Subgroups — C₅₉×#24736 #28436845

Order 15104.

924 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#464	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2545	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2067	C₂	1	1	yes	maximal, characteristic
9	C₅₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2042	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#1958	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#1880	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#464	—	2	4	no	—
27	C₅₉×#464	—	2	4	no	—
28	C₅₉×#462	—	2	4	no	—
29	C₄×Q₁₆×C₅₉	—	2	4	no	—
30	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#396	—	2	1	no	—
46	C₅₉×#396	—	2	1	no	—
47	C₅₉×#391	C₂²	1	1	yes	characteristic
48	C₅₉×#390	C₂²	1	1	yes	characteristic
49	C₅₉×#389	—	2	1	no	—
50	C₅₉×#389	—	2	1	no	—
51	C₅₉×#389	C₂²	1	1	yes	characteristic
52	C₅₉×#389	C₂²	1	1	yes	characteristic
53	C₅₉×#388	—	2	1	no	—
54	C₅₉×#388	—	2	1	no	—
55	C₅₉×#382	—	2	1	no	—
56	C₅₉×#382	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
58	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
59	C₅₉×#340	C₂²	1	1	yes	characteristic
60	C₅₉×#340	C₂²	1	1	yes	characteristic
61	C₅₉×#336	C₂²	1	1	yes	characteristic
62	C₅₉×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
67	C₂×Q₁₆×C₅₉	—	2	2	no	—
68	C₂×Q₁₆×C₅₉	—	2	2	no	—
69	C₂×Q₁₆×C₅₉	—	2	2	no	—
70	C₂×Q₁₆×C₅₉	—	2	2	no	—
71	C₂×Q₁₆×C₅₉	—	2	2	no	—
72	C₂×Q₁₆×C₅₉	D₄	1	4	yes	—
73	C₂×SD₁₆×C₅₉	—	2	2	no	—
74	C₂×SD₁₆×C₅₉	—	2	2	no	—
75	C₂×SD₁₆×C₅₉	—	2	2	no	—
76	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₅₉	—	2	2	no	—
81	C₄⋊Q₈×C₅₉	—	4	1	no	—
82	#124×C₅₉	—	2	2	no	—
83	#124×C₅₉	—	2	2	no	—
84	#124×C₅₉	—	2	2	no	—
85	#124×C₅₉	—	4	1	no	—
86	C₄×Q₈×C₅₉	—	2	2	no	—
87	C₄×Q₈×C₅₉	—	2	2	no	—
88	C₄×Q₈×C₅₉	—	2	2	no	—
89	C₄×Q₈×C₅₉	—	2	2	no	—
90	C₄×Q₈×C₅₉	—	2	2	no	—
91	C₄×Q₈×C₅₉	—	4	1	no	—
92	C₄×Q₈×C₅₉	—	4	1	no	—
93	C₄×Q₈×C₅₉	D₄	1	4	yes	—
94	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
114	C₂×C₄²×C₅₉	—	2	1	no	—
115	C₂×C₄²×C₅₉	—	2	1	no	—
116	C₂×C₄²×C₅₉	—	2	1	no	—
117	C₂×C₄²×C₅₉	—	2	1	no	—
118	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
121	#107×C₅₉	—	2	2	no	—
122	C₄⋊C₈×C₅₉	—	2	2	no	—
123	C₄⋊C₈×C₅₉	—	2	2	no	—
124	C₄⋊C₈×C₅₉	—	2	2	no	—
125	#103×C₅₉	—	2	2	no	—
126	#103×C₅₉	—	2	2	no	—
127	#103×C₅₉	—	2	2	no	—
128	#103×C₅₉	—	2	2	no	—
129	#103×C₅₉	—	2	2	no	—
130	#103×C₅₉	—	2	2	no	—
131	#103×C₅₉	—	4	1	no	—
132	#102×C₅₉	—	2	2	no	—
133	#102×C₅₉	—	2	2	no	—
134	#102×C₅₉	—	4	1	no	—
135	C₄×C₈×C₅₉	—	2	2	no	—
