Subgroups — C₃×#10610254 #14418970

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65417	C₂	1	2	yes	maximal, complemented
4	C₃×#65416	C₂	1	2	yes	maximal, complemented
5	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64995	C₂	1	2	yes	maximal, complemented
7	C₃×#64990	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64974	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64974	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610254	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₄	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
17	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
18	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
20	C₃×#4072	C₄	1	1	yes	characteristic
21	C₂×C₃×#676	C₂²	1	2	yes	—
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
24	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
25	C₃×#4018	C₄	1	1	yes	characteristic
26	C₃×#4018	C₄	1	1	yes	characteristic
27	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
28	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
30	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊#168	C₂²	1	2	yes	—
35	C₃×#3952	C₂²	1	2	yes	—
36	C₃×#3952	C₂²	1	2	yes	—
37	C₃×#3947	C₂²	1	2	yes	—
38	C₃×#3946	C₂²	1	2	yes	—
39	C₃×#3946	C₂²	1	2	yes	—
40	C₃×C₈×Dic₅	C₂²	1	2	yes	—
41	C₃×C₄⋊#168	C₂²	1	2	yes	—
42	C₃×C₄×#168	C₂²	1	1	yes	characteristic
43	C₃×C₄×#168	C₂²	1	1	yes	characteristic
44	C₃×#2965	—	5	1	no	maximal, Hall
45	C₄×#709	C₂×C₃	1	1	yes	characteristic
46	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
47	#65417	C₂×C₃	1	2	yes	complemented
48	#65416	C₂×C₃	1	2	yes	complemented
49	#65214	C₂×C₃	1	1	yes	characteristic, complemented
50	#64995	C₂×C₃	1	2	yes	complemented
51	#64990	C₂×C₃	1	2	yes	complemented
52	C₄×#676	C₂×C₃	1	1	yes	characteristic, complemented
53	#64974	C₂×C₃	1	1	yes	characteristic, complemented
54	#64974	C₂×C₃	1	1	yes	characteristic, complemented
55	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
61	C₃×#709	—	2	4	no	—
62	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
70	C₃×C₅×M₁₆	—	2	4	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×#685	C₂×C₄	1	1	yes	characteristic
80	C₃×#685	C₂×C₄	1	1	yes	characteristic
81	C₃×#685	C₂×C₄	1	1	yes	characteristic
82	C₃×#685	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₃×#683	C₂×C₄	1	1	yes	characteristic
86	C₃×#683	C₂×C₄	1	1	yes	characteristic
87	C₃×#683	C₂×C₄	1	1	yes	characteristic
88	C₃×#683	C₂×C₄	1	1	yes	characteristic
89	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
90	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
91	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
93	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
94	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
95	C₂×C₃×#168	C₂³	1	2	yes	—
96	C₂×C₃×#168	C₂³	1	2	yes	—
97	C₃×#676	—	2	4	no	—
98	C₃×C₈×D₅	—	2	4	no	—
99	C₃×C₄×#41	—	5	1	no	—
100	C₃×#446	—	5	2	no	—
101	C₃×#436	—	5	2	no	—
102	C₃×#435	—	5	2	no	—
103	C₃×#435	—	5	2	no	—
104	C₃×#431	—	5	1	no	—
105	C₃×#431	—	5	1	no	—
106	C₃×#431	—	5	1	no	—
107	C₃×C₄×M₁₆	—	5	1	no	—
108	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
109	C₂×C₃×C₄×C₈	—	5	1	no	—
110	C₂×#709	C₃×C₄	1	1	yes	characteristic
111	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
112	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₂²⋊D₅	C₃×C₄	1	1	yes	characteristic
114	C₄×C₂²⋊D₅	C₃×C₄	1	1	yes	characteristic
115	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
