Subgroups — C₅₉×#17622 #28429731

Order 15104.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3505	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2973	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1519	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1513	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1512	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1509	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1504	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₉×#328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₉×#327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#553	—	2	2	no	—
13	C₅₉×#553	C₄	1	2	yes	complemented
14	C₅₉×#552	C₄	1	2	yes	complemented
15	C₅₉×#551	—	2	2	no	—
16	C₅₉×#548	C₄	1	2	yes	complemented
17	C₅₉×#546	C₄	1	2	yes	complemented
18	C₅₉×#539	—	2	1	no	—
19	C₅₉×#538	—	2	1	no	—
20	C₅₉×#534	—	2	1	no	—
21	C₅₉×#529	C₂²	1	2	yes	—
22	C₅₉×#525	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#518	—	2	1	no	—
26	C₂×C₄×D₄×C₅₉	—	2	1	no	—
27	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₅₉×#435	—	2	2	no	—
29	C₅₉×#435	—	2	2	no	—
30	C₅₉×#432	C₂²	1	2	yes	complemented
31	C₅₉×#407	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₅₉×#389	—	2	1	no	—
35	C₅₉×#385	—	2	1	no	—
36	C₅₉×#385	—	2	1	no	—
37	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
38	C₅₉×#380	C₂²	1	1	yes	characteristic
39	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic, complemented
43	C₅₉×#328	C₂²	1	2	yes	complemented
44	C₅₉×#328	C₂²	1	2	yes	complemented
45	C₅₉×#328	C₂²	1	2	yes	complemented
46	C₅₉×#328	C₂²	1	2	yes	complemented
47	C₅₉×#327	C₂²	1	2	yes	—
48	C₅₉×#327	C₂²	1	2	yes	—
49	C₅₉×#327	C₂²	1	2	yes	—
50	C₅₉×#327	C₂²	1	2	yes	—
51	C₂×#41×C₅₉	C₂×C₄	1	2	yes	complemented
52	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂²×D₄×C₅₉	—	2	1	no	—
54	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₅₉	—	2	1	no	—
57	C₂³×C₄×C₅₉	—	2	1	no	—
58	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₅₉	—	2	2	no	—
61	C₂²×C₈×C₅₉	—	2	1	no	—
62	C₂²×C₈×C₅₉	—	2	1	no	—
63	#126×C₅₉	—	2	2	no	—
64	#126×C₅₉	—	2	2	no	—
65	#126×C₅₉	—	2	2	no	—
66	#125×C₅₉	—	2	2	no	—
67	#125×C₅₉	C₂×C₄	1	2	yes	complemented
68	#124×C₅₉	—	2	2	no	—
69	#124×C₅₉	C₂×C₄	1	2	yes	complemented
70	#123×C₅₉	—	2	2	no	—
71	#123×C₅₉	—	2	2	no	—
72	#123×C₅₉	—	2	2	no	—
73	#123×C₅₉	—	2	2	no	—
74	#123×C₅₉	—	2	2	no	—
75	C₂²⋊Q₈×C₅₉	—	2	1	no	—
76	C₂²⋊Q₈×C₅₉	—	2	1	no	—
77	C₂²⋊Q₈×C₅₉	—	2	2	no	—
78	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	complemented
79	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	complemented
80	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
81	#121×C₅₉	—	2	2	no	—
82	#121×C₅₉	—	2	2	no	—
83	#121×C₅₉	—	2	1	no	—
84	#121×C₅₉	—	2	1	no	—
85	#121×C₅₉	—	2	2	no	—
