Subgroups — #28558151

Order 15104.

730 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433175	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433117	C₂	1	1	yes	maximal, characteristic
3	C₄×SD₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21422910	C₂	1	1	yes	maximal, characteristic, complemented
5	SD₁₆⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422907	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422899	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#11745671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11745670	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422893	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422843	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422489	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422485	C₂	1	1	yes	maximal, characteristic
14	#21422381	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×SD₁₆×D₅₉	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₅₉	C₂²	1	1	yes	characteristic
19	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	C₈×Dic₁₁₈	—	2	1	no	—
21	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic, complemented
22	#16837526	—	2	1	no	—
23	#16837526	C₂²	1	1	yes	characteristic, complemented
24	#16837493	C₄	1	1	yes	characteristic
25	C₄×#11745660	C₂²	1	1	yes	characteristic
26	SD₁₆×Dic₅₉	C₄	1	1	yes	characteristic
27	C₄×#11745671	C₂²	1	1	yes	characteristic
28	#16837489	C₄	1	1	yes	characteristic
29	C₄×#11745670	C₂²	1	1	yes	characteristic
30	#16837487	C₄	1	1	yes	characteristic
31	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
32	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
33	#16837467	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₅₉	—	2	1	no	—
35	(C₂²⋊D₅₉)⋊C₈	—	2	1	no	—
36	#16837454	—	2	1	no	—
37	#16837454	C₂²	1	1	yes	characteristic
38	#16837454	C₂²	1	1	yes	characteristic
39	#16837453	—	2	1	no	—
40	#16837453	C₂²	1	1	yes	characteristic
41	#16837453	C₂²	1	1	yes	characteristic
42	#106×D₅₉	C₄	1	1	yes	characteristic
43	#103×D₅₉	C₄	1	1	yes	characteristic
44	#102×D₅₉	C₄	1	1	yes	characteristic
45	C₂×(C₂×D₅₉)⋊C₈	—	2	1	no	—
46	C₂²⋊C₈×D₅₉	—	2	1	no	—
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837155	C₂²	1	1	yes	characteristic, complemented
49	#16837152	C₂²	1	1	yes	characteristic, complemented
50	#16837152	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	#16837123	C₂²	1	1	yes	characteristic, complemented
58	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₈×C₅₉⋊C₈	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×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	C₈	1	8	yes	complemented
74	C₂²×C₅₉⋊C₈	—	2	1	no	—
75	C₂×C₈×D₅₉	—	2	1	no	—
76	C₂×C₈×D₅₉	—	2	1	no	—
77	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
