Subgroups — D₅₉×#2108 #28741321

Order 15104.

854 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#405×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21425695	C₂	1	1	yes	maximal, characteristic, complemented
5	#21425694	C₂	1	2	yes	maximal, complemented
6	#21425693	C₂	1	1	yes	maximal, characteristic, complemented
7	#21425692	C₂	1	1	yes	maximal, characteristic, complemented
8	#21425691	C₂	1	2	yes	maximal, complemented
9	#346×D₅₉	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₅₉	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₉	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₅₉	C₂²	1	1	yes	characteristic
14	#117×D₅₉	C₄	1	1	yes	characteristic
15	C₂×#14273667	C₂²	1	1	yes	characteristic
16	C₂×#14273666	C₂²	1	2	yes	—
17	M₃₂×D₅₉	C₄	1	8	yes	complemented
18	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₅₉	C₄	1	8	yes	complemented
20	C₂×C₁₆×D₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×D₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₅₉	C₂²	1	2	yes	—
23	C₂×C₁₆×D₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₆×D₅₉	C₂²	1	1	yes	characteristic
25	#16837360	C₄	1	1	yes	characteristic
26	#16837359	C₄	1	2	yes	—
27	#16837358	C₄	1	1	yes	characteristic
28	#16837357	C₂²	1	1	yes	characteristic
29	#16837356	C₂²	1	2	yes	—
30	#97×D₅₉	C₄	1	2	yes	—
31	C₄×C₈×D₅₉	C₂²	1	2	yes	—
32	#16837178	C₂²	1	2	yes	complemented
33	#16837177	C₂²	1	2	yes	complemented
34	#16837177	C₂²	1	2	yes	complemented
35	C₄×C₅₉⋊C₁₆	C₂²	1	2	yes	complemented
36	C₁₆×Dic₅₉	C₂²	1	2	yes	complemented
37	C₁₆×Dic₅₉	C₂²	1	2	yes	complemented
38	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
39	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#405	C₂²	1	1	yes	characteristic
41	C₅₉×#346	C₂²	1	2	yes	complemented
42	C₄×C₁₆×C₅₉	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
44	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
45	C₂×#11745659	C₂×C₄	1	2	yes	—
46	M₁₆×D₅₉	C₈	1	8	yes	—
47	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅₉	C₂×C₄	1	4	yes	—
51	C₂×C₈×D₅₉	C₂×C₄	1	4	yes	—
52	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₅₉	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₅₉	C₂³	1	1	yes	characteristic
55	#14273686	C₂×C₄	1	1	yes	characteristic
56	#14273685	C₈	1	2	yes	—
57	#14273684	C₂×C₄	1	2	yes	—
58	#14273683	C₈	1	2	yes	—
59	C₄⋊C₄×D₅₉	C₈	1	2	yes	—
60	C₂²⋊C₄×D₅₉	C₈	1	2	yes	—
61	C₄²×D₅₉	C₂×C₄	1	2	yes	—
62	#14273667	C₂×C₄	1	4	yes	complemented
63	#14273666	C₂×C₄	1	8	yes	complemented
64	C₂×C₅₉⋊C₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
