Subgroups — C₅₉×#62058 #28474167

Order 15104.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3308	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#3298	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3285	C₂	1	2	yes	maximal, complemented
12	C₅₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#3270	C₂	1	2	yes	maximal, complemented
15	C₅₉×#3258	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3225	C₂	1	2	yes	maximal, complemented
18	C₅₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#3120	C₂	1	2	yes	maximal, complemented
20	C₅₉×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#3046	C₂	1	2	yes	maximal, complemented
22	C₂×C₅₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₉	C₂²	1	2	yes	—
25	C₂×#135×C₅₉	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₅₉	C₂²	1	2	yes	—
27	C₅₉×#563	—	2	2	no	—
28	C₅₉×#559	—	2	1	no	—
29	C₅₉×#559	C₂²	1	1	yes	characteristic
30	Q₈²×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#557	C₂²	1	1	yes	characteristic
32	C₅₉×#556	C₂²	1	1	yes	characteristic
33	C₅₉×#554	—	2	1	no	—
34	C₅₉×#554	—	2	1	no	—
35	C₅₉×#554	C₂²	1	1	yes	characteristic
36	C₅₉×#553	—	2	1	no	—
37	C₅₉×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
39	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#548	C₂²	1	2	yes	—
41	C₅₉×#548	C₂²	1	2	yes	—
42	C₅₉×#547	—	2	2	no	—
43	C₅₉×#547	C₂²	1	1	yes	characteristic
44	C₅₉×#547	C₂²	1	2	yes	—
45	C₅₉×#544	—	2	1	no	—
46	C₅₉×#542	—	2	2	no	—
47	C₅₉×#542	—	2	1	no	—
48	C₅₉×#542	C₂²	1	2	yes	—
49	C₅₉×#541	C₂²	1	2	yes	—
50	C₅₉×#539	—	2	2	no	—
51	C₅₉×#536	C₂²	1	2	yes	—
52	C₅₉×#532	—	2	1	no	—
53	C₅₉×#532	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
55	C₅₉×#529	—	2	1	no	—
56	C₅₉×#529	C₂²	1	1	yes	characteristic
57	C₅₉×#529	C₂²	1	1	yes	characteristic
58	C₅₉×#520	C₂²	1	2	yes	—
59	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
60	C₅₉×#497	C₂²	1	2	yes	—
61	C₅₉×#495	C₂²	1	2	yes	—
62	C₅₉×#492	C₂²	1	1	yes	characteristic
63	C₅₉×#492	C₂²	1	1	yes	characteristic
64	C₅₉×#489	C₂²	1	2	yes	—
65	C₅₉×#487	C₂²	1	2	yes	—
66	C₅₉×#487	C₂²	1	1	yes	characteristic
67	C₅₉×#487	C₂²	1	1	yes	characteristic
68	C₅₉×#484	C₂²	1	2	yes	—
69	C₅₉×#483	C₂²	1	1	yes	characteristic
70	C₅₉×#483	C₂²	1	2	yes	—
71	C₅₉×#480	C₂²	1	1	yes	characteristic
72	C₅₉×#479	C₂²	1	1	yes	characteristic
73	C₅₉×#479	C₂²	1	1	yes	characteristic
74	C₅₉×#478	C₂²	1	2	yes	—
75	C₅₉×#477	C₂²	1	2	yes	—
76	C₅₉×#477	C₂²	1	1	yes	characteristic
77	C₅₉×#476	C₂²	1	1	yes	characteristic
78	C₅₉×#475	C₂²	1	2	yes	—
79	C₅₉×#470	C₂²	1	2	yes	—
80	C₅₉×#468	C₂²	1	2	yes	—
81	C₅₉×#467	C₂²	1	2	yes	—
82	C₅₉×#466	C₂²	1	2	yes	—
83	C₅₉×#465	C₂²	1	2	yes	—
84	C₅₉×#465	C₂²	1	2	yes	—
85	C₅₉×#464	C₂²	1	2	yes	—
86	C₅₉×#464	C₂²	1	2	yes	—
87	C₅₉×#464	C₂²	1	2	yes	—
88	C₅₉×#464	C₂²	1	1	yes	characteristic
89	C₅₉×#464	C₂²	1	1	yes	characteristic
90	C₅₉×#463	C₂²	1	2	yes	—
91	C₅₉×#463	C₂²	1	2	yes	—
92	C₅₉×#462	C₂²	1	2	yes	—
93	C₅₉×#462	C₂²	1	2	yes	—
94	C₅₉×#462	C₂²	1	1	yes	characteristic
95	C₅₉×#462	C₂²	1	1	yes	characteristic
96	C₅₉×#462	C₂²	1	1	yes	characteristic
97	C₅₉×#462	C₂²	1	2	yes	—
98	C₅₉×#462	C₂²	1	1	yes	characteristic
99	C₅₉×#461	C₂²	1	2	yes	—
100	C₅₉×#461	C₂²	1	2	yes	—
101	C₅₉×#461	C₂²	1	2	yes	—
102	C₅₉×#460	C₂²	1	1	yes	characteristic
103	C₅₉×#459	C₂²	1	1	yes	characteristic
104	C₅₉×#452	C₂²	1	2	yes	—
105	C₅₉×#452	C₂²	1	2	yes	—
106	C₅₉×#452	C₂²	1	2	yes	—
107	C₅₉×#451	C₂²	1	1	yes	characteristic
