Subgroups — C₅₉×#61188 #28473297

Order 15104.

2056 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3485	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#3331	C₂	1	2	yes	maximal, complemented
4	C₅₉×#3323	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3315	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3315	C₂	1	2	yes	maximal, complemented
7	C₅₉×#3314	C₂	1	2	yes	maximal, complemented
8	C₅₉×#3311	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3302	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3296	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#137×C₅₉	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
31	C₅₉×#556	C₂²	1	2	yes	complemented
32	C₅₉×#554	C₂²	1	2	yes	complemented
33	C₅₉×#552	—	2	2	no	—
34	C₅₉×#552	C₂²	1	2	yes	complemented
35	C₅₉×#552	C₂²	1	2	yes	complemented
36	C₅₉×#551	—	2	2	no	—
37	C₅₉×#547	—	2	1	no	—
38	C₅₉×#547	—	2	1	no	—
39	C₅₉×#547	C₂²	1	2	yes	—
40	C₅₉×#547	C₂²	1	2	yes	—
41	C₅₉×#546	—	2	1	no	—
42	C₅₉×#546	—	2	1	no	—
43	C₅₉×#546	C₂²	1	2	yes	—
44	C₅₉×#546	C₂²	1	2	yes	—
45	C₅₉×#544	C₂²	1	1	yes	characteristic, complemented
46	C₅₉×#542	—	2	1	no	—
47	C₅₉×#541	—	2	1	no	—
48	C₅₉×#536	C₂²	1	1	yes	characteristic
49	C₅₉×#536	C₂²	1	1	yes	characteristic
50	C₅₉×#536	C₂²	1	1	yes	characteristic
51	C₅₉×#534	—	2	2	no	—
52	C₅₉×#533	—	2	1	no	—
53	C₅₉×#529	—	2	1	no	—
54	C₅₉×#525	C₂²	1	1	yes	characteristic
55	C₅₉×#525	C₂²	1	1	yes	characteristic
56	C₂×#123×C₅₉	—	2	2	no	—
57	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
58	C₅₉×#520	C₂²	1	1	yes	characteristic
59	C₅₉×#519	C₂²	1	1	yes	characteristic, complemented
60	C₅₉×#518	C₂²	1	1	yes	characteristic
61	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
62	C₅₉×#491	C₂²	1	2	yes	complemented
63	C₅₉×#489	C₂²	1	2	yes	complemented
64	C₅₉×#488	C₂²	1	2	yes	complemented
65	C₅₉×#487	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×#484	C₂²	1	2	yes	complemented
71	C₅₉×#484	C₂²	1	1	yes	characteristic, complemented
72	C₅₉×#483	C₂²	1	2	yes	complemented
73	C₅₉×#483	C₂²	1	1	yes	characteristic, complemented
74	C₅₉×#482	C₂²	1	1	yes	characteristic, complemented
75	C₅₉×#482	C₂²	1	1	yes	characteristic, complemented
76	C₅₉×#481	C₂²	1	1	yes	characteristic, complemented
77	C₅₉×#480	C₂²	1	1	yes	characteristic, complemented
78	C₅₉×#478	C₂²	1	2	yes	complemented
79	C₅₉×#478	C₂²	1	2	yes	complemented
80	C₅₉×#476	C₂²	1	2	yes	complemented
81	C₅₉×#474	C₂²	1	2	yes	complemented
82	C₅₉×#470	C₂²	1	2	yes	complemented
83	C₅₉×#470	C₂²	1	2	yes	complemented
84	C₅₉×#470	C₂²	1	2	yes	complemented
85	C₅₉×#468	C₂²	1	2	yes	complemented
86	C₅₉×#467	C₂²	1	2	yes	complemented
87	C₅₉×#467	C₂²	1	2	yes	complemented
88	C₅₉×#467	C₂²	1	2	yes	complemented
89	C₅₉×#465	C₂²	1	2	yes	complemented
90	C₅₉×#464	C₂²	1	2	yes	complemented
91	C₅₉×#464	C₂²	1	2	yes	complemented
92	C₅₉×#462	C₂²	1	2	yes	complemented
93	C₅₉×#462	C₂²	1	2	yes	complemented
94	C₅₉×#452	C₂²	1	2	yes	complemented
95	C₅₉×#452	C₂²	1	2	yes	complemented
96	C₅₉×#452	C₂²	1	2	yes	complemented
97	C₅₉×#452	C₂²	1	2	yes	complemented
98	C₅₉×#452	C₂²	1	2	yes	complemented
99	C₅₉×#452	C₂²	1	2	yes	complemented
100	C₅₉×#450	C₂²	1	2	yes	complemented
101	C₅₉×#450	C₂²	1	2	yes	complemented
102	C₅₉×#440	C₂²	1	2	yes	complemented
103	C₅₉×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
106	C₅₉×#436	C₂²	1	2	yes	complemented
107	C₅₉×#435	C₂²	1	2	yes	complemented
108	C₅₉×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₅₉	C₂²	1	2	yes	complemented
110	C₅₉×#428	C₂²	1	1	yes	characteristic, complemented
111	C₅₉×#427	C₂²	1	1	yes	characteristic, complemented
112	C₅₉×#427	C₂²	1	1	yes	characteristic, complemented
113	C₅₉×#424	C₂²	1	1	yes	characteristic, complemented
114	C₅₉×#419	C₂²	1	1	yes	characteristic, complemented
115	C₅₉×#419	C₂²	1	1	yes	characteristic, complemented
116	C₅₉×#419	C₂²	1	1	yes	characteristic, complemented
117	C₅₉×#418	C₂²	1	1	yes	characteristic
118	C₅₉×#418	C₂²	1	1	yes	characteristic
119	C₅₉×#418	C₂²	1	2	yes	complemented
120	C₅₉×#417	C₂²	1	1	yes	characteristic
121	C₅₉×#417	C₂²	1	2	yes	complemented
122	C₅₉×#417	C₂²	1	2	yes	complemented
123	C₅₉×#417	C₂²	1	2	yes	complemented
124	C₅₉×#416	C₂²	1	1	yes	characteristic
125	C₅₉×#416	C₂²	1	1	yes	characteristic
126	C₅₉×#416	C₂²	1	2	yes	complemented
127	C₅₉×#416	C₂²	1	2	yes	complemented
128	C₅₉×#416	C₂²	1	2	yes	complemented
129	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
131	C₂×#102×C₅₉	C₂²	1	2	yes	complemented
132	C₅₉×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
134	C₅₉×#405	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₅₉	—	2	4	no	—
136	H(5,𝔽₂)×C₅₉	—	4	2	no	—
137	C₂×#41×C₅₉	—	2	1	no	—
138	C₂×#41×C₅₉	—	2	1	no	—
139	C₂×#41×C₅₉	—	2	1	no	—
140	C₂×#41×C₅₉	—	2	4	no	—
141	C₂×#41×C₅₉	—	4	2	no	—
