Subgroups — C₅₉×#35531 #28447640

Order 15104.

2746 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2504	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2501	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2500	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2500	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2448	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2445	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2418	C₂	1	8	yes	maximal, complemented
10	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#535	—	2	8	no	—
18	C₂×#127×C₅₉	C₂²	1	2	yes	—
19	C₂×#124×C₅₉	C₂²	1	2	yes	—
20	C₂×#123×C₅₉	C₂²	1	8	yes	complemented
21	C₂×#121×C₅₉	C₂²	1	2	yes	—
22	C₂×#121×C₅₉	C₂²	1	2	yes	—
23	C₂×#120×C₅₉	C₂²	1	4	yes	—
24	C₅₉×#520	—	2	8	no	—
25	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
28	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
32	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
35	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#399	C₂²	1	8	yes	complemented
37	C₅₉×#397	C₂²	1	8	yes	complemented
38	C₅₉×#394	C₂²	1	8	yes	complemented
39	C₅₉×#394	C₂²	1	8	yes	complemented
40	C₅₉×#391	C₂²	1	2	yes	complemented
41	C₅₉×#390	C₂²	1	2	yes	—
42	C₅₉×#390	C₂²	1	2	yes	—
43	C₅₉×#390	C₂²	1	2	yes	—
44	C₅₉×#390	C₂²	1	2	yes	—
45	C₅₉×#390	C₂²	1	4	yes	—
46	C₅₉×#390	C₂²	1	4	yes	—
47	C₅₉×#390	C₂²	1	2	yes	complemented
48	C₅₉×#389	C₂²	1	4	yes	complemented
49	C₅₉×#388	C₂²	1	8	yes	complemented
50	C₅₉×#388	C₂²	1	8	yes	complemented
51	C₅₉×#386	C₂²	1	4	yes	—
52	C₅₉×#386	C₂²	1	8	yes	complemented
53	C₅₉×#385	C₂²	1	4	yes	—
54	C₅₉×#384	C₂²	1	1	yes	characteristic, complemented
55	C₅₉×#384	C₂²	1	2	yes	complemented
56	C₅₉×#384	C₂²	1	1	yes	characteristic, complemented
57	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
58	C₅₉×#382	C₂²	1	2	yes	complemented
59	C₅₉×#382	C₂²	1	1	yes	characteristic, complemented
60	C₅₉×#380	C₂²	1	4	yes	—
61	C₅₉×#379	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
65	C₂⁵×C₅₉	C₂³	1	2	yes	—
66	C₂×#41×C₅₉	—	2	4	no	—
67	C₂×#41×C₅₉	—	2	4	no	—
68	C₂×#41×C₅₉	D₄	1	8	yes	—
69	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₅₉	—	2	4	no	—
71	C₂²×D₄×C₅₉	—	2	4	no	—
72	C₂²×D₄×C₅₉	—	2	4	no	—
73	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
79	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
83	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
84	#127×C₅₉	—	2	8	no	—
85	#124×C₅₉	—	2	8	no	—
86	#123×C₅₉	—	4	16	no	—
87	#121×C₅₉	—	2	8	no	—
88	#121×C₅₉	—	2	8	no	—
89	#120×C₅₉	—	2	16	no	—
90	C₄×Q₈×C₅₉	—	2	8	no	—
91	C₄×D₄×C₅₉	—	2	16	no	—
92	C₄×D₄×C₅₉	—	2	8	no	—
93	#117×C₅₉	—	2	4	no	—
94	#117×C₅₉	—	2	4	no	—
95	#117×C₅₉	—	2	8	no	—
96	#117×C₅₉	—	2	4	no	—
97	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
98	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	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×C₂²⋊C₄×C₅₉	—	4	8	no	—
111	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
118	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
123	C₂×C₄²×C₅₉	—	2	4	no	—
124	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
131	#95×C₅₉	C₂³	1	4	yes	—
132	#95×C₅₉	C₂³	1	4	yes	—
133	#95×C₅₉	C₂³	1	4	yes	—
134	#95×C₅₉	C₂³	1	4	yes	—
