Subgroups — C₅₉×#26464 #28438573

Order 15104.

950 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#476	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2366	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2065	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2023	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1982	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1957	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1864	C₂	1	2	yes	maximal, complemented
11	C₄×#106×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
14	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₅₉	—	2	1	no	—
16	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
17	C₅₉×#476	—	2	8	no	—
18	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#106×C₅₉	C₂²	1	2	yes	—
20	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
23	C₂×#102×C₅₉	C₂²	1	2	yes	—
24	C₂×#102×C₅₉	C₂²	1	2	yes	—
25	C₂×#102×C₅₉	C₂²	1	2	yes	—
26	C₂×#102×C₅₉	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₅₉×#395	—	2	2	no	—
29	C₅₉×#390	—	2	1	no	—
30	C₅₉×#390	C₂²	1	2	yes	—
31	C₅₉×#389	—	2	1	no	—
32	C₅₉×#389	C₂²	1	2	yes	—
33	C₅₉×#386	—	2	2	no	—
34	C₅₉×#384	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#340	C₂²	1	1	yes	characteristic
39	C₅₉×#340	C₂²	1	2	yes	—
40	C₅₉×#340	C₂²	1	1	yes	characteristic
41	C₅₉×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₅₉	—	2	2	no	—
43	C₂²×D₄×C₅₉	—	2	1	no	—
44	C₂²×D₄×C₅₉	—	2	1	no	—
45	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₅₉	—	2	2	no	—
47	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₅₉	—	2	4	no	—
51	C₄⋊Q₈×C₅₉	—	4	2	no	—
52	C₄⋊Q₈×C₅₉	—	4	4	no	—
53	#127×C₅₉	—	2	2	no	—
54	#127×C₅₉	Q₈	1	4	yes	complemented
55	C₄×D₄×C₅₉	—	2	4	no	—
56	C₄×D₄×C₅₉	—	4	2	no	—
57	C₄×D₄×C₅₉	—	4	4	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
72	C₂×C₄²×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
76	#106×C₅₉	—	2	4	no	—
77	#106×C₅₉	—	2	2	no	—
78	#106×C₅₉	D₄	1	4	yes	complemented
79	C₄⋊C₈×C₅₉	—	2	4	no	—
80	C₄⋊C₈×C₅₉	—	2	2	no	—
81	#102×C₅₉	—	2	4	no	—
82	#102×C₅₉	—	2	4	no	—
83	#102×C₅₉	—	2	4	no	—
84	#102×C₅₉	—	4	2	no	—
85	C₄×C₈×C₅₉	—	2	2	no	—
86	#95×C₅₉	—	2	1	no	—
87	#95×C₅₉	—	2	1	no	—
88	#95×C₅₉	—	2	2	no	—
89	#95×C₅₉	D₄	1	2	yes	—
90	C₂⁴×C₅₉	—	2	2	no	—
91	C₂×Q₈×C₅₉	—	4	4	no	—
92	C₂×Q₈×C₅₉	—	4	4	no	—
93	C₂×Q₈×C₅₉	—	8	2	no	—
94	C₂×D₄×C₅₉	—	2	4	no	—
95	C₂×D₄×C₅₉	—	2	4	no	—
96	C₂×D₄×C₅₉	—	2	2	no	—
97	C₂×D₄×C₅₉	—	2	2	no	—
98	C₂×D₄×C₅₉	—	2	2	no	—
99	C₂×D₄×C₅₉	—	2	2	no	—
100	C₂×D₄×C₅₉	—	2	2	no	—
101	C₂×D₄×C₅₉	—	4	2	no	—
102	C₂×D₄×C₅₉	—	4	2	no	—
103	C₂×D₄×C₅₉	—	8	1	no	—
104	C₂×D₄×C₅₉	—	8	1	no	—
105	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₅₉	—	2	1	no	—
107	C₂²×C₄×C₅₉	—	2	1	no	—
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	—	2	1	no	—
110	C₂²×C₄×C₅₉	—	2	2	no	—
111	C₂²×C₄×C₅₉	—	4	4	no	—
112	C₂²×C₄×C₅₉	—	4	4	no	—
113	C₂²×C₄×C₅₉	—	8	2	no	—
114	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₅₉	—	2	1	no	—
120	C₂×C₈×C₅₉	—	2	1	no	—
121	C₂×C₈×C₅₉	—	2	2	no	—