86	#121×C₅₉	C₂×C₄	1	2	yes	complemented
87	#121×C₅₉	C₂×C₄	1	2	yes	complemented
88	#121×C₅₉	C₂³	1	2	yes	—
89	#120×C₅₉	—	2	2	no	—
90	#120×C₅₉	—	2	2	no	—
91	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	complemented
92	C₄×D₄×C₅₉	—	2	2	no	—
93	C₄×D₄×C₅₉	—	2	2	no	—
94	C₄×D₄×C₅₉	—	2	2	no	—
95	C₄×D₄×C₅₉	—	2	2	no	—
96	C₄×D₄×C₅₉	—	2	2	no	—
97	C₄×D₄×C₅₉	—	4	4	no	—
98	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
99	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
100	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	complemented
101	C₄×D₄×C₅₉	D₄	1	2	yes	—
102	C₄×D₄×C₅₉	D₄	1	2	yes	—
103	#117×C₅₉	—	2	2	no	—
104	#117×C₅₉	—	2	2	no	—
105	#117×C₅₉	C₂×C₄	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
112	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₅₉	—	2	1	no	—
122	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₅₉	—	2	2	no	—
124	C₂²⋊C₈×C₅₉	—	2	1	no	—
125	C₂²⋊C₈×C₅₉	—	2	1	no	—
126	C₂²⋊C₈×C₅₉	—	2	2	no	—
127	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
128	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
129	#97×C₅₉	—	2	2	no	—
130	#95×C₅₉	—	2	1	no	—
131	#95×C₅₉	—	2	1	no	—
132	#95×C₅₉	—	2	1	no	—
133	#95×C₅₉	C₂³	1	1	yes	characteristic
134	#95×C₅₉	C₂³	1	1	yes	characteristic
135	#95×C₅₉	C₂³	1	1	yes	characteristic
136	#95×C₅₉	C₂³	1	1	yes	characteristic
137	C₂⁴×C₅₉	—	2	1	no	—
138	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
140	#41×C₅₉	—	8	2	no	—
141	C₂×Q₈×C₅₉	—	2	1	no	—
142	C₂×Q₈×C₅₉	—	8	1	no	—
143	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
144	C₂×D₄×C₅₉	—	2	2	no	—
145	C₂×D₄×C₅₉	—	2	2	no	—
146	C₂×D₄×C₅₉	—	2	2	no	—
147	C₂×D₄×C₅₉	—	2	2	no	—
148	C₂×D₄×C₅₉	—	2	2	no	—
149	C₂×D₄×C₅₉	—	2	2	no	—
150	C₂×D₄×C₅₉	—	2	1	no	—
151	C₂×D₄×C₅₉	—	4	2	no	—
152	C₂×D₄×C₅₉	—	4	2	no	—
153	C₂×D₄×C₅₉	—	8	1	no	—
154	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
156	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₅₉	—	2	1	no	—
158	C₂²×C₄×C₅₉	—	2	1	no	—
159	C₂²×C₄×C₅₉	—	2	1	no	—
160	C₂²×C₄×C₅₉	—	2	1	no	—
161	C₂²×C₄×C₅₉	—	2	2	no	—
162	C₂²×C₄×C₅₉	—	2	2	no	—
163	C₂²×C₄×C₅₉	—	2	1	no	—
164	C₂²×C₄×C₅₉	—	2	1	no	—
165	C₂²×C₄×C₅₉	—	2	1	no	—
166	C₂²×C₄×C₅₉	—	4	2	no	—
167	C₂²×C₄×C₅₉	—	4	2	no	—
168	C₂²×C₄×C₅₉	—	4	2	no	—
169	C₂²×C₄×C₅₉	—	4	2	no	—
170	C₂²×C₄×C₅₉	—	8	1	no	—
171	C₂²×C₄×C₅₉	—	8	1	no	—
172	C₂²×C₄×C₅₉	—	8	1	no	—
173	C₂²×C₄×C₅₉	—	8	1	no	—
174	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
177	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
185	M₁₆×C₅₉	—	8	2	no	—
186	C₂×C₈×C₅₉	—	2	2	no	—
187	C₂×C₈×C₅₉	—	2	2	no	—
188	C₂×C₈×C₅₉	—	8	1	no	—
189	C₂×C₈×C₅₉	—	8	1	no	—
190	C₄⋊C₄×C₅₉	—	2	2	no	—
191	C₄⋊C₄×C₅₉	—	2	1	no	—
192	C₄⋊C₄×C₅₉	—	2	1	no	—
193	C₄⋊C₄×C₅₉	—	2	2	no	—
194	C₄⋊C₄×C₅₉	—	2	2	no	—
195	C₄⋊C₄×C₅₉	—	2	2	no	—
