Subgroups — C₅₉×#35246 #28447355

Order 15104.

2294 conjugacy classes of subgroups.

The subgroup lattice has 586 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	C₂²×C₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2853	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2637	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2599	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2579	C₂	1	4	yes	maximal, complemented
7	C₅₉×#2565	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2545	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2504	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2436	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2434	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#2327	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2326	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
18	C₅₉×#529	—	2	8	no	—
19	C₂×#126×C₅₉	C₂²	1	2	yes	—
20	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₅₉	C₂²	1	2	yes	—
23	C₂×#123×C₅₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₅₉	—	2	8	no	—
27	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₅₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₅₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#398	C₂²	1	4	yes	—
40	C₅₉×#398	C₂²	1	8	yes	—
41	C₅₉×#397	C₂²	1	4	yes	—
42	C₅₉×#396	C₂²	1	8	yes	—
43	C₅₉×#395	C₂²	1	4	yes	—
44	C₅₉×#393	C₂²	1	4	yes	—
45	C₅₉×#391	C₂²	1	2	yes	—
46	C₅₉×#391	C₂²	1	2	yes	—
47	C₅₉×#391	C₂²	1	2	yes	—
48	C₅₉×#390	C₂²	1	2	yes	—
49	C₅₉×#388	C₂²	1	8	yes	—
50	C₅₉×#388	C₂²	1	8	yes	—
51	C₅₉×#387	C₂²	1	8	yes	—
52	C₅₉×#387	C₂²	1	8	yes	—
53	C₅₉×#387	C₂²	1	8	yes	—
54	C₅₉×#386	C₂²	1	4	yes	—
55	C₅₉×#386	C₂²	1	4	yes	—
56	C₅₉×#385	C₂²	1	4	yes	—
57	C₅₉×#385	C₂²	1	8	yes	—
58	C₅₉×#385	C₂²	1	4	yes	—
59	C₅₉×#384	C₂²	1	2	yes	—
60	C₅₉×#383	C₂²	1	2	yes	—
61	C₅₉×#382	C₂²	1	2	yes	—
62	C₅₉×#382	C₂²	1	2	yes	—
63	C₅₉×#381	C₂²	1	2	yes	—
64	C₅₉×#380	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
68	C₅₉×#376	C₂²	1	2	yes	—
69	C₂²×Q₈×C₅₉	—	2	8	no	—
70	C₂²×Q₈×C₅₉	—	2	4	no	—
71	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
73	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₅₉	—	2	8	no	—
83	#126×C₅₉	—	2	8	no	—
84	#125×C₅₉	—	2	4	no	—
85	#124×C₅₉	—	2	8	no	—
86	#124×C₅₉	—	2	4	no	—
87	#123×C₅₉	—	2	8	no	—
88	C₂²⋊Q₈×C₅₉	—	2	4	no	—
89	#121×C₅₉	—	2	4	no	—
90	C₄×Q₈×C₅₉	—	2	8	no	—
91	C₄×Q₈×C₅₉	—	2	8	no	—
92	C₄×Q₈×C₅₉	—	2	8	no	—
93	C₄×Q₈×C₅₉	—	2	8	no	—
94	C₄×Q₈×C₅₉	—	2	4	no	—
95	C₄×D₄×C₅₉	—	2	8	no	—
96	C₄×D₄×C₅₉	—	2	4	no	—
97	#117×C₅₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
99	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
117	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
122	C₂×C₄²×C₅₉	—	2	8	no	—
123	C₂×C₄²×C₅₉	D₄	1	8	yes	—
124	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
