Subgroups — C₅₉×#24272 #28436381

Order 15104.

1776 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#469	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2408	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2054	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1999	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1972	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1786	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
11	C₂²×D₈×C₅₉	—	2	8	no	—
12	C₂²×D₈×C₅₉	—	2	4	no	—
13	C₂²×D₈×C₅₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₅₉	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#121×C₅₉	C₂²	1	4	yes	complemented
18	C₂×#120×C₅₉	—	2	2	no	—
19	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#469	—	2	8	no	—
21	C₅₉×#435	—	2	4	no	—
22	C₂×#106×C₅₉	C₂²	1	2	yes	complemented
23	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×#102×C₅₉	C₂²	1	4	yes	complemented
25	C₂×#102×C₅₉	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic, complemented
29	C₅₉×#394	—	2	2	no	—
30	C₅₉×#392	—	2	2	no	—
31	C₅₉×#390	C₂²	1	4	yes	complemented
32	C₅₉×#380	C₂²	1	2	yes	—
33	C₅₉×#379	—	2	2	no	—
34	C₅₉×#340	C₂²	1	2	yes	complemented
35	C₂⁵×C₅₉	—	2	2	no	—
36	C₂²×D₄×C₅₉	—	2	8	no	—
37	C₂²×D₄×C₅₉	—	2	4	no	—
38	C₂²×D₄×C₅₉	—	2	4	no	—
39	C₂²×D₄×C₅₉	—	2	2	no	—
40	C₂²×D₄×C₅₉	—	2	4	no	—
41	C₂²×D₄×C₅₉	—	4	4	no	—
42	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
44	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₅₉	—	2	32	no	—
47	C₂×D₈×C₅₉	—	2	8	no	—
48	C₂×D₈×C₅₉	—	2	4	no	—
49	C₂×D₈×C₅₉	—	2	4	no	—
50	C₂×D₈×C₅₉	—	2	4	no	—
51	C₂×D₈×C₅₉	D₄	1	8	yes	complemented
52	C₂×M₁₆×C₅₉	—	2	2	no	—
53	C₂×M₁₆×C₅₉	—	2	4	no	—
54	C₂²×C₈×C₅₉	—	2	4	no	—
55	C₂²×C₈×C₅₉	D₄	1	4	yes	complemented
56	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
60	#121×C₅₉	—	2	8	no	—
61	#121×C₅₉	—	4	4	no	—
62	#120×C₅₉	—	4	8	no	—
63	C₄×D₄×C₅₉	—	2	2	no	—
64	C₄×D₄×C₅₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
74	#106×C₅₉	—	2	4	no	—
75	C₄⋊C₈×C₅₉	—	2	2	no	—
76	#102×C₅₉	—	2	8	no	—
77	#102×C₅₉	—	4	4	no	—
78	C₂²⋊C₈×C₅₉	—	2	2	no	—
79	C₂²⋊C₈×C₅₉	—	2	2	no	—
80	#97×C₅₉	—	2	2	no	—
81	#95×C₅₉	—	2	2	no	—
82	C₂⁴×C₅₉	—	2	4	no	—
83	C₂⁴×C₅₉	—	4	8	no	—
84	C₂⁴×C₅₉	—	4	4	no	—
85	C₂⁴×C₅₉	—	4	4	no	—
86	C₂⁴×C₅₉	—	4	4	no	—
87	C₂⁴×C₅₉	—	8	4	no	—
88	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
89	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₅₉	—	2	16	no	—
91	C₂×D₄×C₅₉	—	2	2	no	—
92	C₂×D₄×C₅₉	—	2	4	no	—
93	C₂×D₄×C₅₉	—	2	4	no	—
94	C₂×D₄×C₅₉	—	2	4	no	—
95	C₂×D₄×C₅₉	—	2	4	no	—
96	C₂×D₄×C₅₉	—	2	4	no	—
97	C₂×D₄×C₅₉	—	2	4	no	—
98	C₂×D₄×C₅₉	—	4	16	no	—
99	C₂×D₄×C₅₉	—	4	8	no	—
100	C₂×D₄×C₅₉	—	4	8	no	—
101	C₂×D₄×C₅₉	—	4	8	no	—
102	C₂×D₄×C₅₉	—	4	8	no	—
103	C₂×D₄×C₅₉	—	4	4	no	—
104	C₂×D₄×C₅₉	—	8	4	no	—
105	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
106	C₂²×C₄×C₅₉	—	2	2	no	—
107	C₂²×C₄×C₅₉	—	2	2	no	—
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	—	2	1	no	—
111	C₂²×C₄×C₅₉	—	2	2	no	—
112	C₂²×C₄×C₅₉	—	2	4	no	—
113	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
118	C₂²×C₄×C₅₉	#41	1	2	yes	—
119	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
120	D₈×C₅₉	—	2	16	no	—
121	D₈×C₅₉	—	2	16	no	—
122	M₁₆×C₅₉	—	4	4	no	—
123	C₂×C₈×C₅₉	—	2	2	no	—
124	C₂×C₈×C₅₉	—	2	8	no	—
