Subgroups — C₅₉×#19401 #28431510

Order 15104.

632 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3207	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3112	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1684	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1678	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1668	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1666	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#532	C₂²	1	1	yes	characteristic
13	C₅₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#493	C₂²	1	1	yes	characteristic
16	C₅₉×#492	C₂²	1	1	yes	characteristic
17	C₅₉×#487	C₂²	1	1	yes	characteristic
18	C₅₉×#486	C₂²	1	1	yes	characteristic
19	C₅₉×#481	—	2	1	no	—
20	C₅₉×#480	—	2	1	no	—
21	C₅₉×#477	C₂²	1	2	yes	—
22	C₅₉×#475	C₂²	1	2	yes	—
23	C₅₉×#463	—	2	2	no	—
24	C₅₉×#460	C₂²	1	2	yes	—
25	C₅₉×#460	C₂²	1	2	yes	—
26	C₅₉×#449	—	2	2	no	—
27	C₅₉×#448	—	2	1	no	—
28	C₅₉×#448	—	2	1	no	—
29	C₈×Q₈×C₅₉	—	2	2	no	—
30	C₈×Q₈×C₅₉	C₂²	1	2	yes	—
31	C₈×Q₈×C₅₉	C₂²	1	2	yes	—
32	C₅₉×#440	—	2	2	no	—
33	C₄×SD₁₆×C₅₉	—	2	2	no	—
34	C₅₉×#432	C₂²	1	1	yes	characteristic
35	C₅₉×#431	—	2	2	no	—
36	C₅₉×#431	C₂²	1	1	yes	characteristic
37	C₅₉×#431	C₂²	1	1	yes	characteristic
38	C₅₉×#431	C₂²	1	1	yes	characteristic
39	C₅₉×#335	C₂²	1	2	yes	—
40	C₅₉×#334	C₂²	1	2	yes	—
41	C₅₉×#333	C₂²	1	2	yes	—
42	C₅₉×#332	C₂²	1	2	yes	—
43	C₅₉×#331	C₂²	1	2	yes	—
44	C₅₉×#331	C₂²	1	2	yes	—
45	C₂×#41×C₅₉	—	2	1	no	—
46	C₂×#41×C₅₉	—	2	1	no	—
47	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₅₉	—	2	2	no	—
49	C₂×SD₁₆×C₅₉	—	2	2	no	—
50	C₂×SD₁₆×C₅₉	—	2	2	no	—
51	C₂×D₈×C₅₉	—	2	2	no	—
52	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
54	#127×C₅₉	C₂³	1	1	yes	characteristic
55	#127×C₅₉	C₂³	1	1	yes	characteristic
56	#124×C₅₉	—	2	1	no	—
57	#124×C₅₉	—	2	1	no	—
58	#121×C₅₉	—	2	1	no	—
59	#121×C₅₉	—	2	1	no	—
60	#121×C₅₉	—	2	1	no	—
61	#121×C₅₉	—	2	1	no	—
62	C₄×Q₈×C₅₉	—	2	1	no	—
63	C₄×Q₈×C₅₉	—	2	1	no	—
64	C₄×Q₈×C₅₉	D₄	1	2	yes	—
65	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
66	C₄×D₄×C₅₉	—	2	1	no	—
67	C₄×D₄×C₅₉	—	2	1	no	—
68	C₄×D₄×C₅₉	—	2	1	no	—
69	C₄×D₄×C₅₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
74	#107×C₅₉	—	2	2	no	—
75	#106×C₅₉	—	2	2	no	—
76	C₄⋊C₈×C₅₉	—	2	2	no	—
77	C₄⋊C₈×C₅₉	—	2	2	no	—
78	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
79	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
80	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
81	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
82	#103×C₅₉	—	2	2	no	—
83	#103×C₅₉	—	2	2	no	—
84	#103×C₅₉	—	2	2	no	—
85	#102×C₅₉	—	2	2	no	—
86	#102×C₅₉	—	2	2	no	—
87	#102×C₅₉	—	2	2	no	—