128	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
129	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
133	#95×C₅₉	C₂³	1	4	yes	—
134	#95×C₅₉	C₂³	1	4	yes	—
135	#95×C₅₉	C₂³	1	2	yes	—
136	#95×C₅₉	C₂³	1	2	yes	—
137	#95×C₅₉	C₂³	1	4	yes	—
138	#95×C₅₉	C₂³	1	8	yes	—
139	#95×C₅₉	C₂³	1	8	yes	—
140	#95×C₅₉	C₂³	1	8	yes	—
141	#95×C₅₉	C₂³	1	8	yes	—
142	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
143	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
144	C₂×Q₈×C₅₉	—	2	32	no	—
145	C₂×Q₈×C₅₉	—	2	4	no	—
146	C₂×Q₈×C₅₉	—	2	4	no	—
147	C₂×Q₈×C₅₉	—	2	2	no	—
148	C₂×Q₈×C₅₉	—	2	8	no	—
149	C₂×Q₈×C₅₉	—	2	4	no	—
150	C₂×Q₈×C₅₉	—	2	4	no	—
151	C₂×Q₈×C₅₉	#41	1	8	yes	—
152	C₂×D₄×C₅₉	—	2	4	no	—
153	C₂×D₄×C₅₉	—	2	8	no	—
154	C₂×D₄×C₅₉	—	2	2	no	—
155	C₂×D₄×C₅₉	—	2	4	no	—
156	C₂²×C₄×C₅₉	—	2	4	no	—
157	C₂²×C₄×C₅₉	—	2	4	no	—
158	C₂²×C₄×C₅₉	—	2	8	no	—
159	C₂²×C₄×C₅₉	—	2	4	no	—
160	C₂²×C₄×C₅₉	—	2	4	no	—
161	C₂²×C₄×C₅₉	—	2	4	no	—
162	C₂²×C₄×C₅₉	—	4	2	no	—
163	C₂²×C₄×C₅₉	—	4	4	no	—
164	C₂²×C₄×C₅₉	—	4	4	no	—
165	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
181	C₄⋊C₄×C₅₉	—	2	8	no	—
182	C₄⋊C₄×C₅₉	—	2	8	no	—
183	C₄⋊C₄×C₅₉	—	2	4	no	—
184	C₄⋊C₄×C₅₉	—	2	4	no	—
185	C₄⋊C₄×C₅₉	—	2	4	no	—
186	C₄⋊C₄×C₅₉	—	2	4	no	—
187	C₄⋊C₄×C₅₉	—	2	2	no	—
188	C₄⋊C₄×C₅₉	—	2	4	no	—
189	C₄⋊C₄×C₅₉	—	2	2	no	—
190	C₄⋊C₄×C₅₉	—	2	4	no	—
191	C₄⋊C₄×C₅₉	—	2	16	no	—
192	C₄⋊C₄×C₅₉	—	4	4	no	—
193	C₄⋊C₄×C₅₉	—	4	8	no	—
194	C₂²⋊C₄×C₅₉	—	2	4	no	—
195	C₂²⋊C₄×C₅₉	—	2	4	no	—
196	C₂²⋊C₄×C₅₉	—	2	4	no	—
197	C₂²⋊C₄×C₅₉	—	2	4	no	—
198	C₂²⋊C₄×C₅₉	—	2	4	no	—
199	C₂²⋊C₄×C₅₉	—	2	4	no	—
200	C₂²⋊C₄×C₅₉	—	2	4	no	—
201	C₂²⋊C₄×C₅₉	—	2	16	no	—
202	C₂²⋊C₄×C₅₉	—	4	8	no	—
203	C₄²×C₅₉	—	2	8	no	—
204	C₄²×C₅₉	—	2	8	no	—
205	C₄²×C₅₉	—	2	4	no	—
206	C₄²×C₅₉	—	2	4	no	—
207	C₄²×C₅₉	—	2	4	no	—
208	C₄²×C₅₉	C₂×D₄	1	4	yes	—
209	C₄²×C₅₉	C₂×D₄	1	4	yes	—
210	C₄²×C₅₉	C₂×D₄	1	4	yes	—
211	C₄²×C₅₉	C₂×D₄	1	4	yes	—
212	C₂³×C₅₉	—	2	2	no	—
213	C₂³×C₅₉	—	2	2	no	—
214	C₂³×C₅₉	—	2	2	no	—
215	C₂³×C₅₉	—	2	4	no	—
216	C₂³×C₅₉	—	2	4	no	—
217	C₂³×C₅₉	—	2	4	no	—
218	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
219	C₂³×C₅₉	2₋¹⁺⁴	1	4	yes	—
220	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
221	Q₈×C₅₉	—	2	16	no	—
222	Q₈×C₅₉	—	2	16	no	—
223	Q₈×C₅₉	—	4	4	no	—
224	D₄×C₅₉	—	4	8	no	—
225	D₄×C₅₉	—	4	4	no	—
226	C₂×C₄×C₅₉	—	2	16	no	—
227	C₂×C₄×C₅₉	—	2	8	no	—
228	C₂×C₄×C₅₉	—	2	4	no	—
229	C₂×C₄×C₅₉	—	2	2	no	—
230	C₂×C₄×C₅₉	—	2	4	no	—
231	C₂×C₄×C₅₉	—	2	2	no	—
232	C₂×C₄×C₅₉	—	2	2	no	—
233	C₂×C₄×C₅₉	—	2	2	no	—
234	C₂×C₄×C₅₉	—	2	2	no	—
235	C₂×C₄×C₅₉	—	2	8	no	—
236	C₂×C₄×C₅₉	—	2	4	no	—
237	C₂×C₄×C₅₉	—	2	2	no	—
238	C₂×C₄×C₅₉	—	2	2	no	—
239	C₂×C₄×C₅₉	—	2	2	no	—
240	C₂×C₄×C₅₉	—	2	4	no	—
241	C₂×C₄×C₅₉	—	2	4	no	—
242	C₂×C₄×C₅₉	—	2	4	no	—
243	C₂×C₄×C₅₉	—	2	4	no	—
244	C₂×C₄×C₅₉	—	2	4	no	—
