Subgroups — C₅₉×#35338 #28447447

Order 15104.

2422 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2861	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2640	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2592	C₂	1	8	yes	maximal, complemented
6	C₅₉×#2561	C₂	1	8	yes	maximal, complemented
7	C₅₉×#2310	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2309	C₂	1	2	yes	maximal
9	C₄×#117×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
12	C₅₉×#533	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
14	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
15	C₂×#124×C₅₉	—	2	8	no	—
16	C₂×#124×C₅₉	C₂²	1	4	yes	—
17	C₂×#124×C₅₉	C₂²	1	2	yes	—
18	C₂×#124×C₅₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	4	yes	complemented
21	C₂×#117×C₅₉	C₂²	1	2	yes	—
22	C₂×#117×C₅₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
24	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#397	C₂²	1	16	yes	complemented
26	C₅₉×#393	C₂²	1	16	yes	complemented
27	C₅₉×#391	C₂²	1	8	yes	complemented
28	C₅₉×#391	C₂²	1	8	yes	complemented
29	C₅₉×#390	C₂²	1	8	yes	—
30	C₅₉×#390	C₂²	1	8	yes	—
31	C₅₉×#388	C₂²	1	32	yes	complemented
32	C₅₉×#381	C₂²	1	8	yes	—
33	C₅₉×#379	C₂²	1	8	yes	—
34	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	complemented
35	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
36	C₅₉×#376	C₂²	1	2	yes	complemented
37	C₄³×C₅₉	C₂²	1	2	yes	complemented
38	C₂⁵×C₅₉	C₂³	1	2	yes	—
39	C₂²×Q₈×C₅₉	—	2	4	no	—
40	C₂²×Q₈×C₅₉	—	2	8	no	—
41	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
42	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
43	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
44	C₂²×D₄×C₅₉	—	2	4	no	—
45	C₂²×D₄×C₅₉	—	2	8	no	—
46	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
47	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₅₉	—	2	8	no	—
52	#125×C₅₉	—	2	8	no	—
53	#124×C₅₉	—	2	16	no	—
54	#124×C₅₉	—	2	8	no	—
55	#124×C₅₉	—	2	8	no	—
56	C₂²⋊Q₈×C₅₉	—	2	16	no	—
57	C₄×Q₈×C₅₉	—	2	16	no	—
58	#117×C₅₉	—	2	8	no	—
59	#117×C₅₉	—	2	8	no	—
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
64	C₂×C₂²⋊C₄×C₅₉	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₅₉	C₂³	1	32	yes	—
70	C₂×C₄²×C₅₉	D₄	1	8	yes	—
71	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
72	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
73	C₂×C₄²×C₅₉	C₂³	1	8	yes	—
74	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
77	#95×C₅₉	C₂³	1	8	yes	—
78	#95×C₅₉	C₂³	1	32	yes	—
79	C₂⁴×C₅₉	—	2	4	no	—
80	C₂⁴×C₅₉	—	2	8	no	—
81	C₂⁴×C₅₉	—	4	8	no	—
82	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
83	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
84	C₂×Q₈×C₅₉	—	2	8	no	—
85	C₂×Q₈×C₅₉	—	2	4	no	—
86	C₂×Q₈×C₅₉	—	2	4	no	—
87	C₂×Q₈×C₅₉	—	2	8	no	—
88	C₂×Q₈×C₅₉	—	2	8	no	—
89	C₂×Q₈×C₅₉	—	4	8	no	—
90	C₂×Q₈×C₅₉	—	4	16	no	—
91	C₂×D₄×C₅₉	—	2	4	no	—
92	C₂×D₄×C₅₉	—	2	4	no	—
93	C₂×D₄×C₅₉	—	2	8	no	—
94	C₂×D₄×C₅₉	—	2	8	no	—
95	C₂×D₄×C₅₉	—	4	16	no	—
96	C₂²×C₄×C₅₉	—	2	4	no	—
97	C₂²×C₄×C₅₉	—	2	8	no	—
98	C₂²×C₄×C₅₉	—	4	4	no	—
99	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
