Subgroups — C₅₉×#62216 #28474325

Order 15104.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3514	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3348	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#3340	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#3311	C₂	1	2	yes	maximal, complemented
13	C₅₉×#3296	C₂	1	2	yes	maximal, complemented
14	C₅₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3258	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3244	C₂	1	2	yes	maximal, complemented
18	C₅₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#3123	C₂	1	2	yes	maximal, complemented
20	C₅₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#3081	C₂	1	2	yes	maximal, complemented
22	C₅₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₉×#563	—	2	2	no	—
25	C₅₉×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₅₉	C₂²	1	1	yes	characteristic, complemented
27	C₅₉×#557	—	2	1	no	—
28	C₅₉×#557	C₂²	1	1	yes	characteristic, complemented
29	C₅₉×#556	—	2	1	no	—
30	C₅₉×#556	C₂²	1	1	yes	characteristic
31	C₅₉×#556	C₂²	1	1	yes	characteristic
32	C₅₉×#556	C₂²	1	2	yes	complemented
33	C₅₉×#555	C₂²	1	2	yes	—
34	C₅₉×#554	C₂²	1	1	yes	characteristic
35	C₅₉×#552	C₂²	1	2	yes	complemented
36	C₅₉×#551	—	2	2	no	—
37	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#548	—	2	1	no	—
39	C₅₉×#546	—	2	1	no	—
40	C₅₉×#546	C₂²	1	2	yes	—
41	D₄²×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#544	C₂²	1	2	yes	complemented
43	C₅₉×#542	—	2	1	no	—
44	C₅₉×#542	C₂²	1	2	yes	—
45	C₅₉×#541	—	2	2	no	—
46	C₅₉×#541	—	2	1	no	—
47	C₅₉×#541	C₂²	1	2	yes	complemented
48	C₅₉×#538	—	2	2	no	—
49	C₅₉×#533	C₂²	1	1	yes	characteristic, complemented
50	C₅₉×#533	C₂²	1	1	yes	characteristic, complemented
51	C₅₉×#532	C₂²	1	1	yes	characteristic
52	C₅₉×#529	—	2	1	no	—
53	C₅₉×#529	C₂²	1	1	yes	characteristic
54	C₂×#124×C₅₉	—	2	1	no	—
55	C₅₉×#518	C₂²	1	2	yes	—
56	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
57	C₅₉×#501	C₂²	1	2	yes	complemented
58	C₅₉×#500	C₂²	1	1	yes	characteristic, complemented
59	C₅₉×#498	C₂²	1	2	yes	complemented
60	C₅₉×#498	C₂²	1	1	yes	characteristic, complemented
61	C₅₉×#489	C₂²	1	2	yes	complemented
62	C₅₉×#488	C₂²	1	2	yes	complemented
63	C₅₉×#486	C₂²	1	1	yes	characteristic
64	C₅₉×#486	C₂²	1	1	yes	characteristic
65	C₅₉×#485	C₂²	1	2	yes	complemented
66	C₅₉×#485	C₂²	1	1	yes	characteristic, complemented
67	C₅₉×#485	C₂²	1	2	yes	complemented
68	C₅₉×#485	C₂²	1	2	yes	complemented
69	C₅₉×#485	C₂²	1	1	yes	characteristic, complemented
70	C₅₉×#483	C₂²	1	2	yes	complemented
71	C₅₉×#482	C₂²	1	2	yes	—
72	C₅₉×#482	C₂²	1	2	yes	complemented
73	C₅₉×#482	C₂²	1	2	yes	complemented
74	C₅₉×#481	C₂²	1	2	yes	—
75	C₅₉×#479	C₂²	1	2	yes	complemented
76	C₅₉×#478	C₂²	1	2	yes	—
77	C₅₉×#478	C₂²	1	2	yes	—
78	C₅₉×#478	C₂²	1	2	yes	complemented
79	C₅₉×#478	C₂²	1	2	yes	complemented
80	C₅₉×#478	C₂²	1	2	yes	complemented
81	C₅₉×#477	C₂²	1	2	yes	complemented
82	C₅₉×#477	C₂²	1	1	yes	characteristic, complemented
83	C₅₉×#476	C₂²	1	1	yes	characteristic
84	C₅₉×#476	C₂²	1	2	yes	—
85	C₅₉×#476	C₂²	1	2	yes	complemented
86	C₅₉×#475	C₂²	1	2	yes	complemented
87	C₅₉×#475	C₂²	1	1	yes	characteristic, complemented
88	C₅₉×#475	C₂²	1	1	yes	characteristic, complemented
89	C₅₉×#475	C₂²	1	1	yes	characteristic, complemented
90	C₅₉×#475	C₂²	1	1	yes	characteristic, complemented
91	C₅₉×#474	C₂²	1	1	yes	characteristic
92	C₅₉×#474	C₂²	1	1	yes	characteristic
93	C₅₉×#474	C₂²	1	2	yes	complemented
94	C₅₉×#470	C₂²	1	2	yes	complemented
95	C₅₉×#468	C₂²	1	2	yes	—
96	C₅₉×#467	C₂²	1	2	yes	complemented
97	C₅₉×#465	C₂²	1	2	yes	—
98	C₅₉×#465	C₂²	1	2	yes	complemented
99	C₅₉×#465	C₂²	1	2	yes	complemented
100	C₅₉×#464	C₂²	1	2	yes	complemented
101	C₅₉×#464	C₂²	1	2	yes	complemented
102	C₅₉×#462	C₂²	1	1	yes	characteristic, complemented
103	C₅₉×#461	C₂²	1	1	yes	characteristic
104	C₅₉×#461	C₂²	1	2	yes	complemented
105	C₅₉×#460	C₂²	1	1	yes	characteristic
106	C₅₉×#460	C₂²	1	1	yes	characteristic