196	C₄⋊C₄×C₅₉	—	2	2	no	—
197	C₄⋊C₄×C₅₉	—	2	2	no	—
198	C₄⋊C₄×C₅₉	—	4	2	no	—
199	C₄⋊C₄×C₅₉	—	4	2	no	—
200	C₄⋊C₄×C₅₉	—	8	1	no	—
201	C₄⋊C₄×C₅₉	—	8	1	no	—
202	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
203	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
204	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
205	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
206	C₂²⋊C₄×C₅₉	—	2	2	no	—
207	C₂²⋊C₄×C₅₉	—	2	2	no	—
208	C₂²⋊C₄×C₅₉	—	2	2	no	—
209	C₂²⋊C₄×C₅₉	—	2	2	no	—
210	C₂²⋊C₄×C₅₉	—	2	2	no	—
211	C₂²⋊C₄×C₅₉	—	2	2	no	—
212	C₂²⋊C₄×C₅₉	—	2	2	no	—
213	C₂²⋊C₄×C₅₉	—	2	2	no	—
214	C₂²⋊C₄×C₅₉	—	2	2	no	—
215	C₂²⋊C₄×C₅₉	—	2	2	no	—
216	C₂²⋊C₄×C₅₉	—	4	2	no	—
217	C₂²⋊C₄×C₅₉	—	4	2	no	—
218	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
219	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
220	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
221	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
222	C₄²×C₅₉	—	2	2	no	—
223	C₄²×C₅₉	—	2	2	no	—
224	C₄²×C₅₉	—	4	2	no	—
225	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
226	C₄²×C₅₉	C₂×D₄	1	2	yes	—
227	C₂³×C₅₉	—	2	1	no	—
228	C₂³×C₅₉	—	2	1	no	—
229	C₂³×C₅₉	—	2	2	no	—
230	C₂³×C₅₉	—	4	1	no	—
231	C₂³×C₅₉	—	4	1	no	—
232	C₂³×C₅₉	—	4	1	no	—
233	C₂³×C₅₉	—	4	1	no	—
234	C₂³×C₅₉	—	4	2	no	—
235	C₂³×C₅₉	—	8	1	no	—
236	C₂³×C₅₉	—	8	1	no	—
237	C₂³×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂³×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
241	C₂³×C₅₉	#137	1	2	yes	—
242	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₅₉	—	4	2	no	—
244	Q₈×C₅₉	—	8	1	no	—
245	D₄×C₅₉	—	2	4	no	—
246	D₄×C₅₉	—	2	4	no	—
247	D₄×C₅₉	—	4	2	no	—
248	D₄×C₅₉	—	4	2	no	—
249	D₄×C₅₉	—	4	2	no	—
250	D₄×C₅₉	—	4	4	no	—
251	D₄×C₅₉	—	8	1	no	—
252	D₄×C₅₉	—	8	2	no	—
253	D₄×C₅₉	—	8	2	no	—
254	C₂×C₄×C₅₉	—	2	1	no	—
255	C₂×C₄×C₅₉	—	2	1	no	—
256	C₂×C₄×C₅₉	—	2	2	no	—
257	C₂×C₄×C₅₉	—	2	2	no	—
258	C₂×C₄×C₅₉	—	2	2	no	—
259	C₂×C₄×C₅₉	—	2	2	no	—
260	C₂×C₄×C₅₉	—	4	1	no	—
261	C₂×C₄×C₅₉	—	4	1	no	—
262	C₂×C₄×C₅₉	—	4	1	no	—
263	C₂×C₄×C₅₉	—	4	1	no	—
264	C₂×C₄×C₅₉	—	4	1	no	—
265	C₂×C₄×C₅₉	—	4	2	no	—
266	C₂×C₄×C₅₉	—	4	1	no	—
267	C₂×C₄×C₅₉	—	4	1	no	—
268	C₂×C₄×C₅₉	—	4	1	no	—
269	C₂×C₄×C₅₉	—	4	2	no	—
270	C₂×C₄×C₅₉	—	4	1	no	—
271	C₂×C₄×C₅₉	—	4	1	no	—
272	C₂×C₄×C₅₉	—	4	2	no	—
273	C₂×C₄×C₅₉	—	4	1	no	—
274	C₂×C₄×C₅₉	—	4	1	no	—
275	C₂×C₄×C₅₉	—	4	1	no	—
276	C₂×C₄×C₅₉	—	4	1	no	—
277	C₂×C₄×C₅₉	—	4	1	no	—
278	C₂×C₄×C₅₉	—	4	1	no	—
279	C₂×C₄×C₅₉	—	4	1	no	—
280	C₂×C₄×C₅₉	—	4	1	no	—
281	C₂×C₄×C₅₉	—	4	1	no	—
282	C₂×C₄×C₅₉	—	8	2	no	—
283	C₂×C₄×C₅₉	—	8	2	no	—
284	C₂×C₄×C₅₉	—	8	1	no	—
285	C₂×C₄×C₅₉	—	8	1	no	—
286	C₂×C₄×C₅₉	—	8	4	no	—
287	C₂×C₄×C₅₉	—	8	4	no	—
288	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
295	C₈×C₅₉	—	4	2	no	—
296	C₈×C₅₉	—	4	2	no	—
