Subgroups — #28558063

Order 15104.

750 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433052	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14273747	C₂	1	1	yes	maximal, characteristic
4	#21422900	C₂	1	2	yes	maximal, complemented
5	#21422899	C₂	1	2	yes	maximal, complemented
6	#21422893	C₂	1	2	yes	maximal, complemented
7	#21422888	C₂	1	2	yes	maximal, complemented
8	#21422842	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₄	1	1	yes	characteristic
13	C₄×#11745685	C₂²	1	1	yes	characteristic
14	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
15	#16837526	C₂²	1	2	yes	—
16	C₄×#11745672	C₄	1	1	yes	characteristic
17	C₄×#11745672	C₂²	1	1	yes	characteristic
18	C₄×#11745671	C₄	1	1	yes	characteristic
19	C₄×#11745671	C₂²	1	1	yes	characteristic
20	C₄×#11745670	C₄	1	1	yes	characteristic
21	C₄×#11745670	C₂²	1	1	yes	characteristic
22	C₄×#11745669	C₄	1	1	yes	characteristic
23	C₄×#11745669	C₂²	1	1	yes	characteristic
24	D₄×C₅₉⋊C₈	—	2	2	no	—
25	D₄×C₅₉⋊C₈	C₂²	1	2	yes	—
26	#16837467	C₂²	1	2	yes	—
27	(C₂²⋊D₅₉)⋊C₈	—	2	2	no	—
28	#16837455	—	2	1	no	—
29	#16837455	C₂²	1	1	yes	characteristic
30	#16837453	—	2	1	no	—
31	#16837438	C₄	1	1	yes	characteristic
32	#16837398	C₄	1	1	yes	characteristic
33	#16837396	C₄	1	1	yes	characteristic
34	C₂×C₄×C₅₉⋊C₈	—	2	1	no	—
35	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
37	C₄×C₈×D₅₉	—	2	1	no	—
38	#16837154	C₂²	1	2	yes	—
39	#16837152	C₂²	1	2	yes	—
40	#16837134	C₂²	1	2	yes	—
41	#16837131	C₂²	1	2	yes	—
42	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
43	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
44	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
49	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
50	#14273747	C₈	1	8	yes	complemented
51	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
52	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
53	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
54	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₅₉⋊C₈	—	2	2	no	—
56	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
59	C₂×C₈×D₅₉	—	2	2	no	—
60	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
62	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₅₉	—	2	1	no	—
65	C₄×C₂²⋊D₅₉	—	2	1	no	—
66	#14273686	C₂×C₄	1	1	yes	characteristic
67	#14273684	—	2	1	no	—
68	C₄²×D₅₉	—	2	1	no	—
69	#14273660	C₂×C₄	1	1	yes	characteristic
70	#14273660	C₂×C₄	1	1	yes	characteristic
71	#14273658	C₂×C₄	1	1	yes	characteristic
72	#14273658	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
74	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
75	Dic₅₉⋊C₈	—	2	2	no	—
76	#14273651	C₂×C₄	1	1	yes	characteristic
77	#14273651	C₂×C₄	1	1	yes	characteristic
78	#14273650	C₂×C₄	1	1	yes	characteristic
79	#14273650	C₂×C₄	1	1	yes	characteristic
80	#14273648	C₂×C₄	1	1	yes	characteristic
81	#14273648	C₂×C₄	1	1	yes	characteristic
82	#14273647	C₂×C₄	1	1	yes	characteristic
