Subgroups — C₃×D₅×#463 #14425918

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65454	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65442	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65133	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65108	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×D₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅×#463	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₅	—	2	1	no	—
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
25	C₃×#4093	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
27	C₃×#4082	C₂²	1	1	yes	characteristic, complemented
28	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#686	C₂²	1	1	yes	characteristic
31	C₂×C₃×#686	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
33	C₃×D₅×SD₁₆	—	2	4	no	—
34	C₃×D₅×D₈	—	2	4	no	—
35	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
36	C₂×C₃×#677	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
39	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
40	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×#4031	—	2	1	no	—
42	C₃×#4031	—	2	1	no	—
43	C₃×#4027	—	2	1	no	—
44	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×#4021	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
54	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
55	C₃×#3953	C₂²	1	1	yes	characteristic, complemented
56	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
58	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
59	C₃×#3942	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×#463	—	5	1	no	maximal, Hall
63	C₂×D₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
65	D₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
66	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
68	#65454	C₂×C₃	1	1	yes	characteristic, complemented
69	#65442	C₂×C₃	1	1	yes	characteristic, complemented
70	#65346	C₂×C₃	1	1	yes	characteristic, complemented
71	#65305	C₂×C₃	1	1	yes	characteristic, complemented
72	#65133	C₂×C₃	1	1	yes	characteristic, complemented
73	D₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
74	#65108	C₂×C₃	1	1	yes	characteristic, complemented
75	D₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
76	#65076	C₂×C₃	1	1	yes	characteristic, complemented
77	D₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂³×C₃×D₅	—	2	1	no	—
79	C₂³×C₃×D₅	—	2	1	no	—
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
85	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
86	C₂²×C₃×Dic₅	—	2	1	no	—
87	C₃×Q₈×D₅	—	2	2	no	—
88	C₃×Q₈×D₅	—	2	2	no	—
89	C₃×D₄×D₅	—	2	2	no	—
90	C₃×D₄×D₅	—	2	2	no	—
91	C₃×D₄×D₅	—	2	2	no	—
92	C₃×D₄×D₅	D₄	1	4	yes	—
93	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
94	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	—	2	1	no	—
96	C₂×C₃×C₄×D₅	—	2	1	no	—
97	C₂×C₃×C₄×D₅	—	2	1	no	—
98	C₂×C₃×C₄×D₅	—	2	1	no	—
99	C₂×C₃×C₄×D₅	—	4	4	no	—
100	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
103	C₂×C₃×Dic₁₀	—	2	1	no	—
104	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
105	C₃×C₅×SD₁₆	—	2	2	no	—
106	C₃×C₅×D₈	—	2	2	no	—
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₃×C₂²⋊Dic₅	—	2	1	no	—
115	C₃×C₂²⋊Dic₅	—	2	1	no	—
116	C₃×C₂²⋊Dic₅	—	2	1	no	—
117	C₃×#688	—	2	2	no	—
118	C₃×#687	—	2	2	no	—
119	C₃×#686	—	2	2	no	—
120	C₃×#686	—	2	2	no	—
121	C₃×#685	—	2	1	no	—