142	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×#41×C₅₉	C₂³	1	2	yes	—
144	C₂×#41×C₅₉	C₂³	1	2	yes	—
145	C₂×#41×C₅₉	C₂³	1	2	yes	—
146	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₅₉	—	2	1	no	—
150	C₂²×D₄×C₅₉	—	2	2	no	—
151	C₂²×D₄×C₅₉	—	2	1	no	—
152	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
153	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₅₉	—	2	1	no	—
155	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
156	#137×C₅₉	—	4	2	no	—
157	C₂×Q₁₆×C₅₉	—	4	2	no	—
158	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₅₉	—	2	4	no	—
162	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
165	#131×C₅₉	—	4	2	no	—
166	C₂×M₁₆×C₅₉	—	4	2	no	—
167	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
170	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
171	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
174	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₅₉	—	2	1	no	—
176	C₄⋊Q₈×C₅₉	—	2	1	no	—
177	C₄⋊Q₈×C₅₉	—	2	1	no	—
178	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
179	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
180	#126×C₅₉	—	2	2	no	—
181	#126×C₅₉	—	2	2	no	—
182	#126×C₅₉	—	2	2	no	—
183	#126×C₅₉	—	2	2	no	—
184	#125×C₅₉	—	2	1	no	—
185	#125×C₅₉	—	2	2	no	—
186	#125×C₅₉	—	2	2	no	—
187	#125×C₅₉	—	2	2	no	—
188	#125×C₅₉	C₂³	1	2	yes	—
189	#124×C₅₉	—	2	1	no	—
190	#124×C₅₉	—	2	1	no	—
191	#124×C₅₉	—	2	2	no	—
192	#124×C₅₉	C₂³	1	2	yes	—
193	#123×C₅₉	—	2	2	no	—
194	#123×C₅₉	—	2	2	no	—
195	#123×C₅₉	—	2	2	no	—
196	#123×C₅₉	—	2	2	no	—
197	#123×C₅₉	—	2	1	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	—	2	2	no	—
205	#123×C₅₉	D₄	1	2	yes	—
206	C₂²⋊Q₈×C₅₉	—	2	1	no	—
207	C₂²⋊Q₈×C₅₉	—	2	1	no	—
208	C₂²⋊Q₈×C₅₉	—	2	1	no	—
209	C₂²⋊Q₈×C₅₉	—	2	1	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	D₄	1	1	yes	characteristic
215	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
216	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
217	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
228	#121×C₅₉	D₄	1	1	yes	characteristic
229	#121×C₅₉	C₂³	1	1	yes	characteristic
230	#121×C₅₉	C₂³	1	1	yes	characteristic
231	#120×C₅₉	—	2	1	no	—
232	#120×C₅₉	—	2	2	no	—
233	#120×C₅₉	—	2	2	no	—
234	#120×C₅₉	D₄	1	2	yes	—
235	C₄×Q₈×C₅₉	—	2	1	no	—
236	C₄×Q₈×C₅₉	—	2	1	no	—
237	C₄×Q₈×C₅₉	—	2	1	no	—
238	C₄×Q₈×C₅₉	—	2	2	no	—
239	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
241	C₄×D₄×C₅₉	—	2	1	no	—
242	C₄×D₄×C₅₉	—	2	2	no	—
243	C₄×D₄×C₅₉	—	2	2	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	C₂³	1	2	yes	—
249	C₄×D₄×C₅₉	C₂³	1	2	yes	—
250	C₄×D₄×C₅₉	C₂³	1	2	yes	—
251	C₄×D₄×C₅₉	C₂³	1	2	yes	—
252	#117×C₅₉	—	2	1	no	—
253	#117×C₅₉	—	2	1	no	—
254	#117×C₅₉	—	2	2	no	—
255	#117×C₅₉	—	2	2	no	—
256	#117×C₅₉	—	2	2	no	—
257	#117×C₅₉	C₂³	1	1	yes	characteristic
258	#117×C₅₉	C₂³	1	1	yes	characteristic
259	#117×C₅₉	C₂³	1	1	yes	characteristic
260	#117×C₅₉	C₂³	1	1	yes	characteristic
261	#117×C₅₉	C₂³	1	2	yes	—
262	#117×C₅₉	C₂³	1	1	yes	characteristic
263	#117×C₅₉	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
266	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
267	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
272	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
273	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
276	C₂×C₄²×C₅₉	—	2	1	no	—
277	#107×C₅₉	C₂³	1	1	yes	characteristic
278	#107×C₅₉	C₂³	1	1	yes	characteristic
279	#107×C₅₉	C₂³	1	1	yes	characteristic
280	#107×C₅₉	C₂³	1	1	yes	characteristic
281	#107×C₅₉	C₂³	1	2	yes	—
282	#106×C₅₉	C₂³	1	1	yes	characteristic
283	#106×C₅₉	C₂³	1	1	yes	characteristic
284	#106×C₅₉	C₂³	1	1	yes	characteristic
285	#106×C₅₉	C₂³	1	1	yes	characteristic
286	#106×C₅₉	C₂³	1	2	yes	—
287	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
288	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
289	#103×C₅₉	C₂³	1	2	yes	—
290	#103×C₅₉	C₂³	1	2	yes	—
291	#103×C₅₉	C₂³	1	1	yes	characteristic
292	#103×C₅₉	C₂³	1	1	yes	characteristic
293	#103×C₅₉	C₂³	1	1	yes	characteristic
294	#103×C₅₉	C₂³	1	1	yes	characteristic
295	#103×C₅₉	C₂³	1	2	yes	—
296	#103×C₅₉	C₂³	1	2	yes	—
297	#103×C₅₉	C₂³	1	2	yes	—
298	#103×C₅₉	C₂³	1	2	yes	—
299	#103×C₅₉	C₂³	1	2	yes	—
300	#103×C₅₉	C₂³	1	2	yes	—
301	#103×C₅₉	C₂³	1	2	yes	—
302	#102×C₅₉	C₂³	1	2	yes	—
303	#102×C₅₉	C₂³	1	2	yes	—
304	#102×C₅₉	C₂³	1	1	yes	characteristic
305	#102×C₅₉	C₂³	1	2	yes	—
306	#102×C₅₉	C₂³	1	2	yes	—
307	#102×C₅₉	C₂³	1	1	yes	characteristic
308	#102×C₅₉	C₂³	1	1	yes	characteristic
309	#102×C₅₉	C₂³	1	1	yes	characteristic
310	#102×C₅₉	C₂³	1	2	yes	—
311	#102×C₅₉	C₂³	1	2	yes	—
312	#102×C₅₉	C₂³	1	2	yes	—
313	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
316	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
317	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
319	#97×C₅₉	C₂³	1	2	yes	—