297	#17622	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂²×C₅₉	—	2	1	no	—
299	C₂²×C₅₉	—	2	1	no	—
300	C₂²×C₅₉	—	2	1	no	—
301	C₂²×C₅₉	—	2	1	no	—
302	C₂²×C₅₉	—	2	1	no	—
303	C₂²×C₅₉	—	2	1	no	—
304	C₂²×C₅₉	—	2	2	no	—
305	C₂²×C₅₉	—	2	2	no	—
306	C₂²×C₅₉	—	2	2	no	—
307	C₂²×C₅₉	—	4	2	no	—
308	C₂²×C₅₉	—	4	2	no	—
309	C₂²×C₅₉	—	4	2	no	—
310	C₂²×C₅₉	—	4	2	no	—
311	C₂²×C₅₉	—	4	2	no	—
312	C₂²×C₅₉	—	4	2	no	—
313	C₂²×C₅₉	—	4	2	no	—
314	C₂²×C₅₉	—	16	2	no	—
315	C₂²×C₅₉	#417	1	2	yes	—
316	C₂²×C₅₉	#417	1	2	yes	—
317	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
320	C₄×C₅₉	—	2	1	no	—
321	C₄×C₅₉	—	2	1	no	—
322	C₄×C₅₉	—	2	2	no	—
323	C₄×C₅₉	—	2	1	no	—
324	C₄×C₅₉	—	2	1	no	—
325	C₄×C₅₉	—	2	2	no	—
326	C₄×C₅₉	—	2	2	no	—
327	C₄×C₅₉	—	4	2	no	—
328	C₄×C₅₉	—	4	2	no	—
329	C₄×C₅₉	—	4	2	no	—
330	C₄×C₅₉	—	4	2	no	—
331	C₄×C₅₉	—	8	1	no	—
332	C₄×C₅₉	—	8	1	no	—
333	C₄×C₅₉	—	8	1	no	—
334	#3505	C₂×C₅₉	1	1	yes	characteristic
335	#2973	C₂×C₅₉	1	1	yes	characteristic, complemented
336	#2349	C₂×C₅₉	1	1	yes	characteristic, complemented
337	#1520	C₂×C₅₉	1	1	yes	characteristic, complemented
338	#1519	C₂×C₅₉	1	1	yes	characteristic, complemented
339	#1513	C₂×C₅₉	1	2	yes	complemented
340	#1512	C₂×C₅₉	1	2	yes	complemented
341	#1509	C₂×C₅₉	1	2	yes	complemented
342	#1504	C₂×C₅₉	1	2	yes	complemented
343	C₂×#328	C₂×C₅₉	1	1	yes	characteristic, complemented
344	C₂×#327	C₂×C₅₉	1	1	yes	characteristic, complemented
345	C₂×C₅₉	—	2	1	no	—
346	C₂×C₅₉	—	2	1	no	—
347	C₂×C₅₉	—	2	2	no	—
348	C₂×C₅₉	—	2	2	no	—
349	C₂×C₅₉	—	4	2	no	—
350	C₂×C₅₉	—	8	2	no	—
351	C₂×C₅₉	#2883	1	1	yes	characteristic
352	C₂×C₅₉	C₂×#417	1	1	yes	characteristic
353	C₂×C₅₉	#2901	1	1	yes	characteristic
354	#553	—	2	2	no	—
355	#553	C₄×C₅₉	1	2	yes	complemented
356	#552	C₄×C₅₉	1	2	yes	complemented
357	#551	—	2	2	no	—
358	#548	C₄×C₅₉	1	2	yes	complemented
359	#546	C₄×C₅₉	1	2	yes	complemented
360	#539	—	2	1	no	—
361	#538	—	2	1	no	—
362	#534	—	2	1	no	—
363	#529	C₂²×C₅₉	1	2	yes	—
364	#525	C₂²×C₅₉	1	2	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
366	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
367	#518	—	2	1	no	—
368	C₂×C₄×D₄	—	2	1	no	—
369	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
370	#435	—	2	2	no	—
371	#435	—	2	2	no	—
372	#432	C₂²×C₅₉	1	2	yes	complemented
373	#407	C₂²×C₅₉	1	2	yes	complemented
374	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
376	#389	—	2	1	no	—
377	#385	—	2	1	no	—
378	#385	—	2	1	no	—
379	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
380	#380	C₂²×C₅₉	1	1	yes	characteristic
381	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
382	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
383	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic
384	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic, complemented
