Subgroups — C₃×#10612818 #14471595

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66064	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65876	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#686	C₂	1	1	yes	maximal, characteristic
6	C₃×#65146	C₂	1	2	yes	maximal, complemented
7	C₃×#65141	C₂	1	2	yes	maximal, complemented
8	C₃×#65130	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65119	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65076	C₂	1	2	yes	maximal
11	C₃×#65057	C₂	1	2	yes	maximal, complemented
12	#10612818	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₃×#4092	—	2	2	no	—
16	C₃×#4082	C₂²	1	2	yes	—
17	C₂×C₃×#686	C₂²	1	1	yes	characteristic
18	C₃×#4072	—	2	1	no	—
19	C₃×#4070	—	2	1	no	—
20	C₂×C₃×#677	C₂²	1	2	yes	—
21	C₃×#4043	—	2	1	no	—
22	C₃×#4039	C₂²	1	2	yes	—
23	C₃×D₅×C₄⋊C₄	—	2	1	no	—
24	C₃×#4036	C₂²	1	2	yes	—
25	C₃×#4033	C₂²	1	2	yes	—
26	C₃×#4025	—	2	2	no	—
27	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
28	C₃×#4015	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	2	yes	—
31	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×#102	C₂²	1	2	yes	—
33	C₃×#3964	C₂²	1	1	yes	characteristic
34	C₃×#3948	C₂²	1	2	yes	—
35	C₃×#3946	C₂²	1	2	yes	—
36	C₃×C₈×Dic₅	C₂²	1	2	yes	—
37	C₃×#3942	C₂²	1	2	yes	—
38	C₃×#3942	C₂²	1	2	yes	—
39	C₃×#3941	C₂²	1	1	yes	characteristic
40	C₃×#3939	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3360	—	5	1	no	maximal, Hall
43	#66064	C₂×C₃	1	1	yes	characteristic, complemented
44	#65876	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
46	#65382	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×#686	C₂×C₃	1	1	yes	characteristic
48	#65146	C₂×C₃	1	2	yes	complemented
49	#65141	C₂×C₃	1	2	yes	complemented
50	#65130	C₂×C₃	1	1	yes	characteristic, complemented
51	#65119	C₂×C₃	1	1	yes	characteristic, complemented
52	#65076	C₂×C₃	1	2	yes	—
53	#65057	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	—	2	1	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	D₄	1	1	yes	characteristic
61	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₂²⋊Dic₅	—	2	2	no	—
69	C₃×C₂²⋊Dic₅	—	2	2	no	—
70	C₃×#686	—	2	2	no	—
71	C₃×#685	—	2	1	no	—
72	C₃×#685	—	2	2	no	—
73	C₃×C₄⋊Dic₅	—	2	1	no	—
74	C₃×C₄⋊Dic₅	—	2	1	no	—
75	C₃×C₄⋊Dic₅	—	2	2	no	—
76	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
77	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
78	C₃×#683	—	2	2	no	—
79	C₃×#683	—	2	2	no	—
80	C₃×#683	D₄	1	2	yes	—
81	C₃×C₄×Dic₅	—	2	2	no	—
82	C₃×C₄×Dic₅	C₂³	1	2	yes	—
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₃×#677	—	2	4	no	—
86	C₃×#556	—	5	1	no	—
87	C₃×#554	—	5	1	no	—
88	C₃×#488	—	5	2	no	—
89	C₃×#487	—	5	1	no	—
90	C₃×#479	—	5	2	no	—
91	C₃×#476	D₅	1	1	yes	characteristic, complemented
92	C₃×#463	—	5	2	no	—
93	C₃×#461	—	5	1	no	—
