Subgroups — C₅₉×#24330 #28436439

Order 15104.

1262 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2058	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2024	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1877	C₂	1	2	yes	maximal
10	C₅₉×#1864	C₂	1	2	yes	maximal
11	C₅₉×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₅₉	—	2	1	no	—
13	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	D₄×Q₈×C₅₉	—	2	4	no	—
15	D₄×Q₈×C₅₉	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₅₉	—	2	2	no	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#475	—	2	4	no	—
25	C₄×SD₁₆×C₅₉	—	2	4	no	—
26	C₂×#106×C₅₉	C₂²	1	2	yes	—
27	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₅₉	C₂²	1	2	yes	—
31	C₂×#102×C₅₉	C₂²	1	2	yes	—
32	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₅₉×#398	—	2	2	no	—
35	C₅₉×#391	—	2	1	no	—
36	C₅₉×#391	C₂²	1	2	yes	—
37	C₅₉×#389	—	2	1	no	—
38	C₅₉×#389	C₂²	1	2	yes	—
39	C₅₉×#384	C₂²	1	1	yes	characteristic
40	C₅₉×#340	C₂²	1	2	yes	—
41	C₅₉×#340	C₂²	1	2	yes	—
42	C₅₉×#340	C₂²	1	2	yes	—
43	C₅₉×#336	C₂²	1	2	yes	—
44	C₅₉×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₅₉	—	2	8	no	—
46	C₂²×Q₈×C₅₉	—	2	2	no	—
47	C₂²×Q₈×C₅₉	—	2	1	no	—
48	C₂²×Q₈×C₅₉	—	4	4	no	—
49	C₂²×Q₈×C₅₉	—	4	4	no	—
50	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₅₉	—	2	2	no	—
54	C₂³×C₄×C₅₉	—	2	1	no	—
55	C₂×SD₁₆×C₅₉	—	2	2	no	—
56	C₂×SD₁₆×C₅₉	—	2	2	no	—
57	C₂×SD₁₆×C₅₉	Q₈	1	4	yes	complemented
58	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₅₉	—	2	4	no	—
62	C₄⋊Q₈×C₅₉	—	2	4	no	—
63	C₄⋊Q₈×C₅₉	—	2	2	no	—
64	C₄⋊Q₈×C₅₉	D₄	1	4	yes	—
65	C₂²⋊Q₈×C₅₉	—	2	8	no	—
66	C₂²⋊Q₈×C₅₉	—	2	16	no	—
67	C₄×Q₈×C₅₉	—	2	2	no	—
68	C₄×Q₈×C₅₉	—	2	2	no	—
69	C₄×Q₈×C₅₉	—	2	2	no	—
70	C₄×Q₈×C₅₉	—	2	2	no	—
71	C₄×D₄×C₅₉	—	2	4	no	—
72	C₄×D₄×C₅₉	—	2	4	no	—
73	C₄×D₄×C₅₉	—	2	2	no	—
74	C₄×D₄×C₅₉	D₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
89	C₂×C₄²×C₅₉	—	2	1	no	—
90	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	#106×C₅₉	—	2	2	no	—
93	#106×C₅₉	—	2	4	no	—
94	C₄⋊C₈×C₅₉	—	2	2	no	—
95	#103×C₅₉	—	2	2	no	—
96	#103×C₅₉	—	2	4	no	—
97	#102×C₅₉	—	2	2	no	—
98	#102×C₅₉	—	2	4	no	—
99	C₄×C₈×C₅₉	—	2	2	no	—
100	#95×C₅₉	—	2	2	no	—
101	#95×C₅₉	—	2	2	no	—
102	#95×C₅₉	—	2	2	no	—
103	C₂⁴×C₅₉	—	2	1	no	—
104	C₂×Q₈×C₅₉	—	2	8	no	—
105	C₂×Q₈×C₅₉	—	2	2	no	—
106	C₂×Q₈×C₅₉	—	2	4	no	—
107	C₂×Q₈×C₅₉	—	2	2	no	—
108	C₂×Q₈×C₅₉	—	2	1	no	—
109	C₂×Q₈×C₅₉	—	2	1	no	—
110	C₂×Q₈×C₅₉	—	2	1	no	—
111	C₂×Q₈×C₅₉	—	2	1	no	—
112	C₂×Q₈×C₅₉	—	2	1	no	—
113	C₂×Q₈×C₅₉	—	4	4	no	—
114	C₂×Q₈×C₅₉	—	4	32	no	—
115	C₂×Q₈×C₅₉	—	4	4	no	—
116	C₂×Q₈×C₅₉	—	4	2	no	—
117	C₂×Q₈×C₅₉	—	4	2	no	—
