Subgroups — C₃×#10614295 #14416992

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4095	C₂	1	1	yes	maximal, characteristic
3	C₃×#65855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65315	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#688	C₂	1	2	yes	maximal, complemented
7	C₃×#65303	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#686	C₂	1	2	yes	maximal, complemented
9	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#3941	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65253	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614295	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
16	C₃×C₄×C₅×D₄	—	2	2	no	—
17	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
18	C₃×C₅×#117	—	2	1	no	—
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×#4095	C₄	1	8	yes	complemented
23	C₂×C₃×#688	C₂²	1	2	yes	—
24	C₂×C₃×#686	C₂²	1	2	yes	—
25	C₃×#4072	C₂²	1	1	yes	characteristic
26	C₂×C₃×#681	C₂²	1	1	yes	characteristic
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
28	C₃×#4039	—	2	1	no	—
29	C₃×#4039	—	2	1	no	—
30	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
31	C₃×C₄×D₂₀	C₂²	1	2	yes	—
32	C₃×C₄×D₂₀	C₂²	1	2	yes	—
33	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3941	C₂²	1	2	yes	—
38	C₃×#3941	C₂²	1	2	yes	—
39	C₃×#3940	C₂²	1	2	yes	complemented
40	C₃×#3939	C₂²	1	2	yes	complemented
41	C₃×#3935	C₂²	1	2	yes	complemented
42	C₃×C₄×#168	C₂²	1	2	yes	complemented
43	C₃×#2946	—	5	1	no	maximal, Hall
44	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#4095	C₂×C₃	1	1	yes	characteristic
46	#65855	C₂×C₃	1	1	yes	characteristic, complemented
47	#65522	C₂×C₃	1	1	yes	characteristic, complemented
48	#65315	C₂×C₃	1	2	yes	complemented
49	C₄×#688	C₂×C₃	1	2	yes	complemented
50	#65303	C₂×C₃	1	2	yes	complemented
51	C₄×#686	C₂×C₃	1	2	yes	complemented
52	#65286	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×#3941	C₂×C₃	1	1	yes	characteristic, complemented
54	#65253	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂³×C₃×D₅	—	2	1	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×D₂₀	—	2	1	no	—
66	C₂×C₃×D₂₀	—	2	2	no	—
67	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	complemented
68	C₂×C₃×D₂₀	C₂³	1	2	yes	—
69	C₂×C₃×C₄×D₅	—	2	2	no	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₃×C₄²×C₅	C₂³	1	2	yes	—
80	C₃×C₂²⋊Dic₅	—	2	1	no	—
81	C₃×#688	C₂×C₄	1	8	yes	complemented
82	C₃×#686	C₂×C₄	1	8	yes	complemented
83	C₃×#685	—	2	2	no	—
84	C₃×#685	—	2	2	no	—
85	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
86	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
87	C₃×C₄×Dic₅	—	2	1	no	—
88	C₃×#681	C₂×C₄	1	4	yes	complemented
89	C₂×C₃×#168	—	2	2	no	—
90	C₂×C₃×#168	C₂³	1	1	yes	characteristic
91	C₂×C₃×#168	C₂³	1	1	yes	characteristic
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
94	C₃×#520	D₅	1	1	yes	characteristic, complemented
95	C₃×#518	—	5	1	no	—
96	C₃×#442	—	5	2	no	—
97	C₃×#440	—	5	2	no	—
98	C₃×C₄×SD₁₆	—	5	2	no	—
99	C₃×C₄×D₈	—	5	2	no	—
100	C₃×#428	—	5	1	no	—
101	C₃×#416	—	5	1	no	—
102	C₂×C₃×#102	—	5	1	no	—
103	C₃×#405	—	5	1	no	—
104	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
105	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
106	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
107	C₄×C₅×D₄	—	2	2	no	—
108	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
109	C₅×#117	—	2	1	no	—
110	C₅×#117	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	—	2	1	no	—
112	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	#4095	C₃×C₄	1	8	yes	complemented
114	C₂×#688	C₂²×C₃	1	2	yes	—
115	C₂×#686	C₂²×C₃	1	2	yes	—
116	#4072	C₂²×C₃	1	1	yes	characteristic
