Subgroups — #28742113

Order 15104.

642 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₅₉	C₂	1	1	yes	maximal, characteristic
2	#21433008	C₂	1	2	yes	maximal, complemented
3	#21425983	C₂	1	1	yes	maximal, characteristic, complemented
4	#21425982	C₂	1	1	yes	maximal, characteristic, complemented
5	#21425981	C₂	1	1	yes	maximal, characteristic, complemented
6	#21425975	C₂	1	2	yes	maximal, complemented
7	#21425974	C₂	1	2	yes	maximal, complemented
8	#368×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#21425822	C₂	1	2	yes	maximal, complemented
10	#21425694	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2179	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₅₉	C₂²	1	2	yes	—
13	#16838167	—	2	2	no	—
14	#16837835	C₄	1	1	yes	characteristic, complemented
15	#16837834	C₂²	1	1	yes	characteristic
16	#16837833	C₄	1	2	yes	complemented
17	#16837832	C₂²	1	2	yes	—
18	#16837831	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₅₉	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₅₉	C₄	1	2	yes	complemented
21	D₁₆×D₅₉	C₄	1	1	yes	characteristic, complemented
22	C₂×#14273666	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₅₉	C₂²	1	1	yes	characteristic
24	#16837522	—	2	2	no	—
25	#16837521	—	2	2	no	—
26	#16837520	C₂²	1	2	yes	complemented
27	#16837519	C₂²	1	2	yes	complemented
28	#16837518	C₂²	1	2	yes	complemented
29	#108×D₅₉	C₂²	1	2	yes	—
30	#16837417	—	2	2	no	—
31	#16837356	C₂²	1	1	yes	characteristic
32	#16837232	C₂²	1	1	yes	characteristic, complemented
33	#16837231	C₂²	1	2	yes	complemented
34	#16837210	C₂²	1	2	yes	complemented
35	#16837209	C₂²	1	2	yes	complemented
36	#16837208	C₂²	1	2	yes	complemented
37	#16837177	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
40	C₅₉×#508	C₂²	1	1	yes	characteristic
41	C₅₉×#443	C₂²	1	2	yes	complemented
42	C₅₉×#368	C₂²	1	1	yes	characteristic, complemented
43	C₅₉×#359	C₂²	1	2	yes	complemented
44	C₅₉×#346	C₂²	1	1	yes	characteristic, complemented
45	#41×D₅₉	—	2	2	no	—
46	#14273750	C₂×C₄	1	2	yes	—
47	#14273749	C₂³	1	2	yes	—
48	#14273748	—	2	2	no	—
49	#14273747	—	2	2	no	—
50	#14273746	C₂×C₄	1	2	yes	—
51	Q₁₆×D₅₉	C₂×C₄	1	2	yes	—
52	SD₁₆×D₅₉	—	2	2	no	—
53	D₈×D₅₉	C₂×C₄	1	2	yes	—
54	#14273735	—	2	2	no	—
55	#14273735	—	4	2	no	—
56	#14273734	—	2	2	no	—
57	#14273733	—	2	2	no	—
58	#14273733	—	4	2	no	—
59	C₂×#11745659	—	4	2	no	—
60	C₂×#11745659	D₄	1	1	yes	characteristic
61	M₁₆×D₅₉	—	2	2	no	—
62	M₁₆×D₅₉	—	4	2	no	—
63	C₂×C₈×D₅₉	C₂³	1	1	yes	characteristic
64	#14273684	D₄	1	1	yes	characteristic
65	Dic₄₇₂	C₂×C₄	1	1	yes	characteristic
66	#14273673	C₂×C₄	1	2	yes	—
67	#14273672	C₂×C₄	1	2	yes	—
68	#14273671	C₂×C₄	1	2	yes	—
69	#14273670	C₂×C₄	1	2	yes	—
70	D₉₄₄	C₂×C₄	1	1	yes	characteristic
71	#14273668	C₂×C₄	1	2	yes	—
