Subgroups — C₃×#10611658 #14471763

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65919	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65136	C₂	1	2	yes	maximal, complemented
6	C₃×#65133	C₂	1	2	yes	maximal, complemented
7	C₃×#65132	C₂	1	1	yes	maximal, characteristic
8	C₃×#64986	C₂	1	2	yes	maximal, complemented
9	C₃×#64983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×D₄₀	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#677	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611658	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×#4093	—	2	1	no	—
15	C₃×#4092	—	2	1	no	—
16	C₂×C₃×D₄₀	C₂²	1	2	yes	—
17	C₂×C₃×#677	C₂²	1	1	yes	characteristic
18	C₃×#4042	—	2	2	no	—
19	C₃×#4040	—	2	2	no	—
20	C₃×#4039	—	2	1	no	—
21	C₃×D₅×C₄⋊C₄	—	2	1	no	—
22	C₃×#4021	C₂²	1	2	yes	—
23	C₃×#4020	C₂²	1	1	yes	characteristic
24	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
25	C₃×C₄×D₂₀	C₂²	1	2	yes	—
26	C₃×C₄×D₂₀	C₂²	1	2	yes	—
27	C₃×#4016	C₂²	1	2	yes	—
28	C₃×#4015	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3953	C₂²	1	2	yes	—
36	C₃×#3953	C₂²	1	1	yes	characteristic
37	C₃×#3953	C₂²	1	2	yes	—
38	C₃×#3950	C₂²	1	2	yes	—
39	C₃×#3949	C₂²	1	1	yes	characteristic
40	C₃×#3948	C₂²	1	2	yes	—
41	C₃×#3948	C₂²	1	1	yes	characteristic
42	C₃×#3361	—	5	1	no	maximal, Hall
43	#65919	C₂×C₃	1	1	yes	characteristic, complemented
44	#65913	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×C₈×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
46	#65139	C₂×C₃	1	1	yes	characteristic, complemented
47	#65136	C₂×C₃	1	2	yes	complemented
48	#65133	C₂×C₃	1	2	yes	complemented
49	#65132	C₂×C₃	1	1	yes	characteristic
50	#64986	C₂×C₃	1	2	yes	complemented
51	#64983	C₂×C₃	1	1	yes	characteristic, complemented
52	C₄×D₄₀	C₂×C₃	1	2	yes	complemented
53	C₄×#677	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
55	C₂×C₃×D₂₀	—	2	1	no	—
56	C₂×C₃×D₂₀	—	2	1	no	—
57	C₂×C₃×D₂₀	C₂³	1	2	yes	—
58	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	—	2	1	no	—
60	C₂×C₃×C₄×D₅	—	2	2	no	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×Dic₁₀	—	2	1	no	—
63	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂³	1	2	yes	—
71	C₃×#685	—	2	2	no	—
72	C₃×#685	—	2	2	no	—
73	C₃×#685	—	2	2	no	—
74	C₃×#685	—	2	1	no	—
75	C₃×#685	—	2	2	no	—
76	C₃×C₄⋊Dic₅	—	2	1	no	—
77	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
78	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
79	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
80	C₃×#683	—	2	2	no	—
81	C₃×#683	—	2	1	no	—
82	C₃×#683	—	2	2	no	—
83	C₃×C₄×Dic₅	—	2	1	no	—
84	C₃×D₄₀	—	2	4	no	—
85	C₃×#677	—	2	2	no	—
86	C₃×#559	—	5	1	no	—
87	C₃×#554	—	5	1	no	—
88	C₃×#488	—	5	2	no	—
89	C₃×#486	—	5	1	no	—
90	C₃×#478	—	5	2	no	—
91	C₃×#477	—	5	1	no	—
92	C₃×#463	—	5	2	no	—
93	C₃×#459	—	5	1	no	—
94	C₃×C₈×Q₈	D₅	1	1	yes	characteristic, complemented
95	C₃×C₄×SD₁₆	—	5	1	no	—
96	C₃×C₄×D₈	—	5	2	no	—
97	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
98	#4093	—	2	1	no	—
99	#4092	—	2	1	no	—
100	C₂×D₄₀	C₂²×C₃	1	2	yes	—