117	C₂×#681	C₂²×C₃	1	1	yes	characteristic
118	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
119	#4039	—	2	1	no	—
120	#4039	—	2	1	no	—
121	D₅×C₂²⋊C₄	—	2	2	no	—
122	C₄×D₂₀	C₂²×C₃	1	2	yes	—
123	C₄×D₂₀	C₂²×C₃	1	2	yes	—
124	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
126	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
127	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
128	#3941	C₂²×C₃	1	2	yes	—
129	#3941	C₂²×C₃	1	2	yes	—
130	#3940	C₂²×C₃	1	2	yes	complemented
131	#3939	C₂²×C₃	1	2	yes	complemented
132	#3935	C₂²×C₃	1	2	yes	complemented
133	C₄×#168	C₂²×C₃	1	2	yes	complemented
134	#2946	—	5	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₃×D₅	—	2	2	no	—
138	C₂²×C₃×D₅	—	2	4	no	—
139	C₂²×C₃×D₅	—	8	1	no	—
140	C₂²×C₃×D₅	—	8	1	no	—
141	C₃×C₅×Q₈	—	2	1	no	—
142	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×D₄	—	2	4	no	—
144	C₃×C₅×D₄	—	2	1	no	—
145	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	4	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	8	2	no	—
150	C₂×C₃×C₄×C₅	—	8	1	no	—
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	#41	1	2	yes	—
156	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
157	C₂×C₃×Dic₅	—	2	1	no	—
158	C₂×C₃×Dic₅	—	2	1	no	—
159	C₃×D₂₀	—	2	4	no	—
160	C₃×D₂₀	—	2	2	no	—
161	C₃×D₂₀	C₂²×C₄	1	4	yes	—
162	C₃×C₄×D₅	—	8	2	no	—
163	C₃×C₄×D₅	—	8	2	no	—
164	C₃×#168	—	2	1	no	—
165	C₃×#168	—	2	1	no	—
166	C₃×#168	C₂²×C₄	1	4	yes	—
167	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
168	C₂²×C₃×D₄	—	5	1	no	—
169	C₃×AGL(1,ℤ/8)	—	5	8	no	—
170	C₂×C₃×SD₁₆	—	5	2	no	—
171	C₂×C₃×D₈	—	5	2	no	—
172	C₂×C₃×M₁₆	—	5	1	no	—
173	C₂²×C₃×C₈	—	5	1	no	—
174	C₃×C₄×Q₈	C₂×D₅	1	2	yes	complemented
175	C₃×C₄×D₄	—	2	2	no	—
176	C₃×C₄×D₄	—	5	2	no	—
177	C₃×C₄×D₄	—	5	2	no	—
178	C₃×C₄×D₄	—	10	1	no	—
179	C₃×C₄×D₄	—	10	1	no	—
180	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
181	C₃×#117	—	2	1	no	—
182	C₃×#117	—	5	1	no	—
183	C₃×#117	C₂×D₅	1	1	yes	characteristic
184	C₂×C₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
186	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
187	C₃×#107	—	5	2	no	—
188	C₃×#106	—	5	2	no	—
189	C₃×#103	—	5	1	no	—
190	C₃×#103	—	5	1	no	—
191	C₃×#102	—	5	1	no	—
192	C₃×#102	—	5	1	no	—
193	C₃×#102	—	5	2	no	—
194	C₃×#102	—	5	2	no	—
195	C₃×#97	—	5	2	no	—
196	C₃×C₄×C₈	—	5	2	no	—
197	C₂³×D₅	—	2	1	no	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	C₂×C₃×C₄	1	4	yes	complemented
200	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×D₂₀	—	2	1	no	—
208	C₂×D₂₀	—	2	2	no	—
209	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
210	C₂×D₂₀	C₂³×C₃	1	2	yes	—
211	C₂×C₄×D₅	—	2	2	no	—
212	C₂×C₄×D₅	—	2	2	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	2	no	—
215	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
218	C₅×C₂²⋊C₄	—	2	2	no	—
219	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
220	C₄²×C₅	—	2	2	no	—
221	C₄²×C₅	C₂³×C₃	1	2	yes	—
222	C₂²⋊Dic₅	—	2	1	no	—
223	#688	C₂×C₃×C₄	1	8	yes	complemented
224	#686	C₂×C₃×C₄	1	8	yes	complemented
225	#685	—	2	2	no	—
226	#685	—	2	2	no	—
227	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
228	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
229	C₄×Dic₅	—	2	1	no	—
230	#681	C₂×C₃×C₄	1	4	yes	complemented
231	C₂×#168	—	2	2	no	—
232	C₂×#168	C₂³×C₃	1	1	yes	characteristic
233	C₂×#168	C₂³×C₃	1	1	yes	characteristic
234	C₂×#168	C₂³×C₃	1	2	yes	—
235	C₂×AGL(1,ℤ/8)	—	5	1	no	—
236	#520	C₃×D₅	1	1	yes	characteristic, complemented
237	#518	—	5	1	no	—
238	#442	—	5	2	no	—
239	#440	—	5	2	no	—
240	C₄×SD₁₆	—	5	2	no	—
241	C₄×D₈	—	5	2	no	—
242	#428	—	5	1	no	—
243	#416	—	5	1	no	—
244	C₂×#102	—	5	1	no	—
