Subgroups — C₅₉×#25084 #28437193

Order 15104.

1226 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#450	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2435	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#467	—	2	4	no	—
28	C₅₉×#464	—	2	4	no	—
29	C₅₉×#450	—	2	4	no	—
30	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×#102×C₅₉	—	2	4	no	—
38	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#102×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×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#394	—	2	1	no	—
46	C₅₉×#394	—	2	1	no	—
47	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
48	C₅₉×#390	C₂²	1	1	yes	characteristic
49	C₅₉×#390	C₂²	1	1	yes	characteristic
50	C₅₉×#389	—	2	1	no	—
51	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
52	C₅₉×#387	—	2	1	no	—
53	C₅₉×#385	—	2	1	no	—
54	C₅₉×#379	—	2	1	no	—
55	C₅₉×#379	—	2	1	no	—
56	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
57	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
59	C₅₉×#340	C₂²	1	1	yes	characteristic, complemented
60	C₅₉×#340	C₂²	1	1	yes	characteristic, complemented
61	C₅₉×#336	C₂²	1	1	yes	characteristic, complemented
62	C₅₉×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₅₉	—	2	1	no	—
64	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₅₉	—	2	2	no	—
67	C₂²×D₄×C₅₉	—	2	2	no	—
68	C₂²×D₄×C₅₉	—	2	2	no	—
69	C₂²×D₄×C₅₉	—	2	1	no	—
70	C₂²×D₄×C₅₉	—	2	2	no	—
71	C₂²×D₄×C₅₉	—	4	1	no	—
72	C₂²×D₄×C₅₉	—	4	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	C₂³	1	1	yes	characteristic
77	C₂×Q₁₆×C₅₉	—	2	2	no	—
78	C₂×Q₁₆×C₅₉	—	2	2	no	—
79	C₂×Q₁₆×C₅₉	—	4	1	no	—
80	C₂×SD₁₆×C₅₉	—	2	2	no	—
81	C₂×SD₁₆×C₅₉	—	2	2	no	—
82	C₂×SD₁₆×C₅₉	—	2	2	no	—
83	C₂×SD₁₆×C₅₉	—	2	2	no	—
84	C₂×SD₁₆×C₅₉	—	4	1	no	—
85	C₂×SD₁₆×C₅₉	—	4	1	no	—
86	C₂²×C₈×C₅₉	—	2	2	no	—
87	C₂²×C₈×C₅₉	—	2	2	no	—
88	C₂²×C₈×C₅₉	—	4	1	no	—
89	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
93	#124×C₅₉	—	2	2	no	—
94	#124×C₅₉	—	2	2	no	—
95	#124×C₅₉	—	4	1	no	—
96	#124×C₅₉	—	4	1	no	—
97	C₂²⋊Q₈×C₅₉	—	2	2	no	—
98	C₂²⋊Q₈×C₅₉	—	2	2	no	—
99	C₂²⋊Q₈×C₅₉	—	2	2	no	—
100	C₂²⋊Q₈×C₅₉	D₄	1	4	yes	—
101	C₄×Q₈×C₅₉	—	2	2	no	—
102	C₄×Q₈×C₅₉	—	4	1	no	—
103	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₅₉	—	4	1	no	—
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₅₉	—	2	1	no	—
127	C₂×C₄²×C₅₉	—	2	1	no	—
128	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
130	#107×C₅₉	—	2	2	no	—
131	C₄⋊C₈×C₅₉	—	2	2	no	—
132	C₄⋊C₈×C₅₉	—	4	1	no	—
133	#103×C₅₉	—	2	2	no	—
134	#103×C₅₉	—	2	2	no	—
135	#103×C₅₉	—	2	2	no	—
136	#103×C₅₉	—	4	1	no	—
137	#102×C₅₉	—	2	2	no	—
138	#102×C₅₉	—	2	2	no	—
139	#102×C₅₉	—	2	2	no	—
140	#102×C₅₉	—	2	2	no	—
141	#102×C₅₉	—	2	2	no	—
142	#102×C₅₉	D₄	1	4	yes	—
143	C₂²⋊C₈×C₅₉	—	2	2	no	—
