Subgroups — C₅₉×#62192 #28474301

Order 15104.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3555	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3523	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3352	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3349	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3328	C₂	1	2	yes	maximal, complemented
12	C₅₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3312	C₂	1	2	yes	maximal, complemented
14	C₅₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3261	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3242	C₂	1	2	yes	maximal, complemented
18	C₅₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#3127	C₂	1	2	yes	maximal, complemented
20	C₅₉×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#3082	C₂	1	2	yes	maximal, complemented
22	C₅₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2993	C₂	1	1	yes	maximal, characteristic
24	C₅₉×#563	—	2	2	no	—
25	Q₈²×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#557	—	2	1	no	—
27	C₅₉×#557	—	2	1	no	—
28	C₅₉×#557	C₂²	1	1	yes	characteristic
29	C₅₉×#557	C₂²	1	1	yes	characteristic
30	C₅₉×#557	C₂²	1	1	yes	characteristic
31	C₅₉×#556	—	2	1	no	—
32	C₅₉×#556	—	2	1	no	—
33	C₅₉×#556	C₂²	1	1	yes	characteristic
34	C₅₉×#556	C₂²	1	1	yes	characteristic
35	C₅₉×#556	C₂²	1	2	yes	—
36	C₅₉×#554	C₂²	1	1	yes	characteristic
37	C₅₉×#552	—	2	2	no	—
38	C₅₉×#552	C₂²	1	2	yes	—
39	C₅₉×#552	C₂²	1	2	yes	—
40	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
42	C₅₉×#544	C₂²	1	2	yes	—
43	C₅₉×#542	—	2	1	no	—
44	C₅₉×#541	—	2	2	no	—
45	C₅₉×#541	—	2	2	no	—
46	C₅₉×#541	—	2	1	no	—
47	C₅₉×#541	C₂²	1	2	yes	—
48	C₅₉×#541	C₂²	1	2	yes	—
49	C₅₉×#533	—	2	1	no	—
50	C₅₉×#533	C₂²	1	1	yes	characteristic
51	C₅₉×#533	C₂²	1	1	yes	characteristic
52	C₅₉×#533	C₂²	1	1	yes	characteristic
53	C₅₉×#529	—	2	1	no	—
54	C₅₉×#529	C₂²	1	1	yes	characteristic
55	C₅₉×#519	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
57	C₅₉×#501	C₂²	1	2	yes	—
58	C₅₉×#500	C₂²	1	1	yes	characteristic
59	C₅₉×#499	C₂²	1	2	yes	—
60	C₅₉×#498	C₂²	1	1	yes	characteristic
61	C₅₉×#491	C₂²	1	2	yes	—
62	C₅₉×#487	C₂²	1	1	yes	characteristic
63	C₅₉×#487	C₂²	1	2	yes	—
64	C₅₉×#487	C₂²	1	1	yes	characteristic
65	C₅₉×#485	C₂²	1	2	yes	—
66	C₅₉×#485	C₂²	1	2	yes	—
67	C₅₉×#485	C₂²	1	2	yes	—
68	C₅₉×#485	C₂²	1	2	yes	—
69	C₅₉×#485	C₂²	1	2	yes	—
70	C₅₉×#485	C₂²	1	2	yes	—
71	C₅₉×#484	C₂²	1	2	yes	—
72	C₅₉×#484	C₂²	1	1	yes	characteristic
73	C₅₉×#484	C₂²	1	1	yes	characteristic
74	C₅₉×#483	C₂²	1	2	yes	—
75	C₅₉×#479	C₂²	1	2	yes	—
76	C₅₉×#479	C₂²	1	2	yes	—
77	C₅₉×#479	C₂²	1	2	yes	—
78	C₅₉×#479	C₂²	1	2	yes	—
79	C₅₉×#479	C₂²	1	2	yes	—
80	C₅₉×#479	C₂²	1	2	yes	—
81	C₅₉×#479	C₂²	1	2	yes	—
82	C₅₉×#479	C₂²	1	2	yes	—
83	C₅₉×#477	C₂²	1	1	yes	characteristic
84	C₅₉×#477	C₂²	1	1	yes	characteristic
85	C₅₉×#477	C₂²	1	1	yes	characteristic
86	C₅₉×#477	C₂²	1	2	yes	—
87	C₅₉×#477	C₂²	1	1	yes	characteristic
88	C₅₉×#475	C₂²	1	2	yes	—
89	C₅₉×#475	C₂²	1	1	yes	characteristic
90	C₅₉×#475	C₂²	1	1	yes	characteristic
91	C₅₉×#475	C₂²	1	1	yes	characteristic
92	C₅₉×#475	C₂²	1	2	yes	—
93	C₅₉×#475	C₂²	1	1	yes	characteristic
94	C₅₉×#470	C₂²	1	2	yes	—
95	C₅₉×#470	C₂²	1	2	yes	—
96	C₅₉×#470	C₂²	1	2	yes	—
97	C₅₉×#470	C₂²	1	2	yes	—
98	C₅₉×#467	C₂²	1	2	yes	—
99	C₅₉×#467	C₂²	1	2	yes	—
100	C₅₉×#462	C₂²	1	2	yes	—
101	C₅₉×#462	C₂²	1	1	yes	characteristic
102	C₅₉×#462	C₂²	1	1	yes	characteristic
