Subgroups — C₅₉×#21984 #28434093

Order 15104.

850 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#431	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1949	C₂	1	4	yes	maximal, complemented
5	C₅₉×#1854	C₂	1	4	yes	maximal
6	C₅₉×#1845	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1844	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#117×C₅₉	—	2	1	no	—
11	C₂×#117×C₅₉	C₂²	1	2	yes	—
12	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
13	C₅₉×#431	C₄	1	8	yes	complemented
14	C₂×#107×C₅₉	C₂²	1	4	yes	—
15	C₂×#106×C₅₉	C₂²	1	4	yes	—
16	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#384	C₂²	1	1	yes	characteristic
21	C₅₉×#384	C₂²	1	1	yes	characteristic
22	C₅₉×#384	C₂²	1	1	yes	characteristic
23	C₅₉×#384	C₂²	1	1	yes	characteristic
24	C₅₉×#382	—	2	1	no	—
25	C₅₉×#382	C₂²	1	2	yes	—
26	C₅₉×#380	—	2	1	no	—
27	C₅₉×#380	—	2	1	no	—
28	C₅₉×#380	—	2	1	no	—
29	C₅₉×#380	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
31	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
34	C₅₉×#340	C₂²	1	4	yes	—
35	C₅₉×#340	C₂²	1	4	yes	—
36	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
41	#117×C₅₉	—	4	4	no	—
42	#117×C₅₉	—	4	4	no	—
43	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
57	C₂×C₄²×C₅₉	—	2	2	no	—
58	C₂×C₄²×C₅₉	—	2	2	no	—
59	C₂×C₄²×C₅₉	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₅₉	Q₈	1	4	yes	—
63	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
65	#107×C₅₉	—	4	4	no	—
66	#106×C₅₉	—	4	4	no	—
67	C₄⋊C₈×C₅₉	C₂×C₄	1	8	yes	—
68	C₂²⋊C₈×C₅₉	C₂×C₄	1	8	yes	—
69	C₄×C₈×C₅₉	C₂×C₄	1	4	yes	—
70	C₄×C₈×C₅₉	C₂×C₄	1	4	yes	—
71	#95×C₅₉	—	2	2	no	—
72	#95×C₅₉	—	2	2	no	—
73	#95×C₅₉	—	2	2	no	—
74	#95×C₅₉	—	2	2	no	—
75	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₉	—	2	2	no	—
77	C₂²×C₄×C₅₉	—	2	2	no	—
78	C₂²×C₄×C₅₉	—	2	2	no	—
79	C₂²×C₄×C₅₉	—	2	2	no	—
80	C₂²×C₄×C₅₉	—	2	2	no	—
81	C₂²×C₄×C₅₉	—	2	2	no	—
82	C₂²×C₄×C₅₉	—	2	2	no	—
83	C₂²×C₄×C₅₉	—	2	2	no	—
84	C₂²×C₄×C₅₉	—	2	2	no	—
85	C₂²×C₄×C₅₉	—	2	2	no	—
86	C₂²×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
87	C₂²×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
88	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₅₉	—	2	2	no	—
97	C₂×C₈×C₅₉	—	2	2	no	—
98	C₂×C₈×C₅₉	—	2	2	no	—
99	C₂×C₈×C₅₉	—	2	2	no	—
100	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
102	C₄⋊C₄×C₅₉	—	2	4	no	—
103	C₄⋊C₄×C₅₉	—	2	4	no	—
104	C₄⋊C₄×C₅₉	—	2	4	no	—
105	C₄⋊C₄×C₅₉	—	2	4	no	—
106	C₄⋊C₄×C₅₉	—	4	2	no	—
107	C₄⋊C₄×C₅₉	—	4	2	no	—
108	C₄⋊C₄×C₅₉	—	4	2	no	—
109	C₄⋊C₄×C₅₉	—	4	2	no	—
110	C₄⋊C₄×C₅₉	—	4	2	no	—
111	C₄⋊C₄×C₅₉	—	4	2	no	—
112	C₄⋊C₄×C₅₉	—	4	2	no	—
113	C₄⋊C₄×C₅₉	—	4	2	no	—
114	C₂²⋊C₄×C₅₉	—	4	4	no	—
115	C₂²⋊C₄×C₅₉	—	4	4	no	—
116	C₄²×C₅₉	—	4	4	no	—
117	C₄²×C₅₉	—	4	4	no	—
118	C₄²×C₅₉	C₄⋊C₄	1	4	yes	—
119	C₄²×C₅₉	C₄⋊C₄	1	4	yes	—
120	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
121	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
122	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
123	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
124	C₂³×C₅₉	—	2	1	no	—
125	C₂³×C₅₉	—	2	1	no	—
126	C₂³×C₅₉	—	2	1	no	—
127	C₂³×C₅₉	—	2	1	no	—
128	C₂³×C₅₉	—	2	1	no	—
129	C₂³×C₅₉	—	2	1	no	—
130	C₂³×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
131	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₅₉	—	2	1	no	—
133	C₂×C₄×C₅₉	—	2	1	no	—
134	C₂×C₄×C₅₉	—	2	1	no	—
