Subgroups — C₃×#10610289 #14419575

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65862	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65289	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64997	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64995	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64990	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#64979	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#64974	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64968	C₂	1	1	yes	maximal, characteristic, complemented
16	#10610289	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×#676	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₃×#4044	C₄	1	1	yes	characteristic
27	C₃×#4042	C₄	1	1	yes	characteristic
28	C₃×#4040	C₄	1	1	yes	characteristic
29	C₃×#4035	C₄	1	1	yes	characteristic
30	C₃×#4031	C₄	1	1	yes	characteristic
31	C₃×#4030	C₄	1	1	yes	characteristic
32	C₃×#4029	C₄	1	1	yes	characteristic
33	C₃×#4025	C₄	1	1	yes	characteristic
34	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
35	C₃×#4018	C₂²	1	1	yes	characteristic
36	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
37	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
38	C₃×C₅×#97	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic
40	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
43	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
44	C₃×#3952	C₂²	1	1	yes	characteristic
45	C₃×#3952	C₂²	1	1	yes	characteristic
46	C₃×#3952	C₂²	1	1	yes	characteristic
47	C₃×#3952	C₂²	1	1	yes	characteristic
48	C₃×#3947	C₂²	1	1	yes	characteristic
49	C₃×#3947	C₂²	1	1	yes	characteristic
50	C₃×#3947	C₂²	1	1	yes	characteristic
51	C₃×#3946	C₂²	1	1	yes	characteristic
52	C₃×#3946	C₂²	1	1	yes	characteristic
53	C₃×#3946	C₂²	1	1	yes	characteristic
54	C₃×#3946	C₂²	1	1	yes	characteristic
55	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
56	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
57	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
58	C₃×#3935	C₂²	1	1	yes	characteristic
59	C₃×C₄×#168	C₂²	1	1	yes	characteristic
60	C₃×#2968	—	5	1	no	maximal, Hall
61	#65862	C₂×C₃	1	1	yes	characteristic
62	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
63	#65416	C₂×C₃	1	1	yes	characteristic, complemented
64	#65416	C₂×C₃	1	1	yes	characteristic, complemented
65	#65400	C₂×C₃	1	1	yes	characteristic, complemented
66	C₈×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
67	#65289	C₂×C₃	1	1	yes	characteristic, complemented
68	#64997	C₂×C₃	1	1	yes	characteristic, complemented
69	#64995	C₂×C₃	1	1	yes	characteristic, complemented
70	D₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
71	#64990	C₂×C₃	1	1	yes	characteristic, complemented
72	#64979	C₂×C₃	1	1	yes	characteristic, complemented
73	C₈×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
74	#64974	C₂×C₃	1	1	yes	characteristic, complemented
75	#64968	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
85	C₃×C₅×M₁₆	—	2	2	no	—
86	C₂×C₃×C₅×C₈	—	2	2	no	—
87	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
98	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₃×#685	C₂×C₄	1	1	yes	characteristic
