Subgroups — C₅₉×#24233 #28436342

Order 15104.

1336 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3499	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#456	C₂	1	2	yes	maximal, complemented
4	C₄×#137×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2038	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2005	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1966	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1806	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	C₂×#137×C₅₉	C₂²	1	2	yes	—
14	C₂×#137×C₅₉	C₂²	1	1	yes	characteristic
15	D₄×Q₈×C₅₉	—	2	1	no	—
16	D₄×Q₈×C₅₉	—	2	1	no	—
17	C₅₉×#547	—	2	1	no	—
18	C₅₉×#547	—	2	1	no	—
19	C₅₉×#547	—	2	2	no	—
20	C₅₉×#547	—	2	2	no	—
21	C₅₉×#536	—	2	2	no	—
22	C₅₉×#536	C₂²	1	2	yes	—
23	C₅₉×#532	—	2	1	no	—
24	C₅₉×#532	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
26	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
27	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#464	—	2	2	no	—
31	C₅₉×#462	—	2	1	no	—
32	C₅₉×#460	—	2	1	no	—
33	C₅₉×#456	—	2	8	no	—
34	C₅₉×#441	—	2	1	no	—
35	C₅₉×#440	—	2	1	no	—
36	C₄×Q₁₆×C₅₉	—	2	1	no	—
37	C₄×SD₁₆×C₅₉	—	2	1	no	—
38	C₅₉×#428	C₂²	1	1	yes	characteristic
39	C₅₉×#423	C₂²	1	1	yes	characteristic
40	C₂×#104×C₅₉	C₂²	1	2	yes	—
41	C₂×#104×C₅₉	C₂²	1	2	yes	—
42	C₂×#104×C₅₉	C₂²	1	2	yes	—
43	C₅₉×#419	C₂²	1	1	yes	characteristic
44	C₅₉×#417	C₂²	1	2	yes	—
45	C₅₉×#417	C₂²	1	1	yes	characteristic
46	C₂×#101×C₅₉	C₂²	1	2	yes	—
47	C₂×#101×C₅₉	C₂²	1	2	yes	—
48	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
49	C₅₉×#398	—	2	2	no	—
50	C₅₉×#391	C₂²	1	2	yes	—
51	C₅₉×#389	—	2	2	no	—
52	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
53	C₅₉×#339	C₂²	1	2	yes	—
54	2₋¹⁺⁴×C₅₉	—	2	4	no	—
55	2₋¹⁺⁴×C₅₉	—	2	4	no	—
56	2₋¹⁺⁴×C₅₉	—	4	2	no	—
57	2₋¹⁺⁴×C₅₉	—	4	2	no	—
58	C₂×#41×C₅₉	—	2	2	no	—
59	C₂×#41×C₅₉	—	2	2	no	—
60	C₂×#41×C₅₉	—	2	4	no	—
61	C₂×#41×C₅₉	C₂³	1	2	yes	—
62	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₅₉	—	2	2	no	—
64	C₂²×Q₈×C₅₉	—	2	2	no	—
65	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
67	#137×C₅₉	—	2	2	no	—
68	#137×C₅₉	—	2	4	no	—
69	#137×C₅₉	—	4	2	no	—
70	#137×C₅₉	D₄	1	4	yes	complemented
71	C₂×Q₁₆×C₅₉	—	2	1	no	—
72	C₂×Q₁₆×C₅₉	—	2	2	no	—
73	C₂×SD₁₆×C₅₉	—	2	1	no	—
74	C₂×SD₁₆×C₅₉	—	2	2	no	—
75	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
76	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₅₉	—	2	2	no	—
79	C₄⋊Q₈×C₅₉	—	2	2	no	—
80	C₄⋊Q₈×C₅₉	—	2	2	no	—
81	C₄⋊Q₈×C₅₉	—	2	4	no	—
82	C₄⋊Q₈×C₅₉	—	2	1	no	—
83	C₄⋊Q₈×C₅₉	—	2	1	no	—
84	C₄⋊Q₈×C₅₉	—	2	1	no	—
85	C₄⋊Q₈×C₅₉	—	2	1	no	—
86	C₄⋊Q₈×C₅₉	—	4	2	no	—
87	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
