Subgroups — C₅₉×#18585 #28430694

Order 15104.

938 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1638	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1635	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1628	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1625	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#556	C₂²	1	2	yes	—
13	C₅₉×#555	—	2	1	no	—
14	C₅₉×#554	—	2	1	no	—
15	C₅₉×#553	—	2	2	no	—
16	C₅₉×#548	—	2	2	no	—
17	C₅₉×#547	C₂²	1	2	yes	—
18	C₅₉×#542	—	2	2	no	—
19	C₅₉×#537	—	2	1	no	—
20	C₅₉×#533	—	2	1	no	—
21	C₅₉×#532	—	2	1	no	—
22	C₅₉×#532	C₂²	1	1	yes	characteristic
23	C₅₉×#532	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#520	—	2	1	no	—
26	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#489	—	2	2	no	—
28	C₅₉×#487	C₂²	1	2	yes	—
29	C₅₉×#486	C₂²	1	2	yes	—
30	C₅₉×#482	—	2	1	no	—
31	C₅₉×#477	C₂²	1	1	yes	characteristic
32	C₅₉×#476	—	2	1	no	—
33	C₅₉×#476	C₂²	1	2	yes	—
34	C₅₉×#476	C₂²	1	1	yes	characteristic
35	C₅₉×#469	—	2	2	no	—
36	C₅₉×#460	C₂²	1	1	yes	characteristic
37	C₅₉×#459	—	2	1	no	—
38	C₅₉×#459	C₂²	1	2	yes	—
39	C₅₉×#459	C₂²	1	1	yes	characteristic
40	C₅₉×#449	—	2	1	no	—
41	C₄×SD₁₆×C₅₉	—	2	1	no	—
42	C₄×D₈×C₅₉	—	2	1	no	—
43	C₅₉×#431	C₂²	1	1	yes	characteristic
44	C₅₉×#423	C₂²	1	1	yes	characteristic
45	C₅₉×#417	—	2	2	no	—
46	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
47	C₅₉×#332	C₂²	1	2	yes	—
48	C₅₉×#332	C₂²	1	2	yes	—
49	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
51	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
52	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₅₉	—	2	2	no	—
54	C₂×#41×C₅₉	—	2	1	no	—
55	C₂×#41×C₅₉	—	2	1	no	—
56	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₅₉	—	2	1	no	—
58	C₂×SD₁₆×C₅₉	—	2	1	no	—
59	C₂×D₈×C₅₉	—	2	1	no	—
60	C₂×D₈×C₅₉	—	2	2	no	—
61	C₂×M₁₆×C₅₉	—	2	1	no	—
62	C₂×M₁₆×C₅₉	—	2	1	no	—
63	C₄⋊Q₈×C₅₉	—	2	1	no	—
64	C₄⋊Q₈×C₅₉	—	2	1	no	—
65	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
67	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
69	#127×C₅₉	D₄	1	1	yes	characteristic
70	#127×C₅₉	C₂³	1	1	yes	characteristic
71	#126×C₅₉	—	2	4	no	—
72	#125×C₅₉	—	2	2	no	—
73	#124×C₅₉	—	2	4	no	—
74	#124×C₅₉	—	2	2	no	—
75	#124×C₅₉	—	2	1	no	—
76	#124×C₅₉	—	2	1	no	—
77	#123×C₅₉	—	2	4	no	—
78	C₂²⋊Q₈×C₅₉	—	2	2	no	—
79	C₂²⋊Q₈×C₅₉	—	2	4	no	—
80	C₂²⋊Q₈×C₅₉	—	2	2	no	—
81	C₂²⋊Q₈×C₅₉	—	2	2	no	—
82	#121×C₅₉	—	2	2	no	—
83	#121×C₅₉	—	2	2	no	—
84	#121×C₅₉	—	2	4	no	—
85	#121×C₅₉	—	2	2	no	—
86	#121×C₅₉	—	2	1	no	—
87	#121×C₅₉	—	2	1	no	—
88	#121×C₅₉	—	2	1	no	—
89	#121×C₅₉	D₄	1	2	yes	—
90	C₄×Q₈×C₅₉	—	2	2	no	—
91	C₄×Q₈×C₅₉	—	2	2	no	—
92	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₅₉	—	2	2	no	—
95	C₄×D₄×C₅₉	—	2	4	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	—	2	1	no	—
102	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
