Subgroups — C₅₉×#62191 #28474300

Order 15104.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3547	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3351	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3348	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3329	C₂	1	2	yes	maximal, complemented
12	C₅₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3320	C₂	1	2	yes	maximal, complemented
14	C₅₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3260	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3254	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×#3126	C₂	1	2	yes	maximal, complemented
20	C₅₉×#3103	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, complemented
24	C₅₉×#562	—	2	2	no	—
25	C₅₉×#557	—	2	1	no	—
26	C₅₉×#557	C₂²	1	1	yes	characteristic
27	C₅₉×#557	C₂²	1	1	yes	characteristic
28	C₅₉×#556	—	2	1	no	—
29	C₅₉×#556	C₂²	1	1	yes	characteristic
30	C₅₉×#555	C₂²	1	1	yes	characteristic
31	C₅₉×#555	C₂²	1	2	yes	—
32	C₅₉×#554	C₂²	1	1	yes	characteristic
33	C₅₉×#553	C₂²	1	2	yes	—
34	C₅₉×#552	—	2	1	no	—
35	C₅₉×#552	—	2	2	no	—
36	C₅₉×#552	C₂²	1	2	yes	—
37	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
39	D₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#548	—	2	1	no	—
41	C₅₉×#547	C₂²	1	1	yes	characteristic
42	C₅₉×#544	C₂²	1	2	yes	—
43	C₅₉×#542	—	2	2	no	—
44	C₅₉×#541	—	2	2	no	—
45	C₅₉×#541	C₂²	1	2	yes	—
46	C₅₉×#540	C₂²	1	2	yes	—
47	C₅₉×#537	—	2	1	no	—
48	C₅₉×#536	—	2	1	no	—
49	C₅₉×#533	—	2	1	no	—
50	C₅₉×#533	C₂²	1	1	yes	characteristic
51	C₅₉×#533	C₂²	1	1	yes	characteristic
52	C₅₉×#532	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×#484	C₂²	1	2	yes	—
70	C₅₉×#483	C₂²	1	2	yes	—
71	C₅₉×#482	C₂²	1	2	yes	—
72	C₅₉×#482	C₂²	1	2	yes	—
73	C₅₉×#481	C₂²	1	1	yes	characteristic
74	C₅₉×#481	C₂²	1	1	yes	characteristic
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×#478	C₂²	1	2	yes	—
82	C₅₉×#478	C₂²	1	2	yes	—
83	C₅₉×#477	C₂²	1	2	yes	—
84	C₅₉×#477	C₂²	1	1	yes	characteristic
85	C₅₉×#477	C₂²	1	2	yes	—
86	C₅₉×#477	C₂²	1	1	yes	characteristic
87	C₅₉×#475	C₂²	1	1	yes	characteristic
88	C₅₉×#475	C₂²	1	1	yes	characteristic
89	C₅₉×#475	C₂²	1	1	yes	characteristic
90	C₅₉×#475	C₂²	1	2	yes	—
91	C₅₉×#475	C₂²	1	1	yes	characteristic
92	C₅₉×#474	C₂²	1	1	yes	characteristic
93	C₅₉×#474	C₂²	1	1	yes	characteristic
94	C₅₉×#468	C₂²	1	2	yes	—
95	C₅₉×#468	C₂²	1	2	yes	—
96	C₅₉×#468	C₂²	1	2	yes	—
97	C₅₉×#468	C₂²	1	2	yes	—
98	C₅₉×#465	C₂²	1	2	yes	—
99	C₅₉×#465	C₂²	1	2	yes	—
100	C₅₉×#461	C₂²	1	1	yes	characteristic
101	C₅₉×#461	C₂²	1	1	yes	characteristic
102	C₅₉×#461	C₂²	1	2	yes	—
103	C₅₉×#461	C₂²	1	2	yes	—
104	C₅₉×#460	C₂²	1	2	yes	—
105	C₅₉×#460	C₂²	1	1	yes	characteristic
106	C₅₉×#460	C₂²	1	1	yes	characteristic
107	C₅₉×#448	C₂²	1	2	yes	—
108	C₅₉×#448	C₂²	1	1	yes	characteristic
109	C₅₉×#448	C₂²	1	2	yes	—
110	C₅₉×#448	C₂²	1	1	yes	characteristic
111	C₅₉×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
113	C₅₉×#440	C₂²	1	2	yes	—
114	C₅₉×#440	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
120	C₄×SD₁₆×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	C₂×#41×C₅₉	—	2	1	no	—
136	C₂×#41×C₅₉	—	2	1	no	—
