Subgroups — #28741905

Order 15104.

682 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837818	C₂	1	2	yes	maximal, complemented
2	#21432803	C₂	1	1	yes	maximal, characteristic
3	#21425929	C₂	1	1	yes	maximal, characteristic, complemented
4	#21425928	C₂	1	1	yes	maximal, characteristic, complemented
5	#21425924	C₂	1	2	yes	maximal, complemented
6	#21425921	C₂	1	2	yes	maximal, complemented
7	#21425915	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#21425708	C₂	1	2	yes	maximal, complemented
10	C₄×#14273666	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273733	C₂²	1	2	yes	—
13	#16837949	C₄	1	1	yes	characteristic
14	#16837818	—	2	8	no	—
15	C₂×#14273667	C₂²	1	2	yes	—
16	C₂×#14273666	C₂²	1	2	yes	—
17	C₂×#14273666	C₂²	1	1	yes	characteristic
18	C₂×#14273666	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₅₉	C₂²	1	2	yes	—
20	C₂×C₁₆×D₅₉	C₂²	1	2	yes	—
21	#16837480	C₄	1	1	yes	characteristic
22	#16837479	C₄	1	1	yes	characteristic
23	#16837477	C₄	1	2	yes	—
24	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₅₉	C₂²	1	2	yes	—
26	#16837424	C₄	1	1	yes	characteristic
27	#16837367	C₄	1	2	yes	—
28	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
29	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
30	Dic₅₉⋊C₁₆	C₂²	1	2	yes	—
31	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	—
32	(C₂×D₅₉)⋊C₁₆	C₂²	1	2	yes	—
33	(C₂×D₅₉)⋊C₁₆	C₂²	1	2	yes	—
34	#16837177	C₂²	1	1	yes	characteristic
35	#16837177	C₂²	1	1	yes	characteristic
36	C₄×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₂²×C₁₆×C₅₉	C₂²	1	2	yes	—
38	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₅₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#11745685	C₂×C₄	1	2	yes	—
43	#14273733	—	2	4	no	—
44	#14273733	—	2	4	no	—
45	C₂×#11745664	C₂×C₄	1	2	yes	—
46	C₂×#11745659	C₂×C₄	1	2	yes	—
47	C₂×#11745659	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₉	C₂³	1	2	yes	—
50	C₂×C₈×D₅₉	C₂³	1	1	yes	characteristic
51	#14273726	C₈	1	1	yes	characteristic
52	#14273723	C₈	1	1	yes	characteristic
53	#14273713	C₈	1	2	yes	—
54	#14273702	C₈	1	1	yes	characteristic
55	#14273700	C₈	1	2	yes	—
56	#14273698	C₈	1	1	yes	characteristic
57	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₅₉	C₂×C₄	1	2	yes	—
59	C₄²×D₅₉	C₂×C₄	1	1	yes	characteristic
60	#14273667	—	2	4	no	—
61	#14273666	—	2	2	no	—
62	#14273666	—	2	4	no	—
63	#14273666	D₄	1	4	yes	complemented
64	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
66	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
67	C₁₆×D₅₉	—	2	4	no	—
68	C₁₆×D₅₉	—	2	4	no	—
69	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
70	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
72	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
73	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
74	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₅₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
78	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₆×C₅₉	—	2	4	no	—