117	#4072	C₃×C₄	1	1	yes	characteristic
118	C₂×#676	C₂²×C₃	1	2	yes	—
119	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
120	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic
121	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
122	#4018	C₃×C₄	1	1	yes	characteristic
123	#4018	C₃×C₄	1	1	yes	characteristic
124	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
125	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
127	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
128	C₅×#97	C₂²×C₃	1	2	yes	—
129	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
130	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
131	C₂²⋊#168	C₂²×C₃	1	2	yes	—
132	#3952	C₂²×C₃	1	2	yes	—
133	#3952	C₂²×C₃	1	2	yes	—
134	#3947	C₂²×C₃	1	2	yes	—
135	#3946	C₂²×C₃	1	2	yes	—
136	#3946	C₂²×C₃	1	2	yes	—
137	C₈×Dic₅	C₂²×C₃	1	2	yes	—
138	C₄⋊#168	C₂²×C₃	1	2	yes	—
139	C₄×#168	C₂²×C₃	1	1	yes	characteristic
140	C₄×#168	C₂²×C₃	1	1	yes	characteristic
141	#2965	—	5	1	no	Sylow
142	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₂²⋊D₅	—	2	2	no	—
155	C₃×C₂²⋊D₅	—	2	2	no	—
156	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₃×D₂₀	—	2	2	no	—
163	C₃×C₄×D₅	—	2	2	no	—
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	—	2	2	no	—
166	C₃×C₄×D₅	—	2	2	no	—
167	C₃×C₄×D₅	—	2	2	no	—
168	C₃×C₄×D₅	M₁₆	1	4	yes	complemented
169	C₃×Dic₁₀	—	2	2	no	—
170	C₃×C₅×C₈	—	2	2	no	—
171	C₃×C₅×C₈	#41	1	4	yes	complemented
172	C₃×#168	—	2	2	no	—
173	C₃×#168	—	2	2	no	—
174	C₂×C₃×#41	—	5	1	no	—
175	C₂×C₃×M₁₆	—	5	2	no	—
176	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
177	C₂²×C₃×C₈	—	5	2	no	—
178	C₃×C₄×Q₈	—	5	1	no	—
179	C₃×C₄×Q₈	—	5	1	no	—
180	C₃×C₄×D₄	—	5	1	no	—
181	C₃×C₄×D₄	—	5	1	no	—
182	C₃×C₄×D₄	—	5	1	no	—
183	C₃×C₄×D₄	—	5	1	no	—
184	C₃×C₄×D₄	—	5	1	no	—
185	C₃×C₄×D₄	—	5	1	no	—
186	C₃×#117	—	5	1	no	—
187	C₃×#117	—	5	1	no	—
188	C₃×#117	—	5	1	no	—
189	C₂×C₃×C₄²	—	5	1	no	—
190	C₂×C₃×C₄²	—	5	1	no	—
191	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
192	C₃×C₄⋊C₈	—	5	2	no	—
193	C₃×C₄⋊C₈	—	5	2	no	—
194	C₃×C₄⋊C₈	—	5	2	no	—
195	C₃×C₂²⋊C₈	—	5	2	no	—
196	C₃×C₂²⋊C₈	—	5	2	no	—
197	C₃×C₂²⋊C₈	—	5	2	no	—
198	C₃×#97	—	5	2	no	—
199	C₃×#97	C₂×D₅	1	2	yes	—
200	C₃×C₄×C₈	—	5	2	no	—
201	C₃×C₄×C₈	—	5	1	no	—
202	C₃×C₄×C₈	—	5	1	no	—
203	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
204	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
210	#709	—	2	4	no	—
211	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
212	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
214	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
216	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
219	C₅×M₁₆	—	2	4	no	—
220	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
221	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
222	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
223	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
224	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
227	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
228	#685	C₂×C₃×C₄	1	1	yes	characteristic
229	#685	C₂×C₃×C₄	1	1	yes	characteristic
230	#685	C₂×C₃×C₄	1	1	yes	characteristic
231	#685	C₂×C₃×C₄	1	1	yes	characteristic
232	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
233	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
234	#683	C₂×C₃×C₄	1	1	yes	characteristic
235	#683	C₂×C₃×C₄	1	1	yes	characteristic
236	#683	C₂×C₃×C₄	1	1	yes	characteristic