67	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
68	C₁₆×D₅₉	C₂×C₄	1	4	yes	—
69	C₁₆×D₅₉	C₂×C₄	1	4	yes	—
70	C₁₆×D₅₉	C₂×C₄	1	8	yes	—
71	C₁₆×D₅₉	C₂×C₄	1	4	yes	complemented
72	C₁₆×D₅₉	C₂×C₄	1	4	yes	complemented
73	#14273638	C₂×C₄	1	2	yes	—
74	#14273637	C₂×C₄	1	2	yes	—
75	#14273637	C₂×C₄	1	2	yes	—
76	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
77	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
78	C₈×Dic₅₉	C₂³	1	2	yes	—
79	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
81	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
82	M₃₂×C₅₉	C₂×C₄	1	4	yes	complemented
83	C₂×C₁₆×C₅₉	C₂×C₄	1	4	yes	complemented
84	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
85	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
87	#97×C₅₉	C₂×C₄	1	2	yes	—
88	C₄×C₈×C₅₉	C₂³	1	2	yes	—
89	C₂³×D₅₉	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₅₉	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₅₉	C₄²	1	4	yes	—
93	C₂×C₄×D₅₉	C₂×C₈	1	4	yes	—
94	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₅₉	C₂×C₈	1	4	yes	—
97	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
99	M₁₆×C₅₉	C₂×C₈	1	4	yes	—
100	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
106	C₂²⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
107	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
108	C₂²⋊Dic₅₉	C₂×C₈	1	2	yes	—
109	(C₂×D₅₉)⋊C₄	C₂×C₈	1	4	yes	—
110	C₄⋊Dic₅₉	C₂×C₈	1	2	yes	—
111	Dic₅₉⋊C₄	C₂×C₈	1	4	yes	—
112	C₄×Dic₅₉	C₂×C₈	1	4	yes	—
113	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
114	#11745664	C₂×C₈	1	4	yes	—
115	C₂×C₅₉⋊C₈	C₄²	1	4	yes	—
116	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
119	#11745659	C₂×C₈	1	8	yes	—
120	C₈×D₅₉	C₄²	1	4	yes	—
121	C₈×D₅₉	C₄²	1	4	yes	—
122	C₈×D₅₉	C₂×C₈	1	8	yes	—
123	C₈×D₅₉	C₂²×C₄	1	2	yes	—
124	C₈×D₅₉	C₂²×C₄	1	2	yes	—
125	C₈×D₅₉	C₂²×C₄	1	2	yes	—
126	C₈×D₅₉	C₂²×C₄	1	2	yes	—
127	C₁₆×C₅₉	C₂²×C₄	1	2	yes	—
128	C₁₆×C₅₉	C₂²×C₄	1	2	yes	—
129	C₁₆×C₅₉	C₂²×C₄	1	4	yes	—
130	C₅₉⋊C₁₆	C₂²×C₄	1	2	yes	—
131	C₅₉⋊C₁₆	C₂²×C₄	1	2	yes	—
132	C₅₉⋊C₁₆	C₂²×C₄	1	4	yes	—
133	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
134	C₂²×D₅₉	—	2	4	no	—
135	C₂²×D₅₉	C₄×C₈	1	4	yes	—
136	C₂²×D₅₉	C₂²×C₈	1	1	yes	characteristic
137	C₂²×D₅₉	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₅₉	C₂²×C₈	1	4	yes	—
140	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
143	C₂×Dic₅₉	C₄×C₈	1	4	yes	—
144	C₂×Dic₅₉	C₂²×C₈	1	4	yes	—
145	C₂×Dic₅₉	C₂²×C₈	1	1	yes	characteristic
146	C₂×Dic₅₉	C₂²×C₈	1	1	yes	characteristic
147	C₄×D₅₉	—	2	8	no	—
