Subgroups — C₅₉×#35839 #28447948

Order 15104.

1882 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2667	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2626	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2607	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2589	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2556	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2549	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2522	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2473	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2441	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2437	C₂	1	2	yes	maximal
12	C₅₉×#2423	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2396	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₉×#399	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2368	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2360	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2342	C₂	1	2	yes	maximal
19	C₅₉×#2273	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
21	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
25	C₂×#117×C₅₉	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₅₉×#400	C₂²	1	2	yes	complemented
33	C₅₉×#399	C₂²	1	1	yes	characteristic
34	C₅₉×#399	C₂²	1	1	yes	characteristic
35	C₅₉×#399	C₂²	1	2	yes	—
36	C₅₉×#399	C₂²	1	2	yes	—
37	C₅₉×#399	C₂²	1	2	yes	—
38	C₅₉×#399	C₂²	1	1	yes	characteristic
39	C₅₉×#399	C₂²	1	1	yes	characteristic
40	C₅₉×#399	C₂²	1	1	yes	characteristic
41	C₅₉×#399	C₂²	1	1	yes	characteristic
42	C₅₉×#398	C₂²	1	2	yes	complemented
43	C₅₉×#398	C₂²	1	2	yes	complemented
44	C₅₉×#398	C₂²	1	2	yes	complemented
45	C₅₉×#398	C₂²	1	2	yes	complemented
46	C₅₉×#398	C₂²	1	2	yes	complemented
47	C₅₉×#398	C₂²	1	2	yes	complemented
48	C₅₉×#396	C₂²	1	2	yes	—
49	C₅₉×#396	C₂²	1	2	yes	—
50	C₅₉×#396	C₂²	1	2	yes	—
51	C₅₉×#396	C₂²	1	2	yes	—
52	C₅₉×#395	C₂²	1	2	yes	complemented
53	C₅₉×#393	C₂²	1	1	yes	characteristic
54	C₅₉×#393	C₂²	1	1	yes	characteristic
55	C₅₉×#393	C₂²	1	2	yes	—
56	C₅₉×#391	C₂²	1	2	yes	complemented
57	C₅₉×#391	C₂²	1	2	yes	complemented
58	C₅₉×#391	C₂²	1	2	yes	complemented
59	C₅₉×#391	C₂²	1	2	yes	complemented
60	C₅₉×#389	C₂²	1	2	yes	complemented
61	C₅₉×#389	C₂²	1	2	yes	complemented
62	C₅₉×#389	C₂²	1	2	yes	complemented
63	C₅₉×#389	C₂²	1	2	yes	complemented
64	C₅₉×#389	C₂²	1	2	yes	complemented
65	C₅₉×#389	C₂²	1	2	yes	complemented
66	C₅₉×#388	C₂²	1	2	yes	—
67	C₅₉×#388	C₂²	1	2	yes	—
68	C₅₉×#388	C₂²	1	2	yes	—
69	C₅₉×#388	C₂²	1	2	yes	—
70	C₅₉×#387	C₂²	1	2	yes	complemented
71	C₅₉×#387	C₂²	1	2	yes	complemented
72	C₅₉×#387	C₂²	1	2	yes	complemented
73	C₅₉×#387	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×#385	C₂²	1	2	yes	—
79	C₅₉×#385	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	—
84	C₅₉×#385	C₂²	1	2	yes	—
85	C₅₉×#384	C₂²	1	2	yes	complemented
86	C₅₉×#381	C₂²	1	2	yes	—
87	C₅₉×#380	C₂²	1	2	yes	—
88	C₅₉×#380	C₂²	1	1	yes	characteristic
89	C₅₉×#380	C₂²	1	2	yes	—
90	C₅₉×#380	C₂²	1	2	yes	—
91	C₅₉×#379	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
