Subgroups — C₅₉×#25361 #28437470

Order 15104.

732 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3141	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3037	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2935	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2079	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2052	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1908	C₂	1	2	yes	maximal, complemented
10	C₅₉×#1815	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₅₉	C₂²	1	2	yes	—
13	C₂×#131×C₅₉	C₂²	1	2	yes	—
14	C₅₉×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#489	—	2	2	no	—
18	C₅₉×#487	—	2	1	no	—
19	C₅₉×#486	—	2	1	no	—
20	C₅₉×#475	—	2	1	no	—
21	C₅₉×#475	—	2	2	no	—
22	C₅₉×#475	—	2	1	no	—
23	C₅₉×#464	—	2	2	no	—
24	C₅₉×#462	—	2	1	no	—
25	C₅₉×#460	—	2	1	no	—
26	C₅₉×#436	—	2	1	no	—
27	C₅₉×#435	—	2	2	no	—
28	C₈×D₄×C₅₉	—	2	1	no	—
29	C₂×#108×C₅₉	C₂²	1	2	yes	—
30	C₂×#106×C₅₉	C₂²	1	2	yes	—
31	C₅₉×#423	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#417	C₂²	1	2	yes	—
34	C₅₉×#417	C₂²	1	2	yes	—
35	C₅₉×#417	C₂²	1	2	yes	—
36	C₂×#103×C₅₉	C₂²	1	2	yes	—
37	C₂×#101×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#101×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#408	C₂²	1	2	yes	—
40	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#343	C₂²	1	2	yes	—
43	C₅₉×#343	C₂²	1	2	yes	—
44	C₅₉×#343	C₂²	1	1	yes	characteristic
45	C₅₉×#343	C₂²	1	1	yes	characteristic
46	C₅₉×#341	C₂²	1	2	yes	—
47	C₂×#41×C₅₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₅₉	—	2	1	no	—
49	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
50	#137×C₅₉	—	2	4	no	—
51	#137×C₅₉	—	4	2	no	—
52	C₂×Q₁₆×C₅₉	—	2	2	no	—
53	C₂×SD₁₆×C₅₉	—	2	2	no	—
54	#131×C₅₉	—	2	4	no	—
55	#131×C₅₉	—	4	2	no	—
56	C₂×M₁₆×C₅₉	—	2	2	no	—
57	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₅₉	—	2	2	no	—
63	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₅₉	—	2	1	no	—
65	C₄⋊Q₈×C₅₉	—	2	1	no	—
66	C₄⋊Q₈×C₅₉	—	2	1	no	—
67	C₄⋊Q₈×C₅₉	—	2	1	no	—
68	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
69	#127×C₅₉	D₄	1	1	yes	characteristic
70	#124×C₅₉	D₄	1	2	yes	—
71	#121×C₅₉	—	2	1	no	—
72	#121×C₅₉	—	2	1	no	—
73	C₄×Q₈×C₅₉	—	2	1	no	—
74	C₄×Q₈×C₅₉	—	2	1	no	—
75	C₄×Q₈×C₅₉	—	2	1	no	—
76	C₄×Q₈×C₅₉	—	2	1	no	—
77	C₄×D₄×C₅₉	—	2	1	no	—
78	C₄×D₄×C₅₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅₉	—	2	1	no	—
84	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
85	#108×C₅₉	—	4	2	no	—
86	#106×C₅₉	—	2	2	no	—
87	#106×C₅₉	—	2	2	no	—
88	C₄⋊C₈×C₅₉	—	2	1	no	—
89	C₄⋊C₈×C₅₉	—	2	1	no	—
90	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
91	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
92	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
93	#103×C₅₉	—	2	2	no	—
94	#103×C₅₉	—	2	2	no	—
95	#103×C₅₉	—	2	2	no	—
96	#103×C₅₉	—	2	2	no	—
97	#103×C₅₉	—	2	2	no	—
98	#102×C₅₉	—	2	2	no	—
99	#102×C₅₉	—	2	2	no	—
100	#102×C₅₉	—	2	2	no	—
101	#101×C₅₉	—	2	2	no	—
102	#101×C₅₉	—	2	2	no	—
103	C₂²⋊C₈×C₅₉	—	2	2	no	—