136	#95×C₅₉	—	2	1	no	—
137	#95×C₅₉	—	2	1	no	—
138	#95×C₅₉	—	2	1	no	—
139	#95×C₅₉	—	2	1	no	—
140	#95×C₅₉	—	2	1	no	—
141	#95×C₅₉	—	2	1	no	—
142	#95×C₅₉	D₄	1	1	yes	characteristic
143	#95×C₅₉	D₄	1	1	yes	characteristic
144	C₂⁴×C₅₉	—	2	1	no	—
145	C₂×Q₈×C₅₉	—	2	1	no	—
146	C₂×Q₈×C₅₉	—	2	1	no	—
147	C₂×Q₈×C₅₉	—	2	1	no	—
148	C₂×Q₈×C₅₉	—	2	1	no	—
149	C₂×Q₈×C₅₉	—	2	1	no	—
150	C₂×Q₈×C₅₉	—	2	1	no	—
151	C₂×Q₈×C₅₉	—	2	1	no	—
152	C₂×Q₈×C₅₉	—	2	1	no	—
153	C₂×Q₈×C₅₉	—	2	1	no	—
154	C₂×Q₈×C₅₉	—	2	1	no	—
155	C₂×Q₈×C₅₉	—	2	1	no	—
156	C₂×Q₈×C₅₉	—	2	1	no	—
157	C₂×Q₈×C₅₉	—	2	1	no	—
158	C₂×Q₈×C₅₉	—	2	1	no	—
159	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
160	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
162	C₂×Q₈×C₅₉	#41	1	2	yes	—
163	C₂×D₄×C₅₉	—	2	1	no	—
164	C₂×D₄×C₅₉	—	2	1	no	—
165	C₂×D₄×C₅₉	—	2	1	no	—
166	C₂×D₄×C₅₉	—	2	1	no	—
167	C₂×D₄×C₅₉	—	2	1	no	—
168	C₂×D₄×C₅₉	—	2	1	no	—
169	C₂²×C₄×C₅₉	—	2	1	no	—
170	C₂²×C₄×C₅₉	—	2	1	no	—
171	C₂²×C₄×C₅₉	—	2	1	no	—
172	C₂²×C₄×C₅₉	—	2	1	no	—
173	C₂²×C₄×C₅₉	—	2	1	no	—
174	C₂²×C₄×C₅₉	—	2	1	no	—
175	C₂²×C₄×C₅₉	—	2	1	no	—
176	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
183	Q₁₆×C₅₉	—	2	8	no	—
184	Q₁₆×C₅₉	—	4	4	no	—
185	SD₁₆×C₅₉	—	4	4	no	—
186	C₂×C₈×C₅₉	—	2	1	no	—
187	C₂×C₈×C₅₉	—	2	1	no	—
188	C₂×C₈×C₅₉	—	2	1	no	—
189	C₂×C₈×C₅₉	—	2	1	no	—
190	C₂×C₈×C₅₉	—	2	1	no	—
191	C₂×C₈×C₅₉	—	2	1	no	—
192	C₂×C₈×C₅₉	—	2	1	no	—
193	C₂×C₈×C₅₉	—	2	1	no	—
194	C₂×C₈×C₅₉	—	2	1	no	—
195	C₂×C₈×C₅₉	—	2	1	no	—
196	C₂×C₈×C₅₉	—	2	1	no	—
197	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
198	C₄⋊C₄×C₅₉	—	2	4	no	—
199	C₄⋊C₄×C₅₉	—	2	2	no	—
200	C₄⋊C₄×C₅₉	—	2	1	no	—
201	C₄⋊C₄×C₅₉	—	2	1	no	—
202	C₄⋊C₄×C₅₉	—	2	1	no	—
203	C₄⋊C₄×C₅₉	—	2	1	no	—
204	C₄⋊C₄×C₅₉	—	2	1	no	—
205	C₄⋊C₄×C₅₉	—	2	1	no	—
206	C₄⋊C₄×C₅₉	—	2	1	no	—
207	C₄⋊C₄×C₅₉	—	4	1	no	—
208	C₄⋊C₄×C₅₉	—	4	2	no	—
209	C₄⋊C₄×C₅₉	—	4	2	no	—
210	C₄⋊C₄×C₅₉	—	4	2	no	—
211	C₄⋊C₄×C₅₉	—	4	2	no	—
212	C₄⋊C₄×C₅₉	—	4	2	no	—
213	C₄⋊C₄×C₅₉	—	4	2	no	—
214	C₄⋊C₄×C₅₉	—	4	2	no	—
215	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
216	C₂²⋊C₄×C₅₉	—	4	2	no	—
217	C₂²⋊C₄×C₅₉	—	4	2	no	—
218	C₂²⋊C₄×C₅₉	—	4	2	no	—
219	C₂²⋊C₄×C₅₉	—	4	2	no	—
220	C₂²⋊C₄×C₅₉	—	4	2	no	—
221	C₂²⋊C₄×C₅₉	—	4	2	no	—
222	C₄²×C₅₉	—	2	4	no	—
223	C₄²×C₅₉	—	2	1	no	—
224	C₄²×C₅₉	—	2	1	no	—
225	C₄²×C₅₉	—	2	1	no	—
226	C₄²×C₅₉	—	2	1	no	—
227	C₄²×C₅₉	—	4	2	no	—
228	C₄²×C₅₉	—	4	2	no	—
229	C₄²×C₅₉	—	4	2	no	—
230	C₄²×C₅₉	C₂×D₄	1	2	yes	—
231	C₄²×C₅₉	#41	1	2	yes	—
232	C₂³×C₅₉	—	4	1	no	—
233	C₂³×C₅₉	—	4	1	no	—