94	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
106	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
109	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
111	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
114	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
115	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
116	#125×C₅₉	—	4	4	no	—
117	C₂²⋊Q₈×C₅₉	—	2	4	no	—
118	C₂²⋊Q₈×C₅₉	—	2	8	no	—
119	C₂²⋊Q₈×C₅₉	—	4	4	no	—
120	C₄×Q₈×C₅₉	—	4	4	no	—
121	#117×C₅₉	—	4	4	no	—
122	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
123	C₂×C₄⋊C₄×C₅₉	—	4	4	no	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
151	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
152	C₂×C₂²⋊C₄×C₅₉	Q₈	1	8	yes	complemented
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
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	#95×C₅₉	C₂³	1	1	yes	characteristic
182	#95×C₅₉	C₂³	1	1	yes	characteristic
183	#95×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	2	yes	—
185	#95×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	2	yes	—
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	C₂⁴×C₅₉	—	2	2	no	—
207	C₂⁴×C₅₉	—	2	2	no	—
208	C₂⁴×C₅₉	—	4	2	no	—
209	C₂⁴×C₅₉	—	4	2	no	—
210	C₂⁴×C₅₉	C₂×Q₈	1	4	yes	—
211	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
214	C₂×Q₈×C₅₉	—	2	4	no	—
215	C₂×Q₈×C₅₉	—	2	2	no	—
216	C₂×Q₈×C₅₉	—	2	4	no	—
217	C₂×Q₈×C₅₉	—	4	2	no	—
218	C₂×Q₈×C₅₉	—	4	2	no	—
219	C₂²×C₄×C₅₉	—	2	4	no	—
220	C₂²×C₄×C₅₉	—	2	2	no	—
221	C₂²×C₄×C₅₉	—	2	4	no	—
222	C₂²×C₄×C₅₉	—	2	4	no	—
223	C₂²×C₄×C₅₉	—	2	4	no	—
224	C₂²×C₄×C₅₉	—	4	2	no	—
225	C₂²×C₄×C₅₉	—	4	2	no	—
226	C₂²×C₄×C₅₉	—	4	2	no	—
227	C₂²×C₄×C₅₉	—	4	2	no	—
228	C₂²×C₄×C₅₉	—	4	2	no	—
229	C₂²×C₄×C₅₉	—	4	2	no	—
230	C₂²×C₄×C₅₉	—	4	2	no	—
231	C₂²×C₄×C₅₉	—	4	2	no	—
232	C₂²×C₄×C₅₉	—	4	2	no	—
233	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	—
234	C₂²×C₄×C₅₉	#41	1	4	yes	—
235	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅₉	C₂⁴	1	2	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	1	yes	characteristic
248	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₅₉	—	2	2	no	—
252	C₄⋊C₄×C₅₉	—	2	2	no	—
253	C₄⋊C₄×C₅₉	—	2	4	no	—
254	C₄⋊C₄×C₅₉	—	2	4	no	—
255	C₄⋊C₄×C₅₉	—	2	2	no	—
256	C₄⋊C₄×C₅₉	—	2	4	no	—
257	C₄⋊C₄×C₅₉	—	2	4	no	—
258	C₄⋊C₄×C₅₉	—	2	4	no	—
259	C₄⋊C₄×C₅₉	—	2	4	no	—
260	C₄⋊C₄×C₅₉	—	2	4	no	—
261	C₄⋊C₄×C₅₉	—	2	4	no	—
262	C₄⋊C₄×C₅₉	—	2	4	no	—
263	C₄⋊C₄×C₅₉	—	4	2	no	—
264	C₄⋊C₄×C₅₉	—	4	2	no	—
265	C₄⋊C₄×C₅₉	—	4	2	no	—
266	C₄⋊C₄×C₅₉	—	4	2	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	2	no	—
277	C₂²⋊C₄×C₅₉	—	2	4	no	—
278	C₂²⋊C₄×C₅₉	—	2	4	no	—
279	C₂²⋊C₄×C₅₉	—	2	2	no	—
280	C₂²⋊C₄×C₅₉	—	2	2	no	—
281	C₂²⋊C₄×C₅₉	—	2	2	no	—
282	C₂²⋊C₄×C₅₉	—	2	2	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	—	4	2	no	—
287	C₂²⋊C₄×C₅₉	—	4	2	no	—
288	C₂²⋊C₄×C₅₉	—	4	2	no	—
289	C₂²⋊C₄×C₅₉	—	4	2	no	—
290	C₂²⋊C₄×C₅₉	—	4	2	no	—
291	C₂²⋊C₄×C₅₉	—	4	2	no	—
292	C₂²⋊C₄×C₅₉	C₂×Q₈	1	8	yes	—
293	C₂²⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
