Subgroups — #28743427

Order 15104.

524 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434605	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#21426271	C₂	1	2	yes	maximal, complemented
4	#21426270	C₂	1	2	yes	maximal, complemented
5	#21426268	C₂	1	1	yes	maximal, characteristic, complemented
6	#21426267	C₂	1	1	yes	maximal, characteristic, complemented
7	#21426264	C₂	1	1	yes	maximal, characteristic, complemented
8	#21425867	C₂	1	2	yes	maximal, complemented
9	#364×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#21425830	C₂	1	2	yes	maximal
11	C₅₉×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₅₉	C₂²	1	1	yes	characteristic
13	#131×D₅₉	—	2	1	no	—
14	#16837957	—	2	1	no	—
15	M₃₂×D₅₉	C₂²	1	2	yes	—
16	#16837805	—	2	1	no	—
17	#16837802	—	2	1	no	—
18	#16837802	C₂²	1	2	yes	complemented
19	#16837800	C₂²	1	1	yes	characteristic, complemented
20	#16837520	C₂²	1	1	yes	characteristic
21	#16837519	C₂²	1	1	yes	characteristic
22	#16837518	C₂²	1	1	yes	characteristic
23	#16837517	—	2	1	no	—
24	#16837516	—	2	1	no	—
25	#108×D₅₉	C₂²	1	1	yes	characteristic
26	#16837437	—	2	1	no	—
27	#16837437	C₂²	1	2	yes	—
28	#104×D₅₉	—	2	1	no	—
29	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
30	#16837226	C₂²	1	2	yes	complemented
31	#16837225	C₂²	1	2	yes	complemented
32	#16837224	C₂²	1	2	yes	complemented
33	#16837223	C₂²	1	1	yes	characteristic, complemented
34	#16837222	C₂²	1	2	yes	complemented
35	#16837213	C₂²	1	2	yes	—
36	#16837212	C₂²	1	2	yes	—
37	#16837211	C₂²	1	2	yes	—
38	C₅₉×#498	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#443	C₂²	1	1	yes	characteristic
40	C₅₉×#365	C₂²	1	2	yes	complemented
41	C₅₉×#364	C₂²	1	1	yes	characteristic, complemented
42	C₅₉×#360	C₂²	1	2	yes	—
43	#41×D₅₉	—	2	1	no	—
44	#14273750	Q₈	1	1	yes	characteristic, complemented
45	#14273749	C₂³	1	1	yes	characteristic
46	#14273748	—	2	1	no	—
47	#14273747	—	2	1	no	—
48	#14273746	Q₈	1	1	yes	characteristic, complemented
49	Q₁₆×D₅₉	Q₈	1	1	yes	characteristic, complemented
50	SD₁₆×D₅₉	—	2	1	no	—
51	D₈×D₅₉	Q₈	1	1	yes	characteristic, complemented
52	#14273735	—	2	1	no	—
53	#14273735	—	4	1	no	—
54	#14273734	—	2	1	no	—
55	#14273733	—	2	1	no	—
56	#14273733	—	4	1	no	—
57	M₁₆×D₅₉	—	2	1	no	—
58	M₁₆×D₅₉	—	4	1	no	—
59	C₂×C₈×D₅₉	—	4	1	no	—
60	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅₉	C₂³	1	1	yes	characteristic
62	#14273727	—	2	1	no	—
63	#14273718	—	2	2	no	—
64	#14273707	—	4	1	no	—
65	#14273703	—	4	1	no	—
66	Q₈×Dic₅₉	—	4	1	no	—
67	#14273692	—	4	1	no	—
68	#14273685	—	2	2	no	—
69	C₄²×D₅₉	D₄	1	1	yes	characteristic
70	#14273667	C₂³	1	2	yes	—
71	#14273666	—	2	2	no	—
72	C₁₆×D₅₉	—	2	2	no	—
73	#14273663	C₂³	1	1	yes	characteristic
74	#14273662	—	2	1	no	—
75	#14273660	—	2	2	no	—
76	#14273660	—	2	2	no	—
77	#14273659	—	2	1	no	—
