Subgroups — C₅₉×#17406 #28429515

Order 15104.

952 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#539	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2973	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1473	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1472	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1470	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1468	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1465	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1463	C₂	1	2	yes	maximal, complemented
10	C₅₉×#539	—	2	4	no	—
11	C₅₉×#539	—	2	4	no	—
12	C₂×#126×C₅₉	C₄	1	1	yes	characteristic
13	C₂×#126×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#125×C₅₉	C₄	1	1	yes	characteristic
15	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#123×C₅₉	C₄	1	1	yes	characteristic
17	C₂×#123×C₅₉	C₄	1	1	yes	characteristic
18	C₂×#123×C₅₉	C₄	1	1	yes	characteristic
19	C₂×#123×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₅₉	C₄	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₅₉	C₄	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₅₉	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#436	—	2	4	no	—
28	C₅₉×#435	—	2	4	no	—
29	C₅₉×#432	C₂²	1	2	yes	—
30	C₅₉×#431	C₂²	1	2	yes	—
31	C₅₉×#407	C₂²	1	2	yes	—
32	C₅₉×#407	C₂²	1	2	yes	—
33	C₅₉×#407	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
35	C₅₉×#324	C₂²	1	4	yes	—
36	C₅₉×#324	C₂²	1	4	yes	—
37	C₅₉×#324	C₂²	1	4	yes	—
38	C₅₉×#323	C₂²	1	4	yes	—
39	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₅₉	—	2	2	no	—
49	C₂×M₁₆×C₅₉	—	2	2	no	—
50	C₂×M₁₆×C₅₉	—	2	2	no	—
51	C₂²×C₈×C₅₉	—	2	2	no	—
52	#126×C₅₉	—	2	4	no	—
53	#126×C₅₉	—	2	2	no	—
54	#126×C₅₉	—	2	2	no	—
55	#125×C₅₉	—	2	4	no	—
56	#125×C₅₉	—	2	2	no	—
57	#125×C₅₉	—	2	2	no	—
58	#123×C₅₉	—	2	4	no	—
59	#123×C₅₉	—	2	2	no	—
60	#123×C₅₉	—	2	2	no	—
61	#123×C₅₉	—	2	4	no	—
62	#123×C₅₉	—	2	4	no	—
63	C₂²⋊Q₈×C₅₉	—	2	2	no	—
64	C₂²⋊Q₈×C₅₉	—	2	2	no	—
65	C₂²⋊Q₈×C₅₉	—	2	4	no	—
66	C₂²⋊Q₈×C₅₉	—	2	4	no	—
67	#121×C₅₉	—	2	4	no	—
68	C₄×D₄×C₅₉	—	2	2	no	—
69	C₄×D₄×C₅₉	—	2	2	no	—
70	C₄×D₄×C₅₉	D₄	1	4	yes	—
71	C₄×D₄×C₅₉	D₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₅₉	—	2	2	no	—
101	C₄⋊C₈×C₅₉	—	2	2	no	—
102	C₂²⋊C₈×C₅₉	—	2	2	no	—
103	C₂²⋊C₈×C₅₉	—	2	2	no	—
104	C₂²⋊C₈×C₅₉	—	2	2	no	—
105	C₂²⋊C₈×C₅₉	—	2	2	no	—
106	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
107	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
108	#97×C₅₉	—	2	2	no	—
109	C₄×C₈×C₅₉	—	2	2	no	—
110	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
111	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×Q₈×C₅₉	—	2	2	no	—
114	C₂×Q₈×C₅₉	—	8	1	no	—
115	C₂×D₄×C₅₉	—	2	2	no	—
116	C₂×D₄×C₅₉	—	2	2	no	—
117	C₂×D₄×C₅₉	—	4	2	no	—
118	C₂×D₄×C₅₉	—	4	2	no	—
119	C₂×D₄×C₅₉	—	8	1	no	—
120	C₂×D₄×C₅₉	C₂²⋊C₄	1	4	yes	—
121	C₂²×C₄×C₅₉	—	2	2	no	—
122	C₂²×C₄×C₅₉	—	2	2	no	—
123	C₂²×C₄×C₅₉	—	2	2	no	—
