Subgroups — C₅₉×#25607 #28437716

Order 15104.

1152 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2619	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2000	C₂	1	4	yes	maximal, complemented
6	C₅₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1960	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1880	C₂	1	4	yes	maximal, complemented
9	C₅₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₅₉	C₂²	1	4	yes	—
11	C₅₉×#541	—	2	4	no	—
12	C₅₉×#541	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#126×C₅₉	—	2	2	no	—
16	C₂×#125×C₅₉	—	2	2	no	—
17	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
19	C₂×#121×C₅₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
21	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
22	C₅₉×#492	—	2	4	no	—
23	C₅₉×#490	—	2	4	no	—
24	C₂×#103×C₅₉	C₂²	1	4	yes	—
25	C₂×#102×C₅₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
27	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₅₉×#394	—	2	2	no	—
30	C₅₉×#392	—	2	2	no	—
31	C₅₉×#390	C₂²	1	2	yes	—
32	C₅₉×#382	C₂²	1	1	yes	characteristic
33	C₅₉×#340	C₂²	1	4	yes	—
34	C₅₉×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
36	C₂²×D₄×C₅₉	—	2	2	no	—
37	C₂²×D₄×C₅₉	—	2	2	no	—
38	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
40	C₂×SD₁₆×C₅₉	—	2	8	no	—
41	C₂×SD₁₆×C₅₉	—	2	8	no	—
42	C₂×SD₁₆×C₅₉	—	4	4	no	—
43	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
45	C₄⋊Q₈×C₅₉	—	2	2	no	—
46	C₄⋊Q₈×C₅₉	D₄	1	4	yes	complemented
47	#127×C₅₉	—	2	2	no	—
48	#127×C₅₉	—	2	2	no	—
49	#126×C₅₉	—	2	16	no	—
50	#125×C₅₉	—	2	16	no	—
51	#125×C₅₉	—	2	2	no	—
52	#125×C₅₉	D₄	1	4	yes	complemented
53	C₂²⋊Q₈×C₅₉	—	2	4	no	—
54	C₂²⋊Q₈×C₅₉	—	2	4	no	—
55	#121×C₅₉	—	4	4	no	—
56	C₄×Q₈×C₅₉	—	2	4	no	—
57	C₄×Q₈×C₅₉	—	2	4	no	—
58	#117×C₅₉	—	2	2	no	—
59	#117×C₅₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
71	C₂×C₄²×C₅₉	—	2	2	no	—
72	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
74	#103×C₅₉	—	4	4	no	—
75	#102×C₅₉	—	2	8	no	—
76	C₂²⋊C₈×C₅₉	—	2	4	no	—
77	#97×C₅₉	—	2	2	no	—
78	C₄×C₈×C₅₉	—	2	2	no	—
79	#95×C₅₉	—	2	2	no	—
80	C₂⁴×C₅₉	—	2	2	no	—
81	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₅₉	—	2	2	no	—
83	C₂×Q₈×C₅₉	—	2	4	no	—
84	C₂×Q₈×C₅₉	—	2	4	no	—
85	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
86	C₂×D₄×C₅₉	—	2	2	no	—
87	C₂×D₄×C₅₉	—	2	2	no	—
88	C₂×D₄×C₅₉	—	2	4	no	—
89	C₂×D₄×C₅₉	—	2	4	no	—
90	C₂×D₄×C₅₉	—	4	4	no	—
91	C₂×D₄×C₅₉	—	4	4	no	—
92	C₂×D₄×C₅₉	—	8	4	no	—
93	C₂×D₄×C₅₉	—	8	4	no	—
94	C₂²×C₄×C₅₉	—	2	2	no	—
95	C₂²×C₄×C₅₉	—	2	2	no	—
96	C₂²×C₄×C₅₉	—	2	1	no	—
97	C₂²×C₄×C₅₉	—	2	1	no	—
98	C₂²×C₄×C₅₉	—	2	2	no	—
99	C₂²×C₄×C₅₉	—	2	2	no	—
100	C₂²×C₄×C₅₉	—	2	2	no	—
101	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
105	SD₁₆×C₅₉	—	4	16	no	—
106	C₂×C₈×C₅₉	—	2	2	no	—
107	C₂×C₈×C₅₉	—	2	2	no	—
108	C₂×C₈×C₅₉	—	2	2	no	—
109	C₂×C₈×C₅₉	—	2	2	no	—
110	C₂×C₈×C₅₉	—	2	2	no	—
111	C₂×C₈×C₅₉	#41	1	4	yes	—
112	C₄⋊C₄×C₅₉	—	2	8	no	—
113	C₄⋊C₄×C₅₉	—	2	8	no	—
114	C₄⋊C₄×C₅₉	—	2	8	no	—
115	C₄⋊C₄×C₅₉	—	2	8	no	—
116	C₄⋊C₄×C₅₉	—	2	4	no	—
117	C₄⋊C₄×C₅₉	—	2	2	no	—
118	C₄⋊C₄×C₅₉	—	2	4	no	—
119	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
120	C₂²⋊C₄×C₅₉	—	2	8	no	—
121	C₂²⋊C₄×C₅₉	—	2	4	no	—
122	C₂²⋊C₄×C₅₉	—	4	4	no	—
123	C₂²⋊C₄×C₅₉	—	8	4	no	—
