Subgroups — C₃×#10615542 #14418111

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66156	C₂	1	1	yes	maximal, characteristic
3	C₃×#66079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3969	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65434	C₂	1	4	yes	maximal, complemented
6	C₃×#65433	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#3957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65413	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
10	#10615542	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₃×#709	C₂²	1	1	yes	characteristic
13	C₃×C₅×#131	—	2	2	no	—
14	C₃×C₅×#131	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×M₁₆	—	2	2	no	—
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₃×#4097	C₄	1	2	yes	complemented
19	C₃×#4096	C₂²	1	4	yes	—
20	C₃×#4095	C₄	1	2	yes	complemented
21	C₃×#4088	C₄	1	2	yes	complemented
22	C₃×#4078	C₄	1	2	yes	complemented
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×#681	C₂²	1	1	yes	characteristic
25	C₂×C₃×#681	C₂²	1	1	yes	characteristic
26	C₃×#4053	—	2	2	no	—
27	C₃×D₅×M₁₆	—	2	2	no	—
28	C₃×#4047	C₂²	1	4	yes	complemented
29	C₃×#3969	C₂²	1	2	yes	complemented
30	C₃×#3969	C₂²	1	2	yes	complemented
31	C₃×#3957	C₂²	1	2	yes	complemented
32	C₃×#3957	C₂²	1	2	yes	complemented
33	C₃×#3954	C₂²	1	4	yes	complemented
34	C₃×#3947	C₂²	1	2	yes	complemented
35	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
36	C₃×#2956	—	5	1	no	maximal, Hall
37	C₅×#568	C₂×C₃	1	1	yes	characteristic, complemented
38	#66156	C₂×C₃	1	1	yes	characteristic
39	#66079	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×#3969	C₂×C₃	1	1	yes	characteristic, complemented
41	#65434	C₂×C₃	1	4	yes	complemented
42	#65433	C₂×C₃	1	4	yes	complemented
43	C₂×#3957	C₂×C₃	1	1	yes	characteristic, complemented
44	#65413	C₂×C₃	1	1	yes	characteristic, complemented
45	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×C₅×#41	—	2	1	no	—
47	C₃×C₅×#41	—	2	1	no	—
48	C₃×C₅×#41	C₂×C₄	1	2	yes	—
49	C₃×C₅×#41	C₂³	1	2	yes	—
50	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×D₄	—	2	1	no	—
52	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	—	2	1	no	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
56	C₂²×C₃×Dic₅	—	2	1	no	—
57	C₃×#709	—	2	1	no	—
58	C₃×#709	—	2	1	no	—
59	C₃×#709	C₂×C₄	1	2	yes	—
60	C₃×#709	C₂³	1	2	yes	—
61	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	—	2	1	no	—
63	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×M₁₆	—	2	1	no	—
65	C₃×C₅×M₁₆	—	2	4	no	—
66	C₃×C₅×M₁₆	D₄	1	2	yes	—
67	C₃×C₅×M₁₆	D₄	1	2	yes	—
68	C₃×C₅×M₁₆	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	—	2	1	no	—
70	C₂×C₃×C₅×C₈	—	2	4	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×#689	C₂×C₄	1	4	yes	complemented
73	C₃×#688	C₂×C₄	1	4	yes	complemented
74	C₃×#687	C₂×C₄	1	4	yes	complemented
75	C₃×#686	C₂×C₄	1	4	yes	complemented
76	C₃×C₄×Dic₅	—	2	1	no	—
77	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
78	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
79	C₃×#681	—	2	1	no	—
80	C₃×#681	C₂×C₄	1	2	yes	—
81	C₃×#681	C₂×C₄	1	2	yes	—
82	C₃×#681	C₂³	1	2	yes	—
83	C₂×C₃×#168	—	2	1	no	—
84	C₂×C₃×#168	C₂³	1	2	yes	—
85	C₃×#676	—	2	4	no	—
86	C₃×C₈×D₅	—	2	4	no	—
87	C₃×#575	—	5	1	no	—
88	C₃×#568	—	5	1	no	—
89	C₃×#568	D₅	1	1	yes	characteristic, complemented
90	C₃×#444	—	5	4	no	—
91	C₃×#443	—	5	4	no	—
92	C₃×#430	—	5	1	no	—
93	C₂×C₃×#104	—	5	1	no	—
94	C₂×C₃×#104	—	5	1	no	—
95	C₃×C₄×M₁₆	—	5	1	no	—
96	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
