Subgroups — C₅₉×#17504 #28429613

Order 15104.

1112 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1493	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1492	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1489	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1483	C₂	1	4	yes	maximal, complemented
8	C₂²×M₁₆×C₅₉	—	2	1	no	—
9	C₂²×M₁₆×C₅₉	—	2	1	no	—
10	C₅₉×#533	C₄	1	1	yes	characteristic
11	C₅₉×#533	C₄	1	1	yes	characteristic
12	C₅₉×#533	C₂²	1	1	yes	characteristic
13	C₅₉×#532	C₄	1	1	yes	characteristic
14	C₅₉×#532	C₄	1	1	yes	characteristic
15	C₅₉×#532	C₂²	1	1	yes	characteristic
16	C₅₉×#529	—	2	1	no	—
17	C₅₉×#529	—	2	1	no	—
18	C₅₉×#529	—	2	1	no	—
19	C₅₉×#529	—	2	1	no	—
20	C₅₉×#529	C₄	1	2	yes	—
21	C₅₉×#529	C₂²	1	2	yes	—
22	C₅₉×#525	—	2	1	no	—
23	C₅₉×#525	—	2	1	no	—
24	C₅₉×#525	C₄	1	2	yes	—
25	C₄×#41×C₅₉	—	2	1	no	—
26	C₄×#41×C₅₉	—	2	1	no	—
27	C₄×#41×C₅₉	C₂²	1	2	yes	—
28	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
29	C₅₉×#423	—	2	1	no	—
30	C₅₉×#423	—	2	1	no	—
31	C₅₉×#423	C₂²	1	2	yes	—
32	C₅₉×#423	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
34	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
35	C₄×M₁₆×C₅₉	—	2	1	no	—
36	C₄×M₁₆×C₅₉	—	2	1	no	—
37	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
38	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
39	C₂×#97×C₅₉	—	2	1	no	—
40	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
41	C₅₉×Q₈⋊C₈	C₂²	1	8	yes	complemented
42	C₅₉×D₄⋊C₈	C₂²	1	8	yes	complemented
43	C₂×#41×C₅₉	—	2	1	no	—
44	C₂×#41×C₅₉	—	2	1	no	—
45	C₂×#41×C₅₉	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
49	C₂×M₁₆×C₅₉	—	2	8	no	—
50	C₂×M₁₆×C₅₉	—	2	2	no	—
51	C₂×M₁₆×C₅₉	—	2	2	no	—
52	C₂×M₁₆×C₅₉	—	2	2	no	—
53	C₂×M₁₆×C₅₉	—	2	2	no	—
54	C₂×M₁₆×C₅₉	—	4	4	no	—
55	C₂²×C₈×C₅₉	—	2	2	no	—
56	C₂²×C₈×C₅₉	—	2	2	no	—
57	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
59	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
60	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
61	#126×C₅₉	—	2	2	no	—
62	#126×C₅₉	—	2	2	no	—
63	#125×C₅₉	—	2	1	no	—
64	#125×C₅₉	—	2	1	no	—
65	#125×C₅₉	C₂×C₄	1	2	yes	—
66	#124×C₅₉	—	2	1	no	—
67	#124×C₅₉	—	2	1	no	—
68	#124×C₅₉	C₂×C₄	1	2	yes	—
69	#123×C₅₉	—	2	2	no	—
70	#123×C₅₉	—	2	2	no	—
71	#123×C₅₉	—	2	2	no	—
72	C₂²⋊Q₈×C₅₉	—	2	1	no	—
73	C₂²⋊Q₈×C₅₉	—	2	1	no	—
74	C₂²⋊Q₈×C₅₉	—	2	1	no	—
75	C₂²⋊Q₈×C₅₉	—	2	1	no	—
76	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
77	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
78	#121×C₅₉	—	2	1	no	—
79	#121×C₅₉	—	2	1	no	—
80	#121×C₅₉	—	2	1	no	—
81	#121×C₅₉	—	2	1	no	—
82	#121×C₅₉	C₂×C₄	1	2	yes	—
83	#121×C₅₉	C₂×C₄	1	2	yes	—
84	#120×C₅₉	—	2	2	no	—
85	C₄×Q₈×C₅₉	—	2	1	no	—
86	C₄×Q₈×C₅₉	—	2	1	no	—
87	C₄×Q₈×C₅₉	—	2	1	no	—
88	C₄×Q₈×C₅₉	—	2	1	no	—
89	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
90	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
91	C₄×D₄×C₅₉	—	2	2	no	—
92	C₄×D₄×C₅₉	—	2	2	no	—
93	C₄×D₄×C₅₉	—	2	2	no	—
94	C₄×D₄×C₅₉	—	2	2	no	—
95	C₄×D₄×C₅₉	—	2	2	no	—
96	C₄×D₄×C₅₉	—	2	2	no	—
97	C₄×D₄×C₅₉	—	2	1	no	—
98	C₄×D₄×C₅₉	—	2	1	no	—
99	C₄×D₄×C₅₉	—	2	1	no	—
