Subgroups — C₅₉×#62251 #28474360

Order 15104.

2014 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3519	C₂	1	2	yes	maximal, complemented
2	C₅₉×#3341	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3339	C₂	1	2	yes	maximal, complemented
4	C₅₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3305	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3297	C₂	1	4	yes	maximal, complemented
7	C₅₉×#3295	C₂	1	2	yes	maximal, complemented
8	C₅₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3247	C₂	1	2	yes	maximal, complemented
12	C₅₉×#3188	C₂	1	4	yes	maximal, complemented
13	C₅₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3050	C₂	1	2	yes	maximal, complemented
16	C₂×C₅₉×#466	C₂	1	2	yes	maximal, complemented
17	C₂×C₈×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₅₉	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₅₉	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₅₉	C₂²	1	2	yes	complemented
21	C₅₉×#555	C₂²	1	2	yes	complemented
22	C₅₉×#554	C₂²	1	2	yes	—
23	C₅₉×#553	—	2	2	no	—
24	C₅₉×#553	C₂²	1	4	yes	complemented
25	C₅₉×#550	C₂²	1	2	yes	complemented
26	C₅₉×#546	—	2	4	no	—
27	C₅₉×#546	C₂²	1	4	yes	complemented
28	D₄²×C₅₉	—	2	2	no	—
29	D₄²×C₅₉	C₂²	1	2	yes	—
30	C₅₉×#540	—	2	2	no	—
31	C₅₉×#538	—	2	4	no	—
32	C₅₉×#532	C₂²	1	2	yes	complemented
33	C₅₉×#529	C₂²	1	2	yes	complemented
34	C₅₉×#525	C₂²	1	4	yes	complemented
35	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
36	C₅₉×#518	—	2	2	no	—
37	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#500	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#499	C₂²	1	1	yes	characteristic, complemented
40	C₅₉×#495	C₂²	1	1	yes	characteristic, complemented
41	C₅₉×#493	C₂²	1	1	yes	characteristic, complemented
42	C₅₉×#488	C₂²	1	2	yes	complemented
43	C₅₉×#486	C₂²	1	2	yes	complemented
44	C₅₉×#484	C₂²	1	4	yes	complemented
45	C₅₉×#482	C₂²	1	4	yes	complemented
46	C₅₉×#482	C₂²	1	4	yes	complemented
47	C₅₉×#481	C₂²	1	4	yes	complemented
48	C₅₉×#478	C₂²	1	4	yes	complemented
49	C₅₉×#477	C₂²	1	2	yes	complemented
50	C₅₉×#476	C₂²	1	2	yes	complemented
51	C₅₉×#467	C₂²	1	2	yes	complemented
52	C₅₉×#467	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#466	C₂²	1	1	yes	characteristic
54	C₅₉×#466	C₂²	1	2	yes	complemented
55	C₅₉×#466	C₂²	1	2	yes	complemented
56	C₅₉×#466	C₂²	1	2	yes	complemented
57	C₅₉×#466	C₂²	1	4	yes	complemented
58	C₅₉×#466	C₂²	1	2	yes	complemented
59	C₅₉×#466	C₂²	1	4	yes	complemented
60	C₅₉×#466	C₂²	1	2	yes	complemented
61	C₅₉×#465	C₂²	1	4	yes	complemented
62	C₅₉×#465	C₂²	1	4	yes	complemented
63	C₅₉×#465	C₂²	1	2	yes	complemented
64	C₅₉×#463	C₂²	1	4	yes	complemented
65	C₅₉×#460	C₂²	1	2	yes	complemented
66	C₅₉×#459	C₂²	1	2	yes	complemented
67	C₅₉×#450	C₂²	1	4	yes	complemented
68	C₅₉×#449	C₂²	1	4	yes	complemented
69	C₅₉×#449	C₂²	1	4	yes	complemented
70	C₅₉×#447	C₂²	1	4	yes	complemented
71	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
72	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
73	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
74	C₄×D₈×C₅₉	C₂²	1	2	yes	complemented
75	C₄×D₈×C₅₉	C₂²	1	2	yes	complemented
76	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₅₉	C₂²	1	2	yes	complemented
79	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₅₉	C₂²	1	2	yes	complemented
81	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
