Subgroups — #28558155

Order 15104.

730 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433177	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433120	C₂	1	1	yes	maximal, characteristic
3	SD₁₆⋊(C₅₉⋊C₈)	C₂	1	4	yes	maximal, complemented
4	SD₁₆×C₅₉⋊C₈	C₂	1	4	yes	maximal, complemented
5	#21422844	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422491	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422487	C₂	1	1	yes	maximal, characteristic
8	#21422379	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
10	Q₈×C₅₉⋊C₈	—	2	2	no	—
11	Q₈×C₅₉⋊C₈	C₂²	1	4	yes	complemented
12	D₄×C₅₉⋊C₈	—	2	2	no	—
13	D₄×C₅₉⋊C₈	C₂²	1	4	yes	—
14	#16837455	—	2	2	no	—
15	#16837455	C₂²	1	1	yes	characteristic
16	#16837455	C₂²	1	1	yes	characteristic
17	#16837455	C₂²	1	1	yes	characteristic
18	#16837455	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
20	#16837155	C₂²	1	2	yes	complemented
21	#16837153	C₂²	1	2	yes	complemented
22	Q₈⋊(C₅₉⋊C₈)	C₂²	1	4	yes	complemented
23	D₄⋊(C₅₉⋊C₈)	C₂²	1	4	yes	—
24	#16837123	C₂²	1	2	yes	complemented
25	C₈×C₅₉⋊C₈	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₅₉	C₄	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₄×SD₁₆×C₅₉	C₄	1	2	yes	—
30	C₄×SD₁₆×C₅₉	C₄	1	2	yes	—
31	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
32	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
33	C₂×#106×C₅₉	C₄	1	1	yes	characteristic
34	C₂×#103×C₅₉	C₄	1	1	yes	characteristic
35	C₂×#102×C₅₉	C₄	1	1	yes	characteristic
36	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₂²×C₅₉⋊C₈	—	2	4	no	—
38	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
40	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
41	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
42	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
43	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
44	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
45	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
46	C₂²⋊(C₅₉⋊C₈)	—	2	4	no	—
47	C₂²⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
48	C₄×C₅₉⋊C₈	—	2	1	no	—
49	C₄×C₅₉⋊C₈	—	2	1	no	—
50	C₄×C₅₉⋊C₈	—	2	4	no	—
51	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
52	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
53	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₅₉	—	2	1	no	—
56	C₂×SD₁₆×C₅₉	C₈	1	8	yes	complemented
57	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
58	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₅₉	—	2	1	no	—
62	C₄×Q₈×C₅₉	—	2	1	no	—
63	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
65	C₄×D₄×C₅₉	—	2	1	no	—
66	C₄×D₄×C₅₉	—	2	1	no	—
67	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₅₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
75	#106×C₅₉	C₂×C₄	1	2	yes	—
76	#106×C₅₉	C₂×C₄	1	2	yes	—
77	#103×C₅₉	C₂×C₄	1	2	yes	—
78	#103×C₅₉	C₂×C₄	1	2	yes	—
79	#102×C₅₉	C₂×C₄	1	2	yes	—
80	#102×C₅₉	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
85	C₂⁴×C₅₉	—	2	1	no	—
