Subgroups — C₅₉×#35532 #28447641

Order 15104.

2462 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2567	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2566	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2565	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2542	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2449	C₂	1	8	yes	maximal, complemented
8	C₅₉×#2441	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2440	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2311	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2297	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#544	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
19	C₂×#125×C₅₉	C₂²	1	2	yes	—
20	C₂×#125×C₅₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	8	yes	—
23	C₅₉×#520	—	2	8	no	—
24	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₅₉	C₂²	1	2	yes	—
30	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
35	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#399	C₂²	1	8	yes	—
37	C₅₉×#398	C₂²	1	8	yes	—
38	C₅₉×#396	C₂²	1	8	yes	—
39	C₅₉×#395	C₂²	1	8	yes	—
40	C₅₉×#391	C₂²	1	1	yes	characteristic
41	C₅₉×#391	C₂²	1	1	yes	characteristic
42	C₅₉×#391	C₂²	1	2	yes	—
43	C₅₉×#390	C₂²	1	1	yes	characteristic
44	C₅₉×#390	C₂²	1	2	yes	—
45	C₅₉×#390	C₂²	1	1	yes	characteristic
46	C₅₉×#389	C₂²	1	2	yes	—
47	C₅₉×#389	C₂²	1	2	yes	—
48	C₅₉×#389	C₂²	1	8	yes	—
49	C₅₉×#389	C₂²	1	4	yes	—
50	C₅₉×#387	C₂²	1	8	yes	—
51	C₅₉×#386	C₂²	1	4	yes	—
52	C₅₉×#386	C₂²	1	4	yes	—
53	C₅₉×#385	C₂²	1	4	yes	—
54	C₅₉×#385	C₂²	1	8	yes	—
55	C₅₉×#385	C₂²	1	4	yes	—
56	C₅₉×#384	C₂²	1	2	yes	—
57	C₅₉×#384	C₂²	1	2	yes	—
58	C₅₉×#384	C₂²	1	4	yes	—
59	C₅₉×#384	C₂²	1	2	yes	—
60	C₅₉×#382	C₂²	1	2	yes	—
61	C₅₉×#380	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
65	C₂×#41×C₅₉	—	2	4	no	—
66	C₂×#41×C₅₉	—	2	4	no	—
67	C₂×#41×C₅₉	Q₈	1	8	yes	complemented
68	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₅₉	—	2	8	no	—
79	C₄⋊Q₈×C₅₉	—	2	8	no	—
80	#125×C₅₉	—	2	8	no	—
81	#125×C₅₉	—	2	8	no	—
82	C₂²⋊Q₈×C₅₉	—	2	16	no	—
83	C₂²⋊Q₈×C₅₉	—	4	16	no	—
84	C₄×Q₈×C₅₉	—	2	8	no	—
85	C₄×D₄×C₅₉	—	2	16	no	—
86	C₄×D₄×C₅₉	—	2	8	no	—
87	#117×C₅₉	—	2	4	no	—
88	#117×C₅₉	—	2	4	no	—
89	#117×C₅₉	—	2	8	no	—
90	#117×C₅₉	D₄	1	8	yes	—
91	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
92	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
93	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
94	C₂×C₄⋊C₄×C₅₉	—	4	8	no	—
95	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₅₉	—	2	4	no	—
121	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
127	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
128	#95×C₅₉	C₂³	1	4	yes	—
129	#95×C₅₉	C₂³	1	4	yes	—
130	#95×C₅₉	C₂³	1	4	yes	—
131	#95×C₅₉	C₂³	1	4	yes	—
132	#95×C₅₉	C₂³	1	8	yes	—
133	#95×C₅₉	C₂³	1	8	yes	—
134	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
135	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
136	#41×C₅₉	—	2	32	no	—
137	C₂×Q₈×C₅₉	—	2	2	no	—
138	C₂×Q₈×C₅₉	—	2	8	no	—
139	C₂×Q₈×C₅₉	—	2	2	no	—
140	C₂×Q₈×C₅₉	—	4	8	no	—
141	C₂×Q₈×C₅₉	C₂×Q₈	1	4	yes	—
142	C₂×D₄×C₅₉	—	2	4	no	—
143	C₂×D₄×C₅₉	—	2	4	no	—
144	C₂×D₄×C₅₉	—	2	2	no	—
145	C₂×D₄×C₅₉	—	2	2	no	—
146	C₂×D₄×C₅₉	C₂×Q₈	1	8	yes	—
