Subgroups — C₅₉×#62259 #28474368

Order 15104.

2130 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3354	C₂	1	2	yes	maximal, complemented
4	C₅₉×#3353	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3332	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3330	C₂	1	2	yes	maximal, complemented
7	C₅₉×#3325	C₂	1	2	yes	maximal, complemented
8	C₅₉×#3324	C₂	1	2	yes	maximal, complemented
9	C₅₉×#3274	C₂	1	2	yes	maximal, complemented
10	C₅₉×#3272	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#3188	C₂	1	4	yes	maximal, complemented
14	C₅₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#3055	C₂	1	4	yes	maximal, complemented
17	C₂×C₅₉×#436	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₅₉	—	2	1	no	—
19	C₂×AGL(1,ℤ/8)×C₅₉	C₂²	1	4	yes	complemented
20	C₂²×M₁₆×C₅₉	C₂²	1	2	yes	complemented
21	C₅₉×#559	—	2	2	no	—
22	C₅₉×#556	C₂²	1	2	yes	complemented
23	C₅₉×#555	C₂²	1	2	yes	complemented
24	C₅₉×#553	—	2	2	no	—
25	C₅₉×#550	C₂²	1	2	yes	complemented
26	C₅₉×#547	C₂²	1	2	yes	—
27	C₅₉×#547	C₂²	1	2	yes	—
28	C₅₉×#547	C₂²	1	2	yes	complemented
29	C₅₉×#546	—	2	2	no	—
30	C₅₉×#546	—	2	2	no	—
31	D₄²×C₅₉	C₂²	1	2	yes	—
32	D₄²×C₅₉	C₂²	1	2	yes	—
33	C₅₉×#538	—	2	2	no	—
34	C₅₉×#537	—	2	1	no	—
35	C₅₉×#535	—	2	1	no	—
36	C₅₉×#534	—	2	2	no	—
37	C₅₉×#533	C₂²	1	1	yes	characteristic, complemented
38	C₅₉×#532	C₂²	1	1	yes	characteristic
39	C₅₉×#532	C₂²	1	1	yes	characteristic
40	C₅₉×#532	C₂²	1	1	yes	characteristic, complemented
41	C₅₉×#525	C₂²	1	4	yes	complemented
42	C₂×#121×C₅₉	C₂²	1	4	yes	—
43	C₅₉×#520	—	2	1	no	—
44	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#500	C₂²	1	1	yes	characteristic, complemented
46	C₅₉×#498	C₂²	1	1	yes	characteristic, complemented
47	C₅₉×#493	C₂²	1	1	yes	characteristic, complemented
48	C₅₉×#492	C₂²	1	1	yes	characteristic, complemented
49	C₅₉×#487	C₂²	1	1	yes	characteristic, complemented
50	C₅₉×#486	C₂²	1	1	yes	characteristic, complemented
51	C₅₉×#486	C₂²	1	1	yes	characteristic, complemented
52	C₅₉×#486	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#484	C₂²	1	4	yes	complemented
54	C₅₉×#482	C₂²	1	4	yes	complemented
55	C₅₉×#482	C₂²	1	4	yes	complemented
56	C₅₉×#481	C₂²	1	4	yes	complemented
57	C₅₉×#476	C₂²	1	2	yes	complemented
58	C₅₉×#475	C₂²	1	2	yes	complemented
59	C₅₉×#474	C₂²	1	2	yes	complemented
60	C₅₉×#474	C₂²	1	2	yes	complemented
61	C₅₉×#469	C₂²	1	4	yes	complemented
62	C₅₉×#469	C₂²	1	4	yes	complemented
63	C₅₉×#468	C₂²	1	4	yes	complemented
64	C₅₉×#468	C₂²	1	4	yes	complemented
65	C₅₉×#466	C₂²	1	2	yes	complemented
66	C₅₉×#466	C₂²	1	4	yes	complemented
67	C₅₉×#466	C₂²	1	2	yes	complemented
68	C₅₉×#465	C₂²	1	2	yes	complemented
69	C₅₉×#465	C₂²	1	4	yes	complemented
70	C₅₉×#465	C₂²	1	2	yes	complemented
71	C₅₉×#461	C₂²	1	2	yes	complemented
72	C₅₉×#460	C₂²	1	2	yes	complemented
73	C₅₉×#459	C₂²	1	2	yes	complemented
74	C₅₉×#459	C₂²	1	2	yes	complemented
75	C₅₉×#450	C₂²	1	4	yes	complemented
76	C₅₉×#449	C₂²	1	4	yes	complemented
77	C₅₉×#449	C₂²	1	4	yes	complemented
78	C₅₉×#447	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
80	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	complemented
81	C₄×D₈×C₅₉	C₂²	1	2	yes	complemented
82	C₄×D₈×C₅₉	C₂²	1	2	yes	complemented
83	C₅₉×#436	C₂²	1	2	yes	complemented
84	C₅₉×#436	C₂²	1	2	yes	complemented
85	C₅₉×#436	C₂²	1	2	yes	complemented
86	C₅₉×#436	C₂²	1	2	yes	complemented
87	C₅₉×#428	C₂²	1	4	yes	complemented
88	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
89	C₅₉×#418	C₂²	1	4	yes	complemented
