Subgroups — C₃×#10612145 #14471504

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66055	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic
4	C₃×#65451	C₂	1	2	yes	maximal
5	C₃×SD₁₆×Dic₅	C₂	1	2	yes	maximal
6	C₃×#65370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#687	C₂	1	1	yes	maximal, characteristic
8	C₃×#65140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65119	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65081	C₂	1	2	yes	maximal, complemented
11	C₃×#65080	C₂	1	2	yes	maximal, complemented
12	#10612145	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×Dic₁₀	—	2	1	no	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
18	C₃×#4090	C₂²	1	2	yes	—
19	C₃×D₄×Dic₅	C₂²	1	2	yes	—
20	C₂×C₃×#687	C₂²	1	1	yes	characteristic
21	C₃×#4070	—	2	1	no	—
22	C₃×#4036	—	2	1	no	—
23	C₃×#4035	—	2	2	no	—
24	C₃×#4034	C₂²	1	2	yes	—
25	C₃×#4033	—	2	1	no	—
26	C₃×#4024	—	2	2	no	—
27	C₃×#4015	C₂²	1	1	yes	characteristic
28	C₃×C₄×Dic₁₀	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×#103	C₂²	1	2	yes	—
32	C₃×#3967	C₂²	1	2	yes	—
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	1	yes	characteristic
35	C₃×#3949	C₂²	1	2	yes	—
36	C₃×#3948	C₂²	1	2	yes	—
37	C₃×#3946	C₂²	1	2	yes	—
38	C₃×C₈×Dic₅	C₂²	1	2	yes	—
39	C₃×#3942	C₂²	1	1	yes	characteristic
40	C₃×#3940	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3359	—	5	1	no	maximal, Hall
43	#66055	C₂×C₃	1	1	yes	characteristic, complemented
44	D₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic
45	C₅×#461	C₂×C₃	1	1	yes	characteristic
46	#65451	C₂×C₃	1	2	yes	—
47	SD₁₆×Dic₅	C₂×C₃	1	2	yes	—
48	#65370	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×#687	C₂×C₃	1	1	yes	characteristic
50	#65140	C₂×C₃	1	1	yes	characteristic, complemented
51	#65119	C₂×C₃	1	1	yes	characteristic, complemented
52	#65081	C₂×C₃	1	2	yes	complemented
53	#65080	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₃×Dic₅	—	2	2	no	—
58	C₂×C₃×Dic₁₀	—	2	1	no	—
59	C₂×C₃×Dic₁₀	—	2	2	no	—
60	C₂×C₃×Dic₁₀	—	4	4	no	—
61	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
62	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₂²⋊Dic₅	—	2	2	no	—
71	C₃×#687	—	2	2	no	—
72	C₃×C₄⋊Dic₅	—	2	1	no	—
73	C₃×C₄⋊Dic₅	—	2	2	no	—
74	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
75	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
76	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
77	C₃×#683	—	2	1	no	—
78	C₃×#683	—	2	2	no	—
79	C₃×#683	—	2	2	no	—
80	C₃×#683	—	2	2	no	—
81	C₃×#683	D₄	1	2	yes	—
82	C₃×C₄×Dic₅	—	2	1	no	—
83	C₃×C₄×Dic₅	—	2	2	no	—
84	C₃×C₄×Dic₅	C₂³	1	2	yes	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₃×#557	—	5	1	no	—
88	C₃×D₄×Q₈	—	5	1	no	—
89	C₃×#487	—	5	1	no	—
90	C₃×#487	—	5	2	no	—
91	C₃×#475	—	5	1	no	—
92	C₃×#475	—	5	2	no	—
93	C₃×#461	—	5	2	no	—
94	C₃×#461	D₅	1	1	yes	characteristic
