Subgroups — C₅₉×#24836 #28436945

Order 15104.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2088	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2065	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1893	C₂	1	2	yes	maximal
10	C₅₉×#1807	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₅₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
15	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₅₉	—	2	1	no	—
17	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
19	C₅₉×#476	—	2	4	no	—
20	C₂×#106×C₅₉	C₂²	1	2	yes	—
21	C₂×#106×C₅₉	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₅₉	—	2	4	no	—
23	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#102×C₅₉	C₂²	1	2	yes	—
27	C₂×#102×C₅₉	C₂²	1	2	yes	—
28	C₅₉×#391	—	2	1	no	—
29	C₅₉×#390	C₂²	1	1	yes	characteristic
30	C₅₉×#389	—	2	1	no	—
31	C₅₉×#389	C₂²	1	1	yes	characteristic
32	C₅₉×#389	C₂²	1	2	yes	—
33	C₅₉×#388	—	2	1	no	—
34	C₅₉×#386	—	2	1	no	—
35	C₅₉×#384	C₂²	1	1	yes	characteristic
36	C₅₉×#380	—	2	1	no	—
37	C₅₉×#380	C₂²	1	1	yes	characteristic
38	C₅₉×#380	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
41	C₅₉×#340	C₂²	1	2	yes	—
42	C₅₉×#340	C₂²	1	2	yes	—
43	C₅₉×#340	C₂²	1	2	yes	—
44	C₅₉×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₅₉	—	2	1	no	—
46	C₂²×D₄×C₅₉	—	2	1	no	—
47	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₅₉	—	2	1	no	—
49	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₅₉	—	2	4	no	—
53	C₂²×C₈×C₅₉	—	2	4	no	—
54	C₂²×C₈×C₅₉	—	4	2	no	—
55	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₅₉	—	2	2	no	—
58	C₄⋊Q₈×C₅₉	—	2	2	no	—
59	C₂²⋊Q₈×C₅₉	—	4	4	no	—
60	#121×C₅₉	—	2	2	no	—
61	#121×C₅₉	Q₈	1	4	yes	complemented
62	C₄×D₄×C₅₉	—	2	2	no	—
63	C₄×D₄×C₅₉	—	2	2	no	—
64	C₄×D₄×C₅₉	—	4	4	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
81	C₂×C₄²×C₅₉	—	2	2	no	—
82	C₂×C₄²×C₅₉	—	2	2	no	—
83	C₂×C₄²×C₅₉	—	2	1	no	—
84	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
88	#106×C₅₉	—	2	4	no	—
89	#106×C₅₉	—	4	2	no	—
90	C₄⋊C₈×C₅₉	—	2	4	no	—
91	C₄⋊C₈×C₅₉	—	2	2	no	—
92	C₄⋊C₈×C₅₉	D₄	1	4	yes	complemented
93	#102×C₅₉	—	2	4	no	—
94	#102×C₅₉	—	4	2	no	—
95	#95×C₅₉	—	2	1	no	—
96	#95×C₅₉	—	2	1	no	—
97	#95×C₅₉	—	2	1	no	—
98	#95×C₅₉	—	2	2	no	—
99	#95×C₅₉	—	2	2	no	—
100	C₂⁴×C₅₉	—	2	1	no	—
101	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₅₉	—	4	2	no	—
103	C₂×Q₈×C₅₉	—	4	2	no	—
104	C₂×Q₈×C₅₉	—	4	2	no	—
105	C₂×D₄×C₅₉	—	2	4	no	—
106	C₂×D₄×C₅₉	—	2	1	no	—
107	C₂×D₄×C₅₉	—	2	1	no	—
108	C₂×D₄×C₅₉	—	2	1	no	—
109	C₂×D₄×C₅₉	—	2	1	no	—
110	C₂×D₄×C₅₉	—	2	1	no	—
111	C₂×D₄×C₅₉	—	4	2	no	—
112	C₂×D₄×C₅₉	—	4	2	no	—
113	C₂×D₄×C₅₉	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₅₉	—	2	2	no	—
115	C₂²×C₄×C₅₉	—	2	2	no	—