122	C₃×#685	—	2	1	no	—
123	C₃×#685	—	2	1	no	—
124	C₃×#685	—	2	1	no	—
125	C₃×#685	—	2	1	no	—
126	C₃×#685	—	2	1	no	—
127	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
128	C₃×#683	—	2	1	no	—
129	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
130	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
131	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
132	C₂×C₃×#168	C₂³	1	1	yes	characteristic
133	C₂×C₃×#168	C₂³	1	1	yes	characteristic
134	C₃×D₄₀	—	2	2	no	—
135	C₃×#677	—	2	2	no	—
136	C₃×C₈×D₅	—	2	2	no	—
137	C₃×C₈×D₅	—	2	2	no	—
138	C₂²×C₃×SD₁₆	—	5	1	no	—
139	C₂²×C₃×D₈	—	5	1	no	—
140	C₂×C₃×#124	—	5	1	no	—
141	C₂×C₃×C₄×D₄	—	5	1	no	—
142	C₃×#463	—	5	1	no	—
143	C₃×#463	—	5	1	no	—
144	C₃×#463	—	5	1	no	—
145	C₃×#463	—	5	1	no	—
146	C₃×#463	—	5	1	no	—
147	C₃×#463	—	5	1	no	—
148	C₃×#463	—	5	1	no	—
149	C₃×#463	D₅	1	1	yes	characteristic, direct product factor
150	C₂×C₃×C₄⋊C₈	—	5	1	no	—
151	C₂×C₃×#103	—	5	1	no	—
152	C₂×C₃×#102	—	5	1	no	—
153	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
154	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
155	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
156	C₂²×C₄×D₅	—	2	1	no	—
157	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
161	#4093	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
163	#4082	C₂²×C₃	1	1	yes	characteristic, complemented
164	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×#686	C₂²×C₃	1	1	yes	characteristic
167	C₂×#686	C₂²×C₃	1	1	yes	characteristic
168	C₄×C₂²⋊D₅	—	2	1	no	—
169	D₅×SD₁₆	—	2	4	no	—
170	D₅×D₈	—	2	4	no	—
171	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
172	C₂×#677	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
175	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
176	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	#4031	—	2	1	no	—
178	#4031	—	2	1	no	—
179	#4027	—	2	1	no	—
180	D₅×C₂²⋊C₄	—	2	1	no	—
181	D₅×C₂²⋊C₄	—	2	1	no	—
182	D₅×C₂²⋊C₄	—	2	1	no	—
183	#4021	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
186	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
189	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
190	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
191	#3953	C₂²×C₃	1	1	yes	characteristic, complemented
192	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
193	#3946	C₂²×C₃	1	1	yes	characteristic, complemented
194	#3946	C₂²×C₃	1	1	yes	characteristic, complemented
195	#3942	C₂²×C₃	1	1	yes	characteristic, complemented
196	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₂×#463	—	5	1	no	Sylow
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	—	2	1	no	—
201	C₂²×C₃×D₅	—	2	1	no	—
202	C₂²×C₃×D₅	—	2	4	no	—
203	C₂²×C₃×D₅	—	2	1	no	—
204	C₂²×C₃×D₅	—	4	2	no	—
205	C₂²×C₃×D₅	—	4	2	no	—
206	C₂²×C₃×D₅	—	4	2	no	—
207	C₂²×C₃×D₅	—	4	2	no	—
208	C₂²×C₃×D₅	—	4	2	no	—
209	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
210	C₃×C₅×Q₈	—	2	1	no	—
211	C₃×C₅×Q₈	—	2	1	no	—
212	C₃×C₅×D₄	—	2	1	no	—
213	C₃×C₅×D₄	—	2	1	no	—
214	C₃×C₅×D₄	—	2	1	no	—
215	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	4	2	no	—
219	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
222	C₃×C₂²⋊D₅	—	2	4	no	—
223	C₃×C₂²⋊D₅	—	4	2	no	—
224	C₂×C₃×Dic₅	—	2	1	no	—
225	C₂×C₃×Dic₅	—	2	1	no	—
226	C₂×C₃×Dic₅	—	4	2	no	—
227	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
230	C₃×D₂₀	—	2	1	no	—
231	C₃×D₂₀	—	2	1	no	—
