Subgroups — C₃×#10614649 #14415449

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65523	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65301	C₂	1	2	yes	maximal, complemented
7	C₃×#65300	C₂	1	2	yes	maximal, complemented
8	C₃×#65300	C₂	1	2	yes	maximal, complemented
9	C₃×D₄×#168	C₂	1	2	yes	maximal, complemented
10	C₃×#65288	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614649	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#123	C₄	1	2	yes	—
16	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₃×C₅×#121	C₄	1	1	yes	characteristic
19	C₃×C₅×#121	C₄	1	1	yes	characteristic
20	C₃×C₅×#120	C₄	1	2	yes	—
21	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₃×#4094	—	2	4	no	—
25	C₂×C₃×#681	—	2	4	no	—
26	C₂×C₃×#681	C₂²	1	1	yes	characteristic
27	C₂×C₃×#681	C₂²	1	2	yes	—
28	C₂×C₃×#681	C₂²	1	1	yes	characteristic
29	C₂×C₃×#681	C₂²	1	2	yes	complemented
30	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
31	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
32	C₂²×C₃×#168	C₂²	1	2	yes	—
33	C₂²×C₃×#168	C₂²	1	2	yes	complemented
34	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
37	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
38	C₃×C₂²⋊#168	C₂²	1	2	yes	complemented
39	C₃×C₂²⋊#168	C₂²	1	2	yes	complemented
40	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
41	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
42	C₃×#3935	C₂²	1	2	yes	complemented
43	C₃×C₄×#168	C₂²	1	2	yes	complemented
44	C₃×#2933	—	5	1	no	maximal, Hall
45	C₅×#525	C₂×C₃	1	1	yes	characteristic
46	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂²×#681	C₂×C₃	1	1	yes	characteristic, complemented
48	#65523	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
50	#65301	C₂×C₃	1	2	yes	complemented
51	#65300	C₂×C₃	1	2	yes	complemented
52	#65300	C₂×C₃	1	2	yes	complemented
53	D₄×#168	C₂×C₃	1	2	yes	complemented
54	#65288	C₂×C₃	1	1	yes	characteristic, complemented
55	#65286	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
61	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
62	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
79	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
82	C₃×C₄²×C₅	C₂³	1	2	yes	—
83	C₃×#681	—	2	2	no	—
84	C₃×#681	—	2	4	no	—
85	C₃×#681	—	2	4	no	—
86	C₃×#681	D₄	1	4	yes	complemented
87	C₂×C₃×#168	—	2	2	no	—
88	C₂×C₃×#168	—	2	2	no	—
89	C₂×C₃×#168	—	2	4	no	—
90	C₂×C₃×#168	—	2	4	no	—
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	1	yes	characteristic
93	C₂×C₃×#168	C₂³	1	1	yes	characteristic
94	C₂×C₃×#168	C₂³	1	1	yes	characteristic
95	C₂×C₃×#168	C₂³	1	2	yes	—
96	C₂×C₃×#168	C₂³	1	2	yes	—
97	C₂×C₃×#131	—	5	1	no	—
98	C₂²×C₃×M₁₆	—	5	1	no	—
99	C₃×#525	D₅	1	1	yes	characteristic
100	C₃×#436	—	5	2	no	—
101	C₃×#435	—	5	2	no	—
102	C₃×#435	—	5	2	no	—
103	C₃×C₈×D₄	—	5	2	no	—
104	C₃×#424	—	5	1	no	—
105	C₃×#408	—	5	1	no	—
106	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
107	C₃×#405	—	5	1	no	—
108	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
110	C₅×#123	C₃×C₄	1	2	yes	—
111	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
112	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
113	C₅×#121	C₃×C₄	1	1	yes	characteristic
114	C₅×#121	C₃×C₄	1	1	yes	characteristic
115	C₅×#120	C₃×C₄	1	2	yes	—
116	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
117	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
118	C₅×#117	C₂²×C₃	1	1	yes	characteristic
119	#4094	—	2	4	no	—
120	C₂×#681	—	2	4	no	—
121	C₂×#681	C₂²×C₃	1	1	yes	characteristic
122	C₂×#681	C₂²×C₃	1	2	yes	—
123	C₂×#681	C₂²×C₃	1	1	yes	characteristic
124	C₂×#681	C₂²×C₃	1	2	yes	complemented
125	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
126	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
127	C₂²×#168	C₂²×C₃	1	2	yes	—