90	C₅₉×#417	C₂²	1	4	yes	complemented
91	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	complemented
92	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
93	H(5,𝔽₂)×C₅₉	—	4	8	no	—
94	C₂×#41×C₅₉	—	2	2	no	—
95	C₂×#41×C₅₉	—	2	2	no	—
96	C₂×#41×C₅₉	—	2	1	no	—
97	C₂×#41×C₅₉	—	2	1	no	—
98	C₂×#41×C₅₉	—	2	1	no	—
99	C₂×#41×C₅₉	C₂³	1	4	yes	—
100	C₂²×D₄×C₅₉	—	2	4	no	—
101	C₂²×D₄×C₅₉	—	2	2	no	—
102	C₂²×D₄×C₅₉	—	2	2	no	—
103	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
105	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
106	AGL(1,ℤ/8)×C₅₉	—	4	8	no	—
107	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₅₉	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₅₉	C₂³	1	4	yes	—
110	C₂×D₈×C₅₉	C₂³	1	2	yes	—
111	C₂×D₈×C₅₉	C₂³	1	2	yes	—
112	C₂×D₈×C₅₉	C₂³	1	4	yes	—
113	C₂×M₁₆×C₅₉	—	4	4	no	—
114	C₂×M₁₆×C₅₉	C₂³	1	4	yes	—
115	C₂×M₁₆×C₅₉	C₂³	1	4	yes	—
116	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
124	#127×C₅₉	—	2	2	no	—
125	#127×C₅₉	C₂³	1	1	yes	characteristic
126	#127×C₅₉	C₂³	1	1	yes	characteristic
127	#127×C₅₉	C₂³	1	1	yes	characteristic
128	#126×C₅₉	—	2	4	no	—
129	#125×C₅₉	—	2	1	no	—
130	#124×C₅₉	—	2	2	no	—
131	#124×C₅₉	—	2	4	no	—
132	#124×C₅₉	—	2	1	no	—
133	#124×C₅₉	—	2	1	no	—
134	#124×C₅₉	—	2	1	no	—
135	#123×C₅₉	—	2	4	no	—
136	#123×C₅₉	—	2	4	no	—
137	#123×C₅₉	—	2	4	no	—
138	#123×C₅₉	—	2	4	no	—
139	C₂²⋊Q₈×C₅₉	—	2	1	no	—
140	C₂²⋊Q₈×C₅₉	—	2	2	no	—
141	C₂²⋊Q₈×C₅₉	—	2	2	no	—
142	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
143	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
144	#121×C₅₉	—	2	2	no	—
145	#121×C₅₉	—	2	2	no	—
146	#121×C₅₉	—	2	4	no	—
147	#121×C₅₉	—	2	4	no	—
148	#121×C₅₉	—	2	1	no	—
149	#121×C₅₉	—	2	1	no	—
150	#121×C₅₉	—	2	1	no	—
151	#121×C₅₉	—	2	2	no	—
152	#121×C₅₉	—	2	2	no	—
153	#121×C₅₉	—	2	4	no	—
154	#121×C₅₉	C₂³	1	4	yes	—
155	#121×C₅₉	C₂³	1	4	yes	—
156	#121×C₅₉	C₂³	1	4	yes	—
157	#121×C₅₉	C₂³	1	2	yes	—
158	#121×C₅₉	C₂³	1	2	yes	—
159	#121×C₅₉	C₂³	1	2	yes	—
160	#120×C₅₉	—	2	4	no	—
161	#120×C₅₉	—	2	4	no	—
162	#120×C₅₉	—	2	4	no	—
163	C₄×Q₈×C₅₉	—	2	2	no	—
164	C₄×Q₈×C₅₉	—	2	1	no	—
165	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
166	C₄×D₄×C₅₉	—	2	4	no	—
167	C₄×D₄×C₅₉	—	2	4	no	—
168	C₄×D₄×C₅₉	—	2	2	no	—
169	C₄×D₄×C₅₉	—	2	1	no	—
170	C₄×D₄×C₅₉	—	2	1	no	—
171	C₄×D₄×C₅₉	—	2	1	no	—
172	C₄×D₄×C₅₉	D₄	1	2	yes	—
173	C₄×D₄×C₅₉	D₄	1	2	yes	—
174	C₄×D₄×C₅₉	C₂³	1	2	yes	—
175	C₄×D₄×C₅₉	C₂³	1	2	yes	—
176	C₄×D₄×C₅₉	C₂³	1	2	yes	—
177	C₄×D₄×C₅₉	C₂³	1	2	yes	—
178	C₄×D₄×C₅₉	C₂³	1	2	yes	—
179	#117×C₅₉	—	2	1	no	—
180	#117×C₅₉	—	2	2	no	—
181	#117×C₅₉	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
183	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
185	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
186	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
187	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
188	#107×C₅₉	C₂³	1	2	yes	—
189	#107×C₅₉	C₂³	1	4	yes	—
190	#107×C₅₉	C₂³	1	2	yes	—
191	#106×C₅₉	C₂³	1	2	yes	—
192	#106×C₅₉	C₂³	1	4	yes	—
193	#106×C₅₉	C₂³	1	2	yes	—
194	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
195	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
196	#103×C₅₉	C₂³	1	2	yes	—
197	#103×C₅₉	C₂³	1	4	yes	—
198	#103×C₅₉	C₂³	1	2	yes	—
199	#102×C₅₉	C₂³	1	2	yes	—
200	#102×C₅₉	C₂³	1	4	yes	—
201	#102×C₅₉	C₂³	1	2	yes	—
202	#102×C₅₉	C₂³	1	2	yes	—
203	#102×C₅₉	C₂³	1	4	yes	—
204	#102×C₅₉	C₂³	1	4	yes	—
205	#102×C₅₉	C₂³	1	2	yes	—
206	#102×C₅₉	C₂³	1	2	yes	—
207	#102×C₅₉	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