88	#127×C₅₉	D₄	1	1	yes	characteristic
89	#124×C₅₉	—	2	2	no	—
90	#124×C₅₉	D₄	1	2	yes	—
91	#123×C₅₉	—	2	4	no	—
92	#123×C₅₉	—	2	4	no	—
93	#123×C₅₉	—	2	4	no	—
94	C₂²⋊Q₈×C₅₉	—	2	4	no	—
95	C₂²⋊Q₈×C₅₉	—	2	4	no	—
96	C₂²⋊Q₈×C₅₉	—	2	2	no	—
97	C₂²⋊Q₈×C₅₉	—	2	2	no	—
98	#121×C₅₉	—	2	2	no	—
99	#121×C₅₉	—	2	2	no	—
100	#121×C₅₉	—	2	1	no	—
101	#121×C₅₉	—	2	1	no	—
102	C₄×Q₈×C₅₉	—	2	1	no	—
103	C₄×Q₈×C₅₉	—	2	1	no	—
104	C₄×Q₈×C₅₉	—	2	1	no	—
105	C₄×Q₈×C₅₉	—	2	1	no	—
106	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
107	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
108	C₄×D₄×C₅₉	—	2	2	no	—
109	C₄×D₄×C₅₉	—	2	2	no	—
110	C₄×D₄×C₅₉	—	2	1	no	—
111	C₄×D₄×C₅₉	—	2	1	no	—
112	C₄×D₄×C₅₉	—	2	1	no	—
113	C₄×D₄×C₅₉	—	2	1	no	—
114	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
115	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
116	#117×C₅₉	—	2	1	no	—
117	#117×C₅₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
119	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
120	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
121	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
122	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₅₉	—	2	1	no	—
127	C₂×C₄²×C₅₉	—	2	1	no	—
128	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
130	#107×C₅₉	—	2	1	no	—
131	#106×C₅₉	—	2	1	no	—
132	C₄⋊C₈×C₅₉	—	2	1	no	—
133	C₄⋊C₈×C₅₉	—	2	1	no	—
134	#104×C₅₉	—	2	4	no	—
135	#104×C₅₉	—	2	4	no	—
136	#104×C₅₉	—	4	2	no	—
137	#103×C₅₉	—	2	1	no	—
138	#103×C₅₉	—	2	2	no	—
139	#103×C₅₉	—	2	1	no	—
140	#103×C₅₉	—	2	1	no	—
141	#102×C₅₉	—	2	1	no	—
142	#102×C₅₉	—	2	2	no	—
143	#101×C₅₉	—	2	4	no	—
144	#101×C₅₉	—	4	2	no	—
145	#97×C₅₉	—	2	1	no	—
146	C₄×C₈×C₅₉	—	2	1	no	—
147	#95×C₅₉	—	2	1	no	—
148	#95×C₅₉	—	2	4	no	—
149	#41×C₅₉	—	2	1	no	—
150	#41×C₅₉	—	2	1	no	—
151	#41×C₅₉	—	2	2	no	—
152	#41×C₅₉	—	2	2	no	—
153	#41×C₅₉	—	2	2	no	—
154	#41×C₅₉	—	2	2	no	—
155	#41×C₅₉	—	4	4	no	—
156	#41×C₅₉	—	4	4	no	—
157	#41×C₅₉	—	4	8	no	—
158	#41×C₅₉	—	4	8	no	—
159	#41×C₅₉	—	4	4	no	—
160	#41×C₅₉	—	4	4	no	—
161	#41×C₅₉	C₂×D₄	1	2	yes	—
162	#41×C₅₉	#41	1	2	yes	—
163	C₂×Q₈×C₅₉	—	2	4	no	—
164	C₂×Q₈×C₅₉	—	2	2	no	—
165	C₂×Q₈×C₅₉	—	2	2	no	—
166	C₂×Q₈×C₅₉	—	2	2	no	—
167	C₂×Q₈×C₅₉	—	2	2	no	—
168	C₂×Q₈×C₅₉	—	2	2	no	—
169	C₂×Q₈×C₅₉	—	2	1	no	—
170	C₂×Q₈×C₅₉	—	2	2	no	—
171	C₂×Q₈×C₅₉	—	2	1	no	—
172	C₂×Q₈×C₅₉	—	2	1	no	—
173	C₂×Q₈×C₅₉	—	2	1	no	—
174	C₂×Q₈×C₅₉	—	2	1	no	—
175	C₂×Q₈×C₅₉	—	4	4	no	—
176	C₂×Q₈×C₅₉	—	4	4	no	—
177	C₂×Q₈×C₅₉	—	4	4	no	—
178	C₂×Q₈×C₅₉	—	4	4	no	—
179	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
180	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
181	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
182	C₂×D₄×C₅₉	—	2	1	no	—
