Subgroups — C₅₉×#62253 #28474362

Order 15104.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3345	C₂	1	2	yes	maximal, complemented
4	C₅₉×#3343	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3318	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3310	C₂	1	2	yes	maximal, complemented
7	C₅₉×#3308	C₂	1	2	yes	maximal, complemented
8	C₅₉×#3306	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3265	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3264	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3247	C₂	1	2	yes	maximal, complemented
12	C₅₉×#3188	C₂	1	2	yes	maximal, complemented
13	C₅₉×#3187	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3180	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3055	C₂	1	2	yes	maximal, complemented
17	C₂×C₅₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₅₉	—	2	1	no	—
21	C₂×AGL(1,ℤ/8)×C₅₉	C₂²	1	2	yes	complemented
22	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
26	C₅₉×#553	—	2	2	no	—
27	C₅₉×#553	C₂²	1	2	yes	complemented
28	C₅₉×#552	C₂²	1	2	yes	complemented
29	C₅₉×#551	—	2	2	no	—
30	C₅₉×#548	C₂²	1	2	yes	complemented
31	C₅₉×#547	C₂²	1	2	yes	—
32	C₅₉×#547	C₂²	1	2	yes	complemented
33	C₅₉×#546	—	2	2	no	—
34	C₅₉×#546	—	2	2	no	—
35	C₅₉×#546	C₂²	1	2	yes	complemented
36	D₄²×C₅₉	C₂²	1	2	yes	—
37	D₄²×C₅₉	C₂²	1	2	yes	complemented
38	C₅₉×#539	—	2	1	no	—
39	C₅₉×#538	—	2	1	no	—
40	C₅₉×#537	—	2	1	no	—
41	C₅₉×#534	—	2	1	no	—
42	C₅₉×#534	—	2	1	no	—
43	C₅₉×#534	—	2	1	no	—
44	C₅₉×#532	C₂²	1	2	yes	complemented
45	C₅₉×#529	C₂²	1	2	yes	complemented
46	C₅₉×#525	C₂²	1	2	yes	complemented
47	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
52	C₅₉×#518	—	2	1	no	—
53	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
54	C₅₉×#501	C₂²	1	2	yes	complemented
55	C₅₉×#496	C₂²	1	2	yes	complemented
56	C₅₉×#490	C₂²	1	2	yes	complemented
57	C₅₉×#489	C₂²	1	2	yes	complemented
58	C₅₉×#484	C₂²	1	2	yes	complemented
59	C₅₉×#483	C₂²	1	2	yes	complemented
60	C₅₉×#482	C₂²	1	2	yes	complemented
61	C₅₉×#482	C₂²	1	2	yes	complemented
62	C₅₉×#481	C₂²	1	2	yes	complemented
63	C₅₉×#481	C₂²	1	2	yes	complemented
64	C₅₉×#480	C₂²	1	2	yes	complemented
65	C₅₉×#480	C₂²	1	2	yes	complemented
66	C₅₉×#478	C₂²	1	2	yes	complemented
67	C₅₉×#478	C₂²	1	2	yes	complemented
68	C₅₉×#477	C₂²	1	2	yes	complemented
69	C₅₉×#476	C₂²	1	2	yes	complemented
70	C₅₉×#469	C₂²	1	2	yes	complemented
71	C₅₉×#469	C₂²	1	2	yes	complemented
72	C₅₉×#468	C₂²	1	2	yes	complemented
73	C₅₉×#468	C₂²	1	2	yes	complemented
74	C₅₉×#466	C₂²	1	2	yes	complemented
75	C₅₉×#466	C₂²	1	2	yes	complemented
76	C₅₉×#466	C₂²	1	2	yes	complemented
77	C₅₉×#466	C₂²	1	2	yes	complemented
78	C₅₉×#466	C₂²	1	2	yes	complemented
79	C₅₉×#466	C₂²	1	2	yes	complemented
80	C₅₉×#465	C₂²	1	2	yes	complemented
81	C₅₉×#465	C₂²	1	2	yes	complemented
82	C₅₉×#465	C₂²	1	2	yes	complemented
83	C₅₉×#465	C₂²	1	2	yes	complemented
84	C₅₉×#465	C₂²	1	2	yes	complemented
85	C₅₉×#465	C₂²	1	2	yes	complemented
86	C₅₉×#463	C₂²	1	2	yes	complemented
87	C₅₉×#463	C₂²	1	2	yes	complemented
88	C₅₉×#460	C₂²	1	2	yes	complemented
89	C₅₉×#459	C₂²	1	2	yes	complemented
90	C₅₉×#450	C₂²	1	2	yes	complemented
91	C₅₉×#450	C₂²	1	2	yes	complemented
92	C₅₉×#449	C₂²	1	2	yes	complemented
93	C₅₉×#449	C₂²	1	2	yes	complemented
94	C₅₉×#448	C₂²	1	2	yes	complemented
95	C₅₉×#447	C₂²	1	2	yes	complemented
96	C₅₉×#447	C₂²	1	2	yes	complemented
97	C₅₉×#447	C₂²	1	2	yes	complemented
98	C₅₉×#442	C₂²	1	2	yes	complemented
99	C₅₉×#442	C₂²	1	2	yes	complemented
100	C₅₉×#440	C₂²	1	2	yes	complemented
101	C₅₉×#440	C₂²	1	2	yes	complemented
102	C₅₉×#435	C₂²	1	2	yes	complemented
103	C₅₉×#435	C₂²	1	2	yes	complemented
104	C₅₉×#435	C₂²	1	2	yes	complemented
105	C₅₉×#435	C₂²	1	2	yes	complemented
106	C₅₉×#428	C₂²	1	2	yes	complemented
107	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic, complemented
108	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
110	C₅₉×#418	C₂²	1	2	yes	complemented
111	C₅₉×#417	C₂²	1	2	yes	complemented
112	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
113	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic, complemented
114	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic, complemented
115	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
118	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic, complemented
119	H(5,𝔽₂)×C₅₉	—	4	8	no	—
120	C₂×#41×C₅₉	—	2	2	no	—
121	C₂×#41×C₅₉	—	2	2	no	—
122	C₂×#41×C₅₉	—	2	2	no	—
123	C₂×#41×C₅₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₉	—	2	1	no	—