86	C₂×Q₈×C₅₉	—	2	1	no	—
87	C₂×Q₈×C₅₉	—	2	2	no	—
88	C₂×Q₈×C₅₉	C₂×C₈	1	4	yes	complemented
89	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₅₉	—	2	1	no	—
91	C₂×D₄×C₅₉	—	2	2	no	—
92	C₂×D₄×C₅₉	C₂×C₈	1	4	yes	—
93	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅₉	—	2	1	no	—
95	C₂²×C₄×C₅₉	—	2	1	no	—
96	C₂²×C₄×C₅₉	—	2	1	no	—
97	C₂²×C₄×C₅₉	—	2	2	no	—
98	C₂²×C₄×C₅₉	—	2	2	no	—
99	C₂²×C₄×C₅₉	—	8	2	no	—
100	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
103	SD₁₆×C₅₉	C₂×C₈	1	8	yes	complemented
104	SD₁₆×C₅₉	C₂×C₈	1	8	yes	complemented
105	C₂×C₈×C₅₉	—	2	2	no	—
106	C₂×C₈×C₅₉	C₂×C₈	1	4	yes	complemented
107	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
111	C₄⋊C₄×C₅₉	—	2	2	no	—
112	C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₄⋊C₄×C₅₉	—	2	1	no	—
114	C₄⋊C₄×C₅₉	—	2	2	no	—
115	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
116	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
117	C₂²⋊C₄×C₅₉	—	2	2	no	—
118	C₂²⋊C₄×C₅₉	—	2	2	no	—
119	C₄²×C₅₉	—	2	2	no	—
120	C₄²×C₅₉	—	2	2	no	—
121	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₅₉	#41	1	1	yes	characteristic
124	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
125	C₂×C₅₉⋊C₈	—	2	2	no	—
126	C₂×C₅₉⋊C₈	—	2	2	no	—
127	C₂×C₅₉⋊C₈	—	2	2	no	—
128	C₂×C₅₉⋊C₈	—	8	4	no	—
129	C₂×C₅₉⋊C₈	C₂×D₄	1	4	yes	—
130	C₂³×C₅₉	—	2	2	no	—
131	C₂³×C₅₉	—	2	4	no	—
132	C₂³×C₅₉	—	8	1	no	—
133	C₂³×C₅₉	—	8	1	no	—
134	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
135	Q₈×C₅₉	—	2	2	no	—
136	Q₈×C₅₉	—	2	4	no	—
137	Q₈×C₅₉	C₂²×C₈	1	4	yes	—
138	D₄×C₅₉	—	2	2	no	—
139	D₄×C₅₉	—	2	4	no	—
140	D₄×C₅₉	C₂²×C₈	1	4	yes	—
141	C₂×C₄×C₅₉	—	2	2	no	—
142	C₂×C₄×C₅₉	—	2	4	no	—
143	C₂×C₄×C₅₉	—	2	2	no	—
144	C₂×C₄×C₅₉	—	2	2	no	—
145	C₂×C₄×C₅₉	—	2	2	no	—
146	C₂×C₄×C₅₉	—	4	1	no	—
147	C₂×C₄×C₅₉	—	4	4	no	—
148	C₂×C₄×C₅₉	—	8	2	no	—
149	C₂×C₄×C₅₉	—	8	1	no	—
150	C₂×C₄×C₅₉	—	8	1	no	—
151	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₅₉	#131	1	2	yes	—
156	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
159	C₈×C₅₉	—	2	1	no	—
160	C₈×C₅₉	—	2	1	no	—
161	C₈×C₅₉	C₂²×C₈	1	2	yes	—
162	C₈×C₅₉	C₂²×C₈	1	2	yes	—
163	C₅₉⋊C₈	—	2	4	no	—
164	C₅₉⋊C₈	—	4	2	no	—
165	C₅₉⋊C₈	—	4	2	no	—
166	C₅₉⋊C₈	—	4	2	no	—
167	#17855	—	59	1	no	maximal, Sylow
168	C₂²×C₅₉	—	2	1	no	—
169	C₂²×C₅₉	—	2	1	no	—
170	C₂²×C₅₉	—	2	4	no	—
171	C₂²×C₅₉	—	4	2	no	—
172	C₂²×C₅₉	—	4	2	no	—
173	C₂²×C₅₉	—	8	4	no	—
174	C₂²×C₅₉	C₈×D₄	1	2	yes	—
175	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
176	C₄×C₅₉	—	2	4	no	—
177	C₄×C₅₉	—	2	1	no	—
178	C₄×C₅₉	—	2	1	no	—
179	C₄×C₅₉	—	2	1	no	—
180	C₄×C₅₉	—	4	2	no	—
181	C₄×C₅₉	—	4	2	no	—
182	C₄×C₅₉	C₈×D₄	1	2	yes	—
183	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
184	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
185	C₄×C₅₉	#577	1	2	yes	—
186	#2982	—	59	1	no	—
187	#2972	—	59	1	no	—
188	C₂×C₄×SD₁₆	D₅₉	1	1	yes	characteristic
189	SD₁₆⋊C₈	—	59	4	no	—
190	C₈×SD₁₆	—	59	4	no	—
191	#1564	—	59	1	no	—
192	#1479	—	59	1	no	—
193	#1478	—	59	1	no	—
194	#1450	—	59	1	no	—
