Subgroups — C₅₉×#18748 #28430857

Order 15104.

1020 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3036	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#1643	C₂	1	4	yes	maximal, complemented
6	C₅₉×#1622	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₅₉	—	2	1	no	—
11	C₅₉×#554	—	2	2	no	—
12	C₅₉×#554	—	2	2	no	—
13	C₅₉×#554	—	2	2	no	—
14	C₅₉×#554	C₂²	1	4	yes	—
15	C₅₉×#532	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#125×C₅₉	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₅₉	—	2	2	no	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₅₉	—	2	1	no	—
22	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
24	C₅₉×#492	C₂²	1	2	yes	complemented
25	C₅₉×#487	C₂²	1	2	yes	complemented
26	C₅₉×#481	—	2	1	no	—
27	C₅₉×#475	C₂²	1	2	yes	complemented
28	C₅₉×#463	—	2	2	no	—
29	C₅₉×#461	—	2	2	no	—
30	C₅₉×#461	C₂²	1	2	yes	—
31	C₅₉×#460	C₂²	1	2	yes	complemented
32	C₅₉×#459	C₂²	1	2	yes	—
33	C₅₉×#448	—	2	1	no	—
34	C₅₉×#448	—	2	2	no	—
35	C₄×SD₁₆×C₅₉	—	2	2	no	—
36	C₅₉×#431	C₂²	1	1	yes	characteristic
37	C₅₉×#431	C₂²	1	1	yes	characteristic
38	C₅₉×#423	C₂²	1	1	yes	characteristic
39	C₅₉×#417	—	2	1	no	—
40	C₅₉×#333	C₂²	1	4	yes	complemented
41	C₅₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₅₉×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₅₉	—	2	1	no	—
44	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₅₉	D₄	1	2	yes	—
46	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₅₉	—	2	2	no	—
48	C₂³×C₄×C₅₉	—	2	1	no	—
49	AGL(1,ℤ/8)×C₅₉	—	4	4	no	—
50	C₂×SD₁₆×C₅₉	—	2	2	no	—
51	C₂×SD₁₆×C₅₉	—	2	2	no	—
52	C₂×SD₁₆×C₅₉	—	2	4	no	—
53	C₂×D₈×C₅₉	—	2	2	no	—
54	C₂×M₁₆×C₅₉	—	2	1	no	—
55	C₄⋊Q₈×C₅₉	—	2	1	no	—
56	C₄⋊Q₈×C₅₉	—	2	1	no	—
57	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
58	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
60	#127×C₅₉	C₂³	1	1	yes	characteristic
61	#125×C₅₉	—	2	4	no	—
62	#125×C₅₉	—	2	4	no	—
63	#124×C₅₉	—	2	1	no	—
64	C₂²⋊Q₈×C₅₉	—	2	4	no	—
65	C₂²⋊Q₈×C₅₉	—	2	8	no	—
66	C₂²⋊Q₈×C₅₉	—	2	4	no	—
67	C₂²⋊Q₈×C₅₉	—	2	8	no	—
68	#121×C₅₉	—	2	1	no	—
69	#121×C₅₉	—	2	1	no	—
70	C₄×Q₈×C₅₉	—	2	1	no	—
71	C₄×Q₈×C₅₉	—	2	1	no	—
72	C₄×Q₈×C₅₉	D₄	1	2	yes	—
73	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
74	C₄×D₄×C₅₉	—	2	4	no	—
75	C₄×D₄×C₅₉	—	2	4	no	—
76	C₄×D₄×C₅₉	—	2	1	no	—
77	C₄×D₄×C₅₉	—	2	1	no	—
78	C₄×D₄×C₅₉	—	2	1	no	—
79	C₄×D₄×C₅₉	—	2	1	no	—
80	C₄×D₄×C₅₉	D₄	1	2	yes	—
81	C₄×D₄×C₅₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
85	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
93	C₂×C₄²×C₅₉	—	2	1	no	—
94	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
95	#106×C₅₉	—	2	2	no	—
96	C₄⋊C₈×C₅₉	—	2	1	no	—
97	C₄⋊C₈×C₅₉	—	2	1	no	—
98	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
99	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
100	#103×C₅₉	—	2	2	no	—
101	#103×C₅₉	—	2	4	no	—
102	#103×C₅₉	—	2	2	no	—
103	#102×C₅₉	—	2	2	no	—
104	#102×C₅₉	—	2	2	no	—
105	C₂²⋊C₈×C₅₉	—	2	1	no	—
106	C₂²⋊C₈×C₅₉	—	2	1	no	—
107	C₄×C₈×C₅₉	—	2	1	no	—
108	C₄×C₈×C₅₉	C₂³	1	2	yes	—
109	C₂⁴×C₅₉	—	2	1	no	—
110	#41×C₅₉	—	4	2	no	—
111	#41×C₅₉	—	4	2	no	—
112	C₂×Q₈×C₅₉	—	2	1	no	—
113	C₂×Q₈×C₅₉	—	2	2	no	—
114	C₂×Q₈×C₅₉	—	2	1	no	—
