Subgroups — C₅₉×#18601 #28430710

Order 15104.

910 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3501	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3101	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#1651	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1643	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1637	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1632	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1490	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#554	—	2	1	no	—
13	C₅₉×#554	—	2	2	no	—
14	C₅₉×#554	—	2	2	no	—
15	C₅₉×#554	C₂²	1	2	yes	—
16	D₄×Q₈×C₅₉	—	2	1	no	—
17	D₄×Q₈×C₅₉	C₂²	1	2	yes	—
18	C₅₉×#544	—	2	1	no	—
19	C₅₉×#543	—	2	2	no	—
20	C₅₉×#533	C₂²	1	1	yes	characteristic
21	C₅₉×#533	C₂²	1	1	yes	characteristic
22	C₅₉×#533	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₉	—	2	2	no	—
24	C₅₉×#518	—	2	1	no	—
25	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#501	—	2	1	no	—
27	C₅₉×#498	C₂²	1	1	yes	characteristic, complemented
28	C₅₉×#494	C₂²	1	1	yes	characteristic, complemented
29	C₅₉×#491	—	2	1	no	—
30	C₅₉×#487	C₂²	1	1	yes	characteristic, complemented
31	C₅₉×#487	C₂²	1	1	yes	characteristic, complemented
32	C₅₉×#485	—	2	2	no	—
33	C₅₉×#483	—	2	1	no	—
34	C₅₉×#477	C₂²	1	2	yes	complemented
35	C₅₉×#476	C₂²	1	2	yes	—
36	C₅₉×#475	C₂²	1	2	yes	complemented
37	C₅₉×#470	—	2	2	no	—
38	C₅₉×#461	C₂²	1	2	yes	—
39	C₅₉×#450	—	2	1	no	—
40	C₅₉×#441	—	2	2	no	—
41	C₄×SD₁₆×C₅₉	—	2	2	no	—
42	C₅₉×#432	C₂²	1	1	yes	characteristic
43	C₅₉×#431	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#333	C₂²	1	2	yes	complemented
46	C₅₉×#332	C₂²	1	2	yes	complemented
47	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
48	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	complemented
49	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
50	C₅₉×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂²×Q₈×C₅₉	—	2	2	no	—
52	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₅₉	—	2	1	no	—
54	C₂×Q₁₆×C₅₉	—	2	2	no	—
55	C₂×SD₁₆×C₅₉	—	2	2	no	—
56	C₂×M₁₆×C₅₉	—	2	1	no	—
57	C₄⋊Q₈×C₅₉	—	2	2	no	—
58	C₄⋊Q₈×C₅₉	—	2	2	no	—
59	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
65	#125×C₅₉	—	2	2	no	—
66	#125×C₅₉	—	2	2	no	—
67	#125×C₅₉	—	2	1	no	—
68	#125×C₅₉	—	2	1	no	—
69	#125×C₅₉	—	2	1	no	—
70	C₂²⋊Q₈×C₅₉	—	2	4	no	—
71	C₂²⋊Q₈×C₅₉	—	2	4	no	—
72	C₂²⋊Q₈×C₅₉	—	2	4	no	—
73	C₂²⋊Q₈×C₅₉	—	2	4	no	—
74	C₂²⋊Q₈×C₅₉	—	2	2	no	—
75	C₂²⋊Q₈×C₅₉	—	2	4	no	—
76	C₂²⋊Q₈×C₅₉	—	2	1	no	—
77	C₂²⋊Q₈×C₅₉	—	2	1	no	—
78	C₂²⋊Q₈×C₅₉	—	2	2	no	—
79	C₂²⋊Q₈×C₅₉	—	2	4	no	—
80	C₂²⋊Q₈×C₅₉	—	2	1	no	—
81	C₂²⋊Q₈×C₅₉	—	2	1	no	—
82	C₂²⋊Q₈×C₅₉	D₄	1	2	yes	—
83	C₂²⋊Q₈×C₅₉	D₄	1	2	yes	—
