Subgroups — C₅₉×#62022 #28474131

Order 15104.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3403	C₂	1	2	yes	maximal, complemented
4	C₅₉×#3375	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3314	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3308	C₂	1	2	yes	maximal, complemented
7	C₅₉×#3294	C₂	1	2	yes	maximal, complemented
8	C₅₉×#3285	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3268	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3265	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3262	C₂	1	2	yes	maximal, complemented
12	C₅₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3224	C₂	1	2	yes	maximal, complemented
14	C₅₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3124	C₂	1	2	yes	maximal, complemented
16	C₅₉×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#3045	C₂	1	2	yes	maximal, complemented
18	C₂×C₅₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×AGL(1,ℤ/8)×C₅₉	C₂²	1	2	yes	complemented
21	C₂×#135×C₅₉	C₂²	1	2	yes	complemented
22	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#562	—	2	1	no	—
25	C₅₉×H(3,𝔽₄)	—	2	1	no	—
26	C₅₉×#559	—	2	1	no	—
27	C₅₉×#559	C₂²	1	2	yes	—
28	C₅₉×#559	C₂²	1	1	yes	characteristic, complemented
29	Q₈²×C₅₉	C₂²	1	1	yes	characteristic, complemented
30	C₅₉×#554	—	2	1	no	—
31	C₅₉×#554	C₂²	1	1	yes	characteristic, complemented
32	C₅₉×#550	C₂²	1	1	yes	characteristic, complemented
33	C₅₉×#548	C₂²	1	2	yes	—
34	C₅₉×#548	C₂²	1	2	yes	complemented
35	C₅₉×#547	—	2	2	no	—
36	C₅₉×#547	C₂²	1	2	yes	complemented
37	C₅₉×#546	—	2	2	no	—
38	C₅₉×#546	C₂²	1	2	yes	—
39	D₄²×C₅₉	C₂²	1	2	yes	—
40	C₅₉×#542	—	2	2	no	—
41	C₅₉×#542	C₂²	1	2	yes	—
42	C₅₉×#542	C₂²	1	2	yes	complemented
43	C₅₉×#538	—	2	2	no	—
44	C₅₉×#538	—	2	1	no	—
45	C₅₉×#535	C₂²	1	2	yes	—
46	C₅₉×#534	—	2	1	no	—
47	C₅₉×#532	—	2	1	no	—
48	C₅₉×#532	C₂²	1	1	yes	characteristic
49	C₅₉×#532	C₂²	1	1	yes	characteristic, complemented
50	C₅₉×#529	—	2	1	no	—
51	C₅₉×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
53	C₅₉×#520	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
55	C₅₉×#496	C₂²	1	2	yes	—
56	C₅₉×#496	C₂²	1	2	yes	complemented
57	C₅₉×#495	C₂²	1	2	yes	complemented
58	C₅₉×#489	C₂²	1	2	yes	complemented
59	C₅₉×#489	C₂²	1	2	yes	complemented
60	C₅₉×#486	C₂²	1	2	yes	—
61	C₅₉×#484	C₂²	1	2	yes	complemented
62	C₅₉×#480	C₂²	1	2	yes	—
63	C₅₉×#480	C₂²	1	2	yes	complemented
64	C₅₉×#477	C₂²	1	1	yes	characteristic, complemented
65	C₅₉×#477	C₂²	1	2	yes	complemented
66	C₅₉×#477	C₂²	1	1	yes	characteristic, complemented
67	C₅₉×#474	C₂²	1	2	yes	complemented
68	C₅₉×#474	C₂²	1	2	yes	complemented
69	C₅₉×#474	C₂²	1	2	yes	complemented
70	C₅₉×#468	C₂²	1	2	yes	—
71	C₅₉×#468	C₂²	1	2	yes	complemented
72	C₅₉×#467	C₂²	1	2	yes	complemented
73	C₅₉×#466	C₂²	1	2	yes	—
74	C₅₉×#466	C₂²	1	2	yes	complemented
75	C₅₉×#466	C₂²	1	2	yes	complemented
76	C₅₉×#464	C₂²	1	2	yes	complemented
77	C₅₉×#464	C₂²	1	2	yes	complemented
78	C₅₉×#464	C₂²	1	2	yes	complemented
79	C₅₉×#464	C₂²	1	2	yes	complemented
80	C₅₉×#464	C₂²	1	2	yes	complemented
81	C₅₉×#464	C₂²	1	2	yes	complemented
82	C₅₉×#463	C₂²	1	2	yes	complemented
83	C₅₉×#463	C₂²	1	2	yes	complemented
84	C₅₉×#463	C₂²	1	2	yes	complemented
85	C₅₉×#463	C₂²	1	2	yes	complemented
86	C₅₉×#460	C₂²	1	2	yes	—
87	C₅₉×#460	C₂²	1	1	yes	characteristic, complemented
88	C₅₉×#460	C₂²	1	1	yes	characteristic, complemented
89	C₅₉×#459	C₂²	1	2	yes	—
90	C₅₉×#459	C₂²	1	2	yes	complemented
91	C₅₉×#459	C₂²	1	2	yes	complemented
92	C₅₉×#452	C₂²	1	2	yes	complemented
93	C₅₉×#452	C₂²	1	2	yes	complemented
94	C₅₉×#450	C₂²	1	2	yes	complemented
95	C₅₉×#449	C₂²	1	2	yes	—
96	C₅₉×#449	C₂²	1	2	yes	complemented
97	C₅₉×#448	C₂²	1	2	yes	complemented
98	C₅₉×#448	C₂²	1	2	yes	complemented
99	C₅₉×#447	C₂²	1	2	yes	—
100	C₅₉×#447	C₂²	1	2	yes	complemented
101	C₅₉×#446	C₂²	1	2	yes	complemented
102	C₅₉×#440	C₂²	1	2	yes	complemented
103	C₅₉×#440	C₂²	1	2	yes	complemented
104	C₅₉×#440	C₂²	1	2	yes	complemented
105	C₅₉×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	complemented
107	C₄×D₈×C₅₉	C₂²	1	2	yes	complemented
108	C₅₉×#435	C₂²	1	2	yes	complemented
109	C₅₉×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₅₉	C₂²	1	2	yes	complemented
111	C₅₉×#433	C₂²	1	2	yes	complemented
112	C₅₉×#432	C₂²	1	1	yes	characteristic, complemented
