Subgroups — C₅₉×#35705 #28447814

Order 15104.

1946 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×#2665	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2626	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2607	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2589	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2574	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2549	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2505	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2492	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2465	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2439	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2437	C₂	1	2	yes	maximal
12	C₅₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2396	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₉×#393	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2368	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2368	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#2342	C₂	1	2	yes	maximal
18	Q₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2273	C₂	1	1	yes	maximal, characteristic
20	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
26	C₂×#117×C₅₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#400	C₂²	1	2	yes	complemented
32	C₅₉×#400	C₂²	1	2	yes	complemented
33	C₅₉×#400	C₂²	1	2	yes	complemented
34	C₅₉×#399	C₂²	1	1	yes	characteristic
35	C₅₉×#399	C₂²	1	1	yes	characteristic
36	C₅₉×#399	C₂²	1	2	yes	—
37	C₅₉×#398	C₂²	1	2	yes	complemented
38	C₅₉×#398	C₂²	1	2	yes	complemented
39	C₅₉×#396	C₂²	1	2	yes	—
40	C₅₉×#396	C₂²	1	2	yes	—
41	C₅₉×#396	C₂²	1	2	yes	—
42	C₅₉×#396	C₂²	1	2	yes	—
43	C₅₉×#395	C₂²	1	2	yes	complemented
44	C₅₉×#395	C₂²	1	2	yes	complemented
45	C₅₉×#395	C₂²	1	2	yes	complemented
46	C₅₉×#393	C₂²	1	1	yes	characteristic
47	C₅₉×#393	C₂²	1	2	yes	—
48	C₅₉×#393	C₂²	1	1	yes	characteristic
49	C₅₉×#393	C₂²	1	2	yes	—
50	C₅₉×#393	C₂²	1	2	yes	—
51	C₅₉×#393	C₂²	1	1	yes	characteristic
52	C₅₉×#393	C₂²	1	1	yes	characteristic
53	C₅₉×#393	C₂²	1	1	yes	characteristic
54	C₅₉×#393	C₂²	1	1	yes	characteristic
55	C₅₉×#391	C₂²	1	2	yes	complemented
56	C₅₉×#391	C₂²	1	2	yes	complemented
57	C₅₉×#391	C₂²	1	2	yes	complemented
58	C₅₉×#391	C₂²	1	2	yes	complemented
59	C₅₉×#391	C₂²	1	2	yes	complemented
60	C₅₉×#391	C₂²	1	2	yes	complemented
61	C₅₉×#391	C₂²	1	2	yes	complemented
62	C₅₉×#391	C₂²	1	2	yes	complemented
63	C₅₉×#389	C₂²	1	2	yes	complemented
64	C₅₉×#389	C₂²	1	2	yes	complemented
65	C₅₉×#388	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×#387	C₂²	1	2	yes	complemented
70	C₅₉×#387	C₂²	1	2	yes	complemented
71	C₅₉×#387	C₂²	1	2	yes	complemented
72	C₅₉×#387	C₂²	1	2	yes	complemented
73	C₅₉×#387	C₂²	1	2	yes	complemented
74	C₅₉×#387	C₂²	1	2	yes	complemented
75	C₅₉×#387	C₂²	1	2	yes	complemented
76	C₅₉×#387	C₂²	1	2	yes	complemented
77	C₅₉×#385	C₂²	1	2	yes	—
