Subgroups — C₅₉×#35817 #28447926

Order 15104.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2637	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2620	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2609	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2601	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2582	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2545	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2479	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2477	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2469	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2465	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2446	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2436	C₂	1	1	yes	maximal, characteristic
16	C₅₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₉×#2396	C₂	1	2	yes	maximal, complemented
19	C₅₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₉×#2363	C₂	1	1	yes	maximal, characteristic
22	C₅₉×#2362	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#556	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#126×C₅₉	C₂²	1	2	yes	—
29	C₂×#126×C₅₉	C₂²	1	2	yes	—
30	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
35	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#519	—	2	8	no	—
37	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₅₉	C₂²	1	2	yes	—
47	C₂×#117×C₅₉	C₂²	1	2	yes	—
48	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₅₉	C₂²	1	2	yes	—
51	C₅₉×#400	C₂²	1	2	yes	—
52	C₅₉×#400	C₂²	1	1	yes	characteristic
53	C₅₉×#399	C₂²	1	2	yes	—
54	C₅₉×#399	C₂²	1	1	yes	characteristic
55	C₅₉×#398	C₂²	1	2	yes	—
56	C₅₉×#398	C₂²	1	2	yes	—
57	C₅₉×#398	C₂²	1	1	yes	characteristic
58	C₅₉×#398	C₂²	1	2	yes	—
59	C₅₉×#398	C₂²	1	1	yes	characteristic
60	C₅₉×#397	C₂²	1	2	yes	—
61	C₅₉×#396	C₂²	1	2	yes	—
62	C₅₉×#396	C₂²	1	2	yes	—
63	C₅₉×#396	C₂²	1	1	yes	characteristic
64	C₅₉×#396	C₂²	1	1	yes	characteristic
65	C₅₉×#396	C₂²	1	2	yes	—
66	C₅₉×#396	C₂²	1	2	yes	—
67	C₅₉×#395	C₂²	1	2	yes	—
68	C₅₉×#395	C₂²	1	2	yes	—
69	C₅₉×#395	C₂²	1	1	yes	characteristic
70	C₅₉×#394	C₂²	1	2	yes	—
71	C₅₉×#394	C₂²	1	2	yes	—
72	C₅₉×#393	C₂²	1	2	yes	—
73	C₅₉×#393	C₂²	1	2	yes	—
74	C₅₉×#393	C₂²	1	1	yes	characteristic
75	C₅₉×#391	C₂²	1	1	yes	characteristic
76	C₅₉×#391	C₂²	1	1	yes	characteristic
77	C₅₉×#391	C₂²	1	1	yes	characteristic
78	C₅₉×#391	C₂²	1	2	yes	—
79	C₅₉×#391	C₂²	1	1	yes	characteristic
80	C₅₉×#391	C₂²	1	1	yes	characteristic
81	C₅₉×#391	C₂²	1	1	yes	characteristic
82	C₅₉×#390	C₂²	1	1	yes	characteristic
83	C₅₉×#390	C₂²	1	2	yes	—
84	C₅₉×#390	C₂²	1	1	yes	characteristic
85	C₅₉×#389	C₂²	1	1	yes	characteristic
86	C₅₉×#389	C₂²	1	1	yes	characteristic
87	C₅₉×#389	C₂²	1	2	yes	—
88	C₅₉×#389	C₂²	1	2	yes	—
89	C₅₉×#388	C₂²	1	2	yes	—
90	C₅₉×#388	C₂²	1	2	yes	—
91	C₅₉×#388	C₂²	1	2	yes	—
92	C₅₉×#388	C₂²	1	2	yes	—
93	C₅₉×#388	C₂²	1	2	yes	—
94	C₅₉×#388	C₂²	1	2	yes	—
95	C₅₉×#388	C₂²	1	2	yes	—
96	C₅₉×#388	C₂²	1	2	yes	—
97	C₅₉×#388	C₂²	1	2	yes	—
98	C₅₉×#387	C₂²	1	2	yes	—
99	C₅₉×#387	C₂²	1	2	yes	—
100	C₅₉×#387	C₂²	1	2	yes	—
101	C₅₉×#387	C₂²	1	2	yes	—
102	C₅₉×#387	C₂²	1	2	yes	—
103	C₅₉×#387	C₂²	1	2	yes	—
104	C₅₉×#387	C₂²	1	2	yes	—
105	C₅₉×#386	C₂²	1	2	yes	—
