Subgroups — D₅₉×#1592 #28558441

Order 15104.

730 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#446×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×SD₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#436×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21423001	C₂	1	1	yes	maximal, characteristic, complemented
5	#21423000	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422999	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422998	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422997	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422996	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422995	C₂	1	1	yes	maximal, characteristic, complemented
11	#335×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈⋊C₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄⋊C₈×D₅₉	C₂	1	1	yes	maximal, characteristic
14	#322×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1592	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×SD₁₆×D₅₉	C₄	1	1	yes	characteristic
17	C₂×M₁₆×D₅₉	—	2	1	no	—
18	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₅₉	C₂²	1	1	yes	characteristic
20	#16837533	C₂²	1	1	yes	characteristic, complemented
21	#16837532	C₂²	1	1	yes	characteristic, complemented
22	#16837531	—	2	1	no	—
23	#16837530	—	2	1	no	—
24	#16837529	C₂²	1	1	yes	characteristic, complemented
25	#16837493	C₄	1	1	yes	characteristic
26	C₄×#11745660	C₂²	1	1	yes	characteristic
27	SD₁₆×Dic₅₉	C₄	1	1	yes	characteristic
28	C₄×#11745671	C₂²	1	1	yes	characteristic
29	#16837489	C₄	1	1	yes	characteristic
30	C₄×#11745670	C₂²	1	1	yes	characteristic
31	#16837487	C₄	1	1	yes	characteristic
32	#16837481	C₂²	1	1	yes	characteristic
33	#16837480	C₂²	1	1	yes	characteristic
34	#16837479	C₂²	1	1	yes	characteristic
35	#16837478	—	2	1	no	—
36	#16837477	—	2	1	no	—
37	#106×D₅₉	C₄	1	1	yes	characteristic
38	C₄⋊C₈×D₅₉	—	2	1	no	—
39	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
41	#103×D₅₉	C₄	1	1	yes	characteristic
42	#102×D₅₉	C₄	1	1	yes	characteristic
43	C₂²⋊C₈×D₅₉	—	2	1	no	—
44	#97×D₅₉	—	2	1	no	—
45	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
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	C₅₉×#446	C₂²	1	1	yes	characteristic, complemented
61	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
62	C₅₉×#436	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×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₅₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₅₉	—	2	1	no	—
70	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
73	SD₁₆×D₅₉	—	2	4	no	—
74	C₂×#11745664	—	2	1	no	—
75	C₂×#11745659	—	2	1	no	—
76	C₂×#11745659	—	2	1	no	—