209	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
210	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
213	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
214	C₂⁴×C₅₉	—	2	4	no	—
215	C₂⁴×C₅₉	C₂×D₄	1	2	yes	—
216	#41×C₅₉	—	4	4	no	—
217	#41×C₅₉	—	4	4	no	—
218	#41×C₅₉	—	4	8	no	—
219	#41×C₅₉	—	4	8	no	—
220	#41×C₅₉	—	4	4	no	—
221	#41×C₅₉	—	4	4	no	—
222	#41×C₅₉	—	4	4	no	—
223	C₂×Q₈×C₅₉	—	2	1	no	—
224	C₂×Q₈×C₅₉	—	2	1	no	—
225	C₂×Q₈×C₅₉	—	2	1	no	—
226	C₂×Q₈×C₅₉	—	2	1	no	—
227	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
228	C₂×D₄×C₅₉	—	2	2	no	—
229	C₂×D₄×C₅₉	—	2	4	no	—
230	C₂×D₄×C₅₉	—	2	4	no	—
231	C₂×D₄×C₅₉	—	2	2	no	—
232	C₂×D₄×C₅₉	—	2	2	no	—
233	C₂×D₄×C₅₉	—	2	4	no	—
234	C₂×D₄×C₅₉	—	2	4	no	—
235	C₂×D₄×C₅₉	—	2	4	no	—
236	C₂×D₄×C₅₉	—	2	1	no	—
237	C₂×D₄×C₅₉	—	2	1	no	—
238	C₂×D₄×C₅₉	—	2	1	no	—
239	C₂×D₄×C₅₉	—	2	1	no	—
240	C₂×D₄×C₅₉	—	2	1	no	—
241	C₂×D₄×C₅₉	—	2	1	no	—
242	C₂×D₄×C₅₉	—	2	4	no	—
243	C₂×D₄×C₅₉	—	4	4	no	—
244	C₂×D₄×C₅₉	—	4	4	no	—
245	C₂×D₄×C₅₉	—	4	8	no	—
246	C₂×D₄×C₅₉	—	4	8	no	—
247	C₂×D₄×C₅₉	—	4	16	no	—
248	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
251	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
252	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₅₉	—	2	4	no	—
254	C₂²×C₄×C₅₉	—	2	2	no	—
255	C₂²×C₄×C₅₉	—	2	2	no	—
256	C₂²×C₄×C₅₉	—	2	2	no	—
257	C₂²×C₄×C₅₉	—	2	4	no	—
258	C₂²×C₄×C₅₉	—	4	2	no	—
259	C₂²×C₄×C₅₉	—	4	2	no	—
260	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
262	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
266	SD₁₆×C₅₉	—	2	4	no	—
267	SD₁₆×C₅₉	—	4	2	no	—
268	SD₁₆×C₅₉	—	4	4	no	—
269	D₈×C₅₉	—	2	4	no	—
270	D₈×C₅₉	—	4	2	no	—
271	D₈×C₅₉	—	4	4	no	—
272	M₁₆×C₅₉	—	2	8	no	—
273	M₁₆×C₅₉	—	4	4	no	—
274	C₂×C₈×C₅₉	—	2	2	no	—
275	C₂×C₈×C₅₉	—	4	1	no	—
276	C₂×C₈×C₅₉	—	4	2	no	—
277	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
279	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
280	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
281	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
282	C₄⋊C₄×C₅₉	—	2	1	no	—
283	C₄⋊C₄×C₅₉	—	2	4	no	—
284	C₄⋊C₄×C₅₉	—	2	4	no	—
285	C₄⋊C₄×C₅₉	—	2	1	no	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	2	1	no	—
288	C₄⋊C₄×C₅₉	—	2	1	no	—
289	C₄⋊C₄×C₅₉	—	2	1	no	—
290	C₄⋊C₄×C₅₉	—	2	1	no	—
291	C₄⋊C₄×C₅₉	—	2	2	no	—
292	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
298	C₂²⋊C₄×C₅₉	—	2	2	no	—
299	C₂²⋊C₄×C₅₉	—	2	4	no	—
300	C₂²⋊C₄×C₅₉	—	2	4	no	—
301	C₂²⋊C₄×C₅₉	—	2	2	no	—
302	C₂²⋊C₄×C₅₉	—	2	2	no	—
303	C₂²⋊C₄×C₅₉	—	2	4	no	—
304	C₂²⋊C₄×C₅₉	—	2	4	no	—
305	C₂²⋊C₄×C₅₉	—	2	4	no	—
306	C₂²⋊C₄×C₅₉	—	2	2	no	—
307	C₂²⋊C₄×C₅₉	—	2	2	no	—
308	C₂²⋊C₄×C₅₉	—	2	2	no	—
309	C₂²⋊C₄×C₅₉	—	2	2	no	—
310	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
311	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
312	C₄²×C₅₉	—	2	4	no	—
313	C₄²×C₅₉	—	2	2	no	—
314	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
317	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
318	C₂³×C₅₉	—	2	4	no	—
319	C₂³×C₅₉	—	2	2	no	—
320	C₂³×C₅₉	—	2	2	no	—
321	C₂³×C₅₉	—	2	2	no	—
322	C₂³×C₅₉	—	4	2	no	—
323	C₂³×C₅₉	—	4	2	no	—
324	C₂³×C₅₉	—	4	8	no	—
325	C₂³×C₅₉	—	8	4	no	—
326	C₂³×C₅₉	—	8	4	no	—
327	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
328	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
329	Q₈×C₅₉	—	2	2	no	—
330	Q₈×C₅₉	—	2	2	no	—
331	Q₈×C₅₉	—	4	2	no	—
332	Q₈×C₅₉	—	4	2	no	—
333	Q₈×C₅₉	—	4	2	no	—
334	Q₈×C₅₉	—	8	1	no	—
335	D₄×C₅₉	—	2	4	no	—
336	D₄×C₅₉	—	2	4	no	—
337	D₄×C₅₉	—	2	2	no	—