183	C₂×D₄×C₅₉	—	2	4	no	—
184	C₂×D₄×C₅₉	—	2	2	no	—
185	C₂×D₄×C₅₉	—	2	1	no	—
186	C₂×D₄×C₅₉	—	2	1	no	—
187	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅₉	—	2	1	no	—
190	C₂²×C₄×C₅₉	—	2	4	no	—
191	C₂²×C₄×C₅₉	—	2	4	no	—
192	C₂²×C₄×C₅₉	—	2	2	no	—
193	C₂²×C₄×C₅₉	—	2	1	no	—
194	C₂²×C₄×C₅₉	—	2	1	no	—
195	C₂²×C₄×C₅₉	—	2	1	no	—
196	C₂²×C₄×C₅₉	—	2	2	no	—
197	C₂²×C₄×C₅₉	—	2	1	no	—
198	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
202	Q₁₆×C₅₉	—	2	4	no	—
203	Q₁₆×C₅₉	—	4	4	no	—
204	SD₁₆×C₅₉	—	2	4	no	—
205	SD₁₆×C₅₉	—	4	4	no	—
206	M₁₆×C₅₉	—	2	1	no	—
207	M₁₆×C₅₉	—	2	2	no	—
208	M₁₆×C₅₉	—	2	1	no	—
209	M₁₆×C₅₉	—	2	2	no	—
210	M₁₆×C₅₉	—	2	1	no	—
211	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
212	C₂×C₈×C₅₉	—	2	1	no	—
213	C₂×C₈×C₅₉	—	2	1	no	—
214	C₂×C₈×C₅₉	—	2	2	no	—
215	C₄⋊C₄×C₅₉	—	2	4	no	—
216	C₄⋊C₄×C₅₉	—	2	4	no	—
217	C₄⋊C₄×C₅₉	—	2	4	no	—
218	C₄⋊C₄×C₅₉	—	2	1	no	—
219	C₄⋊C₄×C₅₉	—	2	1	no	—
220	C₄⋊C₄×C₅₉	—	2	2	no	—
221	C₄⋊C₄×C₅₉	—	2	2	no	—
222	C₄⋊C₄×C₅₉	—	2	2	no	—
223	C₄⋊C₄×C₅₉	—	2	2	no	—
224	C₄⋊C₄×C₅₉	—	2	1	no	—
225	C₄⋊C₄×C₅₉	—	2	1	no	—
226	C₄⋊C₄×C₅₉	—	2	1	no	—
227	C₄⋊C₄×C₅₉	—	2	1	no	—
228	C₄⋊C₄×C₅₉	—	4	8	no	—
229	C₄⋊C₄×C₅₉	—	4	1	no	—
230	C₄⋊C₄×C₅₉	—	4	1	no	—
231	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
232	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
233	C₂²⋊C₄×C₅₉	—	2	4	no	—
234	C₂²⋊C₄×C₅₉	—	2	4	no	—
235	C₂²⋊C₄×C₅₉	—	2	1	no	—
236	C₂²⋊C₄×C₅₉	—	2	1	no	—
237	C₂²⋊C₄×C₅₉	—	2	1	no	—
238	C₂²⋊C₄×C₅₉	—	2	2	no	—
239	C₂²⋊C₄×C₅₉	—	2	2	no	—
240	C₄²×C₅₉	—	2	1	no	—
241	C₄²×C₅₉	—	2	1	no	—
242	C₄²×C₅₉	—	2	1	no	—
243	C₄²×C₅₉	—	2	2	no	—
244	C₄²×C₅₉	—	2	2	no	—
245	C₄²×C₅₉	—	4	1	no	—
246	C₄²×C₅₉	—	4	1	no	—
247	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
251	C₂³×C₅₉	—	2	1	no	—
252	C₂³×C₅₉	—	2	2	no	—
253	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₅₉	—	2	1	no	—
255	Q₈×C₅₉	—	2	2	no	—
256	Q₈×C₅₉	—	2	2	no	—
257	Q₈×C₅₉	—	2	2	no	—
258	Q₈×C₅₉	—	2	2	no	—
259	Q₈×C₅₉	—	4	8	no	—
260	Q₈×C₅₉	—	4	2	no	—
261	Q₈×C₅₉	—	4	1	no	—
262	Q₈×C₅₉	—	4	2	no	—
263	Q₈×C₅₉	—	4	2	no	—
264	Q₈×C₅₉	—	4	1	no	—
265	Q₈×C₅₉	—	4	2	no	—
266	Q₈×C₅₉	#121	1	2	yes	—
267	D₄×C₅₉	—	2	2	no	—
268	D₄×C₅₉	—	2	2	no	—
269	D₄×C₅₉	—	2	1	no	—
270	D₄×C₅₉	—	2	2	no	—
271	D₄×C₅₉	—	2	2	no	—
272	D₄×C₅₉	—	4	2	no	—
273	D₄×C₅₉	—	4	8	no	—
274	D₄×C₅₉	—	4	2	no	—
275	D₄×C₅₉	—	4	2	no	—
276	D₄×C₅₉	—	4	2	no	—
277	D₄×C₅₉	#121	1	2	yes	—
278	C₂×C₄×C₅₉	—	2	1	no	—
279	C₂×C₄×C₅₉	—	2	2	no	—
280	C₂×C₄×C₅₉	—	2	2	no	—
281	C₂×C₄×C₅₉	—	2	2	no	—
282	C₂×C₄×C₅₉	—	2	4	no	—
283	C₂×C₄×C₅₉	—	2	1	no	—
284	C₂×C₄×C₅₉	—	2	1	no	—
285	C₂×C₄×C₅₉	—	2	2	no	—
286	C₂×C₄×C₅₉	—	2	4	no	—
287	C₂×C₄×C₅₉	—	2	2	no	—
288	C₂×C₄×C₅₉	—	2	4	no	—
