Subgroups — C₅₉×#33766 #28445875

Order 15104.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3058	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2237	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2234	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2220	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2217	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2187	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2185	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
11	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
13	C₅₉×#536	—	2	1	no	—
14	C₅₉×#535	—	2	1	no	—
15	C₂×SD₃₂×C₅₉	C₂²	1	2	yes	—
16	C₂×SD₃₂×C₅₉	C₂²	1	2	yes	—
17	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
19	C₅₉×#470	—	2	1	no	—
20	C₅₉×#470	—	2	1	no	—
21	C₅₉×#469	—	2	1	no	—
22	C₅₉×#469	—	2	1	no	—
23	C₅₉×#467	C₂²	1	2	yes	—
24	C₅₉×#467	C₂²	1	2	yes	complemented
25	C₅₉×#466	C₂²	1	2	yes	—
26	C₅₉×#466	C₂²	1	2	yes	—
27	C₅₉×#427	C₂²	1	1	yes	characteristic
28	C₅₉×#427	C₂²	1	1	yes	characteristic, complemented
29	C₅₉×#419	—	2	1	no	—
30	C₅₉×#418	—	2	1	no	—
31	C₅₉×#367	C₂²	1	2	yes	complemented
32	C₅₉×#366	C₂²	1	2	yes	complemented
33	C₅₉×#358	C₂²	1	2	yes	complemented
34	C₅₉×#358	C₂²	1	2	yes	complemented
35	C₅₉×#357	C₂²	1	2	yes	—
36	C₅₉×#357	C₂²	1	2	yes	—
37	C₅₉×C₂²⋊C₁₆	C₂²	1	2	yes	—
38	C₅₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
39	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₅₉	—	2	1	no	—
41	C₂²×D₄×C₅₉	—	2	1	no	—
42	C₂×Q₁₆×C₅₉	—	2	1	no	—
43	C₂×Q₁₆×C₅₉	—	4	1	no	—
44	C₂×Q₁₆×C₅₉	—	4	1	no	—
45	C₂×Q₁₆×C₅₉	C₂³	1	2	yes	—
46	C₂×D₈×C₅₉	—	2	1	no	—
47	C₂×D₈×C₅₉	—	4	1	no	—
48	C₂×D₈×C₅₉	—	4	1	no	—
49	C₂×D₈×C₅₉	C₂³	1	2	yes	—
50	#131×C₅₉	—	4	1	no	—
51	#131×C₅₉	—	4	1	no	—
52	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
54	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₅₉	—	4	1	no	—
59	#127×C₅₉	—	4	1	no	—
60	#124×C₅₉	—	4	1	no	—
61	#124×C₅₉	—	4	1	no	—
62	#123×C₅₉	—	4	1	no	—
63	#123×C₅₉	—	4	1	no	—
64	C₂²⋊Q₈×C₅₉	—	2	2	no	—
65	C₂²⋊Q₈×C₅₉	—	2	2	no	—
66	#121×C₅₉	—	2	2	no	—
67	#121×C₅₉	—	2	2	no	—
68	#120×C₅₉	—	4	1	no	—
69	#120×C₅₉	—	4	1	no	—
70	#117×C₅₉	—	2	1	no	—
71	#117×C₅₉	—	2	1	no	—
72	SD₃₂×C₅₉	—	4	2	no	—
73	SD₃₂×C₅₉	—	4	2	no	—
74	M₃₂×C₅₉	—	4	1	no	—
75	C₂×C₁₆×C₅₉	—	4	1	no	—
76	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
77	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
78	#107×C₅₉	C₂³	1	2	yes	—
79	#107×C₅₉	C₂³	1	2	yes	—
80	#106×C₅₉	—	2	1	no	—
81	#106×C₅₉	—	2	1	no	—
82	#103×C₅₉	—	2	2	no	—
83	#103×C₅₉	—	2	2	no	—
84	#102×C₅₉	—	2	2	no	—
85	#102×C₅₉	—	2	2	no	—
86	C₂⁴×C₅₉	—	4	1	no	—
87	#41×C₅₉	—	4	1	no	—
88	#41×C₅₉	—	4	1	no	—
89	C₂×Q₈×C₅₉	—	2	2	no	—
90	C₂×Q₈×C₅₉	—	4	2	no	—
91	C₂×Q₈×C₅₉	—	4	2	no	—
