Subgroups — C₅₉×#35713 #28447822

Order 15104.

3120 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2624	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2622	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2445	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2445	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2444	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2443	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2422	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2420	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2418	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2418	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2412	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2405	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2395	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₉×#394	C₂	1	2	yes	maximal, complemented
19	C₅₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
22	D₄×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
27	D₄²×C₅₉	—	2	8	no	—
28	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
30	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
31	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
32	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#121×C₅₉	C₂²	1	2	yes	—
35	C₂×#120×C₅₉	C₂²	1	2	yes	—
36	C₂×#120×C₅₉	C₂²	1	2	yes	—
37	C₅₉×#518	—	2	8	no	—
38	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
46	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
51	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
52	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
53	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
54	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
55	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
56	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
57	C₅₉×#399	C₂²	1	2	yes	complemented
58	C₅₉×#399	C₂²	1	1	yes	characteristic, complemented
59	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
60	C₅₉×#397	C₂²	1	2	yes	complemented
61	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
62	C₅₉×#397	C₂²	1	2	yes	complemented
63	C₅₉×#397	C₂²	1	2	yes	complemented
64	C₅₉×#397	C₂²	1	2	yes	complemented
65	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
66	C₅₉×#397	C₂²	1	1	yes	characteristic, complemented
67	C₅₉×#394	C₂²	1	2	yes	—
68	C₅₉×#394	C₂²	1	1	yes	characteristic
69	C₅₉×#394	C₂²	1	1	yes	characteristic
70	C₅₉×#394	C₂²	1	2	yes	complemented
71	C₅₉×#394	C₂²	1	2	yes	complemented
72	C₅₉×#394	C₂²	1	2	yes	complemented
73	C₅₉×#394	C₂²	1	2	yes	complemented
74	C₅₉×#394	C₂²	1	2	yes	complemented
75	C₅₉×#394	C₂²	1	2	yes	complemented
76	C₅₉×#394	C₂²	1	2	yes	complemented
77	C₅₉×#394	C₂²	1	2	yes	complemented
78	C₅₉×#394	C₂²	1	2	yes	complemented
79	C₅₉×#394	C₂²	1	2	yes	complemented
80	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
81	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
82	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
83	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
84	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
85	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
86	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
87	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
88	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
89	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
90	C₅₉×#388	C₂²	1	2	yes	complemented
91	C₅₉×#388	C₂²	1	2	yes	complemented
92	C₅₉×#388	C₂²	1	2	yes	complemented
93	C₅₉×#387	C₂²	1	2	yes	complemented
94	C₅₉×#386	C₂²	1	2	yes	complemented
95	C₅₉×#386	C₂²	1	2	yes	complemented
96	C₅₉×#386	C₂²	1	2	yes	complemented
97	C₅₉×#386	C₂²	1	2	yes	complemented
98	C₅₉×#386	C₂²	1	2	yes	complemented
99	C₅₉×#386	C₂²	1	2	yes	complemented
100	C₅₉×#386	C₂²	1	2	yes	complemented
101	C₅₉×#386	C₂²	1	2	yes	complemented
102	C₅₉×#386	C₂²	1	2	yes	complemented
103	C₅₉×#385	C₂²	1	2	yes	complemented
104	C₅₉×#385	C₂²	1	2	yes	complemented
105	C₅₉×#385	C₂²	1	2	yes	complemented
106	C₅₉×#385	C₂²	1	2	yes	complemented
107	C₅₉×#385	C₂²	1	2	yes	complemented
108	C₅₉×#384	C₂²	1	1	yes	characteristic, complemented
109	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
110	C₅₉×#381	C₂²	1	2	yes	complemented
111	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
112	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
113	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
114	C₅₉×#380	C₂²	1	2	yes	complemented
115	C₅₉×#380	C₂²	1	2	yes	complemented
116	C₅₉×#379	C₂²	1	2	yes	complemented
117	C₅₉×#379	C₂²	1	2	yes	complemented
118	C₅₉×#379	C₂²	1	2	yes	complemented
119	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×#95×C₅₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₅₉	C₂³	1	2	yes	—
126	C₂⁵×C₅₉	C₂³	1	2	yes	—
127	C₂²×D₄×C₅₉	—	2	4	no	—
128	C₂²×D₄×C₅₉	—	2	4	no	—
129	C₂²×D₄×C₅₉	—	2	8	no	—
130	C₂²×D₄×C₅₉	—	2	4	no	—
131	C₂²×D₄×C₅₉	—	2	4	no	—
132	C₂²×D₄×C₅₉	—	2	4	no	—
133	C₂²×D₄×C₅₉	—	4	4	no	—