289	C₂×C₄×C₅₉	—	2	4	no	—
290	C₂×C₄×C₅₉	—	4	1	no	—
291	C₂×C₄×C₅₉	—	4	2	no	—
292	C₂×C₄×C₅₉	—	4	8	no	—
293	C₂×C₄×C₅₉	—	4	2	no	—
294	C₂×C₄×C₅₉	—	4	8	no	—
295	C₂×C₄×C₅₉	—	4	1	no	—
296	C₂×C₄×C₅₉	—	4	2	no	—
297	C₂×C₄×C₅₉	—	4	1	no	—
298	C₂×C₄×C₅₉	—	4	2	no	—
299	C₂×C₄×C₅₉	—	4	2	no	—
300	C₂×C₄×C₅₉	—	4	2	no	—
301	C₂×C₄×C₅₉	—	4	2	no	—
302	C₂×C₄×C₅₉	—	4	1	no	—
303	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
304	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
305	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
306	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
307	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
313	C₈×C₅₉	—	2	2	no	—
314	C₈×C₅₉	—	4	1	no	—
315	C₈×C₅₉	—	4	2	no	—
316	#24233	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂²×C₅₉	—	2	1	no	—
318	C₂²×C₅₉	—	2	1	no	—
319	C₂²×C₅₉	—	2	2	no	—
320	C₂²×C₅₉	—	4	1	no	—
321	C₂²×C₅₉	—	4	1	no	—
322	C₂²×C₅₉	—	4	2	no	—
323	C₂²×C₅₉	—	4	2	no	—
324	C₂²×C₅₉	—	4	2	no	—
325	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
326	C₂²×C₅₉	D₄²	1	1	yes	characteristic
327	C₂²×C₅₉	#546	1	1	yes	characteristic
328	C₄×C₅₉	—	2	2	no	—
329	C₄×C₅₉	—	2	1	no	—
330	C₄×C₅₉	—	2	1	no	—
331	C₄×C₅₉	—	2	1	no	—
332	C₄×C₅₉	—	4	4	no	—
333	C₄×C₅₉	—	4	4	no	—
334	C₄×C₅₉	—	4	2	no	—
335	C₄×C₅₉	—	4	2	no	—
336	C₄×C₅₉	—	4	1	no	—
337	C₄×C₅₉	—	4	1	no	—
338	C₄×C₅₉	—	8	1	no	—
339	C₄×C₅₉	#456	1	2	yes	complemented
340	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
341	C₄×C₅₉	#535	1	1	yes	characteristic
342	C₄×C₅₉	D₄²	1	1	yes	characteristic
343	C₄×C₅₉	#546	1	1	yes	characteristic
344	#3499	C₂×C₅₉	1	1	yes	characteristic
345	#3037	C₂×C₅₉	1	1	yes	characteristic, complemented
346	C₂×#456	C₂×C₅₉	1	2	yes	complemented
347	C₄×#137	C₂×C₅₉	1	1	yes	characteristic, complemented
348	#2546	C₂×C₅₉	1	1	yes	characteristic, complemented
349	#2038	C₂×C₅₉	1	2	yes	complemented
350	#2005	C₂×C₅₉	1	2	yes	complemented
351	#1980	C₂×C₅₉	1	1	yes	characteristic, complemented
352	#1966	C₂×C₅₉	1	1	yes	characteristic, complemented
353	#1806	C₂×C₅₉	1	1	yes	characteristic, complemented
354	#1793	C₂×C₅₉	1	2	yes	complemented
355	C₂×C₅₉	—	2	1	no	—
356	C₂×C₅₉	—	2	1	no	—
357	C₂×C₅₉	—	4	2	no	—
358	C₂×C₅₉	—	8	2	no	—
359	C₂×C₅₉	#2408	1	1	yes	characteristic
360	C₂×C₅₉	C₂×#456	1	1	yes	characteristic
361	C₂×C₅₉	#3020	1	1	yes	characteristic
362	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	2	yes	—
363	C₂×#137	C₂²×C₅₉	1	2	yes	—
364	C₂×#137	C₂²×C₅₉	1	1	yes	characteristic
365	D₄×Q₈	—	2	1	no	—
366	D₄×Q₈	—	2	1	no	—
367	#547	—	2	1	no	—
368	#547	—	2	1	no	—
369	#547	—	2	2	no	—
370	#547	—	2	2	no	—
371	#536	—	2	2	no	—
372	#536	C₂²×C₅₉	1	2	yes	—
373	#532	—	2	1	no	—
374	#532	C₂²×C₅₉	1	1	yes	characteristic
