Subgroups — C₅₉×#25923 #28438032

Order 15104.

1014 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3503	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3039	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2028	C₂	1	4	yes	maximal, complemented
6	C₅₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1882	C₂	1	4	yes	maximal
9	C₄×#104×C₅₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#137×C₅₉	C₂²	1	2	yes	—
11	Q₈²×C₅₉	—	2	1	no	—
12	C₅₉×#557	—	2	1	no	—
13	C₅₉×#554	—	2	1	no	—
14	C₅₉×#554	—	2	2	no	—
15	D₄×Q₈×C₅₉	—	2	2	no	—
16	D₄×Q₈×C₅₉	—	2	1	no	—
17	C₅₉×#544	—	2	2	no	—
18	C₅₉×#544	C₂²	1	2	yes	—
19	C₅₉×#533	—	2	1	no	—
20	C₅₉×#533	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#520	C₂²	1	2	yes	—
25	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#491	—	2	2	no	—
27	C₅₉×#487	—	2	1	no	—
28	C₅₉×#487	—	2	1	no	—
29	C₅₉×#462	—	2	1	no	—
30	C₅₉×#462	—	2	1	no	—
31	C₅₉×#461	—	2	1	no	—
32	C₅₉×#461	—	2	1	no	—
33	C₅₉×#423	C₂²	1	1	yes	characteristic
34	C₂×#104×C₅₉	C₂²	1	2	yes	—
35	C₅₉×#419	C₂²	1	2	yes	—
36	C₅₉×#419	C₂²	1	4	yes	—
37	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#391	—	2	2	no	—
39	C₅₉×#391	C₂²	1	4	yes	—
40	C₅₉×#382	—	2	2	no	—
41	C₄³×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#343	C₂²	1	4	yes	—
43	C₅₉×#339	C₂²	1	4	yes	—
44	C₅₉×#339	C₂²	1	2	yes	—
45	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₅₉	—	2	2	no	—
47	C₂²×Q₈×C₅₉	D₄	1	2	yes	—
48	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
49	#137×C₅₉	—	2	8	no	—
50	C₂×Q₁₆×C₅₉	—	2	2	no	—
51	C₂×SD₁₆×C₅₉	—	2	2	no	—
52	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
53	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₅₉	—	2	2	no	—
55	C₄⋊Q₈×C₅₉	—	2	2	no	—
56	C₄⋊Q₈×C₅₉	—	2	4	no	—
57	C₄⋊Q₈×C₅₉	—	2	2	no	—
58	C₄⋊Q₈×C₅₉	—	2	2	no	—
59	C₄⋊Q₈×C₅₉	—	2	1	no	—
60	C₄⋊Q₈×C₅₉	—	2	1	no	—
61	C₄⋊Q₈×C₅₉	—	2	1	no	—
62	C₄⋊Q₈×C₅₉	—	2	1	no	—
63	C₄⋊Q₈×C₅₉	—	2	1	no	—
64	C₄⋊Q₈×C₅₉	—	2	1	no	—
65	C₄⋊Q₈×C₅₉	—	2	1	no	—
66	C₄⋊Q₈×C₅₉	—	2	1	no	—
67	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
69	#125×C₅₉	—	2	4	no	—
70	#125×C₅₉	—	2	2	no	—
71	#125×C₅₉	—	2	2	no	—
72	#125×C₅₉	D₄	1	2	yes	—
73	C₂²⋊Q₈×C₅₉	—	2	2	no	—
74	C₂²⋊Q₈×C₅₉	—	2	2	no	—
75	C₂²⋊Q₈×C₅₉	—	2	4	no	—
76	C₂²⋊Q₈×C₅₉	—	2	4	no	—
77	C₂²⋊Q₈×C₅₉	—	2	1	no	—
78	C₂²⋊Q₈×C₅₉	—	2	1	no	—
79	C₂²⋊Q₈×C₅₉	—	2	4	no	—
80	C₄×Q₈×C₅₉	—	2	2	no	—
81	C₄×Q₈×C₅₉	—	2	2	no	—
82	C₄×Q₈×C₅₉	—	2	2	no	—
83	C₄×Q₈×C₅₉	—	2	1	no	—
84	C₄×Q₈×C₅₉	—	2	1	no	—
85	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
87	C₄×D₄×C₅₉	—	2	2	no	—
88	C₄×D₄×C₅₉	—	2	1	no	—
89	C₄×D₄×C₅₉	—	2	1	no	—
90	C₄×D₄×C₅₉	—	2	4	no	—
91	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
92	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
93	#117×C₅₉	—	2	2	no	—
94	#117×C₅₉	—	2	1	no	—
95	#117×C₅₉	C₂³	1	1	yes	characteristic
96	#117×C₅₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
99	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
103	C₂×C₄²×C₅₉	—	2	1	no	—
104	C₂×C₄²×C₅₉	—	2	1	no	—
105	C₂×C₄²×C₅₉	—	2	1	no	—
