Subgroups — #28587321

Order 15104.

838 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837533	C₂	1	1	yes	maximal, characteristic
2	#21426574	C₂	1	1	yes	maximal, characteristic
3	#21423973	C₂	1	1	yes	maximal, characteristic
4	#21423973	C₂	1	1	yes	maximal, characteristic
5	#21423968	C₂	1	1	yes	maximal, characteristic
6	#21423968	C₂	1	1	yes	maximal, characteristic
7	#21423966	C₂	1	1	yes	maximal, characteristic
8	#21423963	C₂	1	1	yes	maximal, characteristic
9	#21423955	C₂	1	1	yes	maximal, characteristic
10	#21423955	C₂	1	1	yes	maximal, characteristic
11	#21423951	C₂	1	1	yes	maximal, characteristic
12	#21423784	C₂	1	1	yes	maximal, characteristic
13	#21423782	C₂	1	1	yes	maximal, characteristic
14	#97×Dic₅₉	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅₉×#446	C₂	1	1	yes	maximal, characteristic
16	#16837533	C₄	1	8	yes	complemented
17	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#14273638	C₂²	1	1	yes	characteristic
21	C₂×#14273638	C₂²	1	1	yes	characteristic
22	C₂×#14273637	C₂²	1	1	yes	characteristic
23	C₂×#14273637	C₂²	1	1	yes	characteristic
24	C₂×#14273637	C₂²	1	1	yes	characteristic
25	C₂×#14273637	C₂²	1	1	yes	characteristic
26	C₂×#14273637	C₂²	1	1	yes	characteristic
27	C₂×#14273637	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
33	#16837309	C₄	1	2	yes	—
34	#16837301	C₄	1	2	yes	—
35	#16837288	C₄	1	2	yes	—
36	#16837288	C₄	1	2	yes	—
37	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
40	#16837248	C₂²	1	1	yes	characteristic
41	#16837248	C₂²	1	1	yes	characteristic
42	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
43	#16837156	C₂²	1	1	yes	characteristic
44	#16837156	C₂²	1	1	yes	characteristic
45	#16837156	C₂²	1	1	yes	characteristic
46	#16837156	C₂²	1	1	yes	characteristic
47	#16837156	C₂²	1	1	yes	characteristic
48	#16837156	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
50	C₅₉×#446	C₄	1	8	yes	complemented
51	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
54	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
55	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
57	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₅₉	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₅₉	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
70	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
71	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
72	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
73	#14273638	C₂×C₄	1	4	yes	—
74	#14273638	C₂×C₄	1	4	yes	—
75	#14273637	—	2	2	no	—
76	#14273637	—	2	2	no	—
77	#14273637	—	2	2	no	—
78	#14273637	—	2	2	no	—
79	#14273637	—	2	2	no	—
80	#14273637	—	2	2	no	—
81	C₄×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