118	C₂×Q₈×C₅₉	SD₁₆	1	4	yes	complemented
119	C₂×Q₈×C₅₉	C₂×Q₈	1	2	yes	complemented
120	C₂×D₄×C₅₉	—	2	1	no	—
121	C₂×D₄×C₅₉	—	2	1	no	—
122	C₂×D₄×C₅₉	—	2	1	no	—
123	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₅₉	C₂×Q₈	1	2	yes	—
125	C₂×D₄×C₅₉	#41	1	2	yes	—
126	C₂²×C₄×C₅₉	—	2	8	no	—
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	2	no	—
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	—	2	4	no	—
131	C₂²×C₄×C₅₉	—	2	2	no	—
132	C₂²×C₄×C₅₉	—	2	1	no	—
133	C₂²×C₄×C₅₉	—	4	4	no	—
134	C₂²×C₄×C₅₉	—	4	4	no	—
135	C₂²×C₄×C₅₉	—	4	2	no	—
136	C₂²×C₄×C₅₉	—	4	2	no	—
137	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
142	SD₁₆×C₅₉	—	2	8	no	—
143	C₂×C₈×C₅₉	—	2	1	no	—
144	C₂×C₈×C₅₉	—	2	1	no	—
145	C₂×C₈×C₅₉	—	2	1	no	—
146	C₂×C₈×C₅₉	—	2	2	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₂×C₈×C₅₉	—	2	1	no	—
149	C₂×C₈×C₅₉	—	2	1	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	complemented
152	C₄⋊C₄×C₅₉	—	2	8	no	—
153	C₄⋊C₄×C₅₉	—	2	4	no	—
154	C₄⋊C₄×C₅₉	—	2	4	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	2	2	no	—
157	C₄⋊C₄×C₅₉	—	2	1	no	—
158	C₄⋊C₄×C₅₉	—	2	1	no	—
159	C₄⋊C₄×C₅₉	—	2	1	no	—
160	C₄⋊C₄×C₅₉	—	2	2	no	—
161	C₄⋊C₄×C₅₉	—	2	2	no	—
162	C₄⋊C₄×C₅₉	—	4	2	no	—
163	C₄⋊C₄×C₅₉	—	4	2	no	—
164	C₄⋊C₄×C₅₉	—	8	1	no	—
165	C₄⋊C₄×C₅₉	—	8	2	no	—
166	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₅₉	—	2	8	no	—
169	C₂²⋊C₄×C₅₉	—	2	4	no	—
170	C₄²×C₅₉	—	2	2	no	—
171	C₄²×C₅₉	—	2	2	no	—
172	C₄²×C₅₉	—	4	2	no	—
173	C₄²×C₅₉	C₂×D₄	1	2	yes	—
174	C₄²×C₅₉	C₂×D₄	1	2	yes	—
175	C₂³×C₅₉	—	2	2	no	—
176	C₂³×C₅₉	—	2	2	no	—
177	C₂³×C₅₉	—	2	2	no	—
178	C₂³×C₅₉	—	4	1	no	—
179	C₂³×C₅₉	—	4	1	no	—
180	C₂³×C₅₉	—	4	1	no	—
181	C₂³×C₅₉	—	4	1	no	—
182	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₅₉	—	2	8	no	—
184	Q₈×C₅₉	—	2	2	no	—
185	Q₈×C₅₉	—	2	2	no	—
186	Q₈×C₅₉	—	4	16	no	—
187	Q₈×C₅₉	—	4	1	no	—
188	Q₈×C₅₉	—	4	1	no	—
189	Q₈×C₅₉	—	4	8	no	—
190	D₄×C₅₉	—	2	2	no	—
191	D₄×C₅₉	—	2	2	no	—
192	D₄×C₅₉	—	2	2	no	—
193	D₄×C₅₉	C₂²⋊Q₈	1	4	yes	—
194	C₂×C₄×C₅₉	—	2	2	no	—
195	C₂×C₄×C₅₉	—	2	2	no	—
196	C₂×C₄×C₅₉	—	2	1	no	—
197	C₂×C₄×C₅₉	—	2	1	no	—
198	C₂×C₄×C₅₉	—	2	2	no	—
199	C₂×C₄×C₅₉	—	2	4	no	—
200	C₂×C₄×C₅₉	—	2	2	no	—
201	C₂×C₄×C₅₉	—	2	2	no	—
202	C₂×C₄×C₅₉	—	2	2	no	—
203	C₂×C₄×C₅₉	—	2	2	no	—
204	C₂×C₄×C₅₉	—	4	16	no	—
205	C₂×C₄×C₅₉	—	4	1	no	—
206	C₂×C₄×C₅₉	—	4	1	no	—
207	C₂×C₄×C₅₉	—	4	2	no	—
208	C₂×C₄×C₅₉	—	4	1	no	—
209	C₂×C₄×C₅₉	—	4	2	no	—
210	C₂×C₄×C₅₉	—	4	1	no	—
211	C₂×C₄×C₅₉	—	4	8	no	—
212	C₂×C₄×C₅₉	—	4	1	no	—
213	C₂×C₄×C₅₉	—	4	2	no	—
214	C₂×C₄×C₅₉	—	4	2	no	—
215	C₂×C₄×C₅₉	—	4	2	no	—
216	C₂×C₄×C₅₉	—	4	1	no	—
217	C₂×C₄×C₅₉	—	4	1	no	—
218	C₂×C₄×C₅₉	#120	1	2	yes	—