147	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
148	C₂²×C₄×C₅₉	—	2	4	no	—
149	C₂²×C₄×C₅₉	—	2	4	no	—
150	C₂²×C₄×C₅₉	—	2	4	no	—
151	C₂²×C₄×C₅₉	—	2	4	no	—
152	C₂²×C₄×C₅₉	—	2	4	no	—
153	C₂²×C₄×C₅₉	—	2	4	no	—
154	C₂²×C₄×C₅₉	—	2	4	no	—
155	C₂²×C₄×C₅₉	—	2	8	no	—
156	C₂²×C₄×C₅₉	—	4	4	no	—
157	C₂²×C₄×C₅₉	—	4	4	no	—
158	C₂²×C₄×C₅₉	—	4	8	no	—
159	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	—
161	C₂²×C₄×C₅₉	C₂×Q₈	1	4	yes	—
162	C₂²×C₄×C₅₉	#41	1	4	yes	—
163	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
175	C₄⋊C₄×C₅₉	—	2	4	no	—
176	C₄⋊C₄×C₅₉	—	2	8	no	—
177	C₄⋊C₄×C₅₉	—	2	4	no	—
178	C₄⋊C₄×C₅₉	—	2	4	no	—
179	C₄⋊C₄×C₅₉	—	2	4	no	—
180	C₄⋊C₄×C₅₉	—	2	2	no	—
181	C₄⋊C₄×C₅₉	—	2	2	no	—
182	C₄⋊C₄×C₅₉	—	2	8	no	—
183	C₄⋊C₄×C₅₉	—	2	8	no	—
184	C₄⋊C₄×C₅₉	—	2	8	no	—
185	C₄⋊C₄×C₅₉	—	2	4	no	—
186	C₄⋊C₄×C₅₉	—	2	16	no	—
187	C₄⋊C₄×C₅₉	—	2	8	no	—
188	C₄⋊C₄×C₅₉	—	2	8	no	—
189	C₄⋊C₄×C₅₉	—	4	8	no	—
190	C₄⋊C₄×C₅₉	—	4	8	no	—
191	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
192	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
193	C₂²⋊C₄×C₅₉	—	2	4	no	—
194	C₂²⋊C₄×C₅₉	—	2	4	no	—
195	C₂²⋊C₄×C₅₉	—	2	8	no	—
196	C₂²⋊C₄×C₅₉	—	2	8	no	—
197	C₂²⋊C₄×C₅₉	—	2	8	no	—
198	C₂²⋊C₄×C₅₉	—	4	8	no	—
199	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
200	C₄²×C₅₉	—	2	8	no	—
201	C₄²×C₅₉	—	2	4	no	—
202	C₄²×C₅₉	—	2	2	no	—
203	C₄²×C₅₉	—	2	2	no	—
204	C₄²×C₅₉	—	2	4	no	—
205	C₄²×C₅₉	—	2	4	no	—
206	C₄²×C₅₉	C₂×D₄	1	8	yes	—
207	C₂³×C₅₉	—	2	2	no	—
208	C₂³×C₅₉	—	2	2	no	—
209	C₂³×C₅₉	—	2	2	no	—
210	C₂³×C₅₉	—	2	2	no	—
211	C₂³×C₅₉	—	2	4	no	—
212	C₂³×C₅₉	—	2	4	no	—
213	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
214	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
215	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
216	C₂³×C₅₉	C₂×#41	1	2	yes	—
217	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
218	Q₈×C₅₉	—	2	8	no	—
219	Q₈×C₅₉	—	8	8	no	—
220	D₄×C₅₉	—	2	16	no	—
221	D₄×C₅₉	—	2	8	no	—
222	C₂×C₄×C₅₉	—	2	16	no	—
223	C₂×C₄×C₅₉	—	2	2	no	—
224	C₂×C₄×C₅₉	—	2	2	no	—
225	C₂×C₄×C₅₉	—	2	2	no	—
226	C₂×C₄×C₅₉	—	2	2	no	—
227	C₂×C₄×C₅₉	—	2	4	no	—
228	C₂×C₄×C₅₉	—	2	2	no	—
229	C₂×C₄×C₅₉	—	2	4	no	—
230	C₂×C₄×C₅₉	—	2	2	no	—
231	C₂×C₄×C₅₉	—	2	16	no	—
232	C₂×C₄×C₅₉	—	2	2	no	—
233	C₂×C₄×C₅₉	—	2	4	no	—
234	C₂×C₄×C₅₉	—	2	2	no	—
235	C₂×C₄×C₅₉	—	2	4	no	—
236	C₂×C₄×C₅₉	—	2	4	no	—
237	C₂×C₄×C₅₉	—	2	4	no	—
238	C₂×C₄×C₅₉	—	2	4	no	—
239	C₂×C₄×C₅₉	—	2	8	no	—
240	C₂×C₄×C₅₉	—	2	8	no	—
241	C₂×C₄×C₅₉	—	2	4	no	—
242	C₂×C₄×C₅₉	—	2	4	no	—
243	C₂×C₄×C₅₉	—	8	8	no	—
244	C₂×C₄×C₅₉	—	8	4	no	—
245	C₂×C₄×C₅₉	—	8	4	no	—
246	C₂×C₄×C₅₉	C₂²⋊Q₈	1	16	yes	complemented
247	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
252	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
253	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
254	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
255	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
256	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
257	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
258	#35532	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₅₉	—	2	4	no	—
260	C₂²×C₅₉	—	2	2	no	—
261	C₂²×C₅₉	—	2	2	no	—
262	C₂²×C₅₉	—	2	4	no	—
