Subgroups — C₅₉×#23018 #28435127

Order 15104.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2933	C₂	1	2	yes	maximal, complemented
4	C₂²×#108×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1929	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1871	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1866	C₂	1	2	yes	maximal, complemented
10	C₅₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₅₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₅₉	C₂²	1	2	yes	—
15	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#525	C₂²	1	2	yes	—
17	C₅₉×#467	C₄	1	1	yes	characteristic, complemented
18	C₅₉×#467	C₄	1	1	yes	characteristic, complemented
19	C₅₉×#466	C₄	1	1	yes	characteristic, complemented
20	C₅₉×#466	C₄	1	1	yes	characteristic, complemented
21	C₅₉×#465	C₄	1	2	yes	complemented
22	C₅₉×#465	C₄	1	2	yes	complemented
23	C₅₉×#443	—	2	4	no	—
24	C₅₉×#436	—	2	2	no	—
25	C₅₉×#435	—	2	2	no	—
26	C₅₉×#435	—	2	2	no	—
27	C₈×D₄×C₅₉	—	2	2	no	—
28	C₂×#108×C₅₉	—	2	4	no	—
29	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#108×C₅₉	C₂²	1	2	yes	—
31	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
32	C₅₉×#427	C₂²	1	1	yes	characteristic
33	C₅₉×#424	C₂²	1	2	yes	—
34	C₂×#104×C₅₉	C₂²	1	2	yes	—
35	C₂×#104×C₅₉	C₂²	1	2	yes	—
36	C₅₉×#416	C₂²	1	2	yes	—
37	C₅₉×#408	C₂²	1	2	yes	—
38	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#405	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×#339	C₂²	1	2	yes	—
44	C₅₉×#339	C₂²	1	2	yes	—
45	C₅₉×#336	C₂²	1	1	yes	characteristic
46	C₅₉×#336	C₂²	1	1	yes	characteristic
47	C₂×#41×C₅₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
49	#135×C₅₉	—	2	2	no	—
50	#135×C₅₉	—	2	2	no	—
51	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
53	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
54	#131×C₅₉	—	2	4	no	—
55	#131×C₅₉	—	4	2	no	—
56	C₂×M₁₆×C₅₉	—	2	2	no	—
57	C₂×M₁₆×C₅₉	—	2	2	no	—
58	C₂×M₁₆×C₅₉	—	2	4	no	—
59	C₂×M₁₆×C₅₉	—	4	2	no	—
60	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
61	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₅₉	—	2	2	no	—
63	C₂²×C₈×C₅₉	—	2	2	no	—
64	C₂²×C₈×C₅₉	—	2	2	no	—
65	C₂²×C₈×C₅₉	—	2	2	no	—
66	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
74	#123×C₅₉	—	2	2	no	—
75	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
76	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
77	#121×C₅₉	C₂×C₄	1	2	yes	—
78	#121×C₅₉	C₂×C₄	1	2	yes	—
79	#120×C₅₉	—	2	2	no	—
80	C₄×D₄×C₅₉	—	2	2	no	—
81	C₄×D₄×C₅₉	—	2	2	no	—
82	#117×C₅₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
84	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
86	#108×C₅₉	—	2	4	no	—
87	#108×C₅₉	—	2	2	no	—
88	#108×C₅₉	D₄	1	4	yes	complemented
89	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
90	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
91	#106×C₅₉	C₂×C₄	1	2	yes	—
92	C₄⋊C₈×C₅₉	—	2	2	no	—
93	C₄⋊C₈×C₅₉	—	2	2	no	—
94	#104×C₅₉	—	2	4	no	—
95	#104×C₅₉	—	4	2	no	—
96	#103×C₅₉	C₂×C₄	1	2	yes	—
97	#103×C₅₉	C₂×C₄	1	2	yes	—
