Subgroups — C₅₉×#17623 #28429732

Order 15104.

1014 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3505	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2353	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1521	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1513	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1511	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1510	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1508	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1507	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1504	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1500	C₂	1	2	yes	maximal, complemented
12	C₅₉×#553	—	2	2	no	—
13	C₅₉×#553	C₄	1	2	yes	complemented
14	C₅₉×#552	C₄	1	2	yes	complemented
15	C₅₉×#551	—	2	2	no	—
16	C₅₉×#548	C₄	1	2	yes	complemented
17	C₅₉×#546	C₄	1	2	yes	complemented
18	C₅₉×#539	—	2	1	no	—
19	C₅₉×#538	—	2	1	no	—
20	C₅₉×#534	—	2	1	no	—
21	C₅₉×#529	C₂²	1	2	yes	—
22	C₅₉×#525	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#518	—	2	1	no	—
26	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#436	—	2	2	no	—
28	C₅₉×#436	—	2	2	no	—
29	C₅₉×#431	C₂²	1	2	yes	complemented
30	C₅₉×#407	C₂²	1	1	yes	characteristic
31	C₅₉×#407	C₂²	1	1	yes	characteristic
32	C₅₉×#407	C₂²	1	2	yes	complemented
33	C₅₉×#388	—	2	1	no	—
34	C₅₉×#387	—	2	1	no	—
35	C₅₉×#386	—	2	1	no	—
36	C₅₉×#383	C₂²	1	1	yes	characteristic, complemented
37	C₅₉×#381	C₂²	1	1	yes	characteristic
38	C₅₉×#380	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#376	C₂²	1	1	yes	characteristic, complemented
42	C₂×#95×C₅₉	C₂²	1	1	yes	characteristic, complemented
43	C₅₉×#328	C₂²	1	2	yes	complemented
44	C₅₉×#328	C₂²	1	2	yes	complemented
45	C₅₉×#328	C₂²	1	2	yes	complemented
46	C₅₉×#328	C₂²	1	2	yes	complemented
47	C₅₉×#327	C₂²	1	2	yes	—
48	C₅₉×#327	C₂²	1	2	yes	—
49	C₅₉×#327	C₂²	1	2	yes	—
50	C₅₉×#327	C₂²	1	2	yes	—
51	C₂×#41×C₅₉	C₂×C₄	1	2	yes	—
52	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂²×D₄×C₅₉	—	2	1	no	—
54	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₅₉	—	2	1	no	—
57	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₅₉	—	2	1	no	—
60	C₂×M₁₆×C₅₉	—	2	1	no	—
61	C₂×M₁₆×C₅₉	—	2	2	no	—
62	#126×C₅₉	—	2	2	no	—
63	#126×C₅₉	—	2	2	no	—
64	#126×C₅₉	—	2	2	no	—
65	#125×C₅₉	—	2	2	no	—
66	#125×C₅₉	C₂×C₄	1	2	yes	complemented
67	#124×C₅₉	—	2	2	no	—
68	#124×C₅₉	C₂×C₄	1	2	yes	complemented
69	#123×C₅₉	—	2	2	no	—
70	#123×C₅₉	—	2	2	no	—
71	#123×C₅₉	—	2	2	no	—
72	#123×C₅₉	—	2	2	no	—
73	#123×C₅₉	—	2	2	no	—
74	C₂²⋊Q₈×C₅₉	—	2	1	no	—
75	C₂²⋊Q₈×C₅₉	—	2	1	no	—
76	C₂²⋊Q₈×C₅₉	—	2	2	no	—
77	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