92	C₂×Q₈×C₅₉	—	4	1	no	—
93	C₂×Q₈×C₅₉	D₈	1	1	yes	characteristic
94	C₂×D₄×C₅₉	—	2	2	no	—
95	C₂×D₄×C₅₉	—	4	2	no	—
96	C₂×D₄×C₅₉	—	4	2	no	—
97	C₂×D₄×C₅₉	—	4	2	no	—
98	C₂×D₄×C₅₉	—	4	2	no	—
99	C₂×D₄×C₅₉	—	4	1	no	—
100	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
101	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
102	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	—	4	1	no	—
104	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₅₉	—	2	2	no	—
108	Q₁₆×C₅₉	—	2	2	no	—
109	Q₁₆×C₅₉	—	4	2	no	—
110	D₈×C₅₉	—	2	2	no	—
111	D₈×C₅₉	—	2	2	no	—
112	D₈×C₅₉	—	4	2	no	—
113	M₁₆×C₅₉	—	4	1	no	—
114	M₁₆×C₅₉	—	4	1	no	—
115	M₁₆×C₅₉	—	4	1	no	—
116	C₂×C₈×C₅₉	—	2	1	no	—
117	C₂×C₈×C₅₉	—	2	1	no	—
118	C₂×C₈×C₅₉	—	2	1	no	—
119	C₂×C₈×C₅₉	—	2	1	no	—
120	C₂×C₈×C₅₉	—	2	1	no	—
121	C₂×C₈×C₅₉	—	2	1	no	—
122	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
126	C₄⋊C₄×C₅₉	—	2	2	no	—
127	C₄⋊C₄×C₅₉	—	2	2	no	—
128	C₄⋊C₄×C₅₉	—	4	2	no	—
129	C₄⋊C₄×C₅₉	—	4	2	no	—
130	C₂²⋊C₄×C₅₉	—	4	1	no	—
131	C₂²⋊C₄×C₅₉	—	4	1	no	—
132	C₂²⋊C₄×C₅₉	—	4	2	no	—
133	C₂²⋊C₄×C₅₉	—	4	2	no	—
134	C₂²⋊C₄×C₅₉	—	4	2	no	—
135	C₂²⋊C₄×C₅₉	—	4	2	no	—
136	C₄²×C₅₉	—	4	1	no	—
137	C₄²×C₅₉	—	4	1	no	—
138	C₁₆×C₅₉	—	2	2	no	—
139	C₁₆×C₅₉	—	2	2	no	—
140	C₂³×C₅₉	—	4	2	no	—
141	C₂³×C₅₉	—	8	2	no	—
142	C₂³×C₅₉	—	16	2	no	—
143	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
144	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
145	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₅₉	—	4	1	no	—
147	Q₈×C₅₉	—	4	2	no	—
148	Q₈×C₅₉	—	4	2	no	—
149	Q₈×C₅₉	—	8	2	no	—
150	D₄×C₅₉	—	4	1	no	—
151	D₄×C₅₉	—	4	1	no	—
152	D₄×C₅₉	—	4	1	no	—
153	D₄×C₅₉	—	4	2	no	—
154	D₄×C₅₉	—	4	2	no	—
155	D₄×C₅₉	—	8	2	no	—
156	D₄×C₅₉	—	16	2	no	—
157	D₄×C₅₉	—	16	2	no	—
158	C₂×C₄×C₅₉	—	2	1	no	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	2	1	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	4	2	no	—
167	C₂×C₄×C₅₉	—	8	2	no	—
168	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₅₉	—	2	1	no	—
173	C₈×C₅₉	—	2	1	no	—
174	C₈×C₅₉	—	2	1	no	—
175	C₈×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
176	C₈×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
177	#33766	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₅₉	—	2	2	no	—
179	C₂²×C₅₉	—	2	2	no	—
180	C₂²×C₅₉	—	2	2	no	—
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	1	no	—
183	C₂²×C₅₉	—	2	1	no	—
184	C₂²×C₅₉	—	8	2	no	—
185	C₂²×C₅₉	—	8	2	no	—
186	C₂²×C₅₉	—	8	2	no	—
187	C₂²×C₅₉	—	16	4	no	—
188	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₅₉	—	2	1	no	—
190	C₄×C₅₉	—	2	1	no	—
191	C₄×C₅₉	—	2	1	no	—
192	C₄×C₅₉	—	8	2	no	—
193	C₄×C₅₉	—	8	2	no	—
194	C₄×C₅₉	—	8	2	no	—
195	C₄×C₅₉	#534	1	1	yes	characteristic
196	C₄×C₅₉	#575	1	1	yes	characteristic
