Subgroups — C₅₉×#35207 #28447316

Order 15104.

1872 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2854	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2851	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2653	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2537	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#2494	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2494	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2490	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2458	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2422	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2324	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2314	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#125×C₅₉	C₂²	1	2	yes	—
20	C₂×#123×C₅₉	C₂²	1	4	yes	—
21	C₂×#121×C₅₉	C₂²	1	2	yes	—
22	C₂×#121×C₅₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₅₉	C₂²	1	2	yes	—
30	C₅₉×#401	C₂²	1	4	yes	—
31	C₅₉×#398	C₂²	1	4	yes	—
32	C₅₉×#397	C₂²	1	4	yes	—
33	C₅₉×#397	C₂²	1	4	yes	—
34	C₅₉×#394	C₂²	1	4	yes	—
35	C₅₉×#394	C₂²	1	4	yes	—
36	C₅₉×#393	C₂²	1	4	yes	—
37	C₅₉×#393	C₂²	1	4	yes	—
38	C₅₉×#391	C₂²	1	2	yes	—
39	C₅₉×#390	C₂²	1	1	yes	characteristic
40	C₅₉×#390	C₂²	1	2	yes	—
41	C₅₉×#390	C₂²	1	4	yes	—
42	C₅₉×#390	C₂²	1	1	yes	characteristic
43	C₅₉×#390	C₂²	1	2	yes	—
44	C₅₉×#389	C₂²	1	1	yes	characteristic
45	C₅₉×#389	C₂²	1	2	yes	—
46	C₅₉×#389	C₂²	1	2	yes	—
47	C₅₉×#389	C₂²	1	2	yes	—
48	C₅₉×#389	C₂²	1	1	yes	characteristic
49	C₅₉×#389	C₂²	1	2	yes	—
50	C₅₉×#388	C₂²	1	4	yes	—
51	C₅₉×#388	C₂²	1	4	yes	—
52	C₅₉×#388	C₂²	1	4	yes	—
53	C₅₉×#388	C₂²	1	2	yes	—
54	C₅₉×#388	C₂²	1	2	yes	—
55	C₅₉×#388	C₂²	1	4	yes	—
56	C₅₉×#387	C₂²	1	4	yes	—
57	C₅₉×#387	C₂²	1	4	yes	—
58	C₅₉×#387	C₂²	1	4	yes	—
59	C₅₉×#386	C₂²	1	4	yes	—
60	C₅₉×#385	C₂²	1	4	yes	—
61	C₅₉×#385	C₂²	1	4	yes	—
62	C₅₉×#384	C₂²	1	1	yes	characteristic
63	C₅₉×#384	C₂²	1	2	yes	—
64	C₅₉×#382	C₂²	1	2	yes	—
65	C₅₉×#382	C₂²	1	2	yes	—
66	C₅₉×#380	C₂²	1	2	yes	—
67	C₅₉×#380	C₂²	1	2	yes	—
68	C₅₉×#380	C₂²	1	2	yes	—
69	C₅₉×#380	C₂²	1	2	yes	—
70	C₅₉×#380	C₂²	1	2	yes	—
71	C₅₉×#380	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
82	C₄³×C₅₉	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
87	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
91	C₄⋊Q₈×C₅₉	—	2	4	no	—
92	#125×C₅₉	—	4	4	no	—
93	#123×C₅₉	—	4	8	no	—
94	#121×C₅₉	—	2	8	no	—
95	#121×C₅₉	—	4	4	no	—
96	C₄×Q₈×C₅₉	—	4	4	no	—
97	C₄×D₄×C₅₉	—	2	4	no	—
98	C₄×D₄×C₅₉	—	2	4	no	—
99	C₄×D₄×C₅₉	—	2	4	no	—
100	C₄×D₄×C₅₉	—	2	4	no	—
101	#117×C₅₉	—	2	8	no	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
133	C₂×C₄²×C₅₉	—	4	4	no	—
134	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
144	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