115	C₂×Q₈×C₅₉	—	4	2	no	—
116	C₂×Q₈×C₅₉	—	8	2	no	—
117	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
119	C₂×D₄×C₅₉	—	2	1	no	—
120	C₂×D₄×C₅₉	—	2	2	no	—
121	C₂×D₄×C₅₉	—	2	1	no	—
122	C₂×D₄×C₅₉	—	2	1	no	—
123	C₂×D₄×C₅₉	—	2	1	no	—
124	C₂×D₄×C₅₉	—	4	1	no	—
125	C₂×D₄×C₅₉	SD₁₆	1	4	yes	complemented
126	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	1	no	—
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	—	2	2	no	—
131	C₂²×C₄×C₅₉	—	2	8	no	—
132	C₂²×C₄×C₅₉	—	2	2	no	—
133	C₂²×C₄×C₅₉	—	2	2	no	—
134	C₂²×C₄×C₅₉	—	4	4	no	—
135	C₂²×C₄×C₅₉	—	4	1	no	—
136	C₂²×C₄×C₅₉	—	8	4	no	—
137	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
140	SD₁₆×C₅₉	—	4	4	no	—
141	SD₁₆×C₅₉	—	4	4	no	—
142	SD₁₆×C₅₉	—	8	4	no	—
143	D₈×C₅₉	—	4	4	no	—
144	M₁₆×C₅₉	—	4	2	no	—
145	C₂×C₈×C₅₉	—	2	2	no	—
146	C₂×C₈×C₅₉	—	2	2	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₄⋊C₄×C₅₉	—	2	8	no	—
149	C₄⋊C₄×C₅₉	—	2	8	no	—
150	C₄⋊C₄×C₅₉	—	2	1	no	—
151	C₄⋊C₄×C₅₉	—	2	2	no	—
152	C₄⋊C₄×C₅₉	—	2	2	no	—
153	C₄⋊C₄×C₅₉	—	2	2	no	—
154	C₄⋊C₄×C₅₉	—	2	1	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	2	2	no	—
157	C₄⋊C₄×C₅₉	—	2	2	no	—
158	C₄⋊C₄×C₅₉	—	2	1	no	—
159	C₄⋊C₄×C₅₉	—	2	1	no	—
160	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₅₉	—	2	8	no	—
163	C₂²⋊C₄×C₅₉	—	2	2	no	—
164	C₂²⋊C₄×C₅₉	—	2	2	no	—
165	C₂²⋊C₄×C₅₉	—	4	1	no	—
166	C₂²⋊C₄×C₅₉	—	4	1	no	—
167	C₄²×C₅₉	—	2	2	no	—
168	C₄²×C₅₉	—	2	2	no	—
169	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
173	C₂³×C₅₉	—	2	2	no	—
174	C₂³×C₅₉	—	2	4	no	—
175	C₂³×C₅₉	—	4	2	no	—
176	C₂³×C₅₉	—	4	2	no	—
177	C₂³×C₅₉	—	4	1	no	—
178	C₂³×C₅₉	#120	1	1	yes	characteristic
179	Q₈×C₅₉	—	2	2	no	—
180	Q₈×C₅₉	—	2	2	no	—
181	Q₈×C₅₉	—	4	4	no	—
182	Q₈×C₅₉	—	4	2	no	—
183	Q₈×C₅₉	—	4	1	no	—
184	Q₈×C₅₉	—	4	1	no	—
185	Q₈×C₅₉	—	8	2	no	—
186	D₄×C₅₉	—	2	2	no	—
187	D₄×C₅₉	—	2	4	no	—
188	D₄×C₅₉	—	4	2	no	—
189	D₄×C₅₉	—	4	1	no	—
190	D₄×C₅₉	—	4	1	no	—
191	D₄×C₅₉	—	4	2	no	—
192	D₄×C₅₉	—	8	2	no	—
193	D₄×C₅₉	C₂×SD₁₆	1	4	yes	—
194	C₂×C₄×C₅₉	—	2	2	no	—
195	C₂×C₄×C₅₉	—	2	2	no	—
196	C₂×C₄×C₅₉	—	2	2	no	—
197	C₂×C₄×C₅₉	—	2	2	no	—
198	C₂×C₄×C₅₉	—	2	4	no	—
199	C₂×C₄×C₅₉	—	4	1	no	—
200	C₂×C₄×C₅₉	—	4	4	no	—
201	C₂×C₄×C₅₉	—	4	2	no	—
202	C₂×C₄×C₅₉	—	4	2	no	—
203	C₂×C₄×C₅₉	—	4	4	no	—
204	C₂×C₄×C₅₉	—	4	2	no	—
205	C₂×C₄×C₅₉	—	4	4	no	—
206	C₂×C₄×C₅₉	—	4	1	no	—
207	C₂×C₄×C₅₉	—	8	8	no	—
208	C₂×C₄×C₅₉	—	8	2	no	—
209	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
210	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
211	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
212	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₅₉	#137	1	2	yes	—
214	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₅₉	—	4	2	no	—
218	C₈×C₅₉	—	4	2	no	—
219	C₈×C₅₉	—	4	2	no	—
220	#18748	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₅₉	—	2	1	no	—
222	C₂²×C₅₉	—	2	1	no	—
223	C₂²×C₅₉	—	2	4	no	—
224	C₂²×C₅₉	—	4	8	no	—
225	C₂²×C₅₉	—	4	2	no	—
226	C₂²×C₅₉	—	4	2	no	—
227	C₂²×C₅₉	—	8	1	no	—
228	C₂²×C₅₉	—	8	1	no	—
229	C₂²×C₅₉	—	8	1	no	—
230	C₂²×C₅₉	#448	1	2	yes	—
231	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
232	C₄×C₅₉	—	2	1	no	—
233	C₄×C₅₉	—	2	1	no	—
234	C₄×C₅₉	—	2	1	no	—
