Subgroups — C₅₉×#25944 #28438053

Order 15104.

1100 conjugacy classes of subgroups.

The subgroup lattice has 544 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×#490	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×#460	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2548	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2025	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2023	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1880	C₂	1	2	yes	maximal, complemented
10	C₅₉×#1880	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₅₉	C₂²	1	2	yes	—
13	C₅₉×#557	—	2	4	no	—
14	C₅₉×#557	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
16	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×#125×C₅₉	—	2	1	no	—
19	C₂×#125×C₅₉	—	2	1	no	—
20	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₅₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
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	C₅₉×#490	—	2	4	no	—
29	C₅₉×#460	—	2	4	no	—
30	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₅₉	C₂²	1	2	yes	—
32	C₂×#102×C₅₉	C₂²	1	2	yes	—
33	C₂×#102×C₅₉	C₂²	1	2	yes	—
34	C₂×#102×C₅₉	C₂²	1	2	yes	—
35	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#394	—	2	1	no	—
37	C₅₉×#394	—	2	1	no	—
38	C₅₉×#390	—	2	1	no	—
39	C₅₉×#390	C₂²	1	2	yes	—
40	C₅₉×#390	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#340	C₂²	1	2	yes	—
43	C₅₉×#340	C₂²	1	2	yes	—
44	C₅₉×#340	C₂²	1	2	yes	—
45	C₅₉×#336	C₂²	1	2	yes	—
46	C₅₉×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₅₉	—	2	1	no	—
48	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₅₉	—	2	1	no	—
51	C₂²×D₄×C₅₉	—	2	1	no	—
52	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
53	C₂×SD₁₆×C₅₉	—	2	4	no	—
54	C₂×SD₁₆×C₅₉	—	2	4	no	—
55	C₂×SD₁₆×C₅₉	—	2	4	no	—
56	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₅₉	—	2	8	no	—
59	C₄⋊Q₈×C₅₉	—	2	2	no	—
60	C₄⋊Q₈×C₅₉	—	2	2	no	—
61	#127×C₅₉	—	2	2	no	—
62	#127×C₅₉	—	2	2	no	—
63	#125×C₅₉	—	2	8	no	—
64	#125×C₅₉	—	2	8	no	—
65	#125×C₅₉	—	2	2	no	—
66	#125×C₅₉	—	2	2	no	—
67	#125×C₅₉	—	2	2	no	—
68	#125×C₅₉	D₄	1	4	yes	—
69	#124×C₅₉	—	4	4	no	—
70	C₄×Q₈×C₅₉	—	2	8	no	—
71	C₄×Q₈×C₅₉	—	2	2	no	—
72	C₄×Q₈×C₅₉	—	2	2	no	—
73	C₄×Q₈×C₅₉	—	2	2	no	—
74	C₄×Q₈×C₅₉	—	2	2	no	—
75	C₄×Q₈×C₅₉	—	2	2	no	—
76	C₄×Q₈×C₅₉	—	2	2	no	—
77	C₄×Q₈×C₅₉	—	2	2	no	—
78	C₄×Q₈×C₅₉	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
98	C₂×C₄²×C₅₉	—	2	1	no	—
99	C₂×C₄²×C₅₉	—	2	1	no	—
100	C₂×C₄²×C₅₉	—	2	1	no	—
101	C₂×C₄²×C₅₉	—	2	1	no	—
102	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₅₉	—	2	2	no	—
106	#103×C₅₉	—	2	4	no	—
107	#102×C₅₉	—	2	4	no	—
108	#102×C₅₉	—	2	4	no	—
109	#102×C₅₉	—	2	4	no	—
110	#97×C₅₉	—	2	2	no	—
111	#95×C₅₉	—	2	1	no	—
112	C₂⁴×C₅₉	—	2	2	no	—
113	C₂×Q₈×C₅₉	—	2	4	no	—
114	C₂×Q₈×C₅₉	—	2	2	no	—
115	C₂×Q₈×C₅₉	—	2	2	no	—
116	C₂×Q₈×C₅₉	—	2	1	no	—
117	C₂×Q₈×C₅₉	—	2	2	no	—
118	C₂×Q₈×C₅₉	—	4	1	no	—
119	C₂×Q₈×C₅₉	—	4	2	no	—
120	C₂×Q₈×C₅₉	—	4	2	no	—
121	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₅₉	#41	1	4	yes	—
123	C₂×D₄×C₅₉	—	2	2	no	—