77	M₁₆×D₅₉	—	4	4	no	—
78	C₂×C₈×D₅₉	—	2	1	no	—
79	C₂×C₈×D₅₉	—	2	1	no	—
80	C₂×C₈×D₅₉	—	2	1	no	—
81	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
84	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
85	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₁₈	—	2	1	no	—
87	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
88	#14273692	—	2	1	no	—
89	#14273692	C₂×C₄	1	1	yes	characteristic
90	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
91	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
92	#14273689	C₂×C₄	1	1	yes	characteristic
93	C₄×C₂²⋊D₅₉	—	2	1	no	—
94	(C₂²⋊D₅₉)⋊C₄	—	2	1	no	—
95	C₄⋊C₄×D₅₉	—	2	1	no	—
96	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
97	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊C₄×D₅₉	—	2	1	no	—
99	C₄²×D₅₉	—	2	1	no	—
100	C₄²×D₅₉	C₂³	1	1	yes	characteristic
101	#14273659	C₂×C₄	1	1	yes	characteristic
102	#14273658	C₂×C₄	1	1	yes	characteristic
103	#14273658	C₂×C₄	1	1	yes	characteristic
104	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
105	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
106	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
107	Dic₅₉⋊C₈	—	2	1	no	—
108	Dic₅₉⋊C₈	—	2	1	no	—
109	Dic₅₉⋊C₈	—	2	1	no	—
110	Dic₅₉⋊C₈	—	2	1	no	—
111	#14273652	C₂×C₄	1	1	yes	characteristic
112	#14273651	C₂×C₄	1	1	yes	characteristic
113	#14273650	C₂×C₄	1	1	yes	characteristic
114	#14273649	C₂×C₄	1	1	yes	characteristic
115	#14273648	C₂×C₄	1	1	yes	characteristic
116	#14273647	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
118	(C₂×D₅₉)⋊C₈	—	2	1	no	—
119	(C₂×D₅₉)⋊C₈	—	2	1	no	—
120	#14273638	—	2	1	no	—
121	#14273637	—	2	1	no	—
122	#14273637	—	2	1	no	—
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₅₉	D₄	1	1	yes	characteristic
130	C₈×Dic₅₉	D₄	1	1	yes	characteristic
131	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
132	C₂×M₁₆×C₅₉	—	2	1	no	—
133	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
135	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	—	2	1	no	—
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
139	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
140	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₅₉	—	2	1	no	—
142	#97×C₅₉	—	2	1	no	—
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
146	C₂³×D₅₉	—	2	1	no	—
147	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	—	2	1	no	—
150	C₂×C₂²⋊D₅₉	—	2	1	no	—
151	C₂²×Dic₅₉	—	2	1	no	—
152	Q₈×D₅₉	—	2	2	no	—
153	Q₈×D₅₉	—	2	2	no	—
154	D₄×D₅₉	—	2	2	no	—
155	D₄×D₅₉	—	2	2	no	—
156	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₅₉	—	2	1	no	—
158	C₂×C₄×D₅₉	—	2	1	no	—
159	C₂×C₄×D₅₉	—	2	1	no	—
160	C₂×C₄×D₅₉	—	2	1	no	—