232	C₃×D₂₀	—	2	1	no	—
233	C₃×D₂₀	C₂×D₄	1	2	yes	—
234	C₃×C₄×D₅	—	2	2	no	—
235	C₃×C₄×D₅	—	2	2	no	—
236	C₃×C₄×D₅	—	4	2	no	—
237	C₃×C₄×D₅	—	4	2	no	—
238	C₃×C₄×D₅	—	4	2	no	—
239	C₃×C₄×D₅	—	4	2	no	—
240	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
241	C₃×C₄×D₅	#41	1	2	yes	—
242	C₃×Dic₁₀	—	2	1	no	—
243	C₃×Dic₁₀	—	2	1	no	—
244	C₃×Dic₁₀	—	4	2	no	—
245	C₃×C₅×C₈	—	2	1	no	—
246	C₃×C₅×C₈	—	2	1	no	—
247	C₃×#168	—	2	1	no	—
248	C₃×#168	—	2	1	no	—
249	C₂²×C₃×Q₈	—	5	1	no	—
250	C₂²×C₃×D₄	—	5	1	no	—
251	C₂²×C₃×D₄	—	5	1	no	—
252	C₂³×C₃×C₄	—	10	1	no	—
253	C₂×C₃×SD₁₆	—	5	1	no	—
254	C₂×C₃×SD₁₆	—	5	1	no	—
255	C₂×C₃×SD₁₆	—	5	1	no	—
256	C₂×C₃×SD₁₆	—	10	4	no	—
257	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
258	C₂×C₃×D₈	—	5	1	no	—
259	C₂×C₃×D₈	—	5	1	no	—
260	C₂×C₃×D₈	—	5	1	no	—
261	C₂×C₃×D₈	—	10	4	no	—
262	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
263	C₂²×C₃×C₈	—	5	1	no	—
264	C₂²×C₃×C₈	—	5	1	no	—
265	C₃×#124	—	5	1	no	—
266	C₃×#124	—	5	1	no	—
267	C₃×#124	—	5	1	no	—
268	C₃×#124	—	10	1	no	—
269	C₃×#124	—	10	1	no	—
270	C₃×#124	C₂×D₅	1	1	yes	characteristic, complemented
271	C₃×C₄×D₄	—	5	1	no	—
272	C₃×C₄×D₄	—	5	1	no	—
273	C₃×C₄×D₄	—	5	1	no	—
274	C₃×C₄×D₄	—	10	1	no	—
275	C₃×C₄×D₄	—	10	1	no	—
276	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
277	C₂×C₃×C₄⋊C₄	—	5	1	no	—
278	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
279	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
280	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
281	C₂×C₃×C₄²	—	5	1	no	—
282	C₃×C₄⋊C₈	—	5	1	no	—
283	C₃×C₄⋊C₈	—	5	1	no	—
284	C₃×C₄⋊C₈	—	5	1	no	—
285	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
286	C₃×#103	—	5	1	no	—
287	C₃×#103	—	5	1	no	—
288	C₃×#103	—	5	1	no	—
289	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
290	C₃×#102	—	5	1	no	—
291	C₃×#102	—	5	1	no	—
292	C₃×#102	—	5	1	no	—
293	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
294	C₂³×D₅	—	2	1	no	—
295	C₂³×D₅	—	2	1	no	—
296	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₄×C₅	—	2	1	no	—
300	C₂×C₂²⋊D₅	—	2	1	no	—
301	C₂×C₂²⋊D₅	—	2	1	no	—
302	C₂²×Dic₅	—	2	1	no	—
303	Q₈×D₅	—	2	2	no	—
304	Q₈×D₅	—	2	2	no	—
305	D₄×D₅	—	2	2	no	—
306	D₄×D₅	—	2	2	no	—
307	D₄×D₅	—	2	2	no	—
308	D₄×D₅	C₃×D₄	1	4	yes	—
309	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
310	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₄×D₅	—	2	1	no	—
312	C₂×C₄×D₅	—	2	1	no	—
313	C₂×C₄×D₅	—	2	1	no	—
314	C₂×C₄×D₅	—	2	1	no	—
315	C₂×C₄×D₅	—	4	4	no	—
316	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
317	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
318	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
319	C₂×Dic₁₀	—	2	1	no	—
320	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
321	C₅×SD₁₆	—	2	2	no	—
322	C₅×D₈	—	2	2	no	—
323	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
324	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
325	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
326	C₅×C₂²⋊C₄	—	2	1	no	—
327	C₅×C₂²⋊C₄	—	2	1	no	—
328	C₅×C₂²⋊C₄	—	2	1	no	—
329	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
330	C₂²⋊Dic₅	—	2	1	no	—
331	C₂²⋊Dic₅	—	2	1	no	—
332	C₂²⋊Dic₅	—	2	1	no	—
333	#688	—	2	2	no	—
334	#687	—	2	2	no	—
335	#686	—	2	2	no	—
336	#686	—	2	2	no	—
337	#685	—	2	1	no	—
338	#685	—	2	1	no	—
339	#685	—	2	1	no	—
340	#685	—	2	1	no	—
341	#685	—	2	1	no	—
