Subgroups — C₅₉×#10261 #28422370

Order 15104.

678 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#459	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₅₉	—	2	1	no	—
9	C₂²×D₈×C₅₉	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
13	C₅₉×#486	—	2	2	no	—
14	C₅₉×#486	—	2	2	no	—
15	C₅₉×#461	—	2	2	no	—
16	C₅₉×#461	—	2	2	no	—
17	C₅₉×#459	—	2	2	no	—
18	C₅₉×#459	—	2	2	no	—
19	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#103×C₅₉	—	2	1	no	—
23	C₂×#102×C₅₉	—	2	2	no	—
24	C₂×#102×C₅₉	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₅₉	—	2	2	no	—
26	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#332	—	2	2	no	—
28	C₅₉×#331	—	2	2	no	—
29	C₂²×Q₈×C₅₉	—	2	1	no	—
30	C₂²×D₄×C₅₉	—	2	1	no	—
31	C₂²×D₄×C₅₉	—	2	1	no	—
32	C₂²×D₄×C₅₉	—	2	1	no	—
33	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₅₉	—	2	1	no	—
35	C₂×SD₁₆×C₅₉	—	2	4	no	—
36	C₂×SD₁₆×C₅₉	—	4	2	no	—
37	C₂×SD₁₆×C₅₉	—	4	2	no	—
38	C₂×D₈×C₅₉	—	2	4	no	—
39	C₂×D₈×C₅₉	—	4	2	no	—
40	C₂×D₈×C₅₉	—	4	2	no	—
41	C₂²×C₈×C₅₉	—	2	1	no	—
42	C₂²×C₈×C₅₉	—	2	1	no	—
43	C₂²×C₈×C₅₉	—	2	1	no	—
44	C₂²×C₈×C₅₉	D₄	1	2	yes	—
45	C₄⋊Q₈×C₅₉	—	2	1	no	—
46	C₄⋊Q₈×C₅₉	—	2	1	no	—
47	C₄⋊Q₈×C₅₉	—	2	1	no	—
48	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
49	#127×C₅₉	—	2	1	no	—
50	#127×C₅₉	—	2	1	no	—
51	#127×C₅₉	—	2	1	no	—
52	#127×C₅₉	D₄	1	2	yes	—
53	C₄×D₄×C₅₉	—	2	1	no	—
54	C₄×D₄×C₅₉	—	2	1	no	—
55	C₄×D₄×C₅₉	—	2	1	no	—
56	C₄×D₄×C₅₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
61	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₅₉	—	2	1	no	—
63	C₄⋊C₈×C₅₉	—	2	1	no	—
64	C₄⋊C₈×C₅₉	—	2	1	no	—
65	C₄⋊C₈×C₅₉	—	2	1	no	—
66	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
67	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
68	#103×C₅₉	—	2	4	no	—
69	#102×C₅₉	—	2	4	no	—
70	#102×C₅₉	—	2	8	no	—
71	C₂²⋊C₈×C₅₉	—	4	4	no	—
72	C₄×C₈×C₅₉	—	2	1	no	—
73	C₄×C₈×C₅₉	—	2	1	no	—
74	C₂⁴×C₅₉	—	2	1	no	—
75	C₂⁴×C₅₉	—	4	1	no	—
76	C₂×Q₈×C₅₉	—	2	2	no	—
77	C₂×Q₈×C₅₉	—	4	1	no	—
78	C₂×Q₈×C₅₉	—	4	1	no	—
79	C₂×Q₈×C₅₉	—	4	1	no	—
80	C₂×Q₈×C₅₉	—	4	1	no	—
81	C₂×Q₈×C₅₉	—	4	1	no	—
82	C₂×D₄×C₅₉	—	2	1	no	—
83	C₂×D₄×C₅₉	—	2	1	no	—
84	C₂×D₄×C₅₉	—	2	2	no	—
85	C₂×D₄×C₅₉	—	2	2	no	—
86	C₂×D₄×C₅₉	—	2	2	no	—
87	C₂×D₄×C₅₉	—	2	1	no	—
88	C₂×D₄×C₅₉	—	2	1	no	—
89	C₂×D₄×C₅₉	—	2	1	no	—
90	C₂×D₄×C₅₉	—	4	1	no	—
91	C₂×D₄×C₅₉	—	4	1	no	—
92	C₂×D₄×C₅₉	—	4	1	no	—
93	C₂×D₄×C₅₉	—	4	1	no	—
94	C₂×D₄×C₅₉	—	4	1	no	—
95	C₂×D₄×C₅₉	—	4	2	no	—
96	C₂×D₄×C₅₉	—	4	1	no	—
97	C₂×D₄×C₅₉	—	4	1	no	—
98	C₂×D₄×C₅₉	—	4	2	no	—
99	C₂×D₄×C₅₉	—	8	2	no	—
100	C₂×D₄×C₅₉	D₈	1	2	yes	—
