Subgroups — C₅₉×#24062 #28436171

Order 15104.

1352 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#482	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1875	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1864	C₂	1	2	yes	maximal, complemented
10	C₅₉×#1862	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₉	—	2	1	no	—
13	C₅₉×#532	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₅₉	—	2	1	no	—
17	C₂×#121×C₅₉	—	2	1	no	—
18	C₂×#121×C₅₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₅₉	—	2	1	no	—
20	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
21	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#482	—	2	8	no	—
25	C₂×#107×C₅₉	C₂²	1	2	yes	—
26	C₂×#106×C₅₉	C₂²	1	2	yes	—
27	C₂×#102×C₅₉	C₂²	1	2	yes	—
28	C₂×#102×C₅₉	C₂²	1	2	yes	—
29	C₂×#102×C₅₉	C₂²	1	2	yes	—
30	C₂×#102×C₅₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
32	C₅₉×#389	C₂²	1	1	yes	characteristic
33	C₅₉×#389	C₂²	1	1	yes	characteristic
34	C₅₉×#389	C₂²	1	1	yes	characteristic
35	C₅₉×#389	C₂²	1	1	yes	characteristic
36	C₅₉×#385	—	2	1	no	—
37	C₅₉×#385	—	2	1	no	—
38	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
40	C₅₉×#340	C₂²	1	2	yes	—
41	C₅₉×#340	C₂²	1	2	yes	—
42	C₅₉×#336	C₂²	1	1	yes	characteristic
43	C₅₉×#336	C₂²	1	1	yes	characteristic
44	C₅₉×#336	C₂²	1	2	yes	—
45	C₂×#41×C₅₉	—	2	8	no	—
46	C₂×#41×C₅₉	—	4	4	no	—
47	C₂×#41×C₅₉	—	4	4	no	—
48	C₂²×Q₈×C₅₉	—	2	1	no	—
49	C₂²×D₄×C₅₉	—	2	2	no	—
50	C₂²×D₄×C₅₉	—	2	1	no	—
51	C₂²×D₄×C₅₉	—	2	1	no	—
52	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₅₉	—	2	2	no	—
54	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₅₉	—	2	4	no	—
60	#127×C₅₉	—	2	4	no	—
61	#124×C₅₉	—	2	8	no	—
62	#121×C₅₉	—	2	8	no	—
63	#121×C₅₉	—	2	4	no	—
64	#121×C₅₉	D₄	1	8	yes	—
65	C₄×D₄×C₅₉	—	2	8	no	—
66	C₄×D₄×C₅₉	—	2	4	no	—
67	C₄×D₄×C₅₉	—	2	4	no	—
68	#117×C₅₉	—	2	2	no	—
69	#117×C₅₉	—	2	2	no	—
70	#117×C₅₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
85	C₂×C₄²×C₅₉	—	2	1	no	—
86	C₂×C₄²×C₅₉	—	2	4	no	—
87	C₂×C₄²×C₅₉	—	2	1	no	—
88	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	#107×C₅₉	—	2	4	no	—
93	#106×C₅₉	—	2	4	no	—
94	#102×C₅₉	—	2	4	no	—
95	#102×C₅₉	—	2	4	no	—
96	#102×C₅₉	—	2	4	no	—
97	#102×C₅₉	—	2	4	no	—
98	C₂²⋊C₈×C₅₉	—	2	4	no	—
99	#95×C₅₉	—	2	1	no	—
100	#95×C₅₉	—	2	1	no	—
101	#95×C₅₉	—	2	1	no	—
102	#95×C₅₉	—	2	1	no	—
103	C₂⁴×C₅₉	—	2	2	no	—
104	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
105	#41×C₅₉	—	4	32	no	—
106	C₂×Q₈×C₅₉	—	2	4	no	—
107	C₂×Q₈×C₅₉	—	4	2	no	—
108	C₂×Q₈×C₅₉	—	4	2	no	—
109	C₂×D₄×C₅₉	—	2	4	no	—
110	C₂×D₄×C₅₉	—	2	4	no	—
111	C₂×D₄×C₅₉	—	2	8	no	—
112	C₂×D₄×C₅₉	—	2	2	no	—
113	C₂×D₄×C₅₉	—	2	2	no	—
114	C₂×D₄×C₅₉	—	2	2	no	—
115	C₂×D₄×C₅₉	—	2	2	no	—
116	C₂×D₄×C₅₉	—	2	2	no	—
117	C₂×D₄×C₅₉	—	4	2	no	—
118	C₂×D₄×C₅₉	—	4	2	no	—
119	C₂×D₄×C₅₉	—	4	4	no	—
120	C₂×D₄×C₅₉	—	4	4	no	—
121	C₂×D₄×C₅₉	—	4	2	no	—
122	C₂×D₄×C₅₉	—	4	2	no	—
123	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₅₉	—	2	2	no	—
125	C₂²×C₄×C₅₉	—	2	2	no	—
126	C₂²×C₄×C₅₉	—	2	2	no	—
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	1	no	—
129	C₂²×C₄×C₅₉	—	2	2	no	—
130	C₂²×C₄×C₅₉	—	2	8	no	—
131	C₂²×C₄×C₅₉	—	2	2	no	—
132	C₂²×C₄×C₅₉	—	2	1	no	—
