Subgroups — C₅₉×#35745 #28447854

Order 15104.

1798 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2654	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2620	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2592	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2558	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2553	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2522	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2519	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2512	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2511	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2501	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2470	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2458	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2396	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2363	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2354	C₂	1	1	yes	maximal, characteristic, complemented
22	Q₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#126×C₅₉	C₂²	1	2	yes	—
25	C₂×#125×C₅₉	C₂²	1	2	yes	—
26	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#123×C₅₉	C₂²	1	2	yes	—
28	C₂×#123×C₅₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₅₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#400	C₂²	1	2	yes	—
40	C₅₉×#400	C₂²	1	2	yes	—
41	C₅₉×#400	C₂²	1	1	yes	characteristic
42	C₅₉×#399	C₂²	1	2	yes	—
43	C₅₉×#399	C₂²	1	2	yes	—
44	C₅₉×#399	C₂²	1	1	yes	characteristic
45	C₅₉×#398	C₂²	1	2	yes	—
46	C₅₉×#398	C₂²	1	2	yes	—
47	C₅₉×#398	C₂²	1	1	yes	characteristic
48	C₅₉×#398	C₂²	1	1	yes	characteristic
49	C₅₉×#398	C₂²	1	2	yes	—
50	C₅₉×#398	C₂²	1	2	yes	—
51	C₅₉×#397	C₂²	1	2	yes	—
52	C₅₉×#397	C₂²	1	2	yes	—
53	C₅₉×#396	C₂²	1	2	yes	—
54	C₅₉×#396	C₂²	1	2	yes	—
55	C₅₉×#396	C₂²	1	1	yes	characteristic
56	C₅₉×#396	C₂²	1	2	yes	—
57	C₅₉×#396	C₂²	1	1	yes	characteristic
58	C₅₉×#395	C₂²	1	1	yes	characteristic
59	C₅₉×#394	C₂²	1	2	yes	—
60	C₅₉×#394	C₂²	1	2	yes	—
61	C₅₉×#393	C₂²	1	2	yes	—
62	C₅₉×#393	C₂²	1	1	yes	characteristic
63	C₅₉×#391	C₂²	1	1	yes	characteristic
64	C₅₉×#391	C₂²	1	1	yes	characteristic
65	C₅₉×#391	C₂²	1	1	yes	characteristic
66	C₅₉×#391	C₂²	1	1	yes	characteristic
67	C₅₉×#390	C₂²	1	1	yes	characteristic
68	C₅₉×#390	C₂²	1	1	yes	characteristic
69	C₅₉×#390	C₂²	1	1	yes	characteristic
70	C₅₉×#390	C₂²	1	1	yes	characteristic
71	C₅₉×#390	C₂²	1	2	yes	—
72	C₅₉×#389	C₂²	1	1	yes	characteristic
73	C₅₉×#389	C₂²	1	1	yes	characteristic
74	C₅₉×#389	C₂²	1	2	yes	—
75	C₅₉×#389	C₂²	1	2	yes	—
76	C₅₉×#389	C₂²	1	2	yes	—
77	C₅₉×#389	C₂²	1	2	yes	—
78	C₅₉×#388	C₂²	1	2	yes	—
79	C₅₉×#388	C₂²	1	2	yes	—
80	C₅₉×#388	C₂²	1	2	yes	—
81	C₅₉×#388	C₂²	1	2	yes	—
