Subgroups — C₅₉×#17628 #28429737

Order 15104.

942 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3507	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1517	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#1512	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1509	C₂	1	4	yes	maximal, complemented
8	C₅₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1502	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#559	C₄	1	2	yes	complemented
11	C₅₉×#557	C₄	1	2	yes	complemented
12	C₅₉×#556	—	2	2	no	—
13	C₅₉×#556	C₄	1	2	yes	complemented
14	C₅₉×#554	C₄	1	2	yes	complemented
15	C₅₉×#552	—	2	2	no	—
16	C₅₉×#539	—	2	2	no	—
17	C₅₉×#536	—	2	1	no	—
18	C₅₉×#533	C₂²	1	1	yes	characteristic
19	C₅₉×#532	C₂²	1	1	yes	characteristic
20	C₅₉×#529	C₂²	1	4	yes	—
21	C₅₉×#520	—	2	1	no	—
22	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#446	—	2	2	no	—
25	C₅₉×#446	—	2	2	no	—
26	C₅₉×#432	C₂²	1	4	yes	—
27	C₅₉×#431	C₂²	1	1	yes	characteristic
28	C₅₉×#431	C₂²	1	1	yes	characteristic
29	C₅₉×#389	—	2	1	no	—
30	C₅₉×#389	—	2	2	no	—
31	C₅₉×#382	C₂²	1	2	yes	—
32	C₅₉×#382	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
35	C₅₉×#328	C₂²	1	2	yes	—
36	C₅₉×#328	C₂²	1	2	yes	—
37	C₅₉×#328	C₂²	1	4	yes	—
38	C₅₉×#327	C₂²	1	2	yes	—
39	C₅₉×#327	C₂²	1	2	yes	—
40	C₅₉×#327	C₂²	1	4	yes	—
41	C₂×#41×C₅₉	—	2	1	no	—
42	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
43	C₄⋊Q₈×C₅₉	—	2	2	no	—
44	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
45	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
47	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
48	#126×C₅₉	—	2	4	no	—
49	#126×C₅₉	—	2	4	no	—
50	#125×C₅₉	—	2	4	no	—
51	#125×C₅₉	—	2	1	no	—
52	#125×C₅₉	C₂×C₄	1	4	yes	—
53	#124×C₅₉	—	2	2	no	—
54	#124×C₅₉	—	2	1	no	—
55	#124×C₅₉	C₂×C₄	1	4	yes	—
56	#123×C₅₉	—	2	4	no	—
57	#123×C₅₉	—	2	4	no	—
58	C₂²⋊Q₈×C₅₉	—	2	2	no	—
59	C₂²⋊Q₈×C₅₉	—	2	2	no	—
60	C₂²⋊Q₈×C₅₉	—	2	1	no	—
61	C₂²⋊Q₈×C₅₉	—	2	4	no	—
62	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
63	#121×C₅₉	—	2	1	no	—
64	#121×C₅₉	C₂³	1	2	yes	—
65	C₄×Q₈×C₅₉	—	2	2	no	—
66	C₄×Q₈×C₅₉	—	2	1	no	—
67	C₄×Q₈×C₅₉	—	4	4	no	—
68	C₄×Q₈×C₅₉	C₂×C₄	1	4	yes	—
69	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
70	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
71	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
72	C₄×Q₈×C₅₉	D₄	1	2	yes	—
73	C₄×Q₈×C₅₉	D₄	1	2	yes	—
74	C₄×D₄×C₅₉	—	2	4	no	—
75	C₄×D₄×C₅₉	—	2	2	no	—
76	C₄×D₄×C₅₉	—	2	1	no	—
77	C₄×D₄×C₅₉	C₂×C₄	1	4	yes	—
78	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
79	#117×C₅₉	—	2	1	no	—
80	#117×C₅₉	—	2	2	no	—
81	#117×C₅₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
89	C₂×C₄²×C₅₉	—	2	2	no	—
90	C₂×C₄²×C₅₉	—	2	1	no	—
91	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
93	C₄⋊C₈×C₅₉	—	2	1	no	—
94	C₄⋊C₈×C₅₉	—	2	1	no	—
95	C₄⋊C₈×C₅₉	—	2	4	no	—
96	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
97	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
98	#97×C₅₉	—	2	4	no	—
99	C₄×C₈×C₅₉	—	2	1	no	—
100	C₄×C₈×C₅₉	—	2	1	no	—
101	#95×C₅₉	—	2	2	no	—
102	#95×C₅₉	—	2	1	no	—
103	#95×C₅₉	C₂³	1	1	yes	characteristic