144	#95×C₅₉	—	2	1	no	—
145	#95×C₅₉	—	2	1	no	—
146	#95×C₅₉	—	2	1	no	—
147	#95×C₅₉	—	2	1	no	—
148	#95×C₅₉	D₄	1	1	yes	characteristic
149	#95×C₅₉	D₄	1	1	yes	characteristic
150	C₂⁴×C₅₉	—	2	1	no	—
151	C₂⁴×C₅₉	—	2	1	no	—
152	C₂⁴×C₅₉	—	4	2	no	—
153	C₂⁴×C₅₉	—	4	2	no	—
154	C₂⁴×C₅₉	—	4	2	no	—
155	C₂⁴×C₅₉	—	4	2	no	—
156	C₂⁴×C₅₉	—	4	2	no	—
157	C₂⁴×C₅₉	—	8	1	no	—
158	C₂⁴×C₅₉	—	8	1	no	—
159	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
164	C₂×Q₈×C₅₉	—	2	1	no	—
165	C₂×Q₈×C₅₉	—	2	1	no	—
166	C₂×Q₈×C₅₉	—	2	1	no	—
167	C₂×Q₈×C₅₉	—	2	1	no	—
168	C₂×Q₈×C₅₉	—	2	1	no	—
169	C₂×Q₈×C₅₉	—	2	1	no	—
170	C₂×Q₈×C₅₉	—	2	1	no	—
171	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
172	C₂×D₄×C₅₉	—	2	8	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	—	2	1	no	—
179	C₂×D₄×C₅₉	—	2	1	no	—
180	C₂×D₄×C₅₉	—	2	1	no	—
181	C₂×D₄×C₅₉	—	2	1	no	—
182	C₂×D₄×C₅₉	—	2	1	no	—
183	C₂×D₄×C₅₉	—	4	4	no	—
184	C₂×D₄×C₅₉	—	4	4	no	—
185	C₂×D₄×C₅₉	—	4	2	no	—
186	C₂×D₄×C₅₉	—	4	2	no	—
187	C₂×D₄×C₅₉	—	4	4	no	—
188	C₂×D₄×C₅₉	—	4	2	no	—
189	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₅₉	#41	1	2	yes	—
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	1	no	—
196	C₂²×C₄×C₅₉	—	2	1	no	—
197	C₂²×C₄×C₅₉	—	2	1	no	—
198	C₂²×C₄×C₅₉	—	2	1	no	—
199	C₂²×C₄×C₅₉	—	2	1	no	—
200	C₂²×C₄×C₅₉	—	2	1	no	—
201	C₂²×C₄×C₅₉	—	4	2	no	—
202	C₂²×C₄×C₅₉	—	4	2	no	—
203	C₂²×C₄×C₅₉	—	8	1	no	—
204	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₅₉	#41	1	2	yes	—
211	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
212	Q₁₆×C₅₉	—	4	4	no	—
213	SD₁₆×C₅₉	—	4	4	no	—
214	SD₁₆×C₅₉	—	4	4	no	—
215	C₂×C₈×C₅₉	—	2	1	no	—
216	C₂×C₈×C₅₉	—	2	1	no	—
217	C₂×C₈×C₅₉	—	2	1	no	—
218	C₂×C₈×C₅₉	—	2	1	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	—	4	4	no	—
227	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
228	C₄⋊C₄×C₅₉	—	2	4	no	—
229	C₄⋊C₄×C₅₉	—	2	1	no	—
230	C₄⋊C₄×C₅₉	—	2	1	no	—
231	C₄⋊C₄×C₅₉	—	2	1	no	—
232	C₄⋊C₄×C₅₉	—	2	1	no	—
233	C₄⋊C₄×C₅₉	—	2	1	no	—
234	C₄⋊C₄×C₅₉	—	2	1	no	—
235	C₄⋊C₄×C₅₉	—	4	2	no	—
236	C₄⋊C₄×C₅₉	—	4	2	no	—
237	C₄⋊C₄×C₅₉	—	4	2	no	—
238	C₄⋊C₄×C₅₉	—	8	1	no	—
239	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
240	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
241	C₂²⋊C₄×C₅₉	—	2	4	no	—
242	C₂²⋊C₄×C₅₉	—	2	2	no	—
243	C₂²⋊C₄×C₅₉	—	2	2	no	—
244	C₂²⋊C₄×C₅₉	—	4	2	no	—
245	C₂²⋊C₄×C₅₉	—	4	2	no	—
246	C₂²⋊C₄×C₅₉	—	4	2	no	—
247	C₂²⋊C₄×C₅₉	—	4	2	no	—
248	C₂²⋊C₄×C₅₉	—	4	2	no	—
249	C₂²⋊C₄×C₅₉	—	8	1	no	—
250	C₂²⋊C₄×C₅₉	—	8	1	no	—
251	C₂²⋊C₄×C₅₉	—	8	1	no	—
252	C₂²⋊C₄×C₅₉	—	8	1	no	—
253	C₄²×C₅₉	—	2	1	no	—
254	C₄²×C₅₉	—	2	1	no	—
255	C₄²×C₅₉	—	2	1	no	—
256	C₄²×C₅₉	—	2	1	no	—
257	C₄²×C₅₉	—	4	2	no	—
258	C₄²×C₅₉	—	8	1	no	—
259	C₂³×C₅₉	—	2	1	no	—
260	C₂³×C₅₉	—	2	1	no	—
261	C₂³×C₅₉	—	2	1	no	—
