Subgroups — #28558472

Order 15104.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14273752	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837481	C₂	1	1	yes	maximal, characteristic, complemented
3	#21423008	C₂	1	2	yes	maximal, complemented
4	#21422996	C₂	1	2	yes	maximal, complemented
5	#21422986	C₂	1	2	yes	maximal, complemented
6	#21422979	C₂	1	2	yes	maximal, complemented
7	#21422849	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422486	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422483	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11745664	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273752	C₄	1	1	yes	characteristic
13	C₂²×#11745659	—	2	1	no	—
14	C₂×C₄×D₂₃₆	C₂²	1	1	yes	characteristic
15	#16837512	C₄	1	2	yes	—
16	#16837500	C₄	1	2	yes	—
17	C₄×#11745671	C₂²	1	2	yes	—
18	C₄×#11745669	C₂²	1	2	yes	—
19	#16837481	—	2	1	no	—
20	#16837481	—	2	1	no	—
21	#16837481	C₂²	1	2	yes	—
22	#16837481	C₂²	1	2	yes	—
23	#16837455	C₂²	1	1	yes	characteristic
24	#16837445	C₄	1	1	yes	characteristic
25	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
26	#16837406	C₄	1	1	yes	characteristic
27	#16837403	C₄	1	1	yes	characteristic
28	C₂×(C₂×D₅₉)⋊C₈	—	2	1	no	—
29	C₄×#11745664	C₂²	1	1	yes	characteristic
30	#16837154	C₂²	1	2	yes	complemented
31	#16837152	C₂²	1	2	yes	complemented
32	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	complemented
33	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	complemented
34	#16837129	C₂²	1	2	yes	—
35	#16837129	C₂²	1	2	yes	—
36	#16837124	C₂²	1	2	yes	complemented
37	C₈×C₅₉⋊C₈	C₂²	1	2	yes	complemented
38	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#446	C₂²	1	1	yes	characteristic, complemented
40	C₅₉×#446	C₂²	1	1	yes	characteristic, complemented
41	C₅₉×#436	C₂²	1	1	yes	characteristic, complemented
42	C₅₉×#436	C₂²	1	1	yes	characteristic, complemented
43	C₅₉×#435	—	2	1	no	—
44	C₅₉×#435	—	2	1	no	—
45	C₅₉×#431	—	2	1	no	—
46	C₅₉×#431	C₂²	1	1	yes	characteristic
47	C₄×M₁₆×C₅₉	—	2	1	no	—
48	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₂²×D₂₃₆	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₅₉	—	2	1	no	—
51	#14273752	—	2	4	no	—
52	C₂×#11745671	C₂×C₄	1	2	yes	—
53	C₂×#11745669	C₂×C₄	1	2	yes	—
54	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
55	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
56	C₂×#11745659	—	2	2	no	—
57	C₂×#11745659	—	2	2	no	—
58	C₂×#11745659	—	4	4	no	—
59	C₂²×C₅₉⋊C₈	—	2	1	no	—
60	C₄×D₂₃₆	—	2	1	no	—
61	C₄×D₂₃₆	—	2	1	no	—
62	C₄×D₂₃₆	C₂×C₄	1	2	yes	—
63	C₄×D₂₃₆	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
65	C₂×(C₂×D₅₉)⋊C₄	—	2	1	no	—
66	#14273660	C₂×C₄	1	2	yes	—
67	#14273658	C₂×C₄	1	2	yes	—
68	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
71	#14273651	C₂×C₄	1	2	yes	—
72	#14273648	C₂×C₄	1	2	yes	—
73	#14273647	C₂×C₄	1	2	yes	—
74	#14273647	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
76	(C₂×D₅₉)⋊C₈	—	2	2	no	—
