Subgroups — C₅₉×#62038 #28474147

Order 15104.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1158 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×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3326	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3320	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#3278	C₂	1	2	yes	maximal, complemented
13	C₅₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#3271	C₂	1	2	yes	maximal, complemented
15	C₅₉×#3260	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3221	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×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#3046	C₂	1	2	yes	maximal, complemented
22	C₅₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₉	C₂²	1	2	yes	—
25	C₂×#137×C₅₉	C₂²	1	2	yes	—
26	C₂×#135×C₅₉	C₂²	1	2	yes	—
27	C₅₉×#563	—	2	2	no	—
28	C₅₉×#557	C₂²	1	1	yes	characteristic
29	C₅₉×#557	C₂²	1	1	yes	characteristic
30	C₅₉×#556	C₂²	1	1	yes	characteristic
31	C₅₉×#554	—	2	1	no	—
32	C₅₉×#553	—	2	2	no	—
33	C₅₉×#553	—	2	1	no	—
34	C₅₉×#553	C₂²	1	2	yes	—
35	C₅₉×#550	—	2	1	no	—
36	C₅₉×#550	C₂²	1	2	yes	—
37	C₅₉×#550	C₂²	1	1	yes	characteristic
38	C₅₉×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
41	C₅₉×#548	C₂²	1	2	yes	—
42	C₅₉×#547	—	2	1	no	—
43	C₅₉×#547	C₂²	1	1	yes	characteristic
44	C₅₉×#547	C₂²	1	1	yes	characteristic
45	C₅₉×#544	—	2	1	no	—
46	C₅₉×#542	—	2	1	no	—
47	C₅₉×#541	C₂²	1	2	yes	—
48	C₅₉×#540	—	2	2	no	—
49	C₅₉×#540	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	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
60	C₅₉×#496	C₂²	1	2	yes	—
61	C₅₉×#492	C₂²	1	2	yes	—
62	C₅₉×#492	C₂²	1	1	yes	characteristic
63	C₅₉×#492	C₂²	1	1	yes	characteristic
64	C₅₉×#491	C₂²	1	2	yes	—
65	C₅₉×#488	C₂²	1	2	yes	—
66	C₅₉×#487	C₂²	1	1	yes	characteristic
67	C₅₉×#487	C₂²	1	1	yes	characteristic
68	C₅₉×#485	C₂²	1	1	yes	characteristic
69	C₅₉×#484	C₂²	1	2	yes	—
70	C₅₉×#483	C₂²	1	2	yes	—
71	C₅₉×#482	C₂²	1	1	yes	characteristic
72	C₅₉×#479	C₂²	1	2	yes	—
73	C₅₉×#479	C₂²	1	2	yes	—
74	C₅₉×#479	C₂²	1	1	yes	characteristic
75	C₅₉×#478	C₂²	1	2	yes	—
76	C₅₉×#478	C₂²	1	1	yes	characteristic
77	C₅₉×#475	C₂²	1	1	yes	characteristic
78	C₅₉×#474	C₂²	1	1	yes	characteristic
79	C₅₉×#469	C₂²	1	2	yes	—
80	C₅₉×#468	C₂²	1	2	yes	—
81	C₅₉×#468	C₂²	1	2	yes	—
82	C₅₉×#468	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	1	yes	characteristic
87	C₅₉×#463	C₂²	1	2	yes	—
88	C₅₉×#463	C₂²	1	2	yes	—
89	C₅₉×#463	C₂²	1	1	yes	characteristic
90	C₅₉×#462	C₂²	1	1	yes	characteristic
91	C₅₉×#462	C₂²	1	2	yes	—
92	C₅₉×#462	C₂²	1	1	yes	characteristic
93	C₅₉×#462	C₂²	1	2	yes	—
94	C₅₉×#461	C₂²	1	2	yes	—
95	C₅₉×#461	C₂²	1	2	yes	—
96	C₅₉×#461	C₂²	1	1	yes	characteristic
97	C₅₉×#461	C₂²	1	1	yes	characteristic
98	C₅₉×#461	C₂²	1	2	yes	—
99	C₅₉×#461	C₂²	1	2	yes	—
100	C₅₉×#460	C₂²	1	1	yes	characteristic
101	C₅₉×#460	C₂²	1	2	yes	—
102	C₅₉×#460	C₂²	1	2	yes	—
103	C₅₉×#459	C₂²	1	1	yes	characteristic
104	C₅₉×#452	C₂²	1	2	yes	—
105	C₅₉×#452	C₂²	1	1	yes	characteristic
106	C₅₉×#452	C₂²	1	2	yes	—
107	C₅₉×#449	C₂²	1	1	yes	characteristic
