Subgroups — C₅₉×#33891 #28446000

Order 15104.

608 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2234	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2220	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2187	C₂	1	2	yes	maximal, complemented
9	C₄×SD₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2169	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2140	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₅₉	C₂²	1	2	yes	—
13	C₅₉×#556	—	2	1	no	—
14	D₄²×C₅₉	—	2	1	no	—
15	C₂×SD₃₂×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×SD₃₂×C₅₉	C₂²	1	2	yes	complemented
17	C₂×M₃₂×C₅₉	C₂²	1	2	yes	complemented
18	C₅₉×#500	C₂²	1	1	yes	characteristic, complemented
19	C₅₉×#493	C₂²	1	1	yes	characteristic
20	C₅₉×#485	—	2	2	no	—
21	C₅₉×#475	—	2	1	no	—
22	C₅₉×#467	C₂²	1	2	yes	complemented
23	C₅₉×#466	C₂²	1	2	yes	—
24	C₅₉×#459	—	2	1	no	—
25	C₅₉×#447	—	2	2	no	—
26	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₅₉×#427	C₂²	1	2	yes	complemented
30	C₅₉×#367	C₂²	1	1	yes	characteristic, complemented
31	C₅₉×#366	C₂²	1	2	yes	complemented
32	C₅₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₅₉×#358	C₂²	1	1	yes	characteristic, complemented
34	C₅₉×#357	C₂²	1	1	yes	characteristic
35	C₅₉×#357	C₂²	1	2	yes	—
36	C₅₉×#357	C₂²	1	2	yes	complemented
37	C₅₉×#357	C₂²	1	2	yes	complemented
38	C₅₉×#357	C₂²	1	2	yes	complemented
39	C₅₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₄×C₅₉	—	2	2	no	—
42	C₂²×D₄×C₅₉	—	4	1	no	—
43	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
44	C₂×D₈×C₅₉	—	2	4	no	—
45	C₂×D₈×C₅₉	—	2	2	no	—
46	C₂×D₈×C₅₉	—	2	1	no	—
47	C₂×D₈×C₅₉	—	4	2	no	—
48	C₂×D₈×C₅₉	C₂³	1	2	yes	—
49	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₅₉	—	2	1	no	—
52	#127×C₅₉	—	2	1	no	—
53	#126×C₅₉	—	4	2	no	—
54	#124×C₅₉	—	4	1	no	—
55	C₂²⋊Q₈×C₅₉	—	2	2	no	—
56	#121×C₅₉	—	2	2	no	—
57	#121×C₅₉	—	4	1	no	—
58	#120×C₅₉	—	4	2	no	—
59	C₄×Q₈×C₅₉	—	2	1	no	—
60	C₄×Q₈×C₅₉	—	4	1	no	—
61	C₄×D₄×C₅₉	—	2	1	no	—
62	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
63	#117×C₅₉	—	2	2	no	—
64	SD₃₂×C₅₉	—	2	2	no	—
65	SD₃₂×C₅₉	—	4	2	no	—
66	M₃₂×C₅₉	—	4	2	no	—
67	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
69	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
70	#107×C₅₉	—	2	1	no	—
71	#107×C₅₉	C₂³	1	2	yes	—
72	#107×C₅₉	C₂³	1	1	yes	characteristic
73	#107×C₅₉	C₂³	1	1	yes	characteristic
74	#106×C₅₉	—	2	2	no	—
75	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
76	#103×C₅₉	—	2	1	no	—
77	#103×C₅₉	—	2	2	no	—
78	#102×C₅₉	—	2	1	no	—
79	#102×C₅₉	—	2	2	no	—
80	C₂²⋊C₈×C₅₉	D₄	1	2	yes	—
81	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
82	C₂⁴×C₅₉	—	4	2	no	—
83	C₂×Q₈×C₅₉	—	2	1	no	—
84	C₂×Q₈×C₅₉	—	4	1	no	—
85	C₂×D₄×C₅₉	—	2	1	no	—
86	C₂×D₄×C₅₉	—	2	2	no	—
87	C₂×D₄×C₅₉	—	4	4	no	—
88	C₂×D₄×C₅₉	—	4	2	no	—
89	C₂×D₄×C₅₉	—	4	2	no	—
90	C₂×D₄×C₅₉	—	4	1	no	—
91	C₂×D₄×C₅₉	—	4	1	no	—
92	C₂×D₄×C₅₉	—	8	2	no	—
93	C₂×D₄×C₅₉	—	8	4	no	—
94	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	—	4	1	no	—