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	1	no	—
118	C₂²×C₄×C₅₉	—	2	1	no	—
119	C₂²×C₄×C₅₉	—	2	1	no	—
120	C₂²×C₄×C₅₉	—	2	2	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	2	no	—
123	C₂²×C₄×C₅₉	—	2	1	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	—	2	2	no	—
126	C₂²×C₄×C₅₉	—	2	2	no	—
127	C₂²×C₄×C₅₉	—	4	1	no	—
128	C₂²×C₄×C₅₉	—	4	2	no	—
129	C₂²×C₄×C₅₉	—	4	2	no	—
130	C₂²×C₄×C₅₉	—	4	2	no	—
131	C₂²×C₄×C₅₉	SD₁₆	1	4	yes	—
132	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₅₉	#41	1	2	yes	—
139	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₅₉	—	2	2	no	—
141	C₂×C₈×C₅₉	—	2	2	no	—
142	C₂×C₈×C₅₉	—	2	2	no	—
143	C₂×C₈×C₅₉	—	2	2	no	—
144	C₂×C₈×C₅₉	—	2	2	no	—
145	C₂×C₈×C₅₉	—	4	8	no	—
146	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₅₉	—	2	1	no	—
148	C₄⋊C₄×C₅₉	—	2	2	no	—
149	C₄⋊C₄×C₅₉	—	2	1	no	—
150	C₄⋊C₄×C₅₉	—	2	1	no	—
151	C₄⋊C₄×C₅₉	—	2	2	no	—
152	C₄⋊C₄×C₅₉	—	2	2	no	—
153	C₄⋊C₄×C₅₉	—	2	1	no	—
154	C₄⋊C₄×C₅₉	—	2	1	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	4	2	no	—
157	C₄⋊C₄×C₅₉	—	4	4	no	—
158	C₄⋊C₄×C₅₉	—	4	2	no	—
159	C₄⋊C₄×C₅₉	—	4	2	no	—
160	C₄⋊C₄×C₅₉	—	4	2	no	—
161	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
162	C₂²⋊C₄×C₅₉	—	2	4	no	—
163	C₂²⋊C₄×C₅₉	—	4	2	no	—
164	C₂²⋊C₄×C₅₉	—	4	2	no	—
165	C₂²⋊C₄×C₅₉	—	4	4	no	—
166	C₂²⋊C₄×C₅₉	—	4	2	no	—
167	C₂²⋊C₄×C₅₉	—	4	2	no	—
168	C₄²×C₅₉	—	2	2	no	—
169	C₄²×C₅₉	—	2	2	no	—
170	C₄²×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	—	4	2	no	—
173	C₄²×C₅₉	C₂×D₄	1	2	yes	—
174	C₄²×C₅₉	#41	1	2	yes	—
175	C₂³×C₅₉	—	2	1	no	—
176	C₂³×C₅₉	—	2	1	no	—
177	C₂³×C₅₉	—	2	1	no	—
178	C₂³×C₅₉	—	2	1	no	—
179	C₂³×C₅₉	—	2	2	no	—
180	C₂³×C₅₉	—	4	1	no	—
181	C₂³×C₅₉	—	4	1	no	—
182	C₂³×C₅₉	—	4	1	no	—
183	C₂³×C₅₉	—	4	1	no	—
184	C₂³×C₅₉	—	4	1	no	—
185	C₂³×C₅₉	—	4	1	no	—
186	C₂³×C₅₉	C₂²⋊Q₈	1	2	yes	—
187	C₂³×C₅₉	C₂×SD₁₆	1	2	yes	—
188	C₂³×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
189	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₅₉	—	8	4	no	—
191	D₄×C₅₉	—	2	2	no	—
192	D₄×C₅₉	—	2	2	no	—
193	D₄×C₅₉	—	4	8	no	—
194	D₄×C₅₉	—	4	1	no	—
195	D₄×C₅₉	—	4	1	no	—
196	C₂×C₄×C₅₉	—	2	1	no	—
197	C₂×C₄×C₅₉	—	2	1	no	—
198	C₂×C₄×C₅₉	—	2	1	no	—
199	C₂×C₄×C₅₉	—	2	1	no	—
200	C₂×C₄×C₅₉	—	2	1	no	—
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	2	no	—
203	C₂×C₄×C₅₉	—	2	2	no	—
204	C₂×C₄×C₅₉	—	2	2	no	—
205	C₂×C₄×C₅₉	—	2	2	no	—
206	C₂×C₄×C₅₉	—	2	8	no	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	2	no	—
209	C₂×C₄×C₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	4	4	no	—
212	C₂×C₄×C₅₉	—	4	1	no	—
213	C₂×C₄×C₅₉	—	4	1	no	—
214	C₂×C₄×C₅₉	—	4	1	no	—
215	C₂×C₄×C₅₉	—	4	2	no	—
216	C₂×C₄×C₅₉	—	4	1	no	—
217	C₂×C₄×C₅₉	—	4	2	no	—