82	C₅₉×#427	C₂²	1	2	yes	complemented
83	C₂×#107×C₅₉	C₂²	1	2	yes	complemented
84	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
85	C₅₉×#416	C₂²	1	4	yes	complemented
86	C₂×#102×C₅₉	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
89	C₂×#41×C₅₉	—	2	2	no	—
90	C₂×#41×C₅₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₅₉	—	2	4	no	—
92	C₂²×D₄×C₅₉	—	2	2	no	—
93	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
95	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
96	#135×C₅₉	—	4	4	no	—
97	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₅₉	C₂³	1	4	yes	—
100	C₂×D₈×C₅₉	—	4	4	no	—
101	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₅₉	C₂³	1	2	yes	—
103	C₂×D₈×C₅₉	C₂³	1	2	yes	—
104	C₂×D₈×C₅₉	C₂³	1	4	yes	—
105	C₂²×C₈×C₅₉	—	4	4	no	—
106	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
109	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
112	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
114	#127×C₅₉	—	2	2	no	—
115	#127×C₅₉	C₂³	1	2	yes	—
116	#126×C₅₉	—	2	4	no	—
117	#126×C₅₉	—	2	2	no	—
118	#125×C₅₉	—	2	2	no	—
119	#125×C₅₉	C₂³	1	2	yes	—
120	#124×C₅₉	—	2	4	no	—
121	#124×C₅₉	—	2	2	no	—
122	#124×C₅₉	C₂³	1	2	yes	—
123	#123×C₅₉	—	2	4	no	—
124	#123×C₅₉	—	2	2	no	—
125	#123×C₅₉	—	2	4	no	—
126	#123×C₅₉	—	2	4	no	—
127	C₂²⋊Q₈×C₅₉	—	2	4	no	—
128	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
129	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
130	#121×C₅₉	—	2	4	no	—
131	#121×C₅₉	—	2	2	no	—
132	#121×C₅₉	—	2	4	no	—
133	#121×C₅₉	—	2	4	no	—
134	#121×C₅₉	—	2	2	no	—
135	#121×C₅₉	—	2	2	no	—
136	#121×C₅₉	—	2	4	no	—
137	#121×C₅₉	—	2	4	no	—
138	#121×C₅₉	C₂³	1	4	yes	—
139	#121×C₅₉	C₂³	1	4	yes	—
140	#121×C₅₉	C₂³	1	4	yes	—
141	#121×C₅₉	C₂³	1	2	yes	—
142	#121×C₅₉	C₂³	1	4	yes	—
143	#120×C₅₉	—	2	4	no	—
144	#120×C₅₉	—	2	4	no	—
145	#120×C₅₉	—	2	4	no	—
146	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
147	C₄×D₄×C₅₉	—	2	2	no	—
148	C₄×D₄×C₅₉	—	2	4	no	—
149	C₄×D₄×C₅₉	—	2	4	no	—
150	C₄×D₄×C₅₉	—	2	2	no	—
151	C₄×D₄×C₅₉	—	2	2	no	—
152	C₄×D₄×C₅₉	—	2	4	no	—
153	C₄×D₄×C₅₉	—	2	2	no	—
154	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
155	C₄×D₄×C₅₉	D₄	1	2	yes	—
156	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
157	C₄×D₄×C₅₉	C₂³	1	4	yes	—
158	C₄×D₄×C₅₉	C₂³	1	2	yes	—
159	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₅₉	C₂³	1	2	yes	—
161	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
162	#117×C₅₉	—	2	2	no	—
163	#117×C₅₉	—	2	2	no	—
164	#117×C₅₉	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
168	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
169	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
170	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
171	#107×C₅₉	C₂³	1	1	yes	characteristic
172	#107×C₅₉	C₂³	1	2	yes	—
173	#107×C₅₉	C₂³	1	4	yes	—
174	#107×C₅₉	C₂³	1	1	yes	characteristic
175	#107×C₅₉	C₂³	1	2	yes	—
176	#106×C₅₉	C₂³	1	4	yes	—
177	#106×C₅₉	C₂³	1	2	yes	—
178	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
179	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
180	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
181	#103×C₅₉	C₂³	1	2	yes	—
182	#103×C₅₉	C₂³	1	4	yes	—
183	#103×C₅₉	C₂³	1	2	yes	—
184	#102×C₅₉	C₂³	1	2	yes	—
185	#102×C₅₉	C₂³	1	4	yes	—
186	#102×C₅₉	C₂³	1	4	yes	—
187	#102×C₅₉	C₂³	1	4	yes	—
188	#102×C₅₉	C₂³	1	4	yes	—
189	#102×C₅₉	C₂³	1	2	yes	—
190	#102×C₅₉	C₂³	1	4	yes	—
