Subgroups — C₃×#10613532 #14439631

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4064	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66058	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65479	C₂	1	2	yes	maximal, complemented
8	C₃×#65470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65375	C₂	1	2	yes	maximal, complemented
10	C₃×#64985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64978	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613532	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	2	yes	—
14	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₃×#4093	C₂²	1	2	yes	—
20	C₃×#4090	C₂²	1	2	yes	—
21	C₂×C₃×#689	C₂²	1	2	yes	—
22	C₂×C₃×#689	C₂²	1	2	yes	—
23	C₂×C₃×#688	C₂²	1	2	yes	—
24	C₂×C₃×#688	C₂²	1	2	yes	—
25	C₃×#4065	—	2	4	no	—
26	C₃×#4064	—	2	8	no	—
27	C₃×D₅×Q₁₆	—	2	4	no	—
28	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
29	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
30	C₂×C₃×#677	C₂²	1	2	yes	—
31	C₂×C₃×#676	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
33	C₃×#4042	—	2	4	no	—
34	C₃×#4040	—	2	4	no	—
35	C₃×#4021	C₂²	1	2	yes	—
36	C₃×#4018	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₃×#3947	C₂²	1	1	yes	characteristic
39	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×#3935	C₂²	1	1	yes	characteristic
41	C₃×#3156	—	5	1	no	maximal, Hall
42	C₂×#4065	C₂×C₃	1	1	yes	characteristic
43	C₂×#4064	C₂×C₃	1	2	yes	complemented
44	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
45	#66058	C₂×C₃	1	2	yes	complemented
46	C₅×#494	C₂×C₃	1	1	yes	characteristic, complemented
47	#65480	C₂×C₃	1	1	yes	characteristic, complemented
48	#65479	C₂×C₃	1	2	yes	complemented
49	#65470	C₂×C₃	1	1	yes	characteristic, complemented
50	#65375	C₂×C₃	1	2	yes	complemented
51	#64985	C₂×C₃	1	1	yes	characteristic, complemented
52	#64978	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₃×#713	—	2	4	no	—
56	C₃×#713	—	2	4	no	—
57	C₃×Q₈×D₅	—	2	4	no	—
58	C₃×Q₈×D₅	—	2	4	no	—
59	C₂×C₃×D₂₀	—	2	2	no	—
60	C₂×C₃×D₂₀	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×Dic₁₀	—	2	2	no	—
65	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
66	C₃×C₅×Q₁₆	—	2	2	no	—
67	C₃×C₅×Q₁₆	—	2	4	no	—
68	C₃×C₅×Q₁₆	—	2	2	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	4	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×#689	—	2	4	no	—
74	C₃×#689	—	2	4	no	—
75	C₃×#688	—	2	4	no	—
76	C₃×#688	—	2	4	no	—
77	C₃×#685	—	2	4	no	—
78	C₃×#685	—	2	4	no	—
79	C₃×#685	D₄	1	2	yes	—
80	C₃×#683	—	2	4	no	—
81	C₃×#683	D₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₃×Dic₂₀	—	2	2	no	—
86	C₃×D₄₀	—	2	2	no	—
87	C₃×#677	—	2	4	no	—
88	C₃×#676	D₄	1	4	yes	—
89	C₃×C₈×D₅	D₄	1	4	yes	—
90	C₂×C₃×#137	—	5	2	no	—
91	C₂×C₃×#135	—	5	1	no	—
92	C₂²×C₃×Q₁₆	—	5	1	no	—
93	C₃×#536	—	5	2	no	—
94	C₃×#497	—	5	2	no	—
95	C₃×#497	—	5	2	no	—
96	C₃×#495	—	5	1	no	—
97	C₃×#495	—	5	1	no	—
98	C₃×#494	—	5	1	no	—
99	C₃×#494	D₅	1	1	yes	characteristic, complemented
100	C₃×#405	—	5	1	no	—
101	C₂×#713	C₂²×C₃	1	2	yes	—
102	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