82	C₈×Dic₅₉	—	2	2	no	—
83	C₈×Dic₅₉	—	2	2	no	—
84	C₈×Dic₅₉	—	2	2	no	—
85	C₈×Dic₅₉	Q₈	1	4	yes	complemented
86	C₅₉⋊#95	C₂×C₄	1	2	yes	—
87	C₅₉⋊#95	C₂×C₄	1	2	yes	—
88	C₅₉⋊#95	C₂×C₄	1	2	yes	—
89	C₅₉⋊#95	C₂×C₄	1	2	yes	—
90	C₅₉⋊#95	C₂×C₄	1	2	yes	—
91	C₅₉⋊#95	C₂×C₄	1	2	yes	—
92	C₅₉⋊#95	C₂×C₄	1	2	yes	—
93	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₅₉	C₂×C₄	1	4	yes	—
99	C₄×Q₈×C₅₉	C₂×C₄	1	4	yes	—
100	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
107	C₄⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
108	C₄⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
109	#97×C₅₉	C₂×C₄	1	4	yes	—
110	#97×C₅₉	C₂×C₄	1	4	yes	—
111	C₄×C₈×C₅₉	C₂×C₄	1	4	yes	—
112	C₂×Q₈×C₅₉	—	4	2	no	—
113	C₂×Q₈×C₅₉	C₄²	1	4	yes	—
114	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
121	C₂²×Dic₅₉	C₂²×C₄	1	2	yes	—
122	C₂²×Dic₅₉	C₂²×C₄	1	2	yes	—
123	C₂²×Dic₅₉	C₂²×C₄	1	2	yes	—
124	C₂²×Dic₅₉	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₅₉	—	2	1	no	—
126	C₂×C₈×C₅₉	—	2	1	no	—
127	C₂×C₈×C₅₉	—	2	1	no	—
128	C₂×C₈×C₅₉	—	2	1	no	—
129	C₂×C₈×C₅₉	—	2	1	no	—
130	C₂×C₈×C₅₉	—	2	1	no	—
131	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
136	C₂×C₈×C₅₉	#41	1	2	yes	—
137	C₄⋊C₄×C₅₉	C₄²	1	4	yes	—
138	C₄⋊C₄×C₅₉	C₄²	1	4	yes	—
139	C₄⋊C₄×C₅₉	C₄²	1	4	yes	—
140	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
141	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
142	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
143	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
144	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
145	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
146	C₄⋊Dic₅₉	—	4	2	no	—
147	C₄⋊Dic₅₉	—	4	2	no	—
148	C₄⋊Dic₅₉	—	4	2	no	—
149	C₄×Dic₅₉	—	2	1	no	—
150	C₄×Dic₅₉	—	2	1	no	—
151	C₄×Dic₅₉	—	2	1	no	—
152	C₄×Dic₅₉	—	2	1	no	—
153	C₄×Dic₅₉	—	2	1	no	—
154	C₄×Dic₅₉	—	2	1	no	—
155	C₄×Dic₅₉	—	4	2	no	—
156	C₄×Dic₅₉	—	4	2	no	—
157	C₄×Dic₅₉	C₂×Q₈	1	2	yes	—
158	C₄×Dic₅₉	#41	1	2	yes	—
159	C₂×C₅₉⋊C₈	—	2	1	no	—
160	C₂×C₅₉⋊C₈	—	2	1	no	—
161	C₂×C₅₉⋊C₈	—	2	1	no	—
162	C₂×C₅₉⋊C₈	—	2	1	no	—
163	C₂×C₅₉⋊C₈	—	2	1	no	—
164	C₂×C₅₉⋊C₈	—	2	1	no	—
165	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₅₉⋊C₈	C₂×Q₈	1	2	yes	—
170	C₂×C₅₉⋊C₈	#41	1	2	yes	—
171	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
172	Q₈×C₅₉	—	4	4	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	—	2	2	no	—
179	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
180	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
181	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
182	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
183	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
184	C₂×C₄×C₅₉	C₂×C₄²	1	2	yes	—
