Subgroups — #28558603

Order 15104.

698 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434102	C₂	1	1	yes	maximal, characteristic
2	#21433025	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21422956	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422954	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422952	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422950	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422910	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422908	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422906	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422869	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422519	C₂	1	1	yes	maximal, characteristic
13	#21422497	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422387	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₅₉	—	2	1	no	—
17	#16837956	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₅₉	C₂²	1	1	yes	characteristic
19	#16837734	C₄	1	1	yes	characteristic
20	#16837731	C₄	1	1	yes	characteristic
21	#16837691	C₄	1	1	yes	characteristic
22	#16837690	C₄	1	1	yes	characteristic
23	#16837606	C₄	1	1	yes	characteristic
24	#16837605	C₄	1	1	yes	characteristic
25	#16837554	C₄	1	1	yes	characteristic
26	#16837551	C₄	1	1	yes	characteristic
27	#16837533	C₂²	1	1	yes	characteristic, complemented
28	#16837531	—	2	1	no	—
29	#16837529	C₂²	1	1	yes	characteristic, complemented
30	C₈×Dic₁₁₈	—	2	1	no	—
31	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic, complemented
32	C₄×#11745660	C₂²	1	1	yes	characteristic
33	C₄×#11745671	C₂²	1	1	yes	characteristic
34	C₄×#11745670	C₂²	1	1	yes	characteristic
35	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
36	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
37	#16837467	C₂²	1	1	yes	characteristic
38	C₈×C₂²⋊D₅₉	—	2	1	no	—
39	(C₂²⋊D₅₉)⋊C₈	—	2	1	no	—
40	#16837453	C₂²	1	1	yes	characteristic
41	#16837453	C₂²	1	1	yes	characteristic
42	#16837427	—	2	1	no	—
43	#16837424	C₂²	1	1	yes	characteristic
44	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
45	C₂²⋊C₈×D₅₉	—	2	1	no	—
46	#16837356	—	2	1	no	—
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837155	C₂²	1	1	yes	characteristic, complemented
49	#16837154	C₂²	1	1	yes	characteristic, complemented
50	#16837154	C₂²	1	1	yes	characteristic, complemented
51	#16837134	C₂²	1	1	yes	characteristic, complemented
52	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
53	#16837132	C₂²	1	1	yes	characteristic, complemented
54	#16837131	C₂²	1	1	yes	characteristic
55	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
56	#16837129	C₂²	1	1	yes	characteristic
57	#16837124	C₂²	1	1	yes	characteristic, complemented
58	#16837124	C₂²	1	1	yes	characteristic, complemented
59	#16837123	C₂²	1	1	yes	characteristic, complemented
60	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
61	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic, complemented
64	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅₉×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×D₄×D₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₅₉	—	2	1	no	—
