Subgroups — C₅₉×#24293 #28436402

Order 15104.

1290 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3060	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3013	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₉×#444	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2052	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2007	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1975	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1815	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1793	C₂	1	2	yes	maximal, complemented
12	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	2	yes	—
13	C₅₉×#578	—	2	4	no	—
14	C₅₉×#578	—	2	4	no	—
15	C₂×#137×C₅₉	—	2	2	no	—
16	C₂×#137×C₅₉	C₂²	1	2	yes	—
17	C₂×#137×C₅₉	C₂²	1	2	yes	—
18	C₂×#135×C₅₉	—	2	1	no	—
19	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₅₉	—	2	1	no	—
22	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#537	C₂²	1	2	yes	—
26	C₅₉×#473	—	2	4	no	—
27	C₅₉×#470	—	2	1	no	—
28	C₅₉×#469	—	2	1	no	—
29	C₅₉×#465	—	2	2	no	—
30	C₅₉×#452	—	2	2	no	—
31	C₅₉×#451	—	2	2	no	—
32	C₅₉×#449	—	2	2	no	—
33	C₅₉×#448	—	2	2	no	—
34	C₅₉×#444	—	2	4	no	—
35	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#104×C₅₉	C₂²	1	2	yes	—
41	C₅₉×#417	C₂²	1	2	yes	—
42	C₅₉×#417	C₂²	1	2	yes	—
43	C₂×#103×C₅₉	C₂²	1	2	yes	—
44	C₂×#101×C₅₉	C₂²	1	2	yes	—
45	C₅₉×#408	C₂²	1	2	yes	—
46	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
47	C₅₉×#391	C₂²	1	2	yes	—
48	C₅₉×#343	C₂²	1	2	yes	—
49	2₋¹⁺⁴×C₅₉	—	2	4	no	—
50	2₋¹⁺⁴×C₅₉	—	2	4	no	—
51	2₋¹⁺⁴×C₅₉	—	2	4	no	—
52	2₋¹⁺⁴×C₅₉	—	4	2	no	—
53	C₂×#41×C₅₉	—	2	2	no	—
54	C₂×#41×C₅₉	—	2	2	no	—
55	C₂×#41×C₅₉	—	4	2	no	—
56	C₂×#41×C₅₉	C₂³	1	2	yes	—
57	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
58	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₅₉	—	2	2	no	—
60	C₂²×Q₈×C₅₉	—	2	2	no	—
61	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
62	#137×C₅₉	—	2	16	no	—
63	#137×C₅₉	—	2	4	no	—
64	#137×C₅₉	—	2	4	no	—
65	#137×C₅₉	—	2	4	no	—
66	#137×C₅₉	—	4	2	no	—
67	#135×C₅₉	—	2	8	no	—
68	#135×C₅₉	—	2	2	no	—
69	#135×C₅₉	—	2	2	no	—
70	#135×C₅₉	—	2	2	no	—
71	#135×C₅₉	—	2	2	no	—
72	C₂×Q₁₆×C₅₉	—	2	8	no	—
73	C₂×Q₁₆×C₅₉	—	2	2	no	—
74	C₂×Q₁₆×C₅₉	—	2	2	no	—
75	C₂×Q₁₆×C₅₉	—	2	1	no	—
76	C₂×Q₁₆×C₅₉	—	2	1	no	—
77	C₂×Q₁₆×C₅₉	—	2	2	no	—
78	C₂×Q₁₆×C₅₉	D₄	1	1	yes	characteristic
79	C₂×Q₁₆×C₅₉	D₄	1	1	yes	characteristic
80	C₂×Q₁₆×C₅₉	D₄	1	4	yes	complemented
81	C₂×SD₁₆×C₅₉	—	2	2	no	—
82	C₂×SD₁₆×C₅₉	—	2	2	no	—
83	C₂×SD₁₆×C₅₉	D₄	1	1	yes	characteristic
84	C₂×SD₁₆×C₅₉	D₄	1	1	yes	characteristic
85	C₂×SD₁₆×C₅₉	D₄	1	2	yes	—
86	C₂×D₈×C₅₉	D₄	1	1	yes	characteristic
87	C₂×D₈×C₅₉	D₄	1	1	yes	characteristic
88	#131×C₅₉	—	2	2	no	—
89	#131×C₅₉	—	2	2	no	—
90	#131×C₅₉	—	2	2	no	—
91	#131×C₅₉	D₄	1	4	yes	complemented