77	(C₂×D₅₉)⋊C₈	—	2	2	no	—
78	#14273638	C₂×C₄	1	2	yes	—
79	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
80	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
81	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₂×M₁₆×C₅₉	—	2	1	no	—
83	C₂×M₁₆×C₅₉	—	2	1	no	—
84	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₅₉	—	2	1	no	—
89	C₄×D₄×C₅₉	—	2	1	no	—
90	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
91	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
92	#117×C₅₉	—	2	1	no	—
93	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₅₉	—	2	1	no	—
95	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₅₉	—	2	1	no	—
97	C₄⋊C₈×C₅₉	—	2	1	no	—
98	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
100	C₂²⋊C₈×C₅₉	—	2	1	no	—
101	C₂²⋊C₈×C₅₉	—	2	1	no	—
102	C₂²⋊C₈×C₅₉	—	2	1	no	—
103	#97×C₅₉	—	2	1	no	—
104	#97×C₅₉	—	2	1	no	—
105	C₄×C₈×C₅₉	—	2	1	no	—
106	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂³×D₅₉	—	2	1	no	—
111	#41×C₅₉	—	2	2	no	—
112	#41×C₅₉	—	2	2	no	—
113	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₅₉	—	2	1	no	—
115	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	1	no	—
118	C₂²×C₄×C₅₉	—	2	1	no	—
119	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
122	C₂²×Dic₅₉	—	2	1	no	—
123	C₂×D₂₃₆	—	2	2	no	—
124	C₂×D₂₃₆	—	2	2	no	—
125	C₂×D₂₃₆	—	2	1	no	—
126	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
127	C₂×C₄×D₅₉	—	2	2	no	—
128	C₂×C₄×D₅₉	—	2	2	no	—
129	C₂×C₄×D₅₉	—	4	2	no	—
130	C₂×C₄×D₅₉	—	4	2	no	—
131	M₁₆×C₅₉	—	4	2	no	—
132	M₁₆×C₅₉	—	4	2	no	—
133	C₂×C₈×C₅₉	—	2	2	no	—
134	C₂×C₈×C₅₉	—	2	1	no	—
135	C₂×C₈×C₅₉	—	2	1	no	—
136	C₂×C₈×C₅₉	—	4	1	no	—
137	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₅₉	—	2	1	no	—
142	C₄⋊C₄×C₅₉	—	2	1	no	—
143	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²⋊C₄×C₅₉	—	2	1	no	—
146	C₂²⋊C₄×C₅₉	—	2	1	no	—
147	C₂²⋊C₄×C₅₉	—	2	1	no	—
148	C₄²×C₅₉	—	2	1	no	—
149	C₄²×C₅₉	—	2	1	no	—
150	C₄²×C₅₉	—	2	1	no	—
151	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₅₉	#41	1	1	yes	characteristic
154	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
155	#11745671	—	2	4	no	—
156	#11745669	—	2	4	no	—
157	(C₂×D₅₉)⋊C₄	—	2	2	no	—
158	(C₂×D₅₉)⋊C₄	—	2	2	no	—
159	C₄⋊Dic₅₉	—	2	1	no	—
160	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
161	#11745664	—	2	2	no	—
162	#11745664	M₁₆	1	4	yes	complemented
163	C₂×C₅₉⋊C₈	—	2	2	no	—
164	C₂×C₅₉⋊C₈	—	2	2	no	—
165	C₂×C₅₉⋊C₈	—	4	2	no	—
166	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
168	#11745659	—	4	4	no	—
169	#11745659	—	4	4	no	—
170	C₂³×C₅₉	—	2	1	no	—
171	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
172	C₂²×D₅₉	—	2	2	no	—
173	C₂²×D₅₉	—	4	2	no	—
174	C₂²×D₅₉	—	4	2	no	—
175	C₂²×D₅₉	—	4	2	no	—
176	Q₈×C₅₉	—	2	1	no	—
177	Q₈×C₅₉	—	2	1	no	—
178	D₄×C₅₉	—	2	1	no	—
179	D₄×C₅₉	—	2	1	no	—
180	D₄×C₅₉	—	4	2	no	—
181	C₂×C₄×C₅₉	—	2	1	no	—
182	C₂×C₄×C₅₉	—	2	1	no	—
183	C₂×C₄×C₅₉	—	2	1	no	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	1	no	—