338	D₄×C₅₉	—	2	2	no	—
339	D₄×C₅₉	—	2	2	no	—
340	D₄×C₅₉	—	2	2	no	—
341	D₄×C₅₉	—	2	2	no	—
342	D₄×C₅₉	—	2	2	no	—
343	D₄×C₅₉	—	4	8	no	—
344	D₄×C₅₉	—	4	8	no	—
345	D₄×C₅₉	—	4	4	no	—
346	D₄×C₅₉	—	4	4	no	—
347	D₄×C₅₉	—	4	4	no	—
348	D₄×C₅₉	—	4	2	no	—
349	D₄×C₅₉	—	4	2	no	—
350	D₄×C₅₉	—	4	2	no	—
351	D₄×C₅₉	—	8	1	no	—
352	D₄×C₅₉	—	8	1	no	—
353	D₄×C₅₉	—	8	1	no	—
354	D₄×C₅₉	—	8	4	no	—
355	D₄×C₅₉	—	8	4	no	—
356	D₄×C₅₉	—	8	4	no	—
357	C₂×C₄×C₅₉	—	2	1	no	—
358	C₂×C₄×C₅₉	—	2	4	no	—
359	C₂×C₄×C₅₉	—	2	1	no	—
360	C₂×C₄×C₅₉	—	2	4	no	—
361	C₂×C₄×C₅₉	—	2	2	no	—
362	C₂×C₄×C₅₉	—	2	2	no	—
363	C₂×C₄×C₅₉	—	2	2	no	—
364	C₂×C₄×C₅₉	—	2	2	no	—
365	C₂×C₄×C₅₉	—	2	2	no	—
366	C₂×C₄×C₅₉	—	4	4	no	—
367	C₂×C₄×C₅₉	—	4	2	no	—
368	C₂×C₄×C₅₉	—	4	1	no	—
369	C₂×C₄×C₅₉	—	4	8	no	—
370	C₂×C₄×C₅₉	—	4	4	no	—
371	C₂×C₄×C₅₉	—	4	4	no	—
372	C₂×C₄×C₅₉	—	4	4	no	—
373	C₂×C₄×C₅₉	—	8	4	no	—
374	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	4	yes	complemented
375	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
376	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
382	C₈×C₅₉	—	2	1	no	—
383	C₈×C₅₉	—	2	4	no	—
384	C₈×C₅₉	—	2	1	no	—
385	C₈×C₅₉	—	2	1	no	—
386	C₈×C₅₉	H(5,𝔽₂)	1	2	yes	complemented
387	#62259	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂²×C₅₉	—	2	1	no	—
389	C₂²×C₅₉	—	2	1	no	—
390	C₂²×C₅₉	—	2	4	no	—
391	C₂²×C₅₉	—	2	4	no	—
392	C₂²×C₅₉	—	2	4	no	—
393	C₂²×C₅₉	—	4	2	no	—
394	C₂²×C₅₉	—	4	2	no	—
395	C₂²×C₅₉	—	4	2	no	—
396	C₂²×C₅₉	—	4	2	no	—
397	C₂²×C₅₉	—	4	2	no	—
398	C₂²×C₅₉	—	4	2	no	—
399	C₂²×C₅₉	—	4	2	no	—
400	C₂²×C₅₉	—	4	2	no	—
401	C₂²×C₅₉	—	4	2	no	—
402	C₂²×C₅₉	—	8	4	no	—
403	C₂²×C₅₉	—	16	8	no	—
404	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
405	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
406	C₄×C₅₉	—	2	1	no	—
407	C₄×C₅₉	—	2	1	no	—
408	C₄×C₅₉	—	2	1	no	—
409	C₄×C₅₉	—	2	4	no	—
410	C₄×C₅₉	—	4	2	no	—
411	C₄×C₅₉	—	4	2	no	—
412	C₄×C₅₉	—	4	2	no	—
413	C₄×C₅₉	—	4	2	no	—
414	C₄×C₅₉	—	4	2	no	—
415	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
416	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
417	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₄×C₅₉	#585	1	1	yes	characteristic
419	#3506	C₂×C₅₉	1	1	yes	characteristic, complemented
420	#3496	C₂×C₅₉	1	1	yes	characteristic, complemented
421	#3354	C₂×C₅₉	1	2	yes	complemented
422	#3353	C₂×C₅₉	1	2	yes	complemented
423	#3332	C₂×C₅₉	1	2	yes	complemented
424	#3330	C₂×C₅₉	1	2	yes	complemented
425	#3325	C₂×C₅₉	1	2	yes	complemented
426	#3324	C₂×C₅₉	1	2	yes	complemented
427	#3274	C₂×C₅₉	1	2	yes	complemented
428	#3272	C₂×C₅₉	1	2	yes	complemented
429	#3246	C₂×C₅₉	1	1	yes	characteristic, complemented
430	#3245	C₂×C₅₉	1	1	yes	characteristic, complemented
431	#3188	C₂×C₅₉	1	4	yes	complemented
432	#3169	C₂×C₅₉	1	1	yes	characteristic, complemented
433	#3167	C₂×C₅₉	1	1	yes	characteristic, complemented
434	#3055	C₂×C₅₉	1	4	yes	complemented
435	C₂×#436	C₂×C₅₉	1	1	yes	characteristic, complemented
436	C₂×C₅₉	—	2	2	no	—
437	C₂×C₅₉	—	4	4	no	—
438	C₂×C₅₉	—	8	2	no	—
439	C₂×C₅₉	—	8	2	no	—
440	C₂×C₅₉	—	8	2	no	—
441	C₂×C₅₉	#3496	1	1	yes	characteristic
442	C₂×C₅₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
443	C₂×C₅₉	#3584	1	1	yes	characteristic
444	C₂×H(5,𝔽₂)	—	2	1	no	—
445	C₂×AGL(1,ℤ/8)	C₂²×C₅₉	1	4	yes	complemented
446	C₂²×M₁₆	C₂²×C₅₉	1	2	yes	complemented
447	#559	—	2	2	no	—
448	#556	C₂²×C₅₉	1	2	yes	complemented
449	#555	C₂²×C₅₉	1	2	yes	complemented
450	#553	—	2	2	no	—
451	#550	C₂²×C₅₉	1	2	yes	complemented
452	#547	C₂²×C₅₉	1	2	yes	—
