Subgroups — C₅₉×#35747 #28447856

Order 15104.

1722 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2666	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2629	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2606	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2587	C₂	1	2	yes	maximal
5	C₅₉×#2584	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2556	C₂	1	2	yes	maximal
7	C₅₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2550	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2507	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2506	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2465	C₂	1	2	yes	maximal
12	C₅₉×#2440	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2440	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#2429	C₂	1	2	yes	maximal
15	C₅₉×#2399	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic
17	C₅₉×#2370	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2369	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
20	Q₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2347	C₂	1	1	yes	maximal, characteristic
22	C₅₉×#2346	C₂	1	1	yes	maximal, characteristic
23	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
27	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₅₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
34	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#400	C₂²	1	2	yes	—
38	C₅₉×#400	C₂²	1	1	yes	characteristic
39	C₅₉×#399	C₂²	1	1	yes	characteristic
40	C₅₉×#398	C₂²	1	2	yes	—
41	C₅₉×#398	C₂²	1	2	yes	—
42	C₅₉×#398	C₂²	1	2	yes	—
43	C₅₉×#398	C₂²	1	1	yes	characteristic
44	C₅₉×#398	C₂²	1	2	yes	—
45	C₅₉×#398	C₂²	1	2	yes	—
46	C₅₉×#398	C₂²	1	1	yes	characteristic
47	C₅₉×#398	C₂²	1	2	yes	—
48	C₅₉×#398	C₂²	1	2	yes	—
49	C₅₉×#398	C₂²	1	2	yes	—
50	C₅₉×#396	C₂²	1	2	yes	—
51	C₅₉×#396	C₂²	1	1	yes	characteristic
52	C₅₉×#396	C₂²	1	2	yes	—
53	C₅₉×#396	C₂²	1	1	yes	characteristic
54	C₅₉×#395	C₂²	1	2	yes	—
55	C₅₉×#395	C₂²	1	2	yes	—
56	C₅₉×#395	C₂²	1	2	yes	—
57	C₅₉×#395	C₂²	1	2	yes	—
58	C₅₉×#395	C₂²	1	2	yes	—
59	C₅₉×#395	C₂²	1	1	yes	characteristic
60	C₅₉×#393	C₂²	1	1	yes	characteristic
61	C₅₉×#391	C₂²	1	2	yes	—
62	C₅₉×#391	C₂²	1	2	yes	—
63	C₅₉×#391	C₂²	1	2	yes	—
64	C₅₉×#389	C₂²	1	1	yes	characteristic
65	C₅₉×#389	C₂²	1	1	yes	characteristic
66	C₅₉×#389	C₂²	1	1	yes	characteristic
67	C₅₉×#389	C₂²	1	1	yes	characteristic
68	C₅₉×#389	C₂²	1	2	yes	—
69	C₅₉×#389	C₂²	1	1	yes	characteristic
70	C₅₉×#389	C₂²	1	1	yes	characteristic
71	C₅₉×#389	C₂²	1	1	yes	characteristic
72	C₅₉×#389	C₂²	1	1	yes	characteristic
73	C₅₉×#389	C₂²	1	2	yes	—
74	C₅₉×#389	C₂²	1	2	yes	—
75	C₅₉×#389	C₂²	1	2	yes	—
76	C₅₉×#389	C₂²	1	2	yes	—
77	C₅₉×#389	C₂²	1	2	yes	—
78	C₅₉×#389	C₂²	1	2	yes	—
79	C₅₉×#389	C₂²	1	2	yes	—
80	C₅₉×#389	C₂²	1	1	yes	characteristic
81	C₅₉×#389	C₂²	1	1	yes	characteristic
82	C₅₉×#389	C₂²	1	2	yes	—
83	C₅₉×#388	C₂²	1	2	yes	—
84	C₅₉×#388	C₂²	1	2	yes	—
85	C₅₉×#388	C₂²	1	2	yes	—
