Subgroups — C₅₉×#24627 #28436736

Order 15104.

938 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2055	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2012	C₂	1	2	yes	maximal
7	C₅₉×#1983	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1928	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₅₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#124×C₅₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×#117×C₅₉	—	2	1	no	—
19	C₅₉×#461	—	2	4	no	—
20	C₄×D₈×C₅₉	—	2	4	no	—
21	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
24	C₂×#103×C₅₉	C₂²	1	2	yes	—
25	C₂×#103×C₅₉	C₂²	1	2	yes	—
26	C₂×#103×C₅₉	C₂²	1	2	yes	—
27	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#102×C₅₉	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#397	—	2	2	no	—
32	C₅₉×#391	C₂²	1	2	yes	—
33	C₅₉×#390	C₂²	1	2	yes	—
34	C₅₉×#388	—	2	2	no	—
35	C₅₉×#384	C₂²	1	1	yes	characteristic
36	C₅₉×#380	—	2	1	no	—
37	C₅₉×#380	—	2	1	no	—
38	C₅₉×#380	—	2	1	no	—
39	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#340	C₂²	1	2	yes	—
42	C₅₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₅₉	—	2	1	no	—
47	C₂³×C₄×C₅₉	—	2	1	no	—
48	C₂×SD₁₆×C₅₉	—	2	4	no	—
49	C₂×SD₁₆×C₅₉	—	4	2	no	—
50	C₂×SD₁₆×C₅₉	—	4	2	no	—
51	C₂×D₈×C₅₉	—	2	2	no	—
52	C₂×D₈×C₅₉	—	2	2	no	—
53	C₂×D₈×C₅₉	—	2	2	no	—
54	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₅₉	—	2	2	no	—
58	C₄⋊Q₈×C₅₉	—	2	2	no	—
59	#124×C₅₉	—	2	4	no	—
60	#124×C₅₉	—	4	2	no	—
61	C₄×D₄×C₅₉	—	2	2	no	—
62	C₄×D₄×C₅₉	—	2	2	no	—
63	C₄×D₄×C₅₉	—	2	2	no	—
64	C₄×D₄×C₅₉	D₄	1	4	yes	—
65	#117×C₅₉	—	4	4	no	—
66	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
81	C₂×C₄²×C₅₉	—	2	2	no	—
82	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
84	#107×C₅₉	—	2	2	no	—
85	C₄⋊C₈×C₅₉	—	2	2	no	—
86	C₄⋊C₈×C₅₉	—	4	2	no	—
87	#103×C₅₉	—	2	4	no	—
88	#103×C₅₉	—	2	4	no	—
89	#103×C₅₉	—	4	2	no	—
90	#102×C₅₉	—	2	2	no	—
91	#102×C₅₉	—	2	2	no	—
92	#102×C₅₉	—	4	2	no	—
93	C₄×C₈×C₅₉	—	2	2	no	—
94	#95×C₅₉	—	2	2	no	—
95	#95×C₅₉	—	2	2	no	—
96	#95×C₅₉	—	2	2	no	—
97	#95×C₅₉	D₄	1	2	yes	—
98	C₂⁴×C₅₉	—	2	1	no	—
99	C₂⁴×C₅₉	—	2	1	no	—
100	C₂×Q₈×C₅₉	—	2	2	no	—
101	C₂×Q₈×C₅₉	—	2	2	no	—
102	C₂×Q₈×C₅₉	—	2	2	no	—
103	C₂×Q₈×C₅₉	—	2	2	no	—
104	C₂×Q₈×C₅₉	—	2	2	no	—
105	C₂×Q₈×C₅₉	—	2	2	no	—
106	C₂×D₄×C₅₉	—	2	1	no	—
107	C₂×D₄×C₅₉	—	2	1	no	—
108	C₂×D₄×C₅₉	—	2	1	no	—
109	C₂×D₄×C₅₉	—	2	1	no	—
110	C₂×D₄×C₅₉	—	2	1	no	—
111	C₂×D₄×C₅₉	—	2	1	no	—
112	C₂×D₄×C₅₉	—	2	1	no	—
113	C₂×D₄×C₅₉	—	2	1	no	—
114	C₂×D₄×C₅₉	—	2	1	no	—
115	C₂×D₄×C₅₉	—	2	1	no	—
116	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₅₉	#41	1	2	yes	—
118	C₂²×C₄×C₅₉	—	2	1	no	—
119	C₂²×C₄×C₅₉	—	2	4	no	—
120	C₂²×C₄×C₅₉	—	2	1	no	—
121	C₂²×C₄×C₅₉	—	2	2	no	—
122	C₂²×C₄×C₅₉	—	2	2	no	—
123	C₂²×C₄×C₅₉	—	4	2	no	—
124	C₂²×C₄×C₅₉	—	4	2	no	—
125	C₂²×C₄×C₅₉	—	4	2	no	—
126	C₂²×C₄×C₅₉	—	4	2	no	—
127	C₂²×C₄×C₅₉	—	4	2	no	—
128	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
133	SD₁₆×C₅₉	—	4	8	no	—
134	D₈×C₅₉	—	2	8	no	—
135	C₂×C₈×C₅₉	—	2	1	no	—
136	C₂×C₈×C₅₉	—	2	1	no	—
137	C₂×C₈×C₅₉	—	2	1	no	—
138	C₂×C₈×C₅₉	—	2	2	no	—
139	C₂×C₈×C₅₉	—	2	2	no	—