262	C₂³×C₅₉	—	2	1	no	—
263	C₂³×C₅₉	—	2	2	no	—
264	C₂³×C₅₉	—	2	2	no	—
265	C₂³×C₅₉	—	4	8	no	—
266	C₂³×C₅₉	—	4	1	no	—
267	C₂³×C₅₉	—	4	1	no	—
268	C₂³×C₅₉	—	4	1	no	—
269	C₂³×C₅₉	—	4	1	no	—
270	C₂³×C₅₉	—	4	1	no	—
271	C₂³×C₅₉	—	4	1	no	—
272	C₂³×C₅₉	—	4	1	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	—	8	4	no	—
279	C₂³×C₅₉	—	8	4	no	—
280	C₂³×C₅₉	—	8	4	no	—
281	C₂³×C₅₉	—	8	4	no	—
282	C₂³×C₅₉	—	8	4	no	—
283	C₂³×C₅₉	—	8	4	no	—
284	C₂³×C₅₉	#121	1	2	yes	—
285	C₂³×C₅₉	#135	1	2	yes	—
286	C₂³×C₅₉	#137	1	2	yes	—
287	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₅₉	—	2	2	no	—
289	Q₈×C₅₉	—	2	2	no	—
290	Q₈×C₅₉	—	4	1	no	—
291	Q₈×C₅₉	—	4	1	no	—
292	Q₈×C₅₉	—	4	1	no	—
293	Q₈×C₅₉	—	4	1	no	—
294	Q₈×C₅₉	—	4	1	no	—
295	Q₈×C₅₉	—	4	1	no	—
296	D₄×C₅₉	—	2	2	no	—
297	D₄×C₅₉	—	2	2	no	—
298	D₄×C₅₉	—	2	2	no	—
299	D₄×C₅₉	—	2	2	no	—
300	D₄×C₅₉	—	4	8	no	—
301	D₄×C₅₉	—	4	1	no	—
302	D₄×C₅₉	—	4	1	no	—
303	D₄×C₅₉	—	4	1	no	—
304	D₄×C₅₉	—	4	1	no	—
305	C₂×C₄×C₅₉	—	2	1	no	—
306	C₂×C₄×C₅₉	—	2	1	no	—
307	C₂×C₄×C₅₉	—	2	2	no	—
308	C₂×C₄×C₅₉	—	2	2	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	1	no	—
314	C₂×C₄×C₅₉	—	2	1	no	—
315	C₂×C₄×C₅₉	—	2	2	no	—
316	C₂×C₄×C₅₉	—	2	1	no	—
317	C₂×C₄×C₅₉	—	2	1	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	—	2	1	no	—
323	C₂×C₄×C₅₉	—	2	1	no	—
324	C₂×C₄×C₅₉	—	2	1	no	—
325	C₂×C₄×C₅₉	—	2	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	—	4	1	no	—
335	C₂×C₄×C₅₉	—	4	1	no	—
336	C₂×C₄×C₅₉	—	4	1	no	—
337	C₂×C₄×C₅₉	—	4	1	no	—
338	C₂×C₄×C₅₉	—	4	1	no	—
339	C₂×C₄×C₅₉	—	4	1	no	—
340	C₂×C₄×C₅₉	—	4	1	no	—
341	C₂×C₄×C₅₉	—	8	4	no	—
342	C₂×C₄×C₅₉	#121	1	2	yes	—
343	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₅₉	C₂²×D₄	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	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
349	C₈×C₅₉	—	2	2	no	—
350	C₈×C₅₉	—	4	1	no	—
351	C₈×C₅₉	—	4	1	no	—
352	C₈×C₅₉	—	4	1	no	—
353	#25084	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₂²×C₅₉	—	2	2	no	—
355	C₂²×C₅₉	—	2	2	no	—
356	C₂²×C₅₉	—	2	2	no	—
357	C₂²×C₅₉	—	2	2	no	—
358	C₂²×C₅₉	—	2	2	no	—
359	C₂²×C₅₉	—	2	2	no	—
360	C₂²×C₅₉	—	4	2	no	—
361	C₂²×C₅₉	—	4	2	no	—
362	C₂²×C₅₉	—	4	2	no	—
363	C₂²×C₅₉	—	4	2	no	—
364	C₂²×C₅₉	—	4	2	no	—
365	C₂²×C₅₉	—	4	2	no	—
366	C₂²×C₅₉	—	8	16	no	—
367	C₂²×C₅₉	—	8	1	no	—
368	C₂²×C₅₉	—	8	1	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	—	8	1	no	—
374	C₂²×C₅₉	—	8	1	no	—
375	C₂²×C₅₉	#464	1	4	yes	complemented
376	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
377	C₂²×C₅₉	D₄²	1	1	yes	characteristic
378	C₂²×C₅₉	#546	1	1	yes	characteristic
379	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
380	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
381	C₂²×C₅₉	#576	1	1	yes	characteristic
382	C₂²×C₅₉	#577	1	1	yes	characteristic