79	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₁₈	—	2	1	no	—
81	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
82	#14273692	—	2	1	no	—
83	#14273692	C₂×C₄	1	1	yes	characteristic
84	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
85	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
86	#14273689	C₂×C₄	1	1	yes	characteristic
87	C₄×C₂²⋊D₅₉	—	2	1	no	—
88	(C₂²⋊D₅₉)⋊C₄	—	2	1	no	—
89	C₄⋊C₄×D₅₉	—	2	1	no	—
90	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
91	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊C₄×D₅₉	—	2	1	no	—
93	C₄²×D₅₉	—	2	1	no	—
94	C₄²×D₅₉	C₂³	1	1	yes	characteristic
95	#14273659	C₂×C₄	1	1	yes	characteristic
96	#14273658	C₂×C₄	1	1	yes	characteristic
97	#14273658	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
99	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
100	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
101	Dic₅₉⋊C₈	—	2	1	no	—
102	Dic₅₉⋊C₈	—	2	1	no	—
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
105	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
106	#14273652	C₂×C₄	1	1	yes	characteristic
107	#14273651	C₂×C₄	1	1	yes	characteristic
108	#14273650	C₂×C₄	1	1	yes	characteristic
109	#14273649	C₂×C₄	1	1	yes	characteristic
110	#14273648	C₂×C₄	1	1	yes	characteristic
111	#14273647	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
113	(C₂×D₅₉)⋊C₈	—	2	1	no	—
114	(C₂×D₅₉)⋊C₈	—	2	1	no	—
115	(C₂×D₅₉)⋊C₈	—	2	1	no	—
116	(C₂×D₅₉)⋊C₈	—	2	1	no	—
117	(C₂×D₅₉)⋊C₈	—	2	1	no	—
118	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
119	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
120	C₄×C₅₉⋊C₈	—	2	1	no	—
121	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₈×Dic₅₉	—	2	1	no	—
125	C₈×Dic₅₉	—	2	1	no	—
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	—	2	1	no	—
128	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₅₉	C₂×C₄	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	Q₈×D₅₉	—	2	2	no	—
152	Q₈×D₅₉	C₂×C₈	1	4	yes	complemented
153	D₄×D₅₉	—	2	2	no	—
154	D₄×D₅₉	C₂×C₈	1	4	yes	—
155	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₅₉	—	2	1	no	—
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	—	8	1	no	—
162	C₂×C₄×D₅₉	—	8	1	no	—
163	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
166	C₂×Dic₁₁₈	—	2	1	no	—
167	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
168	SD₁₆×C₅₉	C₂×C₈	1	4	yes	complemented
169	C₂×C₈×C₅₉	—	2	1	no	—
170	C₂×C₈×C₅₉	—	2	1	no	—
171	C₂×C₈×C₅₉	—	2	1	no	—
172	C₂×C₈×C₅₉	—	8	1	no	—
173	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₄⋊C₄×C₅₉	—	2	1	no	—
178	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
180	C₂²⋊C₄×C₅₉	—	2	1	no	—
181	C₄²×C₅₉	—	2	1	no	—
182	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
183	C₂²⋊Dic₅₉	—	2	1	no	—
184	#11745671	C₂×C₈	1	4	yes	complemented