82	C₅₉×#388	C₂²	1	2	yes	—
83	C₅₉×#388	C₂²	1	2	yes	—
84	C₅₉×#388	C₂²	1	2	yes	—
85	C₅₉×#388	C₂²	1	2	yes	—
86	C₅₉×#388	C₂²	1	2	yes	—
87	C₅₉×#388	C₂²	1	2	yes	—
88	C₅₉×#387	C₂²	1	2	yes	—
89	C₅₉×#387	C₂²	1	2	yes	—
90	C₅₉×#387	C₂²	1	2	yes	—
91	C₅₉×#387	C₂²	1	2	yes	—
92	C₅₉×#387	C₂²	1	2	yes	—
93	C₅₉×#386	C₂²	1	2	yes	—
94	C₅₉×#385	C₂²	1	2	yes	—
95	C₅₉×#385	C₂²	1	2	yes	—
96	C₅₉×#385	C₂²	1	2	yes	—
97	C₅₉×#384	C₂²	1	1	yes	characteristic
98	C₅₉×#384	C₂²	1	1	yes	characteristic
99	C₅₉×#384	C₂²	1	1	yes	characteristic
100	C₅₉×#384	C₂²	1	1	yes	characteristic
101	C₅₉×#384	C₂²	1	1	yes	characteristic
102	C₅₉×#382	C₂²	1	2	yes	—
103	C₅₉×#380	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
123	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
127	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
130	#126×C₅₉	—	4	4	no	—
131	#125×C₅₉	—	4	4	no	—
132	#124×C₅₉	—	2	4	no	—
133	#123×C₅₉	—	4	4	no	—
134	#123×C₅₉	—	4	4	no	—
135	C₂²⋊Q₈×C₅₉	—	2	4	no	—
136	#121×C₅₉	—	2	4	no	—
137	C₄×Q₈×C₅₉	—	2	4	no	—
138	C₄×Q₈×C₅₉	—	2	4	no	—
139	C₄×Q₈×C₅₉	—	4	4	no	—
140	C₄×D₄×C₅₉	—	2	4	no	—
141	#117×C₅₉	—	2	4	no	—
142	#117×C₅₉	—	2	4	no	—
143	#117×C₅₉	—	4	4	no	—
144	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
205	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
206	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
207	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
209	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
210	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
211	#95×C₅₉	C₂³	1	1	yes	characteristic
212	#95×C₅₉	C₂³	1	1	yes	characteristic
213	#95×C₅₉	C₂³	1	2	yes	—
214	#95×C₅₉	C₂³	1	2	yes	—
215	#95×C₅₉	C₂³	1	2	yes	—
216	#95×C₅₉	C₂³	1	1	yes	characteristic
217	#95×C₅₉	C₂³	1	2	yes	—
218	#95×C₅₉	C₂³	1	2	yes	—
219	#95×C₅₉	C₂³	1	2	yes	—
220	#95×C₅₉	C₂³	1	1	yes	characteristic
221	#95×C₅₉	C₂³	1	1	yes	characteristic
222	#95×C₅₉	C₂³	1	2	yes	—
223	#95×C₅₉	C₂³	1	2	yes	—
224	#95×C₅₉	C₂³	1	2	yes	—
225	#95×C₅₉	C₂³	1	1	yes	characteristic
226	#95×C₅₉	C₂³	1	1	yes	characteristic
227	#95×C₅₉	C₂³	1	1	yes	characteristic
228	#95×C₅₉	C₂³	1	2	yes	—
229	#95×C₅₉	C₂³	1	2	yes	—
230	#95×C₅₉	C₂³	1	1	yes	characteristic
231	#95×C₅₉	C₂³	1	1	yes	characteristic
232	#95×C₅₉	C₂³	1	2	yes	—
233	#95×C₅₉	C₂³	1	2	yes	—
234	#95×C₅₉	C₂³	1	2	yes	—
235	#95×C₅₉	C₂³	1	2	yes	—
236	#95×C₅₉	C₂³	1	2	yes	—
237	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
238	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₅₉	—	2	2	no	—
240	C₂×Q₈×C₅₉	—	2	2	no	—
241	C₂×Q₈×C₅₉	—	2	2	no	—
242	C₂×Q₈×C₅₉	—	2	2	no	—
243	C₂×Q₈×C₅₉	—	2	2	no	—
244	C₂×Q₈×C₅₉	—	2	2	no	—
245	C₂×D₄×C₅₉	—	2	4	no	—
246	C₂×D₄×C₅₉	—	2	2	no	—
247	C₂×D₄×C₅₉	—	2	2	no	—
248	C₂×D₄×C₅₉	—	2	2	no	—
