Subgroups — C₅₉×#35739 #28447848

Order 15104.

2618 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2628	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2627	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2581	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2564	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2451	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2449	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2440	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2438	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2409	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₉×#395	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₄⋊C₄×C₅₉	C₂	1	2	yes	maximal, complemented
17	C₅₉×#2339	C₂	1	2	yes	maximal
18	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₅₉	C₂²	1	2	yes	—
20	D₄×Q₈×C₅₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
26	C₅₉×#520	—	2	8	no	—
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₅₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
41	C₅₉×#400	C₂²	1	2	yes	—
42	C₅₉×#400	C₂²	1	1	yes	characteristic
43	C₅₉×#400	C₂²	1	2	yes	—
44	C₅₉×#399	C₂²	1	1	yes	characteristic
45	C₅₉×#399	C₂²	1	2	yes	—
46	C₅₉×#398	C₂²	1	4	yes	—
47	C₅₉×#398	C₂²	1	4	yes	—
48	C₅₉×#398	C₂²	1	2	yes	—
49	C₅₉×#396	C₂²	1	2	yes	—
50	C₅₉×#395	C₂²	1	2	yes	—
51	C₅₉×#395	C₂²	1	2	yes	—
52	C₅₉×#395	C₂²	1	2	yes	—
53	C₅₉×#395	C₂²	1	2	yes	—
54	C₅₉×#395	C₂²	1	1	yes	characteristic
55	C₅₉×#395	C₂²	1	4	yes	—
56	C₅₉×#395	C₂²	1	4	yes	—
57	C₅₉×#393	C₂²	1	2	yes	—
58	C₅₉×#393	C₂²	1	1	yes	characteristic
59	C₅₉×#391	C₂²	1	2	yes	—
60	C₅₉×#391	C₂²	1	2	yes	—
61	C₅₉×#391	C₂²	1	4	yes	—
62	C₅₉×#389	C₂²	1	4	yes	—
63	C₅₉×#389	C₂²	1	2	yes	—
64	C₅₉×#389	C₂²	1	2	yes	—
65	C₅₉×#389	C₂²	1	2	yes	—
66	C₅₉×#387	C₂²	1	4	yes	—
67	C₅₉×#387	C₂²	1	4	yes	—
68	C₅₉×#386	C₂²	1	4	yes	—
69	C₅₉×#386	C₂²	1	4	yes	—
70	C₅₉×#385	C₂²	1	4	yes	—
71	C₅₉×#385	C₂²	1	4	yes	—
72	C₅₉×#385	C₂²	1	4	yes	—
73	C₅₉×#385	C₂²	1	4	yes	—
74	C₅₉×#384	C₂²	1	2	yes	—
75	C₅₉×#382	C₂²	1	1	yes	characteristic
76	C₅₉×#381	C₂²	1	4	yes	—
77	C₅₉×#380	C₂²	1	4	yes	—
78	C₅₉×#380	C₂²	1	2	yes	—
79	C₅₉×#380	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
83	C₂×#95×C₅₉	C₂²	1	2	yes	—
84	C₂×#95×C₅₉	C₂²	1	4	yes	—
85	C₂×#41×C₅₉	—	2	4	no	—
86	C₂×#41×C₅₉	—	2	4	no	—
87	C₂×#41×C₅₉	Q₈	1	8	yes	complemented
88	C₂²×Q₈×C₅₉	—	2	8	no	—
89	C₂²×Q₈×C₅₉	—	4	8	no	—
90	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
92	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
97	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
103	C₄⋊Q₈×C₅₉	—	2	8	no	—
104	C₄⋊Q₈×C₅₉	—	2	4	no	—
105	C₂²⋊Q₈×C₅₉	—	2	8	no	—
106	C₂²⋊Q₈×C₅₉	—	2	16	no	—