108	C₅₉×#451	C₂²	1	2	yes	—
109	C₅₉×#449	C₂²	1	2	yes	—
110	C₅₉×#448	C₂²	1	2	yes	—
111	C₅₉×#448	C₂²	1	2	yes	—
112	C₅₉×#448	C₂²	1	1	yes	characteristic
113	C₅₉×#448	C₂²	1	2	yes	—
114	C₅₉×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
116	C₅₉×#441	C₂²	1	2	yes	—
117	C₅₉×#440	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	—
120	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
124	C₅₉×#436	C₂²	1	1	yes	characteristic
125	C₅₉×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₅₉	C₂²	1	2	yes	—
128	C₅₉×#433	C₂²	1	2	yes	—
129	C₅₉×#431	C₂²	1	1	yes	characteristic
130	C₅₉×#424	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
132	C₅₉×#417	C₂²	1	2	yes	—
133	C₂×#103×C₅₉	C₂²	1	2	yes	—
134	C₂×#103×C₅₉	C₂²	1	2	yes	—
135	C₂×#41×C₅₉	—	2	2	no	—
136	C₂×#41×C₅₉	—	2	1	no	—
137	C₂×#41×C₅₉	C₂³	1	2	yes	—
138	C₂×#41×C₅₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
141	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
142	#137×C₅₉	—	4	4	no	—
143	#135×C₅₉	—	4	4	no	—
144	C₂×Q₁₆×C₅₉	—	4	4	no	—
145	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
158	C₂×D₈×C₅₉	C₂³	1	2	yes	—
159	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
160	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₅₉	—	2	1	no	—
163	C₄⋊Q₈×C₅₉	—	2	2	no	—
164	C₄⋊Q₈×C₅₉	—	2	1	no	—
165	C₄⋊Q₈×C₅₉	—	2	2	no	—
166	C₄⋊Q₈×C₅₉	—	2	1	no	—
167	C₄⋊Q₈×C₅₉	—	2	1	no	—
168	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
174	#127×C₅₉	—	2	1	no	—
175	#127×C₅₉	C₂³	1	1	yes	characteristic
176	#126×C₅₉	—	2	2	no	—
177	#126×C₅₉	—	2	2	no	—
178	#126×C₅₉	—	2	2	no	—
179	#126×C₅₉	—	2	2	no	—
180	#126×C₅₉	—	2	1	no	—
181	#126×C₅₉	D₄	1	2	yes	—
182	#125×C₅₉	—	2	1	no	—
183	#125×C₅₉	—	2	2	no	—
184	#125×C₅₉	—	2	2	no	—
185	#125×C₅₉	—	2	2	no	—
186	#125×C₅₉	—	2	1	no	—
187	#125×C₅₉	D₄	1	1	yes	characteristic
188	#125×C₅₉	C₂³	1	1	yes	characteristic
189	#124×C₅₉	—	2	1	no	—
190	#124×C₅₉	—	2	2	no	—
191	#124×C₅₉	—	2	2	no	—
192	#124×C₅₉	—	2	2	no	—
193	#124×C₅₉	—	2	1	no	—
194	#124×C₅₉	D₄	1	1	yes	characteristic
195	#124×C₅₉	C₂³	1	1	yes	characteristic
196	#124×C₅₉	C₂³	1	2	yes	—
197	#124×C₅₉	C₂³	1	2	yes	—
198	#123×C₅₉	—	2	1	no	—
199	#123×C₅₉	—	2	2	no	—
200	#123×C₅₉	—	2	2	no	—
201	#123×C₅₉	—	2	2	no	—
202	#123×C₅₉	—	2	2	no	—
203	#123×C₅₉	—	2	2	no	—
204	#123×C₅₉	—	2	2	no	—
205	#123×C₅₉	—	2	2	no	—
206	#123×C₅₉	D₄	1	2	yes	—
207	C₂²⋊Q₈×C₅₉	—	2	1	no	—
208	C₂²⋊Q₈×C₅₉	—	2	2	no	—
209	C₂²⋊Q₈×C₅₉	—	2	2	no	—
210	C₂²⋊Q₈×C₅₉	—	2	2	no	—
211	C₂²⋊Q₈×C₅₉	—	2	2	no	—
212	C₂²⋊Q₈×C₅₉	—	2	2	no	—
213	C₂²⋊Q₈×C₅₉	—	2	2	no	—
214	C₂²⋊Q₈×C₅₉	—	2	2	no	—
215	C₂²⋊Q₈×C₅₉	—	2	2	no	—
216	C₂²⋊Q₈×C₅₉	—	2	2	no	—
217	C₂²⋊Q₈×C₅₉	—	2	2	no	—
218	C₂²⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
219	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
223	#121×C₅₉	—	2	2	no	—
224	#121×C₅₉	—	2	2	no	—
225	#121×C₅₉	—	2	1	no	—
226	#121×C₅₉	—	2	1	no	—
227	#121×C₅₉	—	2	2	no	—
228	#121×C₅₉	D₄	1	1	yes	characteristic
229	#121×C₅₉	C₂³	1	2	yes	—
230	#121×C₅₉	C₂³	1	2	yes	—
231	#121×C₅₉	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₅₉	—	2	1	no	—
233	C₄×Q₈×C₅₉	—	2	1	no	—
234	C₄×Q₈×C₅₉	—	2	1	no	—
235	C₄×Q₈×C₅₉	—	2	1	no	—
236	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
241	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
242	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₅₉	—	2	1	no	—
246	C₄×D₄×C₅₉	—	2	2	no	—
247	C₄×D₄×C₅₉	—	2	1	no	—