100	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₅₉	#41	1	8	yes	—
102	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
104	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
109	C₄⋊C₄×C₅₉	—	2	8	no	—
110	C₄⋊C₄×C₅₉	—	2	16	no	—
111	C₄⋊C₄×C₅₉	—	2	8	no	—
112	C₄⋊C₄×C₅₉	—	2	8	no	—
113	C₂²⋊C₄×C₅₉	—	2	8	no	—
114	C₂²⋊C₄×C₅₉	—	2	8	no	—
115	C₂²⋊C₄×C₅₉	—	2	16	no	—
116	C₂²⋊C₄×C₅₉	—	2	16	no	—
117	C₂²⋊C₄×C₅₉	—	4	32	no	—
118	C₄²×C₅₉	—	2	8	no	—
119	C₄²×C₅₉	—	2	8	no	—
120	C₄²×C₅₉	—	4	8	no	—
121	C₄²×C₅₉	C₂×D₄	1	8	yes	—
122	C₄²×C₅₉	C₂×D₄	1	4	yes	—
123	C₄²×C₅₉	C₂×D₄	1	4	yes	—
124	C₂³×C₅₉	—	2	4	no	—
125	C₂³×C₅₉	—	2	4	no	—
126	C₂³×C₅₉	—	2	8	no	—
127	C₂³×C₅₉	—	2	16	no	—
128	C₂³×C₅₉	—	4	16	no	—
129	C₂³×C₅₉	—	4	8	no	—
130	C₂³×C₅₉	—	8	16	no	—
131	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
132	C₂³×C₅₉	C₂×#41	1	4	yes	—
133	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
134	Q₈×C₅₉	—	4	16	no	—
135	Q₈×C₅₉	—	4	8	no	—
136	Q₈×C₅₉	—	4	8	no	—
137	D₄×C₅₉	—	4	8	no	—
138	D₄×C₅₉	—	4	8	no	—
139	C₂×C₄×C₅₉	—	2	4	no	—
140	C₂×C₄×C₅₉	—	2	4	no	—
141	C₂×C₄×C₅₉	—	2	8	no	—
142	C₂×C₄×C₅₉	—	2	4	no	—
143	C₂×C₄×C₅₉	—	2	8	no	—
144	C₂×C₄×C₅₉	—	2	8	no	—
145	C₂×C₄×C₅₉	—	2	16	no	—
146	C₂×C₄×C₅₉	—	2	16	no	—
147	C₂×C₄×C₅₉	—	4	8	no	—
148	C₂×C₄×C₅₉	—	4	8	no	—
149	C₂×C₄×C₅₉	#124	1	16	yes	—
150	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
155	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
156	#35338	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂²×C₅₉	—	2	4	no	—
158	C₂²×C₅₉	—	2	8	no	—
159	C₂²×C₅₉	—	4	4	no	—
160	C₂²×C₅₉	—	4	8	no	—
161	C₂²×C₅₉	—	4	16	no	—
162	C₂²×C₅₉	—	8	16	no	—
163	C₂²×C₅₉	C₂×#124	1	4	yes	—
164	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
165	C₂²×C₅₉	C₂²×#41	1	2	yes	—
166	C₂²×C₅₉	#585	1	4	yes	—
167	C₄×C₅₉	—	2	4	no	—
168	C₄×C₅₉	—	2	4	no	—
169	C₄×C₅₉	—	4	4	no	—
170	C₄×C₅₉	—	4	8	no	—
171	C₄×C₅₉	—	4	8	no	—
172	C₄×C₅₉	C₂×#124	1	4	yes	—
173	C₄×C₅₉	C₂×#124	1	4	yes	—
174	C₂×#533	C₂×C₅₉	1	1	yes	characteristic, complemented
175	C₂²×#124	C₂×C₅₉	1	1	yes	characteristic
176	#2861	C₂×C₅₉	1	4	yes	complemented
177	#2640	C₂×C₅₉	1	4	yes	complemented
178	#2592	C₂×C₅₉	1	8	yes	complemented
179	#2561	C₂×C₅₉	1	8	yes	complemented
180	#2310	C₂×C₅₉	1	2	yes	complemented
181	#2309	C₂×C₅₉	1	2	yes	—
182	C₄×#117	C₂×C₅₉	1	1	yes	characteristic, complemented
183	C₂×C₅₉	—	2	4	no	—
184	C₂×C₅₉	—	8	4	no	—
185	C₂×C₅₉	C₂²×#124	1	1	yes	characteristic
186	C₂×C₅₉	#3449	1	2	yes	—
187	C₂×C₅₉	#3510	1	4	yes	—
188	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
189	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
190	#533	—	2	8	no	—
191	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
192	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
193	C₂×#124	—	2	8	no	—
194	C₂×#124	C₂²×C₅₉	1	4	yes	—
195	C₂×#124	C₂²×C₅₉	1	2	yes	—
196	C₂×#124	C₂²×C₅₉	1	2	yes	—
197	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
198	C₂×C₄×Q₈	C₂²×C₅₉	1	4	yes	complemented
199	C₂×#117	C₂²×C₅₉	1	2	yes	—
200	C₂×#117	C₂²×C₅₉	1	2	yes	—
201	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
