Subgroups — C₅₉×#18577 #28430686

Order 15104.

916 conjugacy classes of subgroups.

The subgroup lattice has 578 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
2	C₅₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1646	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1646	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1644	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1643	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1548	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	—	2	1	no	—
13	C₅₉×#555	C₂²	1	2	yes	—
14	C₅₉×#554	C₂²	1	2	yes	—
15	C₅₉×#553	—	2	2	no	—
16	C₅₉×#548	—	2	2	no	—
17	C₅₉×#547	—	2	1	no	—
18	C₅₉×#542	—	2	2	no	—
19	C₅₉×#537	—	2	1	no	—
20	C₅₉×#533	—	2	1	no	—
21	C₅₉×#533	C₂²	1	1	yes	characteristic
22	C₅₉×#532	—	2	1	no	—
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×#491	—	2	2	no	—
28	C₅₉×#487	C₂²	1	2	yes	—
29	C₅₉×#487	C₂²	1	2	yes	—
30	C₅₉×#485	—	2	1	no	—
31	C₅₉×#477	—	2	1	no	—
32	C₅₉×#475	C₂²	1	1	yes	characteristic
33	C₅₉×#474	C₂²	1	2	yes	—
34	C₅₉×#474	C₂²	1	1	yes	characteristic
35	C₅₉×#468	—	2	2	no	—
36	C₅₉×#462	C₂²	1	1	yes	characteristic
37	C₅₉×#461	C₂²	1	2	yes	—
38	C₅₉×#461	C₂²	1	1	yes	characteristic
39	C₅₉×#460	—	2	1	no	—
40	C₅₉×#452	—	2	1	no	—
41	C₄×Q₁₆×C₅₉	—	2	1	no	—
42	C₄×SD₁₆×C₅₉	—	2	1	no	—
43	C₅₉×#431	C₂²	1	1	yes	characteristic
44	C₅₉×#423	C₂²	1	1	yes	characteristic
45	C₅₉×#419	—	2	2	no	—
46	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
47	C₅₉×#333	C₂²	1	2	yes	—
48	C₅₉×#333	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	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₅₉	D₄	1	2	yes	—
57	C₂×Q₁₆×C₅₉	—	2	1	no	—
58	C₂×SD₁₆×C₅₉	—	2	1	no	—
59	C₂×SD₁₆×C₅₉	—	2	2	no	—
60	C₂×M₁₆×C₅₉	—	2	1	no	—
61	C₂×M₁₆×C₅₉	—	2	1	no	—
62	C₄⋊Q₈×C₅₉	—	2	1	no	—
63	C₄⋊Q₈×C₅₉	—	2	1	no	—
64	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
65	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
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	#126×C₅₉	—	2	4	no	—
71	#125×C₅₉	—	2	2	no	—
72	#125×C₅₉	—	2	1	no	—
73	#124×C₅₉	—	2	2	no	—
74	#124×C₅₉	—	2	4	no	—
75	#124×C₅₉	—	2	1	no	—
76	#123×C₅₉	—	2	4	no	—
77	C₂²⋊Q₈×C₅₉	—	2	2	no	—
78	C₂²⋊Q₈×C₅₉	—	2	2	no	—
79	C₂²⋊Q₈×C₅₉	—	2	2	no	—
80	C₂²⋊Q₈×C₅₉	—	2	4	no	—
81	C₂²⋊Q₈×C₅₉	—	2	1	no	—
82	C₂²⋊Q₈×C₅₉	—	2	1	no	—
83	#121×C₅₉	—	2	2	no	—
84	#121×C₅₉	—	2	4	no	—
85	#121×C₅₉	—	2	2	no	—
86	#121×C₅₉	—	2	2	no	—
87	#121×C₅₉	—	2	1	no	—
88	#121×C₅₉	D₄	1	2	yes	—
89	C₄×Q₈×C₅₉	—	2	2	no	—
90	C₄×Q₈×C₅₉	—	2	2	no	—
91	C₄×Q₈×C₅₉	—	2	1	no	—
92	C₄×Q₈×C₅₉	—	2	1	no	—
93	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₅₉	—	2	2	no	—
96	C₄×D₄×C₅₉	—	2	4	no	—
97	C₄×D₄×C₅₉	—	2	2	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	D₄	1	1	yes	characteristic