161	C₂×C₄×D₅₉	—	2	1	no	—
162	C₂×C₄×D₅₉	—	4	2	no	—
163	C₂×C₄×D₅₉	—	4	2	no	—
164	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
167	C₂×Dic₁₁₈	—	2	1	no	—
168	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
169	SD₁₆×C₅₉	—	2	2	no	—
170	M₁₆×C₅₉	—	4	2	no	—
171	C₂×C₈×C₅₉	—	2	1	no	—
172	C₂×C₈×C₅₉	—	2	1	no	—
173	C₂×C₈×C₅₉	—	2	1	no	—
174	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
178	C₄⋊C₄×C₅₉	—	2	1	no	—
179	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
181	C₂²⋊C₄×C₅₉	—	2	1	no	—
182	C₄²×C₅₉	—	2	1	no	—
183	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
184	C₂²⋊Dic₅₉	—	2	1	no	—
185	#11745671	—	2	2	no	—
186	#11745670	—	2	2	no	—
187	(C₂×D₅₉)⋊C₄	—	2	1	no	—
188	(C₂×D₅₉)⋊C₄	—	2	1	no	—
189	C₄⋊Dic₅₉	—	2	1	no	—
190	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
192	Dic₅₉⋊C₄	—	2	1	no	—
193	Dic₅₉⋊C₄	—	2	1	no	—
194	Dic₅₉⋊C₄	—	2	1	no	—
195	Dic₅₉⋊C₄	—	2	1	no	—
196	C₄×Dic₅₉	—	2	1	no	—
197	C₄×Dic₅₉	—	2	1	no	—
198	C₄×Dic₅₉	—	2	1	no	—
199	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
201	C₄×Dic₅₉	#41	1	1	yes	characteristic
202	#11745664	—	4	2	no	—
203	C₂×C₅₉⋊C₈	—	2	1	no	—
204	C₂×C₅₉⋊C₈	—	2	1	no	—
205	C₂×C₅₉⋊C₈	—	2	1	no	—
206	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
210	#11745660	—	2	2	no	—
211	#11745659	—	4	2	no	—
212	#11745659	—	4	2	no	—
213	C₈×D₅₉	—	2	2	no	—
214	C₈×D₅₉	—	2	2	no	—
215	C₈×D₅₉	—	2	2	no	—
216	C₈×D₅₉	—	4	2	no	—
217	C₈×D₅₉	—	4	2	no	—
218	C₈×D₅₉	—	4	2	no	—
219	C₈×D₅₉	M₁₆	1	4	yes	complemented
220	C₂³×C₅₉	—	2	1	no	—
221	C₂²×D₅₉	—	2	1	no	—
222	C₂²×D₅₉	—	4	2	no	—
223	C₂²×D₅₉	—	4	2	no	—
224	C₂²×D₅₉	—	4	2	no	—
225	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
226	Q₈×C₅₉	—	2	1	no	—
227	Q₈×C₅₉	—	2	1	no	—
228	D₄×C₅₉	—	2	1	no	—
229	D₄×C₅₉	—	2	1	no	—
230	C₂×C₄×C₅₉	—	2	1	no	—
231	C₂×C₄×C₅₉	—	2	1	no	—
232	C₂×C₄×C₅₉	—	2	1	no	—
233	C₂×C₄×C₅₉	—	4	1	no	—
234	C₂×C₄×C₅₉	—	4	1	no	—
235	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
238	C₂²⋊D₅₉	—	4	2	no	—
239	C₂×Dic₅₉	—	2	1	no	—
240	C₂×Dic₅₉	—	2	1	no	—
241	C₂×Dic₅₉	—	2	1	no	—
242	C₂×Dic₅₉	—	4	2	no	—
243	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
244	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
245	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
246	D₂₃₆	—	2	1	no	—
247	D₂₃₆	—	2	1	no	—
248	C₄×D₅₉	—	2	2	no	—
249	C₄×D₅₉	—	4	2	no	—
250	C₄×D₅₉	—	4	2	no	—
251	C₄×D₅₉	—	4	2	no	—
252	C₄×D₅₉	—	4	1	no	—
253	C₄×D₅₉	—	4	1	no	—
254	C₄×D₅₉	—	4	2	no	—
255	C₄×D₅₉	C₂×M₁₆	1	2	yes	—
256	C₄×D₅₉	#131	1	2	yes	—
257	C₄×D₅₉	AGL(1,ℤ/8)	1	2	yes	—
258	C₄×D₅₉	#137	1	2	yes	—
259	Dic₁₁₈	—	2	1	no	—
260	Dic₁₁₈	—	2	1	no	—
261	Dic₁₁₈	—	4	2	no	—
262	C₈×C₅₉	—	2	1	no	—