122	C₂×C₈×C₅₉	—	2	1	no	—
123	C₂×C₈×C₅₉	—	2	2	no	—
124	C₂×C₈×C₅₉	—	2	2	no	—
125	C₂×C₈×C₅₉	—	2	1	no	—
126	C₂×C₈×C₅₉	—	2	1	no	—
127	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₅₉	—	2	2	no	—
129	C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₄⋊C₄×C₅₉	—	2	1	no	—
131	C₄⋊C₄×C₅₉	—	2	1	no	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	1	no	—
134	C₄⋊C₄×C₅₉	—	2	2	no	—
135	C₄⋊C₄×C₅₉	—	2	1	no	—
136	C₄⋊C₄×C₅₉	—	4	4	no	—
137	C₄⋊C₄×C₅₉	—	4	4	no	—
138	C₄⋊C₄×C₅₉	—	4	2	no	—
139	C₄⋊C₄×C₅₉	—	8	1	no	—
140	C₄⋊C₄×C₅₉	SD₁₆	1	4	yes	—
141	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₅₉	#41	1	2	yes	—
144	C₂²⋊C₄×C₅₉	—	4	4	no	—
145	C₂²⋊C₄×C₅₉	—	4	4	no	—
146	C₂²⋊C₄×C₅₉	—	8	2	no	—
147	C₄²×C₅₉	—	2	2	no	—
148	C₄²×C₅₉	—	2	2	no	—
149	C₄²×C₅₉	—	4	2	no	—
150	C₄²×C₅₉	—	4	2	no	—
151	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
152	C₄²×C₅₉	#41	1	2	yes	—
153	C₂³×C₅₉	—	2	4	no	—
154	C₂³×C₅₉	—	4	2	no	—
155	C₂³×C₅₉	—	4	2	no	—
156	C₂³×C₅₉	—	4	2	no	—
157	C₂³×C₅₉	—	4	2	no	—
158	C₂³×C₅₉	—	4	2	no	—
159	C₂³×C₅₉	—	4	2	no	—
160	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₅₉	—	8	8	no	—
162	D₄×C₅₉	—	2	4	no	—
163	D₄×C₅₉	—	2	4	no	—
164	D₄×C₅₉	—	4	2	no	—
165	D₄×C₅₉	—	4	2	no	—
166	D₄×C₅₉	—	4	8	no	—
167	D₄×C₅₉	—	8	4	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	2	1	no	—
170	C₂×C₄×C₅₉	—	2	2	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	2	2	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	2	2	no	—
175	C₂×C₄×C₅₉	—	2	2	no	—
176	C₂×C₄×C₅₉	—	2	2	no	—
177	C₂×C₄×C₅₉	—	2	2	no	—
178	C₂×C₄×C₅₉	—	4	1	no	—
179	C₂×C₄×C₅₉	—	4	1	no	—
180	C₂×C₄×C₅₉	—	4	1	no	—
181	C₂×C₄×C₅₉	—	4	1	no	—
182	C₂×C₄×C₅₉	—	4	1	no	—
183	C₂×C₄×C₅₉	—	4	1	no	—
184	C₂×C₄×C₅₉	—	4	2	no	—
185	C₂×C₄×C₅₉	—	4	1	no	—
186	C₂×C₄×C₅₉	—	4	1	no	—
187	C₂×C₄×C₅₉	—	4	2	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	4	2	no	—
190	C₂×C₄×C₅₉	—	8	8	no	—
191	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₅₉	C₂×SD₁₆	1	4	yes	—
194	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
202	C₈×C₅₉	—	2	2	no	—
203	C₈×C₅₉	—	4	2	no	—
204	C₈×C₅₉	—	4	1	no	—
205	#26464	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₅₉	—	4	4	no	—
207	C₂²×C₅₉	—	4	4	no	—
208	C₂²×C₅₉	—	4	4	no	—
209	C₂²×C₅₉	—	8	2	no	—
210	C₂²×C₅₉	—	8	2	no	—
211	C₂²×C₅₉	—	8	2	no	—
212	C₂²×C₅₉	—	8	2	no	—
213	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	C₂²×C₅₉	D₄²	1	1	yes	characteristic
215	C₂²×C₅₉	#548	1	1	yes	characteristic
216	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
217	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₅₉	#576	1	1	yes	characteristic
219	C₂²×C₅₉	#577	1	1	yes	characteristic
220	C₄×C₅₉	—	2	2	no	—
221	C₄×C₅₉	—	2	4	no	—
222	C₄×C₅₉	—	4	2	no	—
223	C₄×C₅₉	—	4	2	no	—
224	C₄×C₅₉	—	4	2	no	—
225	C₄×C₅₉	—	4	2	no	—
226	C₄×C₅₉	—	8	1	no	—
227	C₄×C₅₉	—	8	2	no	—
228	C₄×C₅₉	#476	1	4	yes	complemented
229	C₄×C₅₉	#532	1	1	yes	characteristic
230	C₄×C₅₉	#542	1	1	yes	characteristic
231	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