92	C₂×M₁₆×C₅₉	—	2	1	no	—
93	C₂×M₁₆×C₅₉	—	2	1	no	—
94	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
95	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₅₉	—	2	1	no	—
98	C₂²×C₈×C₅₉	—	2	1	no	—
99	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
101	C₂²⋊Q₈×C₅₉	—	2	2	no	—
102	C₂²⋊Q₈×C₅₉	—	2	2	no	—
103	#121×C₅₉	—	2	2	no	—
104	#121×C₅₉	—	2	2	no	—
105	#121×C₅₉	—	4	2	no	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
108	#108×C₅₉	—	2	2	no	—
109	#108×C₅₉	—	2	2	no	—
110	#106×C₅₉	—	2	1	no	—
111	#106×C₅₉	—	2	1	no	—
112	#104×C₅₉	—	2	2	no	—
113	#104×C₅₉	—	2	2	no	—
114	#104×C₅₉	—	4	2	no	—
115	#103×C₅₉	—	2	2	no	—
116	#103×C₅₉	—	2	2	no	—
117	#103×C₅₉	—	2	2	no	—
118	#103×C₅₉	—	2	2	no	—
119	#102×C₅₉	—	2	2	no	—
120	#102×C₅₉	—	2	2	no	—
121	#101×C₅₉	—	2	4	no	—
122	C₂²⋊C₈×C₅₉	—	2	2	no	—
123	C₂²⋊C₈×C₅₉	—	2	2	no	—
124	#97×C₅₉	—	2	2	no	—
125	#95×C₅₉	—	4	2	no	—
126	#41×C₅₉	—	2	1	no	—
127	#41×C₅₉	—	2	1	no	—
128	#41×C₅₉	—	2	8	no	—
129	#41×C₅₉	—	2	1	no	—
130	#41×C₅₉	—	2	1	no	—
131	#41×C₅₉	—	2	2	no	—
132	#41×C₅₉	—	2	2	no	—
133	#41×C₅₉	—	2	1	no	—
134	#41×C₅₉	—	2	2	no	—
135	#41×C₅₉	—	2	2	no	—
136	#41×C₅₉	—	2	1	no	—
137	#41×C₅₉	—	4	4	no	—
138	#41×C₅₉	—	4	8	no	—
139	#41×C₅₉	—	4	4	no	—
140	#41×C₅₉	—	4	8	no	—
141	#41×C₅₉	—	4	4	no	—
142	#41×C₅₉	C₂×D₄	1	2	yes	—
143	#41×C₅₉	#41	1	2	yes	—
144	C₂×Q₈×C₅₉	—	2	2	no	—
145	C₂×Q₈×C₅₉	—	2	8	no	—
146	C₂×Q₈×C₅₉	—	2	2	no	—
147	C₂×Q₈×C₅₉	—	2	2	no	—
148	C₂×Q₈×C₅₉	—	2	2	no	—
149	C₂×Q₈×C₅₉	—	2	2	no	—
150	C₂×Q₈×C₅₉	—	4	2	no	—
151	C₂×Q₈×C₅₉	—	4	4	no	—
152	C₂×Q₈×C₅₉	—	4	4	no	—
153	C₂×Q₈×C₅₉	—	4	4	no	—
154	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
155	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₅₉	—	2	1	no	—
159	C₂×D₄×C₅₉	—	2	1	no	—
160	C₂×D₄×C₅₉	—	2	2	no	—
161	C₂×D₄×C₅₉	—	4	2	no	—
162	C₂×D₄×C₅₉	—	4	2	no	—
163	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
164	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	—	2	1	no	—
167	C₂²×C₄×C₅₉	—	2	2	no	—
168	C₂²×C₄×C₅₉	—	2	2	no	—
169	C₂²×C₄×C₅₉	—	2	1	no	—
170	C₂²×C₄×C₅₉	—	2	1	no	—
171	C₂²×C₄×C₅₉	—	2	2	no	—
172	C₂²×C₄×C₅₉	—	4	2	no	—
173	C₂²×C₄×C₅₉	—	4	2	no	—
174	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
175	Q₁₆×C₅₉	—	2	8	no	—
176	Q₁₆×C₅₉	—	2	2	no	—
177	Q₁₆×C₅₉	—	2	2	no	—
178	Q₁₆×C₅₉	—	2	4	no	—
179	Q₁₆×C₅₉	—	2	4	no	—
180	Q₁₆×C₅₉	—	4	4	no	—
181	SD₁₆×C₅₉	—	2	8	no	—
182	SD₁₆×C₅₉	—	2	2	no	—
183	SD₁₆×C₅₉	—	2	2	no	—
184	SD₁₆×C₅₉	—	2	4	no	—
185	SD₁₆×C₅₉	—	4	4	no	—
186	D₈×C₅₉	—	2	2	no	—
187	D₈×C₅₉	—	2	2	no	—
188	M₁₆×C₅₉	—	2	1	no	—
189	M₁₆×C₅₉	—	2	4	no	—
190	M₁₆×C₅₉	—	2	1	no	—
191	M₁₆×C₅₉	—	2	2	no	—
192	M₁₆×C₅₉	—	2	1	no	—
193	M₁₆×C₅₉	—	2	2	no	—
194	M₁₆×C₅₉	—	4	2	no	—
195	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₅₉	—	2	1	no	—
197	C₂×C₈×C₅₉	—	2	1	no	—
