Subgroups — C₃×#10610275 #14418661

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65851	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic
3	C₃×#65411	C₂	1	1	yes	maximal, characteristic
4	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic
5	C₃×#65391	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic
7	C₃×#65288	C₂	1	1	yes	maximal, characteristic
8	C₃×#64990	C₂	1	2	yes	maximal, complemented
9	C₃×#64990	C₂	1	2	yes	maximal, complemented
10	C₃×#64968	C₂	1	2	yes	maximal, complemented
11	C₃×C₈×Dic₁₀	C₂	1	2	yes	maximal, complemented
12	#10610275	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₃×#4072	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#681	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×#4036	C₄	1	1	yes	characteristic
21	C₃×#4036	C₄	1	1	yes	characteristic
22	C₃×#4034	C₄	1	1	yes	characteristic
23	C₃×#4034	C₄	1	1	yes	characteristic
24	C₃×#4024	C₄	1	2	yes	—
25	C₃×#4024	C₄	1	2	yes	—
26	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
27	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
28	C₃×C₅×#97	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₃×#3947	C₂²	1	2	yes	—
31	C₃×#3947	C₂²	1	2	yes	—
32	C₃×#3946	C₂²	1	1	yes	characteristic
33	C₃×#3946	C₂²	1	1	yes	characteristic
34	C₃×#3946	C₂²	1	1	yes	characteristic
35	C₃×#3946	C₂²	1	1	yes	characteristic
36	C₃×#3946	C₂²	1	2	yes	—
37	C₃×#3946	C₂²	1	2	yes	—
38	C₃×C₈×Dic₅	C₂²	1	2	yes	—
39	C₃×C₈×Dic₅	C₂²	1	2	yes	—
40	C₃×C₄⋊#168	C₂²	1	2	yes	—
41	C₃×C₄⋊#168	C₂²	1	2	yes	—
42	C₃×#2962	—	5	1	no	maximal, Hall
43	#65851	C₂×C₃	1	1	yes	characteristic
44	C₅×#405	C₂×C₃	1	1	yes	characteristic
45	#65411	C₂×C₃	1	1	yes	characteristic
46	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic
47	#65391	C₂×C₃	1	1	yes	characteristic
48	C₂×#3946	C₂×C₃	1	1	yes	characteristic
49	#65288	C₂×C₃	1	1	yes	characteristic
50	#64990	C₂×C₃	1	2	yes	complemented
51	#64990	C₂×C₃	1	2	yes	complemented
52	#64968	C₂×C₃	1	2	yes	complemented
53	C₈×Dic₁₀	C₂×C₃	1	2	yes	complemented
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
58	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
59	C₃×C₅×M₁₆	Q₈	1	4	yes	complemented
60	C₂×C₃×C₅×C₈	—	2	2	no	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
67	C₃×C₄²×C₅	C₂³	1	2	yes	—
68	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
69	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
70	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
71	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₃×#683	C₂×C₄	1	2	yes	—
74	C₃×#683	C₂×C₄	1	2	yes	—
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×#683	C₂×C₄	1	2	yes	—
77	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₃×C₄×Dic₅	C₂³	1	2	yes	—
81	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
82	C₃×#681	—	2	2	no	—
83	C₂×C₃×#168	—	2	2	no	—
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₂×C₃×#168	C₂³	1	2	yes	—
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₃×#533	—	5	1	no	—
88	C₃×#446	—	5	2	no	—
89	C₃×#446	—	5	2	no	—
90	C₃×#446	—	5	2	no	—
91	C₃×C₈×Q₈	—	5	2	no	—
92	C₃×#424	—	5	1	no	—
93	C₃×#424	—	5	1	no	—
94	C₂×C₃×C₄⋊C₈	—	5	1	no	—
95	C₃×#405	—	5	1	no	—
96	C₃×#405	D₅	1	1	yes	characteristic
97	C₃×C₄×M₁₆	—	5	1	no	—
98	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
100	C₅×#117	C₂²×C₃	1	1	yes	characteristic
101	#4072	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
103	C₂×#681	C₂²×C₃	1	1	yes	characteristic
104	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
105	#4036	C₃×C₄	1	1	yes	characteristic
106	#4036	C₃×C₄	1	1	yes	characteristic
107	#4034	C₃×C₄	1	1	yes	characteristic
108	#4034	C₃×C₄	1	1	yes	characteristic
109	#4024	C₃×C₄	1	2	yes	—
110	#4024	C₃×C₄	1	2	yes	—
111	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
