Subgroups — #28558561

Order 15104.

686 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434125	C₂	1	1	yes	maximal, characteristic
2	C₈×Q₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432803	C₂	1	1	yes	maximal, characteristic
4	#21422942	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422940	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422938	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#11745660	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11745671	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11745670	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422865	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422523	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422493	C₂	1	1	yes	maximal, characteristic
14	#21422378	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273733	—	2	1	no	—
17	#16837949	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
19	#16837722	C₄	1	1	yes	characteristic
20	#16837719	C₄	1	1	yes	characteristic
21	#16837686	C₄	1	1	yes	characteristic
22	#16837685	C₄	1	1	yes	characteristic
23	#16837601	C₄	1	1	yes	characteristic
24	#16837600	C₄	1	1	yes	characteristic
25	#16837542	C₄	1	1	yes	characteristic
26	#16837539	C₄	1	1	yes	characteristic
27	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₁₈	—	2	1	no	—
29	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
30	#16837526	—	2	1	no	—
31	#16837526	C₂²	1	1	yes	characteristic
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	#16837480	C₂²	1	1	yes	characteristic
36	#16837479	C₂²	1	1	yes	characteristic
37	#16837477	—	2	1	no	—
38	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
39	C₈×C₂²⋊D₅₉	—	2	1	no	—
40	#16837453	C₂²	1	1	yes	characteristic
41	#16837453	C₂²	1	1	yes	characteristic
42	#16837424	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₅₉	—	2	1	no	—
44	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
45	#16837367	—	2	1	no	—
46	C₄×C₈×D₅₉	—	2	1	no	—
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837153	C₂²	1	1	yes	characteristic
49	#16837152	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837134	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
53	#16837132	C₂²	1	1	yes	characteristic
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
58	#16837124	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#334	C₂²	1	1	yes	characteristic
64	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₅₉	C₂²	1	1	yes	characteristic
67	C₂×#11745685	—	2	1	no	—
68	C₂×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
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	#14273733	—	4	4	no	—
73	C₂×#11745664	—	2	1	no	—
74	C₂×#11745659	—	2	1	no	—
75	C₂×#11745659	—	2	1	no	—
76	C₂×C₈×D₅₉	—	2	1	no	—
77	C₂×C₈×D₅₉	—	2	1	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	#14273723	C₂×C₄	1	1	yes	characteristic
82	#14273713	—	2	1	no	—
83	#14273702	C₂×C₄	1	1	yes	characteristic
84	#14273700	—	2	1	no	—
85	#14273698	C₂×C₄	1	1	yes	characteristic