135	#95×C₅₉	C₂³	1	8	yes	—
136	C₂⁴×C₅₉	—	2	4	no	—
137	C₂⁴×C₅₉	—	2	4	no	—
138	C₂⁴×C₅₉	—	2	4	no	—
139	C₂⁴×C₅₉	—	4	4	no	—
140	C₂⁴×C₅₉	—	4	4	no	—
141	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
142	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
143	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
144	#41×C₅₉	—	2	32	no	—
145	C₂×Q₈×C₅₉	—	2	2	no	—
146	C₂×Q₈×C₅₉	—	2	2	no	—
147	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
148	C₂×D₄×C₅₉	—	2	4	no	—
149	C₂×D₄×C₅₉	—	2	4	no	—
150	C₂×D₄×C₅₉	—	2	8	no	—
151	C₂×D₄×C₅₉	—	2	8	no	—
152	C₂×D₄×C₅₉	—	2	4	no	—
153	C₂×D₄×C₅₉	—	2	4	no	—
154	C₂×D₄×C₅₉	—	2	2	no	—
155	C₂×D₄×C₅₉	—	2	2	no	—
156	C₂×D₄×C₅₉	—	2	4	no	—
157	C₂×D₄×C₅₉	—	2	4	no	—
158	C₂×D₄×C₅₉	—	2	4	no	—
159	C₂×D₄×C₅₉	—	2	4	no	—
160	C₂×D₄×C₅₉	—	4	8	no	—
161	C₂×D₄×C₅₉	—	4	8	no	—
162	C₂×D₄×C₅₉	—	4	16	no	—
163	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
164	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₅₉	—	2	4	no	—
166	C₂²×C₄×C₅₉	—	2	4	no	—
167	C₂²×C₄×C₅₉	—	2	4	no	—
168	C₂²×C₄×C₅₉	—	2	8	no	—
169	C₂²×C₄×C₅₉	—	2	4	no	—
170	C₂²×C₄×C₅₉	—	2	4	no	—
171	C₂²×C₄×C₅₉	—	4	2	no	—
172	C₂²×C₄×C₅₉	—	4	4	no	—
173	C₂²×C₄×C₅₉	—	4	8	no	—
174	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
175	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₅₉	#41	1	4	yes	—
177	C₂²×C₄×C₅₉	#41	1	4	yes	—
178	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
189	C₄⋊C₄×C₅₉	—	2	4	no	—
190	C₄⋊C₄×C₅₉	—	2	2	no	—
191	C₄⋊C₄×C₅₉	—	2	8	no	—
192	C₄⋊C₄×C₅₉	—	2	4	no	—
193	C₄⋊C₄×C₅₉	—	2	2	no	—
194	C₄⋊C₄×C₅₉	—	2	2	no	—
195	C₄⋊C₄×C₅₉	—	2	2	no	—
196	C₄⋊C₄×C₅₉	—	2	4	no	—
197	C₄⋊C₄×C₅₉	—	2	8	no	—
198	C₄⋊C₄×C₅₉	—	4	4	no	—
199	C₄⋊C₄×C₅₉	—	4	8	no	—
200	C₂²⋊C₄×C₅₉	—	2	8	no	—
201	C₂²⋊C₄×C₅₉	—	2	4	no	—
202	C₂²⋊C₄×C₅₉	—	2	4	no	—
203	C₂²⋊C₄×C₅₉	—	2	4	no	—
204	C₂²⋊C₄×C₅₉	—	2	8	no	—
205	C₂²⋊C₄×C₅₉	—	2	8	no	—
206	C₂²⋊C₄×C₅₉	—	2	16	no	—
207	C₂²⋊C₄×C₅₉	—	2	8	no	—
208	C₂²⋊C₄×C₅₉	—	4	8	no	—
209	C₂²⋊C₄×C₅₉	—	4	8	no	—
210	C₂²⋊C₄×C₅₉	—	4	4	no	—
211	C₂²⋊C₄×C₅₉	—	4	8	no	—
212	C₄²×C₅₉	—	2	8	no	—
213	C₄²×C₅₉	—	2	4	no	—
214	C₄²×C₅₉	—	2	4	no	—
215	C₄²×C₅₉	—	2	2	no	—
216	C₄²×C₅₉	—	2	4	no	—
217	C₄²×C₅₉	—	2	2	no	—
218	C₄²×C₅₉	—	2	4	no	—
219	C₂³×C₅₉	—	2	2	no	—
220	C₂³×C₅₉	—	2	2	no	—
221	C₂³×C₅₉	—	2	2	no	—
222	C₂³×C₅₉	—	2	2	no	—
223	C₂³×C₅₉	—	2	4	no	—
224	C₂³×C₅₉	—	2	4	no	—
225	C₂³×C₅₉	—	2	4	no	—
226	C₂³×C₅₉	—	2	4	no	—
227	C₂³×C₅₉	—	2	4	no	—
228	C₂³×C₅₉	—	2	8	no	—
229	C₂³×C₅₉	—	2	8	no	—
230	C₂³×C₅₉	—	4	16	no	—
231	C₂³×C₅₉	—	4	8	no	—
232	C₂³×C₅₉	—	8	8	no	—
233	C₂³×C₅₉	—	8	4	no	—
234	C₂³×C₅₉	—	8	4	no	—
235	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
236	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
237	C₂³×C₅₉	C₂×#41	1	2	yes	—
238	C₂³×C₅₉	C₂×#41	1	2	yes	—
239	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
240	Q₈×C₅₉	—	2	8	no	—
241	D₄×C₅₉	—	2	16	no	—
242	D₄×C₅₉	—	2	8	no	—
243	D₄×C₅₉	—	4	8	no	—
244	D₄×C₅₉	—	4	8	no	—
245	D₄×C₅₉	—	8	8	no	—
246	D₄×C₅₉	—	8	8	no	—
247	C₂×C₄×C₅₉	—	2	2	no	—
248	C₂×C₄×C₅₉	—	2	2	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	2	no	—
251	C₂×C₄×C₅₉	—	2	16	no	—
252	C₂×C₄×C₅₉	—	2	2	no	—
253	C₂×C₄×C₅₉	—	2	2	no	—
254	C₂×C₄×C₅₉	—	2	2	no	—
255	C₂×C₄×C₅₉	—	2	4	no	—