84	C₄×Q₈×C₅₉	—	2	1	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	D₄	1	2	yes	—
89	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
90	C₄×D₄×C₅₉	—	2	2	no	—
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	1	no	—
95	C₄×D₄×C₅₉	—	2	1	no	—
96	C₄×D₄×C₅₉	D₄	1	2	yes	—
97	C₄×D₄×C₅₉	C₂³	1	2	yes	—
98	#117×C₅₉	—	2	1	no	—
99	#117×C₅₉	—	2	1	no	—
100	#117×C₅₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
102	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
106	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
107	#107×C₅₉	—	2	2	no	—
108	#106×C₅₉	—	2	2	no	—
109	#106×C₅₉	—	2	2	no	—
110	#106×C₅₉	—	2	2	no	—
111	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
112	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
113	#103×C₅₉	—	2	2	no	—
114	#103×C₅₉	—	2	2	no	—
115	#103×C₅₉	—	2	2	no	—
116	#103×C₅₉	—	2	2	no	—
117	#103×C₅₉	—	2	2	no	—
118	#102×C₅₉	—	2	2	no	—
119	C₂²⋊C₈×C₅₉	—	2	1	no	—
120	C₂²⋊C₈×C₅₉	—	2	1	no	—
121	#97×C₅₉	—	2	1	no	—
122	#97×C₅₉	—	2	1	no	—
123	C₄×C₈×C₅₉	—	2	1	no	—
124	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
126	C₂⁴×C₅₉	—	2	1	no	—
127	C₂×Q₈×C₅₉	—	2	4	no	—
128	C₂×Q₈×C₅₉	—	2	1	no	—
129	C₂×Q₈×C₅₉	—	2	1	no	—
130	C₂×Q₈×C₅₉	—	2	1	no	—
131	C₂×Q₈×C₅₉	—	2	1	no	—
132	C₂×Q₈×C₅₉	—	8	4	no	—
133	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₅₉	—	2	4	no	—
136	C₂×D₄×C₅₉	—	2	1	no	—
137	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₅₉	—	2	4	no	—
139	C₂²×C₄×C₅₉	—	2	4	no	—
140	C₂²×C₄×C₅₉	—	2	1	no	—
141	C₂²×C₄×C₅₉	—	2	2	no	—
142	C₂²×C₄×C₅₉	—	2	2	no	—
143	C₂²×C₄×C₅₉	—	8	2	no	—
144	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
147	Q₁₆×C₅₉	—	4	4	no	—
148	SD₁₆×C₅₉	—	4	4	no	—
149	M₁₆×C₅₉	—	4	2	no	—
150	C₂×C₈×C₅₉	—	2	1	no	—
151	C₂×C₈×C₅₉	—	2	2	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₄⋊C₄×C₅₉	—	2	4	no	—
155	C₄⋊C₄×C₅₉	—	2	4	no	—
156	C₄⋊C₄×C₅₉	—	2	4	no	—
157	C₄⋊C₄×C₅₉	—	2	2	no	—
158	C₄⋊C₄×C₅₉	—	2	2	no	—
159	C₄⋊C₄×C₅₉	—	2	1	no	—
160	C₄⋊C₄×C₅₉	—	2	1	no	—
161	C₄⋊C₄×C₅₉	—	2	1	no	—
162	C₄⋊C₄×C₅₉	—	2	1	no	—
163	C₄⋊C₄×C₅₉	—	2	2	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	—	2	2	no	—
168	C₄⋊C₄×C₅₉	—	2	1	no	—
169	C₄⋊C₄×C₅₉	—	2	1	no	—
170	C₄⋊C₄×C₅₉	—	2	1	no	—
171	C₄⋊C₄×C₅₉	—	2	1	no	—
172	C₄⋊C₄×C₅₉	—	4	1	no	—
173	C₄⋊C₄×C₅₉	—	4	1	no	—
174	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
177	C₂²⋊C₄×C₅₉	—	2	4	no	—
178	C₂²⋊C₄×C₅₉	—	2	4	no	—
179	C₂²⋊C₄×C₅₉	—	2	2	no	—
180	C₂²⋊C₄×C₅₉	—	2	2	no	—
181	C₂²⋊C₄×C₅₉	—	2	2	no	—
182	C₂²⋊C₄×C₅₉	—	2	2	no	—
183	C₂²⋊C₄×C₅₉	—	4	1	no	—
184	C₄²×C₅₉	—	2	2	no	—
185	C₄²×C₅₉	—	2	2	no	—
186	C₄²×C₅₉	—	4	1	no	—
187	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
191	C₂³×C₅₉	—	2	4	no	—
192	C₂³×C₅₉	—	2	2	no	—