86	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
87	C₄×Dic₁₁₈	—	2	1	no	—
88	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
89	#14273692	—	2	1	no	—
90	#14273692	C₂×C₄	1	1	yes	characteristic
91	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
92	C₄×C₂²⋊D₅₉	—	2	1	no	—
93	C₄⋊C₄×D₅₉	—	2	1	no	—
94	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
95	C₄²×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	C₄×C₅₉⋊C₈	—	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	—	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	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅₉	—	2	1	no	—
148	C₂×C₂²⋊D₅₉	—	2	1	no	—
149	C₂×C₂²⋊D₅₉	—	2	1	no	—
150	C₂×C₂²⋊D₅₉	—	2	1	no	—
151	Q₈×D₅₉	—	2	2	no	—
152	Q₈×D₅₉	—	2	2	no	—
153	#11745685	—	4	2	no	—
154	#11745685	—	4	2	no	—
155	C₂×D₂₃₆	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
163	C₂×Dic₁₁₈	—	2	1	no	—
164	C₂×Dic₁₁₈	—	2	1	no	—
165	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
166	SD₁₆×C₅₉	—	2	2	no	—
167	C₂×C₈×C₅₉	—	2	1	no	—
168	C₂×C₈×C₅₉	—	2	1	no	—
169	C₂×C₈×C₅₉	—	2	1	no	—
170	C₂×C₈×C₅₉	—	4	2	no	—
171	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₅₉	—	2	1	no	—
176	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
178	C₂²⋊C₄×C₅₉	—	2	1	no	—
179	C₄²×C₅₉	—	2	1	no	—
180	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
181	C₂²⋊Dic₅₉	—	2	1	no	—
182	#11745671	—	2	2	no	—
183	#11745670	—	2	2	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	C₄×Dic₅₉	—	2	1	no	—
194	C₄×Dic₅₉	—	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	#11745664	—	4	2	no	—
200	C₂×C₅₉⋊C₈	—	2	1	no	—
201	C₂×C₅₉⋊C₈	—	2	1	no	—
202	C₂×C₅₉⋊C₈	—	2	1	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	#11745659	—	4	2	no	—
210	C₈×D₅₉	—	2	2	no	—
211	C₈×D₅₉	—	4	2	no	—
212	C₈×D₅₉	—	4	2	no	—
213	C₈×D₅₉	SD₁₆	1	4	yes	complemented
214	C₂³×C₅₉	—	2	1	no	—
215	C₂²×D₅₉	—	2	1	no	—
216	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
217	Q₈×C₅₉	—	2	1	no	—
218	Q₈×C₅₉	#131	1	2	yes	complemented
219	D₄×C₅₉	—	2	1	no	—
220	D₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	1	no	—
222	C₂×C₄×C₅₉	—	2	1	no	—
223	C₂×C₄×C₅₉	—	2	1	no	—
224	C₂×C₄×C₅₉	—	4	1	no	—
225	C₂×C₄×C₅₉	—	4	1	no	—
226	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
229	C₂²⋊D₅₉	—	4	2	no	—
230	C₂²⋊D₅₉	—	4	2	no	—
231	C₂²⋊D₅₉	—	4	2	no	—
232	C₂×Dic₅₉	—	2	1	no	—
233	C₂×Dic₅₉	—	2	1	no	—
234	C₂×Dic₅₉	—	2	1	no	—
235	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
236	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
238	D₂₃₆	—	2	1	no	—
239	D₂₃₆	—	2	1	no	—
240	D₂₃₆	—	4	2	no	—
241	C₄×D₅₉	—	2	4	no	—
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	C₂×SD₁₆	1	2	yes	—
249	C₄×D₅₉	#135	1	2	yes	—
250	Dic₁₁₈	—	2	4	no	—
251	Dic₁₁₈	—	2	1	no	—
252	Dic₁₁₈	—	4	2	no	—
253	Dic₁₁₈	#131	1	2	yes	complemented
254	C₈×C₅₉	—	2	1	no	—
255	C₈×C₅₉	—	2	1	no	—
256	C₈×C₅₉	—	2	1	no	—
257	C₈×C₅₉	—	4	1	no	—
258	C₈×C₅₉	—	4	1	no	—
259	C₈×C₅₉	—	4	1	no	—
260	C₈×C₅₉	C₂×SD₁₆	1	2	yes	—
261	C₅₉⋊C₈	—	2	1	no	—
262	C₅₉⋊C₈	—	2	1	no	—
263	C₅₉⋊C₈	—	2	1	no	—