100	C₄×D₄×C₅₉	—	2	1	no	—
101	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
102	C₄×D₄×C₅₉	C₂³	1	2	yes	—
103	#117×C₅₉	—	2	1	no	—
104	#117×C₅₉	—	2	1	no	—
105	#117×C₅₉	—	2	2	no	—
106	#117×C₅₉	—	2	2	no	—
107	#117×C₅₉	—	2	2	no	—
108	#117×C₅₉	C₂×C₄	1	2	yes	—
109	C₂×C₄²×C₅₉	—	2	2	no	—
110	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₅₉	—	2	2	no	—
123	C₄⋊C₈×C₅₉	—	2	2	no	—
124	C₄⋊C₈×C₅₉	—	2	2	no	—
125	C₄⋊C₈×C₅₉	C₂³	1	4	yes	—
126	#97×C₅₉	—	2	2	no	—
127	#97×C₅₉	—	2	2	no	—
128	C₄×C₈×C₅₉	—	2	2	no	—
129	C₄×C₈×C₅₉	C₂³	1	4	yes	—
130	C₂⁴×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
131	#41×C₅₉	—	4	4	no	—
132	#41×C₅₉	—	4	4	no	—
133	#41×C₅₉	—	4	2	no	—
134	#41×C₅₉	—	4	2	no	—
135	C₂×Q₈×C₅₉	—	2	1	no	—
136	C₂×Q₈×C₅₉	—	2	1	no	—
137	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₅₉	—	2	2	no	—
139	C₂×D₄×C₅₉	—	2	2	no	—
140	C₂×D₄×C₅₉	—	2	2	no	—
141	C₂×D₄×C₅₉	—	2	1	no	—
142	C₂×D₄×C₅₉	—	2	1	no	—
143	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₅₉	—	2	4	no	—
145	C₂²×C₄×C₅₉	—	2	2	no	—
146	C₂²×C₄×C₅₉	—	2	2	no	—
147	C₂²×C₄×C₅₉	—	2	2	no	—
148	C₂²×C₄×C₅₉	—	2	2	no	—
149	C₂²×C₄×C₅₉	—	2	2	no	—
150	C₂²×C₄×C₅₉	—	4	2	no	—
151	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
169	M₁₆×C₅₉	—	2	8	no	—
170	M₁₆×C₅₉	—	2	8	no	—
171	M₁₆×C₅₉	—	4	4	no	—
172	M₁₆×C₅₉	—	4	4	no	—
173	C₂×C₈×C₅₉	—	2	8	no	—
174	C₂×C₈×C₅₉	—	2	4	no	—
175	C₂×C₈×C₅₉	—	2	4	no	—
176	C₂×C₈×C₅₉	—	4	4	no	—
177	C₄⋊C₄×C₅₉	—	2	1	no	—
178	C₄⋊C₄×C₅₉	—	2	1	no	—
179	C₄⋊C₄×C₅₉	—	2	1	no	—
180	C₄⋊C₄×C₅₉	—	2	1	no	—
181	C₄⋊C₄×C₅₉	—	2	2	no	—
182	C₄⋊C₄×C₅₉	—	2	2	no	—
183	C₄⋊C₄×C₅₉	—	2	2	no	—
184	C₄⋊C₄×C₅₉	—	2	2	no	—
185	C₄⋊C₄×C₅₉	—	2	2	no	—
186	C₄⋊C₄×C₅₉	—	2	2	no	—
187	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
188	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
189	C₂²⋊C₄×C₅₉	—	2	2	no	—
190	C₂²⋊C₄×C₅₉	—	2	2	no	—
191	C₂²⋊C₄×C₅₉	—	2	2	no	—
192	C₂²⋊C₄×C₅₉	—	2	2	no	—
193	C₂²⋊C₄×C₅₉	—	2	2	no	—
194	C₂²⋊C₄×C₅₉	—	2	2	no	—
195	C₂²⋊C₄×C₅₉	—	2	2	no	—
196	C₂²⋊C₄×C₅₉	—	2	2	no	—
197	C₂²⋊C₄×C₅₉	—	2	2	no	—
198	C₄²×C₅₉	—	2	2	no	—
199	C₄²×C₅₉	—	2	2	no	—
200	C₄²×C₅₉	—	2	2	no	—
201	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
217	C₂³×C₅₉	—	2	2	no	—
218	C₂³×C₅₉	—	2	2	no	—
219	C₂³×C₅₉	—	2	2	no	—
220	C₂³×C₅₉	—	4	1	no	—
221	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	Q₈×C₅₉	—	2	4	no	—
225	Q₈×C₅₉	—	4	2	no	—
226	Q₈×C₅₉	—	4	2	no	—
227	D₄×C₅₉	—	2	4	no	—
228	D₄×C₅₉	—	4	4	no	—
229	D₄×C₅₉	—	4	4	no	—
230	D₄×C₅₉	—	4	4	no	—
231	D₄×C₅₉	—	4	2	no	—
232	D₄×C₅₉	—	4	2	no	—
233	C₂×C₄×C₅₉	—	2	2	no	—
234	C₂×C₄×C₅₉	—	2	2	no	—
235	C₂×C₄×C₅₉	—	2	2	no	—
236	C₂×C₄×C₅₉	—	2	2	no	—
237	C₂×C₄×C₅₉	—	2	2	no	—
238	C₂×C₄×C₅₉	—	2	1	no	—
239	C₂×C₄×C₅₉	—	2	1	no	—
240	C₂×C₄×C₅₉	—	2	1	no	—
241	C₂×C₄×C₅₉	—	2	1	no	—
242	C₂×C₄×C₅₉	—	2	2	no	—
243	C₂×C₄×C₅₉	—	2	2	no	—
244	C₂×C₄×C₅₉	—	2	2	no	—
245	C₂×C₄×C₅₉	—	2	2	no	—
246	C₂×C₄×C₅₉	—	2	2	no	—
247	C₂×C₄×C₅₉	—	2	2	no	—
248	C₂×C₄×C₅₉	—	2	2	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	2	no	—
251	C₂×C₄×C₅₉	—	4	1	no	—
252	C₂×C₄×C₅₉	—	4	1	no	—
253	C₂×C₄×C₅₉	—	4	1	no	—
254	C₂×C₄×C₅₉	—	4	4	no	—
255	C₂×C₄×C₅₉	—	4	2	no	—
