Subgroups — C₅₉×#23697 #28435806

Order 15104.

1062 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#121×C₅₉	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2065	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2034	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1999	C₂	1	1	yes	maximal, characteristic
10	C₄×#106×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₅₉	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#121×C₅₉	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₅₉	—	2	2	no	—
15	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
17	C₄×D₈×C₅₉	—	2	4	no	—
18	C₅₉×#431	—	2	4	no	—
19	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#106×C₅₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₅₉	C₂²	1	2	yes	—
24	C₂×#102×C₅₉	C₂²	1	2	yes	—
25	C₂×#102×C₅₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#390	C₂²	1	2	yes	—
31	C₅₉×#389	C₂²	1	2	yes	—
32	C₅₉×#388	—	2	2	no	—
33	C₅₉×#386	—	2	2	no	—
34	C₅₉×#380	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₅₉	—	2	2	no	—
37	C₅₉×#340	C₂²	1	1	yes	characteristic
38	C₅₉×#340	C₂²	1	2	yes	—
39	C₅₉×#340	C₂²	1	2	yes	—
40	C₅₉×#340	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₅₉	—	2	2	no	—
42	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₅₉	—	2	2	no	—
44	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
47	C₂×D₈×C₅₉	—	2	4	no	—
48	C₂×D₈×C₅₉	—	2	2	no	—
49	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
53	#121×C₅₉	—	2	4	no	—
54	#121×C₅₉	—	2	4	no	—
55	C₄×D₄×C₅₉	—	2	4	no	—
56	C₄×D₄×C₅₉	—	2	4	no	—
57	C₄×D₄×C₅₉	—	4	8	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
67	C₂×C₄²×C₅₉	—	2	2	no	—
68	C₂×C₄²×C₅₉	—	2	2	no	—
69	C₂×C₄²×C₅₉	—	2	2	no	—
70	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
74	#107×C₅₉	—	2	2	no	—
75	#106×C₅₉	—	2	4	no	—
76	C₄⋊C₈×C₅₉	—	2	2	no	—
77	C₄⋊C₈×C₅₉	—	2	2	no	—
78	#102×C₅₉	—	2	4	no	—
79	#102×C₅₉	—	2	4	no	—
80	#102×C₅₉	—	2	4	no	—
81	C₂²⋊C₈×C₅₉	—	2	2	no	—
82	C₂²⋊C₈×C₅₉	—	2	2	no	—
83	C₄×C₈×C₅₉	—	2	2	no	—
84	C₄×C₈×C₅₉	D₄	1	4	yes	complemented
85	#95×C₅₉	—	2	2	no	—
86	#95×C₅₉	—	2	2	no	—
87	#95×C₅₉	—	2	2	no	—
88	C₂⁴×C₅₉	—	2	2	no	—
89	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₅₉	—	2	8	no	—
91	C₂×D₄×C₅₉	—	2	2	no	—
92	C₂×D₄×C₅₉	—	2	2	no	—
93	C₂×D₄×C₅₉	—	2	2	no	—
94	C₂×D₄×C₅₉	—	2	2	no	—
95	C₂×D₄×C₅₉	—	2	2	no	—
96	C₂×D₄×C₅₉	—	4	4	no	—
97	C₂×D₄×C₅₉	—	4	4	no	—
98	C₂×D₄×C₅₉	#41	1	4	yes	—
99	C₂²×C₄×C₅₉	—	2	2	no	—
100	C₂²×C₄×C₅₉	—	2	2	no	—
101	C₂²×C₄×C₅₉	—	2	2	no	—
102	C₂²×C₄×C₅₉	—	2	2	no	—
103	C₂²×C₄×C₅₉	—	2	2	no	—
104	C₂²×C₄×C₅₉	—	2	4	no	—
105	C₂²×C₄×C₅₉	—	2	1	no	—
106	C₂²×C₄×C₅₉	—	2	1	no	—
107	C₂²×C₄×C₅₉	—	2	2	no	—
108	C₂²×C₄×C₅₉	—	2	2	no	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	—	2	2	no	—