108	C₅₉×#449	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	2	yes	—
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×SD₁₆×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×D₈×C₅₉	C₂²	1	1	yes	characteristic
124	C₅₉×#436	C₂²	1	2	yes	—
125	C₅₉×#436	C₂²	1	1	yes	characteristic
126	C₅₉×#435	C₂²	1	2	yes	—
127	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
128	C₅₉×#433	C₂²	1	2	yes	—
129	C₅₉×#431	C₂²	1	1	yes	characteristic
130	C₅₉×#424	C₂²	1	2	yes	—
131	C₅₉×#423	C₂²	1	1	yes	characteristic
132	C₅₉×#419	C₂²	1	2	yes	—
133	C₅₉×#417	C₂²	1	2	yes	—
134	C₂×#103×C₅₉	C₂²	1	2	yes	—
135	C₂×#41×C₅₉	—	2	1	no	—
136	C₂×#41×C₅₉	—	2	1	no	—
137	C₂×#41×C₅₉	—	2	1	no	—
138	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
139	C₂×#41×C₅₉	C₂³	1	2	yes	—
140	C₂×#41×C₅₉	C₂³	1	2	yes	—
141	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
142	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
143	#137×C₅₉	—	4	4	no	—
144	#137×C₅₉	—	4	4	no	—
145	#135×C₅₉	—	4	4	no	—
146	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
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	1	yes	characteristic
159	C₂×D₈×C₅₉	C₂³	1	2	yes	—
160	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
161	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₅₉	—	2	1	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	1	yes	characteristic
170	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
173	#127×C₅₉	—	2	1	no	—
174	#127×C₅₉	—	2	2	no	—
175	#127×C₅₉	C₂³	1	1	yes	characteristic
176	#127×C₅₉	C₂³	1	2	yes	—
177	#126×C₅₉	—	2	2	no	—
178	#126×C₅₉	—	2	2	no	—
179	#126×C₅₉	—	2	2	no	—
180	#126×C₅₉	—	2	2	no	—
181	#126×C₅₉	—	2	1	no	—
182	#126×C₅₉	D₄	1	2	yes	—
183	#125×C₅₉	—	2	2	no	—
184	#125×C₅₉	—	2	2	no	—
185	#125×C₅₉	—	2	2	no	—
186	#125×C₅₉	—	2	2	no	—
187	#125×C₅₉	—	2	1	no	—
188	#125×C₅₉	D₄	1	1	yes	characteristic
189	#125×C₅₉	C₂³	1	1	yes	characteristic
190	#125×C₅₉	C₂³	1	2	yes	—
191	#124×C₅₉	—	2	2	no	—
192	#124×C₅₉	—	2	1	no	—
193	#124×C₅₉	D₄	1	1	yes	characteristic
194	#124×C₅₉	C₂³	1	1	yes	characteristic
195	#124×C₅₉	C₂³	1	2	yes	—
196	#123×C₅₉	—	2	1	no	—
197	#123×C₅₉	—	2	2	no	—
198	#123×C₅₉	—	2	2	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	D₄	1	2	yes	—
205	C₂²⋊Q₈×C₅₉	—	2	1	no	—
206	C₂²⋊Q₈×C₅₉	—	2	1	no	—
207	C₂²⋊Q₈×C₅₉	—	2	2	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	D₄	1	1	yes	characteristic
214	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
217	#121×C₅₉	—	2	2	no	—
218	#121×C₅₉	—	2	2	no	—
219	#121×C₅₉	—	2	1	no	—
220	#121×C₅₉	—	2	1	no	—
221	#121×C₅₉	—	2	1	no	—
222	#121×C₅₉	—	2	2	no	—
223	#121×C₅₉	—	2	2	no	—
224	#121×C₅₉	—	2	2	no	—
225	#121×C₅₉	—	2	2	no	—
226	#121×C₅₉	—	2	2	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	2	yes	—
232	#121×C₅₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₅₉	—	2	1	no	—
234	C₄×Q₈×C₅₉	—	2	1	no	—
235	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₉	—	2	2	no	—
243	C₄×D₄×C₅₉	—	2	1	no	—
244	C₄×D₄×C₅₉	—	2	1	no	—
245	C₄×D₄×C₅₉	—	2	1	no	—
246	C₄×D₄×C₅₉	—	2	1	no	—
247	C₄×D₄×C₅₉	—	2	1	no	—