113	C₅₉×#424	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
115	C₅₉×#417	C₂²	1	2	yes	complemented
116	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
117	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
118	C₂×#102×C₅₉	C₂²	1	2	yes	complemented
119	C₂×#41×C₅₉	—	2	2	no	—
120	C₂×#41×C₅₉	—	2	1	no	—
121	C₂×#41×C₅₉	—	2	1	no	—
122	C₂×#41×C₅₉	C₂³	1	2	yes	—
123	C₂×#41×C₅₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₅₉	—	2	2	no	—
127	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
129	AGL(1,ℤ/8)×C₅₉	—	4	4	no	—
130	#135×C₅₉	—	4	4	no	—
131	C₂×Q₁₆×C₅₉	—	4	2	no	—
132	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₅₉	—	4	2	no	—
135	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
141	C₂×D₈×C₅₉	C₂³	1	2	yes	—
142	C₂×D₈×C₅₉	C₂³	1	2	yes	—
143	C₂×D₈×C₅₉	C₂³	1	2	yes	—
144	C₂×D₈×C₅₉	C₂³	1	2	yes	—
145	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
146	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
148	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
149	C₄⋊Q₈×C₅₉	—	2	1	no	—
150	C₄⋊Q₈×C₅₉	—	2	2	no	—
151	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
154	#127×C₅₉	—	2	1	no	—
155	#127×C₅₉	C₂³	1	2	yes	—
156	#127×C₅₉	C₂³	1	1	yes	characteristic
157	#127×C₅₉	C₂³	1	1	yes	characteristic
158	#126×C₅₉	—	2	2	no	—
159	#126×C₅₉	—	2	2	no	—
160	#126×C₅₉	D₄	1	2	yes	—
161	#125×C₅₉	—	2	1	no	—
162	#125×C₅₉	D₄	1	1	yes	characteristic
163	#124×C₅₉	—	2	1	no	—
164	#124×C₅₉	—	2	2	no	—
165	#124×C₅₉	—	2	2	no	—
166	#124×C₅₉	—	2	2	no	—
167	#124×C₅₉	—	2	2	no	—
168	#124×C₅₉	—	2	2	no	—
169	#124×C₅₉	—	2	1	no	—
170	#124×C₅₉	—	2	1	no	—
171	#124×C₅₉	—	2	1	no	—
172	#124×C₅₉	—	2	1	no	—
173	#124×C₅₉	D₄	1	1	yes	characteristic
174	#124×C₅₉	C₂³	1	2	yes	—
175	#124×C₅₉	C₂³	1	2	yes	—
176	#124×C₅₉	C₂³	1	2	yes	—
177	#124×C₅₉	C₂³	1	2	yes	—
178	#123×C₅₉	—	2	2	no	—
179	#123×C₅₉	—	2	2	no	—
180	#123×C₅₉	—	2	2	no	—
181	#123×C₅₉	—	2	2	no	—
182	#123×C₅₉	—	2	2	no	—
183	#123×C₅₉	—	2	2	no	—
184	#123×C₅₉	—	2	2	no	—
185	#123×C₅₉	—	2	2	no	—
186	#123×C₅₉	D₄	1	2	yes	—
187	C₂²⋊Q₈×C₅₉	—	2	2	no	—
188	C₂²⋊Q₈×C₅₉	—	2	2	no	—
189	C₂²⋊Q₈×C₅₉	—	2	2	no	—
190	C₂²⋊Q₈×C₅₉	—	2	2	no	—
191	C₂²⋊Q₈×C₅₉	—	2	2	no	—
192	C₂²⋊Q₈×C₅₉	—	2	2	no	—
193	C₂²⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
196	#121×C₅₉	—	2	2	no	—
197	#121×C₅₉	—	2	2	no	—
198	#121×C₅₉	—	2	1	no	—
199	#121×C₅₉	—	2	1	no	—
200	#121×C₅₉	—	2	2	no	—
201	#121×C₅₉	—	2	2	no	—
202	#121×C₅₉	—	2	2	no	—
203	#121×C₅₉	—	2	2	no	—
204	#121×C₅₉	—	2	2	no	—
205	#121×C₅₉	D₄	1	1	yes	characteristic
206	#121×C₅₉	C₂³	1	2	yes	—
207	#121×C₅₉	C₂³	1	2	yes	—
208	#121×C₅₉	C₂³	1	2	yes	—
209	#121×C₅₉	C₂³	1	2	yes	—
210	#120×C₅₉	—	2	2	no	—
211	#120×C₅₉	—	2	2	no	—
212	#120×C₅₉	—	2	2	no	—
213	#120×C₅₉	—	2	2	no	—
214	#120×C₅₉	—	2	2	no	—
215	C₄×Q₈×C₅₉	—	2	1	no	—
216	C₄×Q₈×C₅₉	—	2	1	no	—
217	C₄×Q₈×C₅₉	—	2	1	no	—
218	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
219	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
220	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₅₉	—	2	1	no	—
226	C₄×D₄×C₅₉	—	2	1	no	—
227	C₄×D₄×C₅₉	—	2	1	no	—
228	C₄×D₄×C₅₉	—	2	2	no	—
229	C₄×D₄×C₅₉	—	2	2	no	—
230	C₄×D₄×C₅₉	—	2	2	no	—
231	C₄×D₄×C₅₉	—	2	2	no	—
232	C₄×D₄×C₅₉	—	2	2	no	—
233	C₄×D₄×C₅₉	—	2	1	no	—
234	C₄×D₄×C₅₉	—	2	1	no	—
235	C₄×D₄×C₅₉	C₂³	1	2	yes	—
236	C₄×D₄×C₅₉	C₂³	1	2	yes	—
237	C₄×D₄×C₅₉	C₂³	1	2	yes	—
238	C₄×D₄×C₅₉	C₂³	1	2	yes	—
239	C₄×D₄×C₅₉	C₂³	1	2	yes	—
240	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
241	#117×C₅₉	—	2	2	no	—
242	#117×C₅₉	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
244	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
245	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
247	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
250	C₂×C₄²×C₅₉	—	2	1	no	—
251	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
252	#107×C₅₉	C₂³	1	2	yes	—
253	#107×C₅₉	C₂³	1	2	yes	—
254	#107×C₅₉	C₂³	1	2	yes	—
255	#107×C₅₉	C₂³	1	2	yes	—
256	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
257	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
258	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
260	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
261	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
262	#103×C₅₉	C₂³	1	2	yes	—
263	#103×C₅₉	C₂³	1	2	yes	—
264	#103×C₅₉	C₂³	1	2	yes	—
