Subgroups — #28557939

Order 15104.

634 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433060	C₂	1	1	yes	maximal, characteristic
2	#21432763	C₂	1	1	yes	maximal, characteristic
3	#21432661	C₂	1	1	yes	maximal, characteristic
4	#21422886	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422885	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422878	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422869	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422865	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422864	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422860	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422853	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422847	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422846	C₂	1	1	yes	maximal, characteristic, complemented
14	#334×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273733	—	2	1	no	—
17	C₄×#11745685	C₂²	1	1	yes	characteristic
18	#16837531	C₄	1	1	yes	characteristic
19	#16837531	C₄	1	1	yes	characteristic
20	#16837477	C₄	1	1	yes	characteristic
21	#16837477	C₄	1	1	yes	characteristic
22	#16837476	C₄	1	1	yes	characteristic
23	#16837476	C₄	1	1	yes	characteristic
24	#16837472	C₄	1	1	yes	characteristic
25	#16837472	C₄	1	1	yes	characteristic
26	#16837464	—	2	1	no	—
27	#16837460	—	2	1	no	—
28	#16837458	C₂²	1	1	yes	characteristic
29	#16837455	C₂²	1	1	yes	characteristic
30	#16837454	C₂²	1	1	yes	characteristic
31	#16837453	C₂²	1	1	yes	characteristic
32	#16837453	C₂²	1	1	yes	characteristic
33	#16837428	—	2	1	no	—
34	#16837427	—	2	1	no	—
35	#16837427	—	2	1	no	—
36	#16837426	C₂²	1	1	yes	characteristic
37	#16837424	C₂²	1	1	yes	characteristic
38	#16837424	C₂²	1	1	yes	characteristic
39	#16837424	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
41	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
43	#16837367	—	2	1	no	—
44	#16837359	—	2	1	no	—
45	C₄×#11745664	C₂²	1	1	yes	characteristic
46	C₄×#11745659	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837155	C₂²	1	1	yes	characteristic
49	#16837155	C₂²	1	1	yes	characteristic
50	#16837154	C₂²	1	1	yes	characteristic
51	#16837154	C₂²	1	1	yes	characteristic
52	#16837154	C₂²	1	1	yes	characteristic
53	#16837154	C₂²	1	1	yes	characteristic
54	#16837153	C₂²	1	1	yes	characteristic
55	#16837153	C₂²	1	1	yes	characteristic
56	#16837152	C₂²	1	1	yes	characteristic
57	#16837152	C₂²	1	1	yes	characteristic
58	#16837152	C₂²	1	1	yes	characteristic
59	#16837152	C₂²	1	1	yes	characteristic
60	C₅₉×#432	C₂²	1	1	yes	characteristic
61	C₅₉×#431	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×#335	C₂²	1	1	yes	characteristic
65	C₅₉×#334	C₂²	1	1	yes	characteristic
66	C₅₉×#334	C₂²	1	1	yes	characteristic
67	C₂×#11745685	D₄	1	1	yes	characteristic
68	#14273733	—	4	4	no	—
69	C₂×#11745664	—	2	1	no	—
70	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745659	—	2	1	no	—
73	C₂×#11745659	—	2	1	no	—
74	C₂×#11745659	—	2	1	no	—
75	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
76	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₅₉	—	2	1	no	—
78	C₂×C₈×D₅₉	—	2	1	no	—
79	C₂×C₈×D₅₉	—	2	1	no	—
80	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₁₈	Q₈	1	1	yes	characteristic
84	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
85	C₄×D₂₃₆	Q₈	1	1	yes	characteristic
86	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
87	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