78	C₅₉×#385	C₂²	1	2	yes	—
79	C₅₉×#385	C₂²	1	2	yes	—
80	C₅₉×#385	C₂²	1	2	yes	—
81	C₅₉×#385	C₂²	1	2	yes	—
82	C₅₉×#385	C₂²	1	2	yes	—
83	C₅₉×#385	C₂²	1	2	yes	—
84	C₅₉×#382	C₂²	1	2	yes	complemented
85	C₅₉×#381	C₂²	1	2	yes	—
86	C₅₉×#380	C₂²	1	2	yes	—
87	C₅₉×#380	C₂²	1	2	yes	—
88	C₅₉×#380	C₂²	1	1	yes	characteristic
89	C₅₉×#380	C₂²	1	2	yes	—
90	C₅₉×#379	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
92	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
105	C₂×#95×C₅₉	C₂²	1	2	yes	—
106	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
107	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₅₉	—	2	4	no	—
109	C₂²×Q₈×C₅₉	—	4	4	no	—
110	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
112	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
113	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
114	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
116	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
118	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₅₉	—	4	4	no	—
122	C₂²⋊Q₈×C₅₉	—	2	4	no	—
123	C₂²⋊Q₈×C₅₉	—	2	8	no	—
124	C₂²⋊Q₈×C₅₉	—	4	4	no	—
125	C₄×Q₈×C₅₉	—	4	4	no	—
126	#117×C₅₉	—	4	4	no	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
147	C₂×C₂²⋊C₄×C₅₉	—	4	4	no	—
148	C₂×C₂²⋊C₄×C₅₉	Q₈	1	8	yes	complemented
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
175	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
177	#95×C₅₉	C₂³	1	1	yes	characteristic
178	#95×C₅₉	C₂³	1	2	yes	—
179	#95×C₅₉	C₂³	1	2	yes	—
180	#95×C₅₉	C₂³	1	2	yes	—
181	#95×C₅₉	C₂³	1	1	yes	characteristic
182	#95×C₅₉	C₂³	1	2	yes	—
183	#95×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	2	yes	—
185	#95×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	2	yes	—
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	2	yes	—
189	#95×C₅₉	C₂³	1	2	yes	—
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
197	#95×C₅₉	C₂³	1	2	yes	—
198	#95×C₅₉	C₂³	1	2	yes	—
199	#95×C₅₉	C₂³	1	1	yes	characteristic
200	#95×C₅₉	C₂³	1	1	yes	characteristic
201	#95×C₅₉	C₂³	1	2	yes	—
202	#95×C₅₉	C₂³	1	2	yes	—
203	#95×C₅₉	C₂³	1	2	yes	—
204	#95×C₅₉	C₂³	1	2	yes	—
205	#95×C₅₉	C₂³	1	2	yes	—
206	C₂⁴×C₅₉	—	2	2	no	—
207	C₂⁴×C₅₉	—	2	2	no	—
208	C₂⁴×C₅₉	—	4	2	no	—
209	C₂⁴×C₅₉	—	4	2	no	—
210	C₂⁴×C₅₉	C₂×Q₈	1	4	yes	—
211	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
214	C₂×Q₈×C₅₉	—	2	2	no	—
215	C₂×Q₈×C₅₉	—	2	4	no	—
216	C₂×Q₈×C₅₉	—	2	2	no	—
217	C₂×Q₈×C₅₉	—	2	2	no	—
218	C₂×Q₈×C₅₉	—	2	4	no	—
219	C₂×Q₈×C₅₉	—	2	4	no	—
220	C₂×Q₈×C₅₉	—	2	4	no	—
221	C₂×Q₈×C₅₉	—	4	2	no	—
222	C₂×Q₈×C₅₉	—	4	2	no	—
223	C₂×Q₈×C₅₉	—	4	2	no	—
224	C₂×Q₈×C₅₉	—	4	2	no	—
225	C₂×Q₈×C₅₉	—	4	2	no	—
226	C₂×Q₈×C₅₉	—	4	16	no	—
227	C₂²×C₄×C₅₉	—	2	4	no	—
228	C₂²×C₄×C₅₉	—	2	2	no	—
229	C₂²×C₄×C₅₉	—	2	4	no	—
230	C₂²×C₄×C₅₉	—	2	4	no	—
231	C₂²×C₄×C₅₉	—	2	4	no	—
232	C₂²×C₄×C₅₉	—	4	2	no	—
233	C₂²×C₄×C₅₉	—	4	2	no	—
234	C₂²×C₄×C₅₉	—	4	2	no	—