263	C₈×C₅₉	—	2	1	no	—
264	C₈×C₅₉	—	2	1	no	—
265	C₈×C₅₉	—	4	1	no	—
266	C₈×C₅₉	—	4	1	no	—
267	C₈×C₅₉	—	4	1	no	—
268	C₈×C₅₉	C₂×M₁₆	1	2	yes	complemented
269	C₅₉⋊C₈	—	2	1	no	—
270	C₅₉⋊C₈	—	2	1	no	—
271	C₅₉⋊C₈	—	2	1	no	—
272	C₅₉⋊C₈	—	4	1	no	—
273	C₅₉⋊C₈	—	4	1	no	—
274	C₅₉⋊C₈	—	4	1	no	—
275	C₅₉⋊C₈	C₂×M₁₆	1	2	yes	complemented
276	C₂×#1592	—	59	1	no	maximal, Sylow
277	C₂²×C₅₉	—	4	1	no	—
278	C₂²×C₅₉	—	4	1	no	—
279	C₂²×C₅₉	—	4	1	no	—
280	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂×D₅₉	—	4	1	no	—
282	C₂×D₅₉	—	4	1	no	—
283	C₂×D₅₉	—	4	1	no	—
284	C₂×D₅₉	—	8	4	no	—
285	C₂×D₅₉	#436	1	2	yes	—
286	C₂×D₅₉	#440	1	2	yes	—
287	C₂×D₅₉	#444	1	2	yes	—
288	C₄×C₅₉	—	2	1	no	—
289	C₄×C₅₉	—	4	1	no	—
290	C₄×C₅₉	—	4	1	no	—
291	C₄×C₅₉	—	4	1	no	—
292	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
293	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
294	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
296	Dic₅₉	—	2	1	no	—
297	Dic₅₉	—	4	1	no	—
298	Dic₅₉	—	4	1	no	—
299	Dic₅₉	—	4	1	no	—
300	Dic₅₉	#436	1	2	yes	—
301	Dic₅₉	#440	1	2	yes	—
302	C₂×#446	—	59	1	no	—
303	C₂×C₄×SD₁₆	—	59	1	no	—
304	C₂×#436	—	59	1	no	—
305	#1592	—	59	1	no	—
306	#1592	—	59	1	no	—
307	#1592	—	59	1	no	—
308	#1592	—	59	1	no	—
309	#1592	—	59	1	no	—
310	#1592	—	59	1	no	—
311	#1592	—	59	1	no	—
312	#1592	D₅₉	1	1	yes	characteristic, direct product factor
313	C₂×#335	—	59	1	no	—
314	C₂×Q₈⋊C₈	—	59	1	no	—
315	C₂×D₄⋊C₈	—	59	1	no	—
316	C₂×#322	—	59	1	no	—
317	C₂×C₅₉	—	8	1	no	—
318	C₂×C₅₉	C₂×#436	1	1	yes	characteristic
319	C₂×C₅₉	C₂×#440	1	1	yes	characteristic
320	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
321	D₅₉	—	8	1	no	—
322	D₅₉	#1592	1	4	yes	direct product factor
323	C₂²×SD₁₆	—	59	1	no	—
324	C₂²×M₁₆	—	118	1	no	—
325	C₂×C₄×Q₈	—	59	1	no	—
326	C₂×C₄×D₄	—	59	1	no	—
327	#446	—	59	1	no	—
328	#446	—	59	1	no	—
329	#446	—	59	1	no	—
330	#446	—	118	1	no	—
331	#446	—	118	1	no	—
332	#446	C₂×D₅₉	1	1	yes	characteristic, complemented
333	C₄×SD₁₆	—	59	1	no	—
334	C₄×SD₁₆	—	59	1	no	—
335	C₄×SD₁₆	—	59	1	no	—
336	C₄×SD₁₆	—	59	1	no	—
337	C₄×SD₁₆	—	59	1	no	—
338	C₄×SD₁₆	—	59	1	no	—
339	C₄×SD₁₆	—	59	1	no	—
340	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
341	#436	—	59	1	no	—
342	#436	—	59	1	no	—
343	#436	—	59	1	no	—
344	#436	—	118	1	no	—
345	#436	—	118	1	no	—
346	#436	C₂×D₅₉	1	1	yes	characteristic
347	C₂×#106	—	59	1	no	—
348	C₂×C₄⋊C₈	—	59	1	no	—
349	C₂×C₄⋊C₈	—	59	1	no	—
350	C₂×C₄⋊C₈	—	118	1	no	—
351	C₂×#103	—	59	1	no	—
352	C₂×#102	—	59	1	no	—
353	C₂×C₂²⋊C₈	—	118	1	no	—
354	C₂×#97	—	118	1	no	—
355	C₂×C₄×C₈	—	59	1	no	—
356	C₂×C₄×C₈	—	59	1	no	—
357	C₂×C₄×C₈	—	59	1	no	—
358	#335	—	59	1	no	—