126	C₂²×D₄×C₅₉	—	2	1	no	—
127	C₂²×D₄×C₅₉	—	2	1	no	—
128	C₂²×D₄×C₅₉	—	2	2	no	—
129	C₂²×D₄×C₅₉	—	2	2	no	—
130	C₂²×D₄×C₅₉	—	2	2	no	—
131	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
132	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
138	AGL(1,ℤ/8)×C₅₉	—	4	4	no	—
139	C₂×SD₁₆×C₅₉	—	4	2	no	—
140	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
144	C₂×D₈×C₅₉	—	4	2	no	—
145	C₂×D₈×C₅₉	C₂³	1	2	yes	—
146	C₂×D₈×C₅₉	C₂³	1	2	yes	—
147	C₂×D₈×C₅₉	C₂³	1	2	yes	—
148	C₂×D₈×C₅₉	C₂³	1	2	yes	—
149	C₂×M₁₆×C₅₉	—	4	2	no	—
150	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
151	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
152	C₂²×C₈×C₅₉	—	4	2	no	—
153	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
162	#127×C₅₉	C₂³	1	2	yes	—
163	#126×C₅₉	—	2	2	no	—
164	#126×C₅₉	—	2	2	no	—
165	#126×C₅₉	—	2	2	no	—
166	#125×C₅₉	—	2	2	no	—
167	#125×C₅₉	C₂³	1	2	yes	—
168	#124×C₅₉	—	2	2	no	—
169	#124×C₅₉	—	2	2	no	—
170	#124×C₅₉	C₂³	1	2	yes	—
171	#123×C₅₉	—	2	2	no	—
172	#123×C₅₉	—	2	2	no	—
173	#123×C₅₉	—	2	2	no	—
174	#123×C₅₉	—	2	2	no	—
175	#123×C₅₉	—	2	2	no	—
176	#123×C₅₉	—	2	2	no	—
177	#123×C₅₉	—	2	2	no	—
178	#123×C₅₉	—	2	2	no	—
179	#123×C₅₉	—	2	2	no	—
180	C₂²⋊Q₈×C₅₉	—	2	1	no	—
181	C₂²⋊Q₈×C₅₉	—	2	1	no	—
182	C₂²⋊Q₈×C₅₉	—	2	2	no	—
183	C₂²⋊Q₈×C₅₉	—	2	2	no	—
184	C₂²⋊Q₈×C₅₉	—	2	2	no	—
185	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
187	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
188	#121×C₅₉	—	2	2	no	—
189	#121×C₅₉	—	2	2	no	—
190	#121×C₅₉	—	2	1	no	—
191	#121×C₅₉	—	2	1	no	—
192	#121×C₅₉	—	2	1	no	—
193	#121×C₅₉	—	2	1	no	—
194	#121×C₅₉	—	2	2	no	—
195	#121×C₅₉	—	2	1	no	—
196	#121×C₅₉	—	2	2	no	—
197	#121×C₅₉	—	2	1	no	—
198	#121×C₅₉	—	2	2	no	—
199	#121×C₅₉	—	2	2	no	—
200	#121×C₅₉	—	2	2	no	—
201	#121×C₅₉	—	2	2	no	—
202	#121×C₅₉	C₂³	1	2	yes	—
203	#121×C₅₉	C₂³	1	2	yes	—
204	#121×C₅₉	C₂³	1	2	yes	—
205	#121×C₅₉	C₂³	1	2	yes	—
206	#121×C₅₉	C₂³	1	2	yes	—
207	#121×C₅₉	C₂³	1	2	yes	—
208	#121×C₅₉	C₂³	1	2	yes	—
209	#121×C₅₉	C₂³	1	2	yes	—
210	#121×C₅₉	C₂³	1	2	yes	—
211	#120×C₅₉	—	2	2	no	—
212	#120×C₅₉	—	2	2	no	—
213	#120×C₅₉	—	2	2	no	—
214	#120×C₅₉	—	2	2	no	—
215	#120×C₅₉	—	2	2	no	—
216	#120×C₅₉	—	2	2	no	—
217	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
218	C₄×D₄×C₅₉	—	2	2	no	—
219	C₄×D₄×C₅₉	—	2	2	no	—
220	C₄×D₄×C₅₉	—	2	2	no	—
221	C₄×D₄×C₅₉	—	2	2	no	—
222	C₄×D₄×C₅₉	—	2	2	no	—
223	C₄×D₄×C₅₉	—	2	2	no	—
224	C₄×D₄×C₅₉	D₄	1	2	yes	—
225	C₄×D₄×C₅₉	D₄	1	2	yes	—
226	C₄×D₄×C₅₉	C₂³	1	2	yes	—
227	C₄×D₄×C₅₉	C₂³	1	2	yes	—
228	C₄×D₄×C₅₉	C₂³	1	2	yes	—
229	C₄×D₄×C₅₉	C₂³	1	2	yes	—
230	C₄×D₄×C₅₉	C₂³	1	2	yes	—
231	#117×C₅₉	—	2	2	no	—
232	#117×C₅₉	—	2	2	no	—
233	#117×C₅₉	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
235	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
241	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
242	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
243	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
244	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
245	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
246	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
247	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
248	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
249	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
250	#107×C₅₉	C₂³	1	2	yes	—
251	#107×C₅₉	C₂³	1	2	yes	—
252	#107×C₅₉	C₂³	1	2	yes	—
253	#107×C₅₉	C₂³	1	2	yes	—
254	#106×C₅₉	C₂³	1	2	yes	—
255	#106×C₅₉	C₂³	1	2	yes	—
256	#106×C₅₉	C₂³	1	2	yes	—
257	#106×C₅₉	C₂³	1	2	yes	—
258	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
259	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
260	#103×C₅₉	C₂³	1	2	yes	—
261	#103×C₅₉	C₂³	1	2	yes	—
262	#103×C₅₉	C₂³	1	2	yes	—
263	#103×C₅₉	C₂³	1	2	yes	—
264	#102×C₅₉	C₂³	1	2	yes	—
265	#102×C₅₉	C₂³	1	2	yes	—
266	#102×C₅₉	C₂³	1	2	yes	—
267	#102×C₅₉	C₂³	1	2	yes	—
268	#102×C₅₉	C₂³	1	2	yes	—
269	#102×C₅₉	C₂³	1	2	yes	—
270	#102×C₅₉	C₂³	1	2	yes	—
271	#102×C₅₉	C₂³	1	2	yes	—
272	#102×C₅₉	C₂³	1	2	yes	—
273	#102×C₅₉	C₂³	1	2	yes	—
274	#102×C₅₉	C₂³	1	2	yes	—
275	#102×C₅₉	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
280	#97×C₅₉	C₂³	1	2	yes	—
281	#97×C₅₉	C₂³	1	2	yes	—
282	C₂⁴×C₅₉	—	2	1	no	—
283	C₂⁴×C₅₉	—	2	2	no	—
284	C₂⁴×C₅₉	—	2	1	no	—
285	C₂⁴×C₅₉	—	2	1	no	—
286	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
287	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
288	#41×C₅₉	—	4	8	no	—