72	#14273666	—	2	1	no	—
73	#14273666	—	2	1	no	—
74	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
76	C₁₆×D₅₉	C₂×C₄	1	1	yes	characteristic
77	C₁₆×D₅₉	C₂×C₄	1	1	yes	characteristic
78	C₁₆×D₅₉	C₂×C₄	1	1	yes	characteristic
79	C₁₆×D₅₉	C₂×C₄	1	1	yes	characteristic
80	#14273663	C₂³	1	2	yes	—
81	#14273662	—	2	2	no	—
82	#14273655	—	2	2	no	—
83	#14273654	—	2	2	no	—
84	#14273653	—	2	2	no	—
85	#14273638	D₄	1	1	yes	characteristic
86	#14273637	D₄	1	1	yes	characteristic
87	C₈×Dic₅₉	C₂³	1	1	yes	characteristic
88	#135×C₅₉	C₂³	1	2	yes	—
89	#131×C₅₉	—	2	2	no	—
90	Q₃₂×C₅₉	C₂×C₄	1	1	yes	characteristic
91	SD₃₂×C₅₉	C₂×C₄	1	2	yes	—
92	D₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
95	#108×C₅₉	C₂³	1	2	yes	—
96	#104×C₅₉	—	2	2	no	—
97	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	#41×C₅₉	—	2	2	no	—
99	#11745689	—	2	2	no	—
100	Q₈×D₅₉	—	2	2	no	—
101	#11745687	—	2	2	no	—
102	#11745687	—	4	2	no	—
103	D₄×D₅₉	—	2	2	no	—
104	D₄×D₅₉	—	4	2	no	—
105	#11745685	—	2	2	no	—
106	#11745685	—	4	2	no	—
107	C₂×C₄×D₅₉	—	4	2	no	—
108	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
109	Q₁₆×C₅₉	C₂²×C₄	1	2	yes	—
110	SD₁₆×C₅₉	—	2	2	no	—
111	D₈×C₅₉	C₂²×C₄	1	2	yes	—
112	M₁₆×C₅₉	—	2	2	no	—
113	M₁₆×C₅₉	—	4	2	no	—
114	C₂×C₈×C₅₉	—	4	2	no	—
115	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
117	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
118	#11745672	—	2	2	no	—
119	#11745671	—	2	2	no	—
120	#11745670	—	2	2	no	—
121	#11745669	—	2	2	no	—
122	(C₂×D₅₉)⋊C₄	—	2	1	no	—
123	Dic₅₉⋊C₄	—	2	1	no	—
124	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
125	#11745664	—	2	2	no	—
126	#11745664	—	4	2	no	—
127	C₂×C₅₉⋊C₈	—	4	2	no	—
128	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
130	Dic₂₃₆	C₂²×C₄	1	2	yes	—
131	D₄₇₂	C₂²×C₄	1	2	yes	—
132	#11745660	—	2	2	no	—
133	#11745659	—	4	2	no	—
134	#11745659	—	4	2	no	—
135	#11745659	—	4	2	no	—
136	#11745659	D₈	1	2	yes	—
137	#11745659	D₈	1	2	yes	—
138	C₈×D₅₉	—	4	2	no	—
139	C₈×D₅₉	—	4	2	no	—
140	C₈×D₅₉	—	4	2	no	—
141	C₈×D₅₉	C₂²×C₄	1	1	yes	characteristic
142	C₈×D₅₉	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₅₉	#41	1	1	yes	characteristic
144	C₈×D₅₉	#41	1	1	yes	characteristic
145	C₁₆×C₅₉	—	2	1	no	—
146	C₁₆×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₁₆×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₅₉⋊C₁₆	—	2	1	no	—
149	C₅₉⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
150	C₅₉⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
151	C₂²×D₅₉	—	4	2	no	—
152	C₂²×D₅₉	#135	1	1	yes	characteristic
153	Q₈×C₅₉	—	2	2	no	—
154	D₄×C₅₉	—	2	2	no	—
155	D₄×C₅₉	—	4	2	no	—
156	C₂×C₄×C₅₉	—	2	1	no	—
157	C₂×C₄×C₅₉	—	4	2	no	—
158	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
159	C₂²⋊D₅₉	—	4	2	no	—
160	C₂²⋊D₅₉	—	4	2	no	—
