Subgroups — C₅₉×#35731 #28447840

Order 15104.

2054 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2651	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2627	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2595	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2593	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2569	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2521	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2516	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2482	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2480	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2474	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2468	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2435	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2395	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₉×#394	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2368	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2342	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2342	C₂	1	2	yes	maximal, complemented
18	D₄×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₅₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
25	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
28	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
32	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
33	C₅₉×#400	C₂²	1	2	yes	complemented
34	C₅₉×#400	C₂²	1	1	yes	characteristic, complemented
35	C₅₉×#399	C₂²	1	2	yes	complemented
36	C₅₉×#399	C₂²	1	2	yes	complemented
37	C₅₉×#398	C₂²	1	2	yes	complemented
38	C₅₉×#398	C₂²	1	2	yes	complemented
39	C₅₉×#398	C₂²	1	2	yes	complemented
40	C₅₉×#397	C₂²	1	2	yes	complemented
41	C₅₉×#397	C₂²	1	2	yes	complemented
42	C₅₉×#397	C₂²	1	2	yes	complemented
43	C₅₉×#397	C₂²	1	2	yes	complemented
44	C₅₉×#397	C₂²	1	2	yes	complemented
45	C₅₉×#396	C₂²	1	2	yes	complemented
46	C₅₉×#395	C₂²	1	1	yes	characteristic, complemented
47	C₅₉×#395	C₂²	1	1	yes	characteristic, complemented
48	C₅₉×#394	C₂²	1	2	yes	—
49	C₅₉×#394	C₂²	1	1	yes	characteristic
50	C₅₉×#394	C₂²	1	2	yes	—
51	C₅₉×#394	C₂²	1	2	yes	—
52	C₅₉×#394	C₂²	1	1	yes	characteristic
53	C₅₉×#394	C₂²	1	1	yes	characteristic
54	C₅₉×#394	C₂²	1	1	yes	characteristic
55	C₅₉×#394	C₂²	1	2	yes	—
56	C₅₉×#391	C₂²	1	2	yes	complemented
57	C₅₉×#390	C₂²	1	2	yes	—
58	C₅₉×#390	C₂²	1	2	yes	—
59	C₅₉×#388	C₂²	1	2	yes	complemented
60	C₅₉×#388	C₂²	1	2	yes	complemented
61	C₅₉×#388	C₂²	1	2	yes	complemented
62	C₅₉×#388	C₂²	1	2	yes	complemented
63	C₅₉×#388	C₂²	1	2	yes	complemented
64	C₅₉×#388	C₂²	1	2	yes	complemented
65	C₅₉×#388	C₂²	1	2	yes	complemented
66	C₅₉×#388	C₂²	1	2	yes	complemented
67	C₅₉×#388	C₂²	1	2	yes	complemented
68	C₅₉×#388	C₂²	1	2	yes	complemented
69	C₅₉×#388	C₂²	1	2	yes	complemented
70	C₅₉×#388	C₂²	1	2	yes	complemented
71	C₅₉×#388	C₂²	1	2	yes	complemented
72	C₅₉×#388	C₂²	1	2	yes	complemented
73	C₅₉×#388	C₂²	1	2	yes	complemented
74	C₅₉×#387	C₂²	1	2	yes	complemented
75	C₅₉×#387	C₂²	1	2	yes	complemented
