Subgroups — C₅₉×#21464 #28433573

Order 15104.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#449	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#102×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#520	—	2	4	no	—
21	C₅₉×#520	—	2	4	no	—
22	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₅₉	—	2	1	no	—
25	C₂×C₄×D₄×C₅₉	—	2	1	no	—
26	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₅₉	—	2	1	no	—
30	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
32	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#449	C₄	1	8	yes	complemented
34	C₅₉×#442	—	2	4	no	—
35	C₄×SD₁₆×C₅₉	—	2	4	no	—
36	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
50	C₅₉×#390	—	2	1	no	—
51	C₅₉×#390	C₂²	1	1	yes	characteristic
52	C₅₉×#389	C₂²	1	1	yes	characteristic
53	C₅₉×#388	—	2	1	no	—
54	C₅₉×#386	—	2	1	no	—
55	C₅₉×#385	—	2	1	no	—
56	C₅₉×#380	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
58	C₅₉×#340	C₂²	1	1	yes	characteristic
59	C₅₉×#340	C₂²	1	1	yes	characteristic
60	C₅₉×#340	C₂²	1	1	yes	characteristic
61	C₅₉×#340	C₂²	1	1	yes	characteristic
62	C₅₉×#336	C₂²	1	1	yes	characteristic
63	C₅₉×#336	C₂²	1	1	yes	characteristic
64	C₂×#41×C₅₉	—	2	2	no	—
65	C₂×#41×C₅₉	—	2	2	no	—
66	C₂×#41×C₅₉	—	2	2	no	—
67	C₂×#41×C₅₉	—	2	2	no	—
68	C₂×#41×C₅₉	—	2	2	no	—
69	C₂×#41×C₅₉	C₂×C₄	1	4	yes	complemented
70	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₅₉	—	2	1	no	—
72	C₂²×D₄×C₅₉	—	2	1	no	—
73	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅₉	—	2	1	no	—
76	C₂³×C₄×C₅₉	—	2	1	no	—
77	C₂³×C₄×C₅₉	—	2	1	no	—
78	C₂³×C₄×C₅₉	—	2	1	no	—
79	C₂³×C₄×C₅₉	—	2	1	no	—
80	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×SD₁₆×C₅₉	—	2	2	no	—
82	C₂×SD₁₆×C₅₉	—	2	2	no	—
83	C₂×SD₁₆×C₅₉	C₂×C₄	1	4	yes	complemented
84	C₂×D₈×C₅₉	—	2	2	no	—
85	C₂×D₈×C₅₉	—	2	2	no	—
86	C₂×D₈×C₅₉	C₂×C₄	1	4	yes	complemented
87	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
91	#121×C₅₉	—	2	2	no	—
92	#121×C₅₉	C₂×C₄	1	4	yes	complemented
93	C₄×Q₈×C₅₉	—	2	2	no	—
94	C₄×Q₈×C₅₉	—	2	2	no	—
95	C₄×Q₈×C₅₉	—	2	2	no	—
96	C₄×Q₈×C₅₉	D₄	1	4	yes	complemented
97	C₄×D₄×C₅₉	—	2	8	no	—
98	C₄×D₄×C₅₉	—	2	8	no	—
99	C₄×D₄×C₅₉	—	2	2	no	—
100	C₄×D₄×C₅₉	—	2	2	no	—
101	C₄×D₄×C₅₉	—	2	2	no	—
102	C₄×D₄×C₅₉	—	2	2	no	—
103	C₄×D₄×C₅₉	—	2	2	no	—
104	C₄×D₄×C₅₉	D₄	1	4	yes	complemented
105	#117×C₅₉	—	2	8	no	—
106	#117×C₅₉	—	2	2	no	—
107	#117×C₅₉	—	2	2	no	—
108	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
109	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
113	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
114	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₅₉	—	2	1	no	—
132	C₂×C₄²×C₅₉	—	2	1	no	—
133	C₂×C₄²×C₅₉	—	2	1	no	—
134	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
136	#106×C₅₉	—	2	2	no	—
137	#106×C₅₉	—	2	2	no	—
138	#103×C₅₉	—	2	2	no	—
