Subgroups — C₅₉×#35749 #28447858

Order 15104.

2170 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#519	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2634	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2621	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2611	C₂	1	2	yes	maximal
6	C₅₉×#2599	C₂	1	2	yes	maximal
7	C₅₉×#2581	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2475	C₂	1	4	yes	maximal
10	C₅₉×#2462	C₂	1	4	yes	maximal, complemented
11	C₅₉×#2446	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2434	C₂	1	2	yes	maximal
13	C₅₉×#2399	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2365	C₂	1	2	yes	maximal, complemented
16	C₅₉×#2362	C₂	1	2	yes	maximal
17	C₅₉×#2356	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₅₉×#557	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
23	C₂×#125×C₅₉	C₂²	1	2	yes	—
24	C₂×#125×C₅₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
26	C₅₉×#519	—	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	2	yes	—
30	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₉	C₂²	1	2	yes	—
37	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₅₉	C₂²	1	2	yes	—
40	C₅₉×#400	C₂²	1	2	yes	—
41	C₅₉×#400	C₂²	1	1	yes	characteristic
42	C₅₉×#400	C₂²	1	4	yes	—
43	C₅₉×#399	C₂²	1	1	yes	characteristic
44	C₅₉×#398	C₂²	1	2	yes	—
45	C₅₉×#398	C₂²	1	2	yes	—
46	C₅₉×#398	C₂²	1	2	yes	—
47	C₅₉×#398	C₂²	1	2	yes	—
48	C₅₉×#398	C₂²	1	2	yes	—
49	C₅₉×#398	C₂²	1	4	yes	—
50	C₅₉×#397	C₂²	1	2	yes	—
51	C₅₉×#397	C₂²	1	2	yes	—
52	C₅₉×#396	C₂²	1	2	yes	—
53	C₅₉×#395	C₂²	1	2	yes	—
54	C₅₉×#395	C₂²	1	4	yes	—
55	C₅₉×#395	C₂²	1	1	yes	characteristic
56	C₅₉×#395	C₂²	1	4	yes	—
57	C₅₉×#393	C₂²	1	1	yes	characteristic
58	C₅₉×#391	C₂²	1	2	yes	—
59	C₅₉×#391	C₂²	1	2	yes	—
60	C₅₉×#391	C₂²	1	2	yes	—
61	C₅₉×#391	C₂²	1	2	yes	—
62	C₅₉×#389	C₂²	1	4	yes	—
63	C₅₉×#389	C₂²	1	2	yes	—
64	C₅₉×#389	C₂²	1	4	yes	—
65	C₅₉×#388	C₂²	1	4	yes	—
66	C₅₉×#388	C₂²	1	4	yes	—
67	C₅₉×#387	C₂²	1	4	yes	—
68	C₅₉×#387	C₂²	1	4	yes	—
69	C₅₉×#387	C₂²	1	4	yes	—
70	C₅₉×#387	C₂²	1	4	yes	—
71	C₅₉×#387	C₂²	1	4	yes	—
72	C₅₉×#387	C₂²	1	4	yes	—
73	C₅₉×#387	C₂²	1	4	yes	—
74	C₅₉×#385	C₂²	1	4	yes	—
75	C₅₉×#385	C₂²	1	4	yes	—
76	C₅₉×#383	C₂²	1	2	yes	—
77	C₅₉×#382	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
81	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
84	C₅₉×#376	C₂²	1	2	yes	—
85	C₂²×Q₈×C₅₉	—	2	4	no	—
86	C₂²×Q₈×C₅₉	—	2	4	no	—
87	C₂²×Q₈×C₅₉	—	2	4	no	—
88	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
91	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
95	C₄⋊Q₈×C₅₉	—	2	8	no	—
96	C₄⋊Q₈×C₅₉	—	2	8	no	—
97	C₄⋊Q₈×C₅₉	—	2	4	no	—
98	#125×C₅₉	—	2	16	no	—
99	#125×C₅₉	—	2	8	no	—
100	C₂²⋊Q₈×C₅₉	—	2	8	no	—
101	C₄×Q₈×C₅₉	—	2	4	no	—
102	C₄×Q₈×C₅₉	—	2	4	no	—
103	C₄×Q₈×C₅₉	—	2	8	no	—