76	C₅₉×#387	C₂²	1	2	yes	complemented
77	C₅₉×#387	C₂²	1	2	yes	complemented
78	C₅₉×#386	C₂²	1	2	yes	—
79	C₅₉×#386	C₂²	1	2	yes	—
80	C₅₉×#385	C₂²	1	2	yes	—
81	C₅₉×#385	C₂²	1	2	yes	—
82	C₅₉×#385	C₂²	1	2	yes	—
83	C₅₉×#385	C₂²	1	2	yes	complemented
84	C₅₉×#385	C₂²	1	2	yes	complemented
85	C₅₉×#381	C₂²	1	2	yes	—
86	C₅₉×#381	C₂²	1	2	yes	complemented
87	C₅₉×#380	C₂²	1	1	yes	characteristic
88	C₅₉×#380	C₂²	1	2	yes	—
89	C₅₉×#380	C₂²	1	2	yes	complemented
90	C₅₉×#379	C₂²	1	2	yes	—
91	C₅₉×#379	C₂²	1	2	yes	—
92	C₅₉×#379	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
95	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
96	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
97	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
106	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₅₉	—	2	4	no	—
110	C₂²×D₄×C₅₉	—	4	4	no	—
111	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
117	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
120	#126×C₅₉	—	4	4	no	—
121	#124×C₅₉	—	4	4	no	—
122	C₂²⋊Q₈×C₅₉	—	2	4	no	—
123	C₄×D₄×C₅₉	—	4	4	no	—
124	#117×C₅₉	—	2	4	no	—
125	#117×C₅₉	—	2	4	no	—
126	#117×C₅₉	—	4	4	no	—
127	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
146	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
147	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	1	yes	characteristic
185	#95×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	1	yes	characteristic
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	2	yes	—
189	#95×C₅₉	C₂³	1	2	yes	—
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	2	yes	—
193	#95×C₅₉	C₂³	1	2	yes	—
194	#95×C₅₉	C₂³	1	2	yes	—
195	#95×C₅₉	C₂³	1	2	yes	—
196	#95×C₅₉	C₂³	1	2	yes	—
197	#95×C₅₉	C₂³	1	2	yes	—
198	#95×C₅₉	C₂³	1	2	yes	—
199	#95×C₅₉	C₂³	1	2	yes	—
200	#95×C₅₉	C₂³	1	1	yes	characteristic
201	#95×C₅₉	C₂³	1	1	yes	characteristic
202	#95×C₅₉	C₂³	1	2	yes	—
203	#95×C₅₉	C₂³	1	2	yes	—
204	#95×C₅₉	C₂³	1	2	yes	—
205	#95×C₅₉	C₂³	1	2	yes	—
206	#95×C₅₉	C₂³	1	2	yes	—
207	C₂⁴×C₅₉	—	2	4	no	—
208	C₂⁴×C₅₉	—	2	4	no	—
209	C₂⁴×C₅₉	—	2	4	no	—
210	C₂⁴×C₅₉	—	2	4	no	—
211	C₂⁴×C₅₉	—	4	2	no	—
212	C₂⁴×C₅₉	—	4	2	no	—
213	C₂⁴×C₅₉	—	4	2	no	—
214	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
215	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
216	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
217	C₂×Q₈×C₅₉	—	2	2	no	—
218	C₂×Q₈×C₅₉	—	4	2	no	—
219	C₂×D₄×C₅₉	—	2	4	no	—
220	C₂×D₄×C₅₉	—	2	4	no	—
221	C₂×D₄×C₅₉	—	2	2	no	—
222	C₂×D₄×C₅₉	—	2	2	no	—
223	C₂×D₄×C₅₉	—	2	4	no	—
224	C₂×D₄×C₅₉	—	4	2	no	—
225	C₂×D₄×C₅₉	—	4	2	no	—
226	C₂×D₄×C₅₉	—	4	16	no	—
227	C₂²×C₄×C₅₉	—	2	2	no	—
228	C₂²×C₄×C₅₉	—	2	2	no	—
229	C₂²×C₄×C₅₉	—	2	4	no	—
230	C₂²×C₄×C₅₉	—	2	4	no	—
231	C₂²×C₄×C₅₉	—	2	2	no	—
232	C₂²×C₄×C₅₉	—	2	4	no	—
233	C₂²×C₄×C₅₉	—	2	4	no	—
234	C₂²×C₄×C₅₉	—	4	2	no	—
235	C₂²×C₄×C₅₉	—	4	2	no	—
236	C₂²×C₄×C₅₉	—	4	2	no	—
237	C₂²×C₄×C₅₉	—	4	2	no	—
238	C₂²×C₄×C₅₉	—	4	2	no	—
239	C₂²×C₄×C₅₉	—	4	2	no	—
240	C₂²×C₄×C₅₉	—	4	2	no	—
241	C₂²×C₄×C₅₉	#41	1	4	yes	—
242	C₂²×C₄×C₅₉	#41	1	4	yes	—