146	#95×C₅₉	C₂³	1	2	yes	—
147	#95×C₅₉	C₂³	1	2	yes	—
148	#95×C₅₉	C₂³	1	2	yes	—
149	#95×C₅₉	C₂³	1	2	yes	—
150	#95×C₅₉	C₂³	1	2	yes	—
151	#95×C₅₉	C₂³	1	4	yes	—
152	#95×C₅₉	C₂³	1	2	yes	—
153	#95×C₅₉	C₂³	1	4	yes	—
154	#95×C₅₉	C₂³	1	4	yes	—
155	#95×C₅₉	C₂³	1	4	yes	—
156	#95×C₅₉	C₂³	1	4	yes	—
157	#95×C₅₉	C₂³	1	4	yes	—
158	#95×C₅₉	C₂³	1	4	yes	—
159	#95×C₅₉	C₂³	1	4	yes	—
160	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
161	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
162	C₂×Q₈×C₅₉	—	2	4	no	—
163	C₂×Q₈×C₅₉	—	4	2	no	—
164	C₂×Q₈×C₅₉	—	4	2	no	—
165	C₂×D₄×C₅₉	—	2	8	no	—
166	C₂×D₄×C₅₉	—	2	2	no	—
167	C₂×D₄×C₅₉	—	2	2	no	—
168	C₂×D₄×C₅₉	—	2	2	no	—
169	C₂×D₄×C₅₉	—	2	2	no	—
170	C₂×D₄×C₅₉	—	2	2	no	—
171	C₂×D₄×C₅₉	—	4	4	no	—
172	C₂×D₄×C₅₉	—	4	4	no	—
173	C₂×D₄×C₅₉	#41	1	4	yes	—
174	C₂²×C₄×C₅₉	—	2	4	no	—
175	C₂²×C₄×C₅₉	—	2	4	no	—
176	C₂²×C₄×C₅₉	—	2	4	no	—
177	C₂²×C₄×C₅₉	—	2	4	no	—
178	C₂²×C₄×C₅₉	—	2	4	no	—
179	C₂²×C₄×C₅₉	—	2	4	no	—
180	C₂²×C₄×C₅₉	—	2	4	no	—
181	C₂²×C₄×C₅₉	—	2	4	no	—
182	C₂²×C₄×C₅₉	—	2	4	no	—
183	C₂²×C₄×C₅₉	—	4	2	no	—
184	C₂²×C₄×C₅₉	—	4	2	no	—
185	C₂²×C₄×C₅₉	—	4	2	no	—
186	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
201	C₄⋊C₄×C₅₉	—	2	4	no	—
202	C₄⋊C₄×C₅₉	—	2	4	no	—
203	C₄⋊C₄×C₅₉	—	2	2	no	—
204	C₄⋊C₄×C₅₉	—	2	2	no	—
205	C₄⋊C₄×C₅₉	—	2	2	no	—
206	C₄⋊C₄×C₅₉	—	2	2	no	—
207	C₄⋊C₄×C₅₉	—	2	4	no	—
208	C₄⋊C₄×C₅₉	—	2	4	no	—
209	C₄⋊C₄×C₅₉	—	2	4	no	—
210	C₄⋊C₄×C₅₉	—	2	8	no	—
211	C₄⋊C₄×C₅₉	—	2	4	no	—
212	C₄⋊C₄×C₅₉	—	2	2	no	—
213	C₄⋊C₄×C₅₉	—	2	2	no	—
214	C₄⋊C₄×C₅₉	—	4	2	no	—
215	C₄⋊C₄×C₅₉	—	4	4	no	—
216	C₄⋊C₄×C₅₉	—	4	4	no	—
217	C₄⋊C₄×C₅₉	—	4	4	no	—
218	C₂²⋊C₄×C₅₉	—	2	4	no	—
219	C₂²⋊C₄×C₅₉	—	2	8	no	—
220	C₂²⋊C₄×C₅₉	—	2	4	no	—
221	C₂²⋊C₄×C₅₉	—	2	4	no	—
222	C₂²⋊C₄×C₅₉	—	2	4	no	—
223	C₂²⋊C₄×C₅₉	—	2	4	no	—
224	C₂²⋊C₄×C₅₉	—	2	4	no	—
225	C₂²⋊C₄×C₅₉	—	2	4	no	—
226	C₂²⋊C₄×C₅₉	—	4	2	no	—
227	C₂²⋊C₄×C₅₉	—	4	4	no	—
228	C₂²⋊C₄×C₅₉	—	4	4	no	—
229	C₂²⋊C₄×C₅₉	—	4	4	no	—
230	C₂²⋊C₄×C₅₉	—	4	4	no	—
231	C₂²⋊C₄×C₅₉	—	4	4	no	—
232	C₄²×C₅₉	—	2	4	no	—
233	C₄²×C₅₉	—	2	2	no	—
234	C₄²×C₅₉	—	2	2	no	—
235	C₄²×C₅₉	—	2	4	no	—
236	C₄²×C₅₉	—	2	2	no	—
237	C₄²×C₅₉	—	2	2	no	—
238	C₄²×C₅₉	—	4	2	no	—
239	C₄²×C₅₉	—	4	2	no	—
240	C₄²×C₅₉	—	4	1	no	—
241	C₄²×C₅₉	—	4	4	no	—
242	C₄²×C₅₉	#41	1	4	yes	—
243	C₄²×C₅₉	#41	1	4	yes	—
244	C₂³×C₅₉	—	2	2	no	—
245	C₂³×C₅₉	—	2	2	no	—
246	C₂³×C₅₉	—	2	2	no	—
247	C₂³×C₅₉	—	2	2	no	—
248	C₂³×C₅₉	—	2	2	no	—
249	C₂³×C₅₉	—	2	2	no	—
250	C₂³×C₅₉	—	2	2	no	—
251	C₂³×C₅₉	—	2	2	no	—
252	C₂³×C₅₉	—	2	2	no	—
253	C₂³×C₅₉	—	2	2	no	—
254	C₂³×C₅₉	—	2	2	no	—
255	C₂³×C₅₉	—	2	2	no	—
256	C₂³×C₅₉	—	2	2	no	—
257	C₂³×C₅₉	C₂×#41	1	4	yes	—
258	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
259	Q₈×C₅₉	—	4	8	no	—