95	C₃×C₈×Q₈	—	5	1	no	—
96	C₃×C₄×SD₁₆	—	5	2	no	—
97	C₃×C₄×SD₁₆	—	5	1	no	—
98	C₂²×Dic₁₀	—	2	1	no	—
99	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
101	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
102	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
103	#4090	C₂²×C₃	1	2	yes	—
104	D₄×Dic₅	C₂²×C₃	1	2	yes	—
105	C₂×#687	C₂²×C₃	1	1	yes	characteristic
106	#4070	—	2	1	no	—
107	#4036	—	2	1	no	—
108	#4035	—	2	2	no	—
109	#4034	C₂²×C₃	1	2	yes	—
110	#4033	—	2	1	no	—
111	#4024	—	2	2	no	—
112	#4015	C₂²×C₃	1	1	yes	characteristic
113	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
114	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	C₅×#103	C₂²×C₃	1	2	yes	—
117	#3967	C₂²×C₃	1	2	yes	—
118	#3967	C₂²×C₃	1	2	yes	—
119	#3964	C₂²×C₃	1	1	yes	characteristic
120	#3949	C₂²×C₃	1	2	yes	—
121	#3948	C₂²×C₃	1	2	yes	—
122	#3946	C₂²×C₃	1	2	yes	—
123	C₈×Dic₅	C₂²×C₃	1	2	yes	—
124	#3942	C₂²×C₃	1	1	yes	characteristic
125	#3940	C₂²×C₃	1	1	yes	characteristic
126	C₄×#168	C₂²×C₃	1	1	yes	characteristic
127	#3359	—	5	1	no	Sylow
128	C₂³×C₃×C₅	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	#41	1	2	yes	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
139	C₂×C₃×Dic₅	—	2	1	no	—
140	C₂×C₃×Dic₅	—	2	1	no	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	4	4	no	—
143	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
145	C₃×Dic₁₀	—	2	1	no	—
146	C₃×Dic₁₀	—	2	1	no	—
147	C₃×Dic₁₀	—	4	2	no	—
148	C₃×Dic₁₀	—	4	4	no	—
149	C₃×Dic₁₀	SD₁₆	1	4	yes	complemented
150	C₃×C₅×C₈	—	2	2	no	—
151	C₃×#168	—	2	1	no	—
152	C₃×#168	—	2	1	no	—
153	C₂²×C₃×Q₈	—	10	1	no	—
154	C₂×C₃×SD₁₆	—	5	1	no	—
155	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
156	C₃×C₄⋊Q₈	—	5	2	no	—
157	C₃×C₄⋊Q₈	—	5	2	no	—
158	C₃×C₄⋊Q₈	—	5	1	no	—
159	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
160	C₃×#125	—	10	2	no	—
161	C₃×#125	—	10	1	no	—
162	C₃×C₂²⋊Q₈	—	10	2	no	—
163	C₃×C₂²⋊Q₈	—	10	1	no	—
164	C₃×C₄×Q₈	—	5	1	no	—
165	C₃×C₄×Q₈	—	5	2	no	—
166	C₃×C₄×Q₈	—	5	1	no	—
167	C₃×C₄×Q₈	—	10	1	no	—
168	C₃×C₄×D₄	—	5	2	no	—
169	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
170	C₃×#106	—	5	2	no	—
171	C₃×#106	—	5	1	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
174	C₃×#103	—	5	2	no	—
175	C₃×#103	—	5	2	no	—
176	C₃×#103	—	5	2	no	—
177	C₃×#103	—	5	1	no	—
178	C₃×#103	C₂×D₅	1	2	yes	—
179	C₃×#102	—	5	1	no	—
180	C₃×C₄×C₈	—	5	2	no	—
181	C₃×C₄×C₈	—	5	1	no	—
182	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
183	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×Dic₅	—	2	2	no	—
186	C₂×Dic₁₀	—	2	1	no	—
187	C₂×Dic₁₀	—	2	2	no	—
188	C₂×Dic₁₀	—	4	4	no	—
189	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
190	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
191	C₅×SD₁₆	—	2	4	no	—
192	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