107	C₅₉×#452	C₂²	1	1	yes	characteristic
108	C₅₉×#452	C₂²	1	1	yes	characteristic
109	C₅₉×#450	C₂²	1	2	yes	—
110	C₅₉×#450	C₂²	1	2	yes	—
111	C₅₉×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
113	C₅₉×#440	C₂²	1	2	yes	—
114	C₅₉×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
121	C₅₉×#436	C₂²	1	1	yes	characteristic
122	C₅₉×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₅₉	C₂²	1	2	yes	complemented
125	C₅₉×#433	C₂²	1	2	yes	complemented
126	C₅₉×#431	C₂²	1	1	yes	characteristic, complemented
127	C₅₉×#428	C₂²	1	2	yes	complemented
128	C₅₉×#427	C₂²	1	2	yes	complemented
129	C₅₉×#427	C₂²	1	2	yes	complemented
130	C₅₉×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
132	C₅₉×#418	C₂²	1	2	yes	—
133	C₅₉×#416	C₂²	1	2	yes	—
134	C₂×#102×C₅₉	C₂²	1	2	yes	—
135	C₂×#41×C₅₉	—	2	1	no	—
136	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₅₉	—	2	1	no	—
138	C₂²×D₄×C₅₉	—	2	1	no	—
139	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
146	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
147	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
148	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₉	—	2	1	no	—
150	C₄⋊Q₈×C₅₉	—	2	2	no	—
151	C₄⋊Q₈×C₅₉	—	2	1	no	—
152	C₄⋊Q₈×C₅₉	—	2	2	no	—
153	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
160	#127×C₅₉	C₂³	1	1	yes	characteristic
161	#126×C₅₉	—	2	2	no	—
162	#126×C₅₉	—	2	2	no	—
163	#126×C₅₉	—	2	2	no	—
164	#126×C₅₉	—	2	2	no	—
165	#126×C₅₉	—	2	2	no	—
166	#126×C₅₉	—	2	2	no	—
167	#126×C₅₉	—	2	2	no	—
168	#126×C₅₉	—	2	2	no	—
169	#126×C₅₉	D₄	1	2	yes	—
170	#125×C₅₉	—	2	2	no	—
171	#125×C₅₉	—	2	2	no	—
172	#125×C₅₉	—	2	2	no	—
173	#125×C₅₉	—	2	1	no	—
174	#125×C₅₉	—	2	2	no	—
175	#125×C₅₉	—	2	2	no	—
176	#125×C₅₉	—	2	1	no	—
177	#125×C₅₉	D₄	1	1	yes	characteristic
178	#125×C₅₉	C₂³	1	2	yes	—
179	#125×C₅₉	C₂³	1	2	yes	—
180	#124×C₅₉	—	2	1	no	—
181	#124×C₅₉	—	2	1	no	—
182	#124×C₅₉	—	2	1	no	—
183	#124×C₅₉	—	2	2	no	—
184	#124×C₅₉	—	2	2	no	—
185	#124×C₅₉	—	2	2	no	—
186	#124×C₅₉	—	2	2	no	—
187	#124×C₅₉	—	2	1	no	—
188	#124×C₅₉	D₄	1	1	yes	characteristic
189	#124×C₅₉	C₂³	1	2	yes	—
190	#123×C₅₉	—	2	2	no	—
191	#123×C₅₉	—	2	2	no	—
192	#123×C₅₉	—	2	2	no	—
193	#123×C₅₉	—	2	2	no	—
194	#123×C₅₉	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₅₉	—	2	1	no	—
196	C₂²⋊Q₈×C₅₉	—	2	1	no	—
197	C₂²⋊Q₈×C₅₉	—	2	1	no	—
198	C₂²⋊Q₈×C₅₉	—	2	1	no	—
199	C₂²⋊Q₈×C₅₉	—	2	2	no	—
200	C₂²⋊Q₈×C₅₉	—	2	2	no	—
201	C₂²⋊Q₈×C₅₉	—	2	2	no	—
202	C₂²⋊Q₈×C₅₉	—	2	2	no	—
203	C₂²⋊Q₈×C₅₉	—	2	2	no	—
204	C₂²⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
209	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
210	#121×C₅₉	—	2	2	no	—
211	#121×C₅₉	—	2	1	no	—
212	#121×C₅₉	—	2	1	no	—
213	#121×C₅₉	—	2	2	no	—
214	#121×C₅₉	D₄	1	1	yes	characteristic
215	#121×C₅₉	C₂³	1	2	yes	—
216	#121×C₅₉	C₂³	1	2	yes	—
217	#120×C₅₉	—	2	2	no	—
218	#120×C₅₉	—	2	2	no	—
219	C₄×Q₈×C₅₉	—	2	1	no	—
220	C₄×Q₈×C₅₉	—	2	1	no	—
221	C₄×Q₈×C₅₉	—	2	1	no	—
222	C₄×Q₈×C₅₉	—	2	2	no	—
223	C₄×Q₈×C₅₉	—	2	1	no	—
224	C₄×Q₈×C₅₉	—	2	1	no	—
225	C₄×Q₈×C₅₉	—	2	1	no	—
226	C₄×Q₈×C₅₉	—	2	1	no	—
227	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
230	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
231	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₅₉	—	2	1	no	—
235	C₄×D₄×C₅₉	—	2	1	no	—
236	C₄×D₄×C₅₉	—	2	1	no	—
237	C₄×D₄×C₅₉	—	2	2	no	—
238	C₄×D₄×C₅₉	—	2	2	no	—
239	C₄×D₄×C₅₉	—	2	1	no	—
240	C₄×D₄×C₅₉	—	2	1	no	—
241	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₉	C₂³	1	2	yes	—
243	C₄×D₄×C₅₉	C₂³	1	2	yes	—
244	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₅₉	C₂³	1	2	yes	—
246	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₉	C₂³	1	2	yes	—
248	#117×C₅₉	—	2	1	no	—
249	#117×C₅₉	—	2	2	no	—
250	#117×C₅₉	—	2	2	no	—
251	#117×C₅₉	—	2	1	no	—
252	#117×C₅₉	C₂³	1	2	yes	—
253	#117×C₅₉	C₂³	1	2	yes	—
254	#117×C₅₉	C₂³	1	1	yes	characteristic
255	#117×C₅₉	C₂³	1	2	yes	—
256	#117×C₅₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