137	C₂²×Q₈×C₅₉	—	2	1	no	—
138	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
146	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
147	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
148	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₉	—	2	1	no	—
150	C₄⋊Q₈×C₅₉	—	2	1	no	—
151	C₄⋊Q₈×C₅₉	—	2	2	no	—
152	C₄⋊Q₈×C₅₉	—	2	2	no	—
153	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
160	#127×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	D₄	1	2	yes	—
167	#125×C₅₉	—	2	1	no	—
168	#125×C₅₉	—	2	2	no	—
169	#125×C₅₉	—	2	2	no	—
170	#125×C₅₉	—	2	2	no	—
171	#125×C₅₉	—	2	2	no	—
172	#125×C₅₉	—	2	2	no	—
173	#125×C₅₉	—	2	2	no	—
174	#125×C₅₉	—	2	1	no	—
175	#125×C₅₉	D₄	1	1	yes	characteristic
176	#125×C₅₉	C₂³	1	2	yes	—
177	#125×C₅₉	C₂³	1	2	yes	—
178	#125×C₅₉	C₂³	1	2	yes	—
179	#124×C₅₉	—	2	1	no	—
180	#124×C₅₉	—	2	2	no	—
181	#124×C₅₉	—	2	2	no	—
182	#124×C₅₉	—	2	2	no	—
183	#124×C₅₉	—	2	1	no	—
184	#124×C₅₉	D₄	1	1	yes	characteristic
185	#123×C₅₉	—	2	2	no	—
186	#123×C₅₉	—	2	2	no	—
187	#123×C₅₉	—	2	2	no	—
188	#123×C₅₉	—	2	2	no	—
189	#123×C₅₉	—	2	2	no	—
190	#123×C₅₉	D₄	1	2	yes	—
191	C₂²⋊Q₈×C₅₉	—	2	1	no	—
192	C₂²⋊Q₈×C₅₉	—	2	1	no	—
193	C₂²⋊Q₈×C₅₉	—	2	1	no	—
194	C₂²⋊Q₈×C₅₉	—	2	1	no	—
195	C₂²⋊Q₈×C₅₉	—	2	1	no	—
196	C₂²⋊Q₈×C₅₉	—	2	1	no	—
197	C₂²⋊Q₈×C₅₉	—	2	2	no	—
198	C₂²⋊Q₈×C₅₉	—	2	2	no	—
199	C₂²⋊Q₈×C₅₉	—	2	2	no	—
200	C₂²⋊Q₈×C₅₉	—	2	2	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	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
208	#121×C₅₉	—	2	1	no	—
209	#121×C₅₉	—	2	2	no	—
210	#121×C₅₉	—	2	2	no	—
211	#121×C₅₉	—	2	1	no	—
212	#121×C₅₉	—	2	2	no	—
213	#121×C₅₉	—	2	2	no	—
214	#121×C₅₉	D₄	1	1	yes	characteristic
215	#121×C₅₉	C₂³	1	2	yes	—
216	#121×C₅₉	C₂³	1	2	yes	—
217	#121×C₅₉	C₂³	1	1	yes	characteristic
218	#121×C₅₉	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₅₉	—	2	1	no	—
220	C₄×Q₈×C₅₉	—	2	2	no	—
221	C₄×Q₈×C₅₉	—	2	2	no	—
222	C₄×Q₈×C₅₉	—	2	1	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	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
232	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
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	1	yes	characteristic
237	C₄×D₄×C₅₉	—	2	2	no	—
238	C₄×D₄×C₅₉	—	2	1	no	—
239	C₄×D₄×C₅₉	—	2	2	no	—
240	C₄×D₄×C₅₉	—	2	1	no	—
241	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₅₉	C₂³	1	2	yes	—
244	C₄×D₄×C₅₉	C₂³	1	2	yes	—
245	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₅₉	C₂³	1	2	yes	—
247	#117×C₅₉	—	2	1	no	—
248	#117×C₅₉	—	2	1	no	—
249	#117×C₅₉	—	2	2	no	—
250	#117×C₅₉	—	2	2	no	—
251	#117×C₅₉	—	2	2	no	—
252	#117×C₅₉	—	2	2	no	—
253	#117×C₅₉	C₂³	1	2	yes	—
254	#117×C₅₉	C₂³	1	2	yes	—
255	#117×C₅₉	C₂³	1	2	yes	—
256	#117×C₅₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
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	2	yes	—
264	#107×C₅₉	C₂³	1	2	yes	—
265	#107×C₅₉	C₂³	1	2	yes	—
266	#107×C₅₉	C₂³	1	2	yes	—
267	#107×C₅₉	C₂³	1	2	yes	—
268	#107×C₅₉	C₂³	1	2	yes	—
269	#106×C₅₉	C₂³	1	1	yes	characteristic
270	#106×C₅₉	C₂³	1	2	yes	—
271	#106×C₅₉	C₂³	1	2	yes	—
272	#106×C₅₉	C₂³	1	1	yes	characteristic
273	#106×C₅₉	C₂³	1	2	yes	—