237	#683	C₂×C₃×C₄	1	1	yes	characteristic
238	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
239	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
240	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
241	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
242	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
243	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
244	C₂×#168	C₂³×C₃	1	2	yes	—
245	C₂×#168	C₂³×C₃	1	2	yes	—
246	#676	—	2	4	no	—
247	C₈×D₅	—	2	4	no	—
248	C₄×#41	—	5	1	no	—
249	#446	—	5	2	no	—
250	#436	—	5	2	no	—
251	#435	—	5	2	no	—
252	#435	—	5	2	no	—
253	#431	—	5	1	no	—
254	#431	—	5	1	no	—
255	#431	—	5	1	no	—
256	C₄×M₁₆	—	5	1	no	—
257	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
258	C₂×C₄×C₈	—	5	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₃×D₅	—	2	1	no	—
264	C₂×C₃×D₅	—	2	1	no	—
265	C₂×C₃×D₅	—	2	1	no	—
266	C₂×C₃×D₅	—	2	1	no	—
267	C₂×C₃×D₅	—	2	1	no	—
268	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
273	C₃×C₄×C₅	#131	1	2	yes	—
274	C₃×C₄×C₅	C₂×#41	1	2	yes	—
275	C₃×Dic₅	—	2	1	no	—
276	C₃×Dic₅	—	2	1	no	—
277	C₃×Dic₅	—	2	1	no	—
278	C₃×Dic₅	—	2	1	no	—
279	C₃×Dic₅	—	2	1	no	—
280	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
281	C₃×#41	—	10	4	no	—
282	C₂×C₃×Q₈	—	5	1	no	—
283	C₂×C₃×D₄	—	5	1	no	—
284	C₂×C₃×D₄	—	5	1	no	—
285	C₂×C₃×D₄	—	5	1	no	—
286	C₂²×C₃×C₄	—	5	1	no	—
287	C₂²×C₃×C₄	—	5	1	no	—
288	C₂²×C₃×C₄	—	5	1	no	—
289	C₂²×C₃×C₄	—	5	1	no	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	1	no	—
292	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
295	C₃×M₁₆	—	2	4	no	—
296	C₃×M₁₆	—	10	4	no	—
297	C₂×C₃×C₈	—	5	2	no	—
298	C₂×C₃×C₈	—	5	2	no	—
299	C₂×C₃×C₈	—	10	4	no	—
300	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
301	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
302	C₃×C₄⋊C₄	—	5	1	no	—
303	C₃×C₄⋊C₄	—	5	1	no	—
304	C₃×C₄⋊C₄	—	5	1	no	—
305	C₃×C₄⋊C₄	—	5	1	no	—
306	C₃×C₄⋊C₄	—	5	1	no	—
307	C₃×C₄⋊C₄	—	5	1	no	—
308	C₃×C₂²⋊C₄	—	5	1	no	—
309	C₃×C₂²⋊C₄	—	5	1	no	—
310	C₃×C₂²⋊C₄	—	5	1	no	—
311	C₃×C₂²⋊C₄	—	5	1	no	—
312	C₃×C₂²⋊C₄	—	5	1	no	—
313	C₃×C₂²⋊C₄	—	5	1	no	—
314	C₃×C₄²	—	5	1	no	—
315	C₃×C₄²	—	5	1	no	—
316	C₃×C₄²	—	5	1	no	—
317	C₃×C₄²	—	5	1	no	—
318	C₃×C₄²	—	5	1	no	—
319	C₃×C₄²	—	5	1	no	—
320	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
321	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
322	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
323	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
324	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
325	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
336	C₂²⋊D₅	—	2	2	no	—
337	C₂²⋊D₅	—	2	2	no	—
338	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
340	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
341	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
342	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
343	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
344	D₂₀	—	2	2	no	—
345	C₄×D₅	—	2	2	no	—
346	C₄×D₅	—	2	2	no	—
347	C₄×D₅	—	2	2	no	—
348	C₄×D₅	—	2	2	no	—
349	C₄×D₅	—	2	2	no	—
350	C₄×D₅	C₃×M₁₆	1	4	yes	complemented
351	Dic₁₀	—	2	2	no	—
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	C₃×#41	1	4	yes	complemented
354	#168	—	2	2	no	—
355	#168	—	2	2	no	—
356	C₂×#41	—	5	1	no	—
357	C₂×M₁₆	—	5	2	no	—
358	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
359	C₂²×C₈	—	5	2	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×D₄	—	5	1	no	—