248	C₄×D₄×C₅₉	—	2	2	no	—
249	C₄×D₄×C₅₉	—	2	2	no	—
250	C₄×D₄×C₅₉	—	2	2	no	—
251	C₄×D₄×C₅₉	—	2	2	no	—
252	C₄×D₄×C₅₉	—	2	2	no	—
253	C₄×D₄×C₅₉	—	2	1	no	—
254	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₅₉	C₂³	1	2	yes	—
257	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₉	C₂³	1	2	yes	—
259	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₉	C₂³	1	2	yes	—
261	#117×C₅₉	—	2	2	no	—
262	#117×C₅₉	—	2	1	no	—
263	#117×C₅₉	—	2	1	no	—
264	#117×C₅₉	—	2	1	no	—
265	#117×C₅₉	C₂³	1	1	yes	characteristic
266	#117×C₅₉	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
269	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
270	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
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	1	yes	characteristic
288	#103×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
298	#103×C₅₉	C₂³	1	1	yes	characteristic
299	#103×C₅₉	C₂³	1	2	yes	—
300	#102×C₅₉	C₂³	1	1	yes	characteristic
301	#102×C₅₉	C₂³	1	2	yes	—
302	#102×C₅₉	C₂³	1	1	yes	characteristic
303	#102×C₅₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
317	#41×C₅₉	—	4	1	no	—
318	#41×C₅₉	—	4	2	no	—
319	#41×C₅₉	—	4	2	no	—
320	#41×C₅₉	—	4	2	no	—
321	#41×C₅₉	—	8	2	no	—
322	#41×C₅₉	—	8	2	no	—
323	#41×C₅₉	—	8	2	no	—
324	C₂×Q₈×C₅₉	—	2	1	no	—
325	C₂×Q₈×C₅₉	—	2	2	no	—
326	C₂×Q₈×C₅₉	—	2	2	no	—
327	C₂×Q₈×C₅₉	—	4	2	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	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₅₉	—	2	1	no	—
337	C₂×D₄×C₅₉	—	2	2	no	—
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	—	2	2	no	—
346	C₂×D₄×C₅₉	—	2	2	no	—
347	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
351	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅₉	—	2	2	no	—
353	C₂²×C₄×C₅₉	—	2	2	no	—
354	C₂²×C₄×C₅₉	—	2	2	no	—
355	C₂²×C₄×C₅₉	—	2	1	no	—
356	C₂²×C₄×C₅₉	—	2	1	no	—
357	C₂²×C₄×C₅₉	—	2	1	no	—
358	C₂²×C₄×C₅₉	—	2	2	no	—
359	C₂²×C₄×C₅₉	—	2	1	no	—
360	C₂²×C₄×C₅₉	—	2	2	no	—
361	C₂²×C₄×C₅₉	—	2	2	no	—
362	C₂²×C₄×C₅₉	—	2	2	no	—
363	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
367	Q₁₆×C₅₉	—	2	4	no	—
368	Q₁₆×C₅₉	—	2	2	no	—
369	Q₁₆×C₅₉	—	2	4	no	—
370	SD₁₆×C₅₉	—	2	2	no	—
371	SD₁₆×C₅₉	—	4	2	no	—
372	SD₁₆×C₅₉	—	4	1	no	—
373	SD₁₆×C₅₉	—	4	2	no	—
374	SD₁₆×C₅₉	—	4	2	no	—
375	SD₁₆×C₅₉	—	4	2	no	—
376	SD₁₆×C₅₉	—	4	2	no	—
377	SD₁₆×C₅₉	—	4	2	no	—
378	SD₁₆×C₅₉	—	4	2	no	—
379	D₈×C₅₉	—	4	1	no	—
380	D₈×C₅₉	—	4	2	no	—
381	M₁₆×C₅₉	—	4	2	no	—
382	M₁₆×C₅₉	—	4	2	no	—
383	C₂×C₈×C₅₉	—	4	2	no	—
384	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
388	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₅₉	—	2	1	no	—
391	C₄⋊C₄×C₅₉	—	2	1	no	—
392	C₄⋊C₄×C₅₉	—	2	2	no	—
393	C₄⋊C₄×C₅₉	—	2	1	no	—
394	C₄⋊C₄×C₅₉	—	2	2	no	—
395	C₄⋊C₄×C₅₉	—	2	1	no	—
396	C₄⋊C₄×C₅₉	—	2	2	no	—
397	C₄⋊C₄×C₅₉	—	2	2	no	—
398	C₄⋊C₄×C₅₉	—	2	2	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	1	no	—
404	C₄⋊C₄×C₅₉	—	2	2	no	—
405	C₄⋊C₄×C₅₉	—	2	2	no	—
406	C₄⋊C₄×C₅₉	—	2	2	no	—
407	C₄⋊C₄×C₅₉	—	2	1	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	2	no	—
412	C₄⋊C₄×C₅₉	—	2	1	no	—