148	C₄×D₅₉	C₄×C₈	1	4	yes	—
149	C₄×D₅₉	C₄×C₈	1	4	yes	—
150	C₄×D₅₉	C₂×C₄²	1	2	yes	—
151	C₄×D₅₉	C₂×C₄²	1	2	yes	—
152	C₄×D₅₉	C₂²×C₈	1	2	yes	—
153	C₄×D₅₉	C₂²×C₈	1	2	yes	—
154	C₈×C₅₉	C₂×C₄²	1	2	yes	—
155	C₈×C₅₉	C₂²×C₈	1	4	yes	—
156	C₈×C₅₉	C₂³×C₄	1	1	yes	characteristic
157	C₈×C₅₉	C₂³×C₄	1	1	yes	characteristic
158	C₅₉⋊C₈	C₂×C₄²	1	2	yes	—
159	C₅₉⋊C₈	C₂×C₄²	1	2	yes	—
160	C₅₉⋊C₈	C₂²×C₈	1	4	yes	—
161	C₂×#2108	—	59	1	no	maximal, Sylow
162	C₂²×C₅₉	—	2	2	no	—
163	C₂²×C₅₉	C₂×C₄×C₈	1	2	yes	—
164	C₂²×C₅₉	C₂³×C₈	1	1	yes	characteristic
165	C₂×D₅₉	—	2	2	no	—
166	C₂×D₅₉	—	2	8	no	—
167	C₂×D₅₉	C₂×C₄×C₈	1	2	yes	—
168	C₂×D₅₉	C₂×C₄×C₈	1	2	yes	—
169	C₂×D₅₉	#504	1	4	yes	—
170	C₄×C₅₉	—	2	4	no	—
171	C₄×C₅₉	C₂×C₄×C₈	1	2	yes	—
172	C₄×C₅₉	C₂²×C₄²	1	1	yes	characteristic
173	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
174	Dic₅₉	—	2	4	no	—
175	Dic₅₉	C₂×C₄×C₈	1	2	yes	—
176	Dic₅₉	C₂×C₄×C₈	1	2	yes	—
177	C₂²×M₃₂	—	59	1	no	—
178	C₂³×C₁₆	—	59	1	no	—
179	C₂×#405	—	59	1	no	—
180	#2108	—	59	1	no	—
181	#2108	—	59	1	no	—
182	#2108	—	59	1	no	—
183	#2108	—	59	2	no	—
184	#2108	—	59	2	no	—
185	#2108	D₅₉	1	1	yes	characteristic, direct product factor
186	C₂×#346	—	59	2	no	—
187	C₂×C₄×C₁₆	—	59	2	no	—
188	C₂×C₅₉	—	2	2	no	—
189	C₂×C₅₉	C₂²×C₄×C₈	1	1	yes	characteristic
190	C₂×C₅₉	C₂×#504	1	2	yes	—
191	D₅₉	—	2	2	no	—
192	D₅₉	#2108	1	4	yes	direct product factor
193	C₂²×M₁₆	—	59	1	no	—
194	C₂³×C₈	—	59	1	no	—
195	C₂×#117	—	59	1	no	—
196	C₂×M₃₂	—	59	1	no	—
197	C₂×M₃₂	—	59	8	no	—
198	C₂×M₃₂	—	59	2	no	—
199	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
200	C₂²×C₁₆	—	59	1	no	—
201	C₂²×C₁₆	—	59	8	no	—
202	C₂²×C₁₆	—	59	2	no	—
203	C₂²×C₁₆	—	59	1	no	—
204	C₂²×C₁₆	—	59	1	no	—
205	C₂²×C₁₆	—	59	1	no	—
206	C₂²×C₁₆	—	59	1	no	—
207	C₂²×C₁₆	C₂×D₅₉	1	1	yes	characteristic
208	#405	—	59	1	no	—
209	#405	—	59	1	no	—
210	#405	—	59	1	no	—
211	#405	—	59	2	no	—
212	#405	—	59	2	no	—
213	#405	C₂×D₅₉	1	1	yes	characteristic
214	C₂×#97	—	59	2	no	—
215	C₂×C₄×C₈	—	59	2	no	—
216	#346	—	59	2	no	—
217	#346	—	59	2	no	—
218	#346	—	59	2	no	—
219	#346	C₂×D₅₉	1	2	yes	complemented
220	C₄×C₁₆	—	59	2	no	—
221	C₄×C₁₆	—	59	2	no	—
222	C₄×C₁₆	—	59	2	no	—
223	C₄×C₁₆	C₂×D₅₉	1	2	yes	complemented
224	C₅₉	C₂×#2108	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₄	—	59	1	no	—
226	C₂×M₁₆	—	59	1	no	—
227	C₂×M₁₆	—	59	8	no	—
228	C₂×M₁₆	—	59	2	no	—
229	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
230	C₂²×C₈	—	59	1	no	—
231	C₂²×C₈	—	59	1	no	—
232	C₂²×C₈	—	59	1	no	—
233	C₂²×C₈	—	59	4	no	—
234	C₂²×C₈	—	59	4	no	—
235	C₂²×C₈	—	59	2	no	—
