Subgroups — C₅₉×#22531 #28434640

Order 15104.

1136 conjugacy classes of subgroups.

The subgroup lattice has 574 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×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1955	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1954	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1798	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1750	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#529	—	2	4	no	—
13	C₅₉×#529	—	2	4	no	—
14	C₂×#126×C₅₉	C₄	1	2	yes	—
15	C₂×#125×C₅₉	C₄	1	1	yes	characteristic
16	C₂×#124×C₅₉	C₄	1	1	yes	characteristic
17	C₂×#123×C₅₉	C₄	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₅₉	C₄	1	1	yes	characteristic
19	C₂×#121×C₅₉	C₄	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
23	C₂×#117×C₅₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#446	—	2	4	no	—
26	C₈×Q₈×C₅₉	—	2	4	no	—
27	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
38	C₂×#97×C₅₉	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
42	C₅₉×#336	C₂²	1	1	yes	characteristic
43	C₅₉×#336	C₂²	1	1	yes	characteristic
44	C₅₉×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₅₉	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
58	#126×C₅₉	—	2	8	no	—
59	#125×C₅₉	—	2	4	no	—
60	#124×C₅₉	—	2	4	no	—
61	#123×C₅₉	—	2	8	no	—
62	C₂²⋊Q₈×C₅₉	—	2	4	no	—
63	#121×C₅₉	—	2	4	no	—
64	C₄×Q₈×C₅₉	D₄	1	4	yes	—
65	C₄×Q₈×C₅₉	D₄	1	4	yes	—
66	C₄×D₄×C₅₉	—	2	2	no	—
67	C₄×D₄×C₅₉	—	2	2	no	—
68	C₄×D₄×C₅₉	—	2	4	no	—
69	C₄×D₄×C₅₉	—	2	4	no	—
70	#117×C₅₉	—	2	4	no	—
71	#117×C₅₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₅₉	—	2	2	no	—
84	C₂×C₄²×C₅₉	—	2	2	no	—
85	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
90	C₄⋊C₈×C₅₉	—	2	2	no	—
91	C₄⋊C₈×C₅₉	—	2	4	no	—
92	C₄⋊C₈×C₅₉	—	2	2	no	—
93	C₄⋊C₈×C₅₉	—	2	4	no	—
94	C₂²⋊C₈×C₅₉	—	2	2	no	—
95	C₂²⋊C₈×C₅₉	—	2	2	no	—
96	C₂²⋊C₈×C₅₉	—	2	4	no	—
97	C₂²⋊C₈×C₅₉	—	2	4	no	—
98	C₂²⋊C₈×C₅₉	—	4	2	no	—
99	C₂²⋊C₈×C₅₉	—	4	2	no	—
100	C₂²⋊C₈×C₅₉	—	4	2	no	—
101	#97×C₅₉	—	2	4	no	—
102	C₄×C₈×C₅₉	—	2	2	no	—
103	C₄×C₈×C₅₉	—	2	4	no	—
104	C₄×C₈×C₅₉	—	2	2	no	—
105	C₂⁴×C₅₉	C₂²×C₄	1	2	yes	—
106	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×Q₈×C₅₉	—	2	2	no	—
108	C₂×Q₈×C₅₉	—	2	2	no	—
109	C₂×Q₈×C₅₉	C₂²⋊C₄	1	4	yes	—
110	C₂×D₄×C₅₉	—	2	4	no	—
111	C₂×D₄×C₅₉	—	2	4	no	—
112	C₂×D₄×C₅₉	—	2	2	no	—
113	C₂×D₄×C₅₉	—	2	2	no	—
114	C₂×D₄×C₅₉	—	2	2	no	—
115	C₂×D₄×C₅₉	—	4	2	no	—
116	C₂²×C₄×C₅₉	—	2	2	no	—
117	C₂²×C₄×C₅₉	—	2	2	no	—
118	C₂²×C₄×C₅₉	—	2	2	no	—
119	C₂²×C₄×C₅₉	—	2	2	no	—
120	C₂²×C₄×C₅₉	—	2	2	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	1	no	—
123	C₂²×C₄×C₅₉	—	2	2	no	—
124	C₂²×C₄×C₅₉	—	2	2	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	2	1	no	—
127	C₂²×C₄×C₅₉	—	2	2	no	—
128	C₂²×C₄×C₅₉	—	2	2	no	—
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	—	2	2	no	—
131	C₂²×C₄×C₅₉	—	2	1	no	—
132	C₂²×C₄×C₅₉	—	2	2	no	—
133	C₂²×C₄×C₅₉	—	4	1	no	—
134	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
143	C₂×C₈×C₅₉	—	2	1	no	—
144	C₂×C₈×C₅₉	—	2	1	no	—
145	C₂×C₈×C₅₉	—	2	1	no	—
146	C₂×C₈×C₅₉	—	2	1	no	—
147	C₂×C₈×C₅₉	—	2	1	no	—
148	C₂×C₈×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	—	2	1	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	1	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₂×C₈×C₅₉	—	2	2	no	—
155	C₂×C₈×C₅₉	—	2	2	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	—	2	1	no	—
