Subgroups — C₅₉×#32811 #28444920

Order 15104.

742 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	C₅₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#2861	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2056	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2055	C₂	1	2	yes	maximal
5	C₅₉×#2026	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2023	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2015	C₂	1	2	yes	maximal
10	C₅₉×#2013	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₅₉	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₅₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
19	C₂×#103×C₅₉	C₂²	1	2	yes	—
20	C₂×#103×C₅₉	C₂²	1	2	yes	—
21	C₂×#103×C₅₉	C₂²	1	2	yes	—
22	C₂×#102×C₅₉	C₂²	1	2	yes	—
23	C₅₉×#391	—	2	1	no	—
24	C₅₉×#391	—	2	1	no	—
25	C₅₉×#391	C₂²	1	2	yes	—
26	C₅₉×#391	C₂²	1	1	yes	characteristic
27	C₅₉×#391	C₂²	1	2	yes	—
28	C₅₉×#391	C₂²	1	1	yes	characteristic
29	C₅₉×#390	C₂²	1	1	yes	characteristic
30	C₅₉×#390	C₂²	1	1	yes	characteristic
31	C₅₉×#388	—	2	1	no	—
32	C₅₉×#388	—	2	1	no	—
33	C₅₉×#388	—	2	1	no	—
34	C₅₉×#388	—	2	1	no	—
35	C₅₉×#382	—	2	1	no	—
36	C₅₉×#382	—	2	1	no	—
37	C₄³×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#340	C₂²	1	2	yes	—
39	C₅₉×#340	C₂²	1	2	yes	—
40	C₅₉×#336	C₂²	1	1	yes	characteristic
41	C₅₉×#336	C₂²	1	2	yes	—
42	C₅₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₅₉	—	2	1	no	—
44	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₅₉	—	4	2	no	—
48	C₂×Q₁₆×C₅₉	—	4	2	no	—
49	C₂×Q₁₆×C₅₉	—	4	2	no	—
50	C₂×SD₁₆×C₅₉	—	4	2	no	—
51	C₂×SD₁₆×C₅₉	—	4	2	no	—
52	C₂×SD₁₆×C₅₉	—	4	2	no	—
53	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₅₉	—	4	2	no	—
56	C₄⋊Q₈×C₅₉	—	4	2	no	—
57	#125×C₅₉	—	4	2	no	—
58	#124×C₅₉	—	4	2	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₅₉	—	4	2	no	—
81	#103×C₅₉	—	4	2	no	—
82	#103×C₅₉	—	4	2	no	—
83	#103×C₅₉	—	4	2	no	—
84	#102×C₅₉	—	4	2	no	—
85	#95×C₅₉	—	2	2	no	—
86	#95×C₅₉	—	2	2	no	—
87	#95×C₅₉	—	2	2	no	—
88	#95×C₅₉	—	2	2	no	—
89	#95×C₅₉	—	2	1	no	—
90	#95×C₅₉	—	2	1	no	—
91	#95×C₅₉	—	2	1	no	—
92	#95×C₅₉	—	2	1	no	—
93	C₂⁴×C₅₉	—	2	1	no	—
94	C₂×Q₈×C₅₉	—	2	2	no	—
95	C₂×Q₈×C₅₉	—	2	2	no	—
96	C₂×Q₈×C₅₉	—	2	2	no	—
97	C₂×Q₈×C₅₉	—	2	2	no	—
98	C₂×Q₈×C₅₉	—	2	2	no	—
99	C₂×Q₈×C₅₉	—	2	2	no	—
100	C₂×Q₈×C₅₉	—	2	2	no	—
101	C₂×Q₈×C₅₉	—	2	1	no	—
102	C₂×Q₈×C₅₉	—	2	1	no	—
103	C₂×Q₈×C₅₉	—	2	2	no	—
104	C₂×Q₈×C₅₉	—	4	2	no	—
105	C₂×Q₈×C₅₉	—	4	2	no	—
106	C₂×Q₈×C₅₉	—	4	2	no	—
107	C₂×D₄×C₅₉	—	2	2	no	—
108	C₂×D₄×C₅₉	—	2	2	no	—
109	C₂×D₄×C₅₉	—	2	1	no	—
110	C₂×D₄×C₅₉	—	2	1	no	—
111	C₂²×C₄×C₅₉	—	2	1	no	—
112	C₂²×C₄×C₅₉	—	2	2	no	—
113	C₂²×C₄×C₅₉	—	2	2	no	—