107	C₂²⋊Q₈×C₅₉	—	4	8	no	—
108	C₄×Q₈×C₅₉	—	2	4	no	—
109	C₄×Q₈×C₅₉	—	2	4	no	—
110	C₄×Q₈×C₅₉	—	2	4	no	—
111	C₄×D₄×C₅₉	—	2	4	no	—
112	C₄×D₄×C₅₉	—	2	8	no	—
113	C₄×D₄×C₅₉	—	2	8	no	—
114	C₄×D₄×C₅₉	—	2	8	no	—
115	C₄×D₄×C₅₉	—	2	8	no	—
116	C₄×D₄×C₅₉	D₄	1	8	yes	—
117	#117×C₅₉	—	2	8	no	—
118	#117×C₅₉	—	2	4	no	—
119	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
120	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
121	C₂×C₄⋊C₄×C₅₉	—	4	8	no	—
122	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
158	#95×C₅₉	C₂³	1	2	yes	—
159	#95×C₅₉	C₂³	1	1	yes	characteristic
160	#95×C₅₉	C₂³	1	4	yes	—
161	#95×C₅₉	C₂³	1	2	yes	—
162	#95×C₅₉	C₂³	1	4	yes	—
163	#95×C₅₉	C₂³	1	4	yes	—
164	#95×C₅₉	C₂³	1	4	yes	—
165	#95×C₅₉	C₂³	1	2	yes	—
166	#95×C₅₉	C₂³	1	1	yes	characteristic
167	#95×C₅₉	C₂³	1	2	yes	—
168	#95×C₅₉	C₂³	1	2	yes	—
169	#95×C₅₉	C₂³	1	4	yes	—
170	#95×C₅₉	C₂³	1	4	yes	—
171	#95×C₅₉	C₂³	1	4	yes	—
172	#95×C₅₉	C₂³	1	4	yes	—
173	#95×C₅₉	C₂³	1	2	yes	—
174	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
176	#41×C₅₉	—	2	32	no	—
177	C₂×Q₈×C₅₉	—	2	2	no	—
178	C₂×Q₈×C₅₉	—	2	2	no	—
179	C₂×Q₈×C₅₉	—	2	8	no	—
180	C₂×Q₈×C₅₉	—	2	4	no	—
181	C₂×Q₈×C₅₉	—	2	2	no	—
182	C₂×Q₈×C₅₉	—	2	4	no	—
183	C₂×Q₈×C₅₉	—	2	8	no	—
184	C₂×Q₈×C₅₉	—	4	4	no	—
185	C₂×Q₈×C₅₉	—	4	4	no	—
186	C₂×Q₈×C₅₉	—	4	32	no	—
187	C₂×Q₈×C₅₉	C₂×Q₈	1	4	yes	complemented
188	C₂×D₄×C₅₉	—	2	4	no	—
189	C₂×D₄×C₅₉	—	2	4	no	—
190	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
191	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
192	C₂×D₄×C₅₉	C₂×Q₈	1	8	yes	complemented
193	C₂×D₄×C₅₉	#41	1	4	yes	—
194	C₂²×C₄×C₅₉	—	2	4	no	—
195	C₂²×C₄×C₅₉	—	2	4	no	—
196	C₂²×C₄×C₅₉	—	2	2	no	—
197	C₂²×C₄×C₅₉	—	2	2	no	—
198	C₂²×C₄×C₅₉	—	2	8	no	—
199	C₂²×C₄×C₅₉	—	2	8	no	—
200	C₂²×C₄×C₅₉	—	2	4	no	—
201	C₂²×C₄×C₅₉	—	2	8	no	—
202	C₂²×C₄×C₅₉	—	2	8	no	—
203	C₂²×C₄×C₅₉	—	2	4	no	—
204	C₂²×C₄×C₅₉	—	4	4	no	—
205	C₂²×C₄×C₅₉	—	4	4	no	—
206	C₂²×C₄×C₅₉	—	4	4	no	—
207	C₂²×C₄×C₅₉	—	4	4	no	—
208	C₂²×C₄×C₅₉	—	4	4	no	—
209	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
210	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	complemented
211	C₂²×C₄×C₅₉	C₂×Q₈	1	4	yes	complemented
212	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₅₉	—	2	4	no	—
228	C₄⋊C₄×C₅₉	—	2	2	no	—
229	C₄⋊C₄×C₅₉	—	2	4	no	—
230	C₄⋊C₄×C₅₉	—	2	4	no	—
231	C₄⋊C₄×C₅₉	—	2	2	no	—
232	C₄⋊C₄×C₅₉	—	2	2	no	—
233	C₄⋊C₄×C₅₉	—	2	4	no	—
234	C₄⋊C₄×C₅₉	—	2	4	no	—
235	C₄⋊C₄×C₅₉	—	2	2	no	—
236	C₄⋊C₄×C₅₉	—	2	8	no	—
237	C₄⋊C₄×C₅₉	—	2	4	no	—
238	C₄⋊C₄×C₅₉	—	2	4	no	—
239	C₄⋊C₄×C₅₉	—	2	4	no	—
240	C₄⋊C₄×C₅₉	—	2	8	no	—
241	C₄⋊C₄×C₅₉	—	2	4	no	—
242	C₄⋊C₄×C₅₉	—	2	4	no	—
243	C₄⋊C₄×C₅₉	—	4	4	no	—
244	C₄⋊C₄×C₅₉	—	4	4	no	—
245	C₄⋊C₄×C₅₉	—	4	4	no	—