363	C₄×D₄	—	5	1	no	—
364	C₄×D₄	—	5	1	no	—
365	C₄×D₄	—	5	1	no	—
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	5	1	no	—
368	#117	—	5	1	no	—
369	#117	—	5	1	no	—
370	#117	—	5	1	no	—
371	C₂×C₄²	—	5	1	no	—
372	C₂×C₄²	—	5	1	no	—
373	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
374	C₄⋊C₈	—	5	2	no	—
375	C₄⋊C₈	—	5	2	no	—
376	C₄⋊C₈	—	5	2	no	—
377	C₂²⋊C₈	—	5	2	no	—
378	C₂²⋊C₈	—	5	2	no	—
379	C₂²⋊C₈	—	5	2	no	—
380	#97	—	5	2	no	—
381	#97	C₂×C₃×D₅	1	2	yes	—
382	C₄×C₈	—	5	2	no	—
383	C₄×C₈	—	5	1	no	—
384	C₄×C₈	—	5	1	no	—
385	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
386	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
387	C₂×C₃×C₅	—	4	1	no	—
388	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
389	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
391	C₃×D₅	—	2	2	no	—
392	C₃×D₅	—	4	1	no	—
393	C₂³×C₃	—	5	1	no	—
394	C₂³×C₃	—	5	1	no	—
395	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
396	C₃×Q₈	—	10	2	no	—
397	C₃×D₄	—	10	2	no	—
398	C₃×D₄	—	10	2	no	—
399	C₃×D₄	—	10	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	5	1	no	—
404	C₂×C₃×C₄	—	5	4	no	—
405	C₂×C₃×C₄	—	5	1	no	—
406	C₂×C₃×C₄	—	5	1	no	—
407	C₂×C₃×C₄	—	5	1	no	—
408	C₂×C₃×C₄	—	5	1	no	—
409	C₂×C₃×C₄	—	5	1	no	—
410	C₂×C₃×C₄	—	10	2	no	—
411	C₂×C₃×C₄	—	10	2	no	—
412	C₂×C₃×C₄	—	10	2	no	—
413	C₂×C₃×C₄	—	10	2	no	—
414	C₂×C₃×C₄	—	10	2	no	—
415	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
421	C₃×C₈	—	2	2	no	—
422	C₃×C₈	—	10	2	no	—
423	C₃×C₈	—	10	2	no	—
424	C₃×C₈	#709	1	4	yes	complemented
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	1	no	—
428	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	2	1	no	—
432	C₂×D₅	—	2	1	no	—
433	C₂×D₅	—	2	1	no	—
434	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
439	C₄×C₅	C₃×#131	1	2	yes	—
440	C₄×C₅	C₂×C₃×#41	1	2	yes	—
441	Dic₅	—	2	1	no	—
442	Dic₅	—	2	1	no	—
443	Dic₅	—	2	1	no	—
444	Dic₅	—	2	1	no	—
445	Dic₅	—	2	1	no	—
446	Dic₅	C₂×C₃×M₁₆	1	2	yes	—
447	#41	—	10	4	no	—
448	C₂×Q₈	—	5	1	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	—	5	1	no	—
452	C₂²×C₄	—	5	1	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	1	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	5	1	no	—
458	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
459	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
461	M₁₆	—	2	4	no	—
462	M₁₆	—	10	4	no	—
463	C₂×C₈	—	5	2	no	—
464	C₂×C₈	—	5	2	no	—
465	C₂×C₈	—	10	4	no	—
466	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
467	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	5	1	no	—
473	C₄⋊C₄	—	5	1	no	—
474	C₂²⋊C₄	—	5	1	no	—
475	C₂²⋊C₄	—	5	1	no	—
476	C₂²⋊C₄	—	5	1	no	—
477	C₂²⋊C₄	—	5	1	no	—
478	C₂²⋊C₄	—	5	1	no	—
479	C₂²⋊C₄	—	5	1	no	—
480	C₄²	—	5	1	no	—
481	C₄²	—	5	1	no	—
482	C₄²	—	5	1	no	—
483	C₄²	—	5	1	no	—
484	C₄²	—	5	1	no	—
485	C₄²	—	5	1	no	—
486	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
487	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
488	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
489	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
490	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	5	2	no	—
495	C₂²×C₃	—	10	1	no	—
496	C₂²×C₃	—	10	1	no	—
497	C₂²×C₃	—	10	1	no	—
498	C₂²×C₃	—	10	1	no	—
499	C₂²×C₃	—	10	1	no	—
500	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	5	2	no	—
505	C₃×C₄	—	10	1	no	—
506	C₃×C₄	—	10	1	no	—
507	C₃×C₄	—	10	1	no	—
508	C₃×C₄	—	10	1	no	—
509	C₃×C₄	—	10	1	no	—
510	C₃×C₄	D₅×M₁₆	1	2	yes	—