101	C₂×#677	C₂²×C₃	1	1	yes	characteristic
102	#4042	—	2	2	no	—
103	#4040	—	2	2	no	—
104	#4039	—	2	1	no	—
105	D₅×C₄⋊C₄	—	2	1	no	—
106	#4021	C₂²×C₃	1	2	yes	—
107	#4020	C₂²×C₃	1	1	yes	characteristic
108	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
109	C₄×D₂₀	C₂²×C₃	1	2	yes	—
110	C₄×D₂₀	C₂²×C₃	1	2	yes	—
111	#4016	C₂²×C₃	1	2	yes	—
112	#4015	C₂²×C₃	1	1	yes	characteristic
113	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
116	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
118	#3953	C₂²×C₃	1	2	yes	—
119	#3953	C₂²×C₃	1	2	yes	—
120	#3953	C₂²×C₃	1	1	yes	characteristic
121	#3953	C₂²×C₃	1	2	yes	—
122	#3950	C₂²×C₃	1	2	yes	—
123	#3949	C₂²×C₃	1	1	yes	characteristic
124	#3948	C₂²×C₃	1	2	yes	—
125	#3948	C₂²×C₃	1	1	yes	characteristic
126	#3361	—	5	1	no	Sylow
127	C₂²×C₃×D₅	—	2	1	no	—
128	C₂²×C₃×D₅	—	2	2	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₃×Dic₅	—	2	1	no	—
136	C₂×C₃×Dic₅	—	2	1	no	—
137	C₂×C₃×Dic₅	—	2	1	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₃×D₂₀	—	2	2	no	—
140	C₃×D₂₀	—	2	1	no	—
141	C₃×D₂₀	—	2	2	no	—
142	C₃×D₂₀	—	4	2	no	—
143	C₃×D₂₀	—	8	1	no	—
144	C₃×D₂₀	#41	1	2	yes	—
145	C₃×C₄×D₅	—	4	2	no	—
146	C₃×C₄×D₅	—	8	2	no	—
147	C₃×C₄×D₅	—	8	2	no	—
148	C₃×Dic₁₀	—	2	1	no	—
149	C₃×Dic₁₀	—	2	1	no	—
150	C₃×Dic₁₀	—	8	1	no	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	—	2	1	no	—
154	C₂×C₃×SD₁₆	—	5	1	no	—
155	C₂×C₃×D₈	—	5	2	no	—
156	C₃×C₄⋊Q₈	—	5	1	no	—
157	C₃×#127	—	5	1	no	—
158	C₃×#125	—	5	2	no	—
159	C₃×#124	—	5	2	no	—
160	C₃×#124	—	10	1	no	—
161	C₃×#123	—	10	2	no	—
162	C₃×C₂²⋊Q₈	—	10	1	no	—
163	C₃×C₂²⋊Q₈	—	10	2	no	—
164	C₃×C₄×Q₈	—	5	1	no	—
165	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
166	C₃×C₄×D₄	—	5	2	no	—
167	C₃×C₄×D₄	—	5	2	no	—
168	C₃×C₄×D₄	—	5	1	no	—
169	C₃×C₄×D₄	—	10	1	no	—
170	C₂×C₃×C₄⋊C₄	—	10	1	no	—
171	C₃×#107	—	5	2	no	—
172	C₃×#106	—	5	1	no	—
173	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
175	C₃×#103	—	5	1	no	—
176	C₃×#103	—	5	2	no	—
177	C₃×#102	—	5	1	no	—
178	C₃×#102	—	5	2	no	—
179	C₃×#102	—	5	2	no	—
180	C₃×#102	—	5	2	no	—
181	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
182	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
183	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
184	C₂×D₂₀	—	2	1	no	—
185	C₂×D₂₀	—	2	1	no	—
186	C₂×D₂₀	C₂³×C₃	1	2	yes	—
187	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₄×D₅	—	2	1	no	—
189	C₂×C₄×D₅	—	2	2	no	—
190	C₂×C₄×D₅	—	2	2	no	—
191	C₂×Dic₁₀	—	2	1	no	—
192	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
194	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
197	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
198	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
199	C₄²×C₅	C₂³×C₃	1	2	yes	—
200	#685	—	2	2	no	—
201	#685	—	2	1	no	—
202	#685	—	2	2	no	—
203	#685	—	2	2	no	—
204	#685	—	2	2	no	—
205	C₄⋊Dic₅	—	2	1	no	—
206	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
208	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
209	#683	—	2	1	no	—
210	#683	—	2	2	no	—
211	#683	—	2	2	no	—