140	C₂×C₈×C₅₉	—	2	1	no	—
141	C₂×C₈×C₅₉	—	2	1	no	—
142	C₂×C₈×C₅₉	—	2	2	no	—
143	C₂×C₈×C₅₉	#41	1	2	yes	—
144	C₄⋊C₄×C₅₉	—	2	2	no	—
145	C₄⋊C₄×C₅₉	—	2	2	no	—
146	C₄⋊C₄×C₅₉	—	2	1	no	—
147	C₄⋊C₄×C₅₉	—	2	1	no	—
148	C₄⋊C₄×C₅₉	—	2	2	no	—
149	C₄⋊C₄×C₅₉	—	2	1	no	—
150	C₄⋊C₄×C₅₉	—	2	2	no	—
151	C₄⋊C₄×C₅₉	—	4	2	no	—
152	C₄⋊C₄×C₅₉	—	4	2	no	—
153	C₄⋊C₄×C₅₉	—	4	2	no	—
154	C₄⋊C₄×C₅₉	—	8	1	no	—
155	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₅₉	—	2	4	no	—
157	C₂²⋊C₄×C₅₉	—	4	4	no	—
158	C₂²⋊C₄×C₅₉	—	4	4	no	—
159	C₂²⋊C₄×C₅₉	—	4	4	no	—
160	C₂²⋊C₄×C₅₉	—	4	2	no	—
161	C₂²⋊C₄×C₅₉	—	8	2	no	—
162	C₄²×C₅₉	—	2	2	no	—
163	C₄²×C₅₉	—	2	2	no	—
164	C₄²×C₅₉	—	4	4	no	—
165	C₄²×C₅₉	C₂×D₄	1	2	yes	—
166	C₄²×C₅₉	#41	1	2	yes	—
167	C₂³×C₅₉	—	2	2	no	—
168	C₂³×C₅₉	—	2	2	no	—
169	C₂³×C₅₉	—	4	1	no	—
170	C₂³×C₅₉	—	4	1	no	—
171	C₂³×C₅₉	—	4	1	no	—
172	C₂³×C₅₉	—	4	1	no	—
173	C₂³×C₅₉	—	4	1	no	—
174	C₂³×C₅₉	—	4	1	no	—
175	C₂³×C₅₉	—	4	1	no	—
176	C₂³×C₅₉	—	4	1	no	—
177	C₂³×C₅₉	—	4	1	no	—
178	C₂³×C₅₉	—	4	1	no	—
179	C₂³×C₅₉	—	4	1	no	—
180	C₂³×C₅₉	—	4	1	no	—
181	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₅₉	—	4	2	no	—
183	Q₈×C₅₉	—	4	2	no	—
184	Q₈×C₅₉	—	4	2	no	—
185	Q₈×C₅₉	—	4	2	no	—
186	D₄×C₅₉	—	2	2	no	—
187	D₄×C₅₉	—	2	2	no	—
188	D₄×C₅₉	—	2	2	no	—
189	D₄×C₅₉	—	2	2	no	—
190	D₄×C₅₉	—	4	1	no	—
191	D₄×C₅₉	—	4	1	no	—
192	D₄×C₅₉	—	4	1	no	—
193	D₄×C₅₉	—	4	1	no	—
194	C₂×C₄×C₅₉	—	2	1	no	—
195	C₂×C₄×C₅₉	—	2	1	no	—
196	C₂×C₄×C₅₉	—	2	2	no	—
197	C₂×C₄×C₅₉	—	2	2	no	—
198	C₂×C₄×C₅₉	—	2	2	no	—
199	C₂×C₄×C₅₉	—	2	2	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	—	4	1	no	—
204	C₂×C₄×C₅₉	—	4	1	no	—
205	C₂×C₄×C₅₉	—	4	8	no	—
206	C₂×C₄×C₅₉	—	4	1	no	—
207	C₂×C₄×C₅₉	—	4	2	no	—
208	C₂×C₄×C₅₉	—	4	2	no	—
209	C₂×C₄×C₅₉	—	4	2	no	—
210	C₂×C₄×C₅₉	—	4	2	no	—
211	C₂×C₄×C₅₉	—	4	1	no	—
212	C₂×C₄×C₅₉	—	4	2	no	—
213	C₂×C₄×C₅₉	—	4	1	no	—
214	C₂×C₄×C₅₉	—	4	2	no	—
215	C₂×C₄×C₅₉	—	8	4	no	—
216	C₂×C₄×C₅₉	#121	1	2	yes	—
217	C₂×C₄×C₅₉	#121	1	2	yes	—
218	C₂×C₄×C₅₉	#135	1	2	yes	—
219	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
226	C₈×C₅₉	—	2	2	no	—
227	C₈×C₅₉	—	4	1	no	—
228	C₈×C₅₉	—	4	2	no	—
229	#24627	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂²×C₅₉	—	4	2	no	—
231	C₂²×C₅₉	—	4	2	no	—
232	C₂²×C₅₉	—	4	2	no	—
233	C₂²×C₅₉	—	4	2	no	—
234	C₂²×C₅₉	—	4	2	no	—
235	C₂²×C₅₉	—	4	2	no	—
236	C₂²×C₅₉	—	8	1	no	—
237	C₂²×C₅₉	—	8	1	no	—
238	C₂²×C₅₉	—	8	1	no	—
239	C₂²×C₅₉	—	8	1	no	—
240	C₂²×C₅₉	—	8	1	no	—
241	C₂²×C₅₉	—	8	1	no	—
242	C₂²×C₅₉	—	8	1	no	—
243	C₂²×C₅₉	—	8	1	no	—
244	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
245	C₂²×C₅₉	#546	1	1	yes	characteristic
246	C₂²×C₅₉	#550	1	1	yes	characteristic
247	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
248	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂²×C₅₉	#577	1	1	yes	characteristic
250	C₂²×C₅₉	#578	1	1	yes	characteristic
251	C₄×C₅₉	—	2	2	no	—
252	C₄×C₅₉	—	4	2	no	—
253	C₄×C₅₉	—	4	2	no	—
254	C₄×C₅₉	—	4	2	no	—
255	C₄×C₅₉	—	8	2	no	—
256	C₄×C₅₉	—	8	2	no	—
257	C₄×C₅₉	—	8	1	no	—
258	C₄×C₅₉	#463	1	4	yes	—
259	C₄×C₅₉	#525	1	1	yes	characteristic