139	#103×C₅₉	—	2	2	no	—
140	#103×C₅₉	C₂×C₄	1	4	yes	complemented
141	#102×C₅₉	—	2	2	no	—
142	#102×C₅₉	—	2	2	no	—
143	#102×C₅₉	—	2	2	no	—
144	#102×C₅₉	—	2	2	no	—
145	#102×C₅₉	C₂×C₄	1	4	yes	complemented
146	C₂²⋊C₈×C₅₉	—	2	2	no	—
147	C₂²⋊C₈×C₅₉	C₂×C₄	1	4	yes	complemented
148	#97×C₅₉	—	2	2	no	—
149	C₄×C₈×C₅₉	—	2	2	no	—
150	#95×C₅₉	—	2	1	no	—
151	#95×C₅₉	—	2	1	no	—
152	#95×C₅₉	—	2	1	no	—
153	C₂⁴×C₅₉	—	2	1	no	—
154	C₂⁴×C₅₉	—	2	1	no	—
155	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
156	#41×C₅₉	—	2	8	no	—
157	#41×C₅₉	—	2	8	no	—
158	#41×C₅₉	—	2	8	no	—
159	#41×C₅₉	—	2	8	no	—
160	C₂×Q₈×C₅₉	—	2	1	no	—
161	C₂×Q₈×C₅₉	—	2	1	no	—
162	C₂×Q₈×C₅₉	—	2	1	no	—
163	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
164	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
165	C₂×Q₈×C₅₉	#41	1	2	yes	—
166	C₂×D₄×C₅₉	—	2	4	no	—
167	C₂×D₄×C₅₉	—	2	4	no	—
168	C₂×D₄×C₅₉	—	2	4	no	—
169	C₂×D₄×C₅₉	—	2	4	no	—
170	C₂×D₄×C₅₉	—	2	1	no	—
171	C₂×D₄×C₅₉	—	2	1	no	—
172	C₂×D₄×C₅₉	—	2	1	no	—
173	C₂×D₄×C₅₉	—	2	1	no	—
174	C₂×D₄×C₅₉	—	2	1	no	—
175	C₂×D₄×C₅₉	—	2	1	no	—
176	C₂×D₄×C₅₉	—	2	1	no	—
177	C₂×D₄×C₅₉	—	2	1	no	—
178	C₂×D₄×C₅₉	—	8	1	no	—
179	C₂×D₄×C₅₉	—	8	1	no	—
180	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
181	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
182	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
183	C₂×D₄×C₅₉	#41	1	2	yes	—
184	C₂²×C₄×C₅₉	—	2	4	no	—
185	C₂²×C₄×C₅₉	—	2	4	no	—
186	C₂²×C₄×C₅₉	—	2	1	no	—
187	C₂²×C₄×C₅₉	—	2	4	no	—
188	C₂²×C₄×C₅₉	—	2	1	no	—
189	C₂²×C₄×C₅₉	—	2	1	no	—
190	C₂²×C₄×C₅₉	—	2	1	no	—
191	C₂²×C₄×C₅₉	—	2	1	no	—
192	C₂²×C₄×C₅₉	—	2	1	no	—
193	C₂²×C₄×C₅₉	—	2	1	no	—
194	C₂²×C₄×C₅₉	—	2	1	no	—
195	C₂²×C₄×C₅₉	—	2	4	no	—
196	C₂²×C₄×C₅₉	—	2	4	no	—
197	C₂²×C₄×C₅₉	—	2	4	no	—
198	C₂²×C₄×C₅₉	—	2	1	no	—
199	C₂²×C₄×C₅₉	—	2	1	no	—
200	C₂²×C₄×C₅₉	—	4	2	no	—
201	C₂²×C₄×C₅₉	—	8	1	no	—
202	C₂²×C₄×C₅₉	—	8	1	no	—
203	C₂²×C₄×C₅₉	—	8	1	no	—
204	C₂²×C₄×C₅₉	—	8	1	no	—
205	C₂²×C₄×C₅₉	—	8	1	no	—
206	C₂²×C₄×C₅₉	—	8	1	no	—
207	C₂²×C₄×C₅₉	—	8	1	no	—
208	C₂²×C₄×C₅₉	—	8	1	no	—
209	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
210	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅₉	#41	1	2	yes	—
216	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
217	SD₁₆×C₅₉	—	2	8	no	—
218	D₈×C₅₉	—	2	8	no	—
219	C₂×C₈×C₅₉	—	2	1	no	—
220	C₂×C₈×C₅₉	—	2	1	no	—
221	C₂×C₈×C₅₉	—	2	1	no	—
222	C₂×C₈×C₅₉	—	2	1	no	—
223	C₂×C₈×C₅₉	—	2	1	no	—
224	C₂×C₈×C₅₉	—	2	1	no	—
225	C₂×C₈×C₅₉	—	2	1	no	—
226	C₂×C₈×C₅₉	—	2	1	no	—
227	C₂×C₈×C₅₉	—	2	1	no	—
228	C₂×C₈×C₅₉	—	2	1	no	—
229	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
230	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
231	C₄⋊C₄×C₅₉	—	2	4	no	—
232	C₄⋊C₄×C₅₉	—	2	4	no	—
233	C₄⋊C₄×C₅₉	—	2	2	no	—
234	C₄⋊C₄×C₅₉	—	2	4	no	—
235	C₄⋊C₄×C₅₉	—	2	2	no	—
236	C₄⋊C₄×C₅₉	—	2	1	no	—
