Subgroups — C₂×C₅₉×#1903 #28433103

Order 15104.

1782 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#100×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1903	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
13	C₂×AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
14	C₂×AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
15	C₂×AGL(1,ℤ/8)×C₅₉	C₄	1	4	yes	complemented
16	C₂×AGL(1,ℤ/8)×C₅₉	C₂²	1	4	yes	—
17	C₂²×SD₁₆×C₅₉	C₄	1	2	yes	complemented
18	C₂²×D₈×C₅₉	C₄	1	2	yes	complemented
19	C₅₉×#568	—	2	2	no	—
20	C₅₉×#568	—	2	2	no	—
21	C₅₉×#568	—	2	2	no	—
22	C₅₉×#568	C₂²	1	4	yes	complemented
23	C₂×#131×C₅₉	—	2	2	no	—
24	C₂×#131×C₅₉	—	2	2	no	—
25	C₂²×M₁₆×C₅₉	—	2	2	no	—
26	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#421	—	2	2	no	—
32	C₅₉×#421	C₂²	1	4	yes	complemented
33	C₂×#104×C₅₉	—	2	2	no	—
34	C₅₉×#418	—	2	2	no	—
35	C₅₉×#418	C₂²	1	4	yes	complemented
36	C₂×#102×C₅₉	—	2	2	no	—
37	C₂×#100×C₅₉	—	2	2	no	—
38	C₂×#100×C₅₉	—	2	2	no	—
39	C₂×#100×C₅₉	C₂²	1	4	yes	complemented
40	C₅₉×#344	C₂²	1	4	yes	complemented
41	C₅₉×#338	C₂²	1	4	yes	complemented
42	C₂⁵×C₅₉	—	2	1	no	—
43	C₂×#41×C₅₉	—	2	1	no	—
44	C₂×#41×C₅₉	—	2	1	no	—
45	C₂×#41×C₅₉	—	2	1	no	—
46	C₂×#41×C₅₉	—	2	1	no	—
47	C₂×#41×C₅₉	—	2	1	no	—
48	C₂×#41×C₅₉	—	2	1	no	—
49	C₂×#41×C₅₉	C₂×C₄	1	2	yes	—
50	C₂×#41×C₅₉	D₄	1	2	yes	—
51	C₂×#41×C₅₉	D₄	1	2	yes	—
52	C₂×#41×C₅₉	D₄	1	2	yes	—
53	C₂×#41×C₅₉	D₄	1	2	yes	—
54	C₂×#41×C₅₉	C₂³	1	2	yes	—
55	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₄×C₅₉	—	2	1	no	—
57	C₂²×D₄×C₅₉	—	2	1	no	—
58	C₂²×D₄×C₅₉	—	2	1	no	—
59	C₂²×D₄×C₅₉	—	2	1	no	—
60	C₂²×D₄×C₅₉	—	2	1	no	—
61	C₂²×D₄×C₅₉	—	2	1	no	—
62	C₂²×D₄×C₅₉	—	2	1	no	—
63	C₂²×D₄×C₅₉	—	2	1	no	—
64	C₂²×D₄×C₅₉	—	2	1	no	—
65	C₂²×D₄×C₅₉	—	2	1	no	—
66	C₂²×D₄×C₅₉	—	2	1	no	—
67	C₂²×D₄×C₅₉	—	2	1	no	—
68	C₂²×D₄×C₅₉	C₂×C₄	1	2	yes	—
69	C₂²×D₄×C₅₉	C₂×C₄	1	2	yes	—
70	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₅₉	—	2	1	no	—
73	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
74	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
75	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
76	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
77	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
78	C₂×SD₁₆×C₅₉	—	2	4	no	—
79	C₂×SD₁₆×C₅₉	—	2	4	no	—
80	C₂×SD₁₆×C₅₉	C₂×C₄	1	8	yes	complemented
81	C₂×D₈×C₅₉	—	2	4	no	—
82	C₂×D₈×C₅₉	—	2	4	no	—
83	C₂×D₈×C₅₉	C₂×C₄	1	8	yes	complemented
84	#131×C₅₉	—	2	8	no	—
85	#131×C₅₉	—	2	8	no	—
86	#131×C₅₉	—	2	8	no	—
87	#131×C₅₉	—	2	8	no	—
88	C₂×M₁₆×C₅₉	—	2	4	no	—
89	C₂×M₁₆×C₅₉	—	2	8	no	—
90	C₂×M₁₆×C₅₉	—	2	1	no	—
91	C₂×M₁₆×C₅₉	—	2	1	no	—
92	C₂×M₁₆×C₅₉	—	2	1	no	—
93	C₂×M₁₆×C₅₉	—	2	1	no	—
94	C₂×M₁₆×C₅₉	—	2	1	no	—
95	C₂×M₁₆×C₅₉	—	2	1	no	—
96	C₂×M₁₆×C₅₉	—	2	1	no	—
97	C₂×M₁₆×C₅₉	—	2	1	no	—