249	C₂×D₄×C₅₉	—	4	2	no	—
250	C₂×D₄×C₅₉	—	4	2	no	—
251	C₂²×C₄×C₅₉	—	2	2	no	—
252	C₂²×C₄×C₅₉	—	2	2	no	—
253	C₂²×C₄×C₅₉	—	2	4	no	—
254	C₂²×C₄×C₅₉	—	2	4	no	—
255	C₂²×C₄×C₅₉	—	2	4	no	—
256	C₂²×C₄×C₅₉	—	4	2	no	—
257	C₂²×C₄×C₅₉	—	4	2	no	—
258	C₂²×C₄×C₅₉	—	4	2	no	—
259	C₂²×C₄×C₅₉	#41	1	4	yes	—
260	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₅₉	—	2	4	no	—
282	C₄⋊C₄×C₅₉	—	2	2	no	—
283	C₄⋊C₄×C₅₉	—	2	2	no	—
284	C₄⋊C₄×C₅₉	—	2	2	no	—
285	C₄⋊C₄×C₅₉	—	2	2	no	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	2	2	no	—
288	C₄⋊C₄×C₅₉	—	2	2	no	—
289	C₄⋊C₄×C₅₉	—	2	2	no	—
290	C₄⋊C₄×C₅₉	—	2	4	no	—
291	C₄⋊C₄×C₅₉	—	2	2	no	—
292	C₄⋊C₄×C₅₉	—	2	2	no	—
293	C₄⋊C₄×C₅₉	—	2	4	no	—
294	C₄⋊C₄×C₅₉	—	2	2	no	—
295	C₄⋊C₄×C₅₉	—	2	4	no	—
296	C₄⋊C₄×C₅₉	—	2	4	no	—
297	C₄⋊C₄×C₅₉	—	2	2	no	—
298	C₄⋊C₄×C₅₉	—	2	4	no	—
299	C₄⋊C₄×C₅₉	—	2	2	no	—
300	C₄⋊C₄×C₅₉	—	2	2	no	—
301	C₄⋊C₄×C₅₉	—	2	2	no	—
302	C₄⋊C₄×C₅₉	—	2	2	no	—
303	C₄⋊C₄×C₅₉	—	4	2	no	—
304	C₄⋊C₄×C₅₉	—	4	2	no	—
305	C₄⋊C₄×C₅₉	—	4	2	no	—
306	C₄⋊C₄×C₅₉	—	4	2	no	—
307	C₄⋊C₄×C₅₉	—	4	2	no	—
308	C₄⋊C₄×C₅₉	—	4	2	no	—
309	C₄⋊C₄×C₅₉	—	4	2	no	—
310	C₄⋊C₄×C₅₉	—	4	2	no	—
311	C₄⋊C₄×C₅₉	—	4	2	no	—
312	C₄⋊C₄×C₅₉	#41	1	4	yes	—
313	C₂²⋊C₄×C₅₉	—	2	4	no	—
314	C₂²⋊C₄×C₅₉	—	2	4	no	—
315	C₂²⋊C₄×C₅₉	—	2	2	no	—
316	C₂²⋊C₄×C₅₉	—	2	2	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	4	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	2	no	—
326	C₂²⋊C₄×C₅₉	—	2	4	no	—
327	C₂²⋊C₄×C₅₉	—	2	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	C₄²×C₅₉	—	2	4	no	—
334	C₄²×C₅₉	—	2	2	no	—
335	C₄²×C₅₉	—	2	2	no	—
336	C₄²×C₅₉	—	2	2	no	—
337	C₄²×C₅₉	—	2	4	no	—
338	C₄²×C₅₉	—	2	2	no	—
339	C₄²×C₅₉	—	2	2	no	—
340	C₄²×C₅₉	—	2	4	no	—
341	C₄²×C₅₉	—	4	2	no	—
342	C₄²×C₅₉	—	4	2	no	—
343	C₄²×C₅₉	—	4	2	no	—
344	C₄²×C₅₉	—	4	2	no	—
345	C₄²×C₅₉	—	4	2	no	—
346	C₄²×C₅₉	#41	1	4	yes	—
347	C₂³×C₅₉	—	2	1	no	—
348	C₂³×C₅₉	—	2	1	no	—
349	C₂³×C₅₉	—	2	1	no	—
350	C₂³×C₅₉	—	2	1	no	—
351	C₂³×C₅₉	—	2	1	no	—
352	C₂³×C₅₉	—	2	1	no	—
353	C₂³×C₅₉	—	2	2	no	—
354	C₂³×C₅₉	—	2	2	no	—
355	C₂³×C₅₉	—	2	2	no	—
356	C₂³×C₅₉	—	2	2	no	—
357	C₂³×C₅₉	—	2	2	no	—
358	C₂³×C₅₉	—	2	2	no	—
359	C₂³×C₅₉	—	2	2	no	—
360	C₂³×C₅₉	C₂×#41	1	2	yes	—
361	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
362	Q₈×C₅₉	—	2	8	no	—
363	Q₈×C₅₉	—	4	4	no	—
364	D₄×C₅₉	—	4	4	no	—
365	D₄×C₅₉	—	8	4	no	—
366	C₂×C₄×C₅₉	—	2	1	no	—
367	C₂×C₄×C₅₉	—	2	1	no	—
368	C₂×C₄×C₅₉	—	2	1	no	—
369	C₂×C₄×C₅₉	—	2	1	no	—
370	C₂×C₄×C₅₉	—	2	1	no	—
371	C₂×C₄×C₅₉	—	2	1	no	—
372	C₂×C₄×C₅₉	—	2	2	no	—
373	C₂×C₄×C₅₉	—	2	1	no	—
374	C₂×C₄×C₅₉	—	2	1	no	—
375	C₂×C₄×C₅₉	—	2	1	no	—
376	C₂×C₄×C₅₉	—	2	1	no	—
377	C₂×C₄×C₅₉	—	2	1	no	—
378	C₂×C₄×C₅₉	—	2	1	no	—
379	C₂×C₄×C₅₉	—	2	2	no	—
380	C₂×C₄×C₅₉	—	2	1	no	—
