Subgroups — C₅₉×#35620 #28447729

Order 15104.

2294 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2568	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2566	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2565	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2563	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2450	C₂	1	8	yes	maximal, complemented
8	C₅₉×#2442	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2439	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2311	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2297	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#544	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
19	C₂×#125×C₅₉	C₂²	1	2	yes	—
20	C₂×#125×C₅₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
22	C₅₉×#520	—	2	8	no	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
26	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₉	C₂²	1	2	yes	—
29	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
34	C₅₉×#400	C₂²	1	8	yes	—
35	C₅₉×#398	C₂²	1	8	yes	—
36	C₅₉×#396	C₂²	1	8	yes	—
37	C₅₉×#393	C₂²	1	8	yes	—
38	C₅₉×#391	C₂²	1	1	yes	characteristic
39	C₅₉×#391	C₂²	1	1	yes	characteristic
40	C₅₉×#391	C₂²	1	2	yes	—
41	C₅₉×#391	C₂²	1	8	yes	—
42	C₅₉×#390	C₂²	1	1	yes	characteristic
43	C₅₉×#390	C₂²	1	1	yes	characteristic
44	C₅₉×#390	C₂²	1	2	yes	—
45	C₅₉×#389	C₂²	1	2	yes	—
46	C₅₉×#389	C₂²	1	2	yes	—
47	C₅₉×#389	C₂²	1	4	yes	—
48	C₅₉×#387	C₂²	1	8	yes	—
49	C₅₉×#386	C₂²	1	4	yes	—
50	C₅₉×#386	C₂²	1	4	yes	—
51	C₅₉×#385	C₂²	1	4	yes	—
52	C₅₉×#385	C₂²	1	8	yes	—
53	C₅₉×#385	C₂²	1	4	yes	—
54	C₅₉×#384	C₂²	1	2	yes	—
55	C₅₉×#382	C₂²	1	2	yes	—
56	C₅₉×#382	C₂²	1	2	yes	—
57	C₅₉×#382	C₂²	1	4	yes	—
58	C₅₉×#382	C₂²	1	2	yes	—
59	C₅₉×#380	C₂²	1	8	yes	—
60	C₅₉×#380	C₂²	1	4	yes	—
61	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
64	C₂×#95×C₅₉	C₂²	1	4	yes	—
65	C₂×#41×C₅₉	—	2	4	no	—
66	C₂×#41×C₅₉	—	2	4	no	—
67	C₂×#41×C₅₉	Q₈	1	8	yes	complemented
68	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
77	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₅₉	—	2	8	no	—
79	C₄⋊Q₈×C₅₉	—	2	8	no	—
80	#125×C₅₉	—	2	8	no	—
81	#125×C₅₉	—	2	8	no	—
82	C₂²⋊Q₈×C₅₉	—	2	16	no	—
83	C₄×Q₈×C₅₉	—	2	8	no	—
84	C₄×D₄×C₅₉	—	2	16	no	—
85	C₄×D₄×C₅₉	—	2	8	no	—
86	#117×C₅₉	—	2	4	no	—
87	#117×C₅₉	—	2	4	no	—
88	#117×C₅₉	—	2	8	no	—
89	#117×C₅₉	D₄	1	8	yes	—
90	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
91	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
92	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₅₉	—	2	4	no	—
117	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
123	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
124	#95×C₅₉	C₂³	1	8	yes	—
125	#95×C₅₉	C₂³	1	8	yes	—
126	#95×C₅₉	C₂³	1	4	yes	—
127	#95×C₅₉	C₂³	1	4	yes	—
128	#95×C₅₉	C₂³	1	4	yes	—
129	#95×C₅₉	C₂³	1	4	yes	—
130	#95×C₅₉	C₂³	1	8	yes	—
131	#95×C₅₉	C₂³	1	8	yes	—
132	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
133	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
134	#41×C₅₉	—	2	32	no	—