111	C₂²×C₄×C₅₉	—	4	4	no	—
112	C₂²×C₄×C₅₉	—	4	4	no	—
113	C₂²×C₄×C₅₉	—	4	4	no	—
114	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
120	D₈×C₅₉	—	2	8	no	—
121	C₂×C₈×C₅₉	—	2	2	no	—
122	C₂×C₈×C₅₉	—	2	2	no	—
123	C₂×C₈×C₅₉	—	2	1	no	—
124	C₂×C₈×C₅₉	—	2	1	no	—
125	C₂×C₈×C₅₉	—	2	2	no	—
126	C₂×C₈×C₅₉	—	2	2	no	—
127	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₅₉	—	2	2	no	—
130	C₄⋊C₄×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	2	2	no	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	2	no	—
134	C₄⋊C₄×C₅₉	—	4	4	no	—
135	C₄⋊C₄×C₅₉	#41	1	4	yes	—
136	C₂²⋊C₄×C₅₉	—	2	8	no	—
137	C₂²⋊C₄×C₅₉	—	4	4	no	—
138	C₂²⋊C₄×C₅₉	—	4	4	no	—
139	C₂²⋊C₄×C₅₉	—	4	4	no	—
140	C₂²⋊C₄×C₅₉	—	4	4	no	—
141	C₄²×C₅₉	—	2	2	no	—
142	C₄²×C₅₉	—	2	2	no	—
143	C₄²×C₅₉	—	2	1	no	—
144	C₄²×C₅₉	—	2	1	no	—
145	C₄²×C₅₉	—	4	4	no	—
146	C₄²×C₅₉	C₂×D₄	1	2	yes	—
147	C₄²×C₅₉	#41	1	2	yes	—
148	C₂³×C₅₉	—	2	1	no	—
149	C₂³×C₅₉	—	2	2	no	—
150	C₂³×C₅₉	—	2	1	no	—
151	C₂³×C₅₉	—	2	2	no	—
152	C₂³×C₅₉	—	2	4	no	—
153	C₂³×C₅₉	—	4	2	no	—
154	C₂³×C₅₉	—	4	2	no	—
155	C₂³×C₅₉	—	4	2	no	—
156	C₂³×C₅₉	—	4	2	no	—
157	C₂³×C₅₉	—	4	2	no	—
158	C₂³×C₅₉	—	4	2	no	—
159	C₂³×C₅₉	#135	1	2	yes	—
160	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₅₉	—	2	4	no	—
162	D₄×C₅₉	—	2	4	no	—
163	D₄×C₅₉	—	4	16	no	—
164	D₄×C₅₉	—	4	2	no	—
165	D₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	2	8	no	—
167	C₂×C₄×C₅₉	—	2	1	no	—
168	C₂×C₄×C₅₉	—	2	1	no	—
169	C₂×C₄×C₅₉	—	2	1	no	—
170	C₂×C₄×C₅₉	—	2	1	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	2	1	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	2	4	no	—
175	C₂×C₄×C₅₉	—	2	2	no	—
176	C₂×C₄×C₅₉	—	4	2	no	—
177	C₂×C₄×C₅₉	—	4	2	no	—
178	C₂×C₄×C₅₉	—	4	1	no	—
179	C₂×C₄×C₅₉	—	4	2	no	—
180	C₂×C₄×C₅₉	—	4	1	no	—
181	C₂×C₄×C₅₉	—	4	4	no	—
182	C₂×C₄×C₅₉	—	4	2	no	—
183	C₂×C₄×C₅₉	—	4	2	no	—
184	C₂×C₄×C₅₉	—	4	2	no	—
185	C₂×C₄×C₅₉	—	4	2	no	—
186	C₂×C₄×C₅₉	—	4	2	no	—
187	C₂×C₄×C₅₉	—	4	2	no	—
188	C₂×C₄×C₅₉	—	8	8	no	—
189	C₂×C₄×C₅₉	#121	1	2	yes	—
190	C₂×C₄×C₅₉	#121	1	2	yes	—
191	C₂×C₄×C₅₉	#135	1	2	yes	—
192	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	4	yes	—
193	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
195	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
197	C₈×C₅₉	—	2	2	no	—
198	C₈×C₅₉	—	2	2	no	—
199	C₈×C₅₉	—	4	1	no	—
200	C₈×C₅₉	—	4	1	no	—
201	#23697	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₅₉	—	2	4	no	—
203	C₂²×C₅₉	—	2	2	no	—
204	C₂²×C₅₉	—	4	2	no	—
205	C₂²×C₅₉	—	4	1	no	—
206	C₂²×C₅₉	—	4	1	no	—
207	C₂²×C₅₉	—	4	4	no	—
208	C₂²×C₅₉	—	4	4	no	—
209	C₂²×C₅₉	—	4	4	no	—
210	C₂²×C₅₉	—	8	2	no	—
211	C₂²×C₅₉	—	8	2	no	—
212	C₂²×C₅₉	—	8	2	no	—
