Subgroups — D₅₉×#2231 #28743421

Order 15104.

526 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#499×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#21426273	C₂	1	1	yes	maximal, characteristic, complemented
4	#21426272	C₂	1	1	yes	maximal, characteristic, complemented
5	#21426271	C₂	1	2	yes	maximal, complemented
6	#21426270	C₂	1	2	yes	maximal, complemented
7	#21426269	C₂	1	1	yes	maximal, characteristic, complemented
8	#365×D₅₉	C₂	1	2	yes	maximal, complemented
9	#364×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#360×D₅₉	C₂	1	2	yes	maximal
11	C₅₉×#2231	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₅₉	C₂²	1	1	yes	characteristic
13	#131×D₅₉	—	2	1	no	—
14	#125×D₅₉	—	2	1	no	—
15	M₃₂×D₅₉	C₂²	1	2	yes	—
16	#16837804	C₂²	1	1	yes	characteristic, complemented
17	#16837803	—	2	1	no	—
18	#16837802	C₂²	1	2	yes	complemented
19	#16837801	—	2	1	no	—
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	#107×D₅₉	—	2	1	no	—
27	#106×D₅₉	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×#499	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
45	#14273749	C₂³	1	1	yes	characteristic
46	#14273748	—	2	1	no	—
47	#14273747	—	2	1	no	—
48	#14273746	Q₈	1	1	yes	characteristic
49	Q₁₆×D₅₉	Q₈	1	1	yes	characteristic
50	SD₁₆×D₅₉	—	2	1	no	—
51	D₈×D₅₉	Q₈	1	1	yes	characteristic
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	#14273719	—	2	1	no	—
63	#14273718	—	2	2	no	—
64	#14273717	—	4	2	no	—
65	C₄⋊C₄×D₅₉	—	2	2	no	—
66	C₄⋊C₄×D₅₉	—	4	2	no	—
67	C₄²×D₅₉	D₄	1	1	yes	characteristic
68	#14273667	C₂³	1	2	yes	—
69	#14273666	—	2	2	no	—
70	C₁₆×D₅₉	—	2	2	no	—
71	#14273663	C₂³	1	1	yes	characteristic
72	#14273662	—	2	1	no	—
73	#14273661	—	2	1	no	—
74	#14273660	—	2	2	no	—
75	#14273659	C₂³	1	2	yes	—
76	#14273658	—	2	2	no	—
77	#14273655	—	2	1	no	—
78	#14273654	—	2	1	no	—
79	#14273653	—	2	1	no	—
80	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
81	C₈×Dic₅₉	D₄	1	1	yes	characteristic
82	C₈×Dic₅₉	C₂³	1	1	yes	characteristic
83	#135×C₅₉	C₂³	1	1	yes	characteristic
84	#131×C₅₉	—	2	1	no	—
85	#125×C₅₉	—	2	1	no	—
86	M₃₂×C₅₉	C₂³	1	2	yes	—
87	#108×C₅₉	C₂³	1	1	yes	characteristic
88	#107×C₅₉	—	2	1	no	—
89	#106×C₅₉	C₂³	1	2	yes	—
90	#104×C₅₉	—	2	1	no	—
91	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
92	#41×C₅₉	—	2	1	no	—
93	#11745689	—	2	1	no	—
94	Q₈×D₅₉	—	2	1	no	—
95	#11745687	—	2	1	no	—
96	#11745687	—	4	1	no	—
97	D₄×D₅₉	—	2	1	no	—
98	D₄×D₅₉	—	4	1	no	—
99	#11745685	—	2	1	no	—
100	#11745685	—	4	1	no	—
101	C₂×C₄×D₅₉	—	2	1	no	—
102	C₂×C₄×D₅₉	—	4	1	no	—
103	C₂×C₄×D₅₉	—	4	2	no	—
104	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₅₉	C₂×Q₈	1	1	yes	characteristic
106	SD₁₆×C₅₉	—	2	1	no	—
107	D₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
108	M₁₆×C₅₉	—	2	1	no	—
109	M₁₆×C₅₉	—	4	1	no	—
110	C₂×C₈×C₅₉	—	4	1	no	—
111	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
113	C₄⋊C₄×C₅₉	—	2	2	no	—