134	C₂²×D₄×C₅₉	—	4	4	no	—
135	C₂²×D₄×C₅₉	D₄	1	8	yes	—
136	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
137	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
142	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
145	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
148	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
149	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
151	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
152	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
153	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
154	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
155	#127×C₅₉	—	2	4	no	—
156	#123×C₅₉	—	4	4	no	—
157	#123×C₅₉	—	4	4	no	—
158	#123×C₅₉	—	4	4	no	—
159	#121×C₅₉	—	2	4	no	—
160	#121×C₅₉	—	2	8	no	—
161	#121×C₅₉	—	2	4	no	—
162	#120×C₅₉	—	2	8	no	—
163	#120×C₅₉	—	2	8	no	—
164	C₄×D₄×C₅₉	—	2	4	no	—
165	C₄×D₄×C₅₉	—	2	4	no	—
166	C₄×D₄×C₅₉	—	2	4	no	—
167	C₄×D₄×C₅₉	—	2	8	no	—
168	C₄×D₄×C₅₉	—	2	8	no	—
169	C₄×D₄×C₅₉	—	2	4	no	—
170	C₄×D₄×C₅₉	—	2	4	no	—
171	C₄×D₄×C₅₉	—	2	4	no	—
172	C₄×D₄×C₅₉	—	2	4	no	—
173	C₄×D₄×C₅₉	—	2	4	no	—
174	#117×C₅₉	—	2	4	no	—
175	#117×C₅₉	—	2	4	no	—
176	C₂×C₄⋊C₄×C₅₉	—	4	4	no	—
177	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
196	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
197	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
198	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
199	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
235	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
241	#95×C₅₉	C₂³	1	1	yes	characteristic
242	#95×C₅₉	C₂³	1	2	yes	—
243	#95×C₅₉	C₂³	1	2	yes	—
244	#95×C₅₉	C₂³	1	2	yes	—
245	#95×C₅₉	C₂³	1	1	yes	characteristic
246	#95×C₅₉	C₂³	1	1	yes	characteristic
247	#95×C₅₉	C₂³	1	1	yes	characteristic
248	#95×C₅₉	C₂³	1	1	yes	characteristic
249	#95×C₅₉	C₂³	1	1	yes	characteristic
250	#95×C₅₉	C₂³	1	1	yes	characteristic
251	#95×C₅₉	C₂³	1	1	yes	characteristic
252	#95×C₅₉	C₂³	1	1	yes	characteristic
253	#95×C₅₉	C₂³	1	1	yes	characteristic
254	#95×C₅₉	C₂³	1	2	yes	—
255	#95×C₅₉	C₂³	1	2	yes	—
256	#95×C₅₉	C₂³	1	2	yes	—
257	#95×C₅₉	C₂³	1	2	yes	—
258	#95×C₅₉	C₂³	1	2	yes	—
259	#95×C₅₉	C₂³	1	2	yes	—
260	C₂⁴×C₅₉	—	2	4	no	—
261	C₂⁴×C₅₉	—	2	4	no	—
262	C₂⁴×C₅₉	—	2	4	no	—
263	C₂⁴×C₅₉	—	2	4	no	—
264	C₂⁴×C₅₉	—	2	4	no	—
265	C₂⁴×C₅₉	—	2	4	no	—
266	C₂⁴×C₅₉	—	4	2	no	—
267	C₂⁴×C₅₉	—	4	2	no	—
268	C₂⁴×C₅₉	—	4	2	no	—
269	C₂⁴×C₅₉	—	4	2	no	—
270	C₂⁴×C₅₉	—	4	2	no	—
271	C₂⁴×C₅₉	—	4	2	no	—
272	C₂⁴×C₅₉	—	4	2	no	—
273	C₂⁴×C₅₉	C₂×D₄	1	8	yes	—
274	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
275	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
276	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
277	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
278	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
279	C₂×D₄×C₅₉	—	2	2	no	—
280	C₂×D₄×C₅₉	—	2	4	no	—
281	C₂×D₄×C₅₉	—	2	4	no	—
282	C₂×D₄×C₅₉	—	2	2	no	—
283	C₂×D₄×C₅₉	—	2	32	no	—
284	C₂×D₄×C₅₉	—	2	4	no	—
285	C₂×D₄×C₅₉	—	2	4	no	—
286	C₂×D₄×C₅₉	—	2	4	no	—
287	C₂×D₄×C₅₉	—	2	4	no	—
288	C₂×D₄×C₅₉	—	2	4	no	—
289	C₂×D₄×C₅₉	—	2	4	no	—
290	C₂×D₄×C₅₉	—	2	4	no	—
291	C₂×D₄×C₅₉	—	2	4	no	—
292	C₂×D₄×C₅₉	—	2	2	no	—
293	C₂×D₄×C₅₉	—	2	2	no	—
294	C₂×D₄×C₅₉	—	2	2	no	—
295	C₂×D₄×C₅₉	—	2	2	no	—
296	C₂×D₄×C₅₉	—	2	2	no	—
297	C₂×D₄×C₅₉	—	2	2	no	—
298	C₂×D₄×C₅₉	—	2	4	no	—
299	C₂×D₄×C₅₉	—	4	2	no	—
300	C₂×D₄×C₅₉	—	4	2	no	—
301	C₂×D₄×C₅₉	—	4	2	no	—
302	C₂×D₄×C₅₉	—	4	2	no	—
303	C₂×D₄×C₅₉	—	4	2	no	—
304	C₂×D₄×C₅₉	—	4	2	no	—
305	C₂×D₄×C₅₉	—	4	32	no	—
306	C₂×D₄×C₅₉	—	4	16	no	—
307	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
308	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
309	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
310	C₂×D₄×C₅₉	#41	1	4	yes	—
311	C₂×D₄×C₅₉	#41	1	4	yes	—
312	C₂²×C₄×C₅₉	—	2	2	no	—
313	C₂²×C₄×C₅₉	—	2	2	no	—
314	C₂²×C₄×C₅₉	—	2	4	no	—
315	C₂²×C₄×C₅₉	—	2	4	no	—
316	C₂²×C₄×C₅₉	—	2	4	no	—
317	C₂²×C₄×C₅₉	—	2	4	no	—
318	C₂²×C₄×C₅₉	—	2	4	no	—
319	C₂²×C₄×C₅₉	—	2	4	no	—
320	C₂²×C₄×C₅₉	—	2	4	no	—
321	C₂²×C₄×C₅₉	—	2	2	no	—
322	C₂²×C₄×C₅₉	—	2	2	no	—
323	C₂²×C₄×C₅₉	—	2	2	no	—
324	C₂²×C₄×C₅₉	—	2	4	no	—
325	C₂²×C₄×C₅₉	—	2	4	no	—
326	C₂²×C₄×C₅₉	—	4	2	no	—
327	C₂²×C₄×C₅₉	—	4	2	no	—
328	C₂²×C₄×C₅₉	—	4	2	no	—
329	C₂²×C₄×C₅₉	—	4	2	no	—
330	C₂²×C₄×C₅₉	—	4	2	no	—
331	C₂²×C₄×C₅₉	—	4	2	no	—
332	C₂²×C₄×C₅₉	—	4	2	no	—
333	C₂²×C₄×C₅₉	—	4	2	no	—
334	C₂²×C₄×C₅₉	—	4	2	no	—
335	C₂²×C₄×C₅₉	—	4	2	no	—
336	C₂²×C₄×C₅₉	—	4	2	no	—
337	C₂²×C₄×C₅₉	—	4	2	no	—
338	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
339	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₅₉	—	2	2	no	—
358	C₄⋊C₄×C₅₉	—	2	2	no	—
359	C₄⋊C₄×C₅₉	—	2	2	no	—
360	C₄⋊C₄×C₅₉	—	2	2	no	—
361	C₄⋊C₄×C₅₉	—	2	2	no	—
362	C₄⋊C₄×C₅₉	—	2	2	no	—
363	C₄⋊C₄×C₅₉	—	2	2	no	—
364	C₄⋊C₄×C₅₉	—	2	2	no	—
365	C₄⋊C₄×C₅₉	—	2	2	no	—
366	C₄⋊C₄×C₅₉	—	2	4	no	—
367	C₄⋊C₄×C₅₉	—	2	2	no	—
368	C₄⋊C₄×C₅₉	—	2	2	no	—
369	C₄⋊C₄×C₅₉	—	4	2	no	—
370	C₄⋊C₄×C₅₉	—	4	2	no	—
371	C₄⋊C₄×C₅₉	—	4	1	no	—
372	C₄⋊C₄×C₅₉	—	4	2	no	—