97	C₂×#709	C₂²×C₃	1	1	yes	characteristic
98	C₅×#131	—	2	2	no	—
99	C₅×#131	C₂²×C₃	1	4	yes	complemented
100	C₂×C₅×M₁₆	—	2	2	no	—
101	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
103	#4097	C₃×C₄	1	2	yes	complemented
104	#4096	C₂²×C₃	1	4	yes	—
105	#4095	C₃×C₄	1	2	yes	complemented
106	#4088	C₃×C₄	1	2	yes	complemented
107	#4078	C₃×C₄	1	2	yes	complemented
108	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×#681	C₂²×C₃	1	1	yes	characteristic
110	C₂×#681	C₂²×C₃	1	1	yes	characteristic
111	#4053	—	2	2	no	—
112	D₅×M₁₆	—	2	2	no	—
113	#4047	C₂²×C₃	1	4	yes	complemented
114	#3969	C₂²×C₃	1	2	yes	complemented
115	#3969	C₂²×C₃	1	2	yes	complemented
116	#3957	C₂²×C₃	1	2	yes	complemented
117	#3957	C₂²×C₃	1	2	yes	complemented
118	#3954	C₂²×C₃	1	4	yes	complemented
119	#3947	C₂²×C₃	1	2	yes	complemented
120	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
121	#2956	—	5	1	no	Sylow
122	C₂³×C₃×C₅	—	2	1	no	—
123	C₂³×C₃×C₅	#41	1	1	yes	characteristic
124	C₂²×C₃×D₅	—	2	1	no	—
125	C₃×C₅×Q₈	—	2	1	no	—
126	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	—	2	2	no	—
129	C₃×C₅×D₄	—	2	1	no	—
130	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₂²⋊D₅	—	2	2	no	—
141	C₃×C₂²⋊D₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	—	2	1	no	—
144	C₂×C₃×Dic₅	—	2	1	no	—
145	C₂×C₃×Dic₅	—	4	2	no	—
146	C₃×D₂₀	—	2	1	no	—
147	C₃×D₂₀	C₂²×C₄	1	2	yes	—
148	C₃×C₄×D₅	—	2	2	no	—
149	C₃×C₄×D₅	—	2	2	no	—
150	C₃×Dic₁₀	—	2	1	no	—
151	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
154	C₃×#168	—	2	2	no	—
155	C₃×#168	C₂²×C₄	1	4	yes	—
156	C₂×C₃×#41	—	5	1	no	—
157	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
158	C₃×#137	—	5	2	no	—
159	C₃×#137	—	5	2	no	—
160	C₃×AGL(1,ℤ/8)	—	5	2	no	—
161	C₃×AGL(1,ℤ/8)	—	5	2	no	—
162	C₃×#135	—	5	4	no	—
163	C₃×#131	—	2	2	no	—
164	C₃×#131	—	5	4	no	—
165	C₃×#131	—	10	2	no	—
166	C₃×#131	C₂×D₅	1	4	yes	complemented
167	C₂×C₃×M₁₆	—	2	2	no	—
168	C₂×C₃×M₁₆	—	5	1	no	—
169	C₂×C₃×M₁₆	—	5	1	no	—
170	C₂×C₃×M₁₆	—	10	2	no	—
171	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
172	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
173	C₂×C₃×C₄²	—	5	1	no	—
174	C₃×#108	—	5	4	no	—
175	C₃×#104	—	5	2	no	—
176	C₃×#104	—	5	2	no	—
177	C₃×#104	—	5	2	no	—
178	C₃×#104	—	5	2	no	—
179	C₃×#97	—	5	2	no	—
180	C₃×C₄×C₈	—	5	2	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	—	2	1	no	—
183	C₅×#41	C₂×C₃×C₄	1	2	yes	—
184	C₅×#41	C₂³×C₃	1	2	yes	—
185	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₂²⋊D₅	—	2	1	no	—
191	C₂²×Dic₅	—	2	1	no	—
192	#709	—	2	1	no	—
193	#709	—	2	1	no	—
194	#709	C₂×C₃×C₄	1	2	yes	—
195	#709	C₂³×C₃	1	2	yes	—
196	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
197	C₂×C₄×D₅	—	2	1	no	—
198	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
199	C₅×M₁₆	—	2	1	no	—
200	C₅×M₁₆	—	2	4	no	—
201	C₅×M₁₆	C₃×D₄	1	2	yes	—
202	C₅×M₁₆	C₃×D₄	1	2	yes	—
203	C₅×M₁₆	C₂³×C₃	1	2	yes	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	4	no	—
206	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
207	#689	C₂×C₃×C₄	1	4	yes	complemented
208	#688	C₂×C₃×C₄	1	4	yes	complemented
209	#687	C₂×C₃×C₄	1	4	yes	complemented
210	#686	C₂×C₃×C₄	1	4	yes	complemented
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
213	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
214	#681	—	2	1	no	—
215	#681	C₂×C₃×C₄	1	2	yes	—
216	#681	C₂×C₃×C₄	1	2	yes	—
217	#681	C₂³×C₃	1	2	yes	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	C₂³×C₃	1	2	yes	—
220	#676	—	2	4	no	—
221	C₈×D₅	—	2	4	no	—
222	#575	—	5	1	no	—