158	C₂×C₈×C₅₉	—	2	2	no	—
159	C₂×C₈×C₅₉	#41	1	2	yes	—
160	C₂×C₈×C₅₉	#41	1	2	yes	—
161	C₄⋊C₄×C₅₉	—	2	4	no	—
162	C₄⋊C₄×C₅₉	—	2	4	no	—
163	C₄⋊C₄×C₅₉	—	2	2	no	—
164	C₄⋊C₄×C₅₉	—	2	4	no	—
165	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
166	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	8	yes	—
167	C₂²⋊C₄×C₅₉	—	2	4	no	—
168	C₂²⋊C₄×C₅₉	—	2	4	no	—
169	C₂²⋊C₄×C₅₉	—	2	4	no	—
170	C₂²⋊C₄×C₅₉	—	2	4	no	—
171	C₂²⋊C₄×C₅₉	—	2	4	no	—
172	C₄²×C₅₉	—	2	2	no	—
173	C₄²×C₅₉	—	2	2	no	—
174	C₄²×C₅₉	—	2	1	no	—
175	C₄²×C₅₉	—	2	1	no	—
176	C₄²×C₅₉	C₂×D₄	1	2	yes	—
177	C₄²×C₅₉	C₂×D₄	1	2	yes	—
178	C₄²×C₅₉	C₂×D₄	1	4	yes	—
179	C₄²×C₅₉	C₂×D₄	1	4	yes	—
180	C₂³×C₅₉	—	2	1	no	—
181	C₂³×C₅₉	—	2	1	no	—
182	C₂³×C₅₉	—	2	1	no	—
183	C₂³×C₅₉	—	2	1	no	—
184	C₂³×C₅₉	—	2	1	no	—
185	C₂³×C₅₉	—	2	1	no	—
186	C₂³×C₅₉	—	2	2	no	—
187	C₂³×C₅₉	—	2	2	no	—
188	C₂³×C₅₉	—	2	2	no	—
189	C₂³×C₅₉	—	2	2	no	—
190	C₂³×C₅₉	—	2	2	no	—
191	C₂³×C₅₉	—	2	2	no	—
192	C₂³×C₅₉	—	2	2	no	—
193	C₂³×C₅₉	#131	1	2	yes	—
194	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
195	Q₈×C₅₉	—	2	8	no	—
196	D₄×C₅₉	—	4	8	no	—
197	D₄×C₅₉	—	4	4	no	—
198	C₂×C₄×C₅₉	—	2	1	no	—
199	C₂×C₄×C₅₉	—	2	2	no	—
200	C₂×C₄×C₅₉	—	2	2	no	—
201	C₂×C₄×C₅₉	—	2	2	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	2	2	no	—
204	C₂×C₄×C₅₉	—	2	1	no	—
205	C₂×C₄×C₅₉	—	2	1	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	2	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	2	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	4	4	no	—
217	C₂×C₄×C₅₉	—	4	1	no	—
218	C₂×C₄×C₅₉	—	4	1	no	—
219	C₂×C₄×C₅₉	—	4	2	no	—
220	C₂×C₄×C₅₉	—	4	2	no	—
221	C₂×C₄×C₅₉	—	4	1	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	4	2	no	—
224	C₂×C₄×C₅₉	—	4	2	no	—
225	C₂×C₄×C₅₉	—	4	4	no	—
226	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
228	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
229	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂×C₄×C₅₉	#131	1	2	yes	—
231	C₂×C₄×C₅₉	#131	1	2	yes	—
232	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
238	C₈×C₅₉	—	2	2	no	—
239	C₈×C₅₉	—	2	2	no	—
240	C₈×C₅₉	—	4	1	no	—
241	C₈×C₅₉	—	4	2	no	—
242	C₈×C₅₉	—	4	1	no	—
243	C₈×C₅₉	—	4	2	no	—
244	#22531	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂²×C₅₉	—	2	2	no	—
246	C₂²×C₅₉	—	2	2	no	—
247	C₂²×C₅₉	—	2	2	no	—
248	C₂²×C₅₉	—	4	1	no	—
249	C₂²×C₅₉	—	4	1	no	—
250	C₂²×C₅₉	—	4	1	no	—
251	C₂²×C₅₉	—	4	1	no	—
252	C₂²×C₅₉	—	4	2	no	—
253	C₂²×C₅₉	—	4	2	no	—
254	C₂²×C₅₉	—	4	2	no	—
255	C₂²×C₅₉	—	4	2	no	—
256	C₂²×C₅₉	—	4	2	no	—
257	C₂²×C₅₉	—	4	2	no	—
258	C₂²×C₅₉	—	4	2	no	—
259	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
261	C₂²×C₅₉	#520	1	1	yes	characteristic
262	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
263	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
264	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
265	C₂²×C₅₉	#568	1	1	yes	characteristic
266	C₄×C₅₉	—	2	4	no	—
267	C₄×C₅₉	—	2	2	no	—
268	C₄×C₅₉	—	2	4	no	—
269	C₄×C₅₉	—	4	1	no	—
270	C₄×C₅₉	—	4	2	no	—
271	C₄×C₅₉	—	4	1	no	—
272	C₄×C₅₉	—	4	1	no	—
273	C₄×C₅₉	#408	1	4	yes	—
274	C₄×C₅₉	#548	1	1	yes	characteristic
275	C₄×C₅₉	#548	1	1	yes	characteristic
276	C₄×C₅₉	#550	1	1	yes	characteristic
277	C₄×C₅₉	#550	1	1	yes	characteristic
278	C₂×#529	C₂×C₅₉	1	1	yes	characteristic
279	C₂×#446	C₂×C₅₉	1	1	yes	characteristic, complemented