245	C₂×C₄×C₅₉	—	2	4	no	—
246	C₂×C₄×C₅₉	—	2	4	no	—
247	C₂×C₄×C₅₉	—	2	8	no	—
248	C₂×C₄×C₅₉	—	2	4	no	—
249	C₂×C₄×C₅₉	—	2	4	no	—
250	C₂×C₄×C₅₉	—	4	4	no	—
251	C₂×C₄×C₅₉	—	4	8	no	—
252	C₂×C₄×C₅₉	—	4	8	no	—
253	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₅₉	C₂×#41	1	8	yes	—
260	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
261	#35246	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂²×C₅₉	—	2	2	no	—
263	C₂²×C₅₉	—	2	2	no	—
264	C₂²×C₅₉	—	2	8	no	—
265	C₂²×C₅₉	—	4	2	no	—
266	C₂²×C₅₉	—	4	2	no	—
267	C₂²×C₅₉	—	4	2	no	—
268	C₂²×C₅₉	—	4	8	no	—
269	C₂²×C₅₉	#536	1	4	yes	—
270	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
271	C₂²×C₅₉	C₂²×#41	1	2	yes	—
272	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
273	C₂²×C₅₉	#585	1	2	yes	—
274	C₄×C₅₉	—	2	2	no	—
275	C₄×C₅₉	—	2	8	no	—
276	C₄×C₅₉	—	2	2	no	—
277	C₄×C₅₉	—	2	2	no	—
278	C₄×C₅₉	—	2	2	no	—
279	C₄×C₅₉	—	2	2	no	—
280	C₄×C₅₉	—	4	2	no	—
281	C₄×C₅₉	—	4	2	no	—
282	C₄×C₅₉	—	4	4	no	—
283	C₄×C₅₉	—	4	2	no	—
284	C₄×C₅₉	—	4	4	no	—
285	C₄×C₅₉	—	4	4	no	—
286	C₄×C₅₉	#525	1	4	yes	—
287	C₂×#529	C₂×C₅₉	1	1	yes	characteristic
288	C₂²×C₄×Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
289	#2853	C₂×C₅₉	1	4	yes	complemented
290	#2637	C₂×C₅₉	1	4	yes	complemented
291	#2599	C₂×C₅₉	1	4	yes	complemented
292	#2579	C₂×C₅₉	1	4	yes	complemented
293	#2565	C₂×C₅₉	1	2	yes	complemented
294	#2545	C₂×C₅₉	1	2	yes	complemented
295	#2504	C₂×C₅₉	1	1	yes	characteristic
296	#2502	C₂×C₅₉	1	1	yes	characteristic, complemented
297	#2436	C₂×C₅₉	1	1	yes	characteristic
298	#2434	C₂×C₅₉	1	1	yes	characteristic, complemented
299	#2327	C₂×C₅₉	1	2	yes	complemented
300	#2326	C₂×C₅₉	1	2	yes	complemented
301	#2283	C₂×C₅₉	1	1	yes	characteristic, complemented
302	C₂×C₅₉	—	2	4	no	—
303	C₂×C₅₉	—	8	2	no	—
304	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
305	C₂×C₅₉	C₂×#536	1	1	yes	characteristic
306	C₂×C₅₉	#3449	1	1	yes	characteristic
307	C₂×C₅₉	#3516	1	4	yes	—
308	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
310	#529	—	2	8	no	—
311	C₂×#126	C₂²×C₅₉	1	2	yes	—
312	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
313	C₂×#124	C₂²×C₅₉	1	2	yes	—
314	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
315	C₂×#123	C₂²×C₅₉	1	2	yes	—
316	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
317	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
318	C₂×C₄×Q₈	—	2	8	no	—
319	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
320	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
321	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
323	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
324	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
326	C₂×#117	C₂²×C₅₉	1	2	yes	—
327	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
328	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