185	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
191	C₂×Dic₅₉	—	2	2	no	—
192	C₂×Dic₅₉	—	2	2	no	—
193	C₂×Dic₅₉	—	2	2	no	—
194	C₂×Dic₅₉	—	2	2	no	—
195	C₂×Dic₅₉	—	2	2	no	—
196	C₂×Dic₅₉	—	2	2	no	—
197	C₂×Dic₅₉	—	2	2	no	—
198	C₂×Dic₅₉	—	2	2	no	—
199	C₂×Dic₅₉	—	2	2	no	—
200	C₂×Dic₅₉	—	2	2	no	—
201	C₂×Dic₅₉	—	2	2	no	—
202	C₂×Dic₅₉	C₄×Q₈	1	4	yes	—
203	C₈×C₅₉	—	2	2	no	—
204	C₈×C₅₉	—	2	2	no	—
205	C₈×C₅₉	—	2	2	no	—
206	C₈×C₅₉	C₄×Q₈	1	4	yes	—
207	C₅₉⋊C₈	—	2	2	no	—
208	C₅₉⋊C₈	—	2	2	no	—
209	C₅₉⋊C₈	—	2	2	no	—
210	C₅₉⋊C₈	C₄×Q₈	1	4	yes	—
211	#20518	—	59	1	no	maximal, Sylow
212	C₂²×C₅₉	C₂²×C₄²	1	1	yes	characteristic
213	C₂²×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
215	C₂²×C₅₉	#568	1	2	yes	—
216	C₂²×C₅₉	#568	1	2	yes	—
217	C₄×C₅₉	—	2	2	no	—
218	C₄×C₅₉	—	2	2	no	—
219	C₄×C₅₉	—	2	2	no	—
220	C₄×C₅₉	—	2	2	no	—
221	C₄×C₅₉	—	2	2	no	—
222	C₄×C₅₉	—	2	2	no	—
223	C₄×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
224	C₄×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
225	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
226	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
227	Dic₅₉	—	2	4	no	—
228	Dic₅₉	—	4	2	no	—
229	Dic₅₉	—	4	2	no	—
230	Dic₅₉	—	4	2	no	—
231	C₂×#446	—	59	1	no	—
232	C₂×#446	D₅₉	1	1	yes	characteristic
233	#2295	—	59	1	no	—
234	#1771	—	59	1	no	—
235	#1771	—	59	1	no	—
236	#1771	—	59	1	no	—
237	#1771	—	59	1	no	—
238	#1770	—	59	1	no	—
239	#1770	—	59	1	no	—
240	#1768	—	59	1	no	—
241	#1768	—	59	1	no	—
242	#1767	—	59	1	no	—
243	#1726	—	59	1	no	—
244	#1726	—	59	1	no	—
245	C₄×#97	—	59	1	no	—
246	C₂×C₅₉	C₄²×Q₈	1	1	yes	characteristic
247	C₂×C₅₉	#2873	1	1	yes	characteristic
248	C₂×C₅₉	#2875	1	1	yes	characteristic
249	C₂×C₅₉	#2961	1	2	yes	—
250	C₂×C₅₉	#2967	1	2	yes	—
251	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
252	#446	—	59	8	no	—
253	#446	Dic₅₉	1	8	yes	complemented
254	C₂×C₄⋊C₈	—	59	1	no	—
255	C₂×C₄⋊C₈	—	59	1	no	—
256	C₂×C₄⋊C₈	—	59	1	no	—
257	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
260	C₂×#97	—	59	1	no	—
261	C₂×#97	—	59	1	no	—
262	C₂×#97	—	59	1	no	—
263	C₂×#97	—	59	1	no	—
264	C₂×#97	—	59	1	no	—
265	C₂×#97	—	59	1	no	—
266	C₂×#97	—	59	1	no	—
267	C₂×#97	—	59	1	no	—
268	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
269	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
270	C₂×C₄×C₈	—	59	1	no	—
271	C₂×C₄×C₈	—	59	1	no	—
272	C₂×C₄×C₈	—	59	1	no	—
273	C₂×C₄×C₈	—	59	1	no	—
274	C₂×C₄×C₈	—	59	1	no	—
275	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
276	#391	—	59	2	no	—
277	#389	—	59	2	no	—
278	#387	—	59	2	no	—
279	#387	—	59	2	no	—
280	C₄×C₄⋊C₄	—	59	1	no	—
281	C₄×C₄⋊C₄	—	59	1	no	—
282	C₄×C₄⋊C₄	—	59	1	no	—
283	#376	—	59	1	no	—
284	#376	—	59	1	no	—
285	C₄³	—	59	1	no	—