106	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₅₉	—	2	1	no	—
109	C₄⋊C₈×C₅₉	—	2	1	no	—
110	#104×C₅₉	—	2	4	no	—
111	#103×C₅₉	—	2	2	no	—
112	#103×C₅₉	—	2	2	no	—
113	#103×C₅₉	—	2	4	no	—
114	#103×C₅₉	—	2	4	no	—
115	#97×C₅₉	—	2	1	no	—
116	C₄×C₈×C₅₉	—	2	1	no	—
117	#95×C₅₉	—	2	8	no	—
118	#41×C₅₉	—	2	2	no	—
119	#41×C₅₉	#41	1	4	yes	—
120	C₂×Q₈×C₅₉	—	2	4	no	—
121	C₂×Q₈×C₅₉	—	2	1	no	—
122	C₂×Q₈×C₅₉	—	2	2	no	—
123	C₂×Q₈×C₅₉	—	2	1	no	—
124	C₂×Q₈×C₅₉	—	2	2	no	—
125	C₂×Q₈×C₅₉	—	2	2	no	—
126	C₂×Q₈×C₅₉	—	2	2	no	—
127	C₂×Q₈×C₅₉	—	2	4	no	—
128	C₂×Q₈×C₅₉	—	2	4	no	—
129	C₂×Q₈×C₅₉	—	4	4	no	—
130	C₂×Q₈×C₅₉	—	8	4	no	—
131	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
132	C₂×D₄×C₅₉	—	2	1	no	—
133	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	—	2	1	no	—
135	C₂²×C₄×C₅₉	—	2	2	no	—
136	C₂²×C₄×C₅₉	—	2	4	no	—
137	C₂²×C₄×C₅₉	—	2	1	no	—
138	C₂²×C₄×C₅₉	—	2	1	no	—
139	C₂²×C₄×C₅₉	—	2	2	no	—
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	4	yes	—
143	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
144	Q₁₆×C₅₉	—	4	4	no	—
145	SD₁₆×C₅₉	—	4	4	no	—
146	M₁₆×C₅₉	—	2	2	no	—
147	M₁₆×C₅₉	—	2	4	no	—
148	M₁₆×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	—	2	2	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₄⋊C₄×C₅₉	—	2	4	no	—
152	C₄⋊C₄×C₅₉	—	2	4	no	—
153	C₄⋊C₄×C₅₉	—	2	4	no	—
154	C₄⋊C₄×C₅₉	—	2	4	no	—
155	C₄⋊C₄×C₅₉	—	2	1	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	1	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	2	no	—
165	C₄⋊C₄×C₅₉	—	4	1	no	—
166	C₄⋊C₄×C₅₉	—	4	1	no	—
167	C₄⋊C₄×C₅₉	—	4	1	no	—
168	C₄⋊C₄×C₅₉	—	4	1	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	1	yes	characteristic
172	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
173	C₂²⋊C₄×C₅₉	—	2	4	no	—
174	C₂²⋊C₄×C₅₉	—	2	2	no	—
175	C₂²⋊C₄×C₅₉	—	2	1	no	—
176	C₂²⋊C₄×C₅₉	—	2	1	no	—
177	C₂²⋊C₄×C₅₉	—	2	1	no	—
178	C₄²×C₅₉	—	2	4	no	—
179	C₄²×C₅₉	—	2	4	no	—
180	C₄²×C₅₉	—	2	1	no	—
181	C₄²×C₅₉	—	2	1	no	—
182	C₄²×C₅₉	—	2	1	no	—
183	C₄²×C₅₉	—	2	2	no	—
184	C₄²×C₅₉	—	2	2	no	—
185	C₄²×C₅₉	—	2	2	no	—
186	C₄²×C₅₉	—	4	2	no	—
187	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₅₉	—	2	1	no	—
192	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₅₉	—	2	1	no	—
194	Q₈×C₅₉	—	4	4	no	—
195	Q₈×C₅₉	—	4	2	no	—
196	Q₈×C₅₉	—	4	2	no	—
197	Q₈×C₅₉	—	4	2	no	—
198	Q₈×C₅₉	—	4	2	no	—
199	Q₈×C₅₉	—	4	4	no	—
200	Q₈×C₅₉	—	8	2	no	—
201	Q₈×C₅₉	—	8	4	no	—
202	Q₈×C₅₉	#124	1	2	yes	—
203	D₄×C₅₉	—	2	4	no	—
204	D₄×C₅₉	—	2	1	no	—
205	D₄×C₅₉	#124	1	2	yes	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	4	no	—
208	C₂×C₄×C₅₉	—	2	2	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	2	4	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	4	no	—
215	C₂×C₄×C₅₉	—	2	2	no	—
216	C₂×C₄×C₅₉	—	4	2	no	—
217	C₂×C₄×C₅₉	—	4	2	no	—
218	C₂×C₄×C₅₉	—	4	2	no	—
219	C₂×C₄×C₅₉	—	4	2	no	—
220	C₂×C₄×C₅₉	—	4	4	no	—
221	C₂×C₄×C₅₉	—	4	2	no	—
222	C₂×C₄×C₅₉	—	4	4	no	—
223	C₂×C₄×C₅₉	—	8	4	no	—
224	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