98	#102×C₅₉	C₂×C₄	1	2	yes	—
99	#102×C₅₉	C₂×C₄	1	2	yes	—
100	C₂²⋊C₈×C₅₉	—	2	2	no	—
101	C₂²⋊C₈×C₅₉	—	2	2	no	—
102	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
103	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
104	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
105	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
106	#97×C₅₉	—	2	2	no	—
107	C₄×C₈×C₅₉	—	2	2	no	—
108	C₄×C₈×C₅₉	—	2	2	no	—
109	C₄×C₈×C₅₉	—	2	2	no	—
110	#95×C₅₉	—	2	1	no	—
111	C₂⁴×C₅₉	#41	1	1	yes	characteristic
112	#41×C₅₉	—	2	2	no	—
113	#41×C₅₉	—	2	2	no	—
114	#41×C₅₉	—	2	2	no	—
115	#41×C₅₉	—	2	2	no	—
116	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
117	C₂×D₄×C₅₉	—	2	2	no	—
118	C₂×D₄×C₅₉	—	2	2	no	—
119	C₂×D₄×C₅₉	—	2	2	no	—
120	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	1	no	—
123	C₂²×C₄×C₅₉	—	2	1	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	2	1	no	—
127	C₂²×C₄×C₅₉	—	2	2	no	—
128	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂×D₄	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	—	2	2	no	—
135	SD₁₆×C₅₉	—	2	4	no	—
136	D₈×C₅₉	—	2	2	no	—
137	M₁₆×C₅₉	—	2	2	no	—
138	M₁₆×C₅₉	—	2	2	no	—
139	M₁₆×C₅₉	—	2	2	no	—
140	M₁₆×C₅₉	—	4	4	no	—
141	M₁₆×C₅₉	—	4	4	no	—
142	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₅₉	—	2	1	no	—
144	C₂×C₈×C₅₉	—	2	1	no	—
145	C₂×C₈×C₅₉	—	2	2	no	—
146	C₂×C₈×C₅₉	—	2	1	no	—
147	C₂×C₈×C₅₉	—	2	1	no	—
148	C₂×C₈×C₅₉	—	2	1	no	—
149	C₂×C₈×C₅₉	—	2	1	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	2	no	—
152	C₂×C₈×C₅₉	—	2	2	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₂×C₈×C₅₉	—	2	2	no	—
155	C₂×C₈×C₅₉	—	4	4	no	—
156	C₂×C₈×C₅₉	—	4	4	no	—
157	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₅₉	#41	1	2	yes	—
167	C₄⋊C₄×C₅₉	—	2	2	no	—
168	C₄⋊C₄×C₅₉	—	2	2	no	—
169	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
170	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
171	C₂²⋊C₄×C₅₉	—	2	4	no	—
172	C₂²⋊C₄×C₅₉	—	2	2	no	—
173	C₂²⋊C₄×C₅₉	—	2	2	no	—
174	C₂²⋊C₄×C₅₉	—	2	2	no	—
175	C₂²⋊C₄×C₅₉	—	2	2	no	—
176	C₂²⋊C₄×C₅₉	—	2	2	no	—
177	C₄²×C₅₉	—	2	2	no	—
178	C₄²×C₅₉	—	2	1	no	—
179	C₄²×C₅₉	—	2	1	no	—
180	C₄²×C₅₉	—	2	1	no	—
181	C₄²×C₅₉	—	2	1	no	—
182	C₂³×C₅₉	—	2	1	no	—
183	C₂³×C₅₉	—	2	1	no	—
184	C₂³×C₅₉	—	2	2	no	—
185	C₂³×C₅₉	—	2	2	no	—
186	C₂³×C₅₉	—	4	1	no	—
187	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
189	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
190	Q₈×C₅₉	—	2	2	no	—
191	Q₈×C₅₉	—	2	2	no	—
192	D₄×C₅₉	—	2	2	no	—
193	D₄×C₅₉	—	2	2	no	—
194	D₄×C₅₉	—	4	2	no	—
195	D₄×C₅₉	—	4	2	no	—
196	D₄×C₅₉	—	4	4	no	—
197	D₄×C₅₉	—	8	2	no	—
198	C₂×C₄×C₅₉	—	2	1	no	—
199	C₂×C₄×C₅₉	—	2	1	no	—
200	C₂×C₄×C₅₉	—	2	1	no	—
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	2	1	no	—
204	C₂×C₄×C₅₉	—	2	1	no	—
205	C₂×C₄×C₅₉	—	2	1	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	1	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	1	no	—
215	C₂×C₄×C₅₉	—	4	1	no	—
216	C₂×C₄×C₅₉	—	4	1	no	—
217	C₂×C₄×C₅₉	—	4	2	no	—
218	C₂×C₄×C₅₉	—	4	2	no	—