103	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₅₉	C₂³	1	2	yes	—
105	#117×C₅₉	—	2	2	no	—
106	#117×C₅₉	—	2	2	no	—
107	#117×C₅₉	—	2	1	no	—
108	#117×C₅₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
111	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
112	C₂×C₄²×C₅₉	—	2	1	no	—
113	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
114	#107×C₅₉	—	2	1	no	—
115	#106×C₅₉	—	2	1	no	—
116	#106×C₅₉	—	2	2	no	—
117	C₄⋊C₈×C₅₉	—	2	1	no	—
118	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
119	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
121	#103×C₅₉	—	2	1	no	—
122	#103×C₅₉	—	2	4	no	—
123	#102×C₅₉	—	2	1	no	—
124	#102×C₅₉	—	2	2	no	—
125	#102×C₅₉	—	2	4	no	—
126	#102×C₅₉	—	2	1	no	—
127	#102×C₅₉	—	2	1	no	—
128	#102×C₅₉	—	2	2	no	—
129	C₂²⋊C₈×C₅₉	—	2	1	no	—
130	#97×C₅₉	—	2	1	no	—
131	C₄×C₈×C₅₉	—	2	1	no	—
132	C₄×C₈×C₅₉	C₂³	1	2	yes	—
133	#41×C₅₉	—	4	1	no	—
134	#41×C₅₉	—	4	1	no	—
135	#41×C₅₉	—	4	2	no	—
136	#41×C₅₉	—	4	2	no	—
137	#41×C₅₉	—	4	4	no	—
138	#41×C₅₉	—	8	2	no	—
139	#41×C₅₉	—	8	2	no	—
140	C₂×Q₈×C₅₉	—	2	1	no	—
141	C₂×Q₈×C₅₉	—	2	2	no	—
142	C₂×Q₈×C₅₉	—	2	2	no	—
143	C₂×Q₈×C₅₉	—	2	1	no	—
144	C₂×Q₈×C₅₉	—	8	1	no	—
145	C₂×Q₈×C₅₉	—	8	1	no	—
146	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₅₉	—	2	1	no	—
148	C₂×D₄×C₅₉	—	2	2	no	—
149	C₂×D₄×C₅₉	—	2	4	no	—
150	C₂×D₄×C₅₉	—	2	1	no	—
151	C₂×D₄×C₅₉	—	2	1	no	—
152	C₂×D₄×C₅₉	—	2	1	no	—
153	C₂×D₄×C₅₉	—	2	1	no	—
154	C₂×D₄×C₅₉	—	2	1	no	—
155	C₂×D₄×C₅₉	—	4	1	no	—
156	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₅₉	—	2	4	no	—
159	C₂²×C₄×C₅₉	—	2	2	no	—
160	C₂²×C₄×C₅₉	—	2	1	no	—
161	C₂²×C₄×C₅₉	—	2	1	no	—
162	C₂²×C₄×C₅₉	—	2	1	no	—
163	C₂²×C₄×C₅₉	—	2	2	no	—
164	C₂²×C₄×C₅₉	—	4	1	no	—
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	SD₁₆×C₅₉	—	4	2	no	—
169	D₈×C₅₉	—	4	2	no	—
170	D₈×C₅₉	—	8	2	no	—
171	M₁₆×C₅₉	—	4	2	no	—
172	M₁₆×C₅₉	—	8	1	no	—
173	C₂×C₈×C₅₉	—	2	1	no	—
174	C₂×C₈×C₅₉	—	2	1	no	—
175	C₂×C₈×C₅₉	—	2	2	no	—
176	C₂×C₈×C₅₉	—	2	2	no	—
177	C₄⋊C₄×C₅₉	—	2	4	no	—
178	C₄⋊C₄×C₅₉	—	2	4	no	—
179	C₄⋊C₄×C₅₉	—	2	2	no	—
180	C₄⋊C₄×C₅₉	—	2	2	no	—
181	C₄⋊C₄×C₅₉	—	2	1	no	—
182	C₄⋊C₄×C₅₉	—	2	1	no	—
183	C₄⋊C₄×C₅₉	—	2	2	no	—
184	C₄⋊C₄×C₅₉	—	2	1	no	—
185	C₄⋊C₄×C₅₉	—	2	1	no	—
186	C₄⋊C₄×C₅₉	—	2	1	no	—
187	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
188	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
191	C₂²⋊C₄×C₅₉	—	2	4	no	—
192	C₂²⋊C₄×C₅₉	—	2	4	no	—
193	C₂²⋊C₄×C₅₉	—	2	4	no	—
194	C₂²⋊C₄×C₅₉	—	2	1	no	—
195	C₂²⋊C₄×C₅₉	—	2	1	no	—
196	C₂²⋊C₄×C₅₉	—	2	2	no	—
197	C₂²⋊C₄×C₅₉	—	2	1	no	—
198	C₂²⋊C₄×C₅₉	—	2	2	no	—
199	C₂²⋊C₄×C₅₉	—	4	1	no	—
200	C₂²⋊C₄×C₅₉	—	4	1	no	—
201	C₄²×C₅₉	—	2	4	no	—
202	C₄²×C₅₉	—	2	1	no	—
203	C₄²×C₅₉	—	2	1	no	—
204	C₄²×C₅₉	—	2	1	no	—
205	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
209	C₂³×C₅₉	—	2	1	no	—
210	C₂³×C₅₉	—	2	2	no	—