256	C₂×C₄×C₅₉	—	2	2	no	—
257	C₂×C₄×C₅₉	—	2	2	no	—
258	C₂×C₄×C₅₉	—	2	4	no	—
259	C₂×C₄×C₅₉	—	2	4	no	—
260	C₂×C₄×C₅₉	—	2	8	no	—
261	C₂×C₄×C₅₉	—	2	2	no	—
262	C₂×C₄×C₅₉	—	2	4	no	—
263	C₂×C₄×C₅₉	—	2	4	no	—
264	C₂×C₄×C₅₉	—	2	4	no	—
265	C₂×C₄×C₅₉	—	2	4	no	—
266	C₂×C₄×C₅₉	—	2	2	no	—
267	C₂×C₄×C₅₉	—	2	4	no	—
268	C₂×C₄×C₅₉	—	4	8	no	—
269	C₂×C₄×C₅₉	—	8	4	no	—
270	C₂×C₄×C₅₉	—	8	8	no	—
271	C₂×C₄×C₅₉	#123	1	16	yes	complemented
272	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
276	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
277	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
278	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
279	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
280	#35531	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂²×C₅₉	—	2	4	no	—
282	C₂²×C₅₉	—	2	2	no	—
283	C₂²×C₅₉	—	2	2	no	—
284	C₂²×C₅₉	—	2	4	no	—
285	C₂²×C₅₉	—	2	4	no	—
286	C₂²×C₅₉	—	2	4	no	—
287	C₂²×C₅₉	—	2	4	no	—
288	C₂²×C₅₉	—	4	4	no	—
289	C₂²×C₅₉	—	4	4	no	—
290	C₂²×C₅₉	—	4	4	no	—
291	C₂²×C₅₉	—	4	8	no	—
292	C₂²×C₅₉	—	4	4	no	—
293	C₂²×C₅₉	—	4	4	no	—
294	C₂²×C₅₉	—	4	8	no	—
295	C₂²×C₅₉	—	8	16	no	—
296	C₂²×C₅₉	C₂×#123	1	4	yes	—
297	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
298	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
299	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
301	C₂²×C₅₉	#585	1	2	yes	—
302	C₄×C₅₉	—	2	4	no	—
303	C₄×C₅₉	—	2	4	no	—
304	C₄×C₅₉	—	4	2	no	—
305	C₄×C₅₉	—	4	4	no	—
306	C₄×C₅₉	—	4	2	no	—
307	C₄×C₅₉	—	4	2	no	—
308	C₄×C₅₉	—	4	2	no	—
309	C₄×C₅₉	—	4	2	no	—
310	C₄×C₅₉	—	4	4	no	—
311	C₄×C₅₉	C₂×#123	1	4	yes	—
312	C₄×C₅₉	C₂×#123	1	4	yes	—
313	C₂×#535	C₂×C₅₉	1	1	yes	characteristic
314	C₂×#520	C₂×C₅₉	1	1	yes	characteristic, complemented
315	#2504	C₂×C₅₉	1	2	yes	complemented
316	#2501	C₂×C₅₉	1	2	yes	complemented
317	#2500	C₂×C₅₉	1	2	yes	complemented
318	#2500	C₂×C₅₉	1	2	yes	complemented
319	#2448	C₂×C₅₉	1	4	yes	complemented
320	#2445	C₂×C₅₉	1	4	yes	complemented
321	#2418	C₂×C₅₉	1	8	yes	complemented
322	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
323	#2309	C₂×C₅₉	1	1	yes	characteristic, complemented
324	#2297	C₂×C₅₉	1	1	yes	characteristic, complemented
325	C₂×#390	C₂×C₅₉	1	1	yes	characteristic, complemented
326	#2285	C₂×C₅₉	1	1	yes	characteristic, complemented
327	C₂×C₅₉	—	2	4	no	—
328	C₂×C₅₉	—	4	4	no	—
329	C₂×C₅₉	—	8	4	no	—
330	C₂×C₅₉	C₂²×#123	1	1	yes	characteristic
331	C₂×C₅₉	#3494	1	2	yes	—
332	C₂×C₅₉	#3498	1	1	yes	characteristic
333	C₂×C₅₉	#3500	1	1	yes	characteristic
334	C₂×C₅₉	#3506	1	2	yes	—
335	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
336	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
337	#535	—	2	8	no	—
338	C₂×#127	C₂²×C₅₉	1	2	yes	—
339	C₂×#124	C₂²×C₅₉	1	2	yes	—
340	C₂×#123	C₂²×C₅₉	1	8	yes	complemented
341	C₂×#121	C₂²×C₅₉	1	2	yes	—
342	C₂×#121	C₂²×C₅₉	1	2	yes	—
343	C₂×#120	C₂²×C₅₉	1	4	yes	—
344	#520	—	2	8	no	—
345	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
346	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
347	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
348	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
349	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