263	C₂²×C₅₉	—	2	4	no	—
264	C₂²×C₅₉	—	2	8	no	—
265	C₂²×C₅₉	—	4	4	no	—
266	C₂²×C₅₉	—	4	2	no	—
267	C₂²×C₅₉	—	4	2	no	—
268	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
269	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
270	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
271	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
272	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
273	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
274	C₄×C₅₉	—	2	4	no	—
275	C₄×C₅₉	—	2	4	no	—
276	C₄×C₅₉	—	2	4	no	—
277	C₄×C₅₉	—	2	4	no	—
278	C₄×C₅₉	—	2	4	no	—
279	C₄×C₅₉	—	4	4	no	—
280	C₄×C₅₉	—	4	4	no	—
281	C₄×C₅₉	—	4	4	no	—
282	C₄×C₅₉	—	4	2	no	—
283	C₄×C₅₉	—	4	2	no	—
284	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
285	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
286	C₂×#544	C₂×C₅₉	1	1	yes	characteristic, complemented
287	C₂×#520	C₂×C₅₉	1	1	yes	characteristic
288	#2567	C₂×C₅₉	1	2	yes	complemented
289	#2566	C₂×C₅₉	1	2	yes	complemented
290	#2565	C₂×C₅₉	1	2	yes	complemented
291	#2542	C₂×C₅₉	1	2	yes	complemented
292	#2449	C₂×C₅₉	1	8	yes	complemented
293	#2441	C₂×C₅₉	1	4	yes	complemented
294	#2440	C₂×C₅₉	1	4	yes	complemented
295	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
296	#2311	C₂×C₅₉	1	1	yes	characteristic
297	#2297	C₂×C₅₉	1	1	yes	characteristic
298	#2296	C₂×C₅₉	1	1	yes	characteristic, complemented
299	C₂×#384	C₂×C₅₉	1	1	yes	characteristic, complemented
300	C₂×C₅₉	—	2	4	no	—
301	C₂×C₅₉	—	4	4	no	—
302	C₂×C₅₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
303	C₂×C₅₉	#3492	1	2	yes	—
304	C₂×C₅₉	#3498	1	1	yes	characteristic
305	C₂×C₅₉	#3499	1	1	yes	characteristic
306	C₂×C₅₉	#3503	1	2	yes	—
307	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
308	#544	—	2	8	no	—
309	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
310	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
311	C₂×#125	C₂²×C₅₉	1	2	yes	—
312	C₂×#125	C₂²×C₅₉	1	2	yes	—
313	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
314	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	8	yes	—
315	#520	—	2	8	no	—
316	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
317	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
318	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
319	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
320	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
321	C₂×#117	C₂²×C₅₉	1	2	yes	—
322	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
326	C₂²×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
327	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
328	#399	C₂²×C₅₉	1	8	yes	—
329	#398	C₂²×C₅₉	1	8	yes	—
330	#396	C₂²×C₅₉	1	8	yes	—
331	#395	C₂²×C₅₉	1	8	yes	—
332	#391	C₂²×C₅₉	1	1	yes	characteristic
333	#391	C₂²×C₅₉	1	2	yes	—
334	#391	C₂²×C₅₉	1	1	yes	characteristic
335	#390	C₂²×C₅₉	1	1	yes	characteristic
336	#390	C₂²×C₅₉	1	2	yes	—
337	#390	C₂²×C₅₉	1	1	yes	characteristic
338	#389	C₂²×C₅₉	1	8	yes	—
339	#389	C₂²×C₅₉	1	4	yes	—
340	#389	C₂²×C₅₉	1	2	yes	—
341	#389	C₂²×C₅₉	1	2	yes	—
342	#387	C₂²×C₅₉	1	8	yes	—
343	#386	C₂²×C₅₉	1	4	yes	—
344	#386	C₂²×C₅₉	1	4	yes	—
345	#385	C₂²×C₅₉	1	8	yes	—
346	#385	C₂²×C₅₉	1	4	yes	—
347	#385	C₂²×C₅₉	1	4	yes	—
