Subgroups — C₅₉×#35723 #28447832

Order 15104.

2284 conjugacy classes of subgroups.

The subgroup lattice has 612 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
2	C₂×C₅₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2625	C₂	1	3	yes	maximal, complemented
4	C₅₉×#2499	C₂	1	3	yes	maximal, complemented
5	C₅₉×#2485	C₂	1	3	yes	maximal
6	C₅₉×#2446	C₂	1	3	yes	maximal, complemented
7	C₅₉×#2446	C₂	1	3	yes	maximal, complemented
8	C₅₉×#2423	C₂	1	3	yes	maximal, complemented
9	C₅₉×#2421	C₂	1	3	yes	maximal, complemented
10	C₅₉×#2395	C₂	1	3	yes	maximal
11	C₅₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
13	Q₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
14	Q₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₅₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₅₉	C₂²	1	3	yes	—
20	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	3	yes	—
21	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	3	yes	—
22	C₅₉×#519	—	2	8	no	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₅₉	C₂²	1	3	yes	—
29	C₂×C₄×Q₈×C₅₉	C₂²	1	3	yes	—
30	C₂×C₄×D₄×C₅₉	C₂²	1	3	yes	—
31	C₂×#117×C₅₉	C₂²	1	3	yes	—
32	C₂×#117×C₅₉	C₂²	1	3	yes	—
33	C₅₉×#400	C₂²	1	6	yes	—
34	C₅₉×#400	C₂²	1	3	yes	—
35	C₅₉×#399	C₂²	1	3	yes	—
36	C₅₉×#398	C₂²	1	6	yes	—
37	C₅₉×#398	C₂²	1	3	yes	—
38	C₅₉×#397	C₂²	1	6	yes	—
39	C₅₉×#397	C₂²	1	3	yes	—
40	C₅₉×#397	C₂²	1	3	yes	—
41	C₅₉×#397	C₂²	1	3	yes	—
42	C₅₉×#394	C₂²	1	3	yes	—
43	C₅₉×#394	C₂²	1	1	yes	characteristic
44	C₅₉×#391	C₂²	1	3	yes	—
45	C₅₉×#391	C₂²	1	3	yes	—
46	C₅₉×#391	C₂²	1	3	yes	—
47	C₅₉×#391	C₂²	1	3	yes	—
48	C₅₉×#391	C₂²	1	3	yes	—
49	C₅₉×#391	C₂²	1	3	yes	—
50	C₅₉×#389	C₂²	1	3	yes	—
51	C₅₉×#389	C₂²	1	3	yes	—
52	C₅₉×#389	C₂²	1	3	yes	—
53	C₅₉×#389	C₂²	1	3	yes	—
54	C₅₉×#388	C₂²	1	6	yes	—
55	C₅₉×#387	C₂²	1	6	yes	—
56	C₅₉×#387	C₂²	1	6	yes	—
57	C₅₉×#387	C₂²	1	6	yes	—
58	C₅₉×#384	C₂²	1	3	yes	—
59	C₅₉×#382	C₂²	1	3	yes	—
60	C₅₉×#380	C₂²	1	3	yes	—
61	C₅₉×#380	C₂²	1	3	yes	—
62	C₅₉×#380	C₂²	1	3	yes	—
63	C₄×C₄⋊C₄×C₅₉	C₂²	1	3	yes	—
64	C₄×C₄⋊C₄×C₅₉	C₂²	1	3	yes	—
65	C₄×C₂²⋊C₄×C₅₉	C₂²	1	3	yes	—
66	C₄×C₂²⋊C₄×C₅₉	C₂²	1	3	yes	—
67	C₄×C₂²⋊C₄×C₅₉	C₂²	1	3	yes	—
68	C₂²×Q₈×C₅₉	—	2	4	no	—
69	C₂²×Q₈×C₅₉	—	2	4	no	—
70	C₂²×Q₈×C₅₉	—	2	4	no	—
71	C₂²×Q₈×C₅₉	—	2	4	no	—
72	C₂²×Q₈×C₅₉	—	2	4	no	—
73	C₂²×Q₈×C₅₉	D₄	1	8	yes	—
74	C₂²×Q₈×C₅₉	C₂³	1	3	yes	—
75	C₂²×Q₈×C₅₉	C₂³	1	3	yes	—
76	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
79	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
80	C₄⋊Q₈×C₅₉	—	2	12	no	—
81	C₂²⋊Q₈×C₅₉	—	2	12	no	—
82	C₂²⋊Q₈×C₅₉	—	2	12	no	—
83	C₄×Q₈×C₅₉	—	2	12	no	—
84	C₄×Q₈×C₅₉	—	2	12	no	—
85	C₄×Q₈×C₅₉	—	2	4	no	—
86	C₄×Q₈×C₅₉	—	2	4	no	—
87	C₄×Q₈×C₅₉	—	2	4	no	—
88	C₄×Q₈×C₅₉	—	2	4	no	—