161	C₂²⋊D₅₉	—	4	2	no	—
162	C₂×Dic₅₉	—	2	1	no	—
163	C₂×Dic₅₉	—	4	2	no	—
164	C₂×Dic₅₉	#135	1	1	yes	characteristic
165	D₂₃₆	—	2	2	no	—
166	D₂₃₆	—	4	2	no	—
167	C₄×D₅₉	—	4	2	no	—
168	C₄×D₅₉	—	4	2	no	—
169	C₄×D₅₉	—	4	2	no	—
170	C₄×D₅₉	C₄×D₄	1	1	yes	characteristic
171	C₄×D₅₉	C₄×D₄	1	1	yes	characteristic
172	C₄×D₅₉	C₂×D₈	1	1	yes	characteristic
173	C₄×D₅₉	C₂×D₈	1	1	yes	characteristic
174	Dic₁₁₈	—	2	2	no	—
175	Dic₁₁₈	—	4	2	no	—
176	C₈×C₅₉	—	4	2	no	—
177	C₈×C₅₉	C₂×D₈	1	2	yes	—
178	C₈×C₅₉	C₂³×C₄	1	1	yes	characteristic
179	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
180	C₅₉⋊C₈	—	4	2	no	—
181	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
182	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
183	C₅₉⋊C₈	C₂×D₈	1	2	yes	—
184	#33465	—	59	1	no	maximal, Sylow
185	C₂²×C₅₉	—	4	2	no	—
186	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
187	C₂×D₅₉	—	4	1	no	—
188	C₂×D₅₉	—	4	2	no	—
189	C₂×D₅₉	—	16	2	no	—
190	C₂×D₅₉	C₄×D₈	1	1	yes	characteristic
191	C₂×D₅₉	C₄×D₈	1	1	yes	characteristic
192	C₄×C₅₉	—	4	1	no	—
193	C₄×C₅₉	—	4	2	no	—
194	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₅₉	C₂²×D₈	1	1	yes	characteristic
196	Dic₅₉	—	4	1	no	—
197	Dic₅₉	—	4	2	no	—
198	Dic₅₉	C₄×D₈	1	1	yes	characteristic
199	Dic₅₉	C₄×D₈	1	1	yes	characteristic
200	C₂×#508	—	59	1	no	—
201	#2957	—	59	2	no	—
202	#2179	—	59	1	no	—
203	#2179	—	59	1	no	—
204	#2179	—	59	1	no	—
205	#2179	D₅₉	1	1	yes	characteristic, complemented
206	#2178	—	59	2	no	—
207	#2178	—	59	2	no	—
208	C₂×#368	—	59	1	no	—
209	#2143	—	59	2	no	—
210	#2108	—	59	1	no	—
211	C₂×C₅₉	—	2	1	no	—
212	C₂×C₅₉	—	8	2	no	—
213	C₂×C₅₉	C₂×C₄×D₈	1	1	yes	characteristic
214	D₅₉	—	2	1	no	—
215	D₅₉	—	2	1	no	—
216	D₅₉	—	8	2	no	—
217	C₂×#135	—	59	2	no	—
218	#568	—	118	2	no	—
219	#508	—	59	2	no	—
220	#508	—	59	1	no	—
221	#508	—	59	2	no	—
222	#508	—	59	1	no	—
223	#508	—	59	1	no	—
224	#508	C₂×D₅₉	1	1	yes	characteristic
225	C₂×Q₃₂	—	59	1	no	—
226	C₂×SD₃₂	—	59	2	no	—
227	C₂×D₁₆	—	59	1	no	—
228	C₂×M₃₂	—	59	1	no	—
229	C₂²×C₁₆	—	59	1	no	—
230	#444	—	118	2	no	—
231	#444	—	118	2	no	—
232	#443	—	59	2	no	—
233	#443	—	59	2	no	—
234	#443	—	59	2	no	—
235	#443	C₂×D₅₉	1	2	yes	complemented
236	C₂×#108	—	59	2	no	—
237	#421	—	118	2	no	—
238	#405	—	59	1	no	—
239	#368	—	59	1	no	—
240	#368	—	59	2	no	—
241	#368	C₂×D₅₉	1	1	yes	characteristic, complemented
242	#359	—	59	2	no	—
243	#359	—	59	2	no	—
244	#359	—	59	2	no	—
245	#359	C₂×D₅₉	1	2	yes	complemented
246	#346	—	59	1	no	—
247	#346	C₂×D₅₉	1	1	yes	characteristic, complemented
248	C₄×C₁₆	—	59	1	no	—
249	C₄×C₁₆	—	59	1	no	—
250	C₅₉	#33465	1	1	yes	characteristic, complemented, Sylow
251	C₂×#41	—	118	2	no	—
252	#135	—	59	2	no	—
253	#135	—	59	2	no	—
254	#135	—	59	2	no	—
255	#135	—	118	2	no	—
256	#135	—	118	2	no	—