237	C₄⋊C₄×C₅₉	—	2	1	no	—
238	C₄⋊C₄×C₅₉	—	2	1	no	—
239	C₄⋊C₄×C₅₉	—	2	1	no	—
240	C₄⋊C₄×C₅₉	—	2	1	no	—
241	C₄⋊C₄×C₅₉	—	2	1	no	—
242	C₄⋊C₄×C₅₉	—	2	1	no	—
243	C₄⋊C₄×C₅₉	—	8	1	no	—
244	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
245	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
247	C₂²⋊C₄×C₅₉	—	2	4	no	—
248	C₂²⋊C₄×C₅₉	—	2	4	no	—
249	C₂²⋊C₄×C₅₉	—	2	4	no	—
250	C₂²⋊C₄×C₅₉	—	2	2	no	—
251	C₂²⋊C₄×C₅₉	—	2	2	no	—
252	C₂²⋊C₄×C₅₉	—	4	2	no	—
253	C₂²⋊C₄×C₅₉	—	8	1	no	—
254	C₂²⋊C₄×C₅₉	—	8	1	no	—
255	C₂²⋊C₄×C₅₉	—	8	1	no	—
256	C₄²×C₅₉	—	2	4	no	—
257	C₄²×C₅₉	—	2	4	no	—
258	C₄²×C₅₉	—	2	1	no	—
259	C₄²×C₅₉	—	2	1	no	—
260	C₄²×C₅₉	—	8	1	no	—
261	C₄²×C₅₉	C₂×D₄	1	2	yes	—
262	C₄²×C₅₉	C₂×D₄	1	2	yes	—
263	C₂³×C₅₉	—	2	2	no	—
264	C₂³×C₅₉	—	2	1	no	—
265	C₂³×C₅₉	—	2	2	no	—
266	C₂³×C₅₉	—	2	1	no	—
267	C₂³×C₅₉	—	2	2	no	—
268	C₂³×C₅₉	—	2	1	no	—
269	C₂³×C₅₉	—	2	1	no	—
270	C₂³×C₅₉	—	2	1	no	—
271	C₂³×C₅₉	—	2	1	no	—
272	C₂³×C₅₉	—	2	2	no	—
273	C₂³×C₅₉	—	4	1	no	—
274	C₂³×C₅₉	—	4	1	no	—
275	C₂³×C₅₉	—	4	1	no	—
276	C₂³×C₅₉	—	4	1	no	—
277	C₂³×C₅₉	—	4	1	no	—
278	C₂³×C₅₉	—	4	1	no	—
279	C₂³×C₅₉	—	4	1	no	—
280	C₂³×C₅₉	—	4	1	no	—
281	C₂³×C₅₉	—	4	1	no	—
282	C₂³×C₅₉	—	4	1	no	—
283	C₂³×C₅₉	C₄×D₄	1	2	yes	—
284	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₅₉	—	2	2	no	—
286	Q₈×C₅₉	—	2	2	no	—
287	Q₈×C₅₉	—	2	2	no	—
288	Q₈×C₅₉	C₄×D₄	1	4	yes	—
289	D₄×C₅₉	—	2	16	no	—
290	D₄×C₅₉	—	2	2	no	—
291	D₄×C₅₉	—	2	2	no	—
292	D₄×C₅₉	—	2	2	no	—
293	D₄×C₅₉	—	2	2	no	—
294	D₄×C₅₉	—	2	2	no	—
295	D₄×C₅₉	—	4	1	no	—
296	D₄×C₅₉	—	4	1	no	—
297	D₄×C₅₉	—	8	4	no	—
298	D₄×C₅₉	C₄×D₄	1	4	yes	—
299	C₂×C₄×C₅₉	—	2	16	no	—
300	C₂×C₄×C₅₉	—	2	2	no	—
301	C₂×C₄×C₅₉	—	2	2	no	—
302	C₂×C₄×C₅₉	—	2	1	no	—
303	C₂×C₄×C₅₉	—	2	1	no	—
304	C₂×C₄×C₅₉	—	2	2	no	—
305	C₂×C₄×C₅₉	—	2	1	no	—
306	C₂×C₄×C₅₉	—	2	1	no	—
307	C₂×C₄×C₅₉	—	2	1	no	—
308	C₂×C₄×C₅₉	—	2	1	no	—
309	C₂×C₄×C₅₉	—	2	2	no	—
310	C₂×C₄×C₅₉	—	2	2	no	—
311	C₂×C₄×C₅₉	—	2	2	no	—
312	C₂×C₄×C₅₉	—	2	2	no	—
313	C₂×C₄×C₅₉	—	2	2	no	—
314	C₂×C₄×C₅₉	—	2	1	no	—
315	C₂×C₄×C₅₉	—	2	1	no	—
316	C₂×C₄×C₅₉	—	2	2	no	—
317	C₂×C₄×C₅₉	—	2	2	no	—
318	C₂×C₄×C₅₉	—	2	1	no	—
319	C₂×C₄×C₅₉	—	2	1	no	—
320	C₂×C₄×C₅₉	—	2	1	no	—
321	C₂×C₄×C₅₉	—	2	1	no	—
322	C₂×C₄×C₅₉	—	4	1	no	—
323	C₂×C₄×C₅₉	—	4	1	no	—
324	C₂×C₄×C₅₉	—	4	1	no	—
325	C₂×C₄×C₅₉	—	4	1	no	—
326	C₂×C₄×C₅₉	—	4	1	no	—
327	C₂×C₄×C₅₉	—	4	1	no	—
328	C₂×C₄×C₅₉	—	4	1	no	—
329	C₂×C₄×C₅₉	—	4	1	no	—
330	C₂×C₄×C₅₉	—	4	1	no	—
331	C₂×C₄×C₅₉	—	4	1	no	—
332	C₂×C₄×C₅₉	—	4	1	no	—
333	C₂×C₄×C₅₉	—	4	1	no	—
334	C₂×C₄×C₅₉	—	8	4	no	—
335	C₂×C₄×C₅₉	—	8	4	no	—
336	C₂×C₄×C₅₉	—	8	4	no	—
337	C₂×C₄×C₅₉	—	8	4	no	—
338	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
339	C₂×C₄×C₅₉	#120	1	2	yes	—
340	C₂×C₄×C₅₉	#120	1	2	yes	—
341	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
346	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