100	C₃×#685	C₂×C₄	1	1	yes	characteristic
101	C₃×#685	C₂×C₄	1	1	yes	characteristic
102	C₃×#685	C₂×C₄	1	1	yes	characteristic
103	C₃×#685	C₂×C₄	1	1	yes	characteristic
104	C₃×#685	C₂×C₄	1	1	yes	characteristic
105	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
106	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
107	C₃×#683	C₂×C₄	1	1	yes	characteristic
108	C₃×#683	C₂×C₄	1	1	yes	characteristic
109	C₃×#683	C₂×C₄	1	1	yes	characteristic
110	C₃×#683	C₂×C₄	1	1	yes	characteristic
111	C₃×#683	C₂×C₄	1	1	yes	characteristic
112	C₃×#683	C₂×C₄	1	1	yes	characteristic
113	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
114	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
115	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
116	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
117	C₂×C₃×#168	C₂³	1	1	yes	characteristic
118	C₂×C₃×#168	C₂³	1	1	yes	characteristic
119	C₂×C₃×#168	C₂³	1	1	yes	characteristic
120	C₂×C₃×#168	C₂³	1	1	yes	characteristic
121	C₃×#676	—	2	2	no	—
122	C₃×C₈×D₅	—	2	2	no	—
123	C₃×C₈×D₅	—	2	2	no	—
124	C₃×C₈×D₅	—	2	2	no	—
125	C₃×#529	—	5	1	no	—
126	C₃×#446	—	5	1	no	—
127	C₃×#446	—	5	1	no	—
128	C₃×#435	—	5	1	no	—
129	C₃×#435	—	5	1	no	—
130	C₃×#435	—	5	1	no	—
131	C₃×#435	—	5	1	no	—
132	C₃×C₈×D₄	—	5	1	no	—
133	C₃×C₈×D₄	—	5	1	no	—
134	C₃×#433	—	5	1	no	—
135	C₃×#433	—	5	1	no	—
136	C₃×#431	—	5	1	no	—
137	C₃×#405	—	5	1	no	—
138	C₃×#405	D₅	1	1	yes	characteristic, complemented
139	C₂×C₃×#97	—	5	1	no	—
140	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
141	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
142	C₅×#117	C₂²×C₃	1	1	yes	characteristic
143	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
144	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
145	C₂×#676	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
149	#4044	C₃×C₄	1	1	yes	characteristic
150	#4042	C₃×C₄	1	1	yes	characteristic
151	#4040	C₃×C₄	1	1	yes	characteristic
152	#4035	C₃×C₄	1	1	yes	characteristic
153	#4031	C₃×C₄	1	1	yes	characteristic
154	#4030	C₃×C₄	1	1	yes	characteristic
155	#4029	C₃×C₄	1	1	yes	characteristic
156	#4025	C₃×C₄	1	1	yes	characteristic
157	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
158	#4018	C₂²×C₃	1	1	yes	characteristic
159	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
160	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
161	C₅×#97	C₂²×C₃	1	1	yes	characteristic
162	C₅×#97	C₂²×C₃	1	1	yes	characteristic
163	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
165	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
166	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
167	#3952	C₂²×C₃	1	1	yes	characteristic
168	#3952	C₂²×C₃	1	1	yes	characteristic
169	#3952	C₂²×C₃	1	1	yes	characteristic
170	#3952	C₂²×C₃	1	1	yes	characteristic
171	#3947	C₂²×C₃	1	1	yes	characteristic
172	#3947	C₂²×C₃	1	1	yes	characteristic
173	#3947	C₂²×C₃	1	1	yes	characteristic
174	#3946	C₂²×C₃	1	1	yes	characteristic
175	#3946	C₂²×C₃	1	1	yes	characteristic
176	#3946	C₂²×C₃	1	1	yes	characteristic
177	#3946	C₂²×C₃	1	1	yes	characteristic
178	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
179	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
