Subgroups — C₅₉×#17511 #28429620

Order 15104.

1216 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1496	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1490	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1484	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1478	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₉	—	2	1	no	—
13	C₅₉×#550	C₄	1	1	yes	characteristic
14	D₄×Q₈×C₅₉	C₄	1	1	yes	characteristic
15	C₅₉×#548	—	2	1	no	—
16	C₅₉×#547	C₄	1	2	yes	—
17	C₅₉×#547	C₄	1	1	yes	characteristic
18	C₅₉×#546	—	2	2	no	—
19	C₅₉×#546	—	2	1	no	—
20	D₄²×C₅₉	C₄	1	1	yes	characteristic
21	D₄²×C₅₉	C₄	1	2	yes	—
22	C₅₉×#532	C₂²	1	1	yes	characteristic
23	C₅₉×#532	C₂²	1	2	yes	—
24	C₅₉×#525	—	2	1	no	—
25	C₅₉×#525	—	2	2	no	—
26	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
29	C₅₉×#446	—	2	1	no	—
30	C₅₉×#436	—	2	1	no	—
31	C₅₉×#435	—	2	2	no	—
32	C₅₉×#433	—	2	2	no	—
33	C₅₉×#432	C₂²	1	2	yes	complemented
34	C₅₉×#431	C₂²	1	2	yes	complemented
35	C₅₉×#431	C₂²	1	2	yes	complemented
36	C₅₉×#431	C₂²	1	1	yes	characteristic, complemented
37	C₅₉×#423	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#408	—	2	1	no	—
40	C₅₉×#405	—	2	1	no	—
41	C₄×M₁₆×C₅₉	C₂²	1	2	yes	complemented
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
43	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
46	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₅₉×D₄⋊C₈	C₂²	1	2	yes	complemented
49	C₅₉×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₅₉×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₅₉×D₄⋊C₈	C₂²	1	2	yes	complemented
52	C₅₉×D₄⋊C₈	C₂²	1	2	yes	complemented
53	C₂×#41×C₅₉	—	2	1	no	—
54	C₂×#41×C₅₉	—	2	1	no	—
55	C₂×#41×C₅₉	—	2	2	no	—
56	C₂×#41×C₅₉	—	2	2	no	—
57	C₂×#41×C₅₉	—	2	1	no	—
58	C₂×#41×C₅₉	—	4	4	no	—
59	C₂×#41×C₅₉	—	4	4	no	—
60	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₅₉	—	2	1	no	—
62	C₂²×D₄×C₅₉	—	2	2	no	—
63	C₂²×D₄×C₅₉	—	2	1	no	—
64	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₅₉	C₂×C₄	1	2	yes	—
66	C₂³×C₄×C₅₉	—	2	2	no	—
67	C₂³×C₄×C₅₉	—	2	1	no	—
68	C₂×M₁₆×C₅₉	—	2	2	no	—
69	C₂×M₁₆×C₅₉	—	2	1	no	—
70	C₂²×C₈×C₅₉	—	2	1	no	—
71	C₂²×C₈×C₅₉	—	2	1	no	—
72	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
74	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
75	#127×C₅₉	C₂×C₄	1	2	yes	—
76	#124×C₅₉	—	2	1	no	—
77	#124×C₅₉	—	2	2	no	—
78	#123×C₅₉	—	2	2	no	—
79	#123×C₅₉	—	2	2	no	—
80	#123×C₅₉	—	2	2	no	—
81	C₂²⋊Q₈×C₅₉	—	2	2	no	—
82	C₂²⋊Q₈×C₅₉	—	2	1	no	—
83	C₂²⋊Q₈×C₅₉	—	2	2	no	—
84	C₂²⋊Q₈×C₅₉	—	2	1	no	—
85	#121×C₅₉	—	2	1	no	—
86	#121×C₅₉	—	2	2	no	—
87	#121×C₅₉	—	2	2	no	—
88	#121×C₅₉	—	2	1	no	—
89	#121×C₅₉	—	2	2	no	—
90	#121×C₅₉	—	2	1	no	—
91	#121×C₅₉	C₂×C₄	1	2	yes	—
92	#121×C₅₉	C₂×C₄	1	2	yes	—
93	#121×C₅₉	C₂×C₄	1	2	yes	—
94	#120×C₅₉	—	2	2	no	—
95	#120×C₅₉	—	2	2	no	—
96	#120×C₅₉	—	2	2	no	—
97	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
98	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
99	C₄×D₄×C₅₉	—	2	2	no	—