342	#685	—	2	1	no	—
343	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
344	#683	—	2	1	no	—
345	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
346	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
347	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
348	C₂×#168	C₂³×C₃	1	1	yes	characteristic
349	C₂×#168	C₂³×C₃	1	1	yes	characteristic
350	D₄₀	—	2	2	no	—
351	#677	—	2	2	no	—
352	C₈×D₅	—	2	2	no	—
353	C₈×D₅	—	2	2	no	—
354	C₂²×SD₁₆	—	5	1	no	—
355	C₂²×D₈	—	5	1	no	—
356	C₂×#124	—	5	1	no	—
357	C₂×C₄×D₄	—	5	1	no	—
358	#463	—	5	1	no	—
359	#463	—	5	1	no	—
360	#463	—	5	1	no	—
361	#463	—	5	1	no	—
362	#463	—	5	1	no	—
363	#463	—	5	1	no	—
364	#463	—	5	1	no	—
365	#463	C₃×D₅	1	1	yes	characteristic, direct product factor
366	C₂×C₄⋊C₈	—	5	1	no	—
367	C₂×#103	—	5	1	no	—
368	C₂×#102	—	5	1	no	—
369	C₂²×C₃×C₅	—	2	2	no	—
370	C₂²×C₃×C₅	—	4	1	no	—
371	C₂²×C₃×C₅	—	4	1	no	—
372	C₂²×C₃×C₅	—	4	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₃×D₅	—	2	2	no	—
377	C₂×C₃×D₅	—	4	1	no	—
378	C₂×C₃×D₅	—	4	1	no	—
379	C₂×C₃×D₅	—	4	8	no	—
380	C₂×C₃×D₅	—	4	1	no	—
381	C₂×C₃×D₅	—	4	1	no	—
382	C₂×C₃×D₅	—	4	1	no	—
383	C₂×C₃×D₅	—	8	4	no	—
384	C₂×C₃×D₅	#121	1	2	yes	—
385	C₂×C₃×D₅	#135	1	2	yes	—
386	C₂×C₃×D₅	AGL(1,ℤ/8)	1	2	yes	—
387	C₃×C₄×C₅	—	2	1	no	—
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	—	4	1	no	—
390	C₃×C₄×C₅	—	4	1	no	—
391	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
392	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
393	C₃×Dic₅	—	2	1	no	—
394	C₃×Dic₅	—	2	1	no	—
395	C₃×Dic₅	—	4	1	no	—
396	C₃×Dic₅	—	4	1	no	—
397	C₃×Dic₅	#121	1	2	yes	—
398	C₂⁴×C₃	—	10	1	no	—
399	C₂⁴×C₃	—	10	1	no	—
400	C₂×C₃×Q₈	—	5	1	no	—
401	C₂×C₃×Q₈	—	10	1	no	—
402	C₂×C₃×Q₈	—	10	2	no	—
403	C₂×C₃×Q₈	—	10	2	no	—
404	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
405	C₂×C₃×D₄	—	5	4	no	—
406	C₂×C₃×D₄	—	5	1	no	—
407	C₂×C₃×D₄	—	5	1	no	—
408	C₂×C₃×D₄	—	10	2	no	—
409	C₂×C₃×D₄	—	10	2	no	—
410	C₂×C₃×D₄	—	10	2	no	—
411	C₂×C₃×D₄	—	10	1	no	—
412	C₂×C₃×D₄	—	10	1	no	—
413	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
414	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
415	C₂²×C₃×C₄	—	2	1	no	—
416	C₂²×C₃×C₄	—	5	1	no	—
417	C₂²×C₃×C₄	—	5	1	no	—
418	C₂²×C₃×C₄	—	5	1	no	—
419	C₂²×C₃×C₄	—	10	1	no	—
420	C₂²×C₃×C₄	—	10	1	no	—
421	C₂²×C₃×C₄	—	10	1	no	—
422	C₂²×C₃×C₄	—	10	1	no	—
423	C₂²×C₃×C₄	—	10	1	no	—
424	C₂²×C₃×C₄	—	20	4	no	—
425	C₃×SD₁₆	—	2	2	no	—
426	C₃×SD₁₆	—	10	2	no	—
427	C₃×SD₁₆	—	10	2	no	—
428	C₃×SD₁₆	—	10	2	no	—
429	C₃×D₈	—	2	2	no	—
430	C₃×D₈	—	10	2	no	—
431	C₃×D₈	—	10	2	no	—
432	C₃×D₈	—	10	2	no	—
433	C₂×C₃×C₈	—	5	1	no	—
434	C₂×C₃×C₈	—	5	1	no	—
435	C₂×C₃×C₈	—	10	2	no	—
436	C₂×C₃×C₈	—	10	2	no	—
437	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
438	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
439	C₃×C₄⋊C₄	—	5	1	no	—
440	C₃×C₄⋊C₄	—	10	1	no	—
441	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
442	C₃×C₂²⋊C₄	—	2	1	no	—
443	C₃×C₂²⋊C₄	—	2	1	no	—
444	C₃×C₂²⋊C₄	—	2	1	no	—
445	C₃×C₂²⋊C₄	—	10	1	no	—
446	C₃×C₂²⋊C₄	—	10	1	no	—
447	C₃×C₂²⋊C₄	—	10	1	no	—
448	C₃×C₂²⋊C₄	—	10	1	no	—
449	C₃×C₂²⋊C₄	—	10	1	no	—
450	C₃×C₂²⋊C₄	—	10	1	no	—
451	C₃×C₂²⋊C₄	—	10	1	no	—
452	C₃×C₂²⋊C₄	—	10	1	no	—
453	C₃×C₂²⋊C₄	—	10	1	no	—
454	C₃×C₄²	—	5	1	no	—
455	C₃×C₄²	—	5	1	no	—
456	C₃×C₄²	—	5	1	no	—
457	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