102	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₅₉	C₂³	1	2	yes	—
104	#117×C₅₉	—	2	2	no	—
105	#117×C₅₉	—	2	2	no	—
106	#117×C₅₉	—	2	1	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	1	no	—
111	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
112	C₂×C₄²×C₅₉	—	2	1	no	—
113	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
114	#107×C₅₉	—	2	1	no	—
115	#107×C₅₉	—	2	2	no	—
116	#106×C₅₉	—	2	1	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	4	no	—
122	#103×C₅₉	—	2	4	no	—
123	#103×C₅₉	—	2	1	no	—
124	#103×C₅₉	—	2	1	no	—
125	#103×C₅₉	—	2	1	no	—
126	#103×C₅₉	—	2	2	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	—	8	4	no	—
138	C₂×Q₈×C₅₉	—	2	1	no	—
139	C₂×Q₈×C₅₉	—	2	2	no	—
140	C₂×Q₈×C₅₉	—	2	1	no	—
141	C₂×Q₈×C₅₉	—	2	1	no	—
142	C₂×Q₈×C₅₉	—	4	4	no	—
143	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₅₉	—	2	1	no	—
146	C₂×D₄×C₅₉	—	2	2	no	—
147	C₂×D₄×C₅₉	—	2	4	no	—
148	C₂×D₄×C₅₉	—	2	1	no	—
149	C₂×D₄×C₅₉	—	2	1	no	—
150	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅₉	—	2	4	no	—
153	C₂²×C₄×C₅₉	—	2	2	no	—
154	C₂²×C₄×C₅₉	—	2	1	no	—
155	C₂²×C₄×C₅₉	—	2	1	no	—
156	C₂²×C₄×C₅₉	—	2	1	no	—
157	C₂²×C₄×C₅₉	—	2	2	no	—
158	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
161	Q₁₆×C₅₉	—	4	2	no	—
162	SD₁₆×C₅₉	—	4	2	no	—
163	SD₁₆×C₅₉	—	8	2	no	—
164	M₁₆×C₅₉	—	4	2	no	—
165	M₁₆×C₅₉	—	8	1	no	—
166	C₂×C₈×C₅₉	—	2	1	no	—
167	C₂×C₈×C₅₉	—	2	1	no	—
168	C₂×C₈×C₅₉	—	2	2	no	—
169	C₂×C₈×C₅₉	—	2	2	no	—
170	C₄⋊C₄×C₅₉	—	2	4	no	—
171	C₄⋊C₄×C₅₉	—	2	4	no	—
172	C₄⋊C₄×C₅₉	—	2	2	no	—
173	C₄⋊C₄×C₅₉	—	2	2	no	—
174	C₄⋊C₄×C₅₉	—	2	1	no	—
175	C₄⋊C₄×C₅₉	—	2	1	no	—
176	C₄⋊C₄×C₅₉	—	2	2	no	—
177	C₄⋊C₄×C₅₉	—	2	2	no	—
178	C₄⋊C₄×C₅₉	—	2	1	no	—
179	C₄⋊C₄×C₅₉	—	2	1	no	—
180	C₄⋊C₄×C₅₉	—	2	1	no	—
181	C₄⋊C₄×C₅₉	—	2	1	no	—
182	C₄⋊C₄×C₅₉	—	2	1	no	—
183	C₄⋊C₄×C₅₉	—	4	1	no	—
184	C₄⋊C₄×C₅₉	—	4	1	no	—
185	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
186	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
188	C₂²⋊C₄×C₅₉	—	2	4	no	—
189	C₂²⋊C₄×C₅₉	—	2	4	no	—
190	C₂²⋊C₄×C₅₉	—	2	4	no	—
191	C₂²⋊C₄×C₅₉	—	2	1	no	—
192	C₂²⋊C₄×C₅₉	—	2	1	no	—
193	C₂²⋊C₄×C₅₉	—	2	2	no	—
194	C₂²⋊C₄×C₅₉	—	2	1	no	—
195	C₂²⋊C₄×C₅₉	—	2	2	no	—
196	C₂²⋊C₄×C₅₉	—	4	1	no	—
197	C₄²×C₅₉	—	2	4	no	—
198	C₄²×C₅₉	—	2	1	no	—
199	C₄²×C₅₉	—	2	1	no	—
200	C₄²×C₅₉	—	2	1	no	—
201	C₄²×C₅₉	—	4	1	no	—
202	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
206	C₂³×C₅₉	—	2	1	no	—
207	C₂³×C₅₉	—	2	2	no	—
208	C₂³×C₅₉	#120	1	1	yes	characteristic
209	Q₈×C₅₉	—	2	1	no	—
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	—	4	4	no	—
212	Q₈×C₅₉	—	4	2	no	—
213	Q₈×C₅₉	—	4	4	no	—
214	Q₈×C₅₉	—	4	1	no	—
215	Q₈×C₅₉	—	4	1	no	—
216	Q₈×C₅₉	—	4	1	no	—
217	Q₈×C₅₉	—	4	1	no	—