413	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₅₉	—	2	1	no	—
425	C₂²⋊C₄×C₅₉	—	2	1	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	1	no	—
430	C₂²⋊C₄×C₅₉	—	2	1	no	—
431	C₂²⋊C₄×C₅₉	—	2	2	no	—
432	C₂²⋊C₄×C₅₉	—	2	2	no	—
433	C₂²⋊C₄×C₅₉	—	2	1	no	—
434	C₂²⋊C₄×C₅₉	—	2	1	no	—
435	C₂²⋊C₄×C₅₉	—	2	2	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	—	2	2	no	—
440	C₂²⋊C₄×C₅₉	—	2	1	no	—
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	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
446	C₄²×C₅₉	—	2	1	no	—
447	C₄²×C₅₉	—	2	1	no	—
448	C₄²×C₅₉	—	2	1	no	—
449	C₄²×C₅₉	—	2	2	no	—
450	C₄²×C₅₉	—	2	1	no	—
451	C₄²×C₅₉	—	2	2	no	—
452	C₄²×C₅₉	—	2	2	no	—
453	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
456	C₄²×C₅₉	C₂⁴	1	2	yes	—
457	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
458	C₂³×C₅₉	—	2	1	no	—
459	C₂³×C₅₉	—	2	1	no	—
460	C₂³×C₅₉	—	2	2	no	—
461	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
462	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
463	Q₈×C₅₉	—	2	2	no	—
464	Q₈×C₅₉	—	2	1	no	—
465	Q₈×C₅₉	—	2	2	no	—
466	Q₈×C₅₉	—	2	1	no	—
467	Q₈×C₅₉	—	2	2	no	—
468	Q₈×C₅₉	—	2	2	no	—
469	Q₈×C₅₉	—	2	1	no	—
470	Q₈×C₅₉	—	2	2	no	—
471	Q₈×C₅₉	—	4	2	no	—
472	Q₈×C₅₉	—	8	2	no	—
473	Q₈×C₅₉	—	8	2	no	—
474	Q₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
475	D₄×C₅₉	—	2	2	no	—
476	D₄×C₅₉	—	2	1	no	—
477	D₄×C₅₉	—	2	2	no	—
478	D₄×C₅₉	—	2	1	no	—
479	D₄×C₅₉	—	2	1	no	—
480	D₄×C₅₉	—	2	1	no	—
481	D₄×C₅₉	—	2	2	no	—
482	D₄×C₅₉	—	4	2	no	—
483	D₄×C₅₉	—	4	2	no	—
484	D₄×C₅₉	—	4	4	no	—
485	D₄×C₅₉	—	4	2	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	D₄×C₅₉	—	8	2	no	—
491	D₄×C₅₉	—	8	2	no	—
492	D₄×C₅₉	—	8	2	no	—
493	D₄×C₅₉	—	8	2	no	—
494	C₂×C₄×C₅₉	—	2	1	no	—
495	C₂×C₄×C₅₉	—	2	2	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	2	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	1	no	—
504	C₂×C₄×C₅₉	—	2	1	no	—
505	C₂×C₄×C₅₉	—	2	2	no	—
506	C₂×C₄×C₅₉	—	2	2	no	—
507	C₂×C₄×C₅₉	—	2	2	no	—
508	C₂×C₄×C₅₉	—	4	1	no	—
509	C₂×C₄×C₅₉	—	4	4	no	—
510	C₂×C₄×C₅₉	—	4	2	no	—
511	C₂×C₄×C₅₉	—	4	2	no	—
512	C₂×C₄×C₅₉	—	4	2	no	—
513	C₂×C₄×C₅₉	—	8	1	no	—
514	C₂×C₄×C₅₉	—	8	2	no	—
515	C₂×C₄×C₅₉	—	8	2	no	—
516	C₂×C₄×C₅₉	—	8	2	no	—
517	C₂×C₄×C₅₉	—	8	2	no	—
518	C₂×C₄×C₅₉	—	8	2	no	—
519	C₂×C₄×C₅₉	—	8	2	no	—
520	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
529	C₈×C₅₉	—	2	1	no	—
530	C₈×C₅₉	—	2	2	no	—
531	C₈×C₅₉	—	2	1	no	—
532	C₈×C₅₉	—	2	2	no	—
533	C₈×C₅₉	—	2	1	no	—
534	C₈×C₅₉	—	2	1	no	—
535	#62038	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
536	C₂²×C₅₉	—	2	1	no	—
537	C₂²×C₅₉	—	2	2	no	—
538	C₂²×C₅₉	—	2	1	no	—
539	C₂²×C₅₉	—	2	2	no	—
540	C₂²×C₅₉	—	2	1	no	—
541	C₂²×C₅₉	—	2	2	no	—
542	C₂²×C₅₉	—	4	1	no	—
543	C₂²×C₅₉	—	4	1	no	—
544	C₂²×C₅₉	—	4	2	no	—
545	C₂²×C₅₉	—	4	2	no	—
546	C₂²×C₅₉	—	4	1	no	—
547	C₂²×C₅₉	—	4	1	no	—
548	C₂²×C₅₉	—	4	1	no	—
549	C₂²×C₅₉	—	4	1	no	—
550	C₂²×C₅₉	—	4	2	no	—
551	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₅₉	—	2	1	no	—
553	C₄×C₅₉	—	2	1	no	—
554	C₄×C₅₉	—	2	2	no	—
555	C₄×C₅₉	—	2	2	no	—
556	C₄×C₅₉	—	2	1	no	—