383	C₄×C₅₉	—	2	2	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	1	no	—
389	C₄×C₅₉	—	4	2	no	—
390	C₄×C₅₉	—	4	1	no	—
391	C₄×C₅₉	—	8	1	no	—
392	C₄×C₅₉	—	8	1	no	—
393	C₄×C₅₉	—	8	1	no	—
394	C₄×C₅₉	#525	1	1	yes	characteristic
395	C₄×C₅₉	#538	1	1	yes	characteristic
396	C₄×C₅₉	D₄²	1	1	yes	characteristic
397	C₄×C₅₉	#546	1	1	yes	characteristic
398	C₂×#467	C₂×C₅₉	1	1	yes	characteristic, complemented
399	C₂×#464	C₂×C₅₉	1	1	yes	characteristic, complemented
400	C₂×#450	C₂×C₅₉	1	1	yes	characteristic
401	C₂²×#102	C₂×C₅₉	1	1	yes	characteristic
402	#2435	C₂×C₅₉	1	1	yes	characteristic
403	#2360	C₂×C₅₉	1	1	yes	characteristic, complemented
404	#2067	C₂×C₅₉	1	1	yes	characteristic, complemented
405	#2055	C₂×C₅₉	1	1	yes	characteristic, complemented
406	#2042	C₂×C₅₉	1	1	yes	characteristic, complemented
407	#2015	C₂×C₅₉	1	1	yes	characteristic, complemented
408	#1983	C₂×C₅₉	1	1	yes	characteristic, complemented
409	#1925	C₂×C₅₉	1	1	yes	characteristic, complemented
410	#1880	C₂×C₅₉	1	1	yes	characteristic, complemented
411	#1872	C₂×C₅₉	1	1	yes	characteristic, complemented
412	#1850	C₂×C₅₉	1	1	yes	characteristic, complemented
413	C₂×C₅₉	—	2	4	no	—
414	C₂×C₅₉	—	8	2	no	—
415	C₂×C₅₉	—	8	2	no	—
416	C₂×C₅₉	#2424	1	1	yes	characteristic
417	C₂×C₅₉	C₂×#464	1	1	yes	characteristic
418	C₂×C₅₉	#3045	1	1	yes	characteristic
419	C₂×C₅₉	#3266	1	1	yes	characteristic
420	C₂×C₅₉	#3280	1	1	yes	characteristic
421	C₂×C₅₉	#3296	1	1	yes	characteristic
422	C₂×C₅₉	#3314	1	1	yes	characteristic
423	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
424	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
425	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
426	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
427	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
428	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
429	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
431	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
432	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
433	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
434	#467	—	2	4	no	—
435	#464	—	2	4	no	—
436	#450	—	2	4	no	—
437	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic, complemented
438	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
439	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
440	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
441	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
442	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
443	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
444	C₂×#102	—	2	4	no	—
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×#102	C₂²×C₅₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