86	C₅₉×#388	C₂²	1	2	yes	—
87	C₅₉×#387	C₂²	1	2	yes	—
88	C₅₉×#387	C₂²	1	2	yes	—
89	C₅₉×#387	C₂²	1	2	yes	—
90	C₅₉×#387	C₂²	1	2	yes	—
91	C₅₉×#387	C₂²	1	2	yes	—
92	C₅₉×#387	C₂²	1	2	yes	—
93	C₅₉×#385	C₂²	1	2	yes	—
94	C₅₉×#385	C₂²	1	2	yes	—
95	C₅₉×#384	C₂²	1	1	yes	characteristic
96	C₅₉×#384	C₂²	1	1	yes	characteristic
97	C₅₉×#384	C₂²	1	1	yes	characteristic
98	C₅₉×#383	C₂²	1	2	yes	—
99	C₅₉×#382	C₂²	1	2	yes	—
100	C₅₉×#380	C₂²	1	1	yes	characteristic
101	C₅₉×#380	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
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×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
122	C₅₉×#376	C₂²	1	2	yes	—
123	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
125	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₅₉	—	2	4	no	—
129	C₄⋊Q₈×C₅₉	—	2	4	no	—
130	C₄⋊Q₈×C₅₉	—	4	4	no	—
131	#125×C₅₉	—	2	4	no	—
132	#125×C₅₉	—	4	4	no	—
133	C₂²⋊Q₈×C₅₉	—	4	4	no	—
134	C₂²⋊Q₈×C₅₉	—	4	4	no	—
135	C₄×Q₈×C₅₉	—	2	4	no	—
136	C₄×Q₈×C₅₉	—	4	4	no	—
137	C₄×Q₈×C₅₉	—	4	4	no	—
138	#117×C₅₉	—	2	4	no	—
139	#117×C₅₉	Q₈	1	8	yes	complemented
140	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
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	2	yes	—
144	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
164	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
200	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
203	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
204	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
205	#95×C₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
211	#95×C₅₉	C₂³	1	1	yes	characteristic
212	#95×C₅₉	C₂³	1	2	yes	—
213	#95×C₅₉	C₂³	1	2	yes	—
214	#95×C₅₉	C₂³	1	1	yes	characteristic
215	#95×C₅₉	C₂³	1	1	yes	characteristic
216	#95×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
225	#95×C₅₉	C₂³	1	1	yes	characteristic
226	#95×C₅₉	C₂³	1	1	yes	characteristic
227	#95×C₅₉	C₂³	1	1	yes	characteristic
228	#95×C₅₉	C₂³	1	2	yes	—
229	#95×C₅₉	C₂³	1	1	yes	characteristic
230	#95×C₅₉	C₂³	1	2	yes	—
231	#95×C₅₉	C₂³	1	2	yes	—
232	#95×C₅₉	C₂³	1	2	yes	—
233	#95×C₅₉	C₂³	1	2	yes	—
234	#95×C₅₉	C₂³	1	2	yes	—
235	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
236	C₂×Q₈×C₅₉	—	2	2	no	—
237	C₂×Q₈×C₅₉	—	2	4	no	—
238	C₂×Q₈×C₅₉	—	2	4	no	—
239	C₂×Q₈×C₅₉	—	2	2	no	—
240	C₂×Q₈×C₅₉	—	2	4	no	—
241	C₂×Q₈×C₅₉	—	2	2	no	—
242	C₂×Q₈×C₅₉	—	4	2	no	—
243	C₂×Q₈×C₅₉	—	4	2	no	—
244	C₂×Q₈×C₅₉	—	4	2	no	—
245	C₂²×C₄×C₅₉	—	2	2	no	—
246	C₂²×C₄×C₅₉	—	2	2	no	—
247	C₂²×C₄×C₅₉	—	2	4	no	—
248	C₂²×C₄×C₅₉	—	4	2	no	—
249	C₂²×C₄×C₅₉	—	4	2	no	—
250	C₂²×C₄×C₅₉	C₂×Q₈	1	4	yes	—
251	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
259	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
273	C₄⋊C₄×C₅₉	—	2	4	no	—
274	C₄⋊C₄×C₅₉	—	2	2	no	—
275	C₄⋊C₄×C₅₉	—	2	2	no	—
276	C₄⋊C₄×C₅₉	—	2	2	no	—
277	C₄⋊C₄×C₅₉	—	2	2	no	—
278	C₄⋊C₄×C₅₉	—	2	2	no	—
279	C₄⋊C₄×C₅₉	—	2	2	no	—
280	C₄⋊C₄×C₅₉	—	2	4	no	—
281	C₄⋊C₄×C₅₉	—	2	4	no	—
