Subgroups — C₅₉×#32813 #28444922

Order 15104.

704 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2642	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#2640	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	1	yes	maximal, characteristic, complemented
6	C₅₉×#2025	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2024	C₂	1	2	yes	maximal, complemented
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×#1832	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×#400	—	2	2	no	—
24	C₅₉×#400	—	2	2	no	—
25	C₅₉×#397	—	2	2	no	—
26	C₅₉×#393	—	2	2	no	—
27	C₅₉×#391	C₂²	1	2	yes	—
28	C₅₉×#391	C₂²	1	1	yes	characteristic
29	C₅₉×#391	C₂²	1	2	yes	—
30	C₅₉×#391	C₂²	1	1	yes	characteristic
31	C₅₉×#390	C₂²	1	1	yes	characteristic
32	C₅₉×#390	C₂²	1	1	yes	characteristic
33	C₅₉×#376	C₂²	1	1	yes	characteristic
34	C₅₉×#340	C₂²	1	2	yes	—
35	C₅₉×#340	C₂²	1	2	yes	—
36	C₅₉×#336	C₂²	1	1	yes	characteristic
37	C₅₉×#336	C₂²	1	2	yes	—
38	C₅₉×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₅₉	—	2	1	no	—
40	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
42	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
43	C₂×Q₁₆×C₅₉	—	4	2	no	—
44	C₂×Q₁₆×C₅₉	—	4	2	no	—
45	C₂×Q₁₆×C₅₉	—	4	2	no	—
46	C₂×SD₁₆×C₅₉	—	4	2	no	—
47	C₂×SD₁₆×C₅₉	—	4	2	no	—
48	C₂×SD₁₆×C₅₉	—	4	2	no	—
49	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
50	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₅₉	—	4	2	no	—
52	C₄⋊Q₈×C₅₉	—	4	2	no	—
53	#125×C₅₉	—	4	2	no	—
54	#124×C₅₉	—	4	2	no	—
55	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
65	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₅₉	—	4	2	no	—
69	#103×C₅₉	—	4	2	no	—
70	#103×C₅₉	—	4	2	no	—
71	#103×C₅₉	—	4	2	no	—
72	#102×C₅₉	—	4	2	no	—
73	#95×C₅₉	—	2	2	no	—
74	#95×C₅₉	—	2	2	no	—
75	#95×C₅₉	—	2	4	no	—
76	#95×C₅₉	—	2	2	no	—
77	#95×C₅₉	—	2	2	no	—
78	#95×C₅₉	D₄	1	2	yes	—
79	#95×C₅₉	D₄	1	2	yes	—
80	C₂⁴×C₅₉	—	2	1	no	—
81	C₂×Q₈×C₅₉	—	2	2	no	—
82	C₂×Q₈×C₅₉	—	2	2	no	—
83	C₂×Q₈×C₅₉	—	2	2	no	—
84	C₂×Q₈×C₅₉	—	2	2	no	—
85	C₂×Q₈×C₅₉	—	2	2	no	—
86	C₂×Q₈×C₅₉	—	2	2	no	—
87	C₂×Q₈×C₅₉	—	2	2	no	—
88	C₂×Q₈×C₅₉	—	2	1	no	—
89	C₂×Q₈×C₅₉	—	2	1	no	—
90	C₂×Q₈×C₅₉	—	2	2	no	—
91	C₂×Q₈×C₅₉	—	4	2	no	—
92	C₂×Q₈×C₅₉	—	8	2	no	—
93	C₂×D₄×C₅₉	—	2	2	no	—
94	C₂×D₄×C₅₉	—	2	2	no	—
95	C₂×D₄×C₅₉	—	2	1	no	—
96	C₂×D₄×C₅₉	—	2	1	no	—
97	C₂²×C₄×C₅₉	—	2	1	no	—
98	C₂²×C₄×C₅₉	—	2	2	no	—
99	C₂²×C₄×C₅₉	—	2	2	no	—
100	C₂²×C₄×C₅₉	—	2	1	no	—
101	C₂²×C₄×C₅₉	—	2	1	no	—
102	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
107	Q₁₆×C₅₉	—	4	8	no	—
108	SD₁₆×C₅₉	—	4	8	no	—
109	C₂×C₈×C₅₉	—	2	2	no	—
110	C₂×C₈×C₅₉	—	2	2	no	—
111	C₂×C₈×C₅₉	—	2	2	no	—
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₂×C₈×C₅₉	—	2	2	no	—
114	C₂×C₈×C₅₉	—	2	2	no	—
115	C₄⋊C₄×C₅₉	—	2	2	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	4	no	—
120	C₄⋊C₄×C₅₉	—	4	2	no	—
121	C₄⋊C₄×C₅₉	—	4	4	no	—
122	C₂²⋊C₄×C₅₉	—	4	2	no	—
123	C₂²⋊C₄×C₅₉	—	4	2	no	—
124	C₂²⋊C₄×C₅₉	—	8	2	no	—
125	C₂²⋊C₄×C₅₉	—	8	2	no	—
126	C₄²×C₅₉	—	2	1	no	—