243	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₅₉	—	2	2	no	—
260	C₄⋊C₄×C₅₉	—	2	2	no	—
261	C₄⋊C₄×C₅₉	—	2	2	no	—
262	C₄⋊C₄×C₅₉	—	2	2	no	—
263	C₄⋊C₄×C₅₉	—	2	4	no	—
264	C₄⋊C₄×C₅₉	—	2	4	no	—
265	C₄⋊C₄×C₅₉	—	2	2	no	—
266	C₄⋊C₄×C₅₉	—	2	4	no	—
267	C₄⋊C₄×C₅₉	—	4	2	no	—
268	C₄⋊C₄×C₅₉	—	4	2	no	—
269	C₄⋊C₄×C₅₉	—	4	2	no	—
270	C₄⋊C₄×C₅₉	—	4	2	no	—
271	C₄⋊C₄×C₅₉	—	4	2	no	—
272	C₄⋊C₄×C₅₉	—	4	2	no	—
273	C₄⋊C₄×C₅₉	—	4	2	no	—
274	C₄⋊C₄×C₅₉	—	4	2	no	—
275	C₄⋊C₄×C₅₉	—	4	2	no	—
276	C₂²⋊C₄×C₅₉	—	2	4	no	—
277	C₂²⋊C₄×C₅₉	—	2	2	no	—
278	C₂²⋊C₄×C₅₉	—	2	2	no	—
279	C₂²⋊C₄×C₅₉	—	2	2	no	—
280	C₂²⋊C₄×C₅₉	—	2	4	no	—
281	C₂²⋊C₄×C₅₉	—	2	4	no	—
282	C₂²⋊C₄×C₅₉	—	2	4	no	—
283	C₂²⋊C₄×C₅₉	—	2	4	no	—
284	C₂²⋊C₄×C₅₉	—	2	4	no	—
285	C₂²⋊C₄×C₅₉	—	2	4	no	—
286	C₂²⋊C₄×C₅₉	—	2	4	no	—
287	C₂²⋊C₄×C₅₉	—	2	4	no	—
288	C₂²⋊C₄×C₅₉	—	2	4	no	—
289	C₂²⋊C₄×C₅₉	—	2	4	no	—
290	C₂²⋊C₄×C₅₉	—	2	4	no	—
291	C₂²⋊C₄×C₅₉	—	2	4	no	—
292	C₂²⋊C₄×C₅₉	—	4	2	no	—
293	C₂²⋊C₄×C₅₉	—	4	2	no	—
294	C₂²⋊C₄×C₅₉	—	4	2	no	—
295	C₂²⋊C₄×C₅₉	—	4	2	no	—
296	C₂²⋊C₄×C₅₉	—	4	2	no	—
297	C₂²⋊C₄×C₅₉	—	4	2	no	—
298	C₂²⋊C₄×C₅₉	—	4	2	no	—
299	C₂²⋊C₄×C₅₉	—	4	2	no	—
300	C₂²⋊C₄×C₅₉	—	4	2	no	—
301	C₂²⋊C₄×C₅₉	—	4	2	no	—
302	C₂²⋊C₄×C₅₉	—	4	2	no	—
303	C₂²⋊C₄×C₅₉	#41	1	4	yes	—
304	C₄²×C₅₉	—	2	4	no	—
305	C₄²×C₅₉	—	2	4	no	—
306	C₄²×C₅₉	—	4	2	no	—
307	C₄²×C₅₉	—	4	2	no	—
308	C₄²×C₅₉	—	4	2	no	—
309	C₄²×C₅₉	—	4	2	no	—
310	C₄²×C₅₉	—	4	2	no	—
311	C₄²×C₅₉	—	4	2	no	—
312	C₂³×C₅₉	—	2	2	no	—
313	C₂³×C₅₉	—	2	2	no	—
314	C₂³×C₅₉	—	2	2	no	—
315	C₂³×C₅₉	—	2	2	no	—
316	C₂³×C₅₉	—	2	2	no	—
317	C₂³×C₅₉	—	2	2	no	—
318	C₂³×C₅₉	—	2	2	no	—
319	C₂³×C₅₉	—	2	2	no	—
320	C₂³×C₅₉	—	2	2	no	—
321	C₂³×C₅₉	—	2	2	no	—
322	C₂³×C₅₉	—	2	2	no	—
323	C₂³×C₅₉	—	2	2	no	—
324	C₂³×C₅₉	—	2	2	no	—
325	C₂³×C₅₉	—	2	2	no	—
326	C₂³×C₅₉	—	2	2	no	—
327	C₂³×C₅₉	—	4	8	no	—
328	C₂³×C₅₉	—	4	8	no	—
329	C₂³×C₅₉	—	4	8	no	—
330	C₂³×C₅₉	—	4	8	no	—
331	C₂³×C₅₉	—	8	4	no	—
332	C₂³×C₅₉	—	8	4	no	—
333	C₂³×C₅₉	—	8	4	no	—
334	C₂³×C₅₉	C₂×#41	1	2	yes	—
335	C₂³×C₅₉	C₂×#41	1	2	yes	—
336	C₂³×C₅₉	C₂×#41	1	2	yes	—
337	C₂³×C₅₉	H(5,𝔽₂)	1	4	yes	—
338	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
339	Q₈×C₅₉	—	8	2	no	—
340	D₄×C₅₉	—	2	8	no	—
341	D₄×C₅₉	—	4	8	no	—
342	D₄×C₅₉	—	4	4	no	—
343	C₂×C₄×C₅₉	—	2	8	no	—
344	C₂×C₄×C₅₉	—	2	1	no	—
345	C₂×C₄×C₅₉	—	2	1	no	—
346	C₂×C₄×C₅₉	—	2	1	no	—
347	C₂×C₄×C₅₉	—	2	1	no	—
348	C₂×C₄×C₅₉	—	2	2	no	—
349	C₂×C₄×C₅₉	—	2	2	no	—
350	C₂×C₄×C₅₉	—	2	2	no	—
351	C₂×C₄×C₅₉	—	2	2	no	—
352	C₂×C₄×C₅₉	—	2	2	no	—
353	C₂×C₄×C₅₉	—	2	2	no	—
354	C₂×C₄×C₅₉	—	2	2	no	—
355	C₂×C₄×C₅₉	—	2	2	no	—
356	C₂×C₄×C₅₉	—	2	2	no	—
357	C₂×C₄×C₅₉	—	2	2	no	—
358	C₂×C₄×C₅₉	—	2	2	no	—
359	C₂×C₄×C₅₉	—	2	2	no	—
360	C₂×C₄×C₅₉	—	2	2	no	—
361	C₂×C₄×C₅₉	—	2	1	no	—
362	C₂×C₄×C₅₉	—	2	1	no	—
363	C₂×C₄×C₅₉	—	2	2	no	—
364	C₂×C₄×C₅₉	—	2	2	no	—
365	C₂×C₄×C₅₉	—	2	2	no	—
366	C₂×C₄×C₅₉	—	2	2	no	—
367	C₂×C₄×C₅₉	—	2	2	no	—
368	C₂×C₄×C₅₉	—	2	2	no	—
369	C₂×C₄×C₅₉	—	2	2	no	—
370	C₂×C₄×C₅₉	—	2	2	no	—
371	C₂×C₄×C₅₉	—	2	2	no	—
372	C₂×C₄×C₅₉	—	2	2	no	—
373	C₂×C₄×C₅₉	—	2	2	no	—
374	C₂×C₄×C₅₉	—	2	2	no	—
375	C₂×C₄×C₅₉	—	2	2	no	—