282	C₄⋊C₄×C₅₉	—	2	2	no	—
283	C₄⋊C₄×C₅₉	—	2	2	no	—
284	C₄⋊C₄×C₅₉	—	2	4	no	—
285	C₄⋊C₄×C₅₉	—	2	4	no	—
286	C₄⋊C₄×C₅₉	—	2	2	no	—
287	C₄⋊C₄×C₅₉	—	2	2	no	—
288	C₄⋊C₄×C₅₉	—	2	2	no	—
289	C₄⋊C₄×C₅₉	—	2	4	no	—
290	C₄⋊C₄×C₅₉	—	2	4	no	—
291	C₄⋊C₄×C₅₉	—	2	4	no	—
292	C₄⋊C₄×C₅₉	—	2	2	no	—
293	C₄⋊C₄×C₅₉	—	2	4	no	—
294	C₄⋊C₄×C₅₉	—	2	2	no	—
295	C₄⋊C₄×C₅₉	—	2	2	no	—
296	C₄⋊C₄×C₅₉	—	2	2	no	—
297	C₄⋊C₄×C₅₉	—	2	4	no	—
298	C₄⋊C₄×C₅₉	—	2	2	no	—
299	C₄⋊C₄×C₅₉	—	4	2	no	—
300	C₄⋊C₄×C₅₉	—	4	2	no	—
301	C₄⋊C₄×C₅₉	—	4	2	no	—
302	C₄⋊C₄×C₅₉	—	4	2	no	—
303	C₄⋊C₄×C₅₉	—	4	2	no	—
304	C₄⋊C₄×C₅₉	—	4	2	no	—
305	C₄⋊C₄×C₅₉	—	4	2	no	—
306	C₄⋊C₄×C₅₉	—	4	2	no	—
307	C₄⋊C₄×C₅₉	—	4	2	no	—
308	C₄⋊C₄×C₅₉	—	4	2	no	—
309	C₄⋊C₄×C₅₉	—	4	2	no	—
310	C₄⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
311	C₄⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
312	C₄⋊C₄×C₅₉	#41	1	4	yes	—
313	C₂²⋊C₄×C₅₉	—	2	2	no	—
314	C₂²⋊C₄×C₅₉	—	2	2	no	—
315	C₂²⋊C₄×C₅₉	—	2	2	no	—
316	C₂²⋊C₄×C₅₉	—	2	2	no	—
317	C₂²⋊C₄×C₅₉	—	2	2	no	—
318	C₂²⋊C₄×C₅₉	—	2	2	no	—
319	C₂²⋊C₄×C₅₉	—	4	2	no	—
320	C₂²⋊C₄×C₅₉	—	4	2	no	—
321	C₂²⋊C₄×C₅₉	C₂×Q₈	1	8	yes	—
322	C₄²×C₅₉	—	2	2	no	—
323	C₄²×C₅₉	—	2	2	no	—
324	C₄²×C₅₉	—	2	2	no	—
325	C₄²×C₅₉	—	2	2	no	—
326	C₄²×C₅₉	—	2	2	no	—
327	C₄²×C₅₉	—	2	4	no	—
328	C₄²×C₅₉	—	2	4	no	—
329	C₄²×C₅₉	—	4	2	no	—
330	C₄²×C₅₉	—	4	2	no	—
331	C₄²×C₅₉	—	4	2	no	—
332	C₄²×C₅₉	—	4	2	no	—
333	C₄²×C₅₉	—	4	2	no	—
334	C₄²×C₅₉	—	4	2	no	—
335	C₄²×C₅₉	C₂×Q₈	1	8	yes	—
336	C₄²×C₅₉	#41	1	4	yes	—
337	C₂³×C₅₉	—	2	1	no	—
338	C₂³×C₅₉	—	2	1	no	—
339	C₂³×C₅₉	—	2	1	no	—
340	C₂³×C₅₉	—	2	1	no	—
341	C₂³×C₅₉	—	2	1	no	—
342	C₂³×C₅₉	—	2	1	no	—
343	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
344	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
345	Q₈×C₅₉	—	2	8	no	—
346	Q₈×C₅₉	—	4	8	no	—
347	Q₈×C₅₉	—	8	4	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	1	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	1	no	—
357	C₂×C₄×C₅₉	—	2	1	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	2	no	—
363	C₂×C₄×C₅₉	—	2	2	no	—
364	C₂×C₄×C₅₉	—	2	1	no	—
365	C₂×C₄×C₅₉	—	2	1	no	—
366	C₂×C₄×C₅₉	—	2	1	no	—
367	C₂×C₄×C₅₉	—	2	1	no	—
368	C₂×C₄×C₅₉	—	2	8	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	2	no	—
381	C₂×C₄×C₅₉	—	2	1	no	—
382	C₂×C₄×C₅₉	—	2	1	no	—
383	C₂×C₄×C₅₉	—	2	2	no	—
384	C₂×C₄×C₅₉	—	2	2	no	—
385	C₂×C₄×C₅₉	—	2	2	no	—
386	C₂×C₄×C₅₉	—	2	2	no	—
387	C₂×C₄×C₅₉	—	2	1	no	—
388	C₂×C₄×C₅₉	—	2	1	no	—
389	C₂×C₄×C₅₉	—	2	2	no	—
390	C₂×C₄×C₅₉	—	2	2	no	—
391	C₂×C₄×C₅₉	—	2	1	no	—
392	C₂×C₄×C₅₉	—	2	2	no	—
393	C₂×C₄×C₅₉	—	2	1	no	—
394	C₂×C₄×C₅₉	—	2	2	no	—
395	C₂×C₄×C₅₉	—	2	1	no	—
396	C₂×C₄×C₅₉	—	2	1	no	—
397	C₂×C₄×C₅₉	—	2	1	no	—
398	C₂×C₄×C₅₉	—	2	2	no	—
399	C₂×C₄×C₅₉	—	2	1	no	—
400	C₂×C₄×C₅₉	—	2	1	no	—
401	C₂×C₄×C₅₉	—	2	1	no	—
402	C₂×C₄×C₅₉	—	8	4	no	—
403	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
404	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
405	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