195	C₂×C₅₉	—	2	2	no	—
196	C₂×C₅₉	—	4	4	no	—
197	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
198	C₂×C₅₉	#2949	1	1	yes	characteristic
199	C₂×C₅₉	#2957	1	1	yes	characteristic
200	C₂²×SD₁₆	Dic₅₉	1	1	yes	characteristic
201	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
203	C₈×Q₈	—	59	4	no	—
204	C₈×Q₈	—	118	2	no	—
205	C₄×SD₁₆	Dic₅₉	1	2	yes	—
206	C₄×SD₁₆	Dic₅₉	1	2	yes	—
207	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
208	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
209	C₈×D₄	—	59	4	no	—
210	C₈×D₄	—	118	2	no	—
211	#431	—	59	1	no	—
212	#431	—	59	1	no	—
213	#431	—	59	1	no	—
214	#431	—	59	1	no	—
215	#431	—	118	2	no	—
216	C₂×#106	Dic₅₉	1	1	yes	characteristic
217	C₂×#103	Dic₅₉	1	1	yes	characteristic
218	C₂×#102	Dic₅₉	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	—	118	2	no	—
220	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
221	#335	—	59	2	no	—
222	#334	—	59	2	no	—
223	Q₈⋊C₈	—	59	4	no	—
224	D₄⋊C₈	—	59	4	no	—
225	#322	—	59	2	no	—
226	C₈²	—	59	2	no	—
227	C₅₉	#17855	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
229	C₂²×D₄	C₂×Dic₅₉	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂×SD₁₆	C₅₉⋊C₈	1	8	yes	complemented
232	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
233	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
234	C₂²×C₈	—	118	4	no	—
235	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
236	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
240	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
244	C₄×D₄	C₂²×D₅₉	1	2	yes	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₄²	—	2	1	no	—
250	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
251	#106	C₂×Dic₅₉	1	2	yes	—
252	#106	C₂×Dic₅₉	1	2	yes	—
253	C₄⋊C₈	—	59	2	no	—
254	C₄⋊C₈	—	59	2	no	—
255	C₄⋊C₈	—	59	2	no	—
256	C₄⋊C₈	—	118	4	no	—
257	C₄⋊C₈	—	118	1	no	—
258	#103	C₂×Dic₅₉	1	2	yes	—
259	#103	C₂×Dic₅₉	1	2	yes	—
260	#102	C₂×Dic₅₉	1	2	yes	—
261	#102	C₂×Dic₅₉	1	2	yes	—
262	C₂²⋊C₈	—	59	2	no	—
263	C₂²⋊C₈	—	118	4	no	—
264	C₂²⋊C₈	—	118	1	no	—
265	C₂²⋊C₈	—	118	1	no	—
266	C₂²⋊C₈	—	118	1	no	—
267	C₄×C₈	—	59	2	no	—
268	C₄×C₈	—	59	2	no	—
269	C₄×C₈	—	118	4	no	—
270	C₄×C₈	—	118	1	no	—
271	C₄×C₈	—	118	1	no	—
272	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
273	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
274	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
275	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
276	C₂⁴	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	C₂×C₅₉⋊C₈	1	4	yes	complemented
280	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	C₂×C₅₉⋊C₈	1	4	yes	—
284	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
292	C₂²×C₄	#11745687	1	1	yes	characteristic
293	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
294	SD₁₆	C₂×C₅₉⋊C₈	1	8	yes	complemented
295	SD₁₆	C₂×C₅₉⋊C₈	1	8	yes	complemented
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	59	4	no	—
298	C₂×C₈	—	118	2	no	—
299	C₂×C₈	—	118	2	no	—