256	C₂×C₄×C₅₉	—	4	2	no	—
257	C₂×C₄×C₅₉	—	4	4	no	—
258	C₂×C₄×C₅₉	#104	1	4	yes	—
259	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
269	C₂×C₄×C₅₉	#137	1	2	yes	—
270	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
273	C₈×C₅₉	—	2	8	no	—
274	C₈×C₅₉	—	4	4	no	—
275	#17504	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂²×C₅₉	—	2	1	no	—
277	C₂²×C₅₉	—	2	1	no	—
278	C₂²×C₅₉	—	2	1	no	—
279	C₂²×C₅₉	—	2	1	no	—
280	C₂²×C₅₉	—	2	1	no	—
281	C₂²×C₅₉	—	2	1	no	—
282	C₂²×C₅₉	—	2	1	no	—
283	C₂²×C₅₉	—	4	4	no	—
284	C₂²×C₅₉	—	4	2	no	—
285	C₂²×C₅₉	—	4	2	no	—
286	C₂²×C₅₉	—	4	2	no	—
287	C₂²×C₅₉	#417	1	2	yes	—
288	C₂²×C₅₉	C₂×#104	1	2	yes	—
289	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
290	C₄×C₅₉	—	2	1	no	—
291	C₄×C₅₉	—	2	1	no	—
292	C₄×C₅₉	—	2	1	no	—
293	C₄×C₅₉	—	2	1	no	—
294	C₄×C₅₉	—	2	1	no	—
295	C₄×C₅₉	—	2	1	no	—
296	C₄×C₅₉	—	2	1	no	—
297	C₄×C₅₉	—	4	2	no	—
298	C₄×C₅₉	—	4	2	no	—
299	C₄×C₅₉	—	4	2	no	—
300	C₄×C₅₉	#417	1	2	yes	—
301	C₄×C₅₉	C₂×#104	1	2	yes	—
302	C₄×C₅₉	C₂×#104	1	2	yes	—
303	C₄×C₅₉	#568	1	2	yes	—
304	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
305	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
306	#3444	C₂×C₅₉	1	1	yes	characteristic
307	C₂×#423	C₂×C₅₉	1	1	yes	characteristic, complemented
308	C₂×C₄×M₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
309	#1493	C₂×C₅₉	1	2	yes	complemented
310	#1492	C₂×C₅₉	1	2	yes	complemented
311	#1489	C₂×C₅₉	1	4	yes	complemented
312	#1483	C₂×C₅₉	1	4	yes	complemented
313	C₂×C₅₉	—	2	2	no	—
314	C₂×C₅₉	—	2	2	no	—
315	C₂×C₅₉	—	4	1	no	—
316	C₂×C₅₉	—	8	2	no	—
317	C₂×C₅₉	#2879	1	1	yes	characteristic
318	C₂×C₅₉	C₂×#417	1	1	yes	characteristic
319	C₂×C₅₉	C₂²×#104	1	1	yes	characteristic
320	C₂²×M₁₆	—	2	1	no	—
321	C₂²×M₁₆	—	2	1	no	—
322	#533	C₄×C₅₉	1	1	yes	characteristic
323	#533	C₄×C₅₉	1	1	yes	characteristic
324	#533	C₂²×C₅₉	1	1	yes	characteristic
325	#532	C₄×C₅₉	1	1	yes	characteristic
326	#532	C₄×C₅₉	1	1	yes	characteristic
327	#532	C₂²×C₅₉	1	1	yes	characteristic
328	#529	—	2	1	no	—
329	#529	—	2	1	no	—
330	#529	—	2	1	no	—
331	#529	—	2	1	no	—
332	#529	C₄×C₅₉	1	2	yes	—
333	#529	C₂²×C₅₉	1	2	yes	—
334	#525	—	2	1	no	—
335	#525	—	2	1	no	—
336	#525	C₄×C₅₉	1	2	yes	—
337	C₄×#41	—	2	1	no	—
338	C₄×#41	—	2	1	no	—
339	C₄×#41	C₂²×C₅₉	1	2	yes	—
340	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
341	#423	—	2	1	no	—
342	#423	—	2	1	no	—
343	#423	C₂²×C₅₉	1	2	yes	—
344	#423	C₂²×C₅₉	1	2	yes	—
345	C₂×C₄⋊C₈	—	2	1	no	—
346	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
347	C₄×M₁₆	—	2	1	no	—
348	C₄×M₁₆	—	2	1	no	—
349	C₄×M₁₆	C₂²×C₅₉	1	2	yes	—
350	C₄×M₁₆	C₂²×C₅₉	1	2	yes	—
351	C₂×#97	—	2	1	no	—
352	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
353	Q₈⋊C₈	C₂²×C₅₉	1	8	yes	complemented
354	D₄⋊C₈	C₂²×C₅₉	1	8	yes	complemented
355	C₅₉	#17504	1	1	yes	characteristic, direct product factor, Sylow
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	C₂×C₄×C₅₉	1	2	yes	—
359	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
360	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
361	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
362	C₂×M₁₆	—	2	8	no	—