329	C₂²×C₄²	C₂²×C₅₉	1	2	yes	—
330	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
331	#398	C₂²×C₅₉	1	8	yes	—
332	#398	C₂²×C₅₉	1	4	yes	—
333	#397	C₂²×C₅₉	1	4	yes	—
334	#396	C₂²×C₅₉	1	8	yes	—
335	#395	C₂²×C₅₉	1	4	yes	—
336	#393	C₂²×C₅₉	1	4	yes	—
337	#391	C₂²×C₅₉	1	2	yes	—
338	#391	C₂²×C₅₉	1	2	yes	—
339	#391	C₂²×C₅₉	1	2	yes	—
340	#390	C₂²×C₅₉	1	2	yes	—
341	#388	C₂²×C₅₉	1	8	yes	—
342	#388	C₂²×C₅₉	1	8	yes	—
343	#387	C₂²×C₅₉	1	8	yes	—
344	#387	C₂²×C₅₉	1	8	yes	—
345	#387	C₂²×C₅₉	1	8	yes	—
346	#386	C₂²×C₅₉	1	4	yes	—
347	#386	C₂²×C₅₉	1	4	yes	—
348	#385	C₂²×C₅₉	1	8	yes	—
349	#385	C₂²×C₅₉	1	4	yes	—
350	#385	C₂²×C₅₉	1	4	yes	—
351	#384	C₂²×C₅₉	1	2	yes	—
352	#383	C₂²×C₅₉	1	2	yes	—
353	#382	C₂²×C₅₉	1	2	yes	—
354	#382	C₂²×C₅₉	1	2	yes	—
355	#381	C₂²×C₅₉	1	2	yes	—
356	#380	C₂²×C₅₉	1	2	yes	—
357	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
358	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
359	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
360	#376	C₂²×C₅₉	1	2	yes	—
361	C₅₉	#35246	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²×Q₈	—	2	8	no	—
363	C₂²×Q₈	—	2	4	no	—
364	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
365	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
367	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
368	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
370	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
373	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
374	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
375	C₄⋊Q₈	—	2	8	no	—
376	#126	—	2	8	no	—
377	#125	—	2	4	no	—
378	#124	—	2	8	no	—
379	#124	—	2	4	no	—
380	#123	—	2	8	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	#121	—	2	4	no	—
383	C₄×Q₈	—	2	8	no	—
384	C₄×Q₈	—	2	8	no	—
385	C₄×Q₈	—	2	8	no	—
386	C₄×Q₈	—	2	8	no	—
387	C₄×Q₈	—	2	4	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	4	no	—
390	#117	—	2	8	no	—
391	C₂×C₄⋊C₄	—	2	8	no	—
392	C₂×C₄⋊C₄	—	2	4	no	—
393	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
404	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
415	C₂×C₄²	—	2	8	no	—
416	C₂×C₄²	D₄×C₅₉	1	8	yes	—
417	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
418	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
419	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
420	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
421	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
422	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
426	#95	C₂³×C₅₉	1	4	yes	—
427	#95	C₂³×C₅₉	1	4	yes	—
428	#95	C₂³×C₅₉	1	2	yes	—
429	#95	C₂³×C₅₉	1	2	yes	—
430	#95	C₂³×C₅₉	1	4	yes	—
431	#95	C₂³×C₅₉	1	8	yes	—
432	#95	C₂³×C₅₉	1	8	yes	—
433	#95	C₂³×C₅₉	1	8	yes	—
434	#95	C₂³×C₅₉	1	8	yes	—
435	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