406	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
407	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
408	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
409	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
410	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
411	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
412	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
413	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
414	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
415	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
416	#35747	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
417	C₂²×C₅₉	—	2	2	no	—
418	C₂²×C₅₉	—	2	2	no	—
419	C₂²×C₅₉	—	2	2	no	—
420	C₂²×C₅₉	—	4	1	no	—
421	C₂²×C₅₉	—	4	1	no	—
422	C₂²×C₅₉	—	4	1	no	—
423	C₂²×C₅₉	—	4	1	no	—
424	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
425	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
427	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
430	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
431	C₄×C₅₉	—	2	2	no	—
432	C₄×C₅₉	—	2	2	no	—
433	C₄×C₅₉	—	2	2	no	—
434	C₄×C₅₉	—	2	2	no	—
435	C₄×C₅₉	—	2	4	no	—
436	C₄×C₅₉	—	2	4	no	—
437	C₄×C₅₉	—	2	2	no	—
438	C₄×C₅₉	—	2	4	no	—
439	C₄×C₅₉	—	2	2	no	—
440	C₄×C₅₉	—	2	2	no	—
441	C₄×C₅₉	—	4	1	no	—
442	C₄×C₅₉	—	4	2	no	—
443	C₄×C₅₉	—	4	1	no	—
444	C₄×C₅₉	—	4	1	no	—
445	C₄×C₅₉	—	4	1	no	—
446	C₄×C₅₉	—	4	2	no	—
447	C₄×C₅₉	—	4	2	no	—
448	C₄×C₅₉	—	4	2	no	—
449	C₄×C₅₉	—	4	2	no	—
450	C₄×C₅₉	—	4	1	no	—
451	C₄×C₅₉	—	4	1	no	—
452	C₄×C₅₉	#533	1	4	yes	—
453	#2666	C₂×C₅₉	1	2	yes	complemented
454	#2629	C₂×C₅₉	1	1	yes	characteristic
455	#2606	C₂×C₅₉	1	2	yes	complemented
456	#2587	C₂×C₅₉	1	2	yes	—
457	#2584	C₂×C₅₉	1	1	yes	characteristic, complemented
458	#2556	C₂×C₅₉	1	2	yes	—
459	#2551	C₂×C₅₉	1	1	yes	characteristic, complemented
460	#2550	C₂×C₅₉	1	2	yes	complemented
461	#2507	C₂×C₅₉	1	1	yes	characteristic, complemented
462	#2506	C₂×C₅₉	1	1	yes	characteristic, complemented
463	#2465	C₂×C₅₉	1	2	yes	—
464	#2440	C₂×C₅₉	1	1	yes	characteristic
465	#2440	C₂×C₅₉	1	1	yes	characteristic
466	#2429	C₂×C₅₉	1	2	yes	—
467	#2399	C₂×C₅₉	1	2	yes	complemented
468	#2396	C₂×C₅₉	1	1	yes	characteristic
469	#2370	C₂×C₅₉	1	1	yes	characteristic, complemented
470	#2369	C₂×C₅₉	1	1	yes	characteristic, complemented
471	#2365	C₂×C₅₉	1	1	yes	characteristic, complemented
472	Q₈×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
473	#2347	C₂×C₅₉	1	1	yes	characteristic
474	#2346	C₂×C₅₉	1	1	yes	characteristic
475	#2274	C₂×C₅₉	1	1	yes	characteristic
476	C₂×C₅₉	—	4	2	no	—
477	C₂×C₅₉	C₂×#533	1	1	yes	characteristic
478	C₂×C₅₉	#3492	1	1	yes	characteristic
479	C₂×C₅₉	#3503	1	1	yes	characteristic
480	C₂×C₅₉	#3503	1	1	yes	characteristic
481	C₂×C₅₉	#3511	1	1	yes	characteristic
482	C₂×C₅₉	#3519	1	1	yes	characteristic
483	C₂×C₅₉	#3523	1	1	yes	characteristic
484	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