104	C₄×Q₈×C₅₉	—	2	8	no	—
105	C₄×Q₈×C₅₉	—	2	8	no	—
106	C₄×Q₈×C₅₉	—	2	4	no	—
107	C₄×Q₈×C₅₉	—	2	8	no	—
108	C₄×Q₈×C₅₉	—	2	4	no	—
109	C₄×Q₈×C₅₉	D₄	1	8	yes	—
110	#117×C₅₉	—	2	4	no	—
111	#117×C₅₉	—	2	8	no	—
112	#117×C₅₉	—	2	8	no	—
113	#117×C₅₉	—	2	4	no	—
114	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	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	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
144	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
149	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
154	#95×C₅₉	C₂³	1	1	yes	characteristic
155	#95×C₅₉	C₂³	1	2	yes	—
156	#95×C₅₉	C₂³	1	4	yes	—
157	#95×C₅₉	C₂³	1	2	yes	—
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	4	yes	—
162	#95×C₅₉	C₂³	1	2	yes	—
163	#95×C₅₉	C₂³	1	2	yes	—
164	#95×C₅₉	C₂³	1	4	yes	—
165	#95×C₅₉	C₂³	1	4	yes	—
166	#95×C₅₉	C₂³	1	2	yes	—
167	#95×C₅₉	C₂³	1	4	yes	—
168	#95×C₅₉	C₂³	1	4	yes	—
169	#95×C₅₉	C₂³	1	4	yes	—
170	#95×C₅₉	C₂³	1	4	yes	—
171	#95×C₅₉	C₂³	1	4	yes	—
172	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
173	C₂×Q₈×C₅₉	—	2	32	no	—
174	C₂×Q₈×C₅₉	—	2	2	no	—
175	C₂×Q₈×C₅₉	—	2	4	no	—
176	C₂×Q₈×C₅₉	—	2	2	no	—
177	C₂×Q₈×C₅₉	—	2	4	no	—
178	C₂×Q₈×C₅₉	—	2	4	no	—
179	C₂×Q₈×C₅₉	—	2	4	no	—
180	C₂×Q₈×C₅₉	—	2	2	no	—
181	C₂×Q₈×C₅₉	—	2	2	no	—
182	C₂×Q₈×C₅₉	—	2	2	no	—
183	C₂×Q₈×C₅₉	—	2	4	no	—
184	C₂×Q₈×C₅₉	—	2	4	no	—
185	C₂×Q₈×C₅₉	—	2	4	no	—
186	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
187	C₂×Q₈×C₅₉	#41	1	4	yes	—
188	C₂²×C₄×C₅₉	—	2	4	no	—
189	C₂²×C₄×C₅₉	—	2	4	no	—
190	C₂²×C₄×C₅₉	—	2	2	no	—
191	C₂²×C₄×C₅₉	—	2	4	no	—
192	C₂²×C₄×C₅₉	—	2	2	no	—
193	C₂²×C₄×C₅₉	#41	1	4	yes	—
194	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₄×C₅₉	—	2	4	no	—
211	C₄⋊C₄×C₅₉	—	2	2	no	—
212	C₄⋊C₄×C₅₉	—	2	4	no	—
213	C₄⋊C₄×C₅₉	—	2	2	no	—
214	C₄⋊C₄×C₅₉	—	2	4	no	—
215	C₄⋊C₄×C₅₉	—	2	2	no	—
216	C₄⋊C₄×C₅₉	—	2	4	no	—
217	C₄⋊C₄×C₅₉	—	2	2	no	—
218	C₄⋊C₄×C₅₉	—	2	8	no	—
219	C₄⋊C₄×C₅₉	—	2	8	no	—
220	C₄⋊C₄×C₅₉	—	2	4	no	—
221	C₄⋊C₄×C₅₉	—	2	8	no	—
222	C₄⋊C₄×C₅₉	—	2	4	no	—
223	C₄⋊C₄×C₅₉	—	2	4	no	—
224	C₄⋊C₄×C₅₉	—	2	8	no	—
225	C₄⋊C₄×C₅₉	—	2	8	no	—
226	C₄⋊C₄×C₅₉	—	2	8	no	—
227	C₄⋊C₄×C₅₉	—	2	4	no	—
228	C₄⋊C₄×C₅₉	—	2	4	no	—
229	C₄⋊C₄×C₅₉	—	2	4	no	—
230	C₄⋊C₄×C₅₉	—	2	8	no	—
231	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
233	C₂²⋊C₄×C₅₉	—	2	8	no	—
234	C₂²⋊C₄×C₅₉	—	2	4	no	—
235	C₂²⋊C₄×C₅₉	—	2	2	no	—
236	C₂²⋊C₄×C₅₉	—	2	2	no	—
237	C₂²⋊C₄×C₅₉	—	2	4	no	—
238	C₂²⋊C₄×C₅₉	—	2	4	no	—
239	C₄²×C₅₉	—	2	4	no	—
240	C₄²×C₅₉	—	2	4	no	—
241	C₄²×C₅₉	—	2	4	no	—
242	C₄²×C₅₉	—	2	4	no	—
243	C₄²×C₅₉	—	2	2	no	—
244	C₄²×C₅₉	—	2	8	no	—
245	C₄²×C₅₉	—	2	4	no	—
246	C₄²×C₅₉	—	2	4	no	—
247	C₄²×C₅₉	—	2	8	no	—
248	C₄²×C₅₉	C₂×D₄	1	8	yes	—
249	C₄²×C₅₉	C₂×D₄	1	4	yes	—
250	C₂³×C₅₉	—	2	1	no	—
251	C₂³×C₅₉	—	2	1	no	—