106	C₅₉×#386	C₂²	1	2	yes	—
107	C₅₉×#386	C₂²	1	2	yes	—
108	C₅₉×#385	C₂²	1	2	yes	—
109	C₅₉×#385	C₂²	1	2	yes	—
110	C₅₉×#385	C₂²	1	2	yes	—
111	C₅₉×#384	C₂²	1	1	yes	characteristic
112	C₅₉×#382	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
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	2	yes	—
118	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
120	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
124	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
125	C₂²×Q₈×C₅₉	—	2	4	no	—
126	C₂²×Q₈×C₅₉	—	2	4	no	—
127	C₂²×Q₈×C₅₉	—	2	4	no	—
128	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
130	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
135	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
137	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₅₉	—	2	4	no	—
139	C₄⋊Q₈×C₅₉	—	2	4	no	—
140	#126×C₅₉	—	2	8	no	—
141	#126×C₅₉	—	2	8	no	—
142	#124×C₅₉	—	2	4	no	—
143	#124×C₅₉	—	2	4	no	—
144	#124×C₅₉	—	2	4	no	—
145	C₂²⋊Q₈×C₅₉	—	2	4	no	—
146	C₂²⋊Q₈×C₅₉	—	2	8	no	—
147	#121×C₅₉	—	2	4	no	—
148	C₄×Q₈×C₅₉	—	2	4	no	—
149	C₄×Q₈×C₅₉	—	2	4	no	—
150	C₄×Q₈×C₅₉	—	2	8	no	—
151	C₄×Q₈×C₅₉	—	2	4	no	—
152	C₄×Q₈×C₅₉	—	2	8	no	—
153	C₄×Q₈×C₅₉	—	2	4	no	—
154	C₄×Q₈×C₅₉	—	2	4	no	—
155	C₄×Q₈×C₅₉	D₄	1	8	yes	complemented
156	C₄×D₄×C₅₉	—	2	4	no	—
157	#117×C₅₉	—	2	4	no	—
158	#117×C₅₉	—	2	8	no	—
159	#117×C₅₉	—	2	8	no	—
160	#117×C₅₉	—	2	4	no	—
161	#117×C₅₉	—	2	8	no	—
162	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
211	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
214	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
215	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
218	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
220	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
222	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
224	C₂×C₄²×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	2	yes	—
230	#95×C₅₉	C₂³	1	1	yes	characteristic
231	#95×C₅₉	C₂³	1	1	yes	characteristic
232	#95×C₅₉	C₂³	1	2	yes	—
233	#95×C₅₉	C₂³	1	2	yes	—
234	#95×C₅₉	C₂³	1	2	yes	—
235	#95×C₅₉	C₂³	1	2	yes	—
236	#95×C₅₉	C₂³	1	2	yes	—
237	#95×C₅₉	C₂³	1	1	yes	characteristic
238	#95×C₅₉	C₂³	1	1	yes	characteristic
239	#95×C₅₉	C₂³	1	1	yes	characteristic
240	#95×C₅₉	C₂³	1	1	yes	characteristic
241	#95×C₅₉	C₂³	1	1	yes	characteristic
242	#95×C₅₉	C₂³	1	2	yes	—
243	#95×C₅₉	C₂³	1	2	yes	—
244	#95×C₅₉	C₂³	1	2	yes	—
245	#95×C₅₉	C₂³	1	2	yes	—
246	#95×C₅₉	C₂³	1	2	yes	—
247	#95×C₅₉	C₂³	1	2	yes	—
248	#95×C₅₉	C₂³	1	2	yes	—
249	#95×C₅₉	C₂³	1	2	yes	—
250	#95×C₅₉	C₂³	1	2	yes	—
251	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
252	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
253	C₂×Q₈×C₅₉	—	2	32	no	—
254	C₂×Q₈×C₅₉	—	2	4	no	—
255	C₂×Q₈×C₅₉	—	2	2	no	—
256	C₂×Q₈×C₅₉	—	2	2	no	—
257	C₂×Q₈×C₅₉	—	2	2	no	—
258	C₂×Q₈×C₅₉	—	2	4	no	—
259	C₂×Q₈×C₅₉	—	2	4	no	—
260	C₂×Q₈×C₅₉	—	2	2	no	—
261	C₂×Q₈×C₅₉	—	2	2	no	—
262	C₂×Q₈×C₅₉	—	2	2	no	—
263	C₂×Q₈×C₅₉	—	2	2	no	—
264	C₂×Q₈×C₅₉	—	2	2	no	—
265	C₂×Q₈×C₅₉	—	2	2	no	—
266	C₂×Q₈×C₅₉	—	4	1	no	—
267	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
268	C₂×Q₈×C₅₉	#41	1	4	yes	—
269	C₂×D₄×C₅₉	—	2	4	no	—
270	C₂×D₄×C₅₉	—	2	2	no	—
271	C₂×D₄×C₅₉	—	2	2	no	—