211	C₂³×C₅₉	—	4	1	no	—
212	C₂³×C₅₉	#120	1	1	yes	characteristic
213	Q₈×C₅₉	—	2	1	no	—
214	Q₈×C₅₉	—	2	1	no	—
215	Q₈×C₅₉	—	4	2	no	—
216	Q₈×C₅₉	—	4	2	no	—
217	Q₈×C₅₉	—	4	2	no	—
218	Q₈×C₅₉	—	4	2	no	—
219	Q₈×C₅₉	—	8	2	no	—
220	D₄×C₅₉	—	2	1	no	—
221	D₄×C₅₉	—	2	1	no	—
222	D₄×C₅₉	—	2	2	no	—
223	D₄×C₅₉	—	2	2	no	—
224	D₄×C₅₉	—	4	2	no	—
225	D₄×C₅₉	—	4	2	no	—
226	D₄×C₅₉	—	4	2	no	—
227	D₄×C₅₉	—	4	4	no	—
228	D₄×C₅₉	—	4	1	no	—
229	D₄×C₅₉	—	4	1	no	—
230	D₄×C₅₉	—	4	1	no	—
231	D₄×C₅₉	—	4	1	no	—
232	D₄×C₅₉	—	4	2	no	—
233	D₄×C₅₉	—	8	4	no	—
234	D₄×C₅₉	—	8	2	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	1	no	—
238	C₂×C₄×C₅₉	—	2	1	no	—
239	C₂×C₄×C₅₉	—	2	2	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	1	no	—
244	C₂×C₄×C₅₉	—	2	4	no	—
245	C₂×C₄×C₅₉	—	4	2	no	—
246	C₂×C₄×C₅₉	—	4	2	no	—
247	C₂×C₄×C₅₉	—	4	2	no	—
248	C₂×C₄×C₅₉	—	4	1	no	—
249	C₂×C₄×C₅₉	—	4	1	no	—
250	C₂×C₄×C₅₉	—	4	2	no	—
251	C₂×C₄×C₅₉	—	4	1	no	—
252	C₂×C₄×C₅₉	—	8	2	no	—
253	C₂×C₄×C₅₉	—	8	4	no	—
254	C₂×C₄×C₅₉	—	8	2	no	—
255	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
256	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
261	C₈×C₅₉	—	4	2	no	—
262	C₈×C₅₉	—	4	1	no	—
263	C₈×C₅₉	—	4	1	no	—
264	C₈×C₅₉	—	4	2	no	—
265	#18585	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₅₉	—	2	1	no	—
267	C₂²×C₅₉	—	2	1	no	—
268	C₂²×C₅₉	—	2	1	no	—
269	C₂²×C₅₉	—	4	1	no	—
270	C₂²×C₅₉	—	4	2	no	—
271	C₂²×C₅₉	—	4	1	no	—
272	C₂²×C₅₉	—	4	2	no	—
273	C₂²×C₅₉	—	4	1	no	—
274	C₂²×C₅₉	—	4	2	no	—
275	C₂²×C₅₉	—	8	1	no	—
276	C₂²×C₅₉	—	8	1	no	—
277	C₂²×C₅₉	—	8	1	no	—
278	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
279	C₄×C₅₉	—	2	1	no	—
280	C₄×C₅₉	—	2	1	no	—
281	C₄×C₅₉	—	2	1	no	—
282	C₄×C₅₉	—	4	1	no	—
283	C₄×C₅₉	—	4	2	no	—
284	C₄×C₅₉	—	4	1	no	—
285	C₄×C₅₉	—	4	4	no	—
286	C₄×C₅₉	—	4	1	no	—
287	C₄×C₅₉	—	8	1	no	—
288	C₄×C₅₉	#454	1	2	yes	—
289	C₄×C₅₉	#575	1	1	yes	characteristic
290	C₄×C₅₉	#575	1	1	yes	characteristic
291	C₄×C₅₉	#576	1	1	yes	characteristic
292	C₄×C₅₉	#577	1	1	yes	characteristic
293	#3511	C₂×C₅₉	1	1	yes	characteristic, complemented
294	#3253	C₂×C₅₉	1	1	yes	characteristic, complemented
295	#3141	C₂×C₅₉	1	1	yes	characteristic, complemented
296	#3106	C₂×C₅₉	1	1	yes	characteristic, complemented
297	#1638	C₂×C₅₉	1	2	yes	complemented
298	#1635	C₂×C₅₉	1	2	yes	complemented
299	#1628	C₂×C₅₉	1	2	yes	complemented
300	#1625	C₂×C₅₉	1	2	yes	complemented
301	#1546	C₂×C₅₉	1	1	yes	characteristic, complemented
302	#1489	C₂×C₅₉	1	1	yes	characteristic, complemented
303	#1484	C₂×C₅₉	1	1	yes	characteristic, complemented
304	C₂×C₅₉	—	4	1	no	—
305	C₂×C₅₉	—	8	1	no	—
306	C₂×C₅₉	—	8	2	no	—
307	C₂×C₅₉	—	16	1	no	—
308	C₂×C₅₉	#3005	1	1	yes	characteristic
309	C₂×C₅₉	#3012	1	1	yes	characteristic
310	C₂×C₅₉	C₂×#454	1	1	yes	characteristic
311	#556	C₂²×C₅₉	1	2	yes	—
312	#555	—	2	1	no	—
313	#554	—	2	1	no	—
314	#553	—	2	2	no	—