78	#14273659	C₂³	1	2	yes	—
79	#14273655	—	2	1	no	—
80	#14273654	—	2	1	no	—
81	#14273653	—	2	1	no	—
82	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
83	C₈×Dic₅₉	D₄	1	1	yes	characteristic
84	C₈×Dic₅₉	C₂³	1	1	yes	characteristic
85	#135×C₅₉	C₂³	1	1	yes	characteristic
86	#131×C₅₉	—	2	1	no	—
87	C₄⋊Q₈×C₅₉	—	2	1	no	—
88	M₃₂×C₅₉	C₂³	1	2	yes	—
89	#108×C₅₉	C₂³	1	1	yes	characteristic
90	#106×C₅₉	—	2	1	no	—
91	#106×C₅₉	C₂³	1	2	yes	—
92	#104×C₅₉	—	2	1	no	—
93	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
94	#41×C₅₉	—	2	1	no	—
95	C₂×Q₈×C₅₉	—	4	1	no	—
96	#11745689	—	2	1	no	—
97	Q₈×D₅₉	—	2	1	no	—
98	#11745687	—	2	1	no	—
99	#11745687	—	4	1	no	—
100	D₄×D₅₉	—	2	1	no	—
101	D₄×D₅₉	—	4	1	no	—
102	#11745685	—	2	1	no	—
103	#11745685	—	4	1	no	—
104	C₂×C₄×D₅₉	—	2	1	no	—
105	C₂×C₄×D₅₉	—	4	1	no	—
106	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
107	C₂×Dic₁₁₈	—	4	1	no	—
108	Q₁₆×C₅₉	C₂×Q₈	1	1	yes	characteristic
109	SD₁₆×C₅₉	—	2	1	no	—
110	D₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
111	M₁₆×C₅₉	—	2	1	no	—
112	M₁₆×C₅₉	—	4	1	no	—
113	C₂×C₈×C₅₉	—	4	1	no	—
114	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₅₉	—	2	2	no	—
117	C₄⋊C₄×C₅₉	—	4	1	no	—
118	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
119	#11745672	—	2	1	no	—
120	#11745671	—	2	1	no	—
121	#11745670	—	2	1	no	—
122	#11745669	—	2	1	no	—
123	(C₂×D₅₉)⋊C₄	—	4	2	no	—
124	C₄⋊Dic₅₉	—	2	2	no	—
125	C₄⋊Dic₅₉	—	4	2	no	—
126	C₄⋊Dic₅₉	—	4	1	no	—
127	Dic₅₉⋊C₄	—	4	2	no	—
128	C₄×Dic₅₉	—	2	1	no	—
129	C₄×Dic₅₉	—	4	2	no	—
130	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
131	#11745664	—	2	1	no	—
132	#11745664	—	4	1	no	—
133	C₂×C₅₉⋊C₈	—	4	1	no	—
134	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
136	Dic₂₃₆	C₂×Q₈	1	1	yes	characteristic
137	D₄₇₂	C₂×Q₈	1	1	yes	characteristic
138	#11745660	—	2	1	no	—
139	#11745659	—	4	1	no	—
140	#11745659	—	4	1	no	—
141	#11745659	—	4	1	no	—
142	C₈×D₅₉	—	4	1	no	—
143	C₈×D₅₉	—	4	1	no	—
144	C₈×D₅₉	—	4	1	no	—
145	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
146	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
147	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
148	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
149	C₈×D₅₉	C₂×Q₈	1	1	yes	characteristic
150	C₈×D₅₉	C₂×Q₈	1	1	yes	characteristic
151	C₈×D₅₉	#41	1	1	yes	characteristic
152	C₈×D₅₉	#41	1	1	yes	characteristic
153	C₁₆×C₅₉	—	2	2	no	—
154	C₅₉⋊C₁₆	—	2	2	no	—
155	C₂²×D₅₉	—	4	1	no	—
156	C₂²×D₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	Q₈×C₅₉	—	2	1	no	—
158	Q₈×C₅₉	—	8	2	no	—
159	D₄×C₅₉	—	2	1	no	—
160	D₄×C₅₉	—	4	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	4	1	no	—
163	C₂×C₄×C₅₉	—	4	2	no	—
164	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
165	C₂²⋊D₅₉	—	4	1	no	—
