Subgroups — C₅₉×#60726 #28472835

Order 15104.

1842 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3512	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3181	C₂	1	4	yes	maximal, complemented
4	C₅₉×#3177	C₂	1	4	yes	maximal, complemented
5	C₅₉×#3174	C₂	1	4	yes	maximal, complemented
6	C₅₉×#3172	C₂	1	4	yes	maximal, complemented
7	C₅₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3152	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3063	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2947	C₂	1	4	yes	maximal, complemented
13	C₅₉×#2875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#137×C₅₉	C₂²	1	4	yes	—
15	C₂×#131×C₅₉	C₂²	1	2	yes	—
16	C₅₉×#557	—	2	2	no	—
17	C₅₉×#556	—	2	2	no	—
18	C₅₉×#553	—	2	4	no	—
19	C₅₉×#553	—	2	2	no	—
20	C₅₉×#552	—	2	2	no	—
21	C₅₉×#552	—	2	4	no	—
22	C₅₉×#541	C₂²	1	4	yes	—
23	C₅₉×#541	C₂²	1	2	yes	—
24	C₅₉×#540	C₂²	1	2	yes	—
25	C₅₉×#537	C₂²	1	2	yes	—
26	C₅₉×#536	C₂²	1	2	yes	—
27	C₅₉×#533	C₂²	1	4	yes	—
28	C₅₉×#533	C₂²	1	1	yes	characteristic
29	C₅₉×#532	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#529	C₂²	1	4	yes	—
32	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#520	C₂²	1	2	yes	—
34	C₅₉×#519	C₂²	1	2	yes	—
35	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#501	C₂²	1	4	yes	—
37	C₅₉×#499	C₂²	1	4	yes	—
38	C₅₉×#497	C₂²	1	4	yes	—
39	C₅₉×#494	C₂²	1	2	yes	—
40	C₅₉×#492	C₂²	1	2	yes	—
41	C₅₉×#491	C₂²	1	2	yes	—
42	C₅₉×#491	C₂²	1	4	yes	—
43	C₅₉×#491	C₂²	1	2	yes	—
44	C₅₉×#491	C₂²	1	2	yes	—
45	C₅₉×#490	C₂²	1	2	yes	—
46	C₅₉×#489	C₂²	1	2	yes	—
47	C₅₉×#489	C₂²	1	2	yes	—
48	C₅₉×#470	C₂²	1	8	yes	—
49	C₅₉×#468	C₂²	1	8	yes	—
50	C₅₉×#467	C₂²	1	8	yes	—
51	C₅₉×#465	C₂²	1	8	yes	—
52	C₅₉×#441	C₂²	1	8	yes	—
53	C₅₉×#440	C₂²	1	8	yes	—
54	C₄×Q₁₆×C₅₉	C₂²	1	8	yes	—
55	C₄×SD₁₆×C₅₉	C₂²	1	8	yes	—
56	C₅₉×#428	C₂²	1	4	yes	—
57	C₅₉×#416	C₂²	1	4	yes	—
58	C₂×#103×C₅₉	C₂²	1	4	yes	—
59	C₅₉×#405	C₂²	1	4	yes	—
60	C₅₉×#405	C₂²	1	2	yes	—
61	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
63	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
64	C₂×#97×C₅₉	C₂²	1	2	yes	—
65	C₂×#41×C₅₉	C₂³	1	2	yes	—
66	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
68	#137×C₅₉	—	2	16	no	—
69	C₂×Q₁₆×C₅₉	C₂³	1	8	yes	—
70	C₂×SD₁₆×C₅₉	C₂³	1	8	yes	—
71	#131×C₅₉	—	2	8	no	—
72	C₂×M₁₆×C₅₉	C₂³	1	4	yes	—
73	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
74	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
75	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
76	C₄⋊Q₈×C₅₉	—	2	2	no	—
77	C₄⋊Q₈×C₅₉	—	2	2	no	—
78	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
79	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