373	C₄⋊C₄×C₅₉	—	4	2	no	—
374	C₄⋊C₄×C₅₉	—	4	2	no	—
375	C₂²⋊C₄×C₅₉	—	2	2	no	—
376	C₂²⋊C₄×C₅₉	—	2	4	no	—
377	C₂²⋊C₄×C₅₉	—	2	2	no	—
378	C₂²⋊C₄×C₅₉	—	2	4	no	—
379	C₂²⋊C₄×C₅₉	—	2	4	no	—
380	C₂²⋊C₄×C₅₉	—	2	4	no	—
381	C₂²⋊C₄×C₅₉	—	2	4	no	—
382	C₂²⋊C₄×C₅₉	—	2	2	no	—
383	C₂²⋊C₄×C₅₉	—	2	4	no	—
384	C₂²⋊C₄×C₅₉	—	2	4	no	—
385	C₂²⋊C₄×C₅₉	—	2	4	no	—
386	C₂²⋊C₄×C₅₉	—	2	4	no	—
387	C₂²⋊C₄×C₅₉	—	2	2	no	—
388	C₂²⋊C₄×C₅₉	—	2	4	no	—
389	C₂²⋊C₄×C₅₉	—	2	2	no	—
390	C₂²⋊C₄×C₅₉	—	2	2	no	—
391	C₂²⋊C₄×C₅₉	—	2	4	no	—
392	C₂²⋊C₄×C₅₉	—	2	2	no	—
393	C₂²⋊C₄×C₅₉	—	2	2	no	—
394	C₂²⋊C₄×C₅₉	—	2	4	no	—
395	C₂²⋊C₄×C₅₉	—	2	4	no	—
396	C₂²⋊C₄×C₅₉	—	4	2	no	—
397	C₂²⋊C₄×C₅₉	—	4	2	no	—
398	C₂²⋊C₄×C₅₉	—	4	2	no	—
399	C₂²⋊C₄×C₅₉	—	4	2	no	—
400	C₂²⋊C₄×C₅₉	—	4	2	no	—
401	C₂²⋊C₄×C₅₉	—	4	2	no	—
402	C₂²⋊C₄×C₅₉	—	4	1	no	—
403	C₂²⋊C₄×C₅₉	—	4	2	no	—
404	C₂²⋊C₄×C₅₉	—	4	1	no	—
405	C₂²⋊C₄×C₅₉	—	4	2	no	—
406	C₂²⋊C₄×C₅₉	—	4	2	no	—
407	C₂²⋊C₄×C₅₉	—	4	2	no	—
408	C₂²⋊C₄×C₅₉	—	4	2	no	—
409	C₂²⋊C₄×C₅₉	—	4	2	no	—
410	C₄²×C₅₉	—	2	4	no	—
411	C₄²×C₅₉	—	2	2	no	—
412	C₄²×C₅₉	—	2	2	no	—
413	C₄²×C₅₉	—	2	2	no	—
414	C₄²×C₅₉	—	2	2	no	—
415	C₄²×C₅₉	—	2	2	no	—
416	C₂³×C₅₉	—	2	2	no	—
417	C₂³×C₅₉	—	2	2	no	—
418	C₂³×C₅₉	—	2	2	no	—
419	C₂³×C₅₉	—	2	2	no	—
420	C₂³×C₅₉	—	2	1	no	—
421	C₂³×C₅₉	—	2	1	no	—
422	C₂³×C₅₉	—	2	1	no	—
423	C₂³×C₅₉	—	2	1	no	—
424	C₂³×C₅₉	—	2	1	no	—
425	C₂³×C₅₉	—	2	2	no	—
426	C₂³×C₅₉	—	2	2	no	—
427	C₂³×C₅₉	—	2	1	no	—
428	C₂³×C₅₉	—	2	1	no	—
429	C₂³×C₅₉	—	2	2	no	—
430	C₂³×C₅₉	—	2	2	no	—
431	C₂³×C₅₉	—	2	2	no	—
432	C₂³×C₅₉	—	2	1	no	—
433	C₂³×C₅₉	—	2	1	no	—
434	C₂³×C₅₉	—	2	1	no	—
435	C₂³×C₅₉	—	2	1	no	—
436	C₂³×C₅₉	—	2	1	no	—
437	C₂³×C₅₉	—	2	2	no	—
438	C₂³×C₅₉	—	2	16	no	—
439	C₂³×C₅₉	—	2	2	no	—
440	C₂³×C₅₉	—	2	2	no	—
441	C₂³×C₅₉	—	2	2	no	—
442	C₂³×C₅₉	—	2	2	no	—
443	C₂³×C₅₉	—	2	2	no	—
444	C₂³×C₅₉	—	2	2	no	—
445	C₂³×C₅₉	—	2	2	no	—
446	C₂³×C₅₉	—	4	8	no	—
447	C₂³×C₅₉	—	4	8	no	—
448	C₂³×C₅₉	—	4	8	no	—
449	C₂³×C₅₉	—	4	8	no	—
450	C₂³×C₅₉	—	4	8	no	—
451	C₂³×C₅₉	—	4	8	no	—
452	C₂³×C₅₉	—	8	4	no	—
453	C₂³×C₅₉	—	8	4	no	—
454	C₂³×C₅₉	—	8	4	no	—
455	C₂³×C₅₉	—	8	4	no	—
456	C₂³×C₅₉	—	8	4	no	—
457	C₂³×C₅₉	—	8	4	no	—
458	C₂³×C₅₉	—	8	4	no	—
459	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
460	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
461	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
462	C₂³×C₅₉	C₂×#41	1	4	yes	—
463	C₂³×C₅₉	C₂×#41	1	4	yes	—
464	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
465	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
466	D₄×C₅₉	—	2	8	no	—
467	D₄×C₅₉	—	2	16	no	—
468	D₄×C₅₉	—	2	8	no	—
469	D₄×C₅₉	—	4	8	no	—
470	D₄×C₅₉	—	4	8	no	—
471	D₄×C₅₉	—	4	8	no	—
472	D₄×C₅₉	—	4	8	no	—
473	D₄×C₅₉	—	4	4	no	—
474	D₄×C₅₉	—	8	4	no	—
475	D₄×C₅₉	#123	1	16	yes	complemented
476	C₂×C₄×C₅₉	—	2	1	no	—
477	C₂×C₄×C₅₉	—	2	1	no	—
478	C₂×C₄×C₅₉	—	2	1	no	—
479	C₂×C₄×C₅₉	—	2	1	no	—
480	C₂×C₄×C₅₉	—	2	1	no	—
481	C₂×C₄×C₅₉	—	2	1	no	—
482	C₂×C₄×C₅₉	—	2	8	no	—
483	C₂×C₄×C₅₉	—	2	1	no	—
484	C₂×C₄×C₅₉	—	2	1	no	—
485	C₂×C₄×C₅₉	—	2	2	no	—
486	C₂×C₄×C₅₉	—	2	1	no	—
487	C₂×C₄×C₅₉	—	2	1	no	—
488	C₂×C₄×C₅₉	—	2	2	no	—
489	C₂×C₄×C₅₉	—	2	1	no	—
490	C₂×C₄×C₅₉	—	2	1	no	—
491	C₂×C₄×C₅₉	—	2	2	no	—
492	C₂×C₄×C₅₉	—	2	1	no	—
493	C₂×C₄×C₅₉	—	2	1	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	1	no	—
500	C₂×C₄×C₅₉	—	2	2	no	—
501	C₂×C₄×C₅₉	—	2	2	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	1	no	—
506	C₂×C₄×C₅₉	—	2	2	no	—
507	C₂×C₄×C₅₉	—	2	2	no	—
508	C₂×C₄×C₅₉	—	2	1	no	—
509	C₂×C₄×C₅₉	—	2	1	no	—
510	C₂×C₄×C₅₉	—	2	2	no	—
511	C₂×C₄×C₅₉	—	2	2	no	—
512	C₂×C₄×C₅₉	—	2	1	no	—
513	C₂×C₄×C₅₉	—	2	1	no	—
514	C₂×C₄×C₅₉	—	2	2	no	—
515	C₂×C₄×C₅₉	—	2	1	no	—
516	C₂×C₄×C₅₉	—	2	1	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	1	no	—
524	C₂×C₄×C₅₉	—	2	1	no	—
525	C₂×C₄×C₅₉	—	4	8	no	—
526	C₂×C₄×C₅₉	—	4	8	no	—
527	C₂×C₄×C₅₉	—	4	4	no	—
528	C₂×C₄×C₅₉	—	8	4	no	—
529	C₂×C₄×C₅₉	—	8	4	no	—
530	C₂×C₄×C₅₉	—	8	4	no	—
531	C₂×C₄×C₅₉	—	8	4	no	—
532	C₂×C₄×C₅₉	—	8	4	no	—
533	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
536	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
537	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
539	#35713	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
540	C₂²×C₅₉	—	2	4	no	—
541	C₂²×C₅₉	—	2	4	no	—
542	C₂²×C₅₉	—	2	4	no	—
543	C₂²×C₅₉	—	2	4	no	—
544	C₂²×C₅₉	—	2	4	no	—
545	C₂²×C₅₉	—	2	4	no	—
546	C₂²×C₅₉	—	2	2	no	—
547	C₂²×C₅₉	—	2	4	no	—
548	C₂²×C₅₉	—	2	4	no	—
549	C₂²×C₅₉	—	2	2	no	—
550	C₂²×C₅₉	—	2	2	no	—
551	C₂²×C₅₉	—	2	4	no	—
552	C₂²×C₅₉	—	2	2	no	—
553	C₂²×C₅₉	—	2	2	no	—
554	C₂²×C₅₉	—	2	2	no	—
555	C₂²×C₅₉	—	4	1	no	—
556	C₂²×C₅₉	—	4	1	no	—
557	C₂²×C₅₉	—	4	2	no	—
558	C₂²×C₅₉	—	4	1	no	—
559	C₂²×C₅₉	—	4	2	no	—
560	C₂²×C₅₉	—	4	1	no	—
561	C₂²×C₅₉	—	4	1	no	—
562	C₂²×C₅₉	—	4	2	no	—
563	C₂²×C₅₉	—	4	2	no	—
564	C₂²×C₅₉	—	4	1	no	—
565	C₂²×C₅₉	—	4	1	no	—
566	C₂²×C₅₉	—	4	1	no	—
567	C₂²×C₅₉	—	4	2	no	—
568	C₂²×C₅₉	—	4	2	no	—
569	C₂²×C₅₉	—	4	2	no	—
570	C₂²×C₅₉	—	4	2	no	—
571	C₂²×C₅₉	—	4	2	no	—
572	C₂²×C₅₉	—	4	2	no	—
573	C₂²×C₅₉	—	4	2	no	—