381	C₂×C₄×C₅₉	—	2	1	no	—
382	C₂×C₄×C₅₉	—	2	8	no	—
383	C₂×C₄×C₅₉	—	2	1	no	—
384	C₂×C₄×C₅₉	—	2	1	no	—
385	C₂×C₄×C₅₉	—	2	1	no	—
386	C₂×C₄×C₅₉	—	2	2	no	—
387	C₂×C₄×C₅₉	—	2	1	no	—
388	C₂×C₄×C₅₉	—	2	1	no	—
389	C₂×C₄×C₅₉	—	2	1	no	—
390	C₂×C₄×C₅₉	—	2	2	no	—
391	C₂×C₄×C₅₉	—	2	2	no	—
392	C₂×C₄×C₅₉	—	2	2	no	—
393	C₂×C₄×C₅₉	—	2	2	no	—
394	C₂×C₄×C₅₉	—	2	2	no	—
395	C₂×C₄×C₅₉	—	2	2	no	—
396	C₂×C₄×C₅₉	—	2	2	no	—
397	C₂×C₄×C₅₉	—	2	2	no	—
398	C₂×C₄×C₅₉	—	2	1	no	—
399	C₂×C₄×C₅₉	—	2	1	no	—
400	C₂×C₄×C₅₉	—	2	2	no	—
401	C₂×C₄×C₅₉	—	2	2	no	—
402	C₂×C₄×C₅₉	—	2	2	no	—
403	C₂×C₄×C₅₉	—	2	2	no	—
404	C₂×C₄×C₅₉	—	2	2	no	—
405	C₂×C₄×C₅₉	—	2	2	no	—
406	C₂×C₄×C₅₉	—	2	1	no	—
407	C₂×C₄×C₅₉	—	2	1	no	—
408	C₂×C₄×C₅₉	—	2	1	no	—
409	C₂×C₄×C₅₉	—	2	2	no	—
410	C₂×C₄×C₅₉	—	2	1	no	—
411	C₂×C₄×C₅₉	—	2	2	no	—
412	C₂×C₄×C₅₉	—	2	1	no	—
413	C₂×C₄×C₅₉	—	2	2	no	—
414	C₂×C₄×C₅₉	—	2	1	no	—
415	C₂×C₄×C₅₉	—	2	1	no	—
416	C₂×C₄×C₅₉	—	2	1	no	—
417	C₂×C₄×C₅₉	—	2	1	no	—
418	C₂×C₄×C₅₉	—	2	1	no	—
419	C₂×C₄×C₅₉	—	4	8	no	—
420	C₂×C₄×C₅₉	—	8	4	no	—
421	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
422	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
423	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
424	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
425	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
426	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
427	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
428	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
429	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
430	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
431	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
432	#35745	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
433	C₂²×C₅₉	—	2	2	no	—
434	C₂²×C₅₉	—	2	2	no	—
435	C₂²×C₅₉	—	2	2	no	—
436	C₂²×C₅₉	—	4	1	no	—
437	C₂²×C₅₉	—	4	1	no	—
438	C₂²×C₅₉	—	4	1	no	—
439	C₂²×C₅₉	—	4	1	no	—
440	C₂²×C₅₉	—	4	2	no	—
441	C₂²×C₅₉	—	4	2	no	—
442	C₂²×C₅₉	—	4	2	no	—
443	C₂²×C₅₉	—	4	2	no	—
444	C₂²×C₅₉	—	4	2	no	—
445	C₂²×C₅₉	—	4	2	no	—
446	C₂²×C₅₉	—	4	2	no	—
447	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
450	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₄×C₅₉	—	2	2	no	—
455	C₄×C₅₉	—	2	2	no	—
456	C₄×C₅₉	—	2	2	no	—
457	C₄×C₅₉	—	2	2	no	—
458	C₄×C₅₉	—	2	2	no	—
459	C₄×C₅₉	—	2	2	no	—
460	C₄×C₅₉	—	2	4	no	—
461	C₄×C₅₉	—	2	2	no	—
462	C₄×C₅₉	—	4	2	no	—
463	C₄×C₅₉	—	4	1	no	—
464	C₄×C₅₉	—	4	2	no	—
465	C₄×C₅₉	—	4	2	no	—
466	C₄×C₅₉	—	4	2	no	—
467	C₄×C₅₉	—	4	2	no	—
468	C₄×C₅₉	—	4	1	no	—
469	C₄×C₅₉	—	4	1	no	—
470	C₄×C₅₉	—	4	1	no	—
471	C₄×C₅₉	—	4	1	no	—
472	C₄×C₅₉	—	4	1	no	—
473	C₄×C₅₉	—	4	2	no	—
474	C₄×C₅₉	#529	1	4	yes	—
475	#2654	C₂×C₅₉	1	2	yes	complemented