235	C₄×C₅₉	—	4	2	no	—
236	C₄×C₅₉	—	4	2	no	—
237	C₄×C₅₉	—	4	2	no	—
238	C₄×C₅₉	—	4	4	no	—
239	C₄×C₅₉	—	8	1	no	—
240	C₄×C₅₉	#448	1	2	yes	—
241	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
242	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
243	C₄×C₅₉	#575	1	2	yes	—
244	C₂×#554	C₂×C₅₉	1	1	yes	characteristic, complemented
245	#3206	C₂×C₅₉	1	1	yes	characteristic, complemented
246	#3103	C₂×C₅₉	1	1	yes	characteristic, complemented
247	#3036	C₂×C₅₉	1	1	yes	characteristic
248	#1643	C₂×C₅₉	1	4	yes	complemented
249	#1622	C₂×C₅₉	1	4	yes	complemented
250	#1548	C₂×C₅₉	1	1	yes	characteristic, complemented
251	#1487	C₂×C₅₉	1	1	yes	characteristic, complemented
252	#1478	C₂×C₅₉	1	1	yes	characteristic, complemented
253	C₂×C₅₉	—	2	2	no	—
254	C₂×C₅₉	—	4	4	no	—
255	C₂×C₅₉	—	16	1	no	—
256	C₂×C₅₉	C₂×#448	1	1	yes	characteristic
257	C₂×C₅₉	#3005	1	1	yes	characteristic
258	C₂×C₅₉	#3019	1	1	yes	characteristic
259	C₂×AGL(1,ℤ/8)	—	2	1	no	—
260	#554	—	2	2	no	—
261	#554	—	2	2	no	—
262	#554	—	2	2	no	—
263	#554	C₂²×C₅₉	1	4	yes	—
264	#532	C₂²×C₅₉	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
266	C₂×#125	—	2	1	no	—
267	C₂×C₂²⋊Q₈	—	2	1	no	—
268	C₂×C₂²⋊Q₈	—	2	2	no	—
269	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
270	C₂×C₄×D₄	—	2	1	no	—
271	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	—	2	1	no	—
273	#492	C₂²×C₅₉	1	2	yes	complemented
274	#487	C₂²×C₅₉	1	2	yes	complemented
275	#481	—	2	1	no	—
276	#475	C₂²×C₅₉	1	2	yes	complemented
277	#463	—	2	2	no	—
278	#461	—	2	2	no	—
279	#461	C₂²×C₅₉	1	2	yes	—
280	#460	C₂²×C₅₉	1	2	yes	complemented
281	#459	C₂²×C₅₉	1	2	yes	—
282	#448	—	2	1	no	—
283	#448	—	2	2	no	—
284	C₄×SD₁₆	—	2	2	no	—
285	#431	C₂²×C₅₉	1	1	yes	characteristic
286	#431	C₂²×C₅₉	1	1	yes	characteristic
287	#423	C₂²×C₅₉	1	1	yes	characteristic
288	#417	—	2	1	no	—
289	#333	C₂²×C₅₉	1	4	yes	complemented
290	Q₈⋊C₈	C₂²×C₅₉	1	4	yes	complemented
291	D₄⋊C₈	C₂²×C₅₉	1	4	yes	—
292	C₅₉	#18748	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#41	—	2	1	no	—
294	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
295	C₂²×Q₈	D₄×C₅₉	1	2	yes	—
296	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	1	no	—
299	AGL(1,ℤ/8)	—	4	4	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	2	no	—
302	C₂×SD₁₆	—	2	4	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
310	#127	C₂³×C₅₉	1	1	yes	characteristic
311	#125	—	2	4	no	—
312	#125	—	2	4	no	—
313	#124	—	2	1	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	8	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	D₄×C₅₉	1	2	yes	—
323	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	D₄×C₅₉	1	2	yes	—
331	C₄×D₄	C₂³×C₅₉	1	2	yes	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
345	#106	—	2	2	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	—	2	1	no	—
348	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
349	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
350	#103	—	2	2	no	—
351	#103	—	2	4	no	—
352	#103	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	1	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₄×C₈	—	2	1	no	—
358	C₄×C₈	C₂³×C₅₉	1	2	yes	—
359	C₂⁴	—	2	1	no	—
