Subgroups — C₅₉×#35808 #28447917

Order 15104.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2630	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2620	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2534	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2472	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2461	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2457	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2433	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2418	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2411	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2392	C₂	1	2	yes	maximal, complemented
19	C₅₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2366	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2363	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2354	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#559	—	2	8	no	—
26	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
32	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
33	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
34	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
37	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#120×C₅₉	C₂²	1	2	yes	—
39	C₂×#120×C₅₉	C₂²	1	2	yes	—
40	C₅₉×#518	—	2	8	no	—
41	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
46	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
50	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
52	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
53	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
54	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
55	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
56	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
57	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
58	C₅₉×#399	C₂²	1	1	yes	characteristic
59	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
60	C₅₉×#398	C₂²	1	1	yes	characteristic, complemented
61	C₅₉×#397	C₂²	1	2	yes	complemented
62	C₅₉×#397	C₂²	1	2	yes	complemented
63	C₅₉×#396	C₂²	1	1	yes	characteristic
64	C₅₉×#396	C₂²	1	1	yes	characteristic
65	C₅₉×#396	C₂²	1	2	yes	complemented
66	C₅₉×#396	C₂²	1	2	yes	complemented
67	C₅₉×#396	C₂²	1	2	yes	complemented
68	C₅₉×#396	C₂²	1	2	yes	complemented
69	C₅₉×#395	C₂²	1	1	yes	characteristic, complemented
70	C₅₉×#394	C₂²	1	2	yes	—
71	C₅₉×#394	C₂²	1	2	yes	—
72	C₅₉×#394	C₂²	1	2	yes	—
73	C₅₉×#394	C₂²	1	2	yes	—
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×#393	C₂²	1	1	yes	characteristic
79	C₅₉×#392	C₂²	1	2	yes	—
80	C₅₉×#392	C₂²	1	2	yes	—
81	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
82	C₅₉×#391	C₂²	1	1	yes	characteristic, complemented
83	C₅₉×#390	C₂²	1	1	yes	characteristic
84	C₅₉×#390	C₂²	1	1	yes	characteristic
85	C₅₉×#390	C₂²	1	1	yes	characteristic
86	C₅₉×#390	C₂²	1	1	yes	characteristic
87	C₅₉×#390	C₂²	1	2	yes	—
88	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
89	C₅₉×#390	C₂²	1	1	yes	characteristic, complemented
90	C₅₉×#390	C₂²	1	2	yes	complemented
91	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
92	C₅₉×#389	C₂²	1	1	yes	characteristic, complemented
93	C₅₉×#388	C₂²	1	2	yes	—
94	C₅₉×#388	C₂²	1	2	yes	—
95	C₅₉×#388	C₂²	1	2	yes	complemented
96	C₅₉×#388	C₂²	1	2	yes	complemented
97	C₅₉×#388	C₂²	1	2	yes	complemented
98	C₅₉×#388	C₂²	1	2	yes	complemented
99	C₅₉×#388	C₂²	1	2	yes	complemented
100	C₅₉×#387	C₂²	1	2	yes	complemented
101	C₅₉×#386	C₂²	1	2	yes	—
102	C₅₉×#386	C₂²	1	2	yes	complemented
103	C₅₉×#386	C₂²	1	2	yes	complemented
104	C₅₉×#386	C₂²	1	2	yes	complemented
105	C₅₉×#386	C₂²	1	2	yes	complemented
106	C₅₉×#386	C₂²	1	2	yes	complemented
107	C₅₉×#385	C₂²	1	2	yes	complemented
108	C₅₉×#385	C₂²	1	2	yes	complemented
109	C₅₉×#384	C₂²	1	1	yes	characteristic, complemented
110	C₅₉×#381	C₂²	1	2	yes	complemented
111	C₅₉×#380	C₂²	1	2	yes	complemented
112	C₅₉×#380	C₂²	1	2	yes	complemented
113	C₅₉×#379	C₂²	1	2	yes	—
114	C₅₉×#379	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₄⋊C₄×C₅₉	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
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
124	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₅₉	C₂³	1	2	yes	—
126	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₅₉	—	2	4	no	—