78	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	complemented
79	C₂²⋊Q₈×C₅₉	C₂³	1	2	yes	—
80	#121×C₅₉	—	2	2	no	—
81	#121×C₅₉	—	2	2	no	—
82	#121×C₅₉	—	2	1	no	—
83	#121×C₅₉	—	2	1	no	—
84	#121×C₅₉	—	2	2	no	—
85	#121×C₅₉	C₂×C₄	1	2	yes	—
86	#121×C₅₉	C₂×C₄	1	2	yes	complemented
87	#121×C₅₉	C₂³	1	2	yes	—
88	#120×C₅₉	—	2	2	no	—
89	#120×C₅₉	—	2	2	no	—
90	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	complemented
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	C₂×C₄	1	2	yes	—
97	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	complemented
99	C₄×D₄×C₅₉	D₄	1	2	yes	—
100	C₄×D₄×C₅₉	D₄	1	2	yes	—
101	#117×C₅₉	—	2	2	no	—
102	#117×C₅₉	—	2	2	no	—
103	#117×C₅₉	C₂×C₄	1	2	yes	—
104	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
107	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
108	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅₉	—	2	1	no	—
118	C₂×C₄²×C₅₉	—	2	1	no	—
119	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₅₉	—	2	2	no	—
121	C₂²⋊C₈×C₅₉	—	2	1	no	—
122	C₂²⋊C₈×C₅₉	—	2	1	no	—
123	C₂²⋊C₈×C₅₉	—	2	2	no	—
124	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
125	C₂²⋊C₈×C₅₉	C₂³	1	2	yes	—
126	C₄×C₈×C₅₉	—	2	2	no	—
127	#95×C₅₉	—	2	1	no	—
128	#95×C₅₉	—	2	1	no	—
129	#95×C₅₉	—	2	1	no	—
130	#95×C₅₉	—	2	1	no	—
131	#95×C₅₉	—	2	1	no	—
132	#95×C₅₉	C₂³	1	1	yes	characteristic
133	#95×C₅₉	C₂³	1	1	yes	characteristic
134	#95×C₅₉	C₂³	1	1	yes	characteristic
135	#95×C₅₉	C₂³	1	1	yes	characteristic
136	C₂⁴×C₅₉	—	2	1	no	—
137	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
139	#41×C₅₉	—	8	2	no	—
140	C₂×Q₈×C₅₉	—	2	1	no	—
141	C₂×Q₈×C₅₉	—	8	1	no	—
142	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
143	C₂×D₄×C₅₉	—	2	2	no	—
144	C₂×D₄×C₅₉	—	2	2	no	—
145	C₂×D₄×C₅₉	—	2	2	no	—
146	C₂×D₄×C₅₉	—	2	2	no	—
147	C₂×D₄×C₅₉	—	2	1	no	—
148	C₂×D₄×C₅₉	—	4	1	no	—
149	C₂×D₄×C₅₉	—	4	1	no	—
150	C₂×D₄×C₅₉	—	4	2	no	—
151	C₂×D₄×C₅₉	—	4	2	no	—
152	C₂×D₄×C₅₉	—	8	1	no	—
153	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
154	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₅₉	—	2	1	no	—
157	C₂²×C₄×C₅₉	—	2	1	no	—
158	C₂²×C₄×C₅₉	—	2	1	no	—
159	C₂²×C₄×C₅₉	—	2	1	no	—
160	C₂²×C₄×C₅₉	—	2	2	no	—
161	C₂²×C₄×C₅₉	—	2	2	no	—
162	C₂²×C₄×C₅₉	—	2	1	no	—
163	C₂²×C₄×C₅₉	—	2	1	no	—
164	C₂²×C₄×C₅₉	—	2	1	no	—
165	C₂²×C₄×C₅₉	—	4	2	no	—
166	C₂²×C₄×C₅₉	—	4	2	no	—
167	C₂²×C₄×C₅₉	—	8	1	no	—
168	C₂²×C₄×C₅₉	—	8	1	no	—
169	C₂²×C₄×C₅₉	—	8	1	no	—
170	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
181	M₁₆×C₅₉	—	8	1	no	—
182	M₁₆×C₅₉	—	8	1	no	—
183	M₁₆×C₅₉	—	8	2	no	—
184	C₂×C₈×C₅₉	—	2	2	no	—
185	C₂×C₈×C₅₉	—	2	2	no	—
186	C₄⋊C₄×C₅₉	—	2	2	no	—
187	C₄⋊C₄×C₅₉	—	2	1	no	—