124	C₄²×C₅₉	—	2	8	no	—
125	C₄²×C₅₉	—	2	1	no	—
126	C₄²×C₅₉	—	2	1	no	—
127	C₄²×C₅₉	C₂×D₄	1	2	yes	—
128	C₄²×C₅₉	C₂×D₄	1	2	yes	—
129	C₂³×C₅₉	—	2	1	no	—
130	C₂³×C₅₉	—	2	1	no	—
131	C₂³×C₅₉	—	2	1	no	—
132	C₂³×C₅₉	—	2	4	no	—
133	C₂³×C₅₉	—	4	2	no	—
134	C₂³×C₅₉	—	4	2	no	—
135	C₂³×C₅₉	—	4	2	no	—
136	C₂³×C₅₉	—	4	4	no	—
137	C₂³×C₅₉	—	4	4	no	—
138	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₅₉	—	2	8	no	—
140	Q₈×C₅₉	—	4	4	no	—
141	D₄×C₅₉	—	4	4	no	—
142	D₄×C₅₉	—	4	4	no	—
143	D₄×C₅₉	—	8	8	no	—
144	D₄×C₅₉	—	8	8	no	—
145	C₂×C₄×C₅₉	—	2	4	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	2	4	no	—
148	C₂×C₄×C₅₉	—	2	4	no	—
149	C₂×C₄×C₅₉	—	2	1	no	—
150	C₂×C₄×C₅₉	—	2	1	no	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	4	no	—
153	C₂×C₄×C₅₉	—	4	2	no	—
154	C₂×C₄×C₅₉	—	4	2	no	—
155	C₂×C₄×C₅₉	—	4	4	no	—
156	C₂×C₄×C₅₉	—	4	2	no	—
157	C₂×C₄×C₅₉	—	4	2	no	—
158	C₂×C₄×C₅₉	—	4	2	no	—
159	C₂×C₄×C₅₉	—	4	4	no	—
160	C₂×C₄×C₅₉	#120	1	4	yes	—
161	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
164	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
165	C₈×C₅₉	—	2	4	no	—
166	C₈×C₅₉	—	4	2	no	—
167	#25607	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₅₉	—	4	2	no	—
169	C₂²×C₅₉	—	4	1	no	—
170	C₂²×C₅₉	—	4	2	no	—
171	C₂²×C₅₉	—	4	2	no	—
172	C₂²×C₅₉	—	8	4	no	—
173	C₂²×C₅₉	—	8	2	no	—
174	C₂²×C₅₉	—	8	2	no	—
175	C₂²×C₅₉	—	8	2	no	—
176	C₂²×C₅₉	—	8	4	no	—
177	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
178	C₂²×C₅₉	#532	1	1	yes	characteristic
179	C₂²×C₅₉	#535	1	1	yes	characteristic
180	C₂²×C₅₉	#577	1	4	yes	—
181	C₄×C₅₉	—	2	4	no	—
182	C₄×C₅₉	—	4	1	no	—
183	C₄×C₅₉	—	4	4	no	—
184	C₄×C₅₉	—	4	2	no	—
185	C₄×C₅₉	—	4	4	no	—
186	C₄×C₅₉	—	8	2	no	—
187	C₄×C₅₉	#546	1	2	yes	—
188	C₄×C₅₉	#550	1	2	yes	—
189	C₂×#541	C₂×C₅₉	1	1	yes	characteristic, complemented
190	C₂×#492	C₂×C₅₉	1	1	yes	characteristic, complemented
191	C₂×#490	C₂×C₅₉	1	1	yes	characteristic, complemented
192	#2619	C₂×C₅₉	1	1	yes	characteristic
193	#2000	C₂×C₅₉	1	4	yes	complemented
194	#1991	C₂×C₅₉	1	1	yes	characteristic, complemented
195	#1960	C₂×C₅₉	1	1	yes	characteristic, complemented
196	#1880	C₂×C₅₉	1	4	yes	complemented
197	#1750	C₂×C₅₉	1	1	yes	characteristic, complemented
198	C₂×C₅₉	—	8	1	no	—
199	C₂×C₅₉	—	16	2	no	—
200	C₂×C₅₉	#2431	1	1	yes	characteristic
201	C₂×C₅₉	#3010	1	2	yes	—
202	C₂×C₅₉	#3174	1	2	yes	—
203	C₂×C₅₉	#3222	1	2	yes	—
204	C₂²×SD₁₆	C₂²×C₅₉	1	4	yes	—
205	#541	—	2	4	no	—
206	#541	—	2	4	no	—
207	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
208	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
209	C₂×#126	—	2	2	no	—
210	C₂×#125	—	2	2	no	—
211	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
213	C₂×#121	C₂²×C₅₉	1	2	yes	—
214	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
215	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
216	#492	—	2	4	no	—
217	#490	—	2	4	no	—
218	C₂×#103	C₂²×C₅₉	1	4	yes	—
219	C₂×#102	C₂²×C₅₉	1	4	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
221	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
223	#394	—	2	2	no	—
224	#392	—	2	2	no	—
225	#390	C₂²×C₅₉	1	2	yes	—
226	#382	C₂²×C₅₉	1	1	yes	characteristic
227	#340	C₂²×C₅₉	1	4	yes	—
228	#336	C₂²×C₅₉	1	2	yes	—