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	—	4	4	no	—
368	C₂²×C₈	—	2	2	no	—
369	C₂²×C₈	—	2	2	no	—
370	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
371	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
372	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
373	#127	C₂×C₄×C₅₉	1	1	yes	characteristic
374	#126	—	2	2	no	—
375	#126	—	2	2	no	—
376	#125	—	2	1	no	—
377	#125	—	2	1	no	—
378	#125	C₂×C₄×C₅₉	1	2	yes	—
379	#124	—	2	1	no	—
380	#124	—	2	1	no	—
381	#124	C₂×C₄×C₅₉	1	2	yes	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	#123	—	2	2	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
390	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	C₂×C₄×C₅₉	1	2	yes	—
396	#121	C₂×C₄×C₅₉	1	2	yes	—
397	#120	—	2	2	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
403	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
415	C₄×D₄	C₂³×C₅₉	1	2	yes	—
416	#117	—	2	1	no	—
417	#117	—	2	1	no	—
418	#117	—	2	2	no	—
419	#117	—	2	2	no	—
420	#117	—	2	2	no	—
421	#117	C₂×C₄×C₅₉	1	2	yes	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
424	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
425	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
426	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
427	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
428	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
429	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
430	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
431	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
435	C₄⋊C₈	—	2	2	no	—
436	C₄⋊C₈	—	2	2	no	—
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	C₂³×C₅₉	1	4	yes	—
439	#97	—	2	2	no	—
440	#97	—	2	2	no	—
441	C₄×C₈	—	2	2	no	—
442	C₄×C₈	C₂³×C₅₉	1	4	yes	—
443	C₂⁴	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
444	#41	—	4	4	no	—
445	#41	—	4	4	no	—
446	#41	—	4	2	no	—
447	#41	—	4	2	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
465	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
466	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
467	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
468	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
469	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
470	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
471	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
472	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
482	M₁₆	—	2	8	no	—
483	M₁₆	—	2	8	no	—
484	M₁₆	—	4	4	no	—
485	M₁₆	—	4	4	no	—
486	C₂×C₈	—	2	8	no	—
487	C₂×C₈	—	2	4	no	—
488	C₂×C₈	—	2	4	no	—
489	C₂×C₈	—	4	4	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
501	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	2	no	—
514	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
515	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
516	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
517	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
518	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
519	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
520	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