260	D₄×C₅₉	—	2	8	no	—
261	D₄×C₅₉	—	4	4	no	—
262	D₄×C₅₉	—	8	8	no	—
263	C₂×C₄×C₅₉	—	2	1	no	—
264	C₂×C₄×C₅₉	—	2	1	no	—
265	C₂×C₄×C₅₉	—	2	1	no	—
266	C₂×C₄×C₅₉	—	2	1	no	—
267	C₂×C₄×C₅₉	—	2	1	no	—
268	C₂×C₄×C₅₉	—	2	1	no	—
269	C₂×C₄×C₅₉	—	2	1	no	—
270	C₂×C₄×C₅₉	—	2	1	no	—
271	C₂×C₄×C₅₉	—	2	1	no	—
272	C₂×C₄×C₅₉	—	2	2	no	—
273	C₂×C₄×C₅₉	—	2	2	no	—
274	C₂×C₄×C₅₉	—	2	2	no	—
275	C₂×C₄×C₅₉	—	2	2	no	—
276	C₂×C₄×C₅₉	—	2	2	no	—
277	C₂×C₄×C₅₉	—	2	2	no	—
278	C₂×C₄×C₅₉	—	2	2	no	—
279	C₂×C₄×C₅₉	—	2	4	no	—
280	C₂×C₄×C₅₉	—	2	2	no	—
281	C₂×C₄×C₅₉	—	2	4	no	—
282	C₂×C₄×C₅₉	—	2	2	no	—
283	C₂×C₄×C₅₉	—	2	2	no	—
284	C₂×C₄×C₅₉	—	2	2	no	—
285	C₂×C₄×C₅₉	—	2	4	no	—
286	C₂×C₄×C₅₉	—	2	4	no	—
287	C₂×C₄×C₅₉	—	2	2	no	—
288	C₂×C₄×C₅₉	—	2	2	no	—
289	C₂×C₄×C₅₉	—	2	4	no	—
290	C₂×C₄×C₅₉	—	2	2	no	—
291	C₂×C₄×C₅₉	—	2	1	no	—
292	C₂×C₄×C₅₉	—	2	2	no	—
293	C₂×C₄×C₅₉	—	2	2	no	—
294	C₂×C₄×C₅₉	—	2	1	no	—
295	C₂×C₄×C₅₉	—	2	2	no	—
296	C₂×C₄×C₅₉	—	2	2	no	—
297	C₂×C₄×C₅₉	—	2	4	no	—
298	C₂×C₄×C₅₉	—	4	8	no	—
299	C₂×C₄×C₅₉	—	4	8	no	—
300	C₂×C₄×C₅₉	—	4	8	no	—
301	C₂×C₄×C₅₉	—	4	8	no	—
302	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
303	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
304	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
305	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
306	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
307	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
308	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
309	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
310	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
311	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
312	#35207	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂²×C₅₉	—	2	4	no	—
314	C₂²×C₅₉	—	2	4	no	—
315	C₂²×C₅₉	—	2	4	no	—
316	C₂²×C₅₉	—	4	2	no	—
317	C₂²×C₅₉	—	4	2	no	—
318	C₂²×C₅₉	—	4	2	no	—
319	C₂²×C₅₉	—	4	2	no	—
320	C₂²×C₅₉	—	4	2	no	—
321	C₂²×C₅₉	—	4	2	no	—
322	C₂²×C₅₉	—	4	2	no	—
323	C₂²×C₅₉	—	4	2	no	—
324	C₂²×C₅₉	—	4	2	no	—
325	C₂²×C₅₉	—	4	2	no	—
326	C₂²×C₅₉	—	4	2	no	—
327	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
329	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
330	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂²×C₅₉	#585	1	1	yes	characteristic
334	C₄×C₅₉	—	2	2	no	—
335	C₄×C₅₉	—	2	2	no	—
336	C₄×C₅₉	—	2	2	no	—
337	C₄×C₅₉	—	2	2	no	—
338	C₄×C₅₉	—	4	2	no	—
339	C₄×C₅₉	—	4	2	no	—
340	C₄×C₅₉	—	4	4	no	—
341	C₄×C₅₉	—	4	2	no	—
342	C₄×C₅₉	—	4	2	no	—
343	C₄×C₅₉	—	4	2	no	—
344	C₄×C₅₉	—	4	1	no	—
345	C₄×C₅₉	—	4	2	no	—
346	C₄×C₅₉	—	4	4	no	—
347	C₄×C₅₉	#529	1	4	yes	—
348	C₄×C₅₉	#542	1	4	yes	—
349	#2854	C₂×C₅₉	1	2	yes	complemented
350	#2851	C₂×C₅₉	1	2	yes	complemented
351	#2653	C₂×C₅₉	1	4	yes	complemented