235	C₂²×C₄×C₅₉	—	4	2	no	—
236	C₂²×C₄×C₅₉	—	4	2	no	—
237	C₂²×C₄×C₅₉	—	4	2	no	—
238	C₂²×C₄×C₅₉	—	4	2	no	—
239	C₂²×C₄×C₅₉	—	4	2	no	—
240	C₂²×C₄×C₅₉	—	4	2	no	—
241	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	complemented
242	C₂²×C₄×C₅₉	#41	1	4	yes	—
243	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₅₉	—	2	2	no	—
260	C₄⋊C₄×C₅₉	—	2	4	no	—
261	C₄⋊C₄×C₅₉	—	2	4	no	—
262	C₄⋊C₄×C₅₉	—	2	4	no	—
263	C₄⋊C₄×C₅₉	—	2	4	no	—
264	C₄⋊C₄×C₅₉	—	2	4	no	—
265	C₄⋊C₄×C₅₉	—	2	4	no	—
266	C₄⋊C₄×C₅₉	—	2	4	no	—
267	C₄⋊C₄×C₅₉	—	4	2	no	—
268	C₄⋊C₄×C₅₉	—	4	2	no	—
269	C₄⋊C₄×C₅₉	—	4	2	no	—
270	C₄⋊C₄×C₅₉	—	4	2	no	—
271	C₄⋊C₄×C₅₉	—	4	2	no	—
272	C₄⋊C₄×C₅₉	—	4	2	no	—
273	C₄⋊C₄×C₅₉	—	4	2	no	—
274	C₄⋊C₄×C₅₉	—	4	2	no	—
275	C₄⋊C₄×C₅₉	—	4	2	no	—
276	C₄⋊C₄×C₅₉	—	4	2	no	—
277	C₂²⋊C₄×C₅₉	—	2	2	no	—
278	C₂²⋊C₄×C₅₉	—	2	4	no	—
279	C₂²⋊C₄×C₅₉	—	2	4	no	—
280	C₂²⋊C₄×C₅₉	—	2	2	no	—
281	C₂²⋊C₄×C₅₉	—	2	2	no	—
282	C₂²⋊C₄×C₅₉	—	2	2	no	—
283	C₂²⋊C₄×C₅₉	—	2	2	no	—
284	C₂²⋊C₄×C₅₉	—	2	4	no	—
285	C₂²⋊C₄×C₅₉	—	2	4	no	—
286	C₂²⋊C₄×C₅₉	—	2	4	no	—
287	C₂²⋊C₄×C₅₉	—	4	2	no	—
288	C₂²⋊C₄×C₅₉	—	4	2	no	—
289	C₂²⋊C₄×C₅₉	—	4	2	no	—
290	C₂²⋊C₄×C₅₉	—	4	2	no	—
291	C₂²⋊C₄×C₅₉	—	4	2	no	—
292	C₂²⋊C₄×C₅₉	—	4	2	no	—
293	C₂²⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
294	C₂²⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
295	C₂²⋊C₄×C₅₉	C₂×Q₈	1	8	yes	complemented
296	C₂²⋊C₄×C₅₉	#41	1	4	yes	—
297	C₄²×C₅₉	—	2	4	no	—
298	C₄²×C₅₉	—	4	2	no	—
299	C₄²×C₅₉	—	4	2	no	—
300	C₄²×C₅₉	—	4	2	no	—
301	C₄²×C₅₉	—	4	2	no	—
302	C₄²×C₅₉	—	4	2	no	—
303	C₄²×C₅₉	—	4	2	no	—
304	C₄²×C₅₉	—	4	2	no	—
305	C₂³×C₅₉	—	2	2	no	—
306	C₂³×C₅₉	—	2	2	no	—
307	C₂³×C₅₉	—	2	1	no	—
308	C₂³×C₅₉	—	2	1	no	—
309	C₂³×C₅₉	—	2	1	no	—
310	C₂³×C₅₉	—	2	1	no	—
311	C₂³×C₅₉	—	2	2	no	—
312	C₂³×C₅₉	—	2	2	no	—
313	C₂³×C₅₉	—	2	2	no	—
314	C₂³×C₅₉	—	2	2	no	—
315	C₂³×C₅₉	—	2	8	no	—
316	C₂³×C₅₉	—	4	8	no	—
317	C₂³×C₅₉	—	8	2	no	—
318	C₂³×C₅₉	—	8	2	no	—
319	C₂³×C₅₉	—	8	4	no	—
320	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
321	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
322	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
323	C₂³×C₅₉	C₂×#41	1	2	yes	—
324	C₂³×C₅₉	C₂×#41	1	2	yes	—
325	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
326	Q₈×C₅₉	—	2	8	no	—
327	Q₈×C₅₉	—	4	8	no	—
328	Q₈×C₅₉	—	4	4	no	—
329	Q₈×C₅₉	—	8	2	no	—
330	Q₈×C₅₉	—	8	4	no	—
331	C₂×C₄×C₅₉	—	2	2	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	2	no	—
336	C₂×C₄×C₅₉	—	2	2	no	—
337	C₂×C₄×C₅₉	—	2	2	no	—
338	C₂×C₄×C₅₉	—	2	2	no	—
339	C₂×C₄×C₅₉	—	2	2	no	—
340	C₂×C₄×C₅₉	—	2	2	no	—
341	C₂×C₄×C₅₉	—	2	1	no	—
342	C₂×C₄×C₅₉	—	2	1	no	—
343	C₂×C₄×C₅₉	—	2	2	no	—
344	C₂×C₄×C₅₉	—	2	2	no	—
345	C₂×C₄×C₅₉	—	2	2	no	—
346	C₂×C₄×C₅₉	—	2	2	no	—
347	C₂×C₄×C₅₉	—	2	2	no	—
348	C₂×C₄×C₅₉	—	2	2	no	—
349	C₂×C₄×C₅₉	—	2	2	no	—
350	C₂×C₄×C₅₉	—	2	2	no	—
351	C₂×C₄×C₅₉	—	2	2	no	—
352	C₂×C₄×C₅₉	—	2	2	no	—
