027	1	1	yes	characteristic
562	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
563	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
564	C₃	#10610720	1	1	yes	characteristic, direct product factor, Sylow
565	C₂	—	2	1	no	—
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	4	2	no	—
569	C₂	—	20	2	no	—
570	C₂	C₂×C₃×#4027	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×#421	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×#66156	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#421	D₅
hypocenter	C₅	C₃×#2955
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#421

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4094	C₂	semidirect
3. C₂×C₃×#4053	C₂	semidirect
4. C₃×C₅×#421	C₂	semidirect
5. C₃×#65413	C₂	semidirect
6. C₃×#65294	C₂	semidirect
7. C₃×#65286	C₂	semidirect
8. C₃×#65113	C₂	semidirect
9. C₃×#65112	C₂	semidirect
10. #10610720	C₃	direct (N × H)
15. C₃×#4097	C₄	semidirect
17. C₃×#4095	C₄	semidirect
20. C₃×#4094	C₂²	semidirect
21. C₃×#4094	C₂²	semidirect
22. C₃×#4088	C₄	semidirect
23. C₃×#4078	C₄	semidirect
31. C₃×#4053	C₂²	semidirect
32. C₃×#4053	C₂²	semidirect
35. C₃×C₅×#104	C₂²	semidirect
36. C₃×#3954	C₂²	semidirect
37. C₃×#3937	C₂²	semidirect
38. C₃×#3935	C₂²	semidirect
39. C₃×C₄×#168	C₂²	semidirect
42. C₂×#4094	C₂×C₃	semidirect
43. C₂×#4053	C₂×C₃	semidirect
44. C₅×#421	C₂×C₃	semidirect
45. #65413	C₂×C₃	semidirect
46. #65294	C₂×C₃	semidirect
47. #65286	C₂×C₃	semidirect
48. #65113	C₂×C₃	semidirect
49. #65112	C₂×C₃	semidirect
104. C₃×#421	D₅	semidirect
110. #4097	C₃×C₄	semidirect
112. #4095	C₃×C₄	semidirect
115. #4094	C₂²×C₃	semidirect
116. #4094	C₂²×C₃	semidirect
117. #4088	C₃×C₄	semidirect
118. #4078	C₃×C₄	semidirect
126. #4053	C₂²×C₃	semidirect
127. #4053	C₂²×C₃	semidirect
130. C₅×#104	C₂²×C₃	semidirect
131. #3954	C₂²×C₃	semidirect
132. #3937	C₂²×C₃	semidirect
133. #3935	C₂²×C₃	semidirect
134. C₄×#168	C₂²×C₃	semidirect
197. C₃×#104	C₂×D₅	semidirect
254. #421	C₃×D₅	semidirect
379. #104	C₂×C₃×D₅	semidirect
485. C₃×C₅	#2955	semidirect
548. C₅	C₃×#2955	semidirect
564. C₃	#10610720	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×#66156	2
C₂×C₃×#4094	2
C₂×C₃×#4053	2
C₃×C₅×#421	2
C₃×#65413	2
C₃×#65294	2
C₃×#65286	2
C₃×#65113	2
C₃×#65112	2
#10610720	3
C₃×#2955	5

Subgroups — C3×#10610720 #14418009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610720 #14418009