261	C₂×C₄²×C₅₉	—	2	1	no	—
262	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
263	#107×C₅₉	C₂³	1	1	yes	characteristic
264	#107×C₅₉	C₂³	1	2	yes	—
265	#107×C₅₉	C₂³	1	2	yes	—
266	#107×C₅₉	C₂³	1	2	yes	—
267	#107×C₅₉	C₂³	1	1	yes	characteristic
268	#107×C₅₉	C₂³	1	2	yes	—
269	#106×C₅₉	C₂³	1	2	yes	—
270	#106×C₅₉	C₂³	1	2	yes	—
271	#106×C₅₉	C₂³	1	2	yes	—
272	#106×C₅₉	C₂³	1	2	yes	—
273	#106×C₅₉	C₂³	1	2	yes	—
274	#106×C₅₉	C₂³	1	1	yes	characteristic
275	#106×C₅₉	C₂³	1	1	yes	characteristic
276	#106×C₅₉	C₂³	1	2	yes	—
277	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
284	#103×C₅₉	C₂³	1	2	yes	—
285	#103×C₅₉	C₂³	1	2	yes	—
286	#103×C₅₉	C₂³	1	2	yes	—
287	#103×C₅₉	C₂³	1	1	yes	characteristic
288	#103×C₅₉	C₂³	1	1	yes	characteristic
289	#103×C₅₉	C₂³	1	1	yes	characteristic
290	#103×C₅₉	C₂³	1	1	yes	characteristic
291	#103×C₅₉	C₂³	1	1	yes	characteristic
292	#103×C₅₉	C₂³	1	1	yes	characteristic
293	#103×C₅₉	C₂³	1	2	yes	—
294	#102×C₅₉	C₂³	1	1	yes	characteristic
295	#102×C₅₉	C₂³	1	2	yes	—
296	#102×C₅₉	C₂³	1	2	yes	—
297	#102×C₅₉	C₂³	1	2	yes	—
298	#102×C₅₉	C₂³	1	2	yes	—
299	#102×C₅₉	C₂³	1	1	yes	characteristic
300	#102×C₅₉	C₂³	1	2	yes	—
301	#102×C₅₉	C₂³	1	2	yes	—
302	#102×C₅₉	C₂³	1	2	yes	—
303	#102×C₅₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
308	#97×C₅₉	C₂³	1	2	yes	—
309	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₉	C₂³	1	2	yes	—
312	C₂⁴×C₅₉	—	2	2	no	—
313	#41×C₅₉	—	2	2	no	—
314	#41×C₅₉	—	4	1	no	—
315	#41×C₅₉	—	8	2	no	—
316	C₂×Q₈×C₅₉	—	2	1	no	—
317	C₂×Q₈×C₅₉	—	2	1	no	—
318	C₂×Q₈×C₅₉	—	2	1	no	—
319	C₂×Q₈×C₅₉	—	2	1	no	—
320	C₂×Q₈×C₅₉	—	2	2	no	—
321	C₂×Q₈×C₅₉	—	2	2	no	—
322	C₂×Q₈×C₅₉	—	8	2	no	—
323	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₅₉	—	2	4	no	—
328	C₂×D₄×C₅₉	—	2	1	no	—
329	C₂×D₄×C₅₉	—	2	2	no	—
330	C₂×D₄×C₅₉	—	2	2	no	—
331	C₂×D₄×C₅₉	—	2	2	no	—
332	C₂×D₄×C₅₉	—	2	1	no	—
333	C₂×D₄×C₅₉	—	2	1	no	—
334	C₂×D₄×C₅₉	—	4	2	no	—
335	C₂×D₄×C₅₉	—	8	2	no	—
336	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
339	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₉	—	2	2	no	—
341	C₂²×C₄×C₅₉	—	2	1	no	—
342	C₂²×C₄×C₅₉	—	2	1	no	—
343	C₂²×C₄×C₅₉	—	2	1	no	—
344	C₂²×C₄×C₅₉	—	2	2	no	—
345	C₂²×C₄×C₅₉	—	2	2	no	—
346	C₂²×C₄×C₅₉	—	2	2	no	—
347	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
351	Q₁₆×C₅₉	—	4	1	no	—
352	Q₁₆×C₅₉	—	4	1	no	—
353	SD₁₆×C₅₉	—	2	2	no	—
354	SD₁₆×C₅₉	—	2	2	no	—
355	SD₁₆×C₅₉	—	4	2	no	—
356	SD₁₆×C₅₉	—	4	2	no	—
357	M₁₆×C₅₉	—	4	2	no	—
358	C₂×C₈×C₅₉	—	4	2	no	—
359	C₂×C₈×C₅₉	—	4	2	no	—
360	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
365	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₅₉	—	2	2	no	—
367	C₄⋊C₄×C₅₉	—	2	1	no	—
368	C₄⋊C₄×C₅₉	—	2	1	no	—
369	C₄⋊C₄×C₅₉	—	2	1	no	—
370	C₄⋊C₄×C₅₉	—	2	2	no	—
371	C₄⋊C₄×C₅₉	—	2	1	no	—
372	C₄⋊C₄×C₅₉	—	2	2	no	—
373	C₄⋊C₄×C₅₉	—	2	1	no	—
374	C₄⋊C₄×C₅₉	—	2	1	no	—
375	C₄⋊C₄×C₅₉	—	2	1	no	—
376	C₄⋊C₄×C₅₉	—	2	1	no	—
377	C₄⋊C₄×C₅₉	—	2	2	no	—
378	C₄⋊C₄×C₅₉	—	2	2	no	—
379	C₄⋊C₄×C₅₉	—	2	2	no	—
380	C₄⋊C₄×C₅₉	—	2	2	no	—
381	C₄⋊C₄×C₅₉	—	2	2	no	—
382	C₄⋊C₄×C₅₉	—	2	1	no	—
383	C₄⋊C₄×C₅₉	—	2	1	no	—
384	C₄⋊C₄×C₅₉	—	2	2	no	—
385	C₄⋊C₄×C₅₉	—	2	2	no	—
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	2	no	—
390	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₅₉	—	2	2	no	—
404	C₂²⋊C₄×C₅₉	—	2	2	no	—
405	C₂²⋊C₄×C₅₉	—	2	1	no	—
406	C₂²⋊C₄×C₅₉	—	2	1	no	—
407	C₂²⋊C₄×C₅₉	—	2	2	no	—
408	C₂²⋊C₄×C₅₉	—	2	1	no	—
409	C₂²⋊C₄×C₅₉	—	2	2	no	—
410	C₂²⋊C₄×C₅₉	—	2	2	no	—
411	C₂²⋊C₄×C₅₉	—	2	2	no	—
412	C₂²⋊C₄×C₅₉	—	2	1	no	—
413	C₂²⋊C₄×C₅₉	—	2	2	no	—
414	C₂²⋊C₄×C₅₉	—	2	2	no	—
415	C₂²⋊C₄×C₅₉	—	2	2	no	—
416	C₂²⋊C₄×C₅₉	—	2	2	no	—
417	C₂²⋊C₄×C₅₉	—	2	2	no	—
418	C₂²⋊C₄×C₅₉	—	2	1	no	—
419	C₂²⋊C₄×C₅₉	—	2	2	no	—
420	C₂²⋊C₄×C₅₉	—	2	2	no	—
421	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
426	C₄²×C₅₉	—	2	1	no	—
427	C₄²×C₅₉	—	2	1	no	—
428	C₄²×C₅₉	—	2	1	no	—
429	C₄²×C₅₉	—	2	2	no	—
430	C₄²×C₅₉	—	2	2	no	—
431	C₄²×C₅₉	—	2	1	no	—
432	C₄²×C₅₉	—	2	1	no	—