193	C₂³×C₅₉	—	8	1	no	—
194	C₂³×C₅₉	—	8	1	no	—
195	C₂³×C₅₉	#120	1	1	yes	characteristic
196	Q₈×C₅₉	—	2	4	no	—
197	Q₈×C₅₉	—	4	2	no	—
198	Q₈×C₅₉	—	4	2	no	—
199	Q₈×C₅₉	—	4	2	no	—
200	Q₈×C₅₉	—	4	2	no	—
201	Q₈×C₅₉	—	8	1	no	—
202	Q₈×C₅₉	—	8	4	no	—
203	D₄×C₅₉	—	2	4	no	—
204	D₄×C₅₉	—	2	2	no	—
205	D₄×C₅₉	#137	1	4	yes	—
206	C₂×C₄×C₅₉	—	2	2	no	—
207	C₂×C₄×C₅₉	—	2	2	no	—
208	C₂×C₄×C₅₉	—	2	2	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	2	2	no	—
211	C₂×C₄×C₅₉	—	2	2	no	—
212	C₂×C₄×C₅₉	—	2	2	no	—
213	C₂×C₄×C₅₉	—	4	1	no	—
214	C₂×C₄×C₅₉	—	4	4	no	—
215	C₂×C₄×C₅₉	—	4	1	no	—
216	C₂×C₄×C₅₉	—	4	1	no	—
217	C₂×C₄×C₅₉	—	8	2	no	—
218	C₂×C₄×C₅₉	—	8	1	no	—
219	C₂×C₄×C₅₉	—	8	4	no	—
220	C₂×C₄×C₅₉	—	8	4	no	—
221	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
222	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
227	C₈×C₅₉	—	2	2	no	—
228	C₈×C₅₉	—	4	1	no	—
229	C₈×C₅₉	—	4	2	no	—
230	C₈×C₅₉	—	4	2	no	—
231	#18601	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₅₉	—	2	1	no	—
233	C₂²×C₅₉	—	2	4	no	—
234	C₂²×C₅₉	—	2	1	no	—
235	C₂²×C₅₉	—	2	1	no	—
236	C₂²×C₅₉	—	4	2	no	—
237	C₂²×C₅₉	—	4	2	no	—
238	C₂²×C₅₉	—	8	4	no	—
239	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
240	C₄×C₅₉	—	2	1	no	—
241	C₄×C₅₉	—	2	1	no	—
242	C₄×C₅₉	—	2	1	no	—
243	C₄×C₅₉	—	2	1	no	—
244	C₄×C₅₉	—	4	2	no	—
245	C₄×C₅₉	—	4	2	no	—
246	C₄×C₅₉	—	4	2	no	—
247	C₄×C₅₉	—	4	2	no	—
248	C₄×C₅₉	—	4	2	no	—
249	C₄×C₅₉	—	8	1	no	—
250	C₄×C₅₉	—	8	1	no	—
251	C₄×C₅₉	C₂×#137	1	2	yes	—
252	C₄×C₅₉	#577	1	2	yes	—
253	#3501	C₂×C₅₉	1	1	yes	characteristic
254	#3237	C₂×C₅₉	1	1	yes	characteristic, complemented
255	#3185	C₂×C₅₉	1	1	yes	characteristic, complemented
256	#3101	C₂×C₅₉	1	1	yes	characteristic
257	#1651	C₂×C₅₉	1	2	yes	complemented
258	#1643	C₂×C₅₉	1	2	yes	complemented
259	#1637	C₂×C₅₉	1	2	yes	complemented
260	#1632	C₂×C₅₉	1	2	yes	complemented
261	#1554	C₂×C₅₉	1	1	yes	characteristic, complemented
262	#1490	C₂×C₅₉	1	1	yes	characteristic
263	#1485	C₂×C₅₉	1	1	yes	characteristic, complemented
264	C₂×C₅₉	—	4	1	no	—
265	C₂×C₅₉	—	4	4	no	—
266	C₂×C₅₉	#3004	1	1	yes	characteristic
267	C₂×C₅₉	#3009	1	1	yes	characteristic
268	C₂×C₅₉	#3018	1	1	yes	characteristic
269	#554	—	2	1	no	—
270	#554	—	2	2	no	—
271	#554	—	2	2	no	—
272	#554	C₂²×C₅₉	1	2	yes	—
273	D₄×Q₈	—	2	1	no	—
274	D₄×Q₈	C₂²×C₅₉	1	2	yes	—
275	#544	—	2	1	no	—
276	#543	—	2	2	no	—
277	#533	C₂²×C₅₉	1	1	yes	characteristic
278	#533	C₂²×C₅₉	1	1	yes	characteristic
279	#533	C₂²×C₅₉	1	1	yes	characteristic
280	C₂×C₂²⋊Q₈	—	2	2	no	—
281	#518	—	2	1	no	—
282	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
283	#501	—	2	1	no	—
284	#498	C₂²×C₅₉	1	1	yes	characteristic, complemented
285	#494	C₂²×C₅₉	1	1	yes	characteristic, complemented