103	C₅₉×#462	C₂²	1	1	yes	characteristic
104	C₅₉×#462	C₂²	1	2	yes	—
105	C₅₉×#462	C₂²	1	2	yes	—
106	C₅₉×#462	C₂²	1	1	yes	characteristic
107	C₅₉×#451	C₂²	1	2	yes	—
108	C₅₉×#451	C₂²	1	1	yes	characteristic
109	C₅₉×#451	C₂²	1	2	yes	—
110	C₅₉×#451	C₂²	1	1	yes	characteristic
111	C₅₉×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
113	C₅₉×#441	C₂²	1	2	yes	—
114	C₅₉×#441	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	—
120	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
121	C₅₉×#436	C₂²	1	2	yes	—
122	C₅₉×#436	C₂²	1	1	yes	characteristic
123	C₅₉×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
125	C₅₉×#433	C₂²	1	2	yes	—
126	C₅₉×#431	C₂²	1	1	yes	characteristic
127	C₅₉×#428	C₂²	1	2	yes	—
128	C₅₉×#428	C₂²	1	2	yes	—
129	C₅₉×#427	C₂²	1	2	yes	—
130	C₅₉×#424	C₂²	1	2	yes	—
131	C₅₉×#423	C₂²	1	1	yes	characteristic
132	C₅₉×#419	C₂²	1	2	yes	—
133	C₅₉×#419	C₂²	1	2	yes	—
134	C₂×#103×C₅₉	C₂²	1	2	yes	—
135	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
136	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
143	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
144	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
145	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₅₉	—	2	1	no	—
147	C₄⋊Q₈×C₅₉	—	2	1	no	—
148	C₄⋊Q₈×C₅₉	—	2	1	no	—
149	C₄⋊Q₈×C₅₉	—	2	2	no	—
150	C₄⋊Q₈×C₅₉	—	2	2	no	—
151	C₄⋊Q₈×C₅₉	—	2	1	no	—
152	C₄⋊Q₈×C₅₉	—	2	2	no	—
153	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
161	#126×C₅₉	—	2	2	no	—
162	#126×C₅₉	—	2	2	no	—
163	#126×C₅₉	—	2	2	no	—
164	#126×C₅₉	—	2	2	no	—
165	#126×C₅₉	—	2	2	no	—
166	#126×C₅₉	—	2	2	no	—
167	#126×C₅₉	—	2	2	no	—
168	#126×C₅₉	—	2	2	no	—
169	#126×C₅₉	—	2	2	no	—
170	#126×C₅₉	—	2	2	no	—
171	#126×C₅₉	D₄	1	2	yes	—
172	#125×C₅₉	—	2	1	no	—
173	#125×C₅₉	—	2	2	no	—
174	#125×C₅₉	—	2	2	no	—
175	#125×C₅₉	—	2	2	no	—
176	#125×C₅₉	—	2	2	no	—
177	#125×C₅₉	—	2	2	no	—
178	#125×C₅₉	—	2	2	no	—
179	#125×C₅₉	—	2	2	no	—
180	#125×C₅₉	—	2	1	no	—
181	#125×C₅₉	—	2	2	no	—
182	#125×C₅₉	—	2	2	no	—
183	#125×C₅₉	—	2	2	no	—
184	#125×C₅₉	—	2	1	no	—
185	#125×C₅₉	—	2	1	no	—
186	#125×C₅₉	D₄	1	1	yes	characteristic
187	#125×C₅₉	C₂³	1	2	yes	—
188	#125×C₅₉	C₂³	1	2	yes	—
189	#125×C₅₉	C₂³	1	2	yes	—
190	#124×C₅₉	—	2	1	no	—
191	#124×C₅₉	—	2	1	no	—
192	#124×C₅₉	—	2	2	no	—
193	#124×C₅₉	D₄	1	1	yes	characteristic
194	#123×C₅₉	—	2	2	no	—
195	#123×C₅₉	—	2	2	no	—
196	#123×C₅₉	D₄	1	2	yes	—
197	C₂²⋊Q₈×C₅₉	—	2	1	no	—
198	C₂²⋊Q₈×C₅₉	—	2	1	no	—
199	C₂²⋊Q₈×C₅₉	—	2	1	no	—
200	C₂²⋊Q₈×C₅₉	—	2	1	no	—
201	C₂²⋊Q₈×C₅₉	—	2	2	no	—
202	C₂²⋊Q₈×C₅₉	—	2	2	no	—
203	C₂²⋊Q₈×C₅₉	—	2	2	no	—
204	C₂²⋊Q₈×C₅₉	—	2	2	no	—
205	C₂²⋊Q₈×C₅₉	—	2	2	no	—
206	C₂²⋊Q₈×C₅₉	—	2	2	no	—
207	C₂²⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
215	#121×C₅₉	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₅₉	—	2	1	no	—
217	C₄×Q₈×C₅₉	—	2	1	no	—
218	C₄×Q₈×C₅₉	—	2	2	no	—
219	C₄×Q₈×C₅₉	—	2	2	no	—
220	C₄×Q₈×C₅₉	—	2	1	no	—
221	C₄×Q₈×C₅₉	—	2	1	no	—
222	C₄×Q₈×C₅₉	—	2	2	no	—
223	C₄×Q₈×C₅₉	—	2	1	no	—
224	C₄×Q₈×C₅₉	—	2	1	no	—
225	C₄×Q₈×C₅₉	—	2	1	no	—
226	C₄×Q₈×C₅₉	—	2	1	no	—
227	C₄×Q₈×C₅₉	—	2	1	no	—
228	C₄×Q₈×C₅₉	—	2	1	no	—
229	C₄×Q₈×C₅₉	—	2	1	no	—
230	C₄×Q₈×C₅₉	—	2	1	no	—
231	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
236	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
237	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₉	—	2	2	no	—
244	C₄×D₄×C₅₉	—	2	1	no	—
245	C₄×D₄×C₅₉	—	2	1	no	—
