Subgroups — C₅₉×#35637 #28447746

Order 15104.

2086 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2611	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2604	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2601	C₂	1	2	yes	maximal
6	C₅₉×#2565	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2560	C₂	1	2	yes	maximal
8	C₅₉×#2556	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2542	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2536	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2519	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2506	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2492	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2489	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#2429	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2429	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₉×#2290	C₂	1	1	yes	maximal, characteristic
23	C₅₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₉×#541	—	2	8	no	—
25	C₅₉×#533	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#126×C₅₉	C₂²	1	2	yes	—
31	C₂×#126×C₅₉	C₂²	1	2	yes	—
32	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#125×C₅₉	C₂²	1	2	yes	—
34	C₂×#125×C₅₉	C₂²	1	2	yes	—
35	C₂×#125×C₅₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₅₉	C₂²	1	2	yes	—
52	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
53	C₅₉×#400	C₂²	1	2	yes	—
54	C₅₉×#400	C₂²	1	2	yes	—
55	C₅₉×#399	C₂²	1	2	yes	—
56	C₅₉×#399	C₂²	1	2	yes	—
57	C₅₉×#398	C₂²	1	2	yes	—
58	C₅₉×#398	C₂²	1	2	yes	—
59	C₅₉×#398	C₂²	1	2	yes	—
60	C₅₉×#398	C₂²	1	2	yes	—
61	C₅₉×#398	C₂²	1	2	yes	—
62	C₅₉×#398	C₂²	1	2	yes	—
63	C₅₉×#397	C₂²	1	2	yes	—
64	C₅₉×#396	C₂²	1	2	yes	—
65	C₅₉×#396	C₂²	1	2	yes	—
66	C₅₉×#395	C₂²	1	2	yes	—
67	C₅₉×#394	C₂²	1	2	yes	—
68	C₅₉×#393	C₂²	1	2	yes	—
69	C₅₉×#391	C₂²	1	1	yes	characteristic
70	C₅₉×#391	C₂²	1	1	yes	characteristic
71	C₅₉×#391	C₂²	1	1	yes	characteristic
72	C₅₉×#391	C₂²	1	2	yes	—
73	C₅₉×#391	C₂²	1	1	yes	characteristic
74	C₅₉×#391	C₂²	1	2	yes	—
75	C₅₉×#390	C₂²	1	2	yes	—
76	C₅₉×#389	C₂²	1	2	yes	—
77	C₅₉×#389	C₂²	1	2	yes	—
78	C₅₉×#389	C₂²	1	2	yes	—
79	C₅₉×#389	C₂²	1	2	yes	—
80	C₅₉×#389	C₂²	1	2	yes	—
81	C₅₉×#389	C₂²	1	2	yes	—
82	C₅₉×#389	C₂²	1	1	yes	characteristic
83	C₅₉×#389	C₂²	1	1	yes	characteristic
84	C₅₉×#388	C₂²	1	2	yes	—
85	C₅₉×#388	C₂²	1	2	yes	—
86	C₅₉×#388	C₂²	1	1	yes	characteristic
87	C₅₉×#388	C₂²	1	2	yes	—
88	C₅₉×#388	C₂²	1	2	yes	—
89	C₅₉×#388	C₂²	1	2	yes	—
90	C₅₉×#388	C₂²	1	1	yes	characteristic
91	C₅₉×#388	C₂²	1	2	yes	—
92	C₅₉×#388	C₂²	1	2	yes	—
93	C₅₉×#388	C₂²	1	2	yes	—
94	C₅₉×#387	C₂²	1	1	yes	characteristic
95	C₅₉×#387	C₂²	1	2	yes	—
96	C₅₉×#387	C₂²	1	2	yes	—
97	C₅₉×#387	C₂²	1	1	yes	characteristic
98	C₅₉×#387	C₂²	1	2	yes	—
99	C₅₉×#387	C₂²	1	2	yes	—
100	C₅₉×#387	C₂²	1	2	yes	—
101	C₅₉×#387	C₂²	1	2	yes	—
102	C₅₉×#386	C₂²	1	1	yes	characteristic
103	C₅₉×#386	C₂²	1	1	yes	characteristic
104	C₅₉×#385	C₂²	1	1	yes	characteristic
105	C₅₉×#385	C₂²	1	1	yes	characteristic
106	C₅₉×#385	C₂²	1	2	yes	—
107	C₅₉×#384	C₂²	1	2	yes	—