476	#2620	C₂×C₅₉	1	1	yes	characteristic
477	#2592	C₂×C₅₉	1	1	yes	characteristic, complemented
478	#2558	C₂×C₅₉	1	2	yes	complemented
479	#2553	C₂×C₅₉	1	2	yes	complemented
480	#2552	C₂×C₅₉	1	1	yes	characteristic, complemented
481	#2522	C₂×C₅₉	1	2	yes	complemented
482	#2519	C₂×C₅₉	1	2	yes	complemented
483	#2512	C₂×C₅₉	1	1	yes	characteristic, complemented
484	#2511	C₂×C₅₉	1	1	yes	characteristic, complemented
485	#2502	C₂×C₅₉	1	1	yes	characteristic, complemented
486	#2501	C₂×C₅₉	1	1	yes	characteristic
487	#2470	C₂×C₅₉	1	2	yes	complemented
488	#2458	C₂×C₅₉	1	2	yes	complemented
489	#2396	C₂×C₅₉	1	1	yes	characteristic, complemented
490	#2396	C₂×C₅₉	1	2	yes	complemented
491	#2367	C₂×C₅₉	1	1	yes	characteristic, complemented
492	#2363	C₂×C₅₉	1	1	yes	characteristic
493	#2362	C₂×C₅₉	1	1	yes	characteristic, complemented
494	#2355	C₂×C₅₉	1	1	yes	characteristic, complemented
495	#2354	C₂×C₅₉	1	1	yes	characteristic, complemented
496	Q₈×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
497	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
498	C₂×C₅₉	—	4	2	no	—
499	C₂×C₅₉	—	8	2	no	—
500	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
501	C₂×C₅₉	#3492	1	1	yes	characteristic
502	C₂×C₅₉	#3508	1	1	yes	characteristic
503	C₂×C₅₉	#3509	1	1	yes	characteristic
504	C₂×C₅₉	#3511	1	1	yes	characteristic
505	C₂×C₅₉	#3520	1	1	yes	characteristic
506	C₂×C₅₉	#3522	1	1	yes	characteristic
507	C₂×#126	C₂²×C₅₉	1	2	yes	—
508	C₂×#125	C₂²×C₅₉	1	2	yes	—
509	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
510	C₂×#123	C₂²×C₅₉	1	2	yes	—
511	C₂×#123	C₂²×C₅₉	1	2	yes	—
512	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
513	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
514	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
515	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
516	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
517	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
518	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
519	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
520	C₂×#117	C₂²×C₅₉	1	2	yes	—
521	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
522	#400	C₂²×C₅₉	1	1	yes	characteristic
523	#400	C₂²×C₅₉	1	2	yes	—
524	#400	C₂²×C₅₉	1	2	yes	—
525	#399	C₂²×C₅₉	1	2	yes	—
526	#399	C₂²×C₅₉	1	1	yes	characteristic
527	#399	C₂²×C₅₉	1	2	yes	—
528	#398	C₂²×C₅₉	1	2	yes	—
529	#398	C₂²×C₅₉	1	1	yes	characteristic
530	#398	C₂²×C₅₉	1	1	yes	characteristic
531	#398	C₂²×C₅₉	1	2	yes	—
532	#398	C₂²×C₅₉	1	2	yes	—
533	#398	C₂²×C₅₉	1	2	yes	—
534	#397	C₂²×C₅₉	1	2	yes	—
535	#397	C₂²×C₅₉	1	2	yes	—
536	#396	C₂²×C₅₉	1	2	yes	—
537	#396	C₂²×C₅₉	1	2	yes	—
538	#396	C₂²×C₅₉	1	1	yes	characteristic