246	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₅₉	C₂³	1	2	yes	—
248	#117×C₅₉	—	2	1	no	—
249	#117×C₅₉	—	2	1	no	—
250	#117×C₅₉	—	2	2	no	—
251	#117×C₅₉	—	2	2	no	—
252	#117×C₅₉	—	2	2	no	—
253	#117×C₅₉	—	2	2	no	—
254	#117×C₅₉	C₂³	1	2	yes	—
255	#117×C₅₉	C₂³	1	2	yes	—
256	#117×C₅₉	C₂³	1	2	yes	—
257	#117×C₅₉	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
259	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₅₉	—	2	1	no	—
262	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
263	#107×C₅₉	C₂³	1	1	yes	characteristic
264	#107×C₅₉	C₂³	1	2	yes	—
265	#107×C₅₉	C₂³	1	2	yes	—
266	#107×C₅₉	C₂³	1	1	yes	characteristic
267	#107×C₅₉	C₂³	1	2	yes	—
268	#107×C₅₉	C₂³	1	1	yes	characteristic
269	#107×C₅₉	C₂³	1	1	yes	characteristic
270	#107×C₅₉	C₂³	1	2	yes	—
271	#106×C₅₉	C₂³	1	2	yes	—
272	#106×C₅₉	C₂³	1	2	yes	—
273	#106×C₅₉	C₂³	1	2	yes	—
274	#106×C₅₉	C₂³	1	2	yes	—
275	#106×C₅₉	C₂³	1	2	yes	—
276	#106×C₅₉	C₂³	1	2	yes	—
277	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
284	#103×C₅₉	C₂³	1	1	yes	characteristic
285	#103×C₅₉	C₂³	1	2	yes	—
286	#103×C₅₉	C₂³	1	2	yes	—
287	#103×C₅₉	C₂³	1	2	yes	—
288	#103×C₅₉	C₂³	1	1	yes	characteristic
289	#103×C₅₉	C₂³	1	2	yes	—
290	#103×C₅₉	C₂³	1	2	yes	—
291	#103×C₅₉	C₂³	1	2	yes	—
292	#103×C₅₉	C₂³	1	2	yes	—
293	#103×C₅₉	C₂³	1	2	yes	—
294	#103×C₅₉	C₂³	1	1	yes	characteristic
295	#103×C₅₉	C₂³	1	1	yes	characteristic
296	#103×C₅₉	C₂³	1	1	yes	characteristic
297	#103×C₅₉	C₂³	1	1	yes	characteristic
298	#103×C₅₉	C₂³	1	2	yes	—
299	#103×C₅₉	C₂³	1	1	yes	characteristic
300	#103×C₅₉	C₂³	1	2	yes	—
301	#103×C₅₉	C₂³	1	1	yes	characteristic
302	#103×C₅₉	C₂³	1	2	yes	—
303	#103×C₅₉	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
308	#97×C₅₉	C₂³	1	2	yes	—
309	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₅₉	C₂³	1	2	yes	—
312	C₂×Q₈×C₅₉	—	2	1	no	—
313	C₂×Q₈×C₅₉	—	2	1	no	—
314	C₂×Q₈×C₅₉	—	2	1	no	—
315	C₂×Q₈×C₅₉	—	2	2	no	—
316	C₂×Q₈×C₅₉	—	2	1	no	—
317	C₂×Q₈×C₅₉	—	2	1	no	—
318	C₂×Q₈×C₅₉	—	2	2	no	—
319	C₂×Q₈×C₅₉	—	2	4	no	—
320	C₂×Q₈×C₅₉	—	2	2	no	—
321	C₂×Q₈×C₅₉	—	4	2	no	—
322	C₂×Q₈×C₅₉	—	4	1	no	—
323	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
331	C₂²×C₄×C₅₉	—	2	1	no	—
332	C₂²×C₄×C₅₉	—	2	1	no	—
333	C₂²×C₄×C₅₉	—	2	2	no	—
334	C₂²×C₄×C₅₉	—	2	2	no	—
335	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
339	Q₁₆×C₅₉	—	2	2	no	—
340	Q₁₆×C₅₉	—	2	2	no	—
341	Q₁₆×C₅₉	—	4	1	no	—
342	Q₁₆×C₅₉	—	4	2	no	—
343	Q₁₆×C₅₉	—	4	2	no	—
344	Q₁₆×C₅₉	—	4	1	no	—
345	M₁₆×C₅₉	—	4	2	no	—
346	M₁₆×C₅₉	—	4	2	no	—
347	C₂×C₈×C₅₉	—	4	2	no	—
348	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
352	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₅₉	—	2	1	no	—
355	C₄⋊C₄×C₅₉	—	2	1	no	—
356	C₄⋊C₄×C₅₉	—	2	1	no	—
357	C₄⋊C₄×C₅₉	—	2	1	no	—
358	C₄⋊C₄×C₅₉	—	2	1	no	—
359	C₄⋊C₄×C₅₉	—	2	2	no	—
360	C₄⋊C₄×C₅₉	—	2	1	no	—
361	C₄⋊C₄×C₅₉	—	2	2	no	—
362	C₄⋊C₄×C₅₉	—	2	2	no	—
363	C₄⋊C₄×C₅₉	—	2	2	no	—
364	C₄⋊C₄×C₅₉	—	2	1	no	—
365	C₄⋊C₄×C₅₉	—	2	1	no	—
366	C₄⋊C₄×C₅₉	—	2	2	no	—
367	C₄⋊C₄×C₅₉	—	2	2	no	—
368	C₄⋊C₄×C₅₉	—	2	1	no	—
369	C₄⋊C₄×C₅₉	—	2	1	no	—
370	C₄⋊C₄×C₅₉	—	2	2	no	—
371	C₄⋊C₄×C₅₉	—	2	1	no	—
372	C₄⋊C₄×C₅₉	—	2	1	no	—
373	C₄⋊C₄×C₅₉	—	2	2	no	—
374	C₄⋊C₄×C₅₉	—	2	1	no	—
375	C₄⋊C₄×C₅₉	—	2	2	no	—
376	C₄⋊C₄×C₅₉	—	2	2	no	—
377	C₄⋊C₄×C₅₉	—	2	2	no	—
378	C₄⋊C₄×C₅₉	—	2	2	no	—
379	C₄⋊C₄×C₅₉	—	2	2	no	—
380	C₄⋊C₄×C₅₉	—	2	2	no	—
381	C₄⋊C₄×C₅₉	—	2	2	no	—
382	C₄⋊C₄×C₅₉	—	2	1	no	—
383	C₄⋊C₄×C₅₉	—	2	1	no	—
384	C₄⋊C₄×C₅₉	—	2	2	no	—