232	C₄×C₅₉	#554	1	1	yes	characteristic
233	C₂×#476	C₂×C₅₉	1	2	yes	complemented
234	#2551	C₂×C₅₉	1	1	yes	characteristic, complemented
235	#2366	C₂×C₅₉	1	1	yes	characteristic
236	#2065	C₂×C₅₉	1	2	yes	complemented
237	#2023	C₂×C₅₉	1	2	yes	complemented
238	#1982	C₂×C₅₉	1	1	yes	characteristic
239	#1957	C₂×C₅₉	1	1	yes	characteristic
240	#1948	C₂×C₅₉	1	1	yes	characteristic, complemented
241	#1939	C₂×C₅₉	1	1	yes	characteristic, complemented
242	#1864	C₂×C₅₉	1	2	yes	complemented
243	C₄×#106	C₂×C₅₉	1	1	yes	characteristic, complemented
244	C₂×C₅₉	—	8	4	no	—
245	C₂×C₅₉	#2452	1	1	yes	characteristic
246	C₂×C₅₉	C₂×#476	1	1	yes	characteristic
247	C₂×C₅₉	#3081	1	1	yes	characteristic
248	C₂×C₅₉	#3274	1	1	yes	characteristic
249	C₂×C₅₉	D₄×SD₁₆	1	1	yes	characteristic
250	C₂×C₅₉	#3362	1	1	yes	characteristic
251	C₂×C₅₉	#3373	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	—	2	1	no	—
253	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
254	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
255	C₂×C₄×D₄	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
257	#476	—	2	8	no	—
258	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
259	C₂×#106	C₂²×C₅₉	1	2	yes	—
260	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
262	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
263	C₂×#102	C₂²×C₅₉	1	2	yes	—
264	C₂×#102	C₂²×C₅₉	1	2	yes	—
265	C₂×#102	C₂²×C₅₉	1	2	yes	—
266	C₂×#102	C₂²×C₅₉	1	2	yes	—
267	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
268	#395	—	2	2	no	—
269	#390	—	2	1	no	—
270	#390	C₂²×C₅₉	1	2	yes	—
271	#389	—	2	1	no	—
272	#389	C₂²×C₅₉	1	2	yes	—
273	#386	—	2	2	no	—
274	#384	C₂²×C₅₉	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
277	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
278	#340	C₂²×C₅₉	1	2	yes	—
279	#340	C₂²×C₅₉	1	1	yes	characteristic
280	#340	C₂²×C₅₉	1	1	yes	characteristic
281	#336	C₂²×C₅₉	1	2	yes	—
282	C₅₉	#26464	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	—	2	2	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
287	C₂³×C₄	—	2	2	no	—
288	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
290	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	4	no	—
292	C₄⋊Q₈	—	4	2	no	—
293	C₄⋊Q₈	—	4	4	no	—
294	#127	—	2	2	no	—
295	#127	Q₈×C₅₉	1	4	yes	complemented
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	4	2	no	—
298	C₄×D₄	—	4	4	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
316	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
317	#106	—	2	4	no	—
318	#106	—	2	2	no	—
319	#106	D₄×C₅₉	1	4	yes	complemented
320	C₄⋊C₈	—	2	4	no	—
321	C₄⋊C₈	—	2	2	no	—
322	#102	—	2	4	no	—
323	#102	—	2	4	no	—
324	#102	—	2	4	no	—
325	#102	—	4	2	no	—
326	C₄×C₈	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	D₄×C₅₉	1	2	yes	—
331	C₂⁴	—	2	2	no	—
332	C₂×Q₈	—	4	4	no	—
333	C₂×Q₈	—	4	4	no	—
334	C₂×Q₈	—	8	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	8	1	no	—
345	C₂×D₄	—	8	1	no	—
346	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	8	2	no	—