265	#103×C₅₉	C₂³	1	2	yes	—
266	#103×C₅₉	C₂³	1	2	yes	—
267	#103×C₅₉	C₂³	1	2	yes	—
268	#102×C₅₉	C₂³	1	2	yes	—
269	#102×C₅₉	C₂³	1	2	yes	—
270	#102×C₅₉	C₂³	1	2	yes	—
271	#102×C₅₉	C₂³	1	2	yes	—
272	#102×C₅₉	C₂³	1	2	yes	—
273	#102×C₅₉	C₂³	1	2	yes	—
274	#102×C₅₉	C₂³	1	2	yes	—
275	#102×C₅₉	C₂³	1	2	yes	—
276	#102×C₅₉	C₂³	1	2	yes	—
277	#102×C₅₉	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
281	#97×C₅₉	C₂³	1	2	yes	—
282	#97×C₅₉	C₂³	1	2	yes	—
283	C₄×C₈×C₅₉	C₂³	1	2	yes	—
284	C₂⁴×C₅₉	—	2	1	no	—
285	C₂⁴×C₅₉	—	2	2	no	—
286	#41×C₅₉	—	2	4	no	—
287	#41×C₅₉	—	4	2	no	—
288	#41×C₅₉	—	4	2	no	—
289	#41×C₅₉	—	4	2	no	—
290	#41×C₅₉	—	8	2	no	—
291	#41×C₅₉	—	8	2	no	—
292	#41×C₅₉	—	8	4	no	—
293	C₂×Q₈×C₅₉	—	2	1	no	—
294	C₂×Q₈×C₅₉	—	2	1	no	—
295	C₂×Q₈×C₅₉	—	2	1	no	—
296	C₂×Q₈×C₅₉	—	2	2	no	—
297	C₂×Q₈×C₅₉	—	2	1	no	—
298	C₂×Q₈×C₅₉	—	2	2	no	—
299	C₂×Q₈×C₅₉	—	4	1	no	—
300	C₂×Q₈×C₅₉	—	4	1	no	—
301	C₂×Q₈×C₅₉	—	4	1	no	—
302	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
303	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
305	C₂×Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₅₉	—	2	2	no	—
307	C₂×D₄×C₅₉	—	2	2	no	—
308	C₂×D₄×C₅₉	—	2	2	no	—
309	C₂×D₄×C₅₉	—	2	2	no	—
310	C₂×D₄×C₅₉	—	2	2	no	—
311	C₂×D₄×C₅₉	—	2	2	no	—
312	C₂×D₄×C₅₉	—	2	1	no	—
313	C₂×D₄×C₅₉	—	2	2	no	—
314	C₂×D₄×C₅₉	—	2	1	no	—
315	C₂×D₄×C₅₉	—	2	1	no	—
316	C₂×D₄×C₅₉	—	2	1	no	—
317	C₂×D₄×C₅₉	—	2	2	no	—
318	C₂×D₄×C₅₉	—	2	2	no	—
319	C₂×D₄×C₅₉	—	2	1	no	—
320	C₂×D₄×C₅₉	—	4	1	no	—
321	C₂×D₄×C₅₉	—	4	2	no	—
322	C₂×D₄×C₅₉	—	4	1	no	—
323	C₂×D₄×C₅₉	—	4	2	no	—
324	C₂×D₄×C₅₉	—	8	4	no	—
325	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
326	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
327	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
328	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
329	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₅₉	—	2	1	no	—
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	—	2	2	no	—
336	C₂²×C₄×C₅₉	—	2	2	no	—
337	C₂²×C₄×C₅₉	—	2	2	no	—
338	C₂²×C₄×C₅₉	—	2	2	no	—
339	C₂²×C₄×C₅₉	—	2	2	no	—
340	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
344	Q₁₆×C₅₉	—	2	4	no	—
345	Q₁₆×C₅₉	—	4	2	no	—
346	SD₁₆×C₅₉	—	2	4	no	—
347	SD₁₆×C₅₉	—	2	4	no	—
348	SD₁₆×C₅₉	—	4	2	no	—
349	SD₁₆×C₅₉	—	4	2	no	—
350	SD₁₆×C₅₉	—	4	2	no	—
351	SD₁₆×C₅₉	—	4	2	no	—
352	D₈×C₅₉	—	4	2	no	—
353	D₈×C₅₉	—	4	2	no	—
354	D₈×C₅₉	—	4	2	no	—
355	D₈×C₅₉	—	4	2	no	—
356	M₁₆×C₅₉	—	4	2	no	—
357	C₂×C₈×C₅₉	—	4	1	no	—
358	C₂×C₈×C₅₉	—	4	1	no	—
359	C₂×C₈×C₅₉	—	4	2	no	—
360	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
361	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
362	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
363	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₅₉	—	2	1	no	—
365	C₄⋊C₄×C₅₉	—	2	2	no	—
366	C₄⋊C₄×C₅₉	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₅₉	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
387	C₂²⋊C₄×C₅₉	—	2	2	no	—
388	C₂²⋊C₄×C₅₉	—	2	2	no	—
389	C₂²⋊C₄×C₅₉	—	2	2	no	—
390	C₂²⋊C₄×C₅₉	—	2	2	no	—
391	C₂²⋊C₄×C₅₉	—	2	2	no	—
392	C₂²⋊C₄×C₅₉	—	2	2	no	—
393	C₂²⋊C₄×C₅₉	—	2	2	no	—
394	C₂²⋊C₄×C₅₉	—	2	2	no	—
395	C₂²⋊C₄×C₅₉	—	2	2	no	—
396	C₂²⋊C₄×C₅₉	—	2	2	no	—
397	C₂²⋊C₄×C₅₉	—	2	2	no	—
398	C₂²⋊C₄×C₅₉	—	2	2	no	—
399	C₂²⋊C₄×C₅₉	—	2	2	no	—
400	C₂²⋊C₄×C₅₉	—	2	2	no	—
401	C₂²⋊C₄×C₅₉	—	2	2	no	—
402	C₂²⋊C₄×C₅₉	—	2	2	no	—
403	C₂²⋊C₄×C₅₉	—	2	2	no	—
404	C₂²⋊C₄×C₅₉	—	2	2	no	—
405	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
406	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
407	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
408	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
409	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
410	C₄²×C₅₉	—	2	1	no	—
411	C₄²×C₅₉	—	2	1	no	—
412	C₄²×C₅₉	—	2	1	no	—
413	C₄²×C₅₉	—	2	1	no	—
414	C₄²×C₅₉	—	2	2	no	—
415	C₄²×C₅₉	—	2	2	no	—
416	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₅₉	C₂⁴	1	2	yes	—
419	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
420	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
421	C₂³×C₅₉	—	2	2	no	—
422	C₂³×C₅₉	—	2	2	no	—
423	C₂³×C₅₉	—	2	2	no	—
424	C₂³×C₅₉	—	4	2	no	—
425	C₂³×C₅₉	—	8	1	no	—
426	C₂³×C₅₉	—	8	2	no	—
427	C₂³×C₅₉	—	8	2	no	—
428	C₂³×C₅₉	—	8	1	no	—
429	C₂³×C₅₉	—	8	2	no	—
430	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