129	C₂²×D₄×C₅₉	—	2	4	no	—
130	C₂²×D₄×C₅₉	—	2	4	no	—
131	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
133	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
135	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
140	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
142	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
143	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
145	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
146	#127×C₅₉	—	2	4	no	—
147	#127×C₅₉	—	2	4	no	—
148	#124×C₅₉	—	2	4	no	—
149	#124×C₅₉	—	2	4	no	—
150	#124×C₅₉	—	2	8	no	—
151	#124×C₅₉	—	2	4	no	—
152	#123×C₅₉	—	2	8	no	—
153	#123×C₅₉	—	2	8	no	—
154	#123×C₅₉	—	4	4	no	—
155	C₂²⋊Q₈×C₅₉	—	2	4	no	—
156	C₂²⋊Q₈×C₅₉	—	4	4	no	—
157	#121×C₅₉	—	2	4	no	—
158	#120×C₅₉	—	4	4	no	—
159	#120×C₅₉	—	4	4	no	—
160	C₄×Q₈×C₅₉	—	2	4	no	—
161	C₄×Q₈×C₅₉	—	2	4	no	—
162	C₄×D₄×C₅₉	—	2	4	no	—
163	C₄×D₄×C₅₉	—	2	8	no	—
164	C₄×D₄×C₅₉	—	2	8	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	4	no	—
169	C₄×D₄×C₅₉	—	4	4	no	—
170	C₄×D₄×C₅₉	D₄	1	8	yes	complemented
171	#117×C₅₉	—	2	4	no	—
172	#117×C₅₉	—	2	4	no	—
173	#117×C₅₉	—	4	4	no	—
174	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
196	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
197	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
221	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
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×C₄²×C₅₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
234	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
235	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
236	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
239	#95×C₅₉	C₂³	1	1	yes	characteristic
240	#95×C₅₉	C₂³	1	1	yes	characteristic
241	#95×C₅₉	C₂³	1	1	yes	characteristic
242	#95×C₅₉	C₂³	1	1	yes	characteristic
243	#95×C₅₉	C₂³	1	1	yes	characteristic
244	#95×C₅₉	C₂³	1	2	yes	—
245	#95×C₅₉	C₂³	1	2	yes	—
246	#95×C₅₉	C₂³	1	2	yes	—
247	#95×C₅₉	C₂³	1	2	yes	—
248	#95×C₅₉	C₂³	1	1	yes	characteristic
249	#95×C₅₉	C₂³	1	2	yes	—
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	C₂⁴×C₅₉	—	2	4	no	—
258	C₂⁴×C₅₉	—	2	4	no	—
259	C₂⁴×C₅₉	—	2	4	no	—
260	C₂⁴×C₅₉	—	4	2	no	—
261	C₂⁴×C₅₉	—	4	2	no	—
262	C₂⁴×C₅₉	—	4	2	no	—
263	C₂⁴×C₅₉	—	4	2	no	—
264	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
265	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
266	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₅₉	—	2	2	no	—
269	C₂×Q₈×C₅₉	—	2	2	no	—
270	C₂×Q₈×C₅₉	—	2	2	no	—
271	C₂×Q₈×C₅₉	—	2	2	no	—
272	C₂×Q₈×C₅₉	—	2	2	no	—
273	C₂×Q₈×C₅₉	—	4	1	no	—
274	C₂×D₄×C₅₉	—	2	32	no	—
275	C₂×D₄×C₅₉	—	2	4	no	—
276	C₂×D₄×C₅₉	—	2	4	no	—
277	C₂×D₄×C₅₉	—	2	4	no	—
278	C₂×D₄×C₅₉	—	2	4	no	—
279	C₂×D₄×C₅₉	—	2	4	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	2	no	—
284	C₂×D₄×C₅₉	—	2	4	no	—
285	C₂×D₄×C₅₉	—	2	2	no	—
286	C₂×D₄×C₅₉	—	2	2	no	—
287	C₂×D₄×C₅₉	—	2	2	no	—
288	C₂×D₄×C₅₉	—	2	2	no	—
289	C₂×D₄×C₅₉	—	2	2	no	—
290	C₂×D₄×C₅₉	—	2	4	no	—
291	C₂×D₄×C₅₉	—	2	4	no	—
292	C₂×D₄×C₅₉	—	4	2	no	—
293	C₂×D₄×C₅₉	—	4	2	no	—
294	C₂×D₄×C₅₉	—	4	2	no	—
295	C₂×D₄×C₅₉	—	4	2	no	—
296	C₂×D₄×C₅₉	—	4	2	no	—
297	C₂×D₄×C₅₉	—	4	2	no	—
298	C₂×D₄×C₅₉	—	4	2	no	—
299	C₂×D₄×C₅₉	—	4	2	no	—
300	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
301	C₂×D₄×C₅₉	#41	1	4	yes	—
302	C₂²×C₄×C₅₉	—	2	2	no	—
303	C₂²×C₄×C₅₉	—	2	2	no	—
304	C₂²×C₄×C₅₉	—	2	4	no	—
305	C₂²×C₄×C₅₉	—	2	4	no	—
306	C₂²×C₄×C₅₉	—	2	4	no	—
307	C₂²×C₄×C₅₉	—	2	4	no	—
308	C₂²×C₄×C₅₉	—	4	2	no	—
309	C₂²×C₄×C₅₉	—	4	2	no	—
310	C₂²×C₄×C₅₉	—	4	2	no	—
311	C₂²×C₄×C₅₉	—	4	2	no	—
312	C₂²×C₄×C₅₉	—	4	2	no	—
313	C₂²×C₄×C₅₉	—	4	2	no	—
314	C₂²×C₄×C₅₉	—	4	2	no	—
315	C₂²×C₄×C₅₉	—	4	2	no	—
316	C₂²×C₄×C₅₉	—	4	2	no	—
317	C₂²×C₄×C₅₉	—	4	2	no	—
318	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
319	C₂²×C₄×C₅₉	#41	1	4	yes	—
320	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
339	C₄⋊C₄×C₅₉	—	2	2	no	—
340	C₄⋊C₄×C₅₉	—	2	2	no	—
341	C₄⋊C₄×C₅₉	—	2	2	no	—
342	C₄⋊C₄×C₅₉	—	2	2	no	—
343	C₄⋊C₄×C₅₉	—	2	4	no	—
344	C₄⋊C₄×C₅₉	—	2	2	no	—
345	C₄⋊C₄×C₅₉	—	2	2	no	—
346	C₄⋊C₄×C₅₉	—	2	2	no	—
347	C₄⋊C₄×C₅₉	—	2	2	no	—
348	C₄⋊C₄×C₅₉	—	2	4	no	—
349	C₄⋊C₄×C₅₉	—	2	2	no	—
350	C₄⋊C₄×C₅₉	—	2	2	no	—
351	C₄⋊C₄×C₅₉	—	2	4	no	—
352	C₄⋊C₄×C₅₉	—	2	2	no	—
353	C₄⋊C₄×C₅₉	—	4	1	no	—
354	C₄⋊C₄×C₅₉	—	4	1	no	—