225	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
226	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
227	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
231	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
232	C₈×C₅₉	—	4	2	no	—
233	C₈×C₅₉	—	4	2	no	—
234	#25923	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₅₉	—	2	1	no	—
236	C₂²×C₅₉	—	2	1	no	—
237	C₂²×C₅₉	—	2	2	no	—
238	C₂²×C₅₉	—	4	1	no	—
239	C₂²×C₅₉	—	4	1	no	—
240	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
241	C₂²×C₅₉	#548	1	2	yes	—
242	C₄×C₅₉	—	2	2	no	—
243	C₄×C₅₉	—	2	1	no	—
244	C₄×C₅₉	—	2	1	no	—
245	C₄×C₅₉	—	4	4	no	—
246	C₄×C₅₉	—	4	1	no	—
247	C₄×C₅₉	—	4	4	no	—
248	C₄×C₅₉	—	4	2	no	—
249	C₄×C₅₉	—	4	1	no	—
250	C₄×C₅₉	—	4	2	no	—
251	C₄×C₅₉	—	8	2	no	—
252	C₄×C₅₉	#455	1	2	yes	—
253	C₄×C₅₉	#456	1	2	yes	—
254	C₄×C₅₉	C₂×#124	1	1	yes	characteristic
255	C₄×C₅₉	#536	1	1	yes	characteristic
256	C₄×C₅₉	#548	1	2	yes	—
257	#3503	C₂×C₅₉	1	1	yes	characteristic
258	#3139	C₂×C₅₉	1	1	yes	characteristic, complemented
259	#3039	C₂×C₅₉	1	1	yes	characteristic
260	#2862	C₂×C₅₉	1	1	yes	characteristic, complemented
261	#2028	C₂×C₅₉	1	4	yes	complemented
262	#1997	C₂×C₅₉	1	1	yes	characteristic, complemented
263	#1994	C₂×C₅₉	1	1	yes	characteristic, complemented
264	#1882	C₂×C₅₉	1	4	yes	—
265	C₄×#104	C₂×C₅₉	1	1	yes	characteristic
266	C₂×C₅₉	—	2	2	no	—
267	C₂×C₅₉	—	4	2	no	—
268	C₂×C₅₉	#2436	1	1	yes	characteristic
269	C₂×C₅₉	C₂×#455	1	1	yes	characteristic
270	C₂×C₅₉	C₂×#456	1	1	yes	characteristic
271	C₂×#137	C₂²×C₅₉	1	2	yes	—
272	Q₈²	—	2	1	no	—
273	#557	—	2	1	no	—
274	#554	—	2	1	no	—
275	#554	—	2	2	no	—
276	D₄×Q₈	—	2	2	no	—
277	D₄×Q₈	—	2	1	no	—
278	#544	—	2	2	no	—
279	#544	C₂²×C₅₉	1	2	yes	—
280	#533	—	2	1	no	—
281	#533	C₂²×C₅₉	1	1	yes	characteristic
282	C₂×C₄⋊Q₈	—	2	1	no	—
283	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
284	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
285	#520	C₂²×C₅₉	1	2	yes	—
286	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
287	#491	—	2	2	no	—
288	#487	—	2	1	no	—
289	#487	—	2	1	no	—
290	#462	—	2	1	no	—
291	#462	—	2	1	no	—
292	#461	—	2	1	no	—
293	#461	—	2	1	no	—
294	#423	C₂²×C₅₉	1	1	yes	characteristic
295	C₂×#104	C₂²×C₅₉	1	2	yes	—
296	#419	C₂²×C₅₉	1	4	yes	—
297	#419	C₂²×C₅₉	1	2	yes	—
298	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
299	#391	—	2	2	no	—
300	#391	C₂²×C₅₉	1	4	yes	—
301	#382	—	2	2	no	—
302	C₄³	C₂²×C₅₉	1	1	yes	characteristic
303	#343	C₂²×C₅₉	1	4	yes	—
304	#339	C₂²×C₅₉	1	4	yes	—
305	#339	C₂²×C₅₉	1	2	yes	—
306	C₅₉	#25923	1	1	yes	characteristic, direct product factor, Sylow
307	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	D₄×C₅₉	1	2	yes	—
310	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
311	#137	—	2	8	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
315	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	—	2	4	no	—
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	—	2	1	no	—
329	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
330	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