289	#41×C₅₉	—	4	2	no	—
290	#41×C₅₉	—	4	2	no	—
291	#41×C₅₉	—	4	8	no	—
292	#41×C₅₉	—	4	8	no	—
293	C₂×Q₈×C₅₉	—	2	2	no	—
294	C₂×Q₈×C₅₉	—	2	1	no	—
295	C₂×Q₈×C₅₉	—	4	1	no	—
296	C₂×Q₈×C₅₉	—	4	1	no	—
297	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
298	C₂×D₄×C₅₉	—	2	4	no	—
299	C₂×D₄×C₅₉	—	2	2	no	—
300	C₂×D₄×C₅₉	—	2	2	no	—
301	C₂×D₄×C₅₉	—	2	2	no	—
302	C₂×D₄×C₅₉	—	2	2	no	—
303	C₂×D₄×C₅₉	—	2	2	no	—
304	C₂×D₄×C₅₉	—	2	2	no	—
305	C₂×D₄×C₅₉	—	2	2	no	—
306	C₂×D₄×C₅₉	—	2	2	no	—
307	C₂×D₄×C₅₉	—	2	2	no	—
308	C₂×D₄×C₅₉	—	2	2	no	—
309	C₂×D₄×C₅₉	—	2	2	no	—
310	C₂×D₄×C₅₉	—	2	2	no	—
311	C₂×D₄×C₅₉	—	2	2	no	—
312	C₂×D₄×C₅₉	—	2	1	no	—
313	C₂×D₄×C₅₉	—	2	1	no	—
314	C₂×D₄×C₅₉	—	2	1	no	—
315	C₂×D₄×C₅₉	—	4	1	no	—
316	C₂×D₄×C₅₉	—	4	1	no	—
317	C₂×D₄×C₅₉	—	4	1	no	—
318	C₂×D₄×C₅₉	—	4	2	no	—
319	C₂×D₄×C₅₉	—	4	1	no	—
320	C₂×D₄×C₅₉	—	4	1	no	—
321	C₂×D₄×C₅₉	—	4	1	no	—
322	C₂×D₄×C₅₉	—	4	2	no	—
323	C₂×D₄×C₅₉	—	4	8	no	—
324	C₂×D₄×C₅₉	—	4	8	no	—
325	C₂×D₄×C₅₉	—	4	8	no	—
326	C₂×D₄×C₅₉	—	4	4	no	—
327	C₂×D₄×C₅₉	—	4	4	no	—
328	C₂×D₄×C₅₉	—	4	4	no	—
329	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
331	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
332	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
333	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₅₉	—	2	1	no	—
335	C₂²×C₄×C₅₉	—	2	2	no	—
336	C₂²×C₄×C₅₉	—	2	1	no	—
337	C₂²×C₄×C₅₉	—	2	1	no	—
338	C₂²×C₄×C₅₉	—	2	1	no	—
339	C₂²×C₄×C₅₉	—	2	1	no	—
340	C₂²×C₄×C₅₉	—	2	2	no	—
341	C₂²×C₄×C₅₉	—	2	2	no	—
342	C₂²×C₄×C₅₉	—	2	2	no	—
343	C₂²×C₄×C₅₉	—	2	2	no	—
344	C₂²×C₄×C₅₉	—	4	1	no	—
345	C₂²×C₄×C₅₉	—	4	1	no	—
346	C₂²×C₄×C₅₉	—	4	1	no	—
347	C₂²×C₄×C₅₉	—	4	1	no	—
348	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
359	SD₁₆×C₅₉	—	2	4	no	—
360	SD₁₆×C₅₉	—	4	2	no	—
361	SD₁₆×C₅₉	—	4	2	no	—
362	SD₁₆×C₅₉	—	4	2	no	—
363	D₈×C₅₉	—	2	4	no	—
364	D₈×C₅₉	—	4	2	no	—
365	D₈×C₅₉	—	4	2	no	—
366	D₈×C₅₉	—	4	2	no	—
367	M₁₆×C₅₉	—	2	4	no	—
368	M₁₆×C₅₉	—	4	2	no	—
369	C₂×C₈×C₅₉	—	2	2	no	—
370	C₂×C₈×C₅₉	—	2	2	no	—
371	C₂×C₈×C₅₉	—	2	2	no	—
372	C₂×C₈×C₅₉	—	4	1	no	—
373	C₂×C₈×C₅₉	—	4	1	no	—
374	C₂×C₈×C₅₉	—	4	1	no	—
375	C₂×C₈×C₅₉	—	4	1	no	—
376	C₂×C₈×C₅₉	—	4	1	no	—
377	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
378	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
381	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₅₉	—	2	2	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	1	no	—
389	C₄⋊C₄×C₅₉	—	2	1	no	—
390	C₄⋊C₄×C₅₉	—	2	2	no	—
391	C₄⋊C₄×C₅₉	—	2	2	no	—
392	C₄⋊C₄×C₅₉	—	2	2	no	—
393	C₄⋊C₄×C₅₉	—	2	2	no	—
394	C₄⋊C₄×C₅₉	—	2	2	no	—
395	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
401	C₂²⋊C₄×C₅₉	—	2	2	no	—
402	C₂²⋊C₄×C₅₉	—	2	2	no	—
403	C₂²⋊C₄×C₅₉	—	2	2	no	—
404	C₂²⋊C₄×C₅₉	—	2	2	no	—
405	C₂²⋊C₄×C₅₉	—	2	2	no	—
406	C₂²⋊C₄×C₅₉	—	2	2	no	—
407	C₂²⋊C₄×C₅₉	—	2	2	no	—
408	C₂²⋊C₄×C₅₉	—	2	2	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	2	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	2	no	—
419	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
423	C₄²×C₅₉	—	2	2	no	—
424	C₄²×C₅₉	—	2	2	no	—
425	C₄²×C₅₉	C₂×D₄	1	2	yes	—
426	C₄²×C₅₉	C₂⁴	1	2	yes	—
427	C₂³×C₅₉	—	2	2	no	—
428	C₂³×C₅₉	—	2	2	no	—
429	C₂³×C₅₉	—	2	2	no	—
430	C₂³×C₅₉	—	2	2	no	—
431	C₂³×C₅₉	—	4	1	no	—
432	C₂³×C₅₉	—	4	1	no	—
433	C₂³×C₅₉	—	4	1	no	—
434	C₂³×C₅₉	—	4	1	no	—
435	C₂³×C₅₉	—	4	4	no	—
436	C₂³×C₅₉	—	4	2	no	—
437	C₂³×C₅₉	—	4	2	no	—
438	C₂³×C₅₉	—	4	2	no	—
439	C₂³×C₅₉	—	8	1	no	—
440	C₂³×C₅₉	—	8	1	no	—
441	C₂³×C₅₉	—	8	1	no	—
442	C₂³×C₅₉	—	8	2	no	—
443	C₂³×C₅₉	—	8	1	no	—
444	C₂³×C₅₉	—	8	1	no	—
445	C₂³×C₅₉	—	8	1	no	—
446	C₂³×C₅₉	—	8	2	no	—
447	C₂³×C₅₉	AGL(1,ℤ/8)	1	4	yes	complemented
448	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
449	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₅₉	—	2	2	no	—
453	Q₈×C₅₉	—	2	2	no	—
454	Q₈×C₅₉	—	4	4	no	—
455	Q₈×C₅₉	—	8	1	no	—
456	D₄×C₅₉	—	2	4	no	—
457	D₄×C₅₉	—	2	4	no	—
458	D₄×C₅₉	—	2	2	no	—
459	D₄×C₅₉	—	2	2	no	—
460	D₄×C₅₉	—	2	2	no	—
461	D₄×C₅₉	—	2	2	no	—
462	D₄×C₅₉	—	2	2	no	—
463	D₄×C₅₉	—	2	2	no	—
464	D₄×C₅₉	—	4	4	no	—
465	D₄×C₅₉	—	4	4	no	—
466	D₄×C₅₉	—	4	4	no	—
467	D₄×C₅₉	—	4	4	no	—
468	D₄×C₅₉	—	4	4	no	—
469	D₄×C₅₉	—	4	4	no	—
470	D₄×C₅₉	—	4	4	no	—
471	D₄×C₅₉	—	4	4	no	—
472	D₄×C₅₉	—	4	4	no	—
473	D₄×C₅₉	—	8	2	no	—
474	D₄×C₅₉	—	8	2	no	—
475	D₄×C₅₉	—	8	1	no	—
476	D₄×C₅₉	—	8	1	no	—
477	D₄×C₅₉	—	8	1	no	—
478	D₄×C₅₉	—	8	2	no	—
479	D₄×C₅₉	—	8	2	no	—
480	C₂×C₄×C₅₉	—	2	2	no	—
481	C₂×C₄×C₅₉	—	2	1	no	—
482	C₂×C₄×C₅₉	—	2	1	no	—
483	C₂×C₄×C₅₉	—	2	1	no	—
484	C₂×C₄×C₅₉	—	2	2	no	—