124	C₂×D₄×C₅₉	—	2	2	no	—
125	C₂×D₄×C₅₉	—	2	2	no	—
126	C₂×D₄×C₅₉	—	2	2	no	—
127	C₂×D₄×C₅₉	—	2	2	no	—
128	C₂×D₄×C₅₉	—	2	2	no	—
129	C₂×D₄×C₅₉	—	4	2	no	—
130	C₂×D₄×C₅₉	—	4	2	no	—
131	C₂×D₄×C₅₉	—	4	2	no	—
132	C₂×D₄×C₅₉	—	4	2	no	—
133	C₂×D₄×C₅₉	—	8	2	no	—
134	C₂²×C₄×C₅₉	—	2	1	no	—
135	C₂²×C₄×C₅₉	—	2	1	no	—
136	C₂²×C₄×C₅₉	—	2	1	no	—
137	C₂²×C₄×C₅₉	—	2	1	no	—
138	C₂²×C₄×C₅₉	—	2	2	no	—
139	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
146	SD₁₆×C₅₉	—	4	8	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₂×C₈×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	—	2	2	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	2	no	—
152	C₂×C₈×C₅₉	—	2	2	no	—
153	C₄⋊C₄×C₅₉	—	2	4	no	—
154	C₄⋊C₄×C₅₉	—	2	4	no	—
155	C₄⋊C₄×C₅₉	—	2	4	no	—
156	C₄⋊C₄×C₅₉	—	2	4	no	—
157	C₄⋊C₄×C₅₉	—	2	4	no	—
158	C₄⋊C₄×C₅₉	—	2	4	no	—
159	C₄⋊C₄×C₅₉	—	2	4	no	—
160	C₄⋊C₄×C₅₉	—	2	4	no	—
161	C₄⋊C₄×C₅₉	—	2	2	no	—
162	C₄⋊C₄×C₅₉	—	2	2	no	—
163	C₄⋊C₄×C₅₉	—	2	2	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	—	2	2	no	—
168	C₄⋊C₄×C₅₉	—	2	2	no	—
169	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
172	C₂²⋊C₄×C₅₉	—	4	4	no	—
173	C₂²⋊C₄×C₅₉	—	4	4	no	—
174	C₂²⋊C₄×C₅₉	—	8	2	no	—
175	C₂²⋊C₄×C₅₉	—	8	2	no	—
176	C₄²×C₅₉	—	2	4	no	—
177	C₄²×C₅₉	—	2	4	no	—
178	C₄²×C₅₉	—	2	4	no	—
179	C₄²×C₅₉	—	2	1	no	—
180	C₄²×C₅₉	—	2	1	no	—
181	C₄²×C₅₉	—	2	1	no	—
182	C₄²×C₅₉	—	2	1	no	—
183	C₄²×C₅₉	—	4	2	no	—
184	C₄²×C₅₉	C₂×D₄	1	2	yes	—
185	C₄²×C₅₉	C₂×D₄	1	2	yes	—
186	C₂³×C₅₉	—	4	2	no	—
187	C₂³×C₅₉	—	4	2	no	—
188	C₂³×C₅₉	—	4	2	no	—
189	C₂³×C₅₉	—	4	2	no	—
190	C₂³×C₅₉	—	4	2	no	—
191	C₂³×C₅₉	—	4	2	no	—
192	C₂³×C₅₉	—	4	2	no	—
193	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₅₉	—	2	2	no	—
195	Q₈×C₅₉	—	2	4	no	—
196	Q₈×C₅₉	—	4	4	no	—
197	Q₈×C₅₉	—	4	8	no	—
198	Q₈×C₅₉	#124	1	4	yes	complemented
199	D₄×C₅₉	—	4	2	no	—
200	D₄×C₅₉	—	4	2	no	—
201	D₄×C₅₉	—	4	2	no	—
202	D₄×C₅₉	—	4	2	no	—
203	D₄×C₅₉	—	8	4	no	—
204	D₄×C₅₉	—	8	4	no	—
205	C₂×C₄×C₅₉	—	2	2	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	4	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	2	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	2	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	2	no	—
217	C₂×C₄×C₅₉	—	2	2	no	—
218	C₂×C₄×C₅₉	—	2	1	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	2	no	—
221	C₂×C₄×C₅₉	—	2	2	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	4	1	no	—
224	C₂×C₄×C₅₉	—	4	1	no	—
225	C₂×C₄×C₅₉	—	4	1	no	—
226	C₂×C₄×C₅₉	—	4	2	no	—
227	C₂×C₄×C₅₉	—	4	2	no	—
228	C₂×C₄×C₅₉	—	4	2	no	—
229	C₂×C₄×C₅₉	—	4	2	no	—
230	C₂×C₄×C₅₉	#120	1	2	yes	—
231	C₂×C₄×C₅₉	#120	1	2	yes	—
232	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
237	C₈×C₅₉	—	4	2	no	—
238	C₈×C₅₉	—	4	2	no	—
239	#25944	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₅₉	—	8	2	no	—
241	C₂²×C₅₉	—	8	2	no	—
242	C₂²×C₅₉	—	8	2	no	—
243	C₂²×C₅₉	—	8	2	no	—
244	C₂²×C₅₉	—	8	2	no	—
245	C₂²×C₅₉	—	8	2	no	—
246	C₂²×C₅₉	—	8	2	no	—
247	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
248	C₂²×C₅₉	#548	1	2	yes	—