223	#568	—	5	1	no	—
224	#568	C₃×D₅	1	1	yes	characteristic, complemented
225	#444	—	5	4	no	—
226	#443	—	5	4	no	—
227	#430	—	5	1	no	—
228	C₂×#104	—	5	1	no	—
229	C₂×#104	—	5	1	no	—
230	C₄×M₁₆	—	5	1	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	4	1	no	—
233	C₂²×C₃×C₅	—	8	1	no	—
234	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
236	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
237	C₂×C₃×D₅	—	2	2	no	—
238	C₂×C₃×D₅	—	8	1	no	—
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₃×Dic₅	—	2	2	no	—
245	C₃×Dic₅	—	2	2	no	—
246	C₃×Dic₅	—	4	1	no	—
247	C₃×#41	—	2	1	no	—
248	C₃×#41	—	2	1	no	—
249	C₃×#41	—	5	2	no	—
250	C₃×#41	—	5	2	no	—
251	C₃×#41	—	10	1	no	—
252	C₃×#41	—	10	1	no	—
253	C₃×#41	C₄×D₅	1	2	yes	—
254	C₃×#41	C₂²×D₅	1	2	yes	—
255	C₂×C₃×Q₈	—	5	1	no	—
256	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
257	C₂×C₃×D₄	—	2	1	no	—
258	C₂×C₃×D₄	—	5	1	no	—
259	C₂×C₃×D₄	—	10	1	no	—
260	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
261	C₂²×C₃×C₄	—	2	1	no	—
262	C₂²×C₃×C₄	—	10	1	no	—
263	C₂²×C₃×C₄	—	10	1	no	—
264	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
265	C₃×Q₁₆	—	5	4	no	—
266	C₃×SD₁₆	—	5	4	no	—
267	C₃×SD₁₆	—	5	4	no	—
268	C₃×D₈	—	5	4	no	—
269	C₃×M₁₆	—	2	1	no	—
270	C₃×M₁₆	—	2	4	no	—
271	C₃×M₁₆	—	5	2	no	—
272	C₃×M₁₆	—	5	2	no	—
273	C₃×M₁₆	—	5	2	no	—
274	C₃×M₁₆	—	10	1	no	—
275	C₃×M₁₆	—	10	4	no	—
276	C₃×M₁₆	C₂²⋊D₅	1	2	yes	—
277	C₃×M₁₆	C₂²⋊D₅	1	2	yes	—
278	C₃×M₁₆	C₂²×D₅	1	2	yes	—
279	C₂×C₃×C₈	—	2	1	no	—
280	C₂×C₃×C₈	—	2	4	no	—
281	C₂×C₃×C₈	—	5	2	no	—
282	C₂×C₃×C₈	—	10	1	no	—
283	C₂×C₃×C₈	—	10	4	no	—
284	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
285	C₃×C₄²	—	5	1	no	—
286	C₃×C₄²	—	5	1	no	—
287	C₃×C₄²	—	10	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	C₃×#41	1	1	yes	characteristic
290	C₂²×D₅	—	2	1	no	—
291	C₅×Q₈	—	2	1	no	—
292	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	2	1	no	—
296	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
306	C₂²⋊D₅	—	2	2	no	—
307	C₂²⋊D₅	—	2	2	no	—
308	C₂×Dic₅	—	2	1	no	—
309	C₂×Dic₅	—	2	1	no	—
310	C₂×Dic₅	—	2	1	no	—
311	C₂×Dic₅	—	4	2	no	—
312	D₂₀	—	2	1	no	—
313	D₂₀	C₂²×C₃×C₄	1	2	yes	—
314	C₄×D₅	—	2	2	no	—
315	C₄×D₅	—	2	2	no	—
316	Dic₁₀	—	2	1	no	—
317	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
318	C₅×C₈	—	2	2	no	—
319	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
320	#168	—	2	2	no	—
321	#168	C₂²×C₃×C₄	1	4	yes	—
322	C₂×#41	—	5	1	no	—
323	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
324	#137	—	5	2	no	—
325	#137	—	5	2	no	—
326	AGL(1,ℤ/8)	—	5	2	no	—
327	AGL(1,ℤ/8)	—	5	2	no	—
328	#135	—	5	4	no	—
329	#131	—	2	2	no	—
330	#131	—	5	4	no	—
331	#131	—	10	2	no	—
332	#131	C₂×C₃×D₅	1	4	yes	complemented
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	5	1	no	—
335	C₂×M₁₆	—	5	1	no	—
336	C₂×M₁₆	—	10	2	no	—
337	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
338	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
339	C₂×C₄²	—	5	1	no	—
340	#108	—	5	4	no	—
341	#104	—	5	2	no	—
342	#104	—	5	2	no	—
343	#104	—	5	2	no	—
344	#104	—	5	2	no	—
345	#97	—	5	2	no	—
346	C₄×C₈	—	5	2	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	2	1	no	—
349	C₂×C₃×C₅	—	2	1	no	—
350	C₂×C₃×C₅	—	4	2	no	—
351	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	C₃×D₅	—	4	2	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	—	10	1	no	—
355	C₂³×C₃	#709	1	1	yes	characteristic
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	—	5	2	no	—
358	C₃×Q₈	—	10	1	no	—