98	C₂×M₁₆×C₅₉	—	2	1	no	—
99	C₂×M₁₆×C₅₉	—	2	1	no	—
100	C₂×M₁₆×C₅₉	—	2	1	no	—
101	C₂×M₁₆×C₅₉	—	2	8	no	—
102	C₂×M₁₆×C₅₉	—	2	1	no	—
103	C₂×M₁₆×C₅₉	—	2	1	no	—
104	C₂×M₁₆×C₅₉	—	2	1	no	—
105	C₂×M₁₆×C₅₉	—	2	1	no	—
106	C₂×M₁₆×C₅₉	—	2	1	no	—
107	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
108	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
109	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
110	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
111	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
112	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
113	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
114	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
115	C₂²×C₈×C₅₉	—	2	4	no	—
116	C₂²×C₈×C₅₉	—	2	1	no	—
117	C₂²×C₈×C₅₉	—	2	1	no	—
118	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
119	C₂²×C₈×C₅₉	D₄	1	2	yes	—
120	#117×C₅₉	—	2	1	no	—
121	#117×C₅₉	—	2	1	no	—
122	#117×C₅₉	—	2	1	no	—
123	#117×C₅₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
126	C₂×C₄²×C₅₉	—	2	1	no	—
127	#104×C₅₉	—	2	8	no	—
128	#102×C₅₉	—	2	8	no	—
129	#100×C₅₉	—	2	8	no	—
130	C₂⁴×C₅₉	—	2	1	no	—
131	C₂⁴×C₅₉	—	2	2	no	—
132	C₂⁴×C₅₉	—	2	2	no	—
133	C₂⁴×C₅₉	—	2	2	no	—
134	C₂⁴×C₅₉	—	4	1	no	—
135	C₂⁴×C₅₉	—	4	1	no	—
136	C₂⁴×C₅₉	—	4	1	no	—
137	C₂⁴×C₅₉	—	4	1	no	—
138	C₂⁴×C₅₉	—	8	4	no	—
139	C₂⁴×C₅₉	#41	1	1	yes	characteristic
140	#41×C₅₉	—	2	2	no	—
141	#41×C₅₉	—	2	2	no	—
142	#41×C₅₉	—	2	2	no	—
143	#41×C₅₉	—	2	2	no	—
144	#41×C₅₉	—	2	2	no	—
145	#41×C₅₉	—	2	2	no	—
146	#41×C₅₉	—	2	2	no	—
147	#41×C₅₉	—	2	2	no	—
148	#41×C₅₉	—	2	2	no	—
149	#41×C₅₉	—	2	2	no	—
150	#41×C₅₉	—	2	2	no	—
151	#41×C₅₉	—	2	2	no	—
152	#41×C₅₉	C₂²⋊C₄	1	4	yes	—
153	#41×C₅₉	C₂²⋊C₄	1	4	yes	—
154	#41×C₅₉	C₂×D₄	1	4	yes	—
155	#41×C₅₉	C₂×D₄	1	4	yes	—
156	C₂×Q₈×C₅₉	—	2	1	no	—
157	C₂×Q₈×C₅₉	—	2	1	no	—
158	C₂×Q₈×C₅₉	—	2	1	no	—
159	C₂×Q₈×C₅₉	C₂²⋊C₄	1	2	yes	—
160	C₂×Q₈×C₅₉	C₂²⋊C₄	1	2	yes	—
161	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
162	C₂×D₄×C₅₉	—	2	2	no	—
163	C₂×D₄×C₅₉	—	2	2	no	—
164	C₂×D₄×C₅₉	—	2	2	no	—
165	C₂×D₄×C₅₉	—	2	2	no	—
166	C₂×D₄×C₅₉	—	2	2	no	—
167	C₂×D₄×C₅₉	—	2	2	no	—
168	C₂×D₄×C₅₉	—	2	2	no	—
169	C₂×D₄×C₅₉	—	2	2	no	—
170	C₂×D₄×C₅₉	—	2	2	no	—
171	C₂×D₄×C₅₉	—	2	2	no	—
172	C₂×D₄×C₅₉	—	2	1	no	—
173	C₂×D₄×C₅₉	—	2	1	no	—
174	C₂×D₄×C₅₉	—	2	1	no	—
175	C₂×D₄×C₅₉	—	2	2	no	—
176	C₂×D₄×C₅₉	—	2	2	no	—
177	C₂×D₄×C₅₉	—	2	2	no	—
178	C₂×D₄×C₅₉	—	2	2	no	—
179	C₂×D₄×C₅₉	—	2	2	no	—
180	C₂×D₄×C₅₉	—	2	2	no	—
181	C₂×D₄×C₅₉	—	2	2	no	—
182	C₂×D₄×C₅₉	—	2	2	no	—
183	C₂×D₄×C₅₉	—	2	2	no	—
184	C₂×D₄×C₅₉	—	2	2	no	—
185	C₂×D₄×C₅₉	—	2	2	no	—
186	C₂×D₄×C₅₉	—	4	1	no	—
187	C₂×D₄×C₅₉	—	4	1	no	—
188	C₂×D₄×C₅₉	—	4	1	no	—
189	C₂×D₄×C₅₉	—	4	1	no	—
190	C₂×D₄×C₅₉	—	4	1	no	—
191	C₂×D₄×C₅₉	—	4	1	no	—