272	C₂×D₄×C₅₉	—	2	2	no	—
273	C₂×D₄×C₅₉	—	4	2	no	—
274	C₂×D₄×C₅₉	—	4	2	no	—
275	C₂²×C₄×C₅₉	—	2	4	no	—
276	C₂²×C₄×C₅₉	—	2	4	no	—
277	C₂²×C₄×C₅₉	—	2	2	no	—
278	C₂²×C₄×C₅₉	—	2	4	no	—
279	C₂²×C₄×C₅₉	—	2	2	no	—
280	C₂²×C₄×C₅₉	—	2	4	no	—
281	C₂²×C₄×C₅₉	—	2	4	no	—
282	C₂²×C₄×C₅₉	—	4	2	no	—
283	C₂²×C₄×C₅₉	#41	1	4	yes	—
284	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₅₉	—	2	2	no	—
306	C₄⋊C₄×C₅₉	—	2	4	no	—
307	C₄⋊C₄×C₅₉	—	2	2	no	—
308	C₄⋊C₄×C₅₉	—	2	4	no	—
309	C₄⋊C₄×C₅₉	—	2	2	no	—
310	C₄⋊C₄×C₅₉	—	2	4	no	—
311	C₄⋊C₄×C₅₉	—	2	2	no	—
312	C₄⋊C₄×C₅₉	—	2	4	no	—
313	C₄⋊C₄×C₅₉	—	2	4	no	—
314	C₄⋊C₄×C₅₉	—	2	2	no	—
315	C₄⋊C₄×C₅₉	—	2	2	no	—
316	C₄⋊C₄×C₅₉	—	2	4	no	—
317	C₄⋊C₄×C₅₉	—	2	2	no	—
318	C₄⋊C₄×C₅₉	—	2	2	no	—
319	C₄⋊C₄×C₅₉	—	2	4	no	—
320	C₄⋊C₄×C₅₉	—	2	4	no	—
321	C₄⋊C₄×C₅₉	—	2	4	no	—
322	C₄⋊C₄×C₅₉	—	2	2	no	—
323	C₄⋊C₄×C₅₉	—	2	2	no	—
324	C₄⋊C₄×C₅₉	—	2	2	no	—
325	C₄⋊C₄×C₅₉	—	4	1	no	—
326	C₄⋊C₄×C₅₉	—	4	1	no	—
327	C₄⋊C₄×C₅₉	—	4	2	no	—
328	C₄⋊C₄×C₅₉	—	4	2	no	—
329	C₄⋊C₄×C₅₉	—	4	1	no	—
330	C₄⋊C₄×C₅₉	—	4	2	no	—
331	C₄⋊C₄×C₅₉	—	4	2	no	—
332	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
333	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
334	C₂²⋊C₄×C₅₉	—	2	4	no	—
335	C₂²⋊C₄×C₅₉	—	2	4	no	—
336	C₂²⋊C₄×C₅₉	—	2	2	no	—
337	C₂²⋊C₄×C₅₉	—	2	2	no	—
338	C₂²⋊C₄×C₅₉	—	2	4	no	—
339	C₂²⋊C₄×C₅₉	—	2	4	no	—
340	C₂²⋊C₄×C₅₉	—	2	4	no	—
341	C₂²⋊C₄×C₅₉	—	2	4	no	—
342	C₂²⋊C₄×C₅₉	—	2	4	no	—
343	C₂²⋊C₄×C₅₉	—	2	4	no	—
344	C₂²⋊C₄×C₅₉	—	2	4	no	—
345	C₂²⋊C₄×C₅₉	—	2	4	no	—
346	C₂²⋊C₄×C₅₉	—	2	2	no	—
347	C₂²⋊C₄×C₅₉	—	2	4	no	—
348	C₂²⋊C₄×C₅₉	—	2	2	no	—
349	C₂²⋊C₄×C₅₉	—	4	1	no	—
350	C₂²⋊C₄×C₅₉	—	4	2	no	—
351	C₂²⋊C₄×C₅₉	—	4	2	no	—
352	C₂²⋊C₄×C₅₉	—	4	2	no	—
353	C₂²⋊C₄×C₅₉	—	4	1	no	—
354	C₄²×C₅₉	—	2	4	no	—
355	C₄²×C₅₉	—	2	4	no	—
356	C₄²×C₅₉	—	2	4	no	—
357	C₄²×C₅₉	—	2	4	no	—
358	C₄²×C₅₉	—	2	2	no	—
359	C₄²×C₅₉	—	2	4	no	—
360	C₄²×C₅₉	—	2	2	no	—
361	C₄²×C₅₉	—	2	2	no	—
362	C₄²×C₅₉	—	2	2	no	—
363	C₄²×C₅₉	—	2	2	no	—
364	C₄²×C₅₉	—	4	2	no	—
365	C₄²×C₅₉	—	4	2	no	—
366	C₄²×C₅₉	C₂×D₄	1	8	yes	—
367	C₄²×C₅₉	C₂×D₄	1	4	yes	—
368	C₂³×C₅₉	—	2	1	no	—
369	C₂³×C₅₉	—	2	1	no	—
370	C₂³×C₅₉	—	2	1	no	—
371	C₂³×C₅₉	—	2	1	no	—
372	C₂³×C₅₉	—	2	1	no	—
373	C₂³×C₅₉	—	2	1	no	—
374	C₂³×C₅₉	—	2	2	no	—
375	C₂³×C₅₉	—	2	2	no	—
376	C₂³×C₅₉	—	2	2	no	—
377	C₂³×C₅₉	—	2	2	no	—
378	C₂³×C₅₉	—	2	2	no	—
379	C₂³×C₅₉	—	2	2	no	—
380	C₂³×C₅₉	—	2	2	no	—
381	C₂³×C₅₉	C₂×#41	1	2	yes	—
382	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
383	Q₈×C₅₉	—	2	16	no	—
384	Q₈×C₅₉	—	2	8	no	—
385	Q₈×C₅₉	—	2	8	no	—
386	Q₈×C₅₉	—	4	4	no	—
387	Q₈×C₅₉	—	4	4	no	—
388	D₄×C₅₉	—	4	4	no	—
389	D₄×C₅₉	—	8	4	no	—
390	C₂×C₄×C₅₉	—	2	16	no	—
391	C₂×C₄×C₅₉	—	2	2	no	—
392	C₂×C₄×C₅₉	—	2	1	no	—
393	C₂×C₄×C₅₉	—	2	1	no	—
394	C₂×C₄×C₅₉	—	2	1	no	—
395	C₂×C₄×C₅₉	—	2	2	no	—
396	C₂×C₄×C₅₉	—	2	2	no	—
397	C₂×C₄×C₅₉	—	2	2	no	—
398	C₂×C₄×C₅₉	—	2	1	no	—
399	C₂×C₄×C₅₉	—	2	1	no	—
400	C₂×C₄×C₅₉	—	2	2	no	—
401	C₂×C₄×C₅₉	—	2	1	no	—
402	C₂×C₄×C₅₉	—	2	1	no	—
403	C₂×C₄×C₅₉	—	2	2	no	—
404	C₂×C₄×C₅₉	—	2	1	no	—
405	C₂×C₄×C₅₉	—	2	1	no	—
406	C₂×C₄×C₅₉	—	2	1	no	—
407	C₂×C₄×C₅₉	—	2	8	no	—
408	C₂×C₄×C₅₉	—	2	1	no	—
409	C₂×C₄×C₅₉	—	2	1	no	—
410	C₂×C₄×C₅₉	—	2	2	no	—
411	C₂×C₄×C₅₉	—	2	1	no	—
412	C₂×C₄×C₅₉	—	2	1	no	—