355	C₄⋊C₄×C₅₉	—	4	1	no	—
356	C₄⋊C₄×C₅₉	—	4	2	no	—
357	C₄⋊C₄×C₅₉	—	4	2	no	—
358	C₄⋊C₄×C₅₉	—	4	2	no	—
359	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
360	C₂²⋊C₄×C₅₉	—	2	4	no	—
361	C₂²⋊C₄×C₅₉	—	2	4	no	—
362	C₂²⋊C₄×C₅₉	—	2	4	no	—
363	C₂²⋊C₄×C₅₉	—	2	4	no	—
364	C₂²⋊C₄×C₅₉	—	2	4	no	—
365	C₂²⋊C₄×C₅₉	—	2	4	no	—
366	C₂²⋊C₄×C₅₉	—	2	4	no	—
367	C₂²⋊C₄×C₅₉	—	2	2	no	—
368	C₂²⋊C₄×C₅₉	—	2	2	no	—
369	C₂²⋊C₄×C₅₉	—	2	4	no	—
370	C₂²⋊C₄×C₅₉	—	2	4	no	—
371	C₂²⋊C₄×C₅₉	—	2	4	no	—
372	C₂²⋊C₄×C₅₉	—	2	4	no	—
373	C₂²⋊C₄×C₅₉	—	2	4	no	—
374	C₂²⋊C₄×C₅₉	—	2	4	no	—
375	C₂²⋊C₄×C₅₉	—	2	4	no	—
376	C₂²⋊C₄×C₅₉	—	2	2	no	—
377	C₂²⋊C₄×C₅₉	—	2	2	no	—
378	C₂²⋊C₄×C₅₉	—	2	4	no	—
379	C₂²⋊C₄×C₅₉	—	4	1	no	—
380	C₂²⋊C₄×C₅₉	—	4	2	no	—
381	C₂²⋊C₄×C₅₉	—	4	1	no	—
382	C₂²⋊C₄×C₅₉	—	4	2	no	—
383	C₂²⋊C₄×C₅₉	—	4	2	no	—
384	C₂²⋊C₄×C₅₉	—	4	2	no	—
385	C₂²⋊C₄×C₅₉	—	4	2	no	—
386	C₂²⋊C₄×C₅₉	—	4	2	no	—
387	C₂²⋊C₄×C₅₉	—	4	2	no	—
388	C₂²⋊C₄×C₅₉	—	4	2	no	—
389	C₂²⋊C₄×C₅₉	—	4	2	no	—
390	C₂²⋊C₄×C₅₉	—	4	2	no	—
391	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
392	C₄²×C₅₉	—	2	4	no	—
393	C₄²×C₅₉	—	2	2	no	—
394	C₄²×C₅₉	—	2	4	no	—
395	C₄²×C₅₉	—	2	2	no	—
396	C₄²×C₅₉	—	2	2	no	—
397	C₄²×C₅₉	—	2	2	no	—
398	C₄²×C₅₉	—	2	2	no	—
399	C₄²×C₅₉	—	2	4	no	—
400	C₄²×C₅₉	—	4	2	no	—
401	C₄²×C₅₉	C₂×D₄	1	4	yes	—
402	C₂³×C₅₉	—	2	16	no	—
403	C₂³×C₅₉	—	2	1	no	—
404	C₂³×C₅₉	—	2	2	no	—
405	C₂³×C₅₉	—	2	1	no	—
406	C₂³×C₅₉	—	2	2	no	—
407	C₂³×C₅₉	—	2	2	no	—
408	C₂³×C₅₉	—	2	2	no	—
409	C₂³×C₅₉	—	2	2	no	—
410	C₂³×C₅₉	—	2	2	no	—
411	C₂³×C₅₉	—	2	1	no	—
412	C₂³×C₅₉	—	2	1	no	—
413	C₂³×C₅₉	—	2	2	no	—
414	C₂³×C₅₉	—	2	2	no	—
415	C₂³×C₅₉	—	2	1	no	—
416	C₂³×C₅₉	—	2	1	no	—
417	C₂³×C₅₉	—	2	2	no	—
418	C₂³×C₅₉	—	2	2	no	—
419	C₂³×C₅₉	—	2	2	no	—
420	C₂³×C₅₉	—	2	2	no	—
421	C₂³×C₅₉	—	2	2	no	—
422	C₂³×C₅₉	—	2	2	no	—
423	C₂³×C₅₉	—	2	2	no	—
424	C₂³×C₅₉	—	2	2	no	—
425	C₂³×C₅₉	—	2	2	no	—
426	C₂³×C₅₉	—	2	2	no	—
427	C₂³×C₅₉	—	2	2	no	—
428	C₂³×C₅₉	—	8	4	no	—
429	C₂³×C₅₉	—	8	4	no	—
430	C₂³×C₅₉	—	8	4	no	—
431	C₂³×C₅₉	—	8	4	no	—
432	C₂³×C₅₉	—	8	4	no	—
433	C₂³×C₅₉	—	8	4	no	—
434	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
435	C₂³×C₅₉	C₂×#41	1	2	yes	—
436	C₂³×C₅₉	C₂×#41	1	4	yes	—
437	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
438	Q₈×C₅₉	—	4	4	no	—
439	Q₈×C₅₉	—	4	4	no	—
440	D₄×C₅₉	—	2	16	no	—
441	D₄×C₅₉	—	2	8	no	—
442	D₄×C₅₉	—	2	8	no	—
443	D₄×C₅₉	—	4	8	no	—
444	D₄×C₅₉	—	4	8	no	—
445	D₄×C₅₉	—	4	4	no	—
446	D₄×C₅₉	—	8	4	no	—
447	D₄×C₅₉	—	8	4	no	—
448	D₄×C₅₉	—	8	4	no	—
449	C₂×C₄×C₅₉	—	2	1	no	—
450	C₂×C₄×C₅₉	—	2	1	no	—
451	C₂×C₄×C₅₉	—	2	1	no	—
452	C₂×C₄×C₅₉	—	2	1	no	—
453	C₂×C₄×C₅₉	—	2	2	no	—
454	C₂×C₄×C₅₉	—	2	1	no	—
455	C₂×C₄×C₅₉	—	2	1	no	—
456	C₂×C₄×C₅₉	—	2	1	no	—
457	C₂×C₄×C₅₉	—	2	1	no	—
458	C₂×C₄×C₅₉	—	2	2	no	—
459	C₂×C₄×C₅₉	—	2	1	no	—
460	C₂×C₄×C₅₉	—	2	1	no	—
461	C₂×C₄×C₅₉	—	2	8	no	—
462	C₂×C₄×C₅₉	—	2	2	no	—
463	C₂×C₄×C₅₉	—	2	1	no	—
464	C₂×C₄×C₅₉	—	2	2	no	—
465	C₂×C₄×C₅₉	—	2	1	no	—
466	C₂×C₄×C₅₉	—	2	1	no	—
467	C₂×C₄×C₅₉	—	2	1	no	—
468	C₂×C₄×C₅₉	—	2	1	no	—
469	C₂×C₄×C₅₉	—	2	1	no	—
470	C₂×C₄×C₅₉	—	2	1	no	—
471	C₂×C₄×C₅₉	—	2	1	no	—
472	C₂×C₄×C₅₉	—	2	2	no	—
473	C₂×C₄×C₅₉	—	2	2	no	—
474	C₂×C₄×C₅₉	—	2	2	no	—
475	C₂×C₄×C₅₉	—	2	2	no	—
476	C₂×C₄×C₅₉	—	2	2	no	—
477	C₂×C₄×C₅₉	—	2	1	no	—
478	C₂×C₄×C₅₉	—	2	2	no	—
479	C₂×C₄×C₅₉	—	2	1	no	—
480	C₂×C₄×C₅₉	—	2	1	no	—
481	C₂×C₄×C₅₉	—	2	2	no	—
482	C₂×C₄×C₅₉	—	2	1	no	—
483	C₂×C₄×C₅₉	—	2	2	no	—
484	C₂×C₄×C₅₉	—	2	1	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	1	no	—
490	C₂×C₄×C₅₉	—	2	1	no	—
491	C₂×C₄×C₅₉	—	2	1	no	—
492	C₂×C₄×C₅₉	—	2	2	no	—
493	C₂×C₄×C₅₉	—	2	1	no	—
494	C₂×C₄×C₅₉	—	2	1	no	—
495	C₂×C₄×C₅₉	—	2	1	no	—
496	C₂×C₄×C₅₉	—	2	1	no	—
497	C₂×C₄×C₅₉	—	2	1	no	—
498	C₂×C₄×C₅₉	—	4	8	no	—
499	C₂×C₄×C₅₉	—	8	4	no	—
500	C₂×C₄×C₅₉	—	8	4	no	—
501	C₂×C₄×C₅₉	—	8	4	no	—
502	C₂×C₄×C₅₉	—	8	4	no	—
503	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
504	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
508	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
509	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
510	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
511	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
512	#35808	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
513	C₂²×C₅₉	—	2	2	no	—
514	C₂²×C₅₉	—	2	4	no	—
515	C₂²×C₅₉	—	2	4	no	—