135	C₂×Q₈×C₅₉	—	2	2	no	—
136	C₂×Q₈×C₅₉	—	2	8	no	—
137	C₂×Q₈×C₅₉	—	2	2	no	—
138	C₂×Q₈×C₅₉	—	4	8	no	—
139	C₂×Q₈×C₅₉	C₂×Q₈	1	4	yes	—
140	C₂×D₄×C₅₉	—	2	4	no	—
141	C₂×D₄×C₅₉	—	2	4	no	—
142	C₂×D₄×C₅₉	—	2	2	no	—
143	C₂×D₄×C₅₉	—	2	2	no	—
144	C₂×D₄×C₅₉	C₂×Q₈	1	8	yes	—
145	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
146	C₂²×C₄×C₅₉	—	2	4	no	—
147	C₂²×C₄×C₅₉	—	2	4	no	—
148	C₂²×C₄×C₅₉	—	2	4	no	—
149	C₂²×C₄×C₅₉	—	2	4	no	—
150	C₂²×C₄×C₅₉	—	2	4	no	—
151	C₂²×C₄×C₅₉	—	2	8	no	—
152	C₂²×C₄×C₅₉	—	4	2	no	—
153	C₂²×C₄×C₅₉	—	4	2	no	—
154	C₂²×C₄×C₅₉	—	4	8	no	—
155	C₂²×C₄×C₅₉	—	4	4	no	—
156	C₂²×C₄×C₅₉	—	4	4	no	—
157	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	—
159	C₂²×C₄×C₅₉	C₂×Q₈	1	4	yes	—
160	C₂²×C₄×C₅₉	#41	1	4	yes	—
161	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
173	C₄⋊C₄×C₅₉	—	2	4	no	—
174	C₄⋊C₄×C₅₉	—	2	8	no	—
175	C₄⋊C₄×C₅₉	—	2	4	no	—
176	C₄⋊C₄×C₅₉	—	2	4	no	—
177	C₄⋊C₄×C₅₉	—	2	4	no	—
178	C₄⋊C₄×C₅₉	—	2	2	no	—
179	C₄⋊C₄×C₅₉	—	2	2	no	—
180	C₄⋊C₄×C₅₉	—	2	8	no	—
181	C₄⋊C₄×C₅₉	—	2	8	no	—
182	C₄⋊C₄×C₅₉	—	2	8	no	—
183	C₄⋊C₄×C₅₉	—	2	4	no	—
184	C₄⋊C₄×C₅₉	—	4	4	no	—
185	C₄⋊C₄×C₅₉	—	4	4	no	—
186	C₄⋊C₄×C₅₉	—	4	8	no	—
187	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
188	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
189	C₂²⋊C₄×C₅₉	—	2	4	no	—
190	C₂²⋊C₄×C₅₉	—	2	4	no	—
191	C₂²⋊C₄×C₅₉	—	2	8	no	—
192	C₂²⋊C₄×C₅₉	—	4	8	no	—
193	C₂²⋊C₄×C₅₉	—	4	4	no	—
194	C₂²⋊C₄×C₅₉	—	4	4	no	—
195	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
196	C₄²×C₅₉	—	2	8	no	—
197	C₄²×C₅₉	—	2	4	no	—
198	C₄²×C₅₉	—	2	2	no	—
199	C₄²×C₅₉	—	2	2	no	—
200	C₄²×C₅₉	—	2	4	no	—
201	C₄²×C₅₉	—	2	4	no	—
202	C₄²×C₅₉	C₂×D₄	1	8	yes	—
203	C₂³×C₅₉	—	2	2	no	—
204	C₂³×C₅₉	—	2	2	no	—
205	C₂³×C₅₉	—	2	2	no	—
206	C₂³×C₅₉	—	2	2	no	—
207	C₂³×C₅₉	—	2	4	no	—
208	C₂³×C₅₉	—	2	4	no	—
209	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
210	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
211	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
212	C₂³×C₅₉	C₂×#41	1	2	yes	—
213	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
214	Q₈×C₅₉	—	2	8	no	—
215	Q₈×C₅₉	—	8	8	no	—
216	D₄×C₅₉	—	2	16	no	—
217	D₄×C₅₉	—	2	8	no	—
218	C₂×C₄×C₅₉	—	2	2	no	—
219	C₂×C₄×C₅₉	—	2	2	no	—
220	C₂×C₄×C₅₉	—	2	4	no	—
221	C₂×C₄×C₅₉	—	2	4	no	—
222	C₂×C₄×C₅₉	—	2	16	no	—
223	C₂×C₄×C₅₉	—	2	2	no	—
224	C₂×C₄×C₅₉	—	2	4	no	—
225	C₂×C₄×C₅₉	—	2	2	no	—
226	C₂×C₄×C₅₉	—	2	4	no	—
227	C₂×C₄×C₅₉	—	2	2	no	—
228	C₂×C₄×C₅₉	—	2	2	no	—
229	C₂×C₄×C₅₉	—	2	4	no	—
230	C₂×C₄×C₅₉	—	2	4	no	—
231	C₂×C₄×C₅₉	—	2	2	no	—
232	C₂×C₄×C₅₉	—	2	2	no	—
233	C₂×C₄×C₅₉	—	2	4	no	—
234	C₂×C₄×C₅₉	—	2	8	no	—
235	C₂×C₄×C₅₉	—	2	4	no	—
236	C₂×C₄×C₅₉	—	2	4	no	—
237	C₂×C₄×C₅₉	—	2	2	no	—
238	C₂×C₄×C₅₉	—	2	2	no	—
239	C₂×C₄×C₅₉	—	2	8	no	—
240	C₂×C₄×C₅₉	—	4	8	no	—
241	C₂×C₄×C₅₉	—	8	8	no	—
242	C₂×C₄×C₅₉	—	8	4	no	—
243	C₂×C₄×C₅₉	—	8	4	no	—
244	C₂×C₄×C₅₉	C₂²⋊Q₈	1	16	yes	—
245	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
250	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
251	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
