Subgroups — C₃×#10613351 #14471510

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×#66061	C₂	1	1	yes	maximal, characteristic
2	C₃×#66055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65372	C₂	1	1	yes	maximal, characteristic
6	C₃×#65107	C₂	1	2	yes	maximal
7	C₃×#65081	C₂	1	2	yes	maximal, complemented
8	C₃×#65080	C₂	1	2	yes	maximal, complemented
9	C₃×#65077	C₂	1	2	yes	maximal
10	C₃×C₄×#677	C₂	1	1	yes	maximal, characteristic
11	C₃×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613351	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×Q₈×D₅	—	2	1	no	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×#4092	—	2	1	no	—
17	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
18	C₃×#4090	C₂²	1	2	yes	—
19	C₂×C₃×#688	C₂²	1	2	yes	—
20	C₂×C₃×#677	C₂²	1	1	yes	characteristic
21	C₃×#4042	—	2	2	no	—
22	C₃×#4039	C₂²	1	2	yes	—
23	C₃×#4036	—	2	1	no	—
24	C₃×#4035	—	2	2	no	—
25	C₃×#4034	C₂²	1	2	yes	—
26	C₃×#4033	—	2	1	no	—
27	C₃×C₄×D₂₀	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×#103	C₂²	1	2	yes	—
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	1	yes	characteristic
35	C₃×#3949	C₂²	1	1	yes	characteristic
36	C₃×#3948	C₂²	1	1	yes	characteristic
37	C₃×#3946	C₂²	1	2	yes	—
38	C₃×C₈×Dic₅	C₂²	1	2	yes	—
39	C₃×#3942	C₂²	1	2	yes	—
40	C₃×#3940	C₂²	1	2	yes	—
41	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₃×#3359	—	5	1	no	maximal, Hall
43	#66061	C₂×C₃	1	1	yes	characteristic
44	#66055	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
46	#65383	C₂×C₃	1	1	yes	characteristic, complemented
47	#65372	C₂×C₃	1	1	yes	characteristic
48	#65107	C₂×C₃	1	2	yes	—
49	#65081	C₂×C₃	1	2	yes	complemented
50	#65080	C₂×C₃	1	2	yes	complemented
51	#65077	C₂×C₃	1	2	yes	—
52	C₄×#677	C₂×C₃	1	1	yes	characteristic
53	C₈×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₃×Q₈×D₅	—	4	4	no	—
57	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	—	2	1	no	—
59	C₂×C₃×C₄×D₅	—	2	2	no	—
60	C₂×C₃×Dic₁₀	—	2	2	no	—
61	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
62	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×#688	—	2	4	no	—
71	C₃×#685	—	2	1	no	—
72	C₃×#685	—	2	2	no	—
73	C₃×C₄⋊Dic₅	—	2	2	no	—
74	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
75	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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	2	yes	—
86	C₃×#677	—	2	2	no	—
87	C₃×#557	—	5	1	no	—
88	C₃×D₄×Q₈	—	5	1	no	—
89	C₃×#487	—	5	2	no	—
90	C₃×#487	D₅	1	1	yes	characteristic, complemented
91	C₃×#475	—	5	1	no	—
92	C₃×#475	—	5	2	no	—
93	C₃×#461	—	5	1	no	—
94	C₃×#461	—	5	2	no	—
95	C₃×C₈×Q₈	—	5	1	no	—
96	C₃×C₄×SD₁₆	—	5	2	no	—
97	C₃×C₄×SD₁₆	—	5	1	no	—
98	C₂×Q₈×D₅	—	2	1	no	—
99	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
101	#4092	—	2	1	no	—
102	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
103	#4090	C₂²×C₃	1	2	yes	—
104	C₂×#688	C₂²×C₃	1	2	yes	—
105	C₂×#677	C₂²×C₃	1	1	yes	characteristic
106	#4042	—	2	2	no	—
107	#4039	C₂²×C₃	1	2	yes	—
108	#4036	—	2	1	no	—
109	#4035	—	2	2	no	—
110	#4034	C₂²×C₃	1	2	yes	—
111	#4033	—	2	1	no	—
112	C₄×D₂₀	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×#103	C₂²×C₃	1	2	yes	—