128	C₂²×#168	C₂²×C₃	1	2	yes	complemented
129	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
130	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
131	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
132	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
133	C₂²⋊#168	C₂²×C₃	1	2	yes	complemented
134	C₂²⋊#168	C₂²×C₃	1	2	yes	complemented
135	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
136	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
137	#3935	C₂²×C₃	1	2	yes	complemented
138	C₄×#168	C₂²×C₃	1	2	yes	complemented
139	#2933	—	5	1	no	Sylow
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	4	1	no	—
143	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
145	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×D₄	—	2	4	no	—
149	C₃×C₅×D₄	—	2	4	no	—
150	C₃×C₅×D₄	—	2	2	no	—
151	C₃×C₅×D₄	—	4	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	1	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
168	C₂×C₃×C₄×C₅	#41	1	2	yes	—
169	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
170	C₃×#168	—	2	1	no	—
171	C₃×#168	—	2	1	no	—
172	C₃×#168	—	2	2	no	—
173	C₃×#168	—	2	1	no	—
174	C₃×#168	—	2	1	no	—
175	C₃×#168	C₂×D₄	1	4	yes	—
176	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
177	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
178	C₃×#131	—	10	4	no	—
179	C₂×C₃×M₁₆	—	5	1	no	—
180	C₂×C₃×M₁₆	—	5	1	no	—
181	C₂×C₃×M₁₆	—	5	2	no	—
182	C₂×C₃×M₁₆	—	5	2	no	—
183	C₂×C₃×M₁₆	—	10	4	no	—
184	C₂²×C₃×C₈	—	5	2	no	—
185	C₂²×C₃×C₈	—	5	1	no	—
186	C₂²×C₃×C₈	—	5	2	no	—
187	C₂²×C₃×C₈	—	5	1	no	—
188	C₃×#123	Dic₅	1	2	yes	—
189	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
190	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
191	C₃×#121	Dic₅	1	1	yes	characteristic
192	C₃×#121	Dic₅	1	1	yes	characteristic
193	C₃×#120	Dic₅	1	2	yes	—
194	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
195	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
196	C₃×#117	C₂×D₅	1	1	yes	characteristic
197	C₃×C₄⋊C₈	—	5	2	no	—
198	C₃×C₄⋊C₈	—	5	2	no	—
199	C₃×C₂²⋊C₈	—	5	1	no	—
200	C₃×C₂²⋊C₈	—	5	1	no	—
201	C₃×C₂²⋊C₈	—	5	1	no	—
202	C₃×C₂²⋊C₈	—	5	1	no	—
203	C₃×C₂²⋊C₈	—	5	2	no	—
204	C₃×C₂²⋊C₈	—	5	2	no	—
205	C₃×#97	—	5	2	no	—
206	C₃×C₄×C₈	—	5	2	no	—
207	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₅×#41	—	2	2	no	—
209	C₅×#41	—	2	2	no	—
210	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
212	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
213	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
214	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
215	C₂²×C₄×C₅	—	2	2	no	—
216	C₂²×C₄×C₅	—	2	2	no	—
217	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
223	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
225	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
227	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
228	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
229	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
230	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
231	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
232	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
233	C₄²×C₅	C₂³×C₃	1	2	yes	—
234	#681	—	2	2	no	—
235	#681	—	2	4	no	—
236	#681	—	2	4	no	—
237	#681	C₃×D₄	1	4	yes	complemented
238	C₂×#168	—	2	2	no	—
239	C₂×#168	—	2	2	no	—
240	C₂×#168	—	2	4	no	—
241	C₂×#168	—	2	4	no	—
242	C₂×#168	C₂³×C₃	1	1	yes	characteristic
243	C₂×#168	C₂³×C₃	1	1	yes	characteristic
244	C₂×#168	C₂³×C₃	1	1	yes	characteristic
245	C₂×#168	C₂³×C₃	1	1	yes	characteristic
246	C₂×#168	C₂³×C₃	1	2	yes	—
247	C₂×#168	C₂³×C₃	1	2	yes	—
248	C₂×#131	—	5	1	no	—
249	C₂²×M₁₆	—	5	1	no	—
250	#525	C₃×D₅	1	1	yes	characteristic
251	#436	—	5	2	no	—
252	#435	—	5	2	no	—
253	#435	—	5	2	no	—
254	C₈×D₄	—	5	2	no	—
255	#424	—	5	1	no	—
