Subgroups — #28503560

Order 15104.

586 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14273666	C₂	1	1	yes	maximal, characteristic
2	C₂×M₃₂×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#405×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21422186	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422185	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422184	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1379	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₅₉	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₅₉	C₂²	1	1	yes	characteristic
10	#117×D₅₉	C₄	1	1	yes	characteristic
11	C₂×#14273667	C₂²	1	1	yes	characteristic
12	C₂×#14273666	—	2	1	no	—
13	C₂×#14273666	—	2	2	no	—
14	C₂×#14273666	—	2	1	no	—
15	C₂×#14273666	—	2	1	no	—
16	C₂×#14273666	C₄	1	4	yes	complemented
17	M₃₂×D₅₉	—	2	2	no	—
18	M₃₂×D₅₉	C₄	1	4	yes	complemented
19	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×D₅₉	—	2	1	no	—
21	#16837360	C₄	1	1	yes	characteristic
22	#16837359	—	2	1	no	—
23	#16837358	C₄	1	1	yes	characteristic
24	#16837357	C₂²	1	1	yes	characteristic
25	#16837356	—	2	1	no	—
26	#97×D₅₉	—	2	1	no	—
27	C₄×C₈×D₅₉	—	2	1	no	—
28	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#405	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
32	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
33	C₂×#11745659	—	2	1	no	—
34	M₁₆×D₅₉	—	2	2	no	—
35	M₁₆×D₅₉	C₈	1	4	yes	—
36	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×D₅₉	—	2	1	no	—
38	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₅₉	D₄	1	2	yes	—
41	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
42	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
43	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
44	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
45	C₂×C₈×D₅₉	Q₈	1	2	yes	—
46	#14273686	C₂×C₄	1	1	yes	characteristic
47	#14273685	C₈	1	2	yes	—
48	#14273684	—	2	1	no	—
49	#14273683	—	2	1	no	—
50	C₄⋊C₄×D₅₉	C₈	1	2	yes	—
51	C₂²⋊C₄×D₅₉	—	2	1	no	—
52	C₄²×D₅₉	—	2	1	no	—
53	#14273667	—	2	1	no	—
54	#14273667	C₂×C₄	1	2	yes	complemented
55	#14273666	—	2	4	no	—
56	#14273666	—	2	4	no	—
57	#14273666	—	2	4	no	—
58	C₂×C₅₉⋊C₁₆	—	2	1	no	—
59	C₂×C₅₉⋊C₁₆	—	2	1	no	—
60	C₂×C₅₉⋊C₁₆	—	2	1	no	—
61	C₂×C₅₉⋊C₁₆	C₂×C₄	1	2	yes	complemented
62	C₁₆×D₅₉	—	2	4	no	—
63	#14273638	—	2	1	no	—
64	#14273637	—	2	1	no	—
65	#14273637	—	2	1	no	—
66	C₄×C₅₉⋊C₈	—	2	1	no	—
67	C₈×Dic₅₉	—	2	1	no	—
68	C₈×Dic₅₉	—	2	1	no	—
69	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
71	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
72	M₃₂×C₅₉	—	2	1	no	—
73	M₃₂×C₅₉	C₂×C₄	1	2	yes	complemented
74	C₂×C₁₆×C₅₉	—	2	1	no	—
75	C₂×C₁₆×C₅₉	—	2	1	no	—
76	C₂×C₁₆×C₅₉	—	2	1	no	—
77	C₂×C₁₆×C₅₉	C₂×C₄	1	2	yes	complemented
78	#97×C₅₉	—	2	1	no	—
79	C₄×C₈×C₅₉	—	2	1	no	—
80	C₂³×D₅₉	M₁₆	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×Dic₅₉	M₁₆	1	1	yes	characteristic
83	C₂×C₄×D₅₉	—	2	2	no	—
84	C₂×C₄×D₅₉	C₄²	1	2	yes	—
85	C₂×C₄×D₅₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₅₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₅₉	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₅₉	C₂×C₈	1	2	yes	—