83	#14273647	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
86	(C₂×D₅₉)⋊C₈	—	2	2	no	—
87	C₄×C₅₉⋊C₈	—	2	1	no	—
88	C₄×C₅₉⋊C₈	—	2	2	no	—
89	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
96	C₈×Dic₅₉	—	2	2	no	—
97	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₅₉	—	2	1	no	—
99	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₅₉	—	2	1	no	—
102	C₄×D₄×C₅₉	—	2	1	no	—
103	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
105	#117×C₅₉	—	2	1	no	—
106	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₅₉	—	2	1	no	—
108	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
110	C₂²⋊C₈×C₅₉	—	2	1	no	—
111	C₄×C₈×C₅₉	—	2	1	no	—
112	C₄×C₈×C₅₉	—	2	1	no	—
113	C₄×C₈×C₅₉	C₂³	1	2	yes	—
114	#41×C₅₉	—	2	2	no	—
115	#41×C₅₉	C₂×C₈	1	4	yes	complemented
116	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₅₉	—	2	1	no	—
118	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	—	2	1	no	—
120	C₂²×C₄×C₅₉	—	2	1	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₅₉	—	2	1	no	—
126	#11745685	—	2	2	no	—
127	#11745685	C₂×C₈	1	4	yes	complemented
128	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₅₉	—	2	1	no	—
130	C₂×C₄×D₅₉	—	2	1	no	—
131	C₂×C₄×D₅₉	—	2	1	no	—
132	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₅₉	—	2	4	no	—
134	C₂×C₈×C₅₉	—	2	2	no	—
135	C₂×C₈×C₅₉	—	2	2	no	—
136	C₄⋊C₄×C₅₉	—	2	1	no	—
137	C₄⋊C₄×C₅₉	—	2	1	no	—
138	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₅₉	—	2	1	no	—
141	C₂²⋊C₄×C₅₉	—	2	1	no	—
142	C₂²⋊C₄×C₅₉	—	2	1	no	—
143	C₄²×C₅₉	—	2	1	no	—
144	C₄²×C₅₉	—	2	1	no	—
145	C₄²×C₅₉	—	2	1	no	—
146	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₅₉	#41	1	1	yes	characteristic
149	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
150	C₂²⋊Dic₅₉	—	2	1	no	—
151	#11745672	C₂×C₈	1	4	yes	complemented
152	#11745671	C₂×C₈	1	4	yes	complemented
153	#11745670	C₂×C₈	1	4	yes	complemented
154	#11745669	C₂×C₈	1	4	yes	complemented
155	(C₂×D₅₉)⋊C₄	—	2	1	no	—
156	(C₂×D₅₉)⋊C₄	—	2	1	no	—
157	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
159	Dic₅₉⋊C₄	—	2	1	no	—
160	Dic₅₉⋊C₄	—	2	1	no	—
161	C₄×Dic₅₉	—	2	1	no	—
162	C₄×Dic₅₉	—	2	1	no	—
163	C₄×Dic₅₉	—	2	1	no	—
164	C₂×C₅₉⋊C₈	—	2	2	no	—
165	C₂×C₅₉⋊C₈	—	2	4	no	—
166	C₂×C₅₉⋊C₈	—	2	2	no	—
167	C₂×C₅₉⋊C₈	—	4	4	no	—
168	C₂×C₅₉⋊C₈	C₂×C₈	1	4	yes	complemented
169	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
174	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
175	C₈×D₅₉	—	4	4	no	—
176	C₂³×C₅₉	—	2	1	no	—
177	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
178	C₂²×D₅₉	—	2	1	no	—
179	Q₈×C₅₉	—	2	1	no	—
180	Q₈×C₅₉	C₂²×C₈	1	2	yes	—
181	D₄×C₅₉	—	2	4	no	—
182	D₄×C₅₉	—	2	1	no	—
183	D₄×C₅₉	C₂²×C₈	1	2	yes	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	2	4	no	—
187	C₂×C₄×C₅₉	—	2	2	no	—
188	C₂×C₄×C₅₉	—	2	1	no	—
189	C₂×C₄×C₅₉	—	2	1	no	—
190	C₂×C₄×C₅₉	—	4	2	no	—
191	C₂×C₄×C₅₉	—	4	2	no	—
192	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