124	C₂²×C₄×C₅₉	—	4	2	no	—
125	C₂²×C₄×C₅₉	—	8	1	no	—
126	C₂²×C₄×C₅₉	—	8	1	no	—
127	C₂²×C₄×C₅₉	—	8	1	no	—
128	C₂²×C₄×C₅₉	—	8	1	no	—
129	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₅₉	—	8	2	no	—
146	M₁₆×C₅₉	—	8	2	no	—
147	M₁₆×C₅₉	—	8	2	no	—
148	C₂×C₈×C₅₉	—	2	4	no	—
149	C₂×C₈×C₅₉	—	2	4	no	—
150	C₂×C₈×C₅₉	—	8	2	no	—
151	C₄⋊C₄×C₅₉	—	2	2	no	—
152	C₄⋊C₄×C₅₉	—	2	2	no	—
153	C₄⋊C₄×C₅₉	—	2	2	no	—
154	C₄⋊C₄×C₅₉	—	2	2	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	2	2	no	—
157	C₄⋊C₄×C₅₉	—	2	2	no	—
158	C₄⋊C₄×C₅₉	—	2	2	no	—
159	C₄⋊C₄×C₅₉	—	2	2	no	—
160	C₄⋊C₄×C₅₉	—	2	2	no	—
161	C₄⋊C₄×C₅₉	—	2	1	no	—
162	C₄⋊C₄×C₅₉	—	2	1	no	—
163	C₄⋊C₄×C₅₉	—	2	1	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
168	C₂²⋊C₄×C₅₉	—	2	2	no	—
169	C₂²⋊C₄×C₅₉	—	2	2	no	—
170	C₂²⋊C₄×C₅₉	—	2	2	no	—
171	C₂²⋊C₄×C₅₉	—	2	2	no	—
172	C₂²⋊C₄×C₅₉	—	2	2	no	—
173	C₂²⋊C₄×C₅₉	—	2	2	no	—
174	C₂²⋊C₄×C₅₉	—	2	2	no	—
175	C₂²⋊C₄×C₅₉	—	2	1	no	—
176	C₂²⋊C₄×C₅₉	—	2	1	no	—
177	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
178	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
179	C₄²×C₅₉	—	2	2	no	—
180	C₄²×C₅₉	C₂×D₄	1	2	yes	—
181	C₄²×C₅₉	C₂×D₄	1	2	yes	—
182	C₂³×C₅₉	—	2	2	no	—
183	C₂³×C₅₉	—	2	2	no	—
184	C₂³×C₅₉	—	2	1	no	—
185	C₂³×C₅₉	—	2	2	no	—
186	C₂³×C₅₉	—	4	1	no	—
187	C₂³×C₅₉	—	4	1	no	—
188	C₂³×C₅₉	—	4	1	no	—
189	C₂³×C₅₉	—	4	1	no	—
190	C₂³×C₅₉	—	4	1	no	—
191	C₂³×C₅₉	—	4	1	no	—
192	C₂³×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂³×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
195	Q₈×C₅₉	—	8	2	no	—
196	D₄×C₅₉	—	4	4	no	—
197	D₄×C₅₉	—	4	4	no	—
198	D₄×C₅₉	—	8	2	no	—
199	C₂×C₄×C₅₉	—	2	2	no	—
200	C₂×C₄×C₅₉	—	2	1	no	—
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	2	1	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	2	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	4	2	no	—
211	C₂×C₄×C₅₉	—	4	2	no	—
212	C₂×C₄×C₅₉	—	4	2	no	—
213	C₂×C₄×C₅₉	—	4	2	no	—
214	C₂×C₄×C₅₉	—	4	1	no	—
215	C₂×C₄×C₅₉	—	4	1	no	—
216	C₂×C₄×C₅₉	—	4	1	no	—
217	C₂×C₄×C₅₉	—	4	1	no	—
218	C₂×C₄×C₅₉	—	4	4	no	—
219	C₂×C₄×C₅₉	—	4	1	no	—
220	C₂×C₄×C₅₉	—	4	1	no	—
221	C₂×C₄×C₅₉	—	4	1	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	8	2	no	—
224	C₂×C₄×C₅₉	—	8	2	no	—
225	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₅₉	—	4	4	no	—
232	C₈×C₅₉	—	4	4	no	—
233	#17406	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₅₉	—	2	1	no	—
235	C₂²×C₅₉	—	2	1	no	—
236	C₂²×C₅₉	—	2	2	no	—
237	C₂²×C₅₉	—	2	2	no	—
238	C₂²×C₅₉	—	2	2	no	—
239	C₂²×C₅₉	—	2	2	no	—
240	C₂²×C₅₉	—	2	2	no	—
241	C₂²×C₅₉	—	2	2	no	—
242	C₂²×C₅₉	—	4	4	no	—
243	C₂²×C₅₉	—	4	1	no	—
244	C₂²×C₅₉	—	4	1	no	—
245	C₂²×C₅₉	—	4	1	no	—
246	C₂²×C₅₉	—	8	2	no	—
247	C₂²×C₅₉	—	8	2	no	—
248	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₅₉	#568	1	2	yes	—
250	C₄×C₅₉	—	2	2	no	—
251	C₄×C₅₉	—	2	1	no	—
252	C₄×C₅₉	—	2	1	no	—
253	C₄×C₅₉	—	2	2	no	—
254	C₄×C₅₉	—	2	2	no	—