353	C₂×C₄×C₅₉	—	2	2	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	2	no	—
359	C₂×C₄×C₅₉	—	2	2	no	—
360	C₂×C₄×C₅₉	—	2	2	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	—	2	2	no	—
367	C₂×C₄×C₅₉	—	2	2	no	—
368	C₂×C₄×C₅₉	—	2	2	no	—
369	C₂×C₄×C₅₉	—	4	8	no	—
370	C₂×C₄×C₅₉	—	4	4	no	—
371	C₂×C₄×C₅₉	—	4	8	no	—
372	C₂×C₄×C₅₉	—	8	4	no	—
373	C₂×C₄×C₅₉	—	8	2	no	—
374	C₂×C₄×C₅₉	—	8	4	no	—
375	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
376	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
377	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
378	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
379	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
380	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
381	#35705	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂²×C₅₉	—	2	2	no	—
383	C₂²×C₅₉	—	2	4	no	—
384	C₂²×C₅₉	—	2	2	no	—
385	C₂²×C₅₉	—	2	4	no	—
386	C₂²×C₅₉	—	2	2	no	—
387	C₂²×C₅₉	—	2	2	no	—
388	C₂²×C₅₉	—	2	4	no	—
389	C₂²×C₅₉	—	2	4	no	—
390	C₂²×C₅₉	—	4	1	no	—
391	C₂²×C₅₉	—	4	1	no	—
392	C₂²×C₅₉	—	4	1	no	—
393	C₂²×C₅₉	—	4	1	no	—
394	C₂²×C₅₉	—	4	2	no	—
395	C₂²×C₅₉	—	4	2	no	—
396	C₂²×C₅₉	—	8	8	no	—
397	C₂²×C₅₉	#533	1	4	yes	—
398	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
399	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
401	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
402	C₂²×C₅₉	#585	1	2	yes	—
403	C₄×C₅₉	—	2	2	no	—
404	C₄×C₅₉	—	2	2	no	—
405	C₄×C₅₉	—	2	4	no	—
406	C₄×C₅₉	—	2	4	no	—
407	C₄×C₅₉	—	2	4	no	—
408	C₄×C₅₉	—	2	4	no	—
409	C₄×C₅₉	—	4	2	no	—
410	C₄×C₅₉	—	4	2	no	—
411	C₄×C₅₉	—	4	2	no	—
412	C₄×C₅₉	—	4	1	no	—
413	C₄×C₅₉	—	4	1	no	—
414	C₄×C₅₉	—	4	2	no	—
415	C₄×C₅₉	—	4	2	no	—
416	C₄×C₅₉	—	4	2	no	—
417	C₄×C₅₉	—	4	2	no	—
418	C₄×C₅₉	—	4	2	no	—
419	#2665	C₂×C₅₉	1	2	yes	complemented
420	#2626	C₂×C₅₉	1	1	yes	characteristic
421	#2607	C₂×C₅₉	1	2	yes	complemented
422	#2589	C₂×C₅₉	1	2	yes	complemented
423	#2574	C₂×C₅₉	1	2	yes	complemented
424	#2549	C₂×C₅₉	1	1	yes	characteristic, complemented
425	#2505	C₂×C₅₉	1	2	yes	complemented
426	#2492	C₂×C₅₉	1	2	yes	complemented
427	#2465	C₂×C₅₉	1	2	yes	complemented
428	#2439	C₂×C₅₉	1	2	yes	complemented
429	#2437	C₂×C₅₉	1	2	yes	—
430	#2434	C₂×C₅₉	1	1	yes	characteristic, complemented
431	#2396	C₂×C₅₉	1	2	yes	complemented
432	C₂×#393	C₂×C₅₉	1	1	yes	characteristic
433	#2368	C₂×C₅₉	1	1	yes	characteristic, complemented
434	#2368	C₂×C₅₉	1	2	yes	complemented
435	#2342	C₂×C₅₉	1	2	yes	—
436	Q₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
437	#2273	C₂×C₅₉	1	1	yes	characteristic
438	C₂×C₅₉	—	2	4	no	—
439	C₂×C₅₉	—	4	2	no	—
440	C₂×C₅₉	—	4	2	no	—
441	C₂×C₅₉	C₂×#533	1	1	yes	characteristic
442	C₂×C₅₉	#3490	1	1	yes	characteristic
443	C₂×C₅₉	#3501	1	2	yes	—
444	C₂×C₅₉	#3510	1	1	yes	characteristic
445	C₂×C₅₉	#3514	1	2	yes	—
446	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