294	C₂²⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
295	C₂²⋊C₄×C₅₉	#41	1	4	yes	—
296	C₄²×C₅₉	—	2	4	no	—
297	C₄²×C₅₉	—	4	2	no	—
298	C₄²×C₅₉	—	4	2	no	—
299	C₄²×C₅₉	—	4	2	no	—
300	C₄²×C₅₉	—	4	2	no	—
301	C₄²×C₅₉	—	4	2	no	—
302	C₄²×C₅₉	—	4	2	no	—
303	C₄²×C₅₉	—	4	2	no	—
304	C₂³×C₅₉	—	2	2	no	—
305	C₂³×C₅₉	—	2	2	no	—
306	C₂³×C₅₉	—	2	1	no	—
307	C₂³×C₅₉	—	2	1	no	—
308	C₂³×C₅₉	—	2	1	no	—
309	C₂³×C₅₉	—	2	1	no	—
310	C₂³×C₅₉	—	2	2	no	—
311	C₂³×C₅₉	—	2	2	no	—
312	C₂³×C₅₉	—	2	2	no	—
313	C₂³×C₅₉	—	2	2	no	—
314	C₂³×C₅₉	—	2	8	no	—
315	C₂³×C₅₉	—	4	8	no	—
316	C₂³×C₅₉	—	8	2	no	—
317	C₂³×C₅₉	—	8	2	no	—
318	C₂³×C₅₉	—	8	4	no	—
319	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
320	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
321	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
322	C₂³×C₅₉	C₂×#41	1	2	yes	—
323	C₂³×C₅₉	C₂×#41	1	2	yes	—
324	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
325	Q₈×C₅₉	—	4	8	no	—
326	Q₈×C₅₉	—	8	2	no	—
327	C₂×C₄×C₅₉	—	2	2	no	—
328	C₂×C₄×C₅₉	—	2	2	no	—
329	C₂×C₄×C₅₉	—	2	2	no	—
330	C₂×C₄×C₅₉	—	2	2	no	—
331	C₂×C₄×C₅₉	—	2	2	no	—
332	C₂×C₄×C₅₉	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	2	no	—
335	C₂×C₄×C₅₉	—	2	2	no	—
336	C₂×C₄×C₅₉	—	2	2	no	—
337	C₂×C₄×C₅₉	—	2	1	no	—
338	C₂×C₄×C₅₉	—	2	1	no	—
339	C₂×C₄×C₅₉	—	2	2	no	—
340	C₂×C₄×C₅₉	—	2	2	no	—
341	C₂×C₄×C₅₉	—	2	2	no	—
342	C₂×C₄×C₅₉	—	2	2	no	—
343	C₂×C₄×C₅₉	—	2	2	no	—
344	C₂×C₄×C₅₉	—	2	2	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	2	no	—
347	C₂×C₄×C₅₉	—	2	2	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	2	no	—
362	C₂×C₄×C₅₉	—	2	2	no	—
363	C₂×C₄×C₅₉	—	2	2	no	—
364	C₂×C₄×C₅₉	—	2	2	no	—
365	C₂×C₄×C₅₉	—	4	8	no	—
366	C₂×C₄×C₅₉	—	4	4	no	—
367	C₂×C₄×C₅₉	—	4	8	no	—
368	C₂×C₄×C₅₉	—	8	4	no	—
369	C₂×C₄×C₅₉	—	8	2	no	—
370	C₂×C₄×C₅₉	—	8	4	no	—
371	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
372	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
373	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
374	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
375	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
376	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
377	#35839	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂²×C₅₉	—	2	2	no	—
379	C₂²×C₅₉	—	2	4	no	—
380	C₂²×C₅₉	—	2	2	no	—
381	C₂²×C₅₉	—	2	4	no	—
382	C₂²×C₅₉	—	2	2	no	—
383	C₂²×C₅₉	—	2	2	no	—
384	C₂²×C₅₉	—	2	4	no	—
385	C₂²×C₅₉	—	2	4	no	—
386	C₂²×C₅₉	—	4	1	no	—
387	C₂²×C₅₉	—	4	1	no	—
388	C₂²×C₅₉	—	4	1	no	—
389	C₂²×C₅₉	—	4	1	no	—
390	C₂²×C₅₉	—	4	2	no	—
391	C₂²×C₅₉	—	4	2	no	—
392	C₂²×C₅₉	—	8	8	no	—
393	C₂²×C₅₉	#533	1	4	yes	—
394	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
395	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
397	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
398	C₂²×C₅₉	#585	1	2	yes	—
399	C₄×C₅₉	—	2	2	no	—
400	C₄×C₅₉	—	2	2	no	—
401	C₄×C₅₉	—	2	4	no	—
402	C₄×C₅₉	—	2	4	no	—
403	C₄×C₅₉	—	2	4	no	—
404	C₄×C₅₉	—	2	4	no	—
405	C₄×C₅₉	—	4	2	no	—
406	C₄×C₅₉	—	4	2	no	—
407	C₄×C₅₉	—	4	1	no	—