516	C₂²×C₅₉	—	2	4	no	—
517	C₂²×C₅₉	—	2	4	no	—
518	C₂²×C₅₉	—	2	2	no	—
519	C₂²×C₅₉	—	2	2	no	—
520	C₂²×C₅₉	—	2	4	no	—
521	C₂²×C₅₉	—	2	4	no	—
522	C₂²×C₅₉	—	4	2	no	—
523	C₂²×C₅₉	—	4	1	no	—
524	C₂²×C₅₉	—	4	2	no	—
525	C₂²×C₅₉	—	4	1	no	—
526	C₂²×C₅₉	—	4	2	no	—
527	C₂²×C₅₉	—	4	2	no	—
528	C₂²×C₅₉	—	4	2	no	—
529	C₂²×C₅₉	—	4	2	no	—
530	C₂²×C₅₉	—	4	2	no	—
531	C₂²×C₅₉	—	4	1	no	—
532	C₂²×C₅₉	—	4	2	no	—
533	C₂²×C₅₉	—	4	1	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	—	8	16	no	—
542	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
543	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
545	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²×C₅₉	#585	1	1	yes	characteristic
548	C₂²×C₅₉	#585	1	1	yes	characteristic
549	C₄×C₅₉	—	2	2	no	—
550	C₄×C₅₉	—	2	2	no	—
551	C₄×C₅₉	—	2	2	no	—
552	C₄×C₅₉	—	2	2	no	—
553	C₄×C₅₉	—	2	4	no	—
554	C₄×C₅₉	—	2	2	no	—
555	C₄×C₅₉	—	4	2	no	—
556	C₄×C₅₉	—	4	1	no	—
557	C₄×C₅₉	—	4	2	no	—
558	C₄×C₅₉	—	4	1	no	—
559	C₄×C₅₉	—	4	1	no	—
560	C₄×C₅₉	—	4	1	no	—
561	C₄×C₅₉	—	4	1	no	—
562	C₄×C₅₉	—	4	2	no	—
563	C₄×C₅₉	—	4	2	no	—
564	C₄×C₅₉	—	4	1	no	—
565	C₄×C₅₉	—	4	1	no	—
566	C₄×C₅₉	—	4	1	no	—
567	C₄×C₅₉	#525	1	4	yes	—
568	C₂×#559	C₂×C₅₉	1	1	yes	characteristic, complemented
569	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
570	#2630	C₂×C₅₉	1	2	yes	complemented
571	#2620	C₂×C₅₉	1	1	yes	characteristic, complemented
572	#2544	C₂×C₅₉	1	1	yes	characteristic, complemented
573	#2538	C₂×C₅₉	1	1	yes	characteristic, complemented
574	#2534	C₂×C₅₉	1	2	yes	complemented
575	#2472	C₂×C₅₉	1	2	yes	complemented
576	#2461	C₂×C₅₉	1	2	yes	complemented
577	#2457	C₂×C₅₉	1	2	yes	complemented
578	#2447	C₂×C₅₉	1	1	yes	characteristic, complemented
579	#2445	C₂×C₅₉	1	1	yes	characteristic, complemented
580	#2435	C₂×C₅₉	1	1	yes	characteristic, complemented
581	#2433	C₂×C₅₉	1	1	yes	characteristic
582	#2418	C₂×C₅₉	1	2	yes	complemented
583	#2411	C₂×C₅₉	1	2	yes	complemented
584	#2396	C₂×C₅₉	1	1	yes	characteristic, complemented
585	#2392	C₂×C₅₉	1	2	yes	complemented
586	#2367	C₂×C₅₉	1	1	yes	characteristic, complemented
587	#2366	C₂×C₅₉	1	1	yes	characteristic, complemented
588	#2363	C₂×C₅₉	1	1	yes	characteristic, complemented
589	#2362	C₂×C₅₉	1	1	yes	characteristic, complemented
590	#2354	C₂×C₅₉	1	1	yes	characteristic, complemented
591	C₂×C₅₉	—	4	4	no	—
592	C₂×C₅₉	—	4	4	no	—
593	C₂×C₅₉	—	4	2	no	—
594	C₂×C₅₉	—	8	2	no	—
595	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
596	C₂×C₅₉	#3488	1	1	yes	characteristic
597	C₂×C₅₉	#3496	1	1	yes	characteristic
598	C₂×C₅₉	#3508	1	1	yes	characteristic
599	C₂×C₅₉	#3510	1	1	yes	characteristic
600	C₂×C₅₉	#3513	1	1	yes	characteristic
601	C₂×C₅₉	#3514	1	1	yes	characteristic
602	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
603	#559	—	2	8	no	—
604	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
605	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
606	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
607	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
608	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic, complemented
609	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
610	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
611	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
612	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
613	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
614	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
615	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
616	C₂×#120	C₂²×C₅₉	1	2	yes	—
617	C₂×#120	C₂²×C₅₉	1	2	yes	—
618	#518	—	2	8	no	—
619	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
620	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
621	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
622	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
623	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
624	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
625	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
626	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
627	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
628	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
629	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
