Subgroups — C₅₉×#17581 #28429690

Order 15104.

1070 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1520	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1519	C₂	1	2	yes	maximal
6	C₅₉×#1512	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1509	C₂	1	4	yes	maximal, complemented
8	C₅₉×#529	—	2	1	no	—
9	C₅₉×#529	—	2	1	no	—
10	C₅₉×#529	—	2	1	no	—
11	C₅₉×#529	—	2	1	no	—
12	C₅₉×#529	C₄	1	2	yes	complemented
13	C₅₉×#529	C₄	1	2	yes	complemented
14	C₅₉×#529	C₂²	1	2	yes	—
15	C₅₉×#529	C₂²	1	2	yes	—
16	C₂×#126×C₅₉	—	2	1	no	—
17	C₂×#125×C₅₉	C₄	1	1	yes	characteristic, complemented
18	C₂×#124×C₅₉	C₄	1	1	yes	characteristic, complemented
19	C₂×#123×C₅₉	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₅₉	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₅₉	—	2	1	no	—
24	C₂×C₄×D₄×C₅₉	C₄	1	1	yes	characteristic, complemented
25	C₂×#117×C₅₉	—	2	1	no	—
26	C₂×#117×C₅₉	—	2	1	no	—
27	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
28	C₅₉×#432	—	2	1	no	—
29	C₅₉×#432	—	2	1	no	—
30	C₅₉×#432	C₂²	1	2	yes	complemented
31	C₅₉×#432	C₂²	1	2	yes	complemented
32	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
33	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
34	C₂×#97×C₅₉	—	2	1	no	—
35	C₅₉×#384	—	2	1	no	—
36	C₅₉×#382	C₂²	1	2	yes	complemented
37	C₅₉×#380	—	2	1	no	—
38	C₅₉×#380	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
40	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
41	C₅₉×#328	C₂²	1	8	yes	complemented
42	C₅₉×#327	C₂²	1	8	yes	—
43	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₅₉	—	2	1	no	—
45	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅₉	—	2	1	no	—
47	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₅₉	—	2	2	no	—
51	#126×C₅₉	—	2	2	no	—
52	#126×C₅₉	—	2	2	no	—
53	#126×C₅₉	—	2	2	no	—
54	#126×C₅₉	—	2	2	no	—
55	#125×C₅₉	—	2	1	no	—
56	#125×C₅₉	—	2	1	no	—
57	#125×C₅₉	C₂×C₄	1	2	yes	—
58	#125×C₅₉	C₂×C₄	1	2	yes	—
59	#124×C₅₉	—	2	1	no	—
60	#124×C₅₉	—	2	1	no	—
61	#124×C₅₉	C₂×C₄	1	2	yes	—
62	#124×C₅₉	C₂×C₄	1	2	yes	—
63	#123×C₅₉	—	2	2	no	—
64	#123×C₅₉	—	2	2	no	—
65	#123×C₅₉	—	2	2	no	—
66	#123×C₅₉	—	2	2	no	—
67	C₂²⋊Q₈×C₅₉	—	2	1	no	—
68	C₂²⋊Q₈×C₅₉	—	2	1	no	—
69	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
70	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
71	#121×C₅₉	—	2	1	no	—
72	#121×C₅₉	—	2	1	no	—
73	#121×C₅₉	C₂×C₄	1	2	yes	—
74	#121×C₅₉	C₂³	1	2	yes	—
75	C₄×Q₈×C₅₉	—	2	1	no	—
76	C₄×Q₈×C₅₉	—	2	1	no	—
77	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₅₉	—	2	2	no	—
80	C₄×D₄×C₅₉	—	2	2	no	—
81	C₄×D₄×C₅₉	—	2	2	no	—
82	C₄×D₄×C₅₉	—	2	2	no	—
83	C₄×D₄×C₅₉	—	2	1	no	—
84	C₄×D₄×C₅₉	—	2	1	no	—
85	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
87	#117×C₅₉	—	2	2	no	—
88	#117×C₅₉	—	2	2	no	—
89	#117×C₅₉	—	2	2	no	—
90	#117×C₅₉	—	2	2	no	—
91	#117×C₅₉	—	4	4	no	—
92	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
99	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
107	C₂×C₄²×C₅₉	—	2	1	no	—
108	C₂×C₄²×C₅₉	—	2	2	no	—