196	C₂×C₄×C₅₉	#131	1	2	yes	—
197	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
200	C₂²⋊D₅₉	—	2	4	no	—
201	C₂×Dic₅₉	—	2	1	no	—
202	C₂×Dic₅₉	—	2	1	no	—
203	C₂×Dic₅₉	—	2	1	no	—
204	D₂₃₆	—	2	1	no	—
205	D₂₃₆	C₂²×C₈	1	2	yes	—
206	C₄×D₅₉	—	2	4	no	—
207	C₄×D₅₉	—	4	2	no	—
208	C₄×D₅₉	—	4	2	no	—
209	Dic₁₁₈	—	2	1	no	—
210	Dic₁₁₈	C₂²×C₈	1	2	yes	—
211	C₈×C₅₉	—	2	4	no	—
212	C₈×C₅₉	—	4	2	no	—
213	C₅₉⋊C₈	—	2	1	no	—
214	C₅₉⋊C₈	—	2	1	no	—
215	C₅₉⋊C₈	—	2	2	no	—
216	C₅₉⋊C₈	—	4	2	no	—
217	C₅₉⋊C₈	C₂²×C₈	1	2	yes	—
218	C₅₉⋊C₈	C₂²×C₈	1	2	yes	—
219	C₅₉⋊C₈	#135	1	4	yes	complemented
220	C₈×#135	—	59	1	no	maximal, Sylow
221	C₂²×C₅₉	—	2	1	no	—
222	C₂²×C₅₉	—	2	1	no	—
223	C₂²×C₅₉	—	2	2	no	—
224	C₂²×C₅₉	—	4	1	no	—
225	C₂²×C₅₉	—	4	1	no	—
226	C₂²×C₅₉	C₈×D₄	1	2	yes	—
227	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂×D₅₉	—	2	2	no	—
229	C₂×D₅₉	—	4	1	no	—
230	C₂×D₅₉	—	4	1	no	—
231	C₄×C₅₉	—	2	2	no	—
232	C₄×C₅₉	—	2	1	no	—
233	C₄×C₅₉	—	2	1	no	—
234	C₄×C₅₉	—	4	1	no	—
235	C₄×C₅₉	—	4	1	no	—
236	C₄×C₅₉	C₈×D₄	1	2	yes	—
237	C₄×C₅₉	#443	1	2	yes	—
238	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
239	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
240	C₄×C₅₉	C₂×#135	1	2	yes	—
241	Dic₅₉	—	2	2	no	—
242	Dic₅₉	—	4	1	no	—
243	Dic₅₉	—	4	1	no	—
244	C₈×#41	—	59	1	no	—
245	C₈×#41	—	59	1	no	—
246	C₄×#135	—	59	1	no	—
247	C₈×Q₁₆	—	59	2	no	—
248	C₈×SD₁₆	—	59	2	no	—
249	C₈×SD₁₆	—	59	2	no	—
250	C₈×D₈	—	59	2	no	—
251	#1564	—	59	1	no	—
252	#1476	—	59	1	no	—
253	#1476	D₅₉	1	1	yes	characteristic, complemented
254	C₂×C₈²	—	59	1	no	—
255	C₂×C₅₉	—	2	2	no	—
256	C₂×C₅₉	—	4	2	no	—
257	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
258	C₂×C₅₉	C₄×#135	1	1	yes	characteristic
259	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
260	D₅₉	—	4	2	no	—
261	C₂×#135	—	59	1	no	—
262	C₄×#41	—	59	1	no	—
263	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
264	C₈×Q₈	—	59	2	no	—
265	C₈×Q₈	—	59	2	no	—
266	C₄×Q₁₆	—	59	1	no	—
267	C₄×Q₁₆	—	59	1	no	—
268	C₄×SD₁₆	—	59	1	no	—
269	C₄×SD₁₆	—	59	1	no	—
270	C₄×SD₁₆	—	59	1	no	—
271	C₄×SD₁₆	—	59	1	no	—
272	C₄×D₈	—	59	1	no	—
273	C₄×D₈	—	59	1	no	—
274	C₈×D₄	—	59	2	no	—
275	C₈×D₄	—	59	2	no	—
276	C₈×D₄	—	118	2	no	—
277	C₈×D₄	—	118	2	no	—
278	#431	—	59	1	no	—
279	#431	—	118	1	no	—
280	#431	—	118	1	no	—
281	#431	C₂×D₅₉	1	1	yes	characteristic
282	#427	—	59	1	no	—
283	#416	—	59	1	no	—
284	#416	—	59	1	no	—
285	C₂×C₄×C₈	—	59	1	no	—
286	C₂×C₄×C₈	—	59	1	no	—
287	C₂×C₄×C₈	—	118	1	no	—
288	C₂×C₄×C₈	—	118	1	no	—
289	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
290	#335	—	59	2	no	—
291	#334	—	59	2	no	—
292	Q₈⋊C₈	—	59	2	no	—
293	Q₈⋊C₈	C₂×D₅₉	1	2	yes	—
294	D₄⋊C₈	—	59	2	no	—
295	D₄⋊C₈	C₂×D₅₉	1	2	yes	—
296	C₈²	—	59	2	no	—
297	C₈²	—	59	2	no	—
298	C₅₉	C₈×#135	1	1	yes	characteristic, complemented, Sylow
299	C₂×#41	—	59	1	no	—
300	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
301	#135	—	59	8	no	—
302	C₂×Q₁₆	—	59	1	no	—
303	C₂×SD₁₆	—	59	1	no	—