89	C₄×Q₈×C₅₉	—	2	4	no	—
90	C₄×D₄×C₅₉	—	2	12	no	—
91	#117×C₅₉	—	2	12	no	—
92	#117×C₅₉	—	2	12	no	—
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
95	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
96	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
98	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
107	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
111	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
112	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
113	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
115	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
116	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
117	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
118	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
119	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
120	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
121	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
122	C₂×C₄²×C₅₉	C₂³	1	6	yes	—
123	#95×C₅₉	C₂³	1	3	yes	—
124	#95×C₅₉	C₂³	1	3	yes	—
125	#95×C₅₉	C₂³	1	3	yes	—
126	#95×C₅₉	C₂³	1	3	yes	—
127	#95×C₅₉	C₂³	1	3	yes	—
128	#95×C₅₉	C₂³	1	3	yes	—
129	#95×C₅₉	C₂³	1	1	yes	characteristic
130	#95×C₅₉	C₂³	1	3	yes	—
131	#95×C₅₉	C₂³	1	3	yes	—
132	#95×C₅₉	C₂³	1	3	yes	—
133	#95×C₅₉	C₂³	1	6	yes	—
134	#95×C₅₉	C₂³	1	6	yes	—
135	#95×C₅₉	C₂³	1	6	yes	—
136	#95×C₅₉	C₂³	1	6	yes	—
137	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
138	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
139	C₂×Q₈×C₅₉	—	2	32	no	—
140	C₂×Q₈×C₅₉	—	2	6	no	—
141	C₂×Q₈×C₅₉	—	2	6	no	—
142	C₂×Q₈×C₅₉	—	2	6	no	—
143	C₂×Q₈×C₅₉	—	2	6	no	—
144	C₂×Q₈×C₅₉	—	2	6	no	—
145	C₂×Q₈×C₅₉	—	4	16	no	—
146	C₂×Q₈×C₅₉	C₂×D₄	1	12	yes	—
147	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
148	C₂×Q₈×C₅₉	#41	1	4	yes	—
149	C₂×Q₈×C₅₉	#41	1	4	yes	—
150	C₂×D₄×C₅₉	—	2	2	no	—
151	C₂×D₄×C₅₉	—	2	2	no	—
152	C₂×D₄×C₅₉	—	2	2	no	—
153	C₂²×C₄×C₅₉	—	2	6	no	—
154	C₂²×C₄×C₅₉	—	2	6	no	—
155	C₂²×C₄×C₅₉	—	2	6	no	—
156	C₂²×C₄×C₅₉	—	2	6	no	—
157	C₂²×C₄×C₅₉	—	2	6	no	—
158	C₂²×C₄×C₅₉	C₂×D₄	1	12	yes	—
159	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
161	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
162	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
163	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
164	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
167	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
168	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
169	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
172	C₄⋊C₄×C₅₉	—	2	6	no	—
173	C₄⋊C₄×C₅₉	—	2	6	no	—
174	C₄⋊C₄×C₅₉	—	2	6	no	—
175	C₄⋊C₄×C₅₉	—	2	6	no	—
176	C₄⋊C₄×C₅₉	—	2	6	no	—
