Subgroups — C₅₉×#17893 #28430002

Order 15104.

684 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×AGL(1,ℤ/8)×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1594	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1592	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1590	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1589	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₅₉	C₄	1	1	yes	characteristic
13	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#446	C₂²	1	2	yes	complemented
16	C₅₉×#442	C₄	1	2	yes	—
17	C₅₉×#440	C₄	1	2	yes	—
18	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
19	C₄×D₈×C₅₉	C₂²	1	2	yes	—
20	C₅₉×#436	—	2	1	no	—
21	C₅₉×#436	—	2	1	no	—
22	C₅₉×#436	C₂²	1	2	yes	—
23	C₅₉×#436	C₂²	1	2	yes	—
24	C₅₉×#436	C₂²	1	2	yes	complemented
25	C₅₉×#435	—	2	2	no	—
26	C₅₉×#432	—	2	1	no	—
27	C₅₉×#431	C₂²	1	1	yes	characteristic
28	C₅₉×#431	C₂²	1	1	yes	characteristic
29	C₅₉×#428	C₄	1	1	yes	characteristic
30	C₅₉×#423	—	2	1	no	—
31	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₅₉×#418	C₄	1	1	yes	characteristic
33	C₅₉×#417	C₄	1	1	yes	characteristic
34	C₅₉×#407	—	2	2	no	—
35	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#335	C₂²	1	2	yes	complemented
38	C₅₉×#334	C₂²	1	2	yes	complemented
39	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
42	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
43	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₅₉×#322	C₂²	1	2	yes	complemented
46	C₈²×C₅₉	C₂²	1	2	yes	complemented
47	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅₉	—	2	1	no	—
50	AGL(1,ℤ/8)×C₅₉	—	2	4	no	—
51	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
52	C₂×D₈×C₅₉	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₅₉	—	2	2	no	—
54	C₂×M₁₆×C₅₉	—	2	2	no	—
55	C₂×M₁₆×C₅₉	—	2	2	no	—
56	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
57	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₅₉	—	2	1	no	—
59	C₂²×C₈×C₅₉	—	2	1	no	—
60	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₅₉	—	2	1	no	—
63	C₄×D₄×C₅₉	—	2	1	no	—
64	C₄×D₄×C₅₉	—	2	1	no	—
65	C₄×D₄×C₅₉	—	2	1	no	—
66	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₅₉	C₂³	1	2	yes	—
69	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
70	#117×C₅₉	—	2	1	no	—
71	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	—	2	1	no	—
75	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
76	#107×C₅₉	C₂×C₄	1	2	yes	—
77	#106×C₅₉	C₂×C₄	1	2	yes	—
78	C₄⋊C₈×C₅₉	—	2	2	no	—
79	C₄⋊C₈×C₅₉	—	2	1	no	—
80	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
81	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
82	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
84	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
85	#103×C₅₉	C₂×C₄	1	2	yes	—
86	#102×C₅₉	C₂×C₄	1	2	yes	—
87	#102×C₅₉	C₂×C₄	1	2	yes	—
88	#102×C₅₉	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₅₉	—	2	1	no	—
90	C₂²⋊C₈×C₅₉	—	2	2	no	—
91	C₂²⋊C₈×C₅₉	—	2	2	no	—
92	C₂²⋊C₈×C₅₉	—	2	2	no	—
93	C₂²⋊C₈×C₅₉	D₄	1	2	yes	—
94	#97×C₅₉	—	2	2	no	—
95	#97×C₅₉	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₅₉	—	2	1	no	—
97	C₄×C₈×C₅₉	—	2	1	no	—
98	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₅₉	C₂³	1	2	yes	—
101	C₄×C₈×C₅₉	C₂³	1	2	yes	—
102	C₂⁴×C₅₉	—	2	1	no	—
103	#41×C₅₉	—	2	2	no	—
104	#41×C₅₉	—	2	2	no	—