431	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
432	Q₈×C₅₉	—	2	1	no	—
433	Q₈×C₅₉	—	2	1	no	—
434	Q₈×C₅₉	—	2	2	no	—
435	Q₈×C₅₉	—	2	1	no	—
436	Q₈×C₅₉	—	2	2	no	—
437	Q₈×C₅₉	—	4	1	no	—
438	Q₈×C₅₉	—	4	2	no	—
439	Q₈×C₅₉	—	8	1	no	—
440	Q₈×C₅₉	—	8	1	no	—
441	Q₈×C₅₉	—	8	1	no	—
442	Q₈×C₅₉	—	8	2	no	—
443	Q₈×C₅₉	H(5,𝔽₂)	1	2	yes	—
444	D₄×C₅₉	—	2	4	no	—
445	D₄×C₅₉	—	2	2	no	—
446	D₄×C₅₉	—	2	2	no	—
447	D₄×C₅₉	—	2	2	no	—
448	D₄×C₅₉	—	2	2	no	—
449	D₄×C₅₉	—	2	2	no	—
450	D₄×C₅₉	—	2	2	no	—
451	D₄×C₅₉	—	4	1	no	—
452	D₄×C₅₉	—	4	4	no	—
453	D₄×C₅₉	—	4	2	no	—
454	D₄×C₅₉	—	4	4	no	—
455	D₄×C₅₉	—	4	4	no	—
456	D₄×C₅₉	—	8	1	no	—
457	D₄×C₅₉	—	8	2	no	—
458	D₄×C₅₉	—	8	2	no	—
459	D₄×C₅₉	—	8	1	no	—
460	D₄×C₅₉	—	8	2	no	—
461	D₄×C₅₉	—	8	1	no	—
462	D₄×C₅₉	—	8	1	no	—
463	D₄×C₅₉	—	8	2	no	—
464	D₄×C₅₉	—	8	2	no	—
465	D₄×C₅₉	—	8	2	no	—
466	C₂×C₄×C₅₉	—	2	2	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	1	no	—
471	C₂×C₄×C₅₉	—	2	2	no	—
472	C₂×C₄×C₅₉	—	2	1	no	—
473	C₂×C₄×C₅₉	—	2	1	no	—
474	C₂×C₄×C₅₉	—	2	1	no	—
475	C₂×C₄×C₅₉	—	2	2	no	—
476	C₂×C₄×C₅₉	—	2	2	no	—
477	C₂×C₄×C₅₉	—	2	2	no	—
478	C₂×C₄×C₅₉	—	4	1	no	—
479	C₂×C₄×C₅₉	—	4	4	no	—
480	C₂×C₄×C₅₉	—	4	2	no	—
481	C₂×C₄×C₅₉	—	4	2	no	—
482	C₂×C₄×C₅₉	—	8	2	no	—
483	C₂×C₄×C₅₉	—	8	2	no	—
484	C₂×C₄×C₅₉	—	8	2	no	—
485	C₂×C₄×C₅₉	—	8	2	no	—
486	C₂×C₄×C₅₉	—	8	2	no	—
487	C₂×C₄×C₅₉	—	8	1	no	—
488	C₂×C₄×C₅₉	—	8	2	no	—
489	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
498	C₈×C₅₉	—	2	2	no	—
499	C₈×C₅₉	—	2	2	no	—
500	C₈×C₅₉	—	2	2	no	—
501	C₈×C₅₉	—	2	2	no	—
502	#62022	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
503	C₂²×C₅₉	—	2	1	no	—
504	C₂²×C₅₉	—	2	1	no	—
505	C₂²×C₅₉	—	2	2	no	—
506	C₂²×C₅₉	—	2	2	no	—
507	C₂²×C₅₉	—	2	2	no	—
508	C₂²×C₅₉	—	4	2	no	—
509	C₂²×C₅₉	—	4	2	no	—
510	C₂²×C₅₉	—	4	2	no	—
511	C₂²×C₅₉	—	4	2	no	—
512	C₂²×C₅₉	—	4	2	no	—
513	C₂²×C₅₉	—	4	2	no	—
514	C₂²×C₅₉	—	4	2	no	—
515	C₂²×C₅₉	—	4	2	no	—
516	C₂²×C₅₉	—	4	2	no	—
517	C₂²×C₅₉	—	16	2	no	—
518	C₂²×C₅₉	—	16	4	no	—
519	C₂²×C₅₉	#576	1	2	yes	—
520	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
521	C₄×C₅₉	—	2	1	no	—
522	C₄×C₅₉	—	2	1	no	—
523	C₄×C₅₉	—	2	2	no	—
524	C₄×C₅₉	—	2	2	no	—
525	C₄×C₅₉	—	2	1	no	—
526	C₄×C₅₉	—	2	2	no	—
527	C₄×C₅₉	—	2	1	no	—
528	C₄×C₅₉	—	2	1	no	—
529	C₄×C₅₉	—	2	2	no	—
530	C₄×C₅₉	—	4	1	no	—
531	C₄×C₅₉	—	4	2	no	—
532	C₄×C₅₉	—	4	1	no	—
533	C₄×C₅₉	—	4	1	no	—
534	C₄×C₅₉	—	4	2	no	—
535	C₄×C₅₉	—	4	2	no	—
536	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₄×C₅₉	#585	1	1	yes	characteristic
538	#3558	C₂×C₅₉	1	1	yes	characteristic, complemented
539	#3522	C₂×C₅₉	1	1	yes	characteristic, complemented
540	#3403	C₂×C₅₉	1	2	yes	complemented
541	#3375	C₂×C₅₉	1	2	yes	complemented
542	#3314	C₂×C₅₉	1	2	yes	complemented
543	#3308	C₂×C₅₉	1	2	yes	complemented
544	#3294	C₂×C₅₉	1	2	yes	complemented
545	#3285	C₂×C₅₉	1	2	yes	complemented
546	#3268	C₂×C₅₉	1	2	yes	complemented
547	#3265	C₂×C₅₉	1	2	yes	complemented
548	#3262	C₂×C₅₉	1	2	yes	complemented
549	#3245	C₂×C₅₉	1	1	yes	characteristic, complemented
550	#3224	C₂×C₅₉	1	2	yes	complemented
551	#3213	C₂×C₅₉	1	1	yes	characteristic, complemented
552	#3124	C₂×C₅₉	1	2	yes	complemented
553	#3112	C₂×C₅₉	1	1	yes	characteristic, complemented
554	#3045	C₂×C₅₉	1	2	yes	complemented
555	C₂×#464	C₂×C₅₉	1	1	yes	characteristic, complemented
556	#2992	C₂×C₅₉	1	1	yes	characteristic, complemented
557	C₂×C₅₉	—	2	2	no	—
558	C₂×C₅₉	—	4	2	no	—
559	C₂×C₅₉	—	8	2	no	—
560	C₂×C₅₉	—	8	2	no	—
561	C₂×C₅₉	—	8	2	no	—
562	C₂×C₅₉	#3488	1	1	yes	characteristic
563	C₂×C₅₉	C₂×#576	1	1	yes	characteristic
564	C₂×C₅₉	#3586	1	1	yes	characteristic
565	C₂×AGL(1,ℤ/8)	C₂²×C₅₉	1	2	yes	complemented
566	C₂×#135	C₂²×C₅₉	1	2	yes	complemented
567	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
568	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
569	#562	—	2	1	no	—
570	H(3,𝔽₄)	—	2	1	no	—
571	#559	—	2	1	no	—
572	#559	C₂²×C₅₉	1	2	yes	—
573	#559	C₂²×C₅₉	1	1	yes	characteristic, complemented
574	Q₈²	C₂²×C₅₉	1	1	yes	characteristic, complemented
575	#554	—	2	1	no	—
576	#554	C₂²×C₅₉	1	1	yes	characteristic, complemented
577	#550	C₂²×C₅₉	1	1	yes	characteristic, complemented
578	#548	C₂²×C₅₉	1	2	yes	—
579	#548	C₂²×C₅₉	1	2	yes	complemented
580	#547	—	2	2	no	—
581	#547	C₂²×C₅₉	1	2	yes	complemented
582	#546	—	2	2	no	—