101	C₂²×C₄×C₅₉	—	2	1	no	—
102	C₂²×C₄×C₅₉	—	4	1	no	—
103	C₂²×C₄×C₅₉	—	4	1	no	—
104	C₂²×C₄×C₅₉	—	4	1	no	—
105	C₂²×C₄×C₅₉	—	4	2	no	—
106	C₂²×C₄×C₅₉	—	4	2	no	—
107	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
110	SD₁₆×C₅₉	—	4	8	no	—
111	D₈×C₅₉	—	4	8	no	—
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₂×C₈×C₅₉	—	2	2	no	—
114	C₂×C₈×C₅₉	—	2	2	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	—	2	2	no	—
117	C₂×C₈×C₅₉	—	4	1	no	—
118	C₂×C₈×C₅₉	—	4	1	no	—
119	C₂×C₈×C₅₉	—	4	1	no	—
120	C₂×C₈×C₅₉	—	4	1	no	—
121	C₂×C₈×C₅₉	—	4	1	no	—
122	C₂×C₈×C₅₉	—	4	2	no	—
123	C₄⋊C₄×C₅₉	—	2	2	no	—
124	C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₄⋊C₄×C₅₉	—	2	2	no	—
127	C₄⋊C₄×C₅₉	—	4	1	no	—
128	C₄⋊C₄×C₅₉	—	4	1	no	—
129	C₂²⋊C₄×C₅₉	—	4	1	no	—
130	C₂²⋊C₄×C₅₉	—	4	1	no	—
131	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₅₉	—	2	2	no	—
136	C₂³×C₅₉	—	4	1	no	—
137	C₂³×C₅₉	—	4	2	no	—
138	C₂³×C₅₉	—	4	1	no	—
139	C₂³×C₅₉	—	4	2	no	—
140	C₂³×C₅₉	—	4	2	no	—
141	C₂³×C₅₉	—	8	2	no	—
142	C₂³×C₅₉	—	8	1	no	—
143	C₂³×C₅₉	—	8	1	no	—
144	C₂³×C₅₉	—	8	2	no	—
145	C₂³×C₅₉	#121	1	1	yes	characteristic
146	Q₈×C₅₉	—	4	2	no	—
147	Q₈×C₅₉	—	4	2	no	—
148	Q₈×C₅₉	—	8	1	no	—
149	Q₈×C₅₉	—	8	1	no	—
150	D₄×C₅₉	—	2	2	no	—
151	D₄×C₅₉	—	2	2	no	—
152	D₄×C₅₉	—	4	2	no	—
153	D₄×C₅₉	—	4	1	no	—
154	D₄×C₅₉	—	4	1	no	—
155	D₄×C₅₉	—	4	2	no	—
156	D₄×C₅₉	—	4	4	no	—
157	D₄×C₅₉	—	8	2	no	—
158	D₄×C₅₉	—	8	2	no	—
159	D₄×C₅₉	—	8	1	no	—
160	D₄×C₅₉	—	8	1	no	—
161	D₄×C₅₉	—	8	1	no	—
162	D₄×C₅₉	—	8	1	no	—
163	C₂×C₄×C₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	—	4	1	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	4	2	no	—
167	C₂×C₄×C₅₉	—	8	1	no	—
168	C₂×C₄×C₅₉	—	8	1	no	—
169	C₂×C₄×C₅₉	—	8	2	no	—
170	C₂×C₄×C₅₉	—	8	1	no	—
171	C₂×C₄×C₅₉	—	8	1	no	—
172	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
173	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
180	C₂×C₄×C₅₉	#135	1	2	yes	—
181	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
184	C₈×C₅₉	—	4	2	no	—
185	C₈×C₅₉	—	4	2	no	—
186	C₈×C₅₉	—	4	2	no	—
187	C₈×C₅₉	—	8	1	no	—
188	#10261	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₅₉	—	4	4	no	—
190	C₂²×C₅₉	—	4	2	no	—
191	C₂²×C₅₉	—	8	2	no	—
192	C₂²×C₅₉	—	8	1	no	—
193	C₂²×C₅₉	—	8	1	no	—
194	C₂²×C₅₉	—	8	2	no	—
195	C₂²×C₅₉	—	8	2	no	—
196	C₂²×C₅₉	—	8	2	no	—
197	C₂²×C₅₉	—	16	2	no	—
198	C₂²×C₅₉	—	16	2	no	—
199	C₂²×C₅₉	#392	1	1	yes	characteristic
200	C₂²×C₅₉	#463	1	2	yes	—
201	C₂²×C₅₉	#466	1	1	yes	characteristic
202	C₂²×C₅₉	#469	1	1	yes	characteristic
203	C₂²×C₅₉	#471	1	2	yes	—