180	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
181	#3935	C₂²×C₃	1	1	yes	characteristic
182	C₄×#168	C₂²×C₃	1	1	yes	characteristic
183	#2968	—	5	1	no	Sylow
184	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
195	C₃×C₂²⋊D₅	—	2	2	no	—
196	C₃×C₂²⋊D₅	—	4	1	no	—
197	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
203	C₃×D₂₀	—	2	2	no	—
204	C₃×C₄×D₅	—	2	2	no	—
205	C₃×C₄×D₅	—	2	1	no	—
206	C₃×C₄×D₅	—	2	1	no	—
207	C₃×C₄×D₅	—	2	1	no	—
208	C₃×C₄×D₅	—	2	1	no	—
209	C₃×C₄×D₅	—	4	1	no	—
210	C₃×Dic₁₀	—	4	1	no	—
211	C₃×C₅×C₈	—	2	1	no	—
212	C₃×C₅×C₈	—	2	1	no	—
213	C₃×C₅×C₈	#41	1	2	yes	—
214	C₃×C₅×C₈	#41	1	2	yes	—
215	C₃×#168	—	2	1	no	—
216	C₃×#168	—	2	1	no	—
217	C₃×#168	—	2	1	no	—
218	C₃×#168	—	2	1	no	—
219	C₂×C₃×M₁₆	—	5	1	no	—
220	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
221	C₂²×C₃×C₈	—	5	1	no	—
222	C₂²×C₃×C₈	—	5	1	no	—
223	C₂²×C₃×C₈	—	5	1	no	—
224	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
225	C₃×#126	—	5	1	no	—
226	C₃×#126	—	5	1	no	—
227	C₃×#125	—	5	1	no	—
228	C₃×#124	—	5	1	no	—
229	C₃×#123	—	5	1	no	—
230	C₃×#123	—	5	1	no	—
231	C₃×C₂²⋊Q₈	—	5	1	no	—
232	C₃×#121	—	5	1	no	—
233	C₃×C₄×Q₈	—	5	1	no	—
234	C₃×C₄×D₄	—	5	1	no	—
235	C₃×C₄×D₄	—	5	1	no	—
236	C₃×C₄×D₄	—	5	1	no	—
237	C₃×#117	—	5	1	no	—
238	C₃×#117	C₂×D₅	1	1	yes	characteristic
239	C₂×C₃×C₄²	—	5	1	no	—
240	C₃×C₄⋊C₈	—	5	1	no	—
241	C₃×C₄⋊C₈	—	5	1	no	—
242	C₃×C₄⋊C₈	—	5	1	no	—
243	C₃×C₄⋊C₈	—	5	1	no	—
244	C₃×C₄⋊C₈	—	5	1	no	—
245	C₃×C₄⋊C₈	—	5	1	no	—
246	C₃×C₂²⋊C₈	—	5	1	no	—
247	C₃×C₂²⋊C₈	—	5	1	no	—
248	C₃×C₂²⋊C₈	—	5	1	no	—
249	C₃×C₂²⋊C₈	—	5	1	no	—
250	C₃×C₂²⋊C₈	—	5	1	no	—
251	C₃×C₂²⋊C₈	—	5	1	no	—
252	C₃×#97	—	5	1	no	—
253	C₃×#97	—	5	1	no	—
254	C₃×#97	—	5	1	no	—
255	C₃×#97	—	5	1	no	—
256	C₃×#97	C₂×D₅	1	1	yes	characteristic
257	C₃×#97	C₂×D₅	1	1	yes	characteristic
258	C₃×C₄×C₈	—	5	1	no	—
259	C₃×C₄×C₈	—	5	1	no	—
260	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
261	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
264	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
265	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
266	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
268	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
270	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
271	C₅×M₁₆	—	2	2	no	—
272	C₂×C₅×C₈	—	2	2	no	—
273	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
277	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
278	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
279	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
280	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
281	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
282	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
283	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
284	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
285	#685	C₂×C₃×C₄	1	1	yes	characteristic
286	#685	C₂×C₃×C₄	1	1	yes	characteristic
287	#685	C₂×C₃×C₄	1	1	yes	characteristic
288	#685	C₂×C₃×C₄	1	1	yes	characteristic
289	#685	C₂×C₃×C₄	1	1	yes	characteristic
290	#685	C₂×C₃×C₄	1	1	yes	characteristic
291	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
292	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
