Subgroups — C₃×#10614857 #14419147

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₃×#65313	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65301	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65300	C₂	1	2	yes	maximal, complemented
6	C₃×D₄×#168	C₂	1	2	yes	maximal, complemented
7	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65289	C₂	1	2	yes	maximal, complemented
9	C₃×#65286	C₂	1	2	yes	maximal, complemented
10	C₃×#65215	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614857	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×#126	C₄	1	2	yes	—
14	C₃×C₅×#125	C₄	1	1	yes	characteristic
15	C₃×C₅×#124	C₄	1	1	yes	characteristic
16	C₃×C₅×#123	C₄	1	2	yes	—
17	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₃×C₅×#121	C₄	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₃×C₅×#117	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×#681	C₂²	1	2	yes	—
25	C₂²×C₃×#168	C₂²	1	2	yes	—
26	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
28	C₃×C₂²⋊#168	C₂²	1	2	yes	—
29	C₃×C₂²⋊#168	C₂²	1	2	yes	—
30	C₃×C₂²⋊#168	C₂²	1	2	yes	—
31	C₃×C₄⋊#168	C₂²	1	2	yes	—
32	C₃×C₄⋊#168	C₂²	1	2	yes	—
33	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
34	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
35	C₃×#3935	C₂²	1	2	yes	—
36	C₃×#3935	C₂²	1	2	yes	—
37	C₃×C₄×#168	C₂²	1	1	yes	characteristic
38	C₃×C₄×#168	C₂²	1	2	yes	—
39	C₃×C₄×#168	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×#2966	—	5	1	no	maximal, Hall
43	C₅×#529	C₂×C₃	1	1	yes	characteristic
44	#65313	C₂×C₃	1	1	yes	characteristic, complemented
45	Q₈×#168	C₂×C₃	1	1	yes	characteristic, complemented
46	#65301	C₂×C₃	1	1	yes	characteristic, complemented
47	#65300	C₂×C₃	1	2	yes	complemented
48	D₄×#168	C₂×C₃	1	2	yes	complemented
49	D₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
50	#65289	C₂×C₃	1	2	yes	complemented
51	#65286	C₂×C₃	1	2	yes	complemented
52	#65215	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	2	yes	—
77	C₃×#681	—	2	4	no	—
78	C₂×C₃×#168	—	2	4	no	—
79	C₂×C₃×#168	—	2	2	no	—
80	C₂×C₃×#168	—	2	2	no	—
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	2	yes	—
84	C₂×C₃×#168	C₂³	1	2	yes	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₃×#529	D₅	1	1	yes	characteristic
88	C₃×#446	—	5	1	no	—
89	C₃×C₈×Q₈	—	5	1	no	—
90	C₃×#436	—	5	1	no	—
91	C₃×#435	—	5	2	no	—
92	C₃×C₈×D₄	—	5	1	no	—
93	C₃×C₈×D₄	—	5	2	no	—
94	C₃×#433	—	5	2	no	—
95	C₃×#432	—	5	1	no	—
96	C₃×#405	—	5	2	no	—
97	C₂×C₃×C₄×C₈	—	5	1	no	—
98	C₅×#126	C₃×C₄	1	2	yes	—
99	C₅×#125	C₃×C₄	1	1	yes	characteristic
100	C₅×#124	C₃×C₄	1	1	yes	characteristic
101	C₅×#123	C₃×C₄	1	2	yes	—
102	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
103	C₅×#121	C₃×C₄	1	1	yes	characteristic
104	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
106	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
107	C₅×#117	C₂²×C₃	1	2	yes	—
108	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×#681	C₂²×C₃	1	2	yes	—
110	C₂²×#168	C₂²×C₃	1	2	yes	—
111	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
112	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
113	C₂²⋊#168	C₂²×C₃	1	2	yes	—
114	C₂²⋊#168	C₂²×C₃	1	2	yes	—
115	C₂²⋊#168	C₂²×C₃	1	2	yes	—
116	C₄⋊#168	C₂²×C₃	1	2	yes	—
117	C₄⋊#168	C₂²×C₃	1	2	yes	—
118	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
119	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
120	#3935	C₂²×C₃	1	2	yes	—
121	#3935	C₂²×C₃	1	2	yes	—
122	C₄×#168	C₂²×C₃	1	1	yes	characteristic
123	C₄×#168	C₂²×C₃	1	2	yes	—
124	C₄×#168	C₂²×C₃	1	1	yes	characteristic
125	C₄×#168	C₂²×C₃	1	1	yes	characteristic
126	C₄×#168	C₂²×C₃	1	1	yes	characteristic
127	#2966	—	5	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
129	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×D₄	—	2	4	no	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×#168	—	2	1	no	—
149	C₃×#168	—	2	1	no	—
150	C₃×#168	—	2	2	no	—
151	C₃×#168	—	2	2	no	—
152	C₃×#168	#41	1	2	yes	—
153	C₃×#168	#41	1	2	yes	—
154	C₂×C₃×M₁₆	—	5	2	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂²×C₃×C₈	—	5	1	no	—
157	C₂²×C₃×C₈	—	5	2	no	—
158	C₃×#126	Dic₅	1	2	yes	—
159	C₃×#125	Dic₅	1	1	yes	characteristic
160	C₃×#124	Dic₅	1	1	yes	characteristic
161	C₃×#123	Dic₅	1	2	yes	—
162	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
163	C₃×#121	Dic₅	1	1	yes	characteristic
164	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
165	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
166	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
167	C₃×#117	C₂×D₅	1	2	yes	—
168	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×C₄⋊C₈	—	5	1	no	—
171	C₃×C₄⋊C₈	—	5	2	no	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₂²⋊C₈	—	5	2	no	—
174	C₃×C₂²⋊C₈	—	5	2	no	—
175	C₃×C₂²⋊C₈	—	5	2	no	—
176	C₃×#97	—	5	2	no	—
177	C₃×#97	—	5	2	no	—
178	C₃×C₄×C₈	—	5	1	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₃×C₄×C₈	—	5	1	no	—
181	C₃×C₄×C₈	—	5	1	no	—
182	C₃×C₄×C₈	—	5	2	no	—
183	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