385	C₄⋊C₄×C₅₉	—	2	2	no	—
386	C₄⋊C₄×C₅₉	—	2	2	no	—
387	C₄⋊C₄×C₅₉	—	2	1	no	—
388	C₄⋊C₄×C₅₉	—	2	1	no	—
389	C₄⋊C₄×C₅₉	—	2	2	no	—
390	C₄⋊C₄×C₅₉	—	2	2	no	—
391	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₅₉	—	2	2	no	—
405	C₂²⋊C₄×C₅₉	—	2	2	no	—
406	C₂²⋊C₄×C₅₉	—	2	1	no	—
407	C₂²⋊C₄×C₅₉	—	2	1	no	—
408	C₂²⋊C₄×C₅₉	—	2	2	no	—
409	C₂²⋊C₄×C₅₉	—	2	2	no	—
410	C₂²⋊C₄×C₅₉	—	2	2	no	—
411	C₂²⋊C₄×C₅₉	—	2	2	no	—
412	C₂²⋊C₄×C₅₉	—	2	2	no	—
413	C₂²⋊C₄×C₅₉	—	2	2	no	—
414	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
415	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
417	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
419	C₄²×C₅₉	—	2	1	no	—
420	C₄²×C₅₉	—	2	1	no	—
421	C₄²×C₅₉	—	2	1	no	—
422	C₄²×C₅₉	—	2	1	no	—
423	C₄²×C₅₉	—	2	2	no	—
424	C₄²×C₅₉	—	2	2	no	—
425	C₄²×C₅₉	—	2	2	no	—
426	C₄²×C₅₉	—	2	2	no	—
427	C₄²×C₅₉	—	2	2	no	—
428	C₄²×C₅₉	—	2	1	no	—
429	C₄²×C₅₉	—	2	1	no	—
430	C₄²×C₅₉	—	2	2	no	—
431	C₄²×C₅₉	—	2	2	no	—
432	C₄²×C₅₉	—	2	2	no	—
433	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
436	C₄²×C₅₉	C₂⁴	1	2	yes	—
437	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
438	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
439	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
440	Q₈×C₅₉	—	2	2	no	—
441	Q₈×C₅₉	—	2	1	no	—
442	Q₈×C₅₉	—	2	1	no	—
443	Q₈×C₅₉	—	2	1	no	—
444	Q₈×C₅₉	—	2	2	no	—
445	Q₈×C₅₉	—	2	1	no	—
446	Q₈×C₅₉	—	2	1	no	—
447	Q₈×C₅₉	—	2	1	no	—
448	Q₈×C₅₉	—	2	1	no	—
449	Q₈×C₅₉	—	2	2	no	—
450	Q₈×C₅₉	—	4	4	no	—
451	Q₈×C₅₉	—	4	2	no	—
452	Q₈×C₅₉	—	4	2	no	—
453	Q₈×C₅₉	—	4	2	no	—
454	Q₈×C₅₉	—	8	1	no	—
455	Q₈×C₅₉	—	8	1	no	—
456	Q₈×C₅₉	—	8	2	no	—
457	Q₈×C₅₉	2₋¹⁺⁴	1	2	yes	—
458	D₄×C₅₉	—	2	2	no	—
459	D₄×C₅₉	—	4	2	no	—
460	C₂×C₄×C₅₉	—	2	1	no	—
461	C₂×C₄×C₅₉	—	2	2	no	—
462	C₂×C₄×C₅₉	—	2	1	no	—
463	C₂×C₄×C₅₉	—	2	2	no	—
464	C₂×C₄×C₅₉	—	2	2	no	—
465	C₂×C₄×C₅₉	—	2	1	no	—
466	C₂×C₄×C₅₉	—	2	1	no	—
467	C₂×C₄×C₅₉	—	2	1	no	—
468	C₂×C₄×C₅₉	—	2	1	no	—
469	C₂×C₄×C₅₉	—	2	2	no	—
470	C₂×C₄×C₅₉	—	2	2	no	—
471	C₂×C₄×C₅₉	—	2	1	no	—
472	C₂×C₄×C₅₉	—	2	1	no	—
473	C₂×C₄×C₅₉	—	2	1	no	—
474	C₂×C₄×C₅₉	—	2	2	no	—
475	C₂×C₄×C₅₉	—	2	2	no	—
476	C₂×C₄×C₅₉	—	2	1	no	—
477	C₂×C₄×C₅₉	—	4	1	no	—
478	C₂×C₄×C₅₉	—	4	2	no	—
479	C₂×C₄×C₅₉	—	4	4	no	—
480	C₂×C₄×C₅₉	—	4	2	no	—
481	C₂×C₄×C₅₉	—	8	2	no	—
482	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
491	C₈×C₅₉	—	2	1	no	—
492	C₈×C₅₉	—	2	1	no	—
493	C₈×C₅₉	—	2	1	no	—
494	C₈×C₅₉	—	2	2	no	—
495	C₈×C₅₉	—	2	1	no	—
496	C₈×C₅₉	—	2	2	no	—
497	#62192	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
498	C₂²×C₅₉	—	2	1	no	—
499	C₂²×C₅₉	—	2	2	no	—
500	C₂²×C₅₉	—	2	2	no	—
501	C₂²×C₅₉	—	2	1	no	—
502	C₂²×C₅₉	—	2	1	no	—
503	C₂²×C₅₉	—	2	2	no	—
504	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₅₉	—	2	1	no	—
506	C₄×C₅₉	—	2	1	no	—
507	C₄×C₅₉	—	2	2	no	—
508	C₄×C₅₉	—	2	2	no	—
509	C₄×C₅₉	—	2	1	no	—
510	C₄×C₅₉	—	2	2	no	—
511	C₄×C₅₉	—	2	1	no	—
512	C₄×C₅₉	—	2	2	no	—
513	C₄×C₅₉	—	4	1	no	—
514	C₄×C₅₉	—	4	1	no	—
515	C₄×C₅₉	—	4	1	no	—
516	C₄×C₅₉	—	4	2	no	—
517	C₄×C₅₉	—	4	1	no	—
518	C₄×C₅₉	—	4	1	no	—
519	C₄×C₅₉	—	4	2	no	—
520	C₄×C₅₉	—	4	1	no	—
521	C₄×C₅₉	—	4	1	no	—
522	C₄×C₅₉	—	4	2	no	—
523	C₄×C₅₉	—	4	2	no	—
524	C₄×C₅₉	#578	1	2	yes	—
525	C₄×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₄×C₅₉	#585	1	1	yes	characteristic
527	#3555	C₂×C₅₉	1	1	yes	characteristic
528	#3523	C₂×C₅₉	1	1	yes	characteristic
529	#3387	C₂×C₅₉	1	1	yes	characteristic, complemented
