Subgroups — C₅₉×#21076 #28433185

Order 15104.

1022 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#2896	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×#417	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉×#413	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1931	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1930	C₂	1	4	yes	maximal, complemented
8	C₂×C₅₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1738	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#428	—	2	2	no	—
18	C₅₉×#428	C₂²	1	4	yes	—
19	C₂×#107×C₅₉	—	2	1	no	—
20	C₂×#106×C₅₉	—	2	1	no	—
21	C₅₉×#419	C₂²	1	2	yes	—
22	C₅₉×#418	C₂²	1	2	yes	—
23	C₅₉×#417	—	2	2	no	—
24	C₅₉×#417	—	2	2	no	—
25	C₅₉×#417	—	2	1	no	—
26	C₅₉×#417	—	2	1	no	—
27	C₅₉×#416	—	2	2	no	—
28	C₂×#103×C₅₉	C₂²	1	2	yes	—
29	C₂×#102×C₅₉	C₂²	1	2	yes	—
30	C₅₉×#413	C₄	1	8	yes	complemented
31	C₂×#101×C₅₉	C₂²	1	2	yes	—
32	C₂×#100×C₅₉	C₂²	1	2	yes	—
33	C₅₉×#405	—	2	2	no	—
34	C₅₉×#405	C₂²	1	4	yes	—
35	C₄×M₁₆×C₅₉	—	2	2	no	—
36	C₅₉×#343	C₂²	1	4	yes	—
37	C₅₉×#341	C₂²	1	4	yes	—
38	C₂×#41×C₅₉	—	2	2	no	—
39	C₂×#41×C₅₉	—	2	1	no	—
40	C₂×#41×C₅₉	—	2	1	no	—
41	C₂×#41×C₅₉	—	2	1	no	—
42	C₂×#41×C₅₉	—	2	1	no	—
43	C₂×#41×C₅₉	—	2	2	no	—
44	C₂×#41×C₅₉	—	2	2	no	—
45	C₂×#41×C₅₉	C₂×C₄	1	4	yes	—
46	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₅₉	—	2	1	no	—
48	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₅₉	—	2	1	no	—
50	C₂³×C₄×C₅₉	—	2	1	no	—
51	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₅₉	—	2	1	no	—
53	C₂×M₁₆×C₅₉	—	2	1	no	—
54	C₂×M₁₆×C₅₉	—	2	2	no	—
55	C₂×M₁₆×C₅₉	—	2	2	no	—
56	C₂×M₁₆×C₅₉	—	2	2	no	—
57	C₂×M₁₆×C₅₉	—	2	2	no	—
58	C₂×M₁₆×C₅₉	—	2	1	no	—
59	C₂×M₁₆×C₅₉	—	2	2	no	—
60	C₂×M₁₆×C₅₉	—	2	2	no	—
61	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	—
62	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	—
63	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
64	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
65	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
66	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
67	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₅₉	—	2	1	no	—
69	C₂²×C₈×C₅₉	—	2	1	no	—
70	C₂²×C₈×C₅₉	—	2	1	no	—
71	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
72	#117×C₅₉	—	2	1	no	—
73	#117×C₅₉	—	2	1	no	—
74	#117×C₅₉	D₄	1	2	yes	—
75	#117×C₅₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
78	C₂×C₄⋊C₄×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	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
85	C₂×C₄²×C₅₉	—	2	1	no	—
86	#107×C₅₉	—	2	4	no	—
87	#106×C₅₉	—	2	4	no	—
88	#103×C₅₉	—	2	4	no	—
89	#103×C₅₉	—	2	2	no	—
90	#103×C₅₉	—	2	2	no	—
91	#102×C₅₉	—	2	4	no	—
92	#102×C₅₉	—	2	2	no	—