574	C₂²×C₅₉	—	8	16	no	—
575	C₂²×C₅₉	—	8	16	no	—
576	C₂²×C₅₉	C₂×#123	1	8	yes	—
577	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
578	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
579	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
580	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂²×C₅₉	#585	1	1	yes	characteristic
584	C₄×C₅₉	—	2	2	no	—
585	C₄×C₅₉	—	2	2	no	—
586	C₄×C₅₉	—	2	2	no	—
587	C₄×C₅₉	—	4	1	no	—
588	C₄×C₅₉	—	4	2	no	—
589	C₄×C₅₉	—	4	1	no	—
590	C₄×C₅₉	—	4	2	no	—
591	C₄×C₅₉	—	4	1	no	—
592	C₄×C₅₉	—	4	1	no	—
593	C₄×C₅₉	—	4	2	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	—	4	1	no	—
601	C₄×C₅₉	C₂×#123	1	4	yes	—
602	C₂×D₄²	C₂×C₅₉	1	1	yes	characteristic
603	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
604	#2624	C₂×C₅₉	1	1	yes	characteristic, complemented
605	#2622	C₂×C₅₉	1	2	yes	complemented
606	#2500	C₂×C₅₉	1	1	yes	characteristic, complemented
607	#2485	C₂×C₅₉	1	1	yes	characteristic, complemented
608	#2445	C₂×C₅₉	1	1	yes	characteristic, complemented
609	#2445	C₂×C₅₉	1	1	yes	characteristic, complemented
610	#2444	C₂×C₅₉	1	2	yes	complemented
611	#2443	C₂×C₅₉	1	2	yes	complemented
612	#2422	C₂×C₅₉	1	1	yes	characteristic, complemented
613	#2420	C₂×C₅₉	1	1	yes	characteristic, complemented
614	#2418	C₂×C₅₉	1	2	yes	complemented
615	#2418	C₂×C₅₉	1	2	yes	complemented
616	#2412	C₂×C₅₉	1	2	yes	complemented
617	#2405	C₂×C₅₉	1	2	yes	complemented
618	#2395	C₂×C₅₉	1	1	yes	characteristic, complemented
619	C₂×#394	C₂×C₅₉	1	2	yes	complemented
620	#2349	C₂×C₅₉	1	1	yes	characteristic, complemented
621	D₄×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
622	D₄×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
623	D₄×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
624	D₄×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
625	C₂×C₅₉	—	2	8	no	—
626	C₂×C₅₉	—	4	4	no	—
627	C₂×C₅₉	—	4	2	no	—
628	C₂×C₅₉	—	4	2	no	—
629	C₂×C₅₉	—	8	2	no	—
630	C₂×C₅₉	C₂²×#123	1	1	yes	characteristic
631	C₂×C₅₉	#3484	1	1	yes	characteristic
632	C₂×C₅₉	#3496	1	1	yes	characteristic
633	C₂×C₅₉	#3513	1	1	yes	characteristic
634	C₂×C₅₉	#3514	1	1	yes	characteristic
635	C₂×C₅₉	#3519	1	1	yes	characteristic
636	C₂×C₅₉	#3519	1	1	yes	characteristic
637	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
638	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
639	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
640	D₄²	—	2	8	no	—
641	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
642	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
643	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
644	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
645	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
646	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
647	C₂×#121	C₂²×C₅₉	1	2	yes	—
648	C₂×#120	C₂²×C₅₉	1	2	yes	—
649	C₂×#120	C₂²×C₅₉	1	2	yes	—
650	#518	—	2	8	no	—
651	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
652	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
653	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
654	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
655	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
656	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
657	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
658	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
659	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
660	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
661	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
662	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
663	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
664	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
665	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
666	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
667	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
668	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
669	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
670	#399	C₂²×C₅₉	1	2	yes	complemented
671	#399	C₂²×C₅₉	1	1	yes	characteristic, complemented
672	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
673	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
674	#397	C₂²×C₅₉	1	2	yes	complemented
675	#397	C₂²×C₅₉	1	2	yes	complemented
676	#397	C₂²×C₅₉	1	2	yes	complemented
677	#397	C₂²×C₅₉	1	2	yes	complemented
678	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
679	#397	C₂²×C₅₉	1	1	yes	characteristic, complemented
680	#394	C₂²×C₅₉	1	1	yes	characteristic
681	#394	C₂²×C₅₉	1	2	yes	—
682	#394	C₂²×C₅₉	1	1	yes	characteristic
683	#394	C₂²×C₅₉	1	2	yes	complemented
684	#394	C₂²×C₅₉	1	2	yes	complemented
685	#394	C₂²×C₅₉	1	2	yes	complemented
686	#394	C₂²×C₅₉	1	2	yes	complemented
687	#394	C₂²×C₅₉	1	2	yes	complemented
688	#394	C₂²×C₅₉	1	2	yes	complemented
689	#394	C₂²×C₅₉	1	2	yes	complemented
690	#394	C₂²×C₅₉	1	2	yes	complemented
691	#394	C₂²×C₅₉	1	2	yes	complemented