385	#328	C₂²×C₅₉	1	2	yes	complemented
386	#328	C₂²×C₅₉	1	2	yes	complemented
387	#328	C₂²×C₅₉	1	2	yes	complemented
388	#328	C₂²×C₅₉	1	2	yes	complemented
389	#327	C₂²×C₅₉	1	2	yes	—
390	#327	C₂²×C₅₉	1	2	yes	—
391	#327	C₂²×C₅₉	1	2	yes	—
392	#327	C₂²×C₅₉	1	2	yes	—
393	C₅₉	#17622	1	1	yes	characteristic, direct product factor, Sylow
394	C₂×#41	C₂×C₄×C₅₉	1	2	yes	complemented
395	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
398	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
399	C₂³×C₄	—	2	1	no	—
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
403	C₂×M₁₆	—	2	2	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	—	2	1	no	—
406	#126	—	2	2	no	—
407	#126	—	2	2	no	—
408	#126	—	2	2	no	—
409	#125	—	2	2	no	—
410	#125	C₂×C₄×C₅₉	1	2	yes	complemented
411	#124	—	2	2	no	—
412	#124	C₂×C₄×C₅₉	1	2	yes	complemented
413	#123	—	2	2	no	—
414	#123	—	2	2	no	—
415	#123	—	2	2	no	—
416	#123	—	2	2	no	—
417	#123	—	2	2	no	—
418	C₂²⋊Q₈	—	2	1	no	—
419	C₂²⋊Q₈	—	2	1	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	complemented
422	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	complemented
423	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
424	#121	—	2	2	no	—
425	#121	—	2	2	no	—
426	#121	—	2	1	no	—
427	#121	—	2	1	no	—
428	#121	—	2	2	no	—
429	#121	C₂×C₄×C₅₉	1	2	yes	complemented
430	#121	C₂×C₄×C₅₉	1	2	yes	complemented
431	#121	C₂³×C₅₉	1	2	yes	—
432	#120	—	2	2	no	—
433	#120	—	2	2	no	—
434	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	complemented
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	4	4	no	—
441	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
442	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
443	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	complemented
444	C₄×D₄	D₄×C₅₉	1	2	yes	—
445	C₄×D₄	D₄×C₅₉	1	2	yes	—
446	#117	—	2	2	no	—
447	#117	—	2	2	no	—
448	#117	C₂×C₄×C₅₉	1	2	yes	complemented
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
456	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	2	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
466	C₄⋊C₈	—	2	2	no	—
467	C₂²⋊C₈	—	2	1	no	—
468	C₂²⋊C₈	—	2	1	no	—
469	C₂²⋊C₈	—	2	2	no	—
470	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
471	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
472	#97	—	2	2	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	C₂³×C₅₉	1	1	yes	characteristic
477	#95	C₂³×C₅₉	1	1	yes	characteristic
478	#95	C₂³×C₅₉	1	1	yes	characteristic
479	#95	C₂³×C₅₉	1	1	yes	characteristic
480	C₂⁴	—	2	1	no	—
481	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
482	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
483	#41	—	8	2	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	8	1	no	—
486	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	8	1	no	—