320	C₄×C₈×C₅₉	C₂³	1	2	yes	—
321	C₂⁴×C₅₉	—	2	1	no	—
322	C₂⁴×C₅₉	—	2	2	no	—
323	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
324	#41×C₅₉	—	2	2	no	—
325	#41×C₅₉	—	2	2	no	—
326	#41×C₅₉	—	2	4	no	—
327	#41×C₅₉	—	2	4	no	—
328	#41×C₅₉	—	2	4	no	—
329	#41×C₅₉	—	2	2	no	—
330	#41×C₅₉	—	2	2	no	—
331	#41×C₅₉	—	4	2	no	—
332	#41×C₅₉	—	4	2	no	—
333	#41×C₅₉	—	4	2	no	—
334	#41×C₅₉	—	4	4	no	—
335	#41×C₅₉	—	4	4	no	—
336	#41×C₅₉	—	4	4	no	—
337	C₂×Q₈×C₅₉	—	2	1	no	—
338	C₂×Q₈×C₅₉	—	2	1	no	—
339	C₂×Q₈×C₅₉	—	2	2	no	—
340	C₂×Q₈×C₅₉	—	2	2	no	—
341	C₂×Q₈×C₅₉	—	2	2	no	—
342	C₂×Q₈×C₅₉	—	2	2	no	—
343	C₂×Q₈×C₅₉	—	2	2	no	—
344	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
345	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
346	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
347	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
348	C₂×D₄×C₅₉	—	2	4	no	—
349	C₂×D₄×C₅₉	—	2	2	no	—
350	C₂×D₄×C₅₉	—	2	2	no	—
351	C₂×D₄×C₅₉	—	2	1	no	—
352	C₂×D₄×C₅₉	—	2	2	no	—
353	C₂×D₄×C₅₉	—	2	1	no	—
354	C₂×D₄×C₅₉	—	2	1	no	—
355	C₂×D₄×C₅₉	—	2	1	no	—
356	C₂×D₄×C₅₉	—	2	2	no	—
357	C₂×D₄×C₅₉	—	2	2	no	—
358	C₂×D₄×C₅₉	—	4	2	no	—
359	C₂×D₄×C₅₉	—	4	4	no	—
360	C₂×D₄×C₅₉	—	4	8	no	—
361	C₂×D₄×C₅₉	—	4	4	no	—
362	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₅₉	#41	1	4	yes	—
367	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
368	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₅₉	—	2	2	no	—
370	C₂²×C₄×C₅₉	—	2	2	no	—
371	C₂²×C₄×C₅₉	—	2	1	no	—
372	C₂²×C₄×C₅₉	—	2	1	no	—
373	C₂²×C₄×C₅₉	—	2	1	no	—
374	C₂²×C₄×C₅₉	—	2	1	no	—
375	C₂²×C₄×C₅₉	—	2	1	no	—
376	C₂²×C₄×C₅₉	—	2	2	no	—
377	C₂²×C₄×C₅₉	—	2	2	no	—
378	C₂²×C₄×C₅₉	—	2	2	no	—
379	C₂²×C₄×C₅₉	—	2	2	no	—
380	C₂²×C₄×C₅₉	—	2	1	no	—
381	C₂²×C₄×C₅₉	—	2	2	no	—
382	C₂²×C₄×C₅₉	—	2	2	no	—
383	C₂²×C₄×C₅₉	—	4	4	no	—
384	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
391	Q₁₆×C₅₉	—	4	2	no	—
392	Q₁₆×C₅₉	—	4	2	no	—
393	Q₁₆×C₅₉	—	4	2	no	—
394	SD₁₆×C₅₉	—	2	4	no	—
395	SD₁₆×C₅₉	—	2	4	no	—
396	SD₁₆×C₅₉	—	4	2	no	—
397	M₁₆×C₅₉	—	2	2	no	—
398	M₁₆×C₅₉	—	2	2	no	—
399	M₁₆×C₅₉	—	4	2	no	—
400	M₁₆×C₅₉	—	4	2	no	—
401	C₂×C₈×C₅₉	—	2	2	no	—
402	C₂×C₈×C₅₉	—	2	2	no	—
403	C₂×C₈×C₅₉	—	4	2	no	—
404	C₂×C₈×C₅₉	—	4	2	no	—
405	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
407	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₅₉	—	2	1	no	—
412	C₄⋊C₄×C₅₉	—	2	1	no	—
413	C₄⋊C₄×C₅₉	—	2	2	no	—
414	C₄⋊C₄×C₅₉	—	2	2	no	—
415	C₄⋊C₄×C₅₉	—	2	2	no	—
416	C₄⋊C₄×C₅₉	—	2	2	no	—
417	C₄⋊C₄×C₅₉	—	2	2	no	—
418	C₄⋊C₄×C₅₉	—	2	2	no	—
419	C₄⋊C₄×C₅₉	—	2	1	no	—
420	C₄⋊C₄×C₅₉	—	2	1	no	—
421	C₄⋊C₄×C₅₉	—	2	1	no	—
422	C₄⋊C₄×C₅₉	—	2	2	no	—
423	C₄⋊C₄×C₅₉	—	2	2	no	—
424	C₄⋊C₄×C₅₉	—	2	2	no	—
425	C₄⋊C₄×C₅₉	—	2	2	no	—
426	C₄⋊C₄×C₅₉	—	2	2	no	—
427	C₄⋊C₄×C₅₉	—	2	2	no	—
428	C₄⋊C₄×C₅₉	—	2	2	no	—
429	C₄⋊C₄×C₅₉	—	2	2	no	—
430	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
432	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
441	C₂²⋊C₄×C₅₉	—	2	1	no	—
442	C₂²⋊C₄×C₅₉	—	2	1	no	—
443	C₂²⋊C₄×C₅₉	—	2	1	no	—
444	C₂²⋊C₄×C₅₉	—	2	1	no	—
445	C₂²⋊C₄×C₅₉	—	2	1	no	—
446	C₂²⋊C₄×C₅₉	—	2	2	no	—
447	C₂²⋊C₄×C₅₉	—	2	2	no	—
448	C₂²⋊C₄×C₅₉	—	2	2	no	—
449	C₂²⋊C₄×C₅₉	—	2	2	no	—
450	C₂²⋊C₄×C₅₉	—	2	2	no	—
451	C₂²⋊C₄×C₅₉	—	2	2	no	—
452	C₂²⋊C₄×C₅₉	—	2	1	no	—
453	C₂²⋊C₄×C₅₉	—	2	1	no	—
454	C₂²⋊C₄×C₅₉	—	2	2	no	—
455	C₂²⋊C₄×C₅₉	—	2	1	no	—
456	C₂²⋊C₄×C₅₉	—	2	1	no	—
457	C₂²⋊C₄×C₅₉	—	2	2	no	—
458	C₂²⋊C₄×C₅₉	—	2	2	no	—
459	C₂²⋊C₄×C₅₉	—	2	2	no	—
460	C₂²⋊C₄×C₅₉	—	2	2	no	—
461	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
466	C₄²×C₅₉	—	2	1	no	—
467	C₄²×C₅₉	—	2	1	no	—
468	C₄²×C₅₉	—	2	1	no	—
469	C₄²×C₅₉	—	2	1	no	—
470	C₄²×C₅₉	—	2	2	no	—
471	C₄²×C₅₉	—	2	2	no	—
472	C₄²×C₅₉	—	2	2	no	—
473	C₄²×C₅₉	—	2	1	no	—
474	C₄²×C₅₉	C₂⁴	1	2	yes	—
475	C₂³×C₅₉	—	2	2	no	—
476	C₂³×C₅₉	—	2	2	no	—
477	C₂³×C₅₉	—	2	4	no	—
478	C₂³×C₅₉	—	2	1	no	—
479	C₂³×C₅₉	—	4	1	no	—
480	C₂³×C₅₉	—	4	1	no	—
481	C₂³×C₅₉	—	4	4	no	—
482	C₂³×C₅₉	—	8	1	no	—
483	C₂³×C₅₉	—	8	1	no	—
484	C₂³×C₅₉	—	8	2	no	—
485	C₂³×C₅₉	—	8	2	no	—
486	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
487	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
488	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
489	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
490	Q₈×C₅₉	—	2	2	no	—
491	Q₈×C₅₉	—	2	2	no	—
492	Q₈×C₅₉	—	2	2	no	—
493	Q₈×C₅₉	—	2	1	no	—
494	Q₈×C₅₉	—	2	2	no	—
495	Q₈×C₅₉	—	2	2	no	—
496	Q₈×C₅₉	—	2	1	no	—
497	Q₈×C₅₉	—	4	2	no	—
498	Q₈×C₅₉	—	4	2	no	—
499	Q₈×C₅₉	—	8	2	no	—
500	D₄×C₅₉	—	2	4	no	—
501	D₄×C₅₉	—	2	4	no	—
502	D₄×C₅₉	—	2	2	no	—
503	D₄×C₅₉	—	2	1	no	—
504	D₄×C₅₉	—	2	2	no	—
505	D₄×C₅₉	—	2	1	no	—
506	D₄×C₅₉	—	4	2	no	—
507	D₄×C₅₉	—	4	2	no	—
508	D₄×C₅₉	—	4	4	no	—
509	D₄×C₅₉	—	4	4	no	—
510	D₄×C₅₉	—	4	4	no	—
511	D₄×C₅₉	—	4	4	no	—
512	D₄×C₅₉	—	4	2	no	—
513	D₄×C₅₉	—	8	1	no	—