69	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745659	—	2	1	no	—
73	C₂²×C₅₉⋊C₈	—	2	1	no	—
74	C₂×C₈×D₅₉	—	2	1	no	—
75	C₂×C₈×D₅₉	—	2	1	no	—
76	C₂×C₈×D₅₉	—	2	1	no	—
77	C₂×C₈×D₅₉	—	4	4	no	—
78	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
79	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
80	#14273726	C₂×C₄	1	1	yes	characteristic
81	#14273725	C₂×C₄	1	1	yes	characteristic
82	#14273717	—	2	1	no	—
83	#14273707	C₂×C₄	1	1	yes	characteristic
84	#14273705	—	2	1	no	—
85	#14273703	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₁₈	—	2	1	no	—
87	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
88	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
89	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
90	#14273689	C₂×C₄	1	1	yes	characteristic
91	C₄×C₂²⋊D₅₉	—	2	1	no	—
92	(C₂²⋊D₅₉)⋊C₄	—	2	1	no	—
93	#14273684	—	2	1	no	—
94	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₄×D₅₉	—	2	1	no	—
96	C₄²×D₅₉	C₂³	1	1	yes	characteristic
97	#14273659	C₂×C₄	1	1	yes	characteristic
98	#14273658	C₂×C₄	1	1	yes	characteristic
99	#14273658	C₂×C₄	1	1	yes	characteristic
100	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
101	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	—	2	1	no	—
106	Dic₅₉⋊C₈	—	2	1	no	—
107	Dic₅₉⋊C₈	—	2	1	no	—
108	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
109	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
110	#14273652	C₂×C₄	1	1	yes	characteristic
111	#14273651	C₂×C₄	1	1	yes	characteristic
112	#14273650	C₂×C₄	1	1	yes	characteristic
113	#14273649	C₂×C₄	1	1	yes	characteristic
114	#14273648	C₂×C₄	1	1	yes	characteristic
115	#14273647	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
117	(C₂×D₅₉)⋊C₈	—	2	1	no	—
118	(C₂×D₅₉)⋊C₈	—	2	1	no	—
119	(C₂×D₅₉)⋊C₈	—	2	1	no	—
120	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
121	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
122	#14273638	—	2	1	no	—
123	#14273637	—	2	1	no	—
124	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
126	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
127	C₈×Dic₅₉	—	2	1	no	—
128	C₈×Dic₅₉	D₄	1	1	yes	characteristic
129	C₈×Dic₅₉	D₄	1	1	yes	characteristic
130	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₂²×C₈×C₅₉	—	2	1	no	—
132	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
134	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	—	2	1	no	—
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	—	2	1	no	—
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
145	C₂³×D₅₉	—	2	1	no	—
146	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅₉	—	2	1	no	—
149	C₂×C₂²⋊D₅₉	—	2	1	no	—
150	C₂²×Dic₅₉	—	2	1	no	—
151	D₄×D₅₉	—	2	2	no	—
152	D₄×D₅₉	—	2	2	no	—
153	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅₉	—	2	1	no	—
155	C₂×C₄×D₅₉	—	2	1	no	—
156	C₂×C₄×D₅₉	—	2	1	no	—
157	C₂×C₄×D₅₉	—	4	2	no	—
158	C₂×C₄×D₅₉	—	4	2	no	—
159	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
162	C₂×Dic₁₁₈	—	2	1	no	—
163	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
164	SD₁₆×C₅₉	—	2	2	no	—
165	C₂×C₈×C₅₉	—	2	1	no	—
166	C₂×C₈×C₅₉	—	2	1	no	—
167	C₂×C₈×C₅₉	—	2	1	no	—
168	C₂×C₈×C₅₉	—	4	2	no	—