413	C₂×C₄×C₅₉	—	2	2	no	—
414	C₂×C₄×C₅₉	—	2	1	no	—
415	C₂×C₄×C₅₉	—	2	1	no	—
416	C₂×C₄×C₅₉	—	2	1	no	—
417	C₂×C₄×C₅₉	—	2	1	no	—
418	C₂×C₄×C₅₉	—	2	2	no	—
419	C₂×C₄×C₅₉	—	2	2	no	—
420	C₂×C₄×C₅₉	—	2	2	no	—
421	C₂×C₄×C₅₉	—	2	2	no	—
422	C₂×C₄×C₅₉	—	2	2	no	—
423	C₂×C₄×C₅₉	—	2	1	no	—
424	C₂×C₄×C₅₉	—	2	1	no	—
425	C₂×C₄×C₅₉	—	2	1	no	—
426	C₂×C₄×C₅₉	—	2	1	no	—
427	C₂×C₄×C₅₉	—	2	1	no	—
428	C₂×C₄×C₅₉	—	2	1	no	—
429	C₂×C₄×C₅₉	—	2	1	no	—
430	C₂×C₄×C₅₉	—	2	1	no	—
431	C₂×C₄×C₅₉	—	2	1	no	—
432	C₂×C₄×C₅₉	—	2	2	no	—
433	C₂×C₄×C₅₉	—	2	2	no	—
434	C₂×C₄×C₅₉	—	2	1	no	—
435	C₂×C₄×C₅₉	—	2	1	no	—
436	C₂×C₄×C₅₉	—	2	1	no	—
437	C₂×C₄×C₅₉	—	2	1	no	—
438	C₂×C₄×C₅₉	—	2	2	no	—
439	C₂×C₄×C₅₉	—	2	2	no	—
440	C₂×C₄×C₅₉	—	2	1	no	—
441	C₂×C₄×C₅₉	—	2	1	no	—
442	C₂×C₄×C₅₉	—	2	1	no	—
443	C₂×C₄×C₅₉	—	2	2	no	—
444	C₂×C₄×C₅₉	—	4	8	no	—
445	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
446	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
448	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
451	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
452	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
453	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
454	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
455	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
456	#35817	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₂²×C₅₉	—	2	2	no	—
458	C₂²×C₅₉	—	2	2	no	—
459	C₂²×C₅₉	—	2	2	no	—
460	C₂²×C₅₉	—	4	1	no	—
461	C₂²×C₅₉	—	4	1	no	—
462	C₂²×C₅₉	—	4	1	no	—
463	C₂²×C₅₉	—	4	1	no	—
464	C₂²×C₅₉	—	4	2	no	—
465	C₂²×C₅₉	—	4	2	no	—
466	C₂²×C₅₉	—	4	2	no	—
467	C₂²×C₅₉	—	4	2	no	—
468	C₂²×C₅₉	—	4	2	no	—
469	C₂²×C₅₉	—	4	2	no	—
470	C₂²×C₅₉	—	4	2	no	—
471	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
472	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
473	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
474	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
476	C₂²×C₅₉	#585	1	1	yes	characteristic
477	C₂²×C₅₉	#585	1	1	yes	characteristic
478	C₄×C₅₉	—	2	4	no	—
479	C₄×C₅₉	—	2	4	no	—
480	C₄×C₅₉	—	2	2	no	—
481	C₄×C₅₉	—	2	2	no	—
482	C₄×C₅₉	—	2	4	no	—
483	C₄×C₅₉	—	2	2	no	—
484	C₄×C₅₉	—	2	2	no	—
485	C₄×C₅₉	—	2	2	no	—
486	C₄×C₅₉	—	4	2	no	—
487	C₄×C₅₉	—	4	1	no	—
488	C₄×C₅₉	—	4	1	no	—
489	C₄×C₅₉	—	4	1	no	—
490	C₄×C₅₉	—	4	2	no	—
491	C₄×C₅₉	—	4	1	no	—
492	C₄×C₅₉	—	4	1	no	—
493	C₄×C₅₉	—	4	2	no	—
494	C₄×C₅₉	—	4	2	no	—
495	C₄×C₅₉	—	4	1	no	—
496	C₄×C₅₉	—	4	1	no	—
497	C₄×C₅₉	—	4	1	no	—
498	C₄×C₅₉	#525	1	4	yes	—
499	C₂×#556	C₂×C₅₉	1	1	yes	characteristic, complemented
500	C₂×#519	C₂×C₅₉	1	1	yes	characteristic, complemented
501	#2637	C₂×C₅₉	1	2	yes	complemented
502	#2620	C₂×C₅₉	1	1	yes	characteristic
503	#2609	C₂×C₅₉	1	2	yes	complemented
504	#2601	C₂×C₅₉	1	2	yes	complemented
505	#2582	C₂×C₅₉	1	1	yes	characteristic, complemented
506	#2545	C₂×C₅₉	1	1	yes	characteristic, complemented
507	#2479	C₂×C₅₉	1	2	yes	complemented
508	#2477	C₂×C₅₉	1	2	yes	complemented
509	#2469	C₂×C₅₉	1	2	yes	complemented
510	#2465	C₂×C₅₉	1	2	yes	complemented
511	#2448	C₂×C₅₉	1	1	yes	characteristic, complemented
512	#2446	C₂×C₅₉	1	1	yes	characteristic, complemented
513	#2436	C₂×C₅₉	1	1	yes	characteristic