112	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
113	C₅×#97	C₂²×C₃	1	2	yes	—
114	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
115	#3947	C₂²×C₃	1	2	yes	—
116	#3947	C₂²×C₃	1	2	yes	—
117	#3946	C₂²×C₃	1	1	yes	characteristic
118	#3946	C₂²×C₃	1	1	yes	characteristic
119	#3946	C₂²×C₃	1	1	yes	characteristic
120	#3946	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
125	C₄⋊#168	C₂²×C₃	1	2	yes	—
126	C₄⋊#168	C₂²×C₃	1	2	yes	—
127	#2962	—	5	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
133	C₂×C₃×C₄×C₅	#41	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₃×Dic₅	—	2	2	no	—
136	C₂×C₃×Dic₅	—	4	1	no	—
137	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
143	C₃×Dic₁₀	—	2	4	no	—
144	C₃×Dic₁₀	—	4	2	no	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	—	2	1	no	—
147	C₃×C₅×C₈	C₂×Q₈	1	4	yes	—
148	C₃×#168	—	2	1	no	—
149	C₃×#168	—	2	1	no	—
150	C₃×#168	—	2	2	no	—
151	C₂×C₃×M₁₆	—	5	1	no	—
152	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
153	C₂²×C₃×C₈	—	5	1	no	—
154	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
155	C₃×C₄⋊Q₈	—	5	1	no	—
156	C₃×C₄⋊Q₈	—	5	1	no	—
157	C₃×#125	—	5	1	no	—
158	C₃×#125	—	5	1	no	—
159	C₃×C₂²⋊Q₈	—	5	2	no	—
160	C₃×C₂²⋊Q₈	—	5	2	no	—
161	C₃×C₄×Q₈	—	5	2	no	—
162	C₃×C₄×Q₈	—	5	2	no	—
163	C₃×#117	—	5	1	no	—
164	C₃×#117	C₂×D₅	1	1	yes	characteristic
165	C₂×C₃×C₄²	—	5	1	no	—
166	C₃×C₄⋊C₈	—	5	1	no	—
167	C₃×C₄⋊C₈	—	5	1	no	—
168	C₃×C₄⋊C₈	—	5	1	no	—
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×C₄⋊C₈	—	5	2	no	—
171	C₃×C₄⋊C₈	—	5	2	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₄⋊C₈	—	5	2	no	—
174	C₃×#97	—	5	2	no	—
175	C₃×#97	—	5	2	no	—
176	C₃×#97	C₂×D₅	1	2	yes	—
177	C₃×C₄×C₈	—	5	2	no	—
178	C₃×C₄×C₈	—	5	2	no	—
179	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
184	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
185	C₅×M₁₆	C₃×Q₈	1	4	yes	complemented
186	C₂×C₅×C₈	—	2	2	no	—
187	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
190	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
191	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
192	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
193	C₄²×C₅	C₂³×C₃	1	2	yes	—
194	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
195	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
196	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
197	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
198	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
199	#683	C₂×C₃×C₄	1	2	yes	—
200	#683	C₂×C₃×C₄	1	2	yes	—
201	#683	C₂×C₃×C₄	1	2	yes	—
202	#683	C₂×C₃×C₄	1	2	yes	—
203	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
204	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
205	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
206	C₄×Dic₅	C₂³×C₃	1	2	yes	—
207	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
208	#681	—	2	2	no	—
209	C₂×#168	—	2	2	no	—
210	C₂×#168	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	2	yes	—
212	C₂×#168	C₂³×C₃	1	1	yes	characteristic
213	#533	—	5	1	no	—
214	#446	—	5	2	no	—
215	#446	—	5	2	no	—
216	#446	—	5	2	no	—
217	C₈×Q₈	—	5	2	no	—
218	#424	—	5	1	no	—
219	#424	—	5	1	no	—
220	C₂×C₄⋊C₈	—	5	1	no	—
221	#405	—	5	1	no	—
222	#405	C₃×D₅	1	1	yes	characteristic
223	C₄×M₁₆	—	5	1	no	—
224	C₂²×C₃×C₅	—	2	1	no	—
225	C₂²×C₃×C₅	—	2	1	no	—
226	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₃×C₄×C₅	—	2	2	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
231	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₃×Dic₅	—	2	2	no	—
234	C₃×Dic₅	—	2	1	no	—
235	C₃×Dic₅	—	2	1	no	—
236	C₃×Dic₅	—	2	2	no	—
237	C₃×Dic₅	—	2	1	no	—
238	C₃×Dic₅	#131	1	2	yes	—
239	C₂×C₃×Q₈	—	5	2	no	—
240	C₂×C₃×Q₈	—	5	2	no	—
241	C₂²×C₃×C₄	—	5	1	no	—
242	C₂²×C₃×C₄	—	5	1	no	—