260	C₄×C₅₉	#535	1	1	yes	characteristic
261	C₄×C₅₉	#553	1	1	yes	characteristic
262	C₄×C₅₉	#555	1	1	yes	characteristic
263	C₂×#461	C₂×C₅₉	1	1	yes	characteristic, complemented
264	C₂×C₄×D₈	C₂×C₅₉	1	1	yes	characteristic
265	#2547	C₂×C₅₉	1	1	yes	characteristic, complemented
266	#2354	C₂×C₅₉	1	1	yes	characteristic, complemented
267	#2055	C₂×C₅₉	1	2	yes	complemented
268	#2012	C₂×C₅₉	1	2	yes	—
269	#1983	C₂×C₅₉	1	2	yes	complemented
270	#1956	C₂×C₅₉	1	1	yes	characteristic, complemented
271	#1939	C₂×C₅₉	1	1	yes	characteristic, complemented
272	#1928	C₂×C₅₉	1	2	yes	complemented
273	#1802	C₂×C₅₉	1	1	yes	characteristic, complemented
274	C₂×C₅₉	—	8	2	no	—
275	C₂×C₅₉	—	8	2	no	—
276	C₂×C₅₉	#2414	1	1	yes	characteristic
277	C₂×C₅₉	C₂×#463	1	1	yes	characteristic
278	C₂×C₅₉	#3046	1	1	yes	characteristic
279	C₂×C₅₉	#3303	1	1	yes	characteristic
280	C₂×C₅₉	#3330	1	1	yes	characteristic
281	C₂×C₅₉	#3393	1	1	yes	characteristic
282	C₂×C₅₉	#3397	1	1	yes	characteristic
283	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	—
284	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
285	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
286	C₂×#124	C₂²×C₅₉	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
289	C₂×#117	—	2	1	no	—
290	#461	—	2	4	no	—
291	C₄×D₈	—	2	4	no	—
292	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
295	C₂×#103	C₂²×C₅₉	1	2	yes	—
296	C₂×#103	C₂²×C₅₉	1	2	yes	—
297	C₂×#103	C₂²×C₅₉	1	2	yes	—
298	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
299	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
300	C₂×#102	C₂²×C₅₉	1	2	yes	—
301	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
302	#397	—	2	2	no	—
303	#391	C₂²×C₅₉	1	2	yes	—
304	#390	C₂²×C₅₉	1	2	yes	—
305	#388	—	2	2	no	—
306	#384	C₂²×C₅₉	1	1	yes	characteristic
307	#380	—	2	1	no	—
308	#380	—	2	1	no	—
309	#380	—	2	1	no	—
310	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
311	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
312	#340	C₂²×C₅₉	1	2	yes	—
313	#336	C₂²×C₅₉	1	2	yes	—
314	C₅₉	#24627	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
316	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂×SD₁₆	—	2	4	no	—
321	C₂×SD₁₆	—	4	2	no	—
322	C₂×SD₁₆	—	4	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
327	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	#124	—	2	4	no	—
332	#124	—	4	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	D₄×C₅₉	1	4	yes	—
337	#117	—	4	4	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
355	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
356	#107	—	2	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	C₄⋊C₈	—	4	2	no	—
359	#103	—	2	4	no	—
360	#103	—	2	4	no	—
361	#103	—	4	2	no	—
362	#102	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	4	2	no	—
365	C₄×C₈	—	2	2	no	—
366	#95	—	2	2	no	—
367	#95	—	2	2	no	—
368	#95	—	2	2	no	—
369	#95	D₄×C₅₉	1	2	yes	—
370	C₂⁴	—	2	1	no	—
371	C₂⁴	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
389	C₂×D₄	#41×C₅₉	1	2	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
405	SD₁₆	—	4	8	no	—