447	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
448	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
449	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
450	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
451	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
452	C₂×#117	C₂²×C₅₉	1	2	yes	—
453	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
454	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
456	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
457	#400	C₂²×C₅₉	1	2	yes	complemented
458	#400	C₂²×C₅₉	1	2	yes	complemented
459	#400	C₂²×C₅₉	1	2	yes	complemented
460	#399	C₂²×C₅₉	1	1	yes	characteristic
461	#399	C₂²×C₅₉	1	1	yes	characteristic
462	#399	C₂²×C₅₉	1	2	yes	—
463	#398	C₂²×C₅₉	1	2	yes	complemented
464	#398	C₂²×C₅₉	1	2	yes	complemented
465	#396	C₂²×C₅₉	1	2	yes	—
466	#396	C₂²×C₅₉	1	2	yes	—
467	#396	C₂²×C₅₉	1	2	yes	—
468	#396	C₂²×C₅₉	1	2	yes	—
469	#395	C₂²×C₅₉	1	2	yes	complemented
470	#395	C₂²×C₅₉	1	2	yes	complemented
471	#395	C₂²×C₅₉	1	2	yes	complemented
472	#393	C₂²×C₅₉	1	1	yes	characteristic
473	#393	C₂²×C₅₉	1	2	yes	—
474	#393	C₂²×C₅₉	1	2	yes	—
475	#393	C₂²×C₅₉	1	2	yes	—
476	#393	C₂²×C₅₉	1	1	yes	characteristic
477	#393	C₂²×C₅₉	1	1	yes	characteristic
478	#393	C₂²×C₅₉	1	1	yes	characteristic
479	#393	C₂²×C₅₉	1	1	yes	characteristic
480	#393	C₂²×C₅₉	1	1	yes	characteristic
481	#391	C₂²×C₅₉	1	2	yes	complemented
482	#391	C₂²×C₅₉	1	2	yes	complemented
483	#391	C₂²×C₅₉	1	2	yes	complemented
484	#391	C₂²×C₅₉	1	2	yes	complemented
485	#391	C₂²×C₅₉	1	2	yes	complemented
486	#391	C₂²×C₅₉	1	2	yes	complemented
487	#391	C₂²×C₅₉	1	2	yes	complemented
488	#391	C₂²×C₅₉	1	2	yes	complemented
489	#389	C₂²×C₅₉	1	2	yes	complemented
490	#389	C₂²×C₅₉	1	2	yes	complemented
491	#388	C₂²×C₅₉	1	2	yes	—
492	#388	C₂²×C₅₉	1	2	yes	—
493	#388	C₂²×C₅₉	1	2	yes	—
494	#388	C₂²×C₅₉	1	2	yes	—
495	#387	C₂²×C₅₉	1	2	yes	complemented
496	#387	C₂²×C₅₉	1	2	yes	complemented
497	#387	C₂²×C₅₉	1	2	yes	complemented
498	#387	C₂²×C₅₉	1	2	yes	complemented
499	#387	C₂²×C₅₉	1	2	yes	complemented
500	#387	C₂²×C₅₉	1	2	yes	complemented
501	#387	C₂²×C₅₉	1	2	yes	complemented
502	#387	C₂²×C₅₉	1	2	yes	complemented
503	#385	C₂²×C₅₉	1	2	yes	—
504	#385	C₂²×C₅₉	1	2	yes	—
505	#385	C₂²×C₅₉	1	2	yes	—
506	#385	C₂²×C₅₉	1	2	yes	—
507	#385	C₂²×C₅₉	1	2	yes	—
508	#385	C₂²×C₅₉	1	2	yes	—
509	#385	C₂²×C₅₉	1	2	yes	—
510	#382	C₂²×C₅₉	1	2	yes	complemented
511	#381	C₂²×C₅₉	1	2	yes	—
512	#380	C₂²×C₅₉	1	2	yes	—
513	#380	C₂²×C₅₉	1	1	yes	characteristic
514	#380	C₂²×C₅₉	1	2	yes	—
515	#380	C₂²×C₅₉	1	2	yes	—
516	#379	C₂²×C₅₉	1	2	yes	—
517	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
518	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
519	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
520	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
524	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