218	D₄×C₅₉	—	2	1	no	—
219	D₄×C₅₉	—	2	1	no	—
220	D₄×C₅₉	—	2	2	no	—
221	D₄×C₅₉	—	2	2	no	—
222	D₄×C₅₉	—	4	2	no	—
223	D₄×C₅₉	—	4	2	no	—
224	D₄×C₅₉	—	4	4	no	—
225	D₄×C₅₉	—	4	2	no	—
226	D₄×C₅₉	—	8	4	no	—
227	C₂×C₄×C₅₉	—	2	1	no	—
228	C₂×C₄×C₅₉	—	2	1	no	—
229	C₂×C₄×C₅₉	—	2	1	no	—
230	C₂×C₄×C₅₉	—	2	1	no	—
231	C₂×C₄×C₅₉	—	2	2	no	—
232	C₂×C₄×C₅₉	—	2	1	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	2	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	4	no	—
237	C₂×C₄×C₅₉	—	4	2	no	—
238	C₂×C₄×C₅₉	—	4	2	no	—
239	C₂×C₄×C₅₉	—	4	2	no	—
240	C₂×C₄×C₅₉	—	4	1	no	—
241	C₂×C₄×C₅₉	—	4	1	no	—
242	C₂×C₄×C₅₉	—	4	2	no	—
243	C₂×C₄×C₅₉	—	4	1	no	—
244	C₂×C₄×C₅₉	—	4	1	no	—
245	C₂×C₄×C₅₉	—	8	2	no	—
246	C₂×C₄×C₅₉	—	8	4	no	—
247	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
249	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
250	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
253	C₈×C₅₉	—	4	2	no	—
254	C₈×C₅₉	—	4	1	no	—
255	C₈×C₅₉	—	4	1	no	—
256	C₈×C₅₉	—	4	2	no	—
257	#18577	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂²×C₅₉	—	2	1	no	—
259	C₂²×C₅₉	—	2	1	no	—
260	C₂²×C₅₉	—	2	1	no	—
261	C₂²×C₅₉	—	4	1	no	—
262	C₂²×C₅₉	—	4	2	no	—
263	C₂²×C₅₉	—	4	1	no	—
264	C₂²×C₅₉	—	4	2	no	—
265	C₂²×C₅₉	—	4	1	no	—
266	C₂²×C₅₉	—	4	2	no	—
267	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
268	C₄×C₅₉	—	2	1	no	—
269	C₄×C₅₉	—	2	1	no	—
270	C₄×C₅₉	—	2	1	no	—
271	C₄×C₅₉	—	4	1	no	—
272	C₄×C₅₉	—	4	2	no	—
273	C₄×C₅₉	—	4	1	no	—
274	C₄×C₅₉	—	4	1	no	—
275	C₄×C₅₉	—	4	4	no	—
276	C₄×C₅₉	—	8	1	no	—
277	C₄×C₅₉	—	8	1	no	—
278	C₄×C₅₉	#455	1	2	yes	—
279	C₄×C₅₉	#575	1	1	yes	characteristic
280	C₄×C₅₉	#575	1	1	yes	characteristic
281	C₄×C₅₉	#577	1	1	yes	characteristic
282	C₄×C₅₉	#578	1	1	yes	characteristic
283	#3511	C₂×C₅₉	1	1	yes	characteristic
284	#3254	C₂×C₅₉	1	1	yes	characteristic, complemented
285	#3139	C₂×C₅₉	1	1	yes	characteristic, complemented
286	#3107	C₂×C₅₉	1	1	yes	characteristic, complemented
287	#1646	C₂×C₅₉	1	2	yes	complemented
288	#1646	C₂×C₅₉	1	2	yes	complemented
289	#1644	C₂×C₅₉	1	2	yes	complemented
290	#1643	C₂×C₅₉	1	2	yes	complemented
291	#1548	C₂×C₅₉	1	1	yes	characteristic, complemented
292	#1489	C₂×C₅₉	1	1	yes	characteristic, complemented
293	#1484	C₂×C₅₉	1	1	yes	characteristic, complemented
294	C₂×C₅₉	—	4	1	no	—
295	C₂×C₅₉	—	8	1	no	—
296	C₂×C₅₉	—	8	2	no	—
297	C₂×C₅₉	#3005	1	1	yes	characteristic
298	C₂×C₅₉	#3013	1	1	yes	characteristic
299	C₂×C₅₉	C₂×#455	1	1	yes	characteristic
300	#556	—	2	1	no	—
301	#555	C₂²×C₅₉	1	2	yes	—
302	#554	C₂²×C₅₉	1	2	yes	—
303	#553	—	2	2	no	—
304	#548	—	2	2	no	—
305	#547	—	2	1	no	—
306	#542	—	2	2	no	—
307	#537	—	2	1	no	—
308	#533	—	2	1	no	—
309	#533	C₂²×C₅₉	1	1	yes	characteristic