213	C₂²×C₅₉	—	8	2	no	—
214	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
215	C₂²×C₅₉	#525	1	2	yes	—
216	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
217	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
218	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
219	C₄×C₅₉	—	2	2	no	—
220	C₄×C₅₉	—	2	2	no	—
221	C₄×C₅₉	—	4	4	no	—
222	C₄×C₅₉	—	4	1	no	—
223	C₄×C₅₉	—	4	1	no	—
224	C₄×C₅₉	—	8	2	no	—
225	C₄×C₅₉	—	8	2	no	—
226	C₄×C₅₉	#469	1	4	yes	—
227	C₄×C₅₉	#525	1	1	yes	characteristic
228	C₄×C₅₉	#529	1	2	yes	—
229	C₄×C₅₉	#532	1	1	yes	characteristic
230	C₂×C₄×D₈	C₂×C₅₉	1	1	yes	characteristic, complemented
231	C₂×#431	C₂×C₅₉	1	1	yes	characteristic, complemented
232	C₄×#121	C₂×C₅₉	1	2	yes	complemented
233	#2087	C₂×C₅₉	1	1	yes	characteristic, complemented
234	#2076	C₂×C₅₉	1	1	yes	characteristic, complemented
235	#2065	C₂×C₅₉	1	2	yes	complemented
236	#2054	C₂×C₅₉	1	1	yes	characteristic, complemented
237	#2034	C₂×C₅₉	1	2	yes	complemented
238	#1999	C₂×C₅₉	1	1	yes	characteristic
239	C₄×#106	C₂×C₅₉	1	1	yes	characteristic, complemented
240	C₄×#102	C₂×C₅₉	1	2	yes	complemented
241	C₂×C₅₉	—	4	2	no	—
242	C₂×C₅₉	—	8	4	no	—
243	C₂×C₅₉	#2392	1	1	yes	characteristic
244	C₂×C₅₉	#3050	1	1	yes	characteristic
245	C₂×C₅₉	C₂×#469	1	1	yes	characteristic
246	C₂×C₅₉	#3105	1	2	yes	—
247	C₂×C₅₉	#3106	1	2	yes	—
248	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
249	C₂×#121	C₂²×C₅₉	1	2	yes	—
250	C₂×C₄×D₄	—	2	2	no	—
251	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
252	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
253	C₄×D₈	—	2	4	no	—
254	#431	—	2	4	no	—
255	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
256	C₂×#106	C₂²×C₅₉	1	2	yes	—
257	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
259	C₂×#102	C₂²×C₅₉	1	2	yes	—
260	C₂×#102	C₂²×C₅₉	1	2	yes	—
261	C₂×#102	C₂²×C₅₉	1	2	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
266	#390	C₂²×C₅₉	1	2	yes	—
267	#389	C₂²×C₅₉	1	2	yes	—
268	#388	—	2	2	no	—
269	#386	—	2	2	no	—
270	#380	C₂²×C₅₉	1	2	yes	—
271	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
272	C₄×C₂²⋊C₄	—	2	2	no	—
273	#340	C₂²×C₅₉	1	1	yes	characteristic
274	#340	C₂²×C₅₉	1	2	yes	—
275	#340	C₂²×C₅₉	1	1	yes	characteristic
276	#340	C₂²×C₅₉	1	2	yes	—
277	C₅₉	#23697	1	1	yes	characteristic, direct product factor, Sylow
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
282	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
284	C₂×D₈	—	2	4	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
290	#121	—	2	4	no	—
291	#121	—	2	4	no	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	2	4	no	—
294	C₄×D₄	—	4	8	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
311	#107	—	2	2	no	—