177	C₄⋊C₄×C₅₉	—	2	6	no	—
178	C₄⋊C₄×C₅₉	—	2	12	no	—
179	C₄⋊C₄×C₅₉	—	2	6	no	—
180	C₄⋊C₄×C₅₉	—	2	6	no	—
181	C₄⋊C₄×C₅₉	—	2	2	no	—
182	C₄⋊C₄×C₅₉	—	2	6	no	—
183	C₄⋊C₄×C₅₉	—	2	6	no	—
184	C₄⋊C₄×C₅₉	—	4	3	no	—
185	C₄⋊C₄×C₅₉	—	4	6	no	—
186	C₂²⋊C₄×C₅₉	—	2	6	no	—
187	C₂²⋊C₄×C₅₉	—	2	2	no	—
188	C₂²⋊C₄×C₅₉	—	2	6	no	—
189	C₂²⋊C₄×C₅₉	—	2	2	no	—
190	C₂²⋊C₄×C₅₉	—	2	6	no	—
191	C₂²⋊C₄×C₅₉	—	2	6	no	—
192	C₂²⋊C₄×C₅₉	—	2	2	no	—
193	C₂²⋊C₄×C₅₉	—	2	2	no	—
194	C₂²⋊C₄×C₅₉	—	4	3	no	—
195	C₂²⋊C₄×C₅₉	—	4	3	no	—
196	C₄²×C₅₉	—	2	12	no	—
197	C₄²×C₅₉	—	2	6	no	—
198	C₄²×C₅₉	—	2	6	no	—
199	C₄²×C₅₉	—	2	6	no	—
200	C₄²×C₅₉	—	2	6	no	—
201	C₄²×C₅₉	—	2	6	no	—
202	C₂³×C₅₉	—	2	1	no	—
203	C₂³×C₅₉	—	2	1	no	—
204	C₂³×C₅₉	—	2	1	no	—
205	C₂³×C₅₉	—	2	1	no	—
206	C₂³×C₅₉	—	2	1	no	—
207	C₂³×C₅₉	—	2	1	no	—
208	C₂³×C₅₉	—	2	1	no	—
209	C₂³×C₅₉	—	2	1	no	—
210	C₂³×C₅₉	—	2	1	no	—
211	C₂³×C₅₉	—	2	1	no	—
212	C₂³×C₅₉	—	2	1	no	—
213	C₂³×C₅₉	—	2	1	no	—
214	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
215	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
216	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
217	Q₈×C₅₉	—	2	24	no	—
218	Q₈×C₅₉	—	4	12	no	—
219	Q₈×C₅₉	#123	1	16	yes	—
220	D₄×C₅₉	—	2	8	no	—
221	C₂×C₄×C₅₉	—	2	1	no	—
222	C₂×C₄×C₅₉	—	2	1	no	—
223	C₂×C₄×C₅₉	—	2	3	no	—
224	C₂×C₄×C₅₉	—	2	3	no	—
225	C₂×C₄×C₅₉	—	2	1	no	—
226	C₂×C₄×C₅₉	—	2	1	no	—
227	C₂×C₄×C₅₉	—	2	24	no	—
228	C₂×C₄×C₅₉	—	2	3	no	—
229	C₂×C₄×C₅₉	—	2	1	no	—
230	C₂×C₄×C₅₉	—	2	1	no	—
231	C₂×C₄×C₅₉	—	2	3	no	—
232	C₂×C₄×C₅₉	—	2	3	no	—
233	C₂×C₄×C₅₉	—	2	3	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	3	no	—
236	C₂×C₄×C₅₉	—	2	3	no	—
237	C₂×C₄×C₅₉	—	2	3	no	—
238	C₂×C₄×C₅₉	—	2	3	no	—
239	C₂×C₄×C₅₉	—	2	1	no	—
240	C₂×C₄×C₅₉	—	2	3	no	—
241	C₂×C₄×C₅₉	—	2	1	no	—
242	C₂×C₄×C₅₉	—	2	3	no	—
243	C₂×C₄×C₅₉	—	2	1	no	—
244	C₂×C₄×C₅₉	—	2	1	no	—
245	C₂×C₄×C₅₉	—	2	1	no	—
246	C₂×C₄×C₅₉	—	2	3	no	—
247	C₂×C₄×C₅₉	—	2	3	no	—
248	C₂×C₄×C₅₉	—	2	3	no	—
249	C₂×C₄×C₅₉	—	2	3	no	—
250	C₂×C₄×C₅₉	—	2	3	no	—
251	C₂×C₄×C₅₉	—	2	3	no	—
252	C₂×C₄×C₅₉	—	2	3	no	—
253	C₂×C₄×C₅₉	—	2	1	no	—
254	C₂×C₄×C₅₉	—	2	3	no	—
255	C₂×C₄×C₅₉	—	4	12	no	—
256	C₂×C₄×C₅₉	C₂²×D₄	1	6	yes	—
257	C₂×C₄×C₅₉	C₂²×D₄	1	6	yes	—
258	C₂×C₄×C₅₉	C₂×#41	1	6	yes	—
259	C₂×C₄×C₅₉	C₂×#41	1	6	yes	—
260	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
261	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
262	#35723	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂²×C₅₉	—	2	2	no	—
264	C₂²×C₅₉	—	2	2	no	—
265	C₂²×C₅₉	—	2	2	no	—
266	C₂²×C₅₉	—	2	2	no	—
267	C₂²×C₅₉	—	2	2	no	—
268	C₂²×C₅₉	—	2	2	no	—
269	C₂²×C₅₉	—	4	1	no	—
270	C₂²×C₅₉	—	4	1	no	—
271	C₂²×C₅₉	—	4	1	no	—
272	C₂²×C₅₉	—	4	1	no	—
273	C₂²×C₅₉	—	4	1	no	—
274	C₂²×C₅₉	—	4	1	no	—