219	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
227	C₈×C₅₉	—	2	1	no	—
228	C₈×C₅₉	—	2	1	no	—
229	C₈×C₅₉	—	2	1	no	—
230	C₈×C₅₉	—	2	1	no	—
231	C₈×C₅₉	—	2	4	no	—
232	C₈×C₅₉	—	2	1	no	—
233	C₈×C₅₉	—	2	1	no	—
234	C₈×C₅₉	—	4	2	no	—
235	C₈×C₅₉	C₄×D₄	1	2	yes	—
236	C₈×C₅₉	C₄×D₄	1	2	yes	—
237	#23018	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂²×C₅₉	—	2	1	no	—
239	C₂²×C₅₉	—	2	1	no	—
240	C₂²×C₅₉	—	2	1	no	—
241	C₂²×C₅₉	—	2	1	no	—
242	C₂²×C₅₉	—	2	1	no	—
243	C₂²×C₅₉	—	2	1	no	—
244	C₂²×C₅₉	—	2	1	no	—
245	C₂²×C₅₉	—	4	2	no	—
246	C₂²×C₅₉	—	4	2	no	—
247	C₂²×C₅₉	—	4	2	no	—
248	C₂²×C₅₉	—	4	2	no	—
249	C₂²×C₅₉	—	4	2	no	—
250	C₂²×C₅₉	#443	1	2	yes	complemented
251	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₅₉	#548	1	1	yes	characteristic
253	C₂²×C₅₉	#553	1	1	yes	characteristic
254	C₄×C₅₉	—	2	1	no	—
255	C₄×C₅₉	—	2	1	no	—
256	C₄×C₅₉	—	4	2	no	—
257	C₄×C₅₉	—	4	2	no	—
258	C₄×C₅₉	—	4	2	no	—
259	C₄×C₅₉	—	4	2	no	—
260	C₄×C₅₉	—	4	2	no	—
261	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
262	C₄×C₅₉	#520	1	1	yes	characteristic
263	C₄×C₅₉	D₄²	1	1	yes	characteristic
264	C₄×C₅₉	#547	1	1	yes	characteristic
265	#3050	C₂×C₅₉	1	1	yes	characteristic
266	C₂×#443	C₂×C₅₉	1	1	yes	characteristic, complemented
267	#2933	C₂×C₅₉	1	2	yes	complemented
268	C₂²×#108	C₂×C₅₉	1	1	yes	characteristic, complemented
269	#1974	C₂×C₅₉	1	1	yes	characteristic, complemented
270	#1945	C₂×C₅₉	1	1	yes	characteristic, complemented
271	#1929	C₂×C₅₉	1	2	yes	complemented
272	#1871	C₂×C₅₉	1	2	yes	complemented
273	#1866	C₂×C₅₉	1	2	yes	complemented
274	#1772	C₂×C₅₉	1	1	yes	characteristic, complemented
275	C₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
276	C₂×C₅₉	—	2	1	no	—
277	C₂×C₅₉	—	2	1	no	—
278	C₂×C₅₉	—	2	2	no	—
279	C₂×C₅₉	—	4	1	no	—
280	C₂×C₅₉	—	8	2	no	—
281	C₂×C₅₉	#2361	1	1	yes	characteristic
282	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
283	C₂×C₅₉	#2957	1	1	yes	characteristic
284	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic
285	C₂×#131	C₂²×C₅₉	1	2	yes	—
286	C₂²×M₁₆	C₂²×C₅₉	1	2	yes	—
287	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
288	#525	C₂²×C₅₉	1	2	yes	—
289	#467	C₄×C₅₉	1	1	yes	characteristic, complemented
290	#467	C₄×C₅₉	1	1	yes	characteristic, complemented
291	#466	C₄×C₅₉	1	1	yes	characteristic, complemented
292	#466	C₄×C₅₉	1	1	yes	characteristic, complemented
293	#465	C₄×C₅₉	1	2	yes	complemented
294	#465	C₄×C₅₉	1	2	yes	complemented
295	#443	—	2	4	no	—
296	#436	—	2	2	no	—
297	#435	—	2	2	no	—
298	#435	—	2	2	no	—
299	C₈×D₄	—	2	2	no	—
300	C₂×#108	—	2	4	no	—
301	C₂×#108	C₂²×C₅₉	1	2	yes	—
302	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
303	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
304	#427	C₂²×C₅₉	1	1	yes	characteristic
305	#424	C₂²×C₅₉	1	2	yes	—
306	C₂×#104	C₂²×C₅₉	1	2	yes	—
307	C₂×#104	C₂²×C₅₉	1	2	yes	—
308	#416	C₂²×C₅₉	1	2	yes	—
309	#408	C₂²×C₅₉	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
311	#405	C₂²×C₅₉	1	2	yes	—
312	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