255	C₄×C₅₉	—	2	2	no	—
256	C₄×C₅₉	—	4	1	no	—
257	C₄×C₅₉	—	4	1	no	—
258	C₄×C₅₉	—	4	1	no	—
259	C₄×C₅₉	—	4	1	no	—
260	C₄×C₅₉	—	4	1	no	—
261	C₄×C₅₉	—	4	1	no	—
262	C₄×C₅₉	—	4	1	no	—
263	C₂×#539	C₂×C₅₉	1	1	yes	characteristic
264	#2975	C₂×C₅₉	1	1	yes	characteristic, complemented
265	#2973	C₂×C₅₉	1	1	yes	characteristic, complemented
266	#1473	C₂×C₅₉	1	2	yes	complemented
267	#1472	C₂×C₅₉	1	2	yes	complemented
268	#1470	C₂×C₅₉	1	2	yes	complemented
269	#1468	C₂×C₅₉	1	2	yes	complemented
270	#1465	C₂×C₅₉	1	2	yes	complemented
271	#1463	C₂×C₅₉	1	2	yes	complemented
272	C₂×C₅₉	—	2	2	no	—
273	C₂×C₅₉	—	4	2	no	—
274	C₂×C₅₉	—	4	2	no	—
275	C₂×C₅₉	—	8	1	no	—
276	C₂×C₅₉	#2879	1	1	yes	characteristic
277	C₂×C₅₉	#2883	1	1	yes	characteristic
278	C₂×C₅₉	#2889	1	1	yes	characteristic
279	#539	—	2	4	no	—
280	#539	—	2	4	no	—
281	C₂×#126	C₄×C₅₉	1	1	yes	characteristic
282	C₂×#126	C₂²×C₅₉	1	1	yes	characteristic
283	C₂×#125	C₄×C₅₉	1	1	yes	characteristic
284	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
285	C₂×#123	C₄×C₅₉	1	1	yes	characteristic
286	C₂×#123	C₄×C₅₉	1	1	yes	characteristic
287	C₂×#123	C₄×C₅₉	1	1	yes	characteristic
288	C₂×#123	C₂²×C₅₉	1	1	yes	characteristic
289	C₂×C₂²⋊Q₈	C₄×C₅₉	1	1	yes	characteristic
290	C₂×C₂²⋊Q₈	C₄×C₅₉	1	1	yes	characteristic
291	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
292	C₂×#121	C₄×C₅₉	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
295	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
296	#436	—	2	4	no	—
297	#435	—	2	4	no	—
298	#432	C₂²×C₅₉	1	2	yes	—
299	#431	C₂²×C₅₉	1	2	yes	—
300	#407	C₂²×C₅₉	1	2	yes	—
301	#407	C₂²×C₅₉	1	2	yes	—
302	#407	C₂²×C₅₉	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
304	#324	C₂²×C₅₉	1	4	yes	—
305	#324	C₂²×C₅₉	1	4	yes	—
306	#324	C₂²×C₅₉	1	4	yes	—
307	#323	C₂²×C₅₉	1	4	yes	—
308	C₅₉	#17406	1	1	yes	characteristic, direct product factor, Sylow
309	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
310	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
311	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
312	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
313	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
314	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
315	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	—	2	2	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂²×C₈	—	2	2	no	—
322	#126	—	2	4	no	—
323	#126	—	2	2	no	—
324	#126	—	2	2	no	—
325	#125	—	2	4	no	—
326	#125	—	2	2	no	—
327	#125	—	2	2	no	—
328	#123	—	2	4	no	—
329	#123	—	2	2	no	—
330	#123	—	2	2	no	—
331	#123	—	2	4	no	—
332	#123	—	2	4	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	#121	—	2	4	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	D₄×C₅₉	1	4	yes	—
341	C₄×D₄	D₄×C₅₉	1	4	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
368	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	—	2	2	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	C₂²⋊C₈	—	2	2	no	—