436	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
437	C₂×Q₈	—	2	32	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	8	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	#41×C₅₉	1	8	yes	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	16	no	—
485	C₄⋊C₄	—	4	4	no	—
486	C₄⋊C₄	—	4	8	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	16	no	—
495	C₂²⋊C₄	—	4	8	no	—
496	C₄²	—	2	8	no	—
497	C₄²	—	2	8	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	C₂×D₄×C₅₉	1	4	yes	—
502	C₄²	C₂×D₄×C₅₉	1	4	yes	—
503	C₄²	C₂×D₄×C₅₉	1	4	yes	—
504	C₄²	C₂×D₄×C₅₉	1	4	yes	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
512	C₂³	2₋¹⁺⁴×C₅₉	1	4	yes	—
513	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
514	Q₈	—	2	16	no	—
515	Q₈	—	2	16	no	—
516	Q₈	—	4	4	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	4	no	—
519	C₂×C₄	—	2	16	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
552	C₂×C₄	C₂×#41×C₅₉	1	8	yes	—
553	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
554	C₂²	—	2	8	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	8	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₅₉×#536	1	4	yes	—
562	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
563	C₂²	C₂²×#41×C₅₉	1	2	yes	—
564	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
565	C₂²	C₅₉×#585	1	2	yes	—
566	C₄	—	2	2	no	—
567	C₄	—	2	8	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	2	no	—
578	C₄	C₅₉×#525	1	4	yes	—
579	C₂	—	2	4	no	—
580	C₂	—	8	2	no	—
581	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
582	C₂	C₂×C₅₉×#536	1	1	yes	characteristic
583	C₂	C₅₉×#3449	1	1	yes	characteristic
584	C₂	C₅₉×#3516	1	4	yes	—

	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
2. C₂²×C₄×Q₈×C₅₉	C₂	semidirect
3. C₅₉×#2853	C₂	semidirect
4. C₅₉×#2637	C₂	semidirect
5. C₅₉×#2599	C₂	semidirect
6. C₅₉×#2579	C₂	semidirect
7. C₅₉×#2565	C₂	semidirect
8. C₅₉×#2545	C₂	semidirect
10. C₅₉×#2502	C₂	semidirect
12. C₅₉×#2434	C₂	semidirect
13. C₅₉×#2327	C₂	semidirect
14. C₅₉×#2326	C₂	semidirect
15. C₅₉×#2283	C₂	semidirect
261. #35246	C₅₉	direct (N × H)
288. C₂²×C₄×Q₈	C₂×C₅₉	semidirect
289. #2853	C₂×C₅₉	semidirect
290. #2637	C₂×C₅₉	semidirect
291. #2599	C₂×C₅₉	semidirect
292. #2579	C₂×C₅₉	semidirect
293. #2565	C₂×C₅₉	semidirect
294. #2545	C₂×C₅₉	semidirect
296. #2502	C₂×C₅₉	semidirect
298. #2434	C₂×C₅₉	semidirect
299. #2327	C₂×C₅₉	semidirect
300. #2326	C₂×C₅₉	semidirect
301. #2283	C₂×C₅₉	semidirect
361. C₅₉	#35246	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
C₂²×C₄×Q₈×C₅₉	2
C₅₉×#2853	2
C₅₉×#2637	2
C₅₉×#2599	2
C₅₉×#2579	2
C₅₉×#2565	2
C₅₉×#2545	2
C₅₉×#2504	2
C₅₉×#2502	2
C₅₉×#2436	2
C₅₉×#2434	2
C₅₉×#2327	2
C₅₉×#2326	2
C₅₉×#2283	2
#35246	59

Subgroups — C59×#35246 #28447355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35246 #28447355