116	C₅×#103	C₂²×C₃	1	2	yes	—
117	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
118	#3967	C₂²×C₃	1	2	yes	—
119	#3953	C₂²×C₃	1	1	yes	characteristic
120	#3949	C₂²×C₃	1	1	yes	characteristic
121	#3948	C₂²×C₃	1	1	yes	characteristic
122	#3946	C₂²×C₃	1	2	yes	—
123	C₈×Dic₅	C₂²×C₃	1	2	yes	—
124	#3942	C₂²×C₃	1	2	yes	—
125	#3940	C₂²×C₃	1	2	yes	—
126	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
127	#3359	—	5	1	no	Sylow
128	C₂²×C₃×D₅	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×Q₈	—	4	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×C₃×Dic₅	—	2	1	no	—
138	C₂×C₃×Dic₅	—	2	1	no	—
139	C₂×C₃×Dic₅	—	2	1	no	—
140	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
142	C₃×D₂₀	—	2	1	no	—
143	C₃×D₂₀	#41	1	2	yes	—
144	C₃×C₄×D₅	—	4	2	no	—
145	C₃×C₄×D₅	—	4	4	no	—
146	C₃×Dic₁₀	—	2	1	no	—
147	C₃×Dic₁₀	—	2	1	no	—
148	C₃×Dic₁₀	—	4	4	no	—
149	C₃×Dic₁₀	SD₁₆	1	4	yes	complemented
150	C₃×C₅×C₈	—	2	1	no	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×#168	—	2	2	no	—
153	C₂²×C₃×Q₈	—	10	1	no	—
154	C₂×C₃×SD₁₆	—	5	2	no	—
155	C₂×C₃×SD₁₆	—	5	1	no	—
156	C₃×C₄⋊Q₈	—	5	2	no	—
157	C₃×C₄⋊Q₈	—	5	2	no	—
158	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
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	—	5	1	no	—
170	C₃×#106	—	5	1	no	—
171	C₃×#106	—	5	2	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₄⋊C₈	—	5	1	no	—
174	C₃×#103	—	5	2	no	—
175	C₃×#103	—	5	1	no	—
176	C₃×#103	—	5	2	no	—
177	C₃×#103	C₂×D₅	1	2	yes	—
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	C₂×D₅	1	1	yes	characteristic
182	C₂×C₅×Q₈	—	2	1	no	—
183	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
184	Q₈×D₅	—	4	4	no	—
185	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₄×D₅	—	2	1	no	—
187	C₂×C₄×D₅	—	2	2	no	—
188	C₂×Dic₁₀	—	2	2	no	—
189	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
190	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
197	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
198	#688	—	2	4	no	—
199	#685	—	2	1	no	—
200	#685	—	2	2	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	1	yes	characteristic
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	2	yes	—
214	#677	—	2	2	no	—
215	#557	—	5	1	no	—
216	D₄×Q₈	—	5	1	no	—
217	#487	—	5	2	no	—
218	#487	C₃×D₅	1	1	yes	characteristic, complemented
219	#475	—	5	1	no	—
220	#475	—	5	2	no	—
221	#461	—	5	1	no	—
222	#461	—	5	2	no	—
223	C₈×Q₈	—	5	1	no	—
224	C₄×SD₁₆	—	5	2	no	—
225	C₄×SD₁₆	—	5	1	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	C₃×C₄×C₅	—	2	1	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	2	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	1	no	—
239	C₃×Dic₅	—	4	1	no	—
240	C₃×Dic₅	C₂×SD₁₆	1	4	yes	—
241	C₂×C₃×Q₈	—	2	1	no	—
242	C₂×C₃×Q₈	—	5	1	no	—
243	C₂×C₃×Q₈	—	5	1	no	—
244	C₂×C₃×Q₈	—	10	2	no	—
245	C₂×C₃×Q₈	—	20	4	no	—
246	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
247	C₂×C₃×D₄	—	5	1	no	—
248	C₂²×C₃×C₄	—	10	2	no	—
249	C₂²×C₃×C₄	—	10	1	no	—
250	C₃×SD₁₆	—	10	2	no	—
251	C₃×SD₁₆	—	10	4	no	—
252	C₂×C₃×C₈	—	5	2	no	—
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