191	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
195	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
199	C₂⁴×C₅₉	—	2	4	no	—
200	C₂⁴×C₅₉	C₂×D₄	1	2	yes	—
201	#41×C₅₉	—	4	4	no	—
202	#41×C₅₉	—	4	4	no	—
203	#41×C₅₉	—	8	4	no	—
204	C₂×Q₈×C₅₉	—	2	2	no	—
205	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
206	C₂×D₄×C₅₉	—	2	4	no	—
207	C₂×D₄×C₅₉	—	2	4	no	—
208	C₂×D₄×C₅₉	—	2	4	no	—
209	C₂×D₄×C₅₉	—	2	2	no	—
210	C₂×D₄×C₅₉	—	2	4	no	—
211	C₂×D₄×C₅₉	—	2	4	no	—
212	C₂×D₄×C₅₉	—	2	4	no	—
213	C₂×D₄×C₅₉	—	2	2	no	—
214	C₂×D₄×C₅₉	—	2	2	no	—
215	C₂×D₄×C₅₉	—	2	4	no	—
216	C₂×D₄×C₅₉	—	4	4	no	—
217	C₂×D₄×C₅₉	—	4	4	no	—
218	C₂×D₄×C₅₉	—	4	8	no	—
219	C₂×D₄×C₅₉	—	8	8	no	—
220	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
223	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
224	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
225	C₂²×C₄×C₅₉	—	2	4	no	—
226	C₂²×C₄×C₅₉	—	2	2	no	—
227	C₂²×C₄×C₅₉	—	2	4	no	—
228	C₂²×C₄×C₅₉	—	2	4	no	—
229	C₂²×C₄×C₅₉	—	4	2	no	—
230	C₂²×C₄×C₅₉	—	4	2	no	—
231	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
236	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
239	Q₁₆×C₅₉	—	2	2	no	—
240	SD₁₆×C₅₉	—	4	2	no	—
241	SD₁₆×C₅₉	—	4	4	no	—
242	D₈×C₅₉	—	2	2	no	—
243	D₈×C₅₉	—	2	4	no	—
244	D₈×C₅₉	—	4	4	no	—
245	D₈×C₅₉	—	4	2	no	—
246	C₂×C₈×C₅₉	—	2	2	no	—
247	C₂×C₈×C₅₉	—	2	4	no	—
248	C₂×C₈×C₅₉	—	2	4	no	—
249	C₂×C₈×C₅₉	—	4	2	no	—
250	C₂×C₈×C₅₉	—	4	2	no	—
251	C₂×C₈×C₅₉	—	4	2	no	—
252	C₂×C₈×C₅₉	—	4	1	no	—
253	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
257	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
258	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₅₉	—	2	4	no	—
260	C₄⋊C₄×C₅₉	—	2	2	no	—
261	C₄⋊C₄×C₅₉	—	2	2	no	—
262	C₄⋊C₄×C₅₉	—	2	2	no	—
263	C₄⋊C₄×C₅₉	—	2	2	no	—
264	C₄⋊C₄×C₅₉	—	2	4	no	—
265	C₄⋊C₄×C₅₉	—	2	2	no	—
266	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
269	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
272	C₂²⋊C₄×C₅₉	—	2	4	no	—
273	C₂²⋊C₄×C₅₉	—	2	4	no	—
274	C₂²⋊C₄×C₅₉	—	2	2	no	—
275	C₂²⋊C₄×C₅₉	—	2	2	no	—
276	C₂²⋊C₄×C₅₉	—	2	2	no	—
277	C₂²⋊C₄×C₅₉	—	2	4	no	—
278	C₂²⋊C₄×C₅₉	—	2	4	no	—
279	C₂²⋊C₄×C₅₉	—	2	4	no	—
280	C₂²⋊C₄×C₅₉	—	2	2	no	—
281	C₂²⋊C₄×C₅₉	—	2	4	no	—
282	C₂²⋊C₄×C₅₉	—	2	2	no	—
283	C₂²⋊C₄×C₅₉	—	2	4	no	—
284	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
287	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
288	C₄²×C₅₉	—	2	4	no	—
289	C₄²×C₅₉	—	2	2	no	—
290	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
293	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
294	C₂³×C₅₉	—	2	4	no	—
295	C₂³×C₅₉	—	2	4	no	—
296	C₂³×C₅₉	—	2	2	no	—
297	C₂³×C₅₉	—	2	4	no	—
298	C₂³×C₅₉	—	4	2	no	—
299	C₂³×C₅₉	—	4	8	no	—
300	C₂³×C₅₉	—	8	4	no	—
301	C₂³×C₅₉	—	8	4	no	—
302	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
303	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
304	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₅₉	—	2	2	no	—
306	Q₈×C₅₉	—	2	2	no	—
307	Q₈×C₅₉	—	8	2	no	—
308	D₄×C₅₉	—	2	4	no	—
309	D₄×C₅₉	—	2	2	no	—
310	D₄×C₅₉	—	2	2	no	—
311	D₄×C₅₉	—	2	4	no	—
312	D₄×C₅₉	—	2	4	no	—
313	D₄×C₅₉	—	2	2	no	—
314	D₄×C₅₉	—	4	8	no	—
315	D₄×C₅₉	—	4	4	no	—
316	D₄×C₅₉	—	4	8	no	—
317	D₄×C₅₉	—	4	4	no	—
318	D₄×C₅₉	—	8	4	no	—
319	D₄×C₅₉	—	8	2	no	—
320	D₄×C₅₉	—	8	4	no	—
321	D₄×C₅₉	—	8	4	no	—
322	D₄×C₅₉	—	8	4	no	—
323	D₄×C₅₉	#135	1	4	yes	complemented
324	C₂×C₄×C₅₉	—	2	2	no	—