280	C₂×C₈×Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
281	#1955	C₂×C₅₉	1	2	yes	complemented
282	#1954	C₂×C₅₉	1	1	yes	characteristic, complemented
283	#1954	C₂×C₅₉	1	1	yes	characteristic, complemented
284	#1954	C₂×C₅₉	1	2	yes	complemented
285	#1798	C₂×C₅₉	1	2	yes	complemented
286	#1797	C₂×C₅₉	1	1	yes	characteristic, complemented
287	#1750	C₂×C₅₉	1	2	yes	complemented
288	C₄×C₂²⋊C₈	C₂×C₅₉	1	1	yes	characteristic, complemented
289	C₂×C₅₉	—	4	2	no	—
290	C₂×C₅₉	—	8	2	no	—
291	C₂×C₅₉	#2341	1	1	yes	characteristic
292	C₂×C₅₉	C₂×#408	1	1	yes	characteristic
293	C₂×C₅₉	#2880	1	1	yes	characteristic
294	C₂×C₅₉	#2966	1	1	yes	characteristic
295	C₂×C₅₉	#2969	1	1	yes	characteristic
296	C₂×C₅₉	#2993	1	1	yes	characteristic
297	C₂×C₅₉	#2994	1	1	yes	characteristic
298	#529	—	2	4	no	—
299	#529	—	2	4	no	—
300	C₂×#126	C₄×C₅₉	1	2	yes	—
301	C₂×#125	C₄×C₅₉	1	1	yes	characteristic
302	C₂×#124	C₄×C₅₉	1	1	yes	characteristic
303	C₂×#123	C₄×C₅₉	1	2	yes	—
304	C₂×C₂²⋊Q₈	C₄×C₅₉	1	1	yes	characteristic
305	C₂×#121	C₄×C₅₉	1	1	yes	characteristic
306	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
309	C₂×#117	C₂²×C₅₉	1	2	yes	—
310	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
311	#446	—	2	4	no	—
312	C₈×Q₈	—	2	4	no	—
313	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
316	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
319	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
320	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
322	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
323	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
324	C₂×#97	C₂²×C₅₉	1	2	yes	—
325	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
326	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
327	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
328	#336	C₂²×C₅₉	1	2	yes	—
329	#336	C₂²×C₅₉	1	1	yes	characteristic
330	#336	C₂²×C₅₉	1	1	yes	characteristic
331	C₅₉	#22531	1	1	yes	characteristic, direct product factor, Sylow
332	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
333	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
334	C₂²×D₄	C₂×C₄×C₅₉	1	2	yes	—
335	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
336	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
338	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
340	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
343	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
345	#126	—	2	8	no	—
346	#125	—	2	4	no	—
347	#124	—	2	4	no	—
348	#123	—	2	8	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	#121	—	2	4	no	—
351	C₄×Q₈	D₄×C₅₉	1	4	yes	—
352	C₄×Q₈	D₄×C₅₉	1	4	yes	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	2	4	no	—
357	#117	—	2	4	no	—
358	#117	—	2	4	no	—
359	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
361	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
367	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
368	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
369	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	—	2	2	no	—
372	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
373	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
376	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
377	C₄⋊C₈	—	2	2	no	—
378	C₄⋊C₈	—	2	4	no	—
379	C₄⋊C₈	—	2	2	no	—
380	C₄⋊C₈	—	2	4	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	C₂²⋊C₈	—	2	4	no	—