236	C₂²×C₈	—	59	1	no	—
237	C₂²×C₈	—	59	1	no	—
238	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
239	#117	—	59	1	no	—
240	#117	—	59	2	no	—
241	#117	—	59	2	no	—
242	#117	—	59	2	no	—
243	#117	C₄×D₅₉	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	59	2	no	—
245	C₂×C₂²⋊C₄	—	59	2	no	—
246	C₂×C₄²	—	59	2	no	—
247	M₃₂	—	59	4	no	—
248	M₃₂	—	59	8	no	—
249	M₃₂	C₄×D₅₉	1	4	yes	complemented
250	C₂×C₁₆	—	59	4	no	—
251	C₂×C₁₆	—	59	1	no	—
252	C₂×C₁₆	—	59	2	no	—
253	C₂×C₁₆	—	59	1	no	—
254	C₂×C₁₆	—	59	4	no	—
255	C₂×C₁₆	—	59	4	no	—
256	C₂×C₁₆	—	59	8	no	—
257	C₂×C₁₆	—	59	4	no	—
258	C₂×C₁₆	—	59	4	no	—
259	C₂×C₁₆	C₄×D₅₉	1	4	yes	complemented
260	C₂×C₁₆	C₂²×D₅₉	1	2	yes	—
261	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
262	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
263	#97	—	59	2	no	—
264	#97	—	59	2	no	—
265	#97	—	59	2	no	—
266	#97	C₄×D₅₉	1	2	yes	—
267	C₄×C₈	—	59	2	no	—
268	C₄×C₈	—	59	2	no	—
269	C₄×C₈	—	59	2	no	—
270	C₄×C₈	C₂²×D₅₉	1	2	yes	—
271	C₂⁴	—	59	1	no	—
272	C₂²×C₄	—	59	1	no	—
273	C₂²×C₄	—	59	4	no	—
274	C₂²×C₄	—	59	1	no	—
275	C₂²×C₄	—	59	1	no	—
276	C₂²×C₄	—	59	4	no	—
277	C₂²×C₄	—	59	1	no	—
278	C₂²×C₄	—	59	1	no	—
279	C₂²×C₄	—	59	4	no	—
280	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
281	M₁₆	—	59	4	no	—
282	M₁₆	—	59	8	no	—
283	M₁₆	C₈×D₅₉	1	4	yes	—
284	C₂×C₈	—	59	4	no	—
285	C₂×C₈	—	59	1	no	—
286	C₂×C₈	—	59	2	no	—
287	C₂×C₈	—	59	1	no	—
288	C₂×C₈	—	59	4	no	—
289	C₂×C₈	—	59	4	no	—
290	C₂×C₈	—	59	8	no	—
291	C₂×C₈	—	59	2	no	—
292	C₂×C₈	—	59	2	no	—
293	C₂×C₈	—	59	2	no	—
294	C₂×C₈	—	59	2	no	—
295	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
296	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
297	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
298	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
299	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
300	C₄⋊C₄	—	59	4	no	—
301	C₄⋊C₄	—	59	2	no	—
302	C₄⋊C₄	C₈×D₅₉	1	2	yes	—
303	C₂²⋊C₄	—	59	2	no	—
304	C₂²⋊C₄	—	59	4	no	—
305	C₂²⋊C₄	C₈×D₅₉	1	2	yes	—
306	C₄²	—	59	4	no	—
307	C₄²	—	59	2	no	—
308	C₄²	C₂×C₄×D₅₉	1	2	yes	—
309	C₁₆	—	59	2	no	—
310	C₁₆	—	59	2	no	—
311	C₁₆	—	59	4	no	—
312	C₁₆	C₂×C₄×D₅₉	1	2	yes	—
313	C₁₆	C₂×C₄×D₅₉	1	2	yes	—
314	C₁₆	C₂×C₄×D₅₉	1	4	yes	—
315	C₂³	—	59	1	no	—
316	C₂³	—	59	1	no	—
317	C₂³	—	59	4	no	—
318	C₂³	—	118	4	no	—
319	C₂³	C₂×C₈×D₅₉	1	1	yes	characteristic
320	C₂×C₄	—	59	1	no	—
321	C₂×C₄	—	59	1	no	—
322	C₂×C₄	—	59	4	no	—
323	C₂×C₄	—	59	2	no	—
324	C₂×C₄	—	59	2	no	—
325	C₂×C₄	—	59	2	no	—
326	C₂×C₄	—	59	2	no	—
327	C₂×C₄	—	59	4	no	—
328	C₂×C₄	—	59	4	no	—