325	C₂×C₄×C₅₉	—	2	2	no	—
326	C₂×C₄×C₅₉	—	2	1	no	—
327	C₂×C₄×C₅₉	—	2	2	no	—
328	C₂×C₄×C₅₉	—	2	2	no	—
329	C₂×C₄×C₅₉	—	2	1	no	—
330	C₂×C₄×C₅₉	—	2	2	no	—
331	C₂×C₄×C₅₉	—	2	2	no	—
332	C₂×C₄×C₅₉	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	4	no	—
335	C₂×C₄×C₅₉	—	2	2	no	—
336	C₂×C₄×C₅₉	—	4	2	no	—
337	C₂×C₄×C₅₉	—	4	2	no	—
338	C₂×C₄×C₅₉	—	4	2	no	—
339	C₂×C₄×C₅₉	—	4	4	no	—
340	C₂×C₄×C₅₉	—	8	4	no	—
341	C₂×C₄×C₅₉	—	8	4	no	—
342	C₂×C₄×C₅₉	—	8	4	no	—
343	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
351	C₈×C₅₉	—	2	1	no	—
352	C₈×C₅₉	—	2	2	no	—
353	C₈×C₅₉	—	2	2	no	—
354	C₈×C₅₉	—	2	1	no	—
355	C₈×C₅₉	—	2	1	no	—
356	C₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
357	#62251	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂²×C₅₉	—	2	1	no	—
359	C₂²×C₅₉	—	2	2	no	—
360	C₂²×C₅₉	—	2	1	no	—
361	C₂²×C₅₉	—	2	2	no	—
362	C₂²×C₅₉	—	2	2	no	—
363	C₂²×C₅₉	—	2	2	no	—
364	C₂²×C₅₉	—	2	2	no	—
365	C₂²×C₅₉	—	4	8	no	—
366	C₂²×C₅₉	—	4	4	no	—
367	C₂²×C₅₉	—	4	2	no	—
368	C₂²×C₅₉	—	4	2	no	—
369	C₂²×C₅₉	—	4	4	no	—
370	C₂²×C₅₉	—	4	4	no	—
371	C₂²×C₅₉	—	4	2	no	—
372	C₂²×C₅₉	—	16	8	no	—
373	C₂²×C₅₉	C₂×#135	1	4	yes	—
374	C₂²×C₅₉	#576	1	2	yes	—
375	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
376	C₄×C₅₉	—	2	1	no	—
377	C₄×C₅₉	—	2	2	no	—
378	C₄×C₅₉	—	2	2	no	—
379	C₄×C₅₉	—	2	1	no	—
380	C₄×C₅₉	—	2	1	no	—
381	C₄×C₅₉	—	2	1	no	—
382	C₄×C₅₉	—	4	2	no	—
383	C₄×C₅₉	—	4	2	no	—
384	C₄×C₅₉	—	4	2	no	—
385	C₄×C₅₉	—	4	4	no	—
386	C₄×C₅₉	C₂×#135	1	2	yes	—
387	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
388	C₄×C₅₉	#585	1	1	yes	characteristic
389	#3519	C₂×C₅₉	1	2	yes	complemented
390	#3341	C₂×C₅₉	1	1	yes	characteristic, complemented
391	#3339	C₂×C₅₉	1	2	yes	complemented
392	#3338	C₂×C₅₉	1	1	yes	characteristic, complemented
393	#3305	C₂×C₅₉	1	2	yes	complemented
394	#3297	C₂×C₅₉	1	4	yes	complemented
395	#3295	C₂×C₅₉	1	2	yes	complemented
396	#3287	C₂×C₅₉	1	1	yes	characteristic, complemented
397	#3280	C₂×C₅₉	1	2	yes	complemented
398	D₄×D₈	C₂×C₅₉	1	1	yes	characteristic, complemented
399	#3247	C₂×C₅₉	1	2	yes	complemented
400	#3188	C₂×C₅₉	1	4	yes	complemented
401	#3169	C₂×C₅₉	1	1	yes	characteristic, complemented
402	#3168	C₂×C₅₉	1	1	yes	characteristic, complemented
403	#3050	C₂×C₅₉	1	2	yes	complemented
404	C₂×#466	C₂×C₅₉	1	2	yes	complemented
405	C₂×C₈×D₄	C₂×C₅₉	1	1	yes	characteristic, complemented
406	C₂×C₅₉	—	2	2	no	—
407	C₂×C₅₉	—	2	4	no	—
408	C₂×C₅₉	—	4	2	no	—
409	C₂×C₅₉	—	8	4	no	—
410	C₂×C₅₉	—	8	2	no	—
411	C₂×C₅₉	#3496	1	1	yes	characteristic
412	C₂×C₅₉	C₂²×#135	1	1	yes	characteristic
413	C₂×C₅₉	C₂×#576	1	1	yes	characteristic
414	C₂×#135	C₂²×C₅₉	1	2	yes	complemented
415	C₂²×D₈	C₂²×C₅₉	1	2	yes	complemented
416	C₂³×C₈	C₂²×C₅₉	1	2	yes	complemented
417	#555	C₂²×C₅₉	1	2	yes	complemented
418	#554	C₂²×C₅₉	1	2	yes	—
419	#553	—	2	2	no	—
420	#553	C₂²×C₅₉	1	4	yes	complemented
421	#550	C₂²×C₅₉	1	2	yes	complemented
422	#546	—	2	4	no	—
423	#546	C₂²×C₅₉	1	4	yes	complemented
424	D₄²	—	2	2	no	—
425	D₄²	C₂²×C₅₉	1	2	yes	—
426	#540	—	2	2	no	—
427	#538	—	2	4	no	—
428	#532	C₂²×C₅₉	1	2	yes	complemented
429	#529	C₂²×C₅₉	1	2	yes	complemented
430	#525	C₂²×C₅₉	1	4	yes	complemented
431	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
432	#518	—	2	2	no	—
433	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
434	#500	C₂²×C₅₉	1	1	yes	characteristic, complemented
