Subgroups — #28504911

Order 15104.

440 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#405×D₅₉	C₂	1	1	yes	maximal, characteristic
2	#21425706	C₂	1	1	yes	maximal, characteristic
3	C₂×(C₂×D₅₉)⋊C₁₆	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	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	#16837360	C₄	1	1	yes	characteristic
14	#16837359	—	2	1	no	—
15	#16837358	C₄	1	1	yes	characteristic
16	#16837357	C₂²	1	1	yes	characteristic
17	#16837356	—	2	1	no	—
18	#97×D₅₉	—	2	1	no	—
19	C₄×C₈×D₅₉	—	2	1	no	—
20	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
21	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
22	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
23	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
24	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
25	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#405	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
28	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
29	C₂×#11745659	—	2	1	no	—
30	M₁₆×D₅₉	—	2	2	no	—
31	M₁₆×D₅₉	—	2	2	no	—
32	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×D₅₉	—	2	1	no	—
34	C₂×C₈×D₅₉	—	2	1	no	—
35	C₂×C₈×D₅₉	—	2	1	no	—
36	C₂×C₈×D₅₉	—	2	1	no	—
37	C₂×C₈×D₅₉	—	2	1	no	—
38	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
39	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
40	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
41	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
42	#14273686	C₂×C₄	1	1	yes	characteristic
43	#14273685	C₈	1	1	yes	characteristic
44	#14273685	C₈	1	1	yes	characteristic
45	#14273684	—	2	1	no	—
46	#14273683	—	2	1	no	—
47	C₄⋊C₄×D₅₉	C₈	1	1	yes	characteristic
48	C₄⋊C₄×D₅₉	C₈	1	1	yes	characteristic
49	C₂²⋊C₄×D₅₉	—	2	1	no	—
50	C₄²×D₅₉	—	2	1	no	—
51	#14273667	—	2	1	no	—
52	#14273667	—	2	1	no	—
53	C₂×C₅₉⋊C₁₆	—	2	1	no	—
54	C₂×C₅₉⋊C₁₆	—	2	1	no	—
55	C₂×C₅₉⋊C₁₆	—	2	1	no	—
56	C₂×C₅₉⋊C₁₆	—	2	1	no	—
57	#14273638	—	2	1	no	—
58	#14273637	—	2	1	no	—
59	#14273637	—	2	1	no	—
60	C₄×C₅₉⋊C₈	—	2	1	no	—
61	C₈×Dic₅₉	—	2	1	no	—
62	C₈×Dic₅₉	—	2	1	no	—
63	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
65	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
66	M₃₂×C₅₉	—	2	1	no	—
67	M₃₂×C₅₉	—	2	1	no	—
68	C₂×C₁₆×C₅₉	—	2	1	no	—
69	C₂×C₁₆×C₅₉	—	2	1	no	—
70	C₂×C₁₆×C₅₉	—	2	1	no	—
71	C₂×C₁₆×C₅₉	—	2	1	no	—
72	#97×C₅₉	—	2	1	no	—
73	C₄×C₈×C₅₉	—	2	1	no	—
74	C₂³×D₅₉	M₁₆	1	1	yes	characteristic
75	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×Dic₅₉	M₁₆	1	1	yes	characteristic
77	C₂×C₄×D₅₉	—	2	1	no	—
78	C₂×C₄×D₅₉	—	2	1	no	—
79	C₂×C₄×D₅₉	—	2	1	no	—
80	C₂×C₄×D₅₉	—	2	1	no	—
81	C₂×C₄×D₅₉	—	2	1	no	—
82	C₂×C₄×D₅₉	—	2	1	no	—
83	C₂×C₄×D₅₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₅₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
86	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
87	M₁₆×C₅₉	—	2	1	no	—
88	M₁₆×C₅₉	M₁₆	1	2	yes	—
89	C₂×C₈×C₅₉	—	2	1	no	—
90	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
92	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