557	C₄×C₅₉	—	2	2	no	—
558	C₄×C₅₉	—	2	1	no	—
559	C₄×C₅₉	—	2	2	no	—
560	C₄×C₅₉	—	4	1	no	—
561	C₄×C₅₉	—	4	1	no	—
562	C₄×C₅₉	—	4	2	no	—
563	C₄×C₅₉	—	4	1	no	—
564	C₄×C₅₉	—	4	2	no	—
565	C₄×C₅₉	—	4	1	no	—
566	C₄×C₅₉	—	4	1	no	—
567	C₄×C₅₉	—	4	2	no	—
568	C₄×C₅₉	#577	1	2	yes	—
569	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₄×C₅₉	#585	1	1	yes	characteristic
571	#3552	C₂×C₅₉	1	1	yes	characteristic, complemented
572	#3517	C₂×C₅₉	1	1	yes	characteristic, complemented
573	#3397	C₂×C₅₉	1	1	yes	characteristic, complemented
574	#3392	C₂×C₅₉	1	1	yes	characteristic, complemented
575	#3374	C₂×C₅₉	1	1	yes	characteristic, complemented
576	#3364	C₂×C₅₉	1	1	yes	characteristic, complemented
577	#3330	C₂×C₅₉	1	1	yes	characteristic, complemented
578	#3326	C₂×C₅₉	1	2	yes	complemented
579	#3320	C₂×C₅₉	1	2	yes	complemented
580	#3298	C₂×C₅₉	1	1	yes	characteristic, complemented
581	#3284	C₂×C₅₉	1	1	yes	characteristic, complemented
582	#3278	C₂×C₅₉	1	1	yes	characteristic, complemented
583	#3278	C₂×C₅₉	1	2	yes	complemented
584	#3271	C₂×C₅₉	1	2	yes	complemented
585	#3260	C₂×C₅₉	1	2	yes	complemented
586	#3251	C₂×C₅₉	1	1	yes	characteristic, complemented
587	#3221	C₂×C₅₉	1	2	yes	complemented
588	#3206	C₂×C₅₉	1	1	yes	characteristic, complemented
589	#3120	C₂×C₅₉	1	2	yes	complemented
590	#3102	C₂×C₅₉	1	1	yes	characteristic, complemented
591	#3046	C₂×C₅₉	1	2	yes	complemented
592	#3039	C₂×C₅₉	1	1	yes	characteristic, complemented
593	#2993	C₂×C₅₉	1	1	yes	characteristic, complemented
594	C₂×C₅₉	—	4	1	no	—
595	C₂×C₅₉	—	4	2	no	—
596	C₂×C₅₉	—	8	1	no	—
597	C₂×C₅₉	—	8	1	no	—
598	C₂×C₅₉	—	8	2	no	—
599	C₂×C₅₉	#3488	1	1	yes	characteristic
600	C₂×C₅₉	C₂×#577	1	1	yes	characteristic
601	C₂×C₅₉	#3586	1	1	yes	characteristic
602	C₂×#137	C₂²×C₅₉	1	2	yes	—
603	C₂×#137	C₂²×C₅₉	1	2	yes	—
604	C₂×#135	C₂²×C₅₉	1	2	yes	—
605	#563	—	2	2	no	—
606	#557	C₂²×C₅₉	1	1	yes	characteristic
607	#557	C₂²×C₅₉	1	1	yes	characteristic
608	#556	C₂²×C₅₉	1	1	yes	characteristic
609	#554	—	2	1	no	—
610	#553	—	2	2	no	—
611	#553	—	2	1	no	—
612	#553	C₂²×C₅₉	1	2	yes	—
613	#550	—	2	1	no	—
614	#550	C₂²×C₅₉	1	2	yes	—
615	#550	C₂²×C₅₉	1	1	yes	characteristic
616	#550	C₂²×C₅₉	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
618	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
619	#548	C₂²×C₅₉	1	2	yes	—
620	#547	—	2	1	no	—
621	#547	C₂²×C₅₉	1	1	yes	characteristic
622	#547	C₂²×C₅₉	1	1	yes	characteristic
623	#544	—	2	1	no	—
624	#542	—	2	1	no	—
625	#541	C₂²×C₅₉	1	2	yes	—
626	#540	—	2	2	no	—
627	#540	C₂²×C₅₉	1	2	yes	—
628	#539	—	2	2	no	—
629	#536	C₂²×C₅₉	1	2	yes	—
630	#532	—	2	1	no	—
631	#532	C₂²×C₅₉	1	1	yes	characteristic
632	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
633	#529	—	2	1	no	—
634	#529	C₂²×C₅₉	1	1	yes	characteristic
635	#529	C₂²×C₅₉	1	1	yes	characteristic
636	#520	C₂²×C₅₉	1	2	yes	—
637	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
638	#496	C₂²×C₅₉	1	2	yes	—
639	#492	C₂²×C₅₉	1	1	yes	characteristic
640	#492	C₂²×C₅₉	1	2	yes	—
641	#492	C₂²×C₅₉	1	1	yes	characteristic
642	#491	C₂²×C₅₉	1	2	yes	—