114	C₄⋊C₄×C₅₉	—	4	2	no	—
115	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
116	#11745672	—	2	1	no	—
117	#11745671	—	2	1	no	—
118	#11745670	—	2	1	no	—
119	#11745669	—	2	1	no	—
120	C₄⋊Dic₅₉	—	2	2	no	—
121	C₄⋊Dic₅₉	—	4	2	no	—
122	Dic₅₉⋊C₄	—	4	2	no	—
123	Dic₅₉⋊C₄	—	4	2	no	—
124	Dic₅₉⋊C₄	—	4	2	no	—
125	C₄×Dic₅₉	—	2	1	no	—
126	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
127	#11745664	—	2	1	no	—
128	#11745664	—	4	1	no	—
129	C₂×C₅₉⋊C₈	—	4	1	no	—
130	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
132	Dic₂₃₆	C₂×Q₈	1	1	yes	characteristic
133	D₄₇₂	C₂×Q₈	1	1	yes	characteristic
134	#11745660	—	2	1	no	—
135	#11745659	—	4	1	no	—
136	#11745659	—	4	1	no	—
137	#11745659	—	4	1	no	—
138	C₈×D₅₉	—	4	1	no	—
139	C₈×D₅₉	—	4	1	no	—
140	C₈×D₅₉	—	4	1	no	—
141	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
142	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
143	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
144	C₈×D₅₉	SD₁₆	1	1	yes	characteristic
145	C₈×D₅₉	C₂×Q₈	1	1	yes	characteristic
146	C₈×D₅₉	C₂×Q₈	1	1	yes	characteristic
147	C₈×D₅₉	#41	1	1	yes	characteristic
148	C₈×D₅₉	#41	1	1	yes	characteristic
149	C₁₆×C₅₉	—	2	2	no	—
150	C₅₉⋊C₁₆	—	2	2	no	—
151	C₂²×D₅₉	—	4	1	no	—
152	C₂²×D₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	Q₈×C₅₉	—	2	1	no	—
154	D₄×C₅₉	—	2	1	no	—
155	D₄×C₅₉	—	4	1	no	—
156	C₂×C₄×C₅₉	—	2	1	no	—
157	C₂×C₄×C₅₉	—	4	1	no	—
158	C₂×C₄×C₅₉	—	4	2	no	—
159	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
160	C₂²⋊D₅₉	—	4	1	no	—
161	C₂²⋊D₅₉	—	4	1	no	—
162	C₂²⋊D₅₉	—	4	1	no	—
163	C₂×Dic₅₉	—	2	1	no	—
164	C₂×Dic₅₉	—	4	1	no	—
165	C₂×Dic₅₉	—	4	2	no	—
166	C₂×Dic₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
167	D₂₃₆	—	2	1	no	—
168	D₂₃₆	—	4	1	no	—
169	C₄×D₅₉	—	4	2	no	—
170	C₄×D₅₉	—	4	1	no	—
171	C₄×D₅₉	—	4	1	no	—
172	C₄×D₅₉	—	4	1	no	—
173	C₄×D₅₉	—	8	4	no	—
174	C₄×D₅₉	C₂²⋊Q₈	1	1	yes	characteristic
175	C₄×D₅₉	C₂²⋊Q₈	1	1	yes	characteristic
176	C₄×D₅₉	C₂×SD₁₆	1	1	yes	characteristic
177	C₄×D₅₉	C₂×SD₁₆	1	1	yes	characteristic
178	Dic₁₁₈	—	2	1	no	—
179	Dic₁₁₈	—	4	1	no	—
180	C₈×C₅₉	—	4	1	no	—
181	C₈×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
182	C₈×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
183	C₈×C₅₉	C₂²×Q₈	1	1	yes	characteristic
184	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
185	C₅₉⋊C₈	—	4	1	no	—
186	C₅₉⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
187	C₅₉⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
188	C₅₉⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
189	C₅₉⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
190	C₂×#2231	—	59	1	no	maximal, Sylow
191	C₂²×C₅₉	—	4	1	no	—
192	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂×D₅₉	—	2	2	no	—
194	C₂×D₅₉	—	4	1	no	—
195	C₂×D₅₉	—	8	2	no	—
196	C₂×D₅₉	#476	1	1	yes	characteristic
197	C₂×D₅₉	#476	1	1	yes	characteristic
198	C₄×C₅₉	—	4	1	no	—