264	C₅₉⋊C₈	—	4	1	no	—
265	C₅₉⋊C₈	—	4	1	no	—
266	C₅₉⋊C₈	—	4	1	no	—
267	C₅₉⋊C₈	C₂×SD₁₆	1	2	yes	—
268	#17901	—	59	1	no	maximal, Sylow
269	C₂²×C₅₉	—	4	1	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	—	4	1	no	—
276	C₂×D₅₉	—	4	1	no	—
277	C₂×D₅₉	—	4	1	no	—
278	C₂×D₅₉	C₄×SD₁₆	1	2	yes	—
279	C₄×C₅₉	—	2	2	no	—
280	C₄×C₅₉	—	2	1	no	—
281	C₄×C₅₉	—	4	1	no	—
282	C₄×C₅₉	—	4	1	no	—
283	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
284	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
285	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
286	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
287	Dic₅₉	—	2	1	no	—
288	Dic₅₉	—	2	2	no	—
289	Dic₅₉	—	2	1	no	—
290	Dic₅₉	—	4	1	no	—
291	Dic₅₉	—	4	1	no	—
292	Dic₅₉	C₄×SD₁₆	1	2	yes	—
293	#3103	—	59	1	no	—
294	C₂×C₈×Q₈	—	59	1	no	—
295	#2931	—	59	1	no	—
296	#1583	—	59	1	no	—
297	#1583	—	59	1	no	—
298	#1583	—	59	1	no	—
299	#1583	—	59	1	no	—
300	C₈×SD₁₆	—	59	1	no	—
301	C₈×SD₁₆	—	59	1	no	—
302	C₈×SD₁₆	—	59	1	no	—
303	C₈×SD₁₆	D₅₉	1	1	yes	characteristic, complemented
304	#1570	—	59	1	no	—
305	#1487	—	59	1	no	—
306	#1480	—	59	1	no	—
307	#1450	—	59	1	no	—
308	C₂×C₅₉	—	8	1	no	—
309	C₂×C₅₉	#2929	1	1	yes	characteristic
310	C₂×C₅₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
311	C₂×C₅₉	#2955	1	1	yes	characteristic
312	D₅₉	—	2	2	no	—
313	D₅₉	—	8	1	no	—
314	C₂×#131	—	118	1	no	—
315	#532	—	59	1	no	—
316	C₂×C₄×Q₈	—	59	1	no	—
317	#481	—	59	1	no	—
318	#481	—	59	1	no	—
319	#475	—	59	1	no	—
320	#475	—	59	1	no	—
321	#460	—	59	1	no	—
322	#460	—	59	1	no	—
323	#448	—	59	1	no	—
324	#448	—	59	1	no	—
325	C₈×Q₈	—	59	1	no	—
326	C₈×Q₈	—	59	1	no	—
327	C₈×Q₈	—	59	1	no	—
328	C₈×Q₈	—	118	1	no	—
329	C₈×Q₈	—	118	1	no	—
330	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
331	C₄×SD₁₆	—	59	1	no	—
332	C₄×SD₁₆	—	59	1	no	—
333	C₄×SD₁₆	—	59	1	no	—
334	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
335	#436	—	59	1	no	—
336	#436	—	59	1	no	—
337	#436	—	118	1	no	—
338	C₈×D₄	—	59	1	no	—
339	C₈×D₄	—	118	1	no	—
340	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
341	#431	—	59	1	no	—
342	#431	—	59	1	no	—
343	#423	—	59	1	no	—
344	C₂×C₄⋊C₈	—	59	1	no	—
345	C₂×C₄⋊C₈	—	118	1	no	—
346	#408	—	118	1	no	—
347	C₂×C₄×C₈	—	59	1	no	—
348	C₂×C₄×C₈	—	118	1	no	—
349	#334	—	59	1	no	—
350	#334	—	59	1	no	—
351	#334	—	59	1	no	—
352	#334	C₂×D₅₉	1	1	yes	characteristic
353	Q₈⋊C₈	—	59	1	no	—
354	Q₈⋊C₈	—	59	1	no	—
355	Q₈⋊C₈	—	59	1	no	—
356	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
357	D₄⋊C₈	—	59	1	no	—
358	D₄⋊C₈	—	59	1	no	—
359	D₄⋊C₈	—	59	1	no	—
360	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
361	#322	—	59	1	no	—
362	#322	—	59	1	no	—
363	C₈²	—	59	1	no	—
364	C₈²	C₂×D₅₉	1	1	yes	characteristic
365	C₅₉	#17901	1	1	yes	characteristic, complemented, Sylow
366	C₂×#41	—	118	1	no	—
367	C₂²×Q₈	—	59	1	no	—
368	C₂×SD₁₆	—	59	1	no	—
369	C₂×SD₁₆	—	59	1	no	—
370	C₂×SD₁₆	—	59	1	no	—
371	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
372	#131	—	236	4	no	—
373	C₂×M₁₆	—	118	1	no	—