100	C₄×D₄×C₅₉	—	2	1	no	—
101	C₄×D₄×C₅₉	—	2	1	no	—
102	C₄×D₄×C₅₉	—	2	2	no	—
103	C₄×D₄×C₅₉	—	2	2	no	—
104	C₄×D₄×C₅₉	—	2	1	no	—
105	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
109	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
111	C₄×D₄×C₅₉	D₄	1	2	yes	—
112	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
113	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₅₉	C₂³	1	2	yes	—
116	#117×C₅₉	D₄	1	1	yes	characteristic
117	#117×C₅₉	D₄	1	2	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
120	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
122	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
124	C₄⋊C₈×C₅₉	—	2	1	no	—
125	C₄⋊C₈×C₅₉	—	2	1	no	—
126	C₄⋊C₈×C₅₉	—	2	2	no	—
127	C₄⋊C₈×C₅₉	—	2	1	no	—
128	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
131	C₂²⋊C₈×C₅₉	—	2	2	no	—
132	C₂²⋊C₈×C₅₉	—	2	2	no	—
133	C₂²⋊C₈×C₅₉	—	2	1	no	—
134	C₂²⋊C₈×C₅₉	—	2	2	no	—
135	#97×C₅₉	—	2	2	no	—
136	#97×C₅₉	—	2	2	no	—
137	C₄×C₈×C₅₉	—	2	1	no	—
138	C₄×C₈×C₅₉	—	2	2	no	—
139	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₅₉	C₂³	1	2	yes	—
142	C₂⁴×C₅₉	—	2	2	no	—
143	C₂⁴×C₅₉	—	2	1	no	—
144	#41×C₅₉	—	2	2	no	—
145	#41×C₅₉	—	2	2	no	—
146	#41×C₅₉	—	4	4	no	—
147	#41×C₅₉	—	4	4	no	—
148	#41×C₅₉	—	4	8	no	—
149	#41×C₅₉	—	4	4	no	—
150	#41×C₅₉	—	4	4	no	—
151	#41×C₅₉	—	4	2	no	—
152	#41×C₅₉	—	4	2	no	—
153	C₂×Q₈×C₅₉	—	2	2	no	—
154	C₂×Q₈×C₅₉	—	2	1	no	—
155	C₂×Q₈×C₅₉	—	4	4	no	—
156	C₂×Q₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×D₄×C₅₉	—	2	2	no	—
158	C₂×D₄×C₅₉	—	2	4	no	—
159	C₂×D₄×C₅₉	—	2	2	no	—
160	C₂×D₄×C₅₉	—	2	2	no	—
161	C₂×D₄×C₅₉	—	2	2	no	—
162	C₂×D₄×C₅₉	—	2	1	no	—
163	C₂×D₄×C₅₉	—	2	2	no	—
164	C₂×D₄×C₅₉	—	2	2	no	—
165	C₂×D₄×C₅₉	—	2	1	no	—
166	C₂×D₄×C₅₉	—	2	2	no	—
167	C₂×D₄×C₅₉	—	2	1	no	—
168	C₂×D₄×C₅₉	—	4	1	no	—
169	C₂×D₄×C₅₉	—	4	2	no	—
170	C₂×D₄×C₅₉	—	4	8	no	—
171	C₂×D₄×C₅₉	—	4	4	no	—
172	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
173	C₂×D₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
176	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅₉	—	2	2	no	—
178	C₂²×C₄×C₅₉	—	2	1	no	—
179	C₂²×C₄×C₅₉	—	2	2	no	—
180	C₂²×C₄×C₅₉	—	2	1	no	—
181	C₂²×C₄×C₅₉	—	2	2	no	—
182	C₂²×C₄×C₅₉	—	2	1	no	—
183	C₂²×C₄×C₅₉	—	2	1	no	—
184	C₂²×C₄×C₅₉	—	2	2	no	—
185	C₂²×C₄×C₅₉	—	2	1	no	—
186	C₂²×C₄×C₅₉	—	4	4	no	—
187	C₂²×C₄×C₅₉	—	4	4	no	—
188	C₂²×C₄×C₅₉	—	4	2	no	—
189	C₂²×C₄×C₅₉	—	4	2	no	—
190	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
196	M₁₆×C₅₉	—	4	4	no	—
197	M₁₆×C₅₉	—	4	2	no	—
198	C₂×C₈×C₅₉	—	2	1	no	—
199	C₂×C₈×C₅₉	—	2	1	no	—
200	C₂×C₈×C₅₉	—	2	2	no	—
201	C₂×C₈×C₅₉	—	2	1	no	—
202	C₂×C₈×C₅₉	—	2	2	no	—
203	C₂×C₈×C₅₉	—	2	1	no	—
204	C₂×C₈×C₅₉	—	4	2	no	—
205	C₂×C₈×C₅₉	—	4	2	no	—
206	C₄⋊C₄×C₅₉	—	2	1	no	—
207	C₄⋊C₄×C₅₉	—	2	2	no	—
208	C₄⋊C₄×C₅₉	—	2	2	no	—
209	C₄⋊C₄×C₅₉	—	2	1	no	—
210	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
211	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