246	C₄⋊C₄×C₅₉	—	4	4	no	—
247	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
248	C₂²⋊C₄×C₅₉	—	2	4	no	—
249	C₂²⋊C₄×C₅₉	—	2	8	no	—
250	C₂²⋊C₄×C₅₉	—	2	8	no	—
251	C₂²⋊C₄×C₅₉	—	2	2	no	—
252	C₂²⋊C₄×C₅₉	—	2	2	no	—
253	C₂²⋊C₄×C₅₉	—	2	4	no	—
254	C₂²⋊C₄×C₅₉	—	2	4	no	—
255	C₂²⋊C₄×C₅₉	—	4	4	no	—
256	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
257	C₄²×C₅₉	—	2	4	no	—
258	C₄²×C₅₉	—	2	4	no	—
259	C₄²×C₅₉	—	2	2	no	—
260	C₄²×C₅₉	—	2	4	no	—
261	C₄²×C₅₉	—	2	4	no	—
262	C₄²×C₅₉	C₂×D₄	1	4	yes	—
263	C₂³×C₅₉	—	2	4	no	—
264	C₂³×C₅₉	—	2	4	no	—
265	C₂³×C₅₉	—	2	1	no	—
266	C₂³×C₅₉	—	2	1	no	—
267	C₂³×C₅₉	—	2	2	no	—
268	C₂³×C₅₉	—	2	2	no	—
269	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
270	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
271	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
272	C₂³×C₅₉	C₂×#41	1	4	yes	—
273	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
274	Q₈×C₅₉	—	2	8	no	—
275	Q₈×C₅₉	—	2	8	no	—
276	Q₈×C₅₉	—	4	16	no	—
277	Q₈×C₅₉	—	4	8	no	—
278	D₄×C₅₉	—	2	16	no	—
279	D₄×C₅₉	C₂²⋊Q₈	1	16	yes	complemented
280	C₂×C₄×C₅₉	—	2	16	no	—
281	C₂×C₄×C₅₉	—	2	2	no	—
282	C₂×C₄×C₅₉	—	2	2	no	—
283	C₂×C₄×C₅₉	—	2	1	no	—
284	C₂×C₄×C₅₉	—	2	2	no	—
285	C₂×C₄×C₅₉	—	2	1	no	—
286	C₂×C₄×C₅₉	—	2	2	no	—
287	C₂×C₄×C₅₉	—	2	2	no	—
288	C₂×C₄×C₅₉	—	2	4	no	—
289	C₂×C₄×C₅₉	—	2	2	no	—
290	C₂×C₄×C₅₉	—	2	2	no	—
291	C₂×C₄×C₅₉	—	2	2	no	—
292	C₂×C₄×C₅₉	—	2	8	no	—
293	C₂×C₄×C₅₉	—	2	1	no	—
294	C₂×C₄×C₅₉	—	2	2	no	—
295	C₂×C₄×C₅₉	—	2	2	no	—
296	C₂×C₄×C₅₉	—	2	1	no	—
297	C₂×C₄×C₅₉	—	2	4	no	—
298	C₂×C₄×C₅₉	—	2	2	no	—
299	C₂×C₄×C₅₉	—	2	4	no	—
300	C₂×C₄×C₅₉	—	2	2	no	—
301	C₂×C₄×C₅₉	—	2	4	no	—
302	C₂×C₄×C₅₉	—	2	4	no	—
303	C₂×C₄×C₅₉	—	2	2	no	—
304	C₂×C₄×C₅₉	—	2	4	no	—
305	C₂×C₄×C₅₉	—	2	4	no	—
306	C₂×C₄×C₅₉	—	2	2	no	—
307	C₂×C₄×C₅₉	—	2	2	no	—
308	C₂×C₄×C₅₉	—	2	2	no	—
309	C₂×C₄×C₅₉	—	2	2	no	—
310	C₂×C₄×C₅₉	—	2	4	no	—
311	C₂×C₄×C₅₉	—	4	8	no	—
312	C₂×C₄×C₅₉	—	4	16	no	—
313	C₂×C₄×C₅₉	—	4	16	no	—
314	C₂×C₄×C₅₉	—	8	4	no	—
315	C₂×C₄×C₅₉	—	8	4	no	—
316	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
321	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
322	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
323	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
324	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
325	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
326	#35739	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
327	C₂²×C₅₉	—	2	4	no	—
328	C₂²×C₅₉	—	2	4	no	—
329	C₂²×C₅₉	—	2	8	no	—
330	C₂²×C₅₉	—	2	8	no	—
331	C₂²×C₅₉	—	2	2	no	—
332	C₂²×C₅₉	—	2	4	no	—
333	C₂²×C₅₉	—	4	1	no	—
334	C₂²×C₅₉	—	4	1	no	—
335	C₂²×C₅₉	—	4	2	no	—
336	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	8	yes	—