485	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
486	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
487	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
488	C₂×#125	C₂²×C₅₉	1	2	yes	—
489	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
490	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
491	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
493	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
494	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
495	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
496	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
497	#400	C₂²×C₅₉	1	2	yes	—
498	#400	C₂²×C₅₉	1	1	yes	characteristic
499	#399	C₂²×C₅₉	1	1	yes	characteristic
500	#398	C₂²×C₅₉	1	2	yes	—
501	#398	C₂²×C₅₉	1	2	yes	—
502	#398	C₂²×C₅₉	1	1	yes	characteristic
503	#398	C₂²×C₅₉	1	2	yes	—
504	#398	C₂²×C₅₉	1	2	yes	—
505	#398	C₂²×C₅₉	1	2	yes	—
506	#398	C₂²×C₅₉	1	2	yes	—
507	#398	C₂²×C₅₉	1	1	yes	characteristic
508	#398	C₂²×C₅₉	1	2	yes	—
509	#398	C₂²×C₅₉	1	2	yes	—
510	#396	C₂²×C₅₉	1	1	yes	characteristic
511	#396	C₂²×C₅₉	1	2	yes	—
512	#396	C₂²×C₅₉	1	2	yes	—
513	#396	C₂²×C₅₉	1	1	yes	characteristic
514	#395	C₂²×C₅₉	1	2	yes	—
515	#395	C₂²×C₅₉	1	1	yes	characteristic
516	#395	C₂²×C₅₉	1	2	yes	—
517	#395	C₂²×C₅₉	1	2	yes	—
518	#395	C₂²×C₅₉	1	2	yes	—
519	#395	C₂²×C₅₉	1	2	yes	—
520	#393	C₂²×C₅₉	1	1	yes	characteristic
521	#391	C₂²×C₅₉	1	2	yes	—
522	#391	C₂²×C₅₉	1	2	yes	—
523	#391	C₂²×C₅₉	1	2	yes	—
524	#389	C₂²×C₅₉	1	2	yes	—
525	#389	C₂²×C₅₉	1	1	yes	characteristic
526	#389	C₂²×C₅₉	1	1	yes	characteristic
527	#389	C₂²×C₅₉	1	2	yes	—
528	#389	C₂²×C₅₉	1	1	yes	characteristic
529	#389	C₂²×C₅₉	1	1	yes	characteristic
530	#389	C₂²×C₅₉	1	2	yes	—
531	#389	C₂²×C₅₉	1	2	yes	—
532	#389	C₂²×C₅₉	1	1	yes	characteristic
533	#389	C₂²×C₅₉	1	1	yes	characteristic
534	#389	C₂²×C₅₉	1	2	yes	—
535	#389	C₂²×C₅₉	1	2	yes	—
536	#389	C₂²×C₅₉	1	2	yes	—
537	#389	C₂²×C₅₉	1	1	yes	characteristic
538	#389	C₂²×C₅₉	1	1	yes	characteristic
539	#389	C₂²×C₅₉	1	2	yes	—
540	#389	C₂²×C₅₉	1	1	yes	characteristic
541	#389	C₂²×C₅₉	1	1	yes	characteristic
542	#389	C₂²×C₅₉	1	2	yes	—
543	#388	C₂²×C₅₉	1	2	yes	—
544	#388	C₂²×C₅₉	1	2	yes	—
545	#388	C₂²×C₅₉	1	2	yes	—
546	#388	C₂²×C₅₉	1	2	yes	—
547	#387	C₂²×C₅₉	1	2	yes	—
548	#387	C₂²×C₅₉	1	2	yes	—
549	#387	C₂²×C₅₉	1	2	yes	—
550	#387	C₂²×C₅₉	1	2	yes	—
551	#387	C₂²×C₅₉	1	2	yes	—
552	#387	C₂²×C₅₉	1	2	yes	—
553	#385	C₂²×C₅₉	1	2	yes	—
554	#385	C₂²×C₅₉	1	2	yes	—
555	#384	C₂²×C₅₉	1	1	yes	characteristic
556	#384	C₂²×C₅₉	1	1	yes	characteristic
557	#384	C₂²×C₅₉	1	1	yes	characteristic
558	#383	C₂²×C₅₉	1	2	yes	—
559	#382	C₂²×C₅₉	1	2	yes	—
560	#380	C₂²×C₅₉	1	1	yes	characteristic
561	#380	C₂²×C₅₉	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
569	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
571	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
581	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