108	C₅₉×#382	C₂²	1	2	yes	—
109	C₅₉×#382	C₂²	1	1	yes	characteristic
110	C₅₉×#380	C₂²	1	1	yes	characteristic
111	C₅₉×#380	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
119	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
123	C₅₉×#376	C₂²	1	1	yes	characteristic
124	C₅₉×#376	C₂²	1	2	yes	—
125	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
128	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₄⋊Q₈×C₅₉	—	2	4	no	—
135	C₄⋊Q₈×C₅₉	—	2	4	no	—
136	C₄⋊Q₈×C₅₉	—	2	4	no	—
137	C₄⋊Q₈×C₅₉	—	2	4	no	—
138	#126×C₅₉	—	2	8	no	—
139	#126×C₅₉	—	2	8	no	—
140	#125×C₅₉	—	2	8	no	—
141	#125×C₅₉	—	2	4	no	—
142	#125×C₅₉	—	2	8	no	—
143	#125×C₅₉	—	2	8	no	—
144	C₂²⋊Q₈×C₅₉	—	2	4	no	—
145	C₂²⋊Q₈×C₅₉	—	2	4	no	—
146	C₂²⋊Q₈×C₅₉	—	2	4	no	—
147	C₂²⋊Q₈×C₅₉	—	2	8	no	—
148	C₂²⋊Q₈×C₅₉	—	2	4	no	—
149	C₂²⋊Q₈×C₅₉	—	2	4	no	—
150	C₂²⋊Q₈×C₅₉	—	2	4	no	—
151	C₄×Q₈×C₅₉	—	2	4	no	—
152	C₄×Q₈×C₅₉	—	2	8	no	—
153	C₄×Q₈×C₅₉	—	2	4	no	—
154	C₄×Q₈×C₅₉	—	2	4	no	—
155	C₄×Q₈×C₅₉	—	2	4	no	—
156	C₄×Q₈×C₅₉	D₄	1	8	yes	complemented
157	C₄×D₄×C₅₉	—	2	4	no	—
158	#117×C₅₉	—	2	8	no	—
159	#117×C₅₉	—	2	4	no	—
160	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
167	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₅₉	—	2	4	no	—
209	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
211	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
212	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
213	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
218	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
219	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
220	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
224	#95×C₅₉	C₂³	1	1	yes	characteristic
225	#95×C₅₉	C₂³	1	2	yes	—
226	#95×C₅₉	C₂³	1	1	yes	characteristic
227	#95×C₅₉	C₂³	1	1	yes	characteristic
228	#95×C₅₉	C₂³	1	1	yes	characteristic
229	#95×C₅₉	C₂³	1	2	yes	—
230	#95×C₅₉	C₂³	1	2	yes	—
231	#95×C₅₉	C₂³	1	1	yes	characteristic
232	#95×C₅₉	C₂³	1	1	yes	characteristic
233	#95×C₅₉	C₂³	1	1	yes	characteristic
234	#95×C₅₉	C₂³	1	1	yes	characteristic
235	#95×C₅₉	C₂³	1	2	yes	—
236	#95×C₅₉	C₂³	1	2	yes	—
237	#95×C₅₉	C₂³	1	2	yes	—
238	#95×C₅₉	C₂³	1	2	yes	—
239	#95×C₅₉	C₂³	1	1	yes	characteristic
240	#95×C₅₉	C₂³	1	1	yes	characteristic
241	#95×C₅₉	C₂³	1	2	yes	—
242	#95×C₅₉	C₂³	1	2	yes	—
243	#95×C₅₉	C₂³	1	2	yes	—
244	#95×C₅₉	C₂³	1	2	yes	—
245	#95×C₅₉	C₂³	1	2	yes	—
246	#95×C₅₉	C₂³	1	2	yes	—
247	#95×C₅₉	C₂³	1	2	yes	—
248	#95×C₅₉	C₂³	1	2	yes	—
249	#95×C₅₉	C₂³	1	2	yes	—
250	#95×C₅₉	C₂³	1	2	yes	—
251	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
253	C₂×Q₈×C₅₉	—	2	4	no	—
254	C₂×Q₈×C₅₉	—	2	2	no	—
255	C₂×Q₈×C₅₉	—	2	2	no	—
256	C₂×Q₈×C₅₉	—	2	2	no	—
257	C₂×Q₈×C₅₉	—	2	2	no	—
258	C₂×Q₈×C₅₉	—	2	2	no	—
259	C₂×Q₈×C₅₉	—	2	2	no	—
260	C₂×Q₈×C₅₉	—	2	2	no	—
261	C₂×Q₈×C₅₉	—	2	2	no	—
262	C₂×Q₈×C₅₉	—	2	4	no	—
263	C₂×Q₈×C₅₉	—	4	2	no	—
264	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
265	C₂×D₄×C₅₉	—	2	2	no	—
266	C₂×D₄×C₅₉	—	2	2	no	—
267	C₂×D₄×C₅₉	—	4	1	no	—
268	C₂²×C₄×C₅₉	—	2	2	no	—
269	C₂²×C₄×C₅₉	—	2	2	no	—
270	C₂²×C₄×C₅₉	—	2	2	no	—