376	C₂×C₄×C₅₉	—	2	2	no	—
377	C₂×C₄×C₅₉	—	2	2	no	—
378	C₂×C₄×C₅₉	—	2	2	no	—
379	C₂×C₄×C₅₉	—	2	2	no	—
380	C₂×C₄×C₅₉	—	2	2	no	—
381	C₂×C₄×C₅₉	—	2	2	no	—
382	C₂×C₄×C₅₉	—	2	2	no	—
383	C₂×C₄×C₅₉	—	4	4	no	—
384	C₂×C₄×C₅₉	—	4	8	no	—
385	C₂×C₄×C₅₉	—	8	4	no	—
386	C₂×C₄×C₅₉	—	8	2	no	—
387	C₂×C₄×C₅₉	—	8	4	no	—
388	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
389	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
390	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
391	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
392	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
393	#35731	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂²×C₅₉	—	2	2	no	—
395	C₂²×C₅₉	—	2	4	no	—
396	C₂²×C₅₉	—	2	2	no	—
397	C₂²×C₅₉	—	2	4	no	—
398	C₂²×C₅₉	—	2	4	no	—
399	C₂²×C₅₉	—	2	4	no	—
400	C₂²×C₅₉	—	2	4	no	—
401	C₂²×C₅₉	—	4	2	no	—
402	C₂²×C₅₉	—	4	2	no	—
403	C₂²×C₅₉	—	4	2	no	—
404	C₂²×C₅₉	—	4	2	no	—
405	C₂²×C₅₉	—	4	2	no	—
406	C₂²×C₅₉	—	4	2	no	—
407	C₂²×C₅₉	—	4	2	no	—
408	C₂²×C₅₉	—	4	2	no	—
409	C₂²×C₅₉	—	4	2	no	—
410	C₂²×C₅₉	—	4	2	no	—
411	C₂²×C₅₉	—	4	2	no	—
412	C₂²×C₅₉	—	8	16	no	—
413	C₂²×C₅₉	#529	1	4	yes	—
414	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
415	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
416	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
418	C₂²×C₅₉	#585	1	2	yes	—
419	C₄×C₅₉	—	2	2	no	—
420	C₄×C₅₉	—	2	2	no	—
421	C₄×C₅₉	—	2	2	no	—
422	C₄×C₅₉	—	2	2	no	—
423	C₄×C₅₉	—	2	4	no	—
424	C₄×C₅₉	—	4	1	no	—
425	C₄×C₅₉	—	4	1	no	—
426	C₄×C₅₉	—	4	2	no	—
427	C₄×C₅₉	—	4	2	no	—
428	C₄×C₅₉	—	4	2	no	—
429	C₄×C₅₉	—	4	2	no	—
430	C₄×C₅₉	—	4	2	no	—
431	C₄×C₅₉	—	4	2	no	—
432	C₄×C₅₉	—	4	2	no	—
433	C₄×C₅₉	—	4	2	no	—
434	C₄×C₅₉	—	4	2	no	—
435	#2651	C₂×C₅₉	1	2	yes	complemented
436	#2627	C₂×C₅₉	1	1	yes	characteristic, complemented
437	#2595	C₂×C₅₉	1	2	yes	complemented
438	#2593	C₂×C₅₉	1	2	yes	complemented
439	#2569	C₂×C₅₉	1	1	yes	characteristic, complemented
440	#2521	C₂×C₅₉	1	2	yes	complemented
441	#2516	C₂×C₅₉	1	2	yes	complemented
442	#2482	C₂×C₅₉	1	2	yes	complemented
443	#2480	C₂×C₅₉	1	2	yes	complemented
444	#2474	C₂×C₅₉	1	2	yes	complemented
445	#2468	C₂×C₅₉	1	2	yes	complemented
446	#2435	C₂×C₅₉	1	1	yes	characteristic
447	#2395	C₂×C₅₉	1	2	yes	complemented
448	C₂×#394	C₂×C₅₉	1	1	yes	characteristic
449	#2368	C₂×C₅₉	1	1	yes	characteristic, complemented
450	#2342	C₂×C₅₉	1	2	yes	complemented
451	#2342	C₂×C₅₉	1	2	yes	complemented
452	D₄×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic
453	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
454	C₂×C₅₉	—	2	4	no	—
455	C₂×C₅₉	—	4	4	no	—
456	C₂×C₅₉	—	8	2	no	—
457	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
458	C₂×C₅₉	#3490	1	1	yes	characteristic
459	C₂×C₅₉	#3494	1	2	yes	—
460	C₂×C₅₉	#3510	1	1	yes	characteristic
461	C₂×C₅₉	#3513	1	2	yes	—
462	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
463	C₂×#126	C₂²×C₅₉	1	2	yes	complemented
464	C₂×#124	C₂²×C₅₉	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