458	C₂³×C₅	—	2	1	no	—
459	C₂³×C₅	—	2	1	no	—
460	C₂²×D₅	—	2	1	no	—
461	C₂²×D₅	—	2	4	no	—
462	C₂²×D₅	—	2	1	no	—
463	C₂²×D₅	—	4	2	no	—
464	C₂²×D₅	—	4	2	no	—
465	C₂²×D₅	—	4	2	no	—
466	C₂²×D₅	—	4	2	no	—
467	C₂²×D₅	—	4	2	no	—
468	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
469	C₅×Q₈	—	2	1	no	—
470	C₅×Q₈	—	2	1	no	—
471	C₅×D₄	—	2	1	no	—
472	C₅×D₄	—	2	1	no	—
473	C₅×D₄	—	2	1	no	—
474	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	4	2	no	—
478	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
479	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
480	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
481	C₂²⋊D₅	—	2	4	no	—
482	C₂²⋊D₅	—	4	2	no	—
483	C₂×Dic₅	—	2	1	no	—
484	C₂×Dic₅	—	2	1	no	—
485	C₂×Dic₅	—	4	2	no	—
486	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
487	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
488	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
489	D₂₀	—	2	1	no	—
490	D₂₀	—	2	1	no	—
491	D₂₀	—	2	1	no	—
492	D₂₀	C₂×C₃×D₄	1	2	yes	—
493	C₄×D₅	—	2	2	no	—
494	C₄×D₅	—	2	2	no	—
495	C₄×D₅	—	4	2	no	—
496	C₄×D₅	—	4	2	no	—
497	C₄×D₅	—	4	2	no	—
498	C₄×D₅	—	4	2	no	—
499	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
500	C₄×D₅	C₃×#41	1	2	yes	—
501	Dic₁₀	—	2	1	no	—
502	Dic₁₀	—	2	1	no	—
503	Dic₁₀	—	4	2	no	—
504	C₅×C₈	—	2	1	no	—
505	C₅×C₈	—	2	1	no	—
506	#168	—	2	1	no	—
507	#168	—	2	1	no	—
508	C₂²×Q₈	—	5	1	no	—
509	C₂²×D₄	—	5	1	no	—
510	C₂²×D₄	—	5	1	no	—
511	C₂³×C₄	—	10	1	no	—
512	C₂×SD₁₆	—	5	1	no	—
513	C₂×SD₁₆	—	5	1	no	—
514	C₂×SD₁₆	—	5	1	no	—
515	C₂×SD₁₆	—	10	4	no	—
516	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
517	C₂×D₈	—	5	1	no	—
518	C₂×D₈	—	5	1	no	—
519	C₂×D₈	—	5	1	no	—
520	C₂×D₈	—	10	4	no	—
521	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
522	C₂²×C₈	—	5	1	no	—
523	C₂²×C₈	—	5	1	no	—
524	#124	—	5	1	no	—
525	#124	—	5	1	no	—
526	#124	—	5	1	no	—
527	#124	—	10	1	no	—
528	#124	—	10	1	no	—
529	#124	C₂×C₃×D₅	1	1	yes	characteristic, complemented
530	C₄×D₄	—	5	1	no	—
531	C₄×D₄	—	5	1	no	—
532	C₄×D₄	—	5	1	no	—
533	C₄×D₄	—	10	1	no	—
534	C₄×D₄	—	10	1	no	—
535	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
536	C₂×C₄⋊C₄	—	5	1	no	—
537	C₂×C₂²⋊C₄	—	10	1	no	—
538	C₂×C₂²⋊C₄	—	10	1	no	—
539	C₂×C₂²⋊C₄	—	10	1	no	—
540	C₂×C₄²	—	5	1	no	—
541	C₄⋊C₈	—	5	1	no	—
542	C₄⋊C₈	—	5	1	no	—
543	C₄⋊C₈	—	5	1	no	—
544	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
545	#103	—	5	1	no	—
546	#103	—	5	1	no	—
547	#103	—	5	1	no	—
548	#103	C₂×C₃×D₅	1	1	yes	characteristic, complemented
549	#102	—	5	1	no	—
550	#102	—	5	1	no	—
551	#102	—	5	1	no	—
552	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
553	C₂×C₃×C₅	—	4	2	no	—
554	C₂×C₃×C₅	—	8	1	no	—
555	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
556	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
557	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
558	C₃×D₅	—	4	2	no	—
559	C₃×D₅	—	8	1	no	—
560	C₃×D₅	#463	1	4	yes	direct product factor
561	C₂³×C₃	—	2	1	no	—
562	C₂³×C₃	—	2	1	no	—
563	C₂³×C₃	—	5	1	no	—
564	C₂³×C₃	—	10	4	no	—
565	C₂³×C₃	—	10	1	no	—
566	C₂³×C₃	—	10	1	no	—
567	C₂³×C₃	—	20	2	no	—
568	C₂³×C₃	—	20	2	no	—
569	C₂³×C₃	—	20	2	no	—
570	C₂³×C₃	—	20	2	no	—
571	C₂³×C₃	—	20	2	no	—
572	C₃×Q₈	—	2	1	no	—
573	C₃×Q₈	—	2	1	no	—
574	C₃×Q₈	—	10	1	no	—
575	C₃×Q₈	—	10	1	no	—
576	C₃×Q₈	—	20	2	no	—
577	C₃×D₄	—	2	1	no	—
578	C₃×D₄	—	2	1	no	—