582	#376	C₂²×C₅₉	1	2	yes	—
583	C₅₉	#35747	1	1	yes	characteristic, direct product factor, Sylow
584	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
586	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
587	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
589	C₄⋊Q₈	—	2	4	no	—
590	C₄⋊Q₈	—	2	4	no	—
591	C₄⋊Q₈	—	4	4	no	—
592	#125	—	2	4	no	—
593	#125	—	4	4	no	—
594	C₂²⋊Q₈	—	4	4	no	—
595	C₂²⋊Q₈	—	4	4	no	—
596	C₄×Q₈	—	2	4	no	—
597	C₄×Q₈	—	4	4	no	—
598	C₄×Q₈	—	4	4	no	—
599	#117	—	2	4	no	—
600	#117	Q₈×C₅₉	1	8	yes	complemented
601	C₂×C₄⋊C₄	—	2	4	no	—
602	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
651	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
653	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
658	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
659	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
660	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
661	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
662	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
663	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
664	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
665	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
666	#95	C₂³×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
673	#95	C₂³×C₅₉	1	2	yes	—
674	#95	C₂³×C₅₉	1	2	yes	—
675	#95	C₂³×C₅₉	1	1	yes	characteristic
676	#95	C₂³×C₅₉	1	1	yes	characteristic
677	#95	C₂³×C₅₉	1	1	yes	characteristic
678	#95	C₂³×C₅₉	1	2	yes	—
679	#95	C₂³×C₅₉	1	2	yes	—
680	#95	C₂³×C₅₉	1	2	yes	—
681	#95	C₂³×C₅₉	1	2	yes	—
682	#95	C₂³×C₅₉	1	2	yes	—
683	#95	C₂³×C₅₉	1	2	yes	—
684	#95	C₂³×C₅₉	1	2	yes	—
685	#95	C₂³×C₅₉	1	1	yes	characteristic
686	#95	C₂³×C₅₉	1	1	yes	characteristic
687	#95	C₂³×C₅₉	1	1	yes	characteristic
688	#95	C₂³×C₅₉	1	1	yes	characteristic
689	#95	C₂³×C₅₉	1	2	yes	—
690	#95	C₂³×C₅₉	1	1	yes	characteristic
691	#95	C₂³×C₅₉	1	2	yes	—
692	#95	C₂³×C₅₉	1	2	yes	—
693	#95	C₂³×C₅₉	1	2	yes	—
694	#95	C₂³×C₅₉	1	2	yes	—
695	#95	C₂³×C₅₉	1	2	yes	—
696	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	4	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	4	2	no	—
704	C₂×Q₈	—	4	2	no	—
705	C₂×Q₈	—	4	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	C₂×Q₈×C₅₉	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
772	C₄⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
773	C₄⋊C₄	#41×C₅₉	1	4	yes	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	C₂×Q₈×C₅₉	1	8	yes	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	4	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	2	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₄²	C₂×Q₈×C₅₉	1	8	yes	—
797	C₄²	#41×C₅₉	1	4	yes	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
805	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
806	Q₈	—	2	8	no	—
807	Q₈	—	4	8	no	—