185	#11745670	C₂×C₈	1	4	yes	complemented
186	(C₂×D₅₉)⋊C₄	—	2	1	no	—
187	(C₂×D₅₉)⋊C₄	—	2	1	no	—
188	C₄⋊Dic₅₉	—	2	1	no	—
189	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
197	C₄×Dic₅₉	—	2	1	no	—
198	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
200	C₄×Dic₅₉	#41	1	1	yes	characteristic
201	C₂×C₅₉⋊C₈	—	2	1	no	—
202	C₂×C₅₉⋊C₈	—	2	1	no	—
203	C₂×C₅₉⋊C₈	—	2	1	no	—
204	C₂×C₅₉⋊C₈	—	8	1	no	—
205	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
209	#11745660	C₂×C₈	1	4	yes	complemented
210	C₈×D₅₉	—	2	2	no	—
211	C₈×D₅₉	—	8	1	no	—
212	C₈×D₅₉	—	8	1	no	—
213	C₈×D₅₉	C₂×C₈	1	4	yes	complemented
214	C₂³×C₅₉	—	2	1	no	—
215	C₂²×D₅₉	—	2	1	no	—
216	C₂²×D₅₉	—	2	4	no	—
217	C₂²×D₅₉	—	8	1	no	—
218	C₂²×D₅₉	—	8	1	no	—
219	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
220	Q₈×C₅₉	—	2	1	no	—
221	Q₈×C₅₉	C₂²×C₈	1	2	yes	—
222	D₄×C₅₉	—	2	1	no	—
223	D₄×C₅₉	C₂²×C₈	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	—	8	1	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	C₂²×C₈	1	2	yes	—
242	C₄×D₅₉	—	2	4	no	—
243	C₄×D₅₉	—	2	1	no	—
244	C₄×D₅₉	—	2	1	no	—
245	C₄×D₅₉	—	4	1	no	—
246	C₄×D₅₉	—	4	1	no	—
247	C₄×D₅₉	—	4	1	no	—
248	C₄×D₅₉	—	8	1	no	—
249	C₄×D₅₉	—	8	1	no	—
250	C₄×D₅₉	—	8	1	no	—
251	C₄×D₅₉	C₂²×C₈	1	2	yes	—
252	C₄×D₅₉	#131	1	2	yes	—
253	Dic₁₁₈	—	2	1	no	—
254	Dic₁₁₈	—	2	4	no	—
255	Dic₁₁₈	C₂²×C₈	1	2	yes	—
256	C₈×C₅₉	—	2	1	no	—
257	C₈×C₅₉	—	2	1	no	—
258	C₈×C₅₉	—	2	1	no	—
259	C₈×C₅₉	—	4	1	no	—
260	C₈×C₅₉	—	4	1	no	—
261	C₈×C₅₉	—	4	1	no	—
262	C₈×C₅₉	C₂²×C₈	1	2	yes	—
263	C₅₉⋊C₈	—	2	1	no	—
264	C₅₉⋊C₈	—	2	1	no	—
265	C₅₉⋊C₈	—	2	1	no	—
266	C₅₉⋊C₈	—	4	1	no	—
267	C₅₉⋊C₈	—	4	1	no	—
268	C₅₉⋊C₈	—	4	1	no	—
269	C₅₉⋊C₈	C₂²×C₈	1	2	yes	—
270	#17855	—	59	1	no	maximal, Sylow
271	C₂²×C₅₉	—	2	2	no	—
272	C₂²×C₅₉	—	4	1	no	—
273	C₂²×C₅₉	—	4	1	no	—
274	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
275	C₂×D₅₉	—	2	1	no	—
276	C₂×D₅₉	—	2	1	no	—
277	C₂×D₅₉	—	2	2	no	—
278	C₂×D₅₉	—	4	1	no	—
279	C₂×D₅₉	—	4	1	no	—
280	C₂×D₅₉	—	8	4	no	—
281	C₂×D₅₉	C₈×D₄	1	2	yes	—
282	C₄×C₅₉	—	2	2	no	—
283	C₄×C₅₉	—	2	1	no	—
284	C₄×C₅₉	—	4	1	no	—
285	C₄×C₅₉	—	4	1	no	—
286	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
287	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
288	C₄×C₅₉	#577	1	1	yes	characteristic
289	C₄×C₅₉	#577	1	1	yes	characteristic
290	Dic₅₉	—	2	2	no	—
291	Dic₅₉	—	2	1	no	—
292	Dic₅₉	—	2	1	no	—
293	Dic₅₉	—	4	1	no	—
294	Dic₅₉	—	4	1	no	—
295	Dic₅₉	C₈×D₄	1	2	yes	—
296	#2982	—	59	1	no	—
297	#2972	—	59	1	no	—
298	C₂×C₄×SD₁₆	—	59	1	no	—
299	SD₁₆⋊C₈	—	59	1	no	—
300	SD₁₆⋊C₈	—	59	1	no	—
301	SD₁₆⋊C₈	—	59	1	no	—
302	SD₁₆⋊C₈	D₅₉	1	1	yes	characteristic, complemented
303	C₈×SD₁₆	—	59	1	no	—
304	C₈×SD₁₆	—	59	1	no	—
305	C₈×SD₁₆	—	59	1	no	—
306	C₈×SD₁₆	—	59	1	no	—
307	#1564	—	59	1	no	—
308	#1479	—	59	1	no	—