104	C₂²⋊C₈×C₅₉	—	2	2	no	—
105	#97×C₅₉	—	2	1	no	—
106	#97×C₅₉	—	2	1	no	—
107	C₄×C₈×C₅₉	—	2	1	no	—
108	C₄×C₈×C₅₉	—	2	1	no	—
109	#41×C₅₉	—	2	2	no	—
110	#41×C₅₉	—	2	2	no	—
111	#41×C₅₉	—	2	2	no	—
112	#41×C₅₉	—	2	2	no	—
113	C₂×Q₈×C₅₉	—	2	1	no	—
114	C₂×Q₈×C₅₉	—	2	1	no	—
115	C₂×Q₈×C₅₉	—	2	1	no	—
116	C₂×Q₈×C₅₉	—	2	1	no	—
117	C₂×Q₈×C₅₉	—	2	1	no	—
118	C₂×Q₈×C₅₉	—	4	1	no	—
119	C₂×Q₈×C₅₉	—	4	1	no	—
120	C₂×Q₈×C₅₉	—	8	2	no	—
121	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₅₉	#41	1	2	yes	—
123	C₂×D₄×C₅₉	—	2	2	no	—
124	C₂×D₄×C₅₉	—	2	1	no	—
125	C₂×D₄×C₅₉	—	2	1	no	—
126	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	2	no	—
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	—	2	2	no	—
131	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
134	Q₁₆×C₅₉	—	4	4	no	—
135	SD₁₆×C₅₉	—	4	4	no	—
136	M₁₆×C₅₉	—	2	1	no	—
137	M₁₆×C₅₉	—	2	1	no	—
138	M₁₆×C₅₉	—	2	1	no	—
139	M₁₆×C₅₉	—	2	1	no	—
140	M₁₆×C₅₉	—	2	2	no	—
141	M₁₆×C₅₉	—	2	1	no	—
142	M₁₆×C₅₉	—	2	2	no	—
143	M₁₆×C₅₉	—	2	1	no	—
144	M₁₆×C₅₉	—	2	1	no	—
145	M₁₆×C₅₉	—	4	4	no	—
146	M₁₆×C₅₉	#41	1	2	yes	—
147	C₂×C₈×C₅₉	—	2	1	no	—
148	C₂×C₈×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	—	2	2	no	—
150	C₂×C₈×C₅₉	—	2	1	no	—
151	C₂×C₈×C₅₉	—	2	1	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₂×C₈×C₅₉	—	4	4	no	—
155	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₅₉	—	2	1	no	—
158	C₄⋊C₄×C₅₉	—	2	1	no	—
159	C₄⋊C₄×C₅₉	—	2	1	no	—
160	C₄⋊C₄×C₅₉	—	2	2	no	—
161	C₄⋊C₄×C₅₉	—	2	2	no	—
162	C₄⋊C₄×C₅₉	—	2	1	no	—
163	C₄⋊C₄×C₅₉	—	4	1	no	—
164	C₄⋊C₄×C₅₉	—	4	1	no	—
165	C₄⋊C₄×C₅₉	—	4	1	no	—
166	C₄⋊C₄×C₅₉	—	4	1	no	—
167	C₂²⋊C₄×C₅₉	—	2	2	no	—
168	C₂²⋊C₄×C₅₉	—	2	2	no	—
169	C₄²×C₅₉	—	4	1	no	—
170	C₄²×C₅₉	—	4	1	no	—
171	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₅₉	—	2	2	no	—
176	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
177	Q₈×C₅₉	—	2	2	no	—
178	Q₈×C₅₉	—	2	2	no	—
179	Q₈×C₅₉	—	2	2	no	—
180	Q₈×C₅₉	—	2	2	no	—
181	Q₈×C₅₉	—	4	1	no	—
182	Q₈×C₅₉	—	4	1	no	—
183	Q₈×C₅₉	—	8	2	no	—
184	Q₈×C₅₉	—	8	2	no	—
185	D₄×C₅₉	—	2	2	no	—
186	D₄×C₅₉	—	2	2	no	—
187	D₄×C₅₉	—	4	2	no	—
188	D₄×C₅₉	—	4	2	no	—
189	D₄×C₅₉	—	4	2	no	—
190	D₄×C₅₉	—	8	1	no	—
191	C₂×C₄×C₅₉	—	2	2	no	—
192	C₂×C₄×C₅₉	—	2	2	no	—
193	C₂×C₄×C₅₉	—	2	2	no	—
194	C₂×C₄×C₅₉	—	4	1	no	—
195	C₂×C₄×C₅₉	—	4	1	no	—
196	C₂×C₄×C₅₉	—	4	1	no	—
197	C₂×C₄×C₅₉	—	4	2	no	—
198	C₂×C₄×C₅₉	—	4	2	no	—
199	C₂×C₄×C₅₉	—	4	1	no	—
200	C₂×C₄×C₅₉	—	4	2	no	—
201	C₂×C₄×C₅₉	—	8	1	no	—
202	C₂×C₄×C₅₉	—	8	2	no	—
203	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₅₉	—	2	2	no	—
214	C₈×C₅₉	—	2	2	no	—
215	C₈×C₅₉	—	2	2	no	—
216	C₈×C₅₉	—	4	1	no	—
217	C₈×C₅₉	—	4	2	no	—
218	C₈×C₅₉	—	4	1	no	—
219	C₈×C₅₉	—	4	1	no	—
220	#25361	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	—	4	2	no	—
224	C₂²×C₅₉	—	4	2	no	—
225	C₂²×C₅₉	—	4	2	no	—
226	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
227	C₂²×C₅₉	#529	1	1	yes	characteristic
228	C₂²×C₅₉	#542	1	1	yes	characteristic
229	C₄×C₅₉	—	2	1	no	—
230	C₄×C₅₉	—	2	1	no	—
231	C₄×C₅₉	—	2	1	no	—