433	C₄²×C₅₉	—	2	2	no	—
434	C₄²×C₅₉	—	2	2	no	—
435	C₄²×C₅₉	—	2	2	no	—
436	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
439	C₄²×C₅₉	C₂⁴	1	2	yes	—
440	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
441	C₂³×C₅₉	—	2	1	no	—
442	C₂³×C₅₉	—	2	2	no	—
443	C₂³×C₅₉	—	4	4	no	—
444	C₂³×C₅₉	—	8	2	no	—
445	C₂³×C₅₉	—	8	2	no	—
446	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
447	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
448	Q₈×C₅₉	—	2	2	no	—
449	Q₈×C₅₉	—	2	1	no	—
450	Q₈×C₅₉	—	2	1	no	—
451	Q₈×C₅₉	—	2	1	no	—
452	Q₈×C₅₉	—	2	1	no	—
453	Q₈×C₅₉	—	2	1	no	—
454	Q₈×C₅₉	—	2	1	no	—
455	Q₈×C₅₉	—	4	2	no	—
456	Q₈×C₅₉	—	4	2	no	—
457	Q₈×C₅₉	—	8	1	no	—
458	Q₈×C₅₉	—	8	1	no	—
459	Q₈×C₅₉	—	8	2	no	—
460	Q₈×C₅₉	—	8	2	no	—
461	D₄×C₅₉	—	2	2	no	—
462	D₄×C₅₉	—	2	2	no	—
463	D₄×C₅₉	—	2	1	no	—
464	D₄×C₅₉	—	2	2	no	—
465	D₄×C₅₉	—	4	2	no	—
466	D₄×C₅₉	—	4	4	no	—
467	D₄×C₅₉	—	4	2	no	—
468	D₄×C₅₉	—	4	2	no	—
469	D₄×C₅₉	—	8	1	no	—
470	D₄×C₅₉	—	8	2	no	—
471	D₄×C₅₉	—	8	2	no	—
472	D₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
473	C₂×C₄×C₅₉	—	2	2	no	—
474	C₂×C₄×C₅₉	—	2	2	no	—
475	C₂×C₄×C₅₉	—	2	1	no	—
476	C₂×C₄×C₅₉	—	2	1	no	—
477	C₂×C₄×C₅₉	—	2	2	no	—
478	C₂×C₄×C₅₉	—	2	1	no	—
479	C₂×C₄×C₅₉	—	2	1	no	—
480	C₂×C₄×C₅₉	—	2	1	no	—
481	C₂×C₄×C₅₉	—	2	2	no	—
482	C₂×C₄×C₅₉	—	2	1	no	—
483	C₂×C₄×C₅₉	—	2	1	no	—
484	C₂×C₄×C₅₉	—	2	1	no	—
485	C₂×C₄×C₅₉	—	2	2	no	—
486	C₂×C₄×C₅₉	—	2	2	no	—
487	C₂×C₄×C₅₉	—	2	1	no	—
488	C₂×C₄×C₅₉	—	4	1	no	—
489	C₂×C₄×C₅₉	—	4	2	no	—
490	C₂×C₄×C₅₉	—	4	2	no	—
491	C₂×C₄×C₅₉	—	8	1	no	—
492	C₂×C₄×C₅₉	—	8	2	no	—
493	C₂×C₄×C₅₉	—	8	2	no	—
494	C₂×C₄×C₅₉	—	8	2	no	—
495	C₂×C₄×C₅₉	—	8	2	no	—
496	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
505	C₈×C₅₉	—	2	1	no	—
506	C₈×C₅₉	—	2	1	no	—
507	C₈×C₅₉	—	2	2	no	—
508	C₈×C₅₉	—	2	1	no	—
509	C₈×C₅₉	—	2	2	no	—
510	C₈×C₅₉	—	2	1	no	—
511	#62216	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
512	C₂²×C₅₉	—	2	1	no	—
513	C₂²×C₅₉	—	2	2	no	—
514	C₂²×C₅₉	—	2	1	no	—
515	C₂²×C₅₉	—	2	2	no	—
516	C₂²×C₅₉	—	2	2	no	—
517	C₂²×C₅₉	—	2	1	no	—
518	C₂²×C₅₉	—	2	2	no	—
519	C₂²×C₅₉	—	4	1	no	—
520	C₂²×C₅₉	—	4	1	no	—
521	C₂²×C₅₉	—	4	2	no	—
522	C₂²×C₅₉	—	4	2	no	—
523	C₂²×C₅₉	—	4	2	no	—
524	C₂²×C₅₉	—	16	4	no	—
525	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
526	C₄×C₅₉	—	2	1	no	—
527	C₄×C₅₉	—	2	1	no	—
528	C₄×C₅₉	—	2	2	no	—
529	C₄×C₅₉	—	2	1	no	—
530	C₄×C₅₉	—	2	2	no	—
531	C₄×C₅₉	—	2	1	no	—
532	C₄×C₅₉	—	2	2	no	—
533	C₄×C₅₉	—	4	1	no	—
534	C₄×C₅₉	—	4	1	no	—
535	C₄×C₅₉	—	4	2	no	—
536	C₄×C₅₉	—	4	1	no	—
537	C₄×C₅₉	—	4	1	no	—
538	C₄×C₅₉	—	4	1	no	—
539	C₄×C₅₉	—	4	1	no	—
540	C₄×C₅₉	—	4	1	no	—
541	C₄×C₅₉	—	4	2	no	—
542	C₄×C₅₉	—	4	2	no	—
543	C₄×C₅₉	#577	1	2	yes	—
544	C₄×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
545	C₄×C₅₉	#585	1	1	yes	characteristic
546	#3555	C₂×C₅₉	1	1	yes	characteristic, complemented
547	#3514	C₂×C₅₉	1	1	yes	characteristic
548	#3386	C₂×C₅₉	1	1	yes	characteristic, complemented
549	Q₈×SD₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
550	#3375	C₂×C₅₉	1	1	yes	characteristic, complemented
551	#3365	C₂×C₅₉	1	1	yes	characteristic, complemented
552	#3356	C₂×C₅₉	1	1	yes	characteristic, complemented
553	#3348	C₂×C₅₉	1	2	yes	complemented
554	#3342	C₂×C₅₉	1	1	yes	characteristic, complemented
555	#3340	C₂×C₅₉	1	2	yes	complemented
556	#3324	C₂×C₅₉	1	1	yes	characteristic, complemented
557	#3311	C₂×C₅₉	1	2	yes	complemented
558	#3296	C₂×C₅₉	1	2	yes	complemented
559	#3295	C₂×C₅₉	1	1	yes	characteristic, complemented
560	#3258	C₂×C₅₉	1	2	yes	complemented
561	#3246	C₂×C₅₉	1	1	yes	characteristic, complemented
562	#3244	C₂×C₅₉	1	2	yes	complemented
563	#3228	C₂×C₅₉	1	1	yes	characteristic, complemented
564	#3123	C₂×C₅₉	1	2	yes	complemented
565	#3107	C₂×C₅₉	1	1	yes	characteristic, complemented
566	#3081	C₂×C₅₉	1	2	yes	complemented
567	#3076	C₂×C₅₉	1	1	yes	characteristic, complemented
568	#2994	C₂×C₅₉	1	1	yes	characteristic, complemented
569	C₂×C₅₉	—	4	1	no	—