89	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
91	C₂×C₄×D₅₉	M₁₆	1	2	yes	—
92	M₁₆×C₅₉	—	2	1	no	—
93	M₁₆×C₅₉	C₂×C₈	1	2	yes	—
94	C₂×C₈×C₅₉	—	2	1	no	—
95	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
101	C₄⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
102	C₂²⋊C₄×C₅₉	—	2	1	no	—
103	C₄²×C₅₉	—	2	1	no	—
104	C₂²⋊Dic₅₉	—	2	1	no	—
105	(C₂×D₅₉)⋊C₄	—	2	2	no	—
106	C₄⋊Dic₅₉	C₂×C₈	1	2	yes	—
107	Dic₅₉⋊C₄	—	2	2	no	—
108	C₄×Dic₅₉	—	2	1	no	—
109	C₄×Dic₅₉	—	2	2	no	—
110	#11745664	—	2	1	no	—
111	#11745664	C₂×C₈	1	2	yes	—
112	C₂×C₅₉⋊C₈	—	2	1	no	—
113	C₂×C₅₉⋊C₈	C₄²	1	2	yes	—
114	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₅₉⋊C₈	C₄⋊C₄	1	2	yes	—
117	#11745659	—	2	4	no	—
118	C₈×D₅₉	—	2	4	no	—
119	C₈×D₅₉	C₂²⋊C₄	1	2	yes	—
120	C₈×D₅₉	C₂²⋊C₄	1	2	yes	—
121	C₈×D₅₉	C₂²⋊C₄	1	2	yes	—
122	C₈×D₅₉	C₂²⋊C₄	1	2	yes	—
123	C₈×D₅₉	C₄⋊C₄	1	2	yes	—
124	C₈×D₅₉	C₄⋊C₄	1	2	yes	—
125	C₈×D₅₉	C₄⋊C₄	1	2	yes	—
126	C₈×D₅₉	C₄⋊C₄	1	2	yes	—
127	C₁₆×C₅₉	—	2	2	no	—
128	C₁₆×C₅₉	—	2	2	no	—
129	C₅₉⋊C₁₆	—	2	2	no	—
130	C₅₉⋊C₁₆	—	2	2	no	—
131	C₂³×C₅₉	C₂×M₁₆	1	1	yes	characteristic
132	C₂²×D₅₉	—	4	2	no	—
133	C₂²×D₅₉	#97	1	2	yes	—
134	C₂²×D₅₉	C₂²⋊C₈	1	1	yes	characteristic
135	C₂²×D₅₉	C₂²⋊C₈	1	1	yes	characteristic
136	C₂²×D₅₉	C₄⋊C₈	1	2	yes	—
137	C₂×C₄×C₅₉	—	2	2	no	—
138	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
144	C₂×Dic₅₉	—	2	2	no	—
145	C₂×Dic₅₉	#97	1	2	yes	—
146	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
147	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
148	C₂×Dic₅₉	C₄⋊C₈	1	2	yes	—
149	C₄×D₅₉	—	4	4	no	—
150	C₄×D₅₉	#95	1	2	yes	—
151	C₄×D₅₉	#95	1	2	yes	—
152	C₄×D₅₉	C₄×C₈	1	2	yes	—
153	C₄×D₅₉	C₄×C₈	1	2	yes	—
154	C₄×D₅₉	C₂²⋊C₈	1	2	yes	—
155	C₄×D₅₉	C₂²⋊C₈	1	2	yes	—
156	C₄×D₅₉	C₄⋊C₈	1	2	yes	—
157	C₄×D₅₉	C₄⋊C₈	1	2	yes	—
158	C₈×C₅₉	—	2	2	no	—
159	C₈×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₈×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₅₉⋊C₈	—	2	2	no	—
164	C₅₉⋊C₈	#95	1	2	yes	—
165	C₅₉⋊C₈	#95	1	2	yes	—
166	#12554	—	59	1	no	maximal, Sylow
167	C₂²×C₅₉	—	2	2	no	—
168	C₂²×C₅₉	C₂×#97	1	1	yes	characteristic
169	C₂²×C₅₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
170	C₂²×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
171	C₂×D₅₉	—	2	2	no	—
172	C₂×D₅₉	—	2	2	no	—
173	C₂×D₅₉	—	4	2	no	—
174	C₂×D₅₉	—	4	2	no	—
175	C₂×D₅₉	#336	1	2	yes	—
176	C₂×D₅₉	#336	1	2	yes	—
177	C₄×C₅₉	—	4	2	no	—
178	C₄×C₅₉	C₂×#95	1	1	yes	characteristic
179	C₄×C₅₉	C₂×C₄×C₈	1	1	yes	characteristic
180	C₄×C₅₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
181	C₄×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
182	Dic₅₉	—	4	2	no	—
183	Dic₅₉	#336	1	2	yes	—
184	Dic₅₉	#336	1	2	yes	—
185	C₂²×M₃₂	—	59	1	no	—
186	C₂²×M₃₂	—	59	1	no	—
187	C₂×#405	—	59	1	no	—
188	#1379	—	59	1	no	—
189	#1379	—	59	1	no	—
190	#1379	—	59	1	no	—
191	#1379	D₅₉	1	1	yes	characteristic, complemented
192	C₂×C₅₉	—	2	1	no	—
193	C₂×C₅₉	—	2	1	no	—
194	C₂×C₅₉	C₂×#336	1	1	yes	characteristic
