Subgroups — C₅₉×#24732 #28436841

Order 15104.

914 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#462	C₂	1	2	yes	maximal
2	C₂×C₅₉×#462	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2546	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2068	C₂	1	2	yes	maximal
7	C₅₉×#2043	C₂	1	2	yes	maximal
8	C₅₉×#1956	C₂	1	1	yes	maximal, characteristic
9	C₅₉×#1939	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#1878	C₂	1	2	yes	maximal
11	C₅₉×#1803	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₅₉	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₅₉×#462	—	2	8	no	—
20	C₅₉×#462	—	2	4	no	—
21	C₄×Q₁₆×C₅₉	—	2	4	no	—
22	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
25	C₂×#103×C₅₉	C₂²	1	2	yes	—
26	C₂×#103×C₅₉	C₂²	1	2	yes	—
27	C₂×#103×C₅₉	C₂²	1	2	yes	—
28	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₅₉×#398	—	2	2	no	—
33	C₅₉×#391	C₂²	1	2	yes	—
34	C₅₉×#389	—	2	1	no	—
35	C₅₉×#389	—	2	1	no	—
36	C₅₉×#389	—	2	2	no	—
37	C₅₉×#389	C₂²	1	2	yes	—
38	C₅₉×#384	—	2	1	no	—
39	C₅₉×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
41	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#340	C₂²	1	2	yes	—
43	C₅₉×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
45	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₅₉	—	2	2	no	—
48	C₂×Q₁₆×C₅₉	—	2	2	no	—
49	C₂×Q₁₆×C₅₉	—	2	4	no	—
50	C₂×Q₁₆×C₅₉	—	2	4	no	—
51	C₂×Q₁₆×C₅₉	—	2	4	no	—
52	C₂×Q₁₆×C₅₉	D₄	1	4	yes	—
53	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₅₉	—	2	4	no	—
57	C₄⋊Q₈×C₅₉	—	2	2	no	—
58	C₄⋊Q₈×C₅₉	—	2	2	no	—
59	C₄⋊Q₈×C₅₉	—	4	2	no	—
60	C₄×Q₈×C₅₉	—	2	2	no	—
61	C₄×Q₈×C₅₉	—	2	4	no	—
62	C₄×Q₈×C₅₉	—	2	2	no	—
63	C₄×Q₈×C₅₉	—	2	2	no	—
64	C₄×Q₈×C₅₉	—	4	2	no	—
65	C₄×Q₈×C₅₉	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅₉	—	2	1	no	—
82	C₂×C₄²×C₅₉	—	2	2	no	—
83	C₂×C₄²×C₅₉	—	2	1	no	—
84	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
85	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
86	#107×C₅₉	—	2	2	no	—
87	C₄⋊C₈×C₅₉	—	2	4	no	—
88	C₄⋊C₈×C₅₉	—	2	2	no	—
89	#103×C₅₉	—	2	2	no	—
90	#103×C₅₉	—	2	4	no	—
91	#103×C₅₉	—	2	4	no	—
92	#103×C₅₉	—	2	2	no	—
93	#103×C₅₉	—	2	4	no	—
94	#103×C₅₉	—	4	2	no	—
95	C₄×C₈×C₅₉	—	2	2	no	—
96	#95×C₅₉	—	2	2	no	—
97	#95×C₅₉	—	2	2	no	—
98	#95×C₅₉	—	2	2	no	—
99	#95×C₅₉	D₄	1	2	yes	—
100	C₂×Q₈×C₅₉	—	2	1	no	—
101	C₂×Q₈×C₅₉	—	2	1	no	—
102	C₂×Q₈×C₅₉	—	2	1	no	—
103	C₂×Q₈×C₅₉	—	2	1	no	—
104	C₂×Q₈×C₅₉	—	2	1	no	—
105	C₂×Q₈×C₅₉	—	2	2	no	—
106	C₂×Q₈×C₅₉	—	2	2	no	—
107	C₂×Q₈×C₅₉	—	2	1	no	—
108	C₂×Q₈×C₅₉	—	2	1	no	—
109	C₂×Q₈×C₅₉	—	2	2	no	—
110	C₂×Q₈×C₅₉	—	2	2	no	—
111	C₂×Q₈×C₅₉	—	2	2	no	—
112	C₂×Q₈×C₅₉	—	2	1	no	—
113	C₂×Q₈×C₅₉	—	2	2	no	—
114	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
115	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
116	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₅₉	#41	1	2	yes	—