249	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂²×C₅₉	#575	1	1	yes	characteristic
251	C₂²×C₅₉	#577	1	2	yes	—
252	C₄×C₅₉	—	2	4	no	—
253	C₄×C₅₉	—	2	2	no	—
254	C₄×C₅₉	—	2	2	no	—
255	C₄×C₅₉	—	2	2	no	—
256	C₄×C₅₉	—	4	1	no	—
257	C₄×C₅₉	—	4	2	no	—
258	C₄×C₅₉	—	4	2	no	—
259	C₄×C₅₉	—	4	1	no	—
260	C₄×C₅₉	—	4	1	no	—
261	C₄×C₅₉	—	4	2	no	—
262	C₄×C₅₉	—	8	2	no	—
263	C₄×C₅₉	C₂×#124	1	1	yes	characteristic
264	C₄×C₅₉	#536	1	1	yes	characteristic
265	C₄×C₅₉	#548	1	2	yes	—
266	C₂×#557	C₂×C₅₉	1	1	yes	characteristic, complemented
267	C₂×#490	C₂×C₅₉	1	1	yes	characteristic
268	C₂×#460	C₂×C₅₉	1	1	yes	characteristic
269	#2548	C₂×C₅₉	1	1	yes	characteristic
270	#2025	C₂×C₅₉	1	2	yes	complemented
271	#2023	C₂×C₅₉	1	2	yes	complemented
272	#1989	C₂×C₅₉	1	1	yes	characteristic, complemented
273	#1985	C₂×C₅₉	1	1	yes	characteristic, complemented
274	#1880	C₂×C₅₉	1	2	yes	complemented
275	#1880	C₂×C₅₉	1	2	yes	complemented
276	#1763	C₂×C₅₉	1	1	yes	characteristic, complemented
277	C₂×C₅₉	—	16	2	no	—
278	C₂×C₅₉	#2436	1	1	yes	characteristic
279	C₂×C₅₉	#3006	1	1	yes	characteristic
280	C₂×C₅₉	#3010	1	1	yes	characteristic
281	C₂×C₅₉	#3368	1	2	yes	—
282	C₂×C₅₉	#3371	1	2	yes	—
283	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	—
284	#557	—	2	4	no	—
285	#557	—	2	4	no	—
286	C₂×C₄⋊Q₈	—	2	1	no	—
287	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
288	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
289	C₂×#125	—	2	1	no	—
290	C₂×#125	—	2	1	no	—
291	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
292	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
293	C₂×#124	—	2	1	no	—
294	C₂×C₄×Q₈	—	2	1	no	—
295	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
296	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
299	#490	—	2	4	no	—
300	#460	—	2	4	no	—
301	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
302	C₂×#103	C₂²×C₅₉	1	2	yes	—
303	C₂×#102	C₂²×C₅₉	1	2	yes	—
304	C₂×#102	C₂²×C₅₉	1	2	yes	—
305	C₂×#102	C₂²×C₅₉	1	2	yes	—
306	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
307	#394	—	2	1	no	—
308	#394	—	2	1	no	—
309	#390	—	2	1	no	—
310	#390	C₂²×C₅₉	1	2	yes	—
311	#390	C₂²×C₅₉	1	2	yes	—
312	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
313	#340	C₂²×C₅₉	1	2	yes	—
314	#340	C₂²×C₅₉	1	2	yes	—
315	#340	C₂²×C₅₉	1	2	yes	—
316	#336	C₂²×C₅₉	1	2	yes	—
317	#336	C₂²×C₅₉	1	2	yes	—
318	C₅₉	#25944	1	1	yes	characteristic, direct product factor, Sylow
319	C₂²×Q₈	—	2	1	no	—
320	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
321	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	4	no	—
327	C₂×SD₁₆	—	2	4	no	—
328	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
329	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
330	C₄⋊Q₈	—	2	8	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	#127	—	2	2	no	—
334	#127	—	2	2	no	—
335	#125	—	2	8	no	—
336	#125	—	2	8	no	—
337	#125	—	2	2	no	—
338	#125	—	2	2	no	—
339	#125	—	2	2	no	—
340	#125	D₄×C₅₉	1	4	yes	—
341	#124	—	4	4	no	—