252	C₂³×C₅₉	—	2	2	no	—
253	C₂³×C₅₉	—	2	2	no	—
254	C₂³×C₅₉	C₂×#41	1	2	yes	—
255	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
256	Q₈×C₅₉	—	2	8	no	—
257	Q₈×C₅₉	—	2	16	no	—
258	Q₈×C₅₉	—	2	8	no	—
259	Q₈×C₅₉	—	2	8	no	—
260	Q₈×C₅₉	—	4	8	no	—
261	C₂×C₄×C₅₉	—	2	16	no	—
262	C₂×C₄×C₅₉	—	2	2	no	—
263	C₂×C₄×C₅₉	—	2	2	no	—
264	C₂×C₄×C₅₉	—	2	1	no	—
265	C₂×C₄×C₅₉	—	2	2	no	—
266	C₂×C₄×C₅₉	—	2	2	no	—
267	C₂×C₄×C₅₉	—	2	2	no	—
268	C₂×C₄×C₅₉	—	2	2	no	—
269	C₂×C₄×C₅₉	—	2	1	no	—
270	C₂×C₄×C₅₉	—	2	4	no	—
271	C₂×C₄×C₅₉	—	2	2	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	8	no	—
276	C₂×C₄×C₅₉	—	2	1	no	—
277	C₂×C₄×C₅₉	—	2	2	no	—
278	C₂×C₄×C₅₉	—	2	1	no	—
279	C₂×C₄×C₅₉	—	2	2	no	—
280	C₂×C₄×C₅₉	—	2	4	no	—
281	C₂×C₄×C₅₉	—	2	2	no	—
282	C₂×C₄×C₅₉	—	2	4	no	—
283	C₂×C₄×C₅₉	—	2	4	no	—
284	C₂×C₄×C₅₉	—	2	4	no	—
285	C₂×C₄×C₅₉	—	2	4	no	—
286	C₂×C₄×C₅₉	—	2	2	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	2	no	—
292	C₂×C₄×C₅₉	—	2	4	no	—
293	C₂×C₄×C₅₉	—	2	2	no	—
294	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
300	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
301	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
302	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
303	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
304	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
305	#35749	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂²×C₅₉	—	2	2	no	—
307	C₂²×C₅₉	—	2	4	no	—
308	C₂²×C₅₉	—	4	1	no	—
309	C₂²×C₅₉	—	4	1	no	—
310	C₂²×C₅₉	—	4	2	no	—
311	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
312	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
313	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
314	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
315	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
316	C₄×C₅₉	—	2	4	no	—
317	C₄×C₅₉	—	2	4	no	—
318	C₄×C₅₉	—	2	2	no	—
319	C₄×C₅₉	—	2	2	no	—
320	C₄×C₅₉	—	2	4	no	—
321	C₄×C₅₉	—	2	4	no	—
322	C₄×C₅₉	—	2	2	no	—
323	C₄×C₅₉	—	2	4	no	—
324	C₄×C₅₉	—	4	4	no	—
325	C₄×C₅₉	—	4	1	no	—
326	C₄×C₅₉	—	4	2	no	—
327	C₄×C₅₉	—	4	1	no	—
328	C₄×C₅₉	—	4	2	no	—
329	C₄×C₅₉	—	4	4	no	—
330	C₄×C₅₉	—	4	2	no	—
331	C₄×C₅₉	#525	1	4	yes	—
332	C₂×#557	C₂×C₅₉	1	1	yes	characteristic, complemented
333	C₂×#519	C₂×C₅₉	1	1	yes	characteristic
334	#2634	C₂×C₅₉	1	2	yes	complemented
335	#2621	C₂×C₅₉	1	1	yes	characteristic
336	#2611	C₂×C₅₉	1	2	yes	—
337	#2599	C₂×C₅₉	1	2	yes	—
338	#2581	C₂×C₅₉	1	1	yes	characteristic, complemented
339	#2546	C₂×C₅₉	1	1	yes	characteristic, complemented
340	#2475	C₂×C₅₉	1	4	yes	—
341	#2462	C₂×C₅₉	1	4	yes	complemented
342	#2446	C₂×C₅₉	1	2	yes	complemented
343	#2434	C₂×C₅₉	1	2	yes	—
344	#2399	C₂×C₅₉	1	2	yes	complemented
345	#2396	C₂×C₅₉	1	1	yes	characteristic
346	#2365	C₂×C₅₉	1	2	yes	complemented