103	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
105	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
107	#4093	C₂²×C₃	1	2	yes	—
108	#4090	C₂²×C₃	1	2	yes	—
109	C₂×#689	C₂²×C₃	1	2	yes	—
110	C₂×#689	C₂²×C₃	1	2	yes	—
111	C₂×#688	C₂²×C₃	1	2	yes	—
112	C₂×#688	C₂²×C₃	1	2	yes	—
113	#4065	—	2	4	no	—
114	#4064	—	2	8	no	—
115	D₅×Q₁₆	—	2	4	no	—
116	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
117	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
118	C₂×#677	C₂²×C₃	1	2	yes	—
119	C₂×#676	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
121	#4042	—	2	4	no	—
122	#4040	—	2	4	no	—
123	#4021	C₂²×C₃	1	2	yes	—
124	#4018	C₂²×C₃	1	1	yes	characteristic
125	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
126	#3947	C₂²×C₃	1	1	yes	characteristic
127	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
128	#3935	C₂²×C₃	1	1	yes	characteristic
129	#3156	—	5	1	no	Sylow
130	C₂²×C₃×D₅	—	2	2	no	—
131	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
132	C₃×C₅×Q₈	—	2	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₂×C₃×Dic₅	—	2	2	no	—
141	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
143	C₃×D₂₀	—	2	2	no	—
144	C₃×D₂₀	—	2	2	no	—
145	C₃×D₂₀	—	4	4	no	—
146	C₃×C₄×D₅	—	4	4	no	—
147	C₃×C₄×D₅	—	4	4	no	—
148	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
149	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
150	C₃×Dic₁₀	—	2	2	no	—
151	C₃×Dic₁₀	—	2	2	no	—
152	C₃×Dic₁₀	—	4	4	no	—
153	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
155	C₃×#168	C₂×D₄	1	2	yes	—
156	C₃×#168	C₂×D₄	1	2	yes	—
157	C₂×C₃×#41	—	5	2	no	—
158	C₂²×C₃×Q₈	—	5	2	no	—
159	C₃×#137	—	10	8	no	—
160	C₃×#135	—	10	4	no	—
161	C₂×C₃×Q₁₆	—	5	2	no	—
162	C₂×C₃×Q₁₆	—	5	2	no	—
163	C₂×C₃×Q₁₆	—	5	1	no	—
164	C₂×C₃×Q₁₆	—	10	4	no	—
165	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
166	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
167	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	—
168	C₂×C₃×SD₁₆	—	5	2	no	—
169	C₂×C₃×SD₁₆	—	5	2	no	—
170	C₂×C₃×SD₁₆	—	5	2	no	—
171	C₂×C₃×D₈	—	5	1	no	—
172	C₂×C₃×M₁₆	—	5	1	no	—
173	C₂²×C₃×C₈	—	5	1	no	—
174	C₃×C₄⋊Q₈	—	5	2	no	—
175	C₃×C₄⋊Q₈	C₂×D₅	1	2	yes	—
176	C₃×#124	—	5	2	no	—
177	C₃×#124	—	5	2	no	—
178	C₃×#123	—	10	4	no	—
179	C₃×C₂²⋊Q₈	—	10	4	no	—
180	C₃×#117	—	5	1	no	—
181	C₃×#97	—	5	1	no	—
182	C₃×#97	—	5	1	no	—
183	C₃×C₄×C₈	—	5	1	no	—
184	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
185	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
186	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
187	#713	—	2	4	no	—
188	#713	—	2	4	no	—
189	Q₈×D₅	—	2	4	no	—
190	Q₈×D₅	—	2	4	no	—
191	C₂×D₂₀	—	2	2	no	—
192	C₂×D₂₀	C₂³×C₃	1	2	yes	—
193	C₂×C₄×D₅	—	2	2	no	—
194	C₂×C₄×D₅	—	2	2	no	—
195	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
196	C₂×Dic₁₀	—	2	2	no	—
197	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
198	C₅×Q₁₆	—	2	2	no	—
199	C₅×Q₁₆	—	2	4	no	—
200	C₅×Q₁₆	—	2	2	no	—
201	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
203	C₅×C₄⋊C₄	—	2	4	no	—