570	C₂×C₅₉	—	4	2	no	—
571	C₂×C₅₉	—	4	2	no	—
572	C₂×C₅₉	—	8	2	no	—
573	C₂×C₅₉	#3489	1	1	yes	characteristic
574	C₂×C₅₉	C₂×#577	1	1	yes	characteristic
575	C₂×C₅₉	#3584	1	1	yes	characteristic
576	#563	—	2	2	no	—
577	#559	C₂²×C₅₉	1	1	yes	characteristic
578	Q₈²	C₂²×C₅₉	1	1	yes	characteristic, complemented
579	#557	—	2	1	no	—
580	#557	C₂²×C₅₉	1	1	yes	characteristic, complemented
581	#556	—	2	1	no	—
582	#556	C₂²×C₅₉	1	1	yes	characteristic
583	#556	C₂²×C₅₉	1	1	yes	characteristic
584	#556	C₂²×C₅₉	1	2	yes	complemented
585	#555	C₂²×C₅₉	1	2	yes	—
586	#554	C₂²×C₅₉	1	1	yes	characteristic
587	#552	C₂²×C₅₉	1	2	yes	complemented
588	#551	—	2	2	no	—
589	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
590	#548	—	2	1	no	—
591	#546	—	2	1	no	—
592	#546	C₂²×C₅₉	1	2	yes	—
593	D₄²	C₂²×C₅₉	1	1	yes	characteristic
594	#544	C₂²×C₅₉	1	2	yes	complemented
595	#542	—	2	1	no	—
596	#542	C₂²×C₅₉	1	2	yes	—
597	#541	—	2	2	no	—
598	#541	—	2	1	no	—
599	#541	C₂²×C₅₉	1	2	yes	complemented
600	#538	—	2	2	no	—
601	#533	C₂²×C₅₉	1	1	yes	characteristic, complemented
602	#533	C₂²×C₅₉	1	1	yes	characteristic, complemented
603	#532	C₂²×C₅₉	1	1	yes	characteristic
604	#529	—	2	1	no	—
605	#529	C₂²×C₅₉	1	1	yes	characteristic
606	C₂×#124	—	2	1	no	—
607	#518	C₂²×C₅₉	1	2	yes	—
608	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
609	#501	C₂²×C₅₉	1	2	yes	complemented
610	#500	C₂²×C₅₉	1	1	yes	characteristic, complemented
611	#498	C₂²×C₅₉	1	2	yes	complemented
612	#498	C₂²×C₅₉	1	1	yes	characteristic, complemented
613	#489	C₂²×C₅₉	1	2	yes	complemented
614	#488	C₂²×C₅₉	1	2	yes	complemented
615	#486	C₂²×C₅₉	1	1	yes	characteristic
616	#486	C₂²×C₅₉	1	1	yes	characteristic
617	#485	C₂²×C₅₉	1	1	yes	characteristic, complemented
618	#485	C₂²×C₅₉	1	2	yes	complemented
619	#485	C₂²×C₅₉	1	2	yes	complemented
620	#485	C₂²×C₅₉	1	2	yes	complemented
621	#485	C₂²×C₅₉	1	1	yes	characteristic, complemented
622	#483	C₂²×C₅₉	1	2	yes	complemented
623	#482	C₂²×C₅₉	1	2	yes	—
624	#482	C₂²×C₅₉	1	2	yes	complemented
625	#482	C₂²×C₅₉	1	2	yes	complemented
626	#481	C₂²×C₅₉	1	2	yes	—
627	#479	C₂²×C₅₉	1	2	yes	complemented
628	#478	C₂²×C₅₉	1	2	yes	—
629	#478	C₂²×C₅₉	1	2	yes	—
630	#478	C₂²×C₅₉	1	2	yes	complemented
631	#478	C₂²×C₅₉	1	2	yes	complemented
632	#478	C₂²×C₅₉	1	2	yes	complemented
633	#477	C₂²×C₅₉	1	1	yes	characteristic, complemented
634	#477	C₂²×C₅₉	1	2	yes	complemented
635	#476	C₂²×C₅₉	1	1	yes	characteristic
636	#476	C₂²×C₅₉	1	2	yes	—
637	#476	C₂²×C₅₉	1	2	yes	complemented
638	#475	C₂²×C₅₉	1	1	yes	characteristic, complemented
639	#475	C₂²×C₅₉	1	1	yes	characteristic, complemented
640	#475	C₂²×C₅₉	1	2	yes	complemented
641	#475	C₂²×C₅₉	1	1	yes	characteristic, complemented
642	#475	C₂²×C₅₉	1	1	yes	characteristic, complemented
643	#474	C₂²×C₅₉	1	1	yes	characteristic
644	#474	C₂²×C₅₉	1	1	yes	characteristic
645	#474	C₂²×C₅₉	1	2	yes	complemented
646	#470	C₂²×C₅₉	1	2	yes	complemented
647	#468	C₂²×C₅₉	1	2	yes	—
648	#467	C₂²×C₅₉	1	2	yes	complemented
649	#465	C₂²×C₅₉	1	2	yes	—
650	#465	C₂²×C₅₉	1	2	yes	complemented
651	#465	C₂²×C₅₉	1	2	yes	complemented
652	#464	C₂²×C₅₉	1	2	yes	complemented
653	#464	C₂²×C₅₉	1	2	yes	complemented
654	#462	C₂²×C₅₉	1	1	yes	characteristic, complemented
655	#461	C₂²×C₅₉	1	1	yes	characteristic
656	#461	C₂²×C₅₉	1	2	yes	complemented
657	#460	C₂²×C₅₉	1	1	yes	characteristic
658	#460	C₂²×C₅₉	1	1	yes	characteristic
659	#452	C₂²×C₅₉	1	1	yes	characteristic
660	#452	C₂²×C₅₉	1	1	yes	characteristic
661	#450	C₂²×C₅₉	1	2	yes	—
662	#450	C₂²×C₅₉	1	2	yes	—
663	#446	C₂²×C₅₉	1	1	yes	characteristic, complemented
664	C₈×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
665	#440	C₂²×C₅₉	1	2	yes	—
666	#440	C₂²×C₅₉	1	2	yes	complemented
667	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
668	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
669	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
673	#436	C₂²×C₅₉	1	1	yes	characteristic
674	#435	C₂²×C₅₉	1	2	yes	complemented