166	C₂²⋊D₅₉	—	4	1	no	—
167	C₂²⋊D₅₉	—	4	1	no	—
168	C₂×Dic₅₉	—	2	1	no	—
169	C₂×Dic₅₉	—	4	1	no	—
170	C₂×Dic₅₉	—	4	2	no	—
171	C₂×Dic₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
172	D₂₃₆	—	2	1	no	—
173	D₂₃₆	—	4	1	no	—
174	C₄×D₅₉	—	4	2	no	—
175	C₄×D₅₉	—	4	1	no	—
176	C₄×D₅₉	—	4	1	no	—
177	C₄×D₅₉	—	4	1	no	—
178	C₄×D₅₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₄×D₅₉	C₂²⋊Q₈	1	1	yes	characteristic
180	C₄×D₅₉	C₂×SD₁₆	1	1	yes	characteristic
181	C₄×D₅₉	C₂×SD₁₆	1	1	yes	characteristic
182	Dic₁₁₈	—	2	1	no	—
183	Dic₁₁₈	—	4	1	no	—
184	Dic₁₁₈	—	8	2	no	—
185	C₈×C₅₉	—	4	1	no	—
186	C₈×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
187	C₈×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
188	C₈×C₅₉	C₂²×Q₈	1	1	yes	characteristic
189	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
190	C₅₉⋊C₈	—	4	1	no	—
191	C₅₉⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
192	C₅₉⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
193	C₅₉⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
194	C₅₉⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
195	#33637	—	59	1	no	maximal, Sylow
196	C₂²×C₅₉	—	4	1	no	—
197	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂×D₅₉	—	4	1	no	—
199	C₂×D₅₉	—	4	1	no	—
200	C₂×D₅₉	—	8	2	no	—
201	C₂×D₅₉	#476	1	1	yes	characteristic
202	C₂×D₅₉	#476	1	1	yes	characteristic
203	C₄×C₅₉	—	2	2	no	—
204	C₄×C₅₉	—	4	1	no	—
205	C₄×C₅₉	—	8	2	no	—
206	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
208	Dic₅₉	—	4	1	no	—
209	Dic₅₉	—	4	1	no	—
210	Dic₅₉	—	8	2	no	—
211	Dic₅₉	#476	1	1	yes	characteristic
212	Dic₅₉	#476	1	1	yes	characteristic
213	#3160	—	59	1	no	—
214	C₂×#443	—	59	1	no	—
215	#2231	—	59	2	no	—
216	#2231	—	59	2	no	—
217	#2230	—	59	1	no	—
218	#2230	—	59	1	no	—
219	#2230	—	59	1	no	—
220	#2230	D₅₉	1	1	yes	characteristic, complemented
221	#2155	—	59	2	no	—
222	C₂×#364	—	59	1	no	—
223	#2145	—	59	2	no	—
224	C₂×C₅₉	—	2	1	no	—
225	C₂×C₅₉	—	8	1	no	—
226	C₂×C₅₉	C₂×#476	1	1	yes	characteristic
227	D₅₉	—	2	1	no	—
228	D₅₉	—	2	1	no	—
229	D₅₉	—	8	1	no	—
230	C₂×#135	—	59	1	no	—
231	C₂×#131	—	118	1	no	—
232	#533	—	118	1	no	—
233	C₂×M₃₂	—	59	2	no	—
234	#500	—	118	1	no	—
235	#499	—	59	2	no	—
236	#499	—	118	1	no	—
237	#498	—	59	1	no	—
238	#498	C₂×D₅₉	1	1	yes	characteristic, complemented
239	#443	—	59	1	no	—
240	#443	—	59	1	no	—
241	#443	—	59	1	no	—
242	#443	—	118	1	no	—
243	#443	—	118	1	no	—
244	#443	C₂×D₅₉	1	1	yes	characteristic
245	C₂×#108	—	59	1	no	—
246	#427	—	59	2	no	—
247	#427	—	118	1	no	—
248	C₂×#104	—	118	1	no	—
249	C₂×C₄×C₈	—	59	1	no	—
250	#365	—	59	2	no	—
251	#365	—	59	2	no	—
252	#365	—	59	2	no	—
253	#365	C₂×D₅₉	1	2	yes	complemented
254	#364	—	59	2	no	—
255	#364	—	59	1	no	—
256	#364	C₂×D₅₉	1	1	yes	characteristic, complemented
257	#360	—	59	2	no	—