408	C₄×C₅₉	—	4	1	no	—
409	C₄×C₅₉	—	4	2	no	—
410	C₄×C₅₉	—	4	2	no	—
411	C₄×C₅₉	—	4	2	no	—
412	C₄×C₅₉	—	4	2	no	—
413	C₄×C₅₉	—	4	2	no	—
414	C₄×C₅₉	—	4	2	no	—
415	#2667	C₂×C₅₉	1	2	yes	complemented
416	#2626	C₂×C₅₉	1	1	yes	characteristic
417	#2607	C₂×C₅₉	1	2	yes	complemented
418	#2589	C₂×C₅₉	1	2	yes	complemented
419	#2556	C₂×C₅₉	1	2	yes	complemented
420	#2549	C₂×C₅₉	1	1	yes	characteristic, complemented
421	#2522	C₂×C₅₉	1	2	yes	complemented
422	#2502	C₂×C₅₉	1	1	yes	characteristic, complemented
423	#2473	C₂×C₅₉	1	2	yes	complemented
424	#2441	C₂×C₅₉	1	2	yes	complemented
425	#2437	C₂×C₅₉	1	2	yes	—
426	#2423	C₂×C₅₉	1	2	yes	complemented
427	#2396	C₂×C₅₉	1	2	yes	complemented
428	C₂×#399	C₂×C₅₉	1	1	yes	characteristic
429	#2368	C₂×C₅₉	1	1	yes	characteristic, complemented
430	#2360	C₂×C₅₉	1	2	yes	complemented
431	#2345	C₂×C₅₉	1	1	yes	characteristic, complemented
432	#2342	C₂×C₅₉	1	2	yes	—
433	#2273	C₂×C₅₉	1	1	yes	characteristic
434	C₂×C₅₉	—	2	4	no	—
435	C₂×C₅₉	—	4	2	no	—
436	C₂×C₅₉	—	4	2	no	—
437	C₂×C₅₉	C₂×#533	1	1	yes	characteristic
438	C₂×C₅₉	#3491	1	1	yes	characteristic
439	C₂×C₅₉	#3501	1	2	yes	—
440	C₂×C₅₉	#3508	1	1	yes	characteristic
441	C₂×C₅₉	#3513	1	2	yes	—
442	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
443	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
444	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
445	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
446	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
447	C₂×#117	C₂²×C₅₉	1	2	yes	—
448	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
449	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
450	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
453	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
454	#400	C₂²×C₅₉	1	2	yes	complemented
455	#399	C₂²×C₅₉	1	2	yes	—
456	#399	C₂²×C₅₉	1	2	yes	—
457	#399	C₂²×C₅₉	1	2	yes	—
458	#399	C₂²×C₅₉	1	1	yes	characteristic
459	#399	C₂²×C₅₉	1	1	yes	characteristic
460	#399	C₂²×C₅₉	1	1	yes	characteristic
461	#399	C₂²×C₅₉	1	1	yes	characteristic
462	#399	C₂²×C₅₉	1	1	yes	characteristic
463	#399	C₂²×C₅₉	1	1	yes	characteristic
464	#398	C₂²×C₅₉	1	2	yes	complemented
465	#398	C₂²×C₅₉	1	2	yes	complemented
466	#398	C₂²×C₅₉	1	2	yes	complemented
467	#398	C₂²×C₅₉	1	2	yes	complemented
468	#398	C₂²×C₅₉	1	2	yes	complemented
469	#398	C₂²×C₅₉	1	2	yes	complemented
470	#396	C₂²×C₅₉	1	2	yes	—
471	#396	C₂²×C₅₉	1	2	yes	—
472	#396	C₂²×C₅₉	1	2	yes	—
473	#396	C₂²×C₅₉	1	2	yes	—
474	#395	C₂²×C₅₉	1	2	yes	complemented
475	#393	C₂²×C₅₉	1	1	yes	characteristic
476	#393	C₂²×C₅₉	1	1	yes	characteristic
477	#393	C₂²×C₅₉	1	2	yes	—
478	#391	C₂²×C₅₉	1	2	yes	complemented
479	#391	C₂²×C₅₉	1	2	yes	complemented
480	#391	C₂²×C₅₉	1	2	yes	complemented
481	#391	C₂²×C₅₉	1	2	yes	complemented
482	#389	C₂²×C₅₉	1	2	yes	complemented
483	#389	C₂²×C₅₉	1	2	yes	complemented
484	#389	C₂²×C₅₉	1	2	yes	complemented
485	#389	C₂²×C₅₉	1	2	yes	complemented
486	#389	C₂²×C₅₉	1	2	yes	complemented
487	#389	C₂²×C₅₉	1	2	yes	complemented
488	#388	C₂²×C₅₉	1	2	yes	—