692	#394	C₂²×C₅₉	1	2	yes	complemented
693	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
694	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
695	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
696	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
697	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
698	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
699	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
700	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
701	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
702	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
703	#388	C₂²×C₅₉	1	2	yes	complemented
704	#388	C₂²×C₅₉	1	2	yes	complemented
705	#388	C₂²×C₅₉	1	2	yes	complemented
706	#387	C₂²×C₅₉	1	2	yes	complemented
707	#386	C₂²×C₅₉	1	2	yes	complemented
708	#386	C₂²×C₅₉	1	2	yes	complemented
709	#386	C₂²×C₅₉	1	2	yes	complemented
710	#386	C₂²×C₅₉	1	2	yes	complemented
711	#386	C₂²×C₅₉	1	2	yes	complemented
712	#386	C₂²×C₅₉	1	2	yes	complemented
713	#386	C₂²×C₅₉	1	2	yes	complemented
714	#386	C₂²×C₅₉	1	2	yes	complemented
715	#386	C₂²×C₅₉	1	2	yes	complemented
716	#385	C₂²×C₅₉	1	2	yes	complemented
717	#385	C₂²×C₅₉	1	2	yes	complemented
718	#385	C₂²×C₅₉	1	2	yes	complemented
719	#385	C₂²×C₅₉	1	2	yes	complemented
720	#385	C₂²×C₅₉	1	2	yes	complemented
721	#384	C₂²×C₅₉	1	1	yes	characteristic, complemented
722	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
723	#381	C₂²×C₅₉	1	2	yes	complemented
724	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
725	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
726	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
727	#380	C₂²×C₅₉	1	2	yes	complemented
728	#380	C₂²×C₅₉	1	2	yes	complemented
729	#379	C₂²×C₅₉	1	2	yes	complemented
730	#379	C₂²×C₅₉	1	2	yes	complemented
731	#379	C₂²×C₅₉	1	2	yes	complemented
732	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
733	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
734	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
735	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
736	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
737	C₂×#95	C₂²×C₅₉	1	2	yes	complemented
738	C₅₉	#35713	1	1	yes	characteristic, direct product factor, Sylow
739	C₂⁵	C₂³×C₅₉	1	2	yes	—
740	C₂⁵	C₂³×C₅₉	1	2	yes	—
741	C₂²×D₄	—	2	4	no	—
742	C₂²×D₄	—	2	4	no	—
743	C₂²×D₄	—	2	8	no	—
744	C₂²×D₄	—	2	4	no	—
745	C₂²×D₄	—	2	4	no	—
746	C₂²×D₄	—	2	4	no	—
747	C₂²×D₄	—	4	4	no	—
748	C₂²×D₄	—	4	4	no	—
749	C₂²×D₄	D₄×C₅₉	1	8	yes	—
750	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
751	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
752	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
753	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
754	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
755	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
756	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
757	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
758	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
759	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
760	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
761	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
762	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
763	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
764	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
765	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
766	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
767	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
768	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
769	#127	—	2	4	no	—
770	#123	—	4	4	no	—
771	#123	—	4	4	no	—
772	#123	—	4	4	no	—
773	#121	—	2	4	no	—
774	#121	—	2	8	no	—
775	#121	—	2	4	no	—
776	#120	—	2	8	no	—
777	#120	—	2	8	no	—
778	C₄×D₄	—	2	4	no	—
779	C₄×D₄	—	2	4	no	—
780	C₄×D₄	—	2	4	no	—
781	C₄×D₄	—	2	8	no	—
782	C₄×D₄	—	2	8	no	—
783	C₄×D₄	—	2	4	no	—
784	C₄×D₄	—	2	4	no	—
785	C₄×D₄	—	2	4	no	—
786	C₄×D₄	—	2	4	no	—
787	C₄×D₄	—	2	4	no	—
788	#117	—	2	4	no	—
789	#117	—	2	4	no	—
790	C₂×C₄⋊C₄	—	4	4	no	—
791	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
803	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
804	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
805	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
806	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
807	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
808	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
809	C₂×C₂²⋊C₄	—	2	8	no	—
810	C₂×C₂²⋊C₄	—	2	8	no	—
811	C₂×C₂²⋊C₄	—	4	4	no	—
812	C₂×C₂²⋊C₄	—	4	4	no	—
813	C₂×C₂²⋊C₄	—	4	4	no	—
814	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
820	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
831	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
832	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
833	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
835	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