258	#360	—	59	2	no	—
259	#360	—	59	2	no	—
260	#360	C₂×D₅₉	1	2	yes	—
261	C₅₉	#33637	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	118	1	no	—
263	#135	—	59	1	no	—
264	#135	—	59	1	no	—
265	#135	—	59	1	no	—
266	#135	—	118	1	no	—
267	#135	—	118	1	no	—
268	#135	C₂²×D₅₉	1	1	yes	characteristic
269	C₂×Q₁₆	—	59	1	no	—
270	C₂×SD₁₆	—	118	1	no	—
271	C₂×D₈	—	59	1	no	—
272	#131	—	2	1	no	—
273	#131	—	118	1	no	—
274	#131	—	118	1	no	—
275	#131	—	118	1	no	—
276	#131	—	236	1	no	—
277	#131	—	236	1	no	—
278	C₂×M₁₆	—	118	1	no	—
279	C₂×M₁₆	—	236	1	no	—
280	C₂²×C₈	—	59	1	no	—
281	C₂²×C₈	—	59	1	no	—
282	C₂²×C₈	—	236	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	118	1	no	—
285	#125	—	118	2	no	—
286	C₂²⋊Q₈	—	236	1	no	—
287	C₂²⋊Q₈	—	236	1	no	—
288	C₄×Q₈	—	236	1	no	—
289	C₄×Q₈	—	236	1	no	—
290	#117	—	118	2	no	—
291	C₂×C₄²	—	59	1	no	—
292	M₃₂	—	59	2	no	—
293	M₃₂	—	118	2	no	—
294	M₃₂	C₂²×D₅₉	1	2	yes	—
295	C₂×C₁₆	—	118	2	no	—
296	#108	—	59	1	no	—
297	#108	—	118	1	no	—
298	#108	C₂²×D₅₉	1	1	yes	characteristic
299	#107	—	118	2	no	—
300	#107	—	118	2	no	—
301	#106	—	2	1	no	—
302	#106	—	59	2	no	—
303	#106	—	118	1	no	—
304	#106	C₂²×D₅₉	1	2	yes	—
305	#104	—	2	1	no	—
306	#104	—	118	1	no	—
307	#104	—	118	1	no	—
308	#104	—	118	1	no	—
309	C₄×C₈	—	59	1	no	—
310	C₄×C₈	—	59	1	no	—
311	C₄×C₈	—	59	1	no	—
312	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
313	#41	—	2	1	no	—
314	#41	—	118	1	no	—
315	#41	—	118	1	no	—
316	#41	—	118	1	no	—
317	#41	—	236	1	no	—
318	#41	—	236	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	118	1	no	—
321	C₂×Q₈	—	236	1	no	—
322	C₂×D₄	—	118	1	no	—
323	C₂×D₄	—	236	1	no	—
324	C₂²×C₄	—	59	1	no	—
325	C₂²×C₄	—	118	1	no	—
326	C₂²×C₄	—	236	1	no	—
327	Q₁₆	—	59	1	no	—
328	Q₁₆	—	118	1	no	—
329	Q₁₆	Q₈×D₅₉	1	1	yes	characteristic
330	SD₁₆	—	2	1	no	—
331	SD₁₆	—	118	1	no	—
332	SD₁₆	—	118	1	no	—
333	SD₁₆	—	118	1	no	—
334	D₈	—	59	1	no	—
335	D₈	—	118	1	no	—
336	D₈	Q₈×D₅₉	1	1	yes	characteristic
337	M₁₆	—	2	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	118	1	no	—
340	M₁₆	—	236	1	no	—
341	M₁₆	—	236	1	no	—
342	M₁₆	—	236	1	no	—
343	M₁₆	—	236	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	59	1	no	—
346	C₂×C₈	—	59	1	no	—
347	C₂×C₈	—	59	1	no	—
348	C₂×C₈	—	59	1	no	—
349	C₂×C₈	—	59	1	no	—
350	C₂×C₈	—	59	1	no	—
351	C₂×C₈	—	59	1	no	—
352	C₂×C₈	—	59	1	no	—
353	C₂×C₈	—	59	1	no	—
354	C₂×C₈	—	59	1	no	—
355	C₂×C₈	—	236	1	no	—
356	C₂×C₈	—	236	1	no	—
357	C₂×C₈	—	236	1	no	—
358	C₂×C₈	—	236	1	no	—
359	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	118	2	no	—
364	C₄⋊C₄	—	236	1	no	—
365	C₄⋊C₄	—	236	2	no	—
366	C₄⋊C₄	—	236	2	no	—
367	C₂²⋊C₄	—	236	2	no	—
368	C₄²	—	59	1	no	—
369	C₄²	—	118	1	no	—
370	C₄²	—	236	2	no	—
371	C₄²	D₄×D₅₉	1	1	yes	characteristic
372	C₁₆	—	2	2	no	—
373	C₁₆	—	118	2	no	—