485	C₂×C₄×C₅₉	—	2	1	no	—
486	C₂×C₄×C₅₉	—	2	1	no	—
487	C₂×C₄×C₅₉	—	2	1	no	—
488	C₂×C₄×C₅₉	—	2	2	no	—
489	C₂×C₄×C₅₉	—	2	2	no	—
490	C₂×C₄×C₅₉	—	2	2	no	—
491	C₂×C₄×C₅₉	—	2	2	no	—
492	C₂×C₄×C₅₉	—	2	2	no	—
493	C₂×C₄×C₅₉	—	2	2	no	—
494	C₂×C₄×C₅₉	—	4	2	no	—
495	C₂×C₄×C₅₉	—	4	1	no	—
496	C₂×C₄×C₅₉	—	4	1	no	—
497	C₂×C₄×C₅₉	—	4	1	no	—
498	C₂×C₄×C₅₉	—	4	1	no	—
499	C₂×C₄×C₅₉	—	4	1	no	—
500	C₂×C₄×C₅₉	—	4	4	no	—
501	C₂×C₄×C₅₉	—	4	4	no	—
502	C₂×C₄×C₅₉	—	4	4	no	—
503	C₂×C₄×C₅₉	—	4	2	no	—
504	C₂×C₄×C₅₉	—	4	2	no	—
505	C₂×C₄×C₅₉	—	4	2	no	—
506	C₂×C₄×C₅₉	—	8	2	no	—
507	C₂×C₄×C₅₉	—	8	2	no	—
508	C₂×C₄×C₅₉	—	8	1	no	—
509	C₂×C₄×C₅₉	—	8	1	no	—
510	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
517	C₈×C₅₉	—	2	1	no	—
518	C₈×C₅₉	—	2	1	no	—
519	C₈×C₅₉	—	2	1	no	—
520	C₈×C₅₉	—	2	2	no	—
521	C₈×C₅₉	—	2	2	no	—
522	C₈×C₅₉	H(5,𝔽₂)	1	2	yes	complemented
523	#62253	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
524	C₂²×C₅₉	—	2	1	no	—
525	C₂²×C₅₉	—	2	1	no	—
526	C₂²×C₅₉	—	2	1	no	—
527	C₂²×C₅₉	—	2	1	no	—
528	C₂²×C₅₉	—	2	1	no	—
529	C₂²×C₅₉	—	2	1	no	—
530	C₂²×C₅₉	—	2	2	no	—
531	C₂²×C₅₉	—	2	2	no	—
532	C₂²×C₅₉	—	2	2	no	—
533	C₂²×C₅₉	—	4	4	no	—
534	C₂²×C₅₉	—	4	2	no	—
535	C₂²×C₅₉	—	4	2	no	—
536	C₂²×C₅₉	—	4	2	no	—
537	C₂²×C₅₉	—	4	2	no	—
538	C₂²×C₅₉	—	4	2	no	—
539	C₂²×C₅₉	—	4	2	no	—
540	C₂²×C₅₉	—	4	2	no	—
541	C₂²×C₅₉	—	4	2	no	—
542	C₂²×C₅₉	—	4	2	no	—
543	C₂²×C₅₉	—	8	2	no	—
544	C₂²×C₅₉	—	16	2	no	—
545	C₂²×C₅₉	—	16	2	no	—
546	C₂²×C₅₉	—	16	2	no	—
547	C₂²×C₅₉	—	16	4	no	—
548	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
549	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
550	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
551	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₅₉	—	2	2	no	—
553	C₄×C₅₉	—	2	1	no	—
554	C₄×C₅₉	—	2	2	no	—
555	C₄×C₅₉	—	2	1	no	—
556	C₄×C₅₉	—	2	1	no	—
557	C₄×C₅₉	—	2	2	no	—
558	C₄×C₅₉	—	4	2	no	—
559	C₄×C₅₉	—	4	2	no	—
560	C₄×C₅₉	—	4	2	no	—
561	C₄×C₅₉	—	4	2	no	—
562	C₄×C₅₉	—	4	2	no	—
563	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	C₄×C₅₉	#585	1	1	yes	characteristic
565	#3505	C₂×C₅₉	1	1	yes	characteristic, complemented
566	#3496	C₂×C₅₉	1	1	yes	characteristic, complemented
567	#3345	C₂×C₅₉	1	2	yes	complemented
568	#3343	C₂×C₅₉	1	2	yes	complemented
569	#3318	C₂×C₅₉	1	2	yes	complemented
570	#3310	C₂×C₅₉	1	2	yes	complemented
571	#3308	C₂×C₅₉	1	2	yes	complemented
572	#3306	C₂×C₅₉	1	2	yes	complemented
573	#3265	C₂×C₅₉	1	2	yes	complemented
574	#3264	C₂×C₅₉	1	2	yes	complemented
575	#3247	C₂×C₅₉	1	2	yes	complemented
576	#3188	C₂×C₅₉	1	2	yes	complemented
577	#3187	C₂×C₅₉	1	1	yes	characteristic, complemented
578	#3186	C₂×C₅₉	1	1	yes	characteristic, complemented
579	#3180	C₂×C₅₉	1	2	yes	complemented
580	#3055	C₂×C₅₉	1	2	yes	complemented
581	C₂×#466	C₂×C₅₉	1	1	yes	characteristic, complemented
582	C₂×#465	C₂×C₅₉	1	1	yes	characteristic, complemented
583	C₂×#435	C₂×C₅₉	1	1	yes	characteristic, complemented
584	C₂×C₅₉	—	2	2	no	—
585	C₂×C₅₉	—	2	2	no	—
586	C₂×C₅₉	—	2	2	no	—
587	C₂×C₅₉	—	4	2	no	—
588	C₂×C₅₉	—	8	2	no	—
589	C₂×C₅₉	—	8	2	no	—
590	C₂×C₅₉	—	8	2	no	—
591	C₂×C₅₉	#3496	1	1	yes	characteristic
592	C₂×C₅₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
593	C₂×C₅₉	#3584	1	1	yes	characteristic
594	C₂×H(5,𝔽₂)	—	2	1	no	—
595	C₂×AGL(1,ℤ/8)	C₂²×C₅₉	1	2	yes	complemented
596	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
597	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
598	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
599	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
600	#553	—	2	2	no	—
601	#553	C₂²×C₅₉	1	2	yes	complemented
602	#552	C₂²×C₅₉	1	2	yes	complemented
603	#551	—	2	2	no	—
604	#548	C₂²×C₅₉	1	2	yes	complemented
605	#547	C₂²×C₅₉	1	2	yes	—
606	#547	C₂²×C₅₉	1	2	yes	complemented
607	#546	—	2	2	no	—
608	#546	—	2	2	no	—
609	#546	C₂²×C₅₉	1	2	yes	complemented
610	D₄²	C₂²×C₅₉	1	2	yes	—
611	D₄²	C₂²×C₅₉	1	2	yes	complemented
612	#539	—	2	1	no	—
613	#538	—	2	1	no	—
614	#537	—	2	1	no	—
615	#534	—	2	1	no	—
616	#534	—	2	1	no	—
617	#534	—	2	1	no	—
618	#532	C₂²×C₅₉	1	2	yes	complemented
619	#529	C₂²×C₅₉	1	2	yes	complemented
620	#525	C₂²×C₅₉	1	2	yes	complemented
621	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
622	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
623	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
624	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic, complemented
625	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
