Subgroups — C₅₉×#36560 #28448669

Order 15104.

2090 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#557	C₂	1	2	yes	maximal
2	C₅₉×#2868	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2859	C₂	1	2	yes	maximal
4	C₅₉×#2568	C₂	1	2	yes	maximal
5	C₅₉×#2565	C₂	1	4	yes	maximal
6	C₅₉×#2546	C₂	1	4	yes	maximal
7	C₅₉×#2506	C₂	1	8	yes	maximal
8	C₅₉×#2365	C₂	1	4	yes	maximal
9	C₄×C₄⋊Q₈×C₅₉	C₂	1	2	yes	maximal
10	C₄×C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
11	C₄²×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#557	—	2	16	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	4	yes	—
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	4	yes	—
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#125×C₅₉	C₂²	1	8	yes	—
18	C₂×#125×C₅₉	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₅₉	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#400	C₂²	1	8	yes	—
25	C₅₉×#398	C₂²	1	16	yes	—
26	C₅₉×#391	C₂²	1	8	yes	—
27	C₅₉×#391	C₂²	1	2	yes	—
28	C₅₉×#391	C₂²	1	4	yes	—
29	C₅₉×#389	C₂²	1	4	yes	—
30	C₅₉×#389	C₂²	1	8	yes	—
31	C₅₉×#389	C₂²	1	8	yes	—
32	C₅₉×#389	C₂²	1	8	yes	—
33	C₅₉×#387	C₂²	1	16	yes	—
34	C₅₉×#384	C₂²	1	4	yes	—
35	C₅₉×#384	C₂²	1	1	yes	characteristic
36	C₅₉×#384	C₂²	1	2	yes	—
37	C₅₉×#384	C₂²	1	2	yes	—
38	C₅₉×#382	C₂²	1	4	yes	—
39	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
40	C₄×C₄⋊C₄×C₅₉	C₂²	1	8	yes	—
41	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
44	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
45	C₄³×C₅₉	C₂²	1	2	yes	—
46	C₄³×C₅₉	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
48	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₅₉	—	2	16	no	—
51	C₄⋊Q₈×C₅₉	—	2	8	no	—
52	C₄⋊Q₈×C₅₉	—	2	16	no	—
53	C₄⋊Q₈×C₅₉	Q₈	1	8	yes	complemented
54	#125×C₅₉	—	2	32	no	—
55	#125×C₅₉	—	2	16	no	—
56	C₄×Q₈×C₅₉	—	2	16	no	—
57	C₄×Q₈×C₅₉	—	2	16	no	—
58	C₄×Q₈×C₅₉	—	2	8	no	—
59	C₄×Q₈×C₅₉	—	2	8	no	—
60	C₄×Q₈×C₅₉	D₄	1	8	yes	—
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
76	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
77	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
78	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
81	C₂×C₄²×C₅₉	C₂³	1	8	yes	—
82	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
87	#95×C₅₉	C₂³	1	4	yes	—
88	#95×C₅₉	C₂³	1	2	yes	—
89	#95×C₅₉	C₂³	1	8	yes	—
90	#95×C₅₉	C₂³	1	16	yes	—
91	#95×C₅₉	C₂³	1	16	yes	—
92	C₂×Q₈×C₅₉	—	2	4	no	—
93	C₂×Q₈×C₅₉	—	2	8	no	—
94	C₂×Q₈×C₅₉	—	2	4	no	—
95	C₂×Q₈×C₅₉	—	2	16	no	—
96	C₂×Q₈×C₅₉	—	2	4	no	—
97	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
98	C₂×Q₈×C₅₉	C₂×Q₈	1	8	yes	—
99	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
100	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
102	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₅₉	C₂⁴	1	4	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	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
110	C₄⋊C₄×C₅₉	—	2	8	no	—
111	C₄⋊C₄×C₅₉	—	2	4	no	—
112	C₄⋊C₄×C₅₉	—	2	16	no	—
113	C₄⋊C₄×C₅₉	—	2	16	no	—
114	C₄⋊C₄×C₅₉	—	2	8	no	—
115	C₄⋊C₄×C₅₉	—	2	16	no	—
116	C₄⋊C₄×C₅₉	—	2	8	no	—
117	C₄⋊C₄×C₅₉	—	2	8	no	—
118	C₄⋊C₄×C₅₉	—	2	4	no	—
119	C₄⋊C₄×C₅₉	—	2	16	no	—
120	C₄⋊C₄×C₅₉	—	2	16	no	—
121	C₄⋊C₄×C₅₉	—	2	8	no	—
122	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
123	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
124	C₄⋊C₄×C₅₉	C₂×Q₈	1	16	yes	—
125	C₄²×C₅₉	—	2	16	no	—
126	C₄²×C₅₉	—	2	8	no	—
127	C₄²×C₅₉	—	2	8	no	—
128	C₄²×C₅₉	—	2	2	no	—
129	C₄²×C₅₉	—	2	4	no	—
130	C₄²×C₅₉	—	2	8	no	—
131	C₄²×C₅₉	—	2	4	no	—
132	C₄²×C₅₉	C₂×D₄	1	8	yes	—
133	C₄²×C₅₉	C₂×D₄	1	4	yes	—
134	C₄²×C₅₉	C₂×Q₈	1	4	yes	—
135	C₄²×C₅₉	#41	1	8	yes	—
136	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
137	Q₈×C₅₉	—	2	8	no	—
138	Q₈×C₅₉	—	2	16	no	—
139	Q₈×C₅₉	—	4	16	no	—
140	C₂×C₄×C₅₉	—	2	4	no	—