453	#547	C₂²×C₅₉	1	2	yes	—
454	#547	C₂²×C₅₉	1	2	yes	complemented
455	#546	—	2	2	no	—
456	#546	—	2	2	no	—
457	D₄²	C₂²×C₅₉	1	2	yes	—
458	D₄²	C₂²×C₅₉	1	2	yes	—
459	#538	—	2	2	no	—
460	#537	—	2	1	no	—
461	#535	—	2	1	no	—
462	#534	—	2	2	no	—
463	#533	C₂²×C₅₉	1	1	yes	characteristic, complemented
464	#532	C₂²×C₅₉	1	1	yes	characteristic
465	#532	C₂²×C₅₉	1	1	yes	characteristic
466	#532	C₂²×C₅₉	1	1	yes	characteristic, complemented
467	#525	C₂²×C₅₉	1	4	yes	complemented
468	C₂×#121	C₂²×C₅₉	1	4	yes	—
469	#520	—	2	1	no	—
470	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
471	#500	C₂²×C₅₉	1	1	yes	characteristic, complemented
472	#498	C₂²×C₅₉	1	1	yes	characteristic, complemented
473	#493	C₂²×C₅₉	1	1	yes	characteristic, complemented
474	#492	C₂²×C₅₉	1	1	yes	characteristic, complemented
475	#487	C₂²×C₅₉	1	1	yes	characteristic, complemented
476	#486	C₂²×C₅₉	1	1	yes	characteristic, complemented
477	#486	C₂²×C₅₉	1	1	yes	characteristic, complemented
478	#486	C₂²×C₅₉	1	1	yes	characteristic, complemented
479	#484	C₂²×C₅₉	1	4	yes	complemented
480	#482	C₂²×C₅₉	1	4	yes	complemented
481	#482	C₂²×C₅₉	1	4	yes	complemented
482	#481	C₂²×C₅₉	1	4	yes	complemented
483	#476	C₂²×C₅₉	1	2	yes	complemented
484	#475	C₂²×C₅₉	1	2	yes	complemented
485	#474	C₂²×C₅₉	1	2	yes	complemented
486	#474	C₂²×C₅₉	1	2	yes	complemented
487	#469	C₂²×C₅₉	1	4	yes	complemented
488	#469	C₂²×C₅₉	1	4	yes	complemented
489	#468	C₂²×C₅₉	1	4	yes	complemented
490	#468	C₂²×C₅₉	1	4	yes	complemented
491	#466	C₂²×C₅₉	1	2	yes	complemented
492	#466	C₂²×C₅₉	1	2	yes	complemented
493	#466	C₂²×C₅₉	1	4	yes	complemented
494	#465	C₂²×C₅₉	1	2	yes	complemented
495	#465	C₂²×C₅₉	1	2	yes	complemented
496	#465	C₂²×C₅₉	1	4	yes	complemented
497	#461	C₂²×C₅₉	1	2	yes	complemented
498	#460	C₂²×C₅₉	1	2	yes	complemented
499	#459	C₂²×C₅₉	1	2	yes	complemented
500	#459	C₂²×C₅₉	1	2	yes	complemented
501	#450	C₂²×C₅₉	1	4	yes	complemented
502	#449	C₂²×C₅₉	1	4	yes	complemented
503	#449	C₂²×C₅₉	1	4	yes	complemented
504	#447	C₂²×C₅₉	1	4	yes	complemented
505	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
506	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	complemented
507	C₄×D₈	C₂²×C₅₉	1	2	yes	complemented
508	C₄×D₈	C₂²×C₅₉	1	2	yes	complemented
509	#436	C₂²×C₅₉	1	2	yes	complemented
510	#436	C₂²×C₅₉	1	2	yes	complemented
511	#436	C₂²×C₅₉	1	2	yes	complemented
512	#436	C₂²×C₅₉	1	2	yes	complemented
513	#428	C₂²×C₅₉	1	4	yes	complemented
514	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
515	#418	C₂²×C₅₉	1	4	yes	complemented
516	#417	C₂²×C₅₉	1	4	yes	complemented
517	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	complemented
518	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
519	C₅₉	#62259	1	1	yes	characteristic, direct product factor, Sylow
520	H(5,𝔽₂)	—	4	8	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	1	no	—
526	C₂×#41	C₂³×C₅₉	1	4	yes	—
527	C₂²×D₄	—	2	4	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
532	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
533	AGL(1,ℤ/8)	—	4	8	no	—
534	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₅₉	1	4	yes	—
536	C₂×SD₁₆	C₂³×C₅₉	1	2	yes	—
537	C₂×D₈	C₂³×C₅₉	1	2	yes	—
538	C₂×D₈	C₂³×C₅₉	1	4	yes	—
539	C₂×D₈	C₂³×C₅₉	1	2	yes	—
540	C₂×M₁₆	—	4	4	no	—
541	C₂×M₁₆	C₂³×C₅₉	1	4	yes	—
542	C₂×M₁₆	C₂³×C₅₉	1	4	yes	—
543	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
544	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
545	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
