Subgroups — C₅₉×#10066 #28422175

Order 15104.

634 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#461	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2547	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₅₉	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×#124×C₅₉	—	2	1	no	—
12	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
13	C₅₉×#500	—	2	2	no	—
14	C₅₉×#500	—	2	2	no	—
15	C₅₉×#461	—	2	2	no	—
16	C₅₉×#461	—	2	2	no	—
17	C₂×#107×C₅₉	—	2	2	no	—
18	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#103×C₅₉	—	2	1	no	—
21	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₅₉×#397	—	2	2	no	—
23	C₅₉×#391	—	2	1	no	—
24	C₅₉×#380	—	2	2	no	—
25	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#340	—	2	2	no	—
27	C₅₉×#332	—	2	2	no	—
28	C₅₉×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₅₉	—	2	1	no	—
30	C₂²×Q₈×C₅₉	—	2	1	no	—
31	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₅₉	—	2	1	no	—
33	C₂×SD₁₆×C₅₉	—	2	4	no	—
34	C₂×SD₁₆×C₅₉	—	4	2	no	—
35	C₂×SD₁₆×C₅₉	—	4	2	no	—
36	C₂²×C₈×C₅₉	—	2	1	no	—
37	C₂²×C₈×C₅₉	—	2	1	no	—
38	C₂²×C₈×C₅₉	—	2	1	no	—
39	C₄⋊Q₈×C₅₉	—	2	1	no	—
40	C₄⋊Q₈×C₅₉	—	2	1	no	—
41	C₄⋊Q₈×C₅₉	—	2	1	no	—
42	C₄⋊Q₈×C₅₉	—	2	1	no	—
43	C₄⋊Q₈×C₅₉	—	2	1	no	—
44	C₄⋊Q₈×C₅₉	—	2	1	no	—
45	C₄⋊Q₈×C₅₉	—	2	1	no	—
46	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
47	#124×C₅₉	—	4	2	no	—
48	#124×C₅₉	—	4	2	no	—
49	C₄×D₄×C₅₉	—	2	1	no	—
50	C₄×D₄×C₅₉	—	2	1	no	—
51	C₄×D₄×C₅₉	—	2	1	no	—
52	C₄×D₄×C₅₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
61	C₂×C₄²×C₅₉	—	2	1	no	—
62	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
63	#107×C₅₉	—	2	8	no	—
64	C₄⋊C₈×C₅₉	—	2	1	no	—
65	C₄⋊C₈×C₅₉	—	2	1	no	—
66	C₄⋊C₈×C₅₉	—	2	1	no	—
67	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
68	#103×C₅₉	—	2	4	no	—
69	C₄×C₈×C₅₉	—	2	1	no	—
70	C₄×C₈×C₅₉	D₄	1	2	yes	—
71	#95×C₅₉	—	2	4	no	—
72	#95×C₅₉	—	2	1	no	—
73	C₂⁴×C₅₉	—	2	1	no	—
74	C₂×Q₈×C₅₉	—	2	2	no	—
75	C₂×Q₈×C₅₉	—	4	1	no	—
76	C₂×Q₈×C₅₉	—	4	1	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×Q₈×C₅₉	—	4	1	no	—
83	C₂×Q₈×C₅₉	—	4	1	no	—
84	C₂×Q₈×C₅₉	—	4	1	no	—
85	C₂×Q₈×C₅₉	—	4	1	no	—
86	C₂×D₄×C₅₉	—	2	1	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	—	2	1	no	—
91	C₂×D₄×C₅₉	D₈	1	2	yes	—
92	C₂²×C₄×C₅₉	—	2	1	no	—
93	C₂²×C₄×C₅₉	—	2	2	no	—
94	C₂²×C₄×C₅₉	—	2	2	no	—
95	C₂²×C₄×C₅₉	—	4	1	no	—
96	C₂²×C₄×C₅₉	—	4	1	no	—
97	C₂²×C₄×C₅₉	—	4	1	no	—
98	C₂²×C₄×C₅₉	—	4	2	no	—
99	C₂²×C₄×C₅₉	—	4	2	no	—
100	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
103	SD₁₆×C₅₉	—	4	8	no	—
104	C₂×C₈×C₅₉	—	2	4	no	—
105	C₂×C₈×C₅₉	—	2	2	no	—
106	C₂×C₈×C₅₉	—	2	2	no	—
107	C₂×C₈×C₅₉	—	4	1	no	—
108	C₂×C₈×C₅₉	—	4	1	no	—
109	C₂×C₈×C₅₉	—	4	1	no	—
110	C₂×C₈×C₅₉	—	4	2	no	—
111	C₄⋊C₄×C₅₉	—	2	1	no	—
112	C₄⋊C₄×C₅₉	—	2	2	no	—
113	C₄⋊C₄×C₅₉	—	2	2	no	—
114	C₄⋊C₄×C₅₉	—	2	2	no	—
115	C₄⋊C₄×C₅₉	—	2	1	no	—
116	C₄⋊C₄×C₅₉	—	2	2	no	—
117	C₄⋊C₄×C₅₉	—	2	2	no	—
118	C₄⋊C₄×C₅₉	—	2	2	no	—
119	C₄⋊C₄×C₅₉	—	4	1	no	—
120	C₄⋊C₄×C₅₉	—	4	1	no	—
121	C₄⋊C₄×C₅₉	—	4	1	no	—
122	C₄⋊C₄×C₅₉	—	4	1	no	—
123	C₂²⋊C₄×C₅₉	—	4	8	no	—
124	C₂²⋊C₄×C₅₉	—	4	1	no	—
125	C₂²⋊C₄×C₅₉	—	4	1	no	—
126	C₄²×C₅₉	—	4	1	no	—
127	C₄²×C₅₉	—	4	1	no	—
128	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅₉	#41	1	1	yes	characteristic