452	#394	—	2	1	no	—
453	#394	—	2	1	no	—
454	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
455	#390	C₂²×C₅₉	1	1	yes	characteristic
456	#390	C₂²×C₅₉	1	1	yes	characteristic
457	#389	—	2	1	no	—
458	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
459	#387	—	2	1	no	—
460	#385	—	2	1	no	—
461	#379	—	2	1	no	—
462	#379	—	2	1	no	—
463	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
464	C₄×C₂²⋊C₄	—	2	1	no	—
465	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
466	#340	C₂²×C₅₉	1	1	yes	characteristic, complemented
467	#340	C₂²×C₅₉	1	1	yes	characteristic, complemented
468	#336	C₂²×C₅₉	1	1	yes	characteristic, complemented
469	#336	C₂²×C₅₉	1	1	yes	characteristic, complemented
470	C₅₉	#25084	1	1	yes	characteristic, direct product factor, Sylow
471	C₂⁵	—	2	1	no	—
472	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
474	C₂²×D₄	—	2	2	no	—
475	C₂²×D₄	—	2	2	no	—
476	C₂²×D₄	—	2	2	no	—
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	4	1	no	—
480	C₂²×D₄	—	4	1	no	—
481	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
485	C₂×Q₁₆	—	2	2	no	—
486	C₂×Q₁₆	—	2	2	no	—
487	C₂×Q₁₆	—	4	1	no	—
488	C₂×SD₁₆	—	2	2	no	—
489	C₂×SD₁₆	—	2	2	no	—
490	C₂×SD₁₆	—	2	2	no	—
491	C₂×SD₁₆	—	2	2	no	—
492	C₂×SD₁₆	—	4	1	no	—
493	C₂×SD₁₆	—	4	1	no	—
494	C₂²×C₈	—	2	2	no	—
495	C₂²×C₈	—	2	2	no	—
496	C₂²×C₈	—	4	1	no	—
497	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
501	#124	—	2	2	no	—
502	#124	—	2	2	no	—
503	#124	—	4	1	no	—
504	#124	—	4	1	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	D₄×C₅₉	1	4	yes	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	4	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	1	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	—	4	1	no	—
518	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₅₉	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
534	C₂×C₄²	—	2	1	no	—
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
538	#107	—	2	2	no	—
539	C₄⋊C₈	—	2	2	no	—
540	C₄⋊C₈	—	4	1	no	—
541	#103	—	2	2	no	—
542	#103	—	2	2	no	—
543	#103	—	2	2	no	—
544	#103	—	4	1	no	—
545	#102	—	2	2	no	—
546	#102	—	2	2	no	—
547	#102	—	2	2	no	—
548	#102	—	2	2	no	—
549	#102	—	2	2	no	—
550	#102	D₄×C₅₉	1	4	yes	—
551	C₂²⋊C₈	—	2	2	no	—
552	#95	—	2	1	no	—
553	#95	—	2	1	no	—
554	#95	—	2	1	no	—
555	#95	—	2	1	no	—
556	#95	D₄×C₅₉	1	1	yes	characteristic
557	#95	D₄×C₅₉	1	1	yes	characteristic
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	—	4	2	no	—
561	C₂⁴	—	4	2	no	—
562	C₂⁴	—	4	2	no	—
563	C₂⁴	—	4	2	no	—
564	C₂⁴	—	4	2	no	—
565	C₂⁴	—	8	1	no	—
566	C₂⁴	—	8	1	no	—
567	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	4	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
598	C₂×D₄	#41×C₅₉	1	2	yes	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	8	1	no	—