836	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
837	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
838	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
839	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
843	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
844	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
848	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
849	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
850	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
851	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
852	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
853	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
854	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
855	#95	C₂³×C₅₉	1	1	yes	characteristic
856	#95	C₂³×C₅₉	1	2	yes	—
857	#95	C₂³×C₅₉	1	2	yes	—
858	#95	C₂³×C₅₉	1	2	yes	—
859	#95	C₂³×C₅₉	1	1	yes	characteristic
860	#95	C₂³×C₅₉	1	1	yes	characteristic
861	#95	C₂³×C₅₉	1	1	yes	characteristic
862	#95	C₂³×C₅₉	1	1	yes	characteristic
863	#95	C₂³×C₅₉	1	1	yes	characteristic
864	#95	C₂³×C₅₉	1	1	yes	characteristic
865	#95	C₂³×C₅₉	1	1	yes	characteristic
866	#95	C₂³×C₅₉	1	1	yes	characteristic
867	#95	C₂³×C₅₉	1	1	yes	characteristic
868	#95	C₂³×C₅₉	1	2	yes	—
869	#95	C₂³×C₅₉	1	2	yes	—
870	#95	C₂³×C₅₉	1	2	yes	—
871	#95	C₂³×C₅₉	1	2	yes	—
872	#95	C₂³×C₅₉	1	2	yes	—
873	#95	C₂³×C₅₉	1	2	yes	—
874	C₂⁴	—	2	4	no	—
875	C₂⁴	—	2	4	no	—
876	C₂⁴	—	2	4	no	—
877	C₂⁴	—	2	4	no	—
878	C₂⁴	—	2	4	no	—
879	C₂⁴	—	2	4	no	—
880	C₂⁴	—	4	2	no	—
881	C₂⁴	—	4	2	no	—
882	C₂⁴	—	4	2	no	—
883	C₂⁴	—	4	2	no	—
884	C₂⁴	—	4	2	no	—
885	C₂⁴	—	4	2	no	—
886	C₂⁴	—	4	2	no	—
887	C₂⁴	C₂×D₄×C₅₉	1	8	yes	—
888	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
889	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
890	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
891	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
892	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	4	no	—
895	C₂×D₄	—	2	4	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	32	no	—
898	C₂×D₄	—	2	4	no	—
899	C₂×D₄	—	2	4	no	—
900	C₂×D₄	—	2	4	no	—
901	C₂×D₄	—	2	4	no	—
902	C₂×D₄	—	2	4	no	—
903	C₂×D₄	—	2	4	no	—
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	4	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	4	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	32	no	—
920	C₂×D₄	—	4	16	no	—
921	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
922	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
923	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
924	C₂×D₄	#41×C₅₉	1	4	yes	—
925	C₂×D₄	#41×C₅₉	1	4	yes	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	4	no	—
929	C₂²×C₄	—	2	4	no	—
930	C₂²×C₄	—	2	4	no	—
931	C₂²×C₄	—	2	4	no	—
932	C₂²×C₄	—	2	4	no	—
933	C₂²×C₄	—	2	4	no	—
934	C₂²×C₄	—	2	4	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	4	no	—
939	C₂²×C₄	—	2	4	no	—
940	C₂²×C₄	—	4	2	no	—
941	C₂²×C₄	—	4	2	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	—	4	2	no	—
946	C₂²×C₄	—	4	2	no	—
947	C₂²×C₄	—	4	2	no	—
948	C₂²×C₄	—	4	2	no	—
949	C₂²×C₄	—	4	2	no	—
950	C₂²×C₄	—	4	2	no	—
951	C₂²×C₄	—	4	2	no	—
952	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
953	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
959	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
964	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
966	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
967	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
968	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
969	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
970	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	4	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	4	2	no	—
984	C₄⋊C₄	—	4	2	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₄⋊C₄	—	4	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	4	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	4	no	—
994	C₂²⋊C₄	—	2	4	no	—
995	C₂²⋊C₄	—	2	4	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	4	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	4	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	4	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	4	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	4	no	—
1009	C₂²⋊C₄	—	2	4	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	2	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	4	2	no	—
1015	C₂²⋊C₄	—	4	2	no	—
1016	C₂²⋊C₄	—	4	2	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	4	2	no	—
1019	C₂²⋊C₄	—	4	2	no	—
1020	C₂²⋊C₄	—	4	2	no	—
1021	C₂²⋊C₄	—	4	1	no	—
1022	C₂²⋊C₄	—	4	2	no	—
1023	C₂²⋊C₄	—	4	1	no	—
1024	C₄²	—	2	4	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	16	no	—
1053	C₂³	—	2	2	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	4	8	no	—
1061	C₂³	—	4	8	no	—
1062	C₂³	—	4	8	no	—
1063	C₂³	—	4	8	no	—
1064	C₂³	—	4	8	no	—
1065	C₂³	—	4	8	no	—
1066	C₂³	—	8	4	no	—
1067	C₂³	—	8	4	no	—
1068	C₂³	—	8	4	no	—