135	C₂×C₄×C₅₉	—	2	1	no	—
136	C₂×C₄×C₅₉	—	2	1	no	—
137	C₂×C₄×C₅₉	—	2	1	no	—
138	C₂×C₄×C₅₉	—	2	4	no	—
139	C₂×C₄×C₅₉	—	2	4	no	—
140	C₂×C₄×C₅₉	—	2	8	no	—
141	C₂×C₄×C₅₉	—	2	8	no	—
142	C₂×C₄×C₅₉	—	4	2	no	—
143	C₂×C₄×C₅₉	—	4	2	no	—
144	C₂×C₄×C₅₉	—	4	2	no	—
145	C₂×C₄×C₅₉	—	4	2	no	—
146	C₂×C₄×C₅₉	—	4	2	no	—
147	C₂×C₄×C₅₉	—	4	2	no	—
148	C₂×C₄×C₅₉	—	4	2	no	—
149	C₂×C₄×C₅₉	—	4	2	no	—
150	C₂×C₄×C₅₉	—	4	2	no	—
151	C₂×C₄×C₅₉	—	4	2	no	—
152	C₂×C₄×C₅₉	—	4	2	no	—
153	C₂×C₄×C₅₉	—	4	2	no	—
154	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₅₉	#135	1	2	yes	—
160	C₂×C₄×C₅₉	#135	1	2	yes	—
161	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
162	C₂×C₄×C₅₉	#137	1	2	yes	—
163	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
166	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
167	C₈×C₅₉	—	2	4	no	—
168	C₈×C₅₉	—	2	4	no	—
169	#21984	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₅₉	—	2	2	no	—
171	C₂²×C₅₉	—	2	2	no	—
172	C₂²×C₅₉	—	2	2	no	—
173	C₂²×C₅₉	—	4	1	no	—
174	C₂²×C₅₉	—	4	1	no	—
175	C₂²×C₅₉	—	4	1	no	—
176	C₂²×C₅₉	—	4	1	no	—
177	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₅₉	#535	1	1	yes	characteristic
179	C₂²×C₅₉	#536	1	1	yes	characteristic
180	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
181	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
182	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
184	C₄×C₅₉	—	2	2	no	—
185	C₄×C₅₉	—	2	2	no	—
186	C₄×C₅₉	—	2	2	no	—
187	C₄×C₅₉	—	8	2	no	—
188	C₄×C₅₉	—	8	2	no	—
189	C₄×C₅₉	—	8	2	no	—
190	C₄×C₅₉	—	8	2	no	—
191	C₄×C₅₉	#427	1	4	yes	—
192	C₄×C₅₉	#428	1	4	yes	—
193	C₄×C₅₉	#520	1	2	yes	—
194	C₄×C₅₉	#544	1	2	yes	—
195	C₂×#431	C₂×C₅₉	1	1	yes	characteristic
196	#2285	C₂×C₅₉	1	1	yes	characteristic
197	#2285	C₂×C₅₉	1	1	yes	characteristic
198	#1949	C₂×C₅₉	1	4	yes	complemented
199	#1854	C₂×C₅₉	1	4	yes	—
200	#1845	C₂×C₅₉	1	1	yes	characteristic, complemented
201	#1844	C₂×C₅₉	1	1	yes	characteristic, complemented
202	#1834	C₂×C₅₉	1	1	yes	characteristic, complemented
203	#1834	C₂×C₅₉	1	1	yes	characteristic, complemented
204	C₂×C₅₉	—	4	2	no	—
205	C₂×C₅₉	#2317	1	1	yes	characteristic
206	C₂×C₅₉	C₂×#427	1	1	yes	characteristic
207	C₂×C₅₉	C₂×#428	1	1	yes	characteristic
208	C₂×C₅₉	#3207	1	1	yes	characteristic
209	C₂×C₅₉	#3210	1	1	yes	characteristic
210	C₂×C₅₉	#3228	1	1	yes	characteristic
211	C₂×C₅₉	#3231	1	1	yes	characteristic
212	C₂×#117	—	2	1	no	—
213	C₂×#117	C₂²×C₅₉	1	2	yes	—
214	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
215	#431	C₄×C₅₉	1	8	yes	complemented
216	C₂×#107	C₂²×C₅₉	1	4	yes	—
217	C₂×#106	C₂²×C₅₉	1	4	yes	—
218	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
222	#384	C₂²×C₅₉	1	1	yes	characteristic
223	#384	C₂²×C₅₉	1	1	yes	characteristic
224	#384	C₂²×C₅₉	1	1	yes	characteristic
225	#384	C₂²×C₅₉	1	1	yes	characteristic
226	#382	—	2	1	no	—
227	#382	C₂²×C₅₉	1	2	yes	—
228	#380	—	2	1	no	—
229	#380	—	2	1	no	—
230	#380	—	2	1	no	—
231	#380	C₂²×C₅₉	1	2	yes	—
232	C₄×C₄⋊C₄	—	2	1	no	—
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	—	2	1	no	—
235	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
236	#340	C₂²×C₅₉	1	4	yes	—
237	#340	C₂²×C₅₉	1	4	yes	—
238	C₅₉	#21984	1	1	yes	characteristic, direct product factor, Sylow
239	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
240	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