359	#335	—	59	1	no	—
360	#335	—	59	1	no	—
361	#335	C₂×D₅₉	1	1	yes	characteristic, complemented
362	Q₈⋊C₈	—	59	1	no	—
363	Q₈⋊C₈	—	59	1	no	—
364	Q₈⋊C₈	—	59	1	no	—
365	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic, complemented
366	D₄⋊C₈	—	59	1	no	—
367	D₄⋊C₈	—	59	1	no	—
368	D₄⋊C₈	—	59	1	no	—
369	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
370	#322	—	59	1	no	—
371	#322	—	59	1	no	—
372	#322	—	59	1	no	—
373	#322	C₂×D₅₉	1	1	yes	characteristic, complemented
374	C₅₉	C₂×#1592	1	1	yes	characteristic, complemented, Sylow
375	C₂²×Q₈	—	59	1	no	—
376	C₂²×D₄	—	59	1	no	—
377	C₂³×C₄	—	118	1	no	—
378	C₂×SD₁₆	—	59	1	no	—
379	C₂×SD₁₆	—	59	1	no	—
380	C₂×SD₁₆	—	59	1	no	—
381	C₂×SD₁₆	—	118	4	no	—
382	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	118	1	no	—
385	C₂×M₁₆	—	118	1	no	—
386	C₂×M₁₆	—	118	1	no	—
387	C₂×M₁₆	—	236	4	no	—
388	C₂²×C₈	—	59	1	no	—
389	C₂²×C₈	—	59	1	no	—
390	C₂²×C₈	—	59	1	no	—
391	C₂²×C₈	—	59	1	no	—
392	C₂²×C₈	—	118	1	no	—
393	C₂²×C₈	—	118	1	no	—
394	C₂²×C₈	—	118	1	no	—
395	C₄×Q₈	—	59	1	no	—
396	C₄×Q₈	—	59	1	no	—
397	C₄×Q₈	—	59	1	no	—
398	C₄×Q₈	—	118	1	no	—
399	C₄×Q₈	—	118	1	no	—
400	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
401	C₄×D₄	—	59	1	no	—
402	C₄×D₄	—	59	1	no	—
403	C₄×D₄	—	59	1	no	—
404	C₄×D₄	—	118	1	no	—
405	C₄×D₄	—	118	1	no	—
406	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	—	59	1	no	—
408	C₂×C₄⋊C₄	—	59	1	no	—
409	C₂×C₄⋊C₄	—	118	1	no	—
410	C₂×C₂²⋊C₄	—	118	1	no	—
411	C₂×C₄²	—	59	1	no	—
412	C₂×C₄²	—	118	1	no	—
413	#106	—	59	1	no	—
414	#106	—	59	1	no	—
415	#106	—	59	1	no	—
416	#106	C₄×D₅₉	1	1	yes	characteristic
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	—	59	1	no	—
419	C₄⋊C₈	—	59	1	no	—
420	C₄⋊C₈	—	118	1	no	—
421	C₄⋊C₈	—	118	1	no	—
422	C₄⋊C₈	—	118	1	no	—
423	C₄⋊C₈	—	118	1	no	—
424	C₄⋊C₈	—	118	1	no	—
425	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
427	#103	—	59	1	no	—
428	#103	—	59	1	no	—
429	#103	—	59	1	no	—
430	#103	C₄×D₅₉	1	1	yes	characteristic
431	#102	—	59	1	no	—
432	#102	—	59	1	no	—
433	#102	—	59	1	no	—
434	#102	C₄×D₅₉	1	1	yes	characteristic
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	118	1	no	—
437	C₂²⋊C₈	—	118	1	no	—
438	C₂²⋊C₈	—	118	1	no	—
439	#97	—	2	1	no	—
440	#97	—	118	1	no	—
441	#97	—	118	1	no	—
442	#97	—	118	1	no	—
443	C₄×C₈	—	59	1	no	—
444	C₄×C₈	—	59	1	no	—
445	C₄×C₈	—	59	1	no	—
446	C₄×C₈	—	59	1	no	—
447	C₄×C₈	—	59	1	no	—
448	C₄×C₈	—	59	1	no	—
449	C₄×C₈	—	59	1	no	—
450	C₄×C₈	—	118	1	no	—
451	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
452	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
453	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