293	#683	C₂×C₃×C₄	1	1	yes	characteristic
294	#683	C₂×C₃×C₄	1	1	yes	characteristic
295	#683	C₂×C₃×C₄	1	1	yes	characteristic
296	#683	C₂×C₃×C₄	1	1	yes	characteristic
297	#683	C₂×C₃×C₄	1	1	yes	characteristic
298	#683	C₂×C₃×C₄	1	1	yes	characteristic
299	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
300	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
301	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
302	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
303	C₂×#168	C₂³×C₃	1	1	yes	characteristic
304	C₂×#168	C₂³×C₃	1	1	yes	characteristic
305	C₂×#168	C₂³×C₃	1	1	yes	characteristic
306	C₂×#168	C₂³×C₃	1	1	yes	characteristic
307	#676	—	2	2	no	—
308	C₈×D₅	—	2	2	no	—
309	C₈×D₅	—	2	2	no	—
310	C₈×D₅	—	2	2	no	—
311	#529	—	5	1	no	—
312	#446	—	5	1	no	—
313	#446	—	5	1	no	—
314	#435	—	5	1	no	—
315	#435	—	5	1	no	—
316	#435	—	5	1	no	—
317	#435	—	5	1	no	—
318	C₈×D₄	—	5	1	no	—
319	C₈×D₄	—	5	1	no	—
320	#433	—	5	1	no	—
321	#433	—	5	1	no	—
322	#431	—	5	1	no	—
323	#405	—	5	1	no	—
324	#405	C₃×D₅	1	1	yes	characteristic, complemented
325	C₂×#97	—	5	1	no	—
326	C₂²×C₃×C₅	—	2	1	no	—
327	C₂²×C₃×C₅	—	2	1	no	—
328	C₂²×C₃×C₅	—	2	1	no	—
329	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
330	C₂×C₃×D₅	—	2	1	no	—
331	C₂×C₃×D₅	—	2	1	no	—
332	C₂×C₃×D₅	—	2	1	no	—
333	C₂×C₃×D₅	—	2	1	no	—
334	C₂×C₃×D₅	—	2	1	no	—
335	C₂×C₃×D₅	#131	1	2	yes	—
336	C₃×C₄×C₅	—	2	1	no	—
337	C₃×C₄×C₅	—	2	1	no	—
338	C₃×C₄×C₅	—	2	1	no	—
339	C₃×C₄×C₅	—	2	1	no	—
340	C₃×C₄×C₅	—	2	1	no	—
341	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
343	C₃×Dic₅	—	2	1	no	—
344	C₃×Dic₅	—	2	1	no	—
345	C₃×Dic₅	—	2	1	no	—
346	C₃×Dic₅	—	2	1	no	—
347	C₃×Dic₅	—	2	1	no	—
348	C₃×Dic₅	—	2	1	no	—
349	C₂×C₃×Q₈	—	5	1	no	—
350	C₂×C₃×D₄	—	5	1	no	—
351	C₂×C₃×D₄	—	5	1	no	—
352	C₂×C₃×D₄	—	5	1	no	—
353	C₂²×C₃×C₄	—	5	1	no	—
354	C₂²×C₃×C₄	—	5	1	no	—
355	C₂²×C₃×C₄	—	5	1	no	—
356	C₂²×C₃×C₄	—	5	1	no	—
357	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
358	C₃×M₁₆	—	2	2	no	—
359	C₃×M₁₆	—	10	2	no	—
360	C₂×C₃×C₈	—	2	2	no	—
361	C₂×C₃×C₈	—	5	1	no	—
362	C₂×C₃×C₈	—	5	1	no	—
363	C₂×C₃×C₈	—	5	1	no	—
364	C₂×C₃×C₈	—	5	1	no	—
365	C₂×C₃×C₈	—	10	2	no	—
366	C₂×C₃×C₈	—	10	2	no	—
367	C₂×C₃×C₈	—	10	2	no	—
368	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
369	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
370	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
371	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
372	C₃×C₄⋊C₄	—	5	1	no	—
373	C₃×C₄⋊C₄	—	5	1	no	—
374	C₃×C₄⋊C₄	—	5	1	no	—
375	C₃×C₄⋊C₄	—	5	1	no	—
376	C₃×C₄⋊C₄	—	5	1	no	—
377	C₃×C₄⋊C₄	—	5	1	no	—
378	C₃×C₄⋊C₄	—	5	1	no	—
379	C₃×C₄⋊C₄	—	5	1	no	—
380	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
381	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
382	C₃×C₂²⋊C₄	—	5	1	no	—
383	C₃×C₂²⋊C₄	—	5	1	no	—
384	C₃×C₂²⋊C₄	—	5	1	no	—
385	C₃×C₂²⋊C₄	—	5	1	no	—
386	C₃×C₂²⋊C₄	—	5	1	no	—
387	C₃×C₂²⋊C₄	—	5	1	no	—
388	C₃×C₂²⋊C₄	—	5	1	no	—
389	C₃×C₂²⋊C₄	—	5	1	no	—
390	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
391	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
392	C₃×C₄²	—	5	1	no	—
393	C₃×C₄²	—	5	1	no	—
394	C₃×C₄²	—	5	1	no	—
395	C₃×C₄²	—	5	1	no	—