114	C₂²×C₄×C₅₉	—	2	1	no	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
123	Q₁₆×C₅₉	—	4	8	no	—
124	SD₁₆×C₅₉	—	4	8	no	—
125	C₂×C₈×C₅₉	—	2	2	no	—
126	C₂×C₈×C₅₉	—	2	2	no	—
127	C₂×C₈×C₅₉	—	2	2	no	—
128	C₂×C₈×C₅₉	—	2	2	no	—
129	C₂×C₈×C₅₉	—	2	2	no	—
130	C₂×C₈×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	2	2	no	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	2	no	—
134	C₄⋊C₄×C₅₉	—	2	2	no	—
135	C₄⋊C₄×C₅₉	—	4	2	no	—
136	C₄⋊C₄×C₅₉	—	4	2	no	—
137	C₄⋊C₄×C₅₉	—	4	2	no	—
138	C₄⋊C₄×C₅₉	—	4	2	no	—
139	C₄⋊C₄×C₅₉	—	4	2	no	—
140	C₂²⋊C₄×C₅₉	—	4	2	no	—
141	C₂²⋊C₄×C₅₉	—	4	2	no	—
142	C₂²⋊C₄×C₅₉	—	4	2	no	—
143	C₂²⋊C₄×C₅₉	—	4	2	no	—
144	C₂²⋊C₄×C₅₉	—	4	2	no	—
145	C₂²⋊C₄×C₅₉	—	4	2	no	—
146	C₄²×C₅₉	—	2	2	no	—
147	C₄²×C₅₉	—	2	2	no	—
148	C₄²×C₅₉	—	2	2	no	—
149	C₄²×C₅₉	—	2	1	no	—
150	C₄²×C₅₉	—	2	2	no	—
151	C₄²×C₅₉	—	2	2	no	—
152	C₄²×C₅₉	—	2	1	no	—
153	C₄²×C₅₉	—	4	1	no	—
154	C₂³×C₅₉	—	4	1	no	—
155	C₂³×C₅₉	—	4	1	no	—
156	C₂³×C₅₉	—	4	1	no	—
157	C₂³×C₅₉	—	4	1	no	—
158	C₂³×C₅₉	—	4	1	no	—
159	C₂³×C₅₉	—	4	1	no	—
160	C₂³×C₅₉	—	4	1	no	—
161	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₅₉	—	4	2	no	—
163	Q₈×C₅₉	—	4	2	no	—
164	Q₈×C₅₉	—	4	2	no	—
165	Q₈×C₅₉	—	4	2	no	—
166	Q₈×C₅₉	—	4	2	no	—
167	Q₈×C₅₉	—	4	2	no	—
168	Q₈×C₅₉	—	8	4	no	—
169	D₄×C₅₉	—	4	2	no	—
170	D₄×C₅₉	—	4	2	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	2	1	no	—
173	C₂×C₄×C₅₉	—	2	1	no	—
174	C₂×C₄×C₅₉	—	2	1	no	—
175	C₂×C₄×C₅₉	—	2	1	no	—
176	C₂×C₄×C₅₉	—	2	1	no	—
177	C₂×C₄×C₅₉	—	2	1	no	—
178	C₂×C₄×C₅₉	—	2	1	no	—
179	C₂×C₄×C₅₉	—	2	1	no	—
180	C₂×C₄×C₅₉	—	2	1	no	—
181	C₂×C₄×C₅₉	—	2	1	no	—
182	C₂×C₄×C₅₉	—	2	1	no	—
183	C₂×C₄×C₅₉	—	2	1	no	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	1	no	—
186	C₂×C₄×C₅₉	—	4	1	no	—
187	C₂×C₄×C₅₉	—	4	1	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	4	2	no	—
190	C₂×C₄×C₅₉	—	4	2	no	—
191	C₂×C₄×C₅₉	—	4	2	no	—
192	C₂×C₄×C₅₉	—	4	1	no	—
193	C₂×C₄×C₅₉	—	4	1	no	—
194	C₂×C₄×C₅₉	—	4	2	no	—
195	C₂×C₄×C₅₉	—	4	1	no	—
196	C₂×C₄×C₅₉	—	4	2	no	—
197	C₂×C₄×C₅₉	—	4	1	no	—
198	C₂×C₄×C₅₉	—	4	1	no	—
199	C₂×C₄×C₅₉	—	4	1	no	—
200	C₂×C₄×C₅₉	—	4	2	no	—
201	C₂×C₄×C₅₉	#135	1	2	yes	—
202	C₂×C₄×C₅₉	#137	1	2	yes	—
203	C₂×C₄×C₅₉	#137	1	2	yes	—
204	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
206	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
207	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₅₉	—	4	2	no	—
209	C₈×C₅₉	—	4	2	no	—
210	#32811	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₅₉	—	8	1	no	—
212	C₂²×C₅₉	—	8	1	no	—
213	C₂²×C₅₉	—	8	1	no	—
214	C₂²×C₅₉	—	8	1	no	—
215	C₂²×C₅₉	—	8	1	no	—
216	C₂²×C₅₉	—	8	1	no	—