375	C₂²⋊C₈	—	2	2	no	—
376	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
377	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
378	#97	—	2	2	no	—
379	C₄×C₈	—	2	2	no	—
380	C₂⁴	C₂²×C₄×C₅₉	1	1	yes	characteristic
381	C₂⁴	C₂²×C₄×C₅₉	1	1	yes	characteristic
382	C₂⁴	C₂²×C₄×C₅₉	1	1	yes	characteristic
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	8	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	8	1	no	—
390	C₂×D₄	C₂²⋊C₄×C₅₉	1	4	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	8	1	no	—
396	C₂²×C₄	—	8	1	no	—
397	C₂²×C₄	—	8	1	no	—
398	C₂²×C₄	—	8	1	no	—
399	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
408	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
415	M₁₆	—	8	2	no	—
416	M₁₆	—	8	2	no	—
417	M₁₆	—	8	2	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	8	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	4	yes	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	4	yes	—
448	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	4	yes	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂×D₄×C₅₉	1	2	yes	—
451	C₄²	C₂×D₄×C₅₉	1	2	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
463	C₂³	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
464	C₂³	C₂³×C₄×C₅₉	1	1	yes	characteristic
465	Q₈	—	8	2	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	4	no	—
468	D₄	—	8	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
496	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
497	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
498	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
501	C₈	—	4	4	no	—
502	C₈	—	4	4	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
518	C₂²	C₅₉×#568	1	2	yes	—
519	C₄	—	2	2	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₂	—	2	2	no	—
533	C₂	—	4	2	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	1	no	—
536	C₂	C₅₉×#2879	1	1	yes	characteristic
537	C₂	C₅₉×#2883	1	1	yes	characteristic
538	C₂	C₅₉×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×#121×C₅₉	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2975	C₂	semidirect
3. C₅₉×#2973	C₂	semidirect
4. C₅₉×#1473	C₂	semidirect
5. C₅₉×#1472	C₂	semidirect
6. C₅₉×#1470	C₂	semidirect
7. C₅₉×#1468	C₂	semidirect
8. C₅₉×#1465	C₂	semidirect
9. C₅₉×#1463	C₂	semidirect
233. #17406	C₅₉	direct (N × H)
264. #2975	C₂×C₅₉	semidirect
265. #2973	C₂×C₅₉	semidirect
266. #1473	C₂×C₅₉	semidirect
267. #1472	C₂×C₅₉	semidirect
268. #1470	C₂×C₅₉	semidirect
269. #1468	C₂×C₅₉	semidirect
270. #1465	C₂×C₅₉	semidirect
271. #1463	C₂×C₅₉	semidirect
308. C₅₉	#17406	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×#539	2
C₅₉×#2975	2
C₅₉×#2973	2
C₅₉×#1473	2
C₅₉×#1472	2
C₅₉×#1470	2
C₅₉×#1468	2
C₅₉×#1465	2
C₅₉×#1463	2
#17406	59

Subgroups — C59×#17406 #28429515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17406 #28429515