300	C₂×C₈	—	118	2	no	—
301	C₂×C₈	—	472	4	no	—
302	C₂×C₈	C₂×C₅₉⋊C₈	1	4	yes	complemented
303	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
304	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
305	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
306	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
312	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	D₄×D₅₉	1	1	yes	characteristic
318	C₄²	#11745687	1	1	yes	characteristic
319	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
320	C₄²	C₂³×D₅₉	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	8	1	no	—
324	C₂³	—	8	1	no	—
325	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	4	no	—
328	Q₈	C₂²×C₅₉⋊C₈	1	4	yes	—
329	D₄	—	2	2	no	—
330	D₄	—	2	4	no	—
331	D₄	C₂²×C₅₉⋊C₈	1	4	yes	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	1	no	—
341	C₂×C₄	—	8	1	no	—
342	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
343	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
344	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₅₉⋊C₈	1	2	yes	—
346	C₂×C₄	#14273734	1	2	yes	—
347	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
348	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
349	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	118	4	no	—
353	C₈	—	236	2	no	—
354	C₈	—	236	2	no	—
355	C₈	—	236	2	no	—
356	C₈	C₂²×C₅₉⋊C₈	1	2	yes	—
357	C₈	C₂²×C₅₉⋊C₈	1	2	yes	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	4	no	—
364	C₂²	D₄×C₅₉⋊C₈	1	2	yes	—
365	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	D₄×C₅₉⋊C₈	1	2	yes	—
373	C₄	C₂³×C₅₉⋊C₈	1	1	yes	characteristic
374	C₄	C₂×#14273734	1	1	yes	characteristic
375	C₄	#16838208	1	2	yes	—
376	C₂	—	2	2	no	—
377	C₂	—	4	4	no	—
378	C₂	C₂×D₄×C₅₉⋊C₈	1	1	yes	characteristic
379	C₂	#21432956	1	1	yes	characteristic
380	C₂	#21433013	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₄×C₅₉	C₂³×C₈
Frattini	C₄²	C₂³×D₅₉
Fitting	C₂×C₄×SD₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₄×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₅₉
hypocenter	C₅₉	#17855
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #21433177	C₂	semidirect
3. SD₁₆⋊(C₅₉⋊C₈)	C₂	semidirect
4. SD₁₆×C₅₉⋊C₈	C₂	semidirect
5. #21422844	C₂	semidirect
6. #21422491	C₂	semidirect
8. #21422379	C₂	semidirect
11. Q₈×C₅₉⋊C₈	C₂²	semidirect
20. #16837155	C₂²	semidirect
21. #16837153	C₂²	semidirect
22. Q₈⋊(C₅₉⋊C₈)	C₂²	semidirect
24. #16837123	C₂²	semidirect
25. C₈×C₅₉⋊C₈	C₂²	semidirect
56. C₂×SD₁₆×C₅₉	C₈	semidirect
88. C₂×Q₈×C₅₉	C₂×C₈	semidirect
103. SD₁₆×C₅₉	C₂×C₈	semidirect
104. SD₁₆×C₅₉	C₂×C₈	semidirect
106. C₂×C₈×C₅₉	C₂×C₈	semidirect
227. C₅₉	#17855	semidirect
231. C₂×SD₁₆	C₅₉⋊C₈	semidirect
279. C₂×Q₈	C₂×C₅₉⋊C₈	semidirect
294. SD₁₆	C₂×C₅₉⋊C₈	semidirect
295. SD₁₆	C₂×C₅₉⋊C₈	semidirect
302. C₂×C₈	C₂×C₅₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#21433177	2
#21433120	2
SD₁₆⋊(C₅₉⋊C₈)	2
SD₁₆×C₅₉⋊C₈	2
#21422844	2
#21422491	2
#21422487	2
#21422379	2
C₂×C₄×SD₁₆×C₅₉	2
#17855	59