204	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
205	#689	—	2	4	no	—
206	#689	—	2	4	no	—
207	#688	—	2	4	no	—
208	#688	—	2	4	no	—
209	#685	—	2	4	no	—
210	#685	—	2	4	no	—
211	#685	C₃×D₄	1	2	yes	—
212	#683	—	2	4	no	—
213	#683	C₃×D₄	1	2	yes	—
214	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
215	C₂×#168	C₂³×C₃	1	1	yes	characteristic
216	C₂×#168	C₂³×C₃	1	1	yes	characteristic
217	Dic₂₀	—	2	2	no	—
218	D₄₀	—	2	2	no	—
219	#677	—	2	4	no	—
220	#676	C₃×D₄	1	4	yes	—
221	C₈×D₅	C₃×D₄	1	4	yes	—
222	C₂×#137	—	5	2	no	—
223	C₂×#135	—	5	1	no	—
224	C₂²×Q₁₆	—	5	1	no	—
225	#536	—	5	2	no	—
226	#497	—	5	2	no	—
227	#497	—	5	2	no	—
228	#495	—	5	1	no	—
229	#495	—	5	1	no	—
230	#494	—	5	1	no	—
231	#494	C₃×D₅	1	1	yes	characteristic, complemented
232	#405	—	5	1	no	—
233	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₃×D₅	—	2	2	no	—
235	C₂×C₃×D₅	—	4	2	no	—
236	C₂×C₃×D₅	—	4	4	no	—
237	C₂×C₃×D₅	#127	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	4	2	no	—
240	C₃×C₄×C₅	—	4	2	no	—
241	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₃×Dic₅	—	2	2	no	—
244	C₃×Dic₅	—	4	2	no	—
245	C₃×Dic₅	#127	1	2	yes	—
246	C₃×#41	—	10	4	no	—
247	C₃×#41	—	10	4	no	—
248	C₂×C₃×Q₈	—	5	2	no	—
249	C₂×C₃×Q₈	—	10	2	no	—
250	C₂×C₃×Q₈	—	10	4	no	—
251	C₂×C₃×Q₈	—	10	4	no	—
252	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
253	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
254	C₂×C₃×D₄	—	5	2	no	—
255	C₂×C₃×D₄	—	10	2	no	—
256	C₂²×C₃×C₄	—	5	1	no	—
257	C₂²×C₃×C₄	—	10	2	no	—
258	C₂²×C₃×C₄	—	10	2	no	—
259	C₃×Q₁₆	—	2	2	no	—
260	C₃×Q₁₆	—	2	2	no	—
261	C₃×Q₁₆	—	2	4	no	—
262	C₃×Q₁₆	—	10	4	no	—
263	C₃×Q₁₆	—	10	4	no	—
264	C₃×Q₁₆	—	10	2	no	—
265	C₃×SD₁₆	—	10	4	no	—
266	C₃×SD₁₆	—	10	4	no	—
267	C₃×SD₁₆	—	10	4	no	—
268	C₃×D₈	—	10	2	no	—
269	C₃×M₁₆	—	5	4	no	—
270	C₂×C₃×C₈	—	5	1	no	—
271	C₂×C₃×C₈	—	5	1	no	—
272	C₂×C₃×C₈	—	5	4	no	—
273	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
274	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
275	C₃×C₄⋊C₄	—	2	4	no	—
276	C₃×C₄⋊C₄	—	5	2	no	—
277	C₃×C₄⋊C₄	—	10	4	no	—
278	C₃×C₂²⋊C₄	—	5	2	no	—
279	C₃×C₂²⋊C₄	—	10	4	no	—
280	C₃×C₂²⋊C₄	—	10	4	no	—
281	C₃×C₄²	—	5	1	no	—
282	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
283	C₂²×D₅	—	2	2	no	—
284	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	2	2	no	—
288	C₅×Q₈	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
292	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
293	C₂×Dic₅	—	2	2	no	—
294	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
295	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
296	D₂₀	—	2	2	no	—
297	D₂₀	—	2	2	no	—
298	D₂₀	—	4	4	no	—
299	C₄×D₅	—	4	4	no	—
300	C₄×D₅	—	4	4	no	—
301	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
302	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
303	Dic₁₀	—	2	2	no	—
304	Dic₁₀	—	2	2	no	—
305	Dic₁₀	—	4	4	no	—
306	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
307	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
308	#168	C₂×C₃×D₄	1	2	yes	—
309	#168	C₂×C₃×D₄	1	2	yes	—
310	C₂×#41	—	5	2	no	—
311	C₂²×Q₈	—	5	2	no	—