93	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
94	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
95	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
96	C₄⋊C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
97	C₄⋊C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
98	C₂²⋊C₄×C₅₉	—	2	1	no	—
99	C₄²×C₅₉	—	2	1	no	—
100	C₂²⋊Dic₅₉	—	2	1	no	—
101	(C₂×D₅₉)⋊C₄	—	2	1	no	—
102	(C₂×D₅₉)⋊C₄	—	2	1	no	—
103	C₄⋊Dic₅₉	C₂×C₈	1	1	yes	characteristic
104	C₄⋊Dic₅₉	C₂×C₈	1	1	yes	characteristic
105	Dic₅₉⋊C₄	—	2	1	no	—
106	Dic₅₉⋊C₄	—	2	1	no	—
107	C₄×Dic₅₉	—	2	1	no	—
108	C₄×Dic₅₉	—	2	1	no	—
109	C₄×Dic₅₉	—	2	1	no	—
110	#11745664	—	2	1	no	—
111	#11745664	M₁₆	1	2	yes	—
112	C₂×C₅₉⋊C₈	—	2	1	no	—
113	C₂×C₅₉⋊C₈	—	2	1	no	—
114	C₂×C₅₉⋊C₈	—	2	1	no	—
115	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
117	#11745659	—	2	4	no	—
118	C₈×D₅₉	—	2	4	no	—
119	C₈×D₅₉	—	2	1	no	—
120	C₈×D₅₉	—	2	1	no	—
121	C₈×D₅₉	—	2	1	no	—
122	C₈×D₅₉	—	2	1	no	—
123	C₈×D₅₉	—	2	1	no	—
124	C₈×D₅₉	—	2	1	no	—
125	C₈×D₅₉	—	2	1	no	—
126	C₈×D₅₉	—	2	1	no	—
127	C₁₆×C₅₉	—	4	1	no	—
128	C₁₆×C₅₉	—	4	1	no	—
129	C₅₉⋊C₁₆	—	4	1	no	—
130	C₅₉⋊C₁₆	—	4	1	no	—
131	C₂³×C₅₉	C₂×M₁₆	1	1	yes	characteristic
132	C₂²×D₅₉	—	2	1	no	—
133	C₂²×D₅₉	—	2	1	no	—
134	C₂²×D₅₉	—	2	2	no	—
135	C₂²×D₅₉	—	4	1	no	—
136	C₂²×D₅₉	C₂²⋊C₈	1	1	yes	characteristic
137	C₂²×D₅₉	C₂²⋊C₈	1	1	yes	characteristic
138	C₂×C₄×C₅₉	—	2	1	no	—
139	C₂×C₄×C₅₉	—	2	1	no	—
140	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
142	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
145	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
146	C₂×Dic₅₉	—	2	1	no	—
147	C₂×Dic₅₉	—	2	1	no	—
148	C₂×Dic₅₉	—	2	1	no	—
149	C₂×Dic₅₉	—	2	1	no	—
150	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
151	C₂×Dic₅₉	C₂²⋊C₈	1	1	yes	characteristic
152	C₄×D₅₉	—	2	1	no	—
153	C₄×D₅₉	—	2	1	no	—
154	C₄×D₅₉	—	2	1	no	—
155	C₄×D₅₉	—	2	1	no	—
156	C₄×D₅₉	—	2	1	no	—
157	C₄×D₅₉	—	2	1	no	—
158	C₄×D₅₉	—	2	1	no	—
159	C₄×D₅₉	—	2	1	no	—
160	C₄×D₅₉	—	4	2	no	—
161	C₄×D₅₉	—	4	2	no	—
162	C₈×C₅₉	—	2	2	no	—
163	C₈×C₅₉	#123	1	1	yes	characteristic
164	C₈×C₅₉	#123	1	1	yes	characteristic
165	C₈×C₅₉	#123	1	1	yes	characteristic
166	C₈×C₅₉	#123	1	1	yes	characteristic
167	C₅₉⋊C₈	—	2	1	no	—
168	C₅₉⋊C₈	—	2	1	no	—
169	C₅₉⋊C₈	—	2	2	no	—
170	#12848	—	59	1	no	maximal, Sylow
171	C₂²×C₅₉	—	2	1	no	—
172	C₂²×C₅₉	—	2	1	no	—
173	C₂²×C₅₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
174	C₂²×C₅₉	#432	1	1	yes	characteristic
175	C₂²×C₅₉	#432	1	1	yes	characteristic
176	C₂×D₅₉	—	2	1	no	—
177	C₂×D₅₉	—	2	1	no	—
178	C₂×D₅₉	—	2	1	no	—
179	C₂×D₅₉	—	2	1	no	—
180	C₂×D₅₉	—	2	1	no	—
181	C₂×D₅₉	—	4	2	no	—
182	C₂×D₅₉	—	4	2	no	—
183	C₂×D₅₉	#350	1	2	yes	—
184	C₄×C₅₉	—	4	1	no	—
185	C₄×C₅₉	—	4	1	no	—
186	C₄×C₅₉	#381	1	1	yes	characteristic
187	C₄×C₅₉	#407	1	1	yes	characteristic
188	C₄×C₅₉	#431	1	1	yes	characteristic
189	C₄×C₅₉	#431	1	1	yes	characteristic
190	Dic₅₉	—	2	1	no	—
191	Dic₅₉	—	2	1	no	—
192	Dic₅₉	—	4	1	no	—
193	Dic₅₉	—	4	1	no	—
194	C₂×#405	—	59	1	no	—
195	#2112	—	59	1	no	—
196	C₂×C₂²⋊C₁₆	—	59	1	no	—