643	#488	C₂²×C₅₉	1	2	yes	—
644	#487	C₂²×C₅₉	1	1	yes	characteristic
645	#487	C₂²×C₅₉	1	1	yes	characteristic
646	#485	C₂²×C₅₉	1	1	yes	characteristic
647	#484	C₂²×C₅₉	1	2	yes	—
648	#483	C₂²×C₅₉	1	2	yes	—
649	#482	C₂²×C₅₉	1	1	yes	characteristic
650	#479	C₂²×C₅₉	1	1	yes	characteristic
651	#479	C₂²×C₅₉	1	2	yes	—
652	#479	C₂²×C₅₉	1	2	yes	—
653	#478	C₂²×C₅₉	1	1	yes	characteristic
654	#478	C₂²×C₅₉	1	2	yes	—
655	#475	C₂²×C₅₉	1	1	yes	characteristic
656	#474	C₂²×C₅₉	1	1	yes	characteristic
657	#469	C₂²×C₅₉	1	2	yes	—
658	#468	C₂²×C₅₉	1	2	yes	—
659	#468	C₂²×C₅₉	1	2	yes	—
660	#468	C₂²×C₅₉	1	2	yes	—
661	#465	C₂²×C₅₉	1	2	yes	—
662	#465	C₂²×C₅₉	1	2	yes	—
663	#464	C₂²×C₅₉	1	1	yes	characteristic
664	#464	C₂²×C₅₉	1	2	yes	—
665	#463	C₂²×C₅₉	1	1	yes	characteristic
666	#463	C₂²×C₅₉	1	2	yes	—
667	#463	C₂²×C₅₉	1	2	yes	—
668	#462	C₂²×C₅₉	1	1	yes	characteristic
669	#462	C₂²×C₅₉	1	2	yes	—
670	#462	C₂²×C₅₉	1	1	yes	characteristic
671	#462	C₂²×C₅₉	1	2	yes	—
672	#461	C₂²×C₅₉	1	1	yes	characteristic
673	#461	C₂²×C₅₉	1	2	yes	—
674	#461	C₂²×C₅₉	1	2	yes	—
675	#461	C₂²×C₅₉	1	1	yes	characteristic
676	#461	C₂²×C₅₉	1	2	yes	—
677	#461	C₂²×C₅₉	1	2	yes	—
678	#460	C₂²×C₅₉	1	1	yes	characteristic
679	#460	C₂²×C₅₉	1	2	yes	—
680	#460	C₂²×C₅₉	1	2	yes	—
681	#459	C₂²×C₅₉	1	1	yes	characteristic
682	#452	C₂²×C₅₉	1	1	yes	characteristic
683	#452	C₂²×C₅₉	1	2	yes	—
684	#452	C₂²×C₅₉	1	2	yes	—
685	#449	C₂²×C₅₉	1	2	yes	—
686	#449	C₂²×C₅₉	1	1	yes	characteristic
687	#449	C₂²×C₅₉	1	2	yes	—
688	#448	C₂²×C₅₉	1	2	yes	—
689	#448	C₂²×C₅₉	1	2	yes	—
690	#448	C₂²×C₅₉	1	2	yes	—
691	#448	C₂²×C₅₉	1	2	yes	—
692	#446	C₂²×C₅₉	1	1	yes	characteristic
693	C₈×Q₈	C₂²×C₅₉	1	1	yes	characteristic
694	#441	C₂²×C₅₉	1	2	yes	—
695	#440	C₂²×C₅₉	1	2	yes	—
696	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
697	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	—
698	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
700	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	—
701	C₄×D₈	C₂²×C₅₉	1	1	yes	characteristic
702	#436	C₂²×C₅₉	1	1	yes	characteristic
703	#436	C₂²×C₅₉	1	2	yes	—
704	#435	C₂²×C₅₉	1	2	yes	—
705	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
706	#433	C₂²×C₅₉	1	2	yes	—
707	#431	C₂²×C₅₉	1	1	yes	characteristic
708	#424	C₂²×C₅₉	1	2	yes	—
709	#423	C₂²×C₅₉	1	1	yes	characteristic
710	#419	C₂²×C₅₉	1	2	yes	—
711	#417	C₂²×C₅₉	1	2	yes	—
712	C₂×#103	C₂²×C₅₉	1	2	yes	—
713	C₅₉	#62038	1	1	yes	characteristic, direct product factor, Sylow
714	C₂×#41	—	2	1	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
718	C₂×#41	C₂³×C₅₉	1	2	yes	—
719	C₂×#41	C₂³×C₅₉	1	2	yes	—
720	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
721	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
722	#137	—	4	4	no	—
723	#137	—	4	4	no	—
724	#135	—	4	4	no	—
725	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
737	C₂×D₈	C₂³×C₅₉	1	2	yes	—
738	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
740	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
741	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	2	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