314	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
315	#339	C₂²×C₅₉	1	2	yes	—
316	#339	C₂²×C₅₉	1	2	yes	—
317	#336	C₂²×C₅₉	1	1	yes	characteristic
318	#336	C₂²×C₅₉	1	1	yes	characteristic
319	C₅₉	#23018	1	1	yes	characteristic, direct product factor, Sylow
320	C₂×#41	C₂³×C₅₉	1	2	yes	—
321	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
322	#135	—	2	2	no	—
323	#135	—	2	2	no	—
324	C₂×Q₁₆	C₂×C₄×C₅₉	1	1	yes	characteristic
325	C₂×SD₁₆	C₂×C₄×C₅₉	1	2	yes	—
326	C₂×D₈	C₂×C₄×C₅₉	1	1	yes	characteristic
327	#131	—	2	4	no	—
328	#131	—	4	2	no	—
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	4	no	—
332	C₂×M₁₆	—	4	2	no	—
333	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
334	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
340	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
341	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
342	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
347	#123	—	2	2	no	—
348	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
349	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
350	#121	C₂×C₄×C₅₉	1	2	yes	—
351	#121	C₂×C₄×C₅₉	1	2	yes	—
352	#120	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	#117	C₂³×C₅₉	1	2	yes	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
359	#108	—	2	4	no	—
360	#108	—	2	2	no	—
361	#108	D₄×C₅₉	1	4	yes	complemented
362	#107	C₂×C₄×C₅₉	1	1	yes	characteristic
363	#107	C₂×C₄×C₅₉	1	1	yes	characteristic
364	#106	C₂×C₄×C₅₉	1	2	yes	—
365	C₄⋊C₈	—	2	2	no	—
366	C₄⋊C₈	—	2	2	no	—
367	#104	—	2	4	no	—
368	#104	—	4	2	no	—
369	#103	C₂×C₄×C₅₉	1	2	yes	—
370	#103	C₂×C₄×C₅₉	1	2	yes	—
371	#102	C₂×C₄×C₅₉	1	2	yes	—
372	#102	C₂×C₄×C₅₉	1	2	yes	—
373	C₂²⋊C₈	—	2	2	no	—
374	C₂²⋊C₈	—	2	2	no	—
375	C₂²⋊C₈	D₄×C₅₉	1	1	yes	characteristic
376	C₂²⋊C₈	D₄×C₅₉	1	1	yes	characteristic
377	C₂²⋊C₈	D₄×C₅₉	1	1	yes	characteristic
378	C₂²⋊C₈	D₄×C₅₉	1	1	yes	characteristic
379	#97	—	2	2	no	—
380	C₄×C₈	—	2	2	no	—
381	C₄×C₈	—	2	2	no	—
382	C₄×C₈	—	2	2	no	—
383	#95	—	2	1	no	—
384	C₂⁴	#41×C₅₉	1	1	yes	characteristic
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×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	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
407	Q₁₆	—	2	2	no	—
408	SD₁₆	—	2	4	no	—
409	D₈	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	4	4	no	—
414	M₁₆	—	4	4	no	—
415	M₁₆	C₂×D₄×C₅₉	1	4	yes	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	4	4	no	—
429	C₂×C₈	—	4	4	no	—
430	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
431	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
432	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
433	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
434	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
435	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
436	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
437	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
438	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