374	C₂×M₁₆	—	118	1	no	—
375	C₂×M₁₆	—	118	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	59	1	no	—
378	C₂²×C₈	—	59	1	no	—
379	C₂²×C₈	—	118	1	no	—
380	C₂²×C₈	—	118	1	no	—
381	C₄⋊Q₈	—	59	1	no	—
382	#127	—	59	1	no	—
383	#124	—	118	1	no	—
384	#121	—	59	1	no	—
385	#121	—	59	1	no	—
386	#121	—	118	1	no	—
387	C₄×Q₈	—	59	1	no	—
388	C₄×Q₈	—	59	1	no	—
389	C₄×Q₈	—	59	1	no	—
390	C₄×Q₈	—	118	1	no	—
391	C₄×Q₈	—	118	1	no	—
392	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
393	C₄×D₄	—	59	1	no	—
394	C₄×D₄	—	118	1	no	—
395	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	—	59	1	no	—
397	C₂×C₄⋊C₄	—	118	1	no	—
398	C₂×C₄²	—	59	1	no	—
399	C₂×C₄²	—	118	1	no	—
400	#106	—	59	1	no	—
401	#106	—	59	1	no	—
402	#106	—	59	1	no	—
403	#106	C₄×D₅₉	1	1	yes	characteristic
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	59	1	no	—
406	C₄⋊C₈	—	59	1	no	—
407	C₄⋊C₈	—	59	1	no	—
408	C₄⋊C₈	—	59	1	no	—
409	C₄⋊C₈	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
417	#103	—	59	1	no	—
418	#103	—	59	1	no	—
419	#103	—	59	1	no	—
420	#103	C₄×D₅₉	1	1	yes	characteristic
421	#102	—	59	1	no	—
422	#102	—	59	1	no	—
423	#102	—	59	1	no	—
424	#102	C₄×D₅₉	1	1	yes	characteristic
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	59	1	no	—
427	C₂²⋊C₈	—	59	1	no	—
428	C₂²⋊C₈	—	118	1	no	—
429	C₂²⋊C₈	—	118	1	no	—
430	C₂²⋊C₈	—	118	1	no	—
431	C₂²⋊C₈	—	118	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	—	59	1	no	—
434	C₄×C₈	—	59	1	no	—
435	C₄×C₈	—	59	1	no	—
436	C₄×C₈	—	59	1	no	—
437	C₄×C₈	—	59	1	no	—
438	C₄×C₈	—	118	1	no	—
439	C₄×C₈	—	118	1	no	—
440	C₄×C₈	—	118	1	no	—
441	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
442	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
443	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
444	#41	—	236	2	no	—
445	#41	—	236	2	no	—
446	C₂×Q₈	—	59	1	no	—
447	C₂×Q₈	—	118	1	no	—
448	C₂×Q₈	—	118	1	no	—
449	C₂×Q₈	—	118	2	no	—
450	C₂×Q₈	—	118	2	no	—
451	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
452	C₂×D₄	—	59	1	no	—
453	C₂×D₄	—	118	1	no	—
454	C₂×D₄	—	118	1	no	—
455	C₂×D₄	—	118	1	no	—
456	C₂×D₄	—	118	1	no	—
457	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	59	1	no	—
460	C₂²×C₄	—	59	1	no	—
461	C₂²×C₄	—	59	1	no	—
462	C₂²×C₄	—	118	1	no	—
463	C₂²×C₄	—	118	1	no	—
464	C₂²×C₄	—	118	1	no	—
465	SD₁₆	—	2	2	no	—
466	SD₁₆	—	118	2	no	—
467	SD₁₆	—	118	2	no	—
468	SD₁₆	—	118	2	no	—
469	M₁₆	—	236	2	no	—
470	M₁₆	—	236	2	no	—
471	M₁₆	—	236	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	4	2	no	—
476	C₂×C₈	—	59	1	no	—
477	C₂×C₈	—	59	4	no	—
478	C₂×C₈	—	59	1	no	—
479	C₂×C₈	—	59	1	no	—
480	C₂×C₈	—	59	1	no	—
481	C₂×C₈	—	118	2	no	—
482	C₂×C₈	—	118	1	no	—
483	C₂×C₈	—	118	1	no	—
484	C₂×C₈	—	118	1	no	—
485	C₂×C₈	—	236	2	no	—
486	C₂×C₈	—	236	2	no	—
487	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
488	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
489	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
490	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	59	1	no	—