748	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
752	#127	—	2	1	no	—
753	#127	—	2	2	no	—
754	#127	C₂³×C₅₉	1	1	yes	characteristic
755	#127	C₂³×C₅₉	1	2	yes	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	1	no	—
761	#126	D₄×C₅₉	1	2	yes	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	—	2	1	no	—
767	#125	D₄×C₅₉	1	1	yes	characteristic
768	#125	C₂³×C₅₉	1	1	yes	characteristic
769	#125	C₂³×C₅₉	1	2	yes	—
770	#124	—	2	2	no	—
771	#124	—	2	1	no	—
772	#124	D₄×C₅₉	1	1	yes	characteristic
773	#124	C₂³×C₅₉	1	1	yes	characteristic
774	#124	C₂³×C₅₉	1	2	yes	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	D₄×C₅₉	1	2	yes	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
794	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	D₄×C₅₉	1	1	yes	characteristic
808	#121	C₂³×C₅₉	1	1	yes	characteristic
809	#121	C₂³×C₅₉	1	2	yes	—
810	#121	C₂³×C₅₉	1	2	yes	—
811	#121	C₂³×C₅₉	1	2	yes	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
817	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
819	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
820	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₅₉	1	2	yes	—
836	C₄×D₄	C₂³×C₅₉	1	2	yes	—
837	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₅₉	1	2	yes	—
840	#117	—	2	2	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	C₂³×C₅₉	1	1	yes	characteristic
845	#117	C₂³×C₅₉	1	2	yes	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	2	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
853	#107	C₂³×C₅₉	1	1	yes	characteristic
854	#107	C₂³×C₅₉	1	2	yes	—
855	#107	C₂³×C₅₉	1	1	yes	characteristic
856	#106	C₂³×C₅₉	1	1	yes	characteristic
857	#106	C₂³×C₅₉	1	1	yes	characteristic
858	#106	C₂³×C₅₉	1	2	yes	—
859	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
860	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
864	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
865	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
866	#103	C₂³×C₅₉	1	1	yes	characteristic
867	#103	C₂³×C₅₉	1	2	yes	—
868	#103	C₂³×C₅₉	1	2	yes	—
869	#103	C₂³×C₅₉	1	2	yes	—
870	#103	C₂³×C₅₉	1	2	yes	—
871	#103	C₂³×C₅₉	1	2	yes	—
872	#103	C₂³×C₅₉	1	2	yes	—
873	#103	C₂³×C₅₉	1	2	yes	—
874	#103	C₂³×C₅₉	1	1	yes	characteristic
875	#103	C₂³×C₅₉	1	1	yes	characteristic
876	#103	C₂³×C₅₉	1	2	yes	—
877	#103	C₂³×C₅₉	1	1	yes	characteristic
878	#103	C₂³×C₅₉	1	2	yes	—
879	#102	C₂³×C₅₉	1	1	yes	characteristic
880	#102	C₂³×C₅₉	1	2	yes	—
881	#102	C₂³×C₅₉	1	1	yes	characteristic
882	#102	C₂³×C₅₉	1	1	yes	characteristic
883	#102	C₂³×C₅₉	1	1	yes	characteristic
884	#102	C₂³×C₅₉	1	2	yes	—
885	#102	C₂³×C₅₉	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
890	#97	C₂³×C₅₉	1	2	yes	—
891	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₅₉	1	2	yes	—
894	#41	—	2	4	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
927	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
928	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
929	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