248	C₄×D₄×C₅₉	—	2	1	no	—
249	C₄×D₄×C₅₉	—	2	1	no	—
250	C₄×D₄×C₅₉	—	2	1	no	—
251	C₄×D₄×C₅₉	—	2	2	no	—
252	C₄×D₄×C₅₉	—	2	2	no	—
253	C₄×D₄×C₅₉	—	2	2	no	—
254	C₄×D₄×C₅₉	—	2	2	no	—
255	C₄×D₄×C₅₉	—	2	1	no	—
256	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₅₉	C₂³	1	2	yes	—
258	C₄×D₄×C₅₉	C₂³	1	2	yes	—
259	C₄×D₄×C₅₉	C₂³	1	2	yes	—
260	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
261	#117×C₅₉	—	2	2	no	—
262	#117×C₅₉	—	2	1	no	—
263	#117×C₅₉	—	2	1	no	—
264	#117×C₅₉	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
267	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
269	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
272	C₂×C₄²×C₅₉	—	2	1	no	—
273	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
274	#107×C₅₉	C₂³	1	1	yes	characteristic
275	#107×C₅₉	C₂³	1	2	yes	—
276	#107×C₅₉	C₂³	1	1	yes	characteristic
277	#106×C₅₉	C₂³	1	1	yes	characteristic
278	#106×C₅₉	C₂³	1	1	yes	characteristic
279	#106×C₅₉	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
287	#103×C₅₉	C₂³	1	2	yes	—
288	#103×C₅₉	C₂³	1	1	yes	characteristic
289	#103×C₅₉	C₂³	1	2	yes	—
290	#103×C₅₉	C₂³	1	2	yes	—
291	#103×C₅₉	C₂³	1	2	yes	—
292	#103×C₅₉	C₂³	1	2	yes	—
293	#103×C₅₉	C₂³	1	2	yes	—
294	#103×C₅₉	C₂³	1	2	yes	—
295	#103×C₅₉	C₂³	1	1	yes	characteristic
296	#103×C₅₉	C₂³	1	1	yes	characteristic
297	#103×C₅₉	C₂³	1	1	yes	characteristic
298	#103×C₅₉	C₂³	1	1	yes	characteristic
299	#103×C₅₉	C₂³	1	2	yes	—
300	#103×C₅₉	C₂³	1	1	yes	characteristic
301	#103×C₅₉	C₂³	1	2	yes	—
302	#102×C₅₉	C₂³	1	1	yes	characteristic
303	#102×C₅₉	C₂³	1	2	yes	—
304	#102×C₅₉	C₂³	1	1	yes	characteristic
305	#102×C₅₉	C₂³	1	2	yes	—
306	#102×C₅₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
311	#97×C₅₉	C₂³	1	2	yes	—
312	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₉	C₂³	1	2	yes	—
315	#41×C₅₉	—	2	4	no	—
316	#41×C₅₉	—	4	2	no	—
317	#41×C₅₉	—	4	2	no	—
318	#41×C₅₉	—	4	2	no	—
319	#41×C₅₉	—	8	2	no	—
320	#41×C₅₉	—	8	4	no	—
321	C₂×Q₈×C₅₉	—	2	1	no	—
322	C₂×Q₈×C₅₉	—	2	2	no	—
323	C₂×Q₈×C₅₉	—	2	2	no	—
324	C₂×Q₈×C₅₉	—	2	2	no	—
325	C₂×Q₈×C₅₉	—	2	1	no	—
326	C₂×Q₈×C₅₉	—	2	2	no	—
327	C₂×Q₈×C₅₉	—	4	1	no	—
328	C₂×Q₈×C₅₉	—	4	2	no	—
329	C₂×Q₈×C₅₉	—	4	2	no	—
330	C₂×Q₈×C₅₉	—	4	2	no	—
331	C₂×Q₈×C₅₉	—	4	2	no	—
332	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
336	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
337	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₅₉	—	2	1	no	—
339	C₂×D₄×C₅₉	—	2	2	no	—
340	C₂×D₄×C₅₉	—	2	2	no	—
341	C₂×D₄×C₅₉	—	2	2	no	—
342	C₂×D₄×C₅₉	—	2	2	no	—
343	C₂×D₄×C₅₉	—	2	1	no	—
344	C₂×D₄×C₅₉	—	2	1	no	—
345	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₅₉	—	2	1	no	—
350	C₂²×C₄×C₅₉	—	2	1	no	—
351	C₂²×C₄×C₅₉	—	2	2	no	—
352	C₂²×C₄×C₅₉	—	2	2	no	—
353	C₂²×C₄×C₅₉	—	2	2	no	—
354	C₂²×C₄×C₅₉	—	2	1	no	—
355	C₂²×C₄×C₅₉	—	2	2	no	—
356	C₂²×C₄×C₅₉	—	2	2	no	—
357	C₂²×C₄×C₅₉	—	2	2	no	—
358	C₂²×C₄×C₅₉	—	2	2	no	—
359	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
363	Q₁₆×C₅₉	—	2	4	no	—
364	Q₁₆×C₅₉	—	2	4	no	—
365	Q₁₆×C₅₉	—	2	2	no	—
366	Q₁₆×C₅₉	—	4	2	no	—
367	Q₁₆×C₅₉	—	4	2	no	—
368	Q₁₆×C₅₉	—	4	1	no	—
369	SD₁₆×C₅₉	—	2	2	no	—
370	SD₁₆×C₅₉	—	4	2	no	—
371	SD₁₆×C₅₉	—	4	1	no	—
372	SD₁₆×C₅₉	—	4	2	no	—
373	SD₁₆×C₅₉	—	4	2	no	—
374	SD₁₆×C₅₉	—	4	2	no	—
375	SD₁₆×C₅₉	—	4	2	no	—
376	D₈×C₅₉	—	4	2	no	—
377	M₁₆×C₅₉	—	4	2	no	—
378	C₂×C₈×C₅₉	—	4	2	no	—
379	C₂×C₈×C₅₉	—	4	2	no	—
380	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