93	#102×C₅₉	—	2	2	no	—
94	#101×C₅₉	C₂×C₄	1	8	yes	complemented
95	#100×C₅₉	C₂×C₄	1	8	yes	complemented
96	#97×C₅₉	—	2	4	no	—
97	C₄×C₈×C₅₉	—	2	4	no	—
98	C₂⁴×C₅₉	—	2	1	no	—
99	C₂⁴×C₅₉	#41	1	1	yes	characteristic
100	#41×C₅₉	—	2	4	no	—
101	#41×C₅₉	—	2	4	no	—
102	#41×C₅₉	—	2	4	no	—
103	#41×C₅₉	—	2	4	no	—
104	#41×C₅₉	—	4	2	no	—
105	#41×C₅₉	—	4	2	no	—
106	#41×C₅₉	—	4	2	no	—
107	#41×C₅₉	—	4	2	no	—
108	C₂×Q₈×C₅₉	—	2	1	no	—
109	C₂×Q₈×C₅₉	—	2	1	no	—
110	C₂×Q₈×C₅₉	—	2	1	no	—
111	C₂×Q₈×C₅₉	—	2	1	no	—
112	C₂×Q₈×C₅₉	—	2	1	no	—
113	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
114	C₂×D₄×C₅₉	—	2	4	no	—
115	C₂×D₄×C₅₉	—	2	1	no	—
116	C₂×D₄×C₅₉	—	2	1	no	—
117	C₂×D₄×C₅₉	—	2	1	no	—
118	C₂×D₄×C₅₉	—	2	1	no	—
119	C₂×D₄×C₅₉	—	2	1	no	—
120	C₂×D₄×C₅₉	—	4	1	no	—
121	C₂×D₄×C₅₉	—	4	1	no	—
122	C₂×D₄×C₅₉	—	4	2	no	—
123	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
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	4	no	—
128	C₂²×C₄×C₅₉	—	2	2	no	—
129	C₂²×C₄×C₅₉	—	4	1	no	—
130	C₂²×C₄×C₅₉	—	4	1	no	—
131	C₂²×C₄×C₅₉	—	4	2	no	—
132	C₂²×C₄×C₅₉	—	4	1	no	—
133	C₂²×C₄×C₅₉	—	4	1	no	—
134	C₂²×C₄×C₅₉	—	8	2	no	—
135	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
141	C₂²×C₄×C₅₉	#41	1	2	yes	—
142	C₂²×C₄×C₅₉	#41	1	2	yes	—
143	C₂²×C₄×C₅₉	#41	1	2	yes	—
144	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₅₉	—	2	4	no	—
146	M₁₆×C₅₉	—	2	4	no	—
147	M₁₆×C₅₉	—	2	4	no	—
148	M₁₆×C₅₉	—	2	4	no	—
149	M₁₆×C₅₉	—	2	2	no	—
150	M₁₆×C₅₉	—	2	2	no	—
151	M₁₆×C₅₉	—	2	2	no	—
152	M₁₆×C₅₉	—	2	2	no	—
153	M₁₆×C₅₉	—	4	2	no	—
154	M₁₆×C₅₉	C₂²×C₄	1	4	yes	—
155	M₁₆×C₅₉	C₂²×C₄	1	4	yes	—
156	C₂×C₈×C₅₉	—	2	4	no	—
157	C₂×C₈×C₅₉	—	2	4	no	—
158	C₂×C₈×C₅₉	—	2	2	no	—
159	C₂×C₈×C₅₉	—	2	2	no	—
160	C₂×C₈×C₅₉	—	2	2	no	—
161	C₂×C₈×C₅₉	—	2	2	no	—
162	C₂×C₈×C₅₉	—	2	2	no	—
163	C₂×C₈×C₅₉	—	4	2	no	—
164	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	—	2	2	no	—
168	C₄⋊C₄×C₅₉	—	2	2	no	—
169	C₄⋊C₄×C₅₉	—	4	1	no	—
170	C₄⋊C₄×C₅₉	—	4	1	no	—
171	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₅₉	—	2	2	no	—
174	C₂²⋊C₄×C₅₉	—	2	2	no	—
175	C₄²×C₅₉	—	2	2	no	—
176	C₄²×C₅₉	—	2	2	no	—
177	C₂³×C₅₉	—	2	2	no	—
178	C₂³×C₅₉	—	4	1	no	—
179	C₂³×C₅₉	—	4	1	no	—
180	C₂³×C₅₉	—	4	1	no	—
181	C₂³×C₅₉	—	4	1	no	—
182	C₂³×C₅₉	—	8	1	no	—
183	C₂³×C₅₉	—	8	1	no	—
184	C₂³×C₅₉	#117	1	2	yes	—
185	C₂³×C₅₉	#121	1	1	yes	characteristic
186	C₂³×C₅₉	#121	1	1	yes	characteristic
187	C₂³×C₅₉	#126	1	2	yes	—
188	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
189	Q₈×C₅₉	—	2	2	no	—
190	Q₈×C₅₉	—	2	2	no	—
191	Q₈×C₅₉	—	4	1	no	—
192	Q₈×C₅₉	—	4	1	no	—
193	D₄×C₅₉	—	2	2	no	—
194	D₄×C₅₉	—	2	2	no	—
195	D₄×C₅₉	—	4	4	no	—
196	D₄×C₅₉	—	4	4	no	—
197	D₄×C₅₉	—	4	1	no	—
198	D₄×C₅₉	—	4	1	no	—