232	C₄×C₅₉	—	4	2	no	—
233	C₄×C₅₉	—	4	2	no	—
234	C₄×C₅₉	—	8	2	no	—
235	C₄×C₅₉	—	8	1	no	—
236	C₄×C₅₉	#471	1	2	yes	—
237	C₄×C₅₉	#546	1	1	yes	characteristic
238	C₄×C₅₉	#546	1	1	yes	characteristic
239	C₄×C₅₉	#547	1	1	yes	characteristic
240	C₄×C₅₉	#548	1	1	yes	characteristic
241	#3141	C₂×C₅₉	1	1	yes	characteristic
242	C₂×#475	C₂×C₅₉	1	1	yes	characteristic, complemented
243	#3037	C₂×C₅₉	1	1	yes	characteristic
244	#2935	C₂×C₅₉	1	1	yes	characteristic
245	#2079	C₂×C₅₉	1	2	yes	complemented
246	#2052	C₂×C₅₉	1	2	yes	complemented
247	#1997	C₂×C₅₉	1	1	yes	characteristic, complemented
248	#1950	C₂×C₅₉	1	1	yes	characteristic, complemented
249	#1908	C₂×C₅₉	1	2	yes	complemented
250	#1815	C₂×C₅₉	1	2	yes	complemented
251	C₄×#101	C₂×C₅₉	1	1	yes	characteristic, complemented
252	C₂×C₅₉	—	2	1	no	—
253	C₂×C₅₉	—	2	1	no	—
254	C₂×C₅₉	—	8	2	no	—
255	C₂×C₅₉	#2427	1	1	yes	characteristic
256	C₂×C₅₉	C₂×#471	1	1	yes	characteristic
257	C₂×C₅₉	#3069	1	1	yes	characteristic
258	C₂×#137	C₂²×C₅₉	1	2	yes	—
259	C₂×#131	C₂²×C₅₉	1	2	yes	—
260	#532	C₂²×C₅₉	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
263	#489	—	2	2	no	—
264	#487	—	2	1	no	—
265	#486	—	2	1	no	—
266	#475	—	2	1	no	—
267	#475	—	2	2	no	—
268	#475	—	2	1	no	—
269	#464	—	2	2	no	—
270	#462	—	2	1	no	—
271	#460	—	2	1	no	—
272	#436	—	2	1	no	—
273	#435	—	2	2	no	—
274	C₈×D₄	—	2	1	no	—
275	C₂×#108	C₂²×C₅₉	1	2	yes	—
276	C₂×#106	C₂²×C₅₉	1	2	yes	—
277	#423	C₂²×C₅₉	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
279	#417	C₂²×C₅₉	1	2	yes	—
280	#417	C₂²×C₅₉	1	2	yes	—
281	#417	C₂²×C₅₉	1	2	yes	—
282	C₂×#103	C₂²×C₅₉	1	2	yes	—
283	C₂×#101	C₂²×C₅₉	1	1	yes	characteristic
284	C₂×#101	C₂²×C₅₉	1	1	yes	characteristic
285	#408	C₂²×C₅₉	1	2	yes	—
286	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
287	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
288	#343	C₂²×C₅₉	1	2	yes	—
289	#343	C₂²×C₅₉	1	1	yes	characteristic
290	#343	C₂²×C₅₉	1	2	yes	—
291	#343	C₂²×C₅₉	1	1	yes	characteristic
292	#341	C₂²×C₅₉	1	2	yes	—
293	C₅₉	#25361	1	1	yes	characteristic, direct product factor, Sylow
294	C₂×#41	C₂³×C₅₉	1	2	yes	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
297	#137	—	2	4	no	—
298	#137	—	4	2	no	—
299	C₂×Q₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	#131	—	2	4	no	—
302	#131	—	4	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
305	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
306	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
307	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
308	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
316	#127	D₄×C₅₉	1	1	yes	characteristic
317	#124	D₄×C₅₉	1	2	yes	—
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	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
332	#108	—	4	2	no	—
333	#106	—	2	2	no	—
334	#106	—	2	2	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	—	2	1	no	—
337	C₄⋊C₈	D₄×C₅₉	1	1	yes	characteristic
338	C₄⋊C₈	D₄×C₅₉	1	2	yes	—
339	C₄⋊C₈	D₄×C₅₉	1	1	yes	characteristic