439	C₂×C₈	#41×C₅₉	1	2	yes	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
443	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	1	no	—
460	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
461	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
462	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
493	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
494	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
497	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
498	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
499	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
500	C₈	—	2	1	no	—
501	C₈	—	2	1	no	—
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	4	no	—
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	—	4	2	no	—
508	C₈	C₄×D₄×C₅₉	1	2	yes	—
509	C₈	C₄×D₄×C₅₉	1	2	yes	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	C₅₉×#443	1	2	yes	complemented
523	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
524	C₂²	C₅₉×#548	1	1	yes	characteristic
525	C₂²	C₅₉×#553	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	2	no	—
533	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
534	C₄	C₅₉×#520	1	1	yes	characteristic
535	C₄	D₄²×C₅₉	1	1	yes	characteristic
536	C₄	C₅₉×#547	1	1	yes	characteristic
537	C₂	—	2	1	no	—
538	C₂	—	2	1	no	—
539	C₂	—	2	2	no	—
540	C₂	—	4	1	no	—
541	C₂	—	8	2	no	—
542	C₂	C₅₉×#2361	1	1	yes	characteristic
543	C₂	C₂×C₅₉×#443	1	1	yes	characteristic
544	C₂	C₅₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂×C₂²⋊C₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#443	C₂	semidirect
3. C₅₉×#2933	C₂	semidirect
4. C₂²×#108×C₅₉	C₂	semidirect
5. C₅₉×#1974	C₂	semidirect
6. C₅₉×#1945	C₂	semidirect
7. C₅₉×#1929	C₂	semidirect
8. C₅₉×#1871	C₂	semidirect
9. C₅₉×#1866	C₂	semidirect
10. C₅₉×#1772	C₂	semidirect
11. C₈×C₂²⋊C₄×C₅₉	C₂	semidirect
17. C₅₉×#467	C₄	semidirect
18. C₅₉×#467	C₄	semidirect
19. C₅₉×#466	C₄	semidirect
20. C₅₉×#466	C₄	semidirect
21. C₅₉×#465	C₄	semidirect
22. C₅₉×#465	C₄	semidirect
88. #108×C₅₉	D₄	semidirect
237. #23018	C₅₉	direct (N × H)
250. C₂²×C₅₉	#443	semidirect
266. C₂×#443	C₂×C₅₉	semidirect
267. #2933	C₂×C₅₉	semidirect
268. C₂²×#108	C₂×C₅₉	semidirect
269. #1974	C₂×C₅₉	semidirect
270. #1945	C₂×C₅₉	semidirect
271. #1929	C₂×C₅₉	semidirect
272. #1871	C₂×C₅₉	semidirect
273. #1866	C₂×C₅₉	semidirect
274. #1772	C₂×C₅₉	semidirect
275. C₈×C₂²⋊C₄	C₂×C₅₉	semidirect
289. #467	C₄×C₅₉	semidirect
290. #467	C₄×C₅₉	semidirect
291. #466	C₄×C₅₉	semidirect
292. #466	C₄×C₅₉	semidirect
293. #465	C₄×C₅₉	semidirect
294. #465	C₄×C₅₉	semidirect
319. C₅₉	#23018	direct (N × H)
361. #108	D₄×C₅₉	semidirect
522. C₂²	C₅₉×#443	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₉×#3050	2
C₂×C₅₉×#443	2
C₅₉×#2933	2
C₂²×#108×C₅₉	2
C₅₉×#1974	2
C₅₉×#1945	2
C₅₉×#1929	2
C₅₉×#1871	2
C₅₉×#1866	2
C₅₉×#1772	2
C₈×C₂²⋊C₄×C₅₉	2
#23018	59

Subgroups — C59×#23018 #28435127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23018 #28435127