169	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
173	C₄⋊C₄×C₅₉	—	2	1	no	—
174	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²⋊C₄×C₅₉	—	2	1	no	—
177	C₄²×C₅₉	—	2	1	no	—
178	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
179	C₂²⋊Dic₅₉	—	2	1	no	—
180	#11745671	—	2	2	no	—
181	#11745670	—	2	2	no	—
182	(C₂×D₅₉)⋊C₄	—	2	1	no	—
183	(C₂×D₅₉)⋊C₄	—	2	1	no	—
184	(C₂×D₅₉)⋊C₄	—	2	1	no	—
185	(C₂×D₅₉)⋊C₄	—	2	1	no	—
186	C₄⋊Dic₅₉	—	2	1	no	—
187	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
189	Dic₅₉⋊C₄	—	2	1	no	—
190	Dic₅₉⋊C₄	—	2	1	no	—
191	Dic₅₉⋊C₄	—	2	1	no	—
192	Dic₅₉⋊C₄	—	2	1	no	—
193	Dic₅₉⋊C₄	—	2	1	no	—
194	Dic₅₉⋊C₄	—	2	1	no	—
195	C₄×Dic₅₉	—	2	1	no	—
196	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
198	C₄×Dic₅₉	#41	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	—	2	1	no	—
200	C₂×C₅₉⋊C₈	—	2	1	no	—
201	C₂×C₅₉⋊C₈	—	2	1	no	—
202	C₂×C₅₉⋊C₈	—	4	2	no	—
203	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
207	#11745660	—	2	2	no	—
208	#11745659	—	4	2	no	—
209	C₈×D₅₉	—	2	2	no	—
210	C₈×D₅₉	—	2	2	no	—
211	C₈×D₅₉	—	4	2	no	—
212	C₈×D₅₉	—	4	2	no	—
213	C₈×D₅₉	—	4	2	no	—
214	C₂³×C₅₉	—	2	1	no	—
215	C₂²×D₅₉	—	2	4	no	—
216	C₂²×D₅₉	—	2	1	no	—
217	C₂²×D₅₉	—	4	2	no	—
218	C₂²×D₅₉	—	4	2	no	—
219	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
220	Q₈×C₅₉	—	2	1	no	—
221	Q₈×C₅₉	—	2	1	no	—
222	D₄×C₅₉	—	2	1	no	—
223	D₄×C₅₉	#131	1	2	yes	—
224	C₂×C₄×C₅₉	—	2	1	no	—
225	C₂×C₄×C₅₉	—	2	1	no	—
226	C₂×C₄×C₅₉	—	2	1	no	—
227	C₂×C₄×C₅₉	—	4	1	no	—
228	C₂×C₄×C₅₉	—	4	1	no	—
229	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
232	C₂²⋊D₅₉	—	2	4	no	—
233	C₂×Dic₅₉	—	2	1	no	—
234	C₂×Dic₅₉	—	2	1	no	—
235	C₂×Dic₅₉	—	2	1	no	—
236	C₂×Dic₅₉	—	4	2	no	—
237	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
238	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
239	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
240	D₂₃₆	—	2	1	no	—
241	D₂₃₆	#131	1	2	yes	—
242	C₄×D₅₉	—	2	1	no	—
243	C₄×D₅₉	—	2	1	no	—
244	C₄×D₅₉	—	4	1	no	—
245	C₄×D₅₉	—	4	2	no	—
246	C₄×D₅₉	—	4	1	no	—
247	C₄×D₅₉	—	4	1	no	—
248	C₄×D₅₉	—	4	2	no	—
249	C₄×D₅₉	AGL(1,ℤ/8)	1	2	yes	—
250	C₄×D₅₉	#137	1	2	yes	—
251	Dic₁₁₈	—	2	1	no	—
252	Dic₁₁₈	—	2	1	no	—
253	Dic₁₁₈	—	4	2	no	—
254	C₈×C₅₉	—	2	1	no	—
255	C₈×C₅₉	—	2	1	no	—
256	C₈×C₅₉	—	2	1	no	—
257	C₈×C₅₉	—	2	1	no	—
258	C₈×C₅₉	—	4	1	no	—
259	C₈×C₅₉	—	4	1	no	—
260	C₈×C₅₉	—	4	1	no	—
261	C₅₉⋊C₈	—	2	1	no	—
262	C₅₉⋊C₈	—	2	1	no	—
263	C₅₉⋊C₈	—	2	1	no	—
264	C₅₉⋊C₈	—	2	1	no	—
265	C₅₉⋊C₈	—	4	1	no	—
266	C₅₉⋊C₈	—	4	1	no	—
267	C₅₉⋊C₈	—	4	1	no	—
268	#17905	—	59	1	no	maximal, Sylow
269	C₂²×C₅₉	—	2	2	no	—
270	C₂²×C₅₉	—	4	1	no	—
271	C₂²×C₅₉	—	4	1	no	—
272	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×D₅₉	—	2	1	no	—
274	C₂×D₅₉	—	2	1	no	—
275	C₂×D₅₉	—	2	2	no	—
276	C₂×D₅₉	—	4	8	no	—
277	C₂×D₅₉	—	4	1	no	—
278	C₂×D₅₉	—	4	1	no	—
279	C₂×D₅₉	#440	1	2	yes	—
280	C₄×C₅₉	—	2	1	no	—
281	C₄×C₅₉	—	4	1	no	—
282	C₄×C₅₉	—	4	1	no	—
283	C₄×C₅₉	—	4	1	no	—
284	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
285	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
286	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