133	C₂²×C₄×C₅₉	—	2	1	no	—
134	C₂²×C₄×C₅₉	—	2	2	no	—
135	C₂²×C₄×C₅₉	—	2	2	no	—
136	C₂²×C₄×C₅₉	—	2	1	no	—
137	C₂²×C₄×C₅₉	—	2	1	no	—
138	C₂²×C₄×C₅₉	—	4	1	no	—
139	C₂²×C₄×C₅₉	—	4	4	no	—
140	C₂²×C₄×C₅₉	—	4	4	no	—
141	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	—	2	2	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	2	no	—
152	C₂×C₈×C₅₉	—	2	2	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₄⋊C₄×C₅₉	—	2	4	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	2	1	no	—
157	C₄⋊C₄×C₅₉	—	2	1	no	—
158	C₄⋊C₄×C₅₉	—	2	2	no	—
159	C₄⋊C₄×C₅₉	—	2	2	no	—
160	C₄⋊C₄×C₅₉	—	4	2	no	—
161	C₄⋊C₄×C₅₉	—	4	2	no	—
162	C₄⋊C₄×C₅₉	—	4	2	no	—
163	C₄⋊C₄×C₅₉	—	4	2	no	—
164	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₅₉	#41	1	2	yes	complemented
166	C₄⋊C₄×C₅₉	#41	1	2	yes	complemented
167	C₂²⋊C₄×C₅₉	—	2	4	no	—
168	C₂²⋊C₄×C₅₉	—	2	8	no	—
169	C₂²⋊C₄×C₅₉	—	2	8	no	—
170	C₂²⋊C₄×C₅₉	—	4	2	no	—
171	C₄²×C₅₉	—	2	4	no	—
172	C₄²×C₅₉	—	2	2	no	—
173	C₄²×C₅₉	—	2	2	no	—
174	C₄²×C₅₉	—	2	2	no	—
175	C₄²×C₅₉	—	2	2	no	—
176	C₄²×C₅₉	—	4	2	no	—
177	C₂³×C₅₉	—	2	1	no	—
178	C₂³×C₅₉	—	2	1	no	—
179	C₂³×C₅₉	—	2	1	no	—
180	C₂³×C₅₉	—	2	1	no	—
181	C₂³×C₅₉	—	2	1	no	—
182	C₂³×C₅₉	—	2	1	no	—
183	C₂³×C₅₉	—	2	4	no	—
184	C₂³×C₅₉	—	4	2	no	—
185	C₂³×C₅₉	—	4	2	no	—
186	C₂³×C₅₉	—	4	2	no	—
187	C₂³×C₅₉	—	4	2	no	—
188	C₂³×C₅₉	—	4	2	no	—
189	C₂³×C₅₉	—	4	2	no	—
190	C₂³×C₅₉	#120	1	2	yes	—
191	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₅₉	—	4	8	no	—
193	D₄×C₅₉	—	2	4	no	—
194	D₄×C₅₉	—	2	4	no	—
195	D₄×C₅₉	—	4	8	no	—
196	D₄×C₅₉	—	4	8	no	—
197	D₄×C₅₉	—	4	16	no	—
198	D₄×C₅₉	—	4	2	no	—
199	D₄×C₅₉	—	4	2	no	—
200	C₂×C₄×C₅₉	—	2	8	no	—
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	2	1	no	—
204	C₂×C₄×C₅₉	—	2	1	no	—
205	C₂×C₄×C₅₉	—	2	1	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	4	no	—
210	C₂×C₄×C₅₉	—	2	4	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	4	no	—
213	C₂×C₄×C₅₉	—	2	2	no	—
214	C₂×C₄×C₅₉	—	2	2	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	—	4	4	no	—
218	C₂×C₄×C₅₉	—	4	16	no	—
219	C₂×C₄×C₅₉	—	4	1	no	—
220	C₂×C₄×C₅₉	—	4	1	no	—
221	C₂×C₄×C₅₉	—	4	1	no	—
222	C₂×C₄×C₅₉	—	4	2	no	—
223	C₂×C₄×C₅₉	—	4	2	no	—
224	C₂×C₄×C₅₉	—	4	1	no	—
225	C₂×C₄×C₅₉	—	4	1	no	—
226	C₂×C₄×C₅₉	—	4	1	no	—
227	C₂×C₄×C₅₉	—	4	1	no	—
228	C₂×C₄×C₅₉	—	4	1	no	—
229	C₂×C₄×C₅₉	—	4	1	no	—
230	C₂×C₄×C₅₉	—	4	1	no	—
231	C₂×C₄×C₅₉	#120	1	2	yes	—
232	C₂×C₄×C₅₉	#135	1	2	yes	—
233	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
234	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
235	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
239	C₈×C₅₉	—	4	2	no	—
240	C₈×C₅₉	—	4	2	no	—
241	#24062	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂²×C₅₉	—	2	2	no	—
243	C₂²×C₅₉	—	2	2	no	—
244	C₂²×C₅₉	—	2	2	no	—
245	C₂²×C₅₉	—	4	1	no	—
246	C₂²×C₅₉	—	4	1	no	—
247	C₂²×C₅₉	—	4	1	no	—
248	C₂²×C₅₉	—	4	1	no	—
249	C₂²×C₅₉	—	4	4	no	—
250	C₂²×C₅₉	—	4	4	no	—
251	C₂²×C₅₉	—	4	4	no	—
252	C₂²×C₅₉	—	8	2	no	—
253	C₂²×C₅₉	—	8	2	no	—
254	C₂²×C₅₉	—	8	2	no	—
255	C₂²×C₅₉	—	8	2	no	—
256	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
257	C₂²×C₅₉	#525	1	1	yes	characteristic
258	C₂²×C₅₉	#536	1	1	yes	characteristic