196	C₅×C₂²⋊C₄	—	2	1	no	—
197	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
198	C₂²⋊Dic₅	—	2	2	no	—
199	#687	—	2	2	no	—
200	C₄⋊Dic₅	—	2	1	no	—
201	C₄⋊Dic₅	—	2	2	no	—
202	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
203	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
204	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
205	#683	—	2	1	no	—
206	#683	—	2	2	no	—
207	#683	—	2	2	no	—
208	#683	—	2	2	no	—
209	#683	C₃×D₄	1	2	yes	—
210	C₄×Dic₅	—	2	1	no	—
211	C₄×Dic₅	—	2	2	no	—
212	C₄×Dic₅	C₂³×C₃	1	2	yes	—
213	C₂×#168	C₂³×C₃	1	1	yes	characteristic
214	C₂×#168	C₂³×C₃	1	1	yes	characteristic
215	#557	—	5	1	no	—
216	D₄×Q₈	—	5	1	no	—
217	#487	—	5	1	no	—
218	#487	—	5	2	no	—
219	#475	—	5	1	no	—
220	#475	—	5	2	no	—
221	#461	—	5	2	no	—
222	#461	C₃×D₅	1	1	yes	characteristic
223	C₈×Q₈	—	5	1	no	—
224	C₄×SD₁₆	—	5	2	no	—
225	C₄×SD₁₆	—	5	1	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	4	1	no	—
228	C₂²×C₃×C₅	—	4	1	no	—
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₃×C₄×C₅	—	2	1	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
234	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
236	C₃×Dic₅	—	2	2	no	—
237	C₃×Dic₅	—	4	1	no	—
238	C₃×Dic₅	—	4	2	no	—
239	C₃×Dic₅	—	4	1	no	—
240	C₃×Dic₅	C₂×SD₁₆	1	4	yes	—
241	C₂×C₃×Q₈	—	5	1	no	—
242	C₂×C₃×Q₈	—	5	1	no	—
243	C₂×C₃×Q₈	—	10	2	no	—
244	C₂×C₃×Q₈	—	10	1	no	—
245	C₂×C₃×Q₈	—	20	4	no	—
246	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
247	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
248	C₂²×C₃×C₄	—	2	1	no	—
249	C₂²×C₃×C₄	—	10	2	no	—
250	C₃×SD₁₆	—	2	4	no	—
251	C₃×SD₁₆	—	10	2	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
255	C₃×C₄⋊C₄	—	2	1	no	—
256	C₃×C₄⋊C₄	—	2	1	no	—
257	C₃×C₄⋊C₄	—	5	2	no	—
258	C₃×C₄⋊C₄	—	5	1	no	—
259	C₃×C₄⋊C₄	—	5	1	no	—
260	C₃×C₄⋊C₄	—	5	2	no	—
261	C₃×C₄⋊C₄	—	10	2	no	—
262	C₃×C₄⋊C₄	—	10	2	no	—
263	C₃×C₄⋊C₄	—	10	2	no	—
264	C₃×C₄⋊C₄	—	10	2	no	—
265	C₃×C₄⋊C₄	—	10	1	no	—
266	C₃×C₄⋊C₄	—	10	1	no	—
267	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
268	C₃×C₂²⋊C₄	—	2	1	no	—
269	C₃×C₂²⋊C₄	—	10	2	no	—
270	C₃×C₄²	—	5	2	no	—
271	C₃×C₄²	—	10	2	no	—
272	C₃×C₄²	—	10	1	no	—
273	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
274	C₂³×C₅	—	2	1	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×D₄	—	2	1	no	—
278	C₅×D₄	C₃×#41	1	2	yes	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	4	2	no	—
282	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
285	C₂×Dic₅	—	2	1	no	—
286	C₂×Dic₅	—	2	1	no	—
287	C₂×Dic₅	—	2	2	no	—
288	C₂×Dic₅	—	4	4	no	—
289	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
290	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
291	Dic₁₀	—	2	1	no	—
292	Dic₁₀	—	2	1	no	—
293	Dic₁₀	—	4	2	no	—
294	Dic₁₀	—	4	4	no	—
295	Dic₁₀	C₃×SD₁₆	1	4	yes	complemented
296	C₅×C₈	—	2	2	no	—
297	#168	—	2	1	no	—
298	#168	—	2	1	no	—