514	D₄×C₅₉	—	8	1	no	—
515	D₄×C₅₉	C₂×#41	1	4	yes	—
516	C₂×C₄×C₅₉	—	2	2	no	—
517	C₂×C₄×C₅₉	—	2	2	no	—
518	C₂×C₄×C₅₉	—	2	2	no	—
519	C₂×C₄×C₅₉	—	2	1	no	—
520	C₂×C₄×C₅₉	—	2	1	no	—
521	C₂×C₄×C₅₉	—	2	2	no	—
522	C₂×C₄×C₅₉	—	2	1	no	—
523	C₂×C₄×C₅₉	—	2	2	no	—
524	C₂×C₄×C₅₉	—	2	1	no	—
525	C₂×C₄×C₅₉	—	2	1	no	—
526	C₂×C₄×C₅₉	—	2	1	no	—
527	C₂×C₄×C₅₉	—	2	1	no	—
528	C₂×C₄×C₅₉	—	2	2	no	—
529	C₂×C₄×C₅₉	—	2	1	no	—
530	C₂×C₄×C₅₉	—	2	1	no	—
531	C₂×C₄×C₅₉	—	2	1	no	—
532	C₂×C₄×C₅₉	—	2	2	no	—
533	C₂×C₄×C₅₉	—	2	2	no	—
534	C₂×C₄×C₅₉	—	2	1	no	—
535	C₂×C₄×C₅₉	—	4	4	no	—
536	C₂×C₄×C₅₉	—	4	4	no	—
537	C₂×C₄×C₅₉	—	4	4	no	—
538	C₂×C₄×C₅₉	—	4	2	no	—
539	C₂×C₄×C₅₉	—	4	2	no	—
540	C₂×C₄×C₅₉	—	4	2	no	—
541	C₂×C₄×C₅₉	—	4	2	no	—
542	C₂×C₄×C₅₉	—	8	2	no	—
543	C₂×C₄×C₅₉	—	8	2	no	—
544	C₂×C₄×C₅₉	—	8	2	no	—
545	C₂×C₄×C₅₉	—	8	1	no	—
546	C₂×C₄×C₅₉	—	8	1	no	—
547	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
554	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
555	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
556	C₈×C₅₉	—	2	1	no	—
557	C₈×C₅₉	—	2	1	no	—
558	C₈×C₅₉	—	2	1	no	—
559	C₈×C₅₉	—	2	1	no	—
560	C₈×C₅₉	—	2	2	no	—
561	C₈×C₅₉	—	2	2	no	—
562	#61188	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
563	C₂²×C₅₉	—	2	1	no	—
564	C₂²×C₅₉	—	2	1	no	—
565	C₂²×C₅₉	—	2	2	no	—
566	C₂²×C₅₉	—	2	1	no	—
567	C₂²×C₅₉	—	2	1	no	—
568	C₂²×C₅₉	—	2	1	no	—
569	C₂²×C₅₉	—	2	2	no	—
570	C₂²×C₅₉	—	2	1	no	—
571	C₂²×C₅₉	—	2	1	no	—
572	C₂²×C₅₉	—	2	1	no	—
573	C₂²×C₅₉	—	2	2	no	—
574	C₂²×C₅₉	—	2	4	no	—
575	C₂²×C₅₉	—	4	2	no	—
576	C₂²×C₅₉	—	4	2	no	—
577	C₂²×C₅₉	—	4	1	no	—
578	C₂²×C₅₉	—	4	1	no	—
579	C₂²×C₅₉	—	4	1	no	—
580	C₂²×C₅₉	—	8	2	no	—
581	C₂²×C₅₉	—	8	4	no	—
582	C₂²×C₅₉	—	16	4	no	—
583	C₂²×C₅₉	#546	1	2	yes	—
584	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
585	C₄×C₅₉	—	2	2	no	—
586	C₄×C₅₉	—	2	2	no	—
587	C₄×C₅₉	—	2	1	no	—
588	C₄×C₅₉	—	2	1	no	—
589	C₄×C₅₉	—	2	2	no	—
590	C₄×C₅₉	—	4	1	no	—
591	C₄×C₅₉	—	4	1	no	—
592	C₄×C₅₉	—	4	2	no	—
593	C₄×C₅₉	—	4	1	no	—
594	C₄×C₅₉	—	4	1	no	—
595	C₄×C₅₉	—	4	1	no	—
596	C₄×C₅₉	—	4	1	no	—
597	C₄×C₅₉	—	4	1	no	—
598	C₄×C₅₉	—	4	2	no	—
599	C₄×C₅₉	—	4	2	no	—
600	C₄×C₅₉	#546	1	2	yes	—
601	C₄×C₅₉	C₂²×#41	1	1	yes	characteristic
602	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	#3495	C₂×C₅₉	1	1	yes	characteristic, complemented
604	#3485	C₂×C₅₉	1	1	yes	characteristic
605	#3331	C₂×C₅₉	1	2	yes	complemented
606	#3323	C₂×C₅₉	1	2	yes	complemented
607	#3315	C₂×C₅₉	1	2	yes	complemented
608	#3315	C₂×C₅₉	1	2	yes	complemented
609	#3314	C₂×C₅₉	1	2	yes	complemented
610	#3311	C₂×C₅₉	1	2	yes	complemented
611	#3302	C₂×C₅₉	1	2	yes	complemented
612	#3296	C₂×C₅₉	1	2	yes	complemented
613	#3137	C₂×C₅₉	1	1	yes	characteristic, complemented
614	#3097	C₂×C₅₉	1	1	yes	characteristic, complemented
615	#3091	C₂×C₅₉	1	1	yes	characteristic, complemented
616	#3081	C₂×C₅₉	1	1	yes	characteristic, complemented
617	#3059	C₂×C₅₉	1	1	yes	characteristic, complemented
618	#3056	C₂×C₅₉	1	1	yes	characteristic, complemented
619	#3044	C₂×C₅₉	1	1	yes	characteristic, complemented
620	#3009	C₂×C₅₉	1	1	yes	characteristic, complemented
621	C₂×#452	C₂×C₅₉	1	1	yes	characteristic, complemented
622	#2949	C₂×C₅₉	1	1	yes	characteristic, complemented
623	#2933	C₂×C₅₉	1	1	yes	characteristic, complemented
624	#2897	C₂×C₅₉	1	1	yes	characteristic, complemented
625	#2896	C₂×C₅₉	1	1	yes	characteristic, complemented
626	C₂×C₅₉	—	2	2	no	—
627	C₂×C₅₉	—	4	1	no	—
628	C₂×C₅₉	—	4	1	no	—
629	C₂×C₅₉	—	4	2	no	—
630	C₂×C₅₉	—	4	4	no	—
631	C₂×C₅₉	—	8	1	no	—
632	C₂×C₅₉	C₂×#546	1	1	yes	characteristic
633	C₂×C₅₉	#3584	1	1	yes	characteristic
634	C₂×C₅₉	#3586	1	1	yes	characteristic
635	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	1	yes	characteristic
636	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
637	C₂×#137	C₂²×C₅₉	1	1	yes	characteristic
638	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
639	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
640	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
641	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
642	#556	C₂²×C₅₉	1	2	yes	complemented
643	#554	C₂²×C₅₉	1	2	yes	complemented
644	#552	—	2	2	no	—
645	#552	C₂²×C₅₉	1	2	yes	complemented
646	#552	C₂²×C₅₉	1	2	yes	complemented
647	#551	—	2	2	no	—
648	#547	—	2	1	no	—
649	#547	—	2	1	no	—
650	#547	C₂²×C₅₉	1	2	yes	—
651	#547	C₂²×C₅₉	1	2	yes	—
652	#546	—	2	1	no	—
653	#546	—	2	1	no	—
654	#546	C₂²×C₅₉	1	2	yes	—
655	#546	C₂²×C₅₉	1	2	yes	—
656	#544	C₂²×C₅₉	1	1	yes	characteristic, complemented
657	#542	—	2	1	no	—
658	#541	—	2	1	no	—
659	#536	C₂²×C₅₉	1	1	yes	characteristic
660	#536	C₂²×C₅₉	1	1	yes	characteristic
661	#536	C₂²×C₅₉	1	1	yes	characteristic
662	#534	—	2	2	no	—
663	#533	—	2	1	no	—
664	#529	—	2	1	no	—
665	#525	C₂²×C₅₉	1	1	yes	characteristic
