Subgroups — C₅₉×#35645 #28447754

Order 15104.

1558 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2575	C₂	1	2	yes	maximal
2	C₅₉×#2573	C₂	1	2	yes	maximal
3	C₅₉×#2533	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2530	C₂	1	2	yes	maximal
5	C₅₉×#2524	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2524	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2522	C₂	1	2	yes	maximal
8	C₅₉×#2511	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2509	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2508	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2495	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2489	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2453	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2446	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2429	C₂	1	1	yes	maximal, characteristic
16	C₅₉×#2423	C₂	1	1	yes	maximal, characteristic
17	C₅₉×#2330	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2320	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
21	C₄×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
22	C₅₉×#2283	C₂	1	1	yes	maximal, characteristic
23	C₅₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#400	C₂²	1	2	yes	—
34	C₅₉×#400	C₂²	1	2	yes	—
35	C₅₉×#400	C₂²	1	2	yes	—
36	C₅₉×#400	C₂²	1	2	yes	—
37	C₅₉×#400	C₂²	1	2	yes	—
38	C₅₉×#400	C₂²	1	2	yes	—
39	C₅₉×#400	C₂²	1	2	yes	—
40	C₅₉×#400	C₂²	1	2	yes	—
41	C₅₉×#399	C₂²	1	2	yes	—
42	C₅₉×#398	C₂²	1	2	yes	—
43	C₅₉×#398	C₂²	1	2	yes	—
44	C₅₉×#398	C₂²	1	2	yes	—
45	C₅₉×#398	C₂²	1	2	yes	—
46	C₅₉×#397	C₂²	1	2	yes	—
47	C₅₉×#397	C₂²	1	2	yes	—
48	C₅₉×#396	C₂²	1	2	yes	—
49	C₅₉×#391	C₂²	1	1	yes	characteristic
50	C₅₉×#391	C₂²	1	1	yes	characteristic
51	C₅₉×#391	C₂²	1	1	yes	characteristic
52	C₅₉×#391	C₂²	1	1	yes	characteristic
53	C₅₉×#391	C₂²	1	1	yes	characteristic
54	C₅₉×#391	C₂²	1	1	yes	characteristic
55	C₅₉×#389	C₂²	1	1	yes	characteristic
56	C₅₉×#389	C₂²	1	1	yes	characteristic
57	C₅₉×#389	C₂²	1	2	yes	—
58	C₅₉×#389	C₂²	1	2	yes	—
59	C₅₉×#389	C₂²	1	2	yes	—
60	C₅₉×#389	C₂²	1	2	yes	—
61	C₅₉×#389	C₂²	1	1	yes	characteristic
62	C₅₉×#389	C₂²	1	1	yes	characteristic
63	C₅₉×#389	C₂²	1	1	yes	characteristic
64	C₅₉×#389	C₂²	1	1	yes	characteristic
65	C₅₉×#389	C₂²	1	2	yes	—
66	C₅₉×#388	C₂²	1	2	yes	—
67	C₅₉×#388	C₂²	1	2	yes	—
68	C₅₉×#388	C₂²	1	2	yes	—
69	C₅₉×#388	C₂²	1	2	yes	—
70	C₅₉×#387	C₂²	1	2	yes	—
71	C₅₉×#387	C₂²	1	2	yes	—
72	C₅₉×#387	C₂²	1	2	yes	—
73	C₅₉×#387	C₂²	1	2	yes	—
74	C₅₉×#387	C₂²	1	2	yes	—
75	C₅₉×#387	C₂²	1	2	yes	—
76	C₅₉×#387	C₂²	1	2	yes	—