212	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
213	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
214	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
215	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
216	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
217	C₂²⋊C₄×C₅₉	—	2	2	no	—
218	C₂²⋊C₄×C₅₉	—	2	1	no	—
219	C₂²⋊C₄×C₅₉	—	2	2	no	—
220	C₂²⋊C₄×C₅₉	—	2	1	no	—
221	C₂²⋊C₄×C₅₉	—	2	2	no	—
222	C₂²⋊C₄×C₅₉	—	2	2	no	—
223	C₂²⋊C₄×C₅₉	—	2	2	no	—
224	C₂²⋊C₄×C₅₉	—	2	1	no	—
225	C₂²⋊C₄×C₅₉	—	2	1	no	—
226	C₂²⋊C₄×C₅₉	—	2	2	no	—
227	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
228	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
229	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
230	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
231	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
232	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₅₉	C₂×D₄	1	2	yes	—
234	C₄²×C₅₉	C₂×D₄	1	2	yes	—
235	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
237	C₂³×C₅₉	—	2	1	no	—
238	C₂³×C₅₉	—	2	2	no	—
239	C₂³×C₅₉	—	2	1	no	—
240	C₂³×C₅₉	—	4	2	no	—
241	C₂³×C₅₉	—	4	4	no	—
242	C₂³×C₅₉	—	4	4	no	—
243	C₂³×C₅₉	—	4	2	no	—
244	C₂³×C₅₉	—	8	1	no	—
245	C₂³×C₅₉	—	8	2	no	—
246	C₂³×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	Q₈×C₅₉	—	2	2	no	—
249	Q₈×C₅₉	—	4	4	no	—
250	Q₈×C₅₉	—	4	2	no	—
251	D₄×C₅₉	—	2	4	no	—
252	D₄×C₅₉	—	2	1	no	—
253	D₄×C₅₉	—	2	2	no	—
254	D₄×C₅₉	—	2	1	no	—
255	D₄×C₅₉	—	2	1	no	—
256	D₄×C₅₉	—	2	2	no	—
257	D₄×C₅₉	—	2	2	no	—
258	D₄×C₅₉	—	4	2	no	—
259	D₄×C₅₉	—	4	4	no	—
260	D₄×C₅₉	—	4	4	no	—
261	D₄×C₅₉	—	4	4	no	—
262	D₄×C₅₉	—	4	4	no	—
263	D₄×C₅₉	—	4	4	no	—
264	D₄×C₅₉	—	4	2	no	—
265	D₄×C₅₉	—	8	1	no	—
266	D₄×C₅₉	—	8	2	no	—
267	D₄×C₅₉	#131	1	2	yes	—
268	C₂×C₄×C₅₉	—	2	1	no	—
269	C₂×C₄×C₅₉	—	2	2	no	—
270	C₂×C₄×C₅₉	—	2	1	no	—
271	C₂×C₄×C₅₉	—	2	2	no	—
272	C₂×C₄×C₅₉	—	2	2	no	—
273	C₂×C₄×C₅₉	—	2	2	no	—
274	C₂×C₄×C₅₉	—	2	1	no	—
275	C₂×C₄×C₅₉	—	2	2	no	—
276	C₂×C₄×C₅₉	—	2	1	no	—
277	C₂×C₄×C₅₉	—	4	1	no	—
278	C₂×C₄×C₅₉	—	4	2	no	—
279	C₂×C₄×C₅₉	—	4	4	no	—
280	C₂×C₄×C₅₉	—	4	4	no	—
281	C₂×C₄×C₅₉	—	4	4	no	—
282	C₂×C₄×C₅₉	—	4	2	no	—
283	C₂×C₄×C₅₉	—	4	1	no	—
284	C₂×C₄×C₅₉	—	4	1	no	—
285	C₂×C₄×C₅₉	—	4	2	no	—
286	C₂×C₄×C₅₉	—	4	2	no	—
287	C₂×C₄×C₅₉	—	4	1	no	—
288	C₂×C₄×C₅₉	—	4	1	no	—
289	C₂×C₄×C₅₉	—	4	2	no	—
290	C₂×C₄×C₅₉	—	4	2	no	—
291	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
298	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
299	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
302	C₈×C₅₉	—	2	2	no	—
303	C₈×C₅₉	—	4	1	no	—
304	C₈×C₅₉	—	4	2	no	—
305	C₈×C₅₉	—	4	1	no	—
306	C₈×C₅₉	—	4	1	no	—
307	C₈×C₅₉	—	4	2	no	—
308	#17511	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂²×C₅₉	—	2	1	no	—
310	C₂²×C₅₉	—	2	1	no	—
311	C₂²×C₅₉	—	2	2	no	—
312	C₂²×C₅₉	—	2	2	no	—
313	C₂²×C₅₉	—	2	2	no	—
314	C₂²×C₅₉	—	2	2	no	—
315	C₂²×C₅₉	—	4	1	no	—
316	C₂²×C₅₉	—	4	1	no	—
317	C₂²×C₅₉	—	4	1	no	—
318	C₂²×C₅₉	—	4	2	no	—