199	C₄×C₅₉	—	4	1	no	—
200	C₄×C₅₉	—	8	2	no	—
201	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
203	Dic₅₉	—	4	1	no	—
204	Dic₅₉	—	4	1	no	—
205	Dic₅₉	—	8	2	no	—
206	Dic₅₉	#476	1	1	yes	characteristic
207	Dic₅₉	#476	1	1	yes	characteristic
208	C₂×#499	—	59	1	no	—
209	C₂×#443	—	59	1	no	—
210	#2231	—	59	1	no	—
211	#2231	—	59	1	no	—
212	#2231	—	59	2	no	—
213	#2231	—	59	1	no	—
214	#2231	—	59	2	no	—
215	#2231	D₅₉	1	1	yes	characteristic, direct product factor
216	C₂×#365	—	59	2	no	—
217	C₂×#364	—	59	1	no	—
218	C₂×#360	—	59	2	no	—
219	C₂×C₅₉	—	2	1	no	—
220	C₂×C₅₉	—	8	1	no	—
221	C₂×C₅₉	C₂×#476	1	1	yes	characteristic
222	D₅₉	—	2	1	no	—
223	D₅₉	—	8	1	no	—
224	D₅₉	#2231	1	2	yes	direct product factor
225	C₂×#135	—	59	1	no	—
226	C₂×#131	—	118	1	no	—
227	C₂×#125	—	118	1	no	—
228	C₂×M₃₂	—	59	2	no	—
229	#499	—	59	2	no	—
230	#499	—	59	1	no	—
231	#499	—	118	1	no	—
232	#499	—	118	1	no	—
233	#499	C₂×D₅₉	1	1	yes	characteristic, complemented
234	#443	—	59	1	no	—
235	#443	—	59	1	no	—
236	#443	—	59	1	no	—
237	#443	—	118	1	no	—
238	#443	—	118	1	no	—
239	#443	C₂×D₅₉	1	1	yes	characteristic
240	C₂×#108	—	59	1	no	—
241	C₂×#107	—	118	1	no	—
242	C₂×#106	—	59	2	no	—
243	C₂×#104	—	118	1	no	—
244	C₂×C₄×C₈	—	59	1	no	—
245	#365	—	59	2	no	—
246	#365	—	59	2	no	—
247	#365	—	59	2	no	—
248	#365	C₂×D₅₉	1	2	yes	complemented
249	#364	—	59	2	no	—
250	#364	—	59	1	no	—
251	#364	C₂×D₅₉	1	1	yes	characteristic, complemented
252	#360	—	59	2	no	—
253	#360	—	59	2	no	—
254	#360	—	59	2	no	—
255	#360	C₂×D₅₉	1	2	yes	—
256	C₅₉	C₂×#2231	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	118	1	no	—
258	#135	—	59	1	no	—
259	#135	—	59	1	no	—
260	#135	—	59	1	no	—
261	#135	—	118	1	no	—
262	#135	—	118	1	no	—
263	#135	C₂²×D₅₉	1	1	yes	characteristic
264	C₂×Q₁₆	—	59	1	no	—
265	C₂×SD₁₆	—	118	1	no	—
266	C₂×D₈	—	59	1	no	—
267	#131	—	2	1	no	—
268	#131	—	118	1	no	—
269	#131	—	118	1	no	—
270	#131	—	118	1	no	—
271	#131	—	236	1	no	—
272	#131	—	236	1	no	—
273	C₂×M₁₆	—	118	1	no	—
274	C₂×M₁₆	—	236	1	no	—
275	C₂²×C₈	—	59	1	no	—
276	C₂²×C₈	—	59	1	no	—
277	C₂²×C₈	—	236	1	no	—
278	#125	—	2	1	no	—
279	#125	—	118	2	no	—
280	#125	—	118	1	no	—
281	#125	—	236	2	no	—
282	C₂×C₄⋊C₄	—	118	2	no	—
283	C₂×C₄⋊C₄	—	236	2	no	—
284	C₂×C₄²	—	59	1	no	—
285	M₃₂	—	59	2	no	—
286	M₃₂	—	118	2	no	—
287	M₃₂	C₂²×D₅₉	1	2	yes	—
288	C₂×C₁₆	—	118	2	no	—
289	#108	—	59	1	no	—
290	#108	—	118	1	no	—
291	#108	C₂²×D₅₉	1	1	yes	characteristic
292	#107	—	2	1	no	—
293	#107	—	118	2	no	—
294	#107	—	118	1	no	—
295	#106	—	59	2	no	—
296	#106	—	118	2	no	—
297	#106	C₂²×D₅₉	1	2	yes	—
298	#104	—	2	1	no	—
299	#104	—	118	1	no	—
300	#104	—	118	1	no	—
301	#104	—	118	1	no	—
302	C₄×C₈	—	59	1	no	—
303	C₄×C₈	—	59	1	no	—
304	C₄×C₈	—	59	1	no	—
305	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
306	#41	—	2	1	no	—
307	#41	—	118	1	no	—
308	#41	—	118	1	no	—
309	#41	—	118	1	no	—
310	#41	—	236	1	no	—
311	#41	—	236	1	no	—