274	#106×C₅₉	C₂³	1	1	yes	characteristic
275	#106×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
297	#103×C₅₉	C₂³	1	2	yes	—
298	#102×C₅₉	C₂³	1	1	yes	characteristic
299	#102×C₅₉	C₂³	1	1	yes	characteristic
300	#102×C₅₉	C₂³	1	1	yes	characteristic
301	#102×C₅₉	C₂³	1	2	yes	—
302	#102×C₅₉	C₂³	1	1	yes	characteristic
303	#102×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	#41×C₅₉	—	8	2	no	—
313	#41×C₅₉	—	8	2	no	—
314	C₂×Q₈×C₅₉	—	2	1	no	—
315	C₂×Q₈×C₅₉	—	2	1	no	—
316	C₂×Q₈×C₅₉	—	2	2	no	—
317	C₂×Q₈×C₅₉	—	2	1	no	—
318	C₂×Q₈×C₅₉	—	2	1	no	—
319	C₂×Q₈×C₅₉	—	2	2	no	—
320	C₂×Q₈×C₅₉	—	2	1	no	—
321	C₂×Q₈×C₅₉	—	2	4	no	—
322	C₂×Q₈×C₅₉	—	2	2	no	—
323	C₂×Q₈×C₅₉	—	4	2	no	—
324	C₂×Q₈×C₅₉	—	4	1	no	—
325	C₂×Q₈×C₅₉	—	8	2	no	—
326	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₅₉	—	2	2	no	—
331	C₂×D₄×C₅₉	—	2	1	no	—
332	C₂×D₄×C₅₉	—	2	2	no	—
333	C₂×D₄×C₅₉	—	2	1	no	—
334	C₂×D₄×C₅₉	—	2	1	no	—
335	C₂×D₄×C₅₉	—	2	1	no	—
336	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅₉	—	2	1	no	—
341	C₂²×C₄×C₅₉	—	2	1	no	—
342	C₂²×C₄×C₅₉	—	2	2	no	—
343	C₂²×C₄×C₅₉	—	2	2	no	—
344	C₂²×C₄×C₅₉	—	2	1	no	—
345	C₂²×C₄×C₅₉	—	2	1	no	—
346	C₂²×C₄×C₅₉	—	2	2	no	—
347	C₂²×C₄×C₅₉	—	2	2	no	—
348	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
352	SD₁₆×C₅₉	—	2	2	no	—
353	SD₁₆×C₅₉	—	2	2	no	—
354	SD₁₆×C₅₉	—	4	1	no	—
355	SD₁₆×C₅₉	—	4	2	no	—
356	SD₁₆×C₅₉	—	4	2	no	—
357	SD₁₆×C₅₉	—	4	1	no	—
358	M₁₆×C₅₉	—	4	2	no	—
359	M₁₆×C₅₉	—	4	2	no	—
360	C₂×C₈×C₅₉	—	4	2	no	—
361	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
366	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₅₉	—	2	1	no	—
368	C₄⋊C₄×C₅₉	—	2	1	no	—
369	C₄⋊C₄×C₅₉	—	2	1	no	—
370	C₄⋊C₄×C₅₉	—	2	1	no	—
371	C₄⋊C₄×C₅₉	—	2	1	no	—
372	C₄⋊C₄×C₅₉	—	2	2	no	—
373	C₄⋊C₄×C₅₉	—	2	1	no	—
374	C₄⋊C₄×C₅₉	—	2	2	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	1	no	—
380	C₄⋊C₄×C₅₉	—	2	2	no	—
381	C₄⋊C₄×C₅₉	—	2	1	no	—
382	C₄⋊C₄×C₅₉	—	2	2	no	—
383	C₄⋊C₄×C₅₉	—	2	1	no	—
384	C₄⋊C₄×C₅₉	—	2	1	no	—
385	C₄⋊C₄×C₅₉	—	2	2	no	—
386	C₄⋊C₄×C₅₉	—	2	2	no	—
387	C₄⋊C₄×C₅₉	—	2	2	no	—
388	C₄⋊C₄×C₅₉	—	2	2	no	—
389	C₄⋊C₄×C₅₉	—	2	1	no	—
390	C₄⋊C₄×C₅₉	—	2	2	no	—
391	C₄⋊C₄×C₅₉	—	2	2	no	—
392	C₄⋊C₄×C₅₉	—	2	2	no	—
393	C₄⋊C₄×C₅₉	—	2	2	no	—
394	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
407	C₂²⋊C₄×C₅₉	—	2	2	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	1	no	—
414	C₂²⋊C₄×C₅₉	—	2	2	no	—
415	C₂²⋊C₄×C₅₉	—	2	2	no	—
416	C₂²⋊C₄×C₅₉	—	2	1	no	—
417	C₂²⋊C₄×C₅₉	—	2	2	no	—
418	C₂²⋊C₄×C₅₉	—	2	1	no	—
419	C₂²⋊C₄×C₅₉	—	2	2	no	—
420	C₂²⋊C₄×C₅₉	—	2	1	no	—
421	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
426	C₄²×C₅₉	—	2	1	no	—
427	C₄²×C₅₉	—	2	1	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	—	2	2	no	—
434	C₄²×C₅₉	—	2	2	no	—
435	C₄²×C₅₉	—	2	2	no	—
436	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
439	C₄²×C₅₉	C₂⁴	1	2	yes	—
440	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
441	C₂³×C₅₉	—	2	1	no	—
442	C₂³×C₅₉	—	2	1	no	—
443	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
444	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₅₉	—	2	2	no	—
446	Q₈×C₅₉	—	2	1	no	—
447	Q₈×C₅₉	—	2	2	no	—
448	Q₈×C₅₉	—	2	1	no	—
449	Q₈×C₅₉	—	2	1	no	—