467	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
468	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
469	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
470	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
471	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
472	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
473	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
474	#400	C₂²×C₅₉	1	2	yes	complemented
475	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
476	#400	C₂²×C₅₉	1	1	yes	characteristic, complemented
477	#399	C₂²×C₅₉	1	2	yes	complemented
478	#399	C₂²×C₅₉	1	2	yes	complemented
479	#398	C₂²×C₅₉	1	2	yes	complemented
480	#398	C₂²×C₅₉	1	2	yes	complemented
481	#398	C₂²×C₅₉	1	2	yes	complemented
482	#397	C₂²×C₅₉	1	2	yes	complemented
483	#397	C₂²×C₅₉	1	2	yes	complemented
484	#397	C₂²×C₅₉	1	2	yes	complemented
485	#397	C₂²×C₅₉	1	2	yes	complemented
486	#397	C₂²×C₅₉	1	2	yes	complemented
487	#396	C₂²×C₅₉	1	2	yes	complemented
488	#395	C₂²×C₅₉	1	1	yes	characteristic, complemented
489	#395	C₂²×C₅₉	1	1	yes	characteristic, complemented
490	#394	C₂²×C₅₉	1	1	yes	characteristic
491	#394	C₂²×C₅₉	1	2	yes	—
492	#394	C₂²×C₅₉	1	2	yes	—
493	#394	C₂²×C₅₉	1	1	yes	characteristic
494	#394	C₂²×C₅₉	1	1	yes	characteristic
495	#394	C₂²×C₅₉	1	1	yes	characteristic
496	#394	C₂²×C₅₉	1	2	yes	—
497	#394	C₂²×C₅₉	1	2	yes	—
498	#391	C₂²×C₅₉	1	2	yes	complemented
499	#390	C₂²×C₅₉	1	2	yes	—
500	#390	C₂²×C₅₉	1	2	yes	—
501	#388	C₂²×C₅₉	1	2	yes	complemented
502	#388	C₂²×C₅₉	1	2	yes	complemented
503	#388	C₂²×C₅₉	1	2	yes	complemented
504	#388	C₂²×C₅₉	1	2	yes	complemented
505	#388	C₂²×C₅₉	1	2	yes	complemented
506	#388	C₂²×C₅₉	1	2	yes	complemented
507	#388	C₂²×C₅₉	1	2	yes	complemented
508	#388	C₂²×C₅₉	1	2	yes	complemented
509	#388	C₂²×C₅₉	1	2	yes	complemented
510	#388	C₂²×C₅₉	1	2	yes	complemented
511	#388	C₂²×C₅₉	1	2	yes	complemented
512	#388	C₂²×C₅₉	1	2	yes	complemented
513	#388	C₂²×C₅₉	1	2	yes	complemented
514	#388	C₂²×C₅₉	1	2	yes	complemented
515	#388	C₂²×C₅₉	1	2	yes	complemented
516	#387	C₂²×C₅₉	1	2	yes	complemented
517	#387	C₂²×C₅₉	1	2	yes	complemented
518	#387	C₂²×C₅₉	1	2	yes	complemented
519	#387	C₂²×C₅₉	1	2	yes	complemented
520	#386	C₂²×C₅₉	1	2	yes	—
521	#386	C₂²×C₅₉	1	2	yes	—
522	#385	C₂²×C₅₉	1	2	yes	—
523	#385	C₂²×C₅₉	1	2	yes	—
524	#385	C₂²×C₅₉	1	2	yes	—
525	#385	C₂²×C₅₉	1	2	yes	complemented
526	#385	C₂²×C₅₉	1	2	yes	complemented
527	#381	C₂²×C₅₉	1	2	yes	—
528	#381	C₂²×C₅₉	1	2	yes	complemented
529	#380	C₂²×C₅₉	1	1	yes	characteristic
530	#380	C₂²×C₅₉	1	2	yes	—
531	#380	C₂²×C₅₉	1	2	yes	complemented
532	#379	C₂²×C₅₉	1	2	yes	—
533	#379	C₂²×C₅₉	1	2	yes	—
534	#379	C₂²×C₅₉	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
536	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
537	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
538	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
539	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
540	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