309	#1478	—	59	1	no	—
310	#1450	—	59	1	no	—
311	C₂×C₅₉	—	4	2	no	—
312	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
313	C₂×C₅₉	#2949	1	1	yes	characteristic
314	C₂×C₅₉	#2957	1	1	yes	characteristic
315	D₅₉	—	2	2	no	—
316	D₅₉	—	4	2	no	—
317	C₂²×SD₁₆	—	59	1	no	—
318	C₂×C₄×Q₈	—	59	1	no	—
319	C₂×C₄×D₄	—	59	1	no	—
320	C₈×Q₈	—	59	1	no	—
321	C₈×Q₈	—	59	1	no	—
322	C₈×Q₈	—	59	1	no	—
323	C₈×Q₈	—	118	1	no	—
324	C₈×Q₈	—	118	1	no	—
325	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
326	C₄×SD₁₆	—	59	1	no	—
327	C₄×SD₁₆	—	59	1	no	—
328	C₄×SD₁₆	—	59	1	no	—
329	C₄×SD₁₆	—	59	1	no	—
330	C₄×SD₁₆	—	59	1	no	—
331	C₄×SD₁₆	—	59	1	no	—
332	C₄×SD₁₆	—	59	1	no	—
333	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
334	C₈×D₄	—	59	1	no	—
335	C₈×D₄	—	59	1	no	—
336	C₈×D₄	—	59	1	no	—
337	C₈×D₄	—	118	1	no	—
338	C₈×D₄	—	118	1	no	—
339	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
340	#431	—	59	1	no	—
341	#431	—	59	1	no	—
342	#431	—	59	1	no	—
343	#431	—	59	1	no	—
344	#431	—	118	1	no	—
345	#431	—	118	1	no	—
346	C₂×#106	—	59	1	no	—
347	C₂×#103	—	59	1	no	—
348	C₂×#102	—	59	1	no	—
349	C₂×C₂²⋊C₈	—	118	1	no	—
350	C₂×C₂²⋊C₈	—	118	1	no	—
351	C₂×C₄×C₈	—	59	1	no	—
352	#335	—	59	1	no	—
353	#335	C₂×D₅₉	1	1	yes	characteristic, complemented
354	#334	—	59	1	no	—
355	#334	—	59	1	no	—
356	Q₈⋊C₈	—	59	1	no	—
357	Q₈⋊C₈	—	59	1	no	—
358	Q₈⋊C₈	—	59	1	no	—
359	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic, complemented
360	D₄⋊C₈	—	59	1	no	—
361	D₄⋊C₈	—	59	1	no	—
362	D₄⋊C₈	—	59	1	no	—
363	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
364	#322	—	59	1	no	—
365	#322	C₂×D₅₉	1	1	yes	characteristic, complemented
366	C₈²	—	59	1	no	—
367	C₈²	—	59	1	no	—
368	C₅₉	#17855	1	1	yes	characteristic, complemented, Sylow
369	C₂²×Q₈	—	59	1	no	—
370	C₂²×D₄	—	59	1	no	—
371	C₂³×C₄	—	118	1	no	—
372	C₂×SD₁₆	—	59	1	no	—
373	C₂×SD₁₆	—	59	1	no	—
374	C₂×SD₁₆	—	59	8	no	—
375	C₂×SD₁₆	—	59	1	no	—
376	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	59	1	no	—
379	C₂²×C₈	—	59	1	no	—
380	C₂²×C₈	—	118	1	no	—
381	C₂²×C₈	—	118	1	no	—
382	C₂²×C₈	—	118	1	no	—
383	C₄×Q₈	—	59	1	no	—
384	C₄×Q₈	—	59	1	no	—
385	C₄×Q₈	—	59	1	no	—
386	C₄×Q₈	—	118	1	no	—
387	C₄×Q₈	—	118	1	no	—
388	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
389	C₄×D₄	—	59	1	no	—
390	C₄×D₄	—	59	1	no	—
391	C₄×D₄	—	59	1	no	—
392	C₄×D₄	—	118	1	no	—
393	C₄×D₄	—	118	1	no	—
394	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	59	1	no	—
396	C₂×C₄⋊C₄	—	59	1	no	—
397	C₂×C₄⋊C₄	—	118	1	no	—
398	C₂×C₂²⋊C₄	—	118	1	no	—
399	C₂×C₄²	—	59	1	no	—
400	C₂×C₄²	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
416	#103	—	59	1	no	—
417	#103	—	59	1	no	—
418	#103	—	59	1	no	—
419	#103	C₄×D₅₉	1	1	yes	characteristic
420	#102	—	59	1	no	—
421	#102	—	59	1	no	—
422	#102	—	59	1	no	—