337	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
338	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
339	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
341	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
342	C₄×C₅₉	—	2	2	no	—
343	C₄×C₅₉	—	2	4	no	—
344	C₄×C₅₉	—	2	2	no	—
345	C₄×C₅₉	—	2	4	no	—
346	C₄×C₅₉	—	2	4	no	—
347	C₄×C₅₉	—	2	2	no	—
348	C₄×C₅₉	—	2	4	no	—
349	C₄×C₅₉	—	4	4	no	—
350	C₄×C₅₉	—	4	2	no	—
351	C₄×C₅₉	—	4	1	no	—
352	C₄×C₅₉	—	4	1	no	—
353	C₄×C₅₉	—	4	2	no	—
354	C₄×C₅₉	—	4	2	no	—
355	C₄×C₅₉	—	4	4	no	—
356	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
357	C₂×D₄×Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
358	C₂×#520	C₂×C₅₉	1	1	yes	characteristic
359	#2628	C₂×C₅₉	1	1	yes	characteristic, complemented
360	#2627	C₂×C₅₉	1	2	yes	complemented
361	#2581	C₂×C₅₉	1	1	yes	characteristic, complemented
362	#2567	C₂×C₅₉	1	1	yes	characteristic, complemented
363	#2564	C₂×C₅₉	1	2	yes	complemented
364	#2451	C₂×C₅₉	1	2	yes	complemented
365	#2449	C₂×C₅₉	1	4	yes	complemented
366	#2440	C₂×C₅₉	1	2	yes	complemented
367	#2438	C₂×C₅₉	1	4	yes	complemented
368	#2409	C₂×C₅₉	1	2	yes	complemented
369	#2396	C₂×C₅₉	1	1	yes	characteristic, complemented
370	C₂×#395	C₂×C₅₉	1	2	yes	complemented
371	#2349	C₂×C₅₉	1	1	yes	characteristic, complemented
372	D₄×C₄⋊C₄	C₂×C₅₉	1	2	yes	complemented
373	#2339	C₂×C₅₉	1	2	yes	—
374	C₂×C₅₉	—	2	8	no	—
375	C₂×C₅₉	—	4	2	no	—
376	C₂×C₅₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
377	C₂×C₅₉	#3484	1	1	yes	characteristic
378	C₂×C₅₉	#3499	1	1	yes	characteristic
379	C₂×C₅₉	#3503	1	2	yes	—
380	C₂×C₅₉	#3520	1	2	yes	—
381	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
382	C₂³×Q₈	C₂²×C₅₉	1	2	yes	—
383	D₄×Q₈	—	2	8	no	—
384	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
385	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
386	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
388	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
389	#520	—	2	8	no	—
390	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
394	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
395	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
399	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
400	C₂×#117	C₂²×C₅₉	1	2	yes	—
401	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
402	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
404	#400	C₂²×C₅₉	1	2	yes	—
405	#400	C₂²×C₅₉	1	1	yes	characteristic
406	#400	C₂²×C₅₉	1	2	yes	—
407	#399	C₂²×C₅₉	1	1	yes	characteristic
408	#399	C₂²×C₅₉	1	2	yes	—
409	#398	C₂²×C₅₉	1	4	yes	—
410	#398	C₂²×C₅₉	1	4	yes	—
411	#398	C₂²×C₅₉	1	2	yes	—
412	#396	C₂²×C₅₉	1	2	yes	—