82	#127×C₅₉	C₂³	1	1	yes	characteristic
83	#126×C₅₉	—	2	8	no	—
84	#126×C₅₉	—	2	4	no	—
85	#126×C₅₉	—	2	4	no	—
86	#125×C₅₉	—	2	4	no	—
87	#125×C₅₉	—	2	8	no	—
88	#125×C₅₉	—	2	2	no	—
89	#125×C₅₉	—	2	4	no	—
90	#125×C₅₉	C₂³	1	2	yes	—
91	#125×C₅₉	C₂³	1	2	yes	—
92	#125×C₅₉	C₂³	1	2	yes	—
93	#124×C₅₉	—	2	2	no	—
94	#124×C₅₉	C₂³	1	2	yes	—
95	#123×C₅₉	—	2	4	no	—
96	#123×C₅₉	—	2	4	no	—
97	#123×C₅₉	—	2	4	no	—
98	C₂²⋊Q₈×C₅₉	—	2	2	no	—
99	C₂²⋊Q₈×C₅₉	—	2	2	no	—
100	C₂²⋊Q₈×C₅₉	—	2	4	no	—
101	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
102	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
103	#121×C₅₉	—	2	2	no	—
104	#121×C₅₉	—	2	4	no	—
105	#121×C₅₉	—	2	2	no	—
106	#121×C₅₉	—	2	4	no	—
107	#121×C₅₉	C₂³	1	4	yes	—
108	C₄×Q₈×C₅₉	—	2	4	no	—
109	C₄×Q₈×C₅₉	—	2	4	no	—
110	C₄×Q₈×C₅₉	—	2	2	no	—
111	C₄×Q₈×C₅₉	D₄	1	2	yes	—
112	C₄×Q₈×C₅₉	C₂³	1	8	yes	—
113	C₄×Q₈×C₅₉	C₂³	1	4	yes	—
114	C₄×D₄×C₅₉	—	2	4	no	—
115	C₄×D₄×C₅₉	—	2	4	no	—
116	C₄×D₄×C₅₉	—	2	2	no	—
117	C₄×D₄×C₅₉	D₄	1	4	yes	—
118	C₄×D₄×C₅₉	D₄	1	2	yes	—
119	C₄×D₄×C₅₉	C₂³	1	4	yes	—
120	#117×C₅₉	—	2	4	no	—
121	#117×C₅₉	—	2	2	no	—
122	#117×C₅₉	—	2	4	no	—
123	#117×C₅₉	—	2	4	no	—
124	#117×C₅₉	C₂³	1	2	yes	—
125	#117×C₅₉	C₂³	1	1	yes	characteristic
126	#117×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
128	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
129	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
133	#107×C₅₉	C₂³	1	8	yes	—
134	#106×C₅₉	C₂³	1	8	yes	—
135	#103×C₅₉	C₂³	1	8	yes	—
136	#103×C₅₉	C₂³	1	8	yes	—
137	#103×C₅₉	C₂³	1	4	yes	—
138	#103×C₅₉	C₂³	1	4	yes	—
139	#102×C₅₉	C₂³	1	4	yes	—
140	#102×C₅₉	C₂³	1	4	yes	—
141	#97×C₅₉	C₂³	1	1	yes	characteristic
142	#97×C₅₉	C₂³	1	1	yes	characteristic
143	#97×C₅₉	C₂³	1	2	yes	—
144	#97×C₅₉	C₂³	1	4	yes	—
145	#97×C₅₉	C₂³	1	2	yes	—
146	C₄×C₈×C₅₉	C₂³	1	4	yes	—
147	C₄×C₈×C₅₉	C₂³	1	2	yes	—
148	#41×C₅₉	—	2	4	no	—
149	#41×C₅₉	—	2	8	no	—
150	C₂×Q₈×C₅₉	—	2	2	no	—
151	C₂×Q₈×C₅₉	—	2	2	no	—
152	C₂×Q₈×C₅₉	—	2	8	no	—
153	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
155	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
156	C₂×D₄×C₅₉	—	2	2	no	—
157	C₂×D₄×C₅₉	—	2	4	no	—
158	C₂×D₄×C₅₉	—	2	2	no	—
159	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₅₉	—	2	2	no	—
163	C₂²×C₄×C₅₉	—	2	2	no	—
164	C₂²×C₄×C₅₉	—	2	2	no	—
165	C₂²×C₄×C₅₉	—	2	4	no	—
166	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
170	Q₁₆×C₅₉	—	2	16	no	—
171	SD₁₆×C₅₉	—	2	16	no	—
172	M₁₆×C₅₉	—	2	8	no	—
173	M₁₆×C₅₉	#41	1	8	yes	—
174	C₂×C₈×C₅₉	—	2	4	no	—
175	C₂×C₈×C₅₉	—	2	8	no	—
176	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
177	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