396	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
397	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
398	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
399	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
400	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
404	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
406	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
407	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
408	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
409	C₂²⋊D₅	—	2	2	no	—
410	C₂²⋊D₅	—	4	1	no	—
411	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
412	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
413	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
414	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
415	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
416	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
417	D₂₀	—	2	2	no	—
418	C₄×D₅	—	2	2	no	—
419	C₄×D₅	—	2	1	no	—
420	C₄×D₅	—	2	1	no	—
421	C₄×D₅	—	2	1	no	—
422	C₄×D₅	—	2	1	no	—
423	C₄×D₅	—	4	1	no	—
424	Dic₁₀	—	4	1	no	—
425	C₅×C₈	—	2	1	no	—
426	C₅×C₈	—	2	1	no	—
427	C₅×C₈	C₃×#41	1	2	yes	—
428	C₅×C₈	C₃×#41	1	2	yes	—
429	#168	—	2	1	no	—
430	#168	—	2	1	no	—
431	#168	—	2	1	no	—
432	#168	—	2	1	no	—
433	C₂×M₁₆	—	5	1	no	—
434	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
435	C₂²×C₈	—	5	1	no	—
436	C₂²×C₈	—	5	1	no	—
437	C₂²×C₈	—	5	1	no	—
438	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
439	#126	—	5	1	no	—
440	#126	—	5	1	no	—
441	#125	—	5	1	no	—
442	#124	—	5	1	no	—
443	#123	—	5	1	no	—
444	#123	—	5	1	no	—
445	C₂²⋊Q₈	—	5	1	no	—
446	#121	—	5	1	no	—
447	C₄×Q₈	—	5	1	no	—
448	C₄×D₄	—	5	1	no	—
449	C₄×D₄	—	5	1	no	—
450	C₄×D₄	—	5	1	no	—
451	#117	—	5	1	no	—
452	#117	C₂×C₃×D₅	1	1	yes	characteristic
453	C₂×C₄²	—	5	1	no	—
454	C₄⋊C₈	—	5	1	no	—
455	C₄⋊C₈	—	5	1	no	—
456	C₄⋊C₈	—	5	1	no	—
457	C₄⋊C₈	—	5	1	no	—
458	C₄⋊C₈	—	5	1	no	—
459	C₄⋊C₈	—	5	1	no	—
460	C₂²⋊C₈	—	5	1	no	—
461	C₂²⋊C₈	—	5	1	no	—
462	C₂²⋊C₈	—	5	1	no	—
463	C₂²⋊C₈	—	5	1	no	—
464	C₂²⋊C₈	—	5	1	no	—
465	C₂²⋊C₈	—	5	1	no	—
466	#97	—	5	1	no	—
467	#97	—	5	1	no	—
468	#97	—	5	1	no	—
469	#97	—	5	1	no	—
470	#97	C₂×C₃×D₅	1	1	yes	characteristic
471	#97	C₂×C₃×D₅	1	1	yes	characteristic
472	C₄×C₈	—	5	1	no	—
473	C₄×C₈	—	5	1	no	—
474	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
475	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
476	C₂×C₃×C₅	—	4	1	no	—
477	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
478	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
479	C₂×C₃×C₅	#568	1	1	yes	characteristic
480	C₃×D₅	—	2	2	no	—
481	C₃×D₅	—	4	1	no	—
482	C₂³×C₃	—	5	1	no	—
483	C₂³×C₃	—	5	1	no	—
484	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
485	C₃×Q₈	—	20	1	no	—
486	C₃×D₄	—	10	2	no	—
487	C₃×D₄	—	10	2	no	—
488	C₃×D₄	—	20	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	5	1	no	—
492	C₂×C₃×C₄	—	5	1	no	—
493	C₂×C₃×C₄	—	5	1	no	—
494	C₂×C₃×C₄	—	5	1	no	—
495	C₂×C₃×C₄	—	5	1	no	—
496	C₂×C₃×C₄	—	5	1	no	—
497	C₂×C₃×C₄	—	10	2	no	—
498	C₂×C₃×C₄	—	10	1	no	—
499	C₂×C₃×C₄	—	10	1	no	—
500	C₂×C₃×C₄	—	10	1	no	—
501	C₂×C₃×C₄	—	10	1	no	—
502	C₂×C₃×C₄	—	20	1	no	—