352	#2563	C₂×C₅₉	1	1	yes	characteristic, complemented
353	#2563	C₂×C₅₉	1	1	yes	characteristic, complemented
354	#2552	C₂×C₅₉	1	1	yes	characteristic, complemented
355	#2537	C₂×C₅₉	1	1	yes	characteristic
356	#2494	C₂×C₅₉	1	2	yes	complemented
357	#2494	C₂×C₅₉	1	2	yes	complemented
358	#2490	C₂×C₅₉	1	2	yes	complemented
359	#2458	C₂×C₅₉	1	4	yes	complemented
360	#2422	C₂×C₅₉	1	2	yes	complemented
361	#2324	C₂×C₅₉	1	2	yes	complemented
362	#2314	C₂×C₅₉	1	2	yes	complemented
363	C₄×C₄⋊Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
364	#2293	C₂×C₅₉	1	1	yes	characteristic, complemented
365	C₄²×D₄	C₂×C₅₉	1	1	yes	characteristic, complemented
366	C₂×C₅₉	—	4	4	no	—
367	C₂×C₅₉	—	8	2	no	—
368	C₂×C₅₉	C₂×#529	1	1	yes	characteristic
369	C₂×C₅₉	C₂×#542	1	1	yes	characteristic
370	C₂×C₅₉	#3460	1	1	yes	characteristic
371	C₂×C₅₉	#3506	1	1	yes	characteristic
372	C₂×C₅₉	#3511	1	1	yes	characteristic
373	C₂×C₅₉	#3515	1	1	yes	characteristic
374	C₂×C₅₉	#3519	1	1	yes	characteristic
375	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
376	C₂×#125	C₂²×C₅₉	1	2	yes	—
377	C₂×#123	C₂²×C₅₉	1	4	yes	—
378	C₂×#121	C₂²×C₅₉	1	2	yes	—
379	C₂×#121	C₂²×C₅₉	1	2	yes	—
380	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
381	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
385	C₂×#117	C₂²×C₅₉	1	2	yes	—
386	C₂²×C₄²	C₂²×C₅₉	1	2	yes	—
387	#401	C₂²×C₅₉	1	4	yes	—
388	#398	C₂²×C₅₉	1	4	yes	—
389	#397	C₂²×C₅₉	1	4	yes	—
390	#397	C₂²×C₅₉	1	4	yes	—
391	#394	C₂²×C₅₉	1	4	yes	—
392	#394	C₂²×C₅₉	1	4	yes	—
393	#393	C₂²×C₅₉	1	4	yes	—
394	#393	C₂²×C₅₉	1	4	yes	—
395	#391	C₂²×C₅₉	1	2	yes	—
396	#390	C₂²×C₅₉	1	2	yes	—
397	#390	C₂²×C₅₉	1	2	yes	—
398	#390	C₂²×C₅₉	1	4	yes	—
399	#390	C₂²×C₅₉	1	1	yes	characteristic
400	#390	C₂²×C₅₉	1	1	yes	characteristic
401	#389	C₂²×C₅₉	1	2	yes	—
402	#389	C₂²×C₅₉	1	2	yes	—
403	#389	C₂²×C₅₉	1	2	yes	—
404	#389	C₂²×C₅₉	1	1	yes	characteristic
405	#389	C₂²×C₅₉	1	2	yes	—
406	#389	C₂²×C₅₉	1	1	yes	characteristic
407	#388	C₂²×C₅₉	1	4	yes	—
408	#388	C₂²×C₅₉	1	4	yes	—
409	#388	C₂²×C₅₉	1	4	yes	—
410	#388	C₂²×C₅₉	1	4	yes	—
411	#388	C₂²×C₅₉	1	2	yes	—
412	#388	C₂²×C₅₉	1	2	yes	—
413	#387	C₂²×C₅₉	1	4	yes	—
414	#387	C₂²×C₅₉	1	4	yes	—
415	#387	C₂²×C₅₉	1	4	yes	—
416	#386	C₂²×C₅₉	1	4	yes	—
417	#385	C₂²×C₅₉	1	4	yes	—
418	#385	C₂²×C₅₉	1	4	yes	—
419	#384	C₂²×C₅₉	1	1	yes	characteristic
420	#384	C₂²×C₅₉	1	2	yes	—
421	#382	C₂²×C₅₉	1	2	yes	—
422	#382	C₂²×C₅₉	1	2	yes	—
423	#380	C₂²×C₅₉	1	2	yes	—
424	#380	C₂²×C₅₉	1	2	yes	—
425	#380	C₂²×C₅₉	1	2	yes	—
426	#380	C₂²×C₅₉	1	2	yes	—
427	#380	C₂²×C₅₉	1	2	yes	—
428	#380	C₂²×C₅₉	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
436	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
439	C₄³	C₂²×C₅₉	1	1	yes	characteristic