243	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
244	C₃×M₁₆	—	10	2	no	—
245	C₃×M₁₆	Dic₁₀	1	4	yes	complemented
246	C₂×C₃×C₈	—	2	2	no	—
247	C₂×C₃×C₈	—	5	1	no	—
248	C₂×C₃×C₈	—	5	2	no	—
249	C₂×C₃×C₈	—	5	1	no	—
250	C₂×C₃×C₈	—	10	2	no	—
251	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	5	2	no	—
256	C₃×C₄⋊C₄	—	5	2	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	—	5	2	no	—
262	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
264	C₃×C₂²⋊C₄	—	5	2	no	—
265	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
266	C₃×C₄²	—	5	1	no	—
267	C₃×C₄²	—	5	1	no	—
268	C₃×C₄²	—	5	1	no	—
269	C₃×C₄²	—	5	2	no	—
270	C₃×C₄²	—	5	1	no	—
271	C₃×C₄²	C₂²×D₅	1	2	yes	—
272	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
274	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
275	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
277	C₂×C₄×C₅	C₃×#41	1	2	yes	—
278	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
279	C₂×Dic₅	—	2	2	no	—
280	C₂×Dic₅	—	4	1	no	—
281	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
282	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
283	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
284	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
285	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
286	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
287	Dic₁₀	—	2	4	no	—
288	Dic₁₀	—	4	2	no	—
289	C₅×C₈	—	2	1	no	—
290	C₅×C₈	—	2	1	no	—
291	C₅×C₈	C₂×C₃×Q₈	1	4	yes	—
292	#168	—	2	1	no	—
293	#168	—	2	1	no	—
294	#168	—	2	2	no	—
295	C₂×M₁₆	—	5	1	no	—
296	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
297	C₂²×C₈	—	5	1	no	—
298	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
299	C₄⋊Q₈	—	5	1	no	—
300	C₄⋊Q₈	—	5	1	no	—
301	#125	—	5	1	no	—
302	#125	—	5	1	no	—
303	C₂²⋊Q₈	—	5	2	no	—
304	C₂²⋊Q₈	—	5	2	no	—
305	C₄×Q₈	—	5	2	no	—
306	C₄×Q₈	—	5	2	no	—
307	#117	—	5	1	no	—
308	#117	C₂×C₃×D₅	1	1	yes	characteristic
309	C₂×C₄²	—	5	1	no	—
310	C₄⋊C₈	—	5	1	no	—
311	C₄⋊C₈	—	5	1	no	—
312	C₄⋊C₈	—	5	1	no	—
313	C₄⋊C₈	—	5	1	no	—
314	C₄⋊C₈	—	5	2	no	—
315	C₄⋊C₈	—	5	2	no	—
316	C₄⋊C₈	—	5	2	no	—
317	C₄⋊C₈	—	5	2	no	—
318	#97	—	5	2	no	—
319	#97	—	5	2	no	—
320	#97	C₂×C₃×D₅	1	2	yes	—
321	C₄×C₈	—	5	2	no	—
322	C₄×C₈	—	5	2	no	—
323	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
324	C₂×C₃×C₅	—	2	2	no	—
325	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
326	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
327	C₂×C₃×C₅	#568	1	1	yes	characteristic
328	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
329	C₃×Q₈	—	10	4	no	—
330	C₃×Q₈	—	20	2	no	—
331	C₂×C₃×C₄	—	5	1	no	—
332	C₂×C₃×C₄	—	5	1	no	—
333	C₂×C₃×C₄	—	5	1	no	—
334	C₂×C₃×C₄	—	5	1	no	—
335	C₂×C₃×C₄	—	5	2	no	—
336	C₂×C₃×C₄	—	5	2	no	—
337	C₂×C₃×C₄	—	10	2	no	—
338	C₂×C₃×C₄	—	20	1	no	—
339	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
340	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
341	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
342	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
343	C₂×C₃×C₄	#709	1	2	yes	—
344	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	—	10	1	no	—
348	C₃×C₈	—	10	1	no	—
349	C₃×C₈	—	10	2	no	—
350	C₃×C₈	C₂×Dic₁₀	1	4	yes	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	C₃×C₄×Q₈	1	2	yes	—
354	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
358	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
359	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
360	Dic₅	—	2	2	no	—
361	Dic₅	—	2	1	no	—
362	Dic₅	—	2	1	no	—
363	Dic₅	—	2	2	no	—
364	Dic₅	—	2	1	no	—
365	Dic₅	C₃×#131	1	2	yes	—
366	C₂×Q₈	—	5	2	no	—
367	C₂×Q₈	—	5	2	no	—
368	C₂²×C₄	—	5	1	no	—
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
371	M₁₆	—	10	2	no	—
372	M₁₆	C₃×Dic₁₀	1	4	yes	complemented