626	#518	—	2	1	no	—
627	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
628	#501	C₂²×C₅₉	1	2	yes	complemented
629	#496	C₂²×C₅₉	1	2	yes	complemented
630	#490	C₂²×C₅₉	1	2	yes	complemented
631	#489	C₂²×C₅₉	1	2	yes	complemented
632	#484	C₂²×C₅₉	1	2	yes	complemented
633	#483	C₂²×C₅₉	1	2	yes	complemented
634	#482	C₂²×C₅₉	1	2	yes	complemented
635	#482	C₂²×C₅₉	1	2	yes	complemented
636	#481	C₂²×C₅₉	1	2	yes	complemented
637	#481	C₂²×C₅₉	1	2	yes	complemented
638	#480	C₂²×C₅₉	1	2	yes	complemented
639	#480	C₂²×C₅₉	1	2	yes	complemented
640	#478	C₂²×C₅₉	1	2	yes	complemented
641	#478	C₂²×C₅₉	1	2	yes	complemented
642	#477	C₂²×C₅₉	1	2	yes	complemented
643	#476	C₂²×C₅₉	1	2	yes	complemented
644	#469	C₂²×C₅₉	1	2	yes	complemented
645	#469	C₂²×C₅₉	1	2	yes	complemented
646	#468	C₂²×C₅₉	1	2	yes	complemented
647	#468	C₂²×C₅₉	1	2	yes	complemented
648	#466	C₂²×C₅₉	1	2	yes	complemented
649	#466	C₂²×C₅₉	1	2	yes	complemented
650	#466	C₂²×C₅₉	1	2	yes	complemented
651	#466	C₂²×C₅₉	1	2	yes	complemented
652	#466	C₂²×C₅₉	1	2	yes	complemented
653	#466	C₂²×C₅₉	1	2	yes	complemented
654	#465	C₂²×C₅₉	1	2	yes	complemented
655	#465	C₂²×C₅₉	1	2	yes	complemented
656	#465	C₂²×C₅₉	1	2	yes	complemented
657	#465	C₂²×C₅₉	1	2	yes	complemented
658	#465	C₂²×C₅₉	1	2	yes	complemented
659	#465	C₂²×C₅₉	1	2	yes	complemented
660	#463	C₂²×C₅₉	1	2	yes	complemented
661	#463	C₂²×C₅₉	1	2	yes	complemented
662	#460	C₂²×C₅₉	1	2	yes	complemented
663	#459	C₂²×C₅₉	1	2	yes	complemented
664	#450	C₂²×C₅₉	1	2	yes	complemented
665	#450	C₂²×C₅₉	1	2	yes	complemented
666	#449	C₂²×C₅₉	1	2	yes	complemented
667	#449	C₂²×C₅₉	1	2	yes	complemented
668	#448	C₂²×C₅₉	1	2	yes	complemented
669	#447	C₂²×C₅₉	1	2	yes	complemented
670	#447	C₂²×C₅₉	1	2	yes	complemented
671	#447	C₂²×C₅₉	1	2	yes	complemented
672	#442	C₂²×C₅₉	1	2	yes	complemented
673	#442	C₂²×C₅₉	1	2	yes	complemented
674	#440	C₂²×C₅₉	1	2	yes	complemented
675	#440	C₂²×C₅₉	1	2	yes	complemented
676	#435	C₂²×C₅₉	1	2	yes	complemented
677	#435	C₂²×C₅₉	1	2	yes	complemented
678	#435	C₂²×C₅₉	1	2	yes	complemented
679	#435	C₂²×C₅₉	1	2	yes	complemented
680	#428	C₂²×C₅₉	1	2	yes	complemented
681	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic, complemented
682	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic, complemented
683	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
684	#418	C₂²×C₅₉	1	2	yes	complemented
685	#417	C₂²×C₅₉	1	2	yes	complemented
686	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
687	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic, complemented
688	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic, complemented
689	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic, complemented
690	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
691	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
692	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic, complemented
693	C₅₉	#62253	1	1	yes	characteristic, direct product factor, Sylow
694	H(5,𝔽₂)	—	4	8	no	—
695	C₂×#41	—	2	2	no	—
696	C₂×#41	—	2	2	no	—
697	C₂×#41	—	2	2	no	—
698	C₂×#41	C₂³×C₅₉	1	2	yes	—
699	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
700	C₂²×D₄	—	2	1	no	—
701	C₂²×D₄	—	2	1	no	—
702	C₂²×D₄	—	2	1	no	—
703	C₂²×D₄	—	2	2	no	—
704	C₂²×D₄	—	2	2	no	—
705	C₂²×D₄	—	2	2	no	—
706	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
708	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
709	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
710	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
711	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
712	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
713	AGL(1,ℤ/8)	—	4	4	no	—
714	C₂×SD₁₆	—	4	2	no	—
715	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
719	C₂×D₈	—	4	2	no	—
720	C₂×D₈	C₂³×C₅₉	1	2	yes	—
721	C₂×D₈	C₂³×C₅₉	1	2	yes	—
722	C₂×D₈	C₂³×C₅₉	1	2	yes	—
723	C₂×D₈	C₂³×C₅₉	1	2	yes	—
724	C₂×M₁₆	—	4	2	no	—
725	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
726	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
727	C₂²×C₈	—	4	2	no	—
728	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
731	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
732	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
733	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
734	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
735	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