435	#499	C₂²×C₅₉	1	1	yes	characteristic, complemented
436	#495	C₂²×C₅₉	1	1	yes	characteristic, complemented
437	#493	C₂²×C₅₉	1	1	yes	characteristic, complemented
438	#488	C₂²×C₅₉	1	2	yes	complemented
439	#486	C₂²×C₅₉	1	2	yes	complemented
440	#484	C₂²×C₅₉	1	4	yes	complemented
441	#482	C₂²×C₅₉	1	4	yes	complemented
442	#482	C₂²×C₅₉	1	4	yes	complemented
443	#481	C₂²×C₅₉	1	4	yes	complemented
444	#478	C₂²×C₅₉	1	4	yes	complemented
445	#477	C₂²×C₅₉	1	2	yes	complemented
446	#476	C₂²×C₅₉	1	2	yes	complemented
447	#467	C₂²×C₅₉	1	2	yes	complemented
448	#467	C₂²×C₅₉	1	1	yes	characteristic, complemented
449	#466	C₂²×C₅₉	1	1	yes	characteristic
450	#466	C₂²×C₅₉	1	2	yes	complemented
451	#466	C₂²×C₅₉	1	2	yes	complemented
452	#466	C₂²×C₅₉	1	2	yes	complemented
453	#466	C₂²×C₅₉	1	2	yes	complemented
454	#466	C₂²×C₅₉	1	2	yes	complemented
455	#466	C₂²×C₅₉	1	4	yes	complemented
456	#466	C₂²×C₅₉	1	4	yes	complemented
457	#465	C₂²×C₅₉	1	2	yes	complemented
458	#465	C₂²×C₅₉	1	4	yes	complemented
459	#465	C₂²×C₅₉	1	4	yes	complemented
460	#463	C₂²×C₅₉	1	4	yes	complemented
461	#460	C₂²×C₅₉	1	2	yes	complemented
462	#459	C₂²×C₅₉	1	2	yes	complemented
463	#450	C₂²×C₅₉	1	4	yes	complemented
464	#449	C₂²×C₅₉	1	4	yes	complemented
465	#449	C₂²×C₅₉	1	4	yes	complemented
466	#447	C₂²×C₅₉	1	4	yes	complemented
467	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
468	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
469	C₄×D₈	C₂²×C₅₉	1	2	yes	complemented
470	C₄×D₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
471	C₄×D₈	C₂²×C₅₉	1	2	yes	complemented
472	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
473	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
474	C₈×D₄	C₂²×C₅₉	1	2	yes	complemented
475	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
476	C₈×D₄	C₂²×C₅₉	1	2	yes	complemented
477	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
478	#427	C₂²×C₅₉	1	2	yes	complemented
479	C₂×#107	C₂²×C₅₉	1	2	yes	complemented
480	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
481	#416	C₂²×C₅₉	1	4	yes	complemented
482	C₂×#102	C₂²×C₅₉	1	4	yes	complemented
483	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	complemented
484	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
485	C₅₉	#62251	1	1	yes	characteristic, direct product factor, Sylow
486	C₂×#41	—	2	2	no	—
487	C₂×#41	C₂³×C₅₉	1	4	yes	—
488	C₂²×D₄	—	2	4	no	—
489	C₂²×D₄	—	2	2	no	—
490	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
492	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
493	#135	—	4	4	no	—
494	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
495	C₂×SD₁₆	C₂³×C₅₉	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
497	C₂×D₈	—	4	4	no	—
498	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
499	C₂×D₈	C₂³×C₅₉	1	2	yes	—
500	C₂×D₈	C₂³×C₅₉	1	4	yes	—
501	C₂×D₈	C₂³×C₅₉	1	2	yes	—
502	C₂²×C₈	—	4	4	no	—
503	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
505	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
506	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
507	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
508	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
509	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
511	#127	—	2	2	no	—
512	#127	C₂³×C₅₉	1	2	yes	—
513	#126	—	2	4	no	—
514	#126	—	2	2	no	—
515	#125	—	2	2	no	—
516	#125	C₂³×C₅₉	1	2	yes	—