312	C₂×Q₈	—	118	1	no	—
313	C₂×D₄	—	118	1	no	—
314	C₂×D₄	—	236	1	no	—
315	C₂²×C₄	—	59	1	no	—
316	C₂²×C₄	—	118	1	no	—
317	C₂²×C₄	—	236	1	no	—
318	C₂²×C₄	—	236	2	no	—
319	Q₁₆	—	59	1	no	—
320	Q₁₆	—	118	1	no	—
321	Q₁₆	Q₈×D₅₉	1	1	yes	characteristic
322	SD₁₆	—	2	1	no	—
323	SD₁₆	—	118	1	no	—
324	SD₁₆	—	118	1	no	—
325	SD₁₆	—	118	1	no	—
326	D₈	—	59	1	no	—
327	D₈	—	118	1	no	—
328	D₈	Q₈×D₅₉	1	1	yes	characteristic
329	M₁₆	—	2	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	118	1	no	—
332	M₁₆	—	236	1	no	—
333	M₁₆	—	236	1	no	—
334	M₁₆	—	236	1	no	—
335	M₁₆	—	236	1	no	—
336	C₂×C₈	—	4	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	—	59	1	no	—
342	C₂×C₈	—	59	1	no	—
343	C₂×C₈	—	59	1	no	—
344	C₂×C₈	—	59	1	no	—
345	C₂×C₈	—	59	1	no	—
346	C₂×C₈	—	59	1	no	—
347	C₂×C₈	—	236	1	no	—
348	C₂×C₈	—	236	1	no	—
349	C₂×C₈	—	236	1	no	—
350	C₂×C₈	—	236	1	no	—
351	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
352	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	118	2	no	—
356	C₄⋊C₄	—	236	2	no	—
357	C₄⋊C₄	—	236	2	no	—
358	C₄⋊C₄	—	236	2	no	—
359	C₄⋊C₄	—	236	2	no	—
360	C₄²	—	59	1	no	—
361	C₄²	—	118	1	no	—
362	C₄²	D₄×D₅₉	1	1	yes	characteristic
363	C₁₆	—	2	2	no	—
364	C₁₆	—	118	2	no	—
365	C₂³	—	59	1	no	—
366	C₂³	—	236	1	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	118	1	no	—
369	Q₈	—	236	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	118	1	no	—
373	D₄	—	236	1	no	—
374	D₄	—	236	1	no	—
375	D₄	—	236	1	no	—
376	D₄	—	236	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	59	1	no	—
381	C₂×C₄	—	59	1	no	—
382	C₂×C₄	—	59	1	no	—
383	C₂×C₄	—	59	1	no	—
384	C₂×C₄	—	59	1	no	—
385	C₂×C₄	—	118	1	no	—
386	C₂×C₄	—	472	4	no	—
387	C₂×C₄	—	236	1	no	—
388	C₂×C₄	—	236	1	no	—
389	C₂×C₄	—	236	2	no	—
390	C₂×C₄	—	236	1	no	—
391	C₂×C₄	—	236	2	no	—
392	C₂×C₄	—	236	1	no	—
393	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
394	C₈	—	4	1	no	—
395	C₈	—	59	1	no	—
396	C₈	—	59	1	no	—
397	C₈	—	59	1	no	—
398	C₈	—	59	1	no	—
399	C₈	—	236	1	no	—
400	C₈	SD₁₆×D₅₉	1	1	yes	characteristic
401	C₈	SD₁₆×D₅₉	1	1	yes	characteristic
402	C₈	C₂×Q₈×D₅₉	1	1	yes	characteristic
403	C₈	#41×D₅₉	1	1	yes	characteristic
404	C₂²	—	4	1	no	—
405	C₂²	—	59	1	no	—
406	C₂²	—	59	1	no	—
407	C₂²	—	118	2	no	—
408	C₂²	—	472	2	no	—
409	C₂²	—	236	1	no	—
410	C₂²	AGL(1,ℤ/8)×D₅₉	1	1	yes	characteristic
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	59	1	no	—
415	C₄	—	59	1	no	—
416	C₄	—	472	2	no	—
417	C₄	—	236	1	no	—
418	C₄	—	236	1	no	—
419	C₄	C₂²⋊Q₈×D₅₉	1	1	yes	characteristic
420	C₄	C₂×SD₁₆×D₅₉	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	8	1	no	—
423	C₂	—	59	2	no	—
424	C₂	—	118	1	no	—
425	C₂	—	472	1	no	—
426	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×#2231	C₂
socle	C₂×C₅₉	C₂×#476
prime radical	#135×D₅₉	C₂²
hypercenter	#2231	D₅₉
hypocenter	C₅₉	C₂×#2231
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2231