125	C₂×C₈×C₅₉	—	2	1	no	—
126	C₂×C₈×C₅₉	—	2	1	no	—
127	C₂×C₈×C₅₉	—	2	2	no	—
128	C₂×C₈×C₅₉	—	2	2	no	—
129	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	4	no	—
134	C₄⋊C₄×C₅₉	—	2	4	no	—
135	C₂²⋊C₄×C₅₉	—	2	2	no	—
136	C₂²⋊C₄×C₅₉	—	2	2	no	—
137	C₂²⋊C₄×C₅₉	—	4	8	no	—
138	C₂²⋊C₄×C₅₉	—	4	8	no	—
139	C₂²⋊C₄×C₅₉	—	4	4	no	—
140	C₂²⋊C₄×C₅₉	—	8	4	no	—
141	C₄²×C₅₉	—	2	1	no	—
142	C₄²×C₅₉	—	2	1	no	—
143	C₂³×C₅₉	—	2	2	no	—
144	C₂³×C₅₉	—	2	2	no	—
145	C₂³×C₅₉	—	2	1	no	—
146	C₂³×C₅₉	—	2	8	no	—
147	C₂³×C₅₉	—	2	2	no	—
148	C₂³×C₅₉	—	2	2	no	—
149	C₂³×C₅₉	—	2	2	no	—
150	C₂³×C₅₉	—	4	16	no	—
151	C₂³×C₅₉	—	4	4	no	—
152	C₂³×C₅₉	—	4	4	no	—
153	C₂³×C₅₉	—	4	4	no	—
154	C₂³×C₅₉	—	4	4	no	—
155	C₂³×C₅₉	—	4	4	no	—
156	C₂³×C₅₉	—	4	4	no	—
157	C₂³×C₅₉	—	8	16	no	—
158	C₂³×C₅₉	—	8	16	no	—
159	C₂³×C₅₉	—	8	8	no	—
160	C₂³×C₅₉	—	8	8	no	—
161	C₂³×C₅₉	#121	1	2	yes	—
162	C₂³×C₅₉	AGL(1,ℤ/8)	1	4	yes	—
163	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
164	D₄×C₅₉	—	2	8	no	—
165	D₄×C₅₉	—	2	8	no	—
166	D₄×C₅₉	—	4	16	no	—
167	D₄×C₅₉	—	4	4	no	—
168	D₄×C₅₉	—	4	4	no	—
169	D₄×C₅₉	—	4	4	no	—
170	D₄×C₅₉	—	8	16	no	—
171	C₂×C₄×C₅₉	—	2	2	no	—
172	C₂×C₄×C₅₉	—	2	2	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	2	4	no	—
175	C₂×C₄×C₅₉	—	2	1	no	—
176	C₂×C₄×C₅₉	—	2	1	no	—
177	C₂×C₄×C₅₉	—	2	1	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	2	2	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	—	4	1	no	—
182	C₂×C₄×C₅₉	—	4	1	no	—
183	C₂×C₄×C₅₉	—	4	2	no	—
184	C₂×C₄×C₅₉	—	4	4	no	—
185	C₂×C₄×C₅₉	—	4	4	no	—
186	C₂×C₄×C₅₉	—	4	4	no	—
187	C₂×C₄×C₅₉	#121	1	2	yes	—
188	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
192	C₈×C₅₉	—	2	2	no	—
193	C₈×C₅₉	—	4	1	no	—
194	C₈×C₅₉	—	4	1	no	—
195	C₈×C₅₉	#120	1	4	yes	complemented
196	#24272	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₅₉	—	2	2	no	—
198	C₂²×C₅₉	—	2	8	no	—
199	C₂²×C₅₉	—	2	2	no	—
200	C₂²×C₅₉	—	4	1	no	—
201	C₂²×C₅₉	—	4	8	no	—
202	C₂²×C₅₉	—	4	4	no	—
203	C₂²×C₅₉	—	4	8	no	—
204	C₂²×C₅₉	—	4	8	no	—
205	C₂²×C₅₉	—	4	1	no	—
206	C₂²×C₅₉	—	4	1	no	—
207	C₂²×C₅₉	—	8	32	no	—
208	C₂²×C₅₉	—	8	4	no	—
209	C₂²×C₅₉	—	8	4	no	—
210	C₂²×C₅₉	—	8	4	no	—
211	C₂²×C₅₉	—	8	4	no	—
212	C₂²×C₅₉	#469	1	4	yes	complemented
213	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
214	C₂²×C₅₉	D₄²	1	2	yes	—
215	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
216	C₂²×C₅₉	#576	1	2	yes	—
217	C₄×C₅₉	—	2	2	no	—
218	C₄×C₅₉	—	4	1	no	—
219	C₄×C₅₉	—	4	1	no	—
220	C₄×C₅₉	—	4	1	no	—
221	C₄×C₅₉	—	8	4	no	—
222	C₄×C₅₉	C₂×#120	1	1	yes	characteristic
223	C₄×C₅₉	#535	1	1	yes	characteristic
224	C₄×C₅₉	#546	1	2	yes	—
225	C₂³×D₈	C₂×C₅₉	1	1	yes	characteristic, complemented
226	C₂×#469	C₂×C₅₉	1	2	yes	complemented
227	C₂×#435	C₂×C₅₉	1	1	yes	characteristic, complemented
228	#2408	C₂×C₅₉	1	2	yes	complemented
229	#2054	C₂×C₅₉	1	2	yes	complemented
230	#1999	C₂×C₅₉	1	2	yes	complemented
231	#1972	C₂×C₅₉	1	2	yes	complemented
232	#1807	C₂×C₅₉	1	1	yes	characteristic, complemented
233	#1786	C₂×C₅₉	1	2	yes	complemented
234	C₂×C₅₉	—	2	4	no	—
235	C₂×C₅₉	—	8	1	no	—
236	C₂×C₅₉	—	8	8	no	—
237	C₂×C₅₉	#2408	1	1	yes	characteristic
238	C₂×C₅₉	C₂×#469	1	1	yes	characteristic
239	C₂×C₅₉	#3058	1	1	yes	characteristic
240	C₂×C₅₉	#3264	1	4	yes	—
241	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