77	C₅₉×#387	C₂²	1	2	yes	—
78	C₅₉×#387	C₂²	1	2	yes	—
79	C₅₉×#387	C₂²	1	2	yes	—
80	C₅₉×#387	C₂²	1	2	yes	—
81	C₅₉×#387	C₂²	1	2	yes	—
82	C₅₉×#387	C₂²	1	2	yes	—
83	C₅₉×#387	C₂²	1	2	yes	—
84	C₅₉×#387	C₂²	1	2	yes	—
85	C₅₉×#387	C₂²	1	2	yes	—
86	C₅₉×#387	C₂²	1	2	yes	—
87	C₅₉×#385	C₂²	1	2	yes	—
88	C₅₉×#385	C₂²	1	2	yes	—
89	C₅₉×#384	C₂²	1	1	yes	characteristic
90	C₅₉×#383	C₂²	1	2	yes	—
91	C₅₉×#383	C₂²	1	1	yes	characteristic
92	C₅₉×#383	C₂²	1	2	yes	—
93	C₅₉×#383	C₂²	1	1	yes	characteristic
94	C₅₉×#382	C₂²	1	2	yes	—
95	C₅₉×#382	C₂²	1	1	yes	characteristic
96	C₅₉×#382	C₂²	1	1	yes	characteristic
97	C₅₉×#382	C₂²	1	2	yes	—
98	C₅₉×#382	C₂²	1	1	yes	characteristic
99	C₅₉×#381	C₂²	1	1	yes	characteristic
100	C₅₉×#381	C₂²	1	1	yes	characteristic
101	C₅₉×#380	C₂²	1	1	yes	characteristic
102	C₅₉×#380	C₂²	1	1	yes	characteristic
103	C₅₉×#380	C₂²	1	1	yes	characteristic
104	C₅₉×#380	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
120	C₅₉×#376	C₂²	1	2	yes	—
121	C₅₉×#376	C₂²	1	1	yes	characteristic
122	C₅₉×#376	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₄⋊Q₈×C₅₉	—	2	4	no	—
129	#125×C₅₉	—	2	4	no	—
130	C₂²⋊Q₈×C₅₉	—	2	4	no	—
131	C₂²⋊Q₈×C₅₉	—	2	4	no	—
132	C₄×Q₈×C₅₉	—	2	4	no	—
133	C₄×Q₈×C₅₉	—	2	4	no	—
134	C₄×Q₈×C₅₉	—	2	4	no	—
135	C₄×Q₈×C₅₉	—	2	4	no	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₅₉	—	2	4	no	—
173	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
189	#95×C₅₉	C₂³	1	1	yes	characteristic
190	#95×C₅₉	C₂³	1	1	yes	characteristic
191	#95×C₅₉	C₂³	1	1	yes	characteristic
192	#95×C₅₉	C₂³	1	1	yes	characteristic
193	#95×C₅₉	C₂³	1	2	yes	—
194	#95×C₅₉	C₂³	1	2	yes	—
195	#95×C₅₉	C₂³	1	2	yes	—
196	#95×C₅₉	C₂³	1	1	yes	characteristic
197	#95×C₅₉	C₂³	1	1	yes	characteristic
198	#95×C₅₉	C₂³	1	1	yes	characteristic
199	#95×C₅₉	C₂³	1	1	yes	characteristic
200	#95×C₅₉	C₂³	1	1	yes	characteristic
201	#95×C₅₉	C₂³	1	1	yes	characteristic
202	#95×C₅₉	C₂³	1	1	yes	characteristic
203	#95×C₅₉	C₂³	1	1	yes	characteristic
204	#95×C₅₉	C₂³	1	2	yes	—
205	#95×C₅₉	C₂³	1	2	yes	—
206	#95×C₅₉	C₂³	1	2	yes	—
207	#95×C₅₉	C₂³	1	2	yes	—
208	#95×C₅₉	C₂³	1	2	yes	—
209	#95×C₅₉	C₂³	1	2	yes	—
210	#95×C₅₉	C₂³	1	1	yes	characteristic
211	#95×C₅₉	C₂³	1	1	yes	characteristic
212	#95×C₅₉	C₂³	1	1	yes	characteristic
213	#95×C₅₉	C₂³	1	1	yes	characteristic
214	#95×C₅₉	C₂³	1	2	yes	—
215	#95×C₅₉	C₂³	1	2	yes	—
216	#95×C₅₉	C₂³	1	2	yes	—
217	#95×C₅₉	C₂³	1	2	yes	—
218	#95×C₅₉	C₂³	1	2	yes	—
219	#95×C₅₉	C₂³	1	2	yes	—
220	#95×C₅₉	C₂³	1	2	yes	—
221	#95×C₅₉	C₂³	1	2	yes	—
222	#95×C₅₉	C₂³	1	2	yes	—
223	#95×C₅₉	C₂³	1	2	yes	—
224	#95×C₅₉	C₂³	1	2	yes	—
