Subgroups — C₅₉×#23634 #28435743

Order 15104.

1010 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#417	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#416	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2311	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2074	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2073	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2072	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2071	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
19	C₅₉×#417	—	2	4	no	—
20	C₅₉×#416	—	2	4	no	—
21	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#103×C₅₉	C₂²	1	2	yes	—
23	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#102×C₅₉	C₂²	1	2	yes	—
26	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#391	C₂²	1	2	yes	—
28	C₅₉×#390	C₂²	1	2	yes	—
29	C₅₉×#389	—	2	1	no	—
30	C₅₉×#389	—	2	1	no	—
31	C₅₉×#386	—	2	2	no	—
32	C₅₉×#385	—	2	2	no	—
33	C₅₉×#384	C₂²	1	2	yes	—
34	C₅₉×#382	C₂²	1	2	yes	—
35	C₅₉×#380	—	2	1	no	—
36	C₅₉×#380	—	2	1	no	—
37	C₅₉×#340	C₂²	1	2	yes	—
38	C₅₉×#340	C₂²	1	2	yes	—
39	C₅₉×#340	C₂²	1	2	yes	—
40	C₅₉×#340	C₂²	1	2	yes	—
41	C₅₉×#336	C₂²	1	2	yes	—
42	C₅₉×#336	C₂²	1	2	yes	—
43	C₂×#41×C₅₉	—	2	2	no	—
44	C₂×#41×C₅₉	—	2	2	no	—
45	C₂×#41×C₅₉	—	2	2	no	—
46	C₂×#41×C₅₉	—	2	2	no	—
47	C₂×#41×C₅₉	—	2	2	no	—
48	C₂×#41×C₅₉	D₄	1	4	yes	—
49	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₅₉	—	2	1	no	—
51	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₅₉	—	2	1	no	—
53	C₂³×C₄×C₅₉	—	2	1	no	—
54	C₂³×C₄×C₅₉	—	2	1	no	—
55	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₅₉	—	2	2	no	—
57	C₂×M₁₆×C₅₉	—	2	2	no	—
58	C₂×M₁₆×C₅₉	—	2	2	no	—
59	C₂²×C₈×C₅₉	—	2	2	no	—
60	C₂²×C₈×C₅₉	—	2	2	no	—
61	C₂²×C₈×C₅₉	—	2	2	no	—
62	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
65	#117×C₅₉	—	2	2	no	—
66	#117×C₅₉	—	2	2	no	—
67	#117×C₅₉	—	2	2	no	—
68	#117×C₅₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
87	C₂×C₄²×C₅₉	—	2	1	no	—
88	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
89	#103×C₅₉	—	2	2	no	—
90	#103×C₅₉	—	2	2	no	—
91	#103×C₅₉	—	2	4	no	—
92	#102×C₅₉	—	2	2	no	—
93	#102×C₅₉	—	2	2	no	—
94	#102×C₅₉	—	2	4	no	—
95	#95×C₅₉	—	2	2	no	—
96	#95×C₅₉	—	2	2	no	—
97	#95×C₅₉	—	2	2	no	—
98	#95×C₅₉	—	2	2	no	—
99	C₂⁴×C₅₉	—	2	1	no	—
100	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
101	#41×C₅₉	—	2	8	no	—
102	#41×C₅₉	—	2	8	no	—
103	#41×C₅₉	—	4	4	no	—
104	#41×C₅₉	—	4	4	no	—
105	C₂×Q₈×C₅₉	—	2	1	no	—
106	C₂×Q₈×C₅₉	—	2	1	no	—
107	C₂×Q₈×C₅₉	—	2	1	no	—