105	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₄×C₅₉	—	2	1	no	—
107	C₂×D₄×C₅₉	—	2	1	no	—
108	C₂×D₄×C₅₉	—	2	2	no	—
109	C₂×D₄×C₅₉	—	2	2	no	—
110	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₅₉	—	2	1	no	—
113	C₂²×C₄×C₅₉	—	2	1	no	—
114	C₂²×C₄×C₅₉	—	2	1	no	—
115	C₂²×C₄×C₅₉	—	2	2	no	—
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	2	no	—
118	C₂²×C₄×C₅₉	—	8	1	no	—
119	C₂²×C₄×C₅₉	—	8	1	no	—
120	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
123	SD₁₆×C₅₉	—	2	4	no	—
124	D₈×C₅₉	—	2	4	no	—
125	M₁₆×C₅₉	—	2	2	no	—
126	M₁₆×C₅₉	—	8	2	no	—
127	M₁₆×C₅₉	—	8	2	no	—
128	M₁₆×C₅₉	—	8	2	no	—
129	M₁₆×C₅₉	M₁₆	1	4	yes	complemented
130	C₂×C₈×C₅₉	—	2	1	no	—
131	C₂×C₈×C₅₉	—	2	1	no	—
132	C₂×C₈×C₅₉	—	2	1	no	—
133	C₂×C₈×C₅₉	—	2	2	no	—
134	C₂×C₈×C₅₉	—	2	1	no	—
135	C₂×C₈×C₅₉	—	4	2	no	—
136	C₂×C₈×C₅₉	—	8	1	no	—
137	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₅₉	—	2	1	no	—
142	C₄⋊C₄×C₅₉	—	2	1	no	—
143	C₄⋊C₄×C₅₉	—	2	1	no	—
144	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₅₉	—	2	1	no	—
148	C₂²⋊C₄×C₅₉	—	2	2	no	—
149	C₂²⋊C₄×C₅₉	—	2	1	no	—
150	C₂²⋊C₄×C₅₉	—	2	2	no	—
151	C₂²⋊C₄×C₅₉	—	2	1	no	—
152	C₄²×C₅₉	—	2	1	no	—
153	C₄²×C₅₉	—	2	1	no	—
154	C₄²×C₅₉	—	2	1	no	—
155	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₅₉	#41	1	1	yes	characteristic
158	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₅₉	—	2	1	no	—
160	C₂³×C₅₉	—	2	2	no	—
161	C₂³×C₅₉	—	4	2	no	—
162	C₂³×C₅₉	—	8	1	no	—
163	C₂³×C₅₉	—	8	1	no	—
164	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
165	Q₈×C₅₉	—	2	1	no	—
166	Q₈×C₅₉	—	2	1	no	—
167	D₄×C₅₉	—	2	1	no	—
168	D₄×C₅₉	—	2	2	no	—
169	D₄×C₅₉	—	2	2	no	—
170	D₄×C₅₉	—	2	1	no	—
171	D₄×C₅₉	—	4	2	no	—
172	D₄×C₅₉	—	4	2	no	—
173	C₂×C₄×C₅₉	—	2	1	no	—
174	C₂×C₄×C₅₉	—	2	1	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	—	4	1	no	—
180	C₂×C₄×C₅₉	—	4	1	no	—
181	C₂×C₄×C₅₉	—	4	2	no	—
182	C₂×C₄×C₅₉	—	4	2	no	—
183	C₂×C₄×C₅₉	—	4	1	no	—
184	C₂×C₄×C₅₉	—	4	2	no	—
185	C₂×C₄×C₅₉	—	8	1	no	—
186	C₂×C₄×C₅₉	—	8	2	no	—
187	C₂×C₄×C₅₉	—	8	1	no	—
188	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₅₉	#131	1	2	yes	—
193	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
196	C₈×C₅₉	—	2	2	no	—
197	C₈×C₅₉	—	2	2	no	—
198	C₈×C₅₉	—	2	2	no	—
199	C₈×C₅₉	—	2	2	no	—
200	C₈×C₅₉	—	4	1	no	—
201	C₈×C₅₉	—	4	2	no	—
202	C₈×C₅₉	—	4	1	no	—
203	C₈×C₅₉	—	4	1	no	—
204	C₈×C₅₉	C₂×M₁₆	1	4	yes	—
205	#17893	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₅₉	—	2	1	no	—
207	C₂²×C₅₉	—	2	1	no	—
208	C₂²×C₅₉	—	4	1	no	—
209	C₂²×C₅₉	—	4	2	no	—
210	C₂²×C₅₉	—	4	2	no	—
211	C₂²×C₅₉	—	4	1	no	—
212	C₂²×C₅₉	—	4	1	no	—
213	C₂²×C₅₉	—	4	2	no	—
214	C₂²×C₅₉	—	8	4	no	—
215	C₂²×C₅₉	#436	1	2	yes	—
216	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₅₉	—	2	1	no	—
218	C₄×C₅₉	—	2	1	no	—
219	C₄×C₅₉	—	2	1	no	—
220	C₄×C₅₉	—	4	1	no	—
221	C₄×C₅₉	—	4	1	no	—
222	C₄×C₅₉	—	4	2	no	—
223	C₄×C₅₉	—	4	1	no	—
224	C₄×C₅₉	#436	1	2	yes	—
225	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
226	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
227	C₄×C₅₉	#576	1	1	yes	characteristic
228	C₄×C₅₉	#577	1	1	yes	characteristic
229	#2989	C₂×C₅₉	1	1	yes	characteristic, complemented
230	#2975	C₂×C₅₉	1	1	yes	characteristic, complemented
231	C₄×AGL(1,ℤ/8)	C₂×C₅₉	1	1	yes	characteristic
232	#1594	C₂×C₅₉	1	2	yes	complemented
233	#1592	C₂×C₅₉	1	2	yes	complemented