225	#95×C₅₉	C₂³	1	2	yes	—
226	#95×C₅₉	C₂³	1	2	yes	—
227	#95×C₅₉	C₂³	1	2	yes	—
228	#95×C₅₉	C₂³	1	2	yes	—
229	#95×C₅₉	C₂³	1	2	yes	—
230	#95×C₅₉	C₂³	1	2	yes	—
231	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
232	C₂×Q₈×C₅₉	—	2	2	no	—
233	C₂×Q₈×C₅₉	—	2	2	no	—
234	C₂×Q₈×C₅₉	—	2	2	no	—
235	C₂×Q₈×C₅₉	—	2	2	no	—
236	C₂×Q₈×C₅₉	—	2	2	no	—
237	C₂×Q₈×C₅₉	#41	1	4	yes	—
238	C₂²×C₄×C₅₉	—	2	2	no	—
239	C₂²×C₄×C₅₉	—	2	2	no	—
240	C₂²×C₄×C₅₉	—	2	2	no	—
241	C₂²×C₄×C₅₉	—	2	2	no	—
242	C₂²×C₄×C₅₉	—	2	2	no	—
243	C₂²×C₄×C₅₉	—	2	2	no	—
244	C₂²×C₄×C₅₉	—	2	2	no	—
245	C₂²×C₄×C₅₉	—	4	1	no	—
246	C₂²×C₄×C₅₉	—	4	1	no	—
247	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
269	C₄⋊C₄×C₅₉	—	2	4	no	—
270	C₄⋊C₄×C₅₉	—	2	4	no	—
271	C₄⋊C₄×C₅₉	—	2	4	no	—
272	C₄⋊C₄×C₅₉	—	2	2	no	—
273	C₄⋊C₄×C₅₉	—	2	2	no	—
274	C₄⋊C₄×C₅₉	—	2	2	no	—
275	C₄⋊C₄×C₅₉	—	2	4	no	—
276	C₄⋊C₄×C₅₉	—	2	2	no	—
277	C₄⋊C₄×C₅₉	—	2	4	no	—
278	C₄⋊C₄×C₅₉	—	2	4	no	—
279	C₄⋊C₄×C₅₉	—	2	4	no	—
280	C₄⋊C₄×C₅₉	—	2	4	no	—
281	C₄⋊C₄×C₅₉	—	2	2	no	—
282	C₄⋊C₄×C₅₉	—	2	4	no	—
283	C₄⋊C₄×C₅₉	—	2	4	no	—
284	C₄⋊C₄×C₅₉	—	2	4	no	—
285	C₄⋊C₄×C₅₉	—	2	2	no	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	4	2	no	—
288	C₄⋊C₄×C₅₉	—	4	1	no	—
289	C₄⋊C₄×C₅₉	—	4	1	no	—
290	C₄⋊C₄×C₅₉	—	4	2	no	—
291	C₄⋊C₄×C₅₉	—	4	2	no	—
292	C₄⋊C₄×C₅₉	—	4	2	no	—
293	C₄⋊C₄×C₅₉	—	4	2	no	—
294	C₄⋊C₄×C₅₉	—	4	2	no	—
295	C₄⋊C₄×C₅₉	—	4	2	no	—
296	C₄⋊C₄×C₅₉	#41	1	4	yes	—
297	C₂²⋊C₄×C₅₉	—	2	2	no	—
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	4	no	—
302	C₂²⋊C₄×C₅₉	—	4	1	no	—
303	C₂²⋊C₄×C₅₉	—	4	1	no	—
304	C₂²⋊C₄×C₅₉	—	4	2	no	—
305	C₄²×C₅₉	—	2	2	no	—
306	C₄²×C₅₉	—	2	2	no	—
307	C₄²×C₅₉	—	2	2	no	—
308	C₄²×C₅₉	—	2	4	no	—
309	C₄²×C₅₉	—	2	4	no	—
310	C₄²×C₅₉	—	2	4	no	—
311	C₄²×C₅₉	—	2	2	no	—
312	C₄²×C₅₉	—	2	2	no	—
313	C₄²×C₅₉	—	2	4	no	—
314	C₄²×C₅₉	—	2	2	no	—
315	C₄²×C₅₉	—	2	2	no	—
316	C₄²×C₅₉	—	4	2	no	—
317	C₄²×C₅₉	—	4	2	no	—
318	C₄²×C₅₉	—	4	2	no	—
319	C₄²×C₅₉	—	4	2	no	—
320	C₄²×C₅₉	#41	1	4	yes	—
321	C₂³×C₅₉	—	2	1	no	—
322	C₂³×C₅₉	—	2	1	no	—
323	C₂³×C₅₉	—	2	1	no	—
324	C₂³×C₅₉	—	2	1	no	—
325	C₂³×C₅₉	—	2	1	no	—
326	C₂³×C₅₉	—	2	1	no	—
327	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
328	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
329	Q₈×C₅₉	—	2	8	no	—
330	Q₈×C₅₉	—	4	4	no	—
331	C₂×C₄×C₅₉	—	2	1	no	—
332	C₂×C₄×C₅₉	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	2	no	—
335	C₂×C₄×C₅₉	—	2	1	no	—
336	C₂×C₄×C₅₉	—	2	1	no	—
337	C₂×C₄×C₅₉	—	2	2	no	—
338	C₂×C₄×C₅₉	—	2	1	no	—
339	C₂×C₄×C₅₉	—	2	1	no	—
340	C₂×C₄×C₅₉	—	2	1	no	—
341	C₂×C₄×C₅₉	—	2	1	no	—