245	#405	—	5	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₃×D₅	—	2	4	no	—
254	C₂×C₃×D₅	—	4	2	no	—
255	C₂×C₃×D₅	—	4	2	no	—
256	C₂×C₃×D₅	—	8	4	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	2	2	no	—
259	C₃×C₄×C₅	—	2	2	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
262	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
263	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
264	C₃×Dic₅	—	4	1	no	—
265	C₃×Dic₅	—	4	1	no	—
266	C₂⁴×C₃	—	10	1	no	—
267	C₃×#41	—	2	2	no	—
268	C₃×#41	C₄×D₅	1	4	yes	complemented
269	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	—	5	4	no	—
272	C₂×C₃×D₄	—	5	2	no	—
273	C₂×C₃×D₄	—	10	2	no	—
274	C₂×C₃×D₄	—	10	1	no	—
275	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	—	2	1	no	—
277	C₂²×C₃×C₄	—	2	1	no	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	—	10	2	no	—
280	C₂²×C₃×C₄	—	10	2	no	—
281	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
282	C₃×SD₁₆	—	5	8	no	—
283	C₃×D₈	—	5	8	no	—
284	C₃×M₁₆	—	5	4	no	—
285	C₂×C₃×C₈	—	5	2	no	—
286	C₂×C₃×C₈	—	5	1	no	—
287	C₂×C₃×C₈	—	5	1	no	—
288	C₂×C₃×C₈	—	10	2	no	—
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	5	1	no	—
292	C₃×C₄⋊C₄	—	5	1	no	—
293	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
294	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
295	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
296	C₃×C₂²⋊C₄	—	2	2	no	—
297	C₃×C₂²⋊C₄	—	10	1	no	—
298	C₃×C₂²⋊C₄	—	10	2	no	—
299	C₃×C₂²⋊C₄	—	10	2	no	—
300	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
301	C₃×C₄²	—	2	2	no	—
302	C₃×C₄²	—	10	1	no	—
303	C₃×C₄²	C₂²×D₅	1	2	yes	—
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
306	C₂²×D₅	—	2	2	no	—
307	C₂²×D₅	—	2	4	no	—
308	C₂²×D₅	—	8	1	no	—
309	C₂²×D₅	—	8	1	no	—
310	C₅×Q₈	—	2	1	no	—
311	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
312	C₅×D₄	—	2	4	no	—
313	C₅×D₄	—	2	1	no	—
314	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	4	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	8	2	no	—
319	C₂×C₄×C₅	—	8	1	no	—
320	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
321	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
322	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
323	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₃×#41	1	2	yes	—
325	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
326	C₂×Dic₅	—	2	1	no	—
327	C₂×Dic₅	—	2	1	no	—
328	D₂₀	—	2	4	no	—
329	D₂₀	—	2	2	no	—
330	D₂₀	C₂²×C₃×C₄	1	4	yes	—
331	C₄×D₅	—	8	2	no	—
332	C₄×D₅	—	8	2	no	—
333	#168	—	2	1	no	—
334	#168	—	2	1	no	—
335	#168	C₂²×C₃×C₄	1	4	yes	—
336	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
337	C₂²×D₄	—	5	1	no	—
338	AGL(1,ℤ/8)	—	5	8	no	—
339	C₂×SD₁₆	—	5	2	no	—
340	C₂×D₈	—	5	2	no	—
341	C₂×M₁₆	—	5	1	no	—
342	C₂²×C₈	—	5	1	no	—
343	C₄×Q₈	C₂×C₃×D₅	1	2	yes	complemented
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	5	2	no	—
346	C₄×D₄	—	5	2	no	—
347	C₄×D₄	—	10	1	no	—
348	C₄×D₄	—	10	1	no	—
349	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
350	#117	—	2	1	no	—
351	#117	—	5	1	no	—
352	#117	C₂×C₃×D₅	1	1	yes	characteristic
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	10	2	no	—
356	#107	—	5	2	no	—
357	#106	—	5	2	no	—
358	#103	—	5	1	no	—
359	#103	—	5	1	no	—
360	#102	—	5	1	no	—
361	#102	—	5	1	no	—
362	#102	—	5	2	no	—
363	#102	—	5	2	no	—
364	#97	—	5	2	no	—
365	C₄×C₈	—	5	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂×C₃×C₅	#576	1	1	yes	characteristic
370	C₂×C₃×C₅	#577	1	1	yes	characteristic
371	C₃×D₅	—	4	4	no	—
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	—	10	2	no	—
374	C₂³×C₃	—	10	4	no	—
375	C₂³×C₃	—	40	1	no	—
376	C₂³×C₃	—	40	1	no	—