489	#388	C₂²×C₅₉	1	2	yes	—
490	#388	C₂²×C₅₉	1	2	yes	—
491	#388	C₂²×C₅₉	1	2	yes	—
492	#387	C₂²×C₅₉	1	2	yes	complemented
493	#387	C₂²×C₅₉	1	2	yes	complemented
494	#387	C₂²×C₅₉	1	2	yes	complemented
495	#387	C₂²×C₅₉	1	2	yes	complemented
496	#387	C₂²×C₅₉	1	2	yes	complemented
497	#387	C₂²×C₅₉	1	2	yes	complemented
498	#387	C₂²×C₅₉	1	2	yes	complemented
499	#387	C₂²×C₅₉	1	2	yes	complemented
500	#385	C₂²×C₅₉	1	2	yes	—
501	#385	C₂²×C₅₉	1	2	yes	—
502	#385	C₂²×C₅₉	1	2	yes	—
503	#385	C₂²×C₅₉	1	2	yes	—
504	#385	C₂²×C₅₉	1	2	yes	—
505	#385	C₂²×C₅₉	1	2	yes	—
506	#385	C₂²×C₅₉	1	2	yes	—
507	#384	C₂²×C₅₉	1	2	yes	complemented
508	#381	C₂²×C₅₉	1	2	yes	—
509	#380	C₂²×C₅₉	1	2	yes	—
510	#380	C₂²×C₅₉	1	1	yes	characteristic
511	#380	C₂²×C₅₉	1	2	yes	—
512	#380	C₂²×C₅₉	1	2	yes	—
513	#379	C₂²×C₅₉	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
515	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
516	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
517	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
522	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
524	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
526	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
527	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
528	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
529	C₅₉	#35839	1	1	yes	characteristic, direct product factor, Sylow
530	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
532	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
534	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
536	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
537	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
538	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
539	#125	—	4	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	8	no	—
542	C₂²⋊Q₈	—	4	4	no	—
543	C₄×Q₈	—	4	4	no	—
544	#117	—	4	4	no	—
545	C₂×C₄⋊C₄	—	2	4	no	—
546	C₂×C₄⋊C₄	—	4	4	no	—
547	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
572	C₂×C₂²⋊C₄	—	2	4	no	—
573	C₂×C₂²⋊C₄	—	2	4	no	—
574	C₂×C₂²⋊C₄	—	4	4	no	—
575	C₂×C₂²⋊C₄	Q₈×C₅₉	1	8	yes	complemented
576	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
599	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
600	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
601	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
602	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
603	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
604	#95	C₂³×C₅₉	1	1	yes	characteristic
605	#95	C₂³×C₅₉	1	1	yes	characteristic
606	#95	C₂³×C₅₉	1	2	yes	—
607	#95	C₂³×C₅₉	1	2	yes	—
608	#95	C₂³×C₅₉	1	2	yes	—
609	#95	C₂³×C₅₉	1	2	yes	—
610	#95	C₂³×C₅₉	1	2	yes	—
611	#95	C₂³×C₅₉	1	2	yes	—
612	#95	C₂³×C₅₉	1	2	yes	—
613	#95	C₂³×C₅₉	1	2	yes	—
614	#95	C₂³×C₅₉	1	2	yes	—
615	#95	C₂³×C₅₉	1	2	yes	—
616	#95	C₂³×C₅₉	1	2	yes	—
617	#95	C₂³×C₅₉	1	2	yes	—
618	#95	C₂³×C₅₉	1	2	yes	—
619	#95	C₂³×C₅₉	1	2	yes	—
620	#95	C₂³×C₅₉	1	2	yes	—
621	#95	C₂³×C₅₉	1	2	yes	—
622	#95	C₂³×C₅₉	1	2	yes	—
623	#95	C₂³×C₅₉	1	1	yes	characteristic