234	C₂³×C₅₉	—	4	1	no	—
235	C₂³×C₅₉	—	4	1	no	—
236	C₂³×C₅₉	—	4	1	no	—
237	C₂³×C₅₉	—	4	1	no	—
238	C₂³×C₅₉	—	4	1	no	—
239	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₅₉	—	2	2	no	—
241	Q₈×C₅₉	—	2	2	no	—
242	Q₈×C₅₉	—	2	2	no	—
243	Q₈×C₅₉	—	2	2	no	—
244	Q₈×C₅₉	—	2	2	no	—
245	Q₈×C₅₉	—	4	1	no	—
246	Q₈×C₅₉	—	4	1	no	—
247	Q₈×C₅₉	—	4	1	no	—
248	Q₈×C₅₉	—	4	1	no	—
249	Q₈×C₅₉	—	4	1	no	—
250	Q₈×C₅₉	—	4	1	no	—
251	Q₈×C₅₉	#121	1	4	yes	—
252	D₄×C₅₉	—	4	1	no	—
253	D₄×C₅₉	—	4	1	no	—
254	D₄×C₅₉	—	4	1	no	—
255	D₄×C₅₉	—	4	1	no	—
256	C₂×C₄×C₅₉	—	2	2	no	—
257	C₂×C₄×C₅₉	—	2	1	no	—
258	C₂×C₄×C₅₉	—	2	2	no	—
259	C₂×C₄×C₅₉	—	2	2	no	—
260	C₂×C₄×C₅₉	—	2	1	no	—
261	C₂×C₄×C₅₉	—	2	1	no	—
262	C₂×C₄×C₅₉	—	2	1	no	—
263	C₂×C₄×C₅₉	—	2	1	no	—
264	C₂×C₄×C₅₉	—	2	1	no	—
265	C₂×C₄×C₅₉	—	2	2	no	—
266	C₂×C₄×C₅₉	—	2	1	no	—
267	C₂×C₄×C₅₉	—	2	1	no	—
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	1	no	—
272	C₂×C₄×C₅₉	—	2	1	no	—
273	C₂×C₄×C₅₉	—	2	1	no	—
274	C₂×C₄×C₅₉	—	2	1	no	—
275	C₂×C₄×C₅₉	—	2	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	—	4	1	no	—
283	C₂×C₄×C₅₉	—	4	1	no	—
284	C₂×C₄×C₅₉	—	4	1	no	—
285	C₂×C₄×C₅₉	—	4	1	no	—
286	C₂×C₄×C₅₉	—	4	1	no	—
287	C₂×C₄×C₅₉	—	4	1	no	—
288	C₂×C₄×C₅₉	—	4	1	no	—
289	C₂×C₄×C₅₉	—	4	1	no	—
290	C₂×C₄×C₅₉	—	4	1	no	—
291	C₂×C₄×C₅₉	—	4	1	no	—
292	C₂×C₄×C₅₉	#121	1	2	yes	—
293	C₂×C₄×C₅₉	#121	1	2	yes	—
294	C₂×C₄×C₅₉	#135	1	2	yes	—
295	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
301	C₈×C₅₉	—	2	2	no	—
302	C₈×C₅₉	—	4	1	no	—
303	C₈×C₅₉	—	4	1	no	—
304	C₈×C₅₉	—	4	1	no	—
305	#24736	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂²×C₅₉	—	8	1	no	—
307	C₂²×C₅₉	—	8	1	no	—
308	C₂²×C₅₉	—	8	1	no	—
309	C₂²×C₅₉	—	8	1	no	—
310	C₂²×C₅₉	—	8	1	no	—
311	C₂²×C₅₉	—	8	1	no	—
312	C₂²×C₅₉	—	8	1	no	—
313	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
314	C₂²×C₅₉	D₄²	1	1	yes	characteristic
315	C₂²×C₅₉	#548	1	1	yes	characteristic
316	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
317	C₂²×C₅₉	#575	1	1	yes	characteristic
318	C₂²×C₅₉	#578	1	1	yes	characteristic
319	C₂²×C₅₉	#578	1	1	yes	characteristic
320	C₄×C₅₉	—	2	4	no	—
321	C₄×C₅₉	—	2	2	no	—
322	C₄×C₅₉	—	2	2	no	—
323	C₄×C₅₉	—	2	2	no	—
324	C₄×C₅₉	—	4	2	no	—
325	C₄×C₅₉	—	4	1	no	—
326	C₄×C₅₉	—	4	1	no	—
327	C₄×C₅₉	—	4	1	no	—
328	C₄×C₅₉	—	4	2	no	—
329	C₄×C₅₉	—	8	1	no	—
330	C₄×C₅₉	—	8	1	no	—
331	C₄×C₅₉	—	8	1	no	—
332	C₄×C₅₉	—	8	1	no	—
333	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
334	C₄×C₅₉	#537	1	1	yes	characteristic
335	C₄×C₅₉	#547	1	1	yes	characteristic