88	C₄×C₂²⋊D₅₉	Q₈	1	1	yes	characteristic
89	C₄×C₂²⋊D₅₉	Q₈	1	1	yes	characteristic
90	#14273686	D₄	1	1	yes	characteristic
91	#14273684	D₄	1	1	yes	characteristic
92	#14273684	D₄	1	1	yes	characteristic
93	C₄²×D₅₉	C₂³	1	1	yes	characteristic
94	C₄²×D₅₉	C₂³	1	1	yes	characteristic
95	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
96	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
97	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
98	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
99	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
100	Dic₅₉⋊C₈	—	2	1	no	—
101	Dic₅₉⋊C₈	—	2	1	no	—
102	Dic₅₉⋊C₈	—	2	1	no	—
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	—	2	1	no	—
106	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
107	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
108	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
109	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
111	(C₂×D₅₉)⋊C₈	—	2	1	no	—
112	(C₂×D₅₉)⋊C₈	—	2	1	no	—
113	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	#14273638	C₂×C₄	1	1	yes	characteristic
118	#14273638	C₂×C₄	1	1	yes	characteristic
119	#14273637	—	2	1	no	—
120	#14273637	C₂×C₄	1	1	yes	characteristic
121	#14273637	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅₉⋊C₈	—	2	1	no	—
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
125	C₈×Dic₅₉	—	2	1	no	—
126	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
128	C₂²×C₈×C₅₉	—	2	1	no	—
129	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₅₉	—	2	1	no	—
131	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
132	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₂²⋊C₈×C₅₉	—	2	1	no	—
138	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
140	#97×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
146	C₂×C₂²⋊D₅₉	C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₅₉	C₄⋊C₄	1	1	yes	characteristic
148	#11745685	—	2	2	no	—
149	#11745685	—	2	2	no	—
150	C₂×D₂₃₆	C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₅₉	C₂×Q₈	1	1	yes	characteristic
156	C₂×C₄×D₅₉	C₂×Q₈	1	1	yes	characteristic
157	C₂×Dic₁₁₈	C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	—	2	1	no	—
159	C₂×C₈×C₅₉	—	2	1	no	—
160	C₂×C₈×C₅₉	—	2	1	no	—
161	C₂×C₈×C₅₉	—	2	1	no	—
162	C₂×C₈×C₅₉	—	4	2	no	—
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
170	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
171	C₂²⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
172	C₂²⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
173	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
174	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
175	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
176	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
177	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
178	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
179	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
180	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
181	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
182	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
183	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
184	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
185	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
186	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
187	C₄×Dic₅₉	C₂×Q₈	1	1	yes	characteristic