514	#2434	C₂×C₅₉	1	1	yes	characteristic, complemented
515	#2396	C₂×C₅₉	1	2	yes	complemented
516	#2396	C₂×C₅₉	1	1	yes	characteristic, complemented
517	#2367	C₂×C₅₉	1	1	yes	characteristic, complemented
518	#2365	C₂×C₅₉	1	1	yes	characteristic, complemented
519	#2363	C₂×C₅₉	1	1	yes	characteristic
520	#2362	C₂×C₅₉	1	1	yes	characteristic, complemented
521	#2355	C₂×C₅₉	1	1	yes	characteristic, complemented
522	C₂×C₅₉	—	4	2	no	—
523	C₂×C₅₉	—	8	2	no	—
524	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
525	C₂×C₅₉	#3489	1	1	yes	characteristic
526	C₂×C₅₉	#3497	1	1	yes	characteristic
527	C₂×C₅₉	#3509	1	1	yes	characteristic
528	C₂×C₅₉	#3510	1	1	yes	characteristic
529	C₂×C₅₉	#3516	1	1	yes	characteristic
530	C₂×C₅₉	#3518	1	1	yes	characteristic
531	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
532	#556	—	2	8	no	—
533	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
534	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
535	C₂×#126	C₂²×C₅₉	1	2	yes	—
536	C₂×#126	C₂²×C₅₉	1	2	yes	—
537	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
538	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
539	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
540	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
541	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
542	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
543	#519	—	2	8	no	—
544	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
545	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
546	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
547	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
548	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
549	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
550	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
551	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
553	C₂×#117	C₂²×C₅₉	1	2	yes	—
554	C₂×#117	C₂²×C₅₉	1	2	yes	—
555	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
556	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
557	C₂×#117	C₂²×C₅₉	1	2	yes	—
558	#400	C₂²×C₅₉	1	2	yes	—
559	#400	C₂²×C₅₉	1	1	yes	characteristic
560	#399	C₂²×C₅₉	1	2	yes	—
561	#399	C₂²×C₅₉	1	1	yes	characteristic
562	#398	C₂²×C₅₉	1	2	yes	—
563	#398	C₂²×C₅₉	1	2	yes	—
564	#398	C₂²×C₅₉	1	1	yes	characteristic
565	#398	C₂²×C₅₉	1	2	yes	—
566	#398	C₂²×C₅₉	1	1	yes	characteristic
567	#397	C₂²×C₅₉	1	2	yes	—
568	#396	C₂²×C₅₉	1	1	yes	characteristic
569	#396	C₂²×C₅₉	1	2	yes	—
570	#396	C₂²×C₅₉	1	1	yes	characteristic
571	#396	C₂²×C₅₉	1	2	yes	—
572	#396	C₂²×C₅₉	1	2	yes	—
573	#396	C₂²×C₅₉	1	2	yes	—
574	#395	C₂²×C₅₉	1	2	yes	—
575	#395	C₂²×C₅₉	1	2	yes	—
576	#395	C₂²×C₅₉	1	1	yes	characteristic
577	#394	C₂²×C₅₉	1	2	yes	—
578	#394	C₂²×C₅₉	1	2	yes	—
579	#393	C₂²×C₅₉	1	2	yes	—
580	#393	C₂²×C₅₉	1	2	yes	—
581	#393	C₂²×C₅₉	1	1	yes	characteristic
582	#391	C₂²×C₅₉	1	1	yes	characteristic
583	#391	C₂²×C₅₉	1	1	yes	characteristic
584	#391	C₂²×C₅₉	1	2	yes	—
585	#391	C₂²×C₅₉	1	1	yes	characteristic
586	#391	C₂²×C₅₉	1	1	yes	characteristic
587	#391	C₂²×C₅₉	1	1	yes	characteristic
588	#391	C₂²×C₅₉	1	1	yes	characteristic
589	#390	C₂²×C₅₉	1	2	yes	—
590	#390	C₂²×C₅₉	1	1	yes	characteristic
591	#390	C₂²×C₅₉	1	1	yes	characteristic