1069	C₂³	—	8	4	no	—
1070	C₂³	—	8	4	no	—
1071	C₂³	—	8	4	no	—
1072	C₂³	—	8	4	no	—
1073	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
1074	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
1075	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
1076	C₂³	C₂×#41×C₅₉	1	4	yes	—
1077	C₂³	C₂×#41×C₅₉	1	4	yes	—
1078	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
1079	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
1080	D₄	—	2	8	no	—
1081	D₄	—	2	16	no	—
1082	D₄	—	2	8	no	—
1083	D₄	—	4	8	no	—
1084	D₄	—	4	8	no	—
1085	D₄	—	4	8	no	—
1086	D₄	—	4	8	no	—
1087	D₄	—	4	4	no	—
1088	D₄	—	8	4	no	—
1089	D₄	#123×C₅₉	1	16	yes	complemented
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	8	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	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	—	4	8	no	—
1140	C₂×C₄	—	4	8	no	—
1141	C₂×C₄	—	4	4	no	—
1142	C₂×C₄	—	8	4	no	—
1143	C₂×C₄	—	8	4	no	—
1144	C₂×C₄	—	8	4	no	—
1145	C₂×C₄	—	8	4	no	—
1146	C₂×C₄	—	8	4	no	—
1147	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1148	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1149	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1150	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1151	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1152	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	2	4	no	—
1155	C₂²	—	2	4	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	2	4	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	2	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	4	no	—
1163	C₂²	—	2	4	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	4	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	8	16	no	—
1188	C₂²	—	8	16	no	—
1189	C₂²	C₂×#123×C₅₉	1	8	yes	—
1190	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1191	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1192	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1193	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1194	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1195	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1196	C₂²	C₅₉×#585	1	1	yes	characteristic
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	2	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	C₂×#123×C₅₉	1	4	yes	—
1215	C₂	—	2	8	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	4	4	no	—
1219	C₂	—	8	2	no	—
1220	C₂	C₂²×#123×C₅₉	1	1	yes	characteristic
1221	C₂	C₅₉×#3484	1	1	yes	characteristic
1222	C₂	C₅₉×#3496	1	1	yes	characteristic
1223	C₂	C₅₉×#3513	1	1	yes	characteristic
1224	C₂	C₅₉×#3514	1	1	yes	characteristic
1225	C₂	C₅₉×#3519	1	1	yes	characteristic
1226	C₂	C₅₉×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×D₄²×C₅₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#518	C₂	semidirect
3. C₅₉×#2624	C₂	semidirect
4. C₅₉×#2622	C₂	semidirect
5. C₅₉×#2500	C₂	semidirect
6. C₅₉×#2485	C₂	semidirect
7. C₅₉×#2445	C₂	semidirect
8. C₅₉×#2445	C₂	semidirect
9. C₅₉×#2444	C₂	semidirect
10. C₅₉×#2443	C₂	semidirect
11. C₅₉×#2422	C₂	semidirect
12. C₅₉×#2420	C₂	semidirect
13. C₅₉×#2418	C₂	semidirect
14. C₅₉×#2418	C₂	semidirect
15. C₅₉×#2412	C₂	semidirect
16. C₅₉×#2405	C₂	semidirect
17. C₅₉×#2395	C₂	semidirect
18. C₂×C₅₉×#394	C₂	semidirect
19. C₅₉×#2349	C₂	semidirect
20. D₄×C₄⋊C₄×C₅₉	C₂	semidirect
21. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
22. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
23. D₄×C₂²⋊C₄×C₅₉	C₂	semidirect
29. C₂×#123×C₅₉	C₂²	semidirect
30. C₂×#123×C₅₉	C₂²	semidirect
31. C₂×#123×C₅₉	C₂²	semidirect
44. C₂×C₄×D₄×C₅₉	C₂²	semidirect
45. C₂×C₄×D₄×C₅₉	C₂²	semidirect
46. C₂×C₄×D₄×C₅₉	C₂²	semidirect
47. C₂×C₄×D₄×C₅₉	C₂²	semidirect
48. C₂×#117×C₅₉	C₂²	semidirect
49. C₂×#117×C₅₉	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
51. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
52. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
53. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
54. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
55. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
56. C₅₉×#400	C₂²	semidirect
57. C₅₉×#399	C₂²	semidirect
58. C₅₉×#399	C₂²	semidirect
59. C₅₉×#398	C₂²	semidirect
60. C₅₉×#397	C₂²	semidirect
61. C₅₉×#397	C₂²	semidirect
62. C₅₉×#397	C₂²	semidirect
63. C₅₉×#397	C₂²	semidirect
64. C₅₉×#397	C₂²	semidirect
65. C₅₉×#397	C₂²	semidirect
66. C₅₉×#397	C₂²	semidirect
70. C₅₉×#394	C₂²	semidirect
71. C₅₉×#394	C₂²	semidirect
72. C₅₉×#394	C₂²	semidirect
73. C₅₉×#394	C₂²	semidirect
74. C₅₉×#394	C₂²	semidirect
75. C₅₉×#394	C₂²	semidirect
76. C₅₉×#394	C₂²	semidirect
77. C₅₉×#394	C₂²	semidirect
78. C₅₉×#394	C₂²	semidirect
79. C₅₉×#394	C₂²	semidirect
80. C₅₉×#390	C₂²	semidirect
81. C₅₉×#390	C₂²	semidirect
82. C₅₉×#390	C₂²	semidirect
83. C₅₉×#390	C₂²	semidirect
84. C₅₉×#390	C₂²	semidirect
85. C₅₉×#390	C₂²	semidirect
86. C₅₉×#389	C₂²	semidirect
87. C₅₉×#389	C₂²	semidirect
88. C₅₉×#389	C₂²	semidirect
89. C₅₉×#389	C₂²	semidirect
90. C₅₉×#388	C₂²	semidirect