350	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
351	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
352	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
353	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
354	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
355	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
356	#399	C₂²×C₅₉	1	8	yes	complemented
357	#397	C₂²×C₅₉	1	8	yes	complemented
358	#394	C₂²×C₅₉	1	8	yes	complemented
359	#394	C₂²×C₅₉	1	8	yes	complemented
360	#391	C₂²×C₅₉	1	2	yes	complemented
361	#390	C₂²×C₅₉	1	4	yes	—
362	#390	C₂²×C₅₉	1	2	yes	—
363	#390	C₂²×C₅₉	1	2	yes	—
364	#390	C₂²×C₅₉	1	4	yes	—
365	#390	C₂²×C₅₉	1	2	yes	—
366	#390	C₂²×C₅₉	1	2	yes	—
367	#390	C₂²×C₅₉	1	2	yes	complemented
368	#389	C₂²×C₅₉	1	4	yes	complemented
369	#388	C₂²×C₅₉	1	8	yes	complemented
370	#388	C₂²×C₅₉	1	8	yes	complemented
371	#386	C₂²×C₅₉	1	4	yes	—
372	#386	C₂²×C₅₉	1	8	yes	complemented
373	#385	C₂²×C₅₉	1	4	yes	—
374	#384	C₂²×C₅₉	1	2	yes	complemented
375	#384	C₂²×C₅₉	1	1	yes	characteristic, complemented
376	#384	C₂²×C₅₉	1	1	yes	characteristic, complemented
377	#382	C₂²×C₅₉	1	2	yes	complemented
378	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
379	#382	C₂²×C₅₉	1	1	yes	characteristic, complemented
380	#380	C₂²×C₅₉	1	4	yes	—
381	#379	C₂²×C₅₉	1	4	yes	—
382	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	complemented
383	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
384	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
385	C₅₉	#35531	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁵	C₂³×C₅₉	1	2	yes	—
387	C₂×#41	—	2	4	no	—
388	C₂×#41	—	2	4	no	—
389	C₂×#41	D₄×C₅₉	1	8	yes	—
390	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
391	C₂²×D₄	—	2	4	no	—
392	C₂²×D₄	—	2	4	no	—
393	C₂²×D₄	—	2	4	no	—
394	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
395	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
396	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
397	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
398	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
399	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
400	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
401	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
402	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
403	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
404	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
405	#127	—	2	8	no	—
406	#124	—	2	8	no	—
407	#123	—	4	16	no	—
408	#121	—	2	8	no	—
409	#121	—	2	8	no	—
410	#120	—	2	16	no	—
411	C₄×Q₈	—	2	8	no	—
412	C₄×D₄	—	2	16	no	—
413	C₄×D₄	—	2	8	no	—
414	#117	—	2	4	no	—
415	#117	—	2	4	no	—
416	#117	—	2	8	no	—
417	#117	—	2	4	no	—
418	C₂×C₄⋊C₄	—	2	4	no	—
419	C₂×C₄⋊C₄	—	2	8	no	—
420	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
430	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
431	C₂×C₂²⋊C₄	—	4	8	no	—
432	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
444	C₂×C₄²	—	2	4	no	—
445	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
446	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
447	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
448	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