511	C₃×C₄	#4053	1	2	yes	—
512	C₃×C₄	C₂×#709	1	2	yes	—
513	C₂×C₅	—	4	1	no	—
514	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
515	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
516	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
517	D₅	—	2	2	no	—
518	D₅	—	4	1	no	—
519	C₂³	—	5	1	no	—
520	C₂³	—	5	1	no	—
521	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
522	Q₈	—	10	2	no	—
523	D₄	—	10	2	no	—
524	D₄	—	10	2	no	—
525	D₄	—	10	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	5	1	no	—
530	C₂×C₄	—	5	4	no	—
531	C₂×C₄	—	5	1	no	—
532	C₂×C₄	—	5	1	no	—
533	C₂×C₄	—	5	1	no	—
534	C₂×C₄	—	5	1	no	—
535	C₂×C₄	—	5	1	no	—
536	C₂×C₄	—	10	2	no	—
537	C₂×C₄	—	10	2	no	—
538	C₂×C₄	—	10	2	no	—
539	C₂×C₄	—	10	2	no	—
540	C₂×C₄	—	10	2	no	—
541	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
542	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
543	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
544	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
545	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
546	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	10	2	no	—
549	C₈	—	10	2	no	—
550	C₈	C₃×#709	1	4	yes	complemented
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	—	10	2	no	—
553	C₂×C₃	—	20	1	no	—
554	C₂×C₃	C₄×#709	1	1	yes	characteristic
555	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
556	C₂×C₃	C₂×#4053	1	1	yes	characteristic
557	C₅	C₃×#2965	1	1	yes	characteristic, complemented, Sylow
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	5	2	no	—
562	C₂²	—	10	1	no	—
563	C₂²	—	10	1	no	—
564	C₂²	—	10	1	no	—
565	C₂²	—	10	1	no	—
566	C₂²	—	10	1	no	—
567	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	5	2	no	—
572	C₄	—	10	1	no	—
573	C₄	—	10	1	no	—
574	C₄	—	10	1	no	—
575	C₄	—	10	1	no	—
576	C₄	—	10	1	no	—
577	C₄	C₃×D₅×M₁₆	1	2	yes	—
578	C₄	C₃×#4053	1	2	yes	—
579	C₄	C₂×C₃×#709	1	2	yes	—
580	C₃	#10610254	1	1	yes	characteristic, direct product factor, Sylow
581	C₂	—	4	1	no	—
582	C₂	—	10	2	no	—
583	C₂	—	20	1	no	—
584	C₂	C₃×C₄×#709	1	1	yes	characteristic
585	C₂	C₂×C₃×D₅×M₁₆	1	1	yes	characteristic
586	C₂	C₂×C₃×#4053	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×#2965
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
3. C₃×#65417	C₂	semidirect
4. C₃×#65416	C₂	semidirect
5. C₃×#65214	C₂	semidirect
6. C₃×#64995	C₂	semidirect
7. C₃×#64990	C₂	semidirect
8. C₃×C₄×#676	C₂	semidirect
9. C₃×#64974	C₂	semidirect
10. C₃×#64974	C₂	semidirect
11. C₃×C₄×C₈×D₅	C₂	semidirect
12. #10610254	C₃	direct (N × H)
46. C₄×C₅×M₁₆	C₂×C₃	semidirect
47. #65417	C₂×C₃	semidirect
48. #65416	C₂×C₃	semidirect
49. #65214	C₂×C₃	semidirect
50. #64995	C₂×C₃	semidirect
51. #64990	C₂×C₃	semidirect
52. C₄×#676	C₂×C₃	semidirect
53. #64974	C₂×C₃	semidirect
54. #64974	C₂×C₃	semidirect
55. C₄×C₈×D₅	C₂×C₃	semidirect
108. C₃×C₄×M₁₆	D₅	semidirect
168. C₃×C₄×D₅	M₁₆	semidirect
171. C₃×C₅×C₈	#41	semidirect
257. C₄×M₁₆	C₃×D₅	semidirect
350. C₄×D₅	C₃×M₁₆	semidirect
353. C₅×C₈	C₃×#41	semidirect
424. C₃×C₈	#709	semidirect
490. C₃×C₅	#2965	semidirect
550. C₈	C₃×#709	semidirect
557. C₅	C₃×#2965	semidirect
580. C₃	#10610254	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×#709	2
C₃×C₄×C₅×M₁₆	2
C₃×#65417	2
C₃×#65416	2
C₃×#65214	2
C₃×#64995	2
C₃×#64990	2
C₃×C₄×#676	2
C₃×#64974	2
C₃×C₄×C₈×D₅	2
#10610254	3
C₃×#2965	5

Subgroups — C3×#10610254 #14418970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610254 #14418970