109	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₅₉	—	2	2	no	—
122	C₄⋊C₈×C₅₉	—	2	2	no	—
123	C₂²⋊C₈×C₅₉	—	2	2	no	—
124	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
125	#97×C₅₉	—	2	2	no	—
126	#97×C₅₉	—	2	2	no	—
127	#95×C₅₉	—	2	2	no	—
128	#95×C₅₉	C₂³	1	4	yes	—
129	C₂⁴×C₅₉	—	2	1	no	—
130	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Q₈×C₅₉	—	2	1	no	—
132	C₂×Q₈×C₅₉	—	4	2	no	—
133	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₅₉	—	2	2	no	—
135	C₂×D₄×C₅₉	—	2	2	no	—
136	C₂×D₄×C₅₉	—	2	1	no	—
137	C₂×D₄×C₅₉	—	4	2	no	—
138	C₂×D₄×C₅₉	—	4	2	no	—
139	C₂×D₄×C₅₉	—	4	2	no	—
140	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₅₉	—	2	2	no	—
142	C₂²×C₄×C₅₉	—	2	2	no	—
143	C₂²×C₄×C₅₉	—	2	1	no	—
144	C₂²×C₄×C₅₉	—	2	1	no	—
145	C₂²×C₄×C₅₉	—	2	1	no	—
146	C₂²×C₄×C₅₉	—	2	2	no	—
147	C₂²×C₄×C₅₉	—	2	2	no	—
148	C₂²×C₄×C₅₉	—	2	4	no	—
149	C₂²×C₄×C₅₉	—	4	2	no	—
150	C₂²×C₄×C₅₉	—	4	2	no	—
151	C₂²×C₄×C₅₉	—	4	4	no	—
152	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₅₉	—	2	4	no	—
171	C₂×C₈×C₅₉	—	4	4	no	—
172	C₄⋊C₄×C₅₉	—	2	2	no	—
173	C₄⋊C₄×C₅₉	—	2	2	no	—
174	C₄⋊C₄×C₅₉	—	2	2	no	—
175	C₄⋊C₄×C₅₉	—	2	2	no	—
176	C₄⋊C₄×C₅₉	—	2	2	no	—
177	C₄⋊C₄×C₅₉	—	2	2	no	—
178	C₄⋊C₄×C₅₉	—	2	2	no	—
179	C₄⋊C₄×C₅₉	—	2	1	no	—
180	C₄⋊C₄×C₅₉	—	2	1	no	—
181	C₄⋊C₄×C₅₉	—	2	2	no	—
182	C₄⋊C₄×C₅₉	—	4	4	no	—
183	C₄⋊C₄×C₅₉	—	4	4	no	—
184	C₄⋊C₄×C₅₉	—	4	4	no	—
185	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
186	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
187	C₂²⋊C₄×C₅₉	—	2	2	no	—
188	C₂²⋊C₄×C₅₉	—	2	2	no	—
189	C₂²⋊C₄×C₅₉	—	2	2	no	—
190	C₂²⋊C₄×C₅₉	—	2	2	no	—
191	C₂²⋊C₄×C₅₉	—	2	2	no	—
192	C₂²⋊C₄×C₅₉	—	2	2	no	—
193	C₂²⋊C₄×C₅₉	—	2	2	no	—
194	C₂²⋊C₄×C₅₉	—	2	2	no	—
195	C₂²⋊C₄×C₅₉	—	2	2	no	—
196	C₂²⋊C₄×C₅₉	—	2	2	no	—
197	C₂²⋊C₄×C₅₉	—	4	4	no	—
198	C₄²×C₅₉	—	2	2	no	—
199	C₄²×C₅₉	—	2	2	no	—
200	C₄²×C₅₉	—	4	4	no	—
201	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₅₉	—	2	2	no	—
218	C₂³×C₅₉	—	4	1	no	—
219	C₂³×C₅₉	—	4	1	no	—
220	C₂³×C₅₉	—	4	2	no	—
221	C₂³×C₅₉	—	4	2	no	—
222	C₂³×C₅₉	—	4	2	no	—
223	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
226	C₂³×C₅₉	#137	1	2	yes	—
227	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₅₉	—	4	2	no	—
229	Q₈×C₅₉	—	4	2	no	—
230	D₄×C₅₉	—	4	2	no	—
231	D₄×C₅₉	—	4	2	no	—
232	D₄×C₅₉	—	4	2	no	—
233	D₄×C₅₉	—	4	4	no	—
234	D₄×C₅₉	—	4	2	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	1	no	—
238	C₂×C₄×C₅₉	—	2	1	no	—
239	C₂×C₄×C₅₉	—	2	2	no	—
240	C₂×C₄×C₅₉	—	2	2	no	—
241	C₂×C₄×C₅₉	—	2	2	no	—
242	C₂×C₄×C₅₉	—	2	2	no	—
243	C₂×C₄×C₅₉	—	2	2	no	—
244	C₂×C₄×C₅₉	—	2	2	no	—
245	C₂×C₄×C₅₉	—	2	2	no	—
246	C₂×C₄×C₅₉	—	2	2	no	—
247	C₂×C₄×C₅₉	—	2	2	no	—
248	C₂×C₄×C₅₉	—	2	2	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	2	no	—
251	C₂×C₄×C₅₉	—	2	2	no	—
252	C₂×C₄×C₅₉	—	4	1	no	—
253	C₂×C₄×C₅₉	—	4	1	no	—
254	C₂×C₄×C₅₉	—	4	1	no	—
255	C₂×C₄×C₅₉	—	4	1	no	—
256	C₂×C₄×C₅₉	—	4	1	no	—
257	C₂×C₄×C₅₉	—	4	1	no	—
258	C₂×C₄×C₅₉	—	4	4	no	—
259	C₂×C₄×C₅₉	—	4	2	no	—
260	C₂×C₄×C₅₉	—	4	2	no	—
261	C₂×C₄×C₅₉	—	4	2	no	—
262	C₂×C₄×C₅₉	—	4	4	no	—
