Subgroups — C₅₉×#17454 #28429563

Order 15104.

1138 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×2₋¹⁺⁴×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1491	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1489	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1488	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1487	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1477	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₅₉	C₄	1	1	yes	characteristic
13	C₅₉×#520	—	2	2	no	—
14	C₅₉×#520	—	2	1	no	—
15	C₅₉×#520	C₄	1	2	yes	—
16	C₅₉×#520	C₄	1	1	yes	characteristic
17	C₅₉×#520	C₄	1	1	yes	characteristic
18	C₅₉×#519	—	2	1	no	—
19	C₅₉×#519	C₄	1	2	yes	—
20	C₅₉×#519	C₄	1	1	yes	characteristic
21	C₄×#41×C₅₉	—	2	2	no	—
22	C₄×#41×C₅₉	—	2	1	no	—
23	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
24	C₄×#41×C₅₉	C₂²	1	2	yes	—
25	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
29	C₅₉×#446	—	2	1	no	—
30	C₅₉×#446	—	2	1	no	—
31	C₅₉×#436	—	2	1	no	—
32	C₅₉×#436	—	2	1	no	—
33	C₅₉×#435	—	2	2	no	—
34	C₅₉×#435	—	2	2	no	—
35	C₅₉×#432	C₂²	1	2	yes	—
36	C₅₉×#431	C₂²	1	1	yes	characteristic
37	C₅₉×#431	C₂²	1	1	yes	characteristic
38	C₅₉×#431	C₂²	1	2	yes	—
39	C₅₉×#423	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
46	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
47	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
53	2₋¹⁺⁴×C₅₉	—	2	4	no	—
54	2₋¹⁺⁴×C₅₉	—	2	4	no	—
55	C₂×#41×C₅₉	—	2	1	no	—
56	C₂×#41×C₅₉	—	2	2	no	—
57	C₂×#41×C₅₉	C₂×C₄	1	2	yes	—
58	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
59	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
60	C₂²×Q₈×C₅₉	—	2	1	no	—
61	C₂²×Q₈×C₅₉	C₂×C₄	1	2	yes	—
62	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
63	C₂×M₁₆×C₅₉	—	2	2	no	—
64	C₂×M₁₆×C₅₉	—	2	2	no	—
65	C₂²×C₈×C₅₉	—	2	1	no	—
66	C₂²×C₈×C₅₉	—	2	1	no	—
67	C₄×Q₈×C₅₉	—	2	1	no	—
68	C₄×Q₈×C₅₉	—	2	2	no	—
69	C₄×Q₈×C₅₉	—	2	1	no	—
70	C₄×Q₈×C₅₉	—	2	2	no	—
71	C₄×Q₈×C₅₉	—	2	1	no	—
72	C₄×Q₈×C₅₉	—	2	1	no	—
73	C₄×Q₈×C₅₉	—	2	2	no	—
74	C₄×Q₈×C₅₉	—	2	1	no	—
75	C₄×Q₈×C₅₉	—	2	2	no	—
76	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
77	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
81	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
84	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₅₉	—	2	2	no	—
86	C₄×D₄×C₅₉	—	2	1	no	—
87	C₄×D₄×C₅₉	—	2	1	no	—
88	C₄×D₄×C₅₉	—	2	2	no	—
89	C₄×D₄×C₅₉	—	2	1	no	—
90	C₄×D₄×C₅₉	—	2	2	no	—
91	C₄×D₄×C₅₉	—	2	2	no	—
92	C₄×D₄×C₅₉	—	2	2	no	—
93	C₄×D₄×C₅₉	—	2	2	no	—
94	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
95	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
96	C₄×D₄×C₅₉	D₄	1	2	yes	—
97	C₄×D₄×C₅₉	D₄	1	2	yes	—
98	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
99	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
100	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
101	#117×C₅₉	—	2	2	no	—
102	#117×C₅₉	—	2	1	no	—
103	#117×C₅₉	—	2	2	no	—
104	#117×C₅₉	—	2	2	no	—
105	#117×C₅₉	—	2	2	no	—
106	#117×C₅₉	—	2	1	no	—