80	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
82	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
85	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₅₉	C₂×C₈	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
88	C₂×C₂²⋊D₅₉	C₂×C₈	1	2	yes	—
89	C₂×C₂²⋊D₅₉	C₂×C₈	1	2	yes	—
90	C₂×C₂²⋊D₅₉	C₂×C₈	1	2	yes	—
91	#11745685	—	2	4	no	—
92	#11745685	—	2	4	no	—
93	C₂×D₂₃₆	C₂×C₈	1	1	yes	characteristic
94	C₂×D₂₃₆	C₂×C₈	1	2	yes	—
95	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₅₉	C₂²×C₄	1	2	yes	—
98	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×Dic₁₁₈	C₂×C₈	1	2	yes	—
100	C₂×C₈×C₅₉	—	2	2	no	—
101	C₂×C₈×C₅₉	—	2	2	no	—
102	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
106	C₂²⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
107	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²⋊Dic₅₉	C₂×C₈	1	2	yes	—
109	(C₂×D₅₉)⋊C₄	C₂×C₈	1	2	yes	—
110	(C₂×D₅₉)⋊C₄	C₂×C₈	1	2	yes	—
111	C₄⋊Dic₅₉	C₂×C₈	1	1	yes	characteristic
112	Dic₅₉⋊C₄	C₂×C₈	1	2	yes	—
113	C₄×Dic₅₉	C₂×C₈	1	1	yes	characteristic
114	C₄×Dic₅₉	C₂×C₈	1	1	yes	characteristic
115	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
116	#11745664	—	2	4	no	—
117	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
120	#11745659	—	2	4	no	—
121	#11745659	—	2	4	no	—
122	C₈×D₅₉	—	2	2	no	—
123	C₈×D₅₉	—	2	2	no	—
124	C₈×D₅₉	—	2	2	no	—
125	C₈×D₅₉	C₂×D₄	1	2	yes	—
126	C₈×D₅₉	#41	1	2	yes	—
127	C₁₆×C₅₉	—	2	2	no	—
128	C₁₆×C₅₉	—	2	1	no	—
129	C₁₆×C₅₉	C₂×D₄	1	2	yes	—
130	C₅₉⋊C₁₆	—	2	2	no	—
131	C₅₉⋊C₁₆	—	2	1	no	—
132	C₅₉⋊C₁₆	C₂×D₄	1	2	yes	—
133	C₂³×C₅₉	C₂²×C₈	1	2	yes	—
134	C₂²×D₅₉	C₂²×C₈	1	2	yes	—
135	C₂²×D₅₉	C₂²×C₈	1	1	yes	characteristic
136	D₄×C₅₉	—	2	2	no	—
137	C₂×C₄×C₅₉	—	2	2	no	—
138	C₂×C₄×C₅₉	—	2	2	no	—
139	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
143	C₂²⋊D₅₉	—	2	4	no	—
144	C₂²⋊D₅₉	—	2	4	no	—
145	C₂²⋊D₅₉	—	4	2	no	—
146	C₂×Dic₅₉	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₅₉	C₂²×C₈	1	1	yes	characteristic
148	C₂×Dic₅₉	C₂²×C₈	1	2	yes	—
149	C₂×Dic₅₉	C₂²×C₈	1	1	yes	characteristic
150	D₂₃₆	—	2	4	no	—
151	D₂₃₆	—	2	2	no	—
152	C₄×D₅₉	—	2	2	no	—
153	C₄×D₅₉	—	2	2	no	—
154	C₄×D₅₉	—	2	2	no	—
155	C₄×D₅₉	—	4	1	no	—
156	C₄×D₅₉	C₄×D₄	1	2	yes	—
157	C₄×D₅₉	#131	1	2	yes	—
158	Dic₁₁₈	—	2	4	no	—
159	C₈×C₅₉	—	2	2	no	—
160	C₈×C₅₉	—	2	1	no	—
161	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
163	C₅₉⋊C₈	—	2	2	no	—
164	C₅₉⋊C₈	—	2	1	no	—
165	C₅₉⋊C₈	C₄×D₄	1	2	yes	—
166	#33438	—	59	1	no	maximal, Sylow
167	C₂²×C₅₉	—	2	2	no	—
168	C₂²×C₅₉	—	2	2	no	—
169	C₂²×C₅₉	—	2	2	no	—
170	C₂²×C₅₉	C₂³×C₈	1	1	yes	characteristic
171	C₂×D₅₉	—	2	1	no	—
172	C₂×D₅₉	—	2	1	no	—
173	C₂×D₅₉	—	2	2	no	—
174	C₂×D₅₉	—	2	2	no	—
175	C₂×D₅₉	—	2	2	no	—
176	C₂×D₅₉	C₈×D₄	1	2	yes	—
177	C₄×C₅₉	—	2	1	no	—
178	C₄×C₅₉	—	2	2	no	—
179	C₄×C₅₉	#504	1	2	yes	complemented
180	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
182	Dic₅₉	—	2	1	no	—
183	Dic₅₉	—	2	1	no	—
184	Dic₅₉	—	2	2	no	—
185	Dic₅₉	C₈×D₄	1	2	yes	—
186	C₂×#504	—	59	2	no	—
187	#2931	—	59	1	no	—
188	#2169	—	59	1	no	—
189	#2169	—	59	1	no	—