413	#395	C₂²×C₅₉	1	2	yes	—
414	#395	C₂²×C₅₉	1	2	yes	—
415	#395	C₂²×C₅₉	1	2	yes	—
416	#395	C₂²×C₅₉	1	2	yes	—
417	#395	C₂²×C₅₉	1	1	yes	characteristic
418	#395	C₂²×C₅₉	1	4	yes	—
419	#395	C₂²×C₅₉	1	4	yes	—
420	#393	C₂²×C₅₉	1	2	yes	—
421	#393	C₂²×C₅₉	1	1	yes	characteristic
422	#391	C₂²×C₅₉	1	2	yes	—
423	#391	C₂²×C₅₉	1	2	yes	—
424	#391	C₂²×C₅₉	1	4	yes	—
425	#389	C₂²×C₅₉	1	4	yes	—
426	#389	C₂²×C₅₉	1	2	yes	—
427	#389	C₂²×C₅₉	1	2	yes	—
428	#389	C₂²×C₅₉	1	2	yes	—
429	#387	C₂²×C₅₉	1	4	yes	—
430	#387	C₂²×C₅₉	1	4	yes	—
431	#386	C₂²×C₅₉	1	4	yes	—
432	#386	C₂²×C₅₉	1	4	yes	—
433	#385	C₂²×C₅₉	1	4	yes	—
434	#385	C₂²×C₅₉	1	4	yes	—
435	#385	C₂²×C₅₉	1	4	yes	—
436	#385	C₂²×C₅₉	1	4	yes	—
437	#384	C₂²×C₅₉	1	2	yes	—
438	#382	C₂²×C₅₉	1	1	yes	characteristic
439	#381	C₂²×C₅₉	1	4	yes	—
440	#380	C₂²×C₅₉	1	4	yes	—
441	#380	C₂²×C₅₉	1	2	yes	—
442	#380	C₂²×C₅₉	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
445	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
446	C₂×#95	C₂²×C₅₉	1	2	yes	—
447	C₂×#95	C₂²×C₅₉	1	4	yes	—
448	C₅₉	#35739	1	1	yes	characteristic, direct product factor, Sylow
449	C₂×#41	—	2	4	no	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	Q₈×C₅₉	1	8	yes	complemented
452	C₂²×Q₈	—	2	8	no	—
453	C₂²×Q₈	—	4	8	no	—
454	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
456	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
458	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
459	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
461	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
462	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
463	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
465	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
466	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
467	C₄⋊Q₈	—	2	8	no	—
468	C₄⋊Q₈	—	2	4	no	—
469	C₂²⋊Q₈	—	2	8	no	—
470	C₂²⋊Q₈	—	2	16	no	—
471	C₂²⋊Q₈	—	4	8	no	—
472	C₄×Q₈	—	2	4	no	—
473	C₄×Q₈	—	2	4	no	—
474	C₄×Q₈	—	2	4	no	—
475	C₄×D₄	—	2	4	no	—
476	C₄×D₄	—	2	8	no	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	D₄×C₅₉	1	8	yes	—
481	#117	—	2	8	no	—
482	#117	—	2	4	no	—
483	C₂×C₄⋊C₄	—	2	8	no	—
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	—	4	8	no	—
486	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
516	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
518	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
519	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
520	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
521	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
522	#95	C₂³×C₅₉	1	2	yes	—
523	#95	C₂³×C₅₉	1	1	yes	characteristic
524	#95	C₂³×C₅₉	1	4	yes	—
525	#95	C₂³×C₅₉	1	2	yes	—