107	#117×C₅₉	—	2	2	no	—
108	#117×C₅₉	C₂×C₄	1	2	yes	—
109	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
110	#117×C₅₉	C₂×C₄	1	2	yes	—
111	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
114	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
115	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
117	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄²×C₅₉	—	2	1	no	—
119	C₂×C₄²×C₅₉	—	2	2	no	—
120	C₂×C₄²×C₅₉	—	2	1	no	—
121	C₂×C₄²×C₅₉	—	2	2	no	—
122	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
124	C₄⋊C₈×C₅₉	—	2	1	no	—
125	C₄⋊C₈×C₅₉	—	2	2	no	—
126	C₄⋊C₈×C₅₉	—	2	2	no	—
127	C₄⋊C₈×C₅₉	—	2	1	no	—
128	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
129	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
131	C₂²⋊C₈×C₅₉	—	2	1	no	—
132	C₂²⋊C₈×C₅₉	—	2	1	no	—
133	C₂²⋊C₈×C₅₉	—	2	2	no	—
134	C₂²⋊C₈×C₅₉	—	2	2	no	—
135	#97×C₅₉	—	2	2	no	—
136	#97×C₅₉	—	2	2	no	—
137	C₄×C₈×C₅₉	—	2	1	no	—
138	C₄×C₈×C₅₉	—	2	1	no	—
139	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₅₉	C₂³	1	2	yes	—
142	#41×C₅₉	—	2	16	no	—
143	#41×C₅₉	—	2	8	no	—
144	#41×C₅₉	—	2	4	no	—
145	#41×C₅₉	—	2	4	no	—
146	#41×C₅₉	—	2	2	no	—
147	#41×C₅₉	—	2	2	no	—
148	#41×C₅₉	—	2	2	no	—
149	#41×C₅₉	M₁₆	1	4	yes	complemented
150	C₂×Q₈×C₅₉	—	2	8	no	—
151	C₂×Q₈×C₅₉	—	2	4	no	—
152	C₂×Q₈×C₅₉	—	2	4	no	—
153	C₂×Q₈×C₅₉	—	2	2	no	—
154	C₂×Q₈×C₅₉	—	2	1	no	—
155	C₂×Q₈×C₅₉	—	2	2	no	—
156	C₂×Q₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×Q₈×C₅₉	M₁₆	1	4	yes	complemented
158	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₅₉	—	2	2	no	—
161	C₂×D₄×C₅₉	—	2	1	no	—
162	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
163	C₂×D₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅₉	—	2	2	no	—
166	C₂²×C₄×C₅₉	—	2	1	no	—
167	C₂²×C₄×C₅₉	—	2	2	no	—
168	C₂²×C₄×C₅₉	—	2	1	no	—
169	C₂²×C₄×C₅₉	—	2	2	no	—
170	C₂²×C₄×C₅₉	—	2	1	no	—
171	C₂²×C₄×C₅₉	—	2	1	no	—
172	C₂²×C₄×C₅₉	—	2	1	no	—
173	C₂²×C₄×C₅₉	—	2	2	no	—
174	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
180	M₁₆×C₅₉	—	4	4	no	—
181	M₁₆×C₅₉	—	8	2	no	—
182	C₂×C₈×C₅₉	—	2	1	no	—
183	C₂×C₈×C₅₉	—	2	1	no	—
184	C₂×C₈×C₅₉	—	2	2	no	—
185	C₂×C₈×C₅₉	—	2	1	no	—
186	C₂×C₈×C₅₉	—	2	1	no	—
187	C₂×C₈×C₅₉	—	2	2	no	—
188	C₂×C₈×C₅₉	—	4	2	no	—
189	C₂×C₈×C₅₉	—	8	1	no	—
190	C₄⋊C₄×C₅₉	—	2	2	no	—
191	C₄⋊C₄×C₅₉	—	2	2	no	—
192	C₄⋊C₄×C₅₉	—	2	2	no	—
193	C₄⋊C₄×C₅₉	—	2	2	no	—
194	C₄⋊C₄×C₅₉	—	2	1	no	—
195	C₄⋊C₄×C₅₉	—	2	1	no	—
196	C₄⋊C₄×C₅₉	—	2	2	no	—
197	C₄⋊C₄×C₅₉	—	2	2	no	—
198	C₄⋊C₄×C₅₉	—	2	1	no	—
199	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
200	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
201	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
202	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
205	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
206	C₂²⋊C₄×C₅₉	—	2	2	no	—
207	C₂²⋊C₄×C₅₉	—	2	1	no	—
208	C₂²⋊C₄×C₅₉	—	2	1	no	—
209	C₂²⋊C₄×C₅₉	—	2	2	no	—
210	C₂²⋊C₄×C₅₉	—	2	1	no	—
211	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
212	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