287	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
288	Dic₅₉	—	2	1	no	—
289	Dic₅₉	—	2	1	no	—
290	Dic₅₉	—	4	1	no	—
291	Dic₅₉	—	4	1	no	—
292	Dic₅₉	—	4	1	no	—
293	Dic₅₉	#440	1	2	yes	—
294	#3101	—	59	1	no	—
295	#2960	—	59	1	no	—
296	C₂×C₈×D₄	—	59	1	no	—
297	#1585	—	59	1	no	—
298	#1585	—	59	1	no	—
299	#1585	—	59	1	no	—
300	#1585	—	59	1	no	—
301	SD₁₆⋊C₈	—	59	1	no	—
302	SD₁₆⋊C₈	—	59	1	no	—
303	SD₁₆⋊C₈	—	59	1	no	—
304	SD₁₆⋊C₈	D₅₉	1	1	yes	characteristic, complemented
305	#1571	—	59	1	no	—
306	#1486	—	59	1	no	—
307	#1481	—	59	1	no	—
308	#1452	—	59	1	no	—
309	C₂×C₅₉	—	4	2	no	—
310	C₂×C₅₉	#2929	1	1	yes	characteristic
311	C₂×C₅₉	C₂×#440	1	1	yes	characteristic
312	C₂×C₅₉	#2955	1	1	yes	characteristic
313	D₅₉	—	2	2	no	—
314	D₅₉	—	4	2	no	—
315	C₂³×C₈	—	118	1	no	—
316	#533	—	59	1	no	—
317	C₂×C₄×D₄	—	59	1	no	—
318	#483	—	59	1	no	—
319	#483	—	59	1	no	—
320	#476	—	59	1	no	—
321	#476	—	59	1	no	—
322	#461	—	59	1	no	—
323	#461	—	59	1	no	—
324	#450	—	59	1	no	—
325	#450	—	59	1	no	—
326	#446	—	59	1	no	—
327	#446	—	59	1	no	—
328	#446	—	118	1	no	—
329	C₈×Q₈	—	59	1	no	—
330	C₈×Q₈	—	118	1	no	—
331	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
332	C₄×SD₁₆	—	59	1	no	—
333	C₄×SD₁₆	—	59	1	no	—
334	C₄×SD₁₆	—	59	1	no	—
335	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
336	C₈×D₄	—	59	1	no	—
337	C₈×D₄	—	59	1	no	—
338	C₈×D₄	—	59	1	no	—
339	C₈×D₄	—	118	1	no	—
340	C₈×D₄	—	118	1	no	—
341	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
342	#431	—	59	1	no	—
343	#431	—	59	1	no	—
344	#424	—	118	1	no	—
345	#423	—	59	1	no	—
346	C₂×C₄⋊C₈	—	59	1	no	—
347	C₂×C₂²⋊C₈	—	118	1	no	—
348	#405	—	118	1	no	—
349	C₂×C₄×C₈	—	59	1	no	—
350	#335	—	59	1	no	—
351	#335	—	59	1	no	—
352	#335	—	59	1	no	—
353	#335	C₂×D₅₉	1	1	yes	characteristic, complemented
354	Q₈⋊C₈	—	59	1	no	—
355	Q₈⋊C₈	—	59	1	no	—
356	Q₈⋊C₈	—	59	1	no	—
357	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic, complemented
358	D₄⋊C₈	—	59	1	no	—
359	D₄⋊C₈	—	59	1	no	—
360	D₄⋊C₈	—	59	1	no	—
361	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
362	#322	—	59	1	no	—
363	#322	—	59	1	no	—
364	#322	—	59	1	no	—
365	#322	C₂×D₅₉	1	1	yes	characteristic, complemented
366	C₅₉	#17905	1	1	yes	characteristic, complemented, Sylow
367	C₂²×D₄	—	59	1	no	—
368	C₂³×C₄	—	118	1	no	—
369	C₂×SD₁₆	—	59	1	no	—
370	C₂×SD₁₆	—	59	1	no	—
371	C₂×SD₁₆	—	59	1	no	—
372	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
373	C₂×M₁₆	—	118	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	59	1	no	—
376	C₂²×C₈	—	59	1	no	—
377	C₂²×C₈	—	118	1	no	—
378	C₂²×C₈	—	118	1	no	—
379	C₂²×C₈	—	118	1	no	—
380	C₂²×C₈	—	118	1	no	—
381	C₂²×C₈	—	236	4	no	—
382	C₄⋊Q₈	—	59	1	no	—
383	C₄⋊Q₈	—	59	1	no	—
384	#125	—	118	1	no	—
385	C₂²⋊Q₈	—	59	1	no	—
386	C₂²⋊Q₈	—	59	1	no	—
387	C₂²⋊Q₈	—	118	1	no	—
388	C₄×Q₈	—	59	1	no	—
389	C₄×Q₈	—	118	1	no	—
390	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
391	C₄×D₄	—	59	1	no	—
392	C₄×D₄	—	59	1	no	—
393	C₄×D₄	—	59	1	no	—
394	C₄×D₄	—	118	1	no	—
395	C₄×D₄	—	118	1	no	—
396	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
397	#117	—	118	1	no	—
398	C₂×C₄⋊C₄	—	59	1	no	—
399	C₂×C₂²⋊C₄	—	118	1	no	—
400	C₂×C₄²	—	59	1	no	—