186	C₂×C₄×C₅₉	—	4	1	no	—
187	C₂×C₄×C₅₉	—	4	2	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	4	1	no	—
190	C₂×C₄×C₅₉	—	4	2	no	—
191	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₅₉	#131	1	2	yes	—
196	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
199	C₂×Dic₅₉	—	2	2	no	—
200	C₂×Dic₅₉	—	4	2	no	—
201	D₂₃₆	—	2	2	no	—
202	D₂₃₆	—	2	2	no	—
203	D₂₃₆	—	4	2	no	—
204	C₄×D₅₉	—	4	4	no	—
205	C₄×D₅₉	—	4	2	no	—
206	C₄×D₅₉	—	4	2	no	—
207	C₈×C₅₉	—	2	1	no	—
208	C₈×C₅₉	—	2	1	no	—
209	C₈×C₅₉	—	2	1	no	—
210	C₈×C₅₉	—	4	1	no	—
211	C₈×C₅₉	—	4	1	no	—
212	C₈×C₅₉	AGL(1,ℤ/8)	1	2	yes	complemented
213	C₅₉⋊C₈	—	2	2	no	—
214	C₅₉⋊C₈	—	4	2	no	—
215	C₅₉⋊C₈	—	4	2	no	—
216	C₅₉⋊C₈	C₂×M₁₆	1	4	yes	complemented
217	#17891	—	59	1	no	maximal, Sylow
218	C₂²×C₅₉	—	2	1	no	—
219	C₂²×C₅₉	—	2	1	no	—
220	C₂²×C₅₉	—	4	1	no	—
221	C₂²×C₅₉	—	4	1	no	—
222	C₂²×C₅₉	—	4	1	no	—
223	C₂²×C₅₉	#436	1	2	yes	—
224	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂×D₅₉	—	4	2	no	—
226	C₂×D₅₉	—	4	2	no	—
227	C₂×D₅₉	—	4	2	no	—
228	C₂×D₅₉	—	8	4	no	—
229	C₄×C₅₉	—	2	1	no	—
230	C₄×C₅₉	—	2	1	no	—
231	C₄×C₅₉	—	2	1	no	—
232	C₄×C₅₉	—	4	1	no	—
233	C₄×C₅₉	—	4	1	no	—
234	C₄×C₅₉	—	4	1	no	—
235	C₄×C₅₉	#436	1	2	yes	—
236	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
237	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
238	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₄×C₅₉	#575	1	1	yes	characteristic
240	Dic₅₉	—	4	2	no	—
241	#2965	D₅₉	1	1	yes	characteristic, complemented
242	C₄×AGL(1,ℤ/8)	—	59	1	no	—
243	C₂×#436	—	59	1	no	—
244	#1594	—	59	2	no	—
245	#1592	—	59	2	no	—
246	#1590	—	59	2	no	—
247	#1589	—	59	2	no	—
248	#1565	—	59	1	no	—
249	#1478	—	59	1	no	—
250	#1477	—	59	1	no	—
251	C₈×M₁₆	—	59	1	no	—
252	C₂×C₅₉	—	2	2	no	—
253	C₂×C₅₉	—	8	1	no	—
254	C₂×C₅₉	C₂×#436	1	1	yes	characteristic
255	C₂×C₅₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂×C₅₉	#2955	1	1	yes	characteristic
257	D₅₉	—	8	2	no	—
258	C₂×AGL(1,ℤ/8)	—	59	1	no	—
259	C₂²×M₁₆	—	118	1	no	—
260	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
261	C₂×C₄×D₄	—	59	1	no	—
262	#446	C₂×D₅₉	1	1	yes	characteristic, complemented
263	#446	C₂×D₅₉	1	1	yes	characteristic, complemented
264	#442	—	59	2	no	—
265	#440	—	59	2	no	—
266	C₄×SD₁₆	—	59	2	no	—
267	C₄×D₈	—	59	2	no	—
268	#436	—	59	2	no	—
269	#436	—	59	2	no	—
270	#436	—	118	1	no	—
271	#436	—	118	1	no	—
272	#436	C₂×D₅₉	1	1	yes	characteristic, complemented
273	#436	C₂×D₅₉	1	1	yes	characteristic, complemented
274	#435	—	2	1	no	—
275	#435	—	2	1	no	—
276	#431	—	2	1	no	—
277	#431	—	59	1	no	—
278	#431	C₂×D₅₉	1	1	yes	characteristic
279	#428	—	59	1	no	—
280	C₂×C₄⋊C₈	—	59	1	no	—
281	#418	—	59	1	no	—
282	#417	—	59	1	no	—
283	C₂×C₂²⋊C₈	—	118	1	no	—
284	C₄×M₁₆	—	2	1	no	—
285	C₄×M₁₆	—	59	1	no	—
286	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
287	#335	—	59	2	no	—
288	#334	—	59	2	no	—
289	Q₈⋊C₈	—	59	2	no	—
290	D₄⋊C₈	—	59	2	no	—