178	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
179	C₄⋊C₄×C₅₉	—	2	2	no	—
180	C₄⋊C₄×C₅₉	—	2	4	no	—
181	C₄⋊C₄×C₅₉	—	2	4	no	—
182	C₄⋊C₄×C₅₉	—	2	4	no	—
183	C₄⋊C₄×C₅₉	—	2	4	no	—
184	C₄⋊C₄×C₅₉	—	2	4	no	—
185	C₄⋊C₄×C₅₉	—	2	2	no	—
186	C₄⋊C₄×C₅₉	—	2	8	no	—
187	C₄⋊C₄×C₅₉	—	2	4	no	—
188	C₄⋊C₄×C₅₉	—	2	2	no	—
189	C₄⋊C₄×C₅₉	—	2	4	no	—
190	C₄⋊C₄×C₅₉	—	2	8	no	—
191	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
192	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
193	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
194	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
195	C₂²⋊C₄×C₅₉	—	2	2	no	—
196	C₂²⋊C₄×C₅₉	—	2	8	no	—
197	C₂²⋊C₄×C₅₉	—	2	4	no	—
198	C₂²⋊C₄×C₅₉	—	2	2	no	—
199	C₂²⋊C₄×C₅₉	—	2	4	no	—
200	C₂²⋊C₄×C₅₉	—	2	4	no	—
201	C₂²⋊C₄×C₅₉	—	2	2	no	—
202	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
203	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
204	C₄²×C₅₉	—	2	4	no	—
205	C₄²×C₅₉	—	2	8	no	—
206	C₄²×C₅₉	—	2	2	no	—
207	C₄²×C₅₉	C₂×D₄	1	4	yes	—
208	C₄²×C₅₉	C₂×D₄	1	2	yes	—
209	C₄²×C₅₉	C₂⁴	1	2	yes	—
210	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
211	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
212	C₂³×C₅₉	—	2	2	no	—
213	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
214	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₅₉	—	2	2	no	—
216	Q₈×C₅₉	—	2	8	no	—
217	Q₈×C₅₉	—	2	4	no	—
218	Q₈×C₅₉	—	4	4	no	—
219	Q₈×C₅₉	—	4	4	no	—
220	D₄×C₅₉	—	2	4	no	—
221	D₄×C₅₉	—	2	2	no	—
222	D₄×C₅₉	—	2	4	no	—
223	D₄×C₅₉	—	4	4	no	—
224	D₄×C₅₉	—	8	2	no	—
225	D₄×C₅₉	—	8	4	no	—
226	C₂×C₄×C₅₉	—	2	4	no	—
227	C₂×C₄×C₅₉	—	2	4	no	—
228	C₂×C₄×C₅₉	—	2	2	no	—
229	C₂×C₄×C₅₉	—	2	4	no	—
230	C₂×C₄×C₅₉	—	2	4	no	—
231	C₂×C₄×C₅₉	—	4	4	no	—
232	C₂×C₄×C₅₉	—	4	2	no	—
233	C₂×C₄×C₅₉	—	4	4	no	—
234	C₂×C₄×C₅₉	—	4	4	no	—
235	C₂×C₄×C₅₉	—	8	4	no	—
236	C₂×C₄×C₅₉	—	8	2	no	—
237	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
238	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
243	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
244	C₈×C₅₉	—	2	2	no	—
245	C₈×C₅₉	—	2	2	no	—
246	C₈×C₅₉	C₂×#41	1	8	yes	—
247	#60726	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂²×C₅₉	—	2	2	no	—
249	C₂²×C₅₉	—	2	4	no	—
250	C₂²×C₅₉	—	2	2	no	—
251	C₂²×C₅₉	—	4	2	no	—
252	C₂²×C₅₉	—	4	2	no	—
253	C₂²×C₅₉	—	4	2	no	—
254	C₂²×C₅₉	#532	1	2	yes	—
255	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
256	C₄×C₅₉	—	2	2	no	—
257	C₄×C₅₉	—	2	4	no	—
258	C₄×C₅₉	—	2	2	no	—
259	C₄×C₅₉	—	2	2	no	—
260	C₄×C₅₉	—	4	4	no	—
261	C₄×C₅₉	—	4	4	no	—
262	C₄×C₅₉	—	4	2	no	—
263	C₄×C₅₉	—	4	4	no	—
264	C₄×C₅₉	#532	1	2	yes	—
265	C₄×C₅₉	C₂²×#41	1	2	yes	—