257	#135	C₂²×D₅₉	1	2	yes	—
258	C₂×Q₁₆	—	59	2	no	—
259	C₂×SD₁₆	—	118	2	no	—
260	C₂×D₈	—	59	2	no	—
261	#131	—	2	2	no	—
262	#131	—	118	2	no	—
263	#131	—	118	2	no	—
264	#131	—	118	2	no	—
265	#131	—	236	2	no	—
266	#131	—	236	2	no	—
267	C₂×M₁₆	—	59	1	no	—
268	C₂×M₁₆	—	118	2	no	—
269	C₂×M₁₆	—	236	2	no	—
270	C₂×M₁₆	—	236	2	no	—
271	C₂²×C₈	—	59	1	no	—
272	#117	—	59	1	no	—
273	Q₃₂	—	59	2	no	—
274	Q₃₂	—	59	1	no	—
275	Q₃₂	C₄×D₅₉	1	1	yes	characteristic
276	SD₃₂	—	59	2	no	—
277	SD₃₂	—	59	2	no	—
278	SD₃₂	—	59	2	no	—
279	SD₃₂	C₄×D₅₉	1	2	yes	—
280	D₁₆	—	59	2	no	—
281	D₁₆	—	59	1	no	—
282	D₁₆	C₄×D₅₉	1	1	yes	characteristic
283	M₃₂	—	118	1	no	—
284	M₃₂	—	118	1	no	—
285	C₂×C₁₆	—	59	1	no	—
286	C₂×C₁₆	—	59	1	no	—
287	C₂×C₁₆	—	59	1	no	—
288	C₂×C₁₆	—	59	1	no	—
289	C₂×C₁₆	—	59	1	no	—
290	C₂×C₁₆	—	59	1	no	—
291	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
292	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
293	#108	—	59	2	no	—
294	#108	—	118	2	no	—
295	#108	C₂²×D₅₉	1	2	yes	—
296	#104	—	2	2	no	—
297	#104	—	118	2	no	—
298	#104	—	118	2	no	—
299	#104	—	118	2	no	—
300	#97	—	59	1	no	—
301	#97	—	59	1	no	—
302	C₄×C₈	—	59	1	no	—
303	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
304	#41	—	2	2	no	—
305	#41	—	118	2	no	—
306	#41	—	118	2	no	—
307	#41	—	118	2	no	—
308	#41	—	236	2	no	—
309	#41	—	236	2	no	—
310	C₂×Q₈	—	118	2	no	—
311	C₂×D₄	—	118	2	no	—
312	C₂×D₄	—	236	2	no	—
313	C₂²×C₄	—	59	1	no	—
314	C₂²×C₄	—	236	2	no	—
315	Q₁₆	—	59	2	no	—
316	Q₁₆	—	118	2	no	—
317	Q₁₆	C₂×C₄×D₅₉	1	2	yes	—
318	SD₁₆	—	2	2	no	—
319	SD₁₆	—	118	2	no	—
320	SD₁₆	—	118	2	no	—
321	SD₁₆	—	118	2	no	—
322	D₈	—	59	2	no	—
323	D₈	—	118	2	no	—
324	D₈	C₂×C₄×D₅₉	1	2	yes	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	59	2	no	—
328	M₁₆	—	59	2	no	—
329	M₁₆	—	118	2	no	—
330	M₁₆	—	236	2	no	—
331	M₁₆	—	236	2	no	—
332	M₁₆	—	236	2	no	—
333	M₁₆	—	236	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	59	1	no	—
336	C₂×C₈	—	59	1	no	—
337	C₂×C₈	—	59	1	no	—
338	C₂×C₈	—	59	1	no	—
339	C₂×C₈	—	59	1	no	—
340	C₂×C₈	—	59	1	no	—
341	C₂×C₈	—	236	2	no	—
342	C₂×C₈	—	236	2	no	—
343	C₂×C₈	—	236	2	no	—
344	C₂×C₈	—	236	2	no	—
345	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
346	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
347	C₄⋊C₄	—	118	1	no	—
348	C₂²⋊C₄	—	118	1	no	—
349	C₄²	—	59	1	no	—
350	C₄²	D₄×D₅₉	1	1	yes	characteristic
351	C₁₆	—	2	1	no	—
352	C₁₆	—	59	1	no	—
353	C₁₆	—	59	1	no	—
354	C₁₆	—	118	1	no	—
355	C₁₆	C₂×C₄×D₅₉	1	1	yes	characteristic
356	C₁₆	C₂×C₄×D₅₉	1	1	yes	characteristic
357	C₂³	—	59	1	no	—
358	C₂³	—	236	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	118	2	no	—
361	Q₈	—	236	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	118	2	no	—
365	D₄	—	236	2	no	—
366	D₄	—	236	2	no	—