197	#1379	—	59	1	no	—
198	#1379	—	59	1	no	—
199	#1379	—	59	1	no	—
200	#1379	D₅₉	1	1	yes	characteristic, complemented
201	C₂×C₅₉	—	2	1	no	—
202	C₂×C₅₉	—	2	1	no	—
203	C₂×C₅₉	#1817	1	1	yes	characteristic
204	C₂×C₅₉	C₂×#350	1	1	yes	characteristic
205	C₂×C₅₉	#2117	1	1	yes	characteristic
206	D₅₉	—	2	2	no	—
207	D₅₉	—	4	1	no	—
208	C₂²×M₁₆	—	59	1	no	—
209	C₂³×C₈	—	59	1	no	—
210	C₂×#117	—	59	1	no	—
211	C₂×M₃₂	—	59	1	no	—
212	C₂×M₃₂	C₂×D₅₉	1	1	yes	characteristic
213	C₂²×C₁₆	—	59	1	no	—
214	C₂²×C₁₆	C₂×D₅₉	1	1	yes	characteristic
215	#405	—	59	1	no	—
216	#405	—	59	1	no	—
217	#405	—	59	1	no	—
218	#405	—	118	1	no	—
219	#405	—	118	1	no	—
220	#405	C₂×D₅₉	1	1	yes	characteristic
221	C₂×#97	—	118	1	no	—
222	C₂×C₄×C₈	—	118	1	no	—
223	C₂²⋊C₁₆	—	118	1	no	—
224	C₂²⋊C₁₆	—	118	1	no	—
225	C₂²⋊C₁₆	—	118	1	no	—
226	C₂²⋊C₁₆	—	118	1	no	—
227	C₅₉	#12848	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₄	—	59	1	no	—
229	C₂×M₁₆	—	59	1	no	—
230	C₂×M₁₆	—	118	1	no	—
231	C₂×M₁₆	—	118	2	no	—
232	C₂×M₁₆	—	118	2	no	—
233	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
234	C₂²×C₈	—	59	1	no	—
235	C₂²×C₈	—	59	1	no	—
236	C₂²×C₈	—	59	1	no	—
237	C₂²×C₈	—	59	1	no	—
238	C₂²×C₈	—	59	1	no	—
239	C₂²×C₈	—	118	1	no	—
240	C₂²×C₈	—	118	1	no	—
241	C₂²×C₈	—	118	1	no	—
242	C₂²×C₈	—	118	1	no	—
243	C₂²×C₈	—	118	1	no	—
244	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
245	#117	—	59	1	no	—
246	#117	—	59	1	no	—
247	#117	—	59	1	no	—
248	#117	—	118	1	no	—
249	#117	—	118	1	no	—
250	#117	C₄×D₅₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	59	1	no	—
252	C₂×C₄⋊C₄	—	59	1	no	—
253	C₂×C₂²⋊C₄	—	118	1	no	—
254	C₂×C₄²	—	118	1	no	—
255	M₃₂	—	2	1	no	—
256	M₃₂	—	2	1	no	—
257	M₃₂	—	118	1	no	—
258	M₃₂	—	118	1	no	—
259	C₂×C₁₆	—	2	1	no	—
260	C₂×C₁₆	—	2	1	no	—
261	C₂×C₁₆	—	2	1	no	—
262	C₂×C₁₆	—	2	1	no	—
263	C₂×C₁₆	—	118	1	no	—
264	C₂×C₁₆	—	118	1	no	—
265	C₂×C₁₆	—	118	1	no	—
266	C₂×C₁₆	—	118	1	no	—
267	#97	—	2	1	no	—
268	#97	—	118	1	no	—
269	#97	—	118	1	no	—
270	#97	—	118	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	118	1	no	—
273	C₄×C₈	—	118	1	no	—
274	C₄×C₈	—	118	1	no	—
275	C₂⁴	—	59	1	no	—
276	C₂²×C₄	—	59	1	no	—
277	C₂²×C₄	—	59	1	no	—
278	C₂²×C₄	—	59	1	no	—
279	C₂²×C₄	—	59	1	no	—
280	C₂²×C₄	—	59	1	no	—
281	C₂²×C₄	—	118	1	no	—
282	C₂²×C₄	—	118	1	no	—
283	C₂²×C₄	—	118	1	no	—
284	C₂²×C₄	—	118	1	no	—
285	C₂²×C₄	—	118	1	no	—
286	C₂²×C₄	—	118	1	no	—
287	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
288	M₁₆	—	2	1	no	—
289	M₁₆	—	59	2	no	—
290	M₁₆	—	118	4	no	—
291	M₁₆	—	118	1	no	—
292	M₁₆	#11745659	1	2	yes	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	59	1	no	—
295	C₂×C₈	—	59	1	no	—
296	C₂×C₈	—	118	4	no	—
297	C₂×C₈	—	118	1	no	—
298	C₂×C₈	—	118	1	no	—
299	C₂×C₈	—	118	1	no	—
300	C₂×C₈	—	118	1	no	—
301	C₂×C₈	—	118	1	no	—
302	C₂×C₈	—	118	1	no	—
303	C₂×C₈	—	118	1	no	—
304	C₂×C₈	—	118	1	no	—
305	C₂×C₈	—	118	1	no	—
306	C₂×C₈	—	118	1	no	—
307	C₂×C₈	—	118	1	no	—
308	C₂×C₈	#11745685	1	1	yes	characteristic
309	C₂×C₈	#11745685	1	1	yes	characteristic