218	C₂×C₄×C₅₉	—	4	1	no	—
219	C₂×C₄×C₅₉	—	4	1	no	—
220	C₂×C₄×C₅₉	—	4	2	no	—
221	C₂×C₄×C₅₉	—	4	1	no	—
222	C₂×C₄×C₅₉	—	4	2	no	—
223	C₂×C₄×C₅₉	—	4	2	no	—
224	C₂×C₄×C₅₉	—	4	1	no	—
225	C₂×C₄×C₅₉	—	4	2	no	—
226	C₂×C₄×C₅₉	—	8	4	no	—
227	C₂×C₄×C₅₉	#121	1	2	yes	—
228	C₂×C₄×C₅₉	#121	1	2	yes	—
229	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
230	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
231	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
232	C₂×C₄×C₅₉	#135	1	2	yes	—
233	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
235	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₈×C₅₉	—	2	4	no	—
240	C₈×C₅₉	—	4	2	no	—
241	#24836	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂²×C₅₉	—	2	2	no	—
243	C₂²×C₅₉	—	2	2	no	—
244	C₂²×C₅₉	—	2	2	no	—
245	C₂²×C₅₉	—	2	2	no	—
246	C₂²×C₅₉	—	2	2	no	—
247	C₂²×C₅₉	—	2	2	no	—
248	C₂²×C₅₉	—	4	2	no	—
249	C₂²×C₅₉	—	4	2	no	—
250	C₂²×C₅₉	—	4	2	no	—
251	C₂²×C₅₉	—	8	1	no	—
252	C₂²×C₅₉	—	8	1	no	—
253	C₂²×C₅₉	—	8	1	no	—
254	C₂²×C₅₉	—	8	1	no	—
255	C₂²×C₅₉	#476	1	4	yes	complemented
256	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
257	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
258	C₂²×C₅₉	#537	1	1	yes	characteristic
259	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
260	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
261	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂²×C₅₉	#575	1	1	yes	characteristic
263	C₄×C₅₉	—	2	2	no	—
264	C₄×C₅₉	—	2	2	no	—
265	C₄×C₅₉	—	2	2	no	—
266	C₄×C₅₉	—	4	1	no	—
267	C₄×C₅₉	—	4	2	no	—
268	C₄×C₅₉	—	8	1	no	—
269	C₄×C₅₉	—	8	2	no	—
270	C₄×C₅₉	—	8	1	no	—
271	C₄×C₅₉	—	8	2	no	—
272	C₄×C₅₉	#465	1	4	yes	—
273	C₄×C₅₉	#546	1	1	yes	characteristic
274	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
275	C₄×C₅₉	#552	1	1	yes	characteristic
276	C₄×C₅₉	#554	1	1	yes	characteristic
277	C₂×#476	C₂×C₅₉	1	1	yes	characteristic, complemented
278	C₂²×C₄⋊C₈	C₂×C₅₉	1	1	yes	characteristic, complemented
279	#2857	C₂×C₅₉	1	1	yes	characteristic, complemented
280	C₄×#121	C₂×C₅₉	1	1	yes	characteristic
281	#2088	C₂×C₅₉	1	2	yes	complemented
282	#2065	C₂×C₅₉	1	2	yes	complemented
283	#1987	C₂×C₅₉	1	1	yes	characteristic, complemented
284	#1948	C₂×C₅₉	1	1	yes	characteristic, complemented
285	#1893	C₂×C₅₉	1	2	yes	—
286	#1807	C₂×C₅₉	1	2	yes	complemented
287	#1802	C₂×C₅₉	1	1	yes	characteristic, complemented
288	C₂×C₅₉	—	2	4	no	—
289	C₂×C₅₉	—	8	2	no	—
290	C₂×C₅₉	#2417	1	1	yes	characteristic
291	C₂×C₅₉	C₂×#465	1	1	yes	characteristic
292	C₂×C₅₉	#3055	1	1	yes	characteristic
293	C₂×C₅₉	C₂×#476	1	1	yes	characteristic
294	C₂×C₅₉	#3076	1	1	yes	characteristic
295	C₂×C₅₉	#3246	1	1	yes	characteristic
296	C₂×C₅₉	#3247	1	1	yes	characteristic