195	C₂×C₅₉	#2117	1	2	yes	—
196	D₅₉	—	2	2	no	—
197	D₅₉	—	2	2	no	—
198	C₂²×M₁₆	—	59	1	no	—
199	C₂³×C₈	—	59	1	no	—
200	C₂×#117	—	59	1	no	—
201	C₂×M₃₂	—	59	4	no	—
202	C₂×M₃₂	—	59	1	no	—
203	C₂×M₃₂	—	59	4	no	—
204	C₂×M₃₂	—	118	1	no	—
205	C₂×M₃₂	—	118	1	no	—
206	C₂×M₃₂	—	118	2	no	—
207	C₂×M₃₂	—	118	1	no	—
208	C₂×M₃₂	—	118	2	no	—
209	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
210	C₂²×C₁₆	—	59	1	no	—
211	C₂²×C₁₆	—	118	1	no	—
212	C₂²×C₁₆	C₂×D₅₉	1	1	yes	characteristic
213	#405	—	59	1	no	—
214	#405	—	59	1	no	—
215	#405	—	59	1	no	—
216	#405	—	118	1	no	—
217	#405	—	118	1	no	—
218	#405	C₂×D₅₉	1	1	yes	characteristic
219	C₂×#97	—	118	1	no	—
220	C₂×C₄×C₈	—	118	1	no	—
221	C₅₉	#12554	1	1	yes	characteristic, complemented, Sylow
222	C₂³×C₄	—	59	1	no	—
223	C₂×M₁₆	—	59	1	no	—
224	C₂×M₁₆	—	59	4	no	—
225	C₂×M₁₆	—	118	1	no	—
226	C₂×M₁₆	—	118	2	no	—
227	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
228	C₂²×C₈	—	59	1	no	—
229	C₂²×C₈	—	59	2	no	—
230	C₂²×C₈	—	59	2	no	—
231	C₂²×C₈	—	59	1	no	—
232	C₂²×C₈	—	59	1	no	—
233	C₂²×C₈	—	59	2	no	—
234	C₂²×C₈	—	59	1	no	—
235	C₂²×C₈	—	59	1	no	—
236	C₂²×C₈	—	59	2	no	—
237	C₂²×C₈	—	118	1	no	—
238	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
239	#117	—	59	1	no	—
240	#117	—	59	2	no	—
241	#117	—	118	1	no	—
242	#117	—	118	1	no	—
243	#117	C₄×D₅₉	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	59	2	no	—
245	C₂×C₂²⋊C₄	—	118	1	no	—
246	C₂×C₄²	—	118	1	no	—
247	M₃₂	—	2	1	no	—
248	M₃₂	—	59	2	no	—
249	M₃₂	—	118	4	no	—
250	M₃₂	—	118	4	no	—
251	M₃₂	—	118	4	no	—
252	M₃₂	—	118	1	no	—
253	M₃₂	C₄×D₅₉	1	2	yes	complemented
254	C₂×C₁₆	—	2	1	no	—
255	C₂×C₁₆	—	2	1	no	—
256	C₂×C₁₆	—	2	1	no	—
257	C₂×C₁₆	—	59	2	no	—
258	C₂×C₁₆	—	118	4	no	—
259	C₂×C₁₆	—	118	1	no	—
260	C₂×C₁₆	—	118	1	no	—
261	C₂×C₁₆	—	118	1	no	—
262	C₂×C₁₆	C₄×D₅₉	1	2	yes	complemented
263	#97	—	2	1	no	—
264	#97	—	118	1	no	—
265	#97	—	118	1	no	—
266	#97	—	118	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	118	1	no	—
269	C₄×C₈	—	118	1	no	—
270	C₄×C₈	—	118	1	no	—
271	C₂⁴	—	59	1	no	—
272	C₂²×C₄	—	59	1	no	—
273	C₂²×C₄	—	59	2	no	—
274	C₂²×C₄	—	59	1	no	—
275	C₂²×C₄	—	59	1	no	—
276	C₂²×C₄	—	59	2	no	—
277	C₂²×C₄	—	59	1	no	—
278	C₂²×C₄	—	59	1	no	—
279	C₂²×C₄	—	59	2	no	—
280	C₂²×C₄	—	59	2	no	—
281	C₂²×C₄	—	118	2	no	—
282	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
283	M₁₆	—	2	1	no	—
284	M₁₆	—	59	2	no	—
285	M₁₆	—	118	4	no	—
286	M₁₆	—	118	1	no	—
287	M₁₆	C₈×D₅₉	1	2	yes	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	59	2	no	—
290	C₂×C₈	—	59	1	no	—
291	C₂×C₈	—	59	1	no	—
292	C₂×C₈	—	59	2	no	—
293	C₂×C₈	—	59	2	no	—
294	C₂×C₈	—	59	2	no	—
295	C₂×C₈	—	59	2	no	—
296	C₂×C₈	—	59	2	no	—
297	C₂×C₈	—	59	2	no	—
298	C₂×C₈	—	59	2	no	—
299	C₂×C₈	—	59	2	no	—
300	C₂×C₈	—	59	2	no	—
301	C₂×C₈	—	118	4	no	—
302	C₂×C₈	—	118	1	no	—
303	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
304	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
305	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
306	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