217	C₂²×C₅₉	—	8	1	no	—
218	C₂²×C₅₉	#535	1	1	yes	characteristic
219	C₂²×C₅₉	#535	1	1	yes	characteristic
220	C₂²×C₅₉	#537	1	1	yes	characteristic
221	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
222	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
223	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
224	C₂²×C₅₉	#575	1	1	yes	characteristic
225	C₄×C₅₉	—	2	2	no	—
226	C₄×C₅₉	—	2	2	no	—
227	C₄×C₅₉	—	2	2	no	—
228	C₄×C₅₉	—	4	1	no	—
229	C₄×C₅₉	—	4	1	no	—
230	C₄×C₅₉	—	4	1	no	—
231	C₄×C₅₉	—	8	1	no	—
232	C₄×C₅₉	—	8	2	no	—
233	C₄×C₅₉	—	8	1	no	—
234	C₄×C₅₉	—	8	2	no	—
235	C₄×C₅₉	—	8	1	no	—
236	C₄×C₅₉	H(3,𝔽₄)	1	2	yes	—
237	C₄×C₅₉	#562	1	2	yes	—
238	#2862	C₂×C₅₉	1	1	yes	characteristic, complemented
239	#2861	C₂×C₅₉	1	1	yes	characteristic
240	#2056	C₂×C₅₉	1	2	yes	complemented
241	#2055	C₂×C₅₉	1	2	yes	—
242	#2026	C₂×C₅₉	1	2	yes	complemented
243	#2024	C₂×C₅₉	1	1	yes	characteristic, complemented
244	#2023	C₂×C₅₉	1	1	yes	characteristic
245	#2016	C₂×C₅₉	1	1	yes	characteristic, complemented
246	#2015	C₂×C₅₉	1	2	yes	—
247	#2013	C₂×C₅₉	1	1	yes	characteristic
248	#1831	C₂×C₅₉	1	1	yes	characteristic, complemented
249	C₂×C₅₉	—	16	1	no	—
250	C₂×C₅₉	#2819	1	1	yes	characteristic
251	C₂×C₅₉	#3210	1	1	yes	characteristic
252	C₂×C₅₉	#3211	1	1	yes	characteristic
253	C₂×C₅₉	#3216	1	1	yes	characteristic
254	C₂×C₅₉	#3218	1	1	yes	characteristic
255	C₂×C₅₉	#3248	1	1	yes	characteristic
256	C₂×C₅₉	#3252	1	1	yes	characteristic
257	C₂²×Q₁₆	C₂²×C₅₉	1	2	yes	—
258	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	—
259	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
261	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
262	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
264	C₂×#103	C₂²×C₅₉	1	2	yes	—
265	C₂×#103	C₂²×C₅₉	1	2	yes	—
266	C₂×#103	C₂²×C₅₉	1	2	yes	—
267	C₂×#102	C₂²×C₅₉	1	2	yes	—
268	#391	—	2	1	no	—
269	#391	—	2	1	no	—
270	#391	C₂²×C₅₉	1	2	yes	—
271	#391	C₂²×C₅₉	1	1	yes	characteristic
272	#391	C₂²×C₅₉	1	1	yes	characteristic
273	#391	C₂²×C₅₉	1	2	yes	—
274	#390	C₂²×C₅₉	1	1	yes	characteristic
275	#390	C₂²×C₅₉	1	1	yes	characteristic
276	#388	—	2	1	no	—
277	#388	—	2	1	no	—
278	#388	—	2	1	no	—
279	#388	—	2	1	no	—
280	#382	—	2	1	no	—
281	#382	—	2	1	no	—
282	C₄³	C₂²×C₅₉	1	1	yes	characteristic
283	#340	C₂²×C₅₉	1	2	yes	—
284	#340	C₂²×C₅₉	1	2	yes	—
285	#336	C₂²×C₅₉	1	1	yes	characteristic
286	#336	C₂²×C₅₉	1	2	yes	—
287	#336	C₂²×C₅₉	1	1	yes	characteristic
288	C₅₉	#32811	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
292	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
293	C₂×Q₁₆	—	4	2	no	—
294	C₂×Q₁₆	—	4	2	no	—
295	C₂×Q₁₆	—	4	2	no	—