666	#525	C₂²×C₅₉	1	1	yes	characteristic
667	C₂×#123	—	2	2	no	—
668	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
669	#520	C₂²×C₅₉	1	1	yes	characteristic
670	#519	C₂²×C₅₉	1	1	yes	characteristic, complemented
671	#518	C₂²×C₅₉	1	1	yes	characteristic
672	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
673	#491	C₂²×C₅₉	1	2	yes	complemented
674	#489	C₂²×C₅₉	1	2	yes	complemented
675	#488	C₂²×C₅₉	1	2	yes	complemented
676	#487	C₂²×C₅₉	1	2	yes	complemented
677	#485	C₂²×C₅₉	1	1	yes	characteristic, complemented
678	#485	C₂²×C₅₉	1	1	yes	characteristic, complemented
679	#485	C₂²×C₅₉	1	2	yes	complemented
680	#485	C₂²×C₅₉	1	2	yes	complemented
681	#484	C₂²×C₅₉	1	1	yes	characteristic, complemented
682	#484	C₂²×C₅₉	1	2	yes	complemented
683	#483	C₂²×C₅₉	1	1	yes	characteristic, complemented
684	#483	C₂²×C₅₉	1	2	yes	complemented
685	#482	C₂²×C₅₉	1	1	yes	characteristic, complemented
686	#482	C₂²×C₅₉	1	1	yes	characteristic, complemented
687	#481	C₂²×C₅₉	1	1	yes	characteristic, complemented
688	#480	C₂²×C₅₉	1	1	yes	characteristic, complemented
689	#478	C₂²×C₅₉	1	2	yes	complemented
690	#478	C₂²×C₅₉	1	2	yes	complemented
691	#476	C₂²×C₅₉	1	2	yes	complemented
692	#474	C₂²×C₅₉	1	2	yes	complemented
693	#470	C₂²×C₅₉	1	2	yes	complemented
694	#470	C₂²×C₅₉	1	2	yes	complemented
695	#470	C₂²×C₅₉	1	2	yes	complemented
696	#468	C₂²×C₅₉	1	2	yes	complemented
697	#467	C₂²×C₅₉	1	2	yes	complemented
698	#467	C₂²×C₅₉	1	2	yes	complemented
699	#467	C₂²×C₅₉	1	2	yes	complemented
700	#465	C₂²×C₅₉	1	2	yes	complemented
701	#464	C₂²×C₅₉	1	2	yes	complemented
702	#464	C₂²×C₅₉	1	2	yes	complemented
703	#462	C₂²×C₅₉	1	2	yes	complemented
704	#462	C₂²×C₅₉	1	2	yes	complemented
705	#452	C₂²×C₅₉	1	2	yes	complemented
706	#452	C₂²×C₅₉	1	2	yes	complemented
707	#452	C₂²×C₅₉	1	2	yes	complemented
708	#452	C₂²×C₅₉	1	2	yes	complemented
709	#452	C₂²×C₅₉	1	2	yes	complemented
710	#452	C₂²×C₅₉	1	2	yes	complemented
711	#450	C₂²×C₅₉	1	2	yes	complemented
712	#450	C₂²×C₅₉	1	2	yes	complemented
713	#440	C₂²×C₅₉	1	2	yes	complemented
714	#440	C₂²×C₅₉	1	2	yes	complemented
715	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
716	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
717	#436	C₂²×C₅₉	1	2	yes	complemented
718	#435	C₂²×C₅₉	1	2	yes	complemented
719	#435	C₂²×C₅₉	1	2	yes	complemented
720	C₈×D₄	C₂²×C₅₉	1	2	yes	complemented
721	#428	C₂²×C₅₉	1	1	yes	characteristic, complemented
722	#427	C₂²×C₅₉	1	1	yes	characteristic, complemented
723	#427	C₂²×C₅₉	1	1	yes	characteristic, complemented
724	#424	C₂²×C₅₉	1	1	yes	characteristic, complemented
725	#419	C₂²×C₅₉	1	1	yes	characteristic, complemented
726	#419	C₂²×C₅₉	1	1	yes	characteristic, complemented
727	#419	C₂²×C₅₉	1	1	yes	characteristic, complemented
728	#418	C₂²×C₅₉	1	1	yes	characteristic
729	#418	C₂²×C₅₉	1	1	yes	characteristic
730	#418	C₂²×C₅₉	1	2	yes	complemented
731	#417	C₂²×C₅₉	1	1	yes	characteristic
732	#417	C₂²×C₅₉	1	2	yes	complemented
733	#417	C₂²×C₅₉	1	2	yes	complemented
734	#417	C₂²×C₅₉	1	2	yes	complemented
735	#416	C₂²×C₅₉	1	1	yes	characteristic
736	#416	C₂²×C₅₉	1	1	yes	characteristic
737	#416	C₂²×C₅₉	1	2	yes	complemented
738	#416	C₂²×C₅₉	1	2	yes	complemented
739	#416	C₂²×C₅₉	1	2	yes	complemented
740	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
741	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
742	C₂×#102	C₂²×C₅₉	1	2	yes	complemented
743	#408	C₂²×C₅₉	1	1	yes	characteristic
744	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
745	#405	C₂²×C₅₉	1	1	yes	characteristic, complemented
746	C₅₉	#61188	1	1	yes	characteristic, direct product factor, Sylow
747	H(5,𝔽₂)	—	2	4	no	—
748	H(5,𝔽₂)	—	4	2	no	—
749	C₂×#41	—	2	1	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	4	no	—
753	C₂×#41	—	4	2	no	—
754	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
755	C₂×#41	C₂³×C₅₉	1	2	yes	—
756	C₂×#41	C₂³×C₅₉	1	2	yes	—
757	C₂×#41	C₂³×C₅₉	1	2	yes	—
758	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
759	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
760	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
761	C₂²×D₄	—	2	1	no	—
762	C₂²×D₄	—	2	2	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
765	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
766	C₂³×C₄	—	2	1	no	—
767	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
768	#137	—	4	2	no	—
769	C₂×Q₁₆	—	4	2	no	—
770	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
771	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
773	C₂×SD₁₆	—	2	4	no	—
774	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
777	#131	—	4	2	no	—
778	C₂×M₁₆	—	4	2	no	—
779	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
780	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
781	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