271	C₂²×C₄×C₅₉	—	2	2	no	—
272	C₂²×C₄×C₅₉	—	2	2	no	—
273	C₂²×C₄×C₅₉	—	2	2	no	—
274	C₂²×C₄×C₅₉	—	2	2	no	—
275	C₂²×C₄×C₅₉	—	2	2	no	—
276	C₂²×C₄×C₅₉	—	2	2	no	—
277	C₂²×C₄×C₅₉	—	2	2	no	—
278	C₂²×C₄×C₅₉	—	2	2	no	—
279	C₂²×C₄×C₅₉	—	4	1	no	—
280	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₅₉	—	2	2	no	—
302	C₄⋊C₄×C₅₉	—	2	2	no	—
303	C₄⋊C₄×C₅₉	—	2	4	no	—
304	C₄⋊C₄×C₅₉	—	2	4	no	—
305	C₄⋊C₄×C₅₉	—	2	4	no	—
306	C₄⋊C₄×C₅₉	—	2	4	no	—
307	C₄⋊C₄×C₅₉	—	2	2	no	—
308	C₄⋊C₄×C₅₉	—	2	4	no	—
309	C₄⋊C₄×C₅₉	—	2	4	no	—
310	C₄⋊C₄×C₅₉	—	2	2	no	—
311	C₄⋊C₄×C₅₉	—	2	4	no	—
312	C₄⋊C₄×C₅₉	—	2	4	no	—
313	C₄⋊C₄×C₅₉	—	2	4	no	—
314	C₄⋊C₄×C₅₉	—	2	4	no	—
315	C₄⋊C₄×C₅₉	—	2	4	no	—
316	C₄⋊C₄×C₅₉	—	2	4	no	—
317	C₄⋊C₄×C₅₉	—	2	4	no	—
318	C₄⋊C₄×C₅₉	—	2	2	no	—
319	C₄⋊C₄×C₅₉	—	2	4	no	—
320	C₄⋊C₄×C₅₉	—	2	4	no	—
321	C₄⋊C₄×C₅₉	—	2	2	no	—
322	C₄⋊C₄×C₅₉	—	2	4	no	—
323	C₄⋊C₄×C₅₉	—	2	4	no	—
324	C₄⋊C₄×C₅₉	—	2	4	no	—
325	C₄⋊C₄×C₅₉	—	2	4	no	—
326	C₄⋊C₄×C₅₉	—	2	2	no	—
327	C₄⋊C₄×C₅₉	—	2	4	no	—
328	C₄⋊C₄×C₅₉	—	2	2	no	—
329	C₄⋊C₄×C₅₉	—	4	2	no	—
330	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
331	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
332	C₄⋊C₄×C₅₉	#41	1	4	yes	—
333	C₂²⋊C₄×C₅₉	—	2	4	no	—
334	C₂²⋊C₄×C₅₉	—	2	2	no	—
335	C₂²⋊C₄×C₅₉	—	2	4	no	—
336	C₂²⋊C₄×C₅₉	—	2	4	no	—
337	C₂²⋊C₄×C₅₉	—	2	2	no	—
338	C₂²⋊C₄×C₅₉	—	2	2	no	—
339	C₂²⋊C₄×C₅₉	—	2	4	no	—
340	C₂²⋊C₄×C₅₉	—	2	4	no	—
341	C₂²⋊C₄×C₅₉	—	2	2	no	—
342	C₂²⋊C₄×C₅₉	—	2	2	no	—
343	C₂²⋊C₄×C₅₉	—	2	4	no	—
344	C₂²⋊C₄×C₅₉	—	2	4	no	—
345	C₂²⋊C₄×C₅₉	—	2	2	no	—
346	C₂²⋊C₄×C₅₉	—	2	2	no	—
347	C₂²⋊C₄×C₅₉	—	4	1	no	—
348	C₂²⋊C₄×C₅₉	—	4	2	no	—
349	C₄²×C₅₉	—	2	2	no	—
350	C₄²×C₅₉	—	2	2	no	—
351	C₄²×C₅₉	—	2	2	no	—
352	C₄²×C₅₉	—	2	4	no	—
353	C₄²×C₅₉	—	2	2	no	—
354	C₄²×C₅₉	—	2	4	no	—
355	C₄²×C₅₉	—	2	4	no	—
356	C₄²×C₅₉	—	2	4	no	—
357	C₄²×C₅₉	—	2	2	no	—
358	C₄²×C₅₉	—	4	2	no	—
359	C₄²×C₅₉	—	4	2	no	—
360	C₄²×C₅₉	—	4	2	no	—
361	C₄²×C₅₉	C₂×D₄	1	4	yes	—
362	C₄²×C₅₉	C₂×D₄	1	8	yes	—
363	C₄²×C₅₉	#41	1	4	yes	—
364	C₂³×C₅₉	—	2	1	no	—
365	C₂³×C₅₉	—	2	1	no	—
366	C₂³×C₅₉	—	2	1	no	—
367	C₂³×C₅₉	—	2	1	no	—
368	C₂³×C₅₉	—	2	1	no	—
369	C₂³×C₅₉	—	2	1	no	—
370	C₂³×C₅₉	—	2	1	no	—
371	C₂³×C₅₉	—	2	1	no	—
372	C₂³×C₅₉	—	2	1	no	—
373	C₂³×C₅₉	—	2	1	no	—
374	C₂³×C₅₉	—	2	1	no	—
375	C₂³×C₅₉	—	2	1	no	—
376	C₂³×C₅₉	—	2	1	no	—
377	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
378	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
379	Q₈×C₅₉	—	2	8	no	—
380	Q₈×C₅₉	—	4	8	no	—
381	Q₈×C₅₉	—	4	4	no	—
382	Q₈×C₅₉	—	4	4	no	—
383	D₄×C₅₉	—	4	4	no	—
384	C₂×C₄×C₅₉	—	2	8	no	—
385	C₂×C₄×C₅₉	—	2	1	no	—
386	C₂×C₄×C₅₉	—	2	1	no	—
387	C₂×C₄×C₅₉	—	2	2	no	—
388	C₂×C₄×C₅₉	—	2	2	no	—
389	C₂×C₄×C₅₉	—	2	1	no	—
390	C₂×C₄×C₅₉	—	2	1	no	—
391	C₂×C₄×C₅₉	—	2	2	no	—
392	C₂×C₄×C₅₉	—	2	1	no	—
393	C₂×C₄×C₅₉	—	2	1	no	—
394	C₂×C₄×C₅₉	—	2	1	no	—
395	C₂×C₄×C₅₉	—	2	1	no	—
396	C₂×C₄×C₅₉	—	2	1	no	—
397	C₂×C₄×C₅₉	—	2	2	no	—
398	C₂×C₄×C₅₉	—	2	2	no	—
399	C₂×C₄×C₅₉	—	2	1	no	—
400	C₂×C₄×C₅₉	—	2	1	no	—
401	C₂×C₄×C₅₉	—	2	2	no	—
402	C₂×C₄×C₅₉	—	2	1	no	—
403	C₂×C₄×C₅₉	—	2	1	no	—
404	C₂×C₄×C₅₉	—	2	1	no	—