342	C₂×C₄×C₅₉	—	2	1	no	—
343	C₂×C₄×C₅₉	—	2	1	no	—
344	C₂×C₄×C₅₉	—	2	1	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	2	no	—
347	C₂×C₄×C₅₉	—	2	1	no	—
348	C₂×C₄×C₅₉	—	2	1	no	—
349	C₂×C₄×C₅₉	—	2	1	no	—
350	C₂×C₄×C₅₉	—	2	1	no	—
351	C₂×C₄×C₅₉	—	2	1	no	—
352	C₂×C₄×C₅₉	—	2	2	no	—
353	C₂×C₄×C₅₉	—	2	1	no	—
354	C₂×C₄×C₅₉	—	2	2	no	—
355	C₂×C₄×C₅₉	—	2	2	no	—
356	C₂×C₄×C₅₉	—	2	2	no	—
357	C₂×C₄×C₅₉	—	2	2	no	—
358	C₂×C₄×C₅₉	—	2	1	no	—
359	C₂×C₄×C₅₉	—	2	1	no	—
360	C₂×C₄×C₅₉	—	2	2	no	—
361	C₂×C₄×C₅₉	—	2	2	no	—
362	C₂×C₄×C₅₉	—	2	1	no	—
363	C₂×C₄×C₅₉	—	2	1	no	—
364	C₂×C₄×C₅₉	—	2	2	no	—
365	C₂×C₄×C₅₉	—	2	1	no	—
366	C₂×C₄×C₅₉	—	2	1	no	—
367	C₂×C₄×C₅₉	—	2	2	no	—
368	C₂×C₄×C₅₉	—	2	1	no	—
369	C₂×C₄×C₅₉	—	2	1	no	—
370	C₂×C₄×C₅₉	—	2	1	no	—
371	C₂×C₄×C₅₉	—	2	1	no	—
372	C₂×C₄×C₅₉	—	2	1	no	—
373	C₂×C₄×C₅₉	—	2	1	no	—
374	C₂×C₄×C₅₉	—	2	1	no	—
375	C₂×C₄×C₅₉	—	2	2	no	—
376	C₂×C₄×C₅₉	—	2	2	no	—
377	C₂×C₄×C₅₉	—	2	2	no	—
378	C₂×C₄×C₅₉	—	2	2	no	—
379	C₂×C₄×C₅₉	—	2	2	no	—
380	C₂×C₄×C₅₉	—	2	1	no	—
381	C₂×C₄×C₅₉	—	2	1	no	—
382	C₂×C₄×C₅₉	—	2	2	no	—
383	C₂×C₄×C₅₉	—	2	1	no	—
384	C₂×C₄×C₅₉	—	2	1	no	—
385	C₂×C₄×C₅₉	—	2	2	no	—
386	C₂×C₄×C₅₉	—	2	1	no	—
387	C₂×C₄×C₅₉	—	2	1	no	—
388	C₂×C₄×C₅₉	—	2	1	no	—
389	C₂×C₄×C₅₉	—	4	4	no	—
390	C₂×C₄×C₅₉	—	4	4	no	—
391	C₂×C₄×C₅₉	—	4	4	no	—
392	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
393	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
394	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
395	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
396	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
397	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
398	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
399	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
400	#35645	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂²×C₅₉	—	2	2	no	—
402	C₂²×C₅₉	—	2	2	no	—
403	C₂²×C₅₉	—	2	2	no	—
404	C₂²×C₅₉	—	4	1	no	—
405	C₂²×C₅₉	—	4	1	no	—
406	C₂²×C₅₉	—	4	1	no	—
407	C₂²×C₅₉	—	4	1	no	—
408	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
409	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
413	C₂²×C₅₉	#585	1	1	yes	characteristic
414	C₂²×C₅₉	#585	1	1	yes	characteristic
415	C₄×C₅₉	—	2	4	no	—
416	C₄×C₅₉	—	2	2	no	—
417	C₄×C₅₉	—	2	2	no	—
418	C₄×C₅₉	—	2	2	no	—
419	C₄×C₅₉	—	2	4	no	—
420	C₄×C₅₉	—	4	1	no	—
421	C₄×C₅₉	—	4	2	no	—
422	C₄×C₅₉	—	4	2	no	—
423	C₄×C₅₉	—	4	2	no	—
424	C₄×C₅₉	—	4	1	no	—
425	C₄×C₅₉	—	4	1	no	—
426	C₄×C₅₉	—	4	1	no	—
427	C₄×C₅₉	—	4	1	no	—
428	C₄×C₅₉	—	4	1	no	—
429	C₄×C₅₉	—	4	2	no	—
430	C₄×C₅₉	—	4	1	no	—
431	C₄×C₅₉	—	4	1	no	—