359	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	5	2	no	—
364	C₃×D₄	—	10	2	no	—
365	C₃×D₄	—	10	2	no	—
366	C₃×D₄	—	10	1	no	—
367	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	10	1	no	—
372	C₂×C₃×C₄	—	10	1	no	—
373	C₂×C₃×C₄	—	10	2	no	—
374	C₂×C₃×C₄	—	10	2	no	—
375	C₂×C₃×C₄	—	10	1	no	—
376	C₂×C₃×C₄	—	20	2	no	—
377	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
379	C₂×C₃×C₄	#709	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
383	C₃×C₈	—	2	2	no	—
384	C₃×C₈	—	5	4	no	—
385	C₃×C₈	—	10	2	no	—
386	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	—	8	1	no	—
390	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
391	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
392	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
393	C₂×D₅	—	2	2	no	—
394	C₂×D₅	—	8	1	no	—
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
397	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
398	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
399	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
400	Dic₅	—	2	2	no	—
401	Dic₅	—	2	2	no	—
402	Dic₅	—	4	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	5	2	no	—
406	#41	—	5	2	no	—
407	#41	—	10	1	no	—
408	#41	—	10	1	no	—
409	#41	C₃×C₄×D₅	1	2	yes	—
410	#41	C₂²×C₃×D₅	1	2	yes	—
411	C₂×Q₈	—	5	1	no	—
412	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	5	1	no	—
415	C₂×D₄	—	10	1	no	—
416	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	10	1	no	—
419	C₂²×C₄	—	10	1	no	—
420	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
421	Q₁₆	—	5	4	no	—
422	SD₁₆	—	5	4	no	—
423	SD₁₆	—	5	4	no	—
424	D₈	—	5	4	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	4	no	—
427	M₁₆	—	5	2	no	—
428	M₁₆	—	5	2	no	—
429	M₁₆	—	5	2	no	—
430	M₁₆	—	10	1	no	—
431	M₁₆	—	10	4	no	—
432	M₁₆	C₃×C₂²⋊D₅	1	2	yes	—
433	M₁₆	C₃×C₂²⋊D₅	1	2	yes	—
434	M₁₆	C₂²×C₃×D₅	1	2	yes	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	4	no	—
437	C₂×C₈	—	5	2	no	—
438	C₂×C₈	—	10	1	no	—
439	C₂×C₈	—	10	4	no	—
440	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
441	C₄²	—	5	1	no	—
442	C₄²	—	5	1	no	—
443	C₄²	—	10	1	no	—
444	C₃×C₅	#2956	1	1	yes	characteristic, complemented, Hall
445	C₂²×C₃	—	2	2	no	—
446	C₂²×C₃	—	4	1	no	—
447	C₂²×C₃	—	8	1	no	—
448	C₂²×C₃	—	10	2	no	—
449	C₂²×C₃	—	40	1	no	—
450	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
451	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
452	C₂²×C₃	C₂×#709	1	1	yes	characteristic
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	10	2	no	—
455	C₃×C₄	—	10	2	no	—
456	C₃×C₄	—	20	1	no	—
457	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
458	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
459	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
460	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	2	1	no	—
464	C₂×C₅	—	4	2	no	—
465	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
466	D₅	—	4	2	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	10	1	no	—
469	C₂³	C₃×#709	1	1	yes	characteristic
470	Q₈	—	2	1	no	—
471	Q₈	—	5	2	no	—
472	Q₈	—	10	1	no	—
473	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	5	2	no	—
478	D₄	—	10	2	no	—
479	D₄	—	10	2	no	—
480	D₄	—	10	1	no	—
481	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	10	1	no	—
486	C₂×C₄	—	10	1	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	10	2	no	—
489	C₂×C₄	—	10	1	no	—
490	C₂×C₄	—	20	2	no	—
491	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
492	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