405	C₂×C₄×C₅₉	—	2	2	no	—
406	C₂×C₄×C₅₉	—	2	1	no	—
407	C₂×C₄×C₅₉	—	2	2	no	—
408	C₂×C₄×C₅₉	—	2	2	no	—
409	C₂×C₄×C₅₉	—	2	2	no	—
410	C₂×C₄×C₅₉	—	2	1	no	—
411	C₂×C₄×C₅₉	—	2	1	no	—
412	C₂×C₄×C₅₉	—	2	2	no	—
413	C₂×C₄×C₅₉	—	2	1	no	—
414	C₂×C₄×C₅₉	—	2	1	no	—
415	C₂×C₄×C₅₉	—	2	1	no	—
416	C₂×C₄×C₅₉	—	2	2	no	—
417	C₂×C₄×C₅₉	—	2	2	no	—
418	C₂×C₄×C₅₉	—	2	1	no	—
419	C₂×C₄×C₅₉	—	2	1	no	—
420	C₂×C₄×C₅₉	—	2	2	no	—
421	C₂×C₄×C₅₉	—	2	2	no	—
422	C₂×C₄×C₅₉	—	2	2	no	—
423	C₂×C₄×C₅₉	—	2	1	no	—
424	C₂×C₄×C₅₉	—	2	2	no	—
425	C₂×C₄×C₅₉	—	2	1	no	—
426	C₂×C₄×C₅₉	—	2	1	no	—
427	C₂×C₄×C₅₉	—	2	1	no	—
428	C₂×C₄×C₅₉	—	2	1	no	—
429	C₂×C₄×C₅₉	—	2	2	no	—
430	C₂×C₄×C₅₉	—	2	1	no	—
431	C₂×C₄×C₅₉	—	2	2	no	—
432	C₂×C₄×C₅₉	—	2	2	no	—
433	C₂×C₄×C₅₉	—	2	1	no	—
434	C₂×C₄×C₅₉	—	2	1	no	—
435	C₂×C₄×C₅₉	—	2	2	no	—
436	C₂×C₄×C₅₉	—	4	4	no	—
437	C₂×C₄×C₅₉	—	4	4	no	—
438	C₂×C₄×C₅₉	—	4	4	no	—
439	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
442	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
443	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
445	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
446	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
447	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
448	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
449	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
450	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
451	#35637	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂²×C₅₉	—	2	2	no	—
453	C₂²×C₅₉	—	2	2	no	—
454	C₂²×C₅₉	—	2	2	no	—
455	C₂²×C₅₉	—	4	1	no	—
456	C₂²×C₅₉	—	4	1	no	—
457	C₂²×C₅₉	—	4	1	no	—
458	C₂²×C₅₉	—	4	1	no	—
459	C₂²×C₅₉	—	4	1	no	—
460	C₂²×C₅₉	—	4	1	no	—
461	C₂²×C₅₉	—	4	1	no	—
462	C₂²×C₅₉	—	4	1	no	—
463	C₂²×C₅₉	—	4	1	no	—
464	C₂²×C₅₉	—	4	1	no	—
465	C₂²×C₅₉	—	4	1	no	—
466	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
467	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
468	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
469	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
470	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
472	C₂²×C₅₉	#585	1	1	yes	characteristic
473	C₄×C₅₉	—	2	4	no	—
474	C₄×C₅₉	—	2	2	no	—
475	C₄×C₅₉	—	2	2	no	—
476	C₄×C₅₉	—	2	2	no	—
477	C₄×C₅₉	—	2	2	no	—
478	C₄×C₅₉	—	2	4	no	—
479	C₄×C₅₉	—	2	2	no	—
480	C₄×C₅₉	—	2	2	no	—
481	C₄×C₅₉	—	2	4	no	—
482	C₄×C₅₉	—	4	1	no	—
483	C₄×C₅₉	—	4	1	no	—
484	C₄×C₅₉	—	4	2	no	—
485	C₄×C₅₉	—	4	2	no	—
486	C₄×C₅₉	—	4	1	no	—
487	C₄×C₅₉	—	4	2	no	—
488	C₄×C₅₉	—	4	1	no	—
489	C₄×C₅₉	—	4	2	no	—
490	C₄×C₅₉	—	4	2	no	—
491	C₄×C₅₉	—	4	1	no	—
492	C₄×C₅₉	—	4	1	no	—
493	C₄×C₅₉	#532	1	4	yes	—
494	C₂×#541	C₂×C₅₉	1	1	yes	characteristic, complemented
495	C₂×#533	C₂×C₅₉	1	1	yes	characteristic, complemented
496	#2611	C₂×C₅₉	1	2	yes	complemented
497	#2604	C₂×C₅₉	1	2	yes	complemented
498	#2601	C₂×C₅₉	1	2	yes	—
499	#2565	C₂×C₅₉	1	2	yes	complemented
500	#2560	C₂×C₅₉	1	2	yes	—
501	#2556	C₂×C₅₉	1	2	yes	complemented
502	#2550	C₂×C₅₉	1	1	yes	characteristic, complemented
503	#2546	C₂×C₅₉	1	1	yes	characteristic, complemented