348	#384	C₂²×C₅₉	1	2	yes	—
349	#384	C₂²×C₅₉	1	2	yes	—
350	#384	C₂²×C₅₉	1	2	yes	—
351	#384	C₂²×C₅₉	1	4	yes	—
352	#382	C₂²×C₅₉	1	2	yes	—
353	#380	C₂²×C₅₉	1	4	yes	—
354	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
355	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
356	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
357	C₅₉	#35532	1	1	yes	characteristic, direct product factor, Sylow
358	C₂×#41	—	2	4	no	—
359	C₂×#41	—	2	4	no	—
360	C₂×#41	Q₈×C₅₉	1	8	yes	complemented
361	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
363	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
364	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
366	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
367	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
368	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
369	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
370	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
371	C₄⋊Q₈	—	2	8	no	—
372	C₄⋊Q₈	—	2	8	no	—
373	#125	—	2	8	no	—
374	#125	—	2	8	no	—
375	C₂²⋊Q₈	—	2	16	no	—
376	C₂²⋊Q₈	—	4	16	no	—
377	C₄×Q₈	—	2	8	no	—
378	C₄×D₄	—	2	16	no	—
379	C₄×D₄	—	2	8	no	—
380	#117	—	2	4	no	—
381	#117	—	2	4	no	—
382	#117	—	2	8	no	—
383	#117	D₄×C₅₉	1	8	yes	—
384	C₂×C₄⋊C₄	—	2	4	no	—
385	C₂×C₄⋊C₄	—	2	4	no	—
386	C₂×C₄⋊C₄	—	2	8	no	—
387	C₂×C₄⋊C₄	—	4	8	no	—
388	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
403	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
404	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
413	C₂×C₄²	—	2	4	no	—
414	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
415	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
416	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
417	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
418	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
421	#95	C₂³×C₅₉	1	4	yes	—
422	#95	C₂³×C₅₉	1	4	yes	—
423	#95	C₂³×C₅₉	1	4	yes	—
424	#95	C₂³×C₅₉	1	4	yes	—
425	#95	C₂³×C₅₉	1	8	yes	—
426	#95	C₂³×C₅₉	1	8	yes	—
427	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
428	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
429	#41	—	2	32	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	8	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	4	8	no	—
434	C₂×Q₈	C₂×Q₈×C₅₉	1	4	yes	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	C₂×Q₈×C₅₉	1	8	yes	—
440	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	4	8	no	—
452	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
453	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	—
454	C₂²×C₄	C₂×Q₈×C₅₉	1	4	yes	—
455	C₂²×C₄	#41×C₅₉	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	16	no	—
480	C₄⋊C₄	—	2	8	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	4	8	no	—
483	C₄⋊C₄	—	4	8	no	—
484	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
485	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	4	8	no	—
492	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
493	C₄²	—	2	8	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	4	no	—
499	C₄²	C₂×D₄×C₅₉	1	8	yes	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	4	no	—
506	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