219	C₂×C₄×C₅₉	#120	1	2	yes	—
220	C₂×C₄×C₅₉	C₂×SD₁₆	1	4	yes	—
221	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
222	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
223	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
226	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
228	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
229	C₈×C₅₉	—	2	2	no	—
230	C₈×C₅₉	—	4	1	no	—
231	C₈×C₅₉	—	4	2	no	—
232	#24330	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₅₉	—	2	4	no	—
234	C₂²×C₅₉	—	4	2	no	—
235	C₂²×C₅₉	—	4	2	no	—
236	C₂²×C₅₉	—	4	2	no	—
237	C₂²×C₅₉	—	4	2	no	—
238	C₂²×C₅₉	—	4	2	no	—
239	C₂²×C₅₉	—	4	2	no	—
240	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
241	C₂²×C₅₉	#548	1	1	yes	characteristic
242	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
243	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
244	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₅₉	#577	1	1	yes	characteristic
246	C₂²×C₅₉	#578	1	1	yes	characteristic
247	C₄×C₅₉	—	2	4	no	—
248	C₄×C₅₉	—	2	2	no	—
249	C₄×C₅₉	—	4	2	no	—
250	C₄×C₅₉	—	4	4	no	—
251	C₄×C₅₉	—	4	2	no	—
252	C₄×C₅₉	—	4	2	no	—
253	C₄×C₅₉	—	8	2	no	—
254	C₄×C₅₉	—	8	1	no	—
255	C₄×C₅₉	#450	1	4	yes	—
256	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₄×C₅₉	#536	1	1	yes	characteristic
258	C₄×C₅₉	#548	1	1	yes	characteristic
259	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
260	C₂×D₄×Q₈	C₂×C₅₉	1	1	yes	characteristic
261	C₂×#475	C₂×C₅₉	1	1	yes	characteristic, complemented
262	C₂×C₄×SD₁₆	C₂×C₅₉	1	1	yes	characteristic
263	#2582	C₂×C₅₉	1	1	yes	characteristic, complemented
264	#2058	C₂×C₅₉	1	2	yes	complemented
265	#2024	C₂×C₅₉	1	2	yes	complemented
266	#1990	C₂×C₅₉	1	1	yes	characteristic, complemented
267	#1984	C₂×C₅₉	1	1	yes	characteristic, complemented
268	#1877	C₂×C₅₉	1	2	yes	—
269	#1864	C₂×C₅₉	1	2	yes	—
270	#1802	C₂×C₅₉	1	1	yes	characteristic
271	C₂×C₅₉	—	4	4	no	—
272	C₂×C₅₉	#2409	1	1	yes	characteristic
273	C₂×C₅₉	C₂×#450	1	1	yes	characteristic
274	C₂×C₅₉	#3013	1	1	yes	characteristic
275	C₂×C₅₉	#3359	1	1	yes	characteristic
276	C₂×C₅₉	#3373	1	1	yes	characteristic
277	C₂×C₅₉	Q₈×SD₁₆	1	1	yes	characteristic
278	C₂×C₅₉	#3386	1	1	yes	characteristic
279	C₂³×Q₈	—	2	1	no	—
280	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
281	D₄×Q₈	—	2	4	no	—
282	D₄×Q₈	—	2	4	no	—
283	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
284	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
285	C₂×C₂²⋊Q₈	—	2	1	no	—
286	C₂×C₂²⋊Q₈	—	2	2	no	—
287	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
290	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