127	C₄²×C₅₉	—	2	2	no	—
128	C₄²×C₅₉	—	2	2	no	—
129	C₄²×C₅₉	—	2	1	no	—
130	C₂³×C₅₉	—	4	1	no	—
131	C₂³×C₅₉	—	4	1	no	—
132	C₂³×C₅₉	—	4	1	no	—
133	C₂³×C₅₉	—	4	2	no	—
134	C₂³×C₅₉	—	4	2	no	—
135	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₅₉	—	4	2	no	—
137	Q₈×C₅₉	—	4	2	no	—
138	Q₈×C₅₉	—	4	2	no	—
139	Q₈×C₅₉	—	4	2	no	—
140	Q₈×C₅₉	—	4	2	no	—
141	Q₈×C₅₉	—	4	2	no	—
142	Q₈×C₅₉	—	8	4	no	—
143	D₄×C₅₉	—	4	2	no	—
144	D₄×C₅₉	—	4	2	no	—
145	C₂×C₄×C₅₉	—	2	1	no	—
146	C₂×C₄×C₅₉	—	2	1	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	2	no	—
149	C₂×C₄×C₅₉	—	2	2	no	—
150	C₂×C₄×C₅₉	—	2	2	no	—
151	C₂×C₄×C₅₉	—	2	2	no	—
152	C₂×C₄×C₅₉	—	2	2	no	—
153	C₂×C₄×C₅₉	—	2	2	no	—
154	C₂×C₄×C₅₉	—	2	2	no	—
155	C₂×C₄×C₅₉	—	4	1	no	—
156	C₂×C₄×C₅₉	—	4	2	no	—
157	C₂×C₄×C₅₉	—	4	1	no	—
158	C₂×C₄×C₅₉	—	4	1	no	—
159	C₂×C₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	—	4	2	no	—
161	C₂×C₄×C₅₉	—	4	1	no	—
162	C₂×C₄×C₅₉	—	4	1	no	—
163	C₂×C₄×C₅₉	—	4	2	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	4	2	no	—
167	C₂×C₄×C₅₉	—	4	2	no	—
168	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
172	C₈×C₅₉	—	4	2	no	—
173	C₈×C₅₉	—	4	2	no	—
174	#32813	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₅₉	—	8	1	no	—
176	C₂²×C₅₉	—	8	1	no	—
177	C₂²×C₅₉	—	8	1	no	—
178	C₂²×C₅₉	—	8	2	no	—
179	C₂²×C₅₉	—	8	2	no	—
180	C₂²×C₅₉	#535	1	1	yes	characteristic
181	C₂²×C₅₉	#535	1	1	yes	characteristic
182	C₂²×C₅₉	#537	1	1	yes	characteristic
183	C₂²×C₅₉	#577	1	2	yes	—
184	C₂²×C₅₉	#578	1	2	yes	—
185	C₄×C₅₉	—	4	1	no	—
186	C₄×C₅₉	—	4	1	no	—
187	C₄×C₅₉	—	4	2	no	—
188	C₄×C₅₉	—	4	2	no	—
189	C₄×C₅₉	—	8	1	no	—
190	C₄×C₅₉	—	8	2	no	—
191	C₄×C₅₉	—	8	1	no	—
192	C₄×C₅₉	—	8	1	no	—
193	C₄×C₅₉	—	8	2	no	—
194	C₄×C₅₉	H(3,𝔽₄)	1	2	yes	—
195	C₄×C₅₉	#562	1	2	yes	—
196	#2642	C₂×C₅₉	1	1	yes	characteristic, complemented
197	#2640	C₂×C₅₉	1	1	yes	characteristic
198	#2056	C₂×C₅₉	1	2	yes	complemented
199	#2055	C₂×C₅₉	1	2	yes	—
200	#2026	C₂×C₅₉	1	1	yes	characteristic, complemented
201	#2025	C₂×C₅₉	1	1	yes	characteristic
202	#2024	C₂×C₅₉	1	2	yes	complemented
203	#2016	C₂×C₅₉	1	1	yes	characteristic, complemented
204	#2015	C₂×C₅₉	1	2	yes	—
205	#2013	C₂×C₅₉	1	1	yes	characteristic
206	#1832	C₂×C₅₉	1	1	yes	characteristic, complemented
207	C₂×C₅₉	—	16	1	no	—
208	C₂×C₅₉	#2819	1	1	yes	characteristic
209	C₂×C₅₉	#3222	1	1	yes	characteristic
210	C₂×C₅₉	#3223	1	1	yes	characteristic
211	C₂×C₅₉	#3225	1	2	yes	—
212	C₂×C₅₉	#3258	1	2	yes	—
213	C₂²×Q₁₆	C₂²×C₅₉	1	2	yes	—
214	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
217	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
218	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
220	C₂×#103	C₂²×C₅₉	1	2	yes	—
221	C₂×#103	C₂²×C₅₉	1	2	yes	—
222	C₂×#103	C₂²×C₅₉	1	2	yes	—
223	C₂×#102	C₂²×C₅₉	1	2	yes	—
224	#400	—	2	2	no	—
225	#400	—	2	2	no	—
226	#397	—	2	2	no	—
227	#393	—	2	2	no	—
228	#391	C₂²×C₅₉	1	2	yes	—
229	#391	C₂²×C₅₉	1	1	yes	characteristic
230	#391	C₂²×C₅₉	1	1	yes	characteristic
231	#391	C₂²×C₅₉	1	2	yes	—