229	C₅₉	#25607	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
234	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
235	C₂×SD₁₆	—	2	8	no	—
236	C₂×SD₁₆	—	2	8	no	—
237	C₂×SD₁₆	—	4	4	no	—
238	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
239	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	D₄×C₅₉	1	4	yes	complemented
242	#127	—	2	2	no	—
243	#127	—	2	2	no	—
244	#126	—	2	16	no	—
245	#125	—	2	16	no	—
246	#125	—	2	2	no	—
247	#125	D₄×C₅₉	1	4	yes	complemented
248	C₂²⋊Q₈	—	2	4	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	#121	—	4	4	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	4	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
269	#103	—	4	4	no	—
270	#102	—	2	8	no	—
271	C₂²⋊C₈	—	2	4	no	—
272	#97	—	2	2	no	—
273	C₄×C₈	—	2	2	no	—
274	#95	—	2	2	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	8	4	no	—
288	C₂×D₄	—	8	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
299	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
300	SD₁₆	—	4	16	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	#41×C₅₉	1	4	yes	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	8	4	no	—
319	C₄²	—	2	8	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	C₂×D₄×C₅₉	1	2	yes	—
323	C₄²	C₂×D₄×C₅₉	1	2	yes	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	4	no	—
333	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	4	4	no	—
336	D₄	—	4	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	8	8	no	—
339	D₄	—	8	8	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	#120×C₅₉	1	4	yes	—
356	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
359	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
360	C₈	—	2	4	no	—
361	C₈	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	8	4	no	—
367	C₂²	—	8	4	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
372	C₂²	C₅₉×#532	1	1	yes	characteristic
373	C₂²	C₅₉×#535	1	1	yes	characteristic
374	C₂²	C₅₉×#577	1	4	yes	—
375	C₄	—	2	4	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	4	no	—
380	C₄	—	8	2	no	—
381	C₄	C₅₉×#546	1	2	yes	—
382	C₄	C₅₉×#550	1	2	yes	—
383	C₂	—	8	1	no	—
384	C₂	—	16	2	no	—
385	C₂	C₅₉×#2431	1	1	yes	characteristic
386	C₂	C₅₉×#3010	1	2	yes	—
387	C₂	C₅₉×#3174	1	2	yes	—
388	C₂	C₅₉×#3222	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×#117×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#541	C₂	semidirect
2. C₂×C₅₉×#492	C₂	semidirect
3. C₂×C₅₉×#490	C₂	semidirect
5. C₅₉×#2000	C₂	semidirect
6. C₅₉×#1991	C₂	semidirect
7. C₅₉×#1960	C₂	semidirect
8. C₅₉×#1880	C₂	semidirect
9. C₅₉×#1750	C₂	semidirect
46. C₄⋊Q₈×C₅₉	D₄	semidirect
52. #125×C₅₉	D₄	semidirect
167. #25607	C₅₉	direct (N × H)
189. C₂×#541	C₂×C₅₉	semidirect
190. C₂×#492	C₂×C₅₉	semidirect
191. C₂×#490	C₂×C₅₉	semidirect
193. #2000	C₂×C₅₉	semidirect
194. #1991	C₂×C₅₉	semidirect
195. #1960	C₂×C₅₉	semidirect
196. #1880	C₂×C₅₉	semidirect
197. #1750	C₂×C₅₉	semidirect
229. C₅₉	#25607	direct (N × H)
241. C₄⋊Q₈	D₄×C₅₉	semidirect
247. #125	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#541	2
C₂×C₅₉×#492	2
C₂×C₅₉×#490	2
C₅₉×#2619	2
C₅₉×#2000	2
C₅₉×#1991	2
C₅₉×#1960	2
C₅₉×#1880	2
C₅₉×#1750	2
#25607	59

Subgroups — C59×#25607 #28437716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25607 #28437716