541	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
542	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
544	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
545	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
546	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
547	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
548	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
549	C₅₉	#35731	1	1	yes	characteristic, direct product factor, Sylow
550	C₂⁵	C₂³×C₅₉	1	2	yes	—
551	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
552	C₂²×D₄	—	2	4	no	—
553	C₂²×D₄	—	4	4	no	—
554	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
556	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
558	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
561	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
562	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
563	#126	—	4	4	no	—
564	#124	—	4	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₄×D₄	—	4	4	no	—
567	#117	—	2	4	no	—
568	#117	—	2	4	no	—
569	#117	—	4	4	no	—
570	C₂×C₄⋊C₄	—	2	4	no	—
571	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
588	C₂×C₂²⋊C₄	—	2	8	no	—
589	C₂×C₂²⋊C₄	—	2	8	no	—
590	C₂×C₂²⋊C₄	—	4	4	no	—
591	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
620	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
621	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
625	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
626	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
627	#95	C₂³×C₅₉	1	1	yes	characteristic
628	#95	C₂³×C₅₉	1	2	yes	—
629	#95	C₂³×C₅₉	1	1	yes	characteristic
630	#95	C₂³×C₅₉	1	2	yes	—
631	#95	C₂³×C₅₉	1	2	yes	—
632	#95	C₂³×C₅₉	1	2	yes	—
633	#95	C₂³×C₅₉	1	2	yes	—
634	#95	C₂³×C₅₉	1	2	yes	—
635	#95	C₂³×C₅₉	1	2	yes	—
636	#95	C₂³×C₅₉	1	2	yes	—
637	#95	C₂³×C₅₉	1	2	yes	—
638	#95	C₂³×C₅₉	1	2	yes	—
639	#95	C₂³×C₅₉	1	2	yes	—
640	#95	C₂³×C₅₉	1	2	yes	—
641	#95	C₂³×C₅₉	1	2	yes	—
642	#95	C₂³×C₅₉	1	2	yes	—
643	#95	C₂³×C₅₉	1	1	yes	characteristic
644	#95	C₂³×C₅₉	1	1	yes	characteristic
645	#95	C₂³×C₅₉	1	2	yes	—
646	#95	C₂³×C₅₉	1	2	yes	—
647	#95	C₂³×C₅₉	1	2	yes	—
648	#95	C₂³×C₅₉	1	2	yes	—
649	#95	C₂³×C₅₉	1	2	yes	—
650	C₂⁴	—	2	4	no	—
651	C₂⁴	—	2	4	no	—
652	C₂⁴	—	2	4	no	—
653	C₂⁴	—	2	4	no	—
654	C₂⁴	—	4	2	no	—
655	C₂⁴	—	4	2	no	—
656	C₂⁴	—	4	2	no	—
657	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
658	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
659	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	4	2	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	16	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	#41×C₅₉	1	4	yes	—
685	C₂²×C₄	#41×C₅₉	1	4	yes	—
686	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	#41×C₅₉	1	4	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	4	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	2	no	—
751	C₄²	—	4	2	no	—
752	C₄²	—	4	2	no	—
753	C₄²	—	4	2	no	—
754	C₄²	—	4	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	4	8	no	—
771	C₂³	—	4	8	no	—
772	C₂³	—	4	8	no	—