612	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
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	2	yes	—
618	C₂²×C₄	#41×C₅₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
620	Q₁₆	—	4	4	no	—
621	SD₁₆	—	4	4	no	—
622	SD₁₆	—	4	4	no	—
623	C₂×C₈	—	2	1	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	—	4	4	no	—
635	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	8	1	no	—
647	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
648	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	8	1	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₂²⋊C₄	—	8	1	no	—
660	C₂²⋊C₄	—	8	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	4	2	no	—
666	C₄²	—	8	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	4	8	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	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	—	8	4	no	—
687	C₂³	—	8	4	no	—
688	C₂³	—	8	4	no	—
689	C₂³	—	8	4	no	—
690	C₂³	—	8	4	no	—
691	C₂³	—	8	4	no	—
692	C₂³	#121×C₅₉	1	2	yes	—
693	C₂³	#135×C₅₉	1	2	yes	—
694	C₂³	#137×C₅₉	1	2	yes	—
695	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	4	1	no	—
699	Q₈	—	4	1	no	—
700	Q₈	—	4	1	no	—
701	Q₈	—	4	1	no	—
702	Q₈	—	4	1	no	—
703	Q₈	—	4	1	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	2	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	1	no	—
710	D₄	—	4	1	no	—
711	D₄	—	4	1	no	—
712	D₄	—	4	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	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	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	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	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	#121×C₅₉	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
753	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
754	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
755	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
756	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	4	1	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	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	16	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	C₅₉×#464	1	4	yes	complemented
783	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
784	C₂²	D₄²×C₅₉	1	1	yes	characteristic
785	C₂²	C₅₉×#546	1	1	yes	characteristic
786	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
787	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
788	C₂²	C₅₉×#576	1	1	yes	characteristic
789	C₂²	C₅₉×#577	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	8	1	no	—
799	C₄	—	8	1	no	—
800	C₄	—	8	1	no	—
801	C₄	C₅₉×#525	1	1	yes	characteristic
802	C₄	C₅₉×#538	1	1	yes	characteristic
803	C₄	D₄²×C₅₉	1	1	yes	characteristic
804	C₄	C₅₉×#546	1	1	yes	characteristic