188	C₄⋊C₄×C₅₉	—	2	1	no	—
189	C₄⋊C₄×C₅₉	—	2	2	no	—
190	C₄⋊C₄×C₅₉	—	2	2	no	—
191	C₄⋊C₄×C₅₉	—	2	2	no	—
192	C₄⋊C₄×C₅₉	—	2	2	no	—
193	C₄⋊C₄×C₅₉	—	2	2	no	—
194	C₄⋊C₄×C₅₉	—	8	1	no	—
195	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
196	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
197	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
198	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
199	C₂²⋊C₄×C₅₉	—	2	2	no	—
200	C₂²⋊C₄×C₅₉	—	2	2	no	—
201	C₂²⋊C₄×C₅₉	—	2	2	no	—
202	C₂²⋊C₄×C₅₉	—	2	2	no	—
203	C₂²⋊C₄×C₅₉	—	2	2	no	—
204	C₂²⋊C₄×C₅₉	—	2	2	no	—
205	C₂²⋊C₄×C₅₉	—	2	2	no	—
206	C₂²⋊C₄×C₅₉	—	2	2	no	—
207	C₂²⋊C₄×C₅₉	—	2	2	no	—
208	C₂²⋊C₄×C₅₉	—	2	2	no	—
209	C₂²⋊C₄×C₅₉	—	4	2	no	—
210	C₂²⋊C₄×C₅₉	—	4	2	no	—
211	C₂²⋊C₄×C₅₉	—	8	1	no	—
212	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
213	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
214	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
215	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
216	C₄²×C₅₉	—	2	2	no	—
217	C₄²×C₅₉	—	2	2	no	—
218	C₄²×C₅₉	—	4	2	no	—
219	C₄²×C₅₉	—	8	1	no	—
220	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
221	C₄²×C₅₉	C₂×D₄	1	2	yes	—
222	C₂³×C₅₉	—	2	1	no	—
223	C₂³×C₅₉	—	2	1	no	—
224	C₂³×C₅₉	—	2	1	no	—
225	C₂³×C₅₉	—	2	1	no	—
226	C₂³×C₅₉	—	2	2	no	—
227	C₂³×C₅₉	—	4	1	no	—
228	C₂³×C₅₉	—	4	1	no	—
229	C₂³×C₅₉	—	4	1	no	—
230	C₂³×C₅₉	—	4	1	no	—
231	C₂³×C₅₉	—	4	2	no	—
232	C₂³×C₅₉	—	8	1	no	—
233	C₂³×C₅₉	—	8	1	no	—
234	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₅₉	—	4	2	no	—
239	Q₈×C₅₉	—	8	1	no	—
240	D₄×C₅₉	—	4	2	no	—
241	D₄×C₅₉	—	4	2	no	—
242	D₄×C₅₉	—	4	2	no	—
243	D₄×C₅₉	—	4	4	no	—
244	D₄×C₅₉	—	4	2	no	—
245	D₄×C₅₉	—	4	2	no	—
246	D₄×C₅₉	—	8	1	no	—
247	D₄×C₅₉	—	8	2	no	—
248	D₄×C₅₉	—	8	2	no	—
249	C₂×C₄×C₅₉	—	2	1	no	—
250	C₂×C₄×C₅₉	—	2	1	no	—
251	C₂×C₄×C₅₉	—	2	2	no	—
252	C₂×C₄×C₅₉	—	2	2	no	—
253	C₂×C₄×C₅₉	—	2	2	no	—
254	C₂×C₄×C₅₉	—	2	2	no	—
255	C₂×C₄×C₅₉	—	4	1	no	—
256	C₂×C₄×C₅₉	—	4	1	no	—
257	C₂×C₄×C₅₉	—	4	1	no	—
258	C₂×C₄×C₅₉	—	4	2	no	—
259	C₂×C₄×C₅₉	—	4	1	no	—
260	C₂×C₄×C₅₉	—	4	1	no	—
261	C₂×C₄×C₅₉	—	4	1	no	—
262	C₂×C₄×C₅₉	—	4	1	no	—
263	C₂×C₄×C₅₉	—	4	1	no	—
264	C₂×C₄×C₅₉	—	4	2	no	—
265	C₂×C₄×C₅₉	—	4	1	no	—
266	C₂×C₄×C₅₉	—	4	2	no	—
267	C₂×C₄×C₅₉	—	4	1	no	—
268	C₂×C₄×C₅₉	—	4	1	no	—
269	C₂×C₄×C₅₉	—	4	1	no	—
270	C₂×C₄×C₅₉	—	4	1	no	—
271	C₂×C₄×C₅₉	—	4	1	no	—
272	C₂×C₄×C₅₉	—	4	1	no	—
273	C₂×C₄×C₅₉	—	4	1	no	—
274	C₂×C₄×C₅₉	—	4	1	no	—
275	C₂×C₄×C₅₉	—	4	1	no	—
276	C₂×C₄×C₅₉	—	4	1	no	—
277	C₂×C₄×C₅₉	—	8	2	no	—
278	C₂×C₄×C₅₉	—	8	2	no	—
279	C₂×C₄×C₅₉	—	8	1	no	—
280	C₂×C₄×C₅₉	—	8	1	no	—
281	C₂×C₄×C₅₉	—	8	4	no	—
282	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