315	#548	—	2	2	no	—
316	#547	C₂²×C₅₉	1	2	yes	—
317	#542	—	2	2	no	—
318	#537	—	2	1	no	—
319	#533	—	2	1	no	—
320	#532	—	2	1	no	—
321	#532	C₂²×C₅₉	1	1	yes	characteristic
322	#532	C₂²×C₅₉	1	1	yes	characteristic
323	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
324	#520	—	2	1	no	—
325	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
326	#489	—	2	2	no	—
327	#487	C₂²×C₅₉	1	2	yes	—
328	#486	C₂²×C₅₉	1	2	yes	—
329	#482	—	2	1	no	—
330	#477	C₂²×C₅₉	1	1	yes	characteristic
331	#476	—	2	1	no	—
332	#476	C₂²×C₅₉	1	1	yes	characteristic
333	#476	C₂²×C₅₉	1	2	yes	—
334	#469	—	2	2	no	—
335	#460	C₂²×C₅₉	1	1	yes	characteristic
336	#459	—	2	1	no	—
337	#459	C₂²×C₅₉	1	1	yes	characteristic
338	#459	C₂²×C₅₉	1	2	yes	—
339	#449	—	2	1	no	—
340	C₄×SD₁₆	—	2	1	no	—
341	C₄×D₈	—	2	1	no	—
342	#431	C₂²×C₅₉	1	1	yes	characteristic
343	#423	C₂²×C₅₉	1	1	yes	characteristic
344	#417	—	2	2	no	—
345	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
346	#332	C₂²×C₅₉	1	2	yes	—
347	#332	C₂²×C₅₉	1	2	yes	—
348	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	—
349	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
350	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
351	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
352	C₅₉	#18585	1	1	yes	characteristic, direct product factor, Sylow
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
357	C₂²×Q₈	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×D₈	—	2	1	no	—
360	C₂×D₈	—	2	2	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
366	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
369	#127	D₄×C₅₉	1	1	yes	characteristic
370	#127	C₂³×C₅₉	1	1	yes	characteristic
371	#126	—	2	4	no	—
372	#125	—	2	2	no	—
373	#124	—	2	4	no	—
374	#124	—	2	2	no	—
375	#124	—	2	1	no	—
376	#124	—	2	1	no	—
377	#123	—	2	4	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	#121	—	2	2	no	—
383	#121	—	2	2	no	—
384	#121	—	2	4	no	—
385	#121	—	2	2	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	D₄×C₅₉	1	2	yes	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	2	2	no	—
392	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
393	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	4	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
403	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
404	C₄×D₄	C₂³×C₅₉	1	2	yes	—
405	#117	—	2	2	no	—
406	#117	—	2	2	no	—
407	#117	—	2	1	no	—
408	#117	D₄×C₅₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	2	no	—
411	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
414	#107	—	2	1	no	—
415	#106	—	2	1	no	—
416	#106	—	2	2	no	—
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
420	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
421	#103	—	2	1	no	—
422	#103	—	2	4	no	—
423	#102	—	2	1	no	—
424	#102	—	2	2	no	—