526	#95	C₂³×C₅₉	1	4	yes	—
527	#95	C₂³×C₅₉	1	4	yes	—
528	#95	C₂³×C₅₉	1	4	yes	—
529	#95	C₂³×C₅₉	1	2	yes	—
530	#95	C₂³×C₅₉	1	1	yes	characteristic
531	#95	C₂³×C₅₉	1	2	yes	—
532	#95	C₂³×C₅₉	1	2	yes	—
533	#95	C₂³×C₅₉	1	4	yes	—
534	#95	C₂³×C₅₉	1	4	yes	—
535	#95	C₂³×C₅₉	1	4	yes	—
536	#95	C₂³×C₅₉	1	4	yes	—
537	#95	C₂³×C₅₉	1	2	yes	—
538	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
539	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
540	#41	—	2	32	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	8	no	—
544	C₂×Q₈	—	2	4	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	8	no	—
548	C₂×Q₈	—	4	4	no	—
549	C₂×Q₈	—	4	4	no	—
550	C₂×Q₈	—	4	32	no	—
551	C₂×Q₈	C₂×Q₈×C₅₉	1	4	yes	complemented
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
555	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
556	C₂×D₄	C₂×Q₈×C₅₉	1	8	yes	complemented
557	C₂×D₄	#41×C₅₉	1	4	yes	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	8	no	—
563	C₂²×C₄	—	2	8	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	8	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	—	4	4	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	4	no	—
573	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
574	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	complemented
575	C₂²×C₄	C₂×Q₈×C₅₉	1	4	yes	complemented
576	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₄⋊C₄	—	4	4	no	—
609	C₄⋊C₄	—	4	4	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	C₂×D₄×C₅₉	1	4	yes	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
634	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
635	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
636	C₂³	C₂×#41×C₅₉	1	4	yes	—
637	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
638	Q₈	—	2	8	no	—
639	Q₈	—	2	8	no	—
640	Q₈	—	4	16	no	—
641	Q₈	—	4	8	no	—
642	D₄	—	2	16	no	—
643	D₄	C₂²⋊Q₈×C₅₉	1	16	yes	complemented
644	C₂×C₄	—	2	16	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	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	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	8	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	16	no	—
677	C₂×C₄	—	4	16	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	4	no	—
680	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
682	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
684	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
685	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
686	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
687	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
688	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
689	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