94	C₃×C₈×Q₈	—	5	1	no	—
95	C₃×C₄×SD₁₆	—	5	2	no	—
96	C₃×C₄×D₈	—	5	1	no	—
97	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
99	#4092	—	2	2	no	—
100	#4082	C₂²×C₃	1	2	yes	—
101	C₂×#686	C₂²×C₃	1	1	yes	characteristic
102	#4072	—	2	1	no	—
103	#4070	—	2	1	no	—
104	C₂×#677	C₂²×C₃	1	2	yes	—
105	#4043	—	2	1	no	—
106	#4039	C₂²×C₃	1	2	yes	—
107	D₅×C₄⋊C₄	—	2	1	no	—
108	#4036	C₂²×C₃	1	2	yes	—
109	#4033	C₂²×C₃	1	2	yes	—
110	#4025	—	2	2	no	—
111	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
112	#4015	C₂²×C₃	1	1	yes	characteristic
113	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
114	C₅×#106	C₂²×C₃	1	2	yes	—
115	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	C₅×#102	C₂²×C₃	1	2	yes	—
117	#3964	C₂²×C₃	1	1	yes	characteristic
118	#3948	C₂²×C₃	1	2	yes	—
119	#3946	C₂²×C₃	1	2	yes	—
120	C₈×Dic₅	C₂²×C₃	1	2	yes	—
121	#3942	C₂²×C₃	1	2	yes	—
122	#3942	C₂²×C₃	1	2	yes	—
123	#3941	C₂²×C₃	1	1	yes	characteristic
124	#3939	C₂²×C₃	1	1	yes	characteristic
125	C₄×#168	C₂²×C₃	1	1	yes	characteristic
126	#3360	—	5	1	no	Sylow
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂²×C₃×D₅	—	2	1	no	—
129	C₃×C₅×Q₈	—	8	1	no	—
130	C₃×C₅×D₄	—	2	1	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	4	2	no	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₂×C₃×Dic₅	—	2	2	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	—	8	2	no	—
146	C₃×Dic₁₀	—	2	2	no	—
147	C₃×Dic₁₀	—	2	2	no	—
148	C₃×Dic₁₀	—	2	2	no	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃×#168	—	2	1	no	—
151	C₃×#168	—	2	1	no	—
152	C₂×C₃×SD₁₆	—	5	2	no	—
153	C₂×C₃×D₈	—	5	1	no	—
154	C₃×C₄⋊Q₈	—	5	1	no	—
155	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
156	C₃×#126	—	10	2	no	—
157	C₃×#125	—	5	2	no	—
158	C₃×#124	—	5	2	no	—
159	C₃×C₂²⋊Q₈	—	10	1	no	—
160	C₃×C₂²⋊Q₈	—	10	2	no	—
161	C₃×C₂²⋊Q₈	—	10	1	no	—
162	C₃×C₄×Q₈	—	5	1	no	—
163	C₃×C₄×Q₈	—	5	2	no	—
164	C₃×C₄×D₄	—	5	2	no	—
165	C₃×C₄×D₄	—	5	1	no	—
166	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
167	C₃×#117	—	10	1	no	—
168	C₂×C₃×C₄⋊C₄	—	10	1	no	—
169	C₃×#107	—	5	1	no	—
170	C₃×#106	C₂×D₅	1	2	yes	—
171	C₃×C₄⋊C₈	—	5	2	no	—
172	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
173	C₃×#103	—	5	2	no	—
174	C₃×#103	—	5	2	no	—
175	C₃×#103	—	5	2	no	—
176	C₃×#102	—	5	1	no	—
177	C₃×#102	—	5	1	no	—
178	C₃×#102	C₂×D₅	1	2	yes	—
179	C₃×C₄×C₈	—	5	2	no	—
180	C₃×C₄×C₈	—	5	1	no	—
181	C₂×C₅×Q₈	—	2	1	no	—
182	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₄×D₅	—	2	1	no	—
186	C₂×C₄×D₅	—	2	2	no	—
187	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
188	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
189	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
192	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
193	C₅×C₂²⋊C₄	—	2	1	no	—
194	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₂²⋊Dic₅	—	2	2	no	—
