Subgroups — C₃×#10611248 #14418973

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65416	C₂	1	2	yes	maximal, complemented
4	C₃×M₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
5	C₃×#65301	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65122	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65120	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65017	C₂	1	2	yes	maximal, complemented
9	C₃×#65007	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64968	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611248	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₄	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
17	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×#681	C₂²	1	2	yes	—
20	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4038	C₄	1	1	yes	characteristic
23	C₃×#4033	C₄	1	1	yes	characteristic
24	C₃×#4027	C₄	1	2	yes	—
25	C₃×#4023	C₄	1	2	yes	—
26	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
27	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₃×C₂²⋊#168	C₂²	1	2	yes	—
32	C₃×#3952	C₂²	1	2	yes	—
33	C₃×#3947	C₂²	1	2	yes	—
34	C₃×#3947	C₂²	1	2	yes	—
35	C₃×#3946	C₂²	1	2	yes	—
36	C₃×#3946	C₂²	1	2	yes	—
37	C₃×C₈×Dic₅	C₂²	1	2	yes	—
38	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
39	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#2965	—	5	1	no	maximal, Hall
43	C₄×#711	C₂×C₃	1	1	yes	characteristic
44	C₅×#436	C₂×C₃	1	1	yes	characteristic, complemented
45	#65416	C₂×C₃	1	2	yes	complemented
46	M₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
47	#65301	C₂×C₃	1	1	yes	characteristic, complemented
48	#65122	C₂×C₃	1	1	yes	characteristic, complemented
49	#65120	C₂×C₃	1	1	yes	characteristic, complemented
50	#65017	C₂×C₃	1	2	yes	complemented
51	#65007	C₂×C₃	1	2	yes	complemented
52	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
53	#64968	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
57	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
58	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
59	C₃×#711	—	2	4	no	—
60	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×M₁₆	—	2	4	no	—
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
72	C₃×#685	C₂×C₄	1	2	yes	—
73	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×#683	C₂×C₄	1	2	yes	—
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
80	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂³	1	2	yes	—
82	C₃×#681	—	2	4	no	—
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	2	yes	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₃×C₈×D₅	—	2	2	no	—
87	C₃×C₈×D₅	—	2	2	no	—
88	C₃×C₄×#41	—	5	1	no	—
89	C₃×#446	—	5	1	no	—
90	C₃×#446	—	5	1	no	—
91	C₃×#436	—	5	1	no	—
92	C₃×#436	D₅	1	1	yes	characteristic, complemented
93	C₃×#435	—	5	2	no	—
94	C₃×#435	—	5	2	no	—
95	C₃×#431	—	5	1	no	—
96	C₃×#431	—	5	2	no	—
97	C₃×C₄×M₁₆	—	5	2	no	—
98	C₂×C₃×C₄×C₈	—	5	1	no	—
99	C₂×#711	C₃×C₄	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
101	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
102	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
103	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
104	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
105	C₂×#681	C₂²×C₃	1	2	yes	—
106	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
108	#4038	C₃×C₄	1	1	yes	characteristic
109	#4033	C₃×C₄	1	1	yes	characteristic
110	#4027	C₃×C₄	1	2	yes	—
111	#4023	C₃×C₄	1	2	yes	—
112	C₄²×D₅	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×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
116	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
117	C₂²⋊#168	C₂²×C₃	1	2	yes	—
118	#3952	C₂²×C₃	1	2	yes	—
119	#3947	C₂²×C₃	1	2	yes	—
120	#3947	C₂²×C₃	1	2	yes	—
121	#3946	C₂²×C₃	1	2	yes	—
122	#3946	C₂²×C₃	1	2	yes	—
123	C₈×Dic₅	C₂²×C₃	1	2	yes	—
124	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
125	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
126	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
127	C₄×#168	C₂²×C₃	1	1	yes	characteristic
128	#2965	—	5	1	no	Sylow
129	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