805	C₂	—	2	4	no	—
806	C₂	—	8	2	no	—
807	C₂	—	8	2	no	—
808	C₂	C₅₉×#2424	1	1	yes	characteristic
809	C₂	C₂×C₅₉×#464	1	1	yes	characteristic
810	C₂	C₅₉×#3045	1	1	yes	characteristic
811	C₂	C₅₉×#3266	1	1	yes	characteristic
812	C₂	C₅₉×#3280	1	1	yes	characteristic
813	C₂	C₅₉×#3296	1	1	yes	characteristic
814	C₂	C₅₉×#3314	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#467	C₂	semidirect
2. C₂×C₅₉×#464	C₂	semidirect
6. C₅₉×#2360	C₂	semidirect
7. C₅₉×#2067	C₂	semidirect
8. C₅₉×#2055	C₂	semidirect
9. C₅₉×#2042	C₂	semidirect
10. C₅₉×#2015	C₂	semidirect
11. C₅₉×#1983	C₂	semidirect
12. C₅₉×#1925	C₂	semidirect
13. C₅₉×#1880	C₂	semidirect
14. C₅₉×#1872	C₂	semidirect
15. C₅₉×#1850	C₂	semidirect
17. C₂²×Q₁₆×C₅₉	C₂²	semidirect
25. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
30. C₂×#107×C₅₉	C₂²	semidirect
31. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
32. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
33. C₂×#103×C₅₉	C₂²	semidirect
34. C₂×#103×C₅₉	C₂²	semidirect
35. C₂×#103×C₅₉	C₂²	semidirect
36. C₂×#103×C₅₉	C₂²	semidirect
47. C₅₉×#391	C₂²	semidirect
51. C₅₉×#389	C₂²	semidirect
56. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
59. C₅₉×#340	C₂²	semidirect
60. C₅₉×#340	C₂²	semidirect
61. C₅₉×#336	C₂²	semidirect
62. C₅₉×#336	C₂²	semidirect
353. #25084	C₅₉	direct (N × H)
375. C₂²×C₅₉	#464	semidirect
398. C₂×#467	C₂×C₅₉	semidirect
399. C₂×#464	C₂×C₅₉	semidirect
403. #2360	C₂×C₅₉	semidirect
404. #2067	C₂×C₅₉	semidirect
405. #2055	C₂×C₅₉	semidirect
406. #2042	C₂×C₅₉	semidirect
407. #2015	C₂×C₅₉	semidirect
408. #1983	C₂×C₅₉	semidirect
409. #1925	C₂×C₅₉	semidirect
410. #1880	C₂×C₅₉	semidirect
411. #1872	C₂×C₅₉	semidirect
412. #1850	C₂×C₅₉	semidirect
424. C₂²×Q₁₆	C₂²×C₅₉	semidirect
432. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
437. C₂×#107	C₂²×C₅₉	semidirect
438. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
439. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
440. C₂×#103	C₂²×C₅₉	semidirect
441. C₂×#103	C₂²×C₅₉	semidirect
442. C₂×#103	C₂²×C₅₉	semidirect
443. C₂×#103	C₂²×C₅₉	semidirect
454. #391	C₂²×C₅₉	semidirect
458. #389	C₂²×C₅₉	semidirect
463. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
466. #340	C₂²×C₅₉	semidirect
467. #340	C₂²×C₅₉	semidirect
468. #336	C₂²×C₅₉	semidirect
469. #336	C₂²×C₅₉	semidirect
470. C₅₉	#25084	direct (N × H)
782. C₂²	C₅₉×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#467	2
C₂×C₅₉×#464	2
C₂×C₅₉×#450	2
C₂²×#102×C₅₉	2
C₅₉×#2435	2
C₅₉×#2360	2
C₅₉×#2067	2
C₅₉×#2055	2
C₅₉×#2042	2
C₅₉×#2015	2
C₅₉×#1983	2
C₅₉×#1925	2
C₅₉×#1880	2
C₅₉×#1872	2
C₅₉×#1850	2
#25084	59

Subgroups — C59×#25084 #28437193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25084 #28437193