132	C₂³×C₅₉	—	2	2	no	—
133	C₂³×C₅₉	—	4	1	no	—
134	C₂³×C₅₉	—	4	1	no	—
135	C₂³×C₅₉	—	4	2	no	—
136	C₂³×C₅₉	—	4	2	no	—
137	C₂³×C₅₉	#120	1	1	yes	characteristic
138	Q₈×C₅₉	—	4	2	no	—
139	Q₈×C₅₉	—	4	2	no	—
140	Q₈×C₅₉	—	8	1	no	—
141	Q₈×C₅₉	—	8	1	no	—
142	Q₈×C₅₉	—	8	1	no	—
143	Q₈×C₅₉	—	8	1	no	—
144	Q₈×C₅₉	—	8	1	no	—
145	Q₈×C₅₉	—	8	1	no	—
146	D₄×C₅₉	—	2	2	no	—
147	D₄×C₅₉	—	2	2	no	—
148	D₄×C₅₉	—	4	1	no	—
149	D₄×C₅₉	—	4	1	no	—
150	C₂×C₄×C₅₉	—	2	2	no	—
151	C₂×C₄×C₅₉	—	4	1	no	—
152	C₂×C₄×C₅₉	—	4	2	no	—
153	C₂×C₄×C₅₉	—	4	2	no	—
154	C₂×C₄×C₅₉	—	4	2	no	—
155	C₂×C₄×C₅₉	—	4	2	no	—
156	C₂×C₄×C₅₉	—	4	2	no	—
157	C₂×C₄×C₅₉	—	4	2	no	—
158	C₂×C₄×C₅₉	—	4	2	no	—
159	C₂×C₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	—	8	1	no	—
161	C₂×C₄×C₅₉	—	8	1	no	—
162	C₂×C₄×C₅₉	—	8	2	no	—
163	C₂×C₄×C₅₉	—	8	1	no	—
164	C₂×C₄×C₅₉	—	8	1	no	—
165	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
166	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
167	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
173	C₂×C₄×C₅₉	#135	1	2	yes	—
174	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₅₉	#137	1	2	yes	—
177	C₈×C₅₉	—	2	4	no	—
178	C₈×C₅₉	—	4	2	no	—
179	C₈×C₅₉	—	8	1	no	—
180	#10066	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₅₉	—	4	4	no	—
182	C₂²×C₅₉	—	4	2	no	—
183	C₂²×C₅₉	—	8	2	no	—
184	C₂²×C₅₉	—	8	1	no	—
185	C₂²×C₅₉	—	8	1	no	—
186	C₂²×C₅₉	#392	1	1	yes	characteristic
187	C₂²×C₅₉	#447	1	1	yes	characteristic
188	C₂²×C₅₉	#449	1	1	yes	characteristic
189	C₂²×C₅₉	#452	1	2	yes	—
190	C₂²×C₅₉	#456	1	2	yes	—
191	C₄×C₅₉	—	2	1	no	—
192	C₄×C₅₉	—	2	1	no	—
193	C₄×C₅₉	—	8	2	no	—
194	C₄×C₅₉	—	8	2	no	—
195	C₄×C₅₉	—	8	2	no	—
196	C₄×C₅₉	—	8	1	no	—
197	C₄×C₅₉	#447	1	1	yes	characteristic
198	C₄×C₅₉	#449	1	1	yes	characteristic
199	C₄×C₅₉	#464	1	2	yes	—
200	C₄×C₅₉	#466	1	1	yes	characteristic
201	C₄×C₅₉	#469	1	1	yes	characteristic
202	C₄×C₅₉	#495	1	1	yes	characteristic
203	C₄×C₅₉	#497	1	1	yes	characteristic
204	C₂×#500	C₂×C₅₉	1	1	yes	characteristic, complemented
205	C₂×#461	C₂×C₅₉	1	1	yes	characteristic
206	#2547	C₂×C₅₉	1	1	yes	characteristic
207	#1988	C₂×C₅₉	1	1	yes	characteristic, complemented
208	C₂×#332	C₂×C₅₉	1	1	yes	characteristic, complemented
209	C₂×D₄⋊C₈	C₂×C₅₉	1	1	yes	characteristic
210	#1279	C₂×C₅₉	1	1	yes	characteristic, complemented
211	C₂×C₅₉	—	8	2	no	—
212	C₂×C₅₉	#1647	1	2	yes	—
213	C₂×C₅₉	#1650	1	2	yes	—
214	C₂×C₅₉	#1999	1	1	yes	characteristic
215	C₂×C₅₉	#2005	1	1	yes	characteristic
216	C₂×C₅₉	#2015	1	1	yes	characteristic
217	C₂²×SD₁₆	—	2	1	no	—
218	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
220	C₂×#124	—	2	1	no	—
221	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
222	#500	—	2	2	no	—
223	#500	—	2	2	no	—
224	#461	—	2	2	no	—
225	#461	—	2	2	no	—
226	C₂×#107	—	2	2	no	—
227	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
229	C₂×#103	—	2	1	no	—
230	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
231	#397	—	2	2	no	—
232	#391	—	2	1	no	—
233	#380	—	2	2	no	—
234	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
235	#340	—	2	2	no	—
236	#332	—	2	2	no	—
237	D₄⋊C₈	—	2	2	no	—
238	C₅₉	#10066	1	1	yes	characteristic, direct product factor, Sylow