275	C₂²×C₅₉	—	4	1	no	—
276	C₂²×C₅₉	—	4	1	no	—
277	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
278	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
279	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
280	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
281	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
282	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
283	C₂²×C₅₉	#585	1	1	yes	characteristic
284	C₄×C₅₉	—	2	6	no	—
285	C₄×C₅₉	—	2	2	no	—
286	C₄×C₅₉	—	2	2	no	—
287	C₄×C₅₉	—	4	3	no	—
288	C₄×C₅₉	—	4	3	no	—
289	C₄×C₅₉	—	4	1	no	—
290	C₄×C₅₉	—	4	1	no	—
291	C₄×C₅₉	—	4	3	no	—
292	C₄×C₅₉	—	4	3	no	—
293	C₄×C₅₉	—	4	3	no	—
294	C₄×C₅₉	—	4	3	no	—
295	C₄×C₅₉	—	4	1	no	—
296	C₄×C₅₉	C₂×#123	1	12	yes	—
297	C₂×D₄×Q₈	C₂×C₅₉	1	1	yes	characteristic
298	C₂×#519	C₂×C₅₉	1	1	yes	characteristic, complemented
299	#2625	C₂×C₅₉	1	3	yes	complemented
300	#2499	C₂×C₅₉	1	3	yes	complemented
301	#2485	C₂×C₅₉	1	3	yes	—
302	#2446	C₂×C₅₉	1	3	yes	complemented
303	#2446	C₂×C₅₉	1	3	yes	complemented
304	#2423	C₂×C₅₉	1	3	yes	complemented
305	#2421	C₂×C₅₉	1	3	yes	complemented
306	#2395	C₂×C₅₉	1	3	yes	—
307	#2351	C₂×C₅₉	1	1	yes	characteristic, complemented
308	Q₈×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
309	Q₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
310	Q₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
311	Q₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
312	C₂×C₅₉	—	4	2	no	—
313	C₂×C₅₉	—	4	2	no	—
314	C₂×C₅₉	C₂²×#123	1	1	yes	characteristic
315	C₂×C₅₉	#3486	1	1	yes	characteristic
316	C₂×C₅₉	#3497	1	1	yes	characteristic
317	C₂×C₅₉	#3516	1	1	yes	characteristic
318	C₂×C₅₉	#3518	1	1	yes	characteristic
319	C₂×C₅₉	#3523	1	1	yes	characteristic
320	C₂×C₅₉	#3523	1	1	yes	characteristic
321	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
322	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
323	D₄×Q₈	—	2	8	no	—
324	C₂×C₄⋊Q₈	C₂²×C₅₉	1	3	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	3	yes	—
326	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	3	yes	—
327	#519	—	2	8	no	—
328	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
329	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
332	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
333	C₂×C₄×Q₈	C₂²×C₅₉	1	3	yes	—
334	C₂×C₄×Q₈	C₂²×C₅₉	1	3	yes	—
335	C₂×C₄×D₄	C₂²×C₅₉	1	3	yes	—
336	C₂×#117	C₂²×C₅₉	1	3	yes	—
337	C₂×#117	C₂²×C₅₉	1	3	yes	—
338	#400	C₂²×C₅₉	1	6	yes	—
339	#400	C₂²×C₅₉	1	3	yes	—
340	#399	C₂²×C₅₉	1	3	yes	—
341	#398	C₂²×C₅₉	1	6	yes	—
342	#398	C₂²×C₅₉	1	3	yes	—
343	#397	C₂²×C₅₉	1	3	yes	—
344	#397	C₂²×C₅₉	1	6	yes	—
345	#397	C₂²×C₅₉	1	3	yes	—
346	#397	C₂²×C₅₉	1	3	yes	—
347	#394	C₂²×C₅₉	1	1	yes	characteristic