243	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
244	#117	—	4	4	no	—
245	#117	—	4	4	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	C₂×C₄×C₅₉	1	4	yes	—
263	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
265	C₂×C₄²	Q₈×C₅₉	1	4	yes	—
266	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
268	#107	—	4	4	no	—
269	#106	—	4	4	no	—
270	C₄⋊C₈	C₂×C₄×C₅₉	1	8	yes	—
271	C₂²⋊C₈	C₂×C₄×C₅₉	1	8	yes	—
272	C₄×C₈	C₂×C₄×C₅₉	1	4	yes	—
273	C₄×C₈	C₂×C₄×C₅₉	1	4	yes	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	C₄⋊C₄×C₅₉	1	4	yes	—
290	C₂²×C₄	C₄⋊C₄×C₅₉	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×Q₈×C₅₉	1	2	yes	—
298	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	C₂²×C₄×C₅₉	1	4	yes	—
304	C₂×C₈	C₂²×C₄×C₅₉	1	4	yes	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₄²	—	4	4	no	—
320	C₄²	—	4	4	no	—
321	C₄²	C₄⋊C₄×C₅₉	1	4	yes	—
322	C₄²	C₄⋊C₄×C₅₉	1	4	yes	—
323	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
324	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
325	C₄²	C₂×Q₈×C₅₉	1	2	yes	—
326	C₄²	C₂×Q₈×C₅₉	1	2	yes	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	C₂×C₄⋊C₄×C₅₉	1	2	yes	—
334	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	2	yes	—
358	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	2	yes	—
359	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	2	yes	—
360	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	2	yes	—
361	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	2	yes	—
362	C₂×C₄	#135×C₅₉	1	2	yes	—
363	C₂×C₄	#135×C₅₉	1	2	yes	—
364	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
365	C₂×C₄	#137×C₅₉	1	2	yes	—
366	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
367	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
368	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
369	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₂²×C₄⋊C₄×C₅₉	1	1	yes	characteristic
380	C₂²	C₅₉×#535	1	1	yes	characteristic
381	C₂²	C₅₉×#536	1	1	yes	characteristic
382	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
383	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
384	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
385	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	2	no	—
393	C₄	C₅₉×#427	1	4	yes	—
394	C₄	C₅₉×#428	1	4	yes	—
395	C₄	C₅₉×#520	1	2	yes	—
396	C₄	C₅₉×#544	1	2	yes	—
397	C₂	—	4	2	no	—
398	C₂	C₅₉×#2317	1	1	yes	characteristic
399	C₂	C₂×C₅₉×#427	1	1	yes	characteristic
400	C₂	C₂×C₅₉×#428	1	1	yes	characteristic
401	C₂	C₅₉×#3207	1	1	yes	characteristic
402	C₂	C₅₉×#3210	1	1	yes	characteristic
403	C₂	C₅₉×#3228	1	1	yes	characteristic
404	C₂	C₅₉×#3231	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂⁴×C₅₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₉×#1949	C₂	semidirect
6. C₅₉×#1845	C₂	semidirect
7. C₅₉×#1844	C₂	semidirect
8. C₅₉×#1834	C₂	semidirect
9. C₅₉×#1834	C₂	semidirect
13. C₅₉×#431	C₄	semidirect
169. #21984	C₅₉	direct (N × H)
198. #1949	C₂×C₅₉	semidirect
200. #1845	C₂×C₅₉	semidirect
201. #1844	C₂×C₅₉	semidirect
202. #1834	C₂×C₅₉	semidirect
203. #1834	C₂×C₅₉	semidirect
215. #431	C₄×C₅₉	semidirect
238. C₅₉	#21984	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×#431	2
C₅₉×#2285	2
C₅₉×#1949	2
C₅₉×#1854	2
C₅₉×#1845	2
C₅₉×#1844	2
C₅₉×#1834	2
#21984	59

Subgroups — C59×#21984 #28434093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21984 #28434093