737	#127	C₂³×C₅₉	1	2	yes	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	C₂³×C₅₉	1	2	yes	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	C₂³×C₅₉	1	2	yes	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
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	2	no	—
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	C₂³×C₅₉	1	2	yes	—
778	#121	C₂³×C₅₉	1	2	yes	—
779	#121	C₂³×C₅₉	1	2	yes	—
780	#121	C₂³×C₅₉	1	2	yes	—
781	#121	C₂³×C₅₉	1	2	yes	—
782	#121	C₂³×C₅₉	1	2	yes	—
783	#121	C₂³×C₅₉	1	2	yes	—
784	#121	C₂³×C₅₉	1	2	yes	—
785	#121	C₂³×C₅₉	1	2	yes	—
786	#120	—	2	2	no	—
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	#120	—	2	2	no	—
792	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	D₄×C₅₉	1	2	yes	—
800	C₄×D₄	D₄×C₅₉	1	2	yes	—
801	C₄×D₄	C₂³×C₅₉	1	2	yes	—
802	C₄×D₄	C₂³×C₅₉	1	2	yes	—
803	C₄×D₄	C₂³×C₅₉	1	2	yes	—
804	C₄×D₄	C₂³×C₅₉	1	2	yes	—
805	C₄×D₄	C₂³×C₅₉	1	2	yes	—
806	#117	—	2	2	no	—
807	#117	—	2	2	no	—
808	#117	C₂³×C₅₉	1	2	yes	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
811	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
812	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
813	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
814	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
815	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	2	1	no	—
818	C₂×C₂²⋊C₄	—	2	1	no	—
819	C₂×C₂²⋊C₄	—	2	2	no	—
820	C₂×C₂²⋊C₄	—	2	1	no	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
823	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
824	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
825	#107	C₂³×C₅₉	1	2	yes	—
826	#107	C₂³×C₅₉	1	2	yes	—
827	#107	C₂³×C₅₉	1	2	yes	—
828	#107	C₂³×C₅₉	1	2	yes	—
829	#106	C₂³×C₅₉	1	2	yes	—
830	#106	C₂³×C₅₉	1	2	yes	—
831	#106	C₂³×C₅₉	1	2	yes	—
832	#106	C₂³×C₅₉	1	2	yes	—
833	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
834	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
835	#103	C₂³×C₅₉	1	2	yes	—
836	#103	C₂³×C₅₉	1	2	yes	—
837	#103	C₂³×C₅₉	1	2	yes	—
838	#103	C₂³×C₅₉	1	2	yes	—
839	#102	C₂³×C₅₉	1	2	yes	—
840	#102	C₂³×C₅₉	1	2	yes	—
841	#102	C₂³×C₅₉	1	2	yes	—
842	#102	C₂³×C₅₉	1	2	yes	—
843	#102	C₂³×C₅₉	1	2	yes	—
844	#102	C₂³×C₅₉	1	2	yes	—
845	#102	C₂³×C₅₉	1	2	yes	—
846	#102	C₂³×C₅₉	1	2	yes	—
847	#102	C₂³×C₅₉	1	2	yes	—
848	#102	C₂³×C₅₉	1	2	yes	—
849	#102	C₂³×C₅₉	1	2	yes	—
850	#102	C₂³×C₅₉	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
852	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
855	#97	C₂³×C₅₉	1	2	yes	—
856	#97	C₂³×C₅₉	1	2	yes	—
857	C₂⁴	—	2	1	no	—
858	C₂⁴	—	2	2	no	—
859	C₂⁴	—	2	1	no	—
860	C₂⁴	—	2	1	no	—
861	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
862	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
863	#41	—	4	8	no	—
864	#41	—	4	2	no	—
865	#41	—	4	2	no	—
866	#41	—	4	8	no	—
867	#41	—	4	8	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	4	1	no	—
871	C₂×Q₈	—	4	1	no	—
872	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	4	1	no	—
891	C₂×D₄	—	4	1	no	—
892	C₂×D₄	—	4	1	no	—
893	C₂×D₄	—	4	2	no	—
894	C₂×D₄	—	4	1	no	—
895	C₂×D₄	—	4	1	no	—
896	C₂×D₄	—	4	1	no	—
897	C₂×D₄	—	4	2	no	—
898	C₂×D₄	—	4	8	no	—
899	C₂×D₄	—	4	8	no	—
900	C₂×D₄	—	4	8	no	—
901	C₂×D₄	—	4	4	no	—
902	C₂×D₄	—	4	4	no	—
903	C₂×D₄	—	4	4	no	—
904	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
905	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
906	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
907	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
908	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	4	1	no	—
920	C₂²×C₄	—	4	1	no	—
921	C₂²×C₄	—	4	1	no	—
922	C₂²×C₄	—	4	1	no	—
923	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
924	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
925	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
928	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
929	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
934	SD₁₆	—	2	4	no	—
935	SD₁₆	—	4	2	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	D₈	—	2	4	no	—
939	D₈	—	4	2	no	—
940	D₈	—	4	2	no	—
941	D₈	—	4	2	no	—
942	M₁₆	—	2	4	no	—
943	M₁₆	—	4	2	no	—
944	C₂×C₈	—	2	2	no	—
945	C₂×C₈	—	2	2	no	—
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	4	1	no	—
948	C₂×C₈	—	4	1	no	—
949	C₂×C₈	—	4	1	no	—
950	C₂×C₈	—	4	1	no	—
951	C₂×C₈	—	4	1	no	—
952	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
953	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
956	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	C₂×D₄×C₅₉	1	2	yes	—