96	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
97	Q₁₆×C₅₉	—	2	1	no	—
98	Q₁₆×C₅₉	—	2	1	no	—
99	D₈×C₅₉	—	2	2	no	—
100	D₈×C₅₉	—	2	1	no	—
101	D₈×C₅₉	—	2	2	no	—
102	D₈×C₅₉	—	4	4	no	—
103	D₈×C₅₉	—	8	1	no	—
104	D₈×C₅₉	#41	1	2	yes	—
105	C₂×C₈×C₅₉	—	2	2	no	—
106	C₂×C₈×C₅₉	—	2	2	no	—
107	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₅₉	—	2	1	no	—
111	C₄⋊C₄×C₅₉	—	2	1	no	—
112	C₄⋊C₄×C₅₉	—	2	2	no	—
113	C₄⋊C₄×C₅₉	—	4	1	no	—
114	C₄⋊C₄×C₅₉	—	4	2	no	—
115	C₄⋊C₄×C₅₉	—	4	1	no	—
116	C₄⋊C₄×C₅₉	D₈	1	1	yes	characteristic
117	C₂²⋊C₄×C₅₉	—	4	2	no	—
118	C₂²⋊C₄×C₅₉	—	4	2	no	—
119	C₂²⋊C₄×C₅₉	—	4	1	no	—
120	C₂²⋊C₄×C₅₉	—	4	2	no	—
121	C₂²⋊C₄×C₅₉	D₈	1	2	yes	—
122	C₄²×C₅₉	—	4	2	no	—
123	C₄²×C₅₉	—	4	1	no	—
124	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₅₉	—	2	1	no	—
126	C₁₆×C₅₉	—	2	1	no	—
127	C₁₆×C₅₉	—	2	2	no	—
128	C₂³×C₅₉	—	4	1	no	—
129	C₂³×C₅₉	—	4	2	no	—
130	C₂³×C₅₉	—	8	4	no	—
131	C₂³×C₅₉	—	8	4	no	—
132	C₂³×C₅₉	—	16	2	no	—
133	C₂³×C₅₉	C₂×D₈	1	2	yes	—
134	Q₈×C₅₉	—	4	1	no	—
135	Q₈×C₅₉	—	4	1	no	—
136	Q₈×C₅₉	—	8	2	no	—
137	D₄×C₅₉	—	2	2	no	—
138	D₄×C₅₉	—	2	2	no	—
139	D₄×C₅₉	—	4	2	no	—
140	D₄×C₅₉	—	4	1	no	—
141	D₄×C₅₉	—	4	2	no	—
142	D₄×C₅₉	—	8	4	no	—
143	D₄×C₅₉	—	8	4	no	—
144	D₄×C₅₉	—	8	2	no	—
145	D₄×C₅₉	—	16	1	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	4	1	no	—
149	C₂×C₄×C₅₉	—	4	2	no	—
150	C₂×C₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	—	4	1	no	—
152	C₂×C₄×C₅₉	—	8	2	no	—
153	C₂×C₄×C₅₉	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₅₉	—	2	2	no	—
158	C₈×C₅₉	—	2	1	no	—
159	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
160	C₈×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
161	#33891	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂²×C₅₉	—	2	2	no	—
163	C₂²×C₅₉	—	2	2	no	—
164	C₂²×C₅₉	—	2	2	no	—
165	C₂²×C₅₉	—	4	2	no	—
166	C₂²×C₅₉	—	8	1	no	—
167	C₂²×C₅₉	—	8	1	no	—
168	C₂²×C₅₉	—	8	2	no	—
169	C₂²×C₅₉	—	8	2	no	—
170	C₂²×C₅₉	—	8	2	no	—
171	C₂²×C₅₉	—	16	8	no	—
172	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
173	C₄×C₅₉	—	2	1	no	—
174	C₄×C₅₉	—	2	2	no	—
175	C₄×C₅₉	—	8	1	no	—
176	C₄×C₅₉	—	8	2	no	—
177	C₄×C₅₉	—	8	1	no	—
178	C₄×C₅₉	—	8	1	no	—
179	C₄×C₅₉	#509	1	2	yes	—
180	C₄×C₅₉	#546	1	1	yes	characteristic
181	C₄×C₅₉	#577	1	1	yes	characteristic
182	#3342	C₂×C₅₉	1	1	yes	characteristic, complemented
183	D₄×D₈	C₂×C₅₉	1	1	yes	characteristic
184	#2240	C₂×C₅₉	1	1	yes	characteristic, complemented
185	#2234	C₂×C₅₉	1	2	yes	complemented
186	#2224	C₂×C₅₉	1	1	yes	characteristic, complemented
187	#2220	C₂×C₅₉	1	2	yes	complemented
188	#2207	C₂×C₅₉	1	1	yes	characteristic, complemented
189	#2187	C₂×C₅₉	1	2	yes	complemented
190	C₄×SD₃₂	C₂×C₅₉	1	1	yes	characteristic, complemented
191	#2169	C₂×C₅₉	1	1	yes	characteristic, complemented
192	#2140	C₂×C₅₉	1	2	yes	complemented
193	C₂×C₅₉	—	4	2	no	—
194	C₂×C₅₉	—	8	2	no	—
195	C₂×C₅₉	—	16	2	no	—
196	C₂×C₅₉	#3294	1	1	yes	characteristic
197	C₂×C₅₉	C₂×#509	1	1	yes	characteristic
198	C₂×C₅₉	#3416	1	1	yes	characteristic
199	C₂²×D₈	C₂²×C₅₉	1	2	yes	—