782	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
783	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
784	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
785	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
786	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
791	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#125	—	2	1	no	—
797	#125	—	2	2	no	—
798	#125	—	2	2	no	—
799	#125	—	2	2	no	—
800	#125	C₂³×C₅₉	1	2	yes	—
801	#124	—	2	1	no	—
802	#124	—	2	1	no	—
803	#124	—	2	2	no	—
804	#124	C₂³×C₅₉	1	2	yes	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	1	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	D₄×C₅₉	1	2	yes	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
826	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
827	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
828	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
829	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
831	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
834	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	D₄×C₅₉	1	1	yes	characteristic
840	#121	D₄×C₅₉	1	1	yes	characteristic
841	#121	C₂³×C₅₉	1	1	yes	characteristic
842	#121	C₂³×C₅₉	1	1	yes	characteristic
843	#120	—	2	1	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	D₄×C₅₉	1	2	yes	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	—	2	2	no	—
851	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
852	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	C₂³×C₅₉	1	2	yes	—
861	C₄×D₄	C₂³×C₅₉	1	2	yes	—
862	C₄×D₄	C₂³×C₅₉	1	2	yes	—
863	C₄×D₄	C₂³×C₅₉	1	2	yes	—
864	#117	—	2	1	no	—
865	#117	—	2	1	no	—
866	#117	—	2	2	no	—
867	#117	—	2	2	no	—
868	#117	—	2	2	no	—
869	#117	C₂³×C₅₉	1	1	yes	characteristic
870	#117	C₂³×C₅₉	1	1	yes	characteristic
871	#117	C₂³×C₅₉	1	1	yes	characteristic
872	#117	C₂³×C₅₉	1	1	yes	characteristic
873	#117	C₂³×C₅₉	1	1	yes	characteristic
874	#117	C₂³×C₅₉	1	2	yes	—
875	#117	C₂³×C₅₉	1	1	yes	characteristic
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	—	2	2	no	—
878	C₂×C₄⋊C₄	—	2	2	no	—
879	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
883	C₂×C₂²⋊C₄	—	2	1	no	—
884	C₂×C₂²⋊C₄	—	2	1	no	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₄²	—	2	1	no	—
889	#107	C₂³×C₅₉	1	1	yes	characteristic
890	#107	C₂³×C₅₉	1	1	yes	characteristic
891	#107	C₂³×C₅₉	1	1	yes	characteristic
892	#107	C₂³×C₅₉	1	1	yes	characteristic
893	#107	C₂³×C₅₉	1	2	yes	—
894	#106	C₂³×C₅₉	1	1	yes	characteristic
895	#106	C₂³×C₅₉	1	1	yes	characteristic
896	#106	C₂³×C₅₉	1	1	yes	characteristic
897	#106	C₂³×C₅₉	1	1	yes	characteristic
898	#106	C₂³×C₅₉	1	2	yes	—
899	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
900	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
901	#103	C₂³×C₅₉	1	2	yes	—
902	#103	C₂³×C₅₉	1	2	yes	—
903	#103	C₂³×C₅₉	1	1	yes	characteristic
904	#103	C₂³×C₅₉	1	1	yes	characteristic
905	#103	C₂³×C₅₉	1	1	yes	characteristic
906	#103	C₂³×C₅₉	1	1	yes	characteristic
907	#103	C₂³×C₅₉	1	2	yes	—
908	#103	C₂³×C₅₉	1	2	yes	—
909	#103	C₂³×C₅₉	1	2	yes	—
910	#103	C₂³×C₅₉	1	2	yes	—
911	#103	C₂³×C₅₉	1	2	yes	—
912	#103	C₂³×C₅₉	1	2	yes	—
913	#103	C₂³×C₅₉	1	2	yes	—
914	#102	C₂³×C₅₉	1	2	yes	—
915	#102	C₂³×C₅₉	1	2	yes	—
916	#102	C₂³×C₅₉	1	1	yes	characteristic
917	#102	C₂³×C₅₉	1	2	yes	—
918	#102	C₂³×C₅₉	1	2	yes	—
919	#102	C₂³×C₅₉	1	1	yes	characteristic
920	#102	C₂³×C₅₉	1	1	yes	characteristic
921	#102	C₂³×C₅₉	1	1	yes	characteristic
922	#102	C₂³×C₅₉	1	2	yes	—
923	#102	C₂³×C₅₉	1	2	yes	—
924	#102	C₂³×C₅₉	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
926	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
931	#97	C₂³×C₅₉	1	2	yes	—
932	C₄×C₈	C₂³×C₅₉	1	2	yes	—
933	C₂⁴	—	2	1	no	—
934	C₂⁴	—	2	2	no	—
935	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	2	4	no	—
939	#41	—	2	4	no	—
940	#41	—	2	4	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	4	2	no	—
944	#41	—	4	2	no	—
945	#41	—	4	2	no	—
946	#41	—	4	4	no	—
947	#41	—	4	4	no	—
948	#41	—	4	4	no	—
949	C₂×Q₈	—	2	1	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
959	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
960	C₂×D₄	—	2	4	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	4	no	—
972	C₂×D₄	—	4	8	no	—
973	C₂×D₄	—	4	4	no	—
974	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
975	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
976	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
977	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
978	C₂×D₄	#41×C₅₉	1	4	yes	—
979	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	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	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	4	4	no	—
996	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