1001	C₄²	C₂⁴×C₅₉	1	2	yes	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	4	1	no	—
1007	C₂³	—	4	1	no	—
1008	C₂³	—	4	1	no	—
1009	C₂³	—	4	1	no	—
1010	C₂³	—	4	4	no	—
1011	C₂³	—	4	2	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	4	2	no	—
1014	C₂³	—	8	1	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	2	no	—
1018	C₂³	—	8	1	no	—
1019	C₂³	—	8	1	no	—
1020	C₂³	—	8	1	no	—
1021	C₂³	—	8	2	no	—
1022	C₂³	AGL(1,ℤ/8)×C₅₉	1	4	yes	complemented
1023	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1024	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1025	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1026	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	4	4	no	—
1030	Q₈	—	8	1	no	—
1031	D₄	—	2	4	no	—
1032	D₄	—	2	4	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	4	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	1	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	4	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	1	no	—
1084	C₂×C₄	—	8	1	no	—
1085	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1091	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	2	2	no	—
1096	C₈	—	2	2	no	—
1097	C₈	H(5,𝔽₂)×C₅₉	1	2	yes	complemented
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	4	4	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	8	2	no	—
1118	C₂²	—	16	2	no	—
1119	C₂²	—	16	2	no	—
1120	C₂²	—	16	2	no	—
1121	C₂²	—	16	4	no	—
1122	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
1123	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
1124	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
1125	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	2	no	—
1137	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1138	C₄	C₅₉×#585	1	1	yes	characteristic
1139	C₂	—	2	2	no	—
1140	C₂	—	2	2	no	—
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	8	2	no	—
1144	C₂	—	8	2	no	—
1145	C₂	—	8	2	no	—
1146	C₂	C₅₉×#3496	1	1	yes	characteristic
1147	C₂	C₂²×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
1148	C₂	C₅₉×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3505	C₂	semidirect
2. C₅₉×#3496	C₂	semidirect
3. C₅₉×#3345	C₂	semidirect
4. C₅₉×#3343	C₂	semidirect
5. C₅₉×#3318	C₂	semidirect
6. C₅₉×#3310	C₂	semidirect
7. C₅₉×#3308	C₂	semidirect
8. C₅₉×#3306	C₂	semidirect
9. C₅₉×#3265	C₂	semidirect
10. C₅₉×#3264	C₂	semidirect
11. C₅₉×#3247	C₂	semidirect
12. C₅₉×#3188	C₂	semidirect
13. C₅₉×#3187	C₂	semidirect
14. C₅₉×#3186	C₂	semidirect
15. C₅₉×#3180	C₂	semidirect
16. C₅₉×#3055	C₂	semidirect
17. C₂×C₅₉×#466	C₂	semidirect
18. C₂×C₅₉×#465	C₂	semidirect
19. C₂×C₅₉×#435	C₂	semidirect
21. C₂×AGL(1,ℤ/8)×C₅₉	C₂²	semidirect
22. C₂²×SD₁₆×C₅₉	C₂²	semidirect
23. C₂²×D₈×C₅₉	C₂²	semidirect
24. C₂²×M₁₆×C₅₉	C₂²	semidirect
25. C₂³×C₈×C₅₉	C₂²	semidirect
27. C₅₉×#553	C₂²	semidirect
28. C₅₉×#552	C₂²	semidirect
30. C₅₉×#548	C₂²	semidirect
32. C₅₉×#547	C₂²	semidirect
35. C₅₉×#546	C₂²	semidirect
37. D₄²×C₅₉	C₂²	semidirect
44. C₅₉×#532	C₂²	semidirect
45. C₅₉×#529	C₂²	semidirect
46. C₅₉×#525	C₂²	semidirect
47. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
50. C₂×#121×C₅₉	C₂²	semidirect
51. C₂×#121×C₅₉	C₂²	semidirect
54. C₅₉×#501	C₂²	semidirect
55. C₅₉×#496	C₂²	semidirect
56. C₅₉×#490	C₂²	semidirect
57. C₅₉×#489	C₂²	semidirect
58. C₅₉×#484	C₂²	semidirect
59. C₅₉×#483	C₂²	semidirect
60. C₅₉×#482	C₂²	semidirect
61. C₅₉×#482	C₂²	semidirect
62. C₅₉×#481	C₂²	semidirect
63. C₅₉×#481	C₂²	semidirect
64. C₅₉×#480	C₂²	semidirect
65. C₅₉×#480	C₂²	semidirect
66. C₅₉×#478	C₂²	semidirect
67. C₅₉×#478	C₂²	semidirect
68. C₅₉×#477	C₂²	semidirect
69. C₅₉×#476	C₂²	semidirect
70. C₅₉×#469	C₂²	semidirect
71. C₅₉×#469	C₂²	semidirect
72. C₅₉×#468	C₂²	semidirect
73. C₅₉×#468	C₂²	semidirect
74. C₅₉×#466	C₂²	semidirect
75. C₅₉×#466	C₂²	semidirect
76. C₅₉×#466	C₂²	semidirect
77. C₅₉×#466	C₂²	semidirect
78. C₅₉×#466	C₂²	semidirect
79. C₅₉×#466	C₂²	semidirect
80. C₅₉×#465	C₂²	semidirect
81. C₅₉×#465	C₂²	semidirect
82. C₅₉×#465	C₂²	semidirect
83. C₅₉×#465	C₂²	semidirect
84. C₅₉×#465	C₂²	semidirect
85. C₅₉×#465	C₂²	semidirect
86. C₅₉×#463	C₂²	semidirect
87. C₅₉×#463	C₂²	semidirect
88. C₅₉×#460	C₂²	semidirect
89. C₅₉×#459	C₂²	semidirect
90. C₅₉×#450	C₂²	semidirect
91. C₅₉×#450	C₂²	semidirect
92. C₅₉×#449	C₂²	semidirect
93. C₅₉×#449	C₂²	semidirect
94. C₅₉×#448	C₂²	semidirect
95. C₅₉×#447	C₂²	semidirect
96. C₅₉×#447	C₂²	semidirect
97. C₅₉×#447	C₂²	semidirect
98. C₅₉×#442	C₂²	semidirect