202	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
203	#397	C₂²×C₅₉	1	16	yes	complemented
204	#393	C₂²×C₅₉	1	16	yes	complemented
205	#391	C₂²×C₅₉	1	8	yes	complemented
206	#391	C₂²×C₅₉	1	8	yes	complemented
207	#390	C₂²×C₅₉	1	8	yes	—
208	#390	C₂²×C₅₉	1	8	yes	—
209	#388	C₂²×C₅₉	1	32	yes	complemented
210	#381	C₂²×C₅₉	1	8	yes	—
211	#379	C₂²×C₅₉	1	8	yes	—
212	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	complemented
213	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
214	#376	C₂²×C₅₉	1	2	yes	complemented
215	C₄³	C₂²×C₅₉	1	2	yes	complemented
216	C₅₉	#35338	1	1	yes	characteristic, direct product factor, Sylow
217	C₂⁵	C₂³×C₅₉	1	2	yes	—
218	C₂²×Q₈	—	2	4	no	—
219	C₂²×Q₈	—	2	8	no	—
220	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
221	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
222	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
223	C₂²×D₄	—	2	4	no	—
224	C₂²×D₄	—	2	8	no	—
225	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
226	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
227	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
228	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
229	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
230	C₄⋊Q₈	—	2	8	no	—
231	#125	—	2	8	no	—
232	#124	—	2	16	no	—
233	#124	—	2	8	no	—
234	#124	—	2	8	no	—
235	C₂²⋊Q₈	—	2	16	no	—
236	C₄×Q₈	—	2	16	no	—
237	#117	—	2	8	no	—
238	#117	—	2	8	no	—
239	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
240	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
241	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
242	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	16	no	—
244	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
245	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
246	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₅₉	1	32	yes	—
249	C₂×C₄²	D₄×C₅₉	1	8	yes	—
250	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
251	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
252	C₂×C₄²	C₂³×C₅₉	1	8	yes	—
253	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
254	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
256	#95	C₂³×C₅₉	1	8	yes	—
257	#95	C₂³×C₅₉	1	32	yes	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	—	4	8	no	—
261	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
262	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
263	C₂×Q₈	—	2	8	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	8	no	—
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	4	8	no	—
269	C₂×Q₈	—	4	16	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂×D₄	—	4	16	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
279	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
280	C₂²×C₄	#41×C₅₉	1	8	yes	—
281	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
282	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
283	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
284	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₂²⋊C₄	—	2	8	no	—
293	C₂²⋊C₄	—	2	8	no	—
294	C₂²⋊C₄	—	2	16	no	—
295	C₂²⋊C₄	—	2	16	no	—