383	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₅₉	—	2	1	no	—
387	C₄⋊C₄×C₅₉	—	2	1	no	—
388	C₄⋊C₄×C₅₉	—	2	2	no	—
389	C₄⋊C₄×C₅₉	—	2	1	no	—
390	C₄⋊C₄×C₅₉	—	2	2	no	—
391	C₄⋊C₄×C₅₉	—	2	1	no	—
392	C₄⋊C₄×C₅₉	—	2	1	no	—
393	C₄⋊C₄×C₅₉	—	2	1	no	—
394	C₄⋊C₄×C₅₉	—	2	1	no	—
395	C₄⋊C₄×C₅₉	—	2	2	no	—
396	C₄⋊C₄×C₅₉	—	2	2	no	—
397	C₄⋊C₄×C₅₉	—	2	2	no	—
398	C₄⋊C₄×C₅₉	—	2	1	no	—
399	C₄⋊C₄×C₅₉	—	2	1	no	—
400	C₄⋊C₄×C₅₉	—	2	1	no	—
401	C₄⋊C₄×C₅₉	—	2	1	no	—
402	C₄⋊C₄×C₅₉	—	2	1	no	—
403	C₄⋊C₄×C₅₉	—	2	2	no	—
404	C₄⋊C₄×C₅₉	—	2	2	no	—
405	C₄⋊C₄×C₅₉	—	2	2	no	—
406	C₄⋊C₄×C₅₉	—	2	1	no	—
407	C₄⋊C₄×C₅₉	—	2	2	no	—
408	C₄⋊C₄×C₅₉	—	2	2	no	—
409	C₄⋊C₄×C₅₉	—	2	2	no	—
410	C₄⋊C₄×C₅₉	—	2	2	no	—
411	C₄⋊C₄×C₅₉	—	2	1	no	—
412	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₅₉	—	2	1	no	—
424	C₂²⋊C₄×C₅₉	—	2	2	no	—
425	C₂²⋊C₄×C₅₉	—	2	2	no	—
426	C₂²⋊C₄×C₅₉	—	2	2	no	—
427	C₂²⋊C₄×C₅₉	—	2	2	no	—
428	C₂²⋊C₄×C₅₉	—	2	2	no	—
429	C₂²⋊C₄×C₅₉	—	2	2	no	—
430	C₂²⋊C₄×C₅₉	—	2	1	no	—
431	C₂²⋊C₄×C₅₉	—	2	1	no	—
432	C₂²⋊C₄×C₅₉	—	2	2	no	—
433	C₂²⋊C₄×C₅₉	—	2	2	no	—
434	C₂²⋊C₄×C₅₉	—	2	2	no	—
435	C₂²⋊C₄×C₅₉	—	2	1	no	—
436	C₂²⋊C₄×C₅₉	—	2	2	no	—
437	C₂²⋊C₄×C₅₉	—	2	2	no	—
438	C₂²⋊C₄×C₅₉	—	2	1	no	—
439	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
444	C₄²×C₅₉	—	2	1	no	—
445	C₄²×C₅₉	—	2	1	no	—
446	C₄²×C₅₉	—	2	1	no	—
447	C₄²×C₅₉	—	2	1	no	—
448	C₄²×C₅₉	—	2	2	no	—
449	C₄²×C₅₉	—	2	1	no	—
450	C₄²×C₅₉	—	2	2	no	—
451	C₄²×C₅₉	—	2	2	no	—
452	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
455	C₄²×C₅₉	C₂⁴	1	2	yes	—
456	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
457	C₂³×C₅₉	—	2	1	no	—
458	C₂³×C₅₉	—	2	2	no	—
459	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
460	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₅₉	—	2	2	no	—
462	Q₈×C₅₉	—	2	1	no	—
463	Q₈×C₅₉	—	2	1	no	—
464	Q₈×C₅₉	—	2	2	no	—
465	Q₈×C₅₉	—	2	2	no	—
466	Q₈×C₅₉	—	2	1	no	—
467	Q₈×C₅₉	—	2	1	no	—
468	Q₈×C₅₉	—	2	2	no	—
469	Q₈×C₅₉	—	2	2	no	—
470	Q₈×C₅₉	—	2	1	no	—
471	Q₈×C₅₉	—	4	2	no	—
472	Q₈×C₅₉	—	8	2	no	—
473	Q₈×C₅₉	—	8	2	no	—
474	Q₈×C₅₉	—	8	1	no	—
475	Q₈×C₅₉	—	8	2	no	—
476	Q₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
477	D₄×C₅₉	—	2	4	no	—
478	D₄×C₅₉	—	2	2	no	—
479	D₄×C₅₉	—	2	1	no	—
480	D₄×C₅₉	—	2	2	no	—
481	D₄×C₅₉	—	2	2	no	—
482	D₄×C₅₉	—	2	1	no	—
483	D₄×C₅₉	—	4	4	no	—
484	D₄×C₅₉	—	4	2	no	—
485	D₄×C₅₉	—	4	4	no	—
486	D₄×C₅₉	—	4	2	no	—
487	D₄×C₅₉	—	8	1	no	—
488	D₄×C₅₉	—	8	2	no	—
489	D₄×C₅₉	—	8	2	no	—
490	C₂×C₄×C₅₉	—	2	2	no	—
491	C₂×C₄×C₅₉	—	2	1	no	—
492	C₂×C₄×C₅₉	—	2	2	no	—
493	C₂×C₄×C₅₉	—	2	1	no	—
494	C₂×C₄×C₅₉	—	2	2	no	—
495	C₂×C₄×C₅₉	—	2	1	no	—
496	C₂×C₄×C₅₉	—	2	2	no	—
497	C₂×C₄×C₅₉	—	2	1	no	—
498	C₂×C₄×C₅₉	—	2	1	no	—
499	C₂×C₄×C₅₉	—	2	1	no	—
500	C₂×C₄×C₅₉	—	2	1	no	—
501	C₂×C₄×C₅₉	—	2	1	no	—
502	C₂×C₄×C₅₉	—	2	1	no	—
503	C₂×C₄×C₅₉	—	2	2	no	—
504	C₂×C₄×C₅₉	—	2	2	no	—
505	C₂×C₄×C₅₉	—	2	2	no	—
506	C₂×C₄×C₅₉	—	4	4	no	—
507	C₂×C₄×C₅₉	—	4	2	no	—
508	C₂×C₄×C₅₉	—	4	2	no	—
509	C₂×C₄×C₅₉	—	4	2	no	—
510	C₂×C₄×C₅₉	—	8	2	no	—
511	C₂×C₄×C₅₉	—	8	2	no	—
512	C₂×C₄×C₅₉	—	8	2	no	—
513	C₂×C₄×C₅₉	—	8	2	no	—
514	C₂×C₄×C₅₉	—	8	2	no	—
515	C₂×C₄×C₅₉	—	8	2	no	—
516	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
525	C₈×C₅₉	—	2	2	no	—
526	C₈×C₅₉	—	2	1	no	—
527	C₈×C₅₉	—	2	2	no	—
528	C₈×C₅₉	—	2	1	no	—
529	C₈×C₅₉	—	2	1	no	—
530	C₈×C₅₉	—	2	1	no	—
531	#62058	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
532	C₂²×C₅₉	—	2	1	no	—