192	C₂×D₄×C₅₉	—	4	1	no	—
193	C₂×D₄×C₅₉	—	4	1	no	—
194	C₂×D₄×C₅₉	—	4	1	no	—
195	C₂×D₄×C₅₉	—	4	1	no	—
196	C₂×D₄×C₅₉	—	4	1	no	—
197	C₂×D₄×C₅₉	—	4	1	no	—
198	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
199	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
200	C₂×D₄×C₅₉	C₂²×C₄	1	4	yes	—
201	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
202	C₂²×C₄×C₅₉	—	2	1	no	—
203	C₂²×C₄×C₅₉	—	2	2	no	—
204	C₂²×C₄×C₅₉	—	2	2	no	—
205	C₂²×C₄×C₅₉	—	2	2	no	—
206	C₂²×C₄×C₅₉	—	2	2	no	—
207	C₂²×C₄×C₅₉	—	2	2	no	—
208	C₂²×C₄×C₅₉	—	2	2	no	—
209	C₂²×C₄×C₅₉	—	4	1	no	—
210	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
221	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
222	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
223	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
224	SD₁₆×C₅₉	—	2	16	no	—
225	D₈×C₅₉	—	2	16	no	—
226	M₁₆×C₅₉	—	2	16	no	—
227	M₁₆×C₅₉	—	2	2	no	—
228	M₁₆×C₅₉	—	2	2	no	—
229	M₁₆×C₅₉	—	2	2	no	—
230	M₁₆×C₅₉	—	2	2	no	—
231	M₁₆×C₅₉	—	2	2	no	—
232	M₁₆×C₅₉	—	2	2	no	—
233	M₁₆×C₅₉	—	2	2	no	—
234	M₁₆×C₅₉	—	2	2	no	—
235	M₁₆×C₅₉	—	2	2	no	—
236	M₁₆×C₅₉	—	2	2	no	—
237	M₁₆×C₅₉	—	2	2	no	—
238	M₁₆×C₅₉	—	2	2	no	—
239	M₁₆×C₅₉	—	2	2	no	—
240	M₁₆×C₅₉	—	4	1	no	—
241	M₁₆×C₅₉	—	4	1	no	—
242	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
243	C₂×C₈×C₅₉	—	2	16	no	—
244	C₂×C₈×C₅₉	—	2	2	no	—
245	C₂×C₈×C₅₉	—	2	2	no	—
246	C₂×C₈×C₅₉	—	2	2	no	—
247	C₂×C₈×C₅₉	—	2	2	no	—
248	C₂×C₈×C₅₉	—	2	2	no	—
249	C₂×C₈×C₅₉	—	2	2	no	—
250	C₂×C₈×C₅₉	—	2	2	no	—
251	C₂×C₈×C₅₉	—	2	2	no	—
252	C₂×C₈×C₅₉	—	4	1	no	—
253	C₂×C₈×C₅₉	—	4	1	no	—
254	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
255	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₅₉	—	2	2	no	—
257	C₄⋊C₄×C₅₉	—	4	1	no	—
258	C₂²⋊C₄×C₅₉	—	2	2	no	—
259	C₂²⋊C₄×C₅₉	—	4	1	no	—
260	C₄²×C₅₉	—	2	2	no	—
261	C₄²×C₅₉	—	4	1	no	—
262	C₂³×C₅₉	—	2	2	no	—
263	C₂³×C₅₉	—	2	2	no	—
264	C₂³×C₅₉	—	2	2	no	—
265	C₂³×C₅₉	—	2	4	no	—
266	C₂³×C₅₉	—	4	2	no	—
267	C₂³×C₅₉	—	4	2	no	—
268	C₂³×C₅₉	—	4	2	no	—
269	C₂³×C₅₉	—	4	2	no	—
270	C₂³×C₅₉	—	4	2	no	—
271	C₂³×C₅₉	—	4	2	no	—
272	C₂³×C₅₉	—	4	2	no	—
273	C₂³×C₅₉	—	8	2	no	—
274	C₂³×C₅₉	—	8	4	no	—
275	C₂³×C₅₉	—	8	4	no	—
276	C₂³×C₅₉	—	8	4	no	—
277	C₂³×C₅₉	—	8	4	no	—
278	C₂³×C₅₉	—	8	4	no	—
279	C₂³×C₅₉	—	8	4	no	—
280	C₂³×C₅₉	—	8	4	no	—
281	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
282	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
283	C₂³×C₅₉	#121	1	1	yes	characteristic
284	C₂³×C₅₉	#121	1	1	yes	characteristic
285	C₂³×C₅₉	#123	1	1	yes	characteristic
286	C₂³×C₅₉	#123	1	1	yes	characteristic
287	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
288	Q₈×C₅₉	—	2	2	no	—
289	Q₈×C₅₉	—	2	2	no	—
290	Q₈×C₅₉	—	2	2	no	—
291	Q₈×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