592	#389	C₂²×C₅₉	1	1	yes	characteristic
593	#389	C₂²×C₅₉	1	1	yes	characteristic
594	#389	C₂²×C₅₉	1	2	yes	—
595	#389	C₂²×C₅₉	1	2	yes	—
596	#388	C₂²×C₅₉	1	2	yes	—
597	#388	C₂²×C₅₉	1	2	yes	—
598	#388	C₂²×C₅₉	1	2	yes	—
599	#388	C₂²×C₅₉	1	2	yes	—
600	#388	C₂²×C₅₉	1	2	yes	—
601	#388	C₂²×C₅₉	1	2	yes	—
602	#388	C₂²×C₅₉	1	2	yes	—
603	#388	C₂²×C₅₉	1	2	yes	—
604	#388	C₂²×C₅₉	1	2	yes	—
605	#387	C₂²×C₅₉	1	2	yes	—
606	#387	C₂²×C₅₉	1	2	yes	—
607	#387	C₂²×C₅₉	1	2	yes	—
608	#387	C₂²×C₅₉	1	2	yes	—
609	#387	C₂²×C₅₉	1	2	yes	—
610	#387	C₂²×C₅₉	1	2	yes	—
611	#387	C₂²×C₅₉	1	2	yes	—
612	#386	C₂²×C₅₉	1	2	yes	—
613	#386	C₂²×C₅₉	1	2	yes	—
614	#386	C₂²×C₅₉	1	2	yes	—
615	#385	C₂²×C₅₉	1	2	yes	—
616	#385	C₂²×C₅₉	1	2	yes	—
617	#385	C₂²×C₅₉	1	2	yes	—
618	#384	C₂²×C₅₉	1	1	yes	characteristic
619	#382	C₂²×C₅₉	1	2	yes	—
620	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
621	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
624	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
625	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
626	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
627	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
628	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
629	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
630	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
631	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
632	C₅₉	#35817	1	1	yes	characteristic, direct product factor, Sylow
633	C₂²×Q₈	—	2	4	no	—
634	C₂²×Q₈	—	2	4	no	—
635	C₂²×Q₈	—	2	4	no	—
636	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
637	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
638	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
639	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
640	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
641	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
642	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
643	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
644	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
645	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
646	C₄⋊Q₈	—	2	4	no	—
647	C₄⋊Q₈	—	2	4	no	—
648	#126	—	2	8	no	—
649	#126	—	2	8	no	—
650	#124	—	2	4	no	—
651	#124	—	2	4	no	—
652	#124	—	2	4	no	—
653	C₂²⋊Q₈	—	2	4	no	—
654	C₂²⋊Q₈	—	2	8	no	—
655	#121	—	2	4	no	—
656	C₄×Q₈	—	2	4	no	—
657	C₄×Q₈	—	2	4	no	—
658	C₄×Q₈	—	2	8	no	—
659	C₄×Q₈	—	2	4	no	—
660	C₄×Q₈	—	2	8	no	—
661	C₄×Q₈	—	2	4	no	—
662	C₄×Q₈	—	2	4	no	—
663	C₄×Q₈	D₄×C₅₉	1	8	yes	complemented
664	C₄×D₄	—	2	4	no	—
665	#117	—	2	4	no	—
666	#117	—	2	8	no	—
667	#117	—	2	8	no	—
668	#117	—	2	4	no	—
669	#117	—	2	8	no	—
670	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
719	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
720	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
721	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
723	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
724	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
725	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
730	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
731	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