263	C₂×C₄×C₅₉	—	4	4	no	—
264	C₂×C₄×C₅₉	—	4	4	no	—
265	C₂×C₄×C₅₉	—	4	4	no	—
266	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
278	C₈×C₅₉	—	4	4	no	—
279	#17581	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂²×C₅₉	—	2	1	no	—
281	C₂²×C₅₉	—	2	1	no	—
282	C₂²×C₅₉	—	2	1	no	—
283	C₂²×C₅₉	—	2	1	no	—
284	C₂²×C₅₉	—	2	1	no	—
285	C₂²×C₅₉	—	2	1	no	—
286	C₂²×C₅₉	—	4	2	no	—
287	C₂²×C₅₉	—	4	2	no	—
288	C₂²×C₅₉	—	4	2	no	—
289	C₂²×C₅₉	—	4	2	no	—
290	C₂²×C₅₉	—	4	2	no	—
291	C₂²×C₅₉	—	8	4	no	—
292	C₂²×C₅₉	#417	1	2	yes	—
293	C₂²×C₅₉	#417	1	2	yes	—
294	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
296	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
297	C₄×C₅₉	—	2	1	no	—
298	C₄×C₅₉	—	2	1	no	—
299	C₄×C₅₉	—	2	1	no	—
300	C₄×C₅₉	—	2	1	no	—
301	C₄×C₅₉	—	2	1	no	—
302	C₄×C₅₉	—	2	1	no	—
303	C₄×C₅₉	—	2	1	no	—
304	C₄×C₅₉	—	2	1	no	—
305	C₄×C₅₉	—	2	1	no	—
306	C₄×C₅₉	—	2	1	no	—
307	C₄×C₅₉	—	4	2	no	—
308	C₄×C₅₉	—	4	2	no	—
309	C₄×C₅₉	—	4	2	no	—
310	C₄×C₅₉	—	8	4	no	—
311	C₄×C₅₉	#410	1	2	yes	—
312	C₄×C₅₉	#421	1	2	yes	—
313	C₂×#529	C₂×C₅₉	1	1	yes	characteristic
314	C₂×#432	C₂×C₅₉	1	1	yes	characteristic, complemented
315	#2285	C₂×C₅₉	1	1	yes	characteristic, complemented
316	#1520	C₂×C₅₉	1	2	yes	complemented
317	#1519	C₂×C₅₉	1	2	yes	—
318	#1512	C₂×C₅₉	1	4	yes	complemented
319	#1509	C₂×C₅₉	1	4	yes	complemented
320	C₂×C₅₉	—	2	1	no	—
321	C₂×C₅₉	—	2	2	no	—
322	C₂×C₅₉	—	2	1	no	—
323	C₂×C₅₉	—	2	2	no	—
324	C₂×C₅₉	—	8	2	no	—
325	C₂×C₅₉	C₂×#410	1	1	yes	characteristic
326	C₂×C₅₉	C₂×#417	1	1	yes	characteristic
327	C₂×C₅₉	C₂×#421	1	1	yes	characteristic
328	#529	—	2	1	no	—
329	#529	—	2	1	no	—
330	#529	—	2	1	no	—
331	#529	—	2	1	no	—
332	#529	C₄×C₅₉	1	2	yes	complemented
333	#529	C₄×C₅₉	1	2	yes	complemented
334	#529	C₂²×C₅₉	1	2	yes	—
335	#529	C₂²×C₅₉	1	2	yes	—
336	C₂×#126	—	2	1	no	—
337	C₂×#125	C₄×C₅₉	1	1	yes	characteristic, complemented
338	C₂×#124	C₄×C₅₉	1	1	yes	characteristic, complemented
339	C₂×#123	—	2	1	no	—
340	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
341	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
342	C₂×C₄×Q₈	C₄×C₅₉	1	1	yes	characteristic, complemented
343	C₂×C₄×D₄	—	2	1	no	—
344	C₂×C₄×D₄	C₄×C₅₉	1	1	yes	characteristic, complemented
345	C₂×#117	—	2	1	no	—
346	C₂×#117	—	2	1	no	—
347	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
348	#432	—	2	1	no	—
349	#432	—	2	1	no	—
350	#432	C₂²×C₅₉	1	2	yes	complemented
351	#432	C₂²×C₅₉	1	2	yes	complemented
352	C₂×C₄⋊C₈	—	2	1	no	—
353	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
354	C₂×#97	—	2	1	no	—
355	#384	—	2	1	no	—
356	#382	C₂²×C₅₉	1	2	yes	complemented
357	#380	—	2	1	no	—
358	#380	C₂²×C₅₉	1	2	yes	—
359	C₄×C₄⋊C₄	—	2	1	no	—
360	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
361	#328	C₂²×C₅₉	1	8	yes	complemented
362	#327	C₂²×C₅₉	1	8	yes	—
363	C₅₉	#17581	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
369	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
371	C₂²×C₈	—	2	2	no	—
372	#126	—	2	2	no	—
373	#126	—	2	2	no	—
374	#126	—	2	2	no	—