292	D₄×C₅₉	—	2	4	no	—
293	D₄×C₅₉	—	2	4	no	—
294	D₄×C₅₉	—	2	4	no	—
295	D₄×C₅₉	—	2	4	no	—
296	D₄×C₅₉	—	2	4	no	—
297	D₄×C₅₉	—	2	2	no	—
298	D₄×C₅₉	—	2	4	no	—
299	D₄×C₅₉	—	2	2	no	—
300	D₄×C₅₉	—	2	2	no	—
301	D₄×C₅₉	—	4	2	no	—
302	D₄×C₅₉	—	4	2	no	—
303	D₄×C₅₉	—	4	2	no	—
304	D₄×C₅₉	—	4	2	no	—
305	D₄×C₅₉	—	4	2	no	—
306	D₄×C₅₉	—	4	2	no	—
307	D₄×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
308	C₂×C₄×C₅₉	—	2	2	no	—
309	C₂×C₄×C₅₉	—	2	2	no	—
310	C₂×C₄×C₅₉	—	2	2	no	—
311	C₂×C₄×C₅₉	—	2	4	no	—
312	C₂×C₄×C₅₉	—	2	4	no	—
313	C₂×C₄×C₅₉	—	2	4	no	—
314	C₂×C₄×C₅₉	—	2	4	no	—
315	C₂×C₄×C₅₉	—	4	2	no	—
316	C₂×C₄×C₅₉	—	8	2	no	—
317	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
328	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
329	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
330	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
331	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
332	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
333	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
334	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
335	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
336	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
337	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
338	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
339	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
340	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
345	C₈×C₅₉	—	2	4	no	—
346	C₈×C₅₉	—	2	4	no	—
347	C₈×C₅₉	—	2	4	no	—
348	C₈×C₅₉	—	4	2	no	—
349	C₂×#1903	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂²×C₅₉	—	2	2	no	—
351	C₂²×C₅₉	—	2	2	no	—
352	C₂²×C₅₉	—	2	2	no	—
353	C₂²×C₅₉	—	2	4	no	—
354	C₂²×C₅₉	—	4	1	no	—
355	C₂²×C₅₉	—	4	1	no	—
356	C₂²×C₅₉	—	4	1	no	—
357	C₂²×C₅₉	—	4	1	no	—
358	C₂²×C₅₉	—	4	4	no	—
359	C₂²×C₅₉	—	4	4	no	—
360	C₂²×C₅₉	—	8	2	no	—
361	C₂²×C₅₉	—	8	2	no	—
362	C₂²×C₅₉	—	8	4	no	—
363	C₂²×C₅₉	—	8	4	no	—
364	C₂²×C₅₉	—	8	4	no	—
365	C₂²×C₅₉	—	8	4	no	—
366	C₂²×C₅₉	—	8	4	no	—
367	C₂²×C₅₉	—	8	4	no	—
368	C₂²×C₅₉	—	8	4	no	—
369	C₂²×C₅₉	#386	1	1	yes	characteristic
370	C₂²×C₅₉	#386	1	1	yes	characteristic
371	C₂²×C₅₉	#386	1	1	yes	characteristic
372	C₂²×C₅₉	#386	1	1	yes	characteristic
373	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
375	C₂²×C₅₉	C₂×#123	1	1	yes	characteristic
376	C₄×C₅₉	—	2	4	no	—
377	C₄×C₅₉	—	8	2	no	—
378	C₄×C₅₉	#386	1	1	yes	characteristic
379	C₄×C₅₉	#386	1	1	yes	characteristic
380	C₄×C₅₉	#386	1	1	yes	characteristic
381	C₄×C₅₉	#386	1	1	yes	characteristic
382	C₄×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
383	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
384	C₄×C₅₉	C₂×#120	1	1	yes	characteristic
385	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