497	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
498	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
499	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	8	1	no	—
514	C₂²×C₄	—	8	1	no	—
515	C₂²×C₄	—	8	1	no	—
516	C₂²×C₄	—	8	1	no	—
517	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
520	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
528	M₁₆	—	8	2	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	—	2	2	no	—
531	C₂×C₈	—	8	1	no	—
532	C₂×C₈	—	8	1	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	8	1	no	—
544	C₄⋊C₄	—	8	1	no	—
545	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
546	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
547	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
548	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
562	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
563	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
564	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	4	2	no	—
568	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
569	C₄²	C₂×D₄×C₅₉	1	2	yes	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	8	1	no	—
579	C₂³	—	8	1	no	—
580	C₂³	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
581	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
582	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
583	C₂³	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
584	C₂³	#137×C₅₉	1	2	yes	—
585	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
586	Q₈	—	4	2	no	—
587	Q₈	—	8	1	no	—
588	D₄	—	2	4	no	—
589	D₄	—	2	4	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	4	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	8	1	no	—
595	D₄	—	8	2	no	—
596	D₄	—	8	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	8	2	no	—
626	C₂×C₄	—	8	2	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	8	1	no	—
629	C₂×C₄	—	8	4	no	—
630	C₂×C₄	—	8	4	no	—
631	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
632	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
633	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
634	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
635	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
637	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
638	C₈	—	4	2	no	—
639	C₈	—	4	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	16	2	no	—
657	C₂²	C₅₉×#417	1	2	yes	—
658	C₂²	C₅₉×#417	1	2	yes	—
659	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
660	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
661	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₂	—	2	1	no	—
677	C₂	—	2	1	no	—
678	C₂	—	2	2	no	—
679	C₂	—	2	2	no	—
680	C₂	—	4	2	no	—
681	C₂	—	8	2	no	—
682	C₂	C₅₉×#2883	1	1	yes	characteristic
683	C₂	C₂×C₅₉×#417	1	1	yes	characteristic