310	#532	—	2	1	no	—
311	#532	C₂²×C₅₉	1	1	yes	characteristic
312	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
313	#520	—	2	1	no	—
314	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
315	#491	—	2	2	no	—
316	#487	C₂²×C₅₉	1	2	yes	—
317	#487	C₂²×C₅₉	1	2	yes	—
318	#485	—	2	1	no	—
319	#477	—	2	1	no	—
320	#475	C₂²×C₅₉	1	1	yes	characteristic
321	#474	C₂²×C₅₉	1	1	yes	characteristic
322	#474	C₂²×C₅₉	1	2	yes	—
323	#468	—	2	2	no	—
324	#462	C₂²×C₅₉	1	1	yes	characteristic
325	#461	C₂²×C₅₉	1	1	yes	characteristic
326	#461	C₂²×C₅₉	1	2	yes	—
327	#460	—	2	1	no	—
328	#452	—	2	1	no	—
329	C₄×Q₁₆	—	2	1	no	—
330	C₄×SD₁₆	—	2	1	no	—
331	#431	C₂²×C₅₉	1	1	yes	characteristic
332	#423	C₂²×C₅₉	1	1	yes	characteristic
333	#419	—	2	2	no	—
334	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
335	#333	C₂²×C₅₉	1	2	yes	—
336	#333	C₂²×C₅₉	1	2	yes	—
337	Q₈⋊C₈	C₂²×C₅₉	1	2	yes	—
338	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
339	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
340	D₄⋊C₈	C₂²×C₅₉	1	2	yes	—
341	C₅₉	#18577	1	1	yes	characteristic, direct product factor, Sylow
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
345	C₂²×Q₈	D₄×C₅₉	1	2	yes	—
346	C₂×Q₁₆	—	2	1	no	—
347	C₂×SD₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	2	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₄⋊Q₈	—	2	1	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
354	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
356	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
358	#127	D₄×C₅₉	1	1	yes	characteristic
359	#126	—	2	4	no	—
360	#125	—	2	2	no	—
361	#125	—	2	1	no	—
362	#124	—	2	2	no	—
363	#124	—	2	4	no	—
364	#124	—	2	1	no	—
365	#123	—	2	4	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	#121	—	2	2	no	—
373	#121	—	2	4	no	—
374	#121	—	2	2	no	—
375	#121	—	2	2	no	—
376	#121	—	2	1	no	—
377	#121	D₄×C₅₉	1	2	yes	—
378	C₄×Q₈	—	2	2	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
383	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	4	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
391	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
392	C₄×D₄	C₂³×C₅₉	1	2	yes	—
393	#117	—	2	2	no	—
394	#117	—	2	2	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	D₄×C₅₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
403	#107	—	2	1	no	—
404	#107	—	2	2	no	—
405	#106	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
410	#103	—	2	4	no	—
411	#103	—	2	4	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	2	no	—
416	#102	—	2	1	no	—
417	#102	—	2	2	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	#97	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	C₂³×C₅₉	1	2	yes	—
422	#41	—	4	1	no	—