319	C₂²×C₅₉	—	4	2	no	—
320	C₂²×C₅₉	—	4	1	no	—
321	C₂²×C₅₉	—	4	1	no	—
322	C₂²×C₅₉	—	4	2	no	—
323	C₂²×C₅₉	—	8	4	no	—
324	C₂²×C₅₉	—	8	8	no	—
325	C₂²×C₅₉	#418	1	2	yes	—
326	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
327	C₄×C₅₉	—	2	1	no	—
328	C₄×C₅₉	—	2	2	no	—
329	C₄×C₅₉	—	2	2	no	—
330	C₄×C₅₉	—	2	1	no	—
331	C₄×C₅₉	—	2	1	no	—
332	C₄×C₅₉	—	2	2	no	—
333	C₄×C₅₉	—	4	1	no	—
334	C₄×C₅₉	—	4	2	no	—
335	C₄×C₅₉	—	4	1	no	—
336	C₄×C₅₉	#418	1	2	yes	—
337	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
338	C₄×C₅₉	#568	1	1	yes	characteristic
339	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
341	D₄×#41	C₂×C₅₉	1	1	yes	characteristic
342	#2965	C₂×C₅₉	1	1	yes	characteristic, complemented
343	#2925	C₂×C₅₉	1	1	yes	characteristic, complemented
344	#1496	C₂×C₅₉	1	2	yes	complemented
345	#1492	C₂×C₅₉	1	1	yes	characteristic, complemented
346	#1490	C₂×C₅₉	1	2	yes	complemented
347	#1486	C₂×C₅₉	1	1	yes	characteristic, complemented
348	#1484	C₂×C₅₉	1	2	yes	complemented
349	#1480	C₂×C₅₉	1	1	yes	characteristic, complemented
350	#1478	C₂×C₅₉	1	2	yes	complemented
351	C₂×D₄⋊C₈	C₂×C₅₉	1	1	yes	characteristic, complemented
352	C₂×C₅₉	—	2	2	no	—
353	C₂×C₅₉	—	4	2	no	—
354	C₂×C₅₉	—	4	2	no	—
355	C₂×C₅₉	—	8	1	no	—
356	C₂×C₅₉	—	8	2	no	—
357	C₂×C₅₉	#2880	1	1	yes	characteristic
358	C₂×C₅₉	C₂×#418	1	1	yes	characteristic
359	C₂×C₅₉	#2901	1	1	yes	characteristic
360	C₂²×#41	—	2	1	no	—
361	#550	C₄×C₅₉	1	1	yes	characteristic
362	D₄×Q₈	C₄×C₅₉	1	1	yes	characteristic
363	#548	—	2	1	no	—
364	#547	C₄×C₅₉	1	2	yes	—
365	#547	C₄×C₅₉	1	1	yes	characteristic
366	#546	—	2	2	no	—
367	#546	—	2	1	no	—
368	D₄²	C₄×C₅₉	1	1	yes	characteristic
369	D₄²	C₄×C₅₉	1	2	yes	—
370	#532	C₂²×C₅₉	1	1	yes	characteristic
371	#532	C₂²×C₅₉	1	2	yes	—
372	#525	—	2	1	no	—
373	#525	—	2	2	no	—
374	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
375	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
376	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
377	#446	—	2	1	no	—
378	#436	—	2	1	no	—
379	#435	—	2	2	no	—
380	#433	—	2	2	no	—
381	#432	C₂²×C₅₉	1	2	yes	complemented
382	#431	C₂²×C₅₉	1	2	yes	complemented
383	#431	C₂²×C₅₉	1	2	yes	complemented
384	#431	C₂²×C₅₉	1	1	yes	characteristic, complemented
385	#423	C₂²×C₅₉	1	1	yes	characteristic, complemented
386	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
387	#408	—	2	1	no	—
388	#405	—	2	1	no	—
389	C₄×M₁₆	C₂²×C₅₉	1	2	yes	complemented
390	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
391	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
392	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
393	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
394	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
395	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
396	D₄⋊C₈	C₂²×C₅₉	1	2	yes	complemented
397	D₄⋊C₈	C₂²×C₅₉	1	2	yes	complemented
398	D₄⋊C₈	C₂²×C₅₉	1	2	yes	complemented
399	D₄⋊C₈	C₂²×C₅₉	1	2	yes	complemented