283	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
284	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
289	C₈×C₅₉	—	4	2	no	—
290	C₈×C₅₉	—	4	2	no	—
291	#17623	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂²×C₅₉	—	2	1	no	—
293	C₂²×C₅₉	—	2	1	no	—
294	C₂²×C₅₉	—	2	1	no	—
295	C₂²×C₅₉	—	2	2	no	—
296	C₂²×C₅₉	—	2	1	no	—
297	C₂²×C₅₉	—	2	1	no	—
298	C₂²×C₅₉	—	2	1	no	—
299	C₂²×C₅₉	—	2	2	no	—
300	C₂²×C₅₉	—	2	1	no	—
301	C₂²×C₅₉	—	2	2	no	—
302	C₂²×C₅₉	—	2	1	no	—
303	C₂²×C₅₉	—	4	2	no	—
304	C₂²×C₅₉	—	4	2	no	—
305	C₂²×C₅₉	—	4	2	no	—
306	C₂²×C₅₉	—	4	2	no	—
307	C₂²×C₅₉	—	4	2	no	—
308	C₂²×C₅₉	—	8	1	no	—
309	C₂²×C₅₉	—	8	1	no	—
310	C₂²×C₅₉	—	16	2	no	—
311	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
312	C₂²×C₅₉	#575	1	1	yes	characteristic
313	C₂²×C₅₉	#575	1	1	yes	characteristic
314	C₄×C₅₉	—	2	1	no	—
315	C₄×C₅₉	—	2	1	no	—
316	C₄×C₅₉	—	2	2	no	—
317	C₄×C₅₉	—	2	1	no	—
318	C₄×C₅₉	—	2	1	no	—
319	C₄×C₅₉	—	2	2	no	—
320	C₄×C₅₉	—	2	2	no	—
321	C₄×C₅₉	—	4	2	no	—
322	C₄×C₅₉	—	4	2	no	—
323	C₄×C₅₉	—	4	2	no	—
324	C₄×C₅₉	—	4	2	no	—
325	C₄×C₅₉	—	8	1	no	—
326	C₄×C₅₉	—	8	1	no	—
327	C₄×C₅₉	—	8	1	no	—
328	#3505	C₂×C₅₉	1	1	yes	characteristic
329	#2975	C₂×C₅₉	1	1	yes	characteristic, complemented
330	#2353	C₂×C₅₉	1	1	yes	characteristic, complemented
331	#1521	C₂×C₅₉	1	2	yes	complemented
332	#1513	C₂×C₅₉	1	2	yes	complemented
333	#1511	C₂×C₅₉	1	1	yes	characteristic, complemented
334	#1510	C₂×C₅₉	1	1	yes	characteristic, complemented
335	#1508	C₂×C₅₉	1	1	yes	characteristic, complemented
336	#1507	C₂×C₅₉	1	1	yes	characteristic, complemented
337	#1504	C₂×C₅₉	1	2	yes	complemented
338	#1500	C₂×C₅₉	1	2	yes	complemented
339	C₂×C₅₉	—	2	1	no	—
340	C₂×C₅₉	—	2	1	no	—
341	C₂×C₅₉	—	4	2	no	—
342	C₂×C₅₉	—	4	1	no	—
343	C₂×C₅₉	—	4	1	no	—
344	C₂×C₅₉	—	8	2	no	—
345	C₂×C₅₉	#2883	1	1	yes	characteristic
346	C₂×C₅₉	#2896	1	1	yes	characteristic
347	C₂×C₅₉	#2901	1	1	yes	characteristic
348	#553	—	2	2	no	—
349	#553	C₄×C₅₉	1	2	yes	complemented
350	#552	C₄×C₅₉	1	2	yes	complemented
351	#551	—	2	2	no	—
352	#548	C₄×C₅₉	1	2	yes	complemented
353	#546	C₄×C₅₉	1	2	yes	complemented
354	#539	—	2	1	no	—
355	#538	—	2	1	no	—
356	#534	—	2	1	no	—
357	#529	C₂²×C₅₉	1	2	yes	—
358	#525	C₂²×C₅₉	1	2	yes	—
359	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
360	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
361	#518	—	2	1	no	—
362	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
363	#436	—	2	2	no	—
364	#436	—	2	2	no	—
365	#431	C₂²×C₅₉	1	2	yes	complemented
366	#407	C₂²×C₅₉	1	1	yes	characteristic
367	#407	C₂²×C₅₉	1	1	yes	characteristic
368	#407	C₂²×C₅₉	1	2	yes	complemented
369	#388	—	2	1	no	—