299	C₂²×Q₈	—	10	1	no	—
300	C₂×SD₁₆	—	5	1	no	—
301	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
302	C₄⋊Q₈	—	5	2	no	—
303	C₄⋊Q₈	—	5	2	no	—
304	C₄⋊Q₈	—	5	1	no	—
305	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
306	#125	—	10	2	no	—
307	#125	—	10	1	no	—
308	C₂²⋊Q₈	—	10	2	no	—
309	C₂²⋊Q₈	—	10	1	no	—
310	C₄×Q₈	—	5	1	no	—
311	C₄×Q₈	—	5	2	no	—
312	C₄×Q₈	—	5	1	no	—
313	C₄×Q₈	—	10	1	no	—
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
316	#106	—	5	2	no	—
317	#106	—	5	1	no	—
318	C₄⋊C₈	—	5	2	no	—
319	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
320	#103	—	5	2	no	—
321	#103	—	5	2	no	—
322	#103	—	5	2	no	—
323	#103	—	5	1	no	—
324	#103	C₂×C₃×D₅	1	2	yes	—
325	#102	—	5	1	no	—
326	C₄×C₈	—	5	2	no	—
327	C₄×C₈	—	5	1	no	—
328	C₂×C₃×C₅	—	4	2	no	—
329	C₂×C₃×C₅	#548	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
331	C₂×C₃×C₅	#578	1	1	yes	characteristic
332	C₂³×C₃	—	2	1	no	—
333	C₃×Q₈	—	2	2	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	5	4	no	—
336	C₃×Q₈	—	10	1	no	—
337	C₃×Q₈	—	10	1	no	—
338	C₃×Q₈	—	20	4	no	—
339	C₃×Q₈	—	20	2	no	—
340	C₃×D₄	—	2	1	no	—
341	C₃×D₄	#711	1	2	yes	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	5	2	no	—
346	C₂×C₃×C₄	—	5	2	no	—
347	C₂×C₃×C₄	—	10	1	no	—
348	C₂×C₃×C₄	—	10	1	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	—	20	4	no	—
351	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
352	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
354	C₃×C₈	—	2	2	no	—
355	C₃×C₈	—	10	1	no	—
356	C₃×C₈	—	10	1	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	4	1	no	—
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
365	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
366	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
367	Dic₅	—	2	2	no	—
368	Dic₅	—	4	2	no	—
369	Dic₅	—	4	1	no	—
370	Dic₅	—	4	1	no	—
371	Dic₅	C₂×C₃×SD₁₆	1	4	yes	—
372	C₂×Q₈	—	5	1	no	—
373	C₂×Q₈	—	5	1	no	—
374	C₂×Q₈	—	10	2	no	—
375	C₂×Q₈	—	10	1	no	—
376	C₂×Q₈	—	20	4	no	—
377	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
378	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	10	2	no	—
381	SD₁₆	—	2	4	no	—
382	SD₁₆	—	10	2	no	—
383	C₂×C₈	—	5	1	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	5	2	no	—
389	C₄⋊C₄	—	5	1	no	—
390	C₄⋊C₄	—	5	1	no	—
391	C₄⋊C₄	—	5	2	no	—
392	C₄⋊C₄	—	10	2	no	—
393	C₄⋊C₄	—	10	2	no	—
394	C₄⋊C₄	—	10	2	no	—
395	C₄⋊C₄	—	10	2	no	—
396	C₄⋊C₄	—	10	1	no	—
397	C₄⋊C₄	—	10	1	no	—
398	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	10	2	no	—
401	C₄²	—	5	2	no	—
402	C₄²	—	10	2	no	—
403	C₄²	—	10	1	no	—
404	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
405	C₃×C₅	#3359	1	1	yes	characteristic, complemented, Hall
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	4	1	no	—
408	C₂²×C₃	—	4	1	no	—
