Subgroups — C₅₉×#21524 #28433633

Order 15104.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2324	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1936	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1895	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1808	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#107×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1762	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#121×C₅₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
17	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×#466	C₄	1	8	yes	complemented
19	C₄×D₈×C₅₉	—	2	4	no	—
20	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₅₉	C₂²	1	2	yes	—
24	C₂×#102×C₅₉	C₂²	1	2	yes	—
25	C₂×#102×C₅₉	C₂²	1	2	yes	—
26	C₅₉×#405	—	2	4	no	—
27	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#390	—	2	2	no	—
32	C₅₉×#390	C₂²	1	2	yes	—
33	C₅₉×#389	C₂²	1	2	yes	—
34	C₅₉×#388	—	2	2	no	—
35	C₅₉×#386	—	2	2	no	—
36	C₅₉×#385	—	2	2	no	—
37	C₅₉×#380	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
39	C₅₉×#340	C₂²	1	2	yes	—
40	C₅₉×#340	C₂²	1	2	yes	—
41	C₅₉×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₅₉	—	2	2	no	—
43	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₅₉	—	2	2	no	—
45	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₅₉	—	2	2	no	—
47	C₂×D₈×C₅₉	—	2	2	no	—
48	C₂×D₈×C₅₉	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₅₉	—	2	2	no	—
50	C₂×M₁₆×C₅₉	—	2	2	no	—
51	C₂×M₁₆×C₅₉	—	2	2	no	—
52	C₂²×C₈×C₅₉	—	2	2	no	—
53	C₂²×C₈×C₅₉	—	2	2	no	—
54	C₂²×C₈×C₅₉	C₂×C₄	1	4	yes	complemented
55	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
59	#121×C₅₉	—	2	4	no	—
60	#121×C₅₉	C₂×C₄	1	8	yes	complemented
61	C₄×D₄×C₅₉	—	2	4	no	—
62	C₄×D₄×C₅₉	—	2	4	no	—
63	#117×C₅₉	—	2	2	no	—
64	#117×C₅₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₅₉	—	2	2	no	—
79	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
81	#107×C₅₉	—	2	2	no	—
82	#107×C₅₉	—	2	2	no	—
83	#107×C₅₉	C₂×C₄	1	4	yes	complemented
84	#102×C₅₉	—	2	4	no	—
85	#102×C₅₉	—	2	4	no	—
86	#102×C₅₉	C₂×C₄	1	8	yes	complemented
87	#97×C₅₉	—	2	2	no	—
88	#97×C₅₉	—	2	2	no	—
89	C₄×C₈×C₅₉	—	2	2	no	—
90	C₄×C₈×C₅₉	D₄	1	4	yes	complemented
91	#95×C₅₉	—	2	2	no	—
92	#95×C₅₉	—	2	2	no	—
93	#95×C₅₉	—	2	2	no	—
94	C₂⁴×C₅₉	—	2	2	no	—
95	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₅₉	—	2	8	no	—
97	C₂×D₄×C₅₉	—	2	2	no	—
98	C₂×D₄×C₅₉	—	2	2	no	—
99	C₂×D₄×C₅₉	—	2	2	no	—
100	C₂×D₄×C₅₉	—	2	2	no	—
101	C₂×D₄×C₅₉	—	2	2	no	—
102	C₂×D₄×C₅₉	—	8	2	no	—
103	C₂×D₄×C₅₉	—	8	2	no	—
104	C₂×D₄×C₅₉	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₅₉	—	2	1	no	—
106	C₂²×C₄×C₅₉	—	2	1	no	—
107	C₂²×C₄×C₅₉	—	2	1	no	—
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	—	2	2	no	—
111	C₂²×C₄×C₅₉	—	2	2	no	—
112	C₂²×C₄×C₅₉	—	4	4	no	—
113	C₂²×C₄×C₅₉	—	8	2	no	—
114	C₂²×C₄×C₅₉	—	8	2	no	—
115	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	#41	1	2	yes	—
122	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
123	D₈×C₅₉	—	2	8	no	—
124	M₁₆×C₅₉	—	2	8	no	—
125	C₂×C₈×C₅₉	—	2	1	no	—
126	C₂×C₈×C₅₉	—	2	1	no	—
127	C₂×C₈×C₅₉	—	2	1	no	—
128	C₂×C₈×C₅₉	—	2	1	no	—
129	C₂×C₈×C₅₉	—	2	1	no	—
130	C₂×C₈×C₅₉	—	2	1	no	—