141	C₂×C₄×C₅₉	—	2	4	no	—
142	C₂×C₄×C₅₉	—	2	4	no	—
143	C₂×C₄×C₅₉	—	2	2	no	—
144	C₂×C₄×C₅₉	—	2	2	no	—
145	C₂×C₄×C₅₉	—	2	2	no	—
146	C₂×C₄×C₅₉	—	2	4	no	—
147	C₂×C₄×C₅₉	—	2	4	no	—
148	C₂×C₄×C₅₉	—	2	8	no	—
149	C₂×C₄×C₅₉	—	2	4	no	—
150	C₂×C₄×C₅₉	—	2	16	no	—
151	C₂×C₄×C₅₉	—	2	4	no	—
152	C₂×C₄×C₅₉	—	2	4	no	—
153	C₂×C₄×C₅₉	—	2	8	no	—
154	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
157	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
158	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₅₉	C₂²×Q₈	1	8	yes	—
160	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
161	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
162	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
163	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
164	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
165	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
166	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
167	#36560	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
169	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
170	C₂²×C₅₉	C₂²×#41	1	2	yes	—
171	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
172	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
173	C₄×C₅₉	—	2	4	no	—
174	C₄×C₅₉	—	2	8	no	—
175	C₄×C₅₉	—	2	4	no	—
176	C₄×C₅₉	—	2	2	no	—
177	C₄×C₅₉	—	2	4	no	—
178	C₄×C₅₉	—	4	8	no	—
179	C₄×C₅₉	—	4	4	no	—
180	C₄×C₅₉	—	4	4	no	—
181	C₄×C₅₉	#532	1	4	yes	—
182	C₄×C₅₉	D₄×Q₈	1	4	yes	—
183	C₄×C₅₉	#557	1	8	yes	complemented
184	C₂×#557	C₂×C₅₉	1	2	yes	—
185	#2868	C₂×C₅₉	1	1	yes	characteristic
186	#2859	C₂×C₅₉	1	2	yes	—
187	#2568	C₂×C₅₉	1	2	yes	—
188	#2565	C₂×C₅₉	1	4	yes	—
189	#2546	C₂×C₅₉	1	4	yes	—
190	#2506	C₂×C₅₉	1	8	yes	—
191	#2365	C₂×C₅₉	1	4	yes	—
192	C₄×C₄⋊Q₈	C₂×C₅₉	1	2	yes	—
193	C₄×C₄⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
194	C₄²×Q₈	C₂×C₅₉	1	1	yes	characteristic
195	C₂×C₅₉	C₂×#532	1	1	yes	characteristic
196	C₂×C₅₉	C₂×D₄×Q₈	1	1	yes	characteristic
197	C₂×C₅₉	C₂×#557	1	2	yes	—
198	C₂×C₅₉	#3499	1	1	yes	characteristic
199	C₂×C₅₉	#3509	1	2	yes	—
200	#557	—	2	16	no	—
201	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
202	C₂×C₄⋊Q₈	C₂²×C₅₉	1	4	yes	—
203	C₂×C₄⋊Q₈	C₂²×C₅₉	1	4	yes	—
204	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
205	C₂×#125	C₂²×C₅₉	1	4	yes	—
206	C₂×#125	C₂²×C₅₉	1	8	yes	—
207	C₂×C₄×Q₈	C₂²×C₅₉	1	4	yes	—
208	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
209	C₂×C₄×Q₈	C₂²×C₅₉	1	4	yes	—
210	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
212	#400	C₂²×C₅₉	1	8	yes	—
213	#398	C₂²×C₅₉	1	16	yes	—
214	#391	C₂²×C₅₉	1	2	yes	—
215	#391	C₂²×C₅₉	1	4	yes	—
216	#391	C₂²×C₅₉	1	8	yes	—
217	#389	C₂²×C₅₉	1	4	yes	—
218	#389	C₂²×C₅₉	1	8	yes	—
219	#389	C₂²×C₅₉	1	8	yes	—
220	#389	C₂²×C₅₉	1	8	yes	—
221	#387	C₂²×C₅₉	1	16	yes	—
222	#384	C₂²×C₅₉	1	1	yes	characteristic
223	#384	C₂²×C₅₉	1	2	yes	—
224	#384	C₂²×C₅₉	1	2	yes	—
225	#384	C₂²×C₅₉	1	4	yes	—
226	#382	C₂²×C₅₉	1	4	yes	—
227	C₄×C₄⋊C₄	C₂²×C₅₉	1	8	yes	—
228	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
229	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
233	C₄³	C₂²×C₅₉	1	2	yes	—
234	C₄³	C₂²×C₅₉	1	1	yes	characteristic
235	C₅₉	#36560	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
237	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
239	C₄⋊Q₈	—	2	16	no	—
240	C₄⋊Q₈	—	2	8	no	—
241	C₄⋊Q₈	—	2	16	no	—
242	C₄⋊Q₈	Q₈×C₅₉	1	8	yes	complemented
243	#125	—	2	32	no	—
244	#125	—	2	16	no	—
245	C₄×Q₈	—	2	16	no	—
246	C₄×Q₈	—	2	16	no	—
247	C₄×Q₈	—	2	8	no	—
248	C₄×Q₈	—	2	8	no	—
249	C₄×Q₈	D₄×C₅₉	1	8	yes	—
250	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
252	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
253	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
255	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