449	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
452	#95	C₂³×C₅₉	1	4	yes	—
453	#95	C₂³×C₅₉	1	4	yes	—
454	#95	C₂³×C₅₉	1	4	yes	—
455	#95	C₂³×C₅₉	1	4	yes	—
456	#95	C₂³×C₅₉	1	8	yes	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	4	no	—
460	C₂⁴	—	4	4	no	—
461	C₂⁴	—	4	4	no	—
462	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
463	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
464	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
465	#41	—	2	32	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	8	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	4	8	no	—
482	C₂×D₄	—	4	8	no	—
483	C₂×D₄	—	4	16	no	—
484	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
485	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	8	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	4	no	—
494	C₂²×C₄	—	4	8	no	—
495	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
496	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
497	C₂²×C₄	#41×C₅₉	1	4	yes	—
498	C₂²×C₄	#41×C₅₉	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	8	no	—
519	C₄⋊C₄	—	4	8	no	—
520	C₄⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	8	no	—
526	C₂²⋊C₄	—	2	8	no	—
527	C₂²⋊C₄	—	2	16	no	—
528	C₂²⋊C₄	—	2	8	no	—
529	C₂²⋊C₄	—	4	8	no	—
530	C₂²⋊C₄	—	4	8	no	—
531	C₂²⋊C₄	—	4	8	no	—
532	C₂²⋊C₄	—	4	4	no	—
533	C₄²	—	2	8	no	—
534	C₄²	—	2	4	no	—
535	C₄²	—	2	4	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	4	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	4	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	8	no	—
550	C₂³	—	2	8	no	—
551	C₂³	—	4	16	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	8	8	no	—
554	C₂³	—	8	4	no	—
555	C₂³	—	8	4	no	—
556	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
557	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
558	C₂³	C₂×#41×C₅₉	1	2	yes	—
559	C₂³	C₂×#41×C₅₉	1	2	yes	—
560	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
561	Q₈	—	2	8	no	—
562	D₄	—	2	16	no	—
563	D₄	—	2	8	no	—
564	D₄	—	4	8	no	—
565	D₄	—	4	8	no	—
566	D₄	—	8	8	no	—
567	D₄	—	8	8	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	16	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	—	8	4	no	—
591	C₂×C₄	—	8	8	no	—
592	C₂×C₄	#123×C₅₉	1	16	yes	complemented
593	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
594	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
596	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
597	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
598	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
599	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
600	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	8	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	8	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	8	16	no	—
616	C₂²	C₂×#123×C₅₉	1	4	yes	—
617	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
618	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
619	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
620	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
621	C₂²	C₅₉×#585	1	2	yes	—
622	C₄	—	2	4	no	—
623	C₄	—	2	4	no	—