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	5	1	no	—
375	C₂×C₈	—	5	2	no	—
376	C₂×C₈	—	5	1	no	—
377	C₂×C₈	—	10	2	no	—
378	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
380	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
381	C₄⋊C₄	—	5	1	no	—
382	C₄⋊C₄	—	5	1	no	—
383	C₄⋊C₄	—	5	2	no	—
384	C₄⋊C₄	—	5	2	no	—
385	C₄⋊C₄	—	5	2	no	—
386	C₄⋊C₄	—	5	2	no	—
387	C₄⋊C₄	—	5	2	no	—
388	C₄⋊C₄	—	5	2	no	—
389	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
390	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
391	C₂²⋊C₄	—	5	2	no	—
392	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
393	C₄²	—	5	1	no	—
394	C₄²	—	5	1	no	—
395	C₄²	—	5	1	no	—
396	C₄²	—	5	2	no	—
397	C₄²	—	5	1	no	—
398	C₄²	C₂²×C₃×D₅	1	2	yes	—
399	C₃×C₅	#2962	1	1	yes	characteristic, complemented, Hall
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	C₄×Dic₁₀	1	2	yes	—
403	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	5	2	no	—
407	C₃×C₄	—	10	1	no	—
408	C₃×C₄	—	10	2	no	—
409	C₃×C₄	—	10	1	no	—
410	C₃×C₄	—	10	1	no	—
411	C₃×C₄	—	10	2	no	—
412	C₃×C₄	C₄×Dic₁₀	1	2	yes	—
413	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
414	C₃×C₄	C₂×#709	1	1	yes	characteristic
415	C₂×C₅	—	2	2	no	—
416	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
417	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
418	C₂×C₅	C₃×#568	1	1	yes	characteristic
419	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
420	Q₈	—	10	4	no	—
421	Q₈	—	20	2	no	—
422	C₂×C₄	—	5	1	no	—
423	C₂×C₄	—	5	1	no	—
424	C₂×C₄	—	5	1	no	—
425	C₂×C₄	—	5	1	no	—
426	C₂×C₄	—	5	2	no	—
427	C₂×C₄	—	5	2	no	—
428	C₂×C₄	—	10	2	no	—
429	C₂×C₄	—	20	1	no	—
430	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
431	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
432	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
433	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
434	C₂×C₄	C₃×#709	1	2	yes	—
435	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	10	1	no	—
439	C₈	—	10	1	no	—
440	C₈	—	10	2	no	—
441	C₈	C₂×C₃×Dic₁₀	1	4	yes	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	C₂×C₄×Dic₁₀	1	1	yes	characteristic
444	C₂×C₃	D₅×#131	1	1	yes	characteristic
445	C₂×C₃	#66084	1	1	yes	characteristic
446	C₅	C₃×#2962	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	C₃×C₄×Dic₁₀	1	2	yes	—
450	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	5	2	no	—
454	C₄	—	10	1	no	—
455	C₄	—	10	2	no	—
456	C₄	—	10	1	no	—
457	C₄	—	10	1	no	—
458	C₄	—	10	2	no	—
459	C₄	C₃×C₄×Dic₁₀	1	2	yes	—
460	C₄	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
461	C₄	C₂×C₃×#709	1	1	yes	characteristic
462	C₃	#10610275	1	1	yes	characteristic, direct product factor, Sylow
463	C₂	—	2	2	no	—
464	C₂	C₂×C₃×C₄×Dic₁₀	1	1	yes	characteristic
465	C₂	C₃×D₅×#131	1	1	yes	characteristic
466	C₂	C₃×#66084	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×#405	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2962
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
8. C₃×#64990	C₂	semidirect
9. C₃×#64990	C₂	semidirect
10. C₃×#64968	C₂	semidirect
11. C₃×C₈×Dic₁₀	C₂	semidirect
12. #10610275	C₃	direct (N × H)
50. #64990	C₂×C₃	semidirect
51. #64990	C₂×C₃	semidirect
52. #64968	C₂×C₃	semidirect
53. C₈×Dic₁₀	C₂×C₃	semidirect
59. C₃×C₅×M₁₆	Q₈	semidirect
185. C₅×M₁₆	C₃×Q₈	semidirect
245. C₃×M₁₆	Dic₁₀	semidirect
372. M₁₆	C₃×Dic₁₀	semidirect
399. C₃×C₅	#2962	semidirect
446. C₅	C₃×#2962	semidirect
462. C₃	#10610275	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×#65851	2
C₃×C₅×#405	2
C₃×#65411	2
C₃×M₁₆×Dic₅	2
C₃×#65391	2
C₂×C₃×#3946	2
C₃×#65288	2
C₃×#64990	2
C₃×#64968	2
C₃×C₈×Dic₁₀	2
#10610275	3
C₃×#2962	5

Subgroups — C3×#10610275 #14418661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610275 #14418661