131	C₂×C₈×C₅₉	—	2	8	no	—
132	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₅₉	#41	1	2	yes	—
137	C₂×C₈×C₅₉	#41	1	2	yes	—
138	C₄⋊C₄×C₅₉	—	2	2	no	—
139	C₄⋊C₄×C₅₉	—	2	2	no	—
140	C₄⋊C₄×C₅₉	—	2	2	no	—
141	C₄⋊C₄×C₅₉	—	2	2	no	—
142	C₄⋊C₄×C₅₉	—	2	2	no	—
143	C₄⋊C₄×C₅₉	—	2	2	no	—
144	C₄⋊C₄×C₅₉	—	2	2	no	—
145	C₄⋊C₄×C₅₉	—	8	2	no	—
146	C₄⋊C₄×C₅₉	C₂²×C₄	1	4	yes	—
147	C₂²⋊C₄×C₅₉	—	2	8	no	—
148	C₂²⋊C₄×C₅₉	—	2	2	no	—
149	C₂²⋊C₄×C₅₉	—	2	2	no	—
150	C₂²⋊C₄×C₅₉	—	4	4	no	—
151	C₂²⋊C₄×C₅₉	—	8	2	no	—
152	C₂²⋊C₄×C₅₉	—	8	2	no	—
153	C₂²⋊C₄×C₅₉	—	8	2	no	—
154	C₄²×C₅₉	—	2	1	no	—
155	C₄²×C₅₉	—	2	1	no	—
156	C₄²×C₅₉	—	8	2	no	—
157	C₄²×C₅₉	C₂×D₄	1	2	yes	—
158	C₄²×C₅₉	#41	1	2	yes	—
159	C₂³×C₅₉	—	2	1	no	—
160	C₂³×C₅₉	—	2	1	no	—
161	C₂³×C₅₉	—	2	1	no	—
162	C₂³×C₅₉	—	2	1	no	—
163	C₂³×C₅₉	—	2	1	no	—
164	C₂³×C₅₉	—	2	1	no	—
165	C₂³×C₅₉	—	2	4	no	—
166	C₂³×C₅₉	—	4	2	no	—
167	C₂³×C₅₉	—	4	2	no	—
168	C₂³×C₅₉	—	4	2	no	—
169	C₂³×C₅₉	—	4	2	no	—
170	C₂³×C₅₉	—	4	2	no	—
171	C₂³×C₅₉	—	4	2	no	—
172	C₂³×C₅₉	C₄×D₄	1	2	yes	—
173	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
174	D₄×C₅₉	—	2	4	no	—
175	D₄×C₅₉	—	2	4	no	—
176	D₄×C₅₉	—	4	2	no	—
177	D₄×C₅₉	—	4	2	no	—
178	D₄×C₅₉	—	8	8	no	—
179	C₂×C₄×C₅₉	—	2	1	no	—
180	C₂×C₄×C₅₉	—	2	1	no	—
181	C₂×C₄×C₅₉	—	2	1	no	—
182	C₂×C₄×C₅₉	—	2	1	no	—
183	C₂×C₄×C₅₉	—	2	1	no	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	2	2	no	—
187	C₂×C₄×C₅₉	—	2	2	no	—
188	C₂×C₄×C₅₉	—	2	2	no	—
189	C₂×C₄×C₅₉	—	2	4	no	—
190	C₂×C₄×C₅₉	—	2	1	no	—
191	C₂×C₄×C₅₉	—	2	1	no	—
192	C₂×C₄×C₅₉	—	2	1	no	—
193	C₂×C₄×C₅₉	—	2	1	no	—
194	C₂×C₄×C₅₉	—	2	1	no	—
195	C₂×C₄×C₅₉	—	2	1	no	—
196	C₂×C₄×C₅₉	—	4	2	no	—
197	C₂×C₄×C₅₉	—	4	2	no	—
198	C₂×C₄×C₅₉	—	4	2	no	—
199	C₂×C₄×C₅₉	—	4	2	no	—
200	C₂×C₄×C₅₉	—	4	2	no	—
201	C₂×C₄×C₅₉	—	4	2	no	—
202	C₂×C₄×C₅₉	—	4	2	no	—
203	C₂×C₄×C₅₉	—	4	2	no	—
204	C₂×C₄×C₅₉	—	8	8	no	—
205	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₅₉	#121	1	2	yes	—
207	C₂×C₄×C₅₉	#121	1	2	yes	—
208	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
214	C₈×C₅₉	—	2	2	no	—
215	C₈×C₅₉	—	2	2	no	—
216	C₈×C₅₉	—	2	2	no	—
217	C₈×C₅₉	C₄×D₄	1	4	yes	—
218	#21524	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₅₉	—	2	2	no	—
220	C₂²×C₅₉	—	2	2	no	—
221	C₂²×C₅₉	—	2	2	no	—
222	C₂²×C₅₉	—	4	1	no	—
223	C₂²×C₅₉	—	4	1	no	—
224	C₂²×C₅₉	—	4	1	no	—
225	C₂²×C₅₉	—	4	1	no	—
226	C₂²×C₅₉	—	4	4	no	—
227	C₂²×C₅₉	—	4	4	no	—
228	C₂²×C₅₉	—	4	4	no	—
229	C₂²×C₅₉	—	8	2	no	—
230	C₂²×C₅₉	—	8	2	no	—
231	C₂²×C₅₉	—	8	2	no	—
232	C₂²×C₅₉	—	8	2	no	—
233	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
235	C₂²×C₅₉	#532	1	1	yes	characteristic
236	C₂²×C₅₉	#576	1	1	yes	characteristic
237	C₂²×C₅₉	#576	1	1	yes	characteristic
238	C₂²×C₅₉	#576	1	1	yes	characteristic
239	C₂²×C₅₉	#578	1	1	yes	characteristic
240	C₄×C₅₉	—	2	2	no	—
241	C₄×C₅₉	—	2	2	no	—
242	C₄×C₅₉	—	2	2	no	—
243	C₄×C₅₉	—	4	4	no	—
244	C₄×C₅₉	—	4	1	no	—
245	C₄×C₅₉	—	4	1	no	—
246	C₄×C₅₉	—	8	2	no	—
247	C₄×C₅₉	—	8	2	no	—
248	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
249	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
250	C₄×C₅₉	#525	1	1	yes	characteristic
251	C₄×C₅₉	#529	1	1	yes	characteristic
252	C₂×#466	C₂×C₅₉	1	1	yes	characteristic