188	C₄×Dic₅₉	C₂×Q₈	1	1	yes	characteristic
189	#11745664	—	2	2	no	—
190	#11745664	—	4	1	no	—
191	#11745664	—	4	2	no	—
192	C₂×C₅₉⋊C₈	—	2	1	no	—
193	C₂×C₅₉⋊C₈	—	2	1	no	—
194	C₂×C₅₉⋊C₈	—	2	1	no	—
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
200	#11745659	—	2	2	no	—
201	#11745659	—	4	1	no	—
202	#11745659	—	4	2	no	—
203	#11745659	—	4	2	no	—
204	#11745659	—	4	2	no	—
205	C₈×D₅₉	—	2	2	no	—
206	C₈×D₅₉	—	4	1	no	—
207	C₈×D₅₉	—	4	2	no	—
208	C₈×D₅₉	—	4	2	no	—
209	C₈×D₅₉	—	4	2	no	—
210	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×D₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×D₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	—	4	1	no	—
218	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
224	C₂²⋊D₅₉	—	2	2	no	—
225	C₂²⋊D₅₉	—	2	2	no	—
226	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
232	D₂₃₆	—	2	2	no	—
233	C₄×D₅₉	—	2	1	no	—
234	C₄×D₅₉	—	2	1	no	—
235	C₄×D₅₉	—	2	1	no	—
236	C₄×D₅₉	—	2	1	no	—
237	C₄×D₅₉	—	2	1	no	—
238	C₄×D₅₉	—	2	1	no	—
239	C₄×D₅₉	—	4	1	no	—
240	C₄×D₅₉	—	4	1	no	—
241	C₄×D₅₉	AGL(1,ℤ/8)	1	2	yes	—
242	C₄×D₅₉	#137	1	2	yes	—
243	Dic₁₁₈	—	2	2	no	—
244	C₈×C₅₉	—	2	1	no	—
245	C₈×C₅₉	—	2	1	no	—
246	C₈×C₅₉	—	2	1	no	—
247	C₈×C₅₉	—	2	1	no	—
248	C₈×C₅₉	—	4	1	no	—
249	C₈×C₅₉	—	4	1	no	—
250	C₈×C₅₉	—	4	1	no	—
251	C₈×C₅₉	—	4	1	no	—
252	C₅₉⋊C₈	—	2	1	no	—
253	C₅₉⋊C₈	—	2	1	no	—
254	C₅₉⋊C₈	—	2	1	no	—
255	C₅₉⋊C₈	—	4	1	no	—
256	C₅₉⋊C₈	—	4	1	no	—
257	C₅₉⋊C₈	—	4	1	no	—
258	C₅₉⋊C₈	—	4	1	no	—
259	C₅₉⋊C₈	#131	1	2	yes	complemented
260	#17830	—	59	1	no	maximal, Sylow
261	C₂²×C₅₉	—	2	1	no	—
262	C₂²×C₅₉	—	2	1	no	—
263	C₂²×C₅₉	—	2	1	no	—
264	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
265	C₂×D₅₉	—	2	1	no	—
266	C₂×D₅₉	—	2	1	no	—
267	C₂×D₅₉	—	2	1	no	—
268	C₂×D₅₉	—	2	1	no	—
269	C₂×D₅₉	—	2	1	no	—
270	C₂×D₅₉	#428	1	2	yes	—
271	C₄×C₅₉	—	2	1	no	—
272	C₄×C₅₉	—	2	1	no	—
273	C₄×C₅₉	—	2	1	no	—
274	C₄×C₅₉	—	2	1	no	—
275	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
276	C₄×C₅₉	#568	1	1	yes	characteristic
277	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
279	Dic₅₉	—	2	1	no	—
280	Dic₅₉	—	2	1	no	—
281	Dic₅₉	—	2	1	no	—
282	Dic₅₉	—	2	1	no	—
283	Dic₅₉	—	2	1	no	—
284	Dic₅₉	#428	1	2	yes	—
285	#2965	—	59	1	no	—
286	#2925	—	59	1	no	—
287	#2906	—	59	1	no	—
288	#1574	—	59	1	no	—
289	#1574	—	59	1	no	—
290	#1573	—	59	1	no	—
291	#1573	D₅₉	1	1	yes	characteristic, complemented
292	#1571	—	59	1	no	—
293	#1570	—	59	1	no	—
294	#1569	—	59	1	no	—
295	#1569	—	59	1	no	—
296	#1567	—	59	1	no	—
297	#1565	—	59	1	no	—
298	#1565	—	59	1	no	—
299	C₂×#334	—	59	1	no	—
300	C₂×C₅₉	—	4	1	no	—
301	C₂×C₅₉	#2906	1	1	yes	characteristic
302	C₂×C₅₉	C₂×#428	1	1	yes	characteristic
303	C₂×C₅₉	#2916	1	1	yes	characteristic
304	D₅₉	—	2	2	no	—
305	D₅₉	—	4	1	no	—
306	C₂×#131	—	118	1	no	—
307	C₄×#41	—	59	1	no	—
308	#446	—	59	1	no	—
309	#446	—	59	1	no	—
310	#436	—	59	1	no	—
311	#436	—	59	1	no	—
312	#435	—	59	1	no	—
313	#435	—	59	1	no	—
314	#435	—	59	1	no	—
315	#435	—	59	1	no	—
316	#433	—	118	1	no	—
317	#433	—	118	1	no	—
318	#432	—	59	1	no	—
319	#432	C₂×D₅₉	1	1	yes	characteristic
320	#431	—	59	1	no	—
321	#431	—	59	1	no	—
322	#431	—	59	1	no	—
323	#431	—	59	1	no	—
324	#431	C₂×D₅₉	1	1	yes	characteristic
325	#424	—	118	1	no	—
326	#424	—	118	1	no	—
327	#424	—	118	1	no	—
328	#423	—	59	1	no	—
329	#423	—	59	1	no	—
330	#423	—	59	1	no	—
331	#423	—	59	1	no	—
332	C₂×C₄⋊C₈	—	59	1	no	—
333	C₂×C₄⋊C₈	—	59	1	no	—
334	C₂×C₄⋊C₈	—	59	1	no	—