675	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
676	C₈×D₄	C₂²×C₅₉	1	2	yes	complemented
677	#433	C₂²×C₅₉	1	2	yes	complemented
678	#431	C₂²×C₅₉	1	1	yes	characteristic, complemented
679	#428	C₂²×C₅₉	1	2	yes	complemented
680	#427	C₂²×C₅₉	1	2	yes	complemented
681	#427	C₂²×C₅₉	1	2	yes	complemented
682	#424	C₂²×C₅₉	1	2	yes	complemented
683	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
684	#418	C₂²×C₅₉	1	2	yes	—
685	#416	C₂²×C₅₉	1	2	yes	—
686	C₂×#102	C₂²×C₅₉	1	2	yes	—
687	C₅₉	#62216	1	1	yes	characteristic, direct product factor, Sylow
688	C₂×#41	—	2	1	no	—
689	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
690	C₂²×Q₈	—	2	1	no	—
691	C₂²×D₄	—	2	1	no	—
692	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
693	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
694	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
699	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
700	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
701	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
712	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
713	#127	C₂³×C₅₉	1	1	yes	characteristic
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	D₄×C₅₉	1	2	yes	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	D₄×C₅₉	1	1	yes	characteristic
731	#125	C₂³×C₅₉	1	2	yes	—
732	#125	C₂³×C₅₉	1	2	yes	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	1	no	—
741	#124	D₄×C₅₉	1	1	yes	characteristic
742	#124	C₂³×C₅₉	1	2	yes	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	D₄×C₅₉	1	2	yes	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	D₄×C₅₉	1	1	yes	characteristic
768	#121	C₂³×C₅₉	1	2	yes	—
769	#121	C₂³×C₅₉	1	2	yes	—
770	#120	—	2	2	no	—
771	#120	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
785	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
786	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₅₉	1	2	yes	—
797	C₄×D₄	C₂³×C₅₉	1	2	yes	—
798	C₄×D₄	C₂³×C₅₉	1	2	yes	—
799	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₅₉	1	2	yes	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	C₂³×C₅₉	1	1	yes	characteristic
806	#117	C₂³×C₅₉	1	2	yes	—
807	#117	C₂³×C₅₉	1	2	yes	—
808	#117	C₂³×C₅₉	1	2	yes	—
809	#117	C₂³×C₅₉	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
811	C₂×C₂²⋊C₄	—	2	2	no	—
812	C₂×C₂²⋊C₄	—	2	2	no	—
813	C₂×C₂²⋊C₄	—	2	2	no	—
814	C₂×C₄²	—	2	1	no	—
815	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
816	#107	C₂³×C₅₉	1	1	yes	characteristic
817	#107	C₂³×C₅₉	1	2	yes	—
818	#107	C₂³×C₅₉	1	2	yes	—
819	#107	C₂³×C₅₉	1	2	yes	—
820	#107	C₂³×C₅₉	1	1	yes	characteristic
821	#107	C₂³×C₅₉	1	2	yes	—
822	#106	C₂³×C₅₉	1	2	yes	—
823	#106	C₂³×C₅₉	1	2	yes	—
824	#106	C₂³×C₅₉	1	2	yes	—
825	#106	C₂³×C₅₉	1	2	yes	—
826	#106	C₂³×C₅₉	1	2	yes	—
827	#106	C₂³×C₅₉	1	1	yes	characteristic
828	#106	C₂³×C₅₉	1	1	yes	characteristic
829	#106	C₂³×C₅₉	1	2	yes	—
830	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
831	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
835	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
836	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
837	#103	C₂³×C₅₉	1	2	yes	—
838	#103	C₂³×C₅₉	1	2	yes	—
839	#103	C₂³×C₅₉	1	2	yes	—
840	#103	C₂³×C₅₉	1	1	yes	characteristic
841	#103	C₂³×C₅₉	1	1	yes	characteristic
842	#103	C₂³×C₅₉	1	1	yes	characteristic
843	#103	C₂³×C₅₉	1	1	yes	characteristic
844	#103	C₂³×C₅₉	1	1	yes	characteristic
845	#103	C₂³×C₅₉	1	1	yes	characteristic
846	#103	C₂³×C₅₉	1	2	yes	—
847	#102	C₂³×C₅₉	1	1	yes	characteristic
848	#102	C₂³×C₅₉	1	2	yes	—
849	#102	C₂³×C₅₉	1	2	yes	—
850	#102	C₂³×C₅₉	1	2	yes	—
851	#102	C₂³×C₅₉	1	2	yes	—
852	#102	C₂³×C₅₉	1	1	yes	characteristic
853	#102	C₂³×C₅₉	1	2	yes	—
854	#102	C₂³×C₅₉	1	2	yes	—
855	#102	C₂³×C₅₉	1	2	yes	—
856	#102	C₂³×C₅₉	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
861	#97	C₂³×C₅₉	1	2	yes	—
862	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₅₉	1	2	yes	—
865	C₂⁴	—	2	2	no	—