291	D₄⋊C₈	—	59	2	no	—
292	D₄⋊C₈	—	59	2	no	—
293	#322	—	59	2	no	—
294	C₈²	—	59	2	no	—
295	C₅₉	#17891	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
297	C₂²×D₄	—	59	1	no	—
298	C₂³×C₄	—	118	1	no	—
299	AGL(1,ℤ/8)	—	118	4	no	—
300	C₂×SD₁₆	—	59	2	no	—
301	C₂×D₈	—	59	2	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	59	1	no	—
305	C₂×M₁₆	—	59	1	no	—
306	C₂×M₁₆	—	118	2	no	—
307	C₂×M₁₆	—	118	2	no	—
308	C₂×M₁₆	—	236	4	no	—
309	C₂²×C₈	—	118	1	no	—
310	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
311	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
312	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	59	2	no	—
317	C₄×D₄	—	59	2	no	—
318	C₄×D₄	—	118	1	no	—
319	C₄×D₄	—	118	1	no	—
320	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	C₄×D₅₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	—	59	1	no	—
325	C₂×C₂²⋊C₄	—	118	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
328	#107	—	59	2	no	—
329	#106	—	59	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	59	2	no	—
333	C₄⋊C₈	—	118	1	no	—
334	C₄⋊C₈	—	118	1	no	—
335	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
336	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
337	#103	—	59	2	no	—
338	#102	—	59	2	no	—
339	#102	—	59	2	no	—
340	#102	—	59	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	C₂²⋊C₈	—	118	1	no	—
345	C₂²⋊C₈	—	118	2	no	—
346	C₂²⋊C₈	—	118	2	no	—
347	#97	—	2	1	no	—
348	#97	—	2	1	no	—
349	#97	—	59	2	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	—	59	2	no	—
352	C₄×C₈	—	59	2	no	—
353	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
354	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
357	C₂⁴	—	118	1	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	59	2	no	—
363	C₂×D₄	—	118	1	no	—
364	C₂×D₄	—	118	2	no	—
365	C₂×D₄	—	118	2	no	—
366	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	118	1	no	—
371	C₂²×C₄	—	118	2	no	—
372	C₂²×C₄	—	118	2	no	—
373	C₂²×C₄	—	236	2	no	—
374	C₂²×C₄	—	236	2	no	—
375	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
376	C₂²×C₄	#11745685	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
378	SD₁₆	—	118	4	no	—
379	D₈	—	118	4	no	—
380	M₁₆	—	4	2	no	—
381	M₁₆	—	4	2	no	—
382	M₁₆	—	59	4	no	—
383	M₁₆	—	118	2	no	—
384	M₁₆	—	236	4	no	—
385	M₁₆	—	236	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	4	1	no	—
390	C₂×C₈	—	59	2	no	—
391	C₂×C₈	—	59	2	no	—
392	C₂×C₈	—	118	2	no	—
393	C₂×C₈	—	118	2	no	—
394	C₂×C₈	—	236	2	no	—
395	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
396	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
397	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
398	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	59	2	no	—
402	C₄⋊C₄	—	118	1	no	—
403	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
404	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	118	2	no	—
409	C₂²⋊C₄	—	118	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