212	C₄×Dic₅	—	2	1	no	—
213	D₄₀	—	2	4	no	—
214	#677	—	2	2	no	—
215	#559	—	5	1	no	—
216	#554	—	5	1	no	—
217	#488	—	5	2	no	—
218	#486	—	5	1	no	—
219	#478	—	5	2	no	—
220	#477	—	5	1	no	—
221	#463	—	5	2	no	—
222	#459	—	5	1	no	—
223	C₈×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
224	C₄×SD₁₆	—	5	1	no	—
225	C₄×D₈	—	5	2	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₃×D₅	—	2	2	no	—
228	C₂×C₃×D₅	—	4	1	no	—
229	C₂×C₃×D₅	—	4	1	no	—
230	C₂×C₃×D₅	—	4	2	no	—
231	C₂×C₃×D₅	—	4	2	no	—
232	C₂×C₃×D₅	—	4	2	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	2	no	—
236	C₃×C₄×C₅	#135	1	2	yes	—
237	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
239	C₃×Dic₅	—	4	1	no	—
240	C₃×Dic₅	—	4	1	no	—
241	C₃×Dic₅	—	4	2	no	—
242	C₃×Dic₅	—	4	1	no	—
243	C₂×C₃×Q₈	—	5	1	no	—
244	C₂×C₃×Q₈	—	10	1	no	—
245	C₂×C₃×Q₈	D₂₀	1	1	yes	characteristic
246	C₂×C₃×D₄	—	5	1	no	—
247	C₂×C₃×D₄	—	5	2	no	—
248	C₂×C₃×D₄	—	10	1	no	—
249	C₂×C₃×D₄	—	10	1	no	—
250	C₂²×C₃×C₄	—	10	1	no	—
251	C₂²×C₃×C₄	—	10	2	no	—
252	C₂²×C₃×C₄	—	10	2	no	—
253	C₃×SD₁₆	—	10	2	no	—
254	C₃×D₈	—	10	4	no	—
255	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
256	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
257	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
258	C₃×C₄⋊C₄	—	5	1	no	—
259	C₃×C₄⋊C₄	—	5	2	no	—
260	C₃×C₄⋊C₄	—	5	1	no	—
261	C₃×C₄⋊C₄	—	10	2	no	—
262	C₃×C₄⋊C₄	—	10	1	no	—
263	C₃×C₄⋊C₄	—	10	2	no	—
264	C₃×C₄⋊C₄	—	10	1	no	—
265	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
266	C₃×C₄⋊C₄	D₂₀	1	2	yes	—
267	C₃×C₂²⋊C₄	—	10	1	no	—
268	C₃×C₂²⋊C₄	—	10	2	no	—
269	C₃×C₂²⋊C₄	—	10	2	no	—
270	C₃×C₂²⋊C₄	—	10	2	no	—
271	C₃×C₂²⋊C₄	—	10	2	no	—
272	C₃×C₄²	—	10	1	no	—
273	C₃×C₄²	C₂²×D₅	1	2	yes	—
274	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
275	C₂²×D₅	—	2	1	no	—
276	C₂²×D₅	—	2	2	no	—
277	C₅×Q₈	—	2	2	no	—
278	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
279	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
281	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
283	C₂×Dic₅	—	2	1	no	—
284	C₂×Dic₅	—	2	1	no	—
285	C₂×Dic₅	—	2	1	no	—
286	C₂×Dic₅	—	2	2	no	—
287	D₂₀	—	2	2	no	—
288	D₂₀	—	2	1	no	—
289	D₂₀	—	2	2	no	—
290	D₂₀	—	4	2	no	—
291	D₂₀	—	8	1	no	—
292	D₂₀	C₃×#41	1	2	yes	—
293	C₄×D₅	—	4	2	no	—
294	C₄×D₅	—	8	2	no	—
295	C₄×D₅	—	8	2	no	—
296	Dic₁₀	—	2	1	no	—
297	Dic₁₀	—	2	1	no	—
298	Dic₁₀	—	8	1	no	—
299	C₅×C₈	—	2	1	no	—
300	C₅×C₈	—	2	2	no	—
301	C₅×C₈	—	2	1	no	—
302	C₂×SD₁₆	—	5	1	no	—
303	C₂×D₈	—	5	2	no	—
304	C₄⋊Q₈	—	5	1	no	—
305	#127	—	5	1	no	—
306	#125	—	5	2	no	—
307	#124	—	5	2	no	—
308	#124	—	10	1	no	—
309	#123	—	10	2	no	—
310	C₂²⋊Q₈	—	10	1	no	—
311	C₂²⋊Q₈	—	10	2	no	—
312	C₄×Q₈	—	5	1	no	—
313	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	—	5	1	no	—
316	C₄×D₄	—	5	2	no	—
317	C₄×D₄	—	10	1	no	—
318	C₂×C₄⋊C₄	—	10	1	no	—
319	#107	—	5	2	no	—
320	#106	—	5	1	no	—
321	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
322	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
323	#103	—	5	1	no	—
324	#103	—	5	2	no	—
325	#102	—	5	1	no	—