331	#125	—	2	4	no	—
332	#125	—	2	2	no	—
333	#125	—	2	2	no	—
334	#125	D₄×C₅₉	1	2	yes	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
348	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
354	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
355	#117	—	2	2	no	—
356	#117	—	2	1	no	—
357	#117	C₂³×C₅₉	1	1	yes	characteristic
358	#117	C₂³×C₅₉	1	2	yes	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
369	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	#104	—	2	4	no	—
373	#103	—	2	2	no	—
374	#103	—	2	2	no	—
375	#103	—	2	4	no	—
376	#103	—	2	4	no	—
377	#97	—	2	1	no	—
378	C₄×C₈	—	2	1	no	—
379	#95	—	2	8	no	—
380	#41	—	2	2	no	—
381	#41	#41×C₅₉	1	4	yes	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	4	4	no	—
392	C₂×Q₈	—	8	4	no	—
393	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
406	Q₁₆	—	4	4	no	—
407	SD₁₆	—	4	4	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
433	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
434	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	4	2	no	—
449	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
452	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
453	C₂³	—	2	1	no	—
454	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
455	Q₈	—	2	1	no	—
456	Q₈	—	4	4	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	4	no	—
462	Q₈	—	8	2	no	—
463	Q₈	—	8	4	no	—
464	Q₈	#124×C₅₉	1	2	yes	—
465	D₄	—	2	4	no	—
466	D₄	—	2	1	no	—
467	D₄	#124×C₅₉	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	8	4	no	—
486	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
487	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
488	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
489	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
492	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
493	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
502	C₂²	C₅₉×#548	1	2	yes	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	2	no	—
512	C₄	—	8	2	no	—
513	C₄	C₅₉×#455	1	2	yes	—
514	C₄	C₅₉×#456	1	2	yes	—
515	C₄	C₂×#124×C₅₉	1	1	yes	characteristic
516	C₄	C₅₉×#536	1	1	yes	characteristic
517	C₄	C₅₉×#548	1	2	yes	—
518	C₂	—	2	2	no	—
519	C₂	—	4	2	no	—
520	C₂	C₅₉×#2436	1	1	yes	characteristic
521	C₂	C₂×C₅₉×#455	1	1	yes	characteristic
522	C₂	C₂×C₅₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×#41×C₅₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#3139	C₂	semidirect
4. C₅₉×#2862	C₂	semidirect
5. C₅₉×#2028	C₂	semidirect
6. C₅₉×#1997	C₂	semidirect
7. C₅₉×#1994	C₂	semidirect
234. #25923	C₅₉	direct (N × H)
258. #3139	C₂×C₅₉	semidirect
260. #2862	C₂×C₅₉	semidirect
261. #2028	C₂×C₅₉	semidirect
262. #1997	C₂×C₅₉	semidirect
263. #1994	C₂×C₅₉	semidirect
306. C₅₉	#25923	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#3503	2
C₅₉×#3139	2
C₅₉×#3039	2
C₅₉×#2862	2
C₅₉×#2028	2
C₅₉×#1997	2
C₅₉×#1994	2
C₅₉×#1882	2
C₄×#104×C₅₉	2
#25923	59

Subgroups — C59×#25923 #28438032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25923 #28438032