551	#127	—	2	2	no	—
552	#127	C₂³×C₅₉	1	1	yes	characteristic
553	#127	C₂³×C₅₉	1	1	yes	characteristic
554	#127	C₂³×C₅₉	1	1	yes	characteristic
555	#126	—	2	4	no	—
556	#125	—	2	1	no	—
557	#124	—	2	2	no	—
558	#124	—	2	4	no	—
559	#124	—	2	1	no	—
560	#124	—	2	1	no	—
561	#124	—	2	1	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	#123	—	2	4	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
570	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	4	no	—
574	#121	—	2	4	no	—
575	#121	—	2	1	no	—
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	4	no	—
581	#121	C₂³×C₅₉	1	2	yes	—
582	#121	C₂³×C₅₉	1	2	yes	—
583	#121	C₂³×C₅₉	1	4	yes	—
584	#121	C₂³×C₅₉	1	4	yes	—
585	#121	C₂³×C₅₉	1	2	yes	—
586	#121	C₂³×C₅₉	1	4	yes	—
587	#120	—	2	4	no	—
588	#120	—	2	4	no	—
589	#120	—	2	4	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
593	C₄×D₄	—	2	4	no	—
594	C₄×D₄	—	2	4	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	D₄×C₅₉	1	2	yes	—
600	C₄×D₄	D₄×C₅₉	1	2	yes	—
601	C₄×D₄	C₂³×C₅₉	1	2	yes	—
602	C₄×D₄	C₂³×C₅₉	1	2	yes	—
603	C₄×D₄	C₂³×C₅₉	1	2	yes	—
604	C₄×D₄	C₂³×C₅₉	1	2	yes	—
605	C₄×D₄	C₂³×C₅₉	1	2	yes	—
606	#117	—	2	1	no	—
607	#117	—	2	2	no	—
608	#117	C₂³×C₅₉	1	4	yes	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
612	C₂×C₂²⋊C₄	—	2	4	no	—
613	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
614	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
615	#107	C₂³×C₅₉	1	2	yes	—
616	#107	C₂³×C₅₉	1	4	yes	—
617	#107	C₂³×C₅₉	1	2	yes	—
618	#106	C₂³×C₅₉	1	2	yes	—
619	#106	C₂³×C₅₉	1	4	yes	—
620	#106	C₂³×C₅₉	1	2	yes	—
621	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
622	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
623	#103	C₂³×C₅₉	1	2	yes	—
624	#103	C₂³×C₅₉	1	4	yes	—
625	#103	C₂³×C₅₉	1	2	yes	—
626	#102	C₂³×C₅₉	1	2	yes	—
627	#102	C₂³×C₅₉	1	4	yes	—
628	#102	C₂³×C₅₉	1	2	yes	—
629	#102	C₂³×C₅₉	1	2	yes	—
630	#102	C₂³×C₅₉	1	4	yes	—
631	#102	C₂³×C₅₉	1	4	yes	—
632	#102	C₂³×C₅₉	1	2	yes	—
633	#102	C₂³×C₅₉	1	2	yes	—
634	#102	C₂³×C₅₉	1	2	yes	—
635	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
636	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
637	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
638	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
639	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
640	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
641	C₂⁴	—	2	4	no	—
642	C₂⁴	C₂×D₄×C₅₉	1	2	yes	—
643	#41	—	4	4	no	—
644	#41	—	4	4	no	—
645	#41	—	4	8	no	—
646	#41	—	4	8	no	—
647	#41	—	4	4	no	—
648	#41	—	4	4	no	—
649	#41	—	4	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	8	no	—
674	C₂×D₄	—	4	16	no	—
675	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
676	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
677	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
678	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
679	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
689	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
690	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
693	SD₁₆	—	2	4	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	2	no	—
696	D₈	—	2	4	no	—
697	D₈	—	4	4	no	—
698	D₈	—	4	2	no	—
699	M₁₆	—	2	8	no	—
700	M₁₆	—	4	4	no	—
701	C₂×C₈	—	2	2	no	—
702	C₂×C₈	—	4	2	no	—
703	C₂×C₈	—	4	1	no	—
704	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
705	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
706	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
707	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