108	C₂×Q₈×C₅₉	—	2	1	no	—
109	C₂×Q₈×C₅₉	—	2	1	no	—
110	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₅₉	—	2	4	no	—
112	C₂×D₄×C₅₉	—	2	1	no	—
113	C₂×D₄×C₅₉	—	2	1	no	—
114	C₂×D₄×C₅₉	—	2	1	no	—
115	C₂×D₄×C₅₉	—	2	1	no	—
116	C₂×D₄×C₅₉	—	2	1	no	—
117	C₂×D₄×C₅₉	—	4	2	no	—
118	C₂×D₄×C₅₉	—	4	2	no	—
119	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₅₉	—	2	1	no	—
121	C₂²×C₄×C₅₉	—	2	4	no	—
122	C₂²×C₄×C₅₉	—	2	1	no	—
123	C₂²×C₄×C₅₉	—	2	2	no	—
124	C₂²×C₄×C₅₉	—	2	2	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	4	2	no	—
127	C₂²×C₄×C₅₉	—	4	2	no	—
128	C₂²×C₄×C₅₉	—	4	2	no	—
129	C₂²×C₄×C₅₉	—	4	2	no	—
130	C₂²×C₄×C₅₉	—	8	1	no	—
131	C₂²×C₄×C₅₉	—	8	1	no	—
132	C₂²×C₄×C₅₉	—	8	1	no	—
133	C₂²×C₄×C₅₉	—	8	1	no	—
134	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₅₉	#41	1	2	yes	—
139	C₂²×C₄×C₅₉	#41	1	2	yes	—
140	C₂²×C₄×C₅₉	#41	1	2	yes	—
141	C₂²×C₄×C₅₉	#41	1	2	yes	—
142	C₂²×C₄×C₅₉	#41	1	2	yes	—
143	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
144	M₁₆×C₅₉	—	4	4	no	—
145	C₂×C₈×C₅₉	—	2	1	no	—
146	C₂×C₈×C₅₉	—	2	1	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₂×C₈×C₅₉	—	2	1	no	—
149	C₂×C₈×C₅₉	—	2	1	no	—
150	C₂×C₈×C₅₉	—	2	1	no	—
151	C₂×C₈×C₅₉	—	2	1	no	—
152	C₂×C₈×C₅₉	—	2	2	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₂×C₈×C₅₉	—	4	4	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	2	2	no	—
157	C₄⋊C₄×C₅₉	—	2	2	no	—
158	C₄⋊C₄×C₅₉	—	2	1	no	—
159	C₄⋊C₄×C₅₉	—	2	1	no	—
160	C₄⋊C₄×C₅₉	—	2	2	no	—
161	C₄⋊C₄×C₅₉	—	2	2	no	—
162	C₄⋊C₄×C₅₉	—	2	2	no	—
163	C₄⋊C₄×C₅₉	—	2	1	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	4	2	no	—
166	C₄⋊C₄×C₅₉	—	4	2	no	—
167	C₄⋊C₄×C₅₉	—	8	2	no	—
168	C₄⋊C₄×C₅₉	—	8	2	no	—
169	C₂²⋊C₄×C₅₉	—	2	4	no	—
170	C₂²⋊C₄×C₅₉	—	4	2	no	—
171	C₂²⋊C₄×C₅₉	—	8	2	no	—
172	C₂²⋊C₄×C₅₉	—	8	2	no	—
173	C₄²×C₅₉	—	2	2	no	—
174	C₄²×C₅₉	—	2	2	no	—
175	C₄²×C₅₉	—	4	2	no	—
176	C₂³×C₅₉	—	2	1	no	—
177	C₂³×C₅₉	—	2	1	no	—
178	C₂³×C₅₉	—	2	1	no	—
179	C₂³×C₅₉	—	2	1	no	—
180	C₂³×C₅₉	—	2	2	no	—
181	C₂³×C₅₉	—	4	1	no	—
182	C₂³×C₅₉	—	4	1	no	—
183	C₂³×C₅₉	—	4	1	no	—
184	C₂³×C₅₉	—	4	1	no	—
185	C₂³×C₅₉	—	4	1	no	—
186	C₂³×C₅₉	—	4	1	no	—
187	C₂³×C₅₉	#121	1	2	yes	—
188	C₂³×C₅₉	#123	1	2	yes	—
189	C₂³×C₅₉	#124	1	2	yes	—
190	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₅₉	—	2	2	no	—
192	Q₈×C₅₉	—	2	2	no	—
193	Q₈×C₅₉	—	4	1	no	—
194	Q₈×C₅₉	—	4	1	no	—
195	D₄×C₅₉	—	2	2	no	—
196	D₄×C₅₉	—	2	2	no	—
197	D₄×C₅₉	—	4	8	no	—
198	D₄×C₅₉	—	4	1	no	—
199	D₄×C₅₉	—	4	1	no	—
200	C₂×C₄×C₅₉	—	2	2	no	—
201	C₂×C₄×C₅₉	—	2	2	no	—
202	C₂×C₄×C₅₉	—	2	2	no	—