200	#556	—	2	1	no	—
201	D₄²	—	2	1	no	—
202	C₂×SD₃₂	C₂²×C₅₉	1	1	yes	characteristic
203	C₂×SD₃₂	C₂²×C₅₉	1	2	yes	complemented
204	C₂×M₃₂	C₂²×C₅₉	1	2	yes	complemented
205	#500	C₂²×C₅₉	1	1	yes	characteristic, complemented
206	#493	C₂²×C₅₉	1	1	yes	characteristic
207	#485	—	2	2	no	—
208	#475	—	2	1	no	—
209	#467	C₂²×C₅₉	1	2	yes	complemented
210	#466	C₂²×C₅₉	1	2	yes	—
211	#459	—	2	1	no	—
212	#447	—	2	2	no	—
213	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
214	C₄×D₈	C₂²×C₅₉	1	1	yes	characteristic
215	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
216	#427	C₂²×C₅₉	1	2	yes	complemented
217	#367	C₂²×C₅₉	1	1	yes	characteristic, complemented
218	#366	C₂²×C₅₉	1	2	yes	complemented
219	C₄⋊C₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
220	#358	C₂²×C₅₉	1	1	yes	characteristic, complemented
221	#357	C₂²×C₅₉	1	1	yes	characteristic
222	#357	C₂²×C₅₉	1	2	yes	—
223	#357	C₂²×C₅₉	1	2	yes	complemented
224	#357	C₂²×C₅₉	1	2	yes	complemented
225	#357	C₂²×C₅₉	1	2	yes	complemented
226	C₂²⋊C₁₆	C₂²×C₅₉	1	2	yes	complemented
227	C₄×C₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
228	C₅₉	#33891	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	—	4	1	no	—
231	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
232	C₂×D₈	—	2	4	no	—
233	C₂×D₈	—	2	2	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	4	2	no	—
236	C₂×D₈	C₂³×C₅₉	1	2	yes	—
237	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
239	C₄⋊Q₈	—	2	1	no	—
240	#127	—	2	1	no	—
241	#126	—	4	2	no	—
242	#124	—	4	1	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	#121	—	2	2	no	—
245	#121	—	4	1	no	—
246	#120	—	4	2	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	4	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
251	#117	—	2	2	no	—
252	SD₃₂	—	2	2	no	—
253	SD₃₂	—	4	2	no	—
254	M₃₂	—	4	2	no	—
255	C₂×C₁₆	C₂³×C₅₉	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₅₉	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₅₉	1	2	yes	—
258	#107	—	2	1	no	—
259	#107	C₂³×C₅₉	1	2	yes	—
260	#107	C₂³×C₅₉	1	1	yes	characteristic
261	#107	C₂³×C₅₉	1	1	yes	characteristic
262	#106	—	2	2	no	—
263	C₄⋊C₈	D₄×C₅₉	1	1	yes	characteristic
264	#103	—	2	1	no	—
265	#103	—	2	2	no	—
266	#102	—	2	1	no	—
267	#102	—	2	2	no	—
268	C₂²⋊C₈	D₄×C₅₉	1	2	yes	—
269	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
270	C₂⁴	—	4	2	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	8	2	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
285	Q₁₆	—	2	1	no	—
286	Q₁₆	—	2	1	no	—
287	D₈	—	2	2	no	—
288	D₈	—	2	1	no	—
289	D₈	—	2	2	no	—
290	D₈	—	4	4	no	—
291	D₈	—	8	1	no	—
292	D₈	#41×C₅₉	1	2	yes	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
297	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	D₈×C₅₉	1	1	yes	characteristic
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	D₈×C₅₉	1	2	yes	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	1	no	—
312	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	1	no	—
315	C₁₆	—	2	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	8	4	no	—