336	C₄×C₅₉	#553	1	1	yes	characteristic
337	C₂×#464	C₂×C₅₉	1	1	yes	characteristic
338	C₂×#464	C₂×C₅₉	1	1	yes	characteristic
339	C₂×#462	C₂×C₅₉	1	1	yes	characteristic, complemented
340	C₂×C₄×Q₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
341	#2545	C₂×C₅₉	1	1	yes	characteristic
342	#2351	C₂×C₅₉	1	1	yes	characteristic, complemented
343	#2068	C₂×C₅₉	1	1	yes	characteristic, complemented
344	#2067	C₂×C₅₉	1	1	yes	characteristic
345	#2043	C₂×C₅₉	1	1	yes	characteristic, complemented
346	#2042	C₂×C₅₉	1	1	yes	characteristic
347	#1958	C₂×C₅₉	1	1	yes	characteristic
348	#1939	C₂×C₅₉	1	1	yes	characteristic, complemented
349	#1880	C₂×C₅₉	1	1	yes	characteristic
350	#1878	C₂×C₅₉	1	1	yes	characteristic, complemented
351	#1805	C₂×C₅₉	1	1	yes	characteristic, complemented
352	C₂×C₅₉	—	16	1	no	—
353	C₂×C₅₉	#2416	1	1	yes	characteristic
354	C₂×C₅₉	#3035	1	1	yes	characteristic
355	C₂×C₅₉	#3044	1	1	yes	characteristic
356	C₂×C₅₉	#3277	1	1	yes	characteristic
357	C₂×C₅₉	#3285	1	1	yes	characteristic
358	C₂×C₅₉	#3364	1	1	yes	characteristic
359	C₂×C₅₉	#3377	1	1	yes	characteristic
360	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
361	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
362	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
363	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
364	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
365	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
367	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
370	#464	—	2	4	no	—
371	#464	—	2	4	no	—
372	#462	—	2	4	no	—
373	C₄×Q₁₆	—	2	4	no	—
374	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
375	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
376	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
378	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
379	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
380	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
381	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
383	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
384	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
385	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
387	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
388	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
389	#396	—	2	1	no	—
390	#396	—	2	1	no	—
391	#391	C₂²×C₅₉	1	1	yes	characteristic
392	#390	C₂²×C₅₉	1	1	yes	characteristic
393	#389	—	2	1	no	—
394	#389	—	2	1	no	—