203	C₂×C₄×C₅₉	—	2	2	no	—
204	C₂×C₄×C₅₉	—	2	2	no	—
205	C₂×C₄×C₅₉	—	2	2	no	—
206	C₂×C₄×C₅₉	—	2	2	no	—
207	C₂×C₄×C₅₉	—	4	1	no	—
208	C₂×C₄×C₅₉	—	4	1	no	—
209	C₂×C₄×C₅₉	—	4	8	no	—
210	C₂×C₄×C₅₉	—	4	1	no	—
211	C₂×C₄×C₅₉	—	4	1	no	—
212	C₂×C₄×C₅₉	—	4	2	no	—
213	C₂×C₄×C₅₉	—	4	2	no	—
214	C₂×C₄×C₅₉	—	4	2	no	—
215	C₂×C₄×C₅₉	—	4	1	no	—
216	C₂×C₄×C₅₉	—	4	2	no	—
217	C₂×C₄×C₅₉	—	4	2	no	—
218	C₂×C₄×C₅₉	—	4	1	no	—
219	C₂×C₄×C₅₉	—	4	2	no	—
220	C₂×C₄×C₅₉	—	4	1	no	—
221	C₂×C₄×C₅₉	—	4	1	no	—
222	C₂×C₄×C₅₉	—	8	4	no	—
223	C₂×C₄×C₅₉	—	8	4	no	—
224	C₂×C₄×C₅₉	#121	1	2	yes	—
225	C₂×C₄×C₅₉	#123	1	4	yes	—
226	C₂×C₄×C₅₉	#123	1	4	yes	—
227	C₂×C₄×C₅₉	#123	1	2	yes	—
228	C₂×C₄×C₅₉	#124	1	2	yes	—
229	C₂×C₄×C₅₉	#126	1	4	yes	—
230	C₂×C₄×C₅₉	#126	1	4	yes	—
231	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
237	C₈×C₅₉	—	4	1	no	—
238	C₈×C₅₉	—	4	1	no	—
239	C₈×C₅₉	—	4	2	no	—
240	#23634	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂²×C₅₉	—	2	2	no	—
242	C₂²×C₅₉	—	2	2	no	—
243	C₂²×C₅₉	—	2	2	no	—
244	C₂²×C₅₉	—	2	2	no	—
245	C₂²×C₅₉	—	2	2	no	—
246	C₂²×C₅₉	—	2	2	no	—
247	C₂²×C₅₉	—	4	2	no	—
248	C₂²×C₅₉	—	4	2	no	—
249	C₂²×C₅₉	—	4	2	no	—
250	C₂²×C₅₉	—	8	1	no	—
251	C₂²×C₅₉	—	8	1	no	—
252	C₂²×C₅₉	—	8	1	no	—
253	C₂²×C₅₉	—	8	1	no	—
254	C₂²×C₅₉	#397	1	4	yes	—
255	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
256	C₂²×C₅₉	C₂×#123	1	1	yes	characteristic
257	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
258	C₂²×C₅₉	#576	1	1	yes	characteristic
259	C₂²×C₅₉	#577	1	1	yes	characteristic
260	C₂²×C₅₉	#577	1	1	yes	characteristic
261	C₂²×C₅₉	#578	1	1	yes	characteristic
262	C₄×C₅₉	—	4	2	no	—
263	C₄×C₅₉	—	4	2	no	—
264	C₄×C₅₉	—	4	2	no	—
265	C₄×C₅₉	—	8	2	no	—
266	C₄×C₅₉	—	8	1	no	—
267	C₄×C₅₉	—	8	2	no	—
268	C₄×C₅₉	—	8	1	no	—
269	C₄×C₅₉	#397	1	4	yes	—
270	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
271	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
272	C₄×C₅₉	C₂×#126	1	1	yes	characteristic
273	C₄×C₅₉	C₂×#126	1	1	yes	characteristic
274	C₂×#417	C₂×C₅₉	1	1	yes	characteristic
275	C₂×#416	C₂×C₅₉	1	1	yes	characteristic
276	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
277	#2311	C₂×C₅₉	1	1	yes	characteristic
278	#2074	C₂×C₅₉	1	2	yes	complemented
279	#2073	C₂×C₅₉	1	2	yes	complemented
280	#2072	C₂×C₅₉	1	2	yes	complemented
281	#2071	C₂×C₅₉	1	2	yes	complemented
282	#1736	C₂×C₅₉	1	1	yes	characteristic, complemented
283	C₂×#340	C₂×C₅₉	1	1	yes	characteristic, complemented
284	#1729	C₂×C₅₉	1	1	yes	characteristic, complemented