624	#95	C₂³×C₅₉	1	1	yes	characteristic
625	#95	C₂³×C₅₉	1	2	yes	—
626	#95	C₂³×C₅₉	1	2	yes	—
627	#95	C₂³×C₅₉	1	2	yes	—
628	#95	C₂³×C₅₉	1	2	yes	—
629	C₂⁴	—	2	2	no	—
630	C₂⁴	—	2	2	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	C₂×Q₈×C₅₉	1	4	yes	—
634	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
635	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
636	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
637	C₂×Q₈	—	2	4	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	—	4	2	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	—
657	C₂²×C₄	#41×C₅₉	1	4	yes	—
658	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	C₂×Q₈×C₅₉	1	8	yes	—
716	C₂²⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
717	C₂²⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
718	C₂²⋊C₄	#41×C₅₉	1	4	yes	—
719	C₄²	—	2	4	no	—
720	C₄²	—	4	2	no	—
721	C₄²	—	4	2	no	—
722	C₄²	—	4	2	no	—
723	C₄²	—	4	2	no	—
724	C₄²	—	4	2	no	—
725	C₄²	—	4	2	no	—
726	C₄²	—	4	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	8	no	—
738	C₂³	—	4	8	no	—
739	C₂³	—	8	2	no	—
740	C₂³	—	8	4	no	—
741	C₂³	—	8	2	no	—
742	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
743	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
744	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
745	C₂³	C₂×#41×C₅₉	1	2	yes	—
746	C₂³	C₂×#41×C₅₉	1	2	yes	—
747	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
748	Q₈	—	4	8	no	—
749	Q₈	—	8	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	8	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	—	8	4	no	—
794	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
795	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
796	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
797	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
798	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
799	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	8	8	no	—
815	C₂²	C₅₉×#533	1	4	yes	—
816	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
817	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
818	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
819	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
820	C₂²	C₅₉×#585	1	2	yes	—
821	C₄	—	2	4	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	4	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₂	—	2	4	no	—
838	C₂	—	4	2	no	—
839	C₂	—	4	2	no	—
840	C₂	C₂×C₅₉×#533	1	1	yes	characteristic
841	C₂	C₅₉×#3491	1	1	yes	characteristic
842	C₂	C₅₉×#3501	1	2	yes	—
843	C₂	C₅₉×#3508	1	1	yes	characteristic
844	C₂	C₅₉×#3513	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁵×C₅₉	C₂³
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×#2667	C₂	semidirect
3. C₅₉×#2607	C₂	semidirect
4. C₅₉×#2589	C₂	semidirect
5. C₅₉×#2556	C₂	semidirect
6. C₅₉×#2549	C₂	semidirect
7. C₅₉×#2522	C₂	semidirect
8. C₅₉×#2502	C₂	semidirect
9. C₅₉×#2473	C₂	semidirect
10. C₅₉×#2441	C₂	semidirect
12. C₅₉×#2423	C₂	semidirect
13. C₅₉×#2396	C₂	semidirect
15. C₅₉×#2368	C₂	semidirect