450	Q₈×C₅₉	—	2	2	no	—
451	Q₈×C₅₉	—	4	4	no	—
452	Q₈×C₅₉	—	4	2	no	—
453	Q₈×C₅₉	—	4	2	no	—
454	Q₈×C₅₉	—	4	2	no	—
455	Q₈×C₅₉	—	8	1	no	—
456	Q₈×C₅₉	—	8	2	no	—
457	Q₈×C₅₉	—	8	1	no	—
458	Q₈×C₅₉	2₋¹⁺⁴	1	2	yes	—
459	D₄×C₅₉	—	2	2	no	—
460	D₄×C₅₉	—	2	1	no	—
461	D₄×C₅₉	—	2	1	no	—
462	D₄×C₅₉	—	2	1	no	—
463	D₄×C₅₉	—	2	1	no	—
464	D₄×C₅₉	—	4	2	no	—
465	D₄×C₅₉	—	8	1	no	—
466	D₄×C₅₉	—	8	1	no	—
467	D₄×C₅₉	—	8	2	no	—
468	D₄×C₅₉	—	8	1	no	—
469	D₄×C₅₉	—	8	1	no	—
470	D₄×C₅₉	—	8	2	no	—
471	C₂×C₄×C₅₉	—	2	1	no	—
472	C₂×C₄×C₅₉	—	2	2	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	—	2	1	no	—
478	C₂×C₄×C₅₉	—	2	2	no	—
479	C₂×C₄×C₅₉	—	2	2	no	—
480	C₂×C₄×C₅₉	—	2	1	no	—
481	C₂×C₄×C₅₉	—	2	1	no	—
482	C₂×C₄×C₅₉	—	2	1	no	—
483	C₂×C₄×C₅₉	—	2	2	no	—
484	C₂×C₄×C₅₉	—	2	2	no	—
485	C₂×C₄×C₅₉	—	2	1	no	—
486	C₂×C₄×C₅₉	—	4	1	no	—
487	C₂×C₄×C₅₉	—	4	2	no	—
488	C₂×C₄×C₅₉	—	4	4	no	—
489	C₂×C₄×C₅₉	—	4	2	no	—
490	C₂×C₄×C₅₉	—	4	2	no	—
491	C₂×C₄×C₅₉	—	4	2	no	—
492	C₂×C₄×C₅₉	—	8	2	no	—
493	C₂×C₄×C₅₉	—	8	2	no	—
494	C₂×C₄×C₅₉	—	8	2	no	—
495	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
504	C₈×C₅₉	—	2	1	no	—
505	C₈×C₅₉	—	2	1	no	—
506	C₈×C₅₉	—	2	1	no	—
507	C₈×C₅₉	—	2	2	no	—
508	C₈×C₅₉	—	2	1	no	—
509	C₈×C₅₉	—	2	2	no	—
510	#62191	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
511	C₂²×C₅₉	—	2	1	no	—
512	C₂²×C₅₉	—	2	2	no	—
513	C₂²×C₅₉	—	2	2	no	—
514	C₂²×C₅₉	—	2	1	no	—
515	C₂²×C₅₉	—	2	1	no	—
516	C₂²×C₅₉	—	2	2	no	—
517	C₂²×C₅₉	—	4	1	no	—
518	C₂²×C₅₉	—	4	1	no	—
519	C₂²×C₅₉	—	4	1	no	—
520	C₂²×C₅₉	—	4	1	no	—
521	C₂²×C₅₉	—	4	1	no	—
522	C₂²×C₅₉	—	4	1	no	—
523	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₅₉	—	2	1	no	—
525	C₄×C₅₉	—	2	1	no	—
526	C₄×C₅₉	—	2	2	no	—
527	C₄×C₅₉	—	2	2	no	—
528	C₄×C₅₉	—	2	1	no	—
529	C₄×C₅₉	—	2	2	no	—
530	C₄×C₅₉	—	2	1	no	—
531	C₄×C₅₉	—	2	2	no	—
532	C₄×C₅₉	—	4	1	no	—
533	C₄×C₅₉	—	4	1	no	—
534	C₄×C₅₉	—	4	2	no	—
535	C₄×C₅₉	—	4	1	no	—
536	C₄×C₅₉	—	4	2	no	—
537	C₄×C₅₉	—	4	1	no	—
538	C₄×C₅₉	—	4	1	no	—
539	C₄×C₅₉	—	4	2	no	—
540	C₄×C₅₉	—	4	2	no	—
541	C₄×C₅₉	#577	1	2	yes	—
542	C₄×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	C₄×C₅₉	#585	1	1	yes	characteristic
544	#3547	C₂×C₅₉	1	1	yes	characteristic
545	#3523	C₂×C₅₉	1	1	yes	characteristic, complemented
546	#3386	C₂×C₅₉	1	1	yes	characteristic, complemented
547	#3381	C₂×C₅₉	1	1	yes	characteristic, complemented
548	#3372	C₂×C₅₉	1	1	yes	characteristic, complemented
549	#3359	C₂×C₅₉	1	1	yes	characteristic, complemented
550	#3353	C₂×C₅₉	1	1	yes	characteristic, complemented
551	#3351	C₂×C₅₉	1	2	yes	complemented
552	#3348	C₂×C₅₉	1	2	yes	complemented
553	#3340	C₂×C₅₉	1	1	yes	characteristic, complemented
554	#3329	C₂×C₅₉	1	1	yes	characteristic, complemented
555	#3329	C₂×C₅₉	1	2	yes	complemented
556	#3320	C₂×C₅₉	1	2	yes	complemented
557	#3298	C₂×C₅₉	1	1	yes	characteristic, complemented
558	#3260	C₂×C₅₉	1	2	yes	complemented
559	#3254	C₂×C₅₉	1	1	yes	characteristic, complemented
560	#3242	C₂×C₅₉	1	2	yes	complemented
561	#3231	C₂×C₅₉	1	1	yes	characteristic, complemented
562	#3126	C₂×C₅₉	1	2	yes	complemented
563	#3103	C₂×C₅₉	1	1	yes	characteristic, complemented
564	#3082	C₂×C₅₉	1	2	yes	complemented