348	#394	C₂²×C₅₉	1	3	yes	—
349	#391	C₂²×C₅₉	1	3	yes	—
350	#391	C₂²×C₅₉	1	3	yes	—
351	#391	C₂²×C₅₉	1	3	yes	—
352	#391	C₂²×C₅₉	1	3	yes	—
353	#391	C₂²×C₅₉	1	3	yes	—
354	#391	C₂²×C₅₉	1	3	yes	—
355	#389	C₂²×C₅₉	1	3	yes	—
356	#389	C₂²×C₅₉	1	3	yes	—
357	#389	C₂²×C₅₉	1	3	yes	—
358	#389	C₂²×C₅₉	1	3	yes	—
359	#388	C₂²×C₅₉	1	6	yes	—
360	#387	C₂²×C₅₉	1	6	yes	—
361	#387	C₂²×C₅₉	1	6	yes	—
362	#387	C₂²×C₅₉	1	6	yes	—
363	#384	C₂²×C₅₉	1	3	yes	—
364	#382	C₂²×C₅₉	1	3	yes	—
365	#380	C₂²×C₅₉	1	3	yes	—
366	#380	C₂²×C₅₉	1	3	yes	—
367	#380	C₂²×C₅₉	1	3	yes	—
368	C₄×C₄⋊C₄	C₂²×C₅₉	1	3	yes	—
369	C₄×C₄⋊C₄	C₂²×C₅₉	1	3	yes	—
370	C₄×C₂²⋊C₄	C₂²×C₅₉	1	3	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₅₉	1	3	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₅₉	1	3	yes	—
373	C₅₉	#35723	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²×Q₈	—	2	4	no	—
375	C₂²×Q₈	—	2	4	no	—
376	C₂²×Q₈	—	2	4	no	—
377	C₂²×Q₈	—	2	4	no	—
378	C₂²×Q₈	—	2	4	no	—
379	C₂²×Q₈	D₄×C₅₉	1	8	yes	—
380	C₂²×Q₈	C₂³×C₅₉	1	3	yes	—
381	C₂²×Q₈	C₂³×C₅₉	1	3	yes	—
382	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₅₉	1	3	yes	—
385	C₂³×C₄	C₂³×C₅₉	1	3	yes	—
386	C₄⋊Q₈	—	2	12	no	—
387	C₂²⋊Q₈	—	2	12	no	—
388	C₂²⋊Q₈	—	2	12	no	—
389	C₄×Q₈	—	2	12	no	—
390	C₄×Q₈	—	2	12	no	—
391	C₄×Q₈	—	2	4	no	—
392	C₄×Q₈	—	2	4	no	—
393	C₄×Q₈	—	2	4	no	—
394	C₄×Q₈	—	2	4	no	—
395	C₄×Q₈	—	2	4	no	—
396	C₄×D₄	—	2	12	no	—
397	#117	—	2	12	no	—
398	#117	—	2	12	no	—
399	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
400	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
401	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
402	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
403	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
404	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
405	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
406	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
407	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
408	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
410	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
411	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
412	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
423	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
424	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
425	C₂×C₄²	C₂³×C₅₉	1	6	yes	—
426	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
427	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
428	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
429	#95	C₂³×C₅₉	1	3	yes	—
430	#95	C₂³×C₅₉	1	3	yes	—
431	#95	C₂³×C₅₉	1	3	yes	—
432	#95	C₂³×C₅₉	1	3	yes	—
433	#95	C₂³×C₅₉	1	3	yes	—
434	#95	C₂³×C₅₉	1	3	yes	—