732	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
733	#95	C₂³×C₅₉	1	1	yes	characteristic
734	#95	C₂³×C₅₉	1	1	yes	characteristic
735	#95	C₂³×C₅₉	1	1	yes	characteristic
736	#95	C₂³×C₅₉	1	2	yes	—
737	#95	C₂³×C₅₉	1	2	yes	—
738	#95	C₂³×C₅₉	1	1	yes	characteristic
739	#95	C₂³×C₅₉	1	1	yes	characteristic
740	#95	C₂³×C₅₉	1	2	yes	—
741	#95	C₂³×C₅₉	1	2	yes	—
742	#95	C₂³×C₅₉	1	2	yes	—
743	#95	C₂³×C₅₉	1	2	yes	—
744	#95	C₂³×C₅₉	1	2	yes	—
745	#95	C₂³×C₅₉	1	1	yes	characteristic
746	#95	C₂³×C₅₉	1	1	yes	characteristic
747	#95	C₂³×C₅₉	1	1	yes	characteristic
748	#95	C₂³×C₅₉	1	1	yes	characteristic
749	#95	C₂³×C₅₉	1	1	yes	characteristic
750	#95	C₂³×C₅₉	1	2	yes	—
751	#95	C₂³×C₅₉	1	2	yes	—
752	#95	C₂³×C₅₉	1	2	yes	—
753	#95	C₂³×C₅₉	1	2	yes	—
754	#95	C₂³×C₅₉	1	2	yes	—
755	#95	C₂³×C₅₉	1	2	yes	—
756	#95	C₂³×C₅₉	1	2	yes	—
757	#95	C₂³×C₅₉	1	2	yes	—
758	#95	C₂³×C₅₉	1	2	yes	—
759	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
760	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
761	C₂×Q₈	—	2	32	no	—
762	C₂×Q₈	—	2	4	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	2	2	no	—
766	C₂×Q₈	—	2	4	no	—
767	C₂×Q₈	—	2	4	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	4	1	no	—
775	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
776	C₂×Q₈	#41×C₅₉	1	4	yes	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂×D₄	—	4	2	no	—
783	C₂²×C₄	—	2	4	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	#41×C₅₉	1	4	yes	—
792	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	4	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	4	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	4	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	4	no	—
828	C₄⋊C₄	—	2	4	no	—
829	C₄⋊C₄	—	2	4	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	4	1	no	—
834	C₄⋊C₄	—	4	1	no	—
835	C₄⋊C₄	—	4	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	1	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
841	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	4	no	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	4	1	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	1	no	—
862	C₄²	—	2	4	no	—
863	C₄²	—	2	4	no	—
864	C₄²	—	2	4	no	—
865	C₄²	—	2	4	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	4	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	4	2	no	—
873	C₄²	—	4	2	no	—
874	C₄²	C₂×D₄×C₅₉	1	8	yes	—
875	C₄²	C₂×D₄×C₅₉	1	4	yes	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	1	no	—
879	C₂³	—	2	1	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	C₂×#41×C₅₉	1	2	yes	—
890	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
891	Q₈	—	2	16	no	—
892	Q₈	—	2	8	no	—
893	Q₈	—	2	8	no	—
894	Q₈	—	4	4	no	—
895	Q₈	—	4	4	no	—
896	D₄	—	4	4	no	—
897	D₄	—	8	4	no	—
898	C₂×C₄	—	2	16	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	8	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	4	8	no	—
953	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
954	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
955	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
956	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
958	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