234	#1590	C₂×C₅₉	1	2	yes	complemented
235	#1589	C₂×C₅₉	1	2	yes	complemented
236	#1565	C₂×C₅₉	1	1	yes	characteristic, complemented
237	#1476	C₂×C₅₉	1	1	yes	characteristic, complemented
238	C₂×D₄⋊C₈	C₂×C₅₉	1	1	yes	characteristic, complemented
239	C₈×M₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
240	C₂×C₅₉	—	2	2	no	—
241	C₂×C₅₉	—	8	1	no	—
242	C₂×C₅₉	—	8	2	no	—
243	C₂×C₅₉	C₂×#436	1	1	yes	characteristic
244	C₂×C₅₉	#2946	1	1	yes	characteristic
245	C₂×C₅₉	#2956	1	1	yes	characteristic
246	C₂×AGL(1,ℤ/8)	C₄×C₅₉	1	1	yes	characteristic
247	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
249	#446	C₂²×C₅₉	1	2	yes	complemented
250	#442	C₄×C₅₉	1	2	yes	—
251	#440	C₄×C₅₉	1	2	yes	—
252	C₄×SD₁₆	C₂²×C₅₉	1	2	yes	—
253	C₄×D₈	C₂²×C₅₉	1	2	yes	—
254	#436	—	2	1	no	—
255	#436	—	2	1	no	—
256	#436	C₂²×C₅₉	1	2	yes	—
257	#436	C₂²×C₅₉	1	2	yes	—
258	#436	C₂²×C₅₉	1	2	yes	complemented
259	#435	—	2	2	no	—
260	#432	—	2	1	no	—
261	#431	C₂²×C₅₉	1	1	yes	characteristic
262	#431	C₂²×C₅₉	1	1	yes	characteristic
263	#428	C₄×C₅₉	1	1	yes	characteristic
264	#423	—	2	1	no	—
265	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
266	#418	C₄×C₅₉	1	1	yes	characteristic
267	#417	C₄×C₅₉	1	1	yes	characteristic
268	#407	—	2	2	no	—
269	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
271	#335	C₂²×C₅₉	1	2	yes	complemented
272	#334	C₂²×C₅₉	1	2	yes	complemented
273	Q₈⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
274	Q₈⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
275	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
276	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
277	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
278	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
279	#322	C₂²×C₅₉	1	2	yes	complemented
280	C₈²	C₂²×C₅₉	1	2	yes	complemented
281	C₅₉	#17893	1	1	yes	characteristic, direct product factor, Sylow
282	C₂×#41	C₂×C₄×C₅₉	1	1	yes	characteristic
283	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	AGL(1,ℤ/8)	—	2	4	no	—
286	C₂×SD₁₆	C₂×C₄×C₅₉	1	2	yes	—
287	C₂×D₈	C₂×C₄×C₅₉	1	2	yes	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	C₂×C₄×C₅₉	1	1	yes	characteristic
292	C₂×M₁₆	C₂×C₄×C₅₉	1	1	yes	characteristic
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₄×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
302	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
303	C₄×D₄	C₂³×C₅₉	1	2	yes	—
304	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₂×C₄×C₅₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
311	#107	C₂×C₄×C₅₉	1	2	yes	—
312	#106	C₂×C₄×C₅₉	1	2	yes	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	D₄×C₅₉	1	1	yes	characteristic
316	C₄⋊C₈	D₄×C₅₉	1	1	yes	characteristic
317	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
318	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
320	#103	C₂×C₄×C₅₉	1	2	yes	—
321	#102	C₂×C₄×C₅₉	1	2	yes	—
322	#102	C₂×C₄×C₅₉	1	2	yes	—
323	#102	C₂×C₄×C₅₉	1	2	yes	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	D₄×C₅₉	1	2	yes	—
329	#97	—	2	2	no	—
330	#97	C₂×C₄×C₅₉	1	2	yes	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₅₉	1	2	yes	—
336	C₄×C₈	C₂³×C₅₉	1	2	yes	—
337	C₂⁴	—	2	1	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	C₂×Q₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
346	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	1	no	—