286	#491	—	2	1	no	—
287	#487	C₂²×C₅₉	1	1	yes	characteristic, complemented
288	#487	C₂²×C₅₉	1	1	yes	characteristic, complemented
289	#485	—	2	2	no	—
290	#483	—	2	1	no	—
291	#477	C₂²×C₅₉	1	2	yes	complemented
292	#476	C₂²×C₅₉	1	2	yes	—
293	#475	C₂²×C₅₉	1	2	yes	complemented
294	#470	—	2	2	no	—
295	#461	C₂²×C₅₉	1	2	yes	—
296	#450	—	2	1	no	—
297	#441	—	2	2	no	—
298	C₄×SD₁₆	—	2	2	no	—
299	#432	C₂²×C₅₉	1	1	yes	characteristic
300	#431	C₂²×C₅₉	1	1	yes	characteristic
301	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
302	#333	C₂²×C₅₉	1	2	yes	complemented
303	#332	C₂²×C₅₉	1	2	yes	complemented
304	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	complemented
305	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	complemented
306	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
307	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
308	C₅₉	#18601	1	1	yes	characteristic, direct product factor, Sylow
309	C₂²×Q₈	—	2	2	no	—
310	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
311	C₂³×C₄	—	2	1	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
318	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
319	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
323	#125	—	2	2	no	—
324	#125	—	2	2	no	—
325	#125	—	2	1	no	—
326	#125	—	2	1	no	—
327	#125	—	2	1	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	4	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	D₄×C₅₉	1	2	yes	—
341	C₂²⋊Q₈	D₄×C₅₉	1	2	yes	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	D₄×C₅₉	1	2	yes	—
347	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	D₄×C₅₉	1	2	yes	—
355	C₄×D₄	C₂³×C₅₉	1	2	yes	—
356	#117	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	4	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
365	#107	—	2	2	no	—
366	#106	—	2	2	no	—
367	#106	—	2	2	no	—
368	#106	—	2	2	no	—
369	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
370	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	2	2	no	—
375	#103	—	2	2	no	—
376	#102	—	2	2	no	—
377	C₂²⋊C₈	—	2	1	no	—
378	C₂²⋊C₈	—	2	1	no	—
379	#97	—	2	1	no	—
380	#97	—	2	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
383	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
384	C₂⁴	—	2	1	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	8	4	no	—
391	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
392	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
405	Q₁₆	—	4	4	no	—
406	SD₁₆	—	4	4	no	—
407	M₁₆	—	4	2	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	1	no	—
432	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
433	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