435	#95	C₂³×C₅₉	1	1	yes	characteristic
436	#95	C₂³×C₅₉	1	3	yes	—
437	#95	C₂³×C₅₉	1	3	yes	—
438	#95	C₂³×C₅₉	1	3	yes	—
439	#95	C₂³×C₅₉	1	6	yes	—
440	#95	C₂³×C₅₉	1	6	yes	—
441	#95	C₂³×C₅₉	1	6	yes	—
442	#95	C₂³×C₅₉	1	6	yes	—
443	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
444	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
445	C₂×Q₈	—	2	32	no	—
446	C₂×Q₈	—	2	6	no	—
447	C₂×Q₈	—	2	6	no	—
448	C₂×Q₈	—	2	6	no	—
449	C₂×Q₈	—	2	6	no	—
450	C₂×Q₈	—	2	6	no	—
451	C₂×Q₈	—	4	16	no	—
452	C₂×Q₈	C₂×D₄×C₅₉	1	12	yes	—
453	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
454	C₂×Q₈	#41×C₅₉	1	4	yes	—
455	C₂×Q₈	#41×C₅₉	1	4	yes	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂²×C₄	—	2	6	no	—
460	C₂²×C₄	—	2	6	no	—
461	C₂²×C₄	—	2	6	no	—
462	C₂²×C₄	—	2	6	no	—
463	C₂²×C₄	—	2	6	no	—
464	C₂²×C₄	C₂×D₄×C₅₉	1	12	yes	—
465	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
467	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
468	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
469	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
470	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
473	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
474	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
475	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
478	C₄⋊C₄	—	2	6	no	—
479	C₄⋊C₄	—	2	6	no	—
480	C₄⋊C₄	—	2	6	no	—
481	C₄⋊C₄	—	2	6	no	—
482	C₄⋊C₄	—	2	6	no	—
483	C₄⋊C₄	—	2	6	no	—
484	C₄⋊C₄	—	2	12	no	—
485	C₄⋊C₄	—	2	6	no	—
486	C₄⋊C₄	—	2	6	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	6	no	—
489	C₄⋊C₄	—	2	6	no	—
490	C₄⋊C₄	—	4	3	no	—
491	C₄⋊C₄	—	4	6	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	6	no	—
494	C₂²⋊C₄	—	2	6	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	6	no	—
497	C₂²⋊C₄	—	2	6	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	4	3	no	—
501	C₂²⋊C₄	—	4	3	no	—
502	C₄²	—	2	12	no	—
503	C₄²	—	2	6	no	—
504	C₄²	—	2	6	no	—
505	C₄²	—	2	6	no	—
506	C₄²	—	2	6	no	—
507	C₄²	—	2	6	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
521	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
522	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
523	Q₈	—	2	24	no	—
524	Q₈	—	4	12	no	—
525	Q₈	#123×C₅₉	1	16	yes	—
526	D₄	—	2	8	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	3	no	—
530	C₂×C₄	—	2	3	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	24	no	—
534	C₂×C₄	—	2	3	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	3	no	—
538	C₂×C₄	—	2	3	no	—
539	C₂×C₄	—	2	3	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	3	no	—
542	C₂×C₄	—	2	3	no	—
543	C₂×C₄	—	2	3	no	—
544	C₂×C₄	—	2	3	no	—