395	#389	C₂²×C₅₉	1	1	yes	characteristic
396	#389	C₂²×C₅₉	1	1	yes	characteristic
397	#388	—	2	1	no	—
398	#388	—	2	1	no	—
399	#382	—	2	1	no	—
400	#382	C₂²×C₅₉	1	1	yes	characteristic
401	C₄×C₄⋊C₄	—	2	1	no	—
402	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
403	#340	C₂²×C₅₉	1	1	yes	characteristic
404	#340	C₂²×C₅₉	1	1	yes	characteristic
405	#336	C₂²×C₅₉	1	1	yes	characteristic
406	#336	C₂²×C₅₉	1	1	yes	characteristic
407	C₅₉	#24736	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
409	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
410	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
412	C₂×Q₁₆	—	2	2	no	—
413	C₂×Q₁₆	—	2	2	no	—
414	C₂×Q₁₆	—	2	2	no	—
415	C₂×Q₁₆	—	2	2	no	—
416	C₂×Q₁₆	—	2	2	no	—
417	C₂×Q₁₆	D₄×C₅₉	1	4	yes	—
418	C₂×SD₁₆	—	2	2	no	—
419	C₂×SD₁₆	—	2	2	no	—
420	C₂×SD₁₆	—	2	2	no	—
421	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
425	C₄⋊Q₈	—	2	2	no	—
426	C₄⋊Q₈	—	4	1	no	—
427	#124	—	2	2	no	—
428	#124	—	2	2	no	—
429	#124	—	2	2	no	—
430	#124	—	4	1	no	—
431	C₄×Q₈	—	2	2	no	—
432	C₄×Q₈	—	2	2	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	4	1	no	—
437	C₄×Q₈	—	4	1	no	—
438	C₄×Q₈	D₄×C₅₉	1	4	yes	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	—	2	1	no	—
463	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
466	#107	—	2	2	no	—
467	C₄⋊C₈	—	2	2	no	—
468	C₄⋊C₈	—	2	2	no	—
469	C₄⋊C₈	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	2	2	no	—
472	#103	—	2	2	no	—
473	#103	—	2	2	no	—
474	#103	—	2	2	no	—
475	#103	—	2	2	no	—
476	#103	—	4	1	no	—
477	#102	—	2	2	no	—
478	#102	—	2	2	no	—
479	#102	—	4	1	no	—
480	C₄×C₈	—	2	2	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	D₄×C₅₉	1	1	yes	characteristic
488	#95	D₄×C₅₉	1	1	yes	characteristic
489	C₂⁴	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
505	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
506	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
507	C₂×Q₈	#41×C₅₉	1	2	yes	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
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	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
528	Q₁₆	—	2	8	no	—
529	Q₁₆	—	4	4	no	—
530	SD₁₆	—	4	4	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	4	1	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	4	2	no	—
573	C₄²	—	4	2	no	—
574	C₄²	—	4	2	no	—
575	C₄²	C₂×D₄×C₅₉	1	2	yes	—
576	C₄²	#41×C₅₉	1	2	yes	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	2	2	no	—