291	#475	—	2	4	no	—
292	C₄×SD₁₆	—	2	4	no	—
293	C₂×#106	C₂²×C₅₉	1	2	yes	—
294	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
295	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
296	C₂×#103	C₂²×C₅₉	1	2	yes	—
297	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
298	C₂×#102	C₂²×C₅₉	1	2	yes	—
299	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
301	#398	—	2	2	no	—
302	#391	—	2	1	no	—
303	#391	C₂²×C₅₉	1	2	yes	—
304	#389	—	2	1	no	—
305	#389	C₂²×C₅₉	1	2	yes	—
306	#384	C₂²×C₅₉	1	1	yes	characteristic
307	#340	C₂²×C₅₉	1	2	yes	—
308	#340	C₂²×C₅₉	1	2	yes	—
309	#340	C₂²×C₅₉	1	2	yes	—
310	#336	C₂²×C₅₉	1	2	yes	—
311	#336	C₂²×C₅₉	1	2	yes	—
312	C₅₉	#24330	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²×Q₈	—	2	8	no	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	—	4	4	no	—
317	C₂²×Q₈	—	4	4	no	—
318	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
319	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
320	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
321	C₂³×C₄	—	2	2	no	—
322	C₂³×C₄	—	2	1	no	—
323	C₂×SD₁₆	—	2	2	no	—
324	C₂×SD₁₆	—	2	2	no	—
325	C₂×SD₁₆	Q₈×C₅₉	1	4	yes	complemented
326	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
328	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	—	2	4	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	D₄×C₅₉	1	4	yes	—
333	C₂²⋊Q₈	—	2	8	no	—
334	C₂²⋊Q₈	—	2	16	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	D₄×C₅₉	1	4	yes	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
359	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
360	#106	—	2	2	no	—
361	#106	—	2	4	no	—
362	C₄⋊C₈	—	2	2	no	—
363	#103	—	2	2	no	—
364	#103	—	2	4	no	—
365	#102	—	2	2	no	—
366	#102	—	2	4	no	—
367	C₄×C₈	—	2	2	no	—
368	#95	—	2	2	no	—
369	#95	—	2	2	no	—
370	#95	—	2	2	no	—
371	C₂⁴	—	2	1	no	—
372	C₂×Q₈	—	2	8	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×Q₈	—	4	32	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	SD₁₆×C₅₉	1	4	yes	complemented
387	C₂×Q₈	C₂×Q₈×C₅₉	1	2	yes	complemented
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
392	C₂×D₄	C₂×Q₈×C₅₉	1	2	yes	—
393	C₂×D₄	#41×C₅₉	1	2	yes	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
410	SD₁₆	—	2	8	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	C₂×Q₈×C₅₉	1	2	yes	complemented
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	8	1	no	—
433	C₄⋊C₄	—	8	2	no	—
434	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
435	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	4	2	no	—
441	C₄²	C₂×D₄×C₅₉	1	2	yes	—
442	C₄²	C₂×D₄×C₅₉	1	2	yes	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	16	no	—