959	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
960	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
961	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
962	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
963	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	1	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
979	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
980	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
981	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
982	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
983	C₂²	C₅₉×#585	1	1	yes	characteristic
984	C₂²	C₅₉×#585	1	1	yes	characteristic
985	C₄	—	2	2	no	—
986	C₄	—	2	4	no	—
987	C₄	—	2	4	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	4	no	—
991	C₄	—	2	2	no	—
992	C₄	—	2	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	1	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	1	no	—
1000	C₄	—	4	1	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	1	no	—
1005	C₄	C₅₉×#525	1	4	yes	—
1006	C₂	—	4	2	no	—
1007	C₂	—	8	2	no	—
1008	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
1009	C₂	C₅₉×#3489	1	1	yes	characteristic
1010	C₂	C₅₉×#3497	1	1	yes	characteristic
1011	C₂	C₅₉×#3509	1	1	yes	characteristic
1012	C₂	C₅₉×#3510	1	1	yes	characteristic
1013	C₂	C₅₉×#3516	1	1	yes	characteristic
1014	C₂	C₅₉×#3518	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×#121×C₅₉	C₂²
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. C₂×C₅₉×#556	C₂	semidirect
2. C₂×C₅₉×#519	C₂	semidirect
3. C₅₉×#2637	C₂	semidirect
5. C₅₉×#2609	C₂	semidirect
6. C₅₉×#2601	C₂	semidirect
7. C₅₉×#2582	C₂	semidirect
8. C₅₉×#2545	C₂	semidirect
9. C₅₉×#2479	C₂	semidirect
10. C₅₉×#2477	C₂	semidirect
11. C₅₉×#2469	C₂	semidirect
12. C₅₉×#2465	C₂	semidirect
13. C₅₉×#2448	C₂	semidirect
14. C₅₉×#2446	C₂	semidirect
16. C₅₉×#2434	C₂	semidirect
17. C₅₉×#2396	C₂	semidirect
18. C₅₉×#2396	C₂	semidirect
19. C₅₉×#2367	C₂	semidirect
20. C₅₉×#2365	C₂	semidirect
22. C₅₉×#2362	C₂	semidirect
23. C₅₉×#2355	C₂	semidirect
155. C₄×Q₈×C₅₉	D₄	semidirect
456. #35817	C₅₉	direct (N × H)
499. C₂×#556	C₂×C₅₉	semidirect
500. C₂×#519	C₂×C₅₉	semidirect
501. #2637	C₂×C₅₉	semidirect
503. #2609	C₂×C₅₉	semidirect
504. #2601	C₂×C₅₉	semidirect
505. #2582	C₂×C₅₉	semidirect
506. #2545	C₂×C₅₉	semidirect
507. #2479	C₂×C₅₉	semidirect
508. #2477	C₂×C₅₉	semidirect
509. #2469	C₂×C₅₉	semidirect
510. #2465	C₂×C₅₉	semidirect
511. #2448	C₂×C₅₉	semidirect
512. #2446	C₂×C₅₉	semidirect
514. #2434	C₂×C₅₉	semidirect
515. #2396	C₂×C₅₉	semidirect
516. #2396	C₂×C₅₉	semidirect
517. #2367	C₂×C₅₉	semidirect
518. #2365	C₂×C₅₉	semidirect
520. #2362	C₂×C₅₉	semidirect
521. #2355	C₂×C₅₉	semidirect
632. C₅₉	#35817	direct (N × H)
663. C₄×Q₈	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#556	2
C₂×C₅₉×#519	2
C₅₉×#2637	2
C₅₉×#2620	2
C₅₉×#2609	2
C₅₉×#2601	2
C₅₉×#2582	2
C₅₉×#2545	2
C₅₉×#2479	2
C₅₉×#2477	2
C₅₉×#2469	2
C₅₉×#2465	2
C₅₉×#2448	2
C₅₉×#2446	2
C₅₉×#2436	2
C₅₉×#2434	2
C₅₉×#2396	2
C₅₉×#2367	2
C₅₉×#2365	2
C₅₉×#2363	2
C₅₉×#2362	2
C₅₉×#2355	2
#35817	59

Subgroups — C59×#35817 #28447926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35817 #28447926