130	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₅×D₄	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×C₂²⋊D₅	—	2	4	no	—
139	C₂×C₃×Dic₅	—	2	4	no	—
140	C₂×C₃×Dic₅	—	2	4	no	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
146	C₃×C₄×D₅	—	2	1	no	—
147	C₃×C₄×D₅	—	2	1	no	—
148	C₃×C₄×D₅	—	2	2	no	—
149	C₃×C₄×D₅	M₁₆	1	4	yes	complemented
150	C₃×Dic₁₀	—	2	2	no	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	#41	1	2	yes	complemented
154	C₃×#168	—	2	1	no	—
155	C₃×#168	—	2	2	no	—
156	C₃×#168	#41	1	2	yes	complemented
157	C₂×C₃×#41	—	5	1	no	—
158	C₂×C₃×M₁₆	—	5	2	no	—
159	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
160	C₂²×C₃×C₈	—	5	1	no	—
161	C₂²×C₃×C₈	—	5	1	no	—
162	C₃×C₄×Q₈	—	5	1	no	—
163	C₃×C₄×Q₈	—	5	1	no	—
164	C₃×C₄×D₄	—	5	1	no	—
165	C₃×C₄×D₄	—	5	2	no	—
166	C₃×C₄×D₄	—	5	2	no	—
167	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
168	C₃×#117	—	5	1	no	—
169	C₃×#117	—	5	2	no	—
170	C₂×C₃×C₄²	—	5	2	no	—
171	C₂×C₃×C₄²	—	5	1	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₄⋊C₈	—	5	2	no	—
174	C₃×C₄⋊C₈	—	5	1	no	—
175	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
176	C₃×C₂²⋊C₈	—	5	2	no	—
177	C₃×C₂²⋊C₈	—	5	2	no	—
178	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
179	C₃×#97	—	5	2	no	—
180	C₃×#97	—	5	2	no	—
181	C₃×C₄×C₈	—	5	1	no	—
182	C₃×C₄×C₈	—	5	1	no	—
183	C₃×C₄×C₈	—	5	2	no	—
184	C₃×C₄×C₈	—	5	1	no	—
185	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
186	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
188	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
189	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
190	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
191	#711	—	2	4	no	—
192	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
193	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
194	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
195	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
196	C₅×M₁₆	—	2	4	no	—
197	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
198	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
201	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
202	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
203	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
204	#685	C₂×C₃×C₄	1	2	yes	—
205	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
206	#683	C₂×C₃×C₄	1	2	yes	—
207	#683	C₂×C₃×C₄	1	2	yes	—
208	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
209	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
210	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
211	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
212	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
213	C₄×Dic₅	C₂³×C₃	1	2	yes	—
214	#681	—	2	4	no	—
215	C₂×#168	C₂³×C₃	1	1	yes	characteristic
216	C₂×#168	C₂³×C₃	1	2	yes	—
217	C₂×#168	C₂³×C₃	1	1	yes	characteristic
218	C₈×D₅	—	2	2	no	—
219	C₈×D₅	—	2	2	no	—
220	C₄×#41	—	5	1	no	—
221	#446	—	5	1	no	—
222	#446	—	5	1	no	—
223	#436	—	5	1	no	—
224	#436	C₃×D₅	1	1	yes	characteristic, complemented
225	#435	—	5	2	no	—
226	#435	—	5	2	no	—
227	#431	—	5	1	no	—
228	#431	—	5	2	no	—
229	C₄×M₁₆	—	5	2	no	—
230	C₂×C₄×C₈	—	5	1	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₃×D₅	—	2	1	no	—
236	C₂×C₃×D₅	—	2	1	no	—
237	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	1	no	—
240	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₃×Dic₅	—	2	1	no	—
244	C₃×Dic₅	—	2	2	no	—
245	C₃×Dic₅	—	2	2	no	—
246	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
247	C₃×Dic₅	#131	1	2	yes	—
248	C₃×#41	—	10	4	no	—
249	C₂×C₃×Q₈	—	5	1	no	—
250	C₂×C₃×D₄	—	5	2	no	—
251	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	—	5	1	no	—
253	C₂²×C₃×C₄	—	5	2	no	—
254	C₂²×C₃×C₄	—	5	2	no	—
255	C₂²×C₃×C₄	—	5	1	no	—
256	C₂²×C₃×C₄	—	5	1	no	—
257	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
258	C₃×M₁₆	—	2	4	no	—
259	C₃×M₁₆	—	10	4	no	—
260	C₂×C₃×C₈	—	5	1	no	—
261	C₂×C₃×C₈	—	5	1	no	—
262	C₂×C₃×C₈	—	5	2	no	—
263	C₂×C₃×C₈	—	10	2	no	—
264	C₂×C₃×C₈	—	10	2	no	—
265	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
267	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