374	C₂³	—	59	1	no	—
375	C₂³	—	236	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	118	1	no	—
379	Q₈	—	472	2	no	—
380	Q₈	—	236	1	no	—
381	D₄	—	2	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	118	1	no	—
384	D₄	—	236	1	no	—
385	D₄	—	236	1	no	—
386	D₄	—	236	1	no	—
387	D₄	—	236	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	59	1	no	—
392	C₂×C₄	—	59	1	no	—
393	C₂×C₄	—	59	1	no	—
394	C₂×C₄	—	59	1	no	—
395	C₂×C₄	—	59	1	no	—
396	C₂×C₄	—	118	1	no	—
397	C₂×C₄	—	236	2	no	—
398	C₂×C₄	—	236	1	no	—
399	C₂×C₄	—	236	1	no	—
400	C₂×C₄	—	236	1	no	—
401	C₂×C₄	—	236	2	no	—
402	C₂×C₄	—	236	1	no	—
403	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
404	C₈	—	4	1	no	—
405	C₈	—	59	1	no	—
406	C₈	—	59	1	no	—
407	C₈	—	59	1	no	—
408	C₈	—	59	1	no	—
409	C₈	—	236	1	no	—
410	C₈	SD₁₆×D₅₉	1	1	yes	characteristic
411	C₈	SD₁₆×D₅₉	1	1	yes	characteristic
412	C₈	C₂×Q₈×D₅₉	1	1	yes	characteristic
413	C₈	#41×D₅₉	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	59	1	no	—
416	C₂²	—	59	1	no	—
417	C₂²	—	472	2	no	—
418	C₂²	—	236	1	no	—
419	C₂²	—	236	1	no	—
420	C₂²	AGL(1,ℤ/8)×D₅₉	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	59	1	no	—
425	C₄	—	59	1	no	—
426	C₄	—	472	2	no	—
427	C₄	—	236	1	no	—
428	C₄	—	236	1	no	—
429	C₄	C₂²⋊Q₈×D₅₉	1	1	yes	characteristic
430	C₄	C₂×SD₁₆×D₅₉	1	1	yes	characteristic
431	C₂	—	2	1	no	—
432	C₂	—	8	1	no	—
433	C₂	—	118	1	no	—
434	C₂	—	118	1	no	—
435	C₂	—	472	1	no	—
436	C₂	#476×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#476×D₅₉
commutator, cosocle	C₂×C₈×C₅₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₅₉×#2230	C₂
socle	C₂×C₅₉	C₂×#476
prime radical	#135×D₅₉	C₂²
hypercenter	#2230	D₅₉
hypocenter	C₅₉	#33637
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. #21434605	C₂	semidirect
3. #21426271	C₂	semidirect
4. #21426270	C₂	semidirect
5. #21426268	C₂	semidirect
6. #21426267	C₂	semidirect
7. #21426264	C₂	semidirect
8. #21425867	C₂	semidirect
9. #364×D₅₉	C₂	semidirect
11. C₅₉×#2230	C₂	semidirect
18. #16837802	C₂²	semidirect
19. #16837800	C₂²	semidirect
30. #16837226	C₂²	semidirect
31. #16837225	C₂²	semidirect
32. #16837224	C₂²	semidirect
33. #16837223	C₂²	semidirect
34. #16837222	C₂²	semidirect
38. C₅₉×#498	C₂²	semidirect
40. C₅₉×#365	C₂²	semidirect
41. C₅₉×#364	C₂²	semidirect
44. #14273750	Q₈	semidirect
48. #14273746	Q₈	semidirect
49. Q₁₆×D₅₉	Q₈	semidirect
51. D₈×D₅₉	Q₈	semidirect
220. #2230	D₅₉	semidirect
238. #498	C₂×D₅₉	semidirect
253. #365	C₂×D₅₉	semidirect
256. #364	C₂×D₅₉	semidirect
261. C₅₉	#33637	semidirect

Maximal subgroups

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

subgroup	index
#21434605	2
#443×D₅₉	2
#21426271	2
#21426270	2
#21426268	2
#21426267	2
#21426264	2
#21425867	2
#364×D₅₉	2
#21425830	2
C₅₉×#2230	2
#33637	59