256	#408	—	5	1	no	—
257	C₂×C₂²⋊C₈	—	5	1	no	—
258	#405	—	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	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	2	1	no	—
267	C₂²×C₃×C₅	—	2	1	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	4	4	no	—
270	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
271	C₂²×C₃×C₅	#131	1	2	yes	complemented
272	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
273	C₃×C₄×C₅	—	2	1	no	—
274	C₃×C₄×C₅	—	2	1	no	—
275	C₃×C₄×C₅	—	2	2	no	—
276	C₃×C₄×C₅	—	2	2	no	—
277	C₃×C₄×C₅	—	2	2	no	—
278	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
279	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
281	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
282	C₃×#41	—	2	2	no	—
283	C₃×#41	—	2	2	no	—
284	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
285	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
286	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
287	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
288	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	2	2	no	—
291	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
296	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
298	C₃×M₁₆	—	5	4	no	—
299	C₃×M₁₆	—	10	4	no	—
300	C₃×M₁₆	—	10	4	no	—
301	C₃×M₁₆	—	10	2	no	—
302	C₂×C₃×C₈	—	5	2	no	—
303	C₂×C₃×C₈	—	5	1	no	—
304	C₂×C₃×C₈	—	5	1	no	—
305	C₂×C₃×C₈	—	5	1	no	—
306	C₂×C₃×C₈	—	5	1	no	—
307	C₂×C₃×C₈	—	5	2	no	—
308	C₂×C₃×C₈	—	10	4	no	—
309	C₂×C₃×C₈	—	10	4	no	—
310	C₂×C₃×C₈	—	10	2	no	—
311	C₂×C₃×C₈	—	10	2	no	—
312	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
313	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
314	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
315	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
316	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
317	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
318	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
319	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
320	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
321	C₃×C₄²	C₂²×D₅	1	2	yes	—
322	C₂³×C₅	—	2	2	no	—
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	4	1	no	—
325	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
327	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
328	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
329	C₅×Q₈	—	2	2	no	—
330	C₅×D₄	—	2	4	no	—
331	C₅×D₄	—	2	4	no	—
332	C₅×D₄	—	2	2	no	—
333	C₅×D₄	—	4	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
344	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
345	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
348	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
350	C₂×C₄×C₅	C₃×#41	1	2	yes	—
351	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
352	#168	—	2	1	no	—
353	#168	—	2	1	no	—
354	#168	—	2	2	no	—
355	#168	—	2	1	no	—
356	#168	—	2	1	no	—
357	#168	C₂×C₃×D₄	1	4	yes	—
358	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
359	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
360	#131	—	10	4	no	—
361	C₂×M₁₆	—	5	1	no	—
362	C₂×M₁₆	—	5	1	no	—
363	C₂×M₁₆	—	5	2	no	—
364	C₂×M₁₆	—	5	2	no	—
365	C₂×M₁₆	—	10	4	no	—
366	C₂²×C₈	—	5	2	no	—
367	C₂²×C₈	—	5	1	no	—
368	C₂²×C₈	—	5	2	no	—
369	C₂²×C₈	—	5	1	no	—
370	#123	C₃×Dic₅	1	2	yes	—
371	C₂²⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
372	C₂²⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
373	#121	C₃×Dic₅	1	1	yes	characteristic
374	#121	C₃×Dic₅	1	1	yes	characteristic
375	#120	C₃×Dic₅	1	2	yes	—
376	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
377	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
378	#117	C₂×C₃×D₅	1	1	yes	characteristic
379	C₄⋊C₈	—	5	2	no	—
380	C₄⋊C₈	—	5	2	no	—
381	C₂²⋊C₈	—	5	1	no	—
382	C₂²⋊C₈	—	5	1	no	—
383	C₂²⋊C₈	—	5	1	no	—