197	#3059	C₂×C₅₉	1	1	yes	characteristic, complemented
198	#3058	C₂×C₅₉	1	1	yes	characteristic
199	#2237	C₂×C₅₉	1	2	yes	complemented
200	#2234	C₂×C₅₉	1	2	yes	complemented
201	#2220	C₂×C₅₉	1	2	yes	complemented
202	#2217	C₂×C₅₉	1	2	yes	complemented
203	#2187	C₂×C₅₉	1	2	yes	complemented
204	#2185	C₂×C₅₉	1	2	yes	complemented
205	#2113	C₂×C₅₉	1	1	yes	characteristic, complemented
206	C₂×C₅₉	—	4	1	no	—
207	C₂×C₅₉	—	4	1	no	—
208	C₂×C₅₉	—	4	1	no	—
209	C₂×C₅₉	—	16	2	no	—
210	C₂×C₅₉	#3186	1	1	yes	characteristic
211	C₂×C₅₉	#3416	1	2	yes	—
212	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
213	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
214	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
215	#536	—	2	1	no	—
216	#535	—	2	1	no	—
217	C₂×SD₃₂	C₂²×C₅₉	1	2	yes	—
218	C₂×SD₃₂	C₂²×C₅₉	1	2	yes	—
219	C₂×M₃₂	C₂²×C₅₉	1	1	yes	characteristic, complemented
220	C₂²×C₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
221	#470	—	2	1	no	—
222	#470	—	2	1	no	—
223	#469	—	2	1	no	—
224	#469	—	2	1	no	—
225	#467	C₂²×C₅₉	1	2	yes	—
226	#467	C₂²×C₅₉	1	2	yes	complemented
227	#466	C₂²×C₅₉	1	2	yes	—
228	#466	C₂²×C₅₉	1	2	yes	—
229	#427	C₂²×C₅₉	1	1	yes	characteristic
230	#427	C₂²×C₅₉	1	1	yes	characteristic, complemented
231	#419	—	2	1	no	—
232	#418	—	2	1	no	—
233	#367	C₂²×C₅₉	1	2	yes	complemented
234	#366	C₂²×C₅₉	1	2	yes	complemented
235	#358	C₂²×C₅₉	1	2	yes	complemented
236	#358	C₂²×C₅₉	1	2	yes	complemented
237	#357	C₂²×C₅₉	1	2	yes	—
238	#357	C₂²×C₅₉	1	2	yes	—
239	C₂²⋊C₁₆	C₂²×C₅₉	1	2	yes	—
240	C₂²⋊C₁₆	C₂²×C₅₉	1	2	yes	complemented
241	C₅₉	#33766	1	1	yes	characteristic, direct product factor, Sylow
242	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	—	4	1	no	—
247	C₂×Q₁₆	—	4	1	no	—
248	C₂×Q₁₆	C₂³×C₅₉	1	2	yes	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	4	1	no	—
251	C₂×D₈	—	4	1	no	—
252	C₂×D₈	C₂³×C₅₉	1	2	yes	—
253	#131	—	4	1	no	—
254	#131	—	4	1	no	—
255	C₂×M₁₆	D₄×C₅₉	1	1	yes	characteristic
256	C₂×M₁₆	D₄×C₅₉	1	1	yes	characteristic
257	C₂×M₁₆	D₄×C₅₉	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
261	C₄⋊Q₈	—	4	1	no	—
262	#127	—	4	1	no	—
263	#124	—	4	1	no	—
264	#124	—	4	1	no	—
265	#123	—	4	1	no	—
266	#123	—	4	1	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	#121	—	2	2	no	—
270	#121	—	2	2	no	—
271	#120	—	4	1	no	—
272	#120	—	4	1	no	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	SD₃₂	—	4	2	no	—
276	SD₃₂	—	4	2	no	—
277	M₃₂	—	4	1	no	—
278	C₂×C₁₆	—	4	1	no	—
279	C₂×C₁₆	C₂³×C₅₉	1	2	yes	—
280	C₂×C₁₆	C₂³×C₅₉	1	2	yes	—
281	#107	C₂³×C₅₉	1	2	yes	—
282	#107	C₂³×C₅₉	1	2	yes	—
283	#106	—	2	1	no	—
284	#106	—	2	1	no	—
285	#103	—	2	2	no	—
286	#103	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	C₂⁴	—	4	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	D₈×C₅₉	1	1	yes	characteristic