304	C₂×SD₁₆	—	59	1	no	—
305	C₂×D₈	—	59	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	59	1	no	—
308	C₂²×C₈	—	59	1	no	—
309	C₂²×C₈	—	59	2	no	—
310	C₂²×C₈	—	118	2	no	—
311	C₂²×C₈	—	118	2	no	—
312	C₄×Q₈	—	59	1	no	—
313	C₄×Q₈	—	59	1	no	—
314	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
315	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	59	1	no	—
319	C₄×D₄	—	59	1	no	—
320	C₄×D₄	—	118	1	no	—
321	C₄×D₄	—	118	1	no	—
322	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
323	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
324	#117	—	2	1	no	—
325	#117	—	59	1	no	—
326	#117	—	118	1	no	—
327	#117	C₄×D₅₉	1	1	yes	characteristic
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	118	1	no	—
330	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
331	#107	—	59	1	no	—
332	#107	—	59	1	no	—
333	#106	—	59	1	no	—
334	#106	—	59	1	no	—
335	C₄⋊C₈	—	59	2	no	—
336	C₄⋊C₈	—	118	2	no	—
337	C₄⋊C₈	—	118	2	no	—
338	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
339	#103	—	59	1	no	—
340	#103	—	59	1	no	—
341	#103	—	59	1	no	—
342	#103	—	59	1	no	—
343	#102	—	59	1	no	—
344	#102	—	59	1	no	—
345	#102	—	59	1	no	—
346	#102	—	59	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	118	2	no	—
349	C₂²⋊C₈	—	118	2	no	—
350	C₂²⋊C₈	—	118	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₄×C₈	—	2	1	no	—
353	C₄×C₈	—	59	1	no	—
354	C₄×C₈	—	59	1	no	—
355	C₄×C₈	—	59	1	no	—
356	C₄×C₈	—	59	1	no	—
357	C₄×C₈	—	59	1	no	—
358	C₄×C₈	—	59	1	no	—
359	C₄×C₈	—	59	2	no	—
360	C₄×C₈	—	118	2	no	—
361	C₄×C₈	—	118	2	no	—
362	C₄×C₈	—	118	1	no	—
363	C₄×C₈	C₂²×D₅₉	1	2	yes	—
364	#41	—	2	2	no	—
365	#41	—	59	4	no	—
366	#41	—	118	2	no	—
367	#41	C₈×D₅₉	1	4	yes	complemented
368	C₂×Q₈	—	59	1	no	—
369	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	59	1	no	—
372	C₂×D₄	—	118	1	no	—
373	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	118	1	no	—
378	C₂²×C₄	—	118	1	no	—
379	C₂²×C₄	—	118	1	no	—
380	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
381	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
382	C₂²×C₄	#11745687	1	1	yes	characteristic
383	Q₁₆	—	59	4	no	—
384	SD₁₆	—	59	4	no	—
385	SD₁₆	—	59	4	no	—
386	D₈	—	59	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	59	4	no	—
391	C₂×C₈	—	59	1	no	—
392	C₂×C₈	—	59	1	no	—
393	C₂×C₈	—	59	2	no	—
394	C₂×C₈	—	59	1	no	—
395	C₂×C₈	—	59	1	no	—
396	C₂×C₈	—	59	2	no	—
397	C₂×C₈	—	118	4	no	—
398	C₂×C₈	—	118	2	no	—
399	C₂×C₈	—	118	2	no	—
400	C₂×C₈	—	236	4	no	—
401	C₂×C₈	—	236	4	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	59	1	no	—
405	C₄⋊C₄	—	59	1	no	—
406	C₄⋊C₄	—	118	1	no	—
407	C₄⋊C₄	—	118	1	no	—
408	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
409	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	118	1	no	—
414	C₂²⋊C₄	—	118	1	no	—
415	C₂²⋊C₄	—	118	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	118	1	no	—
420	C₄²	—	118	1	no	—
421	C₄²	—	118	1	no	—