773	C₂³	—	4	8	no	—
774	C₂³	—	8	4	no	—
775	C₂³	—	8	4	no	—
776	C₂³	—	8	4	no	—
777	C₂³	C₂×#41×C₅₉	1	2	yes	—
778	C₂³	C₂×#41×C₅₉	1	2	yes	—
779	C₂³	C₂×#41×C₅₉	1	2	yes	—
780	C₂³	H(5,𝔽₂)×C₅₉	1	4	yes	—
781	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
782	Q₈	—	8	2	no	—
783	D₄	—	2	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	4	no	—
786	C₂×C₄	—	2	8	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	8	no	—
828	C₂×C₄	—	8	4	no	—
829	C₂×C₄	—	8	2	no	—
830	C₂×C₄	—	8	4	no	—
831	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
832	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
833	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
834	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
835	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	8	16	no	—
855	C₂²	C₅₉×#529	1	4	yes	—
856	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
857	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
858	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
859	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
860	C₂²	C₅₉×#585	1	2	yes	—
861	C₄	—	2	4	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₂	—	2	4	no	—
878	C₂	—	4	4	no	—
879	C₂	—	8	2	no	—
880	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
881	C₂	C₅₉×#3490	1	1	yes	characteristic
882	C₂	C₅₉×#3494	1	2	yes	—
883	C₂	C₅₉×#3510	1	1	yes	characteristic
884	C₂	C₅₉×#3513	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂³×D₄×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×#2651	C₂	semidirect
2. C₅₉×#2627	C₂	semidirect
3. C₅₉×#2595	C₂	semidirect
4. C₅₉×#2593	C₂	semidirect
5. C₅₉×#2569	C₂	semidirect
6. C₅₉×#2521	C₂	semidirect
7. C₅₉×#2516	C₂	semidirect
8. C₅₉×#2482	C₂	semidirect
9. C₅₉×#2480	C₂	semidirect
10. C₅₉×#2474	C₂	semidirect
11. C₅₉×#2468	C₂	semidirect
13. C₅₉×#2395	C₂	semidirect
15. C₅₉×#2368	C₂	semidirect
16. C₅₉×#2342	C₂	semidirect
17. C₅₉×#2342	C₂	semidirect
19. C₅₉×#2274	C₂	semidirect
21. C₂×#126×C₅₉	C₂²	semidirect
27. C₂×#117×C₅₉	C₂²	semidirect
32. C₅₉×#400	C₂²	semidirect
33. C₅₉×#400	C₂²	semidirect
34. C₅₉×#400	C₂²	semidirect
35. C₅₉×#399	C₂²	semidirect
36. C₅₉×#399	C₂²	semidirect
37. C₅₉×#398	C₂²	semidirect
38. C₅₉×#398	C₂²	semidirect
39. C₅₉×#398	C₂²	semidirect
40. C₅₉×#397	C₂²	semidirect
41. C₅₉×#397	C₂²	semidirect
42. C₅₉×#397	C₂²	semidirect
43. C₅₉×#397	C₂²	semidirect
44. C₅₉×#397	C₂²	semidirect
45. C₅₉×#396	C₂²	semidirect
46. C₅₉×#395	C₂²	semidirect
47. C₅₉×#395	C₂²	semidirect
56. C₅₉×#391	C₂²	semidirect
59. C₅₉×#388	C₂²	semidirect
60. C₅₉×#388	C₂²	semidirect
61. C₅₉×#388	C₂²	semidirect
62. C₅₉×#388	C₂²	semidirect
63. C₅₉×#388	C₂²	semidirect
64. C₅₉×#388	C₂²	semidirect
65. C₅₉×#388	C₂²	semidirect
66. C₅₉×#388	C₂²	semidirect
67. C₅₉×#388	C₂²	semidirect
68. C₅₉×#388	C₂²	semidirect
69. C₅₉×#388	C₂²	semidirect
70. C₅₉×#388	C₂²	semidirect
71. C₅₉×#388	C₂²	semidirect
72. C₅₉×#388	C₂²	semidirect
73. C₅₉×#388	C₂²	semidirect
74. C₅₉×#387	C₂²	semidirect
75. C₅₉×#387	C₂²	semidirect
76. C₅₉×#387	C₂²	semidirect