565	#3078	C₂×C₅₉	1	1	yes	characteristic, complemented
566	#2993	C₂×C₅₉	1	1	yes	characteristic, complemented
567	C₂×C₅₉	—	4	1	no	—
568	C₂×C₅₉	—	4	2	no	—
569	C₂×C₅₉	—	8	1	no	—
570	C₂×C₅₉	—	8	1	no	—
571	C₂×C₅₉	#3489	1	1	yes	characteristic
572	C₂×C₅₉	C₂×#577	1	1	yes	characteristic
573	C₂×C₅₉	#3586	1	1	yes	characteristic
574	#562	—	2	2	no	—
575	#557	—	2	1	no	—
576	#557	C₂²×C₅₉	1	1	yes	characteristic
577	#557	C₂²×C₅₉	1	1	yes	characteristic
578	#556	—	2	1	no	—
579	#556	C₂²×C₅₉	1	1	yes	characteristic
580	#555	C₂²×C₅₉	1	1	yes	characteristic
581	#555	C₂²×C₅₉	1	2	yes	—
582	#554	C₂²×C₅₉	1	1	yes	characteristic
583	#553	C₂²×C₅₉	1	2	yes	—
584	#552	—	2	1	no	—
585	#552	—	2	2	no	—
586	#552	C₂²×C₅₉	1	2	yes	—
587	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
588	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
589	D₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
590	#548	—	2	1	no	—
591	#547	C₂²×C₅₉	1	1	yes	characteristic
592	#544	C₂²×C₅₉	1	2	yes	—
593	#542	—	2	2	no	—
594	#541	—	2	2	no	—
595	#541	C₂²×C₅₉	1	2	yes	—
596	#540	C₂²×C₅₉	1	2	yes	—
597	#537	—	2	1	no	—
598	#536	—	2	1	no	—
599	#533	—	2	1	no	—
600	#533	C₂²×C₅₉	1	1	yes	characteristic
601	#533	C₂²×C₅₉	1	1	yes	characteristic
602	#532	C₂²×C₅₉	1	1	yes	characteristic
603	#529	—	2	1	no	—
604	#529	C₂²×C₅₉	1	1	yes	characteristic
605	#519	C₂²×C₅₉	1	2	yes	—
606	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
607	#501	C₂²×C₅₉	1	2	yes	—
608	#500	C₂²×C₅₉	1	1	yes	characteristic
609	#499	C₂²×C₅₉	1	2	yes	—
610	#498	C₂²×C₅₉	1	1	yes	characteristic
611	#491	C₂²×C₅₉	1	2	yes	—
612	#487	C₂²×C₅₉	1	2	yes	—
613	#487	C₂²×C₅₉	1	1	yes	characteristic
614	#487	C₂²×C₅₉	1	1	yes	characteristic
615	#485	C₂²×C₅₉	1	2	yes	—
616	#485	C₂²×C₅₉	1	2	yes	—
617	#485	C₂²×C₅₉	1	2	yes	—
618	#485	C₂²×C₅₉	1	2	yes	—
619	#484	C₂²×C₅₉	1	2	yes	—
620	#483	C₂²×C₅₉	1	2	yes	—
621	#482	C₂²×C₅₉	1	2	yes	—
622	#482	C₂²×C₅₉	1	2	yes	—
623	#481	C₂²×C₅₉	1	1	yes	characteristic
624	#481	C₂²×C₅₉	1	1	yes	characteristic
625	#479	C₂²×C₅₉	1	2	yes	—
626	#479	C₂²×C₅₉	1	2	yes	—
627	#479	C₂²×C₅₉	1	2	yes	—
628	#479	C₂²×C₅₉	1	2	yes	—
629	#479	C₂²×C₅₉	1	2	yes	—
630	#479	C₂²×C₅₉	1	2	yes	—
631	#478	C₂²×C₅₉	1	2	yes	—
632	#478	C₂²×C₅₉	1	2	yes	—
633	#477	C₂²×C₅₉	1	1	yes	characteristic
634	#477	C₂²×C₅₉	1	2	yes	—
635	#477	C₂²×C₅₉	1	1	yes	characteristic
636	#477	C₂²×C₅₉	1	2	yes	—
637	#475	C₂²×C₅₉	1	1	yes	characteristic
638	#475	C₂²×C₅₉	1	1	yes	characteristic
639	#475	C₂²×C₅₉	1	1	yes	characteristic
640	#475	C₂²×C₅₉	1	2	yes	—
641	#475	C₂²×C₅₉	1	1	yes	characteristic
642	#474	C₂²×C₅₉	1	1	yes	characteristic
643	#474	C₂²×C₅₉	1	1	yes	characteristic
644	#468	C₂²×C₅₉	1	2	yes	—
645	#468	C₂²×C₅₉	1	2	yes	—
646	#468	C₂²×C₅₉	1	2	yes	—
647	#468	C₂²×C₅₉	1	2	yes	—
648	#465	C₂²×C₅₉	1	2	yes	—
649	#465	C₂²×C₅₉	1	2	yes	—
650	#461	C₂²×C₅₉	1	1	yes	characteristic
651	#461	C₂²×C₅₉	1	2	yes	—
652	#461	C₂²×C₅₉	1	2	yes	—
653	#461	C₂²×C₅₉	1	1	yes	characteristic
654	#460	C₂²×C₅₉	1	1	yes	characteristic
655	#460	C₂²×C₅₉	1	1	yes	characteristic
656	#460	C₂²×C₅₉	1	2	yes	—
657	#448	C₂²×C₅₉	1	1	yes	characteristic
658	#448	C₂²×C₅₉	1	2	yes	—
659	#448	C₂²×C₅₉	1	2	yes	—