630	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
631	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
632	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
633	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
634	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
635	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
636	#399	C₂²×C₅₉	1	1	yes	characteristic
637	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
638	#398	C₂²×C₅₉	1	1	yes	characteristic, complemented
639	#397	C₂²×C₅₉	1	2	yes	complemented
640	#397	C₂²×C₅₉	1	2	yes	complemented
641	#396	C₂²×C₅₉	1	1	yes	characteristic
642	#396	C₂²×C₅₉	1	1	yes	characteristic
643	#396	C₂²×C₅₉	1	2	yes	complemented
644	#396	C₂²×C₅₉	1	2	yes	complemented
645	#396	C₂²×C₅₉	1	2	yes	complemented
646	#396	C₂²×C₅₉	1	2	yes	complemented
647	#395	C₂²×C₅₉	1	1	yes	characteristic, complemented
648	#394	C₂²×C₅₉	1	2	yes	—
649	#394	C₂²×C₅₉	1	2	yes	—
650	#394	C₂²×C₅₉	1	2	yes	—
651	#394	C₂²×C₅₉	1	2	yes	—
652	#394	C₂²×C₅₉	1	2	yes	complemented
653	#394	C₂²×C₅₉	1	2	yes	complemented
654	#394	C₂²×C₅₉	1	2	yes	complemented
655	#394	C₂²×C₅₉	1	2	yes	complemented
656	#393	C₂²×C₅₉	1	1	yes	characteristic
657	#392	C₂²×C₅₉	1	2	yes	—
658	#392	C₂²×C₅₉	1	2	yes	—
659	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
660	#391	C₂²×C₅₉	1	1	yes	characteristic, complemented
661	#390	C₂²×C₅₉	1	1	yes	characteristic
662	#390	C₂²×C₅₉	1	1	yes	characteristic
663	#390	C₂²×C₅₉	1	2	yes	—
664	#390	C₂²×C₅₉	1	1	yes	characteristic
665	#390	C₂²×C₅₉	1	1	yes	characteristic
666	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
667	#390	C₂²×C₅₉	1	1	yes	characteristic, complemented
668	#390	C₂²×C₅₉	1	2	yes	complemented
669	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
670	#389	C₂²×C₅₉	1	1	yes	characteristic, complemented
671	#388	C₂²×C₅₉	1	2	yes	—
672	#388	C₂²×C₅₉	1	2	yes	—
673	#388	C₂²×C₅₉	1	2	yes	complemented
674	#388	C₂²×C₅₉	1	2	yes	complemented
675	#388	C₂²×C₅₉	1	2	yes	complemented
676	#388	C₂²×C₅₉	1	2	yes	complemented
677	#388	C₂²×C₅₉	1	2	yes	complemented
678	#387	C₂²×C₅₉	1	2	yes	complemented
679	#386	C₂²×C₅₉	1	2	yes	—
680	#386	C₂²×C₅₉	1	2	yes	complemented
681	#386	C₂²×C₅₉	1	2	yes	complemented
682	#386	C₂²×C₅₉	1	2	yes	complemented
683	#386	C₂²×C₅₉	1	2	yes	complemented
684	#386	C₂²×C₅₉	1	2	yes	complemented
685	#385	C₂²×C₅₉	1	2	yes	complemented
686	#385	C₂²×C₅₉	1	2	yes	complemented
687	#384	C₂²×C₅₉	1	1	yes	characteristic, complemented
688	#381	C₂²×C₅₉	1	2	yes	complemented
689	#380	C₂²×C₅₉	1	2	yes	complemented
690	#380	C₂²×C₅₉	1	2	yes	complemented
691	#379	C₂²×C₅₉	1	2	yes	—
692	#379	C₂²×C₅₉	1	2	yes	—
693	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
694	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
695	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
696	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
697	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
698	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
699	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
700	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
701	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
702	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
703	C₅₉	#35808	1	1	yes	characteristic, direct product factor, Sylow
704	C₂⁵	C₂³×C₅₉	1	2	yes	—
705	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
706	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
707	C₂²×D₄	—	2	4	no	—
708	C₂²×D₄	—	2	4	no	—
709	C₂²×D₄	—	2	4	no	—
710	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
711	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
712	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
713	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
714	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
715	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
716	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
717	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
718	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
719	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
720	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
721	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
722	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