190	#2168	—	59	2	no	—
191	#2168	—	59	2	no	—
192	D₄×C₁₆	—	59	1	no	—
193	D₄×C₁₆	D₅₉	1	1	yes	characteristic, complemented
194	C₂×C₄⋊C₁₆	—	59	1	no	—
195	#2113	—	59	2	no	—
196	C₄×M₃₂	—	59	1	no	—
197	C₂×C₅₉	—	4	2	no	—
198	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
199	C₂×C₅₉	C₂×#504	1	1	yes	characteristic
200	C₂×C₅₉	#3407	1	1	yes	characteristic
201	D₅₉	—	2	2	no	—
202	D₅₉	—	4	2	no	—
203	C₂×#131	—	59	2	no	—
204	#532	—	59	1	no	—
205	#504	—	118	8	no	—
206	C₂×M₃₂	—	59	2	no	—
207	C₂×M₃₂	—	59	1	no	—
208	C₂×M₃₂	—	59	1	no	—
209	C₂×M₃₂	—	59	2	no	—
210	C₂²×C₁₆	—	59	2	no	—
211	C₂²×C₁₆	—	59	2	no	—
212	C₂²×C₁₆	C₂×D₅₉	1	2	yes	—
213	#436	—	59	1	no	—
214	#436	—	59	1	no	—
215	#436	—	59	2	no	—
216	C₈×D₄	—	59	2	no	—
217	C₈×D₄	—	59	1	no	—
218	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
219	#423	—	59	1	no	—
220	#408	—	59	2	no	—
221	C₂×C₄×C₈	—	59	1	no	—
222	C₄⋊C₁₆	—	59	2	no	—
223	C₄⋊C₁₆	—	59	1	no	—
224	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
225	C₂²⋊C₁₆	—	59	2	no	—
226	C₂²⋊C₁₆	—	59	2	no	—
227	C₂²⋊C₁₆	—	59	2	no	—
228	C₂²⋊C₁₆	C₂×D₅₉	1	2	yes	—
229	#346	—	59	1	no	—
230	#346	—	59	1	no	—
231	C₄×C₁₆	—	59	1	no	—
232	C₄×C₁₆	C₂×D₅₉	1	1	yes	characteristic
233	C₅₉	#33438	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	59	2	no	—
235	#131	—	118	4	no	—
236	#131	—	118	4	no	—
237	C₂×M₁₆	—	59	2	no	—
238	C₂×M₁₆	—	59	2	no	—
239	C₂×M₁₆	—	59	2	no	—
240	C₂²×C₈	—	59	1	no	—
241	C₂²×C₈	—	59	1	no	—
242	C₂²×C₈	—	59	2	no	—
243	C₂²×C₈	C₂²×D₅₉	1	2	yes	—
244	C₄⋊Q₈	—	59	1	no	—
245	#127	—	59	1	no	—
246	#124	—	59	2	no	—
247	#121	—	59	1	no	—
248	#121	—	59	1	no	—
249	#121	—	59	2	no	—
250	C₄×D₄	—	59	2	no	—
251	C₄×D₄	—	59	1	no	—
252	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
253	C₂×C₄²	—	59	1	no	—
254	M₃₂	—	59	4	no	—
255	M₃₂	—	118	2	no	—
256	M₃₂	—	118	4	no	—
257	M₃₂	—	118	4	no	—
258	C₂×C₁₆	—	2	4	no	—
259	C₂×C₁₆	—	59	1	no	—
260	C₂×C₁₆	—	59	1	no	—
261	C₂×C₁₆	—	59	2	no	—
262	C₂×C₁₆	—	118	4	no	—
263	C₂×C₁₆	—	118	4	no	—
264	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
265	C₂×C₁₆	C₂²×D₅₉	1	2	yes	—
266	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
267	C₄⋊C₈	—	59	2	no	—
268	C₄⋊C₈	—	59	1	no	—
269	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
270	C₂²⋊C₈	—	59	2	no	—
271	C₂²⋊C₈	—	59	2	no	—
272	C₂²⋊C₈	—	59	2	no	—
273	C₂²⋊C₈	C₄×D₅₉	1	2	yes	—
274	C₄×C₈	—	59	1	no	—
275	C₄×C₈	—	59	1	no	—
276	C₄×C₈	—	59	1	no	—
277	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
278	#41	—	118	4	no	—
279	#41	—	118	4	no	—
280	C₂×Q₈	—	59	2	no	—
281	C₂×D₄	—	59	2	no	—
282	C₂×D₄	—	59	2	no	—
283	C₂×D₄	—	59	2	no	—
284	C₂×D₄	—	59	1	no	—
285	C₂×D₄	—	59	2	no	—
286	C₂×D₄	C₈×D₅₉	1	1	yes	characteristic
287	C₂²×C₄	—	59	1	no	—
288	C₂²×C₄	—	59	1	no	—
289	C₂²×C₄	—	59	2	no	—
290	C₂²×C₄	—	59	1	no	—
291	C₂²×C₄	C₂×C₄×D₅₉	1	2	yes	—
292	M₁₆	—	118	4	no	—
293	M₁₆	—	118	4	no	—
294	M₁₆	—	118	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	59	1	no	—
298	C₂×C₈	—	59	2	no	—
299	C₂×C₈	—	59	2	no	—
300	C₂×C₈	—	59	1	no	—
301	C₂×C₈	—	59	2	no	—