997	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
1001	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	Q₁₆	—	4	2	no	—
1006	SD₁₆	—	2	4	no	—
1007	SD₁₆	—	2	4	no	—
1008	SD₁₆	—	4	2	no	—
1009	M₁₆	—	2	2	no	—
1010	M₁₆	—	2	2	no	—
1011	M₁₆	—	4	2	no	—
1012	M₁₆	—	4	2	no	—
1013	C₂×C₈	—	2	2	no	—
1014	C₂×C₈	—	2	2	no	—
1015	C₂×C₈	—	4	2	no	—
1016	C₂×C₈	—	4	2	no	—
1017	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
1019	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1043	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1044	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
1046	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1047	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	1	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	C₂⁴×C₅₉	1	2	yes	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	2	2	no	—
1089	C₂³	—	2	4	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	4	1	no	—
1092	C₂³	—	4	1	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	8	1	no	—
1095	C₂³	—	8	1	no	—
1096	C₂³	—	8	2	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1099	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1100	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1101	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	2	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	2	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	4	2	no	—
1110	Q₈	—	4	2	no	—
1111	Q₈	—	8	2	no	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	4	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	4	2	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	8	1	no	—
1126	D₄	—	8	1	no	—
1127	D₄	C₂×#41×C₅₉	1	4	yes	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	4	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1160	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1161	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1162	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1165	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1166	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1167	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1168	C₈	—	2	1	no	—
1169	C₈	—	2	1	no	—
1170	C₈	—	2	1	no	—
1171	C₈	—	2	1	no	—
1172	C₈	—	2	2	no	—
1173	C₈	—	2	2	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	1	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	4	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	8	2	no	—
1192	C₂²	—	8	4	no	—
1193	C₂²	—	16	4	no	—
1194	C₂²	C₅₉×#546	1	2	yes	—
1195	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	2	no	—
1211	C₄	C₅₉×#546	1	2	yes	—
1212	C₄	C₂²×#41×C₅₉	1	1	yes	characteristic
1213	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1214	C₂	—	2	2	no	—
1215	C₂	—	4	1	no	—
1216	C₂	—	4	1	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	4	no	—
1219	C₂	—	8	1	no	—
1220	C₂	C₂×C₅₉×#546	1	1	yes	characteristic
1221	C₂	C₅₉×#3584	1	1	yes	characteristic
1222	C₂	C₅₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	C₅₉×#3485	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₅₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3495	C₂	semidirect
3. C₅₉×#3331	C₂	semidirect
4. C₅₉×#3323	C₂	semidirect
5. C₅₉×#3315	C₂	semidirect
6. C₅₉×#3315	C₂	semidirect
7. C₅₉×#3314	C₂	semidirect
8. C₅₉×#3311	C₂	semidirect
9. C₅₉×#3302	C₂	semidirect
10. C₅₉×#3296	C₂	semidirect
11. C₅₉×#3137	C₂	semidirect
12. C₅₉×#3097	C₂	semidirect
13. C₅₉×#3091	C₂	semidirect
14. C₅₉×#3081	C₂	semidirect
15. C₅₉×#3059	C₂	semidirect
16. C₅₉×#3056	C₂	semidirect
17. C₅₉×#3044	C₂	semidirect
18. C₅₉×#3009	C₂	semidirect
19. C₂×C₅₉×#452	C₂	semidirect
20. C₅₉×#2949	C₂	semidirect
21. C₅₉×#2933	C₂	semidirect
22. C₅₉×#2897	C₂	semidirect
23. C₅₉×#2896	C₂	semidirect
27. C₂²×Q₁₆×C₅₉	C₂²	semidirect
30. C₂²×M₁₆×C₅₉	C₂²	semidirect
31. C₅₉×#556	C₂²	semidirect
32. C₅₉×#554	C₂²	semidirect
34. C₅₉×#552	C₂²	semidirect
35. C₅₉×#552	C₂²	semidirect
45. C₅₉×#544	C₂²	semidirect
57. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
59. C₅₉×#519	C₂²	semidirect
61. C₂×#117×C₅₉	C₂²	semidirect
62. C₅₉×#491	C₂²	semidirect
63. C₅₉×#489	C₂²	semidirect
64. C₅₉×#488	C₂²	semidirect
65. C₅₉×#487	C₂²	semidirect
66. C₅₉×#485	C₂²	semidirect
67. C₅₉×#485	C₂²	semidirect
68. C₅₉×#485	C₂²	semidirect
69. C₅₉×#485	C₂²	semidirect
70. C₅₉×#484	C₂²	semidirect
71. C₅₉×#484	C₂²	semidirect
72. C₅₉×#483	C₂²	semidirect
73. C₅₉×#483	C₂²	semidirect
74. C₅₉×#482	C₂²	semidirect
75. C₅₉×#482	C₂²	semidirect
76. C₅₉×#481	C₂²	semidirect
77. C₅₉×#480	C₂²	semidirect
78. C₅₉×#478	C₂²	semidirect
79. C₅₉×#478	C₂²	semidirect
80. C₅₉×#476	C₂²	semidirect
81. C₅₉×#474	C₂²	semidirect
82. C₅₉×#470	C₂²	semidirect
83. C₅₉×#470	C₂²	semidirect
84. C₅₉×#470	C₂²	semidirect
85. C₅₉×#468	C₂²	semidirect