528	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
529	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
531	C₂×#95	C₂²×C₅₉	1	2	yes	—
532	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
533	C₅₉	#35705	1	1	yes	characteristic, direct product factor, Sylow
534	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
535	C₂²×Q₈	—	2	4	no	—
536	C₂²×Q₈	—	4	4	no	—
537	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
539	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
540	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
543	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
544	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
545	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
547	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
548	C₄⋊Q₈	—	4	4	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	—	2	8	no	—
551	C₂²⋊Q₈	—	4	4	no	—
552	C₄×Q₈	—	4	4	no	—
553	#117	—	4	4	no	—
554	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
572	C₂×C₂²⋊C₄	—	2	4	no	—
573	C₂×C₂²⋊C₄	—	2	4	no	—
574	C₂×C₂²⋊C₄	—	4	4	no	—
575	C₂×C₂²⋊C₄	Q₈×C₅₉	1	8	yes	complemented
576	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
597	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
598	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
599	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
600	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
601	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
602	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
603	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
604	#95	C₂³×C₅₉	1	1	yes	characteristic
605	#95	C₂³×C₅₉	1	2	yes	—
606	#95	C₂³×C₅₉	1	2	yes	—
607	#95	C₂³×C₅₉	1	2	yes	—
608	#95	C₂³×C₅₉	1	1	yes	characteristic
609	#95	C₂³×C₅₉	1	2	yes	—
610	#95	C₂³×C₅₉	1	2	yes	—
611	#95	C₂³×C₅₉	1	2	yes	—
612	#95	C₂³×C₅₉	1	2	yes	—
613	#95	C₂³×C₅₉	1	2	yes	—
614	#95	C₂³×C₅₉	1	2	yes	—
615	#95	C₂³×C₅₉	1	2	yes	—
616	#95	C₂³×C₅₉	1	2	yes	—
617	#95	C₂³×C₅₉	1	2	yes	—
618	#95	C₂³×C₅₉	1	2	yes	—
619	#95	C₂³×C₅₉	1	2	yes	—
620	#95	C₂³×C₅₉	1	2	yes	—
621	#95	C₂³×C₅₉	1	2	yes	—
622	#95	C₂³×C₅₉	1	2	yes	—
623	#95	C₂³×C₅₉	1	2	yes	—
624	#95	C₂³×C₅₉	1	2	yes	—
625	#95	C₂³×C₅₉	1	2	yes	—
626	#95	C₂³×C₅₉	1	1	yes	characteristic
627	#95	C₂³×C₅₉	1	1	yes	characteristic
628	#95	C₂³×C₅₉	1	2	yes	—
629	#95	C₂³×C₅₉	1	2	yes	—
630	#95	C₂³×C₅₉	1	2	yes	—
631	#95	C₂³×C₅₉	1	2	yes	—
632	#95	C₂³×C₅₉	1	2	yes	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	2	no	—
637	C₂⁴	C₂×Q₈×C₅₉	1	4	yes	—
638	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
639	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	—	4	2	no	—
650	C₂×Q₈	—	4	2	no	—
651	C₂×Q₈	—	4	2	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	—	4	16	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	complemented
669	C₂²×C₄	#41×C₅₉	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
