Subgroups — C₅₉×#24479 #28436588

Order 15104.

1102 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#102×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2435	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2067	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2042	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1983	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1925	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#124×C₅₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#484	—	2	4	no	—
18	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	complemented
21	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#103×C₅₉	C₂²	1	2	yes	complemented
24	C₂×#102×C₅₉	—	2	4	no	—
25	C₂×#102×C₅₉	C₂²	1	2	yes	—
26	C₂×#102×C₅₉	C₂²	1	2	yes	—
27	C₂×#102×C₅₉	C₂²	1	2	yes	—
28	C₂×#102×C₅₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#394	—	2	2	no	—
31	C₅₉×#390	C₂²	1	2	yes	—
32	C₅₉×#389	C₂²	1	2	yes	complemented
33	C₅₉×#387	—	2	2	no	—
34	C₅₉×#380	—	2	1	no	—
35	C₅₉×#380	C₂²	1	1	yes	characteristic
36	C₅₉×#379	—	2	1	no	—
37	C₅₉×#379	—	2	1	no	—
38	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
39	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#340	C₂²	1	2	yes	complemented
42	C₅₉×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₅₉	—	2	1	no	—
44	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₅₉	—	2	4	no	—
46	C₂²×D₄×C₅₉	—	2	2	no	—
47	C₂²×D₄×C₅₉	—	2	1	no	—
48	C₂²×D₄×C₅₉	—	2	2	no	—
49	C₂²×D₄×C₅₉	—	4	2	no	—
50	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₅₉	—	2	1	no	—
52	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₅₉	—	2	2	no	—
54	C₂²×C₈×C₅₉	—	4	2	no	—
55	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
58	#124×C₅₉	—	2	4	no	—
59	#124×C₅₉	—	4	2	no	—
60	C₂²⋊Q₈×C₅₉	—	2	2	no	—
61	C₂²⋊Q₈×C₅₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₅₉	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₅₉	—	2	2	no	—
80	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
81	#107×C₅₉	—	2	2	no	—
82	#107×C₅₉	—	2	2	no	—
83	C₄⋊C₈×C₅₉	—	4	2	no	—
84	#103×C₅₉	—	2	2	no	—
85	#103×C₅₉	—	2	2	no	—
86	#103×C₅₉	—	4	2	no	—
87	#102×C₅₉	—	2	4	no	—
88	#102×C₅₉	—	2	4	no	—
89	#102×C₅₉	—	2	4	no	—
90	#102×C₅₉	—	4	2	no	—
91	C₂²⋊C₈×C₅₉	—	2	2	no	—
92	#95×C₅₉	—	2	2	no	—
93	#95×C₅₉	—	2	2	no	—
94	#95×C₅₉	—	2	1	no	—
95	#95×C₅₉	D₄	1	2	yes	—
96	C₂⁴×C₅₉	—	2	2	no	—
97	C₂⁴×C₅₉	—	4	4	no	—
98	C₂⁴×C₅₉	—	4	2	no	—
99	C₂⁴×C₅₉	—	4	2	no	—
100	C₂⁴×C₅₉	—	4	2	no	—
101	C₂⁴×C₅₉	—	8	2	no	—
102	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₅₉	—	2	1	no	—
104	C₂×Q₈×C₅₉	—	2	1	no	—
105	C₂×Q₈×C₅₉	—	2	2	no	—
106	C₂×Q₈×C₅₉	—	2	2	no	—
107	C₂×D₄×C₅₉	—	2	8	no	—
108	C₂×D₄×C₅₉	—	2	2	no	—
109	C₂×D₄×C₅₉	—	2	2	no	—
110	C₂×D₄×C₅₉	—	2	2	no	—
111	C₂×D₄×C₅₉	—	2	2	no	—
112	C₂×D₄×C₅₉	—	2	2	no	—
113	C₂×D₄×C₅₉	—	4	8	no	—
114	C₂×D₄×C₅₉	—	4	4	no	—
115	C₂×D₄×C₅₉	—	4	4	no	—
116	C₂×D₄×C₅₉	—	4	2	no	—
117	C₂×D₄×C₅₉	#41	1	4	yes	—
118	C₂²×C₄×C₅₉	—	2	2	no	—
119	C₂²×C₄×C₅₉	—	2	2	no	—
120	C₂²×C₄×C₅₉	—	2	1	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	4	no	—
123	C₂²×C₄×C₅₉	—	2	2	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	8	2	no	—
127	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₅₉	#41	1	2	yes	—