347	#2362	C₂×C₅₉	1	2	yes	—
348	#2356	C₂×C₅₉	1	1	yes	characteristic, complemented
349	C₂×C₅₉	—	4	2	no	—
350	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
351	C₂×C₅₉	#3486	1	1	yes	characteristic
352	C₂×C₅₉	#3499	1	1	yes	characteristic
353	C₂×C₅₉	#3509	1	2	yes	—
354	C₂×C₅₉	#3523	1	2	yes	—
355	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
356	#557	—	2	8	no	—
357	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
358	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
359	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
360	C₂×#125	C₂²×C₅₉	1	2	yes	—
361	C₂×#125	C₂²×C₅₉	1	4	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
363	#519	—	2	8	no	—
364	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
367	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
368	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
370	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
372	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
373	C₂×#117	C₂²×C₅₉	1	2	yes	—
374	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
375	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
376	C₂×#117	C₂²×C₅₉	1	2	yes	—
377	#400	C₂²×C₅₉	1	2	yes	—
378	#400	C₂²×C₅₉	1	1	yes	characteristic
379	#400	C₂²×C₅₉	1	4	yes	—
380	#399	C₂²×C₅₉	1	1	yes	characteristic
381	#398	C₂²×C₅₉	1	2	yes	—
382	#398	C₂²×C₅₉	1	2	yes	—
383	#398	C₂²×C₅₉	1	2	yes	—
384	#398	C₂²×C₅₉	1	2	yes	—
385	#398	C₂²×C₅₉	1	2	yes	—
386	#398	C₂²×C₅₉	1	4	yes	—
387	#397	C₂²×C₅₉	1	2	yes	—
388	#397	C₂²×C₅₉	1	2	yes	—
389	#396	C₂²×C₅₉	1	2	yes	—
390	#395	C₂²×C₅₉	1	2	yes	—
391	#395	C₂²×C₅₉	1	4	yes	—
392	#395	C₂²×C₅₉	1	1	yes	characteristic
393	#395	C₂²×C₅₉	1	4	yes	—
394	#393	C₂²×C₅₉	1	1	yes	characteristic
395	#391	C₂²×C₅₉	1	2	yes	—
396	#391	C₂²×C₅₉	1	2	yes	—
397	#391	C₂²×C₅₉	1	2	yes	—
398	#391	C₂²×C₅₉	1	2	yes	—
399	#389	C₂²×C₅₉	1	2	yes	—
400	#389	C₂²×C₅₉	1	4	yes	—
401	#389	C₂²×C₅₉	1	4	yes	—
402	#388	C₂²×C₅₉	1	4	yes	—
403	#388	C₂²×C₅₉	1	4	yes	—
404	#387	C₂²×C₅₉	1	4	yes	—
405	#387	C₂²×C₅₉	1	4	yes	—
406	#387	C₂²×C₅₉	1	4	yes	—
407	#387	C₂²×C₅₉	1	4	yes	—
408	#387	C₂²×C₅₉	1	4	yes	—
409	#387	C₂²×C₅₉	1	4	yes	—
410	#387	C₂²×C₅₉	1	4	yes	—
411	#385	C₂²×C₅₉	1	4	yes	—
412	#385	C₂²×C₅₉	1	4	yes	—
413	#383	C₂²×C₅₉	1	2	yes	—
414	#382	C₂²×C₅₉	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
418	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
419	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
421	#376	C₂²×C₅₉	1	2	yes	—
422	C₅₉	#35749	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²×Q₈	—	2	4	no	—
424	C₂²×Q₈	—	2	4	no	—
425	C₂²×Q₈	—	2	4	no	—
426	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
428	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
429	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