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂×SD₁₆	—	2	4	no	—
244	C₂×SD₁₆	—	4	2	no	—
245	C₂×SD₁₆	—	4	2	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
257	#124	—	4	2	no	—
258	#124	—	4	2	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
268	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	4	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
273	#107	—	2	8	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	D₄×C₅₉	1	2	yes	—
278	#103	—	2	4	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	D₄×C₅₉	1	2	yes	—
281	#95	—	2	4	no	—
282	#95	—	2	1	no	—
283	C₂⁴	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	D₈×C₅₉	1	2	yes	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
313	SD₁₆	—	4	8	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	8	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
341	C₄²	#41×C₅₉	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	#120×C₅₉	1	1	yes	characteristic
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	8	1	no	—
351	Q₈	—	8	1	no	—
352	Q₈	—	8	1	no	—
353	Q₈	—	8	1	no	—
354	Q₈	—	8	1	no	—
355	Q₈	—	8	1	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	1	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
376	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
377	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
378	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
379	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
380	C₂×C₄	#127×C₅₉	1	1	yes	characteristic
381	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
382	C₂×C₄	#135×C₅₉	1	1	yes	characteristic
383	C₂×C₄	#135×C₅₉	1	2	yes	—
384	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
385	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
386	C₂×C₄	#137×C₅₉	1	2	yes	—
387	C₈	—	2	4	no	—
388	C₈	—	4	2	no	—
389	C₈	—	8	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₅₉×#392	1	1	yes	characteristic
396	C₂²	C₅₉×#447	1	1	yes	characteristic
397	C₂²	C₅₉×#449	1	1	yes	characteristic
398	C₂²	C₅₉×#452	1	2	yes	—
399	C₂²	C₅₉×#456	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	2	no	—
406	C₄	C₅₉×#447	1	1	yes	characteristic
407	C₄	C₅₉×#449	1	1	yes	characteristic
408	C₄	C₅₉×#464	1	2	yes	—
409	C₄	C₅₉×#466	1	1	yes	characteristic
410	C₄	C₅₉×#469	1	1	yes	characteristic
411	C₄	C₅₉×#495	1	1	yes	characteristic
412	C₄	C₅₉×#497	1	1	yes	characteristic
413	C₂	—	8	2	no	—
414	C₂	C₅₉×#1647	1	2	yes	—
415	C₂	C₅₉×#1650	1	2	yes	—
416	C₂	C₅₉×#1999	1	1	yes	characteristic
417	C₂	C₅₉×#2005	1	1	yes	characteristic
418	C₂	C₅₉×#2015	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₂²×D₄×C₅₉	D₄
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×#500	C₂	semidirect
4. C₅₉×#1988	C₂	semidirect
5. C₂×C₅₉×#332	C₂	semidirect
7. C₅₉×#1279	C₂	semidirect
180. #10066	C₅₉	direct (N × H)
204. C₂×#500	C₂×C₅₉	semidirect
207. #1988	C₂×C₅₉	semidirect
208. C₂×#332	C₂×C₅₉	semidirect
210. #1279	C₂×C₅₉	semidirect
238. C₅₉	#10066	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×#500	2
C₂×C₅₉×#461	2
C₅₉×#2547	2
C₅₉×#1988	2
C₂×C₅₉×#332	2
C₂×C₅₉×D₄⋊C₈	2
C₅₉×#1279	2
#10066	59

Subgroups — C59×#10066 #28422175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#10066 #28422175