132	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₅₉	—	2	1	no	—
134	C₂×C₈×C₅₉	—	2	1	no	—
135	C₂×C₈×C₅₉	—	2	2	no	—
136	C₂×C₈×C₅₉	—	2	2	no	—
137	C₂×C₈×C₅₉	—	2	2	no	—
138	C₂×C₈×C₅₉	—	2	2	no	—
139	C₂×C₈×C₅₉	—	2	2	no	—
140	C₂×C₈×C₅₉	—	4	4	no	—
141	C₄⋊C₄×C₅₉	—	2	4	no	—
142	C₄⋊C₄×C₅₉	—	2	1	no	—
143	C₄⋊C₄×C₅₉	—	2	1	no	—
144	C₄⋊C₄×C₅₉	—	2	1	no	—
145	C₄⋊C₄×C₅₉	—	2	2	no	—
146	C₄⋊C₄×C₅₉	—	2	1	no	—
147	C₄⋊C₄×C₅₉	—	2	2	no	—
148	C₄⋊C₄×C₅₉	—	4	2	no	—
149	C₄⋊C₄×C₅₉	—	8	2	no	—
150	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
152	C₂²⋊C₄×C₅₉	—	2	2	no	—
153	C₂²⋊C₄×C₅₉	—	2	2	no	—
154	C₂²⋊C₄×C₅₉	—	4	4	no	—
155	C₂²⋊C₄×C₅₉	—	4	4	no	—
156	C₂²⋊C₄×C₅₉	—	4	2	no	—
157	C₂²⋊C₄×C₅₉	—	4	2	no	—
158	C₂²⋊C₄×C₅₉	—	8	2	no	—
159	C₂²⋊C₄×C₅₉	—	8	2	no	—
160	C₄²×C₅₉	—	2	2	no	—
161	C₄²×C₅₉	—	2	2	no	—
162	C₄²×C₅₉	—	8	2	no	—
163	C₂³×C₅₉	—	2	2	no	—
164	C₂³×C₅₉	—	2	2	no	—
165	C₂³×C₅₉	—	2	4	no	—
166	C₂³×C₅₉	—	4	8	no	—
167	C₂³×C₅₉	—	4	2	no	—
168	C₂³×C₅₉	—	4	2	no	—
169	C₂³×C₅₉	—	4	2	no	—
170	C₂³×C₅₉	—	4	2	no	—
171	C₂³×C₅₉	—	4	2	no	—
172	C₂³×C₅₉	—	4	2	no	—
173	C₂³×C₅₉	—	8	8	no	—
174	C₂³×C₅₉	—	8	8	no	—
175	C₂³×C₅₉	—	8	4	no	—
176	C₂³×C₅₉	—	8	4	no	—
177	C₂³×C₅₉	#121	1	2	yes	—
178	C₂³×C₅₉	#135	1	2	yes	—
179	C₂³×C₅₉	#137	1	2	yes	—
180	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₅₉	—	4	1	no	—
182	Q₈×C₅₉	—	4	1	no	—
183	Q₈×C₅₉	—	4	2	no	—
184	D₄×C₅₉	—	2	4	no	—
185	D₄×C₅₉	—	2	4	no	—
186	D₄×C₅₉	—	4	8	no	—
187	D₄×C₅₉	—	4	2	no	—
188	D₄×C₅₉	—	4	2	no	—
189	C₂×C₄×C₅₉	—	2	2	no	—
190	C₂×C₄×C₅₉	—	2	2	no	—
191	C₂×C₄×C₅₉	—	2	2	no	—
192	C₂×C₄×C₅₉	—	2	4	no	—
193	C₂×C₄×C₅₉	—	2	2	no	—
194	C₂×C₄×C₅₉	—	2	2	no	—
195	C₂×C₄×C₅₉	—	2	2	no	—
196	C₂×C₄×C₅₉	—	2	2	no	—
197	C₂×C₄×C₅₉	—	2	2	no	—
198	C₂×C₄×C₅₉	—	2	2	no	—
199	C₂×C₄×C₅₉	—	2	2	no	—
200	C₂×C₄×C₅₉	—	2	2	no	—
201	C₂×C₄×C₅₉	—	4	2	no	—
202	C₂×C₄×C₅₉	—	4	2	no	—
203	C₂×C₄×C₅₉	—	4	1	no	—
204	C₂×C₄×C₅₉	—	4	1	no	—
205	C₂×C₄×C₅₉	—	4	2	no	—
206	C₂×C₄×C₅₉	—	4	2	no	—
207	C₂×C₄×C₅₉	—	4	2	no	—
208	C₂×C₄×C₅₉	—	4	2	no	—
209	C₂×C₄×C₅₉	—	4	2	no	—
210	C₂×C₄×C₅₉	—	8	4	no	—
211	C₂×C₄×C₅₉	#121	1	2	yes	—
212	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
214	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
216	C₈×C₅₉	—	4	1	no	—
217	C₈×C₅₉	—	4	1	no	—
218	C₈×C₅₉	—	4	2	no	—
219	#24479	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₅₉	—	2	2	no	—
221	C₂²×C₅₉	—	2	2	no	—
222	C₂²×C₅₉	—	2	4	no	—
223	C₂²×C₅₉	—	2	4	no	—
224	C₂²×C₅₉	—	4	4	no	—
225	C₂²×C₅₉	—	4	4	no	—
226	C₂²×C₅₉	—	4	4	no	—
227	C₂²×C₅₉	—	8	16	no	—
228	C₂²×C₅₉	—	8	2	no	—
229	C₂²×C₅₉	—	8	2	no	—
230	C₂²×C₅₉	—	8	2	no	—
231	C₂²×C₅₉	—	8	2	no	—
232	C₂²×C₅₉	#464	1	4	yes	—
233	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
234	C₂²×C₅₉	#546	1	2	yes	—
235	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
236	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
237	C₂²×C₅₉	#576	1	2	yes	—
238	C₄×C₅₉	—	2	2	no	—
239	C₄×C₅₉	—	4	2	no	—
240	C₄×C₅₉	—	4	2	no	—
241	C₄×C₅₉	—	4	2	no	—
242	C₄×C₅₉	—	4	2	no	—
243	C₄×C₅₉	—	8	1	no	—
244	C₄×C₅₉	—	8	1	no	—
245	C₄×C₅₉	—	8	2	no	—
246	C₄×C₅₉	#525	1	1	yes	characteristic
247	C₄×C₅₉	#535	1	1	yes	characteristic
248	C₄×C₅₉	#551	1	2	yes	—
249	C₂×#484	C₂×C₅₉	1	1	yes	characteristic, complemented