253	C₂×C₄×D₈	C₂×C₅₉	1	1	yes	characteristic, complemented
254	C₂×#405	C₂×C₅₉	1	1	yes	characteristic, complemented
255	#2324	C₂×C₅₉	1	2	yes	complemented
256	#1970	C₂×C₅₉	1	1	yes	characteristic, complemented
257	#1942	C₂×C₅₉	1	1	yes	characteristic, complemented
258	#1936	C₂×C₅₉	1	2	yes	complemented
259	#1895	C₂×C₅₉	1	2	yes	complemented
260	#1808	C₂×C₅₉	1	1	yes	characteristic, complemented
261	C₄×#107	C₂×C₅₉	1	1	yes	characteristic, complemented
262	#1762	C₂×C₅₉	1	2	yes	complemented
263	C₂×C₅₉	—	4	2	no	—
264	C₂×C₅₉	—	8	4	no	—
265	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
266	C₂×C₅₉	#2948	1	1	yes	characteristic
267	C₂×C₅₉	#2951	1	1	yes	characteristic
268	C₂×C₅₉	#3058	1	1	yes	characteristic
269	C₂×C₅₉	#3061	1	1	yes	characteristic
270	C₂×C₅₉	#3175	1	1	yes	characteristic
271	C₂×C₅₉	#3176	1	1	yes	characteristic
272	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
273	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
274	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
275	C₂×#121	C₂²×C₅₉	1	2	yes	—
276	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
277	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
278	#466	C₄×C₅₉	1	8	yes	complemented
279	C₄×D₈	—	2	4	no	—
280	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
281	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
282	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
283	C₂×#102	C₂²×C₅₉	1	2	yes	—
284	C₂×#102	C₂²×C₅₉	1	2	yes	—
285	C₂×#102	C₂²×C₅₉	1	2	yes	—
286	#405	—	2	4	no	—
287	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
288	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
291	#390	—	2	2	no	—
292	#390	C₂²×C₅₉	1	2	yes	—
293	#389	C₂²×C₅₉	1	2	yes	—
294	#388	—	2	2	no	—
295	#386	—	2	2	no	—
296	#385	—	2	2	no	—
297	#380	C₂²×C₅₉	1	2	yes	—
298	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
299	#340	C₂²×C₅₉	1	2	yes	—
300	#340	C₂²×C₅₉	1	2	yes	—
301	#340	C₂²×C₅₉	1	2	yes	—
302	C₅₉	#21524	1	1	yes	characteristic, direct product factor, Sylow
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
307	C₂×D₈	—	2	2	no	—
308	C₂×D₈	—	2	2	no	—
309	C₂×D₈	C₂×C₄×C₅₉	1	4	yes	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	C₂×C₄×C₅₉	1	4	yes	complemented
316	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
320	#121	—	2	4	no	—
321	#121	C₂×C₄×C₅₉	1	8	yes	complemented
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	4	no	—
324	#117	—	2	2	no	—
325	#117	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
342	#107	—	2	2	no	—
343	#107	—	2	2	no	—
344	#107	C₂×C₄×C₅₉	1	4	yes	complemented
345	#102	—	2	4	no	—
346	#102	—	2	4	no	—
347	#102	C₂×C₄×C₅₉	1	8	yes	complemented
348	#97	—	2	2	no	—
349	#97	—	2	2	no	—
350	C₄×C₈	—	2	2	no	—
351	C₄×C₈	D₄×C₅₉	1	4	yes	complemented
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	C₂²×C₄×C₅₉	1	4	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
382	C₂²×C₄	#41×C₅₉	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
384	D₈	—	2	8	no	—
385	M₁₆	—	2	8	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	8	no	—
393	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
394	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