232	#390	C₂²×C₅₉	1	1	yes	characteristic
233	#390	C₂²×C₅₉	1	1	yes	characteristic
234	#376	C₂²×C₅₉	1	1	yes	characteristic
235	#340	C₂²×C₅₉	1	2	yes	—
236	#340	C₂²×C₅₉	1	2	yes	—
237	#336	C₂²×C₅₉	1	1	yes	characteristic
238	#336	C₂²×C₅₉	1	2	yes	—
239	#336	C₂²×C₅₉	1	1	yes	characteristic
240	C₅₉	#32813	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
244	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
245	C₂×Q₁₆	—	4	2	no	—
246	C₂×Q₁₆	—	4	2	no	—
247	C₂×Q₁₆	—	4	2	no	—
248	C₂×SD₁₆	—	4	2	no	—
249	C₂×SD₁₆	—	4	2	no	—
250	C₂×SD₁₆	—	4	2	no	—
251	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
252	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
253	C₄⋊Q₈	—	4	2	no	—
254	C₄⋊Q₈	—	4	2	no	—
255	#125	—	4	2	no	—
256	#124	—	4	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
270	C₄⋊C₈	—	4	2	no	—
271	#103	—	4	2	no	—
272	#103	—	4	2	no	—
273	#103	—	4	2	no	—
274	#102	—	4	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	4	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	D₄×C₅₉	1	2	yes	—
281	#95	D₄×C₅₉	1	2	yes	—
282	C₂⁴	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	8	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
309	Q₁₆	—	4	8	no	—
310	SD₁₆	—	4	8	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	4	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	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	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
371	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
372	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
373	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₅₉×#535	1	1	yes	characteristic
382	C₂²	C₅₉×#535	1	1	yes	characteristic
383	C₂²	C₅₉×#537	1	1	yes	characteristic
384	C₂²	C₅₉×#577	1	2	yes	—
385	C₂²	C₅₉×#578	1	2	yes	—
386	C₄	—	4	2	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	8	1	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	1	no	—
394	C₄	—	8	2	no	—
395	C₄	C₅₉×H(3,𝔽₄)	1	2	yes	—
396	C₄	C₅₉×#562	1	2	yes	—
397	C₂	—	16	1	no	—
398	C₂	C₅₉×#2819	1	1	yes	characteristic
399	C₂	C₅₉×#3222	1	1	yes	characteristic
400	C₂	C₅₉×#3223	1	1	yes	characteristic
401	C₂	C₅₉×#3225	1	2	yes	—
402	C₂	C₅₉×#3258	1	2	yes	—

	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 ◁ C₅₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2642	C₂	semidirect
3. C₅₉×#2056	C₂	semidirect
5. C₅₉×#2026	C₂	semidirect
7. C₅₉×#2024	C₂	semidirect
8. C₅₉×#2016	C₂	semidirect
11. C₅₉×#1832	C₂	semidirect
174. #32813	C₅₉	direct (N × H)
196. #2642	C₂×C₅₉	semidirect
198. #2056	C₂×C₅₉	semidirect
200. #2026	C₂×C₅₉	semidirect
202. #2024	C₂×C₅₉	semidirect
203. #2016	C₂×C₅₉	semidirect
206. #1832	C₂×C₅₉	semidirect
240. C₅₉	#32813	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×#2642	2
C₅₉×#2640	2
C₅₉×#2056	2
C₅₉×#2055	2
C₅₉×#2026	2
C₅₉×#2025	2
C₅₉×#2024	2
C₅₉×#2016	2
C₅₉×#2015	2
C₅₉×#2013	2
C₅₉×#1832	2
#32813	59

Subgroups — C59×#32813 #28444922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#32813 #28444922