297	C₂³×C₈	C₂²×C₅₉	1	2	yes	—
298	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
299	C₂×C₂²⋊Q₈	—	2	1	no	—
300	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
301	C₂×C₄×D₄	—	2	1	no	—
302	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
304	#476	—	2	4	no	—
305	C₂×#106	C₂²×C₅₉	1	2	yes	—
306	C₂×#106	C₂²×C₅₉	1	2	yes	—
307	C₂×C₄⋊C₈	—	2	4	no	—
308	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
309	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
310	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
311	C₂×#102	C₂²×C₅₉	1	2	yes	—
312	C₂×#102	C₂²×C₅₉	1	2	yes	—
313	#391	—	2	1	no	—
314	#390	C₂²×C₅₉	1	1	yes	characteristic
315	#389	—	2	1	no	—
316	#389	C₂²×C₅₉	1	2	yes	—
317	#389	C₂²×C₅₉	1	1	yes	characteristic
318	#388	—	2	1	no	—
319	#386	—	2	1	no	—
320	#384	C₂²×C₅₉	1	1	yes	characteristic
321	#380	—	2	1	no	—
322	#380	C₂²×C₅₉	1	1	yes	characteristic
323	#380	C₂²×C₅₉	1	2	yes	—
324	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
325	C₄×C₂²⋊C₄	—	2	1	no	—
326	#340	C₂²×C₅₉	1	2	yes	—
327	#340	C₂²×C₅₉	1	2	yes	—
328	#340	C₂²×C₅₉	1	2	yes	—
329	#340	C₂²×C₅₉	1	2	yes	—
330	C₅₉	#24836	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
336	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
338	C₂²×C₈	—	2	4	no	—
339	C₂²×C₈	—	2	4	no	—
340	C₂²×C₈	—	4	2	no	—
341	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
342	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	4	4	no	—
346	#121	—	2	2	no	—
347	#121	Q₈×C₅₉	1	4	yes	complemented
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	4	4	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
371	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
374	#106	—	2	4	no	—
375	#106	—	4	2	no	—
376	C₄⋊C₈	—	2	4	no	—
377	C₄⋊C₈	—	2	2	no	—
378	C₄⋊C₈	D₄×C₅₉	1	4	yes	complemented
379	#102	—	2	4	no	—
380	#102	—	4	2	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	2	no	—
385	#95	—	2	2	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	—	4	2	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	C₂×Q₈×C₅₉	1	2	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	SD₁₆×C₅₉	1	4	yes	—
418	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
423	C₂²×C₄	C₂×Q₈×C₅₉	1	2	yes	—
424	C₂²×C₄	#41×C₅₉	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	4	8	no	—
432	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	4	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	4	2	no	—
459	C₄²	C₂×D₄×C₅₉	1	2	yes	—
460	C₄²	#41×C₅₉	1	2	yes	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	C₂²⋊Q₈×C₅₉	1	2	yes	—
473	C₂³	C₂×SD₁₆×C₅₉	1	2	yes	—
474	C₂³	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
475	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