370	#387	—	2	1	no	—
371	#386	—	2	1	no	—
372	#383	C₂²×C₅₉	1	1	yes	characteristic, complemented
373	#381	C₂²×C₅₉	1	1	yes	characteristic
374	#380	C₂²×C₅₉	1	1	yes	characteristic, complemented
375	C₄×C₂²⋊C₄	—	2	1	no	—
376	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
377	#376	C₂²×C₅₉	1	1	yes	characteristic, complemented
378	C₂×#95	C₂²×C₅₉	1	1	yes	characteristic, complemented
379	#328	C₂²×C₅₉	1	2	yes	complemented
380	#328	C₂²×C₅₉	1	2	yes	complemented
381	#328	C₂²×C₅₉	1	2	yes	complemented
382	#328	C₂²×C₅₉	1	2	yes	complemented
383	#327	C₂²×C₅₉	1	2	yes	—
384	#327	C₂²×C₅₉	1	2	yes	—
385	#327	C₂²×C₅₉	1	2	yes	—
386	#327	C₂²×C₅₉	1	2	yes	—
387	C₅₉	#17623	1	1	yes	characteristic, direct product factor, Sylow
388	C₂×#41	C₂×C₄×C₅₉	1	2	yes	—
389	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
392	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	2	no	—
399	#126	—	2	2	no	—
400	#126	—	2	2	no	—
401	#126	—	2	2	no	—
402	#125	—	2	2	no	—
403	#125	C₂×C₄×C₅₉	1	2	yes	complemented
404	#124	—	2	2	no	—
405	#124	C₂×C₄×C₅₉	1	2	yes	complemented
406	#123	—	2	2	no	—
407	#123	—	2	2	no	—
408	#123	—	2	2	no	—
409	#123	—	2	2	no	—
410	#123	—	2	2	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
415	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	complemented
416	C₂²⋊Q₈	C₂³×C₅₉	1	2	yes	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#121	—	2	1	no	—
420	#121	—	2	1	no	—
421	#121	—	2	2	no	—
422	#121	C₂×C₄×C₅₉	1	2	yes	—
423	#121	C₂×C₄×C₅₉	1	2	yes	complemented
424	#121	C₂³×C₅₉	1	2	yes	—
425	#120	—	2	2	no	—
426	#120	—	2	2	no	—
427	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	complemented
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
434	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
435	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	complemented
436	C₄×D₄	D₄×C₅₉	1	2	yes	—
437	C₄×D₄	D₄×C₅₉	1	2	yes	—
438	#117	—	2	2	no	—
439	#117	—	2	2	no	—
440	#117	C₂×C₄×C₅₉	1	2	yes	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
444	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	2	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
457	C₄⋊C₈	—	2	2	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	2	2	no	—
461	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
462	C₂²⋊C₈	C₂³×C₅₉	1	2	yes	—
463	C₄×C₈	—	2	2	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	C₂³×C₅₉	1	1	yes	characteristic
470	#95	C₂³×C₅₉	1	1	yes	characteristic
471	#95	C₂³×C₅₉	1	1	yes	characteristic
472	#95	C₂³×C₅₉	1	1	yes	characteristic
473	C₂⁴	—	2	1	no	—
474	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
475	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