401	#106	—	59	1	no	—
402	#106	—	59	1	no	—
403	#106	—	59	1	no	—
404	#106	C₄×D₅₉	1	1	yes	characteristic
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	59	1	no	—
407	C₄⋊C₈	—	59	1	no	—
408	C₄⋊C₈	—	59	1	no	—
409	C₄⋊C₈	—	59	1	no	—
410	C₄⋊C₈	—	118	1	no	—
411	C₄⋊C₈	—	118	1	no	—
412	C₄⋊C₈	—	118	1	no	—
413	C₄⋊C₈	—	118	1	no	—
414	C₄⋊C₈	—	118	1	no	—
415	C₄⋊C₈	—	118	1	no	—
416	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
417	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
418	#103	—	59	1	no	—
419	#103	—	59	1	no	—
420	#103	—	59	1	no	—
421	#103	C₄×D₅₉	1	1	yes	characteristic
422	#102	—	59	1	no	—
423	#102	—	59	1	no	—
424	#102	—	59	1	no	—
425	#102	C₄×D₅₉	1	1	yes	characteristic
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	59	1	no	—
428	C₂²⋊C₈	—	59	1	no	—
429	C₂²⋊C₈	—	118	1	no	—
430	C₂²⋊C₈	—	118	1	no	—
431	C₂²⋊C₈	—	118	1	no	—
432	C₂²⋊C₈	—	118	1	no	—
433	#97	—	118	1	no	—
434	#97	—	118	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	59	1	no	—
437	C₄×C₈	—	59	1	no	—
438	C₄×C₈	—	59	1	no	—
439	C₄×C₈	—	59	1	no	—
440	C₄×C₈	—	59	1	no	—
441	C₄×C₈	—	118	1	no	—
442	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
443	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
444	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
445	C₂⁴	—	118	1	no	—
446	C₂×Q₈	—	59	1	no	—
447	C₂×Q₈	—	118	1	no	—
448	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
449	C₂×D₄	—	59	1	no	—
450	C₂×D₄	—	118	1	no	—
451	C₂×D₄	—	118	2	no	—
452	C₂×D₄	—	118	2	no	—
453	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	59	1	no	—
456	C₂²×C₄	—	59	1	no	—
457	C₂²×C₄	—	59	1	no	—
458	C₂²×C₄	—	118	1	no	—
459	C₂²×C₄	—	118	1	no	—
460	C₂²×C₄	—	118	1	no	—
461	C₂²×C₄	—	118	1	no	—
462	C₂²×C₄	—	236	2	no	—
463	C₂²×C₄	—	236	2	no	—
464	SD₁₆	—	2	2	no	—
465	SD₁₆	—	118	2	no	—
466	SD₁₆	—	118	2	no	—
467	SD₁₆	—	118	2	no	—
468	M₁₆	—	236	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	4	2	no	—
473	C₂×C₈	—	59	1	no	—
474	C₂×C₈	—	59	1	no	—
475	C₂×C₈	—	59	1	no	—
476	C₂×C₈	—	59	1	no	—
477	C₂×C₈	—	118	2	no	—
478	C₂×C₈	—	118	2	no	—
479	C₂×C₈	—	118	1	no	—
480	C₂×C₈	—	118	1	no	—
481	C₂×C₈	—	118	1	no	—
482	C₂×C₈	—	236	2	no	—
483	C₂×C₈	—	236	2	no	—
484	C₂×C₈	—	236	2	no	—
485	C₂×C₈	—	236	2	no	—
486	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
487	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
488	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
489	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	59	1	no	—
492	C₄⋊C₄	—	59	1	no	—
493	C₄⋊C₄	—	118	1	no	—
494	C₄⋊C₄	—	118	1	no	—
495	C₄⋊C₄	—	118	1	no	—
496	C₄⋊C₄	—	118	1	no	—
497	C₄⋊C₄	—	118	1	no	—
498	C₄⋊C₄	—	118	1	no	—
499	C₄⋊C₄	—	118	1	no	—
500	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	118	1	no	—
504	C₂²⋊C₄	—	118	1	no	—
505	C₂²⋊C₄	—	118	1	no	—
506	C₂²⋊C₄	—	118	1	no	—
507	C₂²⋊C₄	—	118	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	59	1	no	—
510	C₄²	—	59	1	no	—
511	C₄²	—	59	1	no	—
512	C₄²	—	118	1	no	—
513	C₄²	C₂³×D₅₉	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	59	1	no	—
516	C₂³	—	118	4	no	—
517	C₂³	—	118	1	no	—
518	C₂³	—	236	2	no	—