504	#2542	C₂×C₅₉	1	1	yes	characteristic
505	#2536	C₂×C₅₉	1	1	yes	characteristic
506	#2519	C₂×C₅₉	1	2	yes	complemented
507	#2506	C₂×C₅₉	1	2	yes	complemented
508	#2492	C₂×C₅₉	1	1	yes	characteristic, complemented
509	#2489	C₂×C₅₉	1	1	yes	characteristic, complemented
510	#2429	C₂×C₅₉	1	1	yes	characteristic, complemented
511	#2429	C₂×C₅₉	1	1	yes	characteristic, complemented
512	#2327	C₂×C₅₉	1	1	yes	characteristic, complemented
513	#2323	C₂×C₅₉	1	1	yes	characteristic, complemented
514	C₄×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
515	#2290	C₂×C₅₉	1	1	yes	characteristic
516	#2276	C₂×C₅₉	1	1	yes	characteristic, complemented
517	C₂×C₅₉	—	4	2	no	—
518	C₂×C₅₉	—	8	1	no	—
519	C₂×C₅₉	C₂×#532	1	1	yes	characteristic
520	C₂×C₅₉	#3486	1	1	yes	characteristic
521	C₂×C₅₉	#3489	1	1	yes	characteristic
522	C₂×C₅₉	#3495	1	1	yes	characteristic
523	C₂×C₅₉	#3509	1	1	yes	characteristic
524	C₂×C₅₉	#3515	1	1	yes	characteristic
525	C₂×C₅₉	#3523	1	1	yes	characteristic
526	#541	—	2	8	no	—
527	#533	—	2	8	no	—
528	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
529	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
530	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
531	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
532	C₂×#126	C₂²×C₅₉	1	2	yes	—
533	C₂×#126	C₂²×C₅₉	1	2	yes	—
534	C₂×#125	C₂²×C₅₉	1	2	yes	—
535	C₂×#125	C₂²×C₅₉	1	2	yes	—
536	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
537	C₂×#125	C₂²×C₅₉	1	2	yes	—
538	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
539	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
540	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
541	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
542	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
543	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
544	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
545	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
546	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
547	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
548	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
549	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
550	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
552	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
553	C₂×#117	C₂²×C₅₉	1	2	yes	—
554	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
555	#400	C₂²×C₅₉	1	2	yes	—
556	#400	C₂²×C₅₉	1	2	yes	—
557	#399	C₂²×C₅₉	1	2	yes	—
558	#399	C₂²×C₅₉	1	2	yes	—
559	#398	C₂²×C₅₉	1	2	yes	—
560	#398	C₂²×C₅₉	1	2	yes	—
561	#398	C₂²×C₅₉	1	2	yes	—
562	#398	C₂²×C₅₉	1	2	yes	—
563	#398	C₂²×C₅₉	1	2	yes	—
564	#398	C₂²×C₅₉	1	2	yes	—
565	#397	C₂²×C₅₉	1	2	yes	—
566	#396	C₂²×C₅₉	1	2	yes	—
567	#396	C₂²×C₅₉	1	2	yes	—
568	#395	C₂²×C₅₉	1	2	yes	—
569	#394	C₂²×C₅₉	1	2	yes	—
570	#393	C₂²×C₅₉	1	2	yes	—
571	#391	C₂²×C₅₉	1	2	yes	—
572	#391	C₂²×C₅₉	1	2	yes	—
573	#391	C₂²×C₅₉	1	1	yes	characteristic
574	#391	C₂²×C₅₉	1	1	yes	characteristic
575	#391	C₂²×C₅₉	1	1	yes	characteristic
576	#391	C₂²×C₅₉	1	1	yes	characteristic