329	C₂×C₄	—	59	4	no	—
330	C₂×C₄	—	118	8	no	—
331	C₂×C₄	C₄²×D₅₉	1	2	yes	—
332	C₂×C₄	C₂×C₈×D₅₉	1	4	yes	—
333	C₂×C₄	C₂×C₈×D₅₉	1	2	yes	—
334	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
336	C₈	—	59	4	no	—
337	C₈	—	59	2	no	—
338	C₈	—	59	2	no	—
339	C₈	C₄²×D₅₉	1	2	yes	—
340	C₈	C₂×C₈×D₅₉	1	4	yes	—
341	C₈	C₂²×C₄×D₅₉	1	1	yes	characteristic
342	C₈	C₂²×C₄×D₅₉	1	1	yes	characteristic
343	C₂²	—	2	2	no	—
344	C₂²	—	59	4	no	—
345	C₂²	—	59	2	no	—
346	C₂²	—	59	2	no	—
347	C₂²	—	118	8	no	—
348	C₂²	—	118	2	no	—
349	C₂²	C₄×C₈×D₅₉	1	2	yes	—
350	C₂²	C₂²×C₈×D₅₉	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	59	2	no	—
353	C₄	—	59	2	no	—
354	C₄	—	118	4	no	—
355	C₄	C₄×C₈×D₅₉	1	2	yes	—
356	C₄	C₂×C₄²×D₅₉	1	1	yes	characteristic
357	C₄	C₂²×C₈×D₅₉	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	59	4	no	—
360	C₂	—	118	2	no	—
361	C₂	C₂×C₄×C₈×D₅₉	1	1	yes	characteristic
362	C₂	#504×D₅₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₅₉
commutator	C₂×C₅₉	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₅₉×#2108	C₂
socle	C₂²×C₅₉	C₂³×C₈
prime radical	C₂³×D₅₉	C₂×C₈
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	#2108	D₅₉
hypocenter	C₅₉	C₂×#2108
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₁₆ ◁ #2108

Complements

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

N	H ≅ G/N	type
4. #21425695	C₂	semidirect
5. #21425694	C₂	semidirect
6. #21425693	C₂	semidirect
7. #21425692	C₂	semidirect
8. #21425691	C₂	semidirect
9. #346×D₅₉	C₂	semidirect
10. C₄×C₁₆×D₅₉	C₂	semidirect
11. C₅₉×#2108	C₂	semidirect
17. M₃₂×D₅₉	C₄	semidirect
19. C₂×C₁₆×D₅₉	C₄	semidirect
32. #16837178	C₂²	semidirect
33. #16837177	C₂²	semidirect
34. #16837177	C₂²	semidirect
35. C₄×C₅₉⋊C₁₆	C₂²	semidirect
36. C₁₆×Dic₅₉	C₂²	semidirect
37. C₁₆×Dic₅₉	C₂²	semidirect
41. C₅₉×#346	C₂²	semidirect
42. C₄×C₁₆×C₅₉	C₂²	semidirect
62. #14273667	C₂×C₄	semidirect
63. #14273666	C₂×C₄	semidirect
64. C₂×C₅₉⋊C₁₆	C₂×C₄	semidirect
71. C₁₆×D₅₉	C₂×C₄	semidirect
72. C₁₆×D₅₉	C₂×C₄	semidirect
82. M₃₂×C₅₉	C₂×C₄	semidirect
83. C₂×C₁₆×C₅₉	C₂×C₄	semidirect
185. #2108	D₅₉	direct (N × H)
192. D₅₉	#2108	direct (N × H)
219. #346	C₂×D₅₉	semidirect
223. C₄×C₁₆	C₂×D₅₉	semidirect
224. C₅₉	C₂×#2108	semidirect
249. M₃₂	C₄×D₅₉	semidirect
259. C₂×C₁₆	C₄×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₅₉	2
C₂²×C₁₆×D₅₉	2
#405×D₅₉	2
#21425695	2
#21425694	2
#21425693	2
#21425692	2
#21425691	2
#346×D₅₉	2
C₄×C₁₆×D₅₉	2
C₅₉×#2108	2
C₂×#2108	59

Subgroups — D59×#2108 #28741321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×#2108 #28741321