77. C₅₉×#387	C₂²	semidirect
83. C₅₉×#385	C₂²	semidirect
84. C₅₉×#385	C₂²	semidirect
86. C₅₉×#381	C₂²	semidirect
89. C₅₉×#380	C₂²	semidirect
93. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
95. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
96. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
97. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
393. #35731	C₅₉	direct (N × H)
435. #2651	C₂×C₅₉	semidirect
436. #2627	C₂×C₅₉	semidirect
437. #2595	C₂×C₅₉	semidirect
438. #2593	C₂×C₅₉	semidirect
439. #2569	C₂×C₅₉	semidirect
440. #2521	C₂×C₅₉	semidirect
441. #2516	C₂×C₅₉	semidirect
442. #2482	C₂×C₅₉	semidirect
443. #2480	C₂×C₅₉	semidirect
444. #2474	C₂×C₅₉	semidirect
445. #2468	C₂×C₅₉	semidirect
447. #2395	C₂×C₅₉	semidirect
449. #2368	C₂×C₅₉	semidirect
450. #2342	C₂×C₅₉	semidirect
451. #2342	C₂×C₅₉	semidirect
453. #2274	C₂×C₅₉	semidirect
463. C₂×#126	C₂²×C₅₉	semidirect
469. C₂×#117	C₂²×C₅₉	semidirect
474. #400	C₂²×C₅₉	semidirect
475. #400	C₂²×C₅₉	semidirect
476. #400	C₂²×C₅₉	semidirect
477. #399	C₂²×C₅₉	semidirect
478. #399	C₂²×C₅₉	semidirect
479. #398	C₂²×C₅₉	semidirect
480. #398	C₂²×C₅₉	semidirect
481. #398	C₂²×C₅₉	semidirect
482. #397	C₂²×C₅₉	semidirect
483. #397	C₂²×C₅₉	semidirect
484. #397	C₂²×C₅₉	semidirect
485. #397	C₂²×C₅₉	semidirect
486. #397	C₂²×C₅₉	semidirect
487. #396	C₂²×C₅₉	semidirect
488. #395	C₂²×C₅₉	semidirect
489. #395	C₂²×C₅₉	semidirect
498. #391	C₂²×C₅₉	semidirect
501. #388	C₂²×C₅₉	semidirect
502. #388	C₂²×C₅₉	semidirect
503. #388	C₂²×C₅₉	semidirect
504. #388	C₂²×C₅₉	semidirect
505. #388	C₂²×C₅₉	semidirect
506. #388	C₂²×C₅₉	semidirect
507. #388	C₂²×C₅₉	semidirect
508. #388	C₂²×C₅₉	semidirect
509. #388	C₂²×C₅₉	semidirect
510. #388	C₂²×C₅₉	semidirect
511. #388	C₂²×C₅₉	semidirect
512. #388	C₂²×C₅₉	semidirect
513. #388	C₂²×C₅₉	semidirect
514. #388	C₂²×C₅₉	semidirect
515. #388	C₂²×C₅₉	semidirect
516. #387	C₂²×C₅₉	semidirect
517. #387	C₂²×C₅₉	semidirect
518. #387	C₂²×C₅₉	semidirect
519. #387	C₂²×C₅₉	semidirect
525. #385	C₂²×C₅₉	semidirect
526. #385	C₂²×C₅₉	semidirect
528. #381	C₂²×C₅₉	semidirect
531. #380	C₂²×C₅₉	semidirect
535. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
536. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
537. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
538. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
539. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
545. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
546. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
547. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
549. C₅₉	#35731	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×#2651	2
C₅₉×#2627	2
C₅₉×#2595	2
C₅₉×#2593	2
C₅₉×#2569	2
C₅₉×#2521	2
C₅₉×#2516	2
C₅₉×#2482	2
C₅₉×#2480	2
C₅₉×#2474	2
C₅₉×#2468	2
C₅₉×#2435	2
C₅₉×#2395	2
C₂×C₅₉×#394	2
C₅₉×#2368	2
C₅₉×#2342	2
D₄×C₂²⋊C₄×C₅₉	2
C₅₉×#2274	2
#35731	59

Subgroups — C59×#35731 #28447840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35731 #28447840