266	#3512	C₂×C₅₉	1	1	yes	characteristic
267	#3509	C₂×C₅₉	1	1	yes	characteristic, complemented
268	#3181	C₂×C₅₉	1	4	yes	complemented
269	#3177	C₂×C₅₉	1	4	yes	complemented
270	#3174	C₂×C₅₉	1	4	yes	complemented
271	#3172	C₂×C₅₉	1	4	yes	complemented
272	#3166	C₂×C₅₉	1	1	yes	characteristic, complemented
273	#3152	C₂×C₅₉	1	1	yes	characteristic, complemented
274	#3135	C₂×C₅₉	1	1	yes	characteristic, complemented
275	C₂×#491	C₂×C₅₉	1	1	yes	characteristic, complemented
276	#3063	C₂×C₅₉	1	4	yes	complemented
277	#2947	C₂×C₅₉	1	4	yes	complemented
278	#2875	C₂×C₅₉	1	1	yes	characteristic, complemented
279	C₂×C₅₉	—	2	2	no	—
280	C₂×C₅₉	—	4	2	no	—
281	C₂×C₅₉	—	8	2	no	—
282	C₂×C₅₉	C₂×#532	1	1	yes	characteristic
283	C₂×C₅₉	#3586	1	2	yes	—
284	C₂×#137	C₂²×C₅₉	1	4	yes	—
285	C₂×#131	C₂²×C₅₉	1	2	yes	—
286	#557	—	2	2	no	—
287	#556	—	2	2	no	—
288	#553	—	2	4	no	—
289	#553	—	2	2	no	—
290	#552	—	2	2	no	—
291	#552	—	2	4	no	—
292	#541	C₂²×C₅₉	1	4	yes	—
293	#541	C₂²×C₅₉	1	2	yes	—
294	#540	C₂²×C₅₉	1	2	yes	—
295	#537	C₂²×C₅₉	1	2	yes	—
296	#536	C₂²×C₅₉	1	2	yes	—
297	#533	C₂²×C₅₉	1	4	yes	—
298	#533	C₂²×C₅₉	1	1	yes	characteristic
299	#532	C₂²×C₅₉	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
301	#529	C₂²×C₅₉	1	4	yes	—
302	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
303	#520	C₂²×C₅₉	1	2	yes	—
304	#519	C₂²×C₅₉	1	2	yes	—
305	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
306	#501	C₂²×C₅₉	1	4	yes	—
307	#499	C₂²×C₅₉	1	4	yes	—
308	#497	C₂²×C₅₉	1	4	yes	—
309	#494	C₂²×C₅₉	1	2	yes	—
310	#492	C₂²×C₅₉	1	2	yes	—
311	#491	C₂²×C₅₉	1	2	yes	—
312	#491	C₂²×C₅₉	1	4	yes	—
313	#491	C₂²×C₅₉	1	2	yes	—
314	#491	C₂²×C₅₉	1	2	yes	—
315	#490	C₂²×C₅₉	1	2	yes	—
316	#489	C₂²×C₅₉	1	2	yes	—
317	#489	C₂²×C₅₉	1	2	yes	—
318	#470	C₂²×C₅₉	1	8	yes	—
319	#468	C₂²×C₅₉	1	8	yes	—
320	#467	C₂²×C₅₉	1	8	yes	—
321	#465	C₂²×C₅₉	1	8	yes	—
322	#441	C₂²×C₅₉	1	8	yes	—
323	#440	C₂²×C₅₉	1	8	yes	—
324	C₄×Q₁₆	C₂²×C₅₉	1	8	yes	—
325	C₄×SD₁₆	C₂²×C₅₉	1	8	yes	—
326	#428	C₂²×C₅₉	1	4	yes	—
327	#416	C₂²×C₅₉	1	4	yes	—
328	C₂×#103	C₂²×C₅₉	1	4	yes	—
329	#405	C₂²×C₅₉	1	4	yes	—
330	#405	C₂²×C₅₉	1	2	yes	—
331	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
332	C₄×M₁₆	C₂²×C₅₉	1	2	yes	—
333	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
334	C₂×#97	C₂²×C₅₉	1	2	yes	—
335	C₅₉	#60726	1	1	yes	characteristic, direct product factor, Sylow
336	C₂×#41	C₂³×C₅₉	1	2	yes	—
337	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
339	#137	—	2	16	no	—
340	C₂×Q₁₆	C₂³×C₅₉	1	8	yes	—
341	C₂×SD₁₆	C₂³×C₅₉	1	8	yes	—
342	#131	—	2	8	no	—
343	C₂×M₁₆	C₂³×C₅₉	1	4	yes	—
344	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