199	C₂×C₄×C₅₉	—	2	2	no	—
200	C₂×C₄×C₅₉	—	2	2	no	—
201	C₂×C₄×C₅₉	—	2	2	no	—
202	C₂×C₄×C₅₉	—	4	1	no	—
203	C₂×C₄×C₅₉	—	4	1	no	—
204	C₂×C₄×C₅₉	—	4	4	no	—
205	C₂×C₄×C₅₉	—	4	4	no	—
206	C₂×C₄×C₅₉	—	4	2	no	—
207	C₂×C₄×C₅₉	—	8	1	no	—
208	C₂×C₄×C₅₉	—	8	1	no	—
209	C₂×C₄×C₅₉	—	8	2	no	—
210	C₂×C₄×C₅₉	—	8	2	no	—
211	C₂×C₄×C₅₉	—	8	2	no	—
212	C₂×C₄×C₅₉	#117	1	2	yes	—
213	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
218	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
219	C₂×C₄×C₅₉	#123	1	2	yes	—
220	C₂×C₄×C₅₉	#123	1	2	yes	—
221	C₂×C₄×C₅₉	#124	1	2	yes	—
222	C₂×C₄×C₅₉	#124	1	2	yes	—
223	C₂×C₄×C₅₉	#126	1	2	yes	—
224	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
230	C₈×C₅₉	—	2	4	no	—
231	C₈×C₅₉	—	2	4	no	—
232	C₈×C₅₉	—	2	4	no	—
233	C₈×C₅₉	—	4	2	no	—
234	#21076	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₅₉	—	2	1	no	—
236	C₂²×C₅₉	—	2	1	no	—
237	C₂²×C₅₉	—	2	1	no	—
238	C₂²×C₅₉	—	2	1	no	—
239	C₂²×C₅₉	—	2	1	no	—
240	C₂²×C₅₉	—	2	1	no	—
241	C₂²×C₅₉	—	4	2	no	—
242	C₂²×C₅₉	—	4	2	no	—
243	C₂²×C₅₉	—	4	2	no	—
244	C₂²×C₅₉	—	8	2	no	—
245	C₂²×C₅₉	—	8	2	no	—
246	C₂²×C₅₉	—	8	1	no	—
247	C₂²×C₅₉	—	8	1	no	—
248	C₂²×C₅₉	#388	1	2	yes	—
249	C₂²×C₅₉	#388	1	2	yes	—
250	C₂²×C₅₉	C₂×#117	1	1	yes	characteristic
251	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
252	C₂²×C₅₉	C₂×#126	1	1	yes	characteristic
253	C₄×C₅₉	—	4	2	no	—
254	C₄×C₅₉	—	4	2	no	—
255	C₄×C₅₉	—	4	2	no	—
256	C₄×C₅₉	—	8	2	no	—
257	C₄×C₅₉	#388	1	2	yes	—
258	C₄×C₅₉	#388	1	2	yes	—
259	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
261	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
262	C₄×C₅₉	C₂×#124	1	1	yes	characteristic
263	C₂×#428	C₂×C₅₉	1	1	yes	characteristic, complemented
264	#2896	C₂×C₅₉	1	1	yes	characteristic
265	C₂×#417	C₂×C₅₉	1	1	yes	characteristic
266	C₂×#413	C₂×C₅₉	1	1	yes	characteristic
267	#2873	C₂×C₅₉	1	1	yes	characteristic, complemented
268	#1931	C₂×C₅₉	1	4	yes	complemented
269	#1930	C₂×C₅₉	1	4	yes	complemented
270	C₂×#343	C₂×C₅₉	1	1	yes	characteristic, complemented
271	#1738	C₂×C₅₉	1	1	yes	characteristic, complemented
272	C₂×C₅₉	—	2	1	no	—
273	C₂×C₅₉	—	2	1	no	—
274	C₂×C₅₉	—	2	2	no	—
275	C₂×C₅₉	—	2	2	no	—
276	C₂×C₅₉	—	8	2	no	—
277	C₂×C₅₉	C₂×#388	1	1	yes	characteristic
278	C₂×C₅₉	#3068	1	1	yes	characteristic
279	C₂×C₅₉	#3069	1	1	yes	characteristic
280	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
281	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
282	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
283	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
284	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
285	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
287	#428	—	2	2	no	—
288	#428	C₂²×C₅₉	1	4	yes	—