440	C₅₉	#35207	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
442	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
443	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
445	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
446	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
447	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
448	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
449	C₄⋊Q₈	—	2	4	no	—
450	#125	—	4	4	no	—
451	#123	—	4	8	no	—
452	#121	—	2	8	no	—
453	#121	—	4	4	no	—
454	C₄×Q₈	—	4	4	no	—
455	C₄×D₄	—	2	4	no	—
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	4	no	—
458	C₄×D₄	—	2	4	no	—
459	#117	—	2	8	no	—
460	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
491	C₂×C₄²	—	4	4	no	—
492	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
493	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
496	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
499	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
504	#95	C₂³×C₅₉	1	2	yes	—
505	#95	C₂³×C₅₉	1	2	yes	—
506	#95	C₂³×C₅₉	1	2	yes	—
507	#95	C₂³×C₅₉	1	2	yes	—
508	#95	C₂³×C₅₉	1	2	yes	—
509	#95	C₂³×C₅₉	1	4	yes	—
510	#95	C₂³×C₅₉	1	2	yes	—
511	#95	C₂³×C₅₉	1	4	yes	—
512	#95	C₂³×C₅₉	1	4	yes	—
513	#95	C₂³×C₅₉	1	4	yes	—
514	#95	C₂³×C₅₉	1	4	yes	—
515	#95	C₂³×C₅₉	1	4	yes	—
516	#95	C₂³×C₅₉	1	4	yes	—
517	#95	C₂³×C₅₉	1	4	yes	—
518	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
519	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	4	2	no	—
522	C₂×Q₈	—	4	2	no	—
523	C₂×D₄	—	2	8	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	#41×C₅₉	1	4	yes	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	8	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₄⋊C₄	—	4	4	no	—
574	C₄⋊C₄	—	4	4	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	4	4	no	—
585	C₂²⋊C₄	—	4	4	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	4	no	—
589	C₂²⋊C₄	—	4	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	4	2	no	—
597	C₄²	—	4	2	no	—
598	C₄²	—	4	4	no	—
599	C₄²	—	4	1	no	—
600	C₄²	#41×C₅₉	1	4	yes	—
601	C₄²	#41×C₅₉	1	4	yes	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	C₂×#41×C₅₉	1	4	yes	—
616	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
617	Q₈	—	4	8	no	—
618	D₄	—	2	8	no	—
619	D₄	—	4	4	no	—
620	D₄	—	8	8	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
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	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	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	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	4	8	no	—
657	C₂×C₄	—	4	8	no	—
658	C₂×C₄	—	4	8	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
661	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