255	C₃×C₄⋊C₄	—	2	1	no	—
256	C₃×C₄⋊C₄	—	2	1	no	—
257	C₃×C₄⋊C₄	—	2	1	no	—
258	C₃×C₄⋊C₄	—	5	2	no	—
259	C₃×C₄⋊C₄	—	5	1	no	—
260	C₃×C₄⋊C₄	—	5	1	no	—
261	C₃×C₄⋊C₄	—	5	1	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	2	no	—
266	C₃×C₄⋊C₄	—	10	1	no	—
267	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
268	C₃×C₂²⋊C₄	—	10	2	no	—
269	C₃×C₂²⋊C₄	—	10	1	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	C₂²×D₅	—	2	1	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	4	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
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	C₂×C₃×D₄	1	2	yes	—
287	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
288	D₂₀	—	2	1	no	—
289	D₂₀	C₃×#41	1	2	yes	—
290	C₄×D₅	—	4	2	no	—
291	C₄×D₅	—	4	4	no	—
292	Dic₁₀	—	2	1	no	—
293	Dic₁₀	—	2	1	no	—
294	Dic₁₀	—	4	4	no	—
295	Dic₁₀	C₃×SD₁₆	1	4	yes	complemented
296	C₅×C₈	—	2	1	no	—
297	C₅×C₈	—	2	1	no	—
298	#168	—	2	2	no	—
299	C₂²×Q₈	—	10	1	no	—
300	C₂×SD₁₆	—	5	2	no	—
301	C₂×SD₁₆	—	5	1	no	—
302	C₄⋊Q₈	—	5	2	no	—
303	C₄⋊Q₈	—	5	2	no	—
304	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
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	—	5	1	no	—
316	#106	—	5	1	no	—
317	#106	—	5	2	no	—
318	C₄⋊C₈	—	5	2	no	—
319	C₄⋊C₈	—	5	1	no	—
320	#103	—	5	2	no	—
321	#103	—	5	1	no	—
322	#103	—	5	2	no	—
323	#103	C₂×C₃×D₅	1	2	yes	—
324	#103	C₂×C₃×D₅	1	2	yes	—
325	#102	—	5	1	no	—
326	C₄×C₈	—	5	2	no	—
327	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
328	C₂×C₃×C₅	#548	1	1	yes	characteristic
329	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
330	C₂×C₃×C₅	#578	1	1	yes	characteristic
331	C₃×D₅	—	4	2	no	—
332	C₂³×C₃	—	10	1	no	—
333	C₃×Q₈	—	2	2	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	4	2	no	—
336	C₃×Q₈	—	5	4	no	—
337	C₃×Q₈	—	10	1	no	—
338	C₃×Q₈	—	10	1	no	—
339	C₃×Q₈	—	20	4	no	—
340	C₃×D₄	—	5	2	no	—
341	C₃×D₄	—	10	1	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	5	2	no	—
345	C₂×C₃×C₄	—	5	2	no	—
346	C₂×C₃×C₄	—	10	1	no	—
347	C₂×C₃×C₄	—	10	1	no	—
348	C₂×C₃×C₄	—	10	1	no	—
349	C₂×C₃×C₄	—	20	4	no	—
350	C₂×C₃×C₄	—	20	2	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	1	no	—
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	—	10	2	no	—
357	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
358	C₂×D₅	—	2	2	no	—
359	C₂×D₅	—	4	1	no	—
360	C₂×D₅	—	4	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	4	2	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	1	no	—
369	Dic₅	—	4	1	no	—
370	Dic₅	—	4	1	no	—
371	Dic₅	C₂×C₃×SD₁₆	1	4	yes	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	5	1	no	—
374	C₂×Q₈	—	5	1	no	—
375	C₂×Q₈	—	10	2	no	—
376	C₂×Q₈	—	20	4	no	—
377	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
378	C₂×D₄	—	5	1	no	—
379	C₂²×C₄	—	10	2	no	—
380	C₂²×C₄	—	10	1	no	—
381	SD₁₆	—	10	2	no	—
382	SD₁₆	—	10	4	no	—
383	C₂×C₈	—	5	2	no	—
384	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
385	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	5	2	no	—
390	C₄⋊C₄	—	5	1	no	—
391	C₄⋊C₄	—	5	1	no	—
392	C₄⋊C₄	—	5	1	no	—
393	C₄⋊C₄	—	10	2	no	—
394	C₄⋊C₄	—	10	2	no	—
395	C₄⋊C₄	—	10	2	no	—
396	C₄⋊C₄	—	10	2	no	—