579	C₃×D₄	—	2	1	no	—
580	C₃×D₄	—	5	2	no	—
581	C₃×D₄	—	10	4	no	—
582	C₃×D₄	—	10	1	no	—
583	C₃×D₄	—	10	1	no	—
584	C₃×D₄	—	10	1	no	—
585	C₃×D₄	—	20	2	no	—
586	C₃×D₄	D₄×D₅	1	2	yes	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	4	2	no	—
590	C₂×C₃×C₄	—	5	1	no	—
591	C₂×C₃×C₄	—	5	2	no	—
592	C₂×C₃×C₄	—	5	2	no	—
593	C₂×C₃×C₄	—	5	1	no	—
594	C₂×C₃×C₄	—	5	1	no	—
595	C₂×C₃×C₄	—	10	2	no	—
596	C₂×C₃×C₄	—	10	2	no	—
597	C₂×C₃×C₄	—	10	1	no	—
598	C₂×C₃×C₄	—	10	1	no	—
599	C₂×C₃×C₄	—	20	2	no	—
600	C₂×C₃×C₄	—	20	2	no	—
601	C₂×C₃×C₄	—	20	2	no	—
602	C₂×C₃×C₄	—	20	2	no	—
603	C₂×C₃×C₄	—	20	2	no	—
604	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
605	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
606	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
607	C₃×C₈	—	2	1	no	—
608	C₃×C₈	—	2	1	no	—
609	C₃×C₈	—	10	1	no	—
610	C₃×C₈	—	10	1	no	—
611	C₂²×C₅	—	2	2	no	—
612	C₂²×C₅	—	4	1	no	—
613	C₂²×C₅	—	4	1	no	—
614	C₂²×C₅	—	4	1	no	—
615	C₂²×C₅	—	4	1	no	—
616	C₂²×C₅	—	4	1	no	—
617	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
618	C₂×D₅	—	2	2	no	—
619	C₂×D₅	—	4	1	no	—
620	C₂×D₅	—	4	1	no	—
621	C₂×D₅	—	4	8	no	—
622	C₂×D₅	—	4	1	no	—
623	C₂×D₅	—	4	1	no	—
624	C₂×D₅	—	4	1	no	—
625	C₂×D₅	—	8	4	no	—
626	C₂×D₅	C₃×#121	1	2	yes	—
627	C₂×D₅	C₃×#135	1	2	yes	—
628	C₂×D₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
629	C₄×C₅	—	2	1	no	—
630	C₄×C₅	—	2	1	no	—
631	C₄×C₅	—	4	1	no	—
632	C₄×C₅	—	4	1	no	—
633	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
634	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
635	Dic₅	—	2	1	no	—
636	Dic₅	—	2	1	no	—
637	Dic₅	—	4	1	no	—
638	Dic₅	—	4	1	no	—
639	Dic₅	C₃×#121	1	2	yes	—
640	C₂⁴	—	10	1	no	—
641	C₂⁴	—	10	1	no	—
642	C₂×Q₈	—	5	1	no	—
643	C₂×Q₈	—	10	1	no	—
644	C₂×Q₈	—	10	2	no	—
645	C₂×Q₈	—	10	2	no	—
646	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
647	C₂×D₄	—	5	4	no	—
648	C₂×D₄	—	5	1	no	—
649	C₂×D₄	—	5	1	no	—
650	C₂×D₄	—	10	2	no	—
651	C₂×D₄	—	10	2	no	—
652	C₂×D₄	—	10	2	no	—
653	C₂×D₄	—	10	1	no	—
654	C₂×D₄	—	10	1	no	—
655	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
656	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	5	1	no	—
659	C₂²×C₄	—	5	1	no	—
660	C₂²×C₄	—	5	1	no	—
661	C₂²×C₄	—	10	1	no	—
662	C₂²×C₄	—	10	1	no	—
663	C₂²×C₄	—	10	1	no	—
664	C₂²×C₄	—	10	1	no	—
665	C₂²×C₄	—	10	1	no	—
666	C₂²×C₄	—	20	4	no	—
667	SD₁₆	—	2	2	no	—
668	SD₁₆	—	10	2	no	—
669	SD₁₆	—	10	2	no	—
670	SD₁₆	—	10	2	no	—
671	D₈	—	2	2	no	—
672	D₈	—	10	2	no	—
673	D₈	—	10	2	no	—
674	D₈	—	10	2	no	—
675	C₂×C₈	—	5	1	no	—
676	C₂×C₈	—	5	1	no	—
677	C₂×C₈	—	10	2	no	—
678	C₂×C₈	—	10	2	no	—
679	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
680	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
681	C₄⋊C₄	—	5	1	no	—
682	C₄⋊C₄	—	10	1	no	—
683	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	10	1	no	—
688	C₂²⋊C₄	—	10	1	no	—
689	C₂²⋊C₄	—	10	1	no	—
690	C₂²⋊C₄	—	10	1	no	—
691	C₂²⋊C₄	—	10	1	no	—
692	C₂²⋊C₄	—	10	1	no	—
693	C₂²⋊C₄	—	10	1	no	—
694	C₂²⋊C₄	—	10	1	no	—
695	C₂²⋊C₄	—	10	1	no	—
696	C₄²	—	5	1	no	—
697	C₄²	—	5	1	no	—
698	C₄²	—	5	1	no	—
699	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
700	C₃×C₅	C₂×#463	1	1	yes	characteristic, complemented, Hall
701	C₂²×C₃	—	2	2	no	—
702	C₂²×C₃	—	4	1	no	—
703	C₂²×C₃	—	4	1	no	—
704	C₂²×C₃	—	4	1	no	—
705	C₂²×C₃	—	4	1	no	—
706	C₂²×C₃	—	4	1	no	—
707	C₂²×C₃	—	5	2	no	—