455	Q₈	—	4	8	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	C₂²⋊Q₈×C₅₉	1	4	yes	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	16	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	#120×C₅₉	1	2	yes	—
487	C₂×C₄	#120×C₅₉	1	2	yes	—
488	C₂×C₄	C₂×SD₁₆×C₅₉	1	4	yes	—
489	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
490	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
493	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
495	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
496	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	4	1	no	—
499	C₈	—	4	2	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
508	C₂²	C₅₉×#548	1	1	yes	characteristic
509	C₂²	D₄×Q₈×C₅₉	1	1	yes	characteristic
510	C₂²	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
511	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
512	C₂²	C₅₉×#577	1	1	yes	characteristic
513	C₂²	C₅₉×#578	1	1	yes	characteristic
514	C₄	—	2	4	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	2	no	—
522	C₄	C₅₉×#450	1	4	yes	—
523	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
524	C₄	C₅₉×#536	1	1	yes	characteristic
525	C₄	C₅₉×#548	1	1	yes	characteristic
526	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
527	C₂	—	4	4	no	—
528	C₂	C₅₉×#2409	1	1	yes	characteristic
529	C₂	C₂×C₅₉×#450	1	1	yes	characteristic
530	C₂	C₅₉×#3013	1	1	yes	characteristic
531	C₂	C₅₉×#3359	1	1	yes	characteristic
532	C₂	C₅₉×#3373	1	1	yes	characteristic
533	C₂	Q₈×SD₁₆×C₅₉	1	1	yes	characteristic
534	C₂	C₅₉×#3386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄×Q₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#475	C₂	semidirect
4. C₅₉×#2582	C₂	semidirect
5. C₅₉×#2058	C₂	semidirect
6. C₅₉×#2024	C₂	semidirect
7. C₅₉×#1990	C₂	semidirect
8. C₅₉×#1984	C₂	semidirect
57. C₂×SD₁₆×C₅₉	Q₈	semidirect
118. C₂×Q₈×C₅₉	SD₁₆	semidirect
119. C₂×Q₈×C₅₉	C₂×Q₈	semidirect
151. C₂×C₈×C₅₉	C₂×Q₈	semidirect
232. #24330	C₅₉	direct (N × H)
261. C₂×#475	C₂×C₅₉	semidirect
263. #2582	C₂×C₅₉	semidirect
264. #2058	C₂×C₅₉	semidirect
265. #2024	C₂×C₅₉	semidirect
266. #1990	C₂×C₅₉	semidirect
267. #1984	C₂×C₅₉	semidirect
312. C₅₉	#24330	direct (N × H)
325. C₂×SD₁₆	Q₈×C₅₉	semidirect
386. C₂×Q₈	SD₁₆×C₅₉	semidirect
387. C₂×Q₈	C₂×Q₈×C₅₉	semidirect
419. C₂×C₈	C₂×Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₅₉	2
C₂×C₅₉×#475	2
C₂×C₄×SD₁₆×C₅₉	2
C₅₉×#2582	2
C₅₉×#2058	2
C₅₉×#2024	2
C₅₉×#1990	2
C₅₉×#1984	2
C₅₉×#1877	2
C₅₉×#1864	2
C₅₉×#1802	2
#24330	59

Subgroups — C59×#24330 #28436439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24330 #28436439