104	#95×C₅₉	C₂³	1	1	yes	characteristic
105	#95×C₅₉	C₂³	1	2	yes	—
106	#41×C₅₉	—	4	2	no	—
107	#41×C₅₉	—	4	2	no	—
108	C₂×Q₈×C₅₉	—	2	1	no	—
109	C₂×Q₈×C₅₉	—	2	1	no	—
110	C₂×Q₈×C₅₉	—	2	2	no	—
111	C₂×Q₈×C₅₉	—	2	2	no	—
112	C₂×Q₈×C₅₉	C₂²⋊C₄	1	2	yes	—
113	C₂×Q₈×C₅₉	C₂²⋊C₄	1	2	yes	—
114	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₅₉	—	2	2	no	—
116	C₂×D₄×C₅₉	—	2	1	no	—
117	C₂×D₄×C₅₉	—	2	1	no	—
118	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₅₉	—	2	1	no	—
120	C₂²×C₄×C₅₉	—	2	2	no	—
121	C₂²×C₄×C₅₉	—	2	4	no	—
122	C₂²×C₄×C₅₉	—	2	2	no	—
123	C₂²×C₄×C₅₉	—	2	1	no	—
124	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₅₉	—	2	2	no	—
130	C₂×C₈×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	2	1	no	—
132	C₄⋊C₄×C₅₉	—	2	4	no	—
133	C₄⋊C₄×C₅₉	—	2	1	no	—
134	C₄⋊C₄×C₅₉	—	2	4	no	—
135	C₄⋊C₄×C₅₉	—	2	1	no	—
136	C₄⋊C₄×C₅₉	—	2	1	no	—
137	C₄⋊C₄×C₅₉	—	2	2	no	—
138	C₄⋊C₄×C₅₉	—	2	4	no	—
139	C₄⋊C₄×C₅₉	—	2	2	no	—
140	C₄⋊C₄×C₅₉	—	4	4	no	—
141	C₄⋊C₄×C₅₉	—	4	2	no	—
142	C₄⋊C₄×C₅₉	—	4	4	no	—
143	C₄⋊C₄×C₅₉	—	4	2	no	—
144	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
145	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
146	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
147	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	4	yes	—
148	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
149	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
150	C₂²⋊C₄×C₅₉	—	2	2	no	—
151	C₂²⋊C₄×C₅₉	—	2	4	no	—
152	C₂²⋊C₄×C₅₉	—	2	4	no	—
153	C₂²⋊C₄×C₅₉	—	2	2	no	—
154	C₂²⋊C₄×C₅₉	—	2	4	no	—
155	C₂²⋊C₄×C₅₉	—	2	2	no	—
156	C₄²×C₅₉	—	2	4	no	—
157	C₄²×C₅₉	—	2	2	no	—
158	C₄²×C₅₉	—	4	4	no	—
159	C₄²×C₅₉	—	4	2	no	—
160	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅₉	C₂²×C₄	1	4	yes	—
162	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅₉	C₂×D₄	1	4	yes	—
166	C₂³×C₅₉	—	2	2	no	—
167	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₅₉	—	2	4	no	—
169	Q₈×C₅₉	—	2	4	no	—
170	Q₈×C₅₉	—	4	2	no	—
171	Q₈×C₅₉	—	4	2	no	—
172	Q₈×C₅₉	—	8	1	no	—
173	D₄×C₅₉	—	4	2	no	—
174	D₄×C₅₉	—	4	2	no	—
175	D₄×C₅₉	—	4	2	no	—
176	D₄×C₅₉	—	4	2	no	—
177	D₄×C₅₉	—	8	1	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	2	2	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	—	2	2	no	—
182	C₂×C₄×C₅₉	—	2	2	no	—
183	C₂×C₄×C₅₉	—	2	2	no	—
184	C₂×C₄×C₅₉	—	4	2	no	—
185	C₂×C₄×C₅₉	—	4	1	no	—
186	C₂×C₄×C₅₉	—	4	1	no	—
187	C₂×C₄×C₅₉	—	4	1	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	4	4	no	—
190	C₂×C₄×C₅₉	—	4	2	no	—
191	C₂×C₄×C₅₉	—	4	1	no	—
192	C₂×C₄×C₅₉	—	4	2	no	—
193	C₂×C₄×C₅₉	—	4	1	no	—
194	C₂×C₄×C₅₉	—	4	2	no	—
195	C₂×C₄×C₅₉	—	4	1	no	—
196	C₂×C₄×C₅₉	—	8	4	no	—
197	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
198	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	4	yes	—
199	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₅₉	#137	1	2	yes	—
205	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
207	C₈×C₅₉	—	4	2	no	—
208	C₈×C₅₉	—	4	2	no	—
209	#17628	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₅₉	—	2	1	no	—
211	C₂²×C₅₉	—	2	1	no	—
212	C₂²×C₅₉	—	4	2	no	—
213	C₂²×C₅₉	—	4	2	no	—
214	C₂²×C₅₉	—	4	2	no	—