345	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
346	C₂²×C₈	C₂³×C₅₉	1	4	yes	—
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
350	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
351	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
353	#127	C₂³×C₅₉	1	1	yes	characteristic
354	#126	—	2	8	no	—
355	#126	—	2	4	no	—
356	#126	—	2	4	no	—
357	#125	—	2	4	no	—
358	#125	—	2	8	no	—
359	#125	—	2	2	no	—
360	#125	—	2	4	no	—
361	#125	C₂³×C₅₉	1	2	yes	—
362	#125	C₂³×C₅₉	1	2	yes	—
363	#125	C₂³×C₅₉	1	2	yes	—
364	#124	—	2	2	no	—
365	#124	C₂³×C₅₉	1	2	yes	—
366	#123	—	2	4	no	—
367	#123	—	2	4	no	—
368	#123	—	2	4	no	—
369	C₂²⋊Q₈	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	4	no	—
372	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
373	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
374	#121	—	2	2	no	—
375	#121	—	2	4	no	—
376	#121	—	2	2	no	—
377	#121	—	2	4	no	—
378	#121	C₂³×C₅₉	1	4	yes	—
379	C₄×Q₈	—	2	4	no	—
380	C₄×Q₈	—	2	4	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	D₄×C₅₉	1	2	yes	—
383	C₄×Q₈	C₂³×C₅₉	1	8	yes	—
384	C₄×Q₈	C₂³×C₅₉	1	4	yes	—
385	C₄×D₄	—	2	4	no	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	D₄×C₅₉	1	4	yes	—
389	C₄×D₄	D₄×C₅₉	1	2	yes	—
390	C₄×D₄	C₂³×C₅₉	1	4	yes	—
391	#117	—	2	4	no	—
392	#117	—	2	2	no	—
393	#117	—	2	4	no	—
394	#117	—	2	4	no	—
395	#117	C₂³×C₅₉	1	2	yes	—
396	#117	C₂³×C₅₉	1	1	yes	characteristic
397	#117	C₂³×C₅₉	1	2	yes	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
402	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
404	#107	C₂³×C₅₉	1	8	yes	—
405	#106	C₂³×C₅₉	1	8	yes	—
406	#103	C₂³×C₅₉	1	8	yes	—
407	#103	C₂³×C₅₉	1	8	yes	—
408	#103	C₂³×C₅₉	1	4	yes	—
409	#103	C₂³×C₅₉	1	4	yes	—
410	#102	C₂³×C₅₉	1	4	yes	—
411	#102	C₂³×C₅₉	1	4	yes	—
412	#97	C₂³×C₅₉	1	1	yes	characteristic
413	#97	C₂³×C₅₉	1	1	yes	characteristic
414	#97	C₂³×C₅₉	1	2	yes	—
415	#97	C₂³×C₅₉	1	4	yes	—
416	#97	C₂³×C₅₉	1	2	yes	—
417	C₄×C₈	C₂³×C₅₉	1	4	yes	—
418	C₄×C₈	C₂³×C₅₉	1	2	yes	—
419	#41	—	2	4	no	—
420	#41	—	2	8	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	8	no	—
424	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
425	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
426	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
431	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
432	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
441	Q₁₆	—	2	16	no	—
442	SD₁₆	—	2	16	no	—
443	M₁₆	—	2	8	no	—
444	M₁₆	#41×C₅₉	1	8	yes	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	—	2	8	no	—
447	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
448	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