250	C₂²×#102	C₂×C₅₉	1	1	yes	characteristic
251	#2435	C₂×C₅₉	1	1	yes	characteristic
252	#2345	C₂×C₅₉	1	1	yes	characteristic, complemented
253	#2067	C₂×C₅₉	1	2	yes	complemented
254	#2042	C₂×C₅₉	1	2	yes	complemented
255	#1983	C₂×C₅₉	1	2	yes	complemented
256	#1925	C₂×C₅₉	1	2	yes	complemented
257	#1892	C₂×C₅₉	1	1	yes	characteristic, complemented
258	#1850	C₂×C₅₉	1	1	yes	characteristic, complemented
259	#1786	C₂×C₅₉	1	1	yes	characteristic
260	C₂×C₅₉	—	2	4	no	—
261	C₂×C₅₉	—	8	4	no	—
262	C₂×C₅₉	#2411	1	1	yes	characteristic
263	C₂×C₅₉	C₂×#464	1	1	yes	characteristic
264	C₂×C₅₉	#3041	1	1	yes	characteristic
265	C₂×C₅₉	#3297	1	2	yes	—
266	C₂×C₅₉	#3314	1	2	yes	—
267	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
269	C₂×#124	C₂²×C₅₉	1	2	yes	—
270	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
272	#484	—	2	4	no	—
273	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic, complemented
274	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic, complemented
275	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	complemented
276	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
277	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic, complemented
278	C₂×#103	C₂²×C₅₉	1	2	yes	complemented
279	C₂×#102	—	2	4	no	—
280	C₂×#102	C₂²×C₅₉	1	2	yes	—
281	C₂×#102	C₂²×C₅₉	1	2	yes	—
282	C₂×#102	C₂²×C₅₉	1	2	yes	—
283	C₂×#102	C₂²×C₅₉	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
285	#394	—	2	2	no	—
286	#390	C₂²×C₅₉	1	2	yes	—
287	#389	C₂²×C₅₉	1	2	yes	complemented
288	#387	—	2	2	no	—
289	#380	—	2	1	no	—
290	#380	C₂²×C₅₉	1	1	yes	characteristic
291	#379	—	2	1	no	—
292	#379	—	2	1	no	—
293	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
294	C₄×C₂²⋊C₄	—	2	1	no	—
295	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
296	#340	C₂²×C₅₉	1	2	yes	complemented
297	#336	C₂²×C₅₉	1	2	yes	complemented
298	C₅₉	#24479	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁵	—	2	1	no	—
300	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	4	2	no	—
306	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	4	2	no	—
311	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
312	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
314	#124	—	2	4	no	—
315	#124	—	4	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	D₄×C₅₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
337	#107	—	2	2	no	—
338	#107	—	2	2	no	—
339	C₄⋊C₈	—	4	2	no	—
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	4	2	no	—
343	#102	—	2	4	no	—
344	#102	—	2	4	no	—
345	#102	—	2	4	no	—
346	#102	—	4	2	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	#95	—	2	2	no	—
349	#95	—	2	2	no	—
350	#95	—	2	1	no	—
351	#95	D₄×C₅₉	1	2	yes	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	4	4	no	—
354	C₂⁴	—	4	2	no	—
355	C₂⁴	—	4	2	no	—
356	C₂⁴	—	4	2	no	—
357	C₂⁴	—	8	2	no	—
358	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	#41×C₅₉	1	4	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	8	2	no	—
383	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
387	C₂²×C₄	#41×C₅₉	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	4	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	8	2	no	—