930	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
943	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
946	Q₁₆	—	2	4	no	—
947	Q₁₆	—	2	4	no	—
948	Q₁₆	—	2	2	no	—
949	SD₁₆	—	2	2	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	1	no	—
957	SD₁₆	—	4	2	no	—
958	D₈	—	4	2	no	—
959	D₈	—	4	1	no	—
960	M₁₆	—	4	2	no	—
961	M₁₆	—	4	2	no	—
962	C₂×C₈	—	4	2	no	—
963	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
967	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	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	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₅₉	1	2	yes	—
1036	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1041	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	8	2	no	—
1052	Q₈	—	8	2	no	—
1053	Q₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1107	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	C₅₉×#577	1	2	yes	—
1147	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1148	C₄	C₅₉×#585	1	1	yes	characteristic
1149	C₂	—	4	1	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	8	1	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	2	no	—
1154	C₂	C₅₉×#3488	1	1	yes	characteristic
1155	C₂	C₂×C₅₉×#577	1	1	yes	characteristic
1156	C₂	C₅₉×#3586	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×#3517	C₂	semidirect
3. C₅₉×#3397	C₂	semidirect
4. C₅₉×#3392	C₂	semidirect
5. C₅₉×#3374	C₂	semidirect
6. C₅₉×#3364	C₂	semidirect
7. C₅₉×#3330	C₂	semidirect
8. C₅₉×#3326	C₂	semidirect
9. C₅₉×#3320	C₂	semidirect
10. C₅₉×#3298	C₂	semidirect
11. C₅₉×#3284	C₂	semidirect
12. C₅₉×#3278	C₂	semidirect
13. C₅₉×#3278	C₂	semidirect
14. C₅₉×#3271	C₂	semidirect
15. C₅₉×#3260	C₂	semidirect
16. C₅₉×#3251	C₂	semidirect
17. C₅₉×#3221	C₂	semidirect
18. C₅₉×#3206	C₂	semidirect
19. C₅₉×#3120	C₂	semidirect
20. C₅₉×#3102	C₂	semidirect
21. C₅₉×#3046	C₂	semidirect
22. C₅₉×#3039	C₂	semidirect
23. C₅₉×#2993	C₂	semidirect
535. #62038	C₅₉	direct (N × H)
571. #3552	C₂×C₅₉	semidirect
572. #3517	C₂×C₅₉	semidirect
573. #3397	C₂×C₅₉	semidirect
574. #3392	C₂×C₅₉	semidirect
575. #3374	C₂×C₅₉	semidirect
576. #3364	C₂×C₅₉	semidirect
577. #3330	C₂×C₅₉	semidirect
578. #3326	C₂×C₅₉	semidirect
579. #3320	C₂×C₅₉	semidirect
580. #3298	C₂×C₅₉	semidirect
581. #3284	C₂×C₅₉	semidirect
582. #3278	C₂×C₅₉	semidirect
583. #3278	C₂×C₅₉	semidirect
584. #3271	C₂×C₅₉	semidirect
585. #3260	C₂×C₅₉	semidirect
586. #3251	C₂×C₅₉	semidirect
587. #3221	C₂×C₅₉	semidirect
588. #3206	C₂×C₅₉	semidirect
589. #3120	C₂×C₅₉	semidirect
590. #3102	C₂×C₅₉	semidirect
591. #3046	C₂×C₅₉	semidirect
592. #3039	C₂×C₅₉	semidirect
593. #2993	C₂×C₅₉	semidirect
713. C₅₉	#62038	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×#3517	2
C₅₉×#3397	2
C₅₉×#3392	2
C₅₉×#3374	2
C₅₉×#3364	2
C₅₉×#3330	2
C₅₉×#3326	2
C₅₉×#3320	2
C₅₉×#3298	2
C₅₉×#3284	2
C₅₉×#3278	2
C₅₉×#3271	2
C₅₉×#3260	2
C₅₉×#3251	2
C₅₉×#3221	2
C₅₉×#3206	2
C₅₉×#3120	2
C₅₉×#3102	2
C₅₉×#3046	2
C₅₉×#3039	2
C₅₉×#2993	2
#62038	59

Subgroups — C59×#62038 #28474147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62038 #28474147