406	D₈	—	2	8	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	#41×C₅₉	1	2	yes	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	8	1	no	—
427	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	2	no	—
433	C₂²⋊C₄	—	8	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	4	4	no	—
437	C₄²	C₂×D₄×C₅₉	1	2	yes	—
438	C₄²	#41×C₅₉	1	2	yes	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	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	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	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	—	4	2	no	—
487	C₂×C₄	—	8	4	no	—
488	C₂×C₄	#121×C₅₉	1	2	yes	—
489	C₂×C₄	#121×C₅₉	1	2	yes	—
490	C₂×C₄	#135×C₅₉	1	2	yes	—
491	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
494	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
496	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
497	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	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	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	1	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	8	1	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
516	C₂²	C₅₉×#546	1	1	yes	characteristic
517	C₂²	C₅₉×#550	1	1	yes	characteristic
518	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
519	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
520	C₂²	C₅₉×#577	1	1	yes	characteristic
521	C₂²	C₅₉×#578	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	8	1	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	2	no	—
529	C₄	C₅₉×#463	1	4	yes	—
530	C₄	C₅₉×#525	1	1	yes	characteristic
531	C₄	C₅₉×#535	1	1	yes	characteristic
532	C₄	C₅₉×#553	1	1	yes	characteristic
533	C₄	C₅₉×#555	1	1	yes	characteristic
534	C₂	—	8	2	no	—
535	C₂	—	8	2	no	—
536	C₂	C₅₉×#2414	1	1	yes	characteristic
537	C₂	C₂×C₅₉×#463	1	1	yes	characteristic
538	C₂	C₅₉×#3046	1	1	yes	characteristic
539	C₂	C₅₉×#3303	1	1	yes	characteristic
540	C₂	C₅₉×#3330	1	1	yes	characteristic
541	C₂	C₅₉×#3393	1	1	yes	characteristic
542	C₂	C₅₉×#3397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×D₈×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₄×C₄⋊C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#461	C₂	semidirect
3. C₅₉×#2547	C₂	semidirect
4. C₅₉×#2354	C₂	semidirect
5. C₅₉×#2055	C₂	semidirect
7. C₅₉×#1983	C₂	semidirect
8. C₅₉×#1956	C₂	semidirect
9. C₅₉×#1939	C₂	semidirect
10. C₅₉×#1928	C₂	semidirect
11. C₅₉×#1802	C₂	semidirect
229. #24627	C₅₉	direct (N × H)
263. C₂×#461	C₂×C₅₉	semidirect
265. #2547	C₂×C₅₉	semidirect
266. #2354	C₂×C₅₉	semidirect
267. #2055	C₂×C₅₉	semidirect
269. #1983	C₂×C₅₉	semidirect
270. #1956	C₂×C₅₉	semidirect
271. #1939	C₂×C₅₉	semidirect
272. #1928	C₂×C₅₉	semidirect
273. #1802	C₂×C₅₉	semidirect
314. C₅₉	#24627	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#461	2
C₂×C₄×D₈×C₅₉	2
C₅₉×#2547	2
C₅₉×#2354	2
C₅₉×#2055	2
C₅₉×#2012	2
C₅₉×#1983	2
C₅₉×#1956	2
C₅₉×#1939	2
C₅₉×#1928	2
C₅₉×#1802	2
#24627	59

Subgroups — C59×#24627 #28436736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24627 #28436736