88	C₂²⋊C₈×C₅₉	—	2	1	no	—
89	C₂²⋊C₈×C₅₉	—	2	1	no	—
90	C₂²⋊C₈×C₅₉	—	2	1	no	—
91	C₂²⋊C₈×C₅₉	D₄	1	2	yes	—
92	#97×C₅₉	—	2	1	no	—
93	C₄×C₈×C₅₉	—	2	2	no	—
94	C₄×C₈×C₅₉	—	2	2	no	—
95	C₄×C₈×C₅₉	—	2	1	no	—
96	C₄×C₈×C₅₉	—	2	1	no	—
97	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
99	#41×C₅₉	—	8	2	no	—
100	#41×C₅₉	—	8	2	no	—
101	C₂×Q₈×C₅₉	—	2	4	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	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₅₉	—	2	1	no	—
107	C₂×D₄×C₅₉	—	2	1	no	—
108	C₂×D₄×C₅₉	—	2	1	no	—
109	C₂×D₄×C₅₉	—	2	1	no	—
110	C₂×D₄×C₅₉	—	2	1	no	—
111	C₂×D₄×C₅₉	—	2	1	no	—
112	C₂×D₄×C₅₉	—	4	1	no	—
113	C₂×D₄×C₅₉	—	4	1	no	—
114	C₂²×C₄×C₅₉	—	2	1	no	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	—	4	1	no	—
117	C₂²×C₄×C₅₉	—	4	1	no	—
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
121	SD₁₆×C₅₉	—	4	4	no	—
122	SD₁₆×C₅₉	—	4	4	no	—
123	SD₁₆×C₅₉	—	8	2	no	—
124	D₈×C₅₉	—	8	2	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	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	2	1	no	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	1	no	—
134	C₄⋊C₄×C₅₉	—	2	1	no	—
135	C₄⋊C₄×C₅₉	—	2	1	no	—
136	C₄⋊C₄×C₅₉	—	2	1	no	—
137	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₅₉	—	4	1	no	—
139	C₂²⋊C₄×C₅₉	—	4	1	no	—
140	C₂²⋊C₄×C₅₉	—	4	1	no	—
141	C₂²⋊C₄×C₅₉	—	4	1	no	—
142	C₄²×C₅₉	—	2	2	no	—
143	C₄²×C₅₉	—	2	2	no	—
144	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₅₉	#41	1	1	yes	characteristic
147	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
148	C₂³×C₅₉	—	4	1	no	—
149	C₂³×C₅₉	—	4	1	no	—
150	C₂³×C₅₉	#121	1	1	yes	characteristic
151	Q₈×C₅₉	—	2	4	no	—
152	Q₈×C₅₉	—	2	2	no	—
153	Q₈×C₅₉	—	4	2	no	—
154	Q₈×C₅₉	—	8	1	no	—
155	Q₈×C₅₉	#135	1	4	yes	—
156	D₄×C₅₉	—	4	2	no	—
157	D₄×C₅₉	—	4	2	no	—
158	D₄×C₅₉	—	4	2	no	—
159	D₄×C₅₉	—	4	2	no	—
160	D₄×C₅₉	—	8	1	no	—
161	D₄×C₅₉	—	8	1	no	—
162	D₄×C₅₉	—	8	2	no	—
163	D₄×C₅₉	—	8	2	no	—
164	C₂×C₄×C₅₉	—	2	4	no	—
165	C₂×C₄×C₅₉	—	2	2	no	—
166	C₂×C₄×C₅₉	—	2	2	no	—
167	C₂×C₄×C₅₉	—	2	2	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	4	1	no	—
170	C₂×C₄×C₅₉	—	4	1	no	—
171	C₂×C₄×C₅₉	—	4	1	no	—
172	C₂×C₄×C₅₉	—	8	2	no	—
173	C₂×C₄×C₅₉	—	8	2	no	—
174	C₂×C₄×C₅₉	—	8	1	no	—
175	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
181	C₈×C₅₉	—	2	2	no	—
182	C₈×C₅₉	—	2	2	no	—
183	C₈×C₅₉	—	4	2	no	—
184	C₈×C₅₉	—	4	2	no	—
185	C₈×C₅₉	—	4	2	no	—
186	#19401	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₅₉	—	2	1	no	—
188	C₂²×C₅₉	—	2	1	no	—
189	C₂²×C₅₉	—	2	1	no	—
190	C₂²×C₅₉	—	8	1	no	—
191	C₂²×C₅₉	—	8	1	no	—
192	C₂²×C₅₉	—	8	1	no	—
193	C₂²×C₅₉	—	8	1	no	—
194	C₂²×C₅₉	—	8	1	no	—
195	C₂²×C₅₉	—	8	1	no	—
196	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