583	#546	C₂²×C₅₉	1	2	yes	—
584	D₄²	C₂²×C₅₉	1	2	yes	—
585	#542	—	2	2	no	—
586	#542	C₂²×C₅₉	1	2	yes	—
587	#542	C₂²×C₅₉	1	2	yes	complemented
588	#538	—	2	2	no	—
589	#538	—	2	1	no	—
590	#535	C₂²×C₅₉	1	2	yes	—
591	#534	—	2	1	no	—
592	#532	—	2	1	no	—
593	#532	C₂²×C₅₉	1	1	yes	characteristic
594	#532	C₂²×C₅₉	1	1	yes	characteristic, complemented
595	#529	—	2	1	no	—
596	#529	C₂²×C₅₉	1	1	yes	characteristic
597	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
598	#520	C₂²×C₅₉	1	2	yes	complemented
599	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
600	#496	C₂²×C₅₉	1	2	yes	—
601	#496	C₂²×C₅₉	1	2	yes	complemented
602	#495	C₂²×C₅₉	1	2	yes	complemented
603	#489	C₂²×C₅₉	1	2	yes	complemented
604	#489	C₂²×C₅₉	1	2	yes	complemented
605	#486	C₂²×C₅₉	1	2	yes	—
606	#484	C₂²×C₅₉	1	2	yes	complemented
607	#480	C₂²×C₅₉	1	2	yes	—
608	#480	C₂²×C₅₉	1	2	yes	complemented
609	#477	C₂²×C₅₉	1	1	yes	characteristic, complemented
610	#477	C₂²×C₅₉	1	1	yes	characteristic, complemented
611	#477	C₂²×C₅₉	1	2	yes	complemented
612	#474	C₂²×C₅₉	1	2	yes	complemented
613	#474	C₂²×C₅₉	1	2	yes	complemented
614	#474	C₂²×C₅₉	1	2	yes	complemented
615	#468	C₂²×C₅₉	1	2	yes	—
616	#468	C₂²×C₅₉	1	2	yes	complemented
617	#467	C₂²×C₅₉	1	2	yes	complemented
618	#466	C₂²×C₅₉	1	2	yes	—
619	#466	C₂²×C₅₉	1	2	yes	complemented
620	#466	C₂²×C₅₉	1	2	yes	complemented
621	#464	C₂²×C₅₉	1	2	yes	complemented
622	#464	C₂²×C₅₉	1	2	yes	complemented
623	#464	C₂²×C₅₉	1	2	yes	complemented
624	#464	C₂²×C₅₉	1	2	yes	complemented
625	#464	C₂²×C₅₉	1	2	yes	complemented
626	#464	C₂²×C₅₉	1	2	yes	complemented
627	#463	C₂²×C₅₉	1	2	yes	complemented
628	#463	C₂²×C₅₉	1	2	yes	complemented
629	#463	C₂²×C₅₉	1	2	yes	complemented
630	#463	C₂²×C₅₉	1	2	yes	complemented
631	#460	C₂²×C₅₉	1	2	yes	—
632	#460	C₂²×C₅₉	1	1	yes	characteristic, complemented
633	#460	C₂²×C₅₉	1	1	yes	characteristic, complemented
634	#459	C₂²×C₅₉	1	2	yes	—
635	#459	C₂²×C₅₉	1	2	yes	complemented
636	#459	C₂²×C₅₉	1	2	yes	complemented
637	#452	C₂²×C₅₉	1	2	yes	complemented
638	#452	C₂²×C₅₉	1	2	yes	complemented
639	#450	C₂²×C₅₉	1	2	yes	complemented
640	#449	C₂²×C₅₉	1	2	yes	—
641	#449	C₂²×C₅₉	1	2	yes	complemented
642	#448	C₂²×C₅₉	1	2	yes	complemented
643	#448	C₂²×C₅₉	1	2	yes	complemented
644	#447	C₂²×C₅₉	1	2	yes	—
645	#447	C₂²×C₅₉	1	2	yes	complemented
646	#446	C₂²×C₅₉	1	2	yes	complemented
647	#440	C₂²×C₅₉	1	2	yes	complemented
648	#440	C₂²×C₅₉	1	2	yes	complemented
649	#440	C₂²×C₅₉	1	2	yes	complemented
650	#440	C₂²×C₅₉	1	2	yes	complemented
651	C₄×Q₁₆	C₂²×C₅₉	1	2	yes	complemented
652	C₄×D₈	C₂²×C₅₉	1	2	yes	complemented
653	#435	C₂²×C₅₉	1	2	yes	complemented
654	#435	C₂²×C₅₉	1	2	yes	complemented
655	C₈×D₄	C₂²×C₅₉	1	2	yes	complemented
656	#433	C₂²×C₅₉	1	2	yes	complemented
657	#432	C₂²×C₅₉	1	1	yes	characteristic, complemented
658	#424	C₂²×C₅₉	1	2	yes	complemented
659	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
660	#417	C₂²×C₅₉	1	2	yes	complemented
661	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
662	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
663	C₂×#102	C₂²×C₅₉	1	2	yes	complemented
664	C₅₉	#62022	1	1	yes	characteristic, direct product factor, Sylow
665	C₂×#41	—	2	2	no	—
666	C₂×#41	—	2	1	no	—
667	C₂×#41	—	2	1	no	—
668	C₂×#41	C₂³×C₅₉	1	2	yes	—
669	C₂×#41	C₂³×C₅₉	1	2	yes	—
670	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
671	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
672	C₂²×D₄	—	2	2	no	—
673	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
674	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
675	AGL(1,ℤ/8)	—	4	4	no	—
676	#135	—	4	4	no	—
677	C₂×Q₁₆	—	4	2	no	—
678	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
679	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
680	C₂×SD₁₆	—	4	2	no	—
681	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
683	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
687	C₂×D₈	C₂³×C₅₉	1	2	yes	—
688	C₂×D₈	C₂³×C₅₉	1	2	yes	—
689	C₂×D₈	C₂³×C₅₉	1	2	yes	—
690	C₂×D₈	C₂³×C₅₉	1	2	yes	—
691	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
692	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
693	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
694	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
700	#127	—	2	1	no	—