296	C₂×SD₁₆	—	4	2	no	—
297	C₂×SD₁₆	—	4	2	no	—
298	C₂×SD₁₆	—	4	2	no	—
299	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
300	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
301	C₄⋊Q₈	—	4	2	no	—
302	C₄⋊Q₈	—	4	2	no	—
303	#125	—	4	2	no	—
304	#124	—	4	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
321	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
322	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
326	C₄⋊C₈	—	4	2	no	—
327	#103	—	4	2	no	—
328	#103	—	4	2	no	—
329	#103	—	4	2	no	—
330	#102	—	4	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	C₂⁴	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	—	4	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
369	Q₁₆	—	4	8	no	—
370	SD₁₆	—	4	8	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	#135×C₅₉	1	2	yes	—
448	C₂×C₄	#137×C₅₉	1	2	yes	—
449	C₂×C₄	#137×C₅₉	1	2	yes	—
450	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
451	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
452	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
453	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	C₅₉×#535	1	1	yes	characteristic
464	C₂²	C₅₉×#535	1	1	yes	characteristic
465	C₂²	C₅₉×#537	1	1	yes	characteristic
466	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
467	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
468	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
469	C₂²	C₅₉×#575	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	C₅₉×H(3,𝔽₄)	1	2	yes	—
482	C₄	C₅₉×#562	1	2	yes	—
483	C₂	—	16	1	no	—
484	C₂	C₅₉×#2819	1	1	yes	characteristic
485	C₂	C₅₉×#3210	1	1	yes	characteristic
486	C₂	C₅₉×#3211	1	1	yes	characteristic
487	C₂	C₅₉×#3216	1	1	yes	characteristic
488	C₂	C₅₉×#3218	1	1	yes	characteristic
489	C₂	C₅₉×#3248	1	1	yes	characteristic
490	C₂	C₅₉×#3252	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 ◁ C₄³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2862	C₂	semidirect
3. C₅₉×#2056	C₂	semidirect
5. C₅₉×#2026	C₂	semidirect
6. C₅₉×#2024	C₂	semidirect
8. C₅₉×#2016	C₂	semidirect
11. C₅₉×#1831	C₂	semidirect
210. #32811	C₅₉	direct (N × H)
238. #2862	C₂×C₅₉	semidirect
240. #2056	C₂×C₅₉	semidirect
242. #2026	C₂×C₅₉	semidirect
243. #2024	C₂×C₅₉	semidirect
245. #2016	C₂×C₅₉	semidirect
248. #1831	C₂×C₅₉	semidirect
288. C₅₉	#32811	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2862	2
C₅₉×#2861	2
C₅₉×#2056	2
C₅₉×#2055	2
C₅₉×#2026	2
C₅₉×#2024	2
C₅₉×#2023	2
C₅₉×#2016	2
C₅₉×#2015	2
C₅₉×#2013	2
C₅₉×#1831	2
#32811	59

Subgroups — C59×#32811 #28444920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#32811 #28444920