196	C₂²⋊Dic₅	—	2	2	no	—
197	#686	—	2	2	no	—
198	#685	—	2	1	no	—
199	#685	—	2	2	no	—
200	C₄⋊Dic₅	—	2	1	no	—
201	C₄⋊Dic₅	—	2	1	no	—
202	C₄⋊Dic₅	—	2	2	no	—
203	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
204	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
205	#683	—	2	2	no	—
206	#683	—	2	2	no	—
207	#683	C₃×D₄	1	2	yes	—
208	C₄×Dic₅	—	2	2	no	—
209	C₄×Dic₅	C₂³×C₃	1	2	yes	—
210	C₂×#168	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	1	yes	characteristic
212	#677	—	2	4	no	—
213	#556	—	5	1	no	—
214	#554	—	5	1	no	—
215	#488	—	5	2	no	—
216	#487	—	5	1	no	—
217	#479	—	5	2	no	—
218	#476	C₃×D₅	1	1	yes	characteristic, complemented
219	#463	—	5	2	no	—
220	#461	—	5	1	no	—
221	C₈×Q₈	—	5	1	no	—
222	C₄×SD₁₆	—	5	2	no	—
223	C₄×D₈	—	5	1	no	—
224	C₂²×C₃×C₅	—	4	1	no	—
225	C₂²×C₃×C₅	—	4	1	no	—
226	C₂²×C₃×C₅	—	4	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₃×D₅	—	2	2	no	—
229	C₂×C₃×D₅	—	4	1	no	—
230	C₂×C₃×D₅	—	4	1	no	—
231	C₃×C₄×C₅	—	2	1	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	#135	1	2	yes	—
235	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
237	C₃×Dic₅	—	2	2	no	—
238	C₃×Dic₅	—	2	2	no	—
239	C₃×Dic₅	—	4	2	no	—
240	C₃×Dic₅	—	4	1	no	—
241	C₂×C₃×Q₈	—	2	1	no	—
242	C₂×C₃×Q₈	—	5	1	no	—
243	C₂×C₃×Q₈	—	5	2	no	—
244	C₂×C₃×D₄	—	5	1	no	—
245	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	—	10	2	no	—
248	C₂²×C₃×C₄	—	10	1	no	—
249	C₃×SD₁₆	—	10	4	no	—
250	C₃×D₈	—	10	2	no	—
251	C₂×C₃×C₈	—	5	1	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
254	C₃×C₄⋊C₄	—	2	1	no	—
255	C₃×C₄⋊C₄	—	5	2	no	—
256	C₃×C₄⋊C₄	—	5	1	no	—
257	C₃×C₄⋊C₄	—	5	1	no	—
258	C₃×C₄⋊C₄	—	10	2	no	—
259	C₃×C₄⋊C₄	—	10	2	no	—
260	C₃×C₄⋊C₄	—	10	2	no	—
261	C₃×C₄⋊C₄	—	10	1	no	—
262	C₃×C₄⋊C₄	—	10	1	no	—
263	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
265	C₃×C₂²⋊C₄	—	2	1	no	—
266	C₃×C₂²⋊C₄	—	10	2	no	—
267	C₃×C₂²⋊C₄	—	10	2	no	—
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	C₂²×D₅	1	1	yes	characteristic
273	C₂³×C₅	—	2	1	no	—
274	C₂²×D₅	—	2	1	no	—
275	C₅×Q₈	—	8	1	no	—
276	C₅×D₄	—	2	1	no	—
277	C₅×D₄	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	4	2	no	—
281	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
284	C₂×Dic₅	—	2	2	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	—	8	2	no	—
292	Dic₁₀	—	2	2	no	—
293	Dic₁₀	—	2	2	no	—
294	Dic₁₀	—	2	2	no	—
295	C₅×C₈	—	2	2	no	—
296	#168	—	2	1	no	—
297	#168	—	2	1	no	—
298	C₂×SD₁₆	—	5	2	no	—
299	C₂×D₈	—	5	1	no	—
300	C₄⋊Q₈	—	5	1	no	—
301	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
302	#126	—	10	2	no	—
303	#125	—	5	2	no	—
304	#124	—	5	2	no	—
305	C₂²⋊Q₈	—	10	1	no	—
306	C₂²⋊Q₈	—	10	2	no	—
307	C₂²⋊Q₈	—	10	1	no	—
308	C₄×Q₈	—	5	1	no	—
309	C₄×Q₈	—	5	2	no	—
310	C₄×D₄	—	5	2	no	—
311	C₄×D₄	—	5	1	no	—
312	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