377	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
378	C₃×Q₈	—	2	1	no	—
379	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
380	C₃×D₄	—	2	4	no	—
381	C₃×D₄	—	2	1	no	—
382	C₃×D₄	—	5	4	no	—
383	C₃×D₄	—	10	2	no	—
384	C₃×D₄	—	10	4	no	—
385	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	4	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	8	2	no	—
390	C₂×C₃×C₄	—	8	1	no	—
391	C₂×C₃×C₄	—	10	1	no	—
392	C₂×C₃×C₄	—	10	1	no	—
393	C₂×C₃×C₄	—	40	2	no	—
394	C₂×C₃×C₄	—	40	2	no	—
395	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
396	C₂×C₃×C₄	#709	1	2	yes	—
397	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
398	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
399	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
401	C₃×C₈	—	5	4	no	—
402	C₃×C₈	—	10	1	no	—
403	C₃×C₈	—	10	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
410	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
411	C₂×D₅	—	2	4	no	—
412	C₂×D₅	—	4	2	no	—
413	C₂×D₅	—	4	2	no	—
414	C₂×D₅	—	8	4	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	4	2	no	—
419	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
420	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
421	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
422	Dic₅	—	4	1	no	—
423	Dic₅	—	4	1	no	—
424	C₂⁴	—	10	1	no	—
425	#41	—	2	2	no	—
426	#41	C₃×C₄×D₅	1	4	yes	complemented
427	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	5	4	no	—
430	C₂×D₄	—	5	2	no	—
431	C₂×D₄	—	10	2	no	—
432	C₂×D₄	—	10	1	no	—
433	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	10	2	no	—
438	C₂²×C₄	—	10	2	no	—
439	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
440	SD₁₆	—	5	8	no	—
441	D₈	—	5	8	no	—
442	M₁₆	—	5	4	no	—
443	C₂×C₈	—	5	2	no	—
444	C₂×C₈	—	5	1	no	—
445	C₂×C₈	—	5	1	no	—
446	C₂×C₈	—	10	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	5	1	no	—
450	C₄⋊C₄	—	5	1	no	—
451	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
452	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
453	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	10	1	no	—
456	C₂²⋊C₄	—	10	2	no	—
457	C₂²⋊C₄	—	10	2	no	—
458	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
459	C₄²	—	2	2	no	—
460	C₄²	—	10	1	no	—
461	C₄²	C₂²×C₃×D₅	1	2	yes	—
462	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	4	1	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	—	10	4	no	—
469	C₂²×C₃	—	20	2	no	—
470	C₂²×C₃	—	20	2	no	—
471	C₂²×C₃	—	40	4	no	—
472	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
473	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	4	2	no	—
478	C₃×C₄	—	20	1	no	—
479	C₃×C₄	—	20	1	no	—
480	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
481	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
482	C₃×C₄	C₂×#709	1	1	yes	characteristic
483	C₂×C₅	—	2	2	no	—
484	C₂×C₅	—	4	2	no	—
485	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
486	C₂×C₅	C₃×#576	1	1	yes	characteristic
487	C₂×C₅	C₃×#577	1	1	yes	characteristic
488	D₅	—	4	4	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	10	2	no	—
491	C₂³	—	10	4	no	—
492	C₂³	—	40	1	no	—
493	C₂³	—	40	1	no	—
494	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
495	Q₈	—	2	1	no	—
496	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	—	5	4	no	—
500	D₄	—	10	2	no	—
501	D₄	—	10	4	no	—
502	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	1	no	—
508	C₂×C₄	—	10	1	no	—
509	C₂×C₄	—	10	1	no	—
510	C₂×C₄	—	40	2	no	—
511	C₂×C₄	—	40	2	no	—
512	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
513	C₂×C₄	C₃×#709	1	2	yes	—
514	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
515	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