454	C₂⁴	—	118	1	no	—
455	C₂×Q₈	—	59	1	no	—
456	C₂×Q₈	—	118	1	no	—
457	C₂×Q₈	—	118	2	no	—
458	C₂×Q₈	—	118	2	no	—
459	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
460	C₂×D₄	—	59	1	no	—
461	C₂×D₄	—	118	2	no	—
462	C₂×D₄	—	118	2	no	—
463	C₂×D₄	—	118	1	no	—
464	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	59	1	no	—
467	C₂²×C₄	—	59	1	no	—
468	C₂²×C₄	—	59	1	no	—
469	C₂²×C₄	—	118	1	no	—
470	C₂²×C₄	—	118	1	no	—
471	C₂²×C₄	—	118	1	no	—
472	C₂²×C₄	—	118	1	no	—
473	C₂²×C₄	—	118	1	no	—
474	C₂²×C₄	—	118	1	no	—
475	C₂²×C₄	—	236	2	no	—
476	C₂²×C₄	—	236	2	no	—
477	SD₁₆	—	2	2	no	—
478	SD₁₆	—	118	2	no	—
479	SD₁₆	—	118	2	no	—
480	SD₁₆	—	118	2	no	—
481	M₁₆	—	4	2	no	—
482	M₁₆	—	236	2	no	—
483	M₁₆	—	236	2	no	—
484	M₁₆	—	236	2	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	59	1	no	—
489	C₂×C₈	—	59	4	no	—
490	C₂×C₈	—	59	1	no	—
491	C₂×C₈	—	59	1	no	—
492	C₂×C₈	—	59	1	no	—
493	C₂×C₈	—	118	2	no	—
494	C₂×C₈	—	118	2	no	—
495	C₂×C₈	—	118	2	no	—
496	C₂×C₈	—	118	1	no	—
497	C₂×C₈	—	118	1	no	—
498	C₂×C₈	—	118	1	no	—
499	C₂×C₈	—	236	2	no	—
500	C₂×C₈	—	236	2	no	—
501	C₂×C₈	—	236	2	no	—
502	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
503	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
504	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
505	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	59	1	no	—
508	C₄⋊C₄	—	59	1	no	—
509	C₄⋊C₄	—	118	1	no	—
510	C₄⋊C₄	—	118	1	no	—
511	C₄⋊C₄	—	118	1	no	—
512	C₄⋊C₄	—	118	1	no	—
513	C₄⋊C₄	—	118	1	no	—
514	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	118	1	no	—
518	C₂²⋊C₄	—	118	1	no	—
519	C₂²⋊C₄	—	118	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	59	1	no	—
522	C₄²	—	59	1	no	—
523	C₄²	—	59	1	no	—
524	C₄²	—	118	1	no	—
525	C₄²	—	118	1	no	—
526	C₄²	—	118	1	no	—
527	C₄²	C₂³×D₅₉	1	1	yes	characteristic
528	C₂³	—	2	1	no	—
529	C₂³	—	59	1	no	—
530	C₂³	—	118	1	no	—
531	C₂³	—	236	2	no	—
532	C₂³	—	236	2	no	—
533	C₂³	—	236	2	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	2	1	no	—
536	Q₈	—	118	1	no	—
537	Q₈	—	118	1	no	—
538	Q₈	—	236	2	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	118	1	no	—
542	D₄	—	118	1	no	—
543	D₄	—	236	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	59	1	no	—
550	C₂×C₄	—	59	1	no	—
551	C₂×C₄	—	59	2	no	—
552	C₂×C₄	—	59	2	no	—
553	C₂×C₄	—	59	2	no	—
554	C₂×C₄	—	59	2	no	—
555	C₂×C₄	—	59	1	no	—
556	C₂×C₄	—	118	2	no	—
557	C₂×C₄	—	118	1	no	—
558	C₂×C₄	—	118	1	no	—
559	C₂×C₄	—	118	1	no	—
560	C₂×C₄	—	236	2	no	—
561	C₂×C₄	—	236	2	no	—
562	C₂×C₄	—	236	2	no	—
563	C₂×C₄	—	236	2	no	—
564	C₂×C₄	—	236	2	no	—
565	C₂×C₄	—	236	1	no	—
566	C₂×C₄	—	236	1	no	—
567	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