660	#448	C₂²×C₅₉	1	1	yes	characteristic
661	#446	C₂²×C₅₉	1	1	yes	characteristic
662	C₈×Q₈	C₂²×C₅₉	1	1	yes	characteristic
663	#440	C₂²×C₅₉	1	2	yes	—
664	#440	C₂²×C₅₉	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
666	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	—
667	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
668	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	—
669	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
671	#436	C₂²×C₅₉	1	2	yes	—
672	#436	C₂²×C₅₉	1	1	yes	characteristic
673	#435	C₂²×C₅₉	1	2	yes	—
674	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
675	#433	C₂²×C₅₉	1	2	yes	—
676	#431	C₂²×C₅₉	1	1	yes	characteristic
677	#428	C₂²×C₅₉	1	2	yes	—
678	#428	C₂²×C₅₉	1	2	yes	—
679	#427	C₂²×C₅₉	1	2	yes	—
680	#424	C₂²×C₅₉	1	2	yes	—
681	#423	C₂²×C₅₉	1	1	yes	characteristic
682	#419	C₂²×C₅₉	1	2	yes	—
683	#419	C₂²×C₅₉	1	2	yes	—
684	C₂×#103	C₂²×C₅₉	1	2	yes	—
685	C₅₉	#62191	1	1	yes	characteristic, direct product factor, Sylow
686	C₂×#41	—	2	1	no	—
687	C₂×#41	—	2	1	no	—
688	C₂²×Q₈	—	2	1	no	—
689	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
690	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
693	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
695	C₂×SD₁₆	C₂³×C₅₉	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
697	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
698	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
699	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	2	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
711	#127	C₂³×C₅₉	1	1	yes	characteristic
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	D₄×C₅₉	1	2	yes	—
718	#125	—	2	1	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	D₄×C₅₉	1	1	yes	characteristic
727	#125	C₂³×C₅₉	1	2	yes	—
728	#125	C₂³×C₅₉	1	2	yes	—
729	#125	C₂³×C₅₉	1	2	yes	—
730	#124	—	2	1	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	—	2	1	no	—
735	#124	D₄×C₅₉	1	1	yes	characteristic
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	D₄×C₅₉	1	2	yes	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
759	#121	—	2	1	no	—
760	#121	—	2	2	no	—
761	#121	—	2	2	no	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	D₄×C₅₉	1	1	yes	characteristic
766	#121	C₂³×C₅₉	1	1	yes	characteristic
767	#121	C₂³×C₅₉	1	1	yes	characteristic
768	#121	C₂³×C₅₉	1	2	yes	—
769	#121	C₂³×C₅₉	1	2	yes	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
785	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
786	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
787	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₅₉	1	2	yes	—
795	C₄×D₄	C₂³×C₅₉	1	2	yes	—
796	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₅₉	1	2	yes	—
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	2	no	—
804	#117	C₂³×C₅₉	1	2	yes	—
805	#117	C₂³×C₅₉	1	2	yes	—
806	#117	C₂³×C₅₉	1	2	yes	—
807	#117	C₂³×C₅₉	1	2	yes	—
808	C₂×C₄⋊C₄	—	2	1	no	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
811	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
814	#107	C₂³×C₅₉	1	2	yes	—
815	#107	C₂³×C₅₉	1	2	yes	—
816	#107	C₂³×C₅₉	1	2	yes	—
817	#107	C₂³×C₅₉	1	2	yes	—