386	C₂²×AGL(1,ℤ/8)	C₂×C₅₉	1	1	yes	characteristic
387	C₂×#568	C₂×C₅₉	1	1	yes	characteristic, complemented
388	C₂×#421	C₂×C₅₉	1	1	yes	characteristic, complemented
389	C₂×#418	C₂×C₅₉	1	1	yes	characteristic, complemented
390	C₂²×#100	C₂×C₅₉	1	1	yes	characteristic, complemented
391	#1903	C₂×C₅₉	1	8	yes	direct product factor
392	C₂×#344	C₂×C₅₉	1	1	yes	characteristic, complemented
393	C₂×#338	C₂×C₅₉	1	1	yes	characteristic, complemented
394	C₂×C₅₉	—	2	1	no	—
395	C₂×C₅₉	—	2	1	no	—
396	C₂×C₅₉	—	2	1	no	—
397	C₂×C₅₉	—	2	1	no	—
398	C₂×C₅₉	—	2	1	no	—
399	C₂×C₅₉	—	2	1	no	—
400	C₂×C₅₉	—	4	4	no	—
401	C₂×C₅₉	—	8	4	no	—
402	C₂×C₅₉	#1903	1	2	yes	direct product factor
403	C₂×C₅₉	C₂×#386	1	1	yes	characteristic
404	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
405	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
406	C₂×AGL(1,ℤ/8)	—	2	2	no	—
407	C₂×AGL(1,ℤ/8)	—	2	2	no	—
408	C₂×AGL(1,ℤ/8)	—	2	2	no	—
409	C₂×AGL(1,ℤ/8)	—	2	2	no	—
410	C₂×AGL(1,ℤ/8)	C₄×C₅₉	1	4	yes	complemented
411	C₂×AGL(1,ℤ/8)	C₂²×C₅₉	1	4	yes	—
412	C₂²×SD₁₆	C₄×C₅₉	1	2	yes	complemented
413	C₂²×D₈	C₄×C₅₉	1	2	yes	complemented
414	#568	—	2	2	no	—
415	#568	—	2	2	no	—
416	#568	—	2	2	no	—
417	#568	C₂²×C₅₉	1	4	yes	complemented
418	C₂×#131	—	2	2	no	—
419	C₂×#131	—	2	2	no	—
420	C₂²×M₁₆	—	2	2	no	—
421	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
422	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
423	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
424	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
425	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
426	#421	—	2	2	no	—
427	#421	C₂²×C₅₉	1	4	yes	complemented
428	C₂×#104	—	2	2	no	—
429	#418	—	2	2	no	—
430	#418	C₂²×C₅₉	1	4	yes	complemented
431	C₂×#102	—	2	2	no	—
432	C₂×#100	—	2	2	no	—
433	C₂×#100	—	2	2	no	—
434	C₂×#100	C₂²×C₅₉	1	4	yes	complemented
435	#344	C₂²×C₅₉	1	4	yes	complemented
436	#338	C₂²×C₅₉	1	4	yes	complemented
437	C₅₉	C₂×#1903	1	1	yes	characteristic, direct product factor, Sylow
438	C₂⁵	—	2	1	no	—
439	C₂×#41	—	2	1	no	—
440	C₂×#41	—	2	1	no	—
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	1	no	—
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	C₂×C₄×C₅₉	1	2	yes	—
446	C₂×#41	D₄×C₅₉	1	2	yes	—
447	C₂×#41	D₄×C₅₉	1	2	yes	—
448	C₂×#41	D₄×C₅₉	1	2	yes	—
449	C₂×#41	D₄×C₅₉	1	2	yes	—
450	C₂×#41	C₂³×C₅₉	1	2	yes	—
451	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	C₂×C₄×C₅₉	1	2	yes	—
465	C₂²×D₄	C₂×C₄×C₅₉	1	2	yes	—
466	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
470	AGL(1,ℤ/8)	—	2	8	no	—
471	AGL(1,ℤ/8)	—	2	8	no	—
472	AGL(1,ℤ/8)	—	2	8	no	—
473	AGL(1,ℤ/8)	—	2	8	no	—
474	C₂×SD₁₆	—	2	4	no	—
475	C₂×SD₁₆	—	2	4	no	—
476	C₂×SD₁₆	C₂×C₄×C₅₉	1	8	yes	complemented
477	C₂×D₈	—	2	4	no	—
478	C₂×D₈	—	2	4	no	—