312	#106	—	2	4	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	2	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#102	—	2	4	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	D₄×C₅₉	1	4	yes	complemented
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	#41×C₅₉	1	4	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
357	D₈	—	2	8	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	#41×C₅₉	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	4	4	no	—
383	C₄²	C₂×D₄×C₅₉	1	2	yes	—
384	C₄²	#41×C₅₉	1	2	yes	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	#135×C₅₉	1	2	yes	—
397	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	16	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	8	no	—
426	C₂×C₄	#121×C₅₉	1	2	yes	—
427	C₂×C₄	#121×C₅₉	1	2	yes	—
428	C₂×C₄	#135×C₅₉	1	2	yes	—
429	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	4	yes	—
430	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
432	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
451	C₂²	C₅₉×#525	1	2	yes	—
452	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
453	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
454	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₅₉×#469	1	4	yes	—
463	C₄	C₅₉×#525	1	1	yes	characteristic
464	C₄	C₅₉×#529	1	2	yes	—
465	C₄	C₅₉×#532	1	1	yes	characteristic
466	C₂	—	4	2	no	—
467	C₂	—	8	4	no	—
468	C₂	C₅₉×#2392	1	1	yes	characteristic
469	C₂	C₅₉×#3050	1	1	yes	characteristic
470	C₂	C₂×C₅₉×#469	1	1	yes	characteristic
471	C₂	C₅₉×#3105	1	2	yes	—
472	C₂	C₅₉×#3106	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂³×C₅₉	C₂²×D₄
prime radical	C₅₉×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₈×C₅₉	C₂	semidirect
2. C₂×C₅₉×#431	C₂	semidirect
3. C₄×#121×C₅₉	C₂	semidirect
4. C₅₉×#2087	C₂	semidirect
5. C₅₉×#2076	C₂	semidirect
6. C₅₉×#2065	C₂	semidirect
7. C₅₉×#2054	C₂	semidirect
8. C₅₉×#2034	C₂	semidirect
10. C₄×#106×C₅₉	C₂	semidirect
11. C₄×#102×C₅₉	C₂	semidirect
84. C₄×C₈×C₅₉	D₄	semidirect
201. #23697	C₅₉	direct (N × H)
230. C₂×C₄×D₈	C₂×C₅₉	semidirect
231. C₂×#431	C₂×C₅₉	semidirect
232. C₄×#121	C₂×C₅₉	semidirect
233. #2087	C₂×C₅₉	semidirect
234. #2076	C₂×C₅₉	semidirect
235. #2065	C₂×C₅₉	semidirect
236. #2054	C₂×C₅₉	semidirect
237. #2034	C₂×C₅₉	semidirect
239. C₄×#106	C₂×C₅₉	semidirect
240. C₄×#102	C₂×C₅₉	semidirect
277. C₅₉	#23697	direct (N × H)
321. C₄×C₈	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₅₉	2
C₂×C₅₉×#431	2
C₄×#121×C₅₉	2
C₅₉×#2087	2
C₅₉×#2076	2
C₅₉×#2065	2
C₅₉×#2054	2
C₅₉×#2034	2
C₅₉×#1999	2
C₄×#106×C₅₉	2
C₄×#102×C₅₉	2
#23697	59

Subgroups — C59×#23697 #28435806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23697 #28435806