533	C₂²×C₅₉	—	2	1	no	—
534	C₂²×C₅₉	—	2	2	no	—
535	C₂²×C₅₉	—	2	2	no	—
536	C₂²×C₅₉	—	2	2	no	—
537	C₂²×C₅₉	—	4	2	no	—
538	C₂²×C₅₉	—	4	1	no	—
539	C₂²×C₅₉	—	4	2	no	—
540	C₂²×C₅₉	—	4	1	no	—
541	C₂²×C₅₉	—	4	1	no	—
542	C₂²×C₅₉	—	4	2	no	—
543	C₂²×C₅₉	#577	1	2	yes	—
544	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
545	C₄×C₅₉	—	2	2	no	—
546	C₄×C₅₉	—	2	1	no	—
547	C₄×C₅₉	—	2	2	no	—
548	C₄×C₅₉	—	2	1	no	—
549	C₄×C₅₉	—	2	1	no	—
550	C₄×C₅₉	—	2	2	no	—
551	C₄×C₅₉	—	2	1	no	—
552	C₄×C₅₉	—	2	2	no	—
553	C₄×C₅₉	—	4	1	no	—
554	C₄×C₅₉	—	4	2	no	—
555	C₄×C₅₉	—	4	1	no	—
556	C₄×C₅₉	—	4	2	no	—
557	C₄×C₅₉	—	4	1	no	—
558	C₄×C₅₉	—	4	1	no	—
559	C₄×C₅₉	—	4	2	no	—
560	C₄×C₅₉	—	4	1	no	—
561	C₄×C₅₉	—	4	1	no	—
562	C₄×C₅₉	#578	1	2	yes	—
563	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₄×C₅₉	#585	1	1	yes	characteristic
565	#3552	C₂×C₅₉	1	1	yes	characteristic, complemented
566	#3522	C₂×C₅₉	1	1	yes	characteristic, complemented
567	#3400	C₂×C₅₉	1	1	yes	characteristic, complemented
568	#3394	C₂×C₅₉	1	1	yes	characteristic, complemented
569	#3369	C₂×C₅₉	1	1	yes	characteristic, complemented
570	#3363	C₂×C₅₉	1	1	yes	characteristic, complemented
571	#3331	C₂×C₅₉	1	1	yes	characteristic, complemented
572	#3308	C₂×C₅₉	1	2	yes	complemented
573	#3299	C₂×C₅₉	1	1	yes	characteristic, complemented
574	#3298	C₂×C₅₉	1	2	yes	complemented
575	#3285	C₂×C₅₉	1	2	yes	complemented
576	#3284	C₂×C₅₉	1	1	yes	characteristic, complemented
577	#3278	C₂×C₅₉	1	1	yes	characteristic, complemented
578	#3270	C₂×C₅₉	1	2	yes	complemented
579	#3258	C₂×C₅₉	1	2	yes	complemented
580	#3247	C₂×C₅₉	1	1	yes	characteristic, complemented
581	#3225	C₂×C₅₉	1	2	yes	complemented
582	#3206	C₂×C₅₉	1	1	yes	characteristic, complemented
583	#3120	C₂×C₅₉	1	2	yes	complemented
584	#3108	C₂×C₅₉	1	1	yes	characteristic, complemented
585	#3046	C₂×C₅₉	1	2	yes	complemented
586	C₂×#462	C₂×C₅₉	1	1	yes	characteristic, complemented
587	#2994	C₂×C₅₉	1	1	yes	characteristic, complemented
588	C₂×C₅₉	—	2	2	no	—
589	C₂×C₅₉	—	4	2	no	—
590	C₂×C₅₉	—	8	2	no	—
591	C₂×C₅₉	—	8	1	no	—
592	C₂×C₅₉	#3488	1	1	yes	characteristic
593	C₂×C₅₉	C₂×#577	1	1	yes	characteristic
594	C₂×C₅₉	C₂×#578	1	1	yes	characteristic
595	C₂×#137	C₂²×C₅₉	1	2	yes	—
596	C₂×#135	C₂²×C₅₉	1	2	yes	—
597	C₂²×Q₁₆	C₂²×C₅₉	1	2	yes	—
598	#563	—	2	2	no	—
599	#559	—	2	1	no	—
600	#559	C₂²×C₅₉	1	1	yes	characteristic
601	Q₈²	C₂²×C₅₉	1	1	yes	characteristic
602	#557	C₂²×C₅₉	1	1	yes	characteristic
603	#556	C₂²×C₅₉	1	1	yes	characteristic
604	#554	—	2	1	no	—
605	#554	—	2	1	no	—
606	#554	C₂²×C₅₉	1	1	yes	characteristic
607	#553	—	2	1	no	—
608	#550	C₂²×C₅₉	1	1	yes	characteristic
609	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
610	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
611	#548	C₂²×C₅₉	1	2	yes	—
612	#548	C₂²×C₅₉	1	2	yes	—
613	#547	—	2	2	no	—
614	#547	C₂²×C₅₉	1	1	yes	characteristic
615	#547	C₂²×C₅₉	1	2	yes	—
616	#544	—	2	1	no	—
617	#542	—	2	2	no	—
618	#542	—	2	1	no	—
619	#542	C₂²×C₅₉	1	2	yes	—
620	#541	C₂²×C₅₉	1	2	yes	—
621	#539	—	2	2	no	—
622	#536	C₂²×C₅₉	1	2	yes	—
623	#532	—	2	1	no	—
624	#532	C₂²×C₅₉	1	1	yes	characteristic
625	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
626	#529	—	2	1	no	—
627	#529	C₂²×C₅₉	1	1	yes	characteristic
628	#529	C₂²×C₅₉	1	1	yes	characteristic
629	#520	C₂²×C₅₉	1	2	yes	—
630	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
631	#497	C₂²×C₅₉	1	2	yes	—