479	C₂×D₈	C₂×C₄×C₅₉	1	8	yes	complemented
480	#131	—	2	8	no	—
481	#131	—	2	8	no	—
482	#131	—	2	8	no	—
483	#131	—	2	8	no	—
484	C₂×M₁₆	—	2	4	no	—
485	C₂×M₁₆	—	2	8	no	—
486	C₂×M₁₆	—	2	1	no	—
487	C₂×M₁₆	—	2	1	no	—
488	C₂×M₁₆	—	2	1	no	—
489	C₂×M₁₆	—	2	1	no	—
490	C₂×M₁₆	—	2	1	no	—
491	C₂×M₁₆	—	2	1	no	—
492	C₂×M₁₆	—	2	1	no	—
493	C₂×M₁₆	—	2	1	no	—
494	C₂×M₁₆	—	2	1	no	—
495	C₂×M₁₆	—	2	1	no	—
496	C₂×M₁₆	—	2	1	no	—
497	C₂×M₁₆	—	2	8	no	—
498	C₂×M₁₆	—	2	1	no	—
499	C₂×M₁₆	—	2	1	no	—
500	C₂×M₁₆	—	2	1	no	—
501	C₂×M₁₆	—	2	1	no	—
502	C₂×M₁₆	—	2	1	no	—
503	C₂×M₁₆	C₂×C₄×C₅₉	1	2	yes	—
504	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
505	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
506	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
507	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
508	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
509	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
510	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
511	C₂²×C₈	—	2	4	no	—
512	C₂²×C₈	—	2	1	no	—
513	C₂²×C₈	—	2	1	no	—
514	C₂²×C₈	C₂×C₄×C₅₉	1	2	yes	—
515	C₂²×C₈	D₄×C₅₉	1	2	yes	—
516	#117	—	2	1	no	—
517	#117	—	2	1	no	—
518	#117	—	2	1	no	—
519	#117	C₂³×C₅₉	1	2	yes	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₄²	—	2	1	no	—
523	#104	—	2	8	no	—
524	#102	—	2	8	no	—
525	#100	—	2	8	no	—
526	C₂⁴	—	2	1	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	4	1	no	—
531	C₂⁴	—	4	1	no	—
532	C₂⁴	—	4	1	no	—
533	C₂⁴	—	4	1	no	—
534	C₂⁴	—	8	4	no	—
535	C₂⁴	#41×C₅₉	1	1	yes	characteristic
536	#41	—	2	2	no	—
537	#41	—	2	2	no	—
538	#41	—	2	2	no	—
539	#41	—	2	2	no	—
540	#41	—	2	2	no	—
541	#41	—	2	2	no	—
542	#41	—	2	2	no	—
543	#41	—	2	2	no	—
544	#41	—	2	2	no	—
545	#41	—	2	2	no	—
546	#41	—	2	2	no	—
547	#41	—	2	2	no	—
548	#41	C₂²⋊C₄×C₅₉	1	4	yes	—
549	#41	C₂²⋊C₄×C₅₉	1	4	yes	—
550	#41	C₂×D₄×C₅₉	1	4	yes	—
551	#41	C₂×D₄×C₅₉	1	4	yes	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	C₂²⋊C₄×C₅₉	1	2	yes	—
556	C₂×Q₈	C₂²⋊C₄×C₅₉	1	2	yes	—
557	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
595	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
596	C₂×D₄	C₂²×C₄×C₅₉	1	4	yes	—
597	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	4	1	no	—
606	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
607	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
616	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
617	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
618	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
620	SD₁₆	—	2	16	no	—
621	D₈	—	2	16	no	—
622	M₁₆	—	2	16	no	—
623	M₁₆	—	2	2	no	—
624	M₁₆	—	2	2	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	2	no	—
628	M₁₆	—	2	2	no	—
629	M₁₆	—	2	2	no	—
630	M₁₆	—	2	2	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	2	no	—