286	#336	—	59	1	no	—
287	#336	—	59	1	no	—
288	#336	—	59	1	no	—
289	#336	—	59	1	no	—
290	#336	—	59	1	no	—
291	#336	—	59	1	no	—
292	C₅₉	#20518	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₈	C₄×D₅₉	1	1	yes	characteristic
294	C₂²×C₈	—	59	1	no	—
295	C₂²×C₈	—	59	1	no	—
296	C₂²×C₈	—	59	1	no	—
297	C₂²×C₈	—	59	1	no	—
298	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
301	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
302	C₄×Q₈	C₄×D₅₉	1	4	yes	—
303	C₄×Q₈	C₂×Dic₅₉	1	4	yes	—
304	C₂×C₄⋊C₄	—	59	2	no	—
305	C₂×C₄⋊C₄	—	59	2	no	—
306	C₂×C₄⋊C₄	—	59	2	no	—
307	C₂×C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
310	C₂×C₄²	—	59	1	no	—
311	C₂×C₄²	—	59	1	no	—
312	C₂×C₄²	—	59	1	no	—
313	C₂×C₄²	—	59	1	no	—
314	C₂×C₄²	—	59	2	no	—
315	C₂×C₄²	—	59	2	no	—
316	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
317	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
319	C₄⋊C₈	—	59	4	no	—
320	C₄⋊C₈	—	59	4	no	—
321	C₄⋊C₈	—	59	4	no	—
322	C₄⋊C₈	C₂×Dic₅₉	1	4	yes	—
323	C₄⋊C₈	C₂×Dic₅₉	1	4	yes	—
324	C₄⋊C₈	C₂×Dic₅₉	1	4	yes	—
325	#97	—	59	4	no	—
326	#97	—	59	4	no	—
327	#97	—	118	2	no	—
328	#97	—	118	2	no	—
329	#97	—	118	2	no	—
330	#97	—	118	2	no	—
331	#97	—	118	2	no	—
332	#97	—	118	2	no	—
333	#97	C₂×Dic₅₉	1	4	yes	—
334	#97	C₂×Dic₅₉	1	4	yes	—
335	C₄×C₈	—	59	4	no	—
336	C₄×C₈	—	59	4	no	—
337	C₄×C₈	—	118	2	no	—
338	C₄×C₈	—	118	2	no	—
339	C₄×C₈	—	118	2	no	—
340	C₄×C₈	C₂×Dic₅₉	1	4	yes	—
341	#95	—	59	2	no	—
342	#95	—	59	2	no	—
343	#95	—	59	2	no	—
344	#95	—	59	2	no	—
345	#95	—	59	2	no	—
346	#95	—	59	2	no	—
347	#95	—	59	2	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	C₄×Dic₅₉	1	4	yes	—
350	C₂²×C₄	—	59	2	no	—
351	C₂²×C₄	—	59	2	no	—
352	C₂²×C₄	—	59	2	no	—
353	C₂²×C₄	—	59	2	no	—
354	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
360	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	59	2	no	—
368	C₂×C₈	—	59	2	no	—
369	C₂×C₈	—	59	2	no	—
370	C₂×C₈	—	59	2	no	—
371	C₂×C₈	—	59	2	no	—
372	C₂×C₈	—	59	2	no	—
373	C₂×C₈	—	118	1	no	—
374	C₂×C₈	—	118	1	no	—
375	C₂×C₈	—	118	1	no	—
376	C₂×C₈	—	118	1	no	—
377	C₂×C₈	—	118	1	no	—
378	C₂×C₈	—	118	1	no	—
379	C₂×C₈	Q₈×D₅₉	1	2	yes	—
380	C₂×C₈	#11745689	1	2	yes	—
381	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
382	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
383	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
384	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
385	C₄⋊C₄	—	236	2	no	—
386	C₄⋊C₄	—	236	2	no	—
387	C₄⋊C₄	—	236	2	no	—
388	C₄⋊C₄	C₄×Dic₅₉	1	4	yes	—
389	C₄⋊C₄	C₄×Dic₅₉	1	4	yes	—
390	C₄⋊C₄	C₄×Dic₅₉	1	4	yes	—
391	C₄²	—	59	2	no	—
392	C₄²	—	59	2	no	—
393	C₄²	—	118	1	no	—
394	C₄²	—	118	1	no	—
395	C₄²	—	118	1	no	—
396	C₄²	—	118	1	no	—