723	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
724	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
725	#127	—	2	4	no	—
726	#127	—	2	4	no	—
727	#124	—	2	4	no	—
728	#124	—	2	4	no	—
729	#124	—	2	8	no	—
730	#124	—	2	4	no	—
731	#123	—	2	8	no	—
732	#123	—	2	8	no	—
733	#123	—	4	4	no	—
734	C₂²⋊Q₈	—	2	4	no	—
735	C₂²⋊Q₈	—	4	4	no	—
736	#121	—	2	4	no	—
737	#120	—	4	4	no	—
738	#120	—	4	4	no	—
739	C₄×Q₈	—	2	4	no	—
740	C₄×Q₈	—	2	4	no	—
741	C₄×D₄	—	2	4	no	—
742	C₄×D₄	—	2	8	no	—
743	C₄×D₄	—	2	8	no	—
744	C₄×D₄	—	2	4	no	—
745	C₄×D₄	—	2	4	no	—
746	C₄×D₄	—	2	8	no	—
747	C₄×D₄	—	2	4	no	—
748	C₄×D₄	—	4	4	no	—
749	C₄×D₄	D₄×C₅₉	1	8	yes	complemented
750	#117	—	2	4	no	—
751	#117	—	2	4	no	—
752	#117	—	4	4	no	—
753	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
767	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
773	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
774	C₂×C₂²⋊C₄	—	2	8	no	—
775	C₂×C₂²⋊C₄	—	2	8	no	—
776	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
779	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
787	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
805	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
808	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
809	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
810	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
811	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
812	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
813	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
816	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
817	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
818	#95	C₂³×C₅₉	1	1	yes	characteristic
819	#95	C₂³×C₅₉	1	1	yes	characteristic
820	#95	C₂³×C₅₉	1	1	yes	characteristic
821	#95	C₂³×C₅₉	1	1	yes	characteristic
822	#95	C₂³×C₅₉	1	1	yes	characteristic
823	#95	C₂³×C₅₉	1	2	yes	—
824	#95	C₂³×C₅₉	1	2	yes	—
825	#95	C₂³×C₅₉	1	2	yes	—
826	#95	C₂³×C₅₉	1	2	yes	—
827	#95	C₂³×C₅₉	1	1	yes	characteristic
828	#95	C₂³×C₅₉	1	2	yes	—
829	#95	C₂³×C₅₉	1	1	yes	characteristic
830	#95	C₂³×C₅₉	1	1	yes	characteristic
831	#95	C₂³×C₅₉	1	1	yes	characteristic
832	#95	C₂³×C₅₉	1	1	yes	characteristic
833	#95	C₂³×C₅₉	1	2	yes	—
834	#95	C₂³×C₅₉	1	2	yes	—
835	#95	C₂³×C₅₉	1	2	yes	—
836	C₂⁴	—	2	4	no	—
837	C₂⁴	—	2	4	no	—
838	C₂⁴	—	2	4	no	—
839	C₂⁴	—	4	2	no	—
840	C₂⁴	—	4	2	no	—
841	C₂⁴	—	4	2	no	—
842	C₂⁴	—	4	2	no	—
843	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
844	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
845	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
846	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	2	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	4	1	no	—
853	C₂×D₄	—	2	32	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	2	4	no	—
860	C₂×D₄	—	2	4	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	4	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	4	2	no	—
872	C₂×D₄	—	4	2	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	—	4	2	no	—
875	C₂×D₄	—	4	2	no	—
876	C₂×D₄	—	4	2	no	—
877	C₂×D₄	—	4	2	no	—
878	C₂×D₄	—	4	2	no	—
879	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
880	C₂×D₄	#41×C₅₉	1	4	yes	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	4	no	—
884	C₂²×C₄	—	2	4	no	—
885	C₂²×C₄	—	2	4	no	—
886	C₂²×C₄	—	2	4	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	4	2	no	—
891	C₂²×C₄	—	4	2	no	—
892	C₂²×C₄	—	4	2	no	—
893	C₂²×C₄	—	4	2	no	—
894	C₂²×C₄	—	4	2	no	—
895	C₂²×C₄	—	4	2	no	—
896	C₂²×C₄	—	4	2	no	—
897	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
898	C₂²×C₄	#41×C₅₉	1	4	yes	—
899	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	4	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	4	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	4	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	1	no	—
936	C₄⋊C₄	—	4	1	no	—
937	C₄⋊C₄	—	4	1	no	—
938	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	4	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	4	no	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	4	no	—
952	C₂²⋊C₄	—	2	4	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	4	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	1	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	1	no	—