91. C₅₉×#388	C₂²	semidirect
92. C₅₉×#388	C₂²	semidirect
93. C₅₉×#387	C₂²	semidirect
94. C₅₉×#386	C₂²	semidirect
95. C₅₉×#386	C₂²	semidirect
96. C₅₉×#386	C₂²	semidirect
97. C₅₉×#386	C₂²	semidirect
98. C₅₉×#386	C₂²	semidirect
99. C₅₉×#386	C₂²	semidirect
100. C₅₉×#386	C₂²	semidirect
101. C₅₉×#386	C₂²	semidirect
102. C₅₉×#386	C₂²	semidirect
103. C₅₉×#385	C₂²	semidirect
104. C₅₉×#385	C₂²	semidirect
105. C₅₉×#385	C₂²	semidirect
106. C₅₉×#385	C₂²	semidirect
107. C₅₉×#385	C₂²	semidirect
108. C₅₉×#384	C₂²	semidirect
109. C₅₉×#382	C₂²	semidirect
110. C₅₉×#381	C₂²	semidirect
111. C₅₉×#380	C₂²	semidirect
112. C₅₉×#380	C₂²	semidirect
113. C₅₉×#380	C₂²	semidirect
114. C₅₉×#380	C₂²	semidirect
115. C₅₉×#380	C₂²	semidirect
116. C₅₉×#379	C₂²	semidirect
117. C₅₉×#379	C₂²	semidirect
118. C₅₉×#379	C₂²	semidirect
119. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
120. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
124. C₂×#95×C₅₉	C₂²	semidirect
475. D₄×C₅₉	#123	semidirect
539. #35713	C₅₉	direct (N × H)
603. C₂×#518	C₂×C₅₉	semidirect
604. #2624	C₂×C₅₉	semidirect
605. #2622	C₂×C₅₉	semidirect
606. #2500	C₂×C₅₉	semidirect
607. #2485	C₂×C₅₉	semidirect
608. #2445	C₂×C₅₉	semidirect
609. #2445	C₂×C₅₉	semidirect
610. #2444	C₂×C₅₉	semidirect
611. #2443	C₂×C₅₉	semidirect
612. #2422	C₂×C₅₉	semidirect
613. #2420	C₂×C₅₉	semidirect
614. #2418	C₂×C₅₉	semidirect
615. #2418	C₂×C₅₉	semidirect
616. #2412	C₂×C₅₉	semidirect
617. #2405	C₂×C₅₉	semidirect
618. #2395	C₂×C₅₉	semidirect
619. C₂×#394	C₂×C₅₉	semidirect
620. #2349	C₂×C₅₉	semidirect
621. D₄×C₄⋊C₄	C₂×C₅₉	semidirect
622. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
623. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
624. D₄×C₂²⋊C₄	C₂×C₅₉	semidirect
642. C₂×#123	C₂²×C₅₉	semidirect
643. C₂×#123	C₂²×C₅₉	semidirect
644. C₂×#123	C₂²×C₅₉	semidirect
657. C₂×C₄×D₄	C₂²×C₅₉	semidirect
658. C₂×C₄×D₄	C₂²×C₅₉	semidirect
659. C₂×C₄×D₄	C₂²×C₅₉	semidirect
660. C₂×C₄×D₄	C₂²×C₅₉	semidirect
661. C₂×#117	C₂²×C₅₉	semidirect
662. C₂×#117	C₂²×C₅₉	semidirect
663. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
664. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
665. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
666. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
667. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
668. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
669. #400	C₂²×C₅₉	semidirect
670. #399	C₂²×C₅₉	semidirect
671. #399	C₂²×C₅₉	semidirect
672. #398	C₂²×C₅₉	semidirect
673. #397	C₂²×C₅₉	semidirect
674. #397	C₂²×C₅₉	semidirect
675. #397	C₂²×C₅₉	semidirect
676. #397	C₂²×C₅₉	semidirect
677. #397	C₂²×C₅₉	semidirect
678. #397	C₂²×C₅₉	semidirect
679. #397	C₂²×C₅₉	semidirect
683. #394	C₂²×C₅₉	semidirect
684. #394	C₂²×C₅₉	semidirect
685. #394	C₂²×C₅₉	semidirect
686. #394	C₂²×C₅₉	semidirect
687. #394	C₂²×C₅₉	semidirect
688. #394	C₂²×C₅₉	semidirect
689. #394	C₂²×C₅₉	semidirect
690. #394	C₂²×C₅₉	semidirect
691. #394	C₂²×C₅₉	semidirect
692. #394	C₂²×C₅₉	semidirect
693. #390	C₂²×C₅₉	semidirect
694. #390	C₂²×C₅₉	semidirect
695. #390	C₂²×C₅₉	semidirect
696. #390	C₂²×C₅₉	semidirect
697. #390	C₂²×C₅₉	semidirect
698. #390	C₂²×C₅₉	semidirect
699. #389	C₂²×C₅₉	semidirect
700. #389	C₂²×C₅₉	semidirect
701. #389	C₂²×C₅₉	semidirect
702. #389	C₂²×C₅₉	semidirect
703. #388	C₂²×C₅₉	semidirect
704. #388	C₂²×C₅₉	semidirect
705. #388	C₂²×C₅₉	semidirect
706. #387	C₂²×C₅₉	semidirect
707. #386	C₂²×C₅₉	semidirect
708. #386	C₂²×C₅₉	semidirect
709. #386	C₂²×C₅₉	semidirect
710. #386	C₂²×C₅₉	semidirect
711. #386	C₂²×C₅₉	semidirect
712. #386	C₂²×C₅₉	semidirect
713. #386	C₂²×C₅₉	semidirect
714. #386	C₂²×C₅₉	semidirect
715. #386	C₂²×C₅₉	semidirect
716. #385	C₂²×C₅₉	semidirect
717. #385	C₂²×C₅₉	semidirect
718. #385	C₂²×C₅₉	semidirect
719. #385	C₂²×C₅₉	semidirect
720. #385	C₂²×C₅₉	semidirect
721. #384	C₂²×C₅₉	semidirect
722. #382	C₂²×C₅₉	semidirect
723. #381	C₂²×C₅₉	semidirect
724. #380	C₂²×C₅₉	semidirect
725. #380	C₂²×C₅₉	semidirect
726. #380	C₂²×C₅₉	semidirect
727. #380	C₂²×C₅₉	semidirect
728. #380	C₂²×C₅₉	semidirect
729. #379	C₂²×C₅₉	semidirect
730. #379	C₂²×C₅₉	semidirect
731. #379	C₂²×C₅₉	semidirect
732. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
733. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
734. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
735. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
736. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
737. C₂×#95	C₂²×C₅₉	semidirect
738. C₅₉	#35713	direct (N × H)
1089. D₄	#123×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₅₉	2
C₂×C₅₉×#518	2
C₅₉×#2624	2
C₅₉×#2622	2
C₅₉×#2500	2
C₅₉×#2485	2
C₅₉×#2445	2
C₅₉×#2444	2
C₅₉×#2443	2
C₅₉×#2422	2
C₅₉×#2420	2
C₅₉×#2418	2
C₅₉×#2412	2
C₅₉×#2405	2
C₅₉×#2395	2
C₂×C₅₉×#394	2
C₅₉×#2349	2
D₄×C₄⋊C₄×C₅₉	2
D₄×C₂²⋊C₄×C₅₉	2
#35713	59

Subgroups — C59×#35713 #28447822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35713 #28447822