400	D₄⋊C₈	C₂²×C₅₉	1	2	yes	complemented
401	C₅₉	#17511	1	1	yes	characteristic, direct product factor, Sylow
402	C₂×#41	—	2	1	no	—
403	C₂×#41	—	2	1	no	—
404	C₂×#41	—	2	2	no	—
405	C₂×#41	—	2	2	no	—
406	C₂×#41	—	2	1	no	—
407	C₂×#41	—	4	4	no	—
408	C₂×#41	—	4	4	no	—
409	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
410	C₂²×Q₈	—	2	1	no	—
411	C₂²×D₄	—	2	2	no	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
414	C₂²×D₄	C₂×C₄×C₅₉	1	2	yes	—
415	C₂³×C₄	—	2	2	no	—
416	C₂³×C₄	—	2	1	no	—
417	C₂×M₁₆	—	2	2	no	—
418	C₂×M₁₆	—	2	1	no	—
419	C₂²×C₈	—	2	1	no	—
420	C₂²×C₈	—	2	1	no	—
421	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
422	C₄⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
423	#127	C₂×C₄×C₅₉	1	1	yes	characteristic
424	#127	C₂×C₄×C₅₉	1	2	yes	—
425	#124	—	2	1	no	—
426	#124	—	2	2	no	—
427	#123	—	2	2	no	—
428	#123	—	2	2	no	—
429	#123	—	2	2	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	1	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	1	no	—
434	#121	—	2	1	no	—
435	#121	—	2	2	no	—
436	#121	—	2	2	no	—
437	#121	—	2	1	no	—
438	#121	—	2	2	no	—
439	#121	—	2	1	no	—
440	#121	C₂×C₄×C₅₉	1	2	yes	—
441	#121	C₂×C₄×C₅₉	1	2	yes	—
442	#121	C₂×C₄×C₅₉	1	2	yes	—
443	#120	—	2	2	no	—
444	#120	—	2	2	no	—
445	#120	—	2	2	no	—
446	C₄×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
447	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
455	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
456	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
457	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
458	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
459	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
460	C₄×D₄	D₄×C₅₉	1	2	yes	—
461	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
462	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
463	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
464	C₄×D₄	C₂³×C₅₉	1	2	yes	—
465	#117	D₄×C₅₉	1	1	yes	characteristic
466	#117	D₄×C₅₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	2	no	—
471	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
473	C₄⋊C₈	—	2	1	no	—
474	C₄⋊C₈	—	2	1	no	—
475	C₄⋊C₈	—	2	2	no	—
476	C₄⋊C₈	—	2	1	no	—
477	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
478	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
479	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
480	C₂²⋊C₈	—	2	2	no	—
481	C₂²⋊C₈	—	2	2	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	2	no	—
484	#97	—	2	2	no	—
485	#97	—	2	2	no	—
486	C₄×C₈	—	2	1	no	—
487	C₄×C₈	—	2	2	no	—
488	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
489	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
490	C₄×C₈	C₂³×C₅₉	1	2	yes	—
491	C₂⁴	—	2	2	no	—
492	C₂⁴	—	2	1	no	—
493	#41	—	2	2	no	—
494	#41	—	2	2	no	—
495	#41	—	4	4	no	—
496	#41	—	4	4	no	—
497	#41	—	4	8	no	—
498	#41	—	4	4	no	—
499	#41	—	4	4	no	—
500	#41	—	4	2	no	—
501	#41	—	4	2	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	4	4	no	—