86. C₅₉×#467	C₂²	semidirect
87. C₅₉×#467	C₂²	semidirect
88. C₅₉×#467	C₂²	semidirect
89. C₅₉×#465	C₂²	semidirect
90. C₅₉×#464	C₂²	semidirect
91. C₅₉×#464	C₂²	semidirect
92. C₅₉×#462	C₂²	semidirect
93. C₅₉×#462	C₂²	semidirect
94. C₅₉×#452	C₂²	semidirect
95. C₅₉×#452	C₂²	semidirect
96. C₅₉×#452	C₂²	semidirect
97. C₅₉×#452	C₂²	semidirect
98. C₅₉×#452	C₂²	semidirect
99. C₅₉×#452	C₂²	semidirect
100. C₅₉×#450	C₂²	semidirect
101. C₅₉×#450	C₂²	semidirect
102. C₅₉×#440	C₂²	semidirect
103. C₅₉×#440	C₂²	semidirect
104. C₄×SD₁₆×C₅₉	C₂²	semidirect
105. C₄×SD₁₆×C₅₉	C₂²	semidirect
106. C₅₉×#436	C₂²	semidirect
107. C₅₉×#435	C₂²	semidirect
108. C₅₉×#435	C₂²	semidirect
109. C₈×D₄×C₅₉	C₂²	semidirect
110. C₅₉×#428	C₂²	semidirect
111. C₅₉×#427	C₂²	semidirect
112. C₅₉×#427	C₂²	semidirect
113. C₅₉×#424	C₂²	semidirect
114. C₅₉×#419	C₂²	semidirect
115. C₅₉×#419	C₂²	semidirect
116. C₅₉×#419	C₂²	semidirect
119. C₅₉×#418	C₂²	semidirect
121. C₅₉×#417	C₂²	semidirect
122. C₅₉×#417	C₂²	semidirect
123. C₅₉×#417	C₂²	semidirect
126. C₅₉×#416	C₂²	semidirect
127. C₅₉×#416	C₂²	semidirect
128. C₅₉×#416	C₂²	semidirect
129. C₂×#103×C₅₉	C₂²	semidirect
131. C₂×#102×C₅₉	C₂²	semidirect
133. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
134. C₅₉×#405	C₂²	semidirect
562. #61188	C₅₉	direct (N × H)
603. #3495	C₂×C₅₉	semidirect
605. #3331	C₂×C₅₉	semidirect
606. #3323	C₂×C₅₉	semidirect
607. #3315	C₂×C₅₉	semidirect
608. #3315	C₂×C₅₉	semidirect
609. #3314	C₂×C₅₉	semidirect
610. #3311	C₂×C₅₉	semidirect
611. #3302	C₂×C₅₉	semidirect
612. #3296	C₂×C₅₉	semidirect
613. #3137	C₂×C₅₉	semidirect
614. #3097	C₂×C₅₉	semidirect
615. #3091	C₂×C₅₉	semidirect
616. #3081	C₂×C₅₉	semidirect
617. #3059	C₂×C₅₉	semidirect
618. #3056	C₂×C₅₉	semidirect
619. #3044	C₂×C₅₉	semidirect
620. #3009	C₂×C₅₉	semidirect
621. C₂×#452	C₂×C₅₉	semidirect
622. #2949	C₂×C₅₉	semidirect
623. #2933	C₂×C₅₉	semidirect
624. #2897	C₂×C₅₉	semidirect
625. #2896	C₂×C₅₉	semidirect
638. C₂²×Q₁₆	C₂²×C₅₉	semidirect
641. C₂²×M₁₆	C₂²×C₅₉	semidirect
642. #556	C₂²×C₅₉	semidirect
643. #554	C₂²×C₅₉	semidirect
645. #552	C₂²×C₅₉	semidirect
646. #552	C₂²×C₅₉	semidirect
656. #544	C₂²×C₅₉	semidirect
668. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
670. #519	C₂²×C₅₉	semidirect
672. C₂×#117	C₂²×C₅₉	semidirect
673. #491	C₂²×C₅₉	semidirect
674. #489	C₂²×C₅₉	semidirect
675. #488	C₂²×C₅₉	semidirect
676. #487	C₂²×C₅₉	semidirect
677. #485	C₂²×C₅₉	semidirect
678. #485	C₂²×C₅₉	semidirect
679. #485	C₂²×C₅₉	semidirect
680. #485	C₂²×C₅₉	semidirect
681. #484	C₂²×C₅₉	semidirect
682. #484	C₂²×C₅₉	semidirect
683. #483	C₂²×C₅₉	semidirect
684. #483	C₂²×C₅₉	semidirect
685. #482	C₂²×C₅₉	semidirect
686. #482	C₂²×C₅₉	semidirect
687. #481	C₂²×C₅₉	semidirect
688. #480	C₂²×C₅₉	semidirect
689. #478	C₂²×C₅₉	semidirect
690. #478	C₂²×C₅₉	semidirect
691. #476	C₂²×C₅₉	semidirect
692. #474	C₂²×C₅₉	semidirect
693. #470	C₂²×C₅₉	semidirect
694. #470	C₂²×C₅₉	semidirect
695. #470	C₂²×C₅₉	semidirect
696. #468	C₂²×C₅₉	semidirect
697. #467	C₂²×C₅₉	semidirect
698. #467	C₂²×C₅₉	semidirect
699. #467	C₂²×C₅₉	semidirect
700. #465	C₂²×C₅₉	semidirect
701. #464	C₂²×C₅₉	semidirect
702. #464	C₂²×C₅₉	semidirect
703. #462	C₂²×C₅₉	semidirect
704. #462	C₂²×C₅₉	semidirect
705. #452	C₂²×C₅₉	semidirect
706. #452	C₂²×C₅₉	semidirect
707. #452	C₂²×C₅₉	semidirect
708. #452	C₂²×C₅₉	semidirect
709. #452	C₂²×C₅₉	semidirect
710. #452	C₂²×C₅₉	semidirect
711. #450	C₂²×C₅₉	semidirect
712. #450	C₂²×C₅₉	semidirect
713. #440	C₂²×C₅₉	semidirect
714. #440	C₂²×C₅₉	semidirect
715. C₄×SD₁₆	C₂²×C₅₉	semidirect
716. C₄×SD₁₆	C₂²×C₅₉	semidirect
717. #436	C₂²×C₅₉	semidirect
718. #435	C₂²×C₅₉	semidirect
719. #435	C₂²×C₅₉	semidirect
720. C₈×D₄	C₂²×C₅₉	semidirect
721. #428	C₂²×C₅₉	semidirect
722. #427	C₂²×C₅₉	semidirect
723. #427	C₂²×C₅₉	semidirect
724. #424	C₂²×C₅₉	semidirect
725. #419	C₂²×C₅₉	semidirect
726. #419	C₂²×C₅₉	semidirect
727. #419	C₂²×C₅₉	semidirect
730. #418	C₂²×C₅₉	semidirect
732. #417	C₂²×C₅₉	semidirect
733. #417	C₂²×C₅₉	semidirect
734. #417	C₂²×C₅₉	semidirect
737. #416	C₂²×C₅₉	semidirect
738. #416	C₂²×C₅₉	semidirect
739. #416	C₂²×C₅₉	semidirect
740. C₂×#103	C₂²×C₅₉	semidirect
742. C₂×#102	C₂²×C₅₉	semidirect
744. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
745. #405	C₂²×C₅₉	semidirect
746. C₅₉	#61188	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×#3495	2
C₅₉×#3485	2
C₅₉×#3331	2
C₅₉×#3323	2
C₅₉×#3315	2
C₅₉×#3314	2
C₅₉×#3311	2
C₅₉×#3302	2
C₅₉×#3296	2
C₅₉×#3137	2
C₅₉×#3097	2
C₅₉×#3091	2
C₅₉×#3081	2
C₅₉×#3059	2
C₅₉×#3056	2
C₅₉×#3044	2
C₅₉×#3009	2
C₂×C₅₉×#452	2
C₅₉×#2949	2
C₅₉×#2933	2
C₅₉×#2897	2
C₅₉×#2896	2
#61188	59

Subgroups — C59×#61188 #28473297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#61188 #28473297