493	C₂×C₄	C₃×#709	1	1	yes	characteristic
494	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
495	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
496	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	5	4	no	—
499	C₈	—	10	2	no	—
500	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
501	C₂×C₃	—	2	1	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	—	20	2	no	—
506	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
507	C₅	C₃×#2956	1	1	yes	characteristic, complemented, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	10	2	no	—
512	C₂²	—	40	1	no	—
513	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
514	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
515	C₂²	C₂×C₃×#709	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	10	2	no	—
518	C₄	—	10	2	no	—
519	C₄	—	20	1	no	—
520	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
521	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
522	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
523	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
524	C₃	#10615542	1	1	yes	characteristic, direct product factor, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	4	2	no	—
529	C₂	—	20	2	no	—
530	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#568	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×#66156	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#568	D₅
hypocenter	C₅	C₃×#2956
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×M₁₆ ◁ C₃×#568

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#568	C₂	semidirect
3. C₃×#66079	C₂	semidirect
4. C₂×C₃×#3969	C₂	semidirect
5. C₃×#65434	C₂	semidirect
6. C₃×#65433	C₂	semidirect
7. C₂×C₃×#3957	C₂	semidirect
8. C₃×#65413	C₂	semidirect
9. C₃×M₁₆×Dic₅	C₂	semidirect
10. #10615542	C₃	direct (N × H)
14. C₃×C₅×#131	C₂²	semidirect
18. C₃×#4097	C₄	semidirect
20. C₃×#4095	C₄	semidirect
21. C₃×#4088	C₄	semidirect
22. C₃×#4078	C₄	semidirect
28. C₃×#4047	C₂²	semidirect
29. C₃×#3969	C₂²	semidirect
30. C₃×#3969	C₂²	semidirect
31. C₃×#3957	C₂²	semidirect
32. C₃×#3957	C₂²	semidirect
33. C₃×#3954	C₂²	semidirect
34. C₃×#3947	C₂²	semidirect
35. C₃×C₈×Dic₅	C₂²	semidirect
37. C₅×#568	C₂×C₃	semidirect
39. #66079	C₂×C₃	semidirect
40. C₂×#3969	C₂×C₃	semidirect
41. #65434	C₂×C₃	semidirect
42. #65433	C₂×C₃	semidirect
43. C₂×#3957	C₂×C₃	semidirect
44. #65413	C₂×C₃	semidirect
45. M₁₆×Dic₅	C₂×C₃	semidirect
72. C₃×#689	C₂×C₄	semidirect
73. C₃×#688	C₂×C₄	semidirect
74. C₃×#687	C₂×C₄	semidirect
75. C₃×#686	C₂×C₄	semidirect
89. C₃×#568	D₅	semidirect
99. C₅×#131	C₂²×C₃	semidirect
103. #4097	C₃×C₄	semidirect
105. #4095	C₃×C₄	semidirect
106. #4088	C₃×C₄	semidirect
107. #4078	C₃×C₄	semidirect
113. #4047	C₂²×C₃	semidirect
114. #3969	C₂²×C₃	semidirect
115. #3969	C₂²×C₃	semidirect
116. #3957	C₂²×C₃	semidirect
117. #3957	C₂²×C₃	semidirect
118. #3954	C₂²×C₃	semidirect
119. #3947	C₂²×C₃	semidirect
120. C₈×Dic₅	C₂²×C₃	semidirect
166. C₃×#131	C₂×D₅	semidirect
207. #689	C₂×C₃×C₄	semidirect
208. #688	C₂×C₃×C₄	semidirect
209. #687	C₂×C₃×C₄	semidirect
210. #686	C₂×C₃×C₄	semidirect
224. #568	C₃×D₅	semidirect
332. #131	C₂×C₃×D₅	semidirect
444. C₃×C₅	#2956	semidirect
507. C₅	C₃×#2956	semidirect
524. C₃	#10615542	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×#568	2
C₃×#66156	2
C₃×#66079	2
C₂×C₃×#3969	2
C₃×#65434	2
C₃×#65433	2
C₂×C₃×#3957	2
C₃×#65413	2
C₃×M₁₆×Dic₅	2
#10615542	3
C₃×#2956	5

Subgroups — C3×#10615542 #14418111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615542 #14418111