545	C₂×C₄	—	2	3	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	3	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	3	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	3	no	—
554	C₂×C₄	—	2	3	no	—
555	C₂×C₄	—	2	3	no	—
556	C₂×C₄	—	2	3	no	—
557	C₂×C₄	—	2	3	no	—
558	C₂×C₄	—	2	3	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	3	no	—
561	C₂×C₄	—	4	12	no	—
562	C₂×C₄	C₂²×D₄×C₅₉	1	6	yes	—
563	C₂×C₄	C₂²×D₄×C₅₉	1	6	yes	—
564	C₂×C₄	C₂×#41×C₅₉	1	6	yes	—
565	C₂×C₄	C₂×#41×C₅₉	1	6	yes	—
566	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
567	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
583	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
584	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
585	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
586	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
587	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
588	C₂²	C₅₉×#585	1	1	yes	characteristic
589	C₄	—	2	2	no	—
590	C₄	—	2	6	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	3	no	—
593	C₄	—	4	3	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	3	no	—
596	C₄	—	4	3	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	3	no	—
600	C₄	—	4	3	no	—
601	C₄	C₂×#123×C₅₉	1	12	yes	—
602	C₂	—	4	2	no	—
603	C₂	—	4	2	no	—
604	C₂	C₂²×#123×C₅₉	1	1	yes	characteristic
605	C₂	C₅₉×#3486	1	1	yes	characteristic
606	C₂	C₅₉×#3497	1	1	yes	characteristic
607	C₂	C₅₉×#3516	1	1	yes	characteristic
608	C₂	C₅₉×#3518	1	1	yes	characteristic
609	C₂	C₅₉×#3523	1	1	yes	characteristic
610	C₂	C₅₉×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂³
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×#519	C₂	semidirect
3. C₅₉×#2625	C₂	semidirect
4. C₅₉×#2499	C₂	semidirect
6. C₅₉×#2446	C₂	semidirect
7. C₅₉×#2446	C₂	semidirect
8. C₅₉×#2423	C₂	semidirect
9. C₅₉×#2421	C₂	semidirect
11. C₅₉×#2351	C₂	semidirect
12. Q₈×C₄⋊C₄×C₅₉	C₂	semidirect
13. Q₈×C₂²⋊C₄×C₅₉	C₂	semidirect
14. Q₈×C₂²⋊C₄×C₅₉	C₂	semidirect
15. Q₈×C₂²⋊C₄×C₅₉	C₂	semidirect
262. #35723	C₅₉	direct (N × H)
298. C₂×#519	C₂×C₅₉	semidirect
299. #2625	C₂×C₅₉	semidirect
300. #2499	C₂×C₅₉	semidirect
302. #2446	C₂×C₅₉	semidirect
303. #2446	C₂×C₅₉	semidirect
304. #2423	C₂×C₅₉	semidirect
305. #2421	C₂×C₅₉	semidirect
307. #2351	C₂×C₅₉	semidirect
308. Q₈×C₄⋊C₄	C₂×C₅₉	semidirect
309. Q₈×C₂²⋊C₄	C₂×C₅₉	semidirect
310. Q₈×C₂²⋊C₄	C₂×C₅₉	semidirect
311. Q₈×C₂²⋊C₄	C₂×C₅₉	semidirect
373. C₅₉	#35723	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×D₄×Q₈×C₅₉	2
C₂×C₅₉×#519	2
C₅₉×#2625	2
C₅₉×#2499	2
C₅₉×#2485	2
C₅₉×#2446	2
C₅₉×#2423	2
C₅₉×#2421	2
C₅₉×#2395	2
C₅₉×#2351	2
Q₈×C₄⋊C₄×C₅₉	2
Q₈×C₂²⋊C₄×C₅₉	2
#35723	59

Subgroups — C59×#35723 #28447832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35723 #28447832