354	C₂²×C₄	—	8	1	no	—
355	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
357	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
358	SD₁₆	—	2	4	no	—
359	D₈	—	2	4	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	8	2	no	—
362	M₁₆	—	8	2	no	—
363	M₁₆	—	8	2	no	—
364	M₁₆	M₁₆×C₅₉	1	4	yes	complemented
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	8	1	no	—
372	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
373	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
392	C₄²	#41×C₅₉	1	1	yes	characteristic
393	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	8	1	no	—
398	C₂³	—	8	1	no	—
399	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	—	2	1	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	1	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
424	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
426	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
427	C₂×C₄	#131×C₅₉	1	2	yes	—
428	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₈	C₂×M₁₆×C₅₉	1	4	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₅₉×#436	1	2	yes	—
450	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	C₅₉×#436	1	2	yes	—
459	C₄	C₂²×M₁₆×C₅₉	1	1	yes	characteristic
460	C₄	C₂×#131×C₅₉	1	1	yes	characteristic
461	C₄	C₅₉×#576	1	1	yes	characteristic
462	C₄	C₅₉×#577	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	2	no	—
465	C₂	—	8	1	no	—
466	C₂	C₂×C₅₉×#436	1	1	yes	characteristic
467	C₂	C₅₉×#2946	1	1	yes	characteristic
468	C₂	C₅₉×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₄²	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₅₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₅₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2989	C₂	semidirect
2. C₅₉×#2975	C₂	semidirect
4. C₅₉×#1594	C₂	semidirect
5. C₅₉×#1592	C₂	semidirect
6. C₅₉×#1590	C₂	semidirect
7. C₅₉×#1589	C₂	semidirect
8. C₅₉×#1565	C₂	semidirect
9. C₅₉×#1476	C₂	semidirect
10. C₂×C₅₉×D₄⋊C₈	C₂	semidirect
11. C₈×M₁₆×C₅₉	C₂	semidirect
15. C₅₉×#446	C₂²	semidirect
24. C₅₉×#436	C₂²	semidirect
37. C₅₉×#335	C₂²	semidirect
38. C₅₉×#334	C₂²	semidirect
39. C₅₉×Q₈⋊C₈	C₂²	semidirect
40. C₅₉×Q₈⋊C₈	C₂²	semidirect
43. C₅₉×D₄⋊C₈	C₂²	semidirect
44. C₅₉×D₄⋊C₈	C₂²	semidirect
45. C₅₉×#322	C₂²	semidirect
46. C₈²×C₅₉	C₂²	semidirect
129. M₁₆×C₅₉	M₁₆	semidirect
205. #17893	C₅₉	direct (N × H)
229. #2989	C₂×C₅₉	semidirect
230. #2975	C₂×C₅₉	semidirect
232. #1594	C₂×C₅₉	semidirect
233. #1592	C₂×C₅₉	semidirect
234. #1590	C₂×C₅₉	semidirect
235. #1589	C₂×C₅₉	semidirect
236. #1565	C₂×C₅₉	semidirect
237. #1476	C₂×C₅₉	semidirect
238. C₂×D₄⋊C₈	C₂×C₅₉	semidirect
239. C₈×M₁₆	C₂×C₅₉	semidirect
249. #446	C₂²×C₅₉	semidirect
258. #436	C₂²×C₅₉	semidirect
271. #335	C₂²×C₅₉	semidirect
272. #334	C₂²×C₅₉	semidirect
273. Q₈⋊C₈	C₂²×C₅₉	semidirect
274. Q₈⋊C₈	C₂²×C₅₉	semidirect
277. D₄⋊C₈	C₂²×C₅₉	semidirect
278. D₄⋊C₈	C₂²×C₅₉	semidirect
279. #322	C₂²×C₅₉	semidirect
280. C₈²	C₂²×C₅₉	semidirect
281. C₅₉	#17893	direct (N × H)
364. M₁₆	M₁₆×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2989	2
C₅₉×#2975	2
C₄×AGL(1,ℤ/8)×C₅₉	2
C₅₉×#1594	2
C₅₉×#1592	2
C₅₉×#1590	2
C₅₉×#1589	2
C₅₉×#1565	2
C₅₉×#1476	2
C₂×C₅₉×D₄⋊C₈	2
C₈×M₁₆×C₅₉	2
#17893	59

Subgroups — C59×#17893 #28430002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17893 #28430002