302	C₂×C₈	—	118	2	no	—
303	C₂×C₈	—	118	2	no	—
304	C₂×C₈	—	118	2	no	—
305	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
307	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
308	C₄⋊C₄	—	59	2	no	—
309	C₄⋊C₄	—	59	1	no	—
310	C₄⋊C₄	C₈×D₅₉	1	1	yes	characteristic
311	C₂²⋊C₄	—	59	2	no	—
312	C₂²⋊C₄	—	59	2	no	—
313	C₂²⋊C₄	—	59	2	no	—
314	C₂²⋊C₄	C₈×D₅₉	1	2	yes	—
315	C₄²	—	59	1	no	—
316	C₄²	—	59	1	no	—
317	C₄²	—	59	1	no	—
318	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
319	C₁₆	—	2	2	no	—
320	C₁₆	—	2	1	no	—
321	C₁₆	—	59	2	no	—
322	C₁₆	—	118	2	no	—
323	C₁₆	—	118	1	no	—
324	C₁₆	D₄×D₅₉	1	2	yes	—
325	C₂³	—	59	1	no	—
326	C₂³	—	59	2	no	—
327	C₂³	C₂×C₈×D₅₉	1	2	yes	—
328	Q₈	—	118	4	no	—
329	D₄	—	2	2	no	—
330	D₄	—	118	4	no	—
331	D₄	—	118	4	no	—
332	D₄	—	118	4	no	—
333	D₄	—	118	2	no	—
334	D₄	—	236	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	59	1	no	—
338	C₂×C₄	—	59	2	no	—
339	C₂×C₄	—	59	2	no	—
340	C₂×C₄	—	59	1	no	—
341	C₂×C₄	—	59	1	no	—
342	C₂×C₄	—	59	2	no	—
343	C₂×C₄	—	118	2	no	—
344	C₂×C₄	—	118	2	no	—
345	C₂×C₄	—	118	2	no	—
346	C₂×C₄	—	236	1	no	—
347	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
348	C₂×C₄	C₂×C₈×D₅₉	1	2	yes	—
349	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
350	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
351	C₈	—	2	1	no	—
352	C₈	—	2	2	no	—
353	C₈	—	59	2	no	—
354	C₈	—	118	1	no	—
355	C₈	—	118	2	no	—
356	C₈	C₂×D₄×D₅₉	1	1	yes	characteristic
357	C₈	#41×D₅₉	1	1	yes	characteristic
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	59	2	no	—
362	C₂²	—	118	1	no	—
363	C₂²	—	118	1	no	—
364	C₂²	—	118	2	no	—
365	C₂²	—	118	2	no	—
366	C₂²	—	118	2	no	—
367	C₂²	C₂²×C₈×D₅₉	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	59	2	no	—
371	C₄	—	118	1	no	—
372	C₄	—	118	1	no	—
373	C₄	—	118	2	no	—
374	C₄	#16837818	1	2	yes	complemented
375	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
376	C₄	#131×D₅₉	1	1	yes	characteristic
377	C₂	—	4	2	no	—
378	C₂	—	118	2	no	—
379	C₂	—	236	2	no	—
380	C₂	C₈×D₄×D₅₉	1	1	yes	characteristic
381	C₂	C₂×#16837818	1	1	yes	characteristic
382	C₂	#21437197	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₉
commutator, socle	C₂²×C₅₉	C₂³×C₈
Fitting	D₄×C₁₆×C₅₉	C₂
prime radical	#16837949	C₄
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	D₄×C₁₆	D₅₉
hypocenter	C₅₉	#33438
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#16837818	C₂	semidirect
3. #21425929	C₂	semidirect
4. #21425928	C₂	semidirect
5. #21425924	C₂	semidirect
6. #21425921	C₂	semidirect
7. #21425915	C₂	semidirect
8. C₄⋊C₁₆×D₅₉	C₂	semidirect
9. #21425708	C₂	semidirect
10. C₄×#14273666	C₂	semidirect
11. D₄×C₁₆×C₅₉	C₂	semidirect
63. #14273666	D₄	semidirect
179. C₄×C₅₉	#504	semidirect
193. D₄×C₁₆	D₅₉	semidirect
233. C₅₉	#33438	semidirect
374. C₄	#16837818	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837818	2
#21432803	2
#21425929	2
#21425928	2
#21425924	2
#21425921	2
#21425915	2
C₄⋊C₁₆×D₅₉	2
#21425708	2
C₄×#14273666	2
D₄×C₁₆×C₅₉	2
#33438	59