818	#107	C₂³×C₅₉	1	2	yes	—
819	#107	C₂³×C₅₉	1	2	yes	—
820	#106	C₂³×C₅₉	1	1	yes	characteristic
821	#106	C₂³×C₅₉	1	2	yes	—
822	#106	C₂³×C₅₉	1	2	yes	—
823	#106	C₂³×C₅₉	1	1	yes	characteristic
824	#106	C₂³×C₅₉	1	2	yes	—
825	#106	C₂³×C₅₉	1	1	yes	characteristic
826	#106	C₂³×C₅₉	1	1	yes	characteristic
827	#106	C₂³×C₅₉	1	2	yes	—
828	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
829	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
833	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
834	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
835	#103	C₂³×C₅₉	1	1	yes	characteristic
836	#103	C₂³×C₅₉	1	2	yes	—
837	#103	C₂³×C₅₉	1	2	yes	—
838	#103	C₂³×C₅₉	1	2	yes	—
839	#103	C₂³×C₅₉	1	1	yes	characteristic
840	#103	C₂³×C₅₉	1	2	yes	—
841	#103	C₂³×C₅₉	1	2	yes	—
842	#103	C₂³×C₅₉	1	2	yes	—
843	#103	C₂³×C₅₉	1	2	yes	—
844	#103	C₂³×C₅₉	1	2	yes	—
845	#103	C₂³×C₅₉	1	1	yes	characteristic
846	#103	C₂³×C₅₉	1	1	yes	characteristic
847	#103	C₂³×C₅₉	1	2	yes	—
848	#103	C₂³×C₅₉	1	2	yes	—
849	#102	C₂³×C₅₉	1	1	yes	characteristic
850	#102	C₂³×C₅₉	1	1	yes	characteristic
851	#102	C₂³×C₅₉	1	1	yes	characteristic
852	#102	C₂³×C₅₉	1	2	yes	—
853	#102	C₂³×C₅₉	1	1	yes	characteristic
854	#102	C₂³×C₅₉	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
859	#97	C₂³×C₅₉	1	2	yes	—
860	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
861	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₅₉	1	2	yes	—
863	#41	—	8	2	no	—
864	#41	—	8	2	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	1	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	2	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	2	4	no	—
874	C₂×Q₈	—	4	2	no	—
875	C₂×Q₈	—	4	1	no	—
876	C₂×Q₈	—	8	2	no	—
877	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
879	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
880	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
888	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
889	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
890	C₂×D₄	C₂⁴×C₅₉	1	1	yes	characteristic
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
900	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
903	SD₁₆	—	2	2	no	—
904	SD₁₆	—	2	2	no	—
905	SD₁₆	—	4	1	no	—
906	SD₁₆	—	4	2	no	—
907	SD₁₆	—	4	2	no	—
908	SD₁₆	—	4	1	no	—
909	M₁₆	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	2	no	—
912	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
913	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
917	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
946	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
948	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
949	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
950	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
957	C₄⋊C₄	C₂⁴×C₅₉	1	1	yes	characteristic
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
974	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
975	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
988	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
989	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
990	C₄²	C₂⁴×C₅₉	1	2	yes	—