970	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
971	C₄²	—	2	4	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	4	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	4	no	—
979	C₄²	—	4	2	no	—
980	C₄²	C₂×D₄×C₅₉	1	4	yes	—
981	C₂³	—	2	16	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	8	4	no	—
1008	C₂³	—	8	4	no	—
1009	C₂³	—	8	4	no	—
1010	C₂³	—	8	4	no	—
1011	C₂³	—	8	4	no	—
1012	C₂³	—	8	4	no	—
1013	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
1014	C₂³	C₂×#41×C₅₉	1	2	yes	—
1015	C₂³	C₂×#41×C₅₉	1	4	yes	—
1016	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
1017	Q₈	—	4	4	no	—
1018	Q₈	—	4	4	no	—
1019	D₄	—	2	16	no	—
1020	D₄	—	2	8	no	—
1021	D₄	—	2	8	no	—
1022	D₄	—	4	8	no	—
1023	D₄	—	4	8	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	8	4	no	—
1026	D₄	—	8	4	no	—
1027	D₄	—	8	4	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	4	8	no	—
1078	C₂×C₄	—	8	4	no	—
1079	C₂×C₄	—	8	4	no	—
1080	C₂×C₄	—	8	4	no	—
1081	C₂×C₄	—	8	4	no	—
1082	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
1083	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1086	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1087	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1088	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
1089	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1090	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	4	no	—
1094	C₂²	—	2	4	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	4	no	—
1097	C₂²	—	2	4	no	—
1098	C₂²	—	2	4	no	—
1099	C₂²	—	2	4	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	1	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	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	8	16	no	—
1120	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1121	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1122	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
1123	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1124	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1125	C₂²	C₅₉×#585	1	1	yes	characteristic
1126	C₂²	C₅₉×#585	1	1	yes	characteristic
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	4	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	C₅₉×#525	1	4	yes	—
1146	C₂	—	4	2	no	—
1147	C₂	—	4	4	no	—
1148	C₂	—	4	4	no	—
1149	C₂	—	8	2	no	—
1150	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
1151	C₂	C₅₉×#3488	1	1	yes	characteristic
1152	C₂	C₅₉×#3496	1	1	yes	characteristic
1153	C₂	C₅₉×#3508	1	1	yes	characteristic
1154	C₂	C₅₉×#3510	1	1	yes	characteristic
1155	C₂	C₅₉×#3513	1	1	yes	characteristic
1156	C₂	C₅₉×#3514	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2433	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
1. C₂×C₅₉×#559	C₂	semidirect
2. C₂×C₅₉×#518	C₂	semidirect
3. C₅₉×#2630	C₂	semidirect
4. C₅₉×#2620	C₂	semidirect
5. C₅₉×#2544	C₂	semidirect
6. C₅₉×#2538	C₂	semidirect
7. C₅₉×#2534	C₂	semidirect
8. C₅₉×#2472	C₂	semidirect
9. C₅₉×#2461	C₂	semidirect
10. C₅₉×#2457	C₂	semidirect
11. C₅₉×#2447	C₂	semidirect
12. C₅₉×#2445	C₂	semidirect
13. C₅₉×#2435	C₂	semidirect
15. C₅₉×#2418	C₂	semidirect
16. C₅₉×#2411	C₂	semidirect
17. C₅₉×#2396	C₂	semidirect
18. C₅₉×#2392	C₂	semidirect
19. C₅₉×#2367	C₂	semidirect
20. C₅₉×#2366	C₂	semidirect
21. C₅₉×#2363	C₂	semidirect
22. C₅₉×#2362	C₂	semidirect
23. C₅₉×#2354	C₂	semidirect
30. C₂×#124×C₅₉	C₂²	semidirect
31. C₂×#124×C₅₉	C₂²	semidirect
32. C₂×#123×C₅₉	C₂²	semidirect
33. C₂×#123×C₅₉	C₂²	semidirect
34. C₂×#123×C₅₉	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
41. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
42. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
49. C₂×C₄×D₄×C₅₉	C₂²	semidirect
50. C₂×C₄×D₄×C₅₉	C₂²	semidirect
51. C₂×C₄×D₄×C₅₉	C₂²	semidirect
54. C₂×#117×C₅₉	C₂²	semidirect
57. C₅₉×#400	C₂²	semidirect
59. C₅₉×#398	C₂²	semidirect
60. C₅₉×#398	C₂²	semidirect
61. C₅₉×#397	C₂²	semidirect
62. C₅₉×#397	C₂²	semidirect
65. C₅₉×#396	C₂²	semidirect
66. C₅₉×#396	C₂²	semidirect
67. C₅₉×#396	C₂²	semidirect
68. C₅₉×#396	C₂²	semidirect
69. C₅₉×#395	C₂²	semidirect
74. C₅₉×#394	C₂²	semidirect
75. C₅₉×#394	C₂²	semidirect
76. C₅₉×#394	C₂²	semidirect
77. C₅₉×#394	C₂²	semidirect
81. C₅₉×#391	C₂²	semidirect
82. C₅₉×#391	C₂²	semidirect
88. C₅₉×#390	C₂²	semidirect