197	C₄×C₅₉	—	2	1	no	—
198	C₄×C₅₉	—	2	4	no	—
199	C₄×C₅₉	—	2	1	no	—
200	C₄×C₅₉	—	2	1	no	—
201	C₄×C₅₉	—	2	1	no	—
202	C₄×C₅₉	—	4	2	no	—
203	C₄×C₅₉	—	8	1	no	—
204	C₄×C₅₉	—	8	1	no	—
205	C₄×C₅₉	C₂×#135	1	2	yes	—
206	C₄×C₅₉	#577	1	2	yes	—
207	#3207	C₂×C₅₉	1	1	yes	characteristic
208	#3112	C₂×C₅₉	1	1	yes	characteristic, complemented
209	#3103	C₂×C₅₉	1	1	yes	characteristic, complemented
210	#2982	C₂×C₅₉	1	1	yes	characteristic, complemented
211	#1684	C₂×C₅₉	1	2	yes	complemented
212	#1678	C₂×C₅₉	1	2	yes	complemented
213	#1668	C₂×C₅₉	1	2	yes	complemented
214	#1666	C₂×C₅₉	1	2	yes	complemented
215	#1572	C₂×C₅₉	1	1	yes	characteristic, complemented
216	#1553	C₂×C₅₉	1	1	yes	characteristic, complemented
217	#1543	C₂×C₅₉	1	1	yes	characteristic, complemented
218	C₂×C₅₉	—	4	1	no	—
219	C₂×C₅₉	—	16	1	no	—
220	C₂×C₅₉	—	16	1	no	—
221	C₂×C₅₉	#3043	1	1	yes	characteristic
222	C₂×C₅₉	#3050	1	1	yes	characteristic
223	C₂×C₅₉	#3068	1	1	yes	characteristic
224	#532	C₂²×C₅₉	1	1	yes	characteristic
225	#532	C₂²×C₅₉	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
227	#493	C₂²×C₅₉	1	1	yes	characteristic
228	#492	C₂²×C₅₉	1	1	yes	characteristic
229	#487	C₂²×C₅₉	1	1	yes	characteristic
230	#486	C₂²×C₅₉	1	1	yes	characteristic
231	#481	—	2	1	no	—
232	#480	—	2	1	no	—
233	#477	C₂²×C₅₉	1	2	yes	—
234	#475	C₂²×C₅₉	1	2	yes	—
235	#463	—	2	2	no	—
236	#460	C₂²×C₅₉	1	2	yes	—
237	#460	C₂²×C₅₉	1	2	yes	—
238	#449	—	2	2	no	—
239	#448	—	2	1	no	—
240	#448	—	2	1	no	—
241	C₈×Q₈	—	2	2	no	—
242	C₈×Q₈	C₂²×C₅₉	1	2	yes	—
243	C₈×Q₈	C₂²×C₅₉	1	2	yes	—
244	#440	—	2	2	no	—
245	C₄×SD₁₆	—	2	2	no	—
246	#432	C₂²×C₅₉	1	1	yes	characteristic
247	#431	—	2	2	no	—
248	#431	C₂²×C₅₉	1	1	yes	characteristic
249	#431	C₂²×C₅₉	1	1	yes	characteristic
250	#431	C₂²×C₅₉	1	1	yes	characteristic
251	#335	C₂²×C₅₉	1	2	yes	—
252	#334	C₂²×C₅₉	1	2	yes	—
253	#333	C₂²×C₅₉	1	2	yes	—
254	#332	C₂²×C₅₉	1	2	yes	—
255	#331	C₂²×C₅₉	1	2	yes	—
256	#331	C₂²×C₅₉	1	2	yes	—
257	C₅₉	#19401	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	2	1	no	—
260	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×D₈	—	2	2	no	—
265	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
266	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
267	#127	C₂³×C₅₉	1	1	yes	characteristic
268	#127	C₂³×C₅₉	1	1	yes	characteristic
269	#124	—	2	1	no	—
270	#124	—	2	1	no	—
271	#121	—	2	1	no	—
272	#121	—	2	1	no	—
273	#121	—	2	1	no	—
274	#121	—	2	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	—	2	1	no	—
277	C₄×Q₈	D₄×C₅₉	1	2	yes	—
278	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
287	#107	—	2	2	no	—
288	#106	—	2	2	no	—