118	C₂²×C₄×C₅₉	—	2	1	no	—
119	C₂²×C₄×C₅₉	—	2	1	no	—
120	C₂²×C₄×C₅₉	—	2	1	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	2	no	—
123	C₂²×C₄×C₅₉	—	2	2	no	—
124	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
129	Q₁₆×C₅₉	—	2	8	no	—
130	Q₁₆×C₅₉	—	4	8	no	—
131	C₂×C₈×C₅₉	—	2	1	no	—
132	C₂×C₈×C₅₉	—	2	1	no	—
133	C₂×C₈×C₅₉	—	2	1	no	—
134	C₂×C₈×C₅₉	—	2	2	no	—
135	C₂×C₈×C₅₉	—	2	2	no	—
136	C₂×C₈×C₅₉	—	2	2	no	—
137	C₂×C₈×C₅₉	—	2	1	no	—
138	C₂×C₈×C₅₉	—	2	1	no	—
139	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₅₉	—	2	4	no	—
141	C₄⋊C₄×C₅₉	—	2	2	no	—
142	C₄⋊C₄×C₅₉	—	2	1	no	—
143	C₄⋊C₄×C₅₉	—	2	2	no	—
144	C₄⋊C₄×C₅₉	—	2	1	no	—
145	C₄⋊C₄×C₅₉	—	2	1	no	—
146	C₄⋊C₄×C₅₉	—	2	2	no	—
147	C₄⋊C₄×C₅₉	—	4	4	no	—
148	C₄⋊C₄×C₅₉	—	4	4	no	—
149	C₄⋊C₄×C₅₉	—	4	4	no	—
150	C₄⋊C₄×C₅₉	—	4	2	no	—
151	C₄⋊C₄×C₅₉	—	4	2	no	—
152	C₄⋊C₄×C₅₉	—	4	2	no	—
153	C₄⋊C₄×C₅₉	—	4	2	no	—
154	C₄⋊C₄×C₅₉	—	8	1	no	—
155	C₄⋊C₄×C₅₉	—	8	2	no	—
156	C₄⋊C₄×C₅₉	Q₁₆	1	4	yes	complemented
157	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
158	C₄²×C₅₉	—	2	4	no	—
159	C₄²×C₅₉	—	2	2	no	—
160	C₄²×C₅₉	—	2	2	no	—
161	C₄²×C₅₉	—	4	4	no	—
162	C₄²×C₅₉	—	4	2	no	—
163	C₄²×C₅₉	C₂×D₄	1	2	yes	—
164	C₄²×C₅₉	#41	1	2	yes	—
165	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₅₉	—	2	2	no	—
167	Q₈×C₅₉	—	2	2	no	—
168	Q₈×C₅₉	—	2	2	no	—
169	Q₈×C₅₉	—	2	2	no	—
170	Q₈×C₅₉	—	2	2	no	—
171	Q₈×C₅₉	—	4	1	no	—
172	Q₈×C₅₉	—	4	1	no	—
173	Q₈×C₅₉	—	4	2	no	—
174	Q₈×C₅₉	—	4	2	no	—
175	Q₈×C₅₉	—	4	2	no	—
176	Q₈×C₅₉	—	4	2	no	—
177	Q₈×C₅₉	#121	1	4	yes	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	2	2	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	—	2	2	no	—
182	C₂×C₄×C₅₉	—	2	1	no	—
183	C₂×C₄×C₅₉	—	2	2	no	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	2	2	no	—
187	C₂×C₄×C₅₉	—	2	2	no	—
188	C₂×C₄×C₅₉	—	2	2	no	—
189	C₂×C₄×C₅₉	—	2	2	no	—
190	C₂×C₄×C₅₉	—	4	1	no	—
191	C₂×C₄×C₅₉	—	4	1	no	—
192	C₂×C₄×C₅₉	—	4	1	no	—
193	C₂×C₄×C₅₉	—	4	1	no	—
194	C₂×C₄×C₅₉	—	4	1	no	—
195	C₂×C₄×C₅₉	—	4	2	no	—
196	C₂×C₄×C₅₉	—	4	2	no	—
197	C₂×C₄×C₅₉	—	4	2	no	—
198	C₂×C₄×C₅₉	—	4	2	no	—
199	C₂×C₄×C₅₉	—	4	2	no	—
200	C₂×C₄×C₅₉	—	4	2	no	—
201	C₂×C₄×C₅₉	—	4	1	no	—
202	C₂×C₄×C₅₉	—	4	1	no	—
203	C₂×C₄×C₅₉	#121	1	2	yes	—
204	C₂×C₄×C₅₉	#121	1	2	yes	—
205	C₂×C₄×C₅₉	C₂×Q₁₆	1	4	yes	—
206	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
207	C₂×C₄×C₅₉	#137	1	2	yes	—
208	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
214	C₈×C₅₉	—	2	2	no	—
215	C₈×C₅₉	—	4	2	no	—
216	C₈×C₅₉	—	4	1	no	—
217	#24732	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
219	C₂²×C₅₉	D₄²	1	1	yes	characteristic
220	C₂²×C₅₉	#548	1	1	yes	characteristic
221	C₂²×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
222	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
223	C₂²×C₅₉	#577	1	1	yes	characteristic
224	C₂²×C₅₉	#578	1	1	yes	characteristic