285	C₂×C₅₉	—	2	4	no	—
286	C₂×C₅₉	—	8	2	no	—
287	C₂×C₅₉	C₂×#397	1	1	yes	characteristic
288	C₂×C₅₉	#3045	1	1	yes	characteristic
289	C₂×C₅₉	#3046	1	1	yes	characteristic
290	C₂×C₅₉	#3098	1	1	yes	characteristic
291	C₂×C₅₉	#3099	1	1	yes	characteristic
292	C₂×C₅₉	#3136	1	1	yes	characteristic
293	C₂×C₅₉	#3137	1	1	yes	characteristic
294	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
296	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
297	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
298	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
300	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
301	#417	—	2	4	no	—
302	#416	—	2	4	no	—
303	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
304	C₂×#103	C₂²×C₅₉	1	2	yes	—
305	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
306	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
307	C₂×#102	C₂²×C₅₉	1	2	yes	—
308	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
309	#391	C₂²×C₅₉	1	2	yes	—
310	#390	C₂²×C₅₉	1	2	yes	—
311	#389	—	2	1	no	—
312	#389	—	2	1	no	—
313	#386	—	2	2	no	—
314	#385	—	2	2	no	—
315	#384	C₂²×C₅₉	1	2	yes	—
316	#382	C₂²×C₅₉	1	2	yes	—
317	#380	—	2	1	no	—
318	#380	—	2	1	no	—
319	#340	C₂²×C₅₉	1	2	yes	—
320	#340	C₂²×C₅₉	1	2	yes	—
321	#340	C₂²×C₅₉	1	2	yes	—
322	#340	C₂²×C₅₉	1	2	yes	—
323	#336	C₂²×C₅₉	1	2	yes	—
324	#336	C₂²×C₅₉	1	2	yes	—
325	C₅₉	#23634	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	D₄×C₅₉	1	4	yes	—
332	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
348	#117	—	2	2	no	—
349	#117	—	2	2	no	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	2	4	no	—
375	#102	—	2	2	no	—
376	#102	—	2	2	no	—
377	#102	—	2	4	no	—
378	#95	—	2	2	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	C₂⁴	—	2	1	no	—
383	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
384	#41	—	2	8	no	—
385	#41	—	2	8	no	—
386	#41	—	4	4	no	—
387	#41	—	4	4	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	8	1	no	—
414	C₂²×C₄	—	8	1	no	—
415	C₂²×C₄	—	8	1	no	—
416	C₂²×C₄	—	8	1	no	—
417	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
421	C₂²×C₄	#41×C₅₉	1	2	yes	—
422	C₂²×C₄	#41×C₅₉	1	2	yes	—
423	C₂²×C₄	#41×C₅₉	1	2	yes	—
424	C₂²×C₄	#41×C₅₉	1	2	yes	—
425	C₂²×C₄	#41×C₅₉	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
427	M₁₆	—	4	4	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	8	2	no	—
451	C₄⋊C₄	—	8	2	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₂²⋊C₄	—	8	2	no	—