432	C₄×C₅₉	—	4	1	no	—
433	C₄×C₅₉	—	4	2	no	—
434	C₄×C₅₉	—	4	1	no	—
435	C₄×C₅₉	—	4	2	no	—
436	C₄×C₅₉	#529	1	4	yes	—
437	#2575	C₂×C₅₉	1	2	yes	—
438	#2573	C₂×C₅₉	1	2	yes	—
439	#2533	C₂×C₅₉	1	2	yes	complemented
440	#2530	C₂×C₅₉	1	2	yes	—
441	#2524	C₂×C₅₉	1	2	yes	complemented
442	#2524	C₂×C₅₉	1	2	yes	complemented
443	#2522	C₂×C₅₉	1	2	yes	—
444	#2511	C₂×C₅₉	1	1	yes	characteristic, complemented
445	#2509	C₂×C₅₉	1	1	yes	characteristic, complemented
446	#2508	C₂×C₅₉	1	2	yes	complemented
447	#2495	C₂×C₅₉	1	1	yes	characteristic
448	#2489	C₂×C₅₉	1	1	yes	characteristic
449	#2453	C₂×C₅₉	1	1	yes	characteristic, complemented
450	#2446	C₂×C₅₉	1	1	yes	characteristic, complemented
451	#2429	C₂×C₅₉	1	1	yes	characteristic
452	#2423	C₂×C₅₉	1	1	yes	characteristic
453	#2330	C₂×C₅₉	1	1	yes	characteristic, complemented
454	#2327	C₂×C₅₉	1	1	yes	characteristic, complemented
455	#2320	C₂×C₅₉	1	1	yes	characteristic, complemented
456	C₄×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
457	C₄×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
458	#2283	C₂×C₅₉	1	1	yes	characteristic
459	#2276	C₂×C₅₉	1	1	yes	characteristic, complemented
460	C₂×C₅₉	—	4	2	no	—
461	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
462	C₂×C₅₉	#3495	1	1	yes	characteristic
463	C₂×C₅₉	#3495	1	1	yes	characteristic
464	C₂×C₅₉	#3515	1	1	yes	characteristic
465	C₂×C₅₉	#3516	1	1	yes	characteristic
466	C₂×C₅₉	#3523	1	1	yes	characteristic
467	C₂×C₅₉	#3524	1	1	yes	characteristic
468	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
469	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
470	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
471	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
472	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
474	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
475	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
476	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
477	#400	C₂²×C₅₉	1	2	yes	—
478	#400	C₂²×C₅₉	1	2	yes	—
479	#400	C₂²×C₅₉	1	2	yes	—
480	#400	C₂²×C₅₉	1	2	yes	—
481	#400	C₂²×C₅₉	1	2	yes	—
482	#400	C₂²×C₅₉	1	2	yes	—
483	#400	C₂²×C₅₉	1	2	yes	—
484	#400	C₂²×C₅₉	1	2	yes	—
485	#399	C₂²×C₅₉	1	2	yes	—
486	#398	C₂²×C₅₉	1	2	yes	—
487	#398	C₂²×C₅₉	1	2	yes	—
488	#398	C₂²×C₅₉	1	2	yes	—
489	#398	C₂²×C₅₉	1	2	yes	—
490	#397	C₂²×C₅₉	1	2	yes	—
491	#397	C₂²×C₅₉	1	2	yes	—
492	#396	C₂²×C₅₉	1	2	yes	—
493	#391	C₂²×C₅₉	1	1	yes	characteristic
494	#391	C₂²×C₅₉	1	1	yes	characteristic
495	#391	C₂²×C₅₉	1	1	yes	characteristic
496	#391	C₂²×C₅₉	1	1	yes	characteristic