505	C₂×Q₈	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	4	8	no	—
520	C₂×D₄	—	4	4	no	—
521	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
522	C₂×D₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
523	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
524	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
525	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
540	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
542	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
544	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
545	M₁₆	—	4	4	no	—
546	M₁₆	—	4	2	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	4	2	no	—
554	C₂×C₈	—	4	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
560	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
561	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
562	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
563	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
564	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
565	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
577	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
578	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
579	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
580	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
581	C₄²	C₂×D₄×C₅₉	1	2	yes	—
582	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
583	C₄²	C₂×D₄×C₅₉	1	2	yes	—
584	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
585	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
586	C₂³	—	2	1	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	4	4	no	—
591	C₂³	—	4	4	no	—
592	C₂³	—	4	2	no	—
593	C₂³	—	8	1	no	—
594	C₂³	—	8	2	no	—
595	C₂³	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
596	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	4	4	no	—
599	Q₈	—	4	2	no	—
600	D₄	—	2	4	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	1	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	1	no	—
605	D₄	—	2	1	no	—
606	D₄	—	2	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	4	no	—
609	D₄	—	4	4	no	—
610	D₄	—	4	4	no	—
611	D₄	—	4	4	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	2	no	—
614	D₄	—	8	1	no	—
615	D₄	—	8	2	no	—
616	D₄	#131×C₅₉	1	2	yes	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
641	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
642	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
643	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
644	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
645	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
646	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
647	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
648	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
649	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
650	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