519	C₂³	—	236	2	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	118	1	no	—
523	Q₈	—	118	1	no	—
524	Q₈	—	236	2	no	—
525	D₄	—	2	1	no	—
526	D₄	—	59	2	no	—
527	D₄	—	118	4	no	—
528	D₄	—	118	1	no	—
529	D₄	#14273733	1	2	yes	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	59	1	no	—
536	C₂×C₄	—	59	2	no	—
537	C₂×C₄	—	59	2	no	—
538	C₂×C₄	—	59	1	no	—
539	C₂×C₄	—	59	1	no	—
540	C₂×C₄	—	118	1	no	—
541	C₂×C₄	—	118	1	no	—
542	C₂×C₄	—	118	1	no	—
543	C₂×C₄	—	118	1	no	—
544	C₂×C₄	—	118	1	no	—
545	C₂×C₄	—	236	1	no	—
546	C₂×C₄	—	236	2	no	—
547	C₂×C₄	—	236	2	no	—
548	C₂×C₄	—	236	2	no	—
549	C₂×C₄	—	236	1	no	—
550	C₂×C₄	—	236	1	no	—
551	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
552	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
553	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	118	1	no	—
562	C₈	—	118	1	no	—
563	C₈	—	118	1	no	—
564	C₈	—	118	1	no	—
565	C₈	—	236	1	no	—
566	C₈	—	236	1	no	—
567	C₈	—	236	1	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	59	2	no	—
572	C₂²	—	118	1	no	—
573	C₂²	—	118	1	no	—
574	C₂²	—	118	2	no	—
575	C₂²	—	236	8	no	—
576	C₂²	—	236	1	no	—
577	C₂²	—	236	1	no	—
578	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	59	2	no	—
584	C₄	—	118	1	no	—
585	C₄	—	118	1	no	—
586	C₄	—	236	1	no	—
587	C₄	—	236	1	no	—
588	C₄	—	236	1	no	—
589	C₄	#131×D₅₉	1	1	yes	characteristic
590	C₄	C₂×#14273733	1	1	yes	characteristic
591	C₄	AGL(1,ℤ/8)×D₅₉	1	1	yes	characteristic
592	C₄	#137×D₅₉	1	1	yes	characteristic
593	C₂	—	4	2	no	—
594	C₂	—	118	2	no	—
595	C₂	—	236	2	no	—
596	C₂	#21432785	1	1	yes	characteristic
597	C₂	#440×D₅₉	1	1	yes	characteristic
598	C₂	#21432996	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×SD₁₆⋊C₈	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×D₄×D₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	SD₁₆⋊C₈	D₅₉
hypocenter	C₅₉	#17905
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
2. #21433025	C₂	semidirect
4. #21422956	C₂	semidirect
5. #21422954	C₂	semidirect
6. #21422952	C₂	semidirect
7. #21422950	C₂	semidirect
8. #21422910	C₂	semidirect
9. #21422908	C₂	semidirect
10. #21422906	C₂	semidirect
11. #21422869	C₂	semidirect
13. #21422497	C₂	semidirect
14. #21422387	C₂	semidirect
15. C₅₉×SD₁₆⋊C₈	C₂	semidirect
27. #16837533	C₂²	semidirect
29. #16837529	C₂²	semidirect
31. C₈×Dic₁₁₈	C₂²	semidirect
48. #16837155	C₂²	semidirect
49. #16837154	C₂²	semidirect
50. #16837154	C₂²	semidirect
51. #16837134	C₂²	semidirect
52. Q₈⋊(C₅₉⋊C₈)	C₂²	semidirect
53. #16837132	C₂²	semidirect
57. #16837124	C₂²	semidirect
58. #16837124	C₂²	semidirect
59. #16837123	C₂²	semidirect
60. C₈×Q₈×C₅₉	C₂²	semidirect
63. C₅₉×#335	C₂²	semidirect
64. C₅₉×Q₈⋊C₈	C₂²	semidirect
66. C₅₉×#322	C₂²	semidirect
304. SD₁₆⋊C₈	D₅₉	semidirect
331. C₈×Q₈	C₂×D₅₉	semidirect
353. #335	C₂×D₅₉	semidirect
357. Q₈⋊C₈	C₂×D₅₉	semidirect
365. #322	C₂×D₅₉	semidirect
366. C₅₉	#17905	semidirect

Maximal subgroups

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

subgroup	index
#21434102	2
#21433025	2
C₈×D₄×D₅₉	2
#21422956	2
#21422954	2
#21422952	2
#21422950	2
#21422910	2
#21422908	2
#21422906	2
#21422869	2
#21422519	2
#21422497	2
#21422387	2
C₅₉×SD₁₆⋊C₈	2
#17905	59