268	C₃×C₄⋊C₄	—	5	2	no	—
269	C₃×C₄⋊C₄	—	5	2	no	—
270	C₃×C₄⋊C₄	—	5	1	no	—
271	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
272	C₃×C₂²⋊C₄	—	5	2	no	—
273	C₃×C₂²⋊C₄	—	5	2	no	—
274	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
275	C₃×C₄²	—	5	2	no	—
276	C₃×C₄²	—	5	1	no	—
277	C₃×C₄²	—	5	1	no	—
278	C₃×C₄²	—	5	2	no	—
279	C₃×C₄²	—	5	1	no	—
280	C₃×C₄²	—	5	2	no	—
281	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
282	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
283	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
284	C₅×D₄	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
288	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
291	C₂²⋊D₅	—	2	4	no	—
292	C₂×Dic₅	—	2	4	no	—
293	C₂×Dic₅	—	2	4	no	—
294	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
295	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
296	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
297	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
298	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
299	C₄×D₅	—	2	1	no	—
300	C₄×D₅	—	2	1	no	—
301	C₄×D₅	—	2	2	no	—
302	C₄×D₅	C₃×M₁₆	1	4	yes	complemented
303	Dic₁₀	—	2	2	no	—
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	C₃×#41	1	2	yes	complemented
307	#168	—	2	1	no	—
308	#168	—	2	2	no	—
309	#168	C₃×#41	1	2	yes	complemented
310	C₂×#41	—	5	1	no	—
311	C₂×M₁₆	—	5	2	no	—
312	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
313	C₂²×C₈	—	5	1	no	—
314	C₂²×C₈	—	5	1	no	—
315	C₄×Q₈	—	5	1	no	—
316	C₄×Q₈	—	5	1	no	—
317	C₄×D₄	—	5	1	no	—
318	C₄×D₄	—	5	2	no	—
319	C₄×D₄	—	5	2	no	—
320	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
321	#117	—	5	1	no	—
322	#117	—	5	2	no	—
323	C₂×C₄²	—	5	2	no	—
324	C₂×C₄²	—	5	1	no	—
325	C₄⋊C₈	—	5	2	no	—
326	C₄⋊C₈	—	5	2	no	—
327	C₄⋊C₈	—	5	1	no	—
328	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
329	C₂²⋊C₈	—	5	2	no	—
330	C₂²⋊C₈	—	5	2	no	—
331	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	—
332	#97	—	5	2	no	—
333	#97	—	5	2	no	—
334	C₄×C₈	—	5	1	no	—
335	C₄×C₈	—	5	1	no	—
336	C₄×C₈	—	5	2	no	—
337	C₄×C₈	—	5	1	no	—
338	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
339	C₂×C₃×C₅	—	4	2	no	—
340	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
342	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
343	C₃×D₅	—	2	2	no	—
344	C₂³×C₃	—	5	1	no	—
345	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
346	C₃×Q₈	—	10	2	no	—
347	C₃×D₄	—	2	2	no	—
348	C₃×D₄	—	10	4	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	5	1	no	—
352	C₂×C₃×C₄	—	5	1	no	—
353	C₂×C₃×C₄	—	5	4	no	—
354	C₂×C₃×C₄	—	5	2	no	—
355	C₂×C₃×C₄	—	5	1	no	—
356	C₂×C₃×C₄	—	5	2	no	—
357	C₂×C₃×C₄	—	10	2	no	—
358	C₂×C₃×C₄	—	10	4	no	—
359	C₂×C₃×C₄	—	10	4	no	—
360	C₂×C₃×C₄	—	10	1	no	—
361	C₂×C₃×C₄	—	10	1	no	—
362	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
363	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
366	C₃×C₈	—	2	2	no	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	—	5	2	no	—
369	C₃×C₈	—	10	1	no	—
370	C₃×C₈	—	10	2	no	—
371	C₃×C₈	#711	1	2	yes	complemented
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
376	C₂×D₅	—	2	1	no	—
377	C₂×D₅	—	2	1	no	—
378	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
382	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
383	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
384	Dic₅	—	2	2	no	—
385	Dic₅	—	2	2	no	—
386	Dic₅	—	2	1	no	—
387	Dic₅	C₂×C₃×M₁₆	1	2	yes	—
388	Dic₅	C₃×#131	1	2	yes	—
389	#41	—	10	4	no	—
390	C₂×Q₈	—	5	1	no	—
391	C₂×D₄	—	5	2	no	—
392	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
393	C₂²×C₄	—	5	1	no	—
394	C₂²×C₄	—	5	2	no	—
395	C₂²×C₄	—	5	2	no	—
396	C₂²×C₄	—	5	1	no	—
397	C₂²×C₄	—	5	1	no	—
398	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
399	M₁₆	—	2	4	no	—
400	M₁₆	—	10	4	no	—
401	C₂×C₈	—	5	1	no	—
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	5	2	no	—
404	C₂×C₈	—	10	2	no	—
405	C₂×C₈	—	10	2	no	—
406	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
407	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
408	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
409	C₄⋊C₄	—	5	2	no	—