497	#391	C₂²×C₅₉	1	1	yes	characteristic
498	#391	C₂²×C₅₉	1	1	yes	characteristic
499	#389	C₂²×C₅₉	1	2	yes	—
500	#389	C₂²×C₅₉	1	1	yes	characteristic
501	#389	C₂²×C₅₉	1	1	yes	characteristic
502	#389	C₂²×C₅₉	1	1	yes	characteristic
503	#389	C₂²×C₅₉	1	1	yes	characteristic
504	#389	C₂²×C₅₉	1	2	yes	—
505	#389	C₂²×C₅₉	1	2	yes	—
506	#389	C₂²×C₅₉	1	2	yes	—
507	#389	C₂²×C₅₉	1	1	yes	characteristic
508	#389	C₂²×C₅₉	1	2	yes	—
509	#389	C₂²×C₅₉	1	1	yes	characteristic
510	#388	C₂²×C₅₉	1	2	yes	—
511	#388	C₂²×C₅₉	1	2	yes	—
512	#388	C₂²×C₅₉	1	2	yes	—
513	#388	C₂²×C₅₉	1	2	yes	—
514	#387	C₂²×C₅₉	1	2	yes	—
515	#387	C₂²×C₅₉	1	2	yes	—
516	#387	C₂²×C₅₉	1	2	yes	—
517	#387	C₂²×C₅₉	1	2	yes	—
518	#387	C₂²×C₅₉	1	2	yes	—
519	#387	C₂²×C₅₉	1	2	yes	—
520	#387	C₂²×C₅₉	1	2	yes	—
521	#387	C₂²×C₅₉	1	2	yes	—
522	#387	C₂²×C₅₉	1	2	yes	—
523	#387	C₂²×C₅₉	1	2	yes	—
524	#387	C₂²×C₅₉	1	2	yes	—
525	#387	C₂²×C₅₉	1	2	yes	—
526	#387	C₂²×C₅₉	1	2	yes	—
527	#387	C₂²×C₅₉	1	2	yes	—
528	#387	C₂²×C₅₉	1	2	yes	—
529	#387	C₂²×C₅₉	1	2	yes	—
530	#387	C₂²×C₅₉	1	2	yes	—
531	#385	C₂²×C₅₉	1	2	yes	—
532	#385	C₂²×C₅₉	1	2	yes	—
533	#384	C₂²×C₅₉	1	1	yes	characteristic
534	#383	C₂²×C₅₉	1	2	yes	—
535	#383	C₂²×C₅₉	1	2	yes	—
536	#383	C₂²×C₅₉	1	1	yes	characteristic
537	#383	C₂²×C₅₉	1	1	yes	characteristic
538	#382	C₂²×C₅₉	1	2	yes	—
539	#382	C₂²×C₅₉	1	1	yes	characteristic
540	#382	C₂²×C₅₉	1	2	yes	—
541	#382	C₂²×C₅₉	1	1	yes	characteristic
542	#382	C₂²×C₅₉	1	1	yes	characteristic
543	#381	C₂²×C₅₉	1	1	yes	characteristic
544	#381	C₂²×C₅₉	1	1	yes	characteristic
545	#380	C₂²×C₅₉	1	1	yes	characteristic
546	#380	C₂²×C₅₉	1	1	yes	characteristic
547	#380	C₂²×C₅₉	1	1	yes	characteristic
548	#380	C₂²×C₅₉	1	1	yes	characteristic
549	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
550	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
551	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
553	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
556	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
558	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
559	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
562	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
563	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
564	#376	C₂²×C₅₉	1	1	yes	characteristic
565	#376	C₂²×C₅₉	1	1	yes	characteristic
566	#376	C₂²×C₅₉	1	2	yes	—
567	C₅₉	#35645	1	1	yes	characteristic, direct product factor, Sylow
568	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
569	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