476	#41	—	8	2	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	8	1	no	—
479	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	4	2	no	—
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	8	1	no	—
490	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
491	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
492	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	—	8	1	no	—
505	C₂²×C₄	—	8	1	no	—
506	C₂²×C₄	—	8	1	no	—
507	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
508	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
509	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
510	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
518	M₁₆	—	8	1	no	—
519	M₁₆	—	8	1	no	—
520	M₁₆	—	8	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	8	1	no	—
532	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
533	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
534	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
535	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	8	1	no	—
549	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
550	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
551	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
552	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	2	no	—
555	C₄²	—	4	2	no	—
556	C₄²	—	8	1	no	—
557	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
558	C₄²	C₂×D₄×C₅₉	1	2	yes	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	8	1	no	—
570	C₂³	—	8	1	no	—
571	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
572	C₂³	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
573	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
574	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
575	Q₈	—	4	2	no	—
576	Q₈	—	8	1	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	4	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	8	1	no	—
584	D₄	—	8	2	no	—
585	D₄	—	8	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	8	2	no	—
615	C₂×C₄	—	8	2	no	—
616	C₂×C₄	—	8	1	no	—
617	C₂×C₄	—	8	1	no	—
618	C₂×C₄	—	8	4	no	—
619	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
620	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
621	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
622	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
623	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
625	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
626	C₈	—	4	2	no	—
627	C₈	—	4	2	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	16	2	no	—
647	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
648	C₂²	C₅₉×#575	1	1	yes	characteristic