225	C₄×C₅₉	—	2	4	no	—
226	C₄×C₅₉	—	2	4	no	—
227	C₄×C₅₉	—	2	2	no	—
228	C₄×C₅₉	—	4	2	no	—
229	C₄×C₅₉	—	4	2	no	—
230	C₄×C₅₉	—	4	2	no	—
231	C₄×C₅₉	—	8	2	no	—
232	C₄×C₅₉	—	8	2	no	—
233	C₄×C₅₉	—	8	1	no	—
234	C₄×C₅₉	#462	1	4	yes	complemented
235	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
236	C₄×C₅₉	#537	1	1	yes	characteristic
237	C₄×C₅₉	#547	1	1	yes	characteristic
238	C₄×C₅₉	#553	1	1	yes	characteristic
239	C₂×#462	C₂×C₅₉	1	2	yes	—
240	C₂×#462	C₂×C₅₉	1	1	yes	characteristic
241	C₂×C₄×Q₁₆	C₂×C₅₉	1	1	yes	characteristic
242	#2546	C₂×C₅₉	1	1	yes	characteristic
243	Q₈×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic
244	#2068	C₂×C₅₉	1	2	yes	—
245	#2043	C₂×C₅₉	1	2	yes	—
246	#1956	C₂×C₅₉	1	1	yes	characteristic
247	#1939	C₂×C₅₉	1	1	yes	characteristic
248	#1878	C₂×C₅₉	1	2	yes	—
249	#1803	C₂×C₅₉	1	1	yes	characteristic
250	C₂×C₅₉	#2416	1	1	yes	characteristic
251	C₂×C₅₉	C₂×#462	1	1	yes	characteristic
252	C₂×C₅₉	#3046	1	1	yes	characteristic
253	C₂×C₅₉	#3278	1	1	yes	characteristic
254	C₂×C₅₉	D₄×Q₁₆	1	1	yes	characteristic
255	C₂×C₅₉	#3363	1	1	yes	characteristic
256	C₂×C₅₉	#3374	1	1	yes	characteristic
257	C₂²×Q₁₆	C₂²×C₅₉	1	2	yes	—
258	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
263	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
264	#462	—	2	8	no	—
265	#462	—	2	4	no	—
266	C₄×Q₁₆	—	2	4	no	—
267	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
270	C₂×#103	C₂²×C₅₉	1	2	yes	—
271	C₂×#103	C₂²×C₅₉	1	2	yes	—
272	C₂×#103	C₂²×C₅₉	1	2	yes	—
273	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
274	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
275	C₂×#103	C₂²×C₅₉	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
277	#398	—	2	2	no	—
278	#391	C₂²×C₅₉	1	2	yes	—
279	#389	—	2	1	no	—
280	#389	—	2	1	no	—
281	#389	—	2	2	no	—
282	#389	C₂²×C₅₉	1	2	yes	—
283	#384	—	2	1	no	—
284	#384	C₂²×C₅₉	1	1	yes	characteristic
285	C₄×C₄⋊C₄	—	2	1	no	—
286	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
287	#340	C₂²×C₅₉	1	2	yes	—
288	#336	C₂²×C₅₉	1	2	yes	—
289	C₅₉	#24732	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
291	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×Q₁₆	—	2	4	no	—
296	C₂×Q₁₆	—	2	4	no	—
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×Q₁₆	D₄×C₅₉	1	4	yes	—
299	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
300	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
302	C₄⋊Q₈	—	2	4	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	4	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	4	2	no	—
311	C₄×Q₈	D₄×C₅₉	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
323	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
331	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
332	#107	—	2	2	no	—
333	C₄⋊C₈	—	2	4	no	—
334	C₄⋊C₈	—	2	2	no	—
335	#103	—	2	2	no	—
336	#103	—	2	4	no	—