662	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
663	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
664	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
665	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
666	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
667	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
668	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
669	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
685	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
686	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
687	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
688	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
689	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
690	C₂²	C₅₉×#585	1	1	yes	characteristic
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	4	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	4	no	—
704	C₄	C₅₉×#529	1	4	yes	—
705	C₄	C₅₉×#542	1	4	yes	—
706	C₂	—	4	4	no	—
707	C₂	—	8	2	no	—
708	C₂	C₂×C₅₉×#529	1	1	yes	characteristic
709	C₂	C₂×C₅₉×#542	1	1	yes	characteristic
710	C₂	C₅₉×#3460	1	1	yes	characteristic
711	C₂	C₅₉×#3506	1	1	yes	characteristic
712	C₂	C₅₉×#3511	1	1	yes	characteristic
713	C₂	C₅₉×#3515	1	1	yes	characteristic
714	C₂	C₅₉×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₅₉×#2537	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
1. C₅₉×#2854	C₂	semidirect
2. C₅₉×#2851	C₂	semidirect
3. C₅₉×#2653	C₂	semidirect
4. C₅₉×#2563	C₂	semidirect
5. C₅₉×#2563	C₂	semidirect
6. C₅₉×#2552	C₂	semidirect
8. C₅₉×#2494	C₂	semidirect
9. C₅₉×#2494	C₂	semidirect
10. C₅₉×#2490	C₂	semidirect
11. C₅₉×#2458	C₂	semidirect
12. C₅₉×#2422	C₂	semidirect
13. C₅₉×#2324	C₂	semidirect
14. C₅₉×#2314	C₂	semidirect
15. C₄×C₄⋊Q₈×C₅₉	C₂	semidirect
16. C₅₉×#2293	C₂	semidirect
17. C₄²×D₄×C₅₉	C₂	semidirect
312. #35207	C₅₉	direct (N × H)
349. #2854	C₂×C₅₉	semidirect
350. #2851	C₂×C₅₉	semidirect
351. #2653	C₂×C₅₉	semidirect
352. #2563	C₂×C₅₉	semidirect
353. #2563	C₂×C₅₉	semidirect
354. #2552	C₂×C₅₉	semidirect
356. #2494	C₂×C₅₉	semidirect
357. #2494	C₂×C₅₉	semidirect
358. #2490	C₂×C₅₉	semidirect
359. #2458	C₂×C₅₉	semidirect
360. #2422	C₂×C₅₉	semidirect
361. #2324	C₂×C₅₉	semidirect
362. #2314	C₂×C₅₉	semidirect
363. C₄×C₄⋊Q₈	C₂×C₅₉	semidirect
364. #2293	C₂×C₅₉	semidirect
365. C₄²×D₄	C₂×C₅₉	semidirect
440. C₅₉	#35207	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2854	2
C₅₉×#2851	2
C₅₉×#2653	2
C₅₉×#2563	2
C₅₉×#2552	2
C₅₉×#2537	2
C₅₉×#2494	2
C₅₉×#2490	2
C₅₉×#2458	2
C₅₉×#2422	2
C₅₉×#2324	2
C₅₉×#2314	2
C₄×C₄⋊Q₈×C₅₉	2
C₅₉×#2293	2
C₄²×D₄×C₅₉	2
#35207	59

Subgroups — C59×#35207 #28447316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35207 #28447316