289	C₂×#107	—	2	1	no	—
290	C₂×#106	—	2	1	no	—
291	#419	C₂²×C₅₉	1	2	yes	—
292	#418	C₂²×C₅₉	1	2	yes	—
293	#417	—	2	2	no	—
294	#417	—	2	2	no	—
295	#417	—	2	1	no	—
296	#417	—	2	1	no	—
297	#416	—	2	2	no	—
298	C₂×#103	C₂²×C₅₉	1	2	yes	—
299	C₂×#102	C₂²×C₅₉	1	2	yes	—
300	#413	C₄×C₅₉	1	8	yes	complemented
301	C₂×#101	C₂²×C₅₉	1	2	yes	—
302	C₂×#100	C₂²×C₅₉	1	2	yes	—
303	#405	—	2	2	no	—
304	#405	C₂²×C₅₉	1	4	yes	—
305	C₄×M₁₆	—	2	2	no	—
306	#343	C₂²×C₅₉	1	4	yes	—
307	#341	C₂²×C₅₉	1	4	yes	—
308	C₅₉	#21076	1	1	yes	characteristic, direct product factor, Sylow
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	1	no	—
311	C₂×#41	—	2	1	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	C₂×C₄×C₅₉	1	4	yes	—
317	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	—	2	2	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	C₂×C₄×C₅₉	1	4	yes	—
333	C₂×M₁₆	C₂×C₄×C₅₉	1	4	yes	—
334	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
335	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
336	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
337	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
338	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	D₄×C₅₉	1	2	yes	—
346	#117	C₂³×C₅₉	1	2	yes	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	#107	—	2	4	no	—
358	#106	—	2	4	no	—
359	#103	—	2	4	no	—
360	#103	—	2	2	no	—
361	#103	—	2	2	no	—
362	#102	—	2	4	no	—
363	#102	—	2	2	no	—
364	#102	—	2	2	no	—
365	#101	C₂×C₄×C₅₉	1	8	yes	complemented
366	#100	C₂×C₄×C₅₉	1	8	yes	complemented
367	#97	—	2	4	no	—
368	C₄×C₈	—	2	4	no	—
369	C₂⁴	—	2	1	no	—
370	C₂⁴	#41×C₅₉	1	1	yes	characteristic
371	#41	—	2	4	no	—
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	2	4	no	—
375	#41	—	4	2	no	—
376	#41	—	4	2	no	—
377	#41	—	4	2	no	—
378	#41	—	4	2	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	8	2	no	—
406	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
411	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
412	C₂²×C₄	#41×C₅₉	1	2	yes	—
413	C₂²×C₄	#41×C₅₉	1	2	yes	—
414	C₂²×C₄	#41×C₅₉	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
416	M₁₆	—	2	4	no	—
417	M₁₆	—	2	4	no	—
418	M₁₆	—	2	4	no	—
419	M₁₆	—	2	4	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	2	2	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	4	2	no	—
425	M₁₆	C₂²×C₄×C₅₉	1	4	yes	—
426	M₁₆	C₂²×C₄×C₅₉	1	4	yes	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	4	2	no	—
435	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	1	no	—
453	C₂³	—	8	1	no	—
454	C₂³	—	8	1	no	—
455	C₂³	#117×C₅₉	1	2	yes	—
456	C₂³	#121×C₅₉	1	1	yes	characteristic
457	C₂³	#121×C₅₉	1	1	yes	characteristic
458	C₂³	#126×C₅₉	1	2	yes	—