16. C₅₉×#2360	C₂	semidirect
17. C₅₉×#2345	C₂	semidirect
20. C₂×#125×C₅₉	C₂²	semidirect
24. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
32. C₅₉×#400	C₂²	semidirect
42. C₅₉×#398	C₂²	semidirect
43. C₅₉×#398	C₂²	semidirect
44. C₅₉×#398	C₂²	semidirect
45. C₅₉×#398	C₂²	semidirect
46. C₅₉×#398	C₂²	semidirect
47. C₅₉×#398	C₂²	semidirect
52. C₅₉×#395	C₂²	semidirect
56. C₅₉×#391	C₂²	semidirect
57. C₅₉×#391	C₂²	semidirect
58. C₅₉×#391	C₂²	semidirect
59. C₅₉×#391	C₂²	semidirect
60. C₅₉×#389	C₂²	semidirect
61. C₅₉×#389	C₂²	semidirect
62. C₅₉×#389	C₂²	semidirect
63. C₅₉×#389	C₂²	semidirect
64. C₅₉×#389	C₂²	semidirect
65. C₅₉×#389	C₂²	semidirect
70. C₅₉×#387	C₂²	semidirect
71. C₅₉×#387	C₂²	semidirect
72. C₅₉×#387	C₂²	semidirect
73. C₅₉×#387	C₂²	semidirect
74. C₅₉×#387	C₂²	semidirect
75. C₅₉×#387	C₂²	semidirect
76. C₅₉×#387	C₂²	semidirect
77. C₅₉×#387	C₂²	semidirect
85. C₅₉×#384	C₂²	semidirect
92. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
94. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
152. C₂×C₂²⋊C₄×C₅₉	Q₈	semidirect
377. #35839	C₅₉	direct (N × H)
415. #2667	C₂×C₅₉	semidirect
417. #2607	C₂×C₅₉	semidirect
418. #2589	C₂×C₅₉	semidirect
419. #2556	C₂×C₅₉	semidirect
420. #2549	C₂×C₅₉	semidirect
421. #2522	C₂×C₅₉	semidirect
422. #2502	C₂×C₅₉	semidirect
423. #2473	C₂×C₅₉	semidirect
424. #2441	C₂×C₅₉	semidirect
426. #2423	C₂×C₅₉	semidirect
427. #2396	C₂×C₅₉	semidirect
429. #2368	C₂×C₅₉	semidirect
430. #2360	C₂×C₅₉	semidirect
431. #2345	C₂×C₅₉	semidirect
442. C₂×#125	C₂²×C₅₉	semidirect
446. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
454. #400	C₂²×C₅₉	semidirect
464. #398	C₂²×C₅₉	semidirect
465. #398	C₂²×C₅₉	semidirect
466. #398	C₂²×C₅₉	semidirect
467. #398	C₂²×C₅₉	semidirect
468. #398	C₂²×C₅₉	semidirect
469. #398	C₂²×C₅₉	semidirect
474. #395	C₂²×C₅₉	semidirect
478. #391	C₂²×C₅₉	semidirect
479. #391	C₂²×C₅₉	semidirect
480. #391	C₂²×C₅₉	semidirect
481. #391	C₂²×C₅₉	semidirect
482. #389	C₂²×C₅₉	semidirect
483. #389	C₂²×C₅₉	semidirect
484. #389	C₂²×C₅₉	semidirect
485. #389	C₂²×C₅₉	semidirect
486. #389	C₂²×C₅₉	semidirect
487. #389	C₂²×C₅₉	semidirect
492. #387	C₂²×C₅₉	semidirect
493. #387	C₂²×C₅₉	semidirect
494. #387	C₂²×C₅₉	semidirect
495. #387	C₂²×C₅₉	semidirect
496. #387	C₂²×C₅₉	semidirect
497. #387	C₂²×C₅₉	semidirect
498. #387	C₂²×C₅₉	semidirect
499. #387	C₂²×C₅₉	semidirect
507. #384	C₂²×C₅₉	semidirect
514. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
515. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
516. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
529. C₅₉	#35839	direct (N × H)
575. C₂×C₂²⋊C₄	Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2667	2
C₅₉×#2626	2
C₅₉×#2607	2
C₅₉×#2589	2
C₅₉×#2556	2
C₅₉×#2549	2
C₅₉×#2522	2
C₅₉×#2502	2
C₅₉×#2473	2
C₅₉×#2441	2
C₅₉×#2437	2
C₅₉×#2423	2
C₅₉×#2396	2
C₂×C₅₉×#399	2
C₅₉×#2368	2
C₅₉×#2360	2
C₅₉×#2345	2
C₅₉×#2342	2
C₅₉×#2273	2
#35839	59

Subgroups — C59×#35839 #28447948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35839 #28447948