296	C₂²⋊C₄	—	4	32	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	2	8	no	—
299	C₄²	—	4	8	no	—
300	C₄²	C₂×D₄×C₅₉	1	8	yes	—
301	C₄²	C₂×D₄×C₅₉	1	4	yes	—
302	C₄²	C₂×D₄×C₅₉	1	4	yes	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	16	no	—
307	C₂³	—	4	16	no	—
308	C₂³	—	4	8	no	—
309	C₂³	—	8	16	no	—
310	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
311	C₂³	C₂×#41×C₅₉	1	4	yes	—
312	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
313	Q₈	—	4	16	no	—
314	Q₈	—	4	8	no	—
315	Q₈	—	4	8	no	—
316	D₄	—	4	8	no	—
317	D₄	—	4	8	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	8	no	—
328	C₂×C₄	#124×C₅₉	1	16	yes	—
329	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
331	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
332	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
333	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
334	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	4	16	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	8	no	—
340	C₂²	—	8	16	no	—
341	C₂²	C₂×#124×C₅₉	1	4	yes	—
342	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
343	C₂²	C₂²×#41×C₅₉	1	2	yes	—
344	C₂²	C₅₉×#585	1	4	yes	—
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	4	8	no	—
348	C₄	—	4	4	no	—
349	C₄	—	4	8	no	—
350	C₄	C₂×#124×C₅₉	1	4	yes	—
351	C₄	C₂×#124×C₅₉	1	4	yes	—
352	C₂	—	2	4	no	—
353	C₂	—	8	4	no	—
354	C₂	C₂²×#124×C₅₉	1	1	yes	characteristic
355	C₂	C₅₉×#3449	1	2	yes	—
356	C₂	C₅₉×#3510	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂³×D₄×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#533	C₂	semidirect
3. C₅₉×#2861	C₂	semidirect
4. C₅₉×#2640	C₂	semidirect
5. C₅₉×#2592	C₂	semidirect
6. C₅₉×#2561	C₂	semidirect
7. C₅₉×#2310	C₂	semidirect
9. C₄×#117×C₅₉	C₂	semidirect
13. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
14. C₂×#125×C₅₉	C₂²	semidirect
20. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
25. C₅₉×#397	C₂²	semidirect
26. C₅₉×#393	C₂²	semidirect
27. C₅₉×#391	C₂²	semidirect
28. C₅₉×#391	C₂²	semidirect
31. C₅₉×#388	C₂²	semidirect
34. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
36. C₅₉×#376	C₂²	semidirect
37. C₄³×C₅₉	C₂²	semidirect
156. #35338	C₅₉	direct (N × H)
174. C₂×#533	C₂×C₅₉	semidirect
176. #2861	C₂×C₅₉	semidirect
177. #2640	C₂×C₅₉	semidirect
178. #2592	C₂×C₅₉	semidirect
179. #2561	C₂×C₅₉	semidirect
180. #2310	C₂×C₅₉	semidirect
182. C₄×#117	C₂×C₅₉	semidirect
191. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
192. C₂×#125	C₂²×C₅₉	semidirect
198. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
203. #397	C₂²×C₅₉	semidirect
204. #393	C₂²×C₅₉	semidirect
205. #391	C₂²×C₅₉	semidirect
206. #391	C₂²×C₅₉	semidirect
209. #388	C₂²×C₅₉	semidirect
212. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
214. #376	C₂²×C₅₉	semidirect
215. C₄³	C₂²×C₅₉	semidirect
216. C₅₉	#35338	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#533	2
C₂²×#124×C₅₉	2
C₅₉×#2861	2
C₅₉×#2640	2
C₅₉×#2592	2
C₅₉×#2561	2
C₅₉×#2310	2
C₅₉×#2309	2
C₄×#117×C₅₉	2
#35338	59

Subgroups — C59×#35338 #28447447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35338 #28447447