252	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
253	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
254	#35620	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₅₉	—	2	4	no	—
256	C₂²×C₅₉	—	2	2	no	—
257	C₂²×C₅₉	—	2	2	no	—
258	C₂²×C₅₉	—	2	4	no	—
259	C₂²×C₅₉	—	2	4	no	—
260	C₂²×C₅₉	—	2	8	no	—
261	C₂²×C₅₉	—	4	4	no	—
262	C₂²×C₅₉	—	4	2	no	—
263	C₂²×C₅₉	—	4	2	no	—
264	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
265	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
266	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
267	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
268	C₂²×C₅₉	#585	1	2	yes	—
269	C₂²×C₅₉	#585	1	2	yes	—
270	C₄×C₅₉	—	2	4	no	—
271	C₄×C₅₉	—	2	4	no	—
272	C₄×C₅₉	—	2	4	no	—
273	C₄×C₅₉	—	4	4	no	—
274	C₄×C₅₉	—	4	2	no	—
275	C₄×C₅₉	—	4	2	no	—
276	C₄×C₅₉	—	4	2	no	—
277	C₄×C₅₉	—	4	4	no	—
278	C₄×C₅₉	—	4	4	no	—
279	C₄×C₅₉	—	4	2	no	—
280	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
281	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
282	C₂×#544	C₂×C₅₉	1	1	yes	characteristic, complemented
283	C₂×#520	C₂×C₅₉	1	1	yes	characteristic
284	#2568	C₂×C₅₉	1	2	yes	complemented
285	#2566	C₂×C₅₉	1	2	yes	complemented
286	#2565	C₂×C₅₉	1	2	yes	complemented
287	#2563	C₂×C₅₉	1	2	yes	complemented
288	#2450	C₂×C₅₉	1	8	yes	complemented
289	#2442	C₂×C₅₉	1	4	yes	complemented
290	#2439	C₂×C₅₉	1	4	yes	complemented
291	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
292	#2311	C₂×C₅₉	1	1	yes	characteristic
293	#2297	C₂×C₅₉	1	1	yes	characteristic
294	#2296	C₂×C₅₉	1	1	yes	characteristic, complemented
295	C₂×#382	C₂×C₅₉	1	1	yes	characteristic, complemented
296	C₂×C₅₉	—	2	4	no	—
297	C₂×C₅₉	—	4	4	no	—
298	C₂×C₅₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
299	C₂×C₅₉	#3493	1	2	yes	—
300	C₂×C₅₉	#3500	1	1	yes	characteristic
301	C₂×C₅₉	#3500	1	1	yes	characteristic
302	C₂×C₅₉	#3504	1	2	yes	—
303	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
304	#544	—	2	8	no	—
305	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
306	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
307	C₂×#125	C₂²×C₅₉	1	2	yes	—
308	C₂×#125	C₂²×C₅₉	1	2	yes	—
309	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
310	#520	—	2	8	no	—
311	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
312	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
313	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
314	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
315	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
316	C₂×#117	C₂²×C₅₉	1	2	yes	—
317	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
320	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
321	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
322	#400	C₂²×C₅₉	1	8	yes	—
323	#398	C₂²×C₅₉	1	8	yes	—
324	#396	C₂²×C₅₉	1	8	yes	—
325	#393	C₂²×C₅₉	1	8	yes	—
326	#391	C₂²×C₅₉	1	1	yes	characteristic
327	#391	C₂²×C₅₉	1	2	yes	—
328	#391	C₂²×C₅₉	1	1	yes	characteristic
329	#391	C₂²×C₅₉	1	8	yes	—