259	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
260	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂²×C₅₉	#575	1	1	yes	characteristic
263	C₄×C₅₉	—	2	2	no	—
264	C₄×C₅₉	—	2	2	no	—
265	C₄×C₅₉	—	2	2	no	—
266	C₄×C₅₉	—	2	2	no	—
267	C₄×C₅₉	—	4	2	no	—
268	C₄×C₅₉	—	4	2	no	—
269	C₄×C₅₉	—	4	1	no	—
270	C₄×C₅₉	—	4	4	no	—
271	C₄×C₅₉	—	8	1	no	—
272	C₄×C₅₉	—	8	1	no	—
273	C₄×C₅₉	#547	1	2	yes	—
274	C₄×C₅₉	#547	1	2	yes	—
275	C₂×#532	C₂×C₅₉	1	1	yes	characteristic
276	C₂×#482	C₂×C₅₉	1	2	yes	complemented
277	#2296	C₂×C₅₉	1	1	yes	characteristic, complemented
278	#2058	C₂×C₅₉	1	1	yes	characteristic, complemented
279	#2057	C₂×C₅₉	1	1	yes	characteristic, complemented
280	#2041	C₂×C₅₉	1	1	yes	characteristic, complemented
281	#2041	C₂×C₅₉	1	1	yes	characteristic, complemented
282	#1875	C₂×C₅₉	1	2	yes	complemented
283	#1864	C₂×C₅₉	1	2	yes	complemented
284	#1862	C₂×C₅₉	1	2	yes	complemented
285	#1817	C₂×C₅₉	1	1	yes	characteristic, complemented
286	C₂×C₅₉	—	4	2	no	—
287	C₂×C₅₉	—	8	4	no	—
288	C₂×C₅₉	#2406	1	1	yes	characteristic
289	C₂×C₅₉	#3002	1	1	yes	characteristic
290	C₂×C₅₉	#3003	1	1	yes	characteristic
291	C₂×C₅₉	#3106	1	1	yes	characteristic
292	C₂×C₅₉	#3115	1	1	yes	characteristic
293	C₂×C₅₉	#3228	1	1	yes	characteristic
294	C₂×C₅₉	#3235	1	1	yes	characteristic
295	C₂²×#41	—	2	1	no	—
296	#532	—	2	8	no	—
297	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
298	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
299	C₂×#124	—	2	1	no	—
300	C₂×#121	—	2	1	no	—
301	C₂×#121	C₂²×C₅₉	1	2	yes	—
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
304	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
305	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
307	#482	—	2	8	no	—
308	C₂×#107	C₂²×C₅₉	1	2	yes	—
309	C₂×#106	C₂²×C₅₉	1	2	yes	—
310	C₂×#102	C₂²×C₅₉	1	2	yes	—
311	C₂×#102	C₂²×C₅₉	1	2	yes	—
312	C₂×#102	C₂²×C₅₉	1	2	yes	—
313	C₂×#102	C₂²×C₅₉	1	2	yes	—
314	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
315	#389	C₂²×C₅₉	1	1	yes	characteristic
316	#389	C₂²×C₅₉	1	1	yes	characteristic
317	#389	C₂²×C₅₉	1	1	yes	characteristic
318	#389	C₂²×C₅₉	1	1	yes	characteristic
319	#385	—	2	1	no	—
320	#385	—	2	1	no	—
321	C₄×C₄⋊C₄	—	2	1	no	—
322	C₄×C₄⋊C₄	—	2	1	no	—
323	#340	C₂²×C₅₉	1	2	yes	—
324	#340	C₂²×C₅₉	1	2	yes	—
325	#336	C₂²×C₅₉	1	1	yes	characteristic
326	#336	C₂²×C₅₉	1	1	yes	characteristic
327	#336	C₂²×C₅₉	1	2	yes	—
328	C₅₉	#24062	1	1	yes	characteristic, direct product factor, Sylow
329	C₂×#41	—	2	8	no	—
330	C₂×#41	—	4	4	no	—
331	C₂×#41	—	4	4	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
337	C₂³×C₄	—	2	2	no	—
338	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
339	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
342	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
343	C₄⋊Q₈	—	2	4	no	—
344	#127	—	2	4	no	—
345	#124	—	2	8	no	—
346	#121	—	2	8	no	—
347	#121	—	2	4	no	—
348	#121	D₄×C₅₉	1	8	yes	—
349	C₄×D₄	—	2	8	no	—
350	C₄×D₄	—	2	4	no	—
351	C₄×D₄	—	2	4	no	—
352	#117	—	2	2	no	—
353	#117	—	2	2	no	—
354	#117	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	4	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
373	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