808	Q₈	—	8	4	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	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	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	8	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	8	4	no	—
864	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
865	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
866	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
867	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
868	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
869	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
870	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
871	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
872	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
873	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
874	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
875	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
876	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
885	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
886	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
887	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
888	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
889	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
890	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	4	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	C₅₉×#533	1	4	yes	—
913	C₂	—	4	2	no	—
914	C₂	C₂×C₅₉×#533	1	1	yes	characteristic
915	C₂	C₅₉×#3492	1	1	yes	characteristic
916	C₂	C₅₉×#3503	1	1	yes	characteristic
917	C₂	C₅₉×#3503	1	1	yes	characteristic
918	C₂	C₅₉×#3511	1	1	yes	characteristic
919	C₂	C₅₉×#3519	1	1	yes	characteristic
920	C₂	C₅₉×#3523	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
1. C₅₉×#2666	C₂	semidirect
3. C₅₉×#2606	C₂	semidirect
5. C₅₉×#2584	C₂	semidirect
7. C₅₉×#2551	C₂	semidirect
8. C₅₉×#2550	C₂	semidirect
9. C₅₉×#2507	C₂	semidirect
10. C₅₉×#2506	C₂	semidirect
15. C₅₉×#2399	C₂	semidirect
17. C₅₉×#2370	C₂	semidirect
18. C₅₉×#2369	C₂	semidirect
19. C₅₉×#2365	C₂	semidirect
20. Q₈×C₄⋊C₄×C₅₉	C₂	semidirect
139. #117×C₅₉	Q₈	semidirect
416. #35747	C₅₉	direct (N × H)
453. #2666	C₂×C₅₉	semidirect
455. #2606	C₂×C₅₉	semidirect
457. #2584	C₂×C₅₉	semidirect
459. #2551	C₂×C₅₉	semidirect
460. #2550	C₂×C₅₉	semidirect
461. #2507	C₂×C₅₉	semidirect
462. #2506	C₂×C₅₉	semidirect
467. #2399	C₂×C₅₉	semidirect
469. #2370	C₂×C₅₉	semidirect
470. #2369	C₂×C₅₉	semidirect
471. #2365	C₂×C₅₉	semidirect
472. Q₈×C₄⋊C₄	C₂×C₅₉	semidirect
583. C₅₉	#35747	direct (N × H)
600. #117	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×#2666	2
C₅₉×#2629	2
C₅₉×#2606	2
C₅₉×#2587	2
C₅₉×#2584	2
C₅₉×#2556	2
C₅₉×#2551	2
C₅₉×#2550	2
C₅₉×#2507	2
C₅₉×#2506	2
C₅₉×#2465	2
C₅₉×#2440	2
C₅₉×#2429	2
C₅₉×#2399	2
C₅₉×#2396	2
C₅₉×#2370	2
C₅₉×#2369	2
C₅₉×#2365	2
Q₈×C₄⋊C₄×C₅₉	2
C₅₉×#2347	2
C₅₉×#2346	2
C₅₉×#2274	2
#35747	59

Subgroups — C59×#35747 #28447856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35747 #28447856