521	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
522	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
523	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
524	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
525	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
526	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
527	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
529	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	4	1	no	—
534	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
535	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
536	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
537	Q₈	—	2	4	no	—
538	Q₈	—	4	2	no	—
539	Q₈	—	4	2	no	—
540	D₄	—	2	4	no	—
541	D₄	—	4	4	no	—
542	D₄	—	4	4	no	—
543	D₄	—	4	4	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	#104×C₅₉	1	4	yes	—
572	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
573	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
574	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
575	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
576	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
577	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
578	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
579	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
580	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
581	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
582	C₂×C₄	#137×C₅₉	1	2	yes	—
583	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
586	C₈	—	2	8	no	—
587	C₈	—	4	4	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	C₅₉×#417	1	2	yes	—
600	C₂²	C₂×#104×C₅₉	1	2	yes	—
601	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	C₅₉×#417	1	2	yes	—
613	C₄	C₂×#104×C₅₉	1	2	yes	—
614	C₄	C₂×#104×C₅₉	1	2	yes	—
615	C₄	C₅₉×#568	1	2	yes	—
616	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
617	C₄	C₂×#137×C₅₉	1	1	yes	characteristic
618	C₂	—	2	2	no	—
619	C₂	—	2	2	no	—
620	C₂	—	4	1	no	—
621	C₂	—	8	2	no	—
622	C₂	C₅₉×#2879	1	1	yes	characteristic
623	C₂	C₂×C₅₉×#417	1	1	yes	characteristic
624	C₂	C₂²×#104×C₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₄²	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
prime radical	C₅₉×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#423	C₂	semidirect
3. C₂×C₄×M₁₆×C₅₉	C₂	semidirect
4. C₅₉×#1493	C₂	semidirect
5. C₅₉×#1492	C₂	semidirect
6. C₅₉×#1489	C₂	semidirect
7. C₅₉×#1483	C₂	semidirect
41. C₅₉×Q₈⋊C₈	C₂²	semidirect
42. C₅₉×D₄⋊C₈	C₂²	semidirect
275. #17504	C₅₉	direct (N × H)
307. C₂×#423	C₂×C₅₉	semidirect
308. C₂×C₄×M₁₆	C₂×C₅₉	semidirect
309. #1493	C₂×C₅₉	semidirect
310. #1492	C₂×C₅₉	semidirect
311. #1489	C₂×C₅₉	semidirect
312. #1483	C₂×C₅₉	semidirect
353. Q₈⋊C₈	C₂²×C₅₉	semidirect
354. D₄⋊C₈	C₂²×C₅₉	semidirect
355. C₅₉	#17504	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×#3444	2
C₂×C₅₉×#423	2
C₂×C₄×M₁₆×C₅₉	2
C₅₉×#1493	2
C₅₉×#1492	2
C₅₉×#1489	2
C₅₉×#1483	2
#17504	59

Subgroups — C59×#17504 #28429613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17504 #28429613