215	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
218	C₄×C₅₉	—	2	1	no	—
219	C₄×C₅₉	—	2	1	no	—
220	C₄×C₅₉	—	2	4	no	—
221	C₄×C₅₉	—	2	4	no	—
222	C₄×C₅₉	—	2	1	no	—
223	C₄×C₅₉	—	2	1	no	—
224	C₄×C₅₉	—	4	2	no	—
225	C₄×C₅₉	—	4	2	no	—
226	C₄×C₅₉	—	4	2	no	—
227	C₄×C₅₉	—	4	2	no	—
228	C₄×C₅₉	—	8	2	no	—
229	C₄×C₅₉	—	8	1	no	—
230	C₄×C₅₉	#417	1	2	yes	—
231	C₄×C₅₉	#417	1	2	yes	—
232	#3507	C₂×C₅₉	1	1	yes	characteristic
233	#2983	C₂×C₅₉	1	1	yes	characteristic, complemented
234	#2351	C₂×C₅₉	1	1	yes	characteristic, complemented
235	#1518	C₂×C₅₉	1	1	yes	characteristic, complemented
236	#1517	C₂×C₅₉	1	1	yes	characteristic
237	#1512	C₂×C₅₉	1	4	yes	complemented
238	#1509	C₂×C₅₉	1	4	yes	complemented
239	#1503	C₂×C₅₉	1	1	yes	characteristic, complemented
240	#1502	C₂×C₅₉	1	1	yes	characteristic
241	C₂×C₅₉	—	2	1	no	—
242	C₂×C₅₉	—	2	1	no	—
243	C₂×C₅₉	—	8	2	no	—
244	C₂×C₅₉	#2884	1	1	yes	characteristic
245	C₂×C₅₉	C₂×#417	1	1	yes	characteristic
246	C₂×C₅₉	#2901	1	1	yes	characteristic
247	#559	C₄×C₅₉	1	2	yes	complemented
248	#557	C₄×C₅₉	1	2	yes	complemented
249	#556	—	2	2	no	—
250	#556	C₄×C₅₉	1	2	yes	complemented
251	#554	C₄×C₅₉	1	2	yes	complemented
252	#552	—	2	2	no	—
253	#539	—	2	2	no	—
254	#536	—	2	1	no	—
255	#533	C₂²×C₅₉	1	1	yes	characteristic
256	#532	C₂²×C₅₉	1	1	yes	characteristic
257	#529	C₂²×C₅₉	1	4	yes	—
258	#520	—	2	1	no	—
259	C₂×C₄×Q₈	—	2	1	no	—
260	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
261	#446	—	2	2	no	—
262	#446	—	2	2	no	—
263	#432	C₂²×C₅₉	1	4	yes	—
264	#431	C₂²×C₅₉	1	1	yes	characteristic
265	#431	C₂²×C₅₉	1	1	yes	characteristic
266	#389	—	2	1	no	—
267	#389	—	2	2	no	—
268	#382	C₂²×C₅₉	1	2	yes	—
269	#382	C₂²×C₅₉	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
272	#328	C₂²×C₅₉	1	2	yes	—
273	#328	C₂²×C₅₉	1	2	yes	—
274	#328	C₂²×C₅₉	1	4	yes	—
275	#327	C₂²×C₅₉	1	2	yes	—
276	#327	C₂²×C₅₉	1	2	yes	—
277	#327	C₂²×C₅₉	1	4	yes	—
278	C₅₉	#17628	1	1	yes	characteristic, direct product factor, Sylow
279	C₂×#41	—	2	1	no	—
280	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
283	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
284	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
285	#127	C₂×C₄×C₅₉	1	1	yes	characteristic
286	#126	—	2	4	no	—
287	#126	—	2	4	no	—
288	#125	—	2	4	no	—
289	#125	—	2	1	no	—
290	#125	C₂×C₄×C₅₉	1	4	yes	—
291	#124	—	2	2	no	—
292	#124	—	2	1	no	—
293	#124	C₂×C₄×C₅₉	1	4	yes	—
294	#123	—	2	4	no	—
295	#123	—	2	4	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
301	#121	—	2	1	no	—
302	#121	C₂³×C₅₉	1	2	yes	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	4	4	no	—
306	C₄×Q₈	C₂×C₄×C₅₉	1	4	yes	—
307	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
308	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
309	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
310	C₄×Q₈	D₄×C₅₉	1	2	yes	—
311	C₄×Q₈	D₄×C₅₉	1	2	yes	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	C₂×C₄×C₅₉	1	4	yes	—
316	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
317	#117	—	2	1	no	—
318	#117	—	2	2	no	—
319	#117	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
330	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	4	no	—