530	#3383	C₂×C₅₉	1	1	yes	characteristic, complemented
531	#3374	C₂×C₅₉	1	1	yes	characteristic, complemented
532	#3363	C₂×C₅₉	1	1	yes	characteristic, complemented
533	#3356	C₂×C₅₉	1	1	yes	characteristic, complemented
534	#3352	C₂×C₅₉	1	2	yes	complemented
535	#3349	C₂×C₅₉	1	2	yes	complemented
536	#3342	C₂×C₅₉	1	1	yes	characteristic, complemented
537	#3328	C₂×C₅₉	1	1	yes	characteristic, complemented
538	#3328	C₂×C₅₉	1	2	yes	complemented
539	#3312	C₂×C₅₉	1	2	yes	complemented
540	#3299	C₂×C₅₉	1	1	yes	characteristic, complemented
541	#3261	C₂×C₅₉	1	2	yes	complemented
542	#3255	C₂×C₅₉	1	1	yes	characteristic, complemented
543	#3242	C₂×C₅₉	1	2	yes	complemented
544	#3231	C₂×C₅₉	1	1	yes	characteristic, complemented
545	#3127	C₂×C₅₉	1	2	yes	complemented
546	#3104	C₂×C₅₉	1	1	yes	characteristic, complemented
547	#3082	C₂×C₅₉	1	2	yes	complemented
548	#3078	C₂×C₅₉	1	1	yes	characteristic, complemented
549	#2993	C₂×C₅₉	1	1	yes	characteristic
550	C₂×C₅₉	—	4	1	no	—
551	C₂×C₅₉	—	4	2	no	—
552	C₂×C₅₉	#3489	1	1	yes	characteristic
553	C₂×C₅₉	C₂×#578	1	1	yes	characteristic
554	C₂×C₅₉	#3586	1	1	yes	characteristic
555	#563	—	2	2	no	—
556	Q₈²	C₂²×C₅₉	1	1	yes	characteristic
557	#557	—	2	1	no	—
558	#557	—	2	1	no	—
559	#557	C₂²×C₅₉	1	1	yes	characteristic
560	#557	C₂²×C₅₉	1	1	yes	characteristic
561	#557	C₂²×C₅₉	1	1	yes	characteristic
562	#556	—	2	1	no	—
563	#556	—	2	1	no	—
564	#556	C₂²×C₅₉	1	1	yes	characteristic
565	#556	C₂²×C₅₉	1	2	yes	—
566	#556	C₂²×C₅₉	1	1	yes	characteristic
567	#554	C₂²×C₅₉	1	1	yes	characteristic
568	#552	—	2	2	no	—
569	#552	C₂²×C₅₉	1	2	yes	—
570	#552	C₂²×C₅₉	1	2	yes	—
571	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
572	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
573	#544	C₂²×C₅₉	1	2	yes	—
574	#542	—	2	1	no	—
575	#541	—	2	2	no	—
576	#541	—	2	2	no	—
577	#541	—	2	1	no	—
578	#541	C₂²×C₅₉	1	2	yes	—
579	#541	C₂²×C₅₉	1	2	yes	—
580	#533	—	2	1	no	—
581	#533	C₂²×C₅₉	1	1	yes	characteristic
582	#533	C₂²×C₅₉	1	1	yes	characteristic
583	#533	C₂²×C₅₉	1	1	yes	characteristic
584	#529	—	2	1	no	—
585	#529	C₂²×C₅₉	1	1	yes	characteristic
586	#519	C₂²×C₅₉	1	2	yes	—
587	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
588	#501	C₂²×C₅₉	1	2	yes	—
589	#500	C₂²×C₅₉	1	1	yes	characteristic
590	#499	C₂²×C₅₉	1	2	yes	—
591	#498	C₂²×C₅₉	1	1	yes	characteristic
592	#491	C₂²×C₅₉	1	2	yes	—
593	#487	C₂²×C₅₉	1	2	yes	—
594	#487	C₂²×C₅₉	1	1	yes	characteristic
595	#487	C₂²×C₅₉	1	1	yes	characteristic
596	#485	C₂²×C₅₉	1	2	yes	—
597	#485	C₂²×C₅₉	1	2	yes	—
598	#485	C₂²×C₅₉	1	2	yes	—
599	#485	C₂²×C₅₉	1	2	yes	—
600	#485	C₂²×C₅₉	1	2	yes	—
601	#485	C₂²×C₅₉	1	2	yes	—
602	#484	C₂²×C₅₉	1	1	yes	characteristic
603	#484	C₂²×C₅₉	1	1	yes	characteristic
604	#484	C₂²×C₅₉	1	2	yes	—
605	#483	C₂²×C₅₉	1	2	yes	—
606	#479	C₂²×C₅₉	1	2	yes	—
607	#479	C₂²×C₅₉	1	2	yes	—
608	#479	C₂²×C₅₉	1	2	yes	—
609	#479	C₂²×C₅₉	1	2	yes	—
610	#479	C₂²×C₅₉	1	2	yes	—
611	#479	C₂²×C₅₉	1	2	yes	—
612	#479	C₂²×C₅₉	1	2	yes	—
613	#479	C₂²×C₅₉	1	2	yes	—
614	#477	C₂²×C₅₉	1	1	yes	characteristic
615	#477	C₂²×C₅₉	1	1	yes	characteristic
616	#477	C₂²×C₅₉	1	1	yes	characteristic
617	#477	C₂²×C₅₉	1	2	yes	—
618	#477	C₂²×C₅₉	1	1	yes	characteristic
619	#475	C₂²×C₅₉	1	1	yes	characteristic
620	#475	C₂²×C₅₉	1	2	yes	—
621	#475	C₂²×C₅₉	1	1	yes	characteristic
622	#475	C₂²×C₅₉	1	2	yes	—
623	#475	C₂²×C₅₉	1	1	yes	characteristic
624	#475	C₂²×C₅₉	1	1	yes	characteristic
625	#470	C₂²×C₅₉	1	2	yes	—