449	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
464	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
465	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
474	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	8	no	—
477	C₄²	—	2	2	no	—
478	C₄²	C₂×D₄×C₅₉	1	4	yes	—
479	C₄²	C₂×D₄×C₅₉	1	2	yes	—
480	C₄²	C₂⁴×C₅₉	1	2	yes	—
481	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
482	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
483	C₂³	—	2	2	no	—
484	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
485	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
486	Q₈	—	2	2	no	—
487	Q₈	—	2	8	no	—
488	Q₈	—	2	4	no	—
489	Q₈	—	4	4	no	—
490	Q₈	—	4	4	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	4	no	—
494	D₄	—	4	4	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
509	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
511	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
514	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	2	no	—
517	C₈	C₂×#41×C₅₉	1	8	yes	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	C₅₉×#532	1	2	yes	—
525	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	4	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	4	no	—
534	C₄	C₅₉×#532	1	2	yes	—
535	C₄	C₂²×#41×C₅₉	1	2	yes	—
536	C₂	—	2	2	no	—
537	C₂	—	4	2	no	—
538	C₂	—	8	2	no	—
539	C₂	C₂×C₅₉×#532	1	1	yes	characteristic
540	C₂	C₅₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	C₅₉×#3512	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄×#41×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#3509	C₂	semidirect
3. C₅₉×#3181	C₂	semidirect
4. C₅₉×#3177	C₂	semidirect
5. C₅₉×#3174	C₂	semidirect
6. C₅₉×#3172	C₂	semidirect
7. C₅₉×#3166	C₂	semidirect
8. C₅₉×#3152	C₂	semidirect
9. C₅₉×#3135	C₂	semidirect
10. C₂×C₅₉×#491	C₂	semidirect
11. C₅₉×#3063	C₂	semidirect
12. C₅₉×#2947	C₂	semidirect
13. C₅₉×#2875	C₂	semidirect
247. #60726	C₅₉	direct (N × H)
267. #3509	C₂×C₅₉	semidirect
268. #3181	C₂×C₅₉	semidirect
269. #3177	C₂×C₅₉	semidirect
270. #3174	C₂×C₅₉	semidirect
271. #3172	C₂×C₅₉	semidirect
272. #3166	C₂×C₅₉	semidirect
273. #3152	C₂×C₅₉	semidirect
274. #3135	C₂×C₅₉	semidirect
275. C₂×#491	C₂×C₅₉	semidirect
276. #3063	C₂×C₅₉	semidirect
277. #2947	C₂×C₅₉	semidirect
278. #2875	C₂×C₅₉	semidirect
335. C₅₉	#60726	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×#3512	2
C₅₉×#3509	2
C₅₉×#3181	2
C₅₉×#3177	2
C₅₉×#3174	2
C₅₉×#3172	2
C₅₉×#3166	2
C₅₉×#3152	2
C₅₉×#3135	2
C₂×C₅₉×#491	2
C₅₉×#3063	2
C₅₉×#2947	2
C₅₉×#2875	2
#60726	59

Subgroups — C59×#60726 #28472835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#60726 #28472835