347	C₈×C₅₉	—	2	2	no	—
348	C₈×C₅₉	—	2	2	no	—
349	C₈×C₅₉	—	4	1	no	—
350	C₈×C₅₉	—	4	1	no	—
351	#21464	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂²×C₅₉	—	2	2	no	—
353	C₂²×C₅₉	—	2	2	no	—
354	C₂²×C₅₉	—	2	2	no	—
355	C₂²×C₅₉	—	2	4	no	—
356	C₂²×C₅₉	—	4	1	no	—
357	C₂²×C₅₉	—	4	2	no	—
358	C₂²×C₅₉	—	4	1	no	—
359	C₂²×C₅₉	—	4	2	no	—
360	C₂²×C₅₉	—	4	2	no	—
361	C₂²×C₅₉	—	4	2	no	—
362	C₂²×C₅₉	—	4	1	no	—
363	C₂²×C₅₉	—	4	2	no	—
364	C₂²×C₅₉	—	4	1	no	—
365	C₂²×C₅₉	—	4	2	no	—
366	C₂²×C₅₉	—	4	2	no	—
367	C₂²×C₅₉	—	4	2	no	—
368	C₂²×C₅₉	—	4	2	no	—
369	C₂²×C₅₉	—	8	1	no	—
370	C₂²×C₅₉	—	8	1	no	—
371	C₂²×C₅₉	—	8	1	no	—
372	C₂²×C₅₉	—	8	1	no	—
373	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
375	C₂²×C₅₉	#525	1	1	yes	characteristic
376	C₂²×C₅₉	#576	1	1	yes	characteristic
377	C₂²×C₅₉	#577	1	1	yes	characteristic
378	C₂²×C₅₉	#577	1	1	yes	characteristic
379	C₂²×C₅₉	#577	1	1	yes	characteristic
380	C₄×C₅₉	—	2	2	no	—
381	C₄×C₅₉	—	2	2	no	—
382	C₄×C₅₉	—	2	2	no	—
383	C₄×C₅₉	—	2	4	no	—
384	C₄×C₅₉	—	4	2	no	—
385	C₄×C₅₉	—	4	1	no	—
386	C₄×C₅₉	—	4	1	no	—
387	C₄×C₅₉	—	4	2	no	—
388	C₄×C₅₉	—	4	2	no	—
389	C₄×C₅₉	—	8	1	no	—
390	C₄×C₅₉	—	8	1	no	—
391	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
392	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
393	C₄×C₅₉	#525	1	1	yes	characteristic
394	C₄×C₅₉	#525	1	1	yes	characteristic
395	C₂×#520	C₂×C₅₉	1	1	yes	characteristic, complemented
396	C₂×#449	C₂×C₅₉	1	1	yes	characteristic
397	C₂×#442	C₂×C₅₉	1	1	yes	characteristic, complemented
398	C₂×C₄×SD₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
399	#2324	C₂×C₅₉	1	1	yes	characteristic, complemented
400	#1880	C₂×C₅₉	1	1	yes	characteristic, complemented
401	#1879	C₂×C₅₉	1	1	yes	characteristic, complemented
402	#1874	C₂×C₅₉	1	1	yes	characteristic, complemented
403	#1865	C₂×C₅₉	1	1	yes	characteristic, complemented
404	#1864	C₂×C₅₉	1	1	yes	characteristic, complemented
405	#1853	C₂×C₅₉	1	1	yes	characteristic, complemented
406	#1788	C₂×C₅₉	1	1	yes	characteristic, complemented
407	#1763	C₂×C₅₉	1	1	yes	characteristic, complemented
408	C₄×#102	C₂×C₅₉	1	1	yes	characteristic, complemented
409	#1750	C₂×C₅₉	1	1	yes	characteristic, complemented
410	C₂×C₅₉	—	4	2	no	—
411	C₂×C₅₉	—	4	4	no	—
412	C₂×C₅₉	—	8	2	no	—
413	C₂×C₅₉	C₄×#120	1	1	yes	characteristic
414	C₂×C₅₉	#2946	1	1	yes	characteristic
415	C₂×C₅₉	#2952	1	1	yes	characteristic
416	C₂×C₅₉	#3010	1	1	yes	characteristic
417	C₂×C₅₉	#3012	1	1	yes	characteristic
418	C₂×C₅₉	#3119	1	1	yes	characteristic
419	C₂×C₅₉	#3125	1	1	yes	characteristic
420	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
421	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
422	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
423	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
424	#520	—	2	4	no	—