409	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	4	1	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	—	5	4	no	—
414	C₃×C₄	—	10	2	no	—
415	C₃×C₄	—	20	2	no	—
416	C₃×C₄	—	20	1	no	—
417	C₃×C₄	—	20	1	no	—
418	C₃×C₄	D₅×SD₁₆	1	2	yes	—
419	C₃×C₄	C₂×#711	1	1	yes	characteristic
420	C₃×C₄	#4150	1	1	yes	characteristic
421	C₂×C₅	—	4	2	no	—
422	C₂×C₅	C₃×#548	1	1	yes	characteristic
423	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
424	C₂×C₅	C₃×#578	1	1	yes	characteristic
425	C₂³	—	2	1	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	5	4	no	—
429	Q₈	—	10	1	no	—
430	Q₈	—	10	1	no	—
431	Q₈	—	20	4	no	—
432	Q₈	—	20	2	no	—
433	D₄	—	2	1	no	—
434	D₄	C₃×#711	1	2	yes	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	5	2	no	—
439	C₂×C₄	—	5	2	no	—
440	C₂×C₄	—	10	1	no	—
441	C₂×C₄	—	10	1	no	—
442	C₂×C₄	—	10	2	no	—
443	C₂×C₄	—	20	4	no	—
444	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
445	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	10	1	no	—
449	C₈	—	10	1	no	—
450	C₂×C₃	—	4	2	no	—
451	C₂×C₃	#65932	1	1	yes	characteristic
452	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
453	C₂×C₃	#66113	1	1	yes	characteristic
454	C₅	C₃×#3359	1	1	yes	characteristic, complemented, Sylow
455	C₂²	—	2	2	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	1	no	—
462	C₄	—	5	4	no	—
463	C₄	—	10	2	no	—
464	C₄	—	20	1	no	—
465	C₄	—	20	1	no	—
466	C₄	—	20	2	no	—
467	C₄	C₃×D₅×SD₁₆	1	2	yes	—
468	C₄	C₂×C₃×#711	1	1	yes	characteristic
469	C₄	C₃×#4150	1	1	yes	characteristic
470	C₃	#10612145	1	1	yes	characteristic, direct product factor, Sylow
471	C₂	—	4	2	no	—
472	C₂	C₃×#65932	1	1	yes	characteristic
473	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic
474	C₂	C₃×#66113	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	C₃×C₅×#461	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×D₄	C₂³
hypercenter	C₃×#461	D₅
hypocenter	C₅	C₃×#3359
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#461

Complements

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

N	H ≅ G/N	type
1. C₃×#66055	C₂	semidirect
6. C₃×#65370	C₂	semidirect
8. C₃×#65140	C₂	semidirect
9. C₃×#65119	C₂	semidirect
10. C₃×#65081	C₂	semidirect
11. C₃×#65080	C₂	semidirect
12. #10612145	C₃	direct (N × H)
43. #66055	C₂×C₃	semidirect
48. #65370	C₂×C₃	semidirect
50. #65140	C₂×C₃	semidirect
51. #65119	C₂×C₃	semidirect
52. #65081	C₂×C₃	semidirect
53. #65080	C₂×C₃	semidirect
149. C₃×Dic₁₀	SD₁₆	semidirect
295. Dic₁₀	C₃×SD₁₆	semidirect
405. C₃×C₅	#3359	semidirect
454. C₅	C₃×#3359	semidirect
470. C₃	#10612145	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×#66055	2
C₃×D₄×Dic₁₀	2
C₃×C₅×#461	2
C₃×#65451	2
C₃×SD₁₆×Dic₅	2
C₃×#65370	2
C₃×C₄×#687	2
C₃×#65140	2
C₃×#65119	2
C₃×#65081	2
C₃×#65080	2
#10612145	3
C₃×#3359	5

Subgroups — C3×#10612145 #14471504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612145 #14471504