330	#390	C₂²×C₅₉	1	1	yes	characteristic
331	#390	C₂²×C₅₉	1	2	yes	—
332	#390	C₂²×C₅₉	1	1	yes	characteristic
333	#389	C₂²×C₅₉	1	4	yes	—
334	#389	C₂²×C₅₉	1	2	yes	—
335	#389	C₂²×C₅₉	1	2	yes	—
336	#387	C₂²×C₅₉	1	8	yes	—
337	#386	C₂²×C₅₉	1	4	yes	—
338	#386	C₂²×C₅₉	1	4	yes	—
339	#385	C₂²×C₅₉	1	8	yes	—
340	#385	C₂²×C₅₉	1	4	yes	—
341	#385	C₂²×C₅₉	1	4	yes	—
342	#384	C₂²×C₅₉	1	2	yes	—
343	#382	C₂²×C₅₉	1	2	yes	—
344	#382	C₂²×C₅₉	1	2	yes	—
345	#382	C₂²×C₅₉	1	2	yes	—
346	#382	C₂²×C₅₉	1	4	yes	—
347	#380	C₂²×C₅₉	1	8	yes	—
348	#380	C₂²×C₅₉	1	4	yes	—
349	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
350	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
352	C₂×#95	C₂²×C₅₉	1	4	yes	—
353	C₅₉	#35620	1	1	yes	characteristic, direct product factor, Sylow
354	C₂×#41	—	2	4	no	—
355	C₂×#41	—	2	4	no	—
356	C₂×#41	Q₈×C₅₉	1	8	yes	complemented
357	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
358	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
359	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
360	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
364	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
365	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
366	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
367	C₄⋊Q₈	—	2	8	no	—
368	C₄⋊Q₈	—	2	8	no	—
369	#125	—	2	8	no	—
370	#125	—	2	8	no	—
371	C₂²⋊Q₈	—	2	16	no	—
372	C₄×Q₈	—	2	8	no	—
373	C₄×D₄	—	2	16	no	—
374	C₄×D₄	—	2	8	no	—
375	#117	—	2	4	no	—
376	#117	—	2	4	no	—
377	#117	—	2	8	no	—
378	#117	D₄×C₅₉	1	8	yes	—
379	C₂×C₄⋊C₄	—	2	4	no	—
380	C₂×C₄⋊C₄	—	2	4	no	—
381	C₂×C₄⋊C₄	—	2	8	no	—
382	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
396	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
405	C₂×C₄²	—	2	4	no	—
406	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
407	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
408	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
409	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
410	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
413	#95	C₂³×C₅₉	1	8	yes	—
414	#95	C₂³×C₅₉	1	8	yes	—
415	#95	C₂³×C₅₉	1	4	yes	—
416	#95	C₂³×C₅₉	1	4	yes	—
417	#95	C₂³×C₅₉	1	4	yes	—
418	#95	C₂³×C₅₉	1	4	yes	—
419	#95	C₂³×C₅₉	1	8	yes	—
420	#95	C₂³×C₅₉	1	8	yes	—
421	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
422	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
423	#41	—	2	32	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	8	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	4	8	no	—
428	C₂×Q₈	C₂×Q₈×C₅₉	1	4	yes	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	C₂×Q₈×C₅₉	1	8	yes	—
434	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	8	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
447	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	—
448	C₂²×C₄	C₂×Q₈×C₅₉	1	4	yes	—
449	C₂²×C₄	#41×C₅₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	8	no	—
476	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
477	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	4	8	no	—