432	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
433	C₄⋊Q₈	—	2	8	no	—
434	C₄⋊Q₈	—	2	8	no	—
435	C₄⋊Q₈	—	2	4	no	—
436	#125	—	2	16	no	—
437	#125	—	2	8	no	—
438	C₂²⋊Q₈	—	2	8	no	—
439	C₄×Q₈	—	2	4	no	—
440	C₄×Q₈	—	2	4	no	—
441	C₄×Q₈	—	2	8	no	—
442	C₄×Q₈	—	2	8	no	—
443	C₄×Q₈	—	2	8	no	—
444	C₄×Q₈	—	2	4	no	—
445	C₄×Q₈	—	2	8	no	—
446	C₄×Q₈	—	2	4	no	—
447	C₄×Q₈	D₄×C₅₉	1	8	yes	—
448	#117	—	2	4	no	—
449	#117	—	2	8	no	—
450	#117	—	2	8	no	—
451	#117	—	2	4	no	—
452	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
481	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
482	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
483	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
485	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
486	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
487	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
488	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
489	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
490	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
492	#95	C₂³×C₅₉	1	1	yes	characteristic
493	#95	C₂³×C₅₉	1	2	yes	—
494	#95	C₂³×C₅₉	1	4	yes	—
495	#95	C₂³×C₅₉	1	2	yes	—
496	#95	C₂³×C₅₉	1	2	yes	—
497	#95	C₂³×C₅₉	1	1	yes	characteristic
498	#95	C₂³×C₅₉	1	4	yes	—
499	#95	C₂³×C₅₉	1	4	yes	—
500	#95	C₂³×C₅₉	1	2	yes	—
501	#95	C₂³×C₅₉	1	2	yes	—
502	#95	C₂³×C₅₉	1	4	yes	—
503	#95	C₂³×C₅₉	1	4	yes	—
504	#95	C₂³×C₅₉	1	2	yes	—
505	#95	C₂³×C₅₉	1	4	yes	—
506	#95	C₂³×C₅₉	1	4	yes	—
507	#95	C₂³×C₅₉	1	4	yes	—
508	#95	C₂³×C₅₉	1	4	yes	—
509	#95	C₂³×C₅₉	1	4	yes	—
510	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
511	C₂×Q₈	—	2	32	no	—
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	2	4	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	4	no	—
516	C₂×Q₈	—	2	4	no	—
517	C₂×Q₈	—	2	4	no	—
518	C₂×Q₈	—	2	2	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	—	2	4	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
525	C₂×Q₈	#41×C₅₉	1	4	yes	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	#41×C₅₉	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
534	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
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	1	yes	characteristic
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	8	no	—
557	C₄⋊C₄	—	2	8	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	8	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	8	no	—
564	C₄⋊C₄	—	2	8	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	C₂×D₄×C₅₉	1	4	yes	—
570	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
571	C₂²⋊C₄	—	2	8	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₄²	—	2	4	no	—
578	C₄²	—	2	4	no	—
579	C₄²	—	2	4	no	—
580	C₄²	—	2	4	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	2	8	no	—