335	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
336	#408	—	118	1	no	—
337	#405	—	118	1	no	—
338	C₄×M₁₆	—	59	1	no	—
339	C₄×M₁₆	—	59	1	no	—
340	C₂×C₄×C₈	—	59	1	no	—
341	#335	—	59	1	no	—
342	#335	—	59	1	no	—
343	#335	—	59	1	no	—
344	#335	—	59	1	no	—
345	#335	—	59	1	no	—
346	#335	—	59	1	no	—
347	#335	C₂×D₅₉	1	1	yes	characteristic
348	#335	C₂×D₅₉	1	1	yes	characteristic
349	#334	—	59	1	no	—
350	#334	—	59	1	no	—
351	#334	—	59	1	no	—
352	#334	—	59	1	no	—
353	#334	—	59	1	no	—
354	#334	—	59	1	no	—
355	#334	C₂×D₅₉	1	1	yes	characteristic
356	#334	C₂×D₅₉	1	1	yes	characteristic
357	C₅₉	#17830	1	1	yes	characteristic, complemented, Sylow
358	C₂×#41	—	59	1	no	—
359	#131	—	236	4	no	—
360	C₂×M₁₆	—	59	1	no	—
361	C₂×M₁₆	—	59	1	no	—
362	C₂×M₁₆	—	59	1	no	—
363	C₂×M₁₆	—	59	1	no	—
364	C₂×M₁₆	—	118	1	no	—
365	C₂×M₁₆	—	118	1	no	—
366	C₂×M₁₆	—	118	1	no	—
367	C₂×M₁₆	—	118	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	59	1	no	—
370	C₂²×C₈	—	59	1	no	—
371	C₂²×C₈	—	118	1	no	—
372	C₂²×C₈	—	118	1	no	—
373	C₂²×C₈	—	118	1	no	—
374	C₄×Q₈	—	59	1	no	—
375	C₄×Q₈	—	59	1	no	—
376	C₄×D₄	—	59	1	no	—
377	C₄×D₄	—	59	1	no	—
378	C₄×D₄	—	59	1	no	—
379	C₄×D₄	—	59	1	no	—
380	C₄×D₄	—	59	1	no	—
381	C₄×D₄	—	59	1	no	—
382	#117	—	59	1	no	—
383	#117	—	59	1	no	—
384	#117	—	59	1	no	—
385	C₂×C₄²	—	59	1	no	—
386	C₂×C₄²	—	59	1	no	—
387	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	59	1	no	—
390	C₄⋊C₈	—	59	1	no	—
391	C₄⋊C₈	—	59	1	no	—
392	C₄⋊C₈	—	59	1	no	—
393	C₄⋊C₈	—	59	1	no	—
394	C₄⋊C₈	—	59	1	no	—
395	C₄⋊C₈	—	59	1	no	—
396	C₄⋊C₈	—	59	1	no	—
397	C₄⋊C₈	—	118	1	no	—
398	C₄⋊C₈	—	118	1	no	—
399	C₄⋊C₈	—	118	1	no	—
400	C₄⋊C₈	—	118	1	no	—
401	C₄⋊C₈	—	118	1	no	—
402	C₄⋊C₈	—	118	1	no	—
403	C₄⋊C₈	—	118	1	no	—
404	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
405	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
406	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
408	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	59	1	no	—
412	C₂²⋊C₈	—	59	1	no	—
413	C₂²⋊C₈	—	59	1	no	—
414	C₂²⋊C₈	—	59	1	no	—
415	C₂²⋊C₈	—	118	1	no	—
416	C₂²⋊C₈	—	118	1	no	—
417	C₂²⋊C₈	—	118	1	no	—
418	C₂²⋊C₈	C₄×D₅₉	1	1	yes	characteristic
419	C₂²⋊C₈	C₄×D₅₉	1	1	yes	characteristic
420	#97	—	2	1	no	—
421	#97	—	59	1	no	—
422	#97	—	59	1	no	—
423	#97	—	59	1	no	—
424	#97	—	59	1	no	—
425	#97	—	118	1	no	—
426	C₄×C₈	—	59	1	no	—
427	C₄×C₈	—	59	1	no	—
428	C₄×C₈	—	59	1	no	—
429	C₄×C₈	—	59	1	no	—
430	C₄×C₈	—	118	1	no	—
431	C₄×C₈	—	118	1	no	—
432	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
434	#41	—	118	2	no	—
435	#41	—	118	2	no	—
436	C₂×Q₈	—	59	1	no	—
437	C₂×D₄	—	59	1	no	—
438	C₂×D₄	—	59	1	no	—
439	C₂×D₄	—	59	1	no	—
440	C₂²×C₄	—	59	1	no	—
441	C₂²×C₄	—	59	1	no	—
442	C₂²×C₄	—	59	1	no	—
443	C₂²×C₄	—	59	1	no	—
444	C₂²×C₄	—	59	1	no	—
445	C₂²×C₄	—	59	1	no	—
446	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
448	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
449	M₁₆	—	118	2	no	—
450	M₁₆	—	118	2	no	—
451	M₁₆	—	236	1	no	—
452	M₁₆	—	236	2	no	—
453	M₁₆	—	236	2	no	—
454	M₁₆	—	236	2	no	—
455	M₁₆	—	236	1	no	—
456	M₁₆	—	236	2	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	59	1	no	—
463	C₂×C₈	—	59	1	no	—
464	C₂×C₈	—	59	1	no	—
465	C₂×C₈	—	59	1	no	—
466	C₂×C₈	—	118	2	no	—
467	C₂×C₈	—	118	1	no	—
468	C₂×C₈	—	118	1	no	—
469	C₂×C₈	—	118	1	no	—
470	C₂×C₈	—	118	1	no	—
471	C₂×C₈	—	236	1	no	—
472	C₂×C₈	—	236	2	no	—
473	C₂×C₈	—	236	2	no	—
474	C₂×C₈	—	236	2	no	—