632	#495	C₂²×C₅₉	1	2	yes	—
633	#492	C₂²×C₅₉	1	1	yes	characteristic
634	#492	C₂²×C₅₉	1	1	yes	characteristic
635	#489	C₂²×C₅₉	1	2	yes	—
636	#487	C₂²×C₅₉	1	1	yes	characteristic
637	#487	C₂²×C₅₉	1	2	yes	—
638	#487	C₂²×C₅₉	1	1	yes	characteristic
639	#484	C₂²×C₅₉	1	2	yes	—
640	#483	C₂²×C₅₉	1	2	yes	—
641	#483	C₂²×C₅₉	1	1	yes	characteristic
642	#480	C₂²×C₅₉	1	1	yes	characteristic
643	#479	C₂²×C₅₉	1	1	yes	characteristic
644	#479	C₂²×C₅₉	1	1	yes	characteristic
645	#478	C₂²×C₅₉	1	2	yes	—
646	#477	C₂²×C₅₉	1	1	yes	characteristic
647	#477	C₂²×C₅₉	1	2	yes	—
648	#476	C₂²×C₅₉	1	1	yes	characteristic
649	#475	C₂²×C₅₉	1	2	yes	—
650	#470	C₂²×C₅₉	1	2	yes	—
651	#468	C₂²×C₅₉	1	2	yes	—
652	#467	C₂²×C₅₉	1	2	yes	—
653	#466	C₂²×C₅₉	1	2	yes	—
654	#465	C₂²×C₅₉	1	2	yes	—
655	#465	C₂²×C₅₉	1	2	yes	—
656	#464	C₂²×C₅₉	1	1	yes	characteristic
657	#464	C₂²×C₅₉	1	1	yes	characteristic
658	#464	C₂²×C₅₉	1	2	yes	—
659	#464	C₂²×C₅₉	1	2	yes	—
660	#464	C₂²×C₅₉	1	2	yes	—
661	#463	C₂²×C₅₉	1	2	yes	—
662	#463	C₂²×C₅₉	1	2	yes	—
663	#462	C₂²×C₅₉	1	1	yes	characteristic
664	#462	C₂²×C₅₉	1	2	yes	—
665	#462	C₂²×C₅₉	1	1	yes	characteristic
666	#462	C₂²×C₅₉	1	1	yes	characteristic
667	#462	C₂²×C₅₉	1	2	yes	—
668	#462	C₂²×C₅₉	1	1	yes	characteristic
669	#462	C₂²×C₅₉	1	2	yes	—
670	#461	C₂²×C₅₉	1	2	yes	—
671	#461	C₂²×C₅₉	1	2	yes	—
672	#461	C₂²×C₅₉	1	2	yes	—
673	#460	C₂²×C₅₉	1	1	yes	characteristic
674	#459	C₂²×C₅₉	1	1	yes	characteristic
675	#452	C₂²×C₅₉	1	2	yes	—
676	#452	C₂²×C₅₉	1	2	yes	—
677	#452	C₂²×C₅₉	1	2	yes	—
678	#451	C₂²×C₅₉	1	1	yes	characteristic
679	#451	C₂²×C₅₉	1	2	yes	—
680	#449	C₂²×C₅₉	1	2	yes	—
681	#448	C₂²×C₅₉	1	1	yes	characteristic
682	#448	C₂²×C₅₉	1	2	yes	—
683	#448	C₂²×C₅₉	1	2	yes	—
684	#448	C₂²×C₅₉	1	2	yes	—
685	#446	C₂²×C₅₉	1	1	yes	characteristic
686	C₈×Q₈	C₂²×C₅₉	1	1	yes	characteristic
687	#441	C₂²×C₅₉	1	2	yes	—
688	#440	C₂²×C₅₉	1	2	yes	—
689	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
690	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	—
691	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
692	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
694	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	—
695	#436	C₂²×C₅₉	1	1	yes	characteristic
696	#435	C₂²×C₅₉	1	2	yes	—
697	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
698	C₈×D₄	C₂²×C₅₉	1	2	yes	—
699	#433	C₂²×C₅₉	1	2	yes	—
700	#431	C₂²×C₅₉	1	1	yes	characteristic
701	#424	C₂²×C₅₉	1	2	yes	—
702	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
703	#417	C₂²×C₅₉	1	2	yes	—
704	C₂×#103	C₂²×C₅₉	1	2	yes	—
705	C₂×#103	C₂²×C₅₉	1	2	yes	—
706	C₅₉	#62058	1	1	yes	characteristic, direct product factor, Sylow
707	C₂×#41	—	2	2	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	C₂³×C₅₉	1	2	yes	—
710	C₂×#41	C₂³×C₅₉	1	2	yes	—
711	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
712	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
713	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
714	#137	—	4	4	no	—
715	#135	—	4	4	no	—
716	C₂×Q₁₆	—	4	4	no	—
717	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
720	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
730	C₂×D₈	C₂³×C₅₉	1	2	yes	—
731	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
732	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
733	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	—	2	2	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	2	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