423	#102	C₄×D₅₉	1	1	yes	characteristic
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	59	1	no	—
426	C₂²⋊C₈	—	59	1	no	—
427	C₂²⋊C₈	—	118	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	C₂²⋊C₈	—	118	1	no	—
433	C₄×C₈	—	2	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	—	59	1	no	—
439	C₄×C₈	—	118	1	no	—
440	C₄×C₈	—	118	1	no	—
441	C₄×C₈	—	118	1	no	—
442	C₄×C₈	—	118	1	no	—
443	C₄×C₈	—	118	1	no	—
444	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
445	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
446	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
447	C₂⁴	—	118	1	no	—
448	C₂×Q₈	—	59	4	no	—
449	C₂×Q₈	—	59	1	no	—
450	C₂×Q₈	—	118	1	no	—
451	C₂×Q₈	—	118	2	no	—
452	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
453	C₂×D₄	—	59	4	no	—
454	C₂×D₄	—	59	1	no	—
455	C₂×D₄	—	118	2	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	C₂²×C₄	—	118	1	no	—
466	C₂²×C₄	—	118	1	no	—
467	C₂²×C₄	—	118	1	no	—
468	C₂²×C₄	—	472	1	no	—
469	C₂²×C₄	—	472	1	no	—
470	SD₁₆	—	59	4	no	—
471	SD₁₆	—	59	4	no	—
472	SD₁₆	—	59	4	no	—
473	SD₁₆	C₈×D₅₉	1	4	yes	complemented
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	8	1	no	—
478	C₂×C₈	—	59	1	no	—
479	C₂×C₈	—	59	4	no	—
480	C₂×C₈	—	59	1	no	—
481	C₂×C₈	—	59	1	no	—
482	C₂×C₈	—	59	1	no	—
483	C₂×C₈	—	118	2	no	—
484	C₂×C₈	—	118	1	no	—
485	C₂×C₈	—	118	1	no	—
486	C₂×C₈	—	118	1	no	—
487	C₂×C₈	—	472	1	no	—
488	C₂×C₈	—	472	1	no	—
489	C₂×C₈	—	472	1	no	—
490	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
491	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
492	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
493	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	59	1	no	—
496	C₄⋊C₄	—	59	1	no	—
497	C₄⋊C₄	—	118	1	no	—
498	C₄⋊C₄	—	118	1	no	—
499	C₄⋊C₄	—	118	1	no	—
500	C₄⋊C₄	—	118	1	no	—
501	C₄⋊C₄	—	118	1	no	—
502	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
504	C₂²⋊C₄	—	2	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	—	118	1	no	—
514	C₄²	—	118	1	no	—
515	C₄²	C₂³×D₅₉	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	—	59	1	no	—
518	C₂³	—	118	4	no	—
519	C₂³	—	118	1	no	—
520	C₂³	—	472	1	no	—
521	C₂³	—	472	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	59	2	no	—
524	Q₈	—	118	4	no	—
525	Q₈	—	118	1	no	—
526	Q₈	C₂×C₈×D₅₉	1	2	yes	—
527	D₄	—	2	1	no	—
528	D₄	—	59	2	no	—
529	D₄	—	118	4	no	—
530	D₄	—	118	1	no	—
531	D₄	C₂×C₈×D₅₉	1	2	yes	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	59	1	no	—
538	C₂×C₄	—	59	2	no	—
539	C₂×C₄	—	59	2	no	—
540	C₂×C₄	—	59	1	no	—
541	C₂×C₄	—	59	1	no	—
542	C₂×C₄	—	118	4	no	—
543	C₂×C₄	—	118	1	no	—
544	C₂×C₄	—	118	1	no	—
545	C₂×C₄	—	118	1	no	—
546	C₂×C₄	—	118	1	no	—
547	C₂×C₄	—	118	1	no	—
548	C₂×C₄	—	472	1	no	—
549	C₂×C₄	—	472	1	no	—
550	C₂×C₄	—	472	1	no	—
551	C₂×C₄	—	472	1	no	—