213	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
214	C₄²×C₅₉	—	2	1	no	—
215	C₄²×C₅₉	—	2	2	no	—
216	C₄²×C₅₉	—	2	2	no	—
217	C₄²×C₅₉	—	2	2	no	—
218	C₄²×C₅₉	—	2	2	no	—
219	C₄²×C₅₉	—	2	2	no	—
220	C₄²×C₅₉	—	2	1	no	—
221	C₄²×C₅₉	—	2	2	no	—
222	C₄²×C₅₉	—	2	1	no	—
223	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
224	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
225	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₅₉	C₂×D₄	1	2	yes	—
227	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₅₉	C₂×D₄	1	2	yes	—
229	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
230	C₂³×C₅₉	—	2	1	no	—
231	C₂³×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	Q₈×C₅₉	—	2	8	no	—
234	Q₈×C₅₉	—	2	1	no	—
235	Q₈×C₅₉	—	2	2	no	—
236	Q₈×C₅₉	—	2	2	no	—
237	Q₈×C₅₉	—	2	4	no	—
238	Q₈×C₅₉	C₂×M₁₆	1	2	yes	—
239	Q₈×C₅₉	C₂×M₁₆	1	4	yes	—
240	D₄×C₅₉	—	2	8	no	—
241	D₄×C₅₉	—	2	4	no	—
242	D₄×C₅₉	—	2	4	no	—
243	D₄×C₅₉	—	2	1	no	—
244	D₄×C₅₉	—	2	2	no	—
245	D₄×C₅₉	C₂×M₁₆	1	2	yes	—
246	C₂×C₄×C₅₉	—	2	8	no	—
247	C₂×C₄×C₅₉	—	2	8	no	—
248	C₂×C₄×C₅₉	—	2	2	no	—
249	C₂×C₄×C₅₉	—	2	1	no	—
250	C₂×C₄×C₅₉	—	2	4	no	—
251	C₂×C₄×C₅₉	—	2	2	no	—
252	C₂×C₄×C₅₉	—	2	2	no	—
253	C₂×C₄×C₅₉	—	2	1	no	—
254	C₂×C₄×C₅₉	—	2	2	no	—
255	C₂×C₄×C₅₉	—	2	1	no	—
256	C₂×C₄×C₅₉	—	2	2	no	—
257	C₂×C₄×C₅₉	—	2	4	no	—
258	C₂×C₄×C₅₉	—	2	1	no	—
259	C₂×C₄×C₅₉	—	2	2	no	—
260	C₂×C₄×C₅₉	—	2	1	no	—
261	C₂×C₄×C₅₉	—	4	1	no	—
262	C₂×C₄×C₅₉	—	4	2	no	—
263	C₂×C₄×C₅₉	—	4	1	no	—
264	C₂×C₄×C₅₉	—	4	1	no	—
265	C₂×C₄×C₅₉	—	8	1	no	—
266	C₂×C₄×C₅₉	—	8	2	no	—
267	C₂×C₄×C₅₉	—	8	1	no	—
268	C₂×C₄×C₅₉	—	8	2	no	—
269	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
273	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
274	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
276	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
277	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
280	C₈×C₅₉	—	2	2	no	—
281	C₈×C₅₉	—	4	1	no	—
282	C₈×C₅₉	—	4	2	no	—
283	C₈×C₅₉	—	4	2	no	—
284	C₈×C₅₉	—	4	1	no	—
285	C₈×C₅₉	—	4	1	no	—
286	#17454	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂²×C₅₉	—	2	1	no	—
288	C₂²×C₅₉	—	2	1	no	—
289	C₂²×C₅₉	—	2	2	no	—
290	C₂²×C₅₉	—	2	2	no	—
291	C₂²×C₅₉	—	2	2	no	—
292	C₂²×C₅₉	—	2	2	no	—
293	C₂²×C₅₉	—	4	1	no	—
294	C₂²×C₅₉	—	4	1	no	—
295	C₂²×C₅₉	#407	1	2	yes	—
296	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
297	C₄×C₅₉	—	2	4	no	—
298	C₄×C₅₉	—	2	2	no	—
299	C₄×C₅₉	—	2	2	no	—
300	C₄×C₅₉	—	2	1	no	—
301	C₄×C₅₉	—	2	2	no	—
302	C₄×C₅₉	—	2	1	no	—
303	C₄×C₅₉	—	2	1	no	—
304	C₄×C₅₉	—	2	2	no	—
305	C₄×C₅₉	—	4	1	no	—
306	C₄×C₅₉	—	4	2	no	—
307	C₄×C₅₉	—	4	1	no	—
308	C₄×C₅₉	#407	1	2	yes	—
309	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
310	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
311	C₄×C₅₉	#577	1	1	yes	characteristic
312	C₄×C₅₉	#578	1	1	yes	characteristic
313	C₄×2₋¹⁺⁴	C₂×C₅₉	1	1	yes	characteristic
314	#2989	C₂×C₅₉	1	1	yes	characteristic, complemented
315	#2965	C₂×C₅₉	1	1	yes	characteristic, complemented
316	#1491	C₂×C₅₉	1	2	yes	complemented