259	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
260	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
261	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
265	C₂×C₄²	C₂³×C₅₉	1	8	yes	—
266	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
267	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
268	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
269	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
270	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
271	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
273	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
276	#95	C₂³×C₅₉	1	4	yes	—
277	#95	C₂³×C₅₉	1	2	yes	—
278	#95	C₂³×C₅₉	1	8	yes	—
279	#95	C₂³×C₅₉	1	16	yes	—
280	#95	C₂³×C₅₉	1	16	yes	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	16	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
287	C₂×Q₈	C₂×Q₈×C₅₉	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
291	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
294	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
295	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	16	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	2	16	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	16	no	—
309	C₄⋊C₄	—	2	16	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
312	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
313	C₄⋊C₄	C₂×Q₈×C₅₉	1	16	yes	—
314	C₄²	—	2	16	no	—
315	C₄²	—	2	8	no	—
316	C₄²	—	2	8	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	2	8	no	—
320	C₄²	—	2	4	no	—
321	C₄²	C₂×D₄×C₅₉	1	8	yes	—
322	C₄²	C₂×D₄×C₅₉	1	4	yes	—
323	C₄²	C₂×Q₈×C₅₉	1	4	yes	—
324	C₄²	#41×C₅₉	1	8	yes	—
325	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
326	Q₈	—	2	8	no	—
327	Q₈	—	2	16	no	—
328	Q₈	—	4	16	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	16	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
344	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
345	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
346	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
348	C₂×C₄	C₂²×Q₈×C₅₉	1	8	yes	—
349	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
350	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
351	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
352	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
353	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
354	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
355	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
356	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
357	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
358	C₂²	C₂²×#41×C₅₉	1	2	yes	—
359	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
360	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
361	C₄	—	2	4	no	—
362	C₄	—	2	4	no	—
363	C₄	—	2	8	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	8	no	—
368	C₄	—	4	4	no	—
369	C₄	C₅₉×#532	1	4	yes	—
370	C₄	D₄×Q₈×C₅₉	1	4	yes	—
371	C₄	C₅₉×#557	1	8	yes	complemented
372	C₂	C₂×C₅₉×#532	1	1	yes	characteristic
373	C₂	C₂×D₄×Q₈×C₅₉	1	1	yes	characteristic
374	C₂	C₂×C₅₉×#557	1	2	yes	—
375	C₂	C₅₉×#3499	1	1	yes	characteristic
376	C₂	C₅₉×#3509	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
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
53. C₄⋊Q₈×C₅₉	Q₈	semidirect
167. #36560	C₅₉	direct (N × H)
183. C₄×C₅₉	#557	semidirect
235. C₅₉	#36560	direct (N × H)
242. C₄⋊Q₈	Q₈×C₅₉	semidirect
371. C₄	C₅₉×#557	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#557	2
C₅₉×#2868	2
C₅₉×#2859	2
C₅₉×#2568	2
C₅₉×#2565	2
C₅₉×#2546	2
C₅₉×#2506	2
C₅₉×#2365	2
C₄×C₄⋊Q₈×C₅₉	2
C₄²×Q₈×C₅₉	2
#36560	59

Subgroups — C59×#36560 #28448669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#36560 #28448669