708	C₂²×C₃	—	5	2	no	—
709	C₂²×C₃	—	5	2	no	—
710	C₂²×C₃	—	10	2	no	—
711	C₂²×C₃	—	20	8	no	—
712	C₂²×C₃	—	20	1	no	—
713	C₂²×C₃	—	20	1	no	—
714	C₂²×C₃	—	20	1	no	—
715	C₂²×C₃	—	20	1	no	—
716	C₂²×C₃	—	20	1	no	—
717	C₂²×C₃	—	40	4	no	—
718	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
719	C₃×C₄	—	2	1	no	—
720	C₃×C₄	—	2	1	no	—
721	C₃×C₄	—	4	1	no	—
722	C₃×C₄	—	4	1	no	—
723	C₃×C₄	—	5	2	no	—
724	C₃×C₄	—	10	1	no	—
725	C₃×C₄	—	10	1	no	—
726	C₃×C₄	—	20	1	no	—
727	C₃×C₄	—	20	1	no	—
728	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
729	C₃×C₄	D₅×#41	1	1	yes	characteristic
730	C₂×C₅	—	4	2	no	—
731	C₂×C₅	—	8	1	no	—
732	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
733	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
734	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
735	D₅	—	4	2	no	—
736	D₅	—	8	1	no	—
737	D₅	C₃×#463	1	4	yes	direct product factor
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	5	1	no	—
741	C₂³	—	10	4	no	—
742	C₂³	—	10	1	no	—
743	C₂³	—	10	1	no	—
744	C₂³	—	20	2	no	—
745	C₂³	—	20	2	no	—
746	C₂³	—	20	2	no	—
747	C₂³	—	20	2	no	—
748	C₂³	—	20	2	no	—
749	Q₈	—	2	1	no	—
750	Q₈	—	2	1	no	—
751	Q₈	—	10	1	no	—
752	Q₈	—	10	1	no	—
753	Q₈	—	20	2	no	—
754	D₄	—	2	1	no	—
755	D₄	—	2	1	no	—
756	D₄	—	2	1	no	—
757	D₄	—	5	2	no	—
758	D₄	—	10	4	no	—
759	D₄	—	10	1	no	—
760	D₄	—	10	1	no	—
761	D₄	—	10	1	no	—
762	D₄	—	20	2	no	—
763	D₄	C₃×D₄×D₅	1	2	yes	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	5	1	no	—
768	C₂×C₄	—	5	2	no	—
769	C₂×C₄	—	5	2	no	—
770	C₂×C₄	—	5	1	no	—
771	C₂×C₄	—	5	1	no	—
772	C₂×C₄	—	10	2	no	—
773	C₂×C₄	—	10	2	no	—
774	C₂×C₄	—	10	1	no	—
775	C₂×C₄	—	10	1	no	—
776	C₂×C₄	—	20	2	no	—
777	C₂×C₄	—	20	2	no	—
778	C₂×C₄	—	20	2	no	—
779	C₂×C₄	—	20	2	no	—
780	C₂×C₄	—	20	2	no	—
781	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
782	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
783	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
784	C₈	—	2	1	no	—
785	C₈	—	2	1	no	—
786	C₈	—	10	1	no	—
787	C₈	—	10	1	no	—
788	C₂×C₃	—	4	2	no	—
789	C₂×C₃	—	5	4	no	—
790	C₂×C₃	—	8	1	no	—
791	C₂×C₃	—	20	2	no	—
792	C₂×C₃	—	40	1	no	—
793	C₂×C₃	D₅×#121	1	1	yes	characteristic
794	C₂×C₃	D₅×#135	1	1	yes	characteristic
795	C₂×C₃	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
796	C₅	C₂×C₃×#463	1	1	yes	characteristic, complemented, Sylow
797	C₂²	—	2	2	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	5	2	no	—
804	C₂²	—	5	2	no	—
805	C₂²	—	5	2	no	—
806	C₂²	—	10	2	no	—
807	C₂²	—	20	8	no	—
808	C₂²	—	20	1	no	—
809	C₂²	—	20	1	no	—
810	C₂²	—	20	1	no	—
811	C₂²	—	20	1	no	—
812	C₂²	—	20	1	no	—
813	C₂²	—	40	4	no	—
814	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	5	2	no	—
820	C₄	—	10	1	no	—
821	C₄	—	10	1	no	—
822	C₄	—	20	1	no	—
823	C₄	—	20	1	no	—
824	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
825	C₄	C₃×D₅×#41	1	1	yes	characteristic
826	C₃	D₅×#463	1	1	yes	characteristic, direct product factor, Sylow
827	C₂	—	4	2	no	—
828	C₂	—	5	4	no	—
829	C₂	—	8	1	no	—
830	C₂	—	20	2	no	—
831	C₂	—	40	1	no	—
832	C₂	C₃×D₅×#121	1	1	yes	characteristic
833	C₂	C₃×D₅×#135	1	1	yes	characteristic
834	C₂	C₃×D₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#463	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₅×D₈	C₂
hypercenter	C₃×#463	D₅
hypocenter	C₅	C₂×C₃×#463
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#463