626	#470	C₂²×C₅₉	1	2	yes	—
627	#470	C₂²×C₅₉	1	2	yes	—
628	#470	C₂²×C₅₉	1	2	yes	—
629	#467	C₂²×C₅₉	1	2	yes	—
630	#467	C₂²×C₅₉	1	2	yes	—
631	#462	C₂²×C₅₉	1	1	yes	characteristic
632	#462	C₂²×C₅₉	1	2	yes	—
633	#462	C₂²×C₅₉	1	1	yes	characteristic
634	#462	C₂²×C₅₉	1	1	yes	characteristic
635	#462	C₂²×C₅₉	1	2	yes	—
636	#462	C₂²×C₅₉	1	1	yes	characteristic
637	#462	C₂²×C₅₉	1	2	yes	—
638	#451	C₂²×C₅₉	1	1	yes	characteristic
639	#451	C₂²×C₅₉	1	2	yes	—
640	#451	C₂²×C₅₉	1	2	yes	—
641	#451	C₂²×C₅₉	1	1	yes	characteristic
642	#446	C₂²×C₅₉	1	1	yes	characteristic
643	C₈×Q₈	C₂²×C₅₉	1	1	yes	characteristic
644	#441	C₂²×C₅₉	1	2	yes	—
645	#441	C₂²×C₅₉	1	2	yes	—
646	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
647	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	—
648	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
649	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	—
650	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
651	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
652	#436	C₂²×C₅₉	1	2	yes	—
653	#436	C₂²×C₅₉	1	1	yes	characteristic
654	#435	C₂²×C₅₉	1	2	yes	—
655	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
656	#433	C₂²×C₅₉	1	2	yes	—
657	#431	C₂²×C₅₉	1	1	yes	characteristic
658	#428	C₂²×C₅₉	1	2	yes	—
659	#428	C₂²×C₅₉	1	2	yes	—
660	#427	C₂²×C₅₉	1	2	yes	—
661	#424	C₂²×C₅₉	1	2	yes	—
662	#423	C₂²×C₅₉	1	1	yes	characteristic
663	#419	C₂²×C₅₉	1	2	yes	—
664	#419	C₂²×C₅₉	1	2	yes	—
665	C₂×#103	C₂²×C₅₉	1	2	yes	—
666	C₅₉	#62192	1	1	yes	characteristic, direct product factor, Sylow
667	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
668	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
670	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
671	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
672	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
673	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
674	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
675	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
676	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
677	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	—	2	2	no	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	2	no	—
685	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	D₄×C₅₉	1	2	yes	—
704	#125	—	2	1	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	1	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	1	no	—
718	#125	D₄×C₅₉	1	1	yes	characteristic
719	#125	C₂³×C₅₉	1	2	yes	—
720	#125	C₂³×C₅₉	1	2	yes	—
721	#125	C₂³×C₅₉	1	2	yes	—
722	#124	—	2	1	no	—
723	#124	—	2	1	no	—
724	#124	—	2	2	no	—
725	#124	D₄×C₅₉	1	1	yes	characteristic
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	#123	D₄×C₅₉	1	2	yes	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
740	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
741	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
744	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
746	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
747	#121	D₄×C₅₉	1	1	yes	characteristic
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	2	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
768	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
769	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
770	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
773	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