334	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
335	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
336	#97	—	2	4	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	2	1	no	—
339	#95	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	C₂³×C₅₉	1	1	yes	characteristic
342	#95	C₂³×C₅₉	1	1	yes	characteristic
343	#95	C₂³×C₅₉	1	2	yes	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	C₂²⋊C₄×C₅₉	1	2	yes	—
351	C₂×Q₈	C₂²⋊C₄×C₅₉	1	2	yes	—
352	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
383	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	4	yes	—
385	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	4	yes	—
386	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	4	4	no	—
397	C₄²	—	4	2	no	—
398	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
399	C₄²	C₂²×C₄×C₅₉	1	4	yes	—
400	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
401	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₅₉	1	4	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	8	1	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	8	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	8	4	no	—
435	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	4	yes	—
437	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
438	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
439	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
440	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
441	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
442	C₂×C₄	#137×C₅₉	1	2	yes	—
443	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
445	C₈	—	4	2	no	—
446	C₈	—	4	2	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
453	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
454	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	4	no	—
458	C₄	—	2	4	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	1	no	—
467	C₄	C₅₉×#417	1	2	yes	—
468	C₄	C₅₉×#417	1	2	yes	—
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	8	2	no	—
472	C₂	C₅₉×#2884	1	1	yes	characteristic
473	C₂	C₂×C₅₉×#417	1	1	yes	characteristic
474	C₂	C₅₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×Q₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2983	C₂	semidirect
3. C₅₉×#2351	C₂	semidirect
4. C₅₉×#1518	C₂	semidirect
6. C₅₉×#1512	C₂	semidirect
7. C₅₉×#1509	C₂	semidirect
8. C₅₉×#1503	C₂	semidirect
10. C₅₉×#559	C₄	semidirect
11. C₅₉×#557	C₄	semidirect
13. C₅₉×#556	C₄	semidirect
14. C₅₉×#554	C₄	semidirect
209. #17628	C₅₉	direct (N × H)
233. #2983	C₂×C₅₉	semidirect
234. #2351	C₂×C₅₉	semidirect
235. #1518	C₂×C₅₉	semidirect
237. #1512	C₂×C₅₉	semidirect
238. #1509	C₂×C₅₉	semidirect
239. #1503	C₂×C₅₉	semidirect
247. #559	C₄×C₅₉	semidirect
248. #557	C₄×C₅₉	semidirect
250. #556	C₄×C₅₉	semidirect
251. #554	C₄×C₅₉	semidirect
278. C₅₉	#17628	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×#3507	2
C₅₉×#2983	2
C₅₉×#2351	2
C₅₉×#1518	2
C₅₉×#1517	2
C₅₉×#1512	2
C₅₉×#1509	2
C₅₉×#1503	2
C₅₉×#1502	2
#17628	59

Subgroups — C59×#17628 #28429737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17628 #28429737