289	C₄⋊C₈	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	D₄×C₅₉	1	2	yes	—
292	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
293	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
294	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	#103	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	D₄×C₅₉	1	2	yes	—
305	#97	—	2	1	no	—
306	C₄×C₈	—	2	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
312	#41	—	8	2	no	—
313	#41	—	8	2	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
333	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
334	SD₁₆	—	4	4	no	—
335	SD₁₆	—	4	4	no	—
336	SD₁₆	—	8	2	no	—
337	D₈	—	8	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
342	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
358	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
359	C₄²	#41×C₅₉	1	1	yes	characteristic
360	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	#121×C₅₉	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	8	1	no	—
368	Q₈	#135×C₅₉	1	4	yes	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	1	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	2	no	—
376	D₄	—	8	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	1	no	—
388	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
389	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
390	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	4	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	C₂×#135×C₅₉	1	2	yes	—
418	C₄	C₅₉×#577	1	2	yes	—
419	C₂	—	4	1	no	—
420	C₂	—	16	1	no	—
421	C₂	—	16	1	no	—
422	C₂	C₅₉×#3043	1	1	yes	characteristic
423	C₂	C₅₉×#3050	1	1	yes	characteristic
424	C₂	C₅₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₉
prime radical	C₅₉×#3207	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#3112	C₂	semidirect
3. C₅₉×#3103	C₂	semidirect
4. C₅₉×#2982	C₂	semidirect
5. C₅₉×#1684	C₂	semidirect
6. C₅₉×#1678	C₂	semidirect
7. C₅₉×#1668	C₂	semidirect
8. C₅₉×#1666	C₂	semidirect
9. C₅₉×#1572	C₂	semidirect
10. C₅₉×#1553	C₂	semidirect
11. C₅₉×#1543	C₂	semidirect
186. #19401	C₅₉	direct (N × H)
208. #3112	C₂×C₅₉	semidirect
209. #3103	C₂×C₅₉	semidirect
210. #2982	C₂×C₅₉	semidirect
211. #1684	C₂×C₅₉	semidirect
212. #1678	C₂×C₅₉	semidirect
213. #1668	C₂×C₅₉	semidirect
214. #1666	C₂×C₅₉	semidirect
215. #1572	C₂×C₅₉	semidirect
216. #1553	C₂×C₅₉	semidirect
217. #1543	C₂×C₅₉	semidirect
257. C₅₉	#19401	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×#3207	2
C₅₉×#3112	2
C₅₉×#3103	2
C₅₉×#2982	2
C₅₉×#1684	2
C₅₉×#1678	2
C₅₉×#1668	2
C₅₉×#1666	2
C₅₉×#1572	2
C₅₉×#1553	2
C₅₉×#1543	2
#19401	59

Subgroups — C59×#19401 #28431510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#19401 #28431510