573	C₄⋊Q₈	—	2	4	no	—
574	#125	—	2	4	no	—
575	C₂²⋊Q₈	—	2	4	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₄×Q₈	—	2	4	no	—
578	C₄×Q₈	—	2	4	no	—
579	C₄×Q₈	—	2	4	no	—
580	C₄×Q₈	—	2	4	no	—
581	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
617	C₂×C₄²	—	2	4	no	—
618	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
619	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
622	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
623	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
631	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
632	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
633	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
634	#95	C₂³×C₅₉	1	1	yes	characteristic
635	#95	C₂³×C₅₉	1	1	yes	characteristic
636	#95	C₂³×C₅₉	1	1	yes	characteristic
637	#95	C₂³×C₅₉	1	1	yes	characteristic
638	#95	C₂³×C₅₉	1	2	yes	—
639	#95	C₂³×C₅₉	1	2	yes	—
640	#95	C₂³×C₅₉	1	2	yes	—
641	#95	C₂³×C₅₉	1	1	yes	characteristic
642	#95	C₂³×C₅₉	1	1	yes	characteristic
643	#95	C₂³×C₅₉	1	1	yes	characteristic
644	#95	C₂³×C₅₉	1	1	yes	characteristic
645	#95	C₂³×C₅₉	1	1	yes	characteristic
646	#95	C₂³×C₅₉	1	1	yes	characteristic
647	#95	C₂³×C₅₉	1	1	yes	characteristic
648	#95	C₂³×C₅₉	1	1	yes	characteristic
649	#95	C₂³×C₅₉	1	2	yes	—
650	#95	C₂³×C₅₉	1	2	yes	—
651	#95	C₂³×C₅₉	1	2	yes	—
652	#95	C₂³×C₅₉	1	2	yes	—
653	#95	C₂³×C₅₉	1	2	yes	—
654	#95	C₂³×C₅₉	1	2	yes	—
655	#95	C₂³×C₅₉	1	1	yes	characteristic
656	#95	C₂³×C₅₉	1	1	yes	characteristic
657	#95	C₂³×C₅₉	1	1	yes	characteristic
658	#95	C₂³×C₅₉	1	1	yes	characteristic
659	#95	C₂³×C₅₉	1	2	yes	—
660	#95	C₂³×C₅₉	1	2	yes	—
661	#95	C₂³×C₅₉	1	2	yes	—
662	#95	C₂³×C₅₉	1	2	yes	—
663	#95	C₂³×C₅₉	1	2	yes	—
664	#95	C₂³×C₅₉	1	2	yes	—
665	#95	C₂³×C₅₉	1	2	yes	—
666	#95	C₂³×C₅₉	1	2	yes	—
667	#95	C₂³×C₅₉	1	2	yes	—
668	#95	C₂³×C₅₉	1	2	yes	—
669	#95	C₂³×C₅₉	1	2	yes	—
670	#95	C₂³×C₅₉	1	2	yes	—
671	#95	C₂³×C₅₉	1	2	yes	—
672	#95	C₂³×C₅₉	1	2	yes	—
673	#95	C₂³×C₅₉	1	2	yes	—
674	#95	C₂³×C₅₉	1	2	yes	—
675	#95	C₂³×C₅₉	1	2	yes	—
676	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	#41×C₅₉	1	4	yes	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	4	1	no	—
691	C₂²×C₄	—	4	1	no	—
692	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	#41×C₅₉	1	4	yes	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	4	1	no	—
748	C₂²⋊C₄	—	4	1	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	4	2	no	—
762	C₄²	—	4	2	no	—
763	C₄²	—	4	2	no	—
764	C₄²	—	4	2	no	—
765	C₄²	#41×C₅₉	1	4	yes	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