313	#117	—	10	1	no	—
314	C₂×C₄⋊C₄	—	10	1	no	—
315	#107	—	5	1	no	—
316	#106	C₂×C₃×D₅	1	2	yes	—
317	C₄⋊C₈	—	5	2	no	—
318	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
319	#103	—	5	2	no	—
320	#103	—	5	2	no	—
321	#103	—	5	2	no	—
322	#102	—	5	1	no	—
323	#102	—	5	1	no	—
324	#102	C₂×C₃×D₅	1	2	yes	—
325	C₄×C₈	—	5	2	no	—
326	C₄×C₈	—	5	1	no	—
327	C₂×C₃×C₅	—	8	1	no	—
328	C₂×C₃×C₅	#548	1	1	yes	characteristic
329	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
330	C₂×C₃×C₅	#577	1	1	yes	characteristic
331	C₃×D₅	—	4	2	no	—
332	C₂³×C₃	—	2	1	no	—
333	C₂³×C₃	—	10	1	no	—
334	C₃×Q₈	—	8	1	no	—
335	C₃×Q₈	—	10	2	no	—
336	C₃×Q₈	—	10	2	no	—
337	C₃×Q₈	—	10	2	no	—
338	C₃×D₄	—	2	1	no	—
339	C₃×D₄	—	2	1	no	—
340	C₃×D₄	—	5	2	no	—
341	C₃×D₄	—	10	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	2	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	2	no	—
348	C₂×C₃×C₄	—	10	1	no	—
349	C₂×C₃×C₄	—	20	2	no	—
350	C₂×C₃×C₄	—	40	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	2	no	—
355	C₃×C₈	—	10	1	no	—
356	C₃×C₈	—	10	1	no	—
357	C₂²×C₅	—	4	1	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
361	C₂×D₅	—	2	2	no	—
362	C₂×D₅	—	4	1	no	—
363	C₂×D₅	—	4	1	no	—
364	C₄×C₅	—	2	1	no	—
365	C₄×C₅	—	4	1	no	—
366	C₄×C₅	—	4	2	no	—
367	C₄×C₅	C₃×#135	1	2	yes	—
368	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
369	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
370	Dic₅	—	2	2	no	—
371	Dic₅	—	2	2	no	—
372	Dic₅	—	4	1	no	—
373	Dic₅	—	4	2	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	5	1	no	—
376	C₂×Q₈	—	5	2	no	—
377	C₂×D₄	—	5	1	no	—
378	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	10	2	no	—
381	C₂²×C₄	—	10	1	no	—
382	SD₁₆	—	10	4	no	—
383	D₈	—	10	2	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	—	5	1	no	—
386	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	5	1	no	—
389	C₄⋊C₄	—	5	2	no	—
390	C₄⋊C₄	—	5	1	no	—
391	C₄⋊C₄	—	10	2	no	—
392	C₄⋊C₄	—	10	2	no	—
393	C₄⋊C₄	—	10	2	no	—
394	C₄⋊C₄	—	10	1	no	—
395	C₄⋊C₄	—	10	1	no	—
396	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	10	2	no	—
400	C₂²⋊C₄	—	10	2	no	—
401	C₂²⋊C₄	—	10	2	no	—
402	C₂²⋊C₄	—	10	1	no	—
403	C₄²	—	5	2	no	—
404	C₄²	—	10	2	no	—
405	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
406	C₃×C₅	#3360	1	1	yes	characteristic, complemented, Hall
407	C₂²×C₃	—	4	1	no	—
408	C₂²×C₃	—	4	1	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	—	10	2	no	—
411	C₂²×C₃	—	20	1	no	—
412	C₂²×C₃	—	20	1	no	—
413	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	4	1	no	—
416	C₃×C₄	—	4	2	no	—
417	C₃×C₄	—	10	2	no	—
418	C₃×C₄	—	10	2	no	—
419	C₃×C₄	—	20	1	no	—
420	C₃×C₄	—	20	2	no	—
421	C₃×C₄	#4062	1	2	yes	—
422	C₃×C₄	#4147	1	1	yes	characteristic
423	C₃×C₄	D₅×#41	1	1	yes	characteristic
424	C₂×C₅	—	8	1	no	—
425	C₂×C₅	C₃×#548	1	1	yes	characteristic