422	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
423	C₄²	D₄×D₅₉	1	1	yes	characteristic
424	C₄²	#11745687	1	1	yes	characteristic
425	C₄²	C₂³×D₅₉	1	1	yes	characteristic
426	C₂³	—	2	1	no	—
427	C₂³	—	118	1	no	—
428	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	59	2	no	—
431	Q₈	—	118	1	no	—
432	Q₈	C₂×C₈×D₅₉	1	2	yes	—
433	D₄	—	2	4	no	—
434	D₄	—	2	1	no	—
435	D₄	—	59	2	no	—
436	D₄	—	118	4	no	—
437	D₄	—	118	1	no	—
438	D₄	C₂×C₈×D₅₉	1	2	yes	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	118	1	no	—
448	C₂×C₄	—	118	4	no	—
449	C₂×C₄	—	118	1	no	—
450	C₂×C₄	—	118	1	no	—
451	C₂×C₄	—	236	2	no	—
452	C₂×C₄	—	236	2	no	—
453	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
454	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
455	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
456	C₂×C₄	C₂×C₈×D₅₉	1	2	yes	—
457	C₂×C₄	#14273735	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
459	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
461	C₈	—	2	4	no	—
462	C₈	—	4	2	no	—
463	C₈	—	59	2	no	—
464	C₈	—	59	2	no	—
465	C₈	—	59	4	no	—
466	C₈	—	118	1	no	—
467	C₈	—	118	1	no	—
468	C₈	—	118	2	no	—
469	C₈	—	236	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	118	2	no	—
476	C₂²	—	236	1	no	—
477	C₂²	—	236	1	no	—
478	C₂²	(C₂²⋊D₅₉)⋊C₈	1	2	yes	—
479	C₂²	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	118	2	no	—
486	C₄	—	236	1	no	—
487	C₄	—	236	1	no	—
488	C₄	(C₂²⋊D₅₉)⋊C₈	1	2	yes	—
489	C₄	#16837516	1	2	yes	—
490	C₄	C₂²×C₈×D₅₉	1	1	yes	characteristic
491	C₄	C₂×#14273735	1	1	yes	characteristic
492	C₄	#135×D₅₉	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	236	2	no	—
496	C₂	C₂×(C₂²⋊D₅₉)⋊C₈	1	1	yes	characteristic
497	C₂	#21432864	1	1	yes	characteristic
498	C₂	C₂×#16837516	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₅₉
commutator	C₄×C₅₉	C₂³×C₈
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1476	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273747	C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1476	D₅₉
hypocenter	C₅₉	C₈×#135
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
1. #41×C₅₉⋊C₈	C₂	semidirect
2. #21433052	C₂	semidirect
4. #21422900	C₂	semidirect
5. #21422899	C₂	semidirect
6. #21422893	C₂	semidirect
7. #21422888	C₂	semidirect
8. #21422842	C₂	semidirect
9. #21422479	C₂	semidirect
10. C₂×C₈×C₅₉⋊C₈	C₂	semidirect
11. C₅₉×#1476	C₂	semidirect
50. #14273747	C₈	semidirect
115. #41×C₅₉	C₂×C₈	semidirect
127. #11745685	C₂×C₈	semidirect
151. #11745672	C₂×C₈	semidirect
152. #11745671	C₂×C₈	semidirect
153. #11745670	C₂×C₈	semidirect
154. #11745669	C₂×C₈	semidirect
168. C₂×C₅₉⋊C₈	C₂×C₈	semidirect
219. C₅₉⋊C₈	#135	semidirect
253. #1476	D₅₉	semidirect
298. C₅₉	C₈×#135	semidirect
367. #41	C₈×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#41×C₅₉⋊C₈	2
#21433052	2
C₄×#14273747	2
#21422900	2
#21422899	2
#21422893	2
#21422888	2
#21422842	2
#21422479	2
C₂×C₈×C₅₉⋊C₈	2
C₅₉×#1476	2
C₈×#135	59