624	C₄	—	4	4	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	4	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	C₂×#123×C₅₉	1	4	yes	—
632	C₄	C₂×#123×C₅₉	1	4	yes	—
633	C₂	—	2	4	no	—
634	C₂	—	4	4	no	—
635	C₂	—	8	4	no	—
636	C₂	C₂²×#123×C₅₉	1	1	yes	characteristic
637	C₂	C₅₉×#3494	1	2	yes	—
638	C₂	C₅₉×#3498	1	1	yes	characteristic
639	C₂	C₅₉×#3500	1	1	yes	characteristic
640	C₂	C₅₉×#3506	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×C₅₉×#535	C₂
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
2. C₂×C₅₉×#520	C₂	semidirect
3. C₅₉×#2504	C₂	semidirect
4. C₅₉×#2501	C₂	semidirect
5. C₅₉×#2500	C₂	semidirect
6. C₅₉×#2500	C₂	semidirect
7. C₅₉×#2448	C₂	semidirect
8. C₅₉×#2445	C₂	semidirect
9. C₅₉×#2418	C₂	semidirect
10. C₅₉×#2317	C₂	semidirect
11. C₅₉×#2309	C₂	semidirect
12. C₅₉×#2297	C₂	semidirect
13. C₂×C₅₉×#390	C₂	semidirect
14. C₅₉×#2285	C₂	semidirect
20. C₂×#123×C₅₉	C₂²	semidirect
25. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
27. C₂×C₄×D₄×C₅₉	C₂²	semidirect
31. C₂×#117×C₅₉	C₂²	semidirect
33. C₂²×C₄⋊C₄×C₅₉	C₂²	semidirect
36. C₅₉×#399	C₂²	semidirect
37. C₅₉×#397	C₂²	semidirect
38. C₅₉×#394	C₂²	semidirect
39. C₅₉×#394	C₂²	semidirect
40. C₅₉×#391	C₂²	semidirect
47. C₅₉×#390	C₂²	semidirect
48. C₅₉×#389	C₂²	semidirect
49. C₅₉×#388	C₂²	semidirect
50. C₅₉×#388	C₂²	semidirect
52. C₅₉×#386	C₂²	semidirect
54. C₅₉×#384	C₂²	semidirect
55. C₅₉×#384	C₂²	semidirect
56. C₅₉×#384	C₂²	semidirect
57. C₅₉×#382	C₂²	semidirect
58. C₅₉×#382	C₂²	semidirect
59. C₅₉×#382	C₂²	semidirect
62. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
271. C₂×C₄×C₅₉	#123	semidirect
280. #35531	C₅₉	direct (N × H)
314. C₂×#520	C₂×C₅₉	semidirect
315. #2504	C₂×C₅₉	semidirect
316. #2501	C₂×C₅₉	semidirect
317. #2500	C₂×C₅₉	semidirect
318. #2500	C₂×C₅₉	semidirect
319. #2448	C₂×C₅₉	semidirect
320. #2445	C₂×C₅₉	semidirect
321. #2418	C₂×C₅₉	semidirect
322. #2317	C₂×C₅₉	semidirect
323. #2309	C₂×C₅₉	semidirect
324. #2297	C₂×C₅₉	semidirect
325. C₂×#390	C₂×C₅₉	semidirect
326. #2285	C₂×C₅₉	semidirect
340. C₂×#123	C₂²×C₅₉	semidirect
345. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
347. C₂×C₄×D₄	C₂²×C₅₉	semidirect
351. C₂×#117	C₂²×C₅₉	semidirect
353. C₂²×C₄⋊C₄	C₂²×C₅₉	semidirect
356. #399	C₂²×C₅₉	semidirect
357. #397	C₂²×C₅₉	semidirect
358. #394	C₂²×C₅₉	semidirect
359. #394	C₂²×C₅₉	semidirect
360. #391	C₂²×C₅₉	semidirect
367. #390	C₂²×C₅₉	semidirect
368. #389	C₂²×C₅₉	semidirect
369. #388	C₂²×C₅₉	semidirect
370. #388	C₂²×C₅₉	semidirect
372. #386	C₂²×C₅₉	semidirect
374. #384	C₂²×C₅₉	semidirect
375. #384	C₂²×C₅₉	semidirect
376. #384	C₂²×C₅₉	semidirect
377. #382	C₂²×C₅₉	semidirect
378. #382	C₂²×C₅₉	semidirect
379. #382	C₂²×C₅₉	semidirect
382. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
383. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
384. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
385. C₅₉	#35531	direct (N × H)
592. C₂×C₄	#123×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×#535	2
C₂×C₅₉×#520	2
C₅₉×#2504	2
C₅₉×#2501	2
C₅₉×#2500	2
C₅₉×#2448	2
C₅₉×#2445	2
C₅₉×#2418	2
C₅₉×#2317	2
C₅₉×#2309	2
C₅₉×#2297	2
C₂×C₅₉×#390	2
C₅₉×#2285	2
#35531	59

Subgroups — C59×#35531 #28447640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35531 #28447640