384	C₂²⋊C₈	—	5	1	no	—
385	C₂²⋊C₈	—	5	2	no	—
386	C₂²⋊C₈	—	5	2	no	—
387	#97	—	5	2	no	—
388	C₄×C₈	—	5	2	no	—
389	C₂×C₃×C₅	—	2	2	no	—
390	C₂×C₃×C₅	—	2	2	no	—
391	C₂×C₃×C₅	—	4	2	no	—
392	C₂×C₃×C₅	—	4	1	no	—
393	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
394	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
395	C₂×C₃×C₅	#568	1	1	yes	characteristic
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	2	no	—
398	C₂³×C₃	—	4	1	no	—
399	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
400	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
401	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
402	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
403	C₃×Q₈	—	2	2	no	—
404	C₃×D₄	—	2	4	no	—
405	C₃×D₄	—	2	4	no	—
406	C₃×D₄	—	2	2	no	—
407	C₃×D₄	—	4	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
418	C₂×C₃×C₄	#711	1	2	yes	—
419	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
420	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
421	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
424	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
426	C₃×C₈	—	5	4	no	—
427	C₃×C₈	—	10	1	no	—
428	C₃×C₈	—	10	2	no	—
429	C₃×C₈	—	10	1	no	—
430	C₃×C₈	—	10	1	no	—
431	C₃×C₈	—	10	1	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	2	1	no	—
436	C₂²×C₅	—	2	2	no	—
437	C₂²×C₅	—	2	1	no	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	4	4	no	—
443	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
444	C₂²×C₅	C₃×#131	1	2	yes	complemented
445	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	2	no	—
448	C₄×C₅	—	2	1	no	—
449	C₄×C₅	—	2	1	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
452	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
453	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
454	C₂⁴	C₂×C₃×Dic₅	1	1	yes	characteristic
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
458	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
459	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
460	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
461	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
469	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
471	M₁₆	—	5	4	no	—
472	M₁₆	—	10	4	no	—
473	M₁₆	—	10	4	no	—
474	M₁₆	—	10	2	no	—
475	C₂×C₈	—	5	2	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	5	1	no	—
479	C₂×C₈	—	5	1	no	—
480	C₂×C₈	—	5	2	no	—
481	C₂×C₈	—	10	4	no	—
482	C₂×C₈	—	10	4	no	—
483	C₂×C₈	—	10	2	no	—
484	C₂×C₈	—	10	2	no	—
485	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
486	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
487	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
488	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
489	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
490	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
491	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
492	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
493	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
494	C₄²	C₂²×C₃×D₅	1	2	yes	—
495	C₃×C₅	#2933	1	1	yes	characteristic, complemented, Hall
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	1	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	1	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	4	4	no	—
507	C₂²×C₃	D₄×Dic₅	1	2	yes	—
508	C₂²×C₃	#4094	1	2	yes	complemented
509	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	2	2	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	D₄×Dic₅	1	2	yes	—
516	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
517	C₃×C₄	C₂×#711	1	1	yes	characteristic
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	—	2	2	no	—
520	C₂×C₅	—	4	1	no	—
521	C₂×C₅	—	4	2	no	—
522	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