493	C₄⋊C₄	—	59	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	C₂×C₄×D₅₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	118	1	no	—
503	C₂²⋊C₄	—	118	1	no	—
504	C₂²⋊C₄	—	118	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	59	1	no	—
507	C₄²	—	59	1	no	—
508	C₄²	—	59	1	no	—
509	C₄²	—	118	1	no	—
510	C₄²	—	118	1	no	—
511	C₄²	—	118	1	no	—
512	C₄²	C₂³×D₅₉	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	59	1	no	—
515	C₂³	—	118	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	59	2	no	—
518	Q₈	—	118	4	no	—
519	Q₈	—	118	1	no	—
520	Q₈	—	236	2	no	—
521	Q₈	#14273733	1	2	yes	complemented
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	118	1	no	—
525	D₄	—	118	1	no	—
526	D₄	—	236	2	no	—
527	D₄	—	236	2	no	—
528	D₄	—	236	2	no	—
529	D₄	—	236	2	no	—
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	4	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	—	118	1	no	—
546	C₂×C₄	—	236	1	no	—
547	C₂×C₄	—	236	2	no	—
548	C₂×C₄	—	236	1	no	—
549	C₂×C₄	—	236	1	no	—
550	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
552	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	59	2	no	—
560	C₈	—	118	1	no	—
561	C₈	—	118	1	no	—
562	C₈	—	118	1	no	—
563	C₈	—	236	1	no	—
564	C₈	—	236	1	no	—
565	C₈	—	236	1	no	—
566	C₈	SD₁₆×D₅₉	1	2	yes	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	59	2	no	—
571	C₂²	—	118	1	no	—
572	C₂²	—	118	1	no	—
573	C₂²	—	236	1	no	—
574	C₂²	—	236	1	no	—
575	C₂²	—	236	1	no	—
576	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	59	2	no	—
582	C₄	—	118	1	no	—
583	C₄	—	118	1	no	—
584	C₄	—	118	2	no	—
585	C₄	—	236	1	no	—
586	C₄	—	236	1	no	—
587	C₄	#131×D₅₉	1	1	yes	characteristic
588	C₄	C₂×#14273733	1	1	yes	characteristic
589	C₄	C₂×SD₁₆×D₅₉	1	1	yes	characteristic
590	C₄	#135×D₅₉	1	1	yes	characteristic
591	C₂	—	8	1	no	—
592	C₂	—	118	2	no	—
593	C₂	—	472	1	no	—
594	C₂	#21432785	1	1	yes	characteristic
595	C₂	C₄×SD₁₆×D₅₉	1	1	yes	characteristic
596	C₂	#21432994	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₈×SD₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#16837949	C₂²
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₈×SD₁₆	D₅₉
hypocenter	C₅₉	#17901
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₈×Q₈×D₅₉	C₂	semidirect
4. #21422942	C₂	semidirect
5. #21422940	C₂	semidirect
6. #21422938	C₂	semidirect
7. #21422936	C₂	semidirect
8. C₈×#11745660	C₂	semidirect
9. C₈×#11745671	C₂	semidirect
10. C₈×#11745670	C₂	semidirect
11. #21422865	C₂	semidirect
12. #21422523	C₂	semidirect
14. #21422378	C₂	semidirect
15. C₈×SD₁₆×C₅₉	C₂	semidirect
213. C₈×D₅₉	SD₁₆	semidirect
218. Q₈×C₅₉	#131	semidirect
253. Dic₁₁₈	#131	semidirect
303. C₈×SD₁₆	D₅₉	semidirect
365. C₅₉	#17901	semidirect
521. Q₈	#14273733	semidirect

Maximal subgroups

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

subgroup	index
#21434125	2
C₈×Q₈×D₅₉	2
#21432803	2
#21422942	2
#21422940	2
#21422938	2
#21422936	2
C₈×#11745660	2
C₈×#11745671	2
C₈×#11745670	2
#21422865	2
#21422523	2
#21422493	2
#21422378	2
C₈×SD₁₆×C₅₉	2
#17901	59