425	#520	—	2	4	no	—
426	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
428	C₂×C₄×D₄	—	2	1	no	—
429	C₂×C₄×D₄	—	2	1	no	—
430	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
433	C₂×#117	—	2	1	no	—
434	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	—	2	1	no	—
436	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
437	#449	C₄×C₅₉	1	8	yes	complemented
438	#442	—	2	4	no	—
439	C₄×SD₁₆	—	2	4	no	—
440	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
441	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
442	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
443	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
444	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
445	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
446	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
447	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
448	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
449	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
452	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
453	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
454	#390	—	2	1	no	—
455	#390	C₂²×C₅₉	1	1	yes	characteristic
456	#389	C₂²×C₅₉	1	1	yes	characteristic
457	#388	—	2	1	no	—
458	#386	—	2	1	no	—
459	#385	—	2	1	no	—
460	#380	C₂²×C₅₉	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
462	#340	C₂²×C₅₉	1	1	yes	characteristic
463	#340	C₂²×C₅₉	1	1	yes	characteristic
464	#340	C₂²×C₅₉	1	1	yes	characteristic
465	#340	C₂²×C₅₉	1	1	yes	characteristic
466	#336	C₂²×C₅₉	1	1	yes	characteristic
467	#336	C₂²×C₅₉	1	1	yes	characteristic
468	C₅₉	#21464	1	1	yes	characteristic, direct product factor, Sylow
469	C₂×#41	—	2	2	no	—
470	C₂×#41	—	2	2	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	2	no	—
474	C₂×#41	C₂×C₄×C₅₉	1	4	yes	complemented
475	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
479	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
486	C₂×SD₁₆	—	2	2	no	—
487	C₂×SD₁₆	—	2	2	no	—
488	C₂×SD₁₆	C₂×C₄×C₅₉	1	4	yes	complemented
489	C₂×D₈	—	2	2	no	—
490	C₂×D₈	—	2	2	no	—
491	C₂×D₈	C₂×C₄×C₅₉	1	4	yes	complemented
492	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
496	#121	—	2	2	no	—
497	#121	C₂×C₄×C₅₉	1	4	yes	complemented
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	D₄×C₅₉	1	4	yes	complemented
502	C₄×D₄	—	2	8	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	D₄×C₅₉	1	4	yes	complemented
510	#117	—	2	8	no	—
511	#117	—	2	2	no	—
512	#117	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	8	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	2	no	—
518	C₂×C₄⋊C₄	—	2	2	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
536	C₂×C₄²	—	2	1	no	—
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	—	2	1	no	—
539	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