204	C₄×C₅₉	—	2	1	no	—
205	C₄×C₅₉	—	2	1	no	—
206	C₄×C₅₉	—	8	2	no	—
207	C₄×C₅₉	—	8	1	no	—
208	C₄×C₅₉	#447	1	1	yes	characteristic
209	C₄×C₅₉	#447	1	1	yes	characteristic
210	C₄×C₅₉	#449	1	1	yes	characteristic
211	C₄×C₅₉	#449	1	1	yes	characteristic
212	C₄×C₅₉	#449	1	2	yes	—
213	C₄×C₅₉	#495	1	1	yes	characteristic
214	C₄×C₅₉	#496	1	1	yes	characteristic
215	C₂×#486	C₂×C₅₉	1	1	yes	characteristic, complemented
216	C₂×#461	C₂×C₅₉	1	1	yes	characteristic, complemented
217	C₂×#459	C₂×C₅₉	1	1	yes	characteristic
218	#1954	C₂×C₅₉	1	1	yes	characteristic, complemented
219	C₂×#332	C₂×C₅₉	1	1	yes	characteristic, complemented
220	C₂×#331	C₂×C₅₉	1	1	yes	characteristic, complemented
221	#1277	C₂×C₅₉	1	1	yes	characteristic, complemented
222	C₂×C₅₉	—	8	2	no	—
223	C₂×C₅₉	—	16	2	no	—
224	C₂×C₅₉	#1681	1	2	yes	—
225	C₂×C₅₉	#1701	1	2	yes	—
226	C₂×C₅₉	#1999	1	1	yes	characteristic
227	C₂×C₅₉	#2012	1	1	yes	characteristic
228	C₂×C₅₉	#2019	1	1	yes	characteristic
229	C₂²×SD₁₆	—	2	1	no	—
230	C₂²×D₈	—	2	1	no	—
231	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
232	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
234	#486	—	2	2	no	—
235	#486	—	2	2	no	—
236	#461	—	2	2	no	—
237	#461	—	2	2	no	—
238	#459	—	2	2	no	—
239	#459	—	2	2	no	—
240	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
242	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
243	C₂×#103	—	2	1	no	—
244	C₂×#102	—	2	2	no	—
245	C₂×#102	—	2	1	no	—
246	C₂×C₂²⋊C₈	—	2	2	no	—
247	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
248	#332	—	2	2	no	—
249	#331	—	2	2	no	—
250	C₅₉	#10261	1	1	yes	characteristic, direct product factor, Sylow
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂×SD₁₆	—	4	2	no	—
260	C₂×D₈	—	2	4	no	—
261	C₂×D₈	—	4	2	no	—
262	C₂×D₈	—	4	2	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	D₄×C₅₉	1	2	yes	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	—	2	1	no	—
274	#127	D₄×C₅₉	1	2	yes	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	D₄×C₅₉	1	2	yes	—
289	C₄⋊C₈	D₄×C₅₉	1	2	yes	—
290	#103	—	2	4	no	—
291	#102	—	2	4	no	—
292	#102	—	2	8	no	—
293	C₂²⋊C₈	—	4	4	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₂⁴	—	2	1	no	—
297	C₂⁴	—	4	1	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	8	2	no	—
322	C₂×D₄	D₈×C₅₉	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
331	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
332	SD₁₆	—	4	8	no	—
333	D₈	—	4	8	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	4	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