773	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
774	Q₈	—	2	8	no	—
775	Q₈	—	4	4	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
838	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
839	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
840	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
841	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
842	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
843	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
844	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
853	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
854	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
855	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
856	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
857	C₂²	C₅₉×#585	1	1	yes	characteristic
858	C₂²	C₅₉×#585	1	1	yes	characteristic
859	C₄	—	2	4	no	—
860	C₄	—	2	4	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	C₅₉×#529	1	4	yes	—
881	C₂	—	4	2	no	—
882	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
883	C₂	C₅₉×#3495	1	1	yes	characteristic
884	C₂	C₅₉×#3495	1	1	yes	characteristic
885	C₂	C₅₉×#3515	1	1	yes	characteristic
886	C₂	C₅₉×#3516	1	1	yes	characteristic
887	C₂	C₅₉×#3523	1	1	yes	characteristic
888	C₂	C₅₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁴×C₅₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₉×#2533	C₂	semidirect
5. C₅₉×#2524	C₂	semidirect
6. C₅₉×#2524	C₂	semidirect
8. C₅₉×#2511	C₂	semidirect
9. C₅₉×#2509	C₂	semidirect
10. C₅₉×#2508	C₂	semidirect
13. C₅₉×#2453	C₂	semidirect
14. C₅₉×#2446	C₂	semidirect
17. C₅₉×#2330	C₂	semidirect
18. C₅₉×#2327	C₂	semidirect
19. C₅₉×#2320	C₂	semidirect
23. C₅₉×#2276	C₂	semidirect
400. #35645	C₅₉	direct (N × H)
439. #2533	C₂×C₅₉	semidirect
441. #2524	C₂×C₅₉	semidirect
442. #2524	C₂×C₅₉	semidirect
444. #2511	C₂×C₅₉	semidirect
445. #2509	C₂×C₅₉	semidirect
446. #2508	C₂×C₅₉	semidirect
449. #2453	C₂×C₅₉	semidirect
450. #2446	C₂×C₅₉	semidirect
453. #2330	C₂×C₅₉	semidirect
454. #2327	C₂×C₅₉	semidirect
455. #2320	C₂×C₅₉	semidirect
459. #2276	C₂×C₅₉	semidirect
567. C₅₉	#35645	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×#2575	2
C₅₉×#2573	2
C₅₉×#2533	2
C₅₉×#2530	2
C₅₉×#2524	2
C₅₉×#2522	2
C₅₉×#2511	2
C₅₉×#2509	2
C₅₉×#2508	2
C₅₉×#2495	2
C₅₉×#2489	2
C₅₉×#2453	2
C₅₉×#2446	2
C₅₉×#2429	2
C₅₉×#2423	2
C₅₉×#2330	2
C₅₉×#2327	2
C₅₉×#2320	2
C₄×C₂²⋊Q₈×C₅₉	2
C₅₉×#2283	2
C₅₉×#2276	2
#35645	59

Subgroups — C59×#35645 #28447754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35645 #28447754