539	#396	C₂²×C₅₉	1	2	yes	—
540	#396	C₂²×C₅₉	1	1	yes	characteristic
541	#395	C₂²×C₅₉	1	1	yes	characteristic
542	#394	C₂²×C₅₉	1	2	yes	—
543	#394	C₂²×C₅₉	1	2	yes	—
544	#393	C₂²×C₅₉	1	2	yes	—
545	#393	C₂²×C₅₉	1	1	yes	characteristic
546	#391	C₂²×C₅₉	1	1	yes	characteristic
547	#391	C₂²×C₅₉	1	1	yes	characteristic
548	#391	C₂²×C₅₉	1	1	yes	characteristic
549	#391	C₂²×C₅₉	1	1	yes	characteristic
550	#390	C₂²×C₅₉	1	1	yes	characteristic
551	#390	C₂²×C₅₉	1	1	yes	characteristic
552	#390	C₂²×C₅₉	1	1	yes	characteristic
553	#390	C₂²×C₅₉	1	2	yes	—
554	#390	C₂²×C₅₉	1	1	yes	characteristic
555	#389	C₂²×C₅₉	1	2	yes	—
556	#389	C₂²×C₅₉	1	2	yes	—
557	#389	C₂²×C₅₉	1	2	yes	—
558	#389	C₂²×C₅₉	1	1	yes	characteristic
559	#389	C₂²×C₅₉	1	1	yes	characteristic
560	#389	C₂²×C₅₉	1	2	yes	—
561	#388	C₂²×C₅₉	1	2	yes	—
562	#388	C₂²×C₅₉	1	2	yes	—
563	#388	C₂²×C₅₉	1	2	yes	—
564	#388	C₂²×C₅₉	1	2	yes	—
565	#388	C₂²×C₅₉	1	2	yes	—
566	#388	C₂²×C₅₉	1	2	yes	—
567	#388	C₂²×C₅₉	1	2	yes	—
568	#388	C₂²×C₅₉	1	2	yes	—
569	#388	C₂²×C₅₉	1	2	yes	—
570	#388	C₂²×C₅₉	1	2	yes	—
571	#387	C₂²×C₅₉	1	2	yes	—
572	#387	C₂²×C₅₉	1	2	yes	—
573	#387	C₂²×C₅₉	1	2	yes	—
574	#387	C₂²×C₅₉	1	2	yes	—
575	#387	C₂²×C₅₉	1	2	yes	—
576	#386	C₂²×C₅₉	1	2	yes	—
577	#385	C₂²×C₅₉	1	2	yes	—
578	#385	C₂²×C₅₉	1	2	yes	—
579	#385	C₂²×C₅₉	1	2	yes	—
580	#384	C₂²×C₅₉	1	1	yes	characteristic
581	#384	C₂²×C₅₉	1	1	yes	characteristic
582	#384	C₂²×C₅₉	1	1	yes	characteristic
583	#384	C₂²×C₅₉	1	1	yes	characteristic
584	#384	C₂²×C₅₉	1	1	yes	characteristic
585	#382	C₂²×C₅₉	1	2	yes	—
586	#380	C₂²×C₅₉	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
590	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
595	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
596	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
598	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
600	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
602	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
603	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
604	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
605	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
606	C₅₉	#35745	1	1	yes	characteristic, direct product factor, Sylow
607	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
611	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
612	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
614	#126	—	4	4	no	—
615	#125	—	4	4	no	—
616	#124	—	2	4	no	—
617	#123	—	4	4	no	—
618	#123	—	4	4	no	—
619	C₂²⋊Q₈	—	2	4	no	—
620	#121	—	2	4	no	—
621	C₄×Q₈	—	2	4	no	—
622	C₄×Q₈	—	2	4	no	—
623	C₄×Q₈	—	4	4	no	—
624	C₄×D₄	—	2	4	no	—
625	#117	—	2	4	no	—
626	#117	—	2	4	no	—
627	#117	—	4	4	no	—
628	C₂×C₄⋊C₄	—	2	4	no	—