375	#126	—	2	2	no	—
376	#125	—	2	1	no	—
377	#125	—	2	1	no	—
378	#125	C₂×C₄×C₅₉	1	2	yes	—
379	#125	C₂×C₄×C₅₉	1	2	yes	—
380	#124	—	2	1	no	—
381	#124	—	2	1	no	—
382	#124	C₂×C₄×C₅₉	1	2	yes	—
383	#124	C₂×C₄×C₅₉	1	2	yes	—
384	#123	—	2	2	no	—
385	#123	—	2	2	no	—
386	#123	—	2	2	no	—
387	#123	—	2	2	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	1	no	—
390	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
391	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	C₂×C₄×C₅₉	1	2	yes	—
395	#121	C₂³×C₅₉	1	2	yes	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
399	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
407	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	4	4	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	2	no	—
420	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	2	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	2	no	—
430	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
431	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
432	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
433	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
434	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
435	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
436	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
437	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
438	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
442	C₄⋊C₈	—	2	2	no	—
443	C₄⋊C₈	—	2	2	no	—
444	C₂²⋊C₈	—	2	2	no	—
445	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
446	#97	—	2	2	no	—
447	#97	—	2	2	no	—
448	#95	—	2	2	no	—
449	#95	C₂³×C₅₉	1	4	yes	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
478	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
479	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
480	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
481	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
491	C₂×C₈	—	2	4	no	—
492	C₂×C₈	—	4	4	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	4	4	no	—
504	C₄⋊C₄	—	4	4	no	—
505	C₄⋊C₄	—	4	4	no	—
506	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
507	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	4	4	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	4	4	no	—
522	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
523	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
524	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
525	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
526	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
527	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
528	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
529	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
530	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
531	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
532	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
533	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
534	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