307	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
308	C₂×C₈	Q₈×D₅₉	1	1	yes	characteristic
309	C₄⋊C₄	—	59	2	no	—
310	C₄⋊C₄	—	118	2	no	—
311	C₄⋊C₄	C₈×D₅₉	1	2	yes	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	118	2	no	—
314	C₂²⋊C₄	—	118	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	118	2	no	—
317	C₄²	—	118	1	no	—
318	C₁₆	—	2	2	no	—
319	C₁₆	—	2	2	no	—
320	C₁₆	—	118	2	no	—
321	C₁₆	—	118	2	no	—
322	C₂³	—	59	1	no	—
323	C₂³	—	59	1	no	—
324	C₂³	—	59	2	no	—
325	C₂³	—	59	2	no	—
326	C₂³	—	236	2	no	—
327	C₂³	M₁₆×D₅₉	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	59	2	no	—
330	C₂×C₄	—	59	2	no	—
331	C₂×C₄	—	59	1	no	—
332	C₂×C₄	—	59	1	no	—
333	C₂×C₄	—	59	2	no	—
334	C₂×C₄	—	59	2	no	—
335	C₂×C₄	—	59	2	no	—
336	C₂×C₄	—	59	2	no	—
337	C₂×C₄	—	59	2	no	—
338	C₂×C₄	—	59	2	no	—
339	C₂×C₄	—	59	2	no	—
340	C₂×C₄	—	59	2	no	—
341	C₂×C₄	—	118	2	no	—
342	C₂×C₄	—	236	4	no	—
343	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
344	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
345	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
346	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
348	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
349	C₈	—	2	2	no	—
350	C₈	—	59	2	no	—
351	C₈	—	59	2	no	—
352	C₈	—	118	2	no	—
353	C₈	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
354	C₈	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
355	C₈	C₄⋊C₄×D₅₉	1	1	yes	characteristic
356	C₈	C₄⋊C₄×D₅₉	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	59	2	no	—
359	C₂²	—	59	2	no	—
360	C₂²	—	118	2	no	—
361	C₂²	—	118	2	no	—
362	C₂²	—	236	2	no	—
363	C₂²	—	236	2	no	—
364	C₂²	#97×D₅₉	1	1	yes	characteristic
365	C₂²	C₂²⋊C₈×D₅₉	1	1	yes	characteristic
366	C₂²	C₄⋊C₈×D₅₉	1	1	yes	characteristic
367	C₄	—	4	2	no	—
368	C₄	—	59	2	no	—
369	C₄	—	59	2	no	—
370	C₄	—	236	2	no	—
371	C₄	#95×D₅₉	1	1	yes	characteristic
372	C₄	C₄×C₈×D₅₉	1	1	yes	characteristic
373	C₄	C₂²⋊C₈×D₅₉	1	1	yes	characteristic
374	C₄	C₄⋊C₈×D₅₉	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	118	2	no	—
378	C₂	—	118	2	no	—
379	C₂	#336×D₅₉	1	1	yes	characteristic
380	C₂	#21425722	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₅₉
commutator	C₄×C₅₉	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#1379	C₂
socle	C₂²×C₅₉	C₂×C₂²⋊C₈
prime radical	C₂³×D₅₉	M₁₆
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#1379	D₅₉
hypocenter	C₅₉	#12554
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1379

Complements

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

N	H ≅ G/N	type
4. #21422186	C₂	semidirect
5. #21422185	C₂	semidirect
6. #21422184	C₂	semidirect
7. C₅₉×#1379	C₂	semidirect
16. C₂×#14273666	C₄	semidirect
18. M₃₂×D₅₉	C₄	semidirect
54. #14273667	C₂×C₄	semidirect
61. C₂×C₅₉⋊C₁₆	C₂×C₄	semidirect
73. M₃₂×C₅₉	C₂×C₄	semidirect
77. C₂×C₁₆×C₅₉	C₂×C₄	semidirect
191. #1379	D₅₉	semidirect
221. C₅₉	#12554	semidirect
253. M₃₂	C₄×D₅₉	semidirect
262. 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
C₂²×#14273666	2
C₂×M₃₂×D₅₉	2
#405×D₅₉	2
#21422186	2
#21422185	2
#21422184	2
C₅₉×#1379	2
#12554	59