701	#127	C₂³×C₅₉	1	1	yes	characteristic
702	#127	C₂³×C₅₉	1	1	yes	characteristic
703	#127	C₂³×C₅₉	1	2	yes	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	D₄×C₅₉	1	2	yes	—
707	#125	—	2	1	no	—
708	#125	D₄×C₅₉	1	1	yes	characteristic
709	#124	—	2	1	no	—
710	#124	—	2	2	no	—
711	#124	—	2	2	no	—
712	#124	—	2	2	no	—
713	#124	—	2	2	no	—
714	#124	—	2	2	no	—
715	#124	—	2	1	no	—
716	#124	—	2	1	no	—
717	#124	—	2	1	no	—
718	#124	—	2	1	no	—
719	#124	D₄×C₅₉	1	1	yes	characteristic
720	#124	C₂³×C₅₉	1	2	yes	—
721	#124	C₂³×C₅₉	1	2	yes	—
722	#124	C₂³×C₅₉	1	2	yes	—
723	#124	C₂³×C₅₉	1	2	yes	—
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	D₄×C₅₉	1	2	yes	—
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	2	yes	—
742	#121	—	2	2	no	—
743	#121	—	2	2	no	—
744	#121	—	2	1	no	—
745	#121	—	2	1	no	—
746	#121	—	2	2	no	—
747	#121	—	2	2	no	—
748	#121	—	2	2	no	—
749	#121	—	2	2	no	—
750	#121	—	2	2	no	—
751	#121	D₄×C₅₉	1	1	yes	characteristic
752	#121	C₂³×C₅₉	1	2	yes	—
753	#121	C₂³×C₅₉	1	2	yes	—
754	#121	C₂³×C₅₉	1	2	yes	—
755	#121	C₂³×C₅₉	1	2	yes	—
756	#120	—	2	2	no	—
757	#120	—	2	2	no	—
758	#120	—	2	2	no	—
759	#120	—	2	2	no	—
760	#120	—	2	2	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
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	1	yes	characteristic
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×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	C₂³×C₅₉	1	2	yes	—
782	C₄×D₄	C₂³×C₅₉	1	2	yes	—
783	C₄×D₄	C₂³×C₅₉	1	2	yes	—
784	C₄×D₄	C₂³×C₅₉	1	2	yes	—
785	C₄×D₄	C₂³×C₅₉	1	2	yes	—
786	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
787	#117	—	2	2	no	—
788	#117	C₂³×C₅₉	1	2	yes	—
789	C₂×C₄⋊C₄	—	2	1	no	—
790	C₂×C₄⋊C₄	—	2	2	no	—
791	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
792	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
793	C₂×C₂²⋊C₄	—	2	1	no	—
794	C₂×C₂²⋊C₄	—	2	1	no	—
795	C₂×C₂²⋊C₄	—	2	2	no	—
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
798	#107	C₂³×C₅₉	1	2	yes	—
799	#107	C₂³×C₅₉	1	2	yes	—
800	#107	C₂³×C₅₉	1	2	yes	—
801	#107	C₂³×C₅₉	1	2	yes	—
802	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
803	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
804	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
805	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
806	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
807	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
808	#103	C₂³×C₅₉	1	2	yes	—
809	#103	C₂³×C₅₉	1	2	yes	—
810	#103	C₂³×C₅₉	1	2	yes	—
811	#103	C₂³×C₅₉	1	2	yes	—
812	#103	C₂³×C₅₉	1	2	yes	—
813	#103	C₂³×C₅₉	1	2	yes	—
814	#102	C₂³×C₅₉	1	2	yes	—
815	#102	C₂³×C₅₉	1	2	yes	—
816	#102	C₂³×C₅₉	1	2	yes	—
817	#102	C₂³×C₅₉	1	2	yes	—
818	#102	C₂³×C₅₉	1	2	yes	—
819	#102	C₂³×C₅₉	1	2	yes	—
820	#102	C₂³×C₅₉	1	2	yes	—
821	#102	C₂³×C₅₉	1	2	yes	—
822	#102	C₂³×C₅₉	1	2	yes	—
823	#102	C₂³×C₅₉	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
825	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
826	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
827	#97	C₂³×C₅₉	1	2	yes	—
828	#97	C₂³×C₅₉	1	2	yes	—
829	C₄×C₈	C₂³×C₅₉	1	2	yes	—
830	C₂⁴	—	2	1	no	—
831	C₂⁴	—	2	2	no	—
832	#41	—	2	4	no	—
833	#41	—	4	2	no	—
834	#41	—	4	2	no	—
835	#41	—	4	2	no	—
836	#41	—	8	2	no	—
837	#41	—	8	2	no	—
838	#41	—	8	4	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	4	1	no	—
846	C₂×Q₈	—	4	1	no	—
847	C₂×Q₈	—	4	1	no	—
848	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
849	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
850	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
851	C₂×Q₈	C₂⁴×C₅₉	1	1	yes	characteristic
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	1	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	1	no	—
861	C₂×D₄	—	2	1	no	—
862	C₂×D₄	—	2	1	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	—	4	1	no	—
867	C₂×D₄	—	4	2	no	—
868	C₂×D₄	—	4	1	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	—	8	4	no	—
871	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
872	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
873	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
874	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
875	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
887	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
890	Q₁₆	—	2	4	no	—