Complements

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

N	H ≅ G/N	type
1. #499×D₅₉	C₂	semidirect
3. #21426273	C₂	semidirect
4. #21426272	C₂	semidirect
5. #21426271	C₂	semidirect
6. #21426270	C₂	semidirect
7. #21426269	C₂	semidirect
8. #365×D₅₉	C₂	semidirect
9. #364×D₅₉	C₂	semidirect
11. C₅₉×#2231	C₂	semidirect
16. #16837804	C₂²	semidirect
18. #16837802	C₂²	semidirect
30. #16837226	C₂²	semidirect
31. #16837225	C₂²	semidirect
32. #16837224	C₂²	semidirect
33. #16837223	C₂²	semidirect
34. #16837222	C₂²	semidirect
38. C₅₉×#499	C₂²	semidirect
40. C₅₉×#365	C₂²	semidirect
41. C₅₉×#364	C₂²	semidirect
215. #2231	D₅₉	direct (N × H)
224. D₅₉	#2231	direct (N × H)
233. #499	C₂×D₅₉	semidirect
248. #365	C₂×D₅₉	semidirect
251. #364	C₂×D₅₉	semidirect
256. C₅₉	C₂×#2231	semidirect

Maximal subgroups

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

subgroup	index
#499×D₅₉	2
#443×D₅₉	2
#21426273	2
#21426272	2
#21426271	2
#21426270	2
#21426269	2
#365×D₅₉	2
#364×D₅₉	2
#360×D₅₉	2
C₅₉×#2231	2
C₂×#2231	59

Subgroups — D59×#2231 #28743421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×#2231 #28743421