459	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	4	1	no	—
463	Q₈	—	4	1	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	4	4	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	1	no	—
469	D₄	—	4	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	1	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	#117×C₅₉	1	2	yes	—
484	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
485	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
486	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
487	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
488	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
489	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
490	C₂×C₄	#123×C₅₉	1	2	yes	—
491	C₂×C₄	#123×C₅₉	1	2	yes	—
492	C₂×C₄	#124×C₅₉	1	2	yes	—
493	C₂×C₄	#124×C₅₉	1	2	yes	—
494	C₂×C₄	#126×C₅₉	1	2	yes	—
495	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
498	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	2	4	no	—
503	C₈	—	2	4	no	—
504	C₈	—	4	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	1	no	—
517	C₂²	—	8	1	no	—
518	C₂²	C₅₉×#388	1	2	yes	—
519	C₂²	C₅₉×#388	1	2	yes	—
520	C₂²	C₂×#117×C₅₉	1	1	yes	characteristic
521	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
522	C₂²	C₂×#126×C₅₉	1	1	yes	characteristic
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	8	2	no	—
527	C₄	C₅₉×#388	1	2	yes	—
528	C₄	C₅₉×#388	1	2	yes	—
529	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
530	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
531	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
532	C₄	C₂×#124×C₅₉	1	1	yes	characteristic
533	C₂	—	2	1	no	—
534	C₂	—	2	1	no	—
535	C₂	—	2	2	no	—
536	C₂	—	2	2	no	—
537	C₂	—	8	2	no	—
538	C₂	C₂×C₅₉×#388	1	1	yes	characteristic
539	C₂	C₅₉×#3068	1	1	yes	characteristic
540	C₂	C₅₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#428	C₂	semidirect
5. C₅₉×#2873	C₂	semidirect
6. C₅₉×#1931	C₂	semidirect
7. C₅₉×#1930	C₂	semidirect
8. C₂×C₅₉×#343	C₂	semidirect
9. C₅₉×#1738	C₂	semidirect
30. C₅₉×#413	C₄	semidirect
94. #101×C₅₉	C₂×C₄	semidirect
95. #100×C₅₉	C₂×C₄	semidirect
234. #21076	C₅₉	direct (N × H)
263. C₂×#428	C₂×C₅₉	semidirect
267. #2873	C₂×C₅₉	semidirect
268. #1931	C₂×C₅₉	semidirect
269. #1930	C₂×C₅₉	semidirect
270. C₂×#343	C₂×C₅₉	semidirect
271. #1738	C₂×C₅₉	semidirect
300. #413	C₄×C₅₉	semidirect
308. C₅₉	#21076	direct (N × H)
365. #101	C₂×C₄×C₅₉	semidirect
366. #100	C₂×C₄×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×#428	2
C₅₉×#2896	2
C₂×C₅₉×#417	2
C₂×C₅₉×#413	2
C₅₉×#2873	2
C₅₉×#1931	2
C₅₉×#1930	2
C₂×C₅₉×#343	2
C₅₉×#1738	2
#21076	59

Subgroups — C59×#21076 #28433185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21076 #28433185