317	#1489	C₂×C₅₉	1	2	yes	complemented
318	#1488	C₂×C₅₉	1	2	yes	complemented
319	#1487	C₂×C₅₉	1	2	yes	complemented
320	#1479	C₂×C₅₉	1	1	yes	characteristic, complemented
321	#1477	C₂×C₅₉	1	1	yes	characteristic, complemented
322	#1476	C₂×C₅₉	1	1	yes	characteristic, complemented
323	C₂×Q₈⋊C₈	C₂×C₅₉	1	1	yes	characteristic, complemented
324	C₂×C₅₉	—	2	2	no	—
325	C₂×C₅₉	—	4	2	no	—
326	C₂×C₅₉	—	4	2	no	—
327	C₂×C₅₉	C₂×#407	1	1	yes	characteristic
328	C₂×C₅₉	#2898	1	1	yes	characteristic
329	C₂×C₅₉	#2901	1	1	yes	characteristic
330	C₂×2₋¹⁺⁴	C₄×C₅₉	1	1	yes	characteristic
331	#520	—	2	2	no	—
332	#520	—	2	1	no	—
333	#520	C₄×C₅₉	1	2	yes	—
334	#520	C₄×C₅₉	1	1	yes	characteristic
335	#520	C₄×C₅₉	1	1	yes	characteristic
336	#519	—	2	1	no	—
337	#519	C₄×C₅₉	1	2	yes	—
338	#519	C₄×C₅₉	1	1	yes	characteristic
339	C₄×#41	—	2	2	no	—
340	C₄×#41	—	2	1	no	—
341	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
342	C₄×#41	C₂²×C₅₉	1	2	yes	—
343	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
344	C₂×C₄×Q₈	—	2	1	no	—
345	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
347	#446	—	2	1	no	—
348	#446	—	2	1	no	—
349	#436	—	2	1	no	—
350	#436	—	2	1	no	—
351	#435	—	2	2	no	—
352	#435	—	2	2	no	—
353	#432	C₂²×C₅₉	1	2	yes	—
354	#431	C₂²×C₅₉	1	1	yes	characteristic
355	#431	C₂²×C₅₉	1	1	yes	characteristic
356	#431	C₂²×C₅₉	1	2	yes	—
357	#423	C₂²×C₅₉	1	2	yes	—
358	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
359	C₄×M₁₆	C₂²×C₅₉	1	2	yes	—
360	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
361	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	—
362	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	—
363	Q₈⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
364	Q₈⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
365	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	—
366	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	—
367	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	—
368	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
369	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
370	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
371	C₅₉	#17454	1	1	yes	characteristic, direct product factor, Sylow
372	2₋¹⁺⁴	—	2	4	no	—
373	2₋¹⁺⁴	—	2	4	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	C₂×C₄×C₅₉	1	2	yes	—
377	C₂×#41	C₂×C₄×C₅₉	1	1	yes	characteristic
378	C₂×#41	C₂×C₄×C₅₉	1	1	yes	characteristic
379	C₂²×Q₈	—	2	1	no	—
380	C₂²×Q₈	C₂×C₄×C₅₉	1	2	yes	—
381	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
382	C₂×M₁₆	—	2	2	no	—
383	C₂×M₁₆	—	2	2	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
396	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
397	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
398	C₄×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
399	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
400	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
401	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
402	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