708	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
738	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
743	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
744	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
745	C₂³	—	2	4	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	8	no	—
752	C₂³	—	8	4	no	—
753	C₂³	—	8	4	no	—
754	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
755	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
756	Q₈	—	2	2	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	4	2	no	—
760	Q₈	—	4	2	no	—
761	Q₈	—	8	1	no	—
762	D₄	—	2	4	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	4	8	no	—
771	D₄	—	4	8	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	4	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	8	1	no	—
779	D₄	—	8	1	no	—
780	D₄	—	8	1	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	4	yes	complemented
802	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
803	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
808	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
809	C₈	—	2	1	no	—
810	C₈	—	2	4	no	—
811	C₈	—	2	1	no	—
812	C₈	—	2	1	no	—
813	C₈	H(5,𝔽₂)×C₅₉	1	2	yes	complemented
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	8	4	no	—
829	C₂²	—	16	8	no	—
830	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
831	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	4	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
842	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
843	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
844	C₄	C₅₉×#585	1	1	yes	characteristic
845	C₂	—	2	2	no	—
846	C₂	—	4	4	no	—
847	C₂	—	8	2	no	—
848	C₂	—	8	2	no	—
849	C₂	—	8	2	no	—
850	C₂	C₅₉×#3496	1	1	yes	characteristic
851	C₂	C₂²×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
852	C₂	C₅₉×#3584	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 ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3506	C₂	semidirect
2. C₅₉×#3496	C₂	semidirect
3. C₅₉×#3354	C₂	semidirect
4. C₅₉×#3353	C₂	semidirect
5. C₅₉×#3332	C₂	semidirect
6. C₅₉×#3330	C₂	semidirect
7. C₅₉×#3325	C₂	semidirect
8. C₅₉×#3324	C₂	semidirect
9. C₅₉×#3274	C₂	semidirect
10. C₅₉×#3272	C₂	semidirect
11. C₅₉×#3246	C₂	semidirect
12. C₅₉×#3245	C₂	semidirect
13. C₅₉×#3188	C₂	semidirect
14. C₅₉×#3169	C₂	semidirect
15. C₅₉×#3167	C₂	semidirect
16. C₅₉×#3055	C₂	semidirect
17. C₂×C₅₉×#436	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₅₉	C₂²	semidirect
20. C₂²×M₁₆×C₅₉	C₂²	semidirect
22. C₅₉×#556	C₂²	semidirect
23. C₅₉×#555	C₂²	semidirect
25. C₅₉×#550	C₂²	semidirect
28. C₅₉×#547	C₂²	semidirect
37. C₅₉×#533	C₂²	semidirect
40. C₅₉×#532	C₂²	semidirect
41. C₅₉×#525	C₂²	semidirect
45. C₅₉×#500	C₂²	semidirect
46. C₅₉×#498	C₂²	semidirect
47. C₅₉×#493	C₂²	semidirect
48. C₅₉×#492	C₂²	semidirect
49. C₅₉×#487	C₂²	semidirect
50. C₅₉×#486	C₂²	semidirect
51. C₅₉×#486	C₂²	semidirect
52. C₅₉×#486	C₂²	semidirect
53. C₅₉×#484	C₂²	semidirect
54. C₅₉×#482	C₂²	semidirect
55. C₅₉×#482	C₂²	semidirect
56. C₅₉×#481	C₂²	semidirect
57. C₅₉×#476	C₂²	semidirect
58. C₅₉×#475	C₂²	semidirect
59. C₅₉×#474	C₂²	semidirect
60. C₅₉×#474	C₂²	semidirect
61. C₅₉×#469	C₂²	semidirect
62. C₅₉×#469	C₂²	semidirect
63. C₅₉×#468	C₂²	semidirect
64. C₅₉×#468	C₂²	semidirect
65. C₅₉×#466	C₂²	semidirect
66. C₅₉×#466	C₂²	semidirect
67. C₅₉×#466	C₂²	semidirect
68. C₅₉×#465	C₂²	semidirect
69. C₅₉×#465	C₂²	semidirect
70. C₅₉×#465	C₂²	semidirect
71. C₅₉×#461	C₂²	semidirect