397	C₄²	—	118	1	no	—
398	C₄²	—	118	1	no	—
399	C₄²	—	236	2	no	—
400	C₄²	—	236	2	no	—
401	C₄²	C₂×C₄×D₅₉	1	2	yes	—
402	C₄²	C₂×C₄×D₅₉	1	2	yes	—
403	C₄²	C₂×C₄×D₅₉	1	2	yes	—
404	C₄²	C₂²×Dic₅₉	1	2	yes	—
405	C₄²	C₂²×Dic₅₉	1	2	yes	—
406	C₄²	C₂²×Dic₅₉	1	2	yes	—
407	C₂³	C₂²×C₄×D₅₉	1	1	yes	characteristic
408	Q₈	—	4	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	59	4	no	—
416	C₂×C₄	—	118	2	no	—
417	C₂×C₄	—	118	2	no	—
418	C₂×C₄	—	118	2	no	—
419	C₂×C₄	—	118	2	no	—
420	C₂×C₄	—	118	2	no	—
421	C₂×C₄	—	118	2	no	—
422	C₂×C₄	—	118	2	no	—
423	C₂×C₄	—	118	2	no	—
424	C₂×C₄	—	118	2	no	—
425	C₂×C₄	—	118	2	no	—
426	C₂×C₄	—	118	2	no	—
427	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
428	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
429	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
430	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
431	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
432	C₂×C₄	C₂×C₄×Dic₅₉	1	2	yes	—
433	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
434	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
435	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
436	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
437	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
438	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	—	59	4	no	—
443	C₈	—	118	2	no	—
444	C₈	—	118	2	no	—
445	C₈	—	118	2	no	—
446	C₈	Q₈×Dic₅₉	1	4	yes	—
447	C₂²	C₂²×C₄×Dic₅₉	1	1	yes	characteristic
448	C₂²	C₄×Q₈×D₅₉	1	1	yes	characteristic
449	C₂²	C₄×#11745689	1	1	yes	characteristic
450	C₂²	#16838167	1	2	yes	—
451	C₂²	#16838168	1	2	yes	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	118	4	no	—
459	C₄	—	236	2	no	—
460	C₄	—	236	2	no	—
461	C₄	—	236	2	no	—
462	C₄	C₄×Q₈×D₅₉	1	1	yes	characteristic
463	C₄	C₂×Q₈×Dic₅₉	1	1	yes	characteristic
464	C₄	C₄×#11745689	1	1	yes	characteristic
465	C₄	#41×Dic₅₉	1	1	yes	characteristic
466	C₂	C₄×Q₈×Dic₅₉	1	1	yes	characteristic
467	C₂	#21432514	1	1	yes	characteristic
468	C₂	#21432522	1	1	yes	characteristic
469	C₂	#21433032	1	2	yes	—
470	C₂	#21433080	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₉
commutator	C₂²×C₅₉	C₂²×C₄²
Fitting	C₂×C₅₉×#446	C₂
socle, prime radical	C₂³×C₅₉	C₂³×C₄
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₂×#446	D₅₉
hypocenter	C₅₉	#20518
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
16. #16837533	C₄	semidirect
50. C₅₉×#446	C₄	semidirect
85. C₈×Dic₅₉	Q₈	semidirect
253. #446	Dic₅₉	semidirect
292. C₅₉	#20518	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837533	2
#21426574	2
#21423973	2
#21423968	2
#21423966	2
#21423963	2
#21423955	2
#21423951	2
#21423784	2
#21423782	2
#97×Dic₅₉	2
C₂×C₅₉×#446	2
#20518	59