774	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	C₂³×C₅₉	1	2	yes	—
779	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
780	#117	—	2	1	no	—
781	#117	—	2	1	no	—
782	#117	—	2	2	no	—
783	#117	—	2	2	no	—
784	#117	—	2	2	no	—
785	#117	—	2	2	no	—
786	#117	C₂³×C₅₉	1	2	yes	—
787	#117	C₂³×C₅₉	1	2	yes	—
788	#117	C₂³×C₅₉	1	2	yes	—
789	#117	C₂³×C₅₉	1	2	yes	—
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
793	C₂×C₄²	—	2	1	no	—
794	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
795	#107	C₂³×C₅₉	1	1	yes	characteristic
796	#107	C₂³×C₅₉	1	2	yes	—
797	#107	C₂³×C₅₉	1	2	yes	—
798	#107	C₂³×C₅₉	1	1	yes	characteristic
799	#107	C₂³×C₅₉	1	2	yes	—
800	#107	C₂³×C₅₉	1	1	yes	characteristic
801	#107	C₂³×C₅₉	1	1	yes	characteristic
802	#107	C₂³×C₅₉	1	2	yes	—
803	#106	C₂³×C₅₉	1	2	yes	—
804	#106	C₂³×C₅₉	1	2	yes	—
805	#106	C₂³×C₅₉	1	2	yes	—
806	#106	C₂³×C₅₉	1	2	yes	—
807	#106	C₂³×C₅₉	1	2	yes	—
808	#106	C₂³×C₅₉	1	2	yes	—
809	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
810	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
814	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
815	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
816	#103	C₂³×C₅₉	1	1	yes	characteristic
817	#103	C₂³×C₅₉	1	2	yes	—
818	#103	C₂³×C₅₉	1	2	yes	—
819	#103	C₂³×C₅₉	1	2	yes	—
820	#103	C₂³×C₅₉	1	1	yes	characteristic
821	#103	C₂³×C₅₉	1	2	yes	—
822	#103	C₂³×C₅₉	1	2	yes	—
823	#103	C₂³×C₅₉	1	2	yes	—
824	#103	C₂³×C₅₉	1	2	yes	—
825	#103	C₂³×C₅₉	1	2	yes	—
826	#103	C₂³×C₅₉	1	1	yes	characteristic
827	#103	C₂³×C₅₉	1	1	yes	characteristic
828	#103	C₂³×C₅₉	1	1	yes	characteristic
829	#103	C₂³×C₅₉	1	1	yes	characteristic
830	#103	C₂³×C₅₉	1	2	yes	—
831	#103	C₂³×C₅₉	1	1	yes	characteristic
832	#103	C₂³×C₅₉	1	2	yes	—
833	#103	C₂³×C₅₉	1	1	yes	characteristic
834	#103	C₂³×C₅₉	1	2	yes	—
835	#103	C₂³×C₅₉	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
837	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
838	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
839	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
840	#97	C₂³×C₅₉	1	2	yes	—
841	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
842	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
843	C₄×C₈	C₂³×C₅₉	1	2	yes	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	4	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	1	no	—
855	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
856	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
857	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
858	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
859	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
860	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
861	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
862	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
871	Q₁₆	—	2	2	no	—
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	4	1	no	—
874	Q₁₆	—	4	2	no	—
875	Q₁₆	—	4	2	no	—
876	Q₁₆	—	4	1	no	—
877	M₁₆	—	4	2	no	—
878	M₁₆	—	4	2	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
883	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
884	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
885	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
924	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
926	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
948	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