866	#41	—	2	2	no	—
867	#41	—	4	1	no	—
868	#41	—	8	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	8	2	no	—
876	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
877	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	4	2	no	—
888	C₂×D₄	—	8	2	no	—
889	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
890	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
891	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
892	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
904	Q₁₆	—	4	1	no	—
905	Q₁₆	—	4	1	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	2	2	no	—
908	SD₁₆	—	4	2	no	—
909	SD₁₆	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	2	no	—
912	C₂×C₈	—	4	2	no	—
913	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
918	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
975	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
977	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
978	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
990	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
991	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
992	C₄²	C₂⁴×C₅₉	1	2	yes	—
993	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
994	C₂³	—	2	1	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	4	4	no	—
997	C₂³	—	8	2	no	—
998	C₂³	—	8	2	no	—
999	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1000	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1001	Q₈	—	2	2	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	1	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	8	1	no	—
1011	Q₈	—	8	1	no	—
1012	Q₈	—	8	2	no	—
1013	Q₈	—	8	2	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	8	1	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	2	no	—
1025	D₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	8	2	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1053	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1054	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1057	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	1	no	—
1062	C₈	—	2	2	no	—
1063	C₈	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	16	4	no	—
1077	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	C₅₉×#577	1	2	yes	—
1096	C₄	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
1097	C₄	C₅₉×#585	1	1	yes	characteristic
1098	C₂	—	4	2	no	—
1099	C₂	—	4	1	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	8	2	no	—
1102	C₂	C₅₉×#3489	1	1	yes	characteristic
1103	C₂	C₂×C₅₉×#577	1	1	yes	characteristic
1104	C₂	C₅₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	C₅₉×#3514	C₂
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×#3555	C₂	semidirect
3. C₅₉×#3386	C₂	semidirect
4. Q₈×SD₁₆×C₅₉	C₂	semidirect
5. C₅₉×#3375	C₂	semidirect
6. C₅₉×#3365	C₂	semidirect
7. C₅₉×#3356	C₂	semidirect
8. C₅₉×#3348	C₂	semidirect
9. C₅₉×#3342	C₂	semidirect
10. C₅₉×#3340	C₂	semidirect
11. C₅₉×#3324	C₂	semidirect
12. C₅₉×#3311	C₂	semidirect
13. C₅₉×#3296	C₂	semidirect
14. C₅₉×#3295	C₂	semidirect
15. C₅₉×#3258	C₂	semidirect
16. C₅₉×#3246	C₂	semidirect
17. C₅₉×#3244	C₂	semidirect
18. C₅₉×#3228	C₂	semidirect
19. C₅₉×#3123	C₂	semidirect
20. C₅₉×#3107	C₂	semidirect
21. C₅₉×#3081	C₂	semidirect
22. C₅₉×#3076	C₂	semidirect
23. C₅₉×#2994	C₂	semidirect
26. Q₈²×C₅₉	C₂²	semidirect
28. C₅₉×#557	C₂²	semidirect
32. C₅₉×#556	C₂²	semidirect
35. C₅₉×#552	C₂²	semidirect
42. C₅₉×#544	C₂²	semidirect
47. C₅₉×#541	C₂²	semidirect
49. C₅₉×#533	C₂²	semidirect
50. C₅₉×#533	C₂²	semidirect
57. C₅₉×#501	C₂²	semidirect
58. C₅₉×#500	C₂²	semidirect
59. C₅₉×#498	C₂²	semidirect
60. C₅₉×#498	C₂²	semidirect
61. C₅₉×#489	C₂²	semidirect
62. C₅₉×#488	C₂²	semidirect
65. C₅₉×#485	C₂²	semidirect
66. C₅₉×#485	C₂²	semidirect
67. C₅₉×#485	C₂²	semidirect
68. C₅₉×#485	C₂²	semidirect
69. C₅₉×#485	C₂²	semidirect
70. C₅₉×#483	C₂²	semidirect
72. C₅₉×#482	C₂²	semidirect
73. C₅₉×#482	C₂²	semidirect
75. C₅₉×#479	C₂²	semidirect