721	C₂²⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
722	C₂²⋊C₄	C₂×Q₈×C₅₉	1	8	yes	complemented
723	C₂²⋊C₄	#41×C₅₉	1	4	yes	—
724	C₄²	—	2	4	no	—
725	C₄²	—	4	2	no	—
726	C₄²	—	4	2	no	—
727	C₄²	—	4	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	2	no	—
730	C₄²	—	4	2	no	—
731	C₄²	—	4	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	8	no	—
743	C₂³	—	4	8	no	—
744	C₂³	—	8	2	no	—
745	C₂³	—	8	4	no	—
746	C₂³	—	8	2	no	—
747	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
748	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
749	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
750	C₂³	C₂×#41×C₅₉	1	2	yes	—
751	C₂³	C₂×#41×C₅₉	1	2	yes	—
752	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
753	Q₈	—	2	8	no	—
754	Q₈	—	4	8	no	—
755	Q₈	—	4	4	no	—
756	Q₈	—	8	4	no	—
757	Q₈	—	8	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	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	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	—	8	4	no	—
802	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
803	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
804	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
805	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
806	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
807	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	4	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	8	8	no	—
823	C₂²	C₅₉×#533	1	4	yes	—
824	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
825	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
826	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
828	C₂²	C₅₉×#585	1	2	yes	—
829	C₄	—	2	4	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	4	no	—
833	C₄	—	2	4	no	—
834	C₄	—	2	4	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₂	—	2	4	no	—
846	C₂	—	4	2	no	—
847	C₂	—	4	2	no	—
848	C₂	C₂×C₅₉×#533	1	1	yes	characteristic
849	C₂	C₅₉×#3490	1	1	yes	characteristic
850	C₂	C₅₉×#3501	1	2	yes	—
851	C₂	C₅₉×#3510	1	1	yes	characteristic
852	C₂	C₅₉×#3514	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁵×C₅₉	C₂³
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
1. C₅₉×#2665	C₂	semidirect
3. C₅₉×#2607	C₂	semidirect
4. C₅₉×#2589	C₂	semidirect
5. C₅₉×#2574	C₂	semidirect
6. C₅₉×#2549	C₂	semidirect
7. C₅₉×#2505	C₂	semidirect
8. C₅₉×#2492	C₂	semidirect
9. C₅₉×#2465	C₂	semidirect
10. C₅₉×#2439	C₂	semidirect
12. C₅₉×#2434	C₂	semidirect
13. C₅₉×#2396	C₂	semidirect
15. C₅₉×#2368	C₂	semidirect
16. C₅₉×#2368	C₂	semidirect
18. Q₈×C₂²⋊C₄×C₅₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
25. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
31. C₅₉×#400	C₂²	semidirect
32. C₅₉×#400	C₂²	semidirect
33. C₅₉×#400	C₂²	semidirect
37. C₅₉×#398	C₂²	semidirect
38. C₅₉×#398	C₂²	semidirect
43. C₅₉×#395	C₂²	semidirect
44. C₅₉×#395	C₂²	semidirect
45. C₅₉×#395	C₂²	semidirect