634	M₁₆	—	2	2	no	—
635	M₁₆	—	2	2	no	—
636	M₁₆	—	4	1	no	—
637	M₁₆	—	4	1	no	—
638	M₁₆	C₂×D₄×C₅₉	1	4	yes	—
639	C₂×C₈	—	2	16	no	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	2	2	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	2	no	—
648	C₂×C₈	—	4	1	no	—
649	C₂×C₈	—	4	1	no	—
650	C₂×C₈	C₂²×C₄×C₅₉	1	4	yes	—
651	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	4	1	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	4	1	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	4	2	no	—
669	C₂³	—	8	2	no	—
670	C₂³	—	8	4	no	—
671	C₂³	—	8	4	no	—
672	C₂³	—	8	4	no	—
673	C₂³	—	8	4	no	—
674	C₂³	—	8	4	no	—
675	C₂³	—	8	4	no	—
676	C₂³	—	8	4	no	—
677	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
678	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
679	C₂³	#121×C₅₉	1	1	yes	characteristic
680	C₂³	#121×C₅₉	1	1	yes	characteristic
681	C₂³	#123×C₅₉	1	1	yes	characteristic
682	C₂³	#123×C₅₉	1	1	yes	characteristic
683	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
688	D₄	—	2	4	no	—
689	D₄	—	2	4	no	—
690	D₄	—	2	4	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	8	2	no	—
713	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
714	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
715	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
716	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
717	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
718	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
719	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
720	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
721	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
722	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
723	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
724	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
725	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
726	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
727	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
728	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
729	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
730	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
731	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
732	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
733	C₂×C₄	#123×C₅₉	1	1	yes	characteristic
734	C₂×C₄	#123×C₅₉	1	1	yes	characteristic
735	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
740	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
741	C₈	—	2	4	no	—
742	C₈	—	2	4	no	—
743	C₈	—	2	4	no	—
744	C₈	—	4	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	8	2	no	—
756	C₂²	—	8	2	no	—
757	C₂²	—	8	4	no	—
758	C₂²	—	8	4	no	—
759	C₂²	—	8	4	no	—
760	C₂²	—	8	4	no	—