455	C₂²⋊C₄	—	8	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	4	2	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	#121×C₅₉	1	2	yes	—
471	C₂³	#123×C₅₉	1	2	yes	—
472	C₂³	#124×C₅₉	1	2	yes	—
473	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	1	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	#121×C₅₉	1	2	yes	—
508	C₂×C₄	#123×C₅₉	1	2	yes	—
509	C₂×C₄	#123×C₅₉	1	4	yes	—
510	C₂×C₄	#123×C₅₉	1	4	yes	—
511	C₂×C₄	#124×C₅₉	1	2	yes	—
512	C₂×C₄	#126×C₅₉	1	4	yes	—
513	C₂×C₄	#126×C₅₉	1	4	yes	—
514	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
519	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	C₅₉×#397	1	4	yes	—
537	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
538	C₂²	C₂×#123×C₅₉	1	1	yes	characteristic
539	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
540	C₂²	C₅₉×#576	1	1	yes	characteristic
541	C₂²	C₅₉×#577	1	1	yes	characteristic
542	C₂²	C₅₉×#577	1	1	yes	characteristic
543	C₂²	C₅₉×#578	1	1	yes	characteristic
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	8	2	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	2	no	—
551	C₄	C₅₉×#397	1	4	yes	—
552	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
553	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
554	C₄	C₂×#126×C₅₉	1	1	yes	characteristic
555	C₄	C₂×#126×C₅₉	1	1	yes	characteristic
556	C₂	—	2	4	no	—
557	C₂	—	8	2	no	—
558	C₂	C₂×C₅₉×#397	1	1	yes	characteristic
559	C₂	C₅₉×#3045	1	1	yes	characteristic
560	C₂	C₅₉×#3046	1	1	yes	characteristic
561	C₂	C₅₉×#3098	1	1	yes	characteristic
562	C₂	C₅₉×#3099	1	1	yes	characteristic
563	C₂	C₅₉×#3136	1	1	yes	characteristic
564	C₂	C₅₉×#3137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×#117×C₅₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₅₉×#2317	C₂	semidirect
5. C₅₉×#2074	C₂	semidirect
6. C₅₉×#2073	C₂	semidirect
7. C₅₉×#2072	C₂	semidirect
8. C₅₉×#2071	C₂	semidirect
9. C₅₉×#1736	C₂	semidirect
10. C₂×C₅₉×#340	C₂	semidirect
11. C₅₉×#1729	C₂	semidirect
240. #23634	C₅₉	direct (N × H)
276. #2317	C₂×C₅₉	semidirect
278. #2074	C₂×C₅₉	semidirect
279. #2073	C₂×C₅₉	semidirect
280. #2072	C₂×C₅₉	semidirect
281. #2071	C₂×C₅₉	semidirect
282. #1736	C₂×C₅₉	semidirect
283. C₂×#340	C₂×C₅₉	semidirect
284. #1729	C₂×C₅₉	semidirect
325. C₅₉	#23634	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×#417	2
C₂×C₅₉×#416	2
C₅₉×#2317	2
C₅₉×#2311	2
C₅₉×#2074	2
C₅₉×#2073	2
C₅₉×#2072	2
C₅₉×#2071	2
C₅₉×#1736	2
C₂×C₅₉×#340	2
C₅₉×#1729	2
#23634	59

Subgroups — C59×#23634 #28435743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23634 #28435743