482	C₂²⋊C₄	—	4	4	no	—
483	C₂²⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
485	C₄²	—	2	8	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	4	no	—
491	C₄²	C₂×D₄×C₅₉	1	8	yes	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
499	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
500	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
501	C₂³	C₂×#41×C₅₉	1	2	yes	—
502	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
503	Q₈	—	2	8	no	—
504	Q₈	—	8	8	no	—
505	D₄	—	2	16	no	—
506	D₄	—	2	8	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	8	8	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	—	8	4	no	—
533	C₂×C₄	C₂²⋊Q₈×C₅₉	1	16	yes	—
534	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
535	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
536	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
538	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
539	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
540	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
541	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
542	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
553	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
554	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
555	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
556	C₂²	C₅₉×#585	1	2	yes	—
557	C₂²	C₅₉×#585	1	2	yes	—
558	C₄	—	2	4	no	—
559	C₄	—	2	4	no	—
560	C₄	—	2	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	4	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
569	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
570	C₂	—	2	4	no	—
571	C₂	—	4	4	no	—
572	C₂	C₂²×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
573	C₂	C₅₉×#3493	1	2	yes	—
574	C₂	C₅₉×#3500	1	1	yes	characteristic
575	C₂	C₅₉×#3500	1	1	yes	characteristic
576	C₂	C₅₉×#3504	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×C₅₉×#544	C₂	semidirect
3. C₅₉×#2568	C₂	semidirect
4. C₅₉×#2566	C₂	semidirect
5. C₅₉×#2565	C₂	semidirect
6. C₅₉×#2563	C₂	semidirect
7. C₅₉×#2450	C₂	semidirect
8. C₅₉×#2442	C₂	semidirect
9. C₅₉×#2439	C₂	semidirect
10. C₅₉×#2317	C₂	semidirect
13. C₅₉×#2296	C₂	semidirect
14. C₂×C₅₉×#382	C₂	semidirect
67. C₂×#41×C₅₉	Q₈	semidirect
254. #35620	C₅₉	direct (N × H)
282. C₂×#544	C₂×C₅₉	semidirect
284. #2568	C₂×C₅₉	semidirect
285. #2566	C₂×C₅₉	semidirect
286. #2565	C₂×C₅₉	semidirect
287. #2563	C₂×C₅₉	semidirect
288. #2450	C₂×C₅₉	semidirect
289. #2442	C₂×C₅₉	semidirect
290. #2439	C₂×C₅₉	semidirect
291. #2317	C₂×C₅₉	semidirect
294. #2296	C₂×C₅₉	semidirect
295. C₂×#382	C₂×C₅₉	semidirect
353. C₅₉	#35620	direct (N × H)
356. C₂×#41	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×C₅₉×#544	2
C₂×C₅₉×#520	2
C₅₉×#2568	2
C₅₉×#2566	2
C₅₉×#2565	2
C₅₉×#2563	2
C₅₉×#2450	2
C₅₉×#2442	2
C₅₉×#2439	2
C₅₉×#2317	2
C₅₉×#2311	2
C₅₉×#2297	2
C₅₉×#2296	2
C₂×C₅₉×#382	2
#35620	59

Subgroups — C59×#35620 #28447729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35620 #28447729