397	C₄⋊C₄	—	10	1	no	—
398	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
399	C₂²⋊C₄	—	10	2	no	—
400	C₂²⋊C₄	—	10	1	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	—	10	2	no	—
407	C₂²×C₃	—	20	1	no	—
408	C₂²×C₃	—	20	1	no	—
409	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	—	5	4	no	—
414	C₃×C₄	—	10	2	no	—
415	C₃×C₄	—	20	1	no	—
416	C₃×C₄	—	20	1	no	—
417	C₃×C₄	—	20	1	no	—
418	C₃×C₄	D₅×SD₁₆	1	2	yes	—
419	C₃×C₄	D₅×#41	1	1	yes	characteristic
420	C₃×C₄	#4150	1	1	yes	characteristic
421	C₂×C₅	C₃×#548	1	1	yes	characteristic
422	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
423	C₂×C₅	C₃×#578	1	1	yes	characteristic
424	D₅	—	4	2	no	—
425	C₂³	—	10	1	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	5	4	no	—
430	Q₈	—	10	1	no	—
431	Q₈	—	10	1	no	—
432	Q₈	—	20	4	no	—
433	D₄	—	5	2	no	—
434	D₄	—	10	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	5	2	no	—
438	C₂×C₄	—	5	2	no	—
439	C₂×C₄	—	10	1	no	—
440	C₂×C₄	—	10	1	no	—
441	C₂×C₄	—	10	1	no	—
442	C₂×C₄	—	20	4	no	—
443	C₂×C₄	—	20	2	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	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	10	2	no	—
450	C₂×C₃	—	20	2	no	—
451	C₂×C₃	#66011	1	1	yes	characteristic
452	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
453	C₂×C₃	#66100	1	1	yes	characteristic
454	C₅	C₃×#3359	1	1	yes	characteristic, complemented, Sylow
455	C₂²	—	10	2	no	—
456	C₂²	—	20	1	no	—
457	C₂²	—	20	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	2	no	—
462	C₄	—	5	4	no	—
463	C₄	—	10	2	no	—
464	C₄	—	20	1	no	—
465	C₄	—	20	1	no	—
466	C₄	—	20	1	no	—
467	C₄	C₃×D₅×SD₁₆	1	2	yes	—
468	C₄	C₃×D₅×#41	1	1	yes	characteristic
469	C₄	C₃×#4150	1	1	yes	characteristic
470	C₃	#10613351	1	1	yes	characteristic, direct product factor, Sylow
471	C₂	—	20	2	no	—
472	C₂	C₃×#66011	1	1	yes	characteristic
473	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic
474	C₂	C₃×#66100	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×#487	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₂₀	C₂³
hypercenter	C₃×#487	D₅
hypocenter	C₅	C₃×#3359
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#487

Complements

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

N	H ≅ G/N	type
2. C₃×#66055	C₂	semidirect
3. C₃×C₅×#487	C₂	semidirect
4. C₃×#65383	C₂	semidirect
7. C₃×#65081	C₂	semidirect
8. C₃×#65080	C₂	semidirect
11. C₃×C₈×Dic₁₀	C₂	semidirect
12. #10613351	C₃	direct (N × H)
44. #66055	C₂×C₃	semidirect
45. C₅×#487	C₂×C₃	semidirect
46. #65383	C₂×C₃	semidirect
49. #65081	C₂×C₃	semidirect
50. #65080	C₂×C₃	semidirect
53. C₈×Dic₁₀	C₂×C₃	semidirect
90. C₃×#487	D₅	semidirect
149. C₃×Dic₁₀	SD₁₆	semidirect
218. #487	C₃×D₅	semidirect
295. Dic₁₀	C₃×SD₁₆	semidirect
405. C₃×C₅	#3359	semidirect
454. C₅	C₃×#3359	semidirect
470. C₃	#10613351	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×#66061	2
C₃×#66055	2
C₃×C₅×#487	2
C₃×#65383	2
C₃×#65372	2
C₃×#65107	2
C₃×#65081	2
C₃×#65080	2
C₃×#65077	2
C₃×C₄×#677	2
C₃×C₈×Dic₁₀	2
#10613351	3
C₃×#3359	5

Subgroups — C3×#10613351 #14471510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613351 #14471510