342	C₄×Q₈	—	2	8	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	D₄×C₅₉	1	4	yes	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
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	1	yes	characteristic
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	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
377	C₄⋊C₈	—	2	2	no	—
378	#103	—	2	4	no	—
379	#102	—	2	4	no	—
380	#102	—	2	4	no	—
381	#102	—	2	4	no	—
382	#97	—	2	2	no	—
383	#95	—	2	1	no	—
384	C₂⁴	—	2	2	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
394	C₂×Q₈	#41×C₅₉	1	4	yes	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	8	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
418	SD₁₆	—	4	8	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
444	C₂²⋊C₄	—	4	4	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₂²⋊C₄	—	8	2	no	—
447	C₂²⋊C₄	—	8	2	no	—
448	C₄²	—	2	4	no	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	4	2	no	—
456	C₄²	C₂×D₄×C₅₉	1	2	yes	—
457	C₄²	C₂×D₄×C₅₉	1	2	yes	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	4	4	no	—
469	Q₈	—	4	8	no	—
470	Q₈	#124×C₅₉	1	4	yes	complemented
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	4	no	—
476	D₄	—	8	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	#120×C₅₉	1	2	yes	—
503	C₂×C₄	#120×C₅₉	1	2	yes	—
504	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
507	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
508	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
509	C₈	—	4	2	no	—
510	C₈	—	4	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
519	C₂²	C₅₉×#548	1	2	yes	—
520	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
521	C₂²	C₅₉×#575	1	1	yes	characteristic
522	C₂²	C₅₉×#577	1	2	yes	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	8	2	no	—
534	C₄	C₂×#124×C₅₉	1	1	yes	characteristic
535	C₄	C₅₉×#536	1	1	yes	characteristic
536	C₄	C₅₉×#548	1	2	yes	—
537	C₂	—	16	2	no	—
538	C₂	C₅₉×#2436	1	1	yes	characteristic
539	C₂	C₅₉×#3006	1	1	yes	characteristic
540	C₂	C₅₉×#3010	1	1	yes	characteristic
541	C₂	C₅₉×#3368	1	2	yes	—
542	C₂	C₅₉×#3371	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×#127×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄×Q₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#557	C₂	semidirect
5. C₅₉×#2025	C₂	semidirect
6. C₅₉×#2023	C₂	semidirect
7. C₅₉×#1989	C₂	semidirect
8. C₅₉×#1985	C₂	semidirect
9. C₅₉×#1880	C₂	semidirect
10. C₅₉×#1880	C₂	semidirect
11. C₅₉×#1763	C₂	semidirect
198. Q₈×C₅₉	#124	semidirect
239. #25944	C₅₉	direct (N × H)
266. C₂×#557	C₂×C₅₉	semidirect
270. #2025	C₂×C₅₉	semidirect
271. #2023	C₂×C₅₉	semidirect
272. #1989	C₂×C₅₉	semidirect
273. #1985	C₂×C₅₉	semidirect
274. #1880	C₂×C₅₉	semidirect
275. #1880	C₂×C₅₉	semidirect
276. #1763	C₂×C₅₉	semidirect
318. C₅₉	#25944	direct (N × H)
470. Q₈	#124×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×#557	2
C₂×C₅₉×#490	2
C₂×C₅₉×#460	2
C₅₉×#2548	2
C₅₉×#2025	2
C₅₉×#2023	2
C₅₉×#1989	2
C₅₉×#1985	2
C₅₉×#1880	2
C₅₉×#1763	2
#25944	59

Subgroups — C59×#25944 #28438053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25944 #28438053