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
304	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
305	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	4	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	2	2	no	—
315	D₈	—	4	2	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
328	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	4	1	no	—
340	C₄²	—	4	1	no	—
341	C₁₆	—	2	2	no	—
342	C₁₆	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	8	2	no	—
345	C₂³	—	16	2	no	—
346	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
347	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
348	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	16	2	no	—
360	D₄	—	16	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
372	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
373	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
379	C₈	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₅₉×#534	1	1	yes	characteristic
398	C₄	C₅₉×#575	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	16	2	no	—
403	C₂	C₅₉×#3186	1	1	yes	characteristic
404	C₂	C₅₉×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
prime radical	C₅₉×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×#41×C₅₉ ◁ C₂×#131×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3059	C₂	semidirect
3. C₅₉×#2237	C₂	semidirect
4. C₅₉×#2234	C₂	semidirect
5. C₅₉×#2220	C₂	semidirect
6. C₅₉×#2217	C₂	semidirect
7. C₅₉×#2187	C₂	semidirect
8. C₅₉×#2185	C₂	semidirect
9. C₅₉×#2113	C₂	semidirect
10. C₂²×Q₁₆×C₅₉	C₂²	semidirect
17. C₂×M₃₂×C₅₉	C₂²	semidirect
18. C₂²×C₁₆×C₅₉	C₂²	semidirect
24. C₅₉×#467	C₂²	semidirect
28. C₅₉×#427	C₂²	semidirect
31. C₅₉×#367	C₂²	semidirect
32. C₅₉×#366	C₂²	semidirect
33. C₅₉×#358	C₂²	semidirect
34. C₅₉×#358	C₂²	semidirect
38. C₅₉×C₂²⋊C₁₆	C₂²	semidirect
177. #33766	C₅₉	direct (N × H)
197. #3059	C₂×C₅₉	semidirect
199. #2237	C₂×C₅₉	semidirect
200. #2234	C₂×C₅₉	semidirect
201. #2220	C₂×C₅₉	semidirect
202. #2217	C₂×C₅₉	semidirect
203. #2187	C₂×C₅₉	semidirect
204. #2185	C₂×C₅₉	semidirect
205. #2113	C₂×C₅₉	semidirect
212. C₂²×Q₁₆	C₂²×C₅₉	semidirect
219. C₂×M₃₂	C₂²×C₅₉	semidirect
220. C₂²×C₁₆	C₂²×C₅₉	semidirect
226. #467	C₂²×C₅₉	semidirect
230. #427	C₂²×C₅₉	semidirect
233. #367	C₂²×C₅₉	semidirect
234. #366	C₂²×C₅₉	semidirect
235. #358	C₂²×C₅₉	semidirect
236. #358	C₂²×C₅₉	semidirect
240. C₂²⋊C₁₆	C₂²×C₅₉	semidirect
241. C₅₉	#33766	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#3059	2
C₅₉×#3058	2
C₅₉×#2237	2
C₅₉×#2234	2
C₅₉×#2220	2
C₅₉×#2217	2
C₅₉×#2187	2
C₅₉×#2185	2
C₅₉×#2113	2
#33766	59

Subgroups — C59×#33766 #28445875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33766 #28445875