690	C₂²	—	2	8	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	2	8	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	8	yes	—
700	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
701	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
702	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
703	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
704	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
705	C₄	—	2	4	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	4	no	—
710	C₄	—	2	4	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	4	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	2	no	—
719	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
720	C₂	—	2	8	no	—
721	C₂	—	4	2	no	—
722	C₂	C₂²×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
723	C₂	C₅₉×#3484	1	1	yes	characteristic
724	C₂	C₅₉×#3499	1	1	yes	characteristic
725	C₂	C₅₉×#3503	1	2	yes	—
726	C₂	C₅₉×#3520	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×D₄×Q₈×C₅₉	C₂	semidirect
3. C₅₉×#2628	C₂	semidirect
4. C₅₉×#2627	C₂	semidirect
5. C₅₉×#2581	C₂	semidirect
6. C₅₉×#2567	C₂	semidirect
7. C₅₉×#2564	C₂	semidirect
8. C₅₉×#2451	C₂	semidirect
9. C₅₉×#2449	C₂	semidirect
10. C₅₉×#2440	C₂	semidirect
11. C₅₉×#2438	C₂	semidirect
12. C₅₉×#2409	C₂	semidirect
13. C₅₉×#2396	C₂	semidirect
14. C₂×C₅₉×#395	C₂	semidirect
15. C₅₉×#2349	C₂	semidirect
16. D₄×C₄⋊C₄×C₅₉	C₂	semidirect
87. C₂×#41×C₅₉	Q₈	semidirect
187. C₂×Q₈×C₅₉	C₂×Q₈	semidirect
192. C₂×D₄×C₅₉	C₂×Q₈	semidirect
210. C₂²×C₄×C₅₉	C₂×Q₈	semidirect
211. C₂²×C₄×C₅₉	C₂×Q₈	semidirect
279. D₄×C₅₉	C₂²⋊Q₈	semidirect
326. #35739	C₅₉	direct (N × H)
357. C₂×D₄×Q₈	C₂×C₅₉	semidirect
359. #2628	C₂×C₅₉	semidirect
360. #2627	C₂×C₅₉	semidirect
361. #2581	C₂×C₅₉	semidirect
362. #2567	C₂×C₅₉	semidirect
363. #2564	C₂×C₅₉	semidirect
364. #2451	C₂×C₅₉	semidirect
365. #2449	C₂×C₅₉	semidirect
366. #2440	C₂×C₅₉	semidirect
367. #2438	C₂×C₅₉	semidirect
368. #2409	C₂×C₅₉	semidirect
369. #2396	C₂×C₅₉	semidirect
370. C₂×#395	C₂×C₅₉	semidirect
371. #2349	C₂×C₅₉	semidirect
372. D₄×C₄⋊C₄	C₂×C₅₉	semidirect
448. C₅₉	#35739	direct (N × H)
451. C₂×#41	Q₈×C₅₉	semidirect
551. C₂×Q₈	C₂×Q₈×C₅₉	semidirect
556. C₂×D₄	C₂×Q₈×C₅₉	semidirect
574. C₂²×C₄	C₂×Q₈×C₅₉	semidirect
575. C₂²×C₄	C₂×Q₈×C₅₉	semidirect
643. D₄	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×D₄×Q₈×C₅₉	2
C₂×C₅₉×#520	2
C₅₉×#2628	2
C₅₉×#2627	2
C₅₉×#2581	2
C₅₉×#2567	2
C₅₉×#2564	2
C₅₉×#2451	2
C₅₉×#2449	2
C₅₉×#2440	2
C₅₉×#2438	2
C₅₉×#2409	2
C₅₉×#2396	2
C₂×C₅₉×#395	2
C₅₉×#2349	2
D₄×C₄⋊C₄×C₅₉	2
C₅₉×#2339	2
#35739	59

Subgroups — C59×#35739 #28447848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35739 #28447848