949	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
950	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	1	no	—
953	C₄²	—	2	1	no	—
954	C₄²	—	2	1	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
966	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
967	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
968	C₄²	C₂⁴×C₅₉	1	2	yes	—
969	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
970	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
971	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
972	Q₈	—	2	2	no	—
973	Q₈	—	2	1	no	—
974	Q₈	—	2	1	no	—
975	Q₈	—	2	1	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	4	4	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	2	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	1	no	—
988	Q₈	—	8	2	no	—
989	Q₈	2₋¹⁺⁴×C₅₉	1	2	yes	—
990	D₄	—	2	2	no	—
991	D₄	—	4	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1018	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1020	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1022	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1023	C₈	—	2	1	no	—
1024	C₈	—	2	1	no	—
1025	C₈	—	2	1	no	—
1026	C₈	—	2	2	no	—
1027	C₈	—	2	1	no	—
1028	C₈	—	2	2	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1036	C₄	—	2	1	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	C₅₉×#578	1	2	yes	—
1056	C₄	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
1057	C₄	C₅₉×#585	1	1	yes	characteristic
1058	C₂	—	4	1	no	—
1059	C₂	—	4	2	no	—
1060	C₂	C₅₉×#3489	1	1	yes	characteristic
1061	C₂	C₂×C₅₉×#578	1	1	yes	characteristic
1062	C₂	C₅₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	#121×C₅₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₅₉×#529 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₅₉×#3387	C₂	semidirect
4. C₅₉×#3383	C₂	semidirect
5. C₅₉×#3374	C₂	semidirect
6. C₅₉×#3363	C₂	semidirect
7. C₅₉×#3356	C₂	semidirect
8. C₅₉×#3352	C₂	semidirect
9. C₅₉×#3349	C₂	semidirect
10. C₅₉×#3342	C₂	semidirect
11. C₅₉×#3328	C₂	semidirect
12. C₅₉×#3328	C₂	semidirect
13. C₅₉×#3312	C₂	semidirect
14. C₅₉×#3299	C₂	semidirect
15. C₅₉×#3261	C₂	semidirect
16. C₅₉×#3255	C₂	semidirect
17. C₅₉×#3242	C₂	semidirect
18. C₅₉×#3231	C₂	semidirect
19. C₅₉×#3127	C₂	semidirect
20. C₅₉×#3104	C₂	semidirect
21. C₅₉×#3082	C₂	semidirect
22. C₅₉×#3078	C₂	semidirect
497. #62192	C₅₉	direct (N × H)
529. #3387	C₂×C₅₉	semidirect
530. #3383	C₂×C₅₉	semidirect
531. #3374	C₂×C₅₉	semidirect
532. #3363	C₂×C₅₉	semidirect
533. #3356	C₂×C₅₉	semidirect
534. #3352	C₂×C₅₉	semidirect
535. #3349	C₂×C₅₉	semidirect
536. #3342	C₂×C₅₉	semidirect
537. #3328	C₂×C₅₉	semidirect
538. #3328	C₂×C₅₉	semidirect
539. #3312	C₂×C₅₉	semidirect
540. #3299	C₂×C₅₉	semidirect
541. #3261	C₂×C₅₉	semidirect
542. #3255	C₂×C₅₉	semidirect
543. #3242	C₂×C₅₉	semidirect
544. #3231	C₂×C₅₉	semidirect
545. #3127	C₂×C₅₉	semidirect
546. #3104	C₂×C₅₉	semidirect
547. #3082	C₂×C₅₉	semidirect
548. #3078	C₂×C₅₉	semidirect
666. C₅₉	#62192	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×#3555	2
C₅₉×#3523	2
C₅₉×#3387	2
C₅₉×#3383	2
C₅₉×#3374	2
C₅₉×#3363	2
C₅₉×#3356	2
C₅₉×#3352	2
C₅₉×#3349	2
C₅₉×#3342	2
C₅₉×#3328	2
C₅₉×#3312	2
C₅₉×#3299	2
C₅₉×#3261	2
C₅₉×#3255	2
C₅₉×#3242	2
C₅₉×#3231	2
C₅₉×#3127	2
C₅₉×#3104	2
C₅₉×#3082	2
C₅₉×#3078	2
C₅₉×#2993	2
#62192	59

Subgroups — C59×#62192 #28474301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62192 #28474301