403	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
414	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
415	C₄×D₄	D₄×C₅₉	1	2	yes	—
416	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
417	C₄×D₄	D₄×C₅₉	1	2	yes	—
418	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
419	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
420	#117	—	2	2	no	—
421	#117	—	2	1	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	—	2	2	no	—
425	#117	—	2	1	no	—
426	#117	—	2	2	no	—
427	#117	C₂×C₄×C₅₉	1	2	yes	—
428	#117	C₂×C₄×C₅₉	1	1	yes	characteristic
429	#117	C₂×C₄×C₅₉	1	2	yes	—
430	#117	C₂×C₄×C₅₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	2	no	—
433	C₂×C₄⋊C₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
436	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	2	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	2	no	—
441	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
443	C₄⋊C₈	—	2	1	no	—
444	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	2	2	no	—
446	C₄⋊C₈	—	2	1	no	—
447	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
448	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
449	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
450	C₂²⋊C₈	—	2	1	no	—
451	C₂²⋊C₈	—	2	1	no	—
452	C₂²⋊C₈	—	2	2	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	#97	—	2	2	no	—
455	#97	—	2	2	no	—
456	C₄×C₈	—	2	1	no	—
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
459	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
460	C₄×C₈	C₂³×C₅₉	1	2	yes	—
461	#41	—	2	16	no	—
462	#41	—	2	8	no	—
463	#41	—	2	4	no	—
464	#41	—	2	4	no	—
465	#41	—	2	2	no	—
466	#41	—	2	2	no	—
467	#41	—	2	2	no	—
468	#41	M₁₆×C₅₉	1	4	yes	complemented
469	C₂×Q₈	—	2	8	no	—
470	C₂×Q₈	—	2	4	no	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	2	no	—
475	C₂×Q₈	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
476	C₂×Q₈	M₁₆×C₅₉	1	4	yes	complemented
477	C₂×Q₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
478	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
482	C₂×D₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
483	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
494	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
499	M₁₆	—	4	4	no	—
500	M₁₆	—	8	2	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	4	2	no	—
508	C₂×C₈	—	8	1	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
519	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
520	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
521	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
524	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
531	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
532	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	2	1	no	—
542	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
543	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
544	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
546	C₄²	C₂×D₄×C₅₉	1	2	yes	—
547	C₄²	C₂×D₄×C₅₉	1	2	yes	—