367	D₄	—	236	2	no	—
368	D₄	—	236	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	59	1	no	—
372	C₂×C₄	—	59	1	no	—
373	C₂×C₄	—	59	1	no	—
374	C₂×C₄	—	59	1	no	—
375	C₂×C₄	—	59	1	no	—
376	C₂×C₄	—	118	1	no	—
377	C₂×C₄	—	236	2	no	—
378	C₂×C₄	—	236	2	no	—
379	C₂×C₄	—	236	2	no	—
380	C₂×C₄	—	236	2	no	—
381	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	59	2	no	—
384	C₈	—	59	1	no	—
385	C₈	—	59	1	no	—
386	C₈	—	236	2	no	—
387	C₈	D₈×D₅₉	1	2	yes	—
388	C₈	C₂²×C₄×D₅₉	1	1	yes	characteristic
389	C₈	#41×D₅₉	1	1	yes	characteristic
390	C₂²	—	4	2	no	—
391	C₂²	—	59	1	no	—
392	C₂²	—	59	1	no	—
393	C₂²	—	944	2	no	—
394	C₂²	—	236	1	no	—
395	C₂²	—	236	2	no	—
396	C₂²	#135×D₅₉	1	1	yes	characteristic
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	59	1	no	—
400	C₄	—	59	1	no	—
401	C₄	—	236	1	no	—
402	C₄	—	236	2	no	—
403	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
404	C₄	C₂×D₈×D₅₉	1	1	yes	characteristic
405	C₂	—	2	1	no	—
406	C₂	—	8	2	no	—
407	C₂	—	118	1	no	—
408	C₂	—	118	1	no	—
409	C₂	—	472	2	no	—
410	C₂	C₄×D₈×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₅₉
commutator	C₈×C₅₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₅₉×#2179	C₂
socle	C₂×C₅₉	C₂×C₄×D₈
prime radical	#508×D₅₉	C₂
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	#2179	D₅₉
hypocenter	C₅₉	#33465
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2179

Complements

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

N	H ≅ G/N	type
2. #21433008	C₂	semidirect
3. #21425983	C₂	semidirect
4. #21425982	C₂	semidirect
5. #21425981	C₂	semidirect
6. #21425975	C₂	semidirect
7. #21425974	C₂	semidirect
8. #368×D₅₉	C₂	semidirect
9. #21425822	C₂	semidirect
10. #21425694	C₂	semidirect
11. C₅₉×#2179	C₂	semidirect
14. #16837835	C₄	semidirect
16. #16837833	C₄	semidirect
18. #16837831	C₄	semidirect
19. Q₃₂×D₅₉	C₄	semidirect
20. SD₃₂×D₅₉	C₄	semidirect
21. D₁₆×D₅₉	C₄	semidirect
26. #16837520	C₂²	semidirect
27. #16837519	C₂²	semidirect
28. #16837518	C₂²	semidirect
32. #16837232	C₂²	semidirect
33. #16837231	C₂²	semidirect
34. #16837210	C₂²	semidirect
35. #16837209	C₂²	semidirect
36. #16837208	C₂²	semidirect
37. #16837177	C₂²	semidirect
38. C₄×C₅₉⋊C₁₆	C₂²	semidirect
39. C₁₆×Dic₅₉	C₂²	semidirect
41. C₅₉×#443	C₂²	semidirect
42. C₅₉×#368	C₂²	semidirect
43. C₅₉×#359	C₂²	semidirect
44. C₅₉×#346	C₂²	semidirect
205. #2179	D₅₉	semidirect
235. #443	C₂×D₅₉	semidirect
241. #368	C₂×D₅₉	semidirect
245. #359	C₂×D₅₉	semidirect
247. #346	C₂×D₅₉	semidirect
250. C₅₉	#33465	semidirect

Maximal subgroups

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

subgroup	index
#508×D₅₉	2
#21433008	2
#21425983	2
#21425982	2
#21425981	2
#21425975	2
#21425974	2
#368×D₅₉	2
#21425822	2
#21425694	2
C₅₉×#2179	2
#33465	59