475	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
476	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
477	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
478	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
479	C₄⋊C₄	—	59	1	no	—
480	C₄⋊C₄	—	59	1	no	—
481	C₄⋊C₄	—	59	1	no	—
482	C₄⋊C₄	—	59	1	no	—
483	C₄⋊C₄	—	59	1	no	—
484	C₄⋊C₄	—	59	1	no	—
485	C₂²⋊C₄	—	59	1	no	—
486	C₂²⋊C₄	—	59	1	no	—
487	C₂²⋊C₄	—	59	1	no	—
488	C₂²⋊C₄	—	59	1	no	—
489	C₂²⋊C₄	—	59	1	no	—
490	C₂²⋊C₄	—	59	1	no	—
491	C₄²	—	59	1	no	—
492	C₄²	—	59	1	no	—
493	C₄²	—	59	1	no	—
494	C₄²	—	59	1	no	—
495	C₄²	—	59	1	no	—
496	C₄²	—	59	1	no	—
497	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
498	C₄²	D₄×D₅₉	1	1	yes	characteristic
499	C₄²	Q₈×D₅₉	1	1	yes	characteristic
500	C₄²	C₂³×D₅₉	1	1	yes	characteristic
501	C₂³	—	59	1	no	—
502	C₂³	—	59	1	no	—
503	C₂³	C₄⋊C₄×D₅₉	1	1	yes	characteristic
504	Q₈	—	118	2	no	—
505	D₄	—	118	2	no	—
506	D₄	—	118	2	no	—
507	D₄	—	118	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	59	1	no	—
514	C₂×C₄	—	59	2	no	—
515	C₂×C₄	—	59	2	no	—
516	C₂×C₄	—	59	1	no	—
517	C₂×C₄	—	59	1	no	—
518	C₂×C₄	—	59	1	no	—
519	C₂×C₄	—	59	1	no	—
520	C₂×C₄	—	59	1	no	—
521	C₂×C₄	—	118	1	no	—
522	C₂×C₄	—	118	1	no	—
523	C₂×C₄	—	118	1	no	—
524	C₂×C₄	—	118	1	no	—
525	C₂×C₄	—	118	1	no	—
526	C₂×C₄	—	118	1	no	—
527	C₂×C₄	—	236	1	no	—
528	C₂×C₄	—	236	1	no	—
529	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
530	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
531	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
534	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	59	2	no	—
544	C₈	—	118	1	no	—
545	C₈	—	118	1	no	—
546	C₈	—	118	1	no	—
547	C₈	—	236	1	no	—
548	C₈	—	236	1	no	—
549	C₈	—	236	1	no	—
550	C₈	—	236	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	59	2	no	—
555	C₂²	—	118	1	no	—
556	C₂²	—	118	1	no	—
557	C₂²	—	118	1	no	—
558	C₂²	—	118	1	no	—
559	C₂²	—	118	1	no	—
560	C₂²	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	59	2	no	—
566	C₄	—	118	1	no	—
567	C₄	—	118	1	no	—
568	C₄	—	118	1	no	—
569	C₄	—	118	1	no	—
570	C₄	—	118	1	no	—
571	C₄	#131×D₅₉	1	1	yes	characteristic
572	C₄	#16838167	1	1	yes	characteristic
573	C₄	AGL(1,ℤ/8)×D₅₉	1	1	yes	characteristic
574	C₄	#137×D₅₉	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	118	2	no	—
577	C₂	—	236	1	no	—
578	C₂	#21432663	1	1	yes	characteristic
579	C₂	#428×D₅₉	1	1	yes	characteristic
580	C₂	#21432704	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1573	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#11745685	D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1573	D₅₉
hypocenter	C₅₉	#17830
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
4. #21422886	C₂	semidirect
5. #21422885	C₂	semidirect
6. #21422878	C₂	semidirect
7. #21422869	C₂	semidirect
8. #21422865	C₂	semidirect
9. #21422864	C₂	semidirect
10. #21422860	C₂	semidirect
11. #21422853	C₂	semidirect
12. #21422847	C₂	semidirect
13. #21422846	C₂	semidirect
14. #334×D₅₉	C₂	semidirect
15. C₅₉×#1573	C₂	semidirect
259. C₅₉⋊C₈	#131	semidirect
291. #1573	D₅₉	semidirect
357. C₅₉	#17830	semidirect

Maximal subgroups

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

subgroup	index
#21433060	2
#21432763	2
#21432661	2
#21422886	2
#21422885	2
#21422878	2
#21422869	2
#21422865	2
#21422864	2
#21422860	2
#21422853	2
#21422847	2
#21422846	2
#334×D₅₉	2
C₅₉×#1573	2
#17830	59