583	C₄²	—	2	4	no	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	8	no	—
586	C₄²	C₂×D₄×C₅₉	1	8	yes	—
587	C₄²	C₂×D₄×C₅₉	1	4	yes	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	C₂×#41×C₅₉	1	2	yes	—
593	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
594	Q₈	—	2	8	no	—
595	Q₈	—	2	16	no	—
596	Q₈	—	2	8	no	—
597	Q₈	—	2	8	no	—
598	Q₈	—	4	8	no	—
599	C₂×C₄	—	2	16	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
633	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
634	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
635	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
636	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
637	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
638	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
639	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
640	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
641	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
642	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
643	C₂²	—	2	4	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
649	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
650	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
651	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
652	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
653	C₄	—	2	4	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	4	4	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	2	no	—
668	C₄	C₅₉×#525	1	4	yes	—
669	C₂	—	4	2	no	—
670	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
671	C₂	C₅₉×#3486	1	1	yes	characteristic
672	C₂	C₅₉×#3499	1	1	yes	characteristic
673	C₂	C₅₉×#3509	1	2	yes	—
674	C₂	C₅₉×#3523	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁴×C₅₉	C₂⁴
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×#557	C₂	semidirect
3. C₅₉×#2634	C₂	semidirect
7. C₅₉×#2581	C₂	semidirect
8. C₅₉×#2546	C₂	semidirect
10. C₅₉×#2462	C₂	semidirect
11. C₅₉×#2446	C₂	semidirect
13. C₅₉×#2399	C₂	semidirect
15. C₅₉×#2365	C₂	semidirect
17. C₅₉×#2356	C₂	semidirect
305. #35749	C₅₉	direct (N × H)
332. C₂×#557	C₂×C₅₉	semidirect
334. #2634	C₂×C₅₉	semidirect
338. #2581	C₂×C₅₉	semidirect
339. #2546	C₂×C₅₉	semidirect
341. #2462	C₂×C₅₉	semidirect
342. #2446	C₂×C₅₉	semidirect
344. #2399	C₂×C₅₉	semidirect
346. #2365	C₂×C₅₉	semidirect
348. #2356	C₂×C₅₉	semidirect
422. C₅₉	#35749	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#557	2
C₂×C₅₉×#519	2
C₅₉×#2634	2
C₅₉×#2621	2
C₅₉×#2611	2
C₅₉×#2599	2
C₅₉×#2581	2
C₅₉×#2546	2
C₅₉×#2475	2
C₅₉×#2462	2
C₅₉×#2446	2
C₅₉×#2434	2
C₅₉×#2399	2
C₅₉×#2396	2
C₅₉×#2365	2
C₅₉×#2362	2
C₅₉×#2356	2
#35749	59

Subgroups — C59×#35749 #28447858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35749 #28447858