319	C₂³	—	8	4	no	—
320	C₂³	—	16	2	no	—
321	C₂³	C₂×D₈×C₅₉	1	2	yes	—
322	Q₈	—	4	1	no	—
323	Q₈	—	4	1	no	—
324	Q₈	—	8	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	D₄	—	8	2	no	—
333	D₄	—	16	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	C₂×D₈×C₅₉	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
343	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	—	2	1	no	—
347	C₈	C₂×#41×C₅₉	1	1	yes	characteristic
348	C₈	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	8	1	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	16	8	no	—
359	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	2	1	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	1	no	—
366	C₄	C₅₉×#509	1	2	yes	—
367	C₄	C₅₉×#546	1	1	yes	characteristic
368	C₄	C₅₉×#577	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	8	2	no	—
371	C₂	—	16	2	no	—
372	C₂	C₅₉×#3294	1	1	yes	characteristic
373	C₂	C₂×C₅₉×#509	1	1	yes	characteristic
374	C₂	C₅₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
prime radical	D₄×D₈×C₅₉	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄×D₄×C₅₉ ◁ C₈×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3342	C₂	semidirect
3. C₅₉×#2240	C₂	semidirect
4. C₅₉×#2234	C₂	semidirect
5. C₅₉×#2224	C₂	semidirect
6. C₅₉×#2220	C₂	semidirect
7. C₅₉×#2207	C₂	semidirect
8. C₅₉×#2187	C₂	semidirect
9. C₄×SD₃₂×C₅₉	C₂	semidirect
10. C₅₉×#2169	C₂	semidirect
11. C₅₉×#2140	C₂	semidirect
16. C₂×SD₃₂×C₅₉	C₂²	semidirect
17. C₂×M₃₂×C₅₉	C₂²	semidirect
18. C₅₉×#500	C₂²	semidirect
22. C₅₉×#467	C₂²	semidirect
26. C₄×Q₁₆×C₅₉	C₂²	semidirect
29. C₅₉×#427	C₂²	semidirect
30. C₅₉×#367	C₂²	semidirect
31. C₅₉×#366	C₂²	semidirect
32. C₅₉×C₄⋊C₁₆	C₂²	semidirect
33. C₅₉×#358	C₂²	semidirect
36. C₅₉×#357	C₂²	semidirect
37. C₅₉×#357	C₂²	semidirect
38. C₅₉×#357	C₂²	semidirect
39. C₅₉×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₅₉	C₂²	semidirect
161. #33891	C₅₉	direct (N × H)
182. #3342	C₂×C₅₉	semidirect
184. #2240	C₂×C₅₉	semidirect
185. #2234	C₂×C₅₉	semidirect
186. #2224	C₂×C₅₉	semidirect
187. #2220	C₂×C₅₉	semidirect
188. #2207	C₂×C₅₉	semidirect
189. #2187	C₂×C₅₉	semidirect
190. C₄×SD₃₂	C₂×C₅₉	semidirect
191. #2169	C₂×C₅₉	semidirect
192. #2140	C₂×C₅₉	semidirect
203. C₂×SD₃₂	C₂²×C₅₉	semidirect
204. C₂×M₃₂	C₂²×C₅₉	semidirect
205. #500	C₂²×C₅₉	semidirect
209. #467	C₂²×C₅₉	semidirect
213. C₄×Q₁₆	C₂²×C₅₉	semidirect
216. #427	C₂²×C₅₉	semidirect
217. #367	C₂²×C₅₉	semidirect
218. #366	C₂²×C₅₉	semidirect
219. C₄⋊C₁₆	C₂²×C₅₉	semidirect
220. #358	C₂²×C₅₉	semidirect
223. #357	C₂²×C₅₉	semidirect
224. #357	C₂²×C₅₉	semidirect
225. #357	C₂²×C₅₉	semidirect
226. C₂²⋊C₁₆	C₂²×C₅₉	semidirect
227. C₄×C₁₆	C₂²×C₅₉	semidirect
228. C₅₉	#33891	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#3342	2
D₄×D₈×C₅₉	2
C₅₉×#2240	2
C₅₉×#2234	2
C₅₉×#2224	2
C₅₉×#2220	2
C₅₉×#2207	2
C₅₉×#2187	2
C₄×SD₃₂×C₅₉	2
C₅₉×#2169	2
C₅₉×#2140	2
#33891	59

Subgroups — C59×#33891 #28446000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33891 #28446000