375	C₂×C₄⋊Q₈	—	2	1	no	—
376	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
377	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
378	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
379	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
380	#464	—	2	2	no	—
381	#462	—	2	1	no	—
382	#460	—	2	1	no	—
383	#456	—	2	8	no	—
384	#441	—	2	1	no	—
385	#440	—	2	1	no	—
386	C₄×Q₁₆	—	2	1	no	—
387	C₄×SD₁₆	—	2	1	no	—
388	#428	C₂²×C₅₉	1	1	yes	characteristic
389	#423	C₂²×C₅₉	1	1	yes	characteristic
390	C₂×#104	C₂²×C₅₉	1	2	yes	—
391	C₂×#104	C₂²×C₅₉	1	2	yes	—
392	C₂×#104	C₂²×C₅₉	1	2	yes	—
393	#419	C₂²×C₅₉	1	1	yes	characteristic
394	#417	C₂²×C₅₉	1	1	yes	characteristic
395	#417	C₂²×C₅₉	1	2	yes	—
396	C₂×#101	C₂²×C₅₉	1	2	yes	—
397	C₂×#101	C₂²×C₅₉	1	2	yes	—
398	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
399	#398	—	2	2	no	—
400	#391	C₂²×C₅₉	1	2	yes	—
401	#389	—	2	2	no	—
402	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
403	#339	C₂²×C₅₉	1	2	yes	—
404	C₅₉	#24233	1	1	yes	characteristic, direct product factor, Sylow
405	2₋¹⁺⁴	—	2	4	no	—
406	2₋¹⁺⁴	—	2	4	no	—
407	2₋¹⁺⁴	—	4	2	no	—
408	2₋¹⁺⁴	—	4	2	no	—
409	C₂×#41	—	2	2	no	—
410	C₂×#41	—	2	2	no	—
411	C₂×#41	—	2	4	no	—
412	C₂×#41	C₂³×C₅₉	1	2	yes	—
413	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
414	C₂²×Q₈	—	2	2	no	—
415	C₂²×Q₈	—	2	2	no	—
416	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
418	#137	—	2	2	no	—
419	#137	—	2	4	no	—
420	#137	—	4	2	no	—
421	#137	D₄×C₅₉	1	4	yes	complemented
422	C₂×Q₁₆	—	2	1	no	—
423	C₂×Q₁₆	—	2	2	no	—
424	C₂×SD₁₆	—	2	1	no	—
425	C₂×SD₁₆	—	2	2	no	—
426	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
427	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
428	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
429	C₄⋊Q₈	—	2	2	no	—
430	C₄⋊Q₈	—	2	2	no	—
431	C₄⋊Q₈	—	2	2	no	—
432	C₄⋊Q₈	—	2	4	no	—
433	C₄⋊Q₈	—	2	1	no	—
434	C₄⋊Q₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	—	4	2	no	—
438	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
439	#127	D₄×C₅₉	1	1	yes	characteristic
440	#124	—	2	2	no	—
441	#124	D₄×C₅₉	1	2	yes	—
442	#123	—	2	4	no	—
443	#123	—	2	4	no	—
444	#123	—	2	4	no	—
445	C₂²⋊Q₈	—	2	4	no	—
446	C₂²⋊Q₈	—	2	4	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	#121	—	2	2	no	—
450	#121	—	2	2	no	—
451	#121	—	2	1	no	—
452	#121	—	2	1	no	—
453	C₄×Q₈	—	2	1	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×Q₈	—	2	1	no	—
457	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
458	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
459	C₄×D₄	—	2	2	no	—
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
466	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