72. C₅₉×#460	C₂²	semidirect
73. C₅₉×#459	C₂²	semidirect
74. C₅₉×#459	C₂²	semidirect
75. C₅₉×#450	C₂²	semidirect
76. C₅₉×#449	C₂²	semidirect
77. C₅₉×#449	C₂²	semidirect
78. C₅₉×#447	C₂²	semidirect
79. C₄×SD₁₆×C₅₉	C₂²	semidirect
80. C₄×SD₁₆×C₅₉	C₂²	semidirect
81. C₄×D₈×C₅₉	C₂²	semidirect
82. C₄×D₈×C₅₉	C₂²	semidirect
83. C₅₉×#436	C₂²	semidirect
84. C₅₉×#436	C₂²	semidirect
85. C₅₉×#436	C₂²	semidirect
86. C₅₉×#436	C₂²	semidirect
87. C₅₉×#428	C₂²	semidirect
88. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
89. C₅₉×#418	C₂²	semidirect
90. C₅₉×#417	C₂²	semidirect
91. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
92. C₂×C₄×C₈×C₅₉	C₂²	semidirect
374. C₂×C₄×C₅₉	AGL(1,ℤ/8)	semidirect
386. C₈×C₅₉	H(5,𝔽₂)	semidirect
387. #62259	C₅₉	direct (N × H)
419. #3506	C₂×C₅₉	semidirect
420. #3496	C₂×C₅₉	semidirect
421. #3354	C₂×C₅₉	semidirect
422. #3353	C₂×C₅₉	semidirect
423. #3332	C₂×C₅₉	semidirect
424. #3330	C₂×C₅₉	semidirect
425. #3325	C₂×C₅₉	semidirect
426. #3324	C₂×C₅₉	semidirect
427. #3274	C₂×C₅₉	semidirect
428. #3272	C₂×C₅₉	semidirect
429. #3246	C₂×C₅₉	semidirect
430. #3245	C₂×C₅₉	semidirect
431. #3188	C₂×C₅₉	semidirect
432. #3169	C₂×C₅₉	semidirect
433. #3167	C₂×C₅₉	semidirect
434. #3055	C₂×C₅₉	semidirect
435. C₂×#436	C₂×C₅₉	semidirect
445. C₂×AGL(1,ℤ/8)	C₂²×C₅₉	semidirect
446. C₂²×M₁₆	C₂²×C₅₉	semidirect
448. #556	C₂²×C₅₉	semidirect
449. #555	C₂²×C₅₉	semidirect
451. #550	C₂²×C₅₉	semidirect
454. #547	C₂²×C₅₉	semidirect
463. #533	C₂²×C₅₉	semidirect
466. #532	C₂²×C₅₉	semidirect
467. #525	C₂²×C₅₉	semidirect
471. #500	C₂²×C₅₉	semidirect
472. #498	C₂²×C₅₉	semidirect
473. #493	C₂²×C₅₉	semidirect
474. #492	C₂²×C₅₉	semidirect
475. #487	C₂²×C₅₉	semidirect
476. #486	C₂²×C₅₉	semidirect
477. #486	C₂²×C₅₉	semidirect
478. #486	C₂²×C₅₉	semidirect
479. #484	C₂²×C₅₉	semidirect
480. #482	C₂²×C₅₉	semidirect
481. #482	C₂²×C₅₉	semidirect
482. #481	C₂²×C₅₉	semidirect
483. #476	C₂²×C₅₉	semidirect
484. #475	C₂²×C₅₉	semidirect
485. #474	C₂²×C₅₉	semidirect
486. #474	C₂²×C₅₉	semidirect
487. #469	C₂²×C₅₉	semidirect
488. #469	C₂²×C₅₉	semidirect
489. #468	C₂²×C₅₉	semidirect
490. #468	C₂²×C₅₉	semidirect
491. #466	C₂²×C₅₉	semidirect
492. #466	C₂²×C₅₉	semidirect
493. #466	C₂²×C₅₉	semidirect
494. #465	C₂²×C₅₉	semidirect
495. #465	C₂²×C₅₉	semidirect
496. #465	C₂²×C₅₉	semidirect
497. #461	C₂²×C₅₉	semidirect
498. #460	C₂²×C₅₉	semidirect
499. #459	C₂²×C₅₉	semidirect
500. #459	C₂²×C₅₉	semidirect
501. #450	C₂²×C₅₉	semidirect
502. #449	C₂²×C₅₉	semidirect
503. #449	C₂²×C₅₉	semidirect
504. #447	C₂²×C₅₉	semidirect
505. C₄×SD₁₆	C₂²×C₅₉	semidirect
506. C₄×SD₁₆	C₂²×C₅₉	semidirect
507. C₄×D₈	C₂²×C₅₉	semidirect
508. C₄×D₈	C₂²×C₅₉	semidirect
509. #436	C₂²×C₅₉	semidirect
510. #436	C₂²×C₅₉	semidirect
511. #436	C₂²×C₅₉	semidirect
512. #436	C₂²×C₅₉	semidirect
513. #428	C₂²×C₅₉	semidirect
514. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
515. #418	C₂²×C₅₉	semidirect
516. #417	C₂²×C₅₉	semidirect
517. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
518. C₂×C₄×C₈	C₂²×C₅₉	semidirect
519. C₅₉	#62259	direct (N × H)
801. C₂×C₄	AGL(1,ℤ/8)×C₅₉	semidirect
813. C₈	H(5,𝔽₂)×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3506	2
C₅₉×#3496	2
C₅₉×#3354	2
C₅₉×#3353	2
C₅₉×#3332	2
C₅₉×#3330	2
C₅₉×#3325	2
C₅₉×#3324	2
C₅₉×#3274	2
C₅₉×#3272	2
C₅₉×#3246	2
C₅₉×#3245	2
C₅₉×#3188	2
C₅₉×#3169	2
C₅₉×#3167	2
C₅₉×#3055	2
C₂×C₅₉×#436	2
#62259	59

Subgroups — C59×#62259 #28474368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62259 #28474368