397	C₂×C₈	#41×C₅₉	1	2	yes	—
398	C₂×C₈	#41×C₅₉	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	8	2	no	—
407	C₄⋊C₄	C₂²×C₄×C₅₉	1	4	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	8	2	no	—
413	C₂²⋊C₄	—	8	2	no	—
414	C₂²⋊C₄	—	8	2	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	8	2	no	—
418	C₄²	C₂×D₄×C₅₉	1	2	yes	—
419	C₄²	#41×C₅₉	1	2	yes	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₄×D₄×C₅₉	1	2	yes	—
434	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
435	D₄	—	2	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	8	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	8	no	—
466	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
467	C₂×C₄	#121×C₅₉	1	2	yes	—
468	C₂×C₄	#121×C₅₉	1	2	yes	—
469	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	C₄×D₄×C₅₉	1	4	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
494	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
495	C₂²	C₅₉×#532	1	1	yes	characteristic
496	C₂²	C₅₉×#576	1	1	yes	characteristic
497	C₂²	C₅₉×#576	1	1	yes	characteristic
498	C₂²	C₅₉×#576	1	1	yes	characteristic
499	C₂²	C₅₉×#578	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	4	no	—
506	C₄	—	8	2	no	—
507	C₄	—	8	2	no	—
508	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
509	C₄	C₄×#41×C₅₉	1	1	yes	characteristic
510	C₄	C₅₉×#525	1	1	yes	characteristic
511	C₄	C₅₉×#529	1	1	yes	characteristic
512	C₂	—	4	2	no	—
513	C₂	—	8	4	no	—
514	C₂	C₄×#121×C₅₉	1	1	yes	characteristic
515	C₂	C₅₉×#2948	1	1	yes	characteristic
516	C₂	C₅₉×#2951	1	1	yes	characteristic
517	C₂	C₅₉×#3058	1	1	yes	characteristic
518	C₂	C₅₉×#3061	1	1	yes	characteristic
519	C₂	C₅₉×#3175	1	1	yes	characteristic
520	C₂	C₅₉×#3176	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×C₅₉×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×#117×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₅₉	C₂	semidirect
3. C₂×C₅₉×#405	C₂	semidirect
4. C₅₉×#2324	C₂	semidirect
5. C₅₉×#1970	C₂	semidirect
6. C₅₉×#1942	C₂	semidirect
7. C₅₉×#1936	C₂	semidirect
8. C₅₉×#1895	C₂	semidirect
9. C₅₉×#1808	C₂	semidirect
10. C₄×#107×C₅₉	C₂	semidirect
11. C₅₉×#1762	C₂	semidirect
18. C₅₉×#466	C₄	semidirect
54. C₂²×C₈×C₅₉	C₂×C₄	semidirect
60. #121×C₅₉	C₂×C₄	semidirect
83. #107×C₅₉	C₂×C₄	semidirect
86. #102×C₅₉	C₂×C₄	semidirect
90. C₄×C₈×C₅₉	D₄	semidirect
218. #21524	C₅₉	direct (N × H)
253. C₂×C₄×D₈	C₂×C₅₉	semidirect
254. C₂×#405	C₂×C₅₉	semidirect
255. #2324	C₂×C₅₉	semidirect
256. #1970	C₂×C₅₉	semidirect
257. #1942	C₂×C₅₉	semidirect
258. #1936	C₂×C₅₉	semidirect
259. #1895	C₂×C₅₉	semidirect
260. #1808	C₂×C₅₉	semidirect
261. C₄×#107	C₂×C₅₉	semidirect
262. #1762	C₂×C₅₉	semidirect
278. #466	C₄×C₅₉	semidirect
302. C₅₉	#21524	direct (N × H)
315. C₂²×C₈	C₂×C₄×C₅₉	semidirect
321. #121	C₂×C₄×C₅₉	semidirect
344. #107	C₂×C₄×C₅₉	semidirect
347. #102	C₂×C₄×C₅₉	semidirect
351. C₄×C₈	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#466	2
C₂×C₄×D₈×C₅₉	2
C₂×C₅₉×#405	2
C₅₉×#2324	2
C₅₉×#1970	2
C₅₉×#1942	2
C₅₉×#1936	2
C₅₉×#1895	2
C₅₉×#1808	2
C₄×#107×C₅₉	2
C₅₉×#1762	2
#21524	59

Subgroups — C59×#21524 #28433633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21524 #28433633