891	Q₁₆	—	4	2	no	—
892	SD₁₆	—	2	4	no	—
893	SD₁₆	—	2	4	no	—
894	SD₁₆	—	4	2	no	—
895	SD₁₆	—	4	2	no	—
896	SD₁₆	—	4	2	no	—
897	SD₁₆	—	4	2	no	—
898	D₈	—	4	2	no	—
899	D₈	—	4	2	no	—
900	D₈	—	4	2	no	—
901	D₈	—	4	2	no	—
902	M₁₆	—	4	2	no	—
903	C₂×C₈	—	4	1	no	—
904	C₂×C₈	—	4	1	no	—
905	C₂×C₈	—	4	2	no	—
906	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
907	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
908	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
909	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	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	1	yes	characteristic
927	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
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	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
952	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
953	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
954	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
955	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	2	no	—
962	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
963	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
964	C₄²	C₂⁴×C₅₉	1	2	yes	—
965	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
966	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	4	2	no	—
971	C₂³	—	8	1	no	—
972	C₂³	—	8	2	no	—
973	C₂³	—	8	2	no	—
974	C₂³	—	8	1	no	—
975	C₂³	—	8	2	no	—
976	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
977	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	2	no	—
983	Q₈	—	4	1	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	8	1	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	1	no	—
988	Q₈	—	8	2	no	—
989	Q₈	H(5,𝔽₂)×C₅₉	1	2	yes	—
990	D₄	—	2	4	no	—
991	D₄	—	2	2	no	—
992	D₄	—	2	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	2	2	no	—
995	D₄	—	2	2	no	—
996	D₄	—	2	2	no	—
997	D₄	—	4	1	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	4	4	no	—
1001	D₄	—	4	4	no	—
1002	D₄	—	8	1	no	—
1003	D₄	—	8	2	no	—
1004	D₄	—	8	2	no	—
1005	D₄	—	8	1	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	8	1	no	—
1008	D₄	—	8	1	no	—
1009	D₄	—	8	2	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	4	2	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
1043	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
1044	C₈	—	2	2	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	2	no	—
1047	C₈	—	2	2	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	16	2	no	—
1063	C₂²	—	16	4	no	—
1064	C₂²	C₅₉×#576	1	2	yes	—
1065	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
1082	C₄	C₅₉×#585	1	1	yes	characteristic
1083	C₂	—	2	2	no	—
1084	C₂	—	4	2	no	—
1085	C₂	—	8	2	no	—
1086	C₂	—	8	2	no	—
1087	C₂	—	8	2	no	—
1088	C₂	C₅₉×#3488	1	1	yes	characteristic
1089	C₂	C₂×C₅₉×#576	1	1	yes	characteristic
1090	C₂	C₅₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
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
1. C₅₉×#3558	C₂	semidirect
2. C₅₉×#3522	C₂	semidirect
3. C₅₉×#3403	C₂	semidirect
4. C₅₉×#3375	C₂	semidirect
5. C₅₉×#3314	C₂	semidirect
6. C₅₉×#3308	C₂	semidirect
7. C₅₉×#3294	C₂	semidirect
8. C₅₉×#3285	C₂	semidirect
9. C₅₉×#3268	C₂	semidirect
10. C₅₉×#3265	C₂	semidirect
11. C₅₉×#3262	C₂	semidirect
12. C₅₉×#3245	C₂	semidirect
13. C₅₉×#3224	C₂	semidirect
14. C₅₉×#3213	C₂	semidirect
15. C₅₉×#3124	C₂	semidirect
16. C₅₉×#3112	C₂	semidirect
17. C₅₉×#3045	C₂	semidirect
18. C₂×C₅₉×#464	C₂	semidirect
19. C₅₉×#2992	C₂	semidirect
20. C₂×AGL(1,ℤ/8)×C₅₉	C₂²	semidirect
21. C₂×#135×C₅₉	C₂²	semidirect
22. C₂²×Q₁₆×C₅₉	C₂²	semidirect
28. C₅₉×#559	C₂²	semidirect
29. Q₈²×C₅₉	C₂²	semidirect
31. C₅₉×#554	C₂²	semidirect
32. C₅₉×#550	C₂²	semidirect
34. C₅₉×#548	C₂²	semidirect
36. C₅₉×#547	C₂²	semidirect
42. C₅₉×#542	C₂²	semidirect
49. C₅₉×#532	C₂²	semidirect
53. C₅₉×#520	C₂²	semidirect
54. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
56. C₅₉×#496	C₂²	semidirect
57. C₅₉×#495	C₂²	semidirect
58. C₅₉×#489	C₂²	semidirect
59. C₅₉×#489	C₂²	semidirect
61. C₅₉×#484	C₂²	semidirect
63. C₅₉×#480	C₂²	semidirect
64. C₅₉×#477	C₂²	semidirect
65. C₅₉×#477	C₂²	semidirect
66. C₅₉×#477	C₂²	semidirect
67. C₅₉×#474	C₂²	semidirect
68. C₅₉×#474	C₂²	semidirect
69. C₅₉×#474	C₂²	semidirect
71. C₅₉×#468	C₂²	semidirect
72. C₅₉×#467	C₂²	semidirect