516	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
518	C₈	—	5	4	no	—
519	C₈	—	10	1	no	—
520	C₈	—	10	1	no	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	4	2	no	—
523	C₂×C₃	—	20	4	no	—
524	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
525	C₂×C₃	#66169	1	1	yes	characteristic
526	C₂×C₃	#66171	1	1	yes	characteristic
527	C₅	C₃×#2946	1	1	yes	characteristic, complemented, Sylow
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	10	4	no	—
534	C₂²	—	20	2	no	—
535	C₂²	—	20	2	no	—
536	C₂²	—	40	4	no	—
537	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
538	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	20	1	no	—
544	C₄	—	20	1	no	—
545	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
546	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
547	C₄	C₂×C₃×#709	1	1	yes	characteristic
548	C₃	#10614295	1	1	yes	characteristic, direct product factor, Sylow
549	C₂	—	2	2	no	—
550	C₂	—	4	2	no	—
551	C₂	—	20	4	no	—
552	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
553	C₂	C₃×#66169	1	1	yes	characteristic
554	C₂	C₃×#66171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#520	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4095	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#520	D₅
hypocenter	C₅	C₃×#2946
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#520

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#520	C₂	semidirect
3. C₃×#65855	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₃×#65315	C₂	semidirect
6. C₃×C₄×#688	C₂	semidirect
7. C₃×#65303	C₂	semidirect
8. C₃×C₄×#686	C₂	semidirect
9. C₃×#65286	C₂	semidirect
10. C₂×C₃×#3941	C₂	semidirect
11. C₃×#65253	C₂	semidirect
12. #10614295	C₃	direct (N × H)
15. C₃×C₄×C₅×Q₈	C₂²	semidirect
17. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₃×#4095	C₄	semidirect
33. C₃×#3967	C₂²	semidirect
34. C₃×#3967	C₂²	semidirect
35. C₃×#3964	C₂²	semidirect
36. C₃×#3964	C₂²	semidirect
39. C₃×#3940	C₂²	semidirect
40. C₃×#3939	C₂²	semidirect
41. C₃×#3935	C₂²	semidirect
42. C₃×C₄×#168	C₂²	semidirect
44. C₅×#520	C₂×C₃	semidirect
46. #65855	C₂×C₃	semidirect
47. #65522	C₂×C₃	semidirect
48. #65315	C₂×C₃	semidirect
49. C₄×#688	C₂×C₃	semidirect
50. #65303	C₂×C₃	semidirect
51. C₄×#686	C₂×C₃	semidirect
52. #65286	C₂×C₃	semidirect
53. C₂×#3941	C₂×C₃	semidirect
54. #65253	C₂×C₃	semidirect
57. C₃×C₅×#41	C₂×C₄	semidirect
67. C₂×C₃×D₂₀	C₂×C₄	semidirect
81. C₃×#688	C₂×C₄	semidirect
82. C₃×#686	C₂×C₄	semidirect
88. C₃×#681	C₂×C₄	semidirect
94. C₃×#520	D₅	semidirect
106. C₄×C₅×Q₈	C₂²×C₃	semidirect
108. C₄×C₅×D₄	C₂²×C₃	semidirect
113. #4095	C₃×C₄	semidirect
124. #3967	C₂²×C₃	semidirect
125. #3967	C₂²×C₃	semidirect
126. #3964	C₂²×C₃	semidirect
127. #3964	C₂²×C₃	semidirect
130. #3940	C₂²×C₃	semidirect
131. #3939	C₂²×C₃	semidirect
132. #3935	C₂²×C₃	semidirect
133. C₄×#168	C₂²×C₃	semidirect
174. C₃×C₄×Q₈	C₂×D₅	semidirect
180. C₃×C₄×D₄	C₂×D₅	semidirect
199. C₅×#41	C₂×C₃×C₄	semidirect
209. C₂×D₂₀	C₂×C₃×C₄	semidirect
223. #688	C₂×C₃×C₄	semidirect
224. #686	C₂×C₃×C₄	semidirect
230. #681	C₂×C₃×C₄	semidirect
236. #520	C₃×D₅	semidirect
268. C₃×#41	C₄×D₅	semidirect
343. C₄×Q₈	C₂×C₃×D₅	semidirect
349. C₄×D₄	C₂×C₃×D₅	semidirect
426. #41	C₃×C₄×D₅	semidirect
462. C₃×C₅	#2946	semidirect
527. C₅	C₃×#2946	semidirect
548. C₃	#10614295	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×#520	2
C₂×C₃×#4095	2
C₃×#65855	2
C₃×#65522	2
C₃×#65315	2
C₃×C₄×#688	2
C₃×#65303	2
C₃×C₄×#686	2
C₃×#65286	2
C₂×C₃×#3941	2
C₃×#65253	2
#10614295	3
C₃×#2946	5

Subgroups — C3×#10614295 #14416992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614295 #14416992