503	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
509	C₃×C₈	—	2	1	no	—
510	C₃×C₈	—	2	1	no	—
511	C₃×C₈	—	10	1	no	—
512	C₃×C₈	—	10	1	no	—
513	C₃×C₈	—	10	1	no	—
514	C₃×C₈	—	10	1	no	—
515	C₃×C₈	#709	1	2	yes	—
516	C₃×C₈	#709	1	2	yes	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
521	C₂×D₅	—	2	1	no	—
522	C₂×D₅	—	2	1	no	—
523	C₂×D₅	—	2	1	no	—
524	C₂×D₅	—	2	1	no	—
525	C₂×D₅	—	2	1	no	—
526	C₂×D₅	C₃×#131	1	2	yes	—
527	C₄×C₅	—	2	1	no	—
528	C₄×C₅	—	2	1	no	—
529	C₄×C₅	—	2	1	no	—
530	C₄×C₅	—	2	1	no	—
531	C₄×C₅	—	2	1	no	—
532	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
533	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
534	Dic₅	—	2	1	no	—
535	Dic₅	—	2	1	no	—
536	Dic₅	—	2	1	no	—
537	Dic₅	—	2	1	no	—
538	Dic₅	—	2	1	no	—
539	Dic₅	—	2	1	no	—
540	C₂×Q₈	—	5	1	no	—
541	C₂×D₄	—	5	1	no	—
542	C₂×D₄	—	5	1	no	—
543	C₂×D₄	—	5	1	no	—
544	C₂²×C₄	—	5	1	no	—
545	C₂²×C₄	—	5	1	no	—
546	C₂²×C₄	—	5	1	no	—
547	C₂²×C₄	—	5	1	no	—
548	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
549	M₁₆	—	2	2	no	—
550	M₁₆	—	10	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	5	1	no	—
553	C₂×C₈	—	5	1	no	—
554	C₂×C₈	—	5	1	no	—
555	C₂×C₈	—	5	1	no	—
556	C₂×C₈	—	10	2	no	—
557	C₂×C₈	—	10	2	no	—
558	C₂×C₈	—	10	2	no	—
559	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
560	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
561	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
562	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
563	C₄⋊C₄	—	5	1	no	—
564	C₄⋊C₄	—	5	1	no	—
565	C₄⋊C₄	—	5	1	no	—
566	C₄⋊C₄	—	5	1	no	—
567	C₄⋊C₄	—	5	1	no	—
568	C₄⋊C₄	—	5	1	no	—
569	C₄⋊C₄	—	5	1	no	—
570	C₄⋊C₄	—	5	1	no	—
571	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
572	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
573	C₂²⋊C₄	—	5	1	no	—
574	C₂²⋊C₄	—	5	1	no	—
575	C₂²⋊C₄	—	5	1	no	—
576	C₂²⋊C₄	—	5	1	no	—
577	C₂²⋊C₄	—	5	1	no	—
578	C₂²⋊C₄	—	5	1	no	—
579	C₂²⋊C₄	—	5	1	no	—
580	C₂²⋊C₄	—	5	1	no	—
581	C₂²⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
582	C₂²⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
583	C₄²	—	5	1	no	—
584	C₄²	—	5	1	no	—
585	C₄²	—	5	1	no	—
586	C₄²	—	5	1	no	—
587	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
588	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
589	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
590	C₂²×C₃	—	2	1	no	—
591	C₂²×C₃	—	2	1	no	—
592	C₂²×C₃	—	2	1	no	—
593	C₂²×C₃	—	5	2	no	—
594	C₂²×C₃	—	10	1	no	—
595	C₂²×C₃	—	10	1	no	—
596	C₂²×C₃	—	10	1	no	—
597	C₂²×C₃	—	10	1	no	—
598	C₂²×C₃	—	10	1	no	—
599	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	1	no	—
602	C₃×C₄	—	2	1	no	—
603	C₃×C₄	—	2	1	no	—
604	C₃×C₄	—	2	1	no	—
605	C₃×C₄	—	10	1	no	—
606	C₃×C₄	—	10	1	no	—
607	C₃×C₄	—	10	1	no	—
608	C₃×C₄	—	10	1	no	—
609	C₃×C₄	—	10	1	no	—
610	C₃×C₄	—	10	1	no	—
611	C₃×C₄	C₂×#709	1	1	yes	characteristic
612	C₃×C₄	C₂×#709	1	1	yes	characteristic
613	C₂×C₅	—	4	1	no	—
614	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
615	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
616	C₂×C₅	C₃×#568	1	1	yes	characteristic
617	D₅	—	2	2	no	—
618	D₅	—	4	1	no	—
619	C₂³	—	5	1	no	—
620	C₂³	—	5	1	no	—
621	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