89. C₅₉×#390	C₂²	semidirect
90. C₅₉×#390	C₂²	semidirect
91. C₅₉×#389	C₂²	semidirect
92. C₅₉×#389	C₂²	semidirect
95. C₅₉×#388	C₂²	semidirect
96. C₅₉×#388	C₂²	semidirect
97. C₅₉×#388	C₂²	semidirect
98. C₅₉×#388	C₂²	semidirect
99. C₅₉×#388	C₂²	semidirect
100. C₅₉×#387	C₂²	semidirect
102. C₅₉×#386	C₂²	semidirect
103. C₅₉×#386	C₂²	semidirect
104. C₅₉×#386	C₂²	semidirect
105. C₅₉×#386	C₂²	semidirect
106. C₅₉×#386	C₂²	semidirect
107. C₅₉×#385	C₂²	semidirect
108. C₅₉×#385	C₂²	semidirect
109. C₅₉×#384	C₂²	semidirect
110. C₅₉×#381	C₂²	semidirect
111. C₅₉×#380	C₂²	semidirect
112. C₅₉×#380	C₂²	semidirect
115. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
116. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
117. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
118. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
119. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
120. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
170. C₄×D₄×C₅₉	D₄	semidirect
512. #35808	C₅₉	direct (N × H)
568. C₂×#559	C₂×C₅₉	semidirect
569. C₂×#518	C₂×C₅₉	semidirect
570. #2630	C₂×C₅₉	semidirect
571. #2620	C₂×C₅₉	semidirect
572. #2544	C₂×C₅₉	semidirect
573. #2538	C₂×C₅₉	semidirect
574. #2534	C₂×C₅₉	semidirect
575. #2472	C₂×C₅₉	semidirect
576. #2461	C₂×C₅₉	semidirect
577. #2457	C₂×C₅₉	semidirect
578. #2447	C₂×C₅₉	semidirect
579. #2445	C₂×C₅₉	semidirect
580. #2435	C₂×C₅₉	semidirect
582. #2418	C₂×C₅₉	semidirect
583. #2411	C₂×C₅₉	semidirect
584. #2396	C₂×C₅₉	semidirect
585. #2392	C₂×C₅₉	semidirect
586. #2367	C₂×C₅₉	semidirect
587. #2366	C₂×C₅₉	semidirect
588. #2363	C₂×C₅₉	semidirect
589. #2362	C₂×C₅₉	semidirect
590. #2354	C₂×C₅₉	semidirect
608. C₂×#124	C₂²×C₅₉	semidirect
609. C₂×#124	C₂²×C₅₉	semidirect
610. C₂×#123	C₂²×C₅₉	semidirect
611. C₂×#123	C₂²×C₅₉	semidirect
612. C₂×#123	C₂²×C₅₉	semidirect
614. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
619. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
620. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
627. C₂×C₄×D₄	C₂²×C₅₉	semidirect
628. C₂×C₄×D₄	C₂²×C₅₉	semidirect
629. C₂×C₄×D₄	C₂²×C₅₉	semidirect
632. C₂×#117	C₂²×C₅₉	semidirect
635. #400	C₂²×C₅₉	semidirect
637. #398	C₂²×C₅₉	semidirect
638. #398	C₂²×C₅₉	semidirect
639. #397	C₂²×C₅₉	semidirect
640. #397	C₂²×C₅₉	semidirect
643. #396	C₂²×C₅₉	semidirect
644. #396	C₂²×C₅₉	semidirect
645. #396	C₂²×C₅₉	semidirect
646. #396	C₂²×C₅₉	semidirect
647. #395	C₂²×C₅₉	semidirect
652. #394	C₂²×C₅₉	semidirect
653. #394	C₂²×C₅₉	semidirect
654. #394	C₂²×C₅₉	semidirect
655. #394	C₂²×C₅₉	semidirect
659. #391	C₂²×C₅₉	semidirect
660. #391	C₂²×C₅₉	semidirect
666. #390	C₂²×C₅₉	semidirect
667. #390	C₂²×C₅₉	semidirect
668. #390	C₂²×C₅₉	semidirect
669. #389	C₂²×C₅₉	semidirect
670. #389	C₂²×C₅₉	semidirect
673. #388	C₂²×C₅₉	semidirect
674. #388	C₂²×C₅₉	semidirect
675. #388	C₂²×C₅₉	semidirect
676. #388	C₂²×C₅₉	semidirect
677. #388	C₂²×C₅₉	semidirect
678. #387	C₂²×C₅₉	semidirect
680. #386	C₂²×C₅₉	semidirect
681. #386	C₂²×C₅₉	semidirect
682. #386	C₂²×C₅₉	semidirect
683. #386	C₂²×C₅₉	semidirect
684. #386	C₂²×C₅₉	semidirect
685. #385	C₂²×C₅₉	semidirect
686. #385	C₂²×C₅₉	semidirect
687. #384	C₂²×C₅₉	semidirect
688. #381	C₂²×C₅₉	semidirect
689. #380	C₂²×C₅₉	semidirect
690. #380	C₂²×C₅₉	semidirect
693. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
694. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
695. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
696. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
697. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
698. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
701. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
702. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
703. C₅₉	#35808	direct (N × H)
749. C₄×D₄	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#559	2
C₂×C₅₉×#518	2
C₅₉×#2630	2
C₅₉×#2620	2
C₅₉×#2544	2
C₅₉×#2538	2
C₅₉×#2534	2
C₅₉×#2472	2
C₅₉×#2461	2
C₅₉×#2457	2
C₅₉×#2447	2
C₅₉×#2445	2
C₅₉×#2435	2
C₅₉×#2433	2
C₅₉×#2418	2
C₅₉×#2411	2
C₅₉×#2396	2
C₅₉×#2392	2
C₅₉×#2367	2
C₅₉×#2366	2
C₅₉×#2363	2
C₅₉×#2362	2
C₅₉×#2354	2
#35808	59

Subgroups — C59×#35808 #28447917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35808 #28447917