467	#117	—	2	1	no	—
468	#117	C₂³×C₅₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	—	2	2	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	4	no	—
474	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
475	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
477	C₂×C₄²	—	2	1	no	—
478	C₂×C₄²	—	2	1	no	—
479	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
480	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
481	#107	—	2	1	no	—
482	#106	—	2	1	no	—
483	C₄⋊C₈	—	2	1	no	—
484	C₄⋊C₈	—	2	1	no	—
485	#104	—	2	4	no	—
486	#104	—	2	4	no	—
487	#104	—	4	2	no	—
488	#103	—	2	1	no	—
489	#103	—	2	2	no	—
490	#103	—	2	1	no	—
491	#103	—	2	1	no	—
492	#102	—	2	1	no	—
493	#102	—	2	2	no	—
494	#101	—	2	4	no	—
495	#101	—	4	2	no	—
496	#97	—	2	1	no	—
497	C₄×C₈	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	4	no	—
500	#41	—	2	1	no	—
501	#41	—	2	1	no	—
502	#41	—	2	2	no	—
503	#41	—	2	2	no	—
504	#41	—	2	2	no	—
505	#41	—	2	2	no	—
506	#41	—	4	4	no	—
507	#41	—	4	4	no	—
508	#41	—	4	8	no	—
509	#41	—	4	8	no	—
510	#41	—	4	4	no	—
511	#41	—	4	4	no	—
512	#41	C₂×D₄×C₅₉	1	2	yes	—
513	#41	#41×C₅₉	1	2	yes	—
514	C₂×Q₈	—	2	4	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	2	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	4	4	no	—
527	C₂×Q₈	—	4	4	no	—
528	C₂×Q₈	—	4	4	no	—
529	C₂×Q₈	—	4	4	no	—
530	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
531	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
532	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
539	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
550	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
553	Q₁₆	—	2	4	no	—
554	Q₁₆	—	4	4	no	—
555	SD₁₆	—	2	4	no	—
556	SD₁₆	—	4	4	no	—
557	M₁₆	—	2	1	no	—
558	M₁₆	—	2	2	no	—
559	M₁₆	—	2	1	no	—
560	M₁₆	—	2	2	no	—
561	M₁₆	—	2	1	no	—
562	M₁₆	C₂×D₄×C₅₉	1	2	yes	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	4	8	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
583	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	1	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	4	1	no	—
597	C₄²	—	4	1	no	—
598	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
599	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
600	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
601	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
602	C₂³	—	2	1	no	—
603	C₂³	—	2	2	no	—
604	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
605	Q₈	—	2	1	no	—
606	Q₈	—	2	2	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	2	2	no	—
610	Q₈	—	4	8	no	—
611	Q₈	—	4	2	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	2	no	—
614	Q₈	—	4	2	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	2	no	—