649	C₂²	C₅₉×#575	1	1	yes	characteristic
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	1	no	—
668	C₂	—	4	1	no	—
669	C₂	—	8	2	no	—
670	C₂	C₅₉×#2883	1	1	yes	characteristic
671	C₂	C₅₉×#2896	1	1	yes	characteristic
672	C₂	C₅₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2975	C₂	semidirect
3. C₅₉×#2353	C₂	semidirect
4. C₅₉×#1521	C₂	semidirect
5. C₅₉×#1513	C₂	semidirect
6. C₅₉×#1511	C₂	semidirect
7. C₅₉×#1510	C₂	semidirect
8. C₅₉×#1508	C₂	semidirect
9. C₅₉×#1507	C₂	semidirect
10. C₅₉×#1504	C₂	semidirect
11. C₅₉×#1500	C₂	semidirect
13. C₅₉×#553	C₄	semidirect
14. C₅₉×#552	C₄	semidirect
16. C₅₉×#548	C₄	semidirect
17. C₅₉×#546	C₄	semidirect
29. C₅₉×#431	C₂²	semidirect
32. C₅₉×#407	C₂²	semidirect
36. C₅₉×#383	C₂²	semidirect
38. C₅₉×#380	C₂²	semidirect
41. C₅₉×#376	C₂²	semidirect
42. C₂×#95×C₅₉	C₂²	semidirect
43. C₅₉×#328	C₂²	semidirect
44. C₅₉×#328	C₂²	semidirect
45. C₅₉×#328	C₂²	semidirect
46. C₅₉×#328	C₂²	semidirect
52. C₂²×Q₈×C₅₉	C₂×C₄	semidirect
54. C₂²×D₄×C₅₉	C₂×C₄	semidirect
66. #125×C₅₉	C₂×C₄	semidirect
68. #124×C₅₉	C₂×C₄	semidirect
78. C₂²⋊Q₈×C₅₉	C₂×C₄	semidirect
86. #121×C₅₉	C₂×C₄	semidirect
90. C₄×Q₈×C₅₉	C₂×C₄	semidirect
98. C₄×D₄×C₅₉	C₂×C₄	semidirect
106. C₂×C₄⋊C₄×C₅₉	C₂×C₄	semidirect
107. C₂×C₄⋊C₄×C₅₉	C₂×C₄	semidirect
291. #17623	C₅₉	direct (N × H)
329. #2975	C₂×C₅₉	semidirect
330. #2353	C₂×C₅₉	semidirect
331. #1521	C₂×C₅₉	semidirect
332. #1513	C₂×C₅₉	semidirect
333. #1511	C₂×C₅₉	semidirect
334. #1510	C₂×C₅₉	semidirect
335. #1508	C₂×C₅₉	semidirect
336. #1507	C₂×C₅₉	semidirect
337. #1504	C₂×C₅₉	semidirect
338. #1500	C₂×C₅₉	semidirect
349. #553	C₄×C₅₉	semidirect
350. #552	C₄×C₅₉	semidirect
352. #548	C₄×C₅₉	semidirect
353. #546	C₄×C₅₉	semidirect
365. #431	C₂²×C₅₉	semidirect
368. #407	C₂²×C₅₉	semidirect
372. #383	C₂²×C₅₉	semidirect
374. #380	C₂²×C₅₉	semidirect
377. #376	C₂²×C₅₉	semidirect
378. C₂×#95	C₂²×C₅₉	semidirect
379. #328	C₂²×C₅₉	semidirect
380. #328	C₂²×C₅₉	semidirect
381. #328	C₂²×C₅₉	semidirect
382. #328	C₂²×C₅₉	semidirect
387. C₅₉	#17623	direct (N × H)
389. C₂²×Q₈	C₂×C₄×C₅₉	semidirect
391. C₂²×D₄	C₂×C₄×C₅₉	semidirect
403. #125	C₂×C₄×C₅₉	semidirect
405. #124	C₂×C₄×C₅₉	semidirect
415. C₂²⋊Q₈	C₂×C₄×C₅₉	semidirect
423. #121	C₂×C₄×C₅₉	semidirect
427. C₄×Q₈	C₂×C₄×C₅₉	semidirect
435. C₄×D₄	C₂×C₄×C₅₉	semidirect
443. C₂×C₄⋊C₄	C₂×C₄×C₅₉	semidirect
444. C₂×C₄⋊C₄	C₂×C₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3505	2
C₅₉×#2975	2
C₅₉×#2353	2
C₅₉×#1521	2
C₅₉×#1513	2
C₅₉×#1511	2
C₅₉×#1510	2
C₅₉×#1508	2
C₅₉×#1507	2
C₅₉×#1504	2
C₅₉×#1500	2
#17623	59

Subgroups — C59×#17623 #28429732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17623 #28429732