991	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
992	C₂³	—	2	1	no	—
993	C₂³	—	2	1	no	—
994	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
995	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
996	Q₈	—	2	2	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	2	2	no	—
1002	Q₈	—	4	4	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	4	2	no	—
1005	Q₈	—	4	2	no	—
1006	Q₈	—	8	1	no	—
1007	Q₈	—	8	2	no	—
1008	Q₈	—	8	1	no	—
1009	Q₈	2₋¹⁺⁴×C₅₉	1	2	yes	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	1	no	—
1012	D₄	—	2	1	no	—
1013	D₄	—	2	1	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	8	1	no	—
1017	D₄	—	8	1	no	—
1018	D₄	—	8	2	no	—
1019	D₄	—	8	1	no	—
1020	D₄	—	8	1	no	—
1021	D₄	—	8	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	4	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1054	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	2	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	C₅₉×#577	1	2	yes	—
1092	C₄	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
1093	C₄	C₅₉×#585	1	1	yes	characteristic
1094	C₂	—	4	1	no	—
1095	C₂	—	4	2	no	—
1096	C₂	—	8	1	no	—
1097	C₂	—	8	1	no	—
1098	C₂	C₅₉×#3489	1	1	yes	characteristic
1099	C₂	C₂×C₅₉×#577	1	1	yes	characteristic
1100	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	C₅₉×#3547	C₂
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
2. C₅₉×#3523	C₂	semidirect
3. C₅₉×#3386	C₂	semidirect
4. C₅₉×#3381	C₂	semidirect
5. C₅₉×#3372	C₂	semidirect
6. C₅₉×#3359	C₂	semidirect
7. C₅₉×#3353	C₂	semidirect
8. C₅₉×#3351	C₂	semidirect
9. C₅₉×#3348	C₂	semidirect
10. C₅₉×#3340	C₂	semidirect
11. C₅₉×#3329	C₂	semidirect
12. C₅₉×#3329	C₂	semidirect
13. C₅₉×#3320	C₂	semidirect
14. C₅₉×#3298	C₂	semidirect
15. C₅₉×#3260	C₂	semidirect
16. C₅₉×#3254	C₂	semidirect
17. C₅₉×#3242	C₂	semidirect
18. C₅₉×#3231	C₂	semidirect
19. C₅₉×#3126	C₂	semidirect
20. C₅₉×#3103	C₂	semidirect
21. C₅₉×#3082	C₂	semidirect
22. C₅₉×#3078	C₂	semidirect
23. C₅₉×#2993	C₂	semidirect
510. #62191	C₅₉	direct (N × H)
545. #3523	C₂×C₅₉	semidirect
546. #3386	C₂×C₅₉	semidirect
547. #3381	C₂×C₅₉	semidirect
548. #3372	C₂×C₅₉	semidirect
549. #3359	C₂×C₅₉	semidirect
550. #3353	C₂×C₅₉	semidirect
551. #3351	C₂×C₅₉	semidirect
552. #3348	C₂×C₅₉	semidirect
553. #3340	C₂×C₅₉	semidirect
554. #3329	C₂×C₅₉	semidirect
555. #3329	C₂×C₅₉	semidirect
556. #3320	C₂×C₅₉	semidirect
557. #3298	C₂×C₅₉	semidirect
558. #3260	C₂×C₅₉	semidirect
559. #3254	C₂×C₅₉	semidirect
560. #3242	C₂×C₅₉	semidirect
561. #3231	C₂×C₅₉	semidirect
562. #3126	C₂×C₅₉	semidirect
563. #3103	C₂×C₅₉	semidirect
564. #3082	C₂×C₅₉	semidirect
565. #3078	C₂×C₅₉	semidirect
566. #2993	C₂×C₅₉	semidirect
685. C₅₉	#62191	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×#3547	2
C₅₉×#3523	2
C₅₉×#3386	2
C₅₉×#3381	2
C₅₉×#3372	2
C₅₉×#3359	2
C₅₉×#3353	2
C₅₉×#3351	2
C₅₉×#3348	2
C₅₉×#3340	2
C₅₉×#3329	2
C₅₉×#3320	2
C₅₉×#3298	2
C₅₉×#3260	2
C₅₉×#3254	2
C₅₉×#3242	2
C₅₉×#3231	2
C₅₉×#3126	2
C₅₉×#3103	2
C₅₉×#3082	2
C₅₉×#3078	2
C₅₉×#2993	2
#62191	59

Subgroups — C59×#62191 #28474300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62191 #28474300