74. C₅₉×#466	C₂²	semidirect
75. C₅₉×#466	C₂²	semidirect
76. C₅₉×#464	C₂²	semidirect
77. C₅₉×#464	C₂²	semidirect
78. C₅₉×#464	C₂²	semidirect
79. C₅₉×#464	C₂²	semidirect
80. C₅₉×#464	C₂²	semidirect
81. C₅₉×#464	C₂²	semidirect
82. C₅₉×#463	C₂²	semidirect
83. C₅₉×#463	C₂²	semidirect
84. C₅₉×#463	C₂²	semidirect
85. C₅₉×#463	C₂²	semidirect
87. C₅₉×#460	C₂²	semidirect
88. C₅₉×#460	C₂²	semidirect
90. C₅₉×#459	C₂²	semidirect
91. C₅₉×#459	C₂²	semidirect
92. C₅₉×#452	C₂²	semidirect
93. C₅₉×#452	C₂²	semidirect
94. C₅₉×#450	C₂²	semidirect
96. C₅₉×#449	C₂²	semidirect
97. C₅₉×#448	C₂²	semidirect
98. C₅₉×#448	C₂²	semidirect
100. C₅₉×#447	C₂²	semidirect
101. C₅₉×#446	C₂²	semidirect
102. C₅₉×#440	C₂²	semidirect
103. C₅₉×#440	C₂²	semidirect
104. C₅₉×#440	C₂²	semidirect
105. C₅₉×#440	C₂²	semidirect
106. C₄×Q₁₆×C₅₉	C₂²	semidirect
107. C₄×D₈×C₅₉	C₂²	semidirect
108. C₅₉×#435	C₂²	semidirect
109. C₅₉×#435	C₂²	semidirect
110. C₈×D₄×C₅₉	C₂²	semidirect
111. C₅₉×#433	C₂²	semidirect
112. C₅₉×#432	C₂²	semidirect
113. C₅₉×#424	C₂²	semidirect
114. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
115. C₅₉×#417	C₂²	semidirect
116. C₂×#103×C₅₉	C₂²	semidirect
118. C₂×#102×C₅₉	C₂²	semidirect
502. #62022	C₅₉	direct (N × H)
538. #3558	C₂×C₅₉	semidirect
539. #3522	C₂×C₅₉	semidirect
540. #3403	C₂×C₅₉	semidirect
541. #3375	C₂×C₅₉	semidirect
542. #3314	C₂×C₅₉	semidirect
543. #3308	C₂×C₅₉	semidirect
544. #3294	C₂×C₅₉	semidirect
545. #3285	C₂×C₅₉	semidirect
546. #3268	C₂×C₅₉	semidirect
547. #3265	C₂×C₅₉	semidirect
548. #3262	C₂×C₅₉	semidirect
549. #3245	C₂×C₅₉	semidirect
550. #3224	C₂×C₅₉	semidirect
551. #3213	C₂×C₅₉	semidirect
552. #3124	C₂×C₅₉	semidirect
553. #3112	C₂×C₅₉	semidirect
554. #3045	C₂×C₅₉	semidirect
555. C₂×#464	C₂×C₅₉	semidirect
556. #2992	C₂×C₅₉	semidirect
565. C₂×AGL(1,ℤ/8)	C₂²×C₅₉	semidirect
566. C₂×#135	C₂²×C₅₉	semidirect
567. C₂²×Q₁₆	C₂²×C₅₉	semidirect
573. #559	C₂²×C₅₉	semidirect
574. Q₈²	C₂²×C₅₉	semidirect
576. #554	C₂²×C₅₉	semidirect
577. #550	C₂²×C₅₉	semidirect
579. #548	C₂²×C₅₉	semidirect
581. #547	C₂²×C₅₉	semidirect
587. #542	C₂²×C₅₉	semidirect
594. #532	C₂²×C₅₉	semidirect
598. #520	C₂²×C₅₉	semidirect
599. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
601. #496	C₂²×C₅₉	semidirect
602. #495	C₂²×C₅₉	semidirect
603. #489	C₂²×C₅₉	semidirect
604. #489	C₂²×C₅₉	semidirect
606. #484	C₂²×C₅₉	semidirect
608. #480	C₂²×C₅₉	semidirect
609. #477	C₂²×C₅₉	semidirect
610. #477	C₂²×C₅₉	semidirect
611. #477	C₂²×C₅₉	semidirect
612. #474	C₂²×C₅₉	semidirect
613. #474	C₂²×C₅₉	semidirect
614. #474	C₂²×C₅₉	semidirect
616. #468	C₂²×C₅₉	semidirect
617. #467	C₂²×C₅₉	semidirect
619. #466	C₂²×C₅₉	semidirect
620. #466	C₂²×C₅₉	semidirect
621. #464	C₂²×C₅₉	semidirect
622. #464	C₂²×C₅₉	semidirect
623. #464	C₂²×C₅₉	semidirect
624. #464	C₂²×C₅₉	semidirect
625. #464	C₂²×C₅₉	semidirect
626. #464	C₂²×C₅₉	semidirect
627. #463	C₂²×C₅₉	semidirect
628. #463	C₂²×C₅₉	semidirect
629. #463	C₂²×C₅₉	semidirect
630. #463	C₂²×C₅₉	semidirect
632. #460	C₂²×C₅₉	semidirect
633. #460	C₂²×C₅₉	semidirect
635. #459	C₂²×C₅₉	semidirect
636. #459	C₂²×C₅₉	semidirect
637. #452	C₂²×C₅₉	semidirect
638. #452	C₂²×C₅₉	semidirect
639. #450	C₂²×C₅₉	semidirect
641. #449	C₂²×C₅₉	semidirect
642. #448	C₂²×C₅₉	semidirect
643. #448	C₂²×C₅₉	semidirect
645. #447	C₂²×C₅₉	semidirect
646. #446	C₂²×C₅₉	semidirect
647. #440	C₂²×C₅₉	semidirect
648. #440	C₂²×C₅₉	semidirect
649. #440	C₂²×C₅₉	semidirect
650. #440	C₂²×C₅₉	semidirect
651. C₄×Q₁₆	C₂²×C₅₉	semidirect
652. C₄×D₈	C₂²×C₅₉	semidirect
653. #435	C₂²×C₅₉	semidirect
654. #435	C₂²×C₅₉	semidirect
655. C₈×D₄	C₂²×C₅₉	semidirect
656. #433	C₂²×C₅₉	semidirect
657. #432	C₂²×C₅₉	semidirect
658. #424	C₂²×C₅₉	semidirect
659. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
660. #417	C₂²×C₅₉	semidirect
661. C₂×#103	C₂²×C₅₉	semidirect
663. C₂×#102	C₂²×C₅₉	semidirect
664. C₅₉	#62022	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×#3558	2
C₅₉×#3522	2
C₅₉×#3403	2
C₅₉×#3375	2
C₅₉×#3314	2
C₅₉×#3308	2
C₅₉×#3294	2
C₅₉×#3285	2
C₅₉×#3268	2
C₅₉×#3265	2
C₅₉×#3262	2
C₅₉×#3245	2
C₅₉×#3224	2
C₅₉×#3213	2
C₅₉×#3124	2
C₅₉×#3112	2
C₅₉×#3045	2
C₂×C₅₉×#464	2
C₅₉×#2992	2
#62022	59

Subgroups — C59×#62022 #28474131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62022 #28474131