577	#390	C₂²×C₅₉	1	2	yes	—
578	#389	C₂²×C₅₉	1	1	yes	characteristic
579	#389	C₂²×C₅₉	1	2	yes	—
580	#389	C₂²×C₅₉	1	2	yes	—
581	#389	C₂²×C₅₉	1	2	yes	—
582	#389	C₂²×C₅₉	1	2	yes	—
583	#389	C₂²×C₅₉	1	2	yes	—
584	#389	C₂²×C₅₉	1	2	yes	—
585	#389	C₂²×C₅₉	1	1	yes	characteristic
586	#388	C₂²×C₅₉	1	2	yes	—
587	#388	C₂²×C₅₉	1	2	yes	—
588	#388	C₂²×C₅₉	1	2	yes	—
589	#388	C₂²×C₅₉	1	2	yes	—
590	#388	C₂²×C₅₉	1	2	yes	—
591	#388	C₂²×C₅₉	1	2	yes	—
592	#388	C₂²×C₅₉	1	1	yes	characteristic
593	#388	C₂²×C₅₉	1	2	yes	—
594	#388	C₂²×C₅₉	1	2	yes	—
595	#388	C₂²×C₅₉	1	1	yes	characteristic
596	#387	C₂²×C₅₉	1	2	yes	—
597	#387	C₂²×C₅₉	1	1	yes	characteristic
598	#387	C₂²×C₅₉	1	2	yes	—
599	#387	C₂²×C₅₉	1	2	yes	—
600	#387	C₂²×C₅₉	1	2	yes	—
601	#387	C₂²×C₅₉	1	2	yes	—
602	#387	C₂²×C₅₉	1	2	yes	—
603	#387	C₂²×C₅₉	1	1	yes	characteristic
604	#386	C₂²×C₅₉	1	1	yes	characteristic
605	#386	C₂²×C₅₉	1	1	yes	characteristic
606	#385	C₂²×C₅₉	1	2	yes	—
607	#385	C₂²×C₅₉	1	1	yes	characteristic
608	#385	C₂²×C₅₉	1	1	yes	characteristic
609	#384	C₂²×C₅₉	1	2	yes	—
610	#382	C₂²×C₅₉	1	2	yes	—
611	#382	C₂²×C₅₉	1	1	yes	characteristic
612	#380	C₂²×C₅₉	1	1	yes	characteristic
613	#380	C₂²×C₅₉	1	1	yes	characteristic
614	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
615	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
616	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
619	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
620	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
622	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
623	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
624	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
625	#376	C₂²×C₅₉	1	1	yes	characteristic
626	#376	C₂²×C₅₉	1	2	yes	—
627	C₅₉	#35637	1	1	yes	characteristic, direct product factor, Sylow
628	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
631	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
632	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
633	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
634	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
637	C₄⋊Q₈	—	2	4	no	—
638	C₄⋊Q₈	—	2	4	no	—
639	C₄⋊Q₈	—	2	4	no	—
640	C₄⋊Q₈	—	2	4	no	—
641	#126	—	2	8	no	—
642	#126	—	2	8	no	—
643	#125	—	2	8	no	—
644	#125	—	2	4	no	—
645	#125	—	2	8	no	—
646	#125	—	2	8	no	—
647	C₂²⋊Q₈	—	2	4	no	—
648	C₂²⋊Q₈	—	2	4	no	—
649	C₂²⋊Q₈	—	2	4	no	—
650	C₂²⋊Q₈	—	2	8	no	—
651	C₂²⋊Q₈	—	2	4	no	—
652	C₂²⋊Q₈	—	2	4	no	—
653	C₂²⋊Q₈	—	2	4	no	—
654	C₄×Q₈	—	2	4	no	—
655	C₄×Q₈	—	2	8	no	—
656	C₄×Q₈	—	2	4	no	—
657	C₄×Q₈	—	2	4	no	—
658	C₄×Q₈	—	2	4	no	—
659	C₄×Q₈	D₄×C₅₉	1	8	yes	complemented
660	C₄×D₄	—	2	4	no	—
661	#117	—	2	8	no	—
662	#117	—	2	4	no	—
663	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
711	C₂×C₄²	—	2	4	no	—
712	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
713	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
716	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
718	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
719	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