651	C₈	—	2	2	no	—
652	C₈	—	4	1	no	—
653	C₈	—	4	2	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₈	—	4	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	8	4	no	—
672	C₂²	—	8	8	no	—
673	C₂²	C₅₉×#418	1	2	yes	—
674	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
675	C₄	—	2	1	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	1	no	—
684	C₄	C₅₉×#418	1	2	yes	—
685	C₄	C₂×#131×C₅₉	1	1	yes	characteristic
686	C₄	C₅₉×#568	1	1	yes	characteristic
687	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
688	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
689	C₂	—	2	2	no	—
690	C₂	—	4	2	no	—
691	C₂	—	4	2	no	—
692	C₂	—	8	1	no	—
693	C₂	—	8	2	no	—
694	C₂	C₅₉×#2880	1	1	yes	characteristic
695	C₂	C₂×C₅₉×#418	1	1	yes	characteristic
696	C₂	C₅₉×#2901	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	C₂²×C₂²⋊C₄
prime radical	D₄×#41×C₅₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₄×#41×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2965	C₂	semidirect
3. C₅₉×#2925	C₂	semidirect
4. C₅₉×#1496	C₂	semidirect
5. C₅₉×#1492	C₂	semidirect
6. C₅₉×#1490	C₂	semidirect
7. C₅₉×#1486	C₂	semidirect
8. C₅₉×#1484	C₂	semidirect
9. C₅₉×#1480	C₂	semidirect
10. C₅₉×#1478	C₂	semidirect
11. C₂×C₅₉×D₄⋊C₈	C₂	semidirect
33. C₅₉×#432	C₂²	semidirect
34. C₅₉×#431	C₂²	semidirect
35. C₅₉×#431	C₂²	semidirect
36. C₅₉×#431	C₂²	semidirect
37. C₅₉×#423	C₂²	semidirect
38. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
41. C₄×M₁₆×C₅₉	C₂²	semidirect
42. C₂×C₄×C₈×C₅₉	C₂²	semidirect
46. C₅₉×D₄⋊C₈	C₂²	semidirect
47. C₅₉×D₄⋊C₈	C₂²	semidirect
48. C₅₉×D₄⋊C₈	C₂²	semidirect
49. C₅₉×D₄⋊C₈	C₂²	semidirect
50. C₅₉×D₄⋊C₈	C₂²	semidirect
51. C₅₉×D₄⋊C₈	C₂²	semidirect
52. C₅₉×D₄⋊C₈	C₂²	semidirect
308. #17511	C₅₉	direct (N × H)
342. #2965	C₂×C₅₉	semidirect
343. #2925	C₂×C₅₉	semidirect
344. #1496	C₂×C₅₉	semidirect
345. #1492	C₂×C₅₉	semidirect
346. #1490	C₂×C₅₉	semidirect
347. #1486	C₂×C₅₉	semidirect
348. #1484	C₂×C₅₉	semidirect
349. #1480	C₂×C₅₉	semidirect
350. #1478	C₂×C₅₉	semidirect
351. C₂×D₄⋊C₈	C₂×C₅₉	semidirect
381. #432	C₂²×C₅₉	semidirect
382. #431	C₂²×C₅₉	semidirect
383. #431	C₂²×C₅₉	semidirect
384. #431	C₂²×C₅₉	semidirect
385. #423	C₂²×C₅₉	semidirect
386. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
389. C₄×M₁₆	C₂²×C₅₉	semidirect
390. C₂×C₄×C₈	C₂²×C₅₉	semidirect
394. D₄⋊C₈	C₂²×C₅₉	semidirect
395. D₄⋊C₈	C₂²×C₅₉	semidirect
396. D₄⋊C₈	C₂²×C₅₉	semidirect
397. D₄⋊C₈	C₂²×C₅₉	semidirect
398. D₄⋊C₈	C₂²×C₅₉	semidirect
399. D₄⋊C₈	C₂²×C₅₉	semidirect
400. D₄⋊C₈	C₂²×C₅₉	semidirect
401. C₅₉	#17511	direct (N × H)

Maximal subgroups

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

subgroup	index
D₄×#41×C₅₉	2
C₅₉×#2965	2
C₅₉×#2925	2
C₅₉×#1496	2
C₅₉×#1492	2
C₅₉×#1490	2
C₅₉×#1486	2
C₅₉×#1484	2
C₅₉×#1480	2
C₅₉×#1478	2
C₂×C₅₉×D₄⋊C₈	2
#17511	59

Subgroups — C59×#17511 #28429620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17511 #28429620