517	#124	—	2	4	no	—
518	#124	—	2	2	no	—
519	#124	C₂³×C₅₉	1	2	yes	—
520	#123	—	2	4	no	—
521	#123	—	2	2	no	—
522	#123	—	2	4	no	—
523	#123	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
526	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
527	#121	—	2	4	no	—
528	#121	—	2	2	no	—
529	#121	—	2	4	no	—
530	#121	—	2	4	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	4	no	—
534	#121	—	2	4	no	—
535	#121	C₂³×C₅₉	1	2	yes	—
536	#121	C₂³×C₅₉	1	4	yes	—
537	#121	C₂³×C₅₉	1	4	yes	—
538	#121	C₂³×C₅₉	1	4	yes	—
539	#121	C₂³×C₅₉	1	4	yes	—
540	#120	—	2	4	no	—
541	#120	—	2	4	no	—
542	#120	—	2	4	no	—
543	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	4	no	—
546	C₄×D₄	—	2	4	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	4	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
552	C₄×D₄	D₄×C₅₉	1	2	yes	—
553	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
554	C₄×D₄	C₂³×C₅₉	1	2	yes	—
555	C₄×D₄	C₂³×C₅₉	1	4	yes	—
556	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
557	C₄×D₄	C₂³×C₅₉	1	2	yes	—
558	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
559	#117	—	2	2	no	—
560	#117	—	2	2	no	—
561	#117	C₂³×C₅₉	1	4	yes	—
562	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
567	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
568	#107	C₂³×C₅₉	1	1	yes	characteristic
569	#107	C₂³×C₅₉	1	2	yes	—
570	#107	C₂³×C₅₉	1	4	yes	—
571	#107	C₂³×C₅₉	1	1	yes	characteristic
572	#107	C₂³×C₅₉	1	2	yes	—
573	#106	C₂³×C₅₉	1	4	yes	—
574	#106	C₂³×C₅₉	1	2	yes	—
575	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
576	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
577	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
578	#103	C₂³×C₅₉	1	2	yes	—
579	#103	C₂³×C₅₉	1	4	yes	—
580	#103	C₂³×C₅₉	1	2	yes	—
581	#102	C₂³×C₅₉	1	2	yes	—
582	#102	C₂³×C₅₉	1	4	yes	—
583	#102	C₂³×C₅₉	1	4	yes	—
584	#102	C₂³×C₅₉	1	4	yes	—
585	#102	C₂³×C₅₉	1	4	yes	—
586	#102	C₂³×C₅₉	1	2	yes	—
587	#102	C₂³×C₅₉	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
591	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
592	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
594	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
595	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
596	C₂⁴	—	2	4	no	—
597	C₂⁴	C₂×D₄×C₅₉	1	2	yes	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	8	4	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	8	no	—
616	C₂×D₄	—	8	8	no	—
617	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
619	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
620	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
621	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
632	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
636	Q₁₆	—	2	2	no	—
637	SD₁₆	—	4	4	no	—
638	SD₁₆	—	4	2	no	—
639	D₈	—	2	2	no	—
640	D₈	—	2	4	no	—
641	D₈	—	4	4	no	—
642	D₈	—	4	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	4	no	—
645	C₂×C₈	—	2	4	no	—
646	C₂×C₈	—	4	2	no	—
647	C₂×C₈	—	4	2	no	—
648	C₂×C₈	—	4	2	no	—
649	C₂×C₈	—	4	1	no	—
650	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
653	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
654	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
655	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
664	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
665	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