310	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
311	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
312	C₂×C₈	#11745687	1	1	yes	characteristic
313	C₂×C₈	#11745689	1	1	yes	characteristic
314	C₄⋊C₄	—	59	1	no	—
315	C₄⋊C₄	—	59	1	no	—
316	C₄⋊C₄	—	118	1	no	—
317	C₄⋊C₄	—	118	1	no	—
318	C₄⋊C₄	C₈×D₅₉	1	1	yes	characteristic
319	C₄⋊C₄	C₈×D₅₉	1	1	yes	characteristic
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	118	1	no	—
322	C₂²⋊C₄	—	118	1	no	—
323	C₂²⋊C₄	—	118	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	118	1	no	—
326	C₄²	—	118	1	no	—
327	C₄²	—	118	1	no	—
328	C₁₆	—	4	1	no	—
329	C₁₆	—	4	1	no	—
330	C₁₆	—	236	1	no	—
331	C₁₆	—	236	1	no	—
332	C₂³	—	59	1	no	—
333	C₂³	—	59	1	no	—
334	C₂³	—	118	2	no	—
335	C₂³	—	118	1	no	—
336	C₂³	—	118	1	no	—
337	C₂³	—	236	1	no	—
338	C₂³	M₁₆×D₅₉	1	1	yes	characteristic
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	59	1	no	—
342	C₂×C₄	—	59	1	no	—
343	C₂×C₄	—	118	1	no	—
344	C₂×C₄	—	118	1	no	—
345	C₂×C₄	—	118	1	no	—
346	C₂×C₄	—	118	1	no	—
347	C₂×C₄	—	118	1	no	—
348	C₂×C₄	—	118	1	no	—
349	C₂×C₄	—	118	1	no	—
350	C₂×C₄	—	118	1	no	—
351	C₂×C₄	—	118	1	no	—
352	C₂×C₄	—	118	1	no	—
353	C₂×C₄	—	118	1	no	—
354	C₂×C₄	—	118	1	no	—
355	C₂×C₄	—	236	2	no	—
356	C₂×C₄	—	236	2	no	—
357	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
358	C₂×C₄	#14273684	1	1	yes	characteristic
359	C₂×C₄	#14273685	1	1	yes	characteristic
360	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
361	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
362	C₂×C₄	C₂×#11745659	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	118	1	no	—
365	C₈	—	118	1	no	—
366	C₈	—	118	2	no	—
367	C₈	#14273709	1	1	yes	characteristic
368	C₈	#14273709	1	1	yes	characteristic
369	C₈	#14273712	1	1	yes	characteristic
370	C₈	#14273712	1	1	yes	characteristic
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	59	2	no	—
374	C₂²	—	118	1	no	—
375	C₂²	—	118	1	no	—
376	C₂²	—	118	1	no	—
377	C₂²	—	118	1	no	—
378	C₂²	—	118	1	no	—
379	C₂²	—	236	2	no	—
380	C₂²	—	236	2	no	—
381	C₂²	C₂²⋊C₈×D₅₉	1	1	yes	characteristic
382	C₂²	#16837457	1	1	yes	characteristic
383	C₂²	#16837458	1	1	yes	characteristic
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	118	1	no	—
387	C₄	—	118	1	no	—
388	C₄	—	236	1	no	—
389	C₄	—	236	1	no	—
390	C₄	#16837264	1	1	yes	characteristic
391	C₄	#16837364	1	1	yes	characteristic
392	C₄	#16837453	1	1	yes	characteristic
393	C₄	#16837454	1	1	yes	characteristic
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	118	2	no	—
397	C₂	—	236	1	no	—
398	C₂	#21424163	1	1	yes	characteristic
399	C₂	#350×D₅₉	1	1	yes	characteristic
400	C₂	#21425722	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×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	#12848
LCS	G ▷ C₂×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
200. #1379	D₅₉	semidirect
227. C₅₉	#12848	semidirect

Maximal subgroups

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

subgroup	index
#405×D₅₉	2
#21425706	2
C₂×(C₂×D₅₉)⋊C₁₆	2
#21422186	2
#21422185	2
#21422184	2
C₅₉×#1379	2
#12848	59