536	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
537	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
538	C₂³	—	2	2	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
545	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
546	C₂³	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
547	C₂³	#137×C₅₉	1	2	yes	—
548	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
549	Q₈	—	4	2	no	—
550	Q₈	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	4	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
588	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
590	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
591	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
592	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
593	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
594	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
595	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
596	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
599	C₈	—	4	4	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	8	4	no	—
612	C₂²	C₅₉×#417	1	2	yes	—
613	C₂²	C₅₉×#417	1	2	yes	—
614	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
615	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
616	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	4	no	—
631	C₄	C₅₉×#410	1	2	yes	—
632	C₄	C₅₉×#421	1	2	yes	—
633	C₂	—	2	1	no	—
634	C₂	—	2	2	no	—
635	C₂	—	2	2	no	—
636	C₂	—	2	1	no	—
637	C₂	—	8	2	no	—
638	C₂	C₂×C₅₉×#410	1	1	yes	characteristic
639	C₂	C₂×C₅₉×#417	1	1	yes	characteristic
640	C₂	C₂×C₅₉×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×#121×C₅₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#432	C₂	semidirect
3. C₅₉×#2285	C₂	semidirect
4. C₅₉×#1520	C₂	semidirect
6. C₅₉×#1512	C₂	semidirect
7. C₅₉×#1509	C₂	semidirect
12. C₅₉×#529	C₄	semidirect
13. C₅₉×#529	C₄	semidirect
17. C₂×#125×C₅₉	C₄	semidirect
18. C₂×#124×C₅₉	C₄	semidirect
22. C₂×C₄×Q₈×C₅₉	C₄	semidirect
24. C₂×C₄×D₄×C₅₉	C₄	semidirect
30. C₅₉×#432	C₂²	semidirect
31. C₅₉×#432	C₂²	semidirect
36. C₅₉×#382	C₂²	semidirect
40. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
41. C₅₉×#328	C₂²	semidirect
279. #17581	C₅₉	direct (N × H)
314. C₂×#432	C₂×C₅₉	semidirect
315. #2285	C₂×C₅₉	semidirect
316. #1520	C₂×C₅₉	semidirect
318. #1512	C₂×C₅₉	semidirect
319. #1509	C₂×C₅₉	semidirect
332. #529	C₄×C₅₉	semidirect
333. #529	C₄×C₅₉	semidirect
337. C₂×#125	C₄×C₅₉	semidirect
338. C₂×#124	C₄×C₅₉	semidirect
342. C₂×C₄×Q₈	C₄×C₅₉	semidirect
344. C₂×C₄×D₄	C₄×C₅₉	semidirect
350. #432	C₂²×C₅₉	semidirect
351. #432	C₂²×C₅₉	semidirect
356. #382	C₂²×C₅₉	semidirect
360. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
361. #328	C₂²×C₅₉	semidirect
363. C₅₉	#17581	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#529	2
C₂×C₅₉×#432	2
C₅₉×#2285	2
C₅₉×#1520	2
C₅₉×#1519	2
C₅₉×#1512	2
C₅₉×#1509	2
#17581	59

Subgroups — C59×#17581 #28429690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17581 #28429690