741	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
744	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
746	#127	—	2	1	no	—
747	#127	C₂³×C₅₉	1	1	yes	characteristic
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	1	no	—
753	#126	D₄×C₅₉	1	2	yes	—
754	#125	—	2	1	no	—
755	#125	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	1	no	—
759	#125	D₄×C₅₉	1	1	yes	characteristic
760	#125	C₂³×C₅₉	1	1	yes	characteristic
761	#124	—	2	1	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	D₄×C₅₉	1	1	yes	characteristic
767	#124	C₂³×C₅₉	1	1	yes	characteristic
768	#124	C₂³×C₅₉	1	2	yes	—
769	#124	C₂³×C₅₉	1	2	yes	—
770	#123	—	2	1	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	D₄×C₅₉	1	2	yes	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
792	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	D₄×C₅₉	1	1	yes	characteristic
801	#121	C₂³×C₅₉	1	1	yes	characteristic
802	#121	C₂³×C₅₉	1	2	yes	—
803	#121	C₂³×C₅₉	1	2	yes	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
813	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
815	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
816	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	C₂³×C₅₉	1	2	yes	—
829	C₄×D₄	C₂³×C₅₉	1	2	yes	—
830	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₅₉	1	2	yes	—
832	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
833	#117	—	2	2	no	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	C₂³×C₅₉	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	—	2	2	no	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
846	#107	C₂³×C₅₉	1	1	yes	characteristic
847	#107	C₂³×C₅₉	1	2	yes	—
848	#107	C₂³×C₅₉	1	1	yes	characteristic
849	#106	C₂³×C₅₉	1	1	yes	characteristic
850	#106	C₂³×C₅₉	1	1	yes	characteristic
851	#106	C₂³×C₅₉	1	2	yes	—
852	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
853	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
857	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
858	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
859	#103	C₂³×C₅₉	1	2	yes	—
860	#103	C₂³×C₅₉	1	1	yes	characteristic
861	#103	C₂³×C₅₉	1	2	yes	—
862	#103	C₂³×C₅₉	1	2	yes	—
863	#103	C₂³×C₅₉	1	2	yes	—
864	#103	C₂³×C₅₉	1	2	yes	—
865	#103	C₂³×C₅₉	1	2	yes	—
866	#103	C₂³×C₅₉	1	2	yes	—
867	#103	C₂³×C₅₉	1	1	yes	characteristic
868	#103	C₂³×C₅₉	1	1	yes	characteristic
869	#103	C₂³×C₅₉	1	1	yes	characteristic
870	#103	C₂³×C₅₉	1	1	yes	characteristic
871	#103	C₂³×C₅₉	1	2	yes	—
872	#103	C₂³×C₅₉	1	1	yes	characteristic
873	#103	C₂³×C₅₉	1	2	yes	—
874	#102	C₂³×C₅₉	1	1	yes	characteristic
875	#102	C₂³×C₅₉	1	2	yes	—
876	#102	C₂³×C₅₉	1	1	yes	characteristic
877	#102	C₂³×C₅₉	1	2	yes	—
878	#102	C₂³×C₅₉	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
883	#97	C₂³×C₅₉	1	2	yes	—
884	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₅₉	1	2	yes	—
887	#41	—	2	4	no	—
888	#41	—	4	2	no	—
889	#41	—	4	2	no	—
890	#41	—	4	2	no	—
891	#41	—	8	2	no	—
892	#41	—	8	4	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	4	1	no	—
900	C₂×Q₈	—	4	2	no	—
901	C₂×Q₈	—	4	2	no	—
902	C₂×Q₈	—	4	2	no	—
903	C₂×Q₈	—	4	2	no	—
904	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
907	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
908	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
918	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