722	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
723	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
724	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
726	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
727	#95	C₂³×C₅₉	1	1	yes	characteristic
728	#95	C₂³×C₅₉	1	2	yes	—
729	#95	C₂³×C₅₉	1	1	yes	characteristic
730	#95	C₂³×C₅₉	1	1	yes	characteristic
731	#95	C₂³×C₅₉	1	1	yes	characteristic
732	#95	C₂³×C₅₉	1	2	yes	—
733	#95	C₂³×C₅₉	1	2	yes	—
734	#95	C₂³×C₅₉	1	1	yes	characteristic
735	#95	C₂³×C₅₉	1	1	yes	characteristic
736	#95	C₂³×C₅₉	1	1	yes	characteristic
737	#95	C₂³×C₅₉	1	1	yes	characteristic
738	#95	C₂³×C₅₉	1	2	yes	—
739	#95	C₂³×C₅₉	1	2	yes	—
740	#95	C₂³×C₅₉	1	2	yes	—
741	#95	C₂³×C₅₉	1	2	yes	—
742	#95	C₂³×C₅₉	1	1	yes	characteristic
743	#95	C₂³×C₅₉	1	1	yes	characteristic
744	#95	C₂³×C₅₉	1	2	yes	—
745	#95	C₂³×C₅₉	1	2	yes	—
746	#95	C₂³×C₅₉	1	2	yes	—
747	#95	C₂³×C₅₉	1	2	yes	—
748	#95	C₂³×C₅₉	1	2	yes	—
749	#95	C₂³×C₅₉	1	2	yes	—
750	#95	C₂³×C₅₉	1	2	yes	—
751	#95	C₂³×C₅₉	1	2	yes	—
752	#95	C₂³×C₅₉	1	2	yes	—
753	#95	C₂³×C₅₉	1	2	yes	—
754	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
755	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
756	C₂×Q₈	—	2	4	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	2	2	no	—
759	C₂×Q₈	—	2	2	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	2	4	no	—
766	C₂×Q₈	—	4	2	no	—
767	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	4	1	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	4	no	—
812	C₄⋊C₄	—	2	4	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	4	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	4	no	—
818	C₄⋊C₄	—	2	4	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	4	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	4	no	—
826	C₄⋊C₄	—	2	4	no	—
827	C₄⋊C₄	—	2	4	no	—
828	C₄⋊C₄	—	2	4	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	4	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
834	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
835	C₄⋊C₄	#41×C₅₉	1	4	yes	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	4	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	4	1	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	4	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	4	no	—
858	C₄²	—	2	4	no	—
859	C₄²	—	2	4	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	4	2	no	—
862	C₄²	—	4	2	no	—
863	C₄²	—	4	2	no	—
864	C₄²	C₂×D₄×C₅₉	1	4	yes	—
865	C₄²	C₂×D₄×C₅₉	1	8	yes	—
866	C₄²	#41×C₅₉	1	4	yes	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	1	no	—
870	C₂³	—	2	1	no	—
871	C₂³	—	2	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	1	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
881	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
882	Q₈	—	2	8	no	—
883	Q₈	—	4	8	no	—
884	Q₈	—	4	4	no	—
885	Q₈	—	4	4	no	—
886	D₄	—	4	4	no	—
887	C₂×C₄	—	2	8	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
943	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
944	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