242	C₂²×D₈	—	2	8	no	—
243	C₂²×D₈	—	2	4	no	—
244	C₂²×D₈	C₂²×C₅₉	1	2	yes	—
245	C₂²×D₈	C₂²×C₅₉	1	2	yes	—
246	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
247	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
248	C₂×#121	C₂²×C₅₉	1	4	yes	complemented
249	C₂×#120	—	2	2	no	—
250	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
251	#469	—	2	8	no	—
252	#435	—	2	4	no	—
253	C₂×#106	C₂²×C₅₉	1	2	yes	complemented
254	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
255	C₂×#102	C₂²×C₅₉	1	4	yes	complemented
256	C₂×#102	C₂²×C₅₉	1	4	yes	complemented
257	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
259	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic, complemented
260	#394	—	2	2	no	—
261	#392	—	2	2	no	—
262	#390	C₂²×C₅₉	1	4	yes	complemented
263	#380	C₂²×C₅₉	1	2	yes	—
264	#379	—	2	2	no	—
265	#340	C₂²×C₅₉	1	2	yes	complemented
266	C₅₉	#24272	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁵	—	2	2	no	—
268	C₂²×D₄	—	2	8	no	—
269	C₂²×D₄	—	2	4	no	—
270	C₂²×D₄	—	2	4	no	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	—	2	4	no	—
273	C₂²×D₄	—	4	4	no	—
274	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
275	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
276	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
278	C₂×D₈	—	2	32	no	—
279	C₂×D₈	—	2	8	no	—
280	C₂×D₈	—	2	4	no	—
281	C₂×D₈	—	2	4	no	—
282	C₂×D₈	—	2	4	no	—
283	C₂×D₈	D₄×C₅₉	1	8	yes	complemented
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	4	no	—
286	C₂²×C₈	—	2	4	no	—
287	C₂²×C₈	D₄×C₅₉	1	4	yes	complemented
288	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
292	#121	—	2	8	no	—
293	#121	—	4	4	no	—
294	#120	—	4	8	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	—	2	4	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
306	#106	—	2	4	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	8	no	—
309	#102	—	4	4	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	#97	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₂⁴	—	2	4	no	—
315	C₂⁴	—	4	8	no	—
316	C₂⁴	—	4	4	no	—
317	C₂⁴	—	4	4	no	—
318	C₂⁴	—	4	4	no	—
319	C₂⁴	—	8	4	no	—
320	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
321	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
322	C₂×D₄	—	2	16	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	4	16	no	—
331	C₂×D₄	—	4	8	no	—
332	C₂×D₄	—	4	8	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	—	4	8	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	8	4	no	—
337	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
350	C₂²×C₄	#41×C₅₉	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
352	D₈	—	2	16	no	—
353	D₈	—	2	16	no	—
354	M₁₆	—	4	4	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	8	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	4	8	no	—
370	C₂²⋊C₄	—	4	8	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	8	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	8	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	16	no	—
383	C₂³	—	4	4	no	—
384	C₂³	—	4	4	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	8	16	no	—
390	C₂³	—	8	16	no	—
391	C₂³	—	8	8	no	—
392	C₂³	—	8	8	no	—
393	C₂³	#121×C₅₉	1	2	yes	—
394	C₂³	AGL(1,ℤ/8)×C₅₉	1	4	yes	—
395	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