426	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
427	C₂×C₅	C₃×#577	1	1	yes	characteristic
428	D₅	—	4	2	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	10	1	no	—
431	Q₈	—	8	1	no	—
432	Q₈	—	10	2	no	—
433	Q₈	—	10	2	no	—
434	Q₈	—	10	2	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	5	2	no	—
438	D₄	—	10	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	5	2	no	—
443	C₂×C₄	—	5	2	no	—
444	C₂×C₄	—	10	2	no	—
445	C₂×C₄	—	10	1	no	—
446	C₂×C₄	—	20	2	no	—
447	C₂×C₄	—	40	2	no	—
448	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
449	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
450	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	10	1	no	—
453	C₈	—	10	1	no	—
454	C₂×C₃	—	8	1	no	—
455	C₂×C₃	—	20	2	no	—
456	C₂×C₃	#65967	1	1	yes	characteristic
457	C₂×C₃	C₂×#4062	1	1	yes	characteristic
458	C₂×C₃	#66109	1	1	yes	characteristic
459	C₅	C₃×#3360	1	1	yes	characteristic, complemented, Sylow
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	10	2	no	—
464	C₂²	—	20	1	no	—
465	C₂²	—	20	1	no	—
466	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	1	no	—
470	C₄	—	10	2	no	—
471	C₄	—	10	2	no	—
472	C₄	—	20	2	no	—
473	C₄	—	20	1	no	—
474	C₄	C₃×#4062	1	2	yes	—
475	C₄	C₃×#4147	1	1	yes	characteristic
476	C₄	C₃×D₅×#41	1	1	yes	characteristic
477	C₃	#10612818	1	1	yes	characteristic, direct product factor, Sylow
478	C₂	—	8	1	no	—
479	C₂	—	20	2	no	—
480	C₂	C₃×#65967	1	1	yes	characteristic
481	C₂	C₂×C₃×#4062	1	1	yes	characteristic
482	C₂	C₃×#66109	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×#476	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#686	C₂²
hypercenter	C₃×#476	D₅
hypocenter	C₅	C₃×#3360
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#476

Complements

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

N	H ≅ G/N	type
1. C₃×#66064	C₂	semidirect
2. C₃×#65876	C₂	semidirect
3. C₃×C₅×#476	C₂	semidirect
4. C₃×#65382	C₂	semidirect
6. C₃×#65146	C₂	semidirect
7. C₃×#65141	C₂	semidirect
8. C₃×#65130	C₂	semidirect
9. C₃×#65119	C₂	semidirect
11. C₃×#65057	C₂	semidirect
12. #10612818	C₃	direct (N × H)
43. #66064	C₂×C₃	semidirect
44. #65876	C₂×C₃	semidirect
45. C₅×#476	C₂×C₃	semidirect
46. #65382	C₂×C₃	semidirect
48. #65146	C₂×C₃	semidirect
49. #65141	C₂×C₃	semidirect
50. #65130	C₂×C₃	semidirect
51. #65119	C₂×C₃	semidirect
53. #65057	C₂×C₃	semidirect
91. C₃×#476	D₅	semidirect
218. #476	C₃×D₅	semidirect
406. C₃×C₅	#3360	semidirect
459. C₅	C₃×#3360	semidirect
477. C₃	#10612818	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×#66064	2
C₃×#65876	2
C₃×C₅×#476	2
C₃×#65382	2
C₃×C₄×#686	2
C₃×#65146	2
C₃×#65141	2
C₃×#65130	2
C₃×#65119	2
C₃×#65076	2
C₃×#65057	2
#10612818	3
C₃×#3360	5

Subgroups — C3×#10612818 #14471595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612818 #14471595