326	#102	—	5	2	no	—
327	#102	—	5	2	no	—
328	#102	—	5	2	no	—
329	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
330	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
331	C₂×C₃×C₅	#548	1	1	yes	characteristic
332	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
333	C₂×C₃×C₅	#576	1	1	yes	characteristic
334	C₃×D₅	—	4	2	no	—
335	C₃×D₅	—	8	2	no	—
336	C₂³×C₃	—	10	1	no	—
337	C₂³×C₃	—	10	2	no	—
338	C₃×Q₈	—	2	2	no	—
339	C₃×Q₈	—	10	1	no	—
340	C₃×Q₈	—	10	1	no	—
341	C₃×Q₈	—	40	1	no	—
342	C₃×D₄	—	5	2	no	—
343	C₃×D₄	—	10	1	no	—
344	C₃×D₄	—	10	2	no	—
345	C₃×D₄	—	10	2	no	—
346	C₃×D₄	—	20	2	no	—
347	C₃×D₄	—	40	1	no	—
348	C₂×C₃×C₄	—	10	1	no	—
349	C₂×C₃×C₄	—	10	1	no	—
350	C₂×C₃×C₄	—	10	1	no	—
351	C₂×C₃×C₄	—	10	2	no	—
352	C₂×C₃×C₄	—	20	2	no	—
353	C₂×C₃×C₄	—	40	2	no	—
354	C₂×C₃×C₄	—	40	2	no	—
355	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
356	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
357	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
360	C₃×C₈	—	2	1	no	—
361	C₃×C₈	—	2	2	no	—
362	C₃×C₈	—	2	1	no	—
363	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
364	C₂×D₅	—	2	2	no	—
365	C₂×D₅	—	4	1	no	—
366	C₂×D₅	—	4	1	no	—
367	C₂×D₅	—	4	2	no	—
368	C₂×D₅	—	4	2	no	—
369	C₂×D₅	—	4	2	no	—
370	C₄×C₅	—	2	2	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	2	no	—
373	C₄×C₅	C₃×#135	1	2	yes	—
374	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
375	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
376	Dic₅	—	4	1	no	—
377	Dic₅	—	4	2	no	—
378	Dic₅	—	4	1	no	—
379	Dic₅	—	4	1	no	—
380	C₂×Q₈	—	5	1	no	—
381	C₂×Q₈	—	10	1	no	—
382	C₂×Q₈	C₃×D₂₀	1	1	yes	characteristic
383	C₂×D₄	—	5	1	no	—
384	C₂×D₄	—	5	2	no	—
385	C₂×D₄	—	10	1	no	—
386	C₂×D₄	—	10	1	no	—
387	C₂²×C₄	—	10	1	no	—
388	C₂²×C₄	—	10	2	no	—
389	C₂²×C₄	—	10	2	no	—
390	SD₁₆	—	10	2	no	—
391	D₈	—	10	4	no	—
392	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
393	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
394	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
395	C₄⋊C₄	—	5	1	no	—
396	C₄⋊C₄	—	5	2	no	—
397	C₄⋊C₄	—	5	1	no	—
398	C₄⋊C₄	—	10	2	no	—
399	C₄⋊C₄	—	10	1	no	—
400	C₄⋊C₄	—	10	1	no	—
401	C₄⋊C₄	—	10	2	no	—
402	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
403	C₄⋊C₄	C₃×D₂₀	1	2	yes	—
404	C₂²⋊C₄	—	10	1	no	—
405	C₂²⋊C₄	—	10	2	no	—
406	C₂²⋊C₄	—	10	2	no	—
407	C₂²⋊C₄	—	10	2	no	—
408	C₂²⋊C₄	—	10	2	no	—
409	C₄²	—	10	1	no	—
410	C₄²	C₂²×C₃×D₅	1	2	yes	—
411	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
412	C₃×C₅	#3361	1	1	yes	characteristic, complemented, Hall
413	C₂²×C₃	—	10	2	no	—
414	C₂²×C₃	—	20	1	no	—
415	C₂²×C₃	—	20	1	no	—
416	C₂²×C₃	—	20	2	no	—
417	C₂²×C₃	—	20	2	no	—
418	C₂²×C₃	—	20	2	no	—
419	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
420	C₃×C₄	—	2	2	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	20	1	no	—
424	C₃×C₄	—	20	1	no	—
425	C₃×C₄	—	20	2	no	—
426	C₃×C₄	—	20	1	no	—
427	C₃×C₄	#4050	1	2	yes	—
428	C₃×C₄	#4147	1	1	yes	characteristic
429	C₃×C₄	D₅×#41	1	1	yes	characteristic
430	C₂×C₅	C₃×#548	1	1	yes	characteristic