356	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	8	2	no	—
364	C₂³	—	8	1	no	—
365	C₂³	—	8	1	no	—
366	C₂³	—	8	2	no	—
367	C₂³	#121×C₅₉	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	4	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	1	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
395	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
396	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
397	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
398	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
399	C₂×C₄	#127×C₅₉	1	1	yes	characteristic
400	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
401	C₂×C₄	#135×C₅₉	1	1	yes	characteristic
402	C₂×C₄	#135×C₅₉	1	2	yes	—
403	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
404	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
405	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
406	C₈	—	4	2	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	8	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	16	2	no	—
419	C₂²	—	16	2	no	—
420	C₂²	C₅₉×#392	1	1	yes	characteristic
421	C₂²	C₅₉×#463	1	2	yes	—
422	C₂²	C₅₉×#466	1	1	yes	characteristic
423	C₂²	C₅₉×#469	1	1	yes	characteristic
424	C₂²	C₅₉×#471	1	2	yes	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	1	no	—
429	C₄	C₅₉×#447	1	1	yes	characteristic
430	C₄	C₅₉×#447	1	1	yes	characteristic
431	C₄	C₅₉×#449	1	1	yes	characteristic
432	C₄	C₅₉×#449	1	1	yes	characteristic
433	C₄	C₅₉×#449	1	2	yes	—
434	C₄	C₅₉×#495	1	1	yes	characteristic
435	C₄	C₅₉×#496	1	1	yes	characteristic
436	C₂	—	8	2	no	—
437	C₂	—	16	2	no	—
438	C₂	C₅₉×#1681	1	2	yes	—
439	C₂	C₅₉×#1701	1	2	yes	—
440	C₂	C₅₉×#1999	1	1	yes	characteristic
441	C₂	C₅₉×#2012	1	1	yes	characteristic
442	C₂	C₅₉×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₂×C₅₉×#459	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#486	C₂	semidirect
2. C₂×C₅₉×#461	C₂	semidirect
4. C₅₉×#1954	C₂	semidirect
5. C₂×C₅₉×#332	C₂	semidirect
6. C₂×C₅₉×#331	C₂	semidirect
7. C₅₉×#1277	C₂	semidirect
188. #10261	C₅₉	direct (N × H)
215. C₂×#486	C₂×C₅₉	semidirect
216. C₂×#461	C₂×C₅₉	semidirect
218. #1954	C₂×C₅₉	semidirect
219. C₂×#332	C₂×C₅₉	semidirect
220. C₂×#331	C₂×C₅₉	semidirect
221. #1277	C₂×C₅₉	semidirect
250. C₅₉	#10261	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×#486	2
C₂×C₅₉×#461	2
C₂×C₅₉×#459	2
C₅₉×#1954	2
C₂×C₅₉×#332	2
C₂×C₅₉×#331	2
C₅₉×#1277	2
#10261	59

Subgroups — C59×#10261 #28422370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#10261 #28422370