919	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
935	Q₁₆	—	2	4	no	—
936	Q₁₆	—	2	4	no	—
937	Q₁₆	—	2	2	no	—
938	Q₁₆	—	4	2	no	—
939	Q₁₆	—	4	2	no	—
940	Q₁₆	—	4	1	no	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	—	4	2	no	—
946	SD₁₆	—	4	1	no	—
947	SD₁₆	—	4	2	no	—
948	D₈	—	4	2	no	—
949	M₁₆	—	4	2	no	—
950	C₂×C₈	—	4	2	no	—
951	C₂×C₈	—	4	2	no	—
952	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
955	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1025	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1027	C₄²	C₂⁴×C₅₉	1	2	yes	—
1028	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1032	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	2	no	—
1046	Q₈	—	8	1	no	—
1047	Q₈	—	8	2	no	—
1048	Q₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
1049	D₄	—	2	4	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	4	4	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1096	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1097	C₈	—	2	2	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	1	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	C₅₉×#577	1	2	yes	—
1115	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	C₅₉×#578	1	2	yes	—
1134	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1135	C₄	C₅₉×#585	1	1	yes	characteristic
1136	C₂	—	2	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	C₅₉×#3488	1	1	yes	characteristic
1141	C₂	C₂×C₅₉×#577	1	1	yes	characteristic
1142	C₂	C₂×C₅₉×#578	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 ◁ C₅₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3552	C₂	semidirect
2. C₅₉×#3522	C₂	semidirect
3. C₅₉×#3400	C₂	semidirect
4. C₅₉×#3394	C₂	semidirect
5. C₅₉×#3369	C₂	semidirect
6. C₅₉×#3363	C₂	semidirect
7. C₅₉×#3331	C₂	semidirect
8. C₅₉×#3308	C₂	semidirect
9. C₅₉×#3299	C₂	semidirect
10. C₅₉×#3298	C₂	semidirect
11. C₅₉×#3285	C₂	semidirect
12. C₅₉×#3284	C₂	semidirect
13. C₅₉×#3278	C₂	semidirect
14. C₅₉×#3270	C₂	semidirect
15. C₅₉×#3258	C₂	semidirect
16. C₅₉×#3247	C₂	semidirect
17. C₅₉×#3225	C₂	semidirect
18. C₅₉×#3206	C₂	semidirect
19. C₅₉×#3120	C₂	semidirect
20. C₅₉×#3108	C₂	semidirect
21. C₅₉×#3046	C₂	semidirect
22. C₂×C₅₉×#462	C₂	semidirect
23. C₅₉×#2994	C₂	semidirect
531. #62058	C₅₉	direct (N × H)
565. #3552	C₂×C₅₉	semidirect
566. #3522	C₂×C₅₉	semidirect
567. #3400	C₂×C₅₉	semidirect
568. #3394	C₂×C₅₉	semidirect
569. #3369	C₂×C₅₉	semidirect
570. #3363	C₂×C₅₉	semidirect
571. #3331	C₂×C₅₉	semidirect
572. #3308	C₂×C₅₉	semidirect
573. #3299	C₂×C₅₉	semidirect
574. #3298	C₂×C₅₉	semidirect
575. #3285	C₂×C₅₉	semidirect
576. #3284	C₂×C₅₉	semidirect
577. #3278	C₂×C₅₉	semidirect
578. #3270	C₂×C₅₉	semidirect
579. #3258	C₂×C₅₉	semidirect
580. #3247	C₂×C₅₉	semidirect
581. #3225	C₂×C₅₉	semidirect
582. #3206	C₂×C₅₉	semidirect
583. #3120	C₂×C₅₉	semidirect
584. #3108	C₂×C₅₉	semidirect
585. #3046	C₂×C₅₉	semidirect
586. C₂×#462	C₂×C₅₉	semidirect
587. #2994	C₂×C₅₉	semidirect
706. C₅₉	#62058	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#3552	2
C₅₉×#3522	2
C₅₉×#3400	2
C₅₉×#3394	2
C₅₉×#3369	2
C₅₉×#3363	2
C₅₉×#3331	2
C₅₉×#3308	2
C₅₉×#3299	2
C₅₉×#3298	2
C₅₉×#3285	2
C₅₉×#3284	2
C₅₉×#3278	2
C₅₉×#3270	2
C₅₉×#3258	2
C₅₉×#3247	2
C₅₉×#3225	2
C₅₉×#3206	2
C₅₉×#3120	2
C₅₉×#3108	2
C₅₉×#3046	2
C₂×C₅₉×#462	2
C₅₉×#2994	2
#62058	59

Subgroups — C59×#62058 #28474167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62058 #28474167