360	#41	—	4	2	no	—
361	#41	—	4	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	8	2	no	—
367	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
368	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	SD₁₆×C₅₉	1	4	yes	complemented
376	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	8	4	no	—
387	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
390	SD₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	SD₁₆	—	8	4	no	—
393	D₈	—	4	4	no	—
394	M₁₆	—	4	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
411	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
420	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
422	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	1	no	—
428	C₂³	#120×C₅₉	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	4	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	8	2	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	1	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	2	no	—
442	D₄	—	8	2	no	—
443	D₄	C₂×SD₁₆×C₅₉	1	4	yes	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	8	8	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
460	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
461	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
462	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
463	C₂×C₄	#137×C₅₉	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	C₅₉×#448	1	2	yes	—
480	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	8	1	no	—
489	C₄	C₅₉×#448	1	2	yes	—
490	C₄	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
491	C₄	C₂×#137×C₅₉	1	1	yes	characteristic
492	C₄	C₅₉×#575	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	4	4	no	—
495	C₂	—	16	1	no	—
496	C₂	C₂×C₅₉×#448	1	1	yes	characteristic
497	C₂	C₅₉×#3005	1	1	yes	characteristic
498	C₂	C₅₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₉
prime radical	C₅₉×#3036	C₂
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. C₂×C₅₉×#554	C₂	semidirect
2. C₅₉×#3206	C₂	semidirect
3. C₅₉×#3103	C₂	semidirect
5. C₅₉×#1643	C₂	semidirect
6. C₅₉×#1622	C₂	semidirect
7. C₅₉×#1548	C₂	semidirect
8. C₅₉×#1487	C₂	semidirect
9. C₅₉×#1478	C₂	semidirect
24. C₅₉×#492	C₂²	semidirect
25. C₅₉×#487	C₂²	semidirect
27. C₅₉×#475	C₂²	semidirect
31. C₅₉×#460	C₂²	semidirect
40. C₅₉×#333	C₂²	semidirect
41. C₅₉×Q₈⋊C₈	C₂²	semidirect
125. C₂×D₄×C₅₉	SD₁₆	semidirect
220. #18748	C₅₉	direct (N × H)
244. C₂×#554	C₂×C₅₉	semidirect
245. #3206	C₂×C₅₉	semidirect
246. #3103	C₂×C₅₉	semidirect
248. #1643	C₂×C₅₉	semidirect
249. #1622	C₂×C₅₉	semidirect
250. #1548	C₂×C₅₉	semidirect
251. #1487	C₂×C₅₉	semidirect
252. #1478	C₂×C₅₉	semidirect
273. #492	C₂²×C₅₉	semidirect
274. #487	C₂²×C₅₉	semidirect
276. #475	C₂²×C₅₉	semidirect
280. #460	C₂²×C₅₉	semidirect
289. #333	C₂²×C₅₉	semidirect
290. Q₈⋊C₈	C₂²×C₅₉	semidirect
292. C₅₉	#18748	direct (N × H)
375. C₂×D₄	SD₁₆×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×#554	2
C₅₉×#3206	2
C₅₉×#3103	2
C₅₉×#3036	2
C₅₉×#1643	2
C₅₉×#1622	2
C₅₉×#1548	2
C₅₉×#1487	2
C₅₉×#1478	2
#18748	59

Subgroups — C59×#18748 #28430857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#18748 #28430857