541	#106	—	2	2	no	—
542	#106	—	2	2	no	—
543	#103	—	2	2	no	—
544	#103	—	2	2	no	—
545	#103	C₂×C₄×C₅₉	1	4	yes	complemented
546	#102	—	2	2	no	—
547	#102	—	2	2	no	—
548	#102	—	2	2	no	—
549	#102	—	2	2	no	—
550	#102	C₂×C₄×C₅₉	1	4	yes	complemented
551	C₂²⋊C₈	—	2	2	no	—
552	C₂²⋊C₈	C₂×C₄×C₅₉	1	4	yes	complemented
553	#97	—	2	2	no	—
554	C₄×C₈	—	2	2	no	—
555	#95	—	2	1	no	—
556	#95	—	2	1	no	—
557	#95	—	2	1	no	—
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
561	#41	—	2	8	no	—
562	#41	—	2	8	no	—
563	#41	—	2	8	no	—
564	#41	—	2	8	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
569	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
570	C₂×Q₈	#41×C₅₉	1	2	yes	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	8	1	no	—
584	C₂×D₄	—	8	1	no	—
585	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
586	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
587	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
588	C₂×D₄	#41×C₅₉	1	2	yes	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	8	1	no	—
607	C₂²×C₄	—	8	1	no	—
608	C₂²×C₄	—	8	1	no	—
609	C₂²×C₄	—	8	1	no	—
610	C₂²×C₄	—	8	1	no	—
611	C₂²×C₄	—	8	1	no	—
612	C₂²×C₄	—	8	1	no	—
613	C₂²×C₄	—	8	1	no	—
614	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
615	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
620	C₂²×C₄	#41×C₅₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
622	SD₁₆	—	2	8	no	—
623	D₈	—	2	8	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
635	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	8	1	no	—
649	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₂²⋊C₄	—	8	1	no	—
660	C₂²⋊C₄	—	8	1	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	2	4	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	8	1	no	—
666	C₄²	C₂×D₄×C₅₉	1	2	yes	—
667	C₄²	C₂×D₄×C₅₉	1	2	yes	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	C₄×D₄×C₅₉	1	2	yes	—
689	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	C₄×D₄×C₅₉	1	4	yes	—
694	D₄	—	2	16	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	8	4	no	—
703	D₄	C₄×D₄×C₅₉	1	4	yes	—
704	C₂×C₄	—	2	16	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	—	8	4	no	—
743	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
744	C₂×C₄	#120×C₅₉	1	2	yes	—
745	C₂×C₄	#120×C₅₉	1	2	yes	—
746	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
749	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
750	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
751	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
752	C₈	—	2	2	no	—
753	C₈	—	2	2	no	—
754	C₈	—	4	1	no	—
755	C₈	—	4	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
778	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
779	C₂²	C₅₉×#525	1	1	yes	characteristic
780	C₂²	C₅₉×#576	1	1	yes	characteristic
781	C₂²	C₅₉×#577	1	1	yes	characteristic