568	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
569	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
570	C₈	—	2	1	no	—
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	59	2	no	—
577	C₈	—	118	1	no	—
578	C₈	—	118	1	no	—
579	C₈	—	118	1	no	—
580	C₈	—	236	1	no	—
581	C₈	—	236	1	no	—
582	C₈	—	236	1	no	—
583	C₈	M₁₆×D₅₉	1	2	yes	complemented
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	59	2	no	—
588	C₂²	—	59	2	no	—
589	C₂²	—	59	2	no	—
590	C₂²	—	472	4	no	—
591	C₂²	—	236	1	no	—
592	C₂²	—	236	1	no	—
593	C₂²	—	236	1	no	—
594	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	59	2	no	—
600	C₄	—	59	2	no	—
601	C₄	—	118	1	no	—
602	C₄	—	236	1	no	—
603	C₄	—	236	1	no	—
604	C₄	—	236	1	no	—
605	C₄	C₂×M₁₆×D₅₉	1	1	yes	characteristic
606	C₄	#131×D₅₉	1	1	yes	characteristic
607	C₄	AGL(1,ℤ/8)×D₅₉	1	1	yes	characteristic
608	C₄	#137×D₅₉	1	1	yes	characteristic
609	C₂	—	8	1	no	—
610	C₂	—	59	4	no	—
611	C₂	—	472	1	no	—
612	C₂	#436×D₅₉	1	1	yes	characteristic
613	C₂	#440×D₅₉	1	1	yes	characteristic
614	C₂	#444×D₅₉	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×#1592	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×D₄×D₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1592	D₅₉
hypocenter	C₅₉	C₂×#1592
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1592

Complements

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

N	H ≅ G/N	type
1. #446×D₅₉	C₂	semidirect
4. #21423001	C₂	semidirect
5. #21423000	C₂	semidirect
6. #21422999	C₂	semidirect
7. #21422998	C₂	semidirect
8. #21422997	C₂	semidirect
9. #21422996	C₂	semidirect
10. #21422995	C₂	semidirect
11. #335×D₅₉	C₂	semidirect
12. Q₈⋊C₈×D₅₉	C₂	semidirect
14. #322×D₅₉	C₂	semidirect
15. C₅₉×#1592	C₂	semidirect
20. #16837533	C₂²	semidirect
21. #16837532	C₂²	semidirect
24. #16837529	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. C₅₉×#446	C₂²	semidirect
63. C₅₉×#335	C₂²	semidirect
64. C₅₉×Q₈⋊C₈	C₂²	semidirect
66. C₅₉×#322	C₂²	semidirect
219. C₈×D₅₉	M₁₆	semidirect
268. C₈×C₅₉	C₂×M₁₆	semidirect
275. C₅₉⋊C₈	C₂×M₁₆	semidirect
312. #1592	D₅₉	direct (N × H)
322. D₅₉	#1592	direct (N × H)
332. #446	C₂×D₅₉	semidirect
361. #335	C₂×D₅₉	semidirect
365. Q₈⋊C₈	C₂×D₅₉	semidirect
373. #322	C₂×D₅₉	semidirect
374. C₅₉	C₂×#1592	semidirect
583. C₈	M₁₆×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#446×D₅₉	2
C₄×SD₁₆×D₅₉	2
#436×D₅₉	2
#21423001	2
#21423000	2
#21422999	2
#21422998	2
#21422997	2
#21422996	2
#21422995	2
#335×D₅₉	2
Q₈⋊C₈×D₅₉	2
D₄⋊C₈×D₅₉	2
#322×D₅₉	2
C₅₉×#1592	2
C₂×#1592	59

Subgroups — D59×#1592 #28558441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×#1592 #28558441