589	Q₈	—	2	2	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	1	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	1	no	—
595	Q₈	—	4	1	no	—
596	Q₈	#121×C₅₉	1	4	yes	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	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	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	#121×C₅₉	1	2	yes	—
638	C₂×C₄	#121×C₅₉	1	2	yes	—
639	C₂×C₄	#135×C₅₉	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
642	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
643	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
644	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
645	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
646	C₈	—	2	2	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
658	C₂²	D₄²×C₅₉	1	1	yes	characteristic
659	C₂²	C₅₉×#548	1	1	yes	characteristic
660	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
661	C₂²	C₅₉×#575	1	1	yes	characteristic
662	C₂²	C₅₉×#578	1	1	yes	characteristic
663	C₂²	C₅₉×#578	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	4	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	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	C₄	—	8	1	no	—
677	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
678	C₄	C₅₉×#537	1	1	yes	characteristic
679	C₄	C₅₉×#547	1	1	yes	characteristic
680	C₄	C₅₉×#553	1	1	yes	characteristic
681	C₂	—	16	1	no	—
682	C₂	C₅₉×#2416	1	1	yes	characteristic
683	C₂	C₅₉×#3035	1	1	yes	characteristic
684	C₂	C₅₉×#3044	1	1	yes	characteristic
685	C₂	C₅₉×#3277	1	1	yes	characteristic
686	C₂	C₅₉×#3285	1	1	yes	characteristic
687	C₂	C₅₉×#3364	1	1	yes	characteristic
688	C₂	C₅₉×#3377	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₅₉×#462	C₂	semidirect
4. C₂×C₄×Q₁₆×C₅₉	C₂	semidirect
6. C₅₉×#2351	C₂	semidirect
7. C₅₉×#2068	C₂	semidirect
9. C₅₉×#2043	C₂	semidirect
12. C₅₉×#1939	C₂	semidirect
14. C₅₉×#1878	C₂	semidirect
15. C₅₉×#1805	C₂	semidirect
305. #24736	C₅₉	direct (N × H)
339. C₂×#462	C₂×C₅₉	semidirect
340. C₂×C₄×Q₁₆	C₂×C₅₉	semidirect
342. #2351	C₂×C₅₉	semidirect
343. #2068	C₂×C₅₉	semidirect
345. #2043	C₂×C₅₉	semidirect
348. #1939	C₂×C₅₉	semidirect
350. #1878	C₂×C₅₉	semidirect
351. #1805	C₂×C₅₉	semidirect
407. C₅₉	#24736	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#464	2
C₂×C₅₉×#462	2
C₂×C₄×Q₁₆×C₅₉	2
C₅₉×#2545	2
C₅₉×#2351	2
C₅₉×#2068	2
C₅₉×#2067	2
C₅₉×#2043	2
C₅₉×#2042	2
C₅₉×#1958	2
C₅₉×#1939	2
C₅₉×#1880	2
C₅₉×#1878	2
C₅₉×#1805	2
#24736	59

Subgroups — C59×#24736 #28436845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24736 #28436845