682	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
683	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
684	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	2	no	—
687	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
689	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
690	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
700	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
701	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
702	Q₈	—	2	2	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	8	2	no	—
705	D₄	—	2	4	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	4	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	2	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	2	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	4	no	—
719	D₄	—	8	4	no	—
720	D₄	#135×C₅₉	1	4	yes	complemented
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
747	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
748	C₈	—	2	1	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	4	8	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	16	8	no	—
769	C₂²	C₂×#135×C₅₉	1	4	yes	—
770	C₂²	C₅₉×#576	1	2	yes	—
771	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	4	no	—
781	C₄	—	4	2	no	—
782	C₄	C₂×#135×C₅₉	1	2	yes	—
783	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
784	C₄	C₅₉×#585	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	2	4	no	—
787	C₂	—	4	2	no	—
788	C₂	—	8	2	no	—
789	C₂	—	8	4	no	—
790	C₂	C₅₉×#3496	1	1	yes	characteristic
791	C₂	C₂²×#135×C₅₉	1	1	yes	characteristic
792	C₂	C₂×C₅₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3519	C₂	semidirect
2. C₅₉×#3341	C₂	semidirect
3. C₅₉×#3339	C₂	semidirect
4. C₅₉×#3338	C₂	semidirect
5. C₅₉×#3305	C₂	semidirect
6. C₅₉×#3297	C₂	semidirect
7. C₅₉×#3295	C₂	semidirect
8. C₅₉×#3287	C₂	semidirect
9. C₅₉×#3280	C₂	semidirect
10. D₄×D₈×C₅₉	C₂	semidirect
11. C₅₉×#3247	C₂	semidirect
12. C₅₉×#3188	C₂	semidirect
13. C₅₉×#3169	C₂	semidirect
14. C₅₉×#3168	C₂	semidirect
15. C₅₉×#3050	C₂	semidirect
16. C₂×C₅₉×#466	C₂	semidirect
17. C₂×C₈×D₄×C₅₉	C₂	semidirect
18. C₂×#135×C₅₉	C₂²	semidirect
19. C₂²×D₈×C₅₉	C₂²	semidirect
20. C₂³×C₈×C₅₉	C₂²	semidirect
21. C₅₉×#555	C₂²	semidirect
24. C₅₉×#553	C₂²	semidirect
25. C₅₉×#550	C₂²	semidirect
27. C₅₉×#546	C₂²	semidirect
32. C₅₉×#532	C₂²	semidirect
33. C₅₉×#529	C₂²	semidirect
34. C₅₉×#525	C₂²	semidirect
35. C₂×#121×C₅₉	C₂²	semidirect
38. C₅₉×#500	C₂²	semidirect
39. C₅₉×#499	C₂²	semidirect
40. C₅₉×#495	C₂²	semidirect
41. C₅₉×#493	C₂²	semidirect
42. C₅₉×#488	C₂²	semidirect
43. C₅₉×#486	C₂²	semidirect
44. C₅₉×#484	C₂²	semidirect
45. C₅₉×#482	C₂²	semidirect
46. C₅₉×#482	C₂²	semidirect
47. C₅₉×#481	C₂²	semidirect
48. C₅₉×#478	C₂²	semidirect
49. C₅₉×#477	C₂²	semidirect
50. C₅₉×#476	C₂²	semidirect
51. C₅₉×#467	C₂²	semidirect
52. C₅₉×#467	C₂²	semidirect
54. C₅₉×#466	C₂²	semidirect
55. C₅₉×#466	C₂²	semidirect
56. C₅₉×#466	C₂²	semidirect
57. C₅₉×#466	C₂²	semidirect
58. C₅₉×#466	C₂²	semidirect
59. C₅₉×#466	C₂²	semidirect
60. C₅₉×#466	C₂²	semidirect
61. C₅₉×#465	C₂²	semidirect
62. C₅₉×#465	C₂²	semidirect
63. C₅₉×#465	C₂²	semidirect
64. C₅₉×#463	C₂²	semidirect
65. C₅₉×#460	C₂²	semidirect
66. C₅₉×#459	C₂²	semidirect
67. C₅₉×#450	C₂²	semidirect
68. C₅₉×#449	C₂²	semidirect
69. C₅₉×#449	C₂²	semidirect
70. C₅₉×#447	C₂²	semidirect