185	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
190	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
191	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
192	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
193	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
194	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
196	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
197	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
198	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
199	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
200	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
201	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
202	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
203	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
204	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₄²×C₅	C₂³×C₃	1	2	yes	—
206	#681	—	2	4	no	—
207	C₂×#168	—	2	4	no	—
208	C₂×#168	—	2	2	no	—
209	C₂×#168	—	2	2	no	—
210	C₂×#168	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	1	yes	characteristic
212	C₂×#168	C₂³×C₃	1	2	yes	—
213	C₂×#168	C₂³×C₃	1	2	yes	—
214	C₂×#168	C₂³×C₃	1	1	yes	characteristic
215	C₂×#168	C₂³×C₃	1	1	yes	characteristic
216	#529	C₃×D₅	1	1	yes	characteristic
217	#446	—	5	1	no	—
218	C₈×Q₈	—	5	1	no	—
219	#436	—	5	1	no	—
220	#435	—	5	2	no	—
221	C₈×D₄	—	5	1	no	—
222	C₈×D₄	—	5	2	no	—
223	#433	—	5	2	no	—
224	#432	—	5	1	no	—
225	#405	—	5	2	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂²×C₃×C₅	—	2	1	no	—
228	C₂²×C₃×C₅	—	2	1	no	—
229	C₂²×C₃×C₅	—	2	2	no	—
230	C₂²×C₃×C₅	—	2	2	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	#131	1	2	yes	—
233	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	2	no	—
236	C₃×C₄×C₅	—	2	1	no	—
237	C₃×C₄×C₅	—	2	1	no	—
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	#131	1	2	yes	—
242	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
245	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
246	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
251	C₃×M₁₆	—	10	4	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	1	no	—
254	C₂×C₃×C₈	—	5	1	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	5	2	no	—
257	C₂×C₃×C₈	—	5	2	no	—
258	C₂×C₃×C₈	—	10	2	no	—
259	C₂×C₃×C₈	—	10	4	no	—
260	C₂×C₃×C₈	—	10	2	no	—
261	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
262	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
263	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
265	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
266	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
267	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
268	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
269	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
270	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
271	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
272	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
273	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
274	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
275	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
276	C₃×C₄²	C₂²×D₅	1	2	yes	—
277	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
278	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₅×Q₈	—	2	2	no	—
280	C₅×D₄	—	2	4	no	—
281	C₅×D₄	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
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	C₂²×C₃×C₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
293	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
294	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
295	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
297	#168	—	2	1	no	—
298	#168	—	2	1	no	—
299	#168	—	2	2	no	—
300	#168	—	2	2	no	—
301	#168	C₃×#41	1	2	yes	—
302	#168	C₃×#41	1	2	yes	—
303	C₂×M₁₆	—	5	2	no	—
304	C₂²×C₈	—	5	1	no	—
305	C₂²×C₈	—	5	1	no	—
306	C₂²×C₈	—	5	2	no	—
307	#126	C₃×Dic₅	1	2	yes	—
308	#125	C₃×Dic₅	1	1	yes	characteristic
309	#124	C₃×Dic₅	1	1	yes	characteristic
310	#123	C₃×Dic₅	1	2	yes	—
311	C₂²⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
312	#121	C₃×Dic₅	1	1	yes	characteristic
313	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
314	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
315	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
316	#117	C₂×C₃×D₅	1	2	yes	—
317	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
318	C₄⋊C₈	—	5	1	no	—
319	C₄⋊C₈	—	5	1	no	—
320	C₄⋊C₈	—	5	2	no	—
321	C₄⋊C₈	—	5	2	no	—
322	C₂²⋊C₈	—	5	2	no	—
323	C₂²⋊C₈	—	5	2	no	—
324	C₂²⋊C₈	—	5	2	no	—
325	#97	—	5	2	no	—
326	#97	—	5	2	no	—
327	C₄×C₈	—	5	1	no	—
328	C₄×C₈	—	5	1	no	—
329	C₄×C₈	—	5	1	no	—
330	C₄×C₈	—	5	1	no	—
331	C₄×C₈	—	5	2	no	—
332	C₂×C₃×C₅	—	2	2	no	—
333	C₂×C₃×C₅	—	4	2	no	—
334	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
337	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
338	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
339	C₃×Q₈	—	2	2	no	—
340	C₃×D₄	—	2	4	no	—
341	C₃×D₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