78. C₅₉×#478	C₂²	semidirect
79. C₅₉×#478	C₂²	semidirect
80. C₅₉×#478	C₂²	semidirect
81. C₅₉×#477	C₂²	semidirect
82. C₅₉×#477	C₂²	semidirect
85. C₅₉×#476	C₂²	semidirect
86. C₅₉×#475	C₂²	semidirect
87. C₅₉×#475	C₂²	semidirect
88. C₅₉×#475	C₂²	semidirect
89. C₅₉×#475	C₂²	semidirect
90. C₅₉×#475	C₂²	semidirect
93. C₅₉×#474	C₂²	semidirect
94. C₅₉×#470	C₂²	semidirect
96. C₅₉×#467	C₂²	semidirect
98. C₅₉×#465	C₂²	semidirect
99. C₅₉×#465	C₂²	semidirect
100. C₅₉×#464	C₂²	semidirect
101. C₅₉×#464	C₂²	semidirect
102. C₅₉×#462	C₂²	semidirect
104. C₅₉×#461	C₂²	semidirect
111. C₅₉×#446	C₂²	semidirect
112. C₈×Q₈×C₅₉	C₂²	semidirect
114. C₅₉×#440	C₂²	semidirect
115. C₄×Q₁₆×C₅₉	C₂²	semidirect
116. C₄×Q₁₆×C₅₉	C₂²	semidirect
120. C₄×SD₁₆×C₅₉	C₂²	semidirect
122. C₅₉×#435	C₂²	semidirect
124. C₈×D₄×C₅₉	C₂²	semidirect
125. C₅₉×#433	C₂²	semidirect
126. C₅₉×#431	C₂²	semidirect
127. C₅₉×#428	C₂²	semidirect
128. C₅₉×#427	C₂²	semidirect
129. C₅₉×#427	C₂²	semidirect
130. C₅₉×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
511. #62216	C₅₉	direct (N × H)
546. #3555	C₂×C₅₉	semidirect
548. #3386	C₂×C₅₉	semidirect
549. Q₈×SD₁₆	C₂×C₅₉	semidirect
550. #3375	C₂×C₅₉	semidirect
551. #3365	C₂×C₅₉	semidirect
552. #3356	C₂×C₅₉	semidirect
553. #3348	C₂×C₅₉	semidirect
554. #3342	C₂×C₅₉	semidirect
555. #3340	C₂×C₅₉	semidirect
556. #3324	C₂×C₅₉	semidirect
557. #3311	C₂×C₅₉	semidirect
558. #3296	C₂×C₅₉	semidirect
559. #3295	C₂×C₅₉	semidirect
560. #3258	C₂×C₅₉	semidirect
561. #3246	C₂×C₅₉	semidirect
562. #3244	C₂×C₅₉	semidirect
563. #3228	C₂×C₅₉	semidirect
564. #3123	C₂×C₅₉	semidirect
565. #3107	C₂×C₅₉	semidirect
566. #3081	C₂×C₅₉	semidirect
567. #3076	C₂×C₅₉	semidirect
568. #2994	C₂×C₅₉	semidirect
578. Q₈²	C₂²×C₅₉	semidirect
580. #557	C₂²×C₅₉	semidirect
584. #556	C₂²×C₅₉	semidirect
587. #552	C₂²×C₅₉	semidirect
594. #544	C₂²×C₅₉	semidirect
599. #541	C₂²×C₅₉	semidirect
601. #533	C₂²×C₅₉	semidirect
602. #533	C₂²×C₅₉	semidirect
609. #501	C₂²×C₅₉	semidirect
610. #500	C₂²×C₅₉	semidirect
611. #498	C₂²×C₅₉	semidirect
612. #498	C₂²×C₅₉	semidirect
613. #489	C₂²×C₅₉	semidirect
614. #488	C₂²×C₅₉	semidirect
617. #485	C₂²×C₅₉	semidirect
618. #485	C₂²×C₅₉	semidirect
619. #485	C₂²×C₅₉	semidirect
620. #485	C₂²×C₅₉	semidirect
621. #485	C₂²×C₅₉	semidirect
622. #483	C₂²×C₅₉	semidirect
624. #482	C₂²×C₅₉	semidirect
625. #482	C₂²×C₅₉	semidirect
627. #479	C₂²×C₅₉	semidirect
630. #478	C₂²×C₅₉	semidirect
631. #478	C₂²×C₅₉	semidirect
632. #478	C₂²×C₅₉	semidirect
633. #477	C₂²×C₅₉	semidirect
634. #477	C₂²×C₅₉	semidirect
637. #476	C₂²×C₅₉	semidirect
638. #475	C₂²×C₅₉	semidirect
639. #475	C₂²×C₅₉	semidirect
640. #475	C₂²×C₅₉	semidirect
641. #475	C₂²×C₅₉	semidirect
642. #475	C₂²×C₅₉	semidirect
645. #474	C₂²×C₅₉	semidirect
646. #470	C₂²×C₅₉	semidirect
648. #467	C₂²×C₅₉	semidirect
650. #465	C₂²×C₅₉	semidirect
651. #465	C₂²×C₅₉	semidirect
652. #464	C₂²×C₅₉	semidirect
653. #464	C₂²×C₅₉	semidirect
654. #462	C₂²×C₅₉	semidirect
656. #461	C₂²×C₅₉	semidirect
663. #446	C₂²×C₅₉	semidirect
664. C₈×Q₈	C₂²×C₅₉	semidirect
666. #440	C₂²×C₅₉	semidirect
667. C₄×Q₁₆	C₂²×C₅₉	semidirect
668. C₄×Q₁₆	C₂²×C₅₉	semidirect
672. C₄×SD₁₆	C₂²×C₅₉	semidirect
674. #435	C₂²×C₅₉	semidirect
676. C₈×D₄	C₂²×C₅₉	semidirect
677. #433	C₂²×C₅₉	semidirect
678. #431	C₂²×C₅₉	semidirect
679. #428	C₂²×C₅₉	semidirect
680. #427	C₂²×C₅₉	semidirect
681. #427	C₂²×C₅₉	semidirect
682. #424	C₂²×C₅₉	semidirect
683. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
687. C₅₉	#62216	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×#3555	2
C₅₉×#3514	2
C₅₉×#3386	2
Q₈×SD₁₆×C₅₉	2
C₅₉×#3375	2
C₅₉×#3365	2
C₅₉×#3356	2
C₅₉×#3348	2
C₅₉×#3342	2
C₅₉×#3340	2
C₅₉×#3324	2
C₅₉×#3311	2
C₅₉×#3296	2
C₅₉×#3295	2
C₅₉×#3258	2
C₅₉×#3246	2
C₅₉×#3244	2
C₅₉×#3228	2
C₅₉×#3123	2
C₅₉×#3107	2
C₅₉×#3081	2
C₅₉×#3076	2
C₅₉×#2994	2
#62216	59

Subgroups — C59×#62216 #28474325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62216 #28474325