71. C₄×Q₁₆×C₅₉	C₂²	semidirect
72. C₄×SD₁₆×C₅₉	C₂²	semidirect
73. C₄×D₈×C₅₉	C₂²	semidirect
74. C₄×D₈×C₅₉	C₂²	semidirect
75. C₄×D₈×C₅₉	C₂²	semidirect
78. C₈×D₄×C₅₉	C₂²	semidirect
79. C₈×D₄×C₅₉	C₂²	semidirect
80. C₈×D₄×C₅₉	C₂²	semidirect
81. C₈×D₄×C₅₉	C₂²	semidirect
82. C₅₉×#427	C₂²	semidirect
83. C₂×#107×C₅₉	C₂²	semidirect
84. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
85. C₅₉×#416	C₂²	semidirect
86. C₂×#102×C₅₉	C₂²	semidirect
87. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
88. C₂×C₄×C₈×C₅₉	C₂²	semidirect
323. D₄×C₅₉	#135	semidirect
357. #62251	C₅₉	direct (N × H)
389. #3519	C₂×C₅₉	semidirect
390. #3341	C₂×C₅₉	semidirect
391. #3339	C₂×C₅₉	semidirect
392. #3338	C₂×C₅₉	semidirect
393. #3305	C₂×C₅₉	semidirect
394. #3297	C₂×C₅₉	semidirect
395. #3295	C₂×C₅₉	semidirect
396. #3287	C₂×C₅₉	semidirect
397. #3280	C₂×C₅₉	semidirect
398. D₄×D₈	C₂×C₅₉	semidirect
399. #3247	C₂×C₅₉	semidirect
400. #3188	C₂×C₅₉	semidirect
401. #3169	C₂×C₅₉	semidirect
402. #3168	C₂×C₅₉	semidirect
403. #3050	C₂×C₅₉	semidirect
404. C₂×#466	C₂×C₅₉	semidirect
405. C₂×C₈×D₄	C₂×C₅₉	semidirect
414. C₂×#135	C₂²×C₅₉	semidirect
415. C₂²×D₈	C₂²×C₅₉	semidirect
416. C₂³×C₈	C₂²×C₅₉	semidirect
417. #555	C₂²×C₅₉	semidirect
420. #553	C₂²×C₅₉	semidirect
421. #550	C₂²×C₅₉	semidirect
423. #546	C₂²×C₅₉	semidirect
428. #532	C₂²×C₅₉	semidirect
429. #529	C₂²×C₅₉	semidirect
430. #525	C₂²×C₅₉	semidirect
431. C₂×#121	C₂²×C₅₉	semidirect
434. #500	C₂²×C₅₉	semidirect
435. #499	C₂²×C₅₉	semidirect
436. #495	C₂²×C₅₉	semidirect
437. #493	C₂²×C₅₉	semidirect
438. #488	C₂²×C₅₉	semidirect
439. #486	C₂²×C₅₉	semidirect
440. #484	C₂²×C₅₉	semidirect
441. #482	C₂²×C₅₉	semidirect
442. #482	C₂²×C₅₉	semidirect
443. #481	C₂²×C₅₉	semidirect
444. #478	C₂²×C₅₉	semidirect
445. #477	C₂²×C₅₉	semidirect
446. #476	C₂²×C₅₉	semidirect
447. #467	C₂²×C₅₉	semidirect
448. #467	C₂²×C₅₉	semidirect
450. #466	C₂²×C₅₉	semidirect
451. #466	C₂²×C₅₉	semidirect
452. #466	C₂²×C₅₉	semidirect
453. #466	C₂²×C₅₉	semidirect
454. #466	C₂²×C₅₉	semidirect
455. #466	C₂²×C₅₉	semidirect
456. #466	C₂²×C₅₉	semidirect
457. #465	C₂²×C₅₉	semidirect
458. #465	C₂²×C₅₉	semidirect
459. #465	C₂²×C₅₉	semidirect
460. #463	C₂²×C₅₉	semidirect
461. #460	C₂²×C₅₉	semidirect
462. #459	C₂²×C₅₉	semidirect
463. #450	C₂²×C₅₉	semidirect
464. #449	C₂²×C₅₉	semidirect
465. #449	C₂²×C₅₉	semidirect
466. #447	C₂²×C₅₉	semidirect
467. C₄×Q₁₆	C₂²×C₅₉	semidirect
468. C₄×SD₁₆	C₂²×C₅₉	semidirect
469. C₄×D₈	C₂²×C₅₉	semidirect
470. C₄×D₈	C₂²×C₅₉	semidirect
471. C₄×D₈	C₂²×C₅₉	semidirect
474. C₈×D₄	C₂²×C₅₉	semidirect
475. C₈×D₄	C₂²×C₅₉	semidirect
476. C₈×D₄	C₂²×C₅₉	semidirect
477. C₈×D₄	C₂²×C₅₉	semidirect
478. #427	C₂²×C₅₉	semidirect
479. C₂×#107	C₂²×C₅₉	semidirect
480. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
481. #416	C₂²×C₅₉	semidirect
482. C₂×#102	C₂²×C₅₉	semidirect
483. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
484. C₂×C₄×C₈	C₂²×C₅₉	semidirect
485. C₅₉	#62251	direct (N × H)
720. D₄	#135×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3519	2
C₅₉×#3341	2
C₅₉×#3339	2
C₅₉×#3338	2
C₅₉×#3305	2
C₅₉×#3297	2
C₅₉×#3295	2
C₅₉×#3287	2
C₅₉×#3280	2
D₄×D₈×C₅₉	2
C₅₉×#3247	2
C₅₉×#3188	2
C₅₉×#3169	2
C₅₉×#3168	2
C₅₉×#3050	2
C₂×C₅₉×#466	2
C₂×C₈×D₄×C₅₉	2
#62251	59

Subgroups — C59×#62251 #28474360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62251 #28474360