552	C₂×C₄	—	236	1	no	—
553	C₂×C₄	—	236	1	no	—
554	C₂×C₄	—	236	1	no	—
555	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
556	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
557	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	59	2	no	—
565	C₈	—	118	1	no	—
566	C₈	—	118	1	no	—
567	C₈	—	118	1	no	—
568	C₈	—	236	1	no	—
569	C₈	—	236	1	no	—
570	C₈	—	236	1	no	—
571	C₈	C₂×C₈×D₅₉	1	2	yes	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	59	2	no	—
576	C₂²	—	118	1	no	—
577	C₂²	—	118	1	no	—
578	C₂²	—	118	2	no	—
579	C₂²	—	472	4	no	—
580	C₂²	—	236	1	no	—
581	C₂²	—	236	1	no	—
582	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	59	2	no	—
588	C₄	—	118	1	no	—
589	C₄	—	118	1	no	—
590	C₄	—	118	2	no	—
591	C₄	—	236	1	no	—
592	C₄	—	236	1	no	—
593	C₄	C₂²×C₈×D₅₉	1	1	yes	characteristic
594	C₄	#131×D₅₉	1	1	yes	characteristic
595	C₄	#16838211	1	1	yes	characteristic
596	C₄	#16838212	1	1	yes	characteristic
597	C₂	—	4	2	no	—
598	C₂	—	118	2	no	—
599	C₂	—	236	2	no	—
600	C₂	C₈×D₄×D₅₉	1	1	yes	characteristic
601	C₂	#21432952	1	1	yes	characteristic
602	C₂	#21433010	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₄×C₅₉	C₂³×C₈
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	#17855
LCS	G ▷ 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
1. #21433175	C₂	semidirect
4. #21422910	C₂	semidirect
5. SD₁₆⋊(C₅₉⋊C₈)	C₂	semidirect
6. #21422907	C₂	semidirect
7. #21422899	C₂	semidirect
8. C₈×#11745671	C₂	semidirect
9. C₈×#11745670	C₂	semidirect
10. #21422893	C₂	semidirect
11. #21422843	C₂	semidirect
12. #21422489	C₂	semidirect
14. #21422381	C₂	semidirect
15. C₅₉×SD₁₆⋊C₈	C₂	semidirect
19. Q₈×C₅₉⋊C₈	C₂²	semidirect
21. C₈×Dic₁₁₈	C₂²	semidirect
23. #16837526	C₂²	semidirect
48. #16837155	C₂²	semidirect
49. #16837152	C₂²	semidirect
50. #16837152	C₂²	semidirect
51. #16837134	C₂²	semidirect
52. Q₈⋊(C₅₉⋊C₈)	C₂²	semidirect
53. #16837132	C₂²	semidirect
57. #16837123	C₂²	semidirect
58. C₈×C₅₉⋊C₈	C₂²	semidirect
59. C₈×C₅₉⋊C₈	C₂²	semidirect
60. C₈×Q₈×C₅₉	C₂²	semidirect
63. C₅₉×#335	C₂²	semidirect
64. C₅₉×Q₈⋊C₈	C₂²	semidirect
66. C₅₉×#322	C₂²	semidirect
73. SD₁₆×D₅₉	C₈	semidirect
152. Q₈×D₅₉	C₂×C₈	semidirect
168. SD₁₆×C₅₉	C₂×C₈	semidirect
184. #11745671	C₂×C₈	semidirect
185. #11745670	C₂×C₈	semidirect
209. #11745660	C₂×C₈	semidirect
213. C₈×D₅₉	C₂×C₈	semidirect
302. SD₁₆⋊C₈	D₅₉	semidirect
325. C₈×Q₈	C₂×D₅₉	semidirect
353. #335	C₂×D₅₉	semidirect
359. Q₈⋊C₈	C₂×D₅₉	semidirect
365. #322	C₂×D₅₉	semidirect
368. C₅₉	#17855	semidirect
473. SD₁₆	C₈×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21433175	2
#21433117	2
C₄×SD₁₆×D₅₉	2
#21422910	2
SD₁₆⋊(C₅₉⋊C₈)	2
#21422907	2
#21422899	2
C₈×#11745671	2
C₈×#11745670	2
#21422893	2
#21422843	2
#21422489	2
#21422485	2
#21422381	2
C₅₉×SD₁₆⋊C₈	2
#17855	59