312	#137	—	10	8	no	—
313	#135	—	10	4	no	—
314	C₂×Q₁₆	—	5	2	no	—
315	C₂×Q₁₆	—	5	2	no	—
316	C₂×Q₁₆	—	5	1	no	—
317	C₂×Q₁₆	—	10	4	no	—
318	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
319	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
320	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	—
321	C₂×SD₁₆	—	5	2	no	—
322	C₂×SD₁₆	—	5	2	no	—
323	C₂×SD₁₆	—	5	2	no	—
324	C₂×D₈	—	5	1	no	—
325	C₂×M₁₆	—	5	1	no	—
326	C₂²×C₈	—	5	1	no	—
327	C₄⋊Q₈	—	5	2	no	—
328	C₄⋊Q₈	C₂×C₃×D₅	1	2	yes	—
329	#124	—	5	2	no	—
330	#124	—	5	2	no	—
331	#123	—	10	4	no	—
332	C₂²⋊Q₈	—	10	4	no	—
333	#117	—	5	1	no	—
334	#97	—	5	1	no	—
335	#97	—	5	1	no	—
336	C₄×C₈	—	5	1	no	—
337	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
338	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
339	C₂×C₃×C₅	#578	1	2	yes	—
340	C₃×D₅	—	2	2	no	—
341	C₃×D₅	—	8	2	no	—
342	C₂³×C₃	—	5	1	no	—
343	C₂³×C₃	—	10	2	no	—
344	C₃×Q₈	—	2	2	no	—
345	C₃×Q₈	—	2	2	no	—
346	C₃×Q₈	—	2	2	no	—
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	10	2	no	—
349	C₃×Q₈	—	10	2	no	—
350	C₃×Q₈	—	20	4	no	—
351	C₃×D₄	—	10	2	no	—
352	C₃×D₄	—	10	2	no	—
353	C₃×D₄	—	20	4	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	5	1	no	—
357	C₂×C₃×C₄	—	5	2	no	—
358	C₂×C₃×C₄	—	5	2	no	—
359	C₂×C₃×C₄	—	5	2	no	—
360	C₂×C₃×C₄	—	10	2	no	—
361	C₂×C₃×C₄	—	20	4	no	—
362	C₂×C₃×C₄	—	20	4	no	—
363	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
364	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
365	C₃×C₈	—	5	2	no	—
366	C₃×C₈	—	5	2	no	—
367	C₃×C₈	D₄×D₅	1	2	yes	—
368	C₃×C₈	D₄×D₅	1	2	yes	—
369	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
370	C₂×D₅	—	2	2	no	—
371	C₂×D₅	—	4	4	no	—
372	C₂×D₅	—	4	2	no	—
373	C₂×D₅	C₃×#127	1	2	yes	—
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	4	2	no	—
376	C₄×C₅	—	4	2	no	—
377	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
378	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
379	Dic₅	—	2	2	no	—
380	Dic₅	—	4	2	no	—
381	Dic₅	C₃×#127	1	2	yes	—
382	#41	—	10	4	no	—
383	#41	—	10	4	no	—
384	C₂×Q₈	—	5	2	no	—
385	C₂×Q₈	—	10	2	no	—
386	C₂×Q₈	—	10	4	no	—
387	C₂×Q₈	—	10	4	no	—
388	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
389	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
390	C₂×D₄	—	5	2	no	—
391	C₂×D₄	—	10	2	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	10	2	no	—
394	C₂²×C₄	—	10	2	no	—
395	Q₁₆	—	2	2	no	—
396	Q₁₆	—	2	2	no	—
397	Q₁₆	—	2	4	no	—
398	Q₁₆	—	10	4	no	—
399	Q₁₆	—	10	4	no	—
400	Q₁₆	—	10	2	no	—
401	SD₁₆	—	10	4	no	—
402	SD₁₆	—	10	4	no	—
403	SD₁₆	—	10	4	no	—
404	D₈	—	10	2	no	—
405	M₁₆	—	5	4	no	—
406	C₂×C₈	—	5	1	no	—
407	C₂×C₈	—	5	1	no	—
408	C₂×C₈	—	5	4	no	—
409	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
410	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	5	2	no	—
413	C₄⋊C₄	—	10	4	no	—
414	C₂²⋊C₄	—	5	2	no	—
415	C₂²⋊C₄	—	10	4	no	—
416	C₂²⋊C₄	—	10	4	no	—
417	C₄²	—	5	1	no	—
418	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
419	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	—	5	2	no	—
421	C₂²×C₃	—	10	2	no	—