198	C₂×C₈×C₅₉	—	2	1	no	—
199	C₂×C₈×C₅₉	—	2	4	no	—
200	C₂×C₈×C₅₉	—	2	2	no	—
201	C₂×C₈×C₅₉	—	2	1	no	—
202	C₂×C₈×C₅₉	—	4	2	no	—
203	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
206	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₅₉	—	2	2	no	—
210	C₄⋊C₄×C₅₉	—	2	2	no	—
211	C₄⋊C₄×C₅₉	—	4	2	no	—
212	C₂²⋊C₄×C₅₉	—	4	2	no	—
213	C₂²⋊C₄×C₅₉	—	4	2	no	—
214	C₄²×C₅₉	—	2	1	no	—
215	C₄²×C₅₉	—	2	1	no	—
216	C₂³×C₅₉	—	2	1	no	—
217	C₂³×C₅₉	—	2	1	no	—
218	C₂³×C₅₉	—	2	2	no	—
219	C₂³×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
220	Q₈×C₅₉	—	2	1	no	—
221	Q₈×C₅₉	—	2	4	no	—
222	Q₈×C₅₉	—	2	2	no	—
223	Q₈×C₅₉	—	2	1	no	—
224	Q₈×C₅₉	—	2	4	no	—
225	Q₈×C₅₉	—	2	1	no	—
226	Q₈×C₅₉	—	2	2	no	—
227	Q₈×C₅₉	—	4	8	no	—
228	Q₈×C₅₉	—	4	2	no	—
229	Q₈×C₅₉	—	4	2	no	—
230	Q₈×C₅₉	#121	1	2	yes	—
231	D₄×C₅₉	—	2	2	no	—
232	D₄×C₅₉	—	2	2	no	—
233	D₄×C₅₉	—	2	2	no	—
234	D₄×C₅₉	—	2	1	no	—
235	D₄×C₅₉	—	2	1	no	—
236	D₄×C₅₉	—	2	1	no	—
237	D₄×C₅₉	—	2	2	no	—
238	D₄×C₅₉	—	4	8	no	—
239	D₄×C₅₉	—	4	1	no	—
240	D₄×C₅₉	—	4	2	no	—
241	D₄×C₅₉	—	4	1	no	—
242	D₄×C₅₉	—	4	2	no	—
243	D₄×C₅₉	—	16	2	no	—
244	D₄×C₅₉	#121	1	2	yes	—
245	C₂×C₄×C₅₉	—	2	1	no	—
246	C₂×C₄×C₅₉	—	2	2	no	—
247	C₂×C₄×C₅₉	—	2	2	no	—
248	C₂×C₄×C₅₉	—	2	1	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	4	no	—
251	C₂×C₄×C₅₉	—	4	8	no	—
252	C₂×C₄×C₅₉	—	4	8	no	—
253	C₂×C₄×C₅₉	—	4	2	no	—
254	C₂×C₄×C₅₉	—	4	2	no	—
255	C₂×C₄×C₅₉	—	4	1	no	—
256	C₂×C₄×C₅₉	—	4	2	no	—
257	C₂×C₄×C₅₉	—	4	2	no	—
258	C₂×C₄×C₅₉	—	4	1	no	—
259	C₂×C₄×C₅₉	—	4	2	no	—
260	C₂×C₄×C₅₉	—	4	1	no	—
261	C₂×C₄×C₅₉	—	4	2	no	—
262	C₂×C₄×C₅₉	—	8	2	no	—
263	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
269	C₈×C₅₉	—	2	2	no	—
270	C₈×C₅₉	—	2	1	no	—
271	C₈×C₅₉	—	2	1	no	—
272	C₈×C₅₉	—	4	1	no	—
273	C₈×C₅₉	—	4	2	no	—
274	C₈×C₅₉	#120	1	2	yes	—
275	C₈×C₅₉	#120	1	2	yes	—
276	#24293	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂²×C₅₉	—	2	2	no	—
278	C₂²×C₅₉	—	2	2	no	—
279	C₂²×C₅₉	—	4	2	no	—
280	C₂²×C₅₉	—	4	2	no	—
281	C₂²×C₅₉	—	4	1	no	—
282	C₂²×C₅₉	—	4	2	no	—
283	C₂²×C₅₉	—	4	2	no	—
284	C₂²×C₅₉	—	4	2	no	—
285	C₂²×C₅₉	#535	1	1	yes	characteristic
286	C₂²×C₅₉	D₄²	1	1	yes	characteristic
287	C₂²×C₅₉	#546	1	1	yes	characteristic
288	C₄×C₅₉	—	2	2	no	—
289	C₄×C₅₉	—	4	2	no	—
290	C₄×C₅₉	—	4	4	no	—
291	C₄×C₅₉	—	4	1	no	—
292	C₄×C₅₉	—	8	1	no	—
293	C₄×C₅₉	—	8	2	no	—
294	C₄×C₅₉	C₂×#120	1	1	yes	characteristic
295	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
296	C₄×C₅₉	D₄²	1	1	yes	characteristic
297	C₄×C₅₉	#546	1	1	yes	characteristic
298	C₂×#578	C₂×C₅₉	1	1	yes	characteristic, complemented
299	C₂×#473	C₂×C₅₉	1	1	yes	characteristic, complemented
300	#3060	C₂×C₅₉	1	1	yes	characteristic, complemented
301	#3013	C₂×C₅₉	1	2	yes	complemented
302	C₂×#444	C₂×C₅₉	1	1	yes	characteristic, complemented