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×SD₁₆	C₂	semidirect
3. C₃×D₅×#124	C₂	semidirect
4. C₃×C₄×D₄×D₅	C₂	semidirect
5. C₃×C₅×#463	C₂	semidirect
6. C₃×#65454	C₂	semidirect
7. C₃×#65442	C₂	semidirect
8. C₃×#65346	C₂	semidirect
9. C₃×#65305	C₂	semidirect
10. C₃×#65133	C₂	semidirect
11. C₃×D₅×C₄⋊C₈	C₂	semidirect
12. C₃×#65108	C₂	semidirect
13. C₃×D₅×#103	C₂	semidirect
14. C₃×#65076	C₂	semidirect
15. C₃×D₅×#102	C₂	semidirect
16. D₅×#463	C₃	direct (N × H)
21. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₃×C₅×#124	C₂²	semidirect
24. C₃×C₄×C₅×D₄	C₂²	semidirect
25. C₃×#4093	C₂²	semidirect
26. C₂×C₃×#688	C₂²	semidirect
27. C₃×#4082	C₂²	semidirect
28. C₃×D₄×Dic₅	C₂²	semidirect
29. C₂×C₃×#687	C₂²	semidirect
36. C₂×C₃×#677	C₂²	semidirect
39. C₃×#4039	C₂²	semidirect
47. C₃×#4021	C₂²	semidirect
48. C₃×C₄×D₂₀	C₂²	semidirect
50. C₃×C₅×C₄⋊C₈	C₂²	semidirect
51. C₃×C₅×#103	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×#3967	C₂²	semidirect
54. C₃×#3964	C₂²	semidirect
55. C₃×#3953	C₂²	semidirect
56. C₃×#3948	C₂²	semidirect
57. C₃×#3946	C₂²	semidirect
58. C₃×#3946	C₂²	semidirect
59. C₃×#3942	C₂²	semidirect
60. C₃×#3941	C₂²	semidirect
61. C₃×C₄⋊#168	C₂²	semidirect
63. C₂×D₅×SD₁₆	C₂×C₃	semidirect
65. D₅×#124	C₂×C₃	semidirect
66. C₄×D₄×D₅	C₂×C₃	semidirect
67. C₅×#463	C₂×C₃	semidirect
68. #65454	C₂×C₃	semidirect
69. #65442	C₂×C₃	semidirect
70. #65346	C₂×C₃	semidirect
71. #65305	C₂×C₃	semidirect
72. #65133	C₂×C₃	semidirect
73. D₅×C₄⋊C₈	C₂×C₃	semidirect
74. #65108	C₂×C₃	semidirect
75. D₅×#103	C₂×C₃	semidirect
76. #65076	C₂×C₃	semidirect
77. D₅×#102	C₂×C₃	semidirect
149. C₃×#463	D₅	direct (N × H)
157. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
159. C₅×#124	C₂²×C₃	semidirect
160. C₄×C₅×D₄	C₂²×C₃	semidirect
161. #4093	C₂²×C₃	semidirect
162. C₂×#688	C₂²×C₃	semidirect
163. #4082	C₂²×C₃	semidirect
164. D₄×Dic₅	C₂²×C₃	semidirect
165. C₂×#687	C₂²×C₃	semidirect
172. C₂×#677	C₂²×C₃	semidirect
175. #4039	C₂²×C₃	semidirect
183. #4021	C₂²×C₃	semidirect
184. C₄×D₂₀	C₂²×C₃	semidirect
186. C₅×C₄⋊C₈	C₂²×C₃	semidirect
187. C₅×#103	C₂²×C₃	semidirect
188. C₅×#102	C₂²×C₃	semidirect
189. #3967	C₂²×C₃	semidirect
190. #3964	C₂²×C₃	semidirect
191. #3953	C₂²×C₃	semidirect
192. #3948	C₂²×C₃	semidirect
193. #3946	C₂²×C₃	semidirect
194. #3946	C₂²×C₃	semidirect
195. #3942	C₂²×C₃	semidirect
196. #3941	C₂²×C₃	semidirect
197. C₄⋊#168	C₂²×C₃	semidirect
257. C₂×C₃×SD₁₆	C₂×D₅	semidirect
270. C₃×#124	C₂×D₅	semidirect
276. C₃×C₄×D₄	C₂×D₅	semidirect
285. C₃×C₄⋊C₈	C₂×D₅	semidirect
289. C₃×#103	C₂×D₅	semidirect
293. C₃×#102	C₂×D₅	semidirect
365. #463	C₃×D₅	direct (N × H)
516. C₂×SD₁₆	C₂×C₃×D₅	semidirect
529. #124	C₂×C₃×D₅	semidirect
535. C₄×D₄	C₂×C₃×D₅	semidirect
544. C₄⋊C₈	C₂×C₃×D₅	semidirect
548. #103	C₂×C₃×D₅	semidirect
552. #102	C₂×C₃×D₅	semidirect
560. C₃×D₅	#463	direct (N × H)
700. C₃×C₅	C₂×#463	semidirect
737. D₅	C₃×#463	direct (N × H)
796. C₅	C₂×C₃×#463	semidirect
826. C₃	D₅×#463	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×D₅×SD₁₆	2
C₂×C₃×D₅×D₈	2
C₃×D₅×#124	2
C₃×C₄×D₄×D₅	2
C₃×C₅×#463	2
C₃×#65454	2
C₃×#65442	2
C₃×#65346	2
C₃×#65305	2
C₃×#65133	2
C₃×D₅×C₄⋊C₈	2
C₃×#65108	2
C₃×D₅×#103	2
C₃×#65076	2
C₃×D₅×#102	2
D₅×#463	3
C₂×C₃×#463	5

Subgroups — C3×D5×#463 #14425918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#463 #14425918