422	C₂²×C₃	—	20	2	no	—
423	C₂²×C₃	—	20	4	no	—
424	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	4	2	no	—
427	C₃×C₄	—	4	2	no	—
428	C₃×C₄	—	5	2	no	—
429	C₃×C₄	—	10	2	no	—
430	C₃×C₄	—	20	2	no	—
431	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
432	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
433	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
434	C₂×C₅	C₃×#578	1	2	yes	—
435	D₅	—	2	2	no	—
436	D₅	—	8	2	no	—
437	C₂³	—	5	1	no	—
438	C₂³	—	10	2	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	10	2	no	—
444	Q₈	—	10	2	no	—
445	Q₈	—	20	4	no	—
446	D₄	—	10	2	no	—
447	D₄	—	10	2	no	—
448	D₄	—	20	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	5	1	no	—
452	C₂×C₄	—	5	2	no	—
453	C₂×C₄	—	5	2	no	—
454	C₂×C₄	—	5	2	no	—
455	C₂×C₄	—	10	2	no	—
456	C₂×C₄	—	20	4	no	—
457	C₂×C₄	—	20	4	no	—
458	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
459	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
460	C₈	—	5	2	no	—
461	C₈	—	5	2	no	—
462	C₈	C₃×D₄×D₅	1	2	yes	—
463	C₈	C₃×D₄×D₅	1	2	yes	—
464	C₂×C₃	—	10	2	no	—
465	C₂×C₃	—	40	2	no	—
466	C₂×C₃	D₅×#127	1	1	yes	characteristic
467	C₂×C₃	#66100	1	2	yes	—
468	C₅	C₃×#3156	1	1	yes	characteristic, complemented, Sylow
469	C₂²	—	5	2	no	—
470	C₂²	—	10	2	no	—
471	C₂²	—	20	4	no	—
472	C₂²	—	20	2	no	—
473	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	5	2	no	—
478	C₄	—	10	2	no	—
479	C₄	—	20	2	no	—
480	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
481	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
482	C₃	#10613532	1	1	yes	characteristic, direct product factor, Sylow
483	C₂	—	10	2	no	—
484	C₂	—	40	2	no	—
485	C₂	C₃×D₅×#127	1	1	yes	characteristic
486	C₂	C₃×#66100	1	2	yes	—

	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×#494	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4065	C₂
hypercenter	C₃×#494	D₅
hypocenter	C₅	C₃×#3156
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#494

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4064	C₂	semidirect
3. C₂×C₃×D₅×Q₁₆	C₂	semidirect
4. C₃×#66058	C₂	semidirect
5. C₃×C₅×#494	C₂	semidirect
6. C₃×#65480	C₂	semidirect
7. C₃×#65479	C₂	semidirect
8. C₃×#65470	C₂	semidirect
9. C₃×#65375	C₂	semidirect
10. C₃×#64985	C₂	semidirect
11. C₃×#64978	C₂	semidirect
12. #10613532	C₃	direct (N × H)
43. C₂×#4064	C₂×C₃	semidirect
44. C₂×D₅×Q₁₆	C₂×C₃	semidirect
45. #66058	C₂×C₃	semidirect
46. C₅×#494	C₂×C₃	semidirect
47. #65480	C₂×C₃	semidirect
48. #65479	C₂×C₃	semidirect
49. #65470	C₂×C₃	semidirect
50. #65375	C₂×C₃	semidirect
51. #64985	C₂×C₃	semidirect
52. #64978	C₂×C₃	semidirect
99. C₃×#494	D₅	semidirect
231. #494	C₃×D₅	semidirect
419. C₃×C₅	#3156	semidirect
468. C₅	C₃×#3156	semidirect
482. C₃	#10613532	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#4065	2
C₂×C₃×#4064	2
C₂×C₃×D₅×Q₁₆	2
C₃×#66058	2
C₃×C₅×#494	2
C₃×#65480	2
C₃×#65479	2
C₃×#65470	2
C₃×#65375	2
C₃×#64985	2
C₃×#64978	2
#10613532	3
C₃×#3156	5

Subgroups — C3×#10613532 #14439631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613532 #14439631