99. C₅₉×#442	C₂²	semidirect
100. C₅₉×#440	C₂²	semidirect
101. C₅₉×#440	C₂²	semidirect
102. C₅₉×#435	C₂²	semidirect
103. C₅₉×#435	C₂²	semidirect
104. C₅₉×#435	C₂²	semidirect
105. C₅₉×#435	C₂²	semidirect
106. C₅₉×#428	C₂²	semidirect
107. C₂×#107×C₅₉	C₂²	semidirect
108. C₂×#106×C₅₉	C₂²	semidirect
109. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
110. C₅₉×#418	C₂²	semidirect
111. C₅₉×#417	C₂²	semidirect
112. C₂×#103×C₅₉	C₂²	semidirect
113. C₂×#102×C₅₉	C₂²	semidirect
114. C₂×#102×C₅₉	C₂²	semidirect
115. C₂×#102×C₅₉	C₂²	semidirect
116. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
117. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
118. C₂×#97×C₅₉	C₂²	semidirect
447. C₂³×C₅₉	AGL(1,ℤ/8)	semidirect
522. C₈×C₅₉	H(5,𝔽₂)	semidirect
523. #62253	C₅₉	direct (N × H)
565. #3505	C₂×C₅₉	semidirect
566. #3496	C₂×C₅₉	semidirect
567. #3345	C₂×C₅₉	semidirect
568. #3343	C₂×C₅₉	semidirect
569. #3318	C₂×C₅₉	semidirect
570. #3310	C₂×C₅₉	semidirect
571. #3308	C₂×C₅₉	semidirect
572. #3306	C₂×C₅₉	semidirect
573. #3265	C₂×C₅₉	semidirect
574. #3264	C₂×C₅₉	semidirect
575. #3247	C₂×C₅₉	semidirect
576. #3188	C₂×C₅₉	semidirect
577. #3187	C₂×C₅₉	semidirect
578. #3186	C₂×C₅₉	semidirect
579. #3180	C₂×C₅₉	semidirect
580. #3055	C₂×C₅₉	semidirect
581. C₂×#466	C₂×C₅₉	semidirect
582. C₂×#465	C₂×C₅₉	semidirect
583. C₂×#435	C₂×C₅₉	semidirect
595. C₂×AGL(1,ℤ/8)	C₂²×C₅₉	semidirect
596. C₂²×SD₁₆	C₂²×C₅₉	semidirect
597. C₂²×D₈	C₂²×C₅₉	semidirect
598. C₂²×M₁₆	C₂²×C₅₉	semidirect
599. C₂³×C₈	C₂²×C₅₉	semidirect
601. #553	C₂²×C₅₉	semidirect
602. #552	C₂²×C₅₉	semidirect
604. #548	C₂²×C₅₉	semidirect
606. #547	C₂²×C₅₉	semidirect
609. #546	C₂²×C₅₉	semidirect
611. D₄²	C₂²×C₅₉	semidirect
618. #532	C₂²×C₅₉	semidirect
619. #529	C₂²×C₅₉	semidirect
620. #525	C₂²×C₅₉	semidirect
621. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
624. C₂×#121	C₂²×C₅₉	semidirect
625. C₂×#121	C₂²×C₅₉	semidirect
628. #501	C₂²×C₅₉	semidirect
629. #496	C₂²×C₅₉	semidirect
630. #490	C₂²×C₅₉	semidirect
631. #489	C₂²×C₅₉	semidirect
632. #484	C₂²×C₅₉	semidirect
633. #483	C₂²×C₅₉	semidirect
634. #482	C₂²×C₅₉	semidirect
635. #482	C₂²×C₅₉	semidirect
636. #481	C₂²×C₅₉	semidirect
637. #481	C₂²×C₅₉	semidirect
638. #480	C₂²×C₅₉	semidirect
639. #480	C₂²×C₅₉	semidirect
640. #478	C₂²×C₅₉	semidirect
641. #478	C₂²×C₅₉	semidirect
642. #477	C₂²×C₅₉	semidirect
643. #476	C₂²×C₅₉	semidirect
644. #469	C₂²×C₅₉	semidirect
645. #469	C₂²×C₅₉	semidirect
646. #468	C₂²×C₅₉	semidirect
647. #468	C₂²×C₅₉	semidirect
648. #466	C₂²×C₅₉	semidirect
649. #466	C₂²×C₅₉	semidirect
650. #466	C₂²×C₅₉	semidirect
651. #466	C₂²×C₅₉	semidirect
652. #466	C₂²×C₅₉	semidirect
653. #466	C₂²×C₅₉	semidirect
654. #465	C₂²×C₅₉	semidirect
655. #465	C₂²×C₅₉	semidirect
656. #465	C₂²×C₅₉	semidirect
657. #465	C₂²×C₅₉	semidirect
658. #465	C₂²×C₅₉	semidirect
659. #465	C₂²×C₅₉	semidirect
660. #463	C₂²×C₅₉	semidirect
661. #463	C₂²×C₅₉	semidirect
662. #460	C₂²×C₅₉	semidirect
663. #459	C₂²×C₅₉	semidirect
664. #450	C₂²×C₅₉	semidirect
665. #450	C₂²×C₅₉	semidirect
666. #449	C₂²×C₅₉	semidirect
667. #449	C₂²×C₅₉	semidirect
668. #448	C₂²×C₅₉	semidirect
669. #447	C₂²×C₅₉	semidirect
670. #447	C₂²×C₅₉	semidirect
671. #447	C₂²×C₅₉	semidirect
672. #442	C₂²×C₅₉	semidirect
673. #442	C₂²×C₅₉	semidirect
674. #440	C₂²×C₅₉	semidirect
675. #440	C₂²×C₅₉	semidirect
676. #435	C₂²×C₅₉	semidirect
677. #435	C₂²×C₅₉	semidirect
678. #435	C₂²×C₅₉	semidirect
679. #435	C₂²×C₅₉	semidirect
680. #428	C₂²×C₅₉	semidirect
681. C₂×#107	C₂²×C₅₉	semidirect
682. C₂×#106	C₂²×C₅₉	semidirect
683. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
684. #418	C₂²×C₅₉	semidirect
685. #417	C₂²×C₅₉	semidirect
686. C₂×#103	C₂²×C₅₉	semidirect
687. C₂×#102	C₂²×C₅₉	semidirect
688. C₂×#102	C₂²×C₅₉	semidirect
689. C₂×#102	C₂²×C₅₉	semidirect
690. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
691. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
692. C₂×#97	C₂²×C₅₉	semidirect
693. C₅₉	#62253	direct (N × H)
1022. C₂³	AGL(1,ℤ/8)×C₅₉	semidirect
1097. C₈	H(5,𝔽₂)×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3505	2
C₅₉×#3496	2
C₅₉×#3345	2
C₅₉×#3343	2
C₅₉×#3318	2
C₅₉×#3310	2
C₅₉×#3308	2
C₅₉×#3306	2
C₅₉×#3265	2
C₅₉×#3264	2
C₅₉×#3247	2
C₅₉×#3188	2
C₅₉×#3187	2
C₅₉×#3186	2
C₅₉×#3180	2
C₅₉×#3055	2
C₂×C₅₉×#466	2
C₂×C₅₉×#465	2
C₂×C₅₉×#435	2
#62253	59

Subgroups — C59×#62253 #28474362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62253 #28474362