423	#41	—	4	1	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	#41	—	8	4	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
433	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
440	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
450	Q₁₆	—	4	2	no	—
451	SD₁₆	—	4	2	no	—
452	SD₁₆	—	8	2	no	—
453	M₁₆	—	4	2	no	—
454	M₁₆	—	8	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	1	no	—
491	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
493	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
494	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
495	C₂³	—	2	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	#120×C₅₉	1	1	yes	characteristic
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	4	4	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	4	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	8	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	—	8	4	no	—
536	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
537	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
538	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
542	C₈	—	4	2	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	2	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	2	no	—
555	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	4	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₅₉×#455	1	2	yes	—
567	C₄	C₅₉×#575	1	1	yes	characteristic
568	C₄	C₅₉×#575	1	1	yes	characteristic
569	C₄	C₅₉×#577	1	1	yes	characteristic
570	C₄	C₅₉×#578	1	1	yes	characteristic
571	C₂	—	4	1	no	—
572	C₂	—	8	1	no	—
573	C₂	—	8	2	no	—
574	C₂	C₅₉×#3005	1	1	yes	characteristic
575	C₂	C₅₉×#3013	1	1	yes	characteristic
576	C₂	C₂×C₅₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₉
prime radical	C₅₉×#3511	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
2. C₅₉×#3254	C₂	semidirect
3. C₅₉×#3139	C₂	semidirect
4. C₅₉×#3107	C₂	semidirect
5. C₅₉×#1646	C₂	semidirect
6. C₅₉×#1646	C₂	semidirect
7. C₅₉×#1644	C₂	semidirect
8. C₅₉×#1643	C₂	semidirect
9. C₅₉×#1548	C₂	semidirect
10. C₅₉×#1489	C₂	semidirect
11. C₅₉×#1484	C₂	semidirect
257. #18577	C₅₉	direct (N × H)
284. #3254	C₂×C₅₉	semidirect
285. #3139	C₂×C₅₉	semidirect
286. #3107	C₂×C₅₉	semidirect
287. #1646	C₂×C₅₉	semidirect
288. #1646	C₂×C₅₉	semidirect
289. #1644	C₂×C₅₉	semidirect
290. #1643	C₂×C₅₉	semidirect
291. #1548	C₂×C₅₉	semidirect
292. #1489	C₂×C₅₉	semidirect
293. #1484	C₂×C₅₉	semidirect
341. C₅₉	#18577	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×#3254	2
C₅₉×#3139	2
C₅₉×#3107	2
C₅₉×#1646	2
C₅₉×#1644	2
C₅₉×#1643	2
C₅₉×#1548	2
C₅₉×#1489	2
C₅₉×#1484	2
#18577	59

Subgroups — C59×#18577 #28430686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#18577 #28430686