376	#107	—	2	4	no	—
377	#106	—	2	4	no	—
378	#102	—	2	4	no	—
379	#102	—	2	4	no	—
380	#102	—	2	4	no	—
381	#102	—	2	4	no	—
382	C₂²⋊C₈	—	2	4	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
389	#41	—	4	32	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
428	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
449	C₄⋊C₄	#41×C₅₉	1	2	yes	complemented
450	C₄⋊C₄	#41×C₅₉	1	2	yes	complemented
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₄²	—	2	4	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	4	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	#120×C₅₉	1	2	yes	—
475	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
476	Q₈	—	4	8	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	4	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	16	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	16	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	#120×C₅₉	1	2	yes	—
516	C₂×C₄	#135×C₅₉	1	2	yes	—
517	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
518	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
520	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
522	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
523	C₈	—	4	2	no	—
524	C₈	—	4	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	8	2	no	—
539	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
540	C₂²	C₅₉×#525	1	1	yes	characteristic
541	C₂²	C₅₉×#536	1	1	yes	characteristic
542	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
543	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
544	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
545	C₂²	C₅₉×#575	1	1	yes	characteristic
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	C₅₉×#547	1	2	yes	—
557	C₄	C₅₉×#547	1	2	yes	—
558	C₂	—	4	2	no	—
559	C₂	—	8	4	no	—
560	C₂	C₅₉×#2406	1	1	yes	characteristic
561	C₂	C₅₉×#3002	1	1	yes	characteristic
562	C₂	C₅₉×#3003	1	1	yes	characteristic
563	C₂	C₅₉×#3106	1	1	yes	characteristic
564	C₂	C₅₉×#3115	1	1	yes	characteristic
565	C₂	C₅₉×#3228	1	1	yes	characteristic
566	C₂	C₅₉×#3235	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×C₅₉×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#482	C₂	semidirect
3. C₅₉×#2296	C₂	semidirect
4. C₅₉×#2058	C₂	semidirect
5. C₅₉×#2057	C₂	semidirect
6. C₅₉×#2041	C₂	semidirect
7. C₅₉×#2041	C₂	semidirect
8. C₅₉×#1875	C₂	semidirect
9. C₅₉×#1864	C₂	semidirect
10. C₅₉×#1862	C₂	semidirect
11. C₅₉×#1817	C₂	semidirect
165. C₄⋊C₄×C₅₉	#41	semidirect
166. C₄⋊C₄×C₅₉	#41	semidirect
241. #24062	C₅₉	direct (N × H)
276. C₂×#482	C₂×C₅₉	semidirect
277. #2296	C₂×C₅₉	semidirect
278. #2058	C₂×C₅₉	semidirect
279. #2057	C₂×C₅₉	semidirect
280. #2041	C₂×C₅₉	semidirect
281. #2041	C₂×C₅₉	semidirect
282. #1875	C₂×C₅₉	semidirect
283. #1864	C₂×C₅₉	semidirect
284. #1862	C₂×C₅₉	semidirect
285. #1817	C₂×C₅₉	semidirect
328. C₅₉	#24062	direct (N × H)
449. C₄⋊C₄	#41×C₅₉	semidirect
450. C₄⋊C₄	#41×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#532	2
C₂×C₅₉×#482	2
C₅₉×#2296	2
C₅₉×#2058	2
C₅₉×#2057	2
C₅₉×#2041	2
C₅₉×#1875	2
C₅₉×#1864	2
C₅₉×#1862	2
C₅₉×#1817	2
#24062	59

Subgroups — C59×#24062 #28436171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24062 #28436171