629	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
681	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
682	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
683	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
686	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
690	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
691	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
692	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
693	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
694	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
695	#95	C₂³×C₅₉	1	1	yes	characteristic
696	#95	C₂³×C₅₉	1	1	yes	characteristic
697	#95	C₂³×C₅₉	1	2	yes	—
698	#95	C₂³×C₅₉	1	2	yes	—
699	#95	C₂³×C₅₉	1	2	yes	—
700	#95	C₂³×C₅₉	1	1	yes	characteristic
701	#95	C₂³×C₅₉	1	2	yes	—
702	#95	C₂³×C₅₉	1	2	yes	—
703	#95	C₂³×C₅₉	1	2	yes	—
704	#95	C₂³×C₅₉	1	1	yes	characteristic
705	#95	C₂³×C₅₉	1	1	yes	characteristic
706	#95	C₂³×C₅₉	1	2	yes	—
707	#95	C₂³×C₅₉	1	2	yes	—
708	#95	C₂³×C₅₉	1	2	yes	—
709	#95	C₂³×C₅₉	1	1	yes	characteristic
710	#95	C₂³×C₅₉	1	1	yes	characteristic
711	#95	C₂³×C₅₉	1	1	yes	characteristic
712	#95	C₂³×C₅₉	1	2	yes	—
713	#95	C₂³×C₅₉	1	2	yes	—
714	#95	C₂³×C₅₉	1	1	yes	characteristic
715	#95	C₂³×C₅₉	1	1	yes	characteristic
716	#95	C₂³×C₅₉	1	2	yes	—
717	#95	C₂³×C₅₉	1	2	yes	—
718	#95	C₂³×C₅₉	1	2	yes	—
719	#95	C₂³×C₅₉	1	2	yes	—
720	#95	C₂³×C₅₉	1	2	yes	—
721	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
722	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	#41×C₅₉	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	#41×C₅₉	1	4	yes	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₄²	—	2	4	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	4	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	4	no	—
825	C₄²	—	4	2	no	—
826	C₄²	—	4	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₄²	#41×C₅₉	1	4	yes	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	C₂×#41×C₅₉	1	2	yes	—
845	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
846	Q₈	—	2	8	no	—
847	Q₈	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	8	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	8	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	4	8	no	—
904	C₂×C₄	—	8	4	no	—
905	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
906	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
907	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
908	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
909	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
910	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
911	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