476	Q₈	—	8	4	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	#121×C₅₉	1	2	yes	—
514	C₂×C₄	#121×C₅₉	1	2	yes	—
515	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
516	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
517	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
518	C₂×C₄	#135×C₅₉	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
523	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
524	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	C₅₉×#476	1	4	yes	complemented
541	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
542	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
543	C₂²	C₅₉×#537	1	1	yes	characteristic
544	C₂²	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
545	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
546	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
547	C₂²	C₅₉×#575	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	2	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	2	no	—
557	C₄	C₅₉×#465	1	4	yes	—
558	C₄	C₅₉×#546	1	1	yes	characteristic
559	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
560	C₄	C₅₉×#552	1	1	yes	characteristic
561	C₄	C₅₉×#554	1	1	yes	characteristic
562	C₂	—	2	4	no	—
563	C₂	—	8	2	no	—
564	C₂	C₅₉×#2417	1	1	yes	characteristic
565	C₂	C₂×C₅₉×#465	1	1	yes	characteristic
566	C₂	C₅₉×#3055	1	1	yes	characteristic
567	C₂	C₂×C₅₉×#476	1	1	yes	characteristic
568	C₂	C₅₉×#3076	1	1	yes	characteristic
569	C₂	C₅₉×#3246	1	1	yes	characteristic
570	C₂	C₅₉×#3247	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×#121×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#476	C₂	semidirect
2. C₂²×C₄⋊C₈×C₅₉	C₂	semidirect
3. C₅₉×#2857	C₂	semidirect
5. C₅₉×#2088	C₂	semidirect
6. C₅₉×#2065	C₂	semidirect
7. C₅₉×#1987	C₂	semidirect
8. C₅₉×#1948	C₂	semidirect
10. C₅₉×#1807	C₂	semidirect
11. C₅₉×#1802	C₂	semidirect
61. #121×C₅₉	Q₈	semidirect
92. C₄⋊C₈×C₅₉	D₄	semidirect
241. #24836	C₅₉	direct (N × H)
255. C₂²×C₅₉	#476	semidirect
277. C₂×#476	C₂×C₅₉	semidirect
278. C₂²×C₄⋊C₈	C₂×C₅₉	semidirect
279. #2857	C₂×C₅₉	semidirect
281. #2088	C₂×C₅₉	semidirect
282. #2065	C₂×C₅₉	semidirect
283. #1987	C₂×C₅₉	semidirect
284. #1948	C₂×C₅₉	semidirect
286. #1807	C₂×C₅₉	semidirect
287. #1802	C₂×C₅₉	semidirect
330. C₅₉	#24836	direct (N × H)
347. #121	Q₈×C₅₉	semidirect
378. C₄⋊C₈	D₄×C₅₉	semidirect
540. C₂²	C₅₉×#476	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#476	2
C₂²×C₄⋊C₈×C₅₉	2
C₅₉×#2857	2
C₄×#121×C₅₉	2
C₅₉×#2088	2
C₅₉×#2065	2
C₅₉×#1987	2
C₅₉×#1948	2
C₅₉×#1893	2
C₅₉×#1807	2
C₅₉×#1802	2
#24836	59

Subgroups — C59×#24836 #28436945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24836 #28436945