434	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	4	1	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	4	1	no	—
445	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
448	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
449	C₂³	—	2	4	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	8	1	no	—
452	C₂³	—	8	1	no	—
453	C₂³	#120×C₅₉	1	1	yes	characteristic
454	Q₈	—	2	4	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	8	1	no	—
460	Q₈	—	8	4	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	2	no	—
463	D₄	#137×C₅₉	1	4	yes	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	8	2	no	—
476	C₂×C₄	—	8	1	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
480	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
481	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
485	C₈	—	2	2	no	—
486	C₈	—	4	1	no	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	4	no	—
496	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	1	no	—
508	C₄	C₂×#137×C₅₉	1	2	yes	—
509	C₄	C₅₉×#577	1	2	yes	—
510	C₂	—	4	1	no	—
511	C₂	—	4	4	no	—
512	C₂	C₅₉×#3004	1	1	yes	characteristic
513	C₂	C₅₉×#3009	1	1	yes	characteristic
514	C₂	C₅₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₉
prime radical	C₂²×D₄×C₅₉	D₄
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
2. C₅₉×#3237	C₂	semidirect
3. C₅₉×#3185	C₂	semidirect
5. C₅₉×#1651	C₂	semidirect
6. C₅₉×#1643	C₂	semidirect
7. C₅₉×#1637	C₂	semidirect
8. C₅₉×#1632	C₂	semidirect
9. C₅₉×#1554	C₂	semidirect
11. C₅₉×#1485	C₂	semidirect
27. C₅₉×#498	C₂²	semidirect
28. C₅₉×#494	C₂²	semidirect
30. C₅₉×#487	C₂²	semidirect
31. C₅₉×#487	C₂²	semidirect
34. C₅₉×#477	C₂²	semidirect
36. C₅₉×#475	C₂²	semidirect
45. C₅₉×#333	C₂²	semidirect
46. C₅₉×#332	C₂²	semidirect
47. C₅₉×Q₈⋊C₈	C₂²	semidirect
48. C₅₉×Q₈⋊C₈	C₂²	semidirect
231. #18601	C₅₉	direct (N × H)
254. #3237	C₂×C₅₉	semidirect
255. #3185	C₂×C₅₉	semidirect
257. #1651	C₂×C₅₉	semidirect
258. #1643	C₂×C₅₉	semidirect
259. #1637	C₂×C₅₉	semidirect
260. #1632	C₂×C₅₉	semidirect
261. #1554	C₂×C₅₉	semidirect
263. #1485	C₂×C₅₉	semidirect
284. #498	C₂²×C₅₉	semidirect
285. #494	C₂²×C₅₉	semidirect
287. #487	C₂²×C₅₉	semidirect
288. #487	C₂²×C₅₉	semidirect
291. #477	C₂²×C₅₉	semidirect
293. #475	C₂²×C₅₉	semidirect
302. #333	C₂²×C₅₉	semidirect
303. #332	C₂²×C₅₉	semidirect
304. Q₈⋊C₈	C₂²×C₅₉	semidirect
305. Q₈⋊C₈	C₂²×C₅₉	semidirect
308. C₅₉	#18601	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×#3501	2
C₅₉×#3237	2
C₅₉×#3185	2
C₅₉×#3101	2
C₅₉×#1651	2
C₅₉×#1643	2
C₅₉×#1637	2
C₅₉×#1632	2
C₅₉×#1554	2
C₅₉×#1490	2
C₅₉×#1485	2
#18601	59

Subgroups — C59×#18601 #28430710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#18601 #28430710