406	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
407	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	8	2	no	—
415	C₂²⋊C₄	—	8	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	8	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	8	no	—
430	C₂³	—	8	8	no	—
431	C₂³	—	8	4	no	—
432	C₂³	—	8	4	no	—
433	C₂³	#121×C₅₉	1	2	yes	—
434	C₂³	#135×C₅₉	1	2	yes	—
435	C₂³	#137×C₅₉	1	2	yes	—
436	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
437	Q₈	—	4	1	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	2	no	—
440	D₄	—	2	4	no	—
441	D₄	—	2	4	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	8	4	no	—
467	C₂×C₄	#121×C₅₉	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
470	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
471	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
472	C₈	—	4	1	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	8	16	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	2	no	—
487	C₂²	C₅₉×#464	1	4	yes	—
488	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
489	C₂²	C₅₉×#546	1	2	yes	—
490	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
491	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
492	C₂²	C₅₉×#576	1	2	yes	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	2	no	—
500	C₄	—	8	1	no	—
501	C₄	C₅₉×#525	1	1	yes	characteristic
502	C₄	C₅₉×#535	1	1	yes	characteristic
503	C₄	C₅₉×#551	1	2	yes	—
504	C₂	—	2	4	no	—
505	C₂	—	8	4	no	—
506	C₂	C₅₉×#2411	1	1	yes	characteristic
507	C₂	C₂×C₅₉×#464	1	1	yes	characteristic
508	C₂	C₅₉×#3041	1	1	yes	characteristic
509	C₂	C₅₉×#3297	1	2	yes	—
510	C₂	C₅₉×#3314	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#484	C₂	semidirect
4. C₅₉×#2345	C₂	semidirect
5. C₅₉×#2067	C₂	semidirect
6. C₅₉×#2042	C₂	semidirect
7. C₅₉×#1983	C₂	semidirect
8. C₅₉×#1925	C₂	semidirect
9. C₅₉×#1892	C₂	semidirect
10. C₅₉×#1850	C₂	semidirect
18. C₂×#107×C₅₉	C₂²	semidirect
19. C₂×#107×C₅₉	C₂²	semidirect
20. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
21. C₂×#103×C₅₉	C₂²	semidirect
22. C₂×#103×C₅₉	C₂²	semidirect
23. C₂×#103×C₅₉	C₂²	semidirect
32. C₅₉×#389	C₂²	semidirect
38. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
41. C₅₉×#340	C₂²	semidirect
42. C₅₉×#336	C₂²	semidirect
219. #24479	C₅₉	direct (N × H)
249. C₂×#484	C₂×C₅₉	semidirect
252. #2345	C₂×C₅₉	semidirect
253. #2067	C₂×C₅₉	semidirect
254. #2042	C₂×C₅₉	semidirect
255. #1983	C₂×C₅₉	semidirect
256. #1925	C₂×C₅₉	semidirect
257. #1892	C₂×C₅₉	semidirect
258. #1850	C₂×C₅₉	semidirect
273. C₂×#107	C₂²×C₅₉	semidirect
274. C₂×#107	C₂²×C₅₉	semidirect
275. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
276. C₂×#103	C₂²×C₅₉	semidirect
277. C₂×#103	C₂²×C₅₉	semidirect
278. C₂×#103	C₂²×C₅₉	semidirect
287. #389	C₂²×C₅₉	semidirect
293. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
296. #340	C₂²×C₅₉	semidirect
297. #336	C₂²×C₅₉	semidirect
298. C₅₉	#24479	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×#484	2
C₂²×#102×C₅₉	2
C₅₉×#2435	2
C₅₉×#2345	2
C₅₉×#2067	2
C₅₉×#2042	2
C₅₉×#1983	2
C₅₉×#1925	2
C₅₉×#1892	2
C₅₉×#1850	2
C₅₉×#1786	2
#24479	59

Subgroups — C59×#24479 #28436588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24479 #28436588