425	#102	—	2	4	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	2	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	#97	—	2	1	no	—
431	C₄×C₈	—	2	1	no	—
432	C₄×C₈	C₂³×C₅₉	1	2	yes	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	2	no	—
436	#41	—	4	2	no	—
437	#41	—	4	4	no	—
438	#41	—	8	2	no	—
439	#41	—	8	2	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	8	1	no	—
445	C₂×Q₈	—	8	1	no	—
446	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
457	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
468	SD₁₆	—	4	2	no	—
469	D₈	—	4	2	no	—
470	D₈	—	8	2	no	—
471	M₁₆	—	4	2	no	—
472	M₁₆	—	8	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
488	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
490	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
508	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
509	C₂³	—	2	1	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	4	1	no	—
512	C₂³	#120×C₅₉	1	1	yes	characteristic
513	Q₈	—	2	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	4	2	no	—
516	Q₈	—	4	2	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	8	2	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	8	4	no	—
534	D₄	—	8	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
556	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
557	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
561	C₈	—	4	2	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	4	no	—
585	C₄	—	4	1	no	—
586	C₄	—	8	1	no	—
587	C₄	C₅₉×#454	1	2	yes	—
588	C₄	C₅₉×#575	1	1	yes	characteristic
589	C₄	C₅₉×#575	1	1	yes	characteristic
590	C₄	C₅₉×#576	1	1	yes	characteristic
591	C₄	C₅₉×#577	1	1	yes	characteristic
592	C₂	—	4	1	no	—
593	C₂	—	8	1	no	—
594	C₂	—	8	2	no	—
595	C₂	—	16	1	no	—
596	C₂	C₅₉×#3005	1	1	yes	characteristic
597	C₂	C₅₉×#3012	1	1	yes	characteristic
598	C₂	C₂×C₅₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3511	C₂	semidirect
2. C₅₉×#3253	C₂	semidirect
3. C₅₉×#3141	C₂	semidirect
4. C₅₉×#3106	C₂	semidirect
5. C₅₉×#1638	C₂	semidirect
6. C₅₉×#1635	C₂	semidirect
7. C₅₉×#1628	C₂	semidirect
8. C₅₉×#1625	C₂	semidirect
9. C₅₉×#1546	C₂	semidirect
10. C₅₉×#1489	C₂	semidirect
11. C₅₉×#1484	C₂	semidirect
265. #18585	C₅₉	direct (N × H)
293. #3511	C₂×C₅₉	semidirect
294. #3253	C₂×C₅₉	semidirect
295. #3141	C₂×C₅₉	semidirect
296. #3106	C₂×C₅₉	semidirect
297. #1638	C₂×C₅₉	semidirect
298. #1635	C₂×C₅₉	semidirect
299. #1628	C₂×C₅₉	semidirect
300. #1625	C₂×C₅₉	semidirect
301. #1546	C₂×C₅₉	semidirect
302. #1489	C₂×C₅₉	semidirect
303. #1484	C₂×C₅₉	semidirect
352. C₅₉	#18585	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×#3511	2
C₅₉×#3253	2
C₅₉×#3141	2
C₅₉×#3106	2
C₅₉×#1638	2
C₅₉×#1635	2
C₅₉×#1628	2
C₅₉×#1625	2
C₅₉×#1546	2
C₅₉×#1489	2
C₅₉×#1484	2
#18585	59

Subgroups — C59×#18585 #28430694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#18585 #28430694