431	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
432	C₂×C₅	C₃×#576	1	1	yes	characteristic
433	D₅	—	4	2	no	—
434	D₅	—	8	2	no	—
435	C₂³	—	10	1	no	—
436	C₂³	—	10	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	10	1	no	—
439	Q₈	—	10	1	no	—
440	Q₈	—	40	1	no	—
441	D₄	—	5	2	no	—
442	D₄	—	10	1	no	—
443	D₄	—	10	2	no	—
444	D₄	—	10	2	no	—
445	D₄	—	20	2	no	—
446	D₄	—	40	1	no	—
447	C₂×C₄	—	10	1	no	—
448	C₂×C₄	—	10	1	no	—
449	C₂×C₄	—	10	1	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	20	2	no	—
452	C₂×C₄	—	40	2	no	—
453	C₂×C₄	—	40	2	no	—
454	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
455	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
456	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
457	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
458	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	2	no	—
461	C₈	—	2	1	no	—
462	C₂×C₃	—	20	2	no	—
463	C₂×C₃	—	40	2	no	—
464	C₂×C₃	#65910	1	1	yes	characteristic
465	C₂×C₃	C₂×#4050	1	1	yes	characteristic
466	C₂×C₃	#66086	1	1	yes	characteristic
467	C₅	C₃×#3361	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	10	2	no	—
469	C₂²	—	20	1	no	—
470	C₂²	—	20	1	no	—
471	C₂²	—	20	2	no	—
472	C₂²	—	20	2	no	—
473	C₂²	—	20	2	no	—
474	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	20	1	no	—
479	C₄	—	20	1	no	—
480	C₄	—	20	1	no	—
481	C₄	—	20	2	no	—
482	C₄	C₃×#4050	1	2	yes	—
483	C₄	C₃×#4147	1	1	yes	characteristic
484	C₄	C₃×D₅×#41	1	1	yes	characteristic
485	C₃	#10611658	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	20	2	no	—
487	C₂	—	40	2	no	—
488	C₂	C₃×#65910	1	1	yes	characteristic
489	C₂	C₂×C₃×#4050	1	1	yes	characteristic
490	C₂	C₃×#66086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×C₈×Q₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#65132	C₂
hypercenter	C₃×C₈×Q₈	D₅
hypocenter	C₅	C₃×#3361
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈ ◁ C₃×C₈×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×#65919	C₂	semidirect
2. C₃×#65913	C₂	semidirect
3. C₃×C₅×C₈×Q₈	C₂	semidirect
4. C₃×#65139	C₂	semidirect
5. C₃×#65136	C₂	semidirect
6. C₃×#65133	C₂	semidirect
8. C₃×#64986	C₂	semidirect
9. C₃×#64983	C₂	semidirect
10. C₃×C₄×D₄₀	C₂	semidirect
11. C₃×C₄×#677	C₂	semidirect
12. #10611658	C₃	direct (N × H)
43. #65919	C₂×C₃	semidirect
44. #65913	C₂×C₃	semidirect
45. C₅×C₈×Q₈	C₂×C₃	semidirect
46. #65139	C₂×C₃	semidirect
47. #65136	C₂×C₃	semidirect
48. #65133	C₂×C₃	semidirect
50. #64986	C₂×C₃	semidirect
51. #64983	C₂×C₃	semidirect
52. C₄×D₄₀	C₂×C₃	semidirect
53. C₄×#677	C₂×C₃	semidirect
94. C₃×C₈×Q₈	D₅	semidirect
223. C₈×Q₈	C₃×D₅	semidirect
412. C₃×C₅	#3361	semidirect
467. C₅	C₃×#3361	semidirect
485. C₃	#10611658	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×#65919	2
C₃×#65913	2
C₃×C₅×C₈×Q₈	2
C₃×#65139	2
C₃×#65136	2
C₃×#65133	2
C₃×#65132	2
C₃×#64986	2
C₃×#64983	2
C₃×C₄×D₄₀	2
C₃×C₄×#677	2
#10611658	3
C₃×#3361	5

Subgroups — C3×#10611658 #14471763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611658 #14471763