303	#2052	C₂×C₅₉	1	2	yes	complemented
304	#2007	C₂×C₅₉	1	2	yes	complemented
305	#1975	C₂×C₅₉	1	1	yes	characteristic, complemented
306	#1971	C₂×C₅₉	1	1	yes	characteristic, complemented
307	#1815	C₂×C₅₉	1	1	yes	characteristic, complemented
308	#1793	C₂×C₅₉	1	2	yes	complemented
309	C₂×C₅₉	—	2	1	no	—
310	C₂×C₅₉	—	2	1	no	—
311	C₂×C₅₉	—	4	2	no	—
312	C₂×C₅₉	—	8	2	no	—
313	C₂×C₅₉	—	8	1	no	—
314	C₂×C₅₉	#2408	1	1	yes	characteristic
315	C₂×C₅₉	#3289	1	2	yes	—
316	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	2	yes	—
317	#578	—	2	4	no	—
318	#578	—	2	4	no	—
319	C₂×#137	—	2	2	no	—
320	C₂×#137	C₂²×C₅₉	1	2	yes	—
321	C₂×#137	C₂²×C₅₉	1	2	yes	—
322	C₂×#135	—	2	1	no	—
323	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic
324	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic
325	C₂²×Q₁₆	—	2	1	no	—
326	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
327	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
328	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
329	#537	C₂²×C₅₉	1	2	yes	—
330	#473	—	2	4	no	—
331	#470	—	2	1	no	—
332	#469	—	2	1	no	—
333	#465	—	2	2	no	—
334	#452	—	2	2	no	—
335	#451	—	2	2	no	—
336	#449	—	2	2	no	—
337	#448	—	2	2	no	—
338	#444	—	2	4	no	—
339	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
340	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
341	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
342	C₂×#104	C₂²×C₅₉	1	1	yes	characteristic
343	C₂×#104	C₂²×C₅₉	1	1	yes	characteristic
344	C₂×#104	C₂²×C₅₉	1	2	yes	—
345	#417	C₂²×C₅₉	1	2	yes	—
346	#417	C₂²×C₅₉	1	2	yes	—
347	C₂×#103	C₂²×C₅₉	1	2	yes	—
348	C₂×#101	C₂²×C₅₉	1	2	yes	—
349	#408	C₂²×C₅₉	1	2	yes	—
350	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
351	#391	C₂²×C₅₉	1	2	yes	—
352	#343	C₂²×C₅₉	1	2	yes	—
353	C₅₉	#24293	1	1	yes	characteristic, direct product factor, Sylow
354	2₋¹⁺⁴	—	2	4	no	—
355	2₋¹⁺⁴	—	2	4	no	—
356	2₋¹⁺⁴	—	2	4	no	—
357	2₋¹⁺⁴	—	4	2	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	4	2	no	—
361	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
362	C₂×#41	C₂³×C₅₉	1	2	yes	—
363	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
364	C₂²×Q₈	—	2	2	no	—
365	C₂²×Q₈	—	2	2	no	—
366	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
367	#137	—	2	16	no	—
368	#137	—	2	4	no	—
369	#137	—	2	4	no	—
370	#137	—	2	4	no	—
371	#137	—	4	2	no	—
372	#135	—	2	8	no	—
373	#135	—	2	2	no	—
374	#135	—	2	2	no	—
375	#135	—	2	2	no	—
376	#135	—	2	2	no	—
377	C₂×Q₁₆	—	2	8	no	—
378	C₂×Q₁₆	—	2	2	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×Q₁₆	—	2	1	no	—
381	C₂×Q₁₆	—	2	1	no	—
382	C₂×Q₁₆	—	2	2	no	—
383	C₂×Q₁₆	D₄×C₅₉	1	1	yes	characteristic
384	C₂×Q₁₆	D₄×C₅₉	1	1	yes	characteristic
385	C₂×Q₁₆	D₄×C₅₉	1	4	yes	complemented