355	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	8	1	no	—
381	C₄⋊C₄	SD₁₆×C₅₉	1	4	yes	—
382	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
383	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
384	C₄⋊C₄	#41×C₅₉	1	2	yes	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	8	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	4	2	no	—
391	C₄²	—	4	2	no	—
392	C₄²	C₂×Q₈×C₅₉	1	2	yes	—
393	C₄²	#41×C₅₉	1	2	yes	—
394	C₂³	—	2	4	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
402	Q₈	—	8	8	no	—
403	D₄	—	2	4	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	8	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
433	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
434	C₂×C₄	C₂×SD₁₆×C₅₉	1	4	yes	—
435	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
436	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
441	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
442	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	4	2	no	—
445	C₈	—	4	1	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
454	C₂²	D₄²×C₅₉	1	1	yes	characteristic
455	C₂²	C₅₉×#548	1	1	yes	characteristic
456	C₂²	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
457	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
458	C₂²	C₅₉×#576	1	1	yes	characteristic
459	C₂²	C₅₉×#577	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	C₅₉×#476	1	4	yes	complemented
469	C₄	C₅₉×#532	1	1	yes	characteristic
470	C₄	C₅₉×#542	1	1	yes	characteristic
471	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
472	C₄	C₅₉×#554	1	1	yes	characteristic
473	C₂	—	8	4	no	—
474	C₂	C₅₉×#2452	1	1	yes	characteristic
475	C₂	C₂×C₅₉×#476	1	1	yes	characteristic
476	C₂	C₅₉×#3081	1	1	yes	characteristic
477	C₂	C₅₉×#3274	1	1	yes	characteristic
478	C₂	D₄×SD₁₆×C₅₉	1	1	yes	characteristic
479	C₂	C₅₉×#3362	1	1	yes	characteristic
480	C₂	C₅₉×#3373	1	1	yes	characteristic

	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 ◁ C₄×C₄⋊C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#476	C₂	semidirect
2. C₅₉×#2551	C₂	semidirect
4. C₅₉×#2065	C₂	semidirect
5. C₅₉×#2023	C₂	semidirect
8. C₅₉×#1948	C₂	semidirect
9. C₅₉×#1939	C₂	semidirect
10. C₅₉×#1864	C₂	semidirect
11. C₄×#106×C₅₉	C₂	semidirect
54. #127×C₅₉	Q₈	semidirect
78. #106×C₅₉	D₄	semidirect
205. #26464	C₅₉	direct (N × H)
228. C₄×C₅₉	#476	semidirect
233. C₂×#476	C₂×C₅₉	semidirect
234. #2551	C₂×C₅₉	semidirect
236. #2065	C₂×C₅₉	semidirect
237. #2023	C₂×C₅₉	semidirect
240. #1948	C₂×C₅₉	semidirect
241. #1939	C₂×C₅₉	semidirect
242. #1864	C₂×C₅₉	semidirect
243. C₄×#106	C₂×C₅₉	semidirect
282. C₅₉	#26464	direct (N × H)
295. #127	Q₈×C₅₉	semidirect
319. #106	D₄×C₅₉	semidirect
468. C₄	C₅₉×#476	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#476	2
C₅₉×#2551	2
C₅₉×#2366	2
C₅₉×#2065	2
C₅₉×#2023	2
C₅₉×#1982	2
C₅₉×#1957	2
C₅₉×#1948	2
C₅₉×#1939	2
C₅₉×#1864	2
C₄×#106×C₅₉	2
#26464	59

Subgroups — C59×#26464 #28438573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#26464 #28438573