353	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
354	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
355	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
357	C₃×C₈	—	5	2	no	—
358	C₃×C₈	—	5	2	no	—
359	C₃×C₈	—	10	1	no	—
360	C₃×C₈	—	10	1	no	—
361	C₃×C₈	—	10	2	no	—
362	C₃×C₈	—	10	2	no	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	C₃×#131	1	2	yes	—
369	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	2	no	—
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	2	1	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	C₃×#131	1	2	yes	—
378	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
379	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
380	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
381	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
382	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
387	M₁₆	—	10	4	no	—
388	C₂×C₈	—	5	1	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	5	1	no	—
392	C₂×C₈	—	5	2	no	—
393	C₂×C₈	—	5	2	no	—
394	C₂×C₈	—	10	2	no	—
395	C₂×C₈	—	10	4	no	—
396	C₂×C₈	—	10	2	no	—
397	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
398	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
399	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
400	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
401	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
402	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
403	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
404	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
405	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
406	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
407	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
408	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
409	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
410	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
411	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
412	C₄²	C₂²×C₃×D₅	1	2	yes	—
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	2	2	no	—
418	C₂²×C₃	—	2	2	no	—
419	C₂²×C₃	#4094	1	2	yes	—
420	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	#4094	1	2	yes	—
429	C₃×C₄	D₅×#41	1	1	yes	characteristic
430	C₃×C₄	D₅×#41	1	1	yes	characteristic
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	—	4	2	no	—
433	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
434	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
435	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
436	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
437	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
449	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
452	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
453	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
454	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
455	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
456	C₈	—	5	2	no	—
457	C₈	—	5	2	no	—
458	C₈	—	10	1	no	—
459	C₈	—	10	1	no	—
460	C₈	—	10	2	no	—
461	C₈	—	10	2	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	—	4	2	no	—
464	C₂×C₃	C₂×#4094	1	1	yes	characteristic
465	C₂×C₃	C₂×#4094	1	1	yes	characteristic
466	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
467	C₅	C₃×#2966	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	C₃×#4094	1	2	yes	—
474	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	C₃×#4094	1	2	yes	—
483	C₄	C₃×D₅×#41	1	1	yes	characteristic
484	C₄	C₃×D₅×#41	1	1	yes	characteristic
485	C₃	#10614857	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	2	2	no	—
487	C₂	—	4	2	no	—
488	C₂	C₂×C₃×#4094	1	1	yes	characteristic
489	C₂	C₂×C₃×#4094	1	1	yes	characteristic
490	C₂	C₃×#41×Dic₅	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×#529	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×C₅×#121	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#529	D₅
hypocenter	C₅	C₃×#2966
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
2. C₃×#65313	C₂	semidirect
3. C₃×Q₈×#168	C₂	semidirect
4. C₃×#65301	C₂	semidirect
5. C₃×#65300	C₂	semidirect
6. C₃×D₄×#168	C₂	semidirect
7. C₃×D₄×#168	C₂	semidirect
8. C₃×#65289	C₂	semidirect
9. C₃×#65286	C₂	semidirect
10. C₃×#65215	C₂	semidirect
11. C₂×C₃×C₄×#168	C₂	semidirect
12. #10614857	C₃	direct (N × H)
44. #65313	C₂×C₃	semidirect
45. Q₈×#168	C₂×C₃	semidirect
46. #65301	C₂×C₃	semidirect
47. #65300	C₂×C₃	semidirect
48. D₄×#168	C₂×C₃	semidirect
49. D₄×#168	C₂×C₃	semidirect
50. #65289	C₂×C₃	semidirect
51. #65286	C₂×C₃	semidirect
52. #65215	C₂×C₃	semidirect
53. C₂×C₄×#168	C₂×C₃	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	C₃×#2966	semidirect
485. C₃	#10614857	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×C₅×#529	2
C₃×#65313	2
C₃×Q₈×#168	2
C₃×#65301	2
C₃×#65300	2
C₃×D₄×#168	2
C₃×#65289	2
C₃×#65286	2
C₃×#65215	2
C₂×C₃×C₄×#168	2
#10614857	3
C₃×#2966	5

Subgroups — C3×#10614857 #14419147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614857 #14419147