782	C₂²	C₅₉×#577	1	1	yes	characteristic
783	C₂²	C₅₉×#577	1	1	yes	characteristic
784	C₄	—	2	2	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	4	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	8	1	no	—
794	C₄	—	8	1	no	—
795	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
796	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
797	C₄	C₅₉×#525	1	1	yes	characteristic
798	C₄	C₅₉×#525	1	1	yes	characteristic
799	C₂	—	4	2	no	—
800	C₂	—	4	4	no	—
801	C₂	—	8	2	no	—
802	C₂	C₄×#120×C₅₉	1	1	yes	characteristic
803	C₂	C₅₉×#2946	1	1	yes	characteristic
804	C₂	C₅₉×#2952	1	1	yes	characteristic
805	C₂	C₅₉×#3010	1	1	yes	characteristic
806	C₂	C₅₉×#3012	1	1	yes	characteristic
807	C₂	C₅₉×#3119	1	1	yes	characteristic
808	C₂	C₅₉×#3125	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×C₅₉×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×#117×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#520	C₂	semidirect
3. C₂×C₅₉×#442	C₂	semidirect
4. C₂×C₄×SD₁₆×C₅₉	C₂	semidirect
5. C₅₉×#2324	C₂	semidirect
6. C₅₉×#1880	C₂	semidirect
7. C₅₉×#1879	C₂	semidirect
8. C₅₉×#1874	C₂	semidirect
9. C₅₉×#1865	C₂	semidirect
10. C₅₉×#1864	C₂	semidirect
11. C₅₉×#1853	C₂	semidirect
12. C₅₉×#1788	C₂	semidirect
13. C₅₉×#1763	C₂	semidirect
14. C₄×#102×C₅₉	C₂	semidirect
15. C₅₉×#1750	C₂	semidirect
33. C₅₉×#449	C₄	semidirect
69. C₂×#41×C₅₉	C₂×C₄	semidirect
83. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
86. C₂×D₈×C₅₉	C₂×C₄	semidirect
92. #121×C₅₉	C₂×C₄	semidirect
96. C₄×Q₈×C₅₉	D₄	semidirect
104. C₄×D₄×C₅₉	D₄	semidirect
140. #103×C₅₉	C₂×C₄	semidirect
145. #102×C₅₉	C₂×C₄	semidirect
147. C₂²⋊C₈×C₅₉	C₂×C₄	semidirect
351. #21464	C₅₉	direct (N × H)
395. C₂×#520	C₂×C₅₉	semidirect
397. C₂×#442	C₂×C₅₉	semidirect
398. C₂×C₄×SD₁₆	C₂×C₅₉	semidirect
399. #2324	C₂×C₅₉	semidirect
400. #1880	C₂×C₅₉	semidirect
401. #1879	C₂×C₅₉	semidirect
402. #1874	C₂×C₅₉	semidirect
403. #1865	C₂×C₅₉	semidirect
404. #1864	C₂×C₅₉	semidirect
405. #1853	C₂×C₅₉	semidirect
406. #1788	C₂×C₅₉	semidirect
407. #1763	C₂×C₅₉	semidirect
408. C₄×#102	C₂×C₅₉	semidirect
409. #1750	C₂×C₅₉	semidirect
437. #449	C₄×C₅₉	semidirect
468. C₅₉	#21464	direct (N × H)
474. C₂×#41	C₂×C₄×C₅₉	semidirect
488. C₂×SD₁₆	C₂×C₄×C₅₉	semidirect
491. C₂×D₈	C₂×C₄×C₅₉	semidirect
497. #121	C₂×C₄×C₅₉	semidirect
501. C₄×Q₈	D₄×C₅₉	semidirect
509. C₄×D₄	D₄×C₅₉	semidirect
545. #103	C₂×C₄×C₅₉	semidirect
550. #102	C₂×C₄×C₅₉	semidirect
552. C₂²⋊C₈	C₂×C₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#520	2
C₂×C₅₉×#449	2
C₂×C₅₉×#442	2
C₂×C₄×SD₁₆×C₅₉	2
C₅₉×#2324	2
C₅₉×#1880	2
C₅₉×#1879	2
C₅₉×#1874	2
C₅₉×#1865	2
C₅₉×#1864	2
C₅₉×#1853	2
C₅₉×#1788	2
C₅₉×#1763	2
C₄×#102×C₅₉	2
C₅₉×#1750	2
#21464	59

Subgroups — C59×#21464 #28433573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21464 #28433573