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	2	2	no	—
343	#103	—	2	2	no	—
344	#103	—	2	2	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	#102	—	2	2	no	—
348	#101	—	2	2	no	—
349	#101	—	2	2	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	#97	—	2	1	no	—
353	#97	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	4	1	no	—
366	C₂×Q₈	—	4	1	no	—
367	C₂×Q₈	—	8	2	no	—
368	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
369	C₂×Q₈	#41×C₅₉	1	2	yes	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
379	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
381	Q₁₆	—	4	4	no	—
382	SD₁₆	—	4	4	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	1	no	—
392	M₁₆	—	4	4	no	—
393	M₁₆	#41×C₅₉	1	2	yes	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	4	4	no	—
402	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
403	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₄²	—	4	1	no	—
417	C₄²	—	4	1	no	—
418	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
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	C₂³	—	2	2	no	—
423	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
424	Q₈	—	2	2	no	—
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	8	2	no	—
431	Q₈	—	8	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	1	no	—
449	C₂×C₄	—	8	2	no	—
450	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
451	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
452	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
453	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
458	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
459	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
473	C₂²	C₅₉×#529	1	1	yes	characteristic
474	C₂²	C₅₉×#542	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	1	no	—
482	C₄	C₅₉×#471	1	2	yes	—
483	C₄	C₅₉×#546	1	1	yes	characteristic
484	C₄	C₅₉×#546	1	1	yes	characteristic
485	C₄	C₅₉×#547	1	1	yes	characteristic
486	C₄	C₅₉×#548	1	1	yes	characteristic
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	8	2	no	—
490	C₂	C₅₉×#2427	1	1	yes	characteristic
491	C₂	C₂×C₅₉×#471	1	1	yes	characteristic
492	C₂	C₅₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₂×C₅₉×#475	C₂	semidirect
5. C₅₉×#2079	C₂	semidirect
6. C₅₉×#2052	C₂	semidirect
7. C₅₉×#1997	C₂	semidirect
8. C₅₉×#1950	C₂	semidirect
9. C₅₉×#1908	C₂	semidirect
10. C₅₉×#1815	C₂	semidirect
11. C₄×#101×C₅₉	C₂	semidirect
220. #25361	C₅₉	direct (N × H)
242. C₂×#475	C₂×C₅₉	semidirect
245. #2079	C₂×C₅₉	semidirect
246. #2052	C₂×C₅₉	semidirect
247. #1997	C₂×C₅₉	semidirect
248. #1950	C₂×C₅₉	semidirect
249. #1908	C₂×C₅₉	semidirect
250. #1815	C₂×C₅₉	semidirect
251. C₄×#101	C₂×C₅₉	semidirect
293. C₅₉	#25361	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×#3141	2
C₂×C₅₉×#475	2
C₅₉×#3037	2
C₅₉×#2935	2
C₅₉×#2079	2
C₅₉×#2052	2
C₅₉×#1997	2
C₅₉×#1950	2
C₅₉×#1908	2
C₅₉×#1815	2
C₄×#101×C₅₉	2
#25361	59

Subgroups — C59×#25361 #28437470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25361 #28437470