761	C₂²	—	8	4	no	—
762	C₂²	—	8	4	no	—
763	C₂²	—	8	4	no	—
764	C₂²	C₅₉×#386	1	1	yes	characteristic
765	C₂²	C₅₉×#386	1	1	yes	characteristic
766	C₂²	C₅₉×#386	1	1	yes	characteristic
767	C₂²	C₅₉×#386	1	1	yes	characteristic
768	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
769	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
770	C₂²	C₂×#123×C₅₉	1	1	yes	characteristic
771	C₄	—	2	4	no	—
772	C₄	—	8	2	no	—
773	C₄	C₅₉×#386	1	1	yes	characteristic
774	C₄	C₅₉×#386	1	1	yes	characteristic
775	C₄	C₅₉×#386	1	1	yes	characteristic
776	C₄	C₅₉×#386	1	1	yes	characteristic
777	C₄	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
778	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
779	C₄	C₂×#120×C₅₉	1	1	yes	characteristic
780	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
781	C₂	—	2	1	no	—
782	C₂	—	2	1	no	—
783	C₂	—	2	1	no	—
784	C₂	—	2	1	no	—
785	C₂	—	2	1	no	—
786	C₂	—	2	1	no	—
787	C₂	—	4	4	no	—
788	C₂	—	8	4	no	—
789	C₂	C₅₉×#1903	1	2	yes	direct product factor
790	C₂	C₂×C₅₉×#386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	#386
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×AGL(1,ℤ/8)×C₅₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#568	C₂	semidirect
3. C₂×C₅₉×#421	C₂	semidirect
4. C₂×C₅₉×#418	C₂	semidirect
5. C₂²×#100×C₅₉	C₂	semidirect
6. C₅₉×#1903	C₂	direct (N × H)
7. C₂×C₅₉×#344	C₂	semidirect
8. C₂×C₅₉×#338	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₅₉	C₄	semidirect
17. C₂²×SD₁₆×C₅₉	C₄	semidirect
18. C₂²×D₈×C₅₉	C₄	semidirect
22. C₅₉×#568	C₂²	semidirect
32. C₅₉×#421	C₂²	semidirect
35. C₅₉×#418	C₂²	semidirect
39. C₂×#100×C₅₉	C₂²	semidirect
40. C₅₉×#344	C₂²	semidirect
41. C₅₉×#338	C₂²	semidirect
80. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
83. C₂×D₈×C₅₉	C₂×C₄	semidirect
349. C₂×#1903	C₅₉	direct (N × H)
387. C₂×#568	C₂×C₅₉	semidirect
388. C₂×#421	C₂×C₅₉	semidirect
389. C₂×#418	C₂×C₅₉	semidirect
390. C₂²×#100	C₂×C₅₉	semidirect
391. #1903	C₂×C₅₉	direct (N × H)
392. C₂×#344	C₂×C₅₉	semidirect
393. C₂×#338	C₂×C₅₉	semidirect
402. C₂×C₅₉	#1903	direct (N × H)
410. C₂×AGL(1,ℤ/8)	C₄×C₅₉	semidirect
412. C₂²×SD₁₆	C₄×C₅₉	semidirect
413. C₂²×D₈	C₄×C₅₉	semidirect
417. #568	C₂²×C₅₉	semidirect
427. #421	C₂²×C₅₉	semidirect
430. #418	C₂²×C₅₉	semidirect
434. C₂×#100	C₂²×C₅₉	semidirect
435. #344	C₂²×C₅₉	semidirect
436. #338	C₂²×C₅₉	semidirect
437. C₅₉	C₂×#1903	direct (N × H)
476. C₂×SD₁₆	C₂×C₄×C₅₉	semidirect
479. C₂×D₈	C₂×C₄×C₅₉	semidirect
789. C₂	C₅₉×#1903	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₅₉	2
C₂×C₅₉×#568	2
C₂×C₅₉×#421	2
C₂×C₅₉×#418	2
C₂²×#100×C₅₉	2
C₅₉×#1903	2
C₂×C₅₉×#344	2
C₂×C₅₉×#338	2
C₂×#1903	59

Subgroups — C2×C59×#1903 #28433103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#1903 #28433103