396	D₄	—	2	8	no	—
397	D₄	—	2	8	no	—
398	D₄	—	4	16	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	4	no	—
402	D₄	—	8	16	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	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	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	#121×C₅₉	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
422	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
423	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
424	C₈	—	2	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	#120×C₅₉	1	4	yes	complemented
428	C₂²	—	2	8	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	4	8	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	8	no	—
438	C₂²	—	8	32	no	—
439	C₂²	—	8	4	no	—
440	C₂²	—	8	4	no	—
441	C₂²	—	8	4	no	—
442	C₂²	—	8	4	no	—
443	C₂²	C₅₉×#469	1	4	yes	complemented
444	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
445	C₂²	D₄²×C₅₉	1	2	yes	—
446	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
447	C₂²	C₅₉×#576	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	8	4	no	—
453	C₄	C₂×#120×C₅₉	1	1	yes	characteristic
454	C₄	C₅₉×#535	1	1	yes	characteristic
455	C₄	C₅₉×#546	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	8	1	no	—
458	C₂	—	8	8	no	—
459	C₂	C₅₉×#2408	1	1	yes	characteristic
460	C₂	C₂×C₅₉×#469	1	1	yes	characteristic
461	C₂	C₅₉×#3058	1	1	yes	characteristic
462	C₂	C₅₉×#3264	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈×C₅₉	C₂	semidirect
2. C₂×C₅₉×#469	C₂	semidirect
3. C₂×C₅₉×#435	C₂	semidirect
4. C₅₉×#2408	C₂	semidirect
5. C₅₉×#2054	C₂	semidirect
6. C₅₉×#1999	C₂	semidirect
7. C₅₉×#1972	C₂	semidirect
8. C₅₉×#1807	C₂	semidirect
9. C₅₉×#1786	C₂	semidirect
15. C₂²×M₁₆×C₅₉	C₂²	semidirect
17. C₂×#121×C₅₉	C₂²	semidirect
22. C₂×#106×C₅₉	C₂²	semidirect
23. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
24. C₂×#102×C₅₉	C₂²	semidirect
25. C₂×#102×C₅₉	C₂²	semidirect
27. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
28. C₂×#97×C₅₉	C₂²	semidirect
31. C₅₉×#390	C₂²	semidirect
34. C₅₉×#340	C₂²	semidirect
51. C₂×D₈×C₅₉	D₄	semidirect
55. C₂²×C₈×C₅₉	D₄	semidirect
195. C₈×C₅₉	#120	semidirect
196. #24272	C₅₉	direct (N × H)
212. C₂²×C₅₉	#469	semidirect
225. C₂³×D₈	C₂×C₅₉	semidirect
226. C₂×#469	C₂×C₅₉	semidirect
227. C₂×#435	C₂×C₅₉	semidirect
228. #2408	C₂×C₅₉	semidirect
229. #2054	C₂×C₅₉	semidirect
230. #1999	C₂×C₅₉	semidirect
231. #1972	C₂×C₅₉	semidirect
232. #1807	C₂×C₅₉	semidirect
233. #1786	C₂×C₅₉	semidirect
246. C₂²×M₁₆	C₂²×C₅₉	semidirect
248. C₂×#121	C₂²×C₅₉	semidirect
253. C₂×#106	C₂²×C₅₉	semidirect
254. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
255. C₂×#102	C₂²×C₅₉	semidirect
256. C₂×#102	C₂²×C₅₉	semidirect
258. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
259. C₂×#97	C₂²×C₅₉	semidirect
262. #390	C₂²×C₅₉	semidirect
265. #340	C₂²×C₅₉	semidirect
266. C₅₉	#24272	direct (N × H)
283. C₂×D₈	D₄×C₅₉	semidirect
287. C₂²×C₈	D₄×C₅₉	semidirect
427. C₈	#120×C₅₉	semidirect
443. C₂²	C₅₉×#469	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₅₉	2
C₂×C₅₉×#469	2
C₂×C₅₉×#435	2
C₅₉×#2408	2
C₅₉×#2054	2
C₅₉×#1999	2
C₅₉×#1972	2
C₅₉×#1807	2
C₅₉×#1786	2
#24272	59

Subgroups — C59×#24272 #28436381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24272 #28436381