410	C₄⋊C₄	—	5	2	no	—
411	C₄⋊C₄	—	5	1	no	—
412	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	5	2	no	—
414	C₂²⋊C₄	—	5	2	no	—
415	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
416	C₄²	—	5	2	no	—
417	C₄²	—	5	1	no	—
418	C₄²	—	5	1	no	—
419	C₄²	—	5	2	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	2	no	—
422	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
423	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	5	2	no	—
428	C₂²×C₃	—	10	1	no	—
429	C₂²×C₃	—	10	1	no	—
430	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	5	2	no	—
434	C₃×C₄	—	5	2	no	—
435	C₃×C₄	—	10	2	no	—
436	C₃×C₄	—	10	2	no	—
437	C₃×C₄	—	10	1	no	—
438	C₃×C₄	D₅×M₁₆	1	2	yes	—
439	C₃×C₄	C₂×#711	1	1	yes	characteristic
440	C₃×C₄	D₅×#41	1	1	yes	characteristic
441	C₂×C₅	—	4	2	no	—
442	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
443	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
444	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
445	D₅	—	2	2	no	—
446	C₂³	—	5	1	no	—
447	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
448	Q₈	—	10	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	10	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	5	1	no	—
454	C₂×C₄	—	5	1	no	—
455	C₂×C₄	—	5	4	no	—
456	C₂×C₄	—	5	1	no	—
457	C₂×C₄	—	5	2	no	—
458	C₂×C₄	—	5	2	no	—
459	C₂×C₄	—	10	2	no	—
460	C₂×C₄	—	10	4	no	—
461	C₂×C₄	—	10	4	no	—
462	C₂×C₄	—	10	1	no	—
463	C₂×C₄	—	10	1	no	—
464	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
465	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
466	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
467	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	1	no	—
470	C₈	—	5	2	no	—
471	C₈	—	10	1	no	—
472	C₈	—	10	2	no	—
473	C₈	C₃×#711	1	2	yes	complemented
474	C₂×C₃	—	4	2	no	—
475	C₂×C₃	—	10	2	no	—
476	C₂×C₃	C₄×#711	1	1	yes	characteristic
477	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
478	C₂×C₃	D₅×#131	1	1	yes	characteristic
479	C₅	C₃×#2965	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	5	2	no	—
484	C₂²	—	10	1	no	—
485	C₂²	—	10	1	no	—
486	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	5	2	no	—
490	C₄	—	5	2	no	—
491	C₄	—	10	1	no	—
492	C₄	—	10	2	no	—
493	C₄	—	10	2	no	—
494	C₄	C₃×D₅×M₁₆	1	2	yes	—
495	C₄	C₂×C₃×#711	1	1	yes	characteristic
496	C₄	C₃×D₅×#41	1	1	yes	characteristic
497	C₃	#10611248	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	4	2	no	—
499	C₂	—	10	2	no	—
500	C₂	C₃×C₄×#711	1	1	yes	characteristic
501	C₂	C₂×C₃×D₅×M₁₆	1	1	yes	characteristic
502	C₂	C₃×D₅×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#436	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#711	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#436	D₅
hypocenter	C₅	C₃×#2965
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#436

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#436	C₂	semidirect
3. C₃×#65416	C₂	semidirect
4. C₃×M₁₆×Dic₅	C₂	semidirect
5. C₃×#65301	C₂	semidirect
6. C₃×#65122	C₂	semidirect
7. C₃×#65120	C₂	semidirect
8. C₃×#65017	C₂	semidirect
9. C₃×#65007	C₂	semidirect
10. C₃×C₄×C₈×D₅	C₂	semidirect
11. C₃×#64968	C₂	semidirect
12. #10611248	C₃	direct (N × H)
44. C₅×#436	C₂×C₃	semidirect
45. #65416	C₂×C₃	semidirect
46. M₁₆×Dic₅	C₂×C₃	semidirect
47. #65301	C₂×C₃	semidirect
48. #65122	C₂×C₃	semidirect
49. #65120	C₂×C₃	semidirect
50. #65017	C₂×C₃	semidirect
51. #65007	C₂×C₃	semidirect
52. C₄×C₈×D₅	C₂×C₃	semidirect
53. #64968	C₂×C₃	semidirect
92. C₃×#436	D₅	semidirect
149. C₃×C₄×D₅	M₁₆	semidirect
153. C₃×C₅×C₈	#41	semidirect
156. C₃×#168	#41	semidirect
224. #436	C₃×D₅	semidirect
302. C₄×D₅	C₃×M₁₆	semidirect
306. C₅×C₈	C₃×#41	semidirect
309. #168	C₃×#41	semidirect
371. C₃×C₈	#711	semidirect
423. C₃×C₅	#2965	semidirect
473. C₈	C₃×#711	semidirect
479. C₅	C₃×#2965	semidirect
497. C₃	#10611248	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×C₄×#711	2
C₃×C₅×#436	2
C₃×#65416	2
C₃×M₁₆×Dic₅	2
C₃×#65301	2
C₃×#65122	2
C₃×#65120	2
C₃×#65017	2
C₃×#65007	2
C₃×C₄×C₈×D₅	2
C₃×#64968	2
#10611248	3
C₃×#2965	5

Subgroups — C3×#10611248 #14418973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611248 #14418973