523	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
524	C₂×C₅	C₃×#568	1	1	yes	characteristic
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
529	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
530	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
531	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
532	Q₈	—	2	2	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	4	no	—
535	D₄	—	2	2	no	—
536	D₄	—	4	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
547	C₂×C₄	C₃×#711	1	2	yes	—
548	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
549	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
550	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
551	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
553	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
554	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
555	C₈	—	5	4	no	—
556	C₈	—	10	1	no	—
557	C₈	—	10	2	no	—
558	C₈	—	10	1	no	—
559	C₈	—	10	1	no	—
560	C₈	—	10	1	no	—
561	C₂×C₃	—	2	2	no	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	—	4	1	no	—
564	C₂×C₃	—	4	2	no	—
565	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
566	C₂×C₃	C₂×#4094	1	1	yes	characteristic
567	C₂×C₃	#66153	1	1	yes	characteristic
568	C₅	C₃×#2933	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	4	no	—
580	C₂²	C₃×D₄×Dic₅	1	2	yes	—
581	C₂²	C₃×#4094	1	2	yes	complemented
582	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	C₃×D₄×Dic₅	1	2	yes	—
589	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
590	C₄	C₂×C₃×#711	1	1	yes	characteristic
591	C₃	#10614649	1	1	yes	characteristic, direct product factor, Sylow
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	4	1	no	—
595	C₂	—	4	2	no	—
596	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic
597	C₂	C₂×C₃×#4094	1	1	yes	characteristic
598	C₂	C₃×#66153	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, prime radical	C₃×C₅×#525	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#525	D₅
hypocenter	C₅	C₃×#2933
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#525

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4094	C₂	semidirect
3. C₂²×C₃×#681	C₂	semidirect
4. C₃×#65523	C₂	semidirect
5. C₂×C₃×C₂²⋊#168	C₂	semidirect
6. C₃×#65301	C₂	semidirect
7. C₃×#65300	C₂	semidirect
8. C₃×#65300	C₂	semidirect
9. C₃×D₄×#168	C₂	semidirect
10. C₃×#65288	C₂	semidirect
11. C₃×#65286	C₂	semidirect
12. #10614649	C₃	direct (N × H)
29. C₂×C₃×#681	C₂²	semidirect
33. C₂²×C₃×#168	C₂²	semidirect
38. C₃×C₂²⋊#168	C₂²	semidirect
39. C₃×C₂²⋊#168	C₂²	semidirect
40. C₃×C₄⋊#168	C₂²	semidirect
41. C₃×C₄⋊#168	C₂²	semidirect
42. C₃×#3935	C₂²	semidirect
43. C₃×C₄×#168	C₂²	semidirect
46. C₂×#4094	C₂×C₃	semidirect
47. C₂²×#681	C₂×C₃	semidirect
48. #65523	C₂×C₃	semidirect
49. C₂×C₂²⋊#168	C₂×C₃	semidirect
50. #65301	C₂×C₃	semidirect
51. #65300	C₂×C₃	semidirect
52. #65300	C₂×C₃	semidirect
53. D₄×#168	C₂×C₃	semidirect
54. #65288	C₂×C₃	semidirect
55. #65286	C₂×C₃	semidirect
86. C₃×#681	D₄	semidirect
124. C₂×#681	C₂²×C₃	semidirect
128. C₂²×#168	C₂²×C₃	semidirect
133. C₂²⋊#168	C₂²×C₃	semidirect
134. C₂²⋊#168	C₂²×C₃	semidirect
135. C₄⋊#168	C₂²×C₃	semidirect
136. C₄⋊#168	C₂²×C₃	semidirect
137. #3935	C₂²×C₃	semidirect
138. C₄×#168	C₂²×C₃	semidirect
237. #681	C₃×D₄	semidirect
271. C₂²×C₃×C₅	#131	semidirect
444. C₂²×C₅	C₃×#131	semidirect
495. C₃×C₅	#2933	semidirect
508. C₂²×C₃	#4094	semidirect
568. C₅	C₃×#2933	semidirect
581. C₂²	C₃×#4094	semidirect
591. C₃	#10614649	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×#525	2
C₂×C₃×#4094	2
C₂²×C₃×#681	2
C₃×#65523	2
C₂×C₃×C₂²⋊#168	2
C₃×#65301	2
C₃×#65300	2
C₃×D₄×#168	2
C₃×#65288	2
C₃×#65286	2
#10614649	3
C₃×#2933	5

Subgroups — C3×#10614649 #14415449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614649 #14415449