684	C₂	C₅₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2973	C₂	semidirect
3. C₅₉×#2349	C₂	semidirect
4. C₅₉×#1520	C₂	semidirect
5. C₅₉×#1519	C₂	semidirect
6. C₅₉×#1513	C₂	semidirect
7. C₅₉×#1512	C₂	semidirect
8. C₅₉×#1509	C₂	semidirect
9. C₅₉×#1504	C₂	semidirect
10. C₂×C₅₉×#328	C₂	semidirect
11. C₂×C₅₉×#327	C₂	semidirect
13. C₅₉×#553	C₄	semidirect
14. C₅₉×#552	C₄	semidirect
16. C₅₉×#548	C₄	semidirect
17. C₅₉×#546	C₄	semidirect
30. C₅₉×#432	C₂²	semidirect
31. C₅₉×#407	C₂²	semidirect
37. C₅₉×#382	C₂²	semidirect
39. C₅₉×#380	C₂²	semidirect
40. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
42. C₂×#95×C₅₉	C₂²	semidirect
43. C₅₉×#328	C₂²	semidirect
44. C₅₉×#328	C₂²	semidirect
45. C₅₉×#328	C₂²	semidirect
46. C₅₉×#328	C₂²	semidirect
51. C₂×#41×C₅₉	C₂×C₄	semidirect
52. C₂²×Q₈×C₅₉	C₂×C₄	semidirect
54. C₂²×D₄×C₅₉	C₂×C₄	semidirect
67. #125×C₅₉	C₂×C₄	semidirect
69. #124×C₅₉	C₂×C₄	semidirect
78. C₂²⋊Q₈×C₅₉	C₂×C₄	semidirect
79. C₂²⋊Q₈×C₅₉	C₂×C₄	semidirect
86. #121×C₅₉	C₂×C₄	semidirect
87. #121×C₅₉	C₂×C₄	semidirect
91. C₄×Q₈×C₅₉	C₂×C₄	semidirect
100. C₄×D₄×C₅₉	C₂×C₄	semidirect
105. #117×C₅₉	C₂×C₄	semidirect
111. C₂×C₄⋊C₄×C₅₉	C₂×C₄	semidirect
112. C₂×C₄⋊C₄×C₅₉	C₂×C₄	semidirect
297. #17622	C₅₉	direct (N × H)
335. #2973	C₂×C₅₉	semidirect
336. #2349	C₂×C₅₉	semidirect
337. #1520	C₂×C₅₉	semidirect
338. #1519	C₂×C₅₉	semidirect
339. #1513	C₂×C₅₉	semidirect
340. #1512	C₂×C₅₉	semidirect
341. #1509	C₂×C₅₉	semidirect
342. #1504	C₂×C₅₉	semidirect
343. C₂×#328	C₂×C₅₉	semidirect
344. C₂×#327	C₂×C₅₉	semidirect
355. #553	C₄×C₅₉	semidirect
356. #552	C₄×C₅₉	semidirect
358. #548	C₄×C₅₉	semidirect
359. #546	C₄×C₅₉	semidirect
372. #432	C₂²×C₅₉	semidirect
373. #407	C₂²×C₅₉	semidirect
379. #382	C₂²×C₅₉	semidirect
381. #380	C₂²×C₅₉	semidirect
382. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
384. C₂×#95	C₂²×C₅₉	semidirect
385. #328	C₂²×C₅₉	semidirect
386. #328	C₂²×C₅₉	semidirect
387. #328	C₂²×C₅₉	semidirect
388. #328	C₂²×C₅₉	semidirect
393. C₅₉	#17622	direct (N × H)
394. C₂×#41	C₂×C₄×C₅₉	semidirect
395. C₂²×Q₈	C₂×C₄×C₅₉	semidirect
397. C₂²×D₄	C₂×C₄×C₅₉	semidirect
410. #125	C₂×C₄×C₅₉	semidirect
412. #124	C₂×C₄×C₅₉	semidirect
421. C₂²⋊Q₈	C₂×C₄×C₅₉	semidirect
422. C₂²⋊Q₈	C₂×C₄×C₅₉	semidirect
429. #121	C₂×C₄×C₅₉	semidirect
430. #121	C₂×C₄×C₅₉	semidirect
434. C₄×Q₈	C₂×C₄×C₅₉	semidirect
443. C₄×D₄	C₂×C₄×C₅₉	semidirect
448. #117	C₂×C₄×C₅₉	semidirect
454. C₂×C₄⋊C₄	C₂×C₄×C₅₉	semidirect
455. C₂×C₄⋊C₄	C₂×C₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3505	2
C₅₉×#2973	2
C₅₉×#2349	2
C₅₉×#1520	2
C₅₉×#1519	2
C₅₉×#1513	2
C₅₉×#1512	2
C₅₉×#1509	2
C₅₉×#1504	2
C₂×C₅₉×#328	2
C₂×C₅₉×#327	2
#17622	59

Subgroups — C59×#17622 #28429731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17622 #28429731