337	#103	—	2	4	no	—
338	#103	—	2	2	no	—
339	#103	—	2	4	no	—
340	#103	—	4	2	no	—
341	C₄×C₈	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	D₄×C₅₉	1	2	yes	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
361	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
362	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
363	C₂×Q₈	#41×C₅₉	1	2	yes	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
375	Q₁₆	—	2	8	no	—
376	Q₁₆	—	4	8	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	4	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	8	1	no	—
401	C₄⋊C₄	—	8	2	no	—
402	C₄⋊C₄	Q₁₆×C₅₉	1	4	yes	complemented
403	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	4	no	—
408	C₄²	—	4	2	no	—
409	C₄²	C₂×D₄×C₅₉	1	2	yes	—
410	C₄²	#41×C₅₉	1	2	yes	—
411	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	4	1	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	#121×C₅₉	1	4	yes	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	#121×C₅₉	1	2	yes	—
450	C₂×C₄	#121×C₅₉	1	2	yes	—
451	C₂×C₄	C₂×Q₁₆×C₅₉	1	4	yes	—
452	C₂×C₄	C₂×Q₁₆×C₅₉	1	2	yes	—
453	C₂×C₄	#137×C₅₉	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
458	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
459	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	4	2	no	—
462	C₈	—	4	1	no	—
463	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
464	C₂²	D₄²×C₅₉	1	1	yes	characteristic
465	C₂²	C₅₉×#548	1	1	yes	characteristic
466	C₂²	C₂²×Q₁₆×C₅₉	1	1	yes	characteristic
467	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
468	C₂²	C₅₉×#577	1	1	yes	characteristic
469	C₂²	C₅₉×#578	1	1	yes	characteristic
470	C₄	—	2	4	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	8	2	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	2	no	—
479	C₄	C₅₉×#462	1	4	yes	complemented
480	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
481	C₄	C₅₉×#537	1	1	yes	characteristic
482	C₄	C₅₉×#547	1	1	yes	characteristic
483	C₄	C₅₉×#553	1	1	yes	characteristic
484	C₂	C₅₉×#2416	1	1	yes	characteristic
485	C₂	C₂×C₅₉×#462	1	1	yes	characteristic
486	C₂	C₅₉×#3046	1	1	yes	characteristic
487	C₂	C₅₉×#3278	1	1	yes	characteristic
488	C₂	D₄×Q₁₆×C₅₉	1	1	yes	characteristic
489	C₂	C₅₉×#3363	1	1	yes	characteristic
490	C₂	C₅₉×#3374	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
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
156. C₄⋊C₄×C₅₉	Q₁₆	semidirect
217. #24732	C₅₉	direct (N × H)
234. C₄×C₅₉	#462	semidirect
289. C₅₉	#24732	direct (N × H)
402. C₄⋊C₄	Q₁₆×C₅₉	semidirect
479. C₄	C₅₉×#462	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#462	2
C₂×C₄×Q₁₆×C₅₉	2
C₅₉×#2546	2
Q₈×C₄⋊C₄×C₅₉	2
C₅₉×#2068	2
C₅₉×#2043	2
C₅₉×#1956	2
C₅₉×#1939	2
C₅₉×#1878	2
C₅₉×#1803	2
#24732	59

Subgroups — C59×#24732 #28436841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24732 #28436841