414	C₄²	#11745685	1	1	yes	characteristic
415	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
416	C₄²	C₂³×D₅₉	1	1	yes	characteristic
417	C₂³	—	2	1	no	—
418	C₂³	—	118	2	no	—
419	C₂³	—	236	2	no	—
420	C₂³	—	236	2	no	—
421	C₂³	—	236	2	no	—
422	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	2	1	no	—
427	D₄	—	4	2	no	—
428	D₄	—	118	2	no	—
429	D₄	—	118	2	no	—
430	D₄	—	236	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	118	2	no	—
442	C₂×C₄	—	236	4	no	—
443	C₂×C₄	—	236	2	no	—
444	C₂×C₄	—	236	2	no	—
445	C₂×C₄	—	236	2	no	—
446	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
447	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
448	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
449	C₂×C₄	M₁₆×D₅₉	1	2	yes	—
450	C₂×C₄	#14273735	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	59	4	no	—
460	C₈	—	118	2	no	—
461	C₈	—	236	2	no	—
462	C₈	—	236	2	no	—
463	C₈	#14273752	1	2	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	472	4	no	—
470	C₂²	—	236	2	no	—
471	C₂²	—	236	2	no	—
472	C₂²	—	236	2	no	—
473	C₂²	#16837478	1	2	yes	—
474	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	236	2	no	—
482	C₄	#16837478	1	2	yes	—
483	C₄	C₂×M₁₆×D₅₉	1	1	yes	characteristic
484	C₄	C₂×#14273735	1	1	yes	characteristic
485	C₄	C₂×#14273752	1	1	yes	characteristic
486	C₄	#16838200	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	1	no	—
489	C₂	—	472	2	no	—
490	C₂	C₂×#16837478	1	1	yes	characteristic
491	C₂	C₄×#14273752	1	1	yes	characteristic
492	C₂	#21432997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2965	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273752	C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2965	D₅₉
hypocenter	C₅₉	#17891
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2965

Complements

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

N	H ≅ G/N	type
2. C₂×#16837481	C₂	semidirect
3. #21423008	C₂	semidirect
4. #21422996	C₂	semidirect
5. #21422986	C₂	semidirect
6. #21422979	C₂	semidirect
7. #21422849	C₂	semidirect
8. #21422486	C₂	semidirect
9. #21422483	C₂	semidirect
10. C₈×#11745664	C₂	semidirect
11. C₅₉×#2965	C₂	semidirect
30. #16837154	C₂²	semidirect
31. #16837152	C₂²	semidirect
32. Q₈⋊(C₅₉⋊C₈)	C₂²	semidirect
33. D₄⋊(C₅₉⋊C₈)	C₂²	semidirect
36. #16837124	C₂²	semidirect
37. C₈×C₅₉⋊C₈	C₂²	semidirect
39. C₅₉×#446	C₂²	semidirect
40. C₅₉×#446	C₂²	semidirect
41. C₅₉×#436	C₂²	semidirect
42. C₅₉×#436	C₂²	semidirect
162. #11745664	M₁₆	semidirect
212. C₈×C₅₉	AGL(1,ℤ/8)	semidirect
216. C₅₉⋊C₈	C₂×M₁₆	semidirect
241. #2965	D₅₉	semidirect
262. #446	C₂×D₅₉	semidirect
263. #446	C₂×D₅₉	semidirect
272. #436	C₂×D₅₉	semidirect
273. #436	C₂×D₅₉	semidirect
295. C₅₉	#17891	semidirect
463. C₈	#14273752	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14273752	2
C₂×#16837481	2
#21423008	2
#21422996	2
#21422986	2
#21422979	2
#21422849	2
#21422486	2
#21422483	2
C₈×#11745664	2
C₅₉×#2965	2
#17891	59