383	C₂²⋊C₈	—	2	4	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	—	4	2	no	—
386	C₂²⋊C₈	—	4	2	no	—
387	C₂²⋊C₈	—	4	2	no	—
388	#97	—	2	4	no	—
389	C₄×C₈	—	2	2	no	—
390	C₄×C₈	—	2	4	no	—
391	C₄×C₈	—	2	2	no	—
392	C₂⁴	C₂²×C₄×C₅₉	1	2	yes	—
393	C₂⁴	C₂²×C₄×C₅₉	1	1	yes	characteristic
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	C₂²⋊C₄×C₅₉	1	4	yes	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
425	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
427	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
428	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	#41×C₅₉	1	2	yes	—
447	C₂×C₈	#41×C₅₉	1	2	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	4	yes	—
453	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	8	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	C₂×D₄×C₅₉	1	2	yes	—
464	C₄²	C₂×D₄×C₅₉	1	2	yes	—
465	C₄²	C₂×D₄×C₅₉	1	4	yes	—
466	C₄²	C₂×D₄×C₅₉	1	4	yes	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	#131×C₅₉	1	2	yes	—
481	C₂³	C₂³×C₄×C₅₉	1	1	yes	characteristic
482	Q₈	—	2	8	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	4	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
515	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
516	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
517	C₂×C₄	#131×C₅₉	1	2	yes	—
518	C₂×C₄	#131×C₅₉	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
523	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
524	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	2	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
546	C₂²	C₄×#41×C₅₉	1	1	yes	characteristic
547	C₂²	C₅₉×#520	1	1	yes	characteristic
548	C₂²	C₂×#131×C₅₉	1	1	yes	characteristic
549	C₂²	C₂×#131×C₅₉	1	1	yes	characteristic
550	C₂²	C₂×#131×C₅₉	1	1	yes	characteristic
551	C₂²	C₅₉×#568	1	1	yes	characteristic
552	C₄	—	2	4	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	4	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	C₅₉×#408	1	4	yes	—
560	C₄	C₅₉×#548	1	1	yes	characteristic
561	C₄	C₅₉×#548	1	1	yes	characteristic
562	C₄	C₅₉×#550	1	1	yes	characteristic
563	C₄	C₅₉×#550	1	1	yes	characteristic
564	C₂	—	4	2	no	—
565	C₂	—	8	2	no	—
566	C₂	C₅₉×#2341	1	1	yes	characteristic
567	C₂	C₂×C₅₉×#408	1	1	yes	characteristic
568	C₂	C₅₉×#2880	1	1	yes	characteristic
569	C₂	C₅₉×#2966	1	1	yes	characteristic
570	C₂	C₅₉×#2969	1	1	yes	characteristic
571	C₂	C₅₉×#2993	1	1	yes	characteristic
572	C₂	C₅₉×#2994	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#446	C₂	semidirect
3. C₂×C₈×Q₈×C₅₉	C₂	semidirect
4. C₅₉×#1955	C₂	semidirect
5. C₅₉×#1954	C₂	semidirect
6. C₅₉×#1954	C₂	semidirect
7. C₅₉×#1954	C₂	semidirect
8. C₅₉×#1798	C₂	semidirect
9. C₅₉×#1797	C₂	semidirect
10. C₅₉×#1750	C₂	semidirect
11. C₄×C₂²⋊C₈×C₅₉	C₂	semidirect
244. #22531	C₅₉	direct (N × H)
279. C₂×#446	C₂×C₅₉	semidirect
280. C₂×C₈×Q₈	C₂×C₅₉	semidirect
281. #1955	C₂×C₅₉	semidirect
282. #1954	C₂×C₅₉	semidirect
283. #1954	C₂×C₅₉	semidirect
284. #1954	C₂×C₅₉	semidirect
285. #1798	C₂×C₅₉	semidirect
286. #1797	C₂×C₅₉	semidirect
287. #1750	C₂×C₅₉	semidirect
288. C₄×C₂²⋊C₈	C₂×C₅₉	semidirect
331. C₅₉	#22531	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×#446	2
C₂×C₈×Q₈×C₅₉	2
C₅₉×#1955	2
C₅₉×#1954	2
C₅₉×#1798	2
C₅₉×#1797	2
C₅₉×#1750	2
C₄×C₂²⋊C₈×C₅₉	2
#22531	59

Subgroups — C59×#22531 #28434640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#22531 #28434640