386	C₂×SD₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	D₄×C₅₉	1	2	yes	—
389	C₂×SD₁₆	D₄×C₅₉	1	1	yes	characteristic
390	C₂×SD₁₆	D₄×C₅₉	1	1	yes	characteristic
391	C₂×D₈	D₄×C₅₉	1	1	yes	characteristic
392	C₂×D₈	D₄×C₅₉	1	1	yes	characteristic
393	#131	—	2	2	no	—
394	#131	—	2	2	no	—
395	#131	—	2	2	no	—
396	#131	D₄×C₅₉	1	4	yes	complemented
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	1	no	—
399	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
400	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
401	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	#121	—	2	2	no	—
409	#121	—	2	2	no	—
410	#121	—	4	2	no	—
411	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
412	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
413	#108	—	2	2	no	—
414	#108	—	2	2	no	—
415	#106	—	2	1	no	—
416	#106	—	2	1	no	—
417	#104	—	2	2	no	—
418	#104	—	2	2	no	—
419	#104	—	4	2	no	—
420	#103	—	2	2	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#103	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#101	—	2	4	no	—
427	C₂²⋊C₈	—	2	2	no	—
428	C₂²⋊C₈	—	2	2	no	—
429	#97	—	2	2	no	—
430	#95	—	4	2	no	—
431	#41	—	2	1	no	—
432	#41	—	2	1	no	—
433	#41	—	2	8	no	—
434	#41	—	2	1	no	—
435	#41	—	2	1	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	2	1	no	—
439	#41	—	2	2	no	—
440	#41	—	2	2	no	—
441	#41	—	2	1	no	—
442	#41	—	4	4	no	—
443	#41	—	4	8	no	—
444	#41	—	4	4	no	—
445	#41	—	4	8	no	—
446	#41	—	4	4	no	—
447	#41	C₂×D₄×C₅₉	1	2	yes	—
448	#41	#41×C₅₉	1	2	yes	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	8	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	4	4	no	—
457	C₂×Q₈	—	4	4	no	—
458	C₂×Q₈	—	4	4	no	—
459	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
460	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
461	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
462	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
469	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
470	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
480	Q₁₆	—	2	8	no	—
481	Q₁₆	—	2	2	no	—
482	Q₁₆	—	2	2	no	—
483	Q₁₆	—	2	4	no	—
484	Q₁₆	—	2	4	no	—
485	Q₁₆	—	4	4	no	—
486	SD₁₆	—	2	8	no	—
487	SD₁₆	—	2	2	no	—
488	SD₁₆	—	2	2	no	—
489	SD₁₆	—	2	4	no	—
490	SD₁₆	—	4	4	no	—
491	D₈	—	2	2	no	—
492	D₈	—	2	2	no	—
493	M₁₆	—	2	1	no	—
494	M₁₆	—	2	4	no	—
495	M₁₆	—	2	1	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	—	2	1	no	—
498	M₁₆	—	2	2	no	—
499	M₁₆	—	4	2	no	—
500	M₁₆	C₂×D₄×C₅₉	1	2	yes	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	4	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	4	2	no	—
508	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
509	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
510	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
511	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