507	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
508	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
509	C₂³	C₂×#41×C₅₉	1	2	yes	—
510	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
511	Q₈	—	2	8	no	—
512	Q₈	—	8	8	no	—
513	D₄	—	2	16	no	—
514	D₄	—	2	8	no	—
515	C₂×C₄	—	2	16	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	16	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	8	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	8	8	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	—	8	4	no	—
539	C₂×C₄	C₂²⋊Q₈×C₅₉	1	16	yes	complemented
540	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
541	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
542	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
544	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
545	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
546	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
547	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
548	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
549	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
550	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	8	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
561	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
562	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
563	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
564	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
565	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
566	C₄	—	2	4	no	—
567	C₄	—	2	4	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	4	no	—
570	C₄	—	2	4	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
577	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
578	C₂	—	2	4	no	—
579	C₂	—	4	4	no	—
580	C₂	C₂²×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
581	C₂	C₅₉×#3492	1	2	yes	—
582	C₂	C₅₉×#3498	1	1	yes	characteristic
583	C₂	C₅₉×#3499	1	1	yes	characteristic
584	C₂	C₅₉×#3503	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#544	C₂	semidirect
3. C₅₉×#2567	C₂	semidirect
4. C₅₉×#2566	C₂	semidirect
5. C₅₉×#2565	C₂	semidirect
6. C₅₉×#2542	C₂	semidirect
7. C₅₉×#2449	C₂	semidirect
8. C₅₉×#2441	C₂	semidirect
9. C₅₉×#2440	C₂	semidirect
10. C₅₉×#2317	C₂	semidirect
13. C₅₉×#2296	C₂	semidirect
14. C₂×C₅₉×#384	C₂	semidirect
67. C₂×#41×C₅₉	Q₈	semidirect
246. C₂×C₄×C₅₉	C₂²⋊Q₈	semidirect
258. #35532	C₅₉	direct (N × H)
286. C₂×#544	C₂×C₅₉	semidirect
288. #2567	C₂×C₅₉	semidirect
289. #2566	C₂×C₅₉	semidirect
290. #2565	C₂×C₅₉	semidirect
291. #2542	C₂×C₅₉	semidirect
292. #2449	C₂×C₅₉	semidirect
293. #2441	C₂×C₅₉	semidirect
294. #2440	C₂×C₅₉	semidirect
295. #2317	C₂×C₅₉	semidirect
298. #2296	C₂×C₅₉	semidirect
299. C₂×#384	C₂×C₅₉	semidirect
357. C₅₉	#35532	direct (N × H)
360. C₂×#41	Q₈×C₅₉	semidirect
539. C₂×C₄	C₂²⋊Q₈×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×#544	2
C₂×C₅₉×#520	2
C₅₉×#2567	2
C₅₉×#2566	2
C₅₉×#2565	2
C₅₉×#2542	2
C₅₉×#2449	2
C₅₉×#2441	2
C₅₉×#2440	2
C₅₉×#2317	2
C₅₉×#2311	2
C₅₉×#2297	2
C₅₉×#2296	2
C₂×C₅₉×#384	2
#35532	59

Subgroups — C59×#35532 #28447641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35532 #28447641