912	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
913	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
914	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
915	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
931	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
932	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
933	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
934	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
935	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
936	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	1	no	—
957	C₄	C₅₉×#529	1	4	yes	—
958	C₂	—	4	2	no	—
959	C₂	—	8	2	no	—
960	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
961	C₂	C₅₉×#3492	1	1	yes	characteristic
962	C₂	C₅₉×#3508	1	1	yes	characteristic
963	C₂	C₅₉×#3509	1	1	yes	characteristic
964	C₂	C₅₉×#3511	1	1	yes	characteristic
965	C₂	C₅₉×#3520	1	1	yes	characteristic
966	C₂	C₅₉×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×#121×C₅₉	C₂²
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. C₅₉×#2654	C₂	semidirect
3. C₅₉×#2592	C₂	semidirect
4. C₅₉×#2558	C₂	semidirect
5. C₅₉×#2553	C₂	semidirect
6. C₅₉×#2552	C₂	semidirect
7. C₅₉×#2522	C₂	semidirect
8. C₅₉×#2519	C₂	semidirect
9. C₅₉×#2512	C₂	semidirect
10. C₅₉×#2511	C₂	semidirect
11. C₅₉×#2502	C₂	semidirect
13. C₅₉×#2470	C₂	semidirect
14. C₅₉×#2458	C₂	semidirect
15. C₅₉×#2396	C₂	semidirect
16. C₅₉×#2396	C₂	semidirect
17. C₅₉×#2367	C₂	semidirect
19. C₅₉×#2362	C₂	semidirect
20. C₅₉×#2355	C₂	semidirect
21. C₅₉×#2354	C₂	semidirect
22. Q₈×C₄⋊C₄×C₅₉	C₂	semidirect
23. C₅₉×#2274	C₂	semidirect
432. #35745	C₅₉	direct (N × H)
475. #2654	C₂×C₅₉	semidirect
477. #2592	C₂×C₅₉	semidirect
478. #2558	C₂×C₅₉	semidirect
479. #2553	C₂×C₅₉	semidirect
480. #2552	C₂×C₅₉	semidirect
481. #2522	C₂×C₅₉	semidirect
482. #2519	C₂×C₅₉	semidirect
483. #2512	C₂×C₅₉	semidirect
484. #2511	C₂×C₅₉	semidirect
485. #2502	C₂×C₅₉	semidirect
487. #2470	C₂×C₅₉	semidirect
488. #2458	C₂×C₅₉	semidirect
489. #2396	C₂×C₅₉	semidirect
490. #2396	C₂×C₅₉	semidirect
491. #2367	C₂×C₅₉	semidirect
493. #2362	C₂×C₅₉	semidirect
494. #2355	C₂×C₅₉	semidirect
495. #2354	C₂×C₅₉	semidirect
496. Q₈×C₄⋊C₄	C₂×C₅₉	semidirect
497. #2274	C₂×C₅₉	semidirect
606. C₅₉	#35745	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×#2654	2
C₅₉×#2620	2
C₅₉×#2592	2
C₅₉×#2558	2
C₅₉×#2553	2
C₅₉×#2552	2
C₅₉×#2522	2
C₅₉×#2519	2
C₅₉×#2512	2
C₅₉×#2511	2
C₅₉×#2502	2
C₅₉×#2501	2
C₅₉×#2470	2
C₅₉×#2458	2
C₅₉×#2396	2
C₅₉×#2367	2
C₅₉×#2363	2
C₅₉×#2362	2
C₅₉×#2355	2
C₅₉×#2354	2
Q₈×C₄⋊C₄×C₅₉	2
C₅₉×#2274	2
#35745	59

Subgroups — C59×#35745 #28447854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35745 #28447854