512	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
513	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	2	no	—
524	C₂³	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
525	Q₈	—	2	1	no	—
526	Q₈	—	2	4	no	—
527	Q₈	—	2	2	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	4	8	no	—
533	Q₈	—	4	2	no	—
534	Q₈	—	4	2	no	—
535	Q₈	#121×C₅₉	1	2	yes	—
536	D₄	—	2	2	no	—
537	D₄	—	2	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	8	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	2	no	—
548	D₄	—	16	2	no	—
549	D₄	#121×C₅₉	1	2	yes	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	4	8	no	—
557	C₂×C₄	—	4	8	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
571	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
572	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
573	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
574	C₈	—	2	2	no	—
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	2	no	—
579	C₈	#120×C₅₉	1	2	yes	—
580	C₈	#120×C₅₉	1	2	yes	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	1	no	—
589	C₂²	C₅₉×#535	1	1	yes	characteristic
590	C₂²	D₄²×C₅₉	1	1	yes	characteristic
591	C₂²	C₅₉×#546	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	1	no	—
596	C₄	—	8	1	no	—
597	C₄	—	8	2	no	—
598	C₄	C₂×#120×C₅₉	1	1	yes	characteristic
599	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
600	C₄	D₄²×C₅₉	1	1	yes	characteristic
601	C₄	C₅₉×#546	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	4	2	no	—
605	C₂	—	8	1	no	—
606	C₂	—	8	2	no	—
607	C₂	C₅₉×#2408	1	1	yes	characteristic
608	C₂	C₅₉×#3289	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#578	C₂	semidirect
2. C₂×C₅₉×#473	C₂	semidirect
3. C₅₉×#3060	C₂	semidirect
4. C₅₉×#3013	C₂	semidirect
5. C₂×C₅₉×#444	C₂	semidirect
6. C₅₉×#2052	C₂	semidirect
7. C₅₉×#2007	C₂	semidirect
8. C₅₉×#1975	C₂	semidirect
9. C₅₉×#1971	C₂	semidirect
10. C₅₉×#1815	C₂	semidirect
11. C₅₉×#1793	C₂	semidirect
80. C₂×Q₁₆×C₅₉	D₄	semidirect
91. #131×C₅₉	D₄	semidirect
276. #24293	C₅₉	direct (N × H)
298. C₂×#578	C₂×C₅₉	semidirect
299. C₂×#473	C₂×C₅₉	semidirect
300. #3060	C₂×C₅₉	semidirect
301. #3013	C₂×C₅₉	semidirect
302. C₂×#444	C₂×C₅₉	semidirect
303. #2052	C₂×C₅₉	semidirect
304. #2007	C₂×C₅₉	semidirect
305. #1975	C₂×C₅₉	semidirect
306. #1971	C₂×C₅₉	semidirect
307. #1815	C₂×C₅₉	semidirect
308. #1793	C₂×C₅₉	semidirect
353. C₅₉	#24293	direct (N × H)
385. C₂×Q₁₆	D₄×C₅₉	semidirect
396. #131	D₄×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×#578	2
C₂×C₅₉×#473	2
C₅₉×#3060	2
C₅₉×#3013	2
C₂×C₅₉×#444	2
C₅₉×#2052	2
C₅₉×#2007	2
C₅₉×#1975	2
C₅₉×#1971	2
C₅₉×#1815	2
C₅₉×#1793	2
#24293	59

Subgroups — C59×#24293 #28436402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24293 #28436402