55. C₅₉×#391	C₂²	semidirect
56. C₅₉×#391	C₂²	semidirect
57. C₅₉×#391	C₂²	semidirect
58. C₅₉×#391	C₂²	semidirect
59. C₅₉×#391	C₂²	semidirect
60. C₅₉×#391	C₂²	semidirect
61. C₅₉×#391	C₂²	semidirect
62. C₅₉×#391	C₂²	semidirect
63. C₅₉×#389	C₂²	semidirect
64. C₅₉×#389	C₂²	semidirect
69. C₅₉×#387	C₂²	semidirect
70. C₅₉×#387	C₂²	semidirect
71. C₅₉×#387	C₂²	semidirect
72. C₅₉×#387	C₂²	semidirect
73. C₅₉×#387	C₂²	semidirect
74. C₅₉×#387	C₂²	semidirect
75. C₅₉×#387	C₂²	semidirect
76. C₅₉×#387	C₂²	semidirect
84. C₅₉×#382	C₂²	semidirect
91. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
92. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
93. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
148. C₂×C₂²⋊C₄×C₅₉	Q₈	semidirect
241. C₂²×C₄×C₅₉	C₂×Q₈	semidirect
295. C₂²⋊C₄×C₅₉	C₂×Q₈	semidirect
381. #35705	C₅₉	direct (N × H)
419. #2665	C₂×C₅₉	semidirect
421. #2607	C₂×C₅₉	semidirect
422. #2589	C₂×C₅₉	semidirect
423. #2574	C₂×C₅₉	semidirect
424. #2549	C₂×C₅₉	semidirect
425. #2505	C₂×C₅₉	semidirect
426. #2492	C₂×C₅₉	semidirect
427. #2465	C₂×C₅₉	semidirect
428. #2439	C₂×C₅₉	semidirect
430. #2434	C₂×C₅₉	semidirect
431. #2396	C₂×C₅₉	semidirect
433. #2368	C₂×C₅₉	semidirect
434. #2368	C₂×C₅₉	semidirect
436. Q₈×C₂²⋊C₄	C₂×C₅₉	semidirect
447. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
451. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
457. #400	C₂²×C₅₉	semidirect
458. #400	C₂²×C₅₉	semidirect
459. #400	C₂²×C₅₉	semidirect
463. #398	C₂²×C₅₉	semidirect
464. #398	C₂²×C₅₉	semidirect
469. #395	C₂²×C₅₉	semidirect
470. #395	C₂²×C₅₉	semidirect
471. #395	C₂²×C₅₉	semidirect
481. #391	C₂²×C₅₉	semidirect
482. #391	C₂²×C₅₉	semidirect
483. #391	C₂²×C₅₉	semidirect
484. #391	C₂²×C₅₉	semidirect
485. #391	C₂²×C₅₉	semidirect
486. #391	C₂²×C₅₉	semidirect
487. #391	C₂²×C₅₉	semidirect
488. #391	C₂²×C₅₉	semidirect
489. #389	C₂²×C₅₉	semidirect
490. #389	C₂²×C₅₉	semidirect
495. #387	C₂²×C₅₉	semidirect
496. #387	C₂²×C₅₉	semidirect
497. #387	C₂²×C₅₉	semidirect
498. #387	C₂²×C₅₉	semidirect
499. #387	C₂²×C₅₉	semidirect
500. #387	C₂²×C₅₉	semidirect
501. #387	C₂²×C₅₉	semidirect
502. #387	C₂²×C₅₉	semidirect
510. #382	C₂²×C₅₉	semidirect
517. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
518. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
519. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
533. C₅₉	#35705	direct (N × H)
575. C₂×C₂²⋊C₄	Q₈×C₅₉	semidirect
668. C₂²×C₄	C₂×Q₈×C₅₉	semidirect
722. C₂²⋊C₄	C₂×Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2665	2
C₅₉×#2626	2
C₅₉×#2607	2
C₅₉×#2589	2
C₅₉×#2574	2
C₅₉×#2549	2
C₅₉×#2505	2
C₅₉×#2492	2
C₅₉×#2465	2
C₅₉×#2439	2
C₅₉×#2437	2
C₅₉×#2434	2
C₅₉×#2396	2
C₂×C₅₉×#393	2
C₅₉×#2368	2
C₅₉×#2342	2
Q₈×C₂²⋊C₄×C₅₉	2
C₅₉×#2273	2
#35705	59

Subgroups — C59×#35705 #28447814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35705 #28447814