945	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
946	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
947	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
948	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
949	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
950	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
951	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
952	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
953	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
969	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
970	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
971	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
972	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
973	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
974	C₂²	C₅₉×#585	1	1	yes	characteristic
975	C₄	—	2	2	no	—
976	C₄	—	2	4	no	—
977	C₄	—	2	4	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	C₅₉×#532	1	4	yes	—
996	C₂	—	4	2	no	—
997	C₂	—	8	1	no	—
998	C₂	C₂×C₅₉×#532	1	1	yes	characteristic
999	C₂	C₅₉×#3486	1	1	yes	characteristic
1000	C₂	C₅₉×#3489	1	1	yes	characteristic
1001	C₂	C₅₉×#3495	1	1	yes	characteristic
1002	C₂	C₅₉×#3509	1	1	yes	characteristic
1003	C₂	C₅₉×#3515	1	1	yes	characteristic
1004	C₂	C₅₉×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×D₄×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. C₂×C₅₉×#541	C₂	semidirect
2. C₂×C₅₉×#533	C₂	semidirect
3. C₅₉×#2611	C₂	semidirect
4. C₅₉×#2604	C₂	semidirect
6. C₅₉×#2565	C₂	semidirect
8. C₅₉×#2556	C₂	semidirect
9. C₅₉×#2550	C₂	semidirect
10. C₅₉×#2546	C₂	semidirect
13. C₅₉×#2519	C₂	semidirect
14. C₅₉×#2506	C₂	semidirect
15. C₅₉×#2492	C₂	semidirect
16. C₅₉×#2489	C₂	semidirect
17. C₅₉×#2429	C₂	semidirect
18. C₅₉×#2429	C₂	semidirect
19. C₅₉×#2327	C₂	semidirect
20. C₅₉×#2323	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₅₉	C₂	semidirect
23. C₅₉×#2276	C₂	semidirect
156. C₄×Q₈×C₅₉	D₄	semidirect
451. #35637	C₅₉	direct (N × H)
494. C₂×#541	C₂×C₅₉	semidirect
495. C₂×#533	C₂×C₅₉	semidirect
496. #2611	C₂×C₅₉	semidirect
497. #2604	C₂×C₅₉	semidirect
499. #2565	C₂×C₅₉	semidirect
501. #2556	C₂×C₅₉	semidirect
502. #2550	C₂×C₅₉	semidirect
503. #2546	C₂×C₅₉	semidirect
506. #2519	C₂×C₅₉	semidirect
507. #2506	C₂×C₅₉	semidirect
508. #2492	C₂×C₅₉	semidirect
509. #2489	C₂×C₅₉	semidirect
510. #2429	C₂×C₅₉	semidirect
511. #2429	C₂×C₅₉	semidirect
512. #2327	C₂×C₅₉	semidirect
513. #2323	C₂×C₅₉	semidirect
514. C₄×C₂²⋊Q₈	C₂×C₅₉	semidirect
516. #2276	C₂×C₅₉	semidirect
627. C₅₉	#35637	direct (N × H)
659. C₄×Q₈	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×#541	2
C₂×C₅₉×#533	2
C₅₉×#2611	2
C₅₉×#2604	2
C₅₉×#2601	2
C₅₉×#2565	2
C₅₉×#2560	2
C₅₉×#2556	2
C₅₉×#2550	2
C₅₉×#2546	2
C₅₉×#2542	2
C₅₉×#2536	2
C₅₉×#2519	2
C₅₉×#2506	2
C₅₉×#2492	2
C₅₉×#2489	2
C₅₉×#2429	2
C₅₉×#2327	2
C₅₉×#2323	2
C₄×C₂²⋊Q₈×C₅₉	2
C₅₉×#2290	2
C₅₉×#2276	2
#35637	59

Subgroups — C59×#35637 #28447746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35637 #28447746