617	Q₈	#121×C₅₉	1	2	yes	—
618	D₄	—	2	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	1	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	2	no	—
626	D₄	—	4	2	no	—
627	D₄	—	4	2	no	—
628	D₄	#121×C₅₉	1	2	yes	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	8	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
655	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
656	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
657	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
658	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
661	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
662	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
663	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
664	C₈	—	2	2	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	2	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
676	C₂²	D₄²×C₅₉	1	1	yes	characteristic
677	C₂²	C₅₉×#546	1	1	yes	characteristic
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	4	4	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	8	1	no	—
689	C₄	C₅₉×#456	1	2	yes	complemented
690	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
691	C₄	C₅₉×#535	1	1	yes	characteristic
692	C₄	D₄²×C₅₉	1	1	yes	characteristic
693	C₄	C₅₉×#546	1	1	yes	characteristic
694	C₂	—	2	1	no	—
695	C₂	—	2	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	8	2	no	—
698	C₂	C₅₉×#2408	1	1	yes	characteristic
699	C₂	C₂×C₅₉×#456	1	1	yes	characteristic
700	C₂	C₅₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#3499	C₂
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. C₅₉×#3037	C₂	semidirect
3. C₂×C₅₉×#456	C₂	semidirect
4. C₄×#137×C₅₉	C₂	semidirect
5. C₅₉×#2546	C₂	semidirect
6. C₅₉×#2038	C₂	semidirect
7. C₅₉×#2005	C₂	semidirect
8. C₅₉×#1980	C₂	semidirect
9. C₅₉×#1966	C₂	semidirect
10. C₅₉×#1806	C₂	semidirect
11. C₅₉×#1793	C₂	semidirect
70. #137×C₅₉	D₄	semidirect
316. #24233	C₅₉	direct (N × H)
339. C₄×C₅₉	#456	semidirect
345. #3037	C₂×C₅₉	semidirect
346. C₂×#456	C₂×C₅₉	semidirect
347. C₄×#137	C₂×C₅₉	semidirect
348. #2546	C₂×C₅₉	semidirect
349. #2038	C₂×C₅₉	semidirect
350. #2005	C₂×C₅₉	semidirect
351. #1980	C₂×C₅₉	semidirect
352. #1966	C₂×C₅₉	semidirect
353. #1806	C₂×C₅₉	semidirect
354. #1793	C₂×C₅₉	semidirect
404. C₅₉	#24233	direct (N × H)
421. #137	D₄×C₅₉	semidirect
689. C₄	C₅₉×#456	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3499	2
C₅₉×#3037	2
C₂×C₅₉×#456	2
C₄×#137×C₅₉	2
C₅₉×#2546	2
C₅₉×#2038	2
C₅₉×#2005	2
C₅₉×#1980	2
C₅₉×#1966	2
C₅₉×#1806	2
C₅₉×#1793	2
#24233	59

Subgroups — C59×#24233 #28436342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24233 #28436342