622	Q₈	—	20	1	no	—
623	D₄	—	10	2	no	—
624	D₄	—	10	2	no	—
625	D₄	—	20	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	5	1	no	—
629	C₂×C₄	—	5	1	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	1	no	—
632	C₂×C₄	—	5	1	no	—
633	C₂×C₄	—	5	1	no	—
634	C₂×C₄	—	10	2	no	—
635	C₂×C₄	—	10	1	no	—
636	C₂×C₄	—	10	1	no	—
637	C₂×C₄	—	10	1	no	—
638	C₂×C₄	—	10	1	no	—
639	C₂×C₄	—	20	1	no	—
640	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
641	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
642	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
643	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
644	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	10	1	no	—
649	C₈	—	10	1	no	—
650	C₈	—	10	1	no	—
651	C₈	—	10	1	no	—
652	C₈	C₃×#709	1	2	yes	—
653	C₈	C₃×#709	1	2	yes	—
654	C₂×C₃	—	4	1	no	—
655	C₂×C₃	—	10	2	no	—
656	C₂×C₃	—	20	1	no	—
657	C₂×C₃	C₄×#709	1	1	yes	characteristic
658	C₂×C₃	D₅×#131	1	1	yes	characteristic
659	C₂×C₃	#66084	1	1	yes	characteristic
660	C₅	C₃×#2968	1	1	yes	characteristic, complemented, Sylow
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	5	2	no	—
665	C₂²	—	10	1	no	—
666	C₂²	—	10	1	no	—
667	C₂²	—	10	1	no	—
668	C₂²	—	10	1	no	—
669	C₂²	—	10	1	no	—
670	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	10	1	no	—
677	C₄	—	10	1	no	—
678	C₄	—	10	1	no	—
679	C₄	—	10	1	no	—
680	C₄	—	10	1	no	—
681	C₄	—	10	1	no	—
682	C₄	C₂×C₃×#709	1	1	yes	characteristic
683	C₄	C₂×C₃×#709	1	1	yes	characteristic
684	C₃	#10610289	1	1	yes	characteristic, direct product factor, Sylow
685	C₂	—	4	1	no	—
686	C₂	—	10	2	no	—
687	C₂	—	20	1	no	—
688	C₂	C₃×C₄×#709	1	1	yes	characteristic
689	C₂	C₃×D₅×#131	1	1	yes	characteristic
690	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	C₃×#4030	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2968
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
2. C₃×C₅×#405	C₂	semidirect
3. C₃×#65416	C₂	semidirect
4. C₃×#65416	C₂	semidirect
5. C₃×#65400	C₂	semidirect
6. C₃×C₈×C₂²⋊D₅	C₂	semidirect
7. C₃×#65289	C₂	semidirect
8. C₃×#64997	C₂	semidirect
9. C₃×#64995	C₂	semidirect
10. C₃×D₅×#97	C₂	semidirect
11. C₃×#64990	C₂	semidirect
12. C₃×#64979	C₂	semidirect
13. C₃×C₈×D₂₀	C₂	semidirect
14. C₃×#64974	C₂	semidirect
15. C₃×#64968	C₂	semidirect
16. #10610289	C₃	direct (N × H)
62. C₅×#405	C₂×C₃	semidirect
63. #65416	C₂×C₃	semidirect
64. #65416	C₂×C₃	semidirect
65. #65400	C₂×C₃	semidirect
66. C₈×C₂²⋊D₅	C₂×C₃	semidirect
67. #65289	C₂×C₃	semidirect
68. #64997	C₂×C₃	semidirect
69. #64995	C₂×C₃	semidirect
70. D₅×#97	C₂×C₃	semidirect
71. #64990	C₂×C₃	semidirect
72. #64979	C₂×C₃	semidirect
73. C₈×D₂₀	C₂×C₃	semidirect
74. #64974	C₂×C₃	semidirect
75. #64968	C₂×C₃	semidirect
138. C₃×#405	D₅	semidirect
324. #405	C₃×D₅	semidirect
589. C₃×C₅	#2968	semidirect
660. C₅	C₃×#2968	semidirect
684. C₃	#10610289	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×#65862	2
C₃×C₅×#405	2
C₃×#65416	2
C₃×#65400	2
C₃×C₈×C₂²⋊D₅	2
C₃×#65289	2
C₃×#64997	2
C₃×#64995	2
C₃×D₅×#97	2
C₃×#64990	2
C₃×#64979	2
C₃×C₈×D₂₀	2
C₃×#64974	2
C₃×#64968	2
#10610289	3
C₃×#2968	5

Subgroups — C3×#10610289 #14419575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610289 #14419575