548	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
549	C₂³	—	2	1	no	—
550	C₂³	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
551	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
552	Q₈	—	2	8	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	2	4	no	—
555	Q₈	—	2	1	no	—
556	Q₈	—	2	2	no	—
557	Q₈	C₂×M₁₆×C₅₉	1	2	yes	—
558	Q₈	C₂×M₁₆×C₅₉	1	4	yes	—
559	D₄	—	2	8	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	1	no	—
564	D₄	C₂×M₁₆×C₅₉	1	2	yes	—
565	C₂×C₄	—	2	8	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	8	1	no	—
585	C₂×C₄	—	8	2	no	—
586	C₂×C₄	—	8	1	no	—
587	C₂×C₄	—	8	2	no	—
588	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
590	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
591	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
592	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
593	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
594	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
595	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
596	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
599	C₈	—	2	2	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	2	no	—
602	C₈	—	4	2	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	C₅₉×#407	1	2	yes	—
614	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
615	C₄	—	2	4	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	C₅₉×#407	1	2	yes	—
627	C₄	C₂²×M₁₆×C₅₉	1	1	yes	characteristic
628	C₄	C₂²×M₁₆×C₅₉	1	1	yes	characteristic
629	C₄	C₅₉×#577	1	1	yes	characteristic
630	C₄	C₅₉×#578	1	1	yes	characteristic
631	C₂	—	2	2	no	—
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	C₂×C₅₉×#407	1	1	yes	characteristic
635	C₂	C₅₉×#2898	1	1	yes	characteristic
636	C₂	C₅₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₄²	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
prime radical	C₂×2₋¹⁺⁴×C₅₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₄×#41×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2989	C₂	semidirect
3. C₅₉×#2965	C₂	semidirect
4. C₅₉×#1491	C₂	semidirect
5. C₅₉×#1489	C₂	semidirect
6. C₅₉×#1488	C₂	semidirect
7. C₅₉×#1487	C₂	semidirect
8. C₅₉×#1479	C₂	semidirect
9. C₅₉×#1477	C₂	semidirect
10. C₅₉×#1476	C₂	semidirect
11. C₂×C₅₉×Q₈⋊C₈	C₂	semidirect
149. #41×C₅₉	M₁₆	semidirect
157. C₂×Q₈×C₅₉	M₁₆	semidirect
286. #17454	C₅₉	direct (N × H)
314. #2989	C₂×C₅₉	semidirect
315. #2965	C₂×C₅₉	semidirect
316. #1491	C₂×C₅₉	semidirect
317. #1489	C₂×C₅₉	semidirect
318. #1488	C₂×C₅₉	semidirect
319. #1487	C₂×C₅₉	semidirect
320. #1479	C₂×C₅₉	semidirect
321. #1477	C₂×C₅₉	semidirect
322. #1476	C₂×C₅₉	semidirect
323. C₂×Q₈⋊C₈	C₂×C₅₉	semidirect
371. C₅₉	#17454	direct (N × H)
468. #41	M₁₆×C₅₉	semidirect
476. C₂×Q₈	M₁₆×C₅₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×2₋¹⁺⁴×C₅₉	2
C₅₉×#2989	2
C₅₉×#2965	2
C₅₉×#1491	2
C₅₉×#1489	2
C₅₉×#1488	2
C₅₉×#1487	2
C₅₉×#1479	2
C₅₉×#1477	2
C₅₉×#1476	2
C₂×C₅₉×Q₈⋊C₈	2
#17454	59

Subgroups — C59×#17454 #28429563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17454 #28429563