Subgroups — #28594162

Order 15104.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21424711	C₂	1	1	yes	maximal, characteristic
2	#21424711	C₂	1	1	yes	maximal, characteristic
3	#21424704	C₂	1	1	yes	maximal, characteristic
4	#21424704	C₂	1	1	yes	maximal, characteristic
5	#21424662	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424662	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424655	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424655	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₄⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	#21423862	C₂	1	1	yes	maximal, characteristic
12	#21423862	C₂	1	1	yes	maximal, characteristic
13	#21423848	C₂	1	1	yes	maximal, characteristic, complemented
14	#21423783	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2298	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
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×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×#14273638	C₂²	1	1	yes	characteristic
25	C₂×#14273638	C₂²	1	1	yes	characteristic
26	C₂×#14273638	C₂²	1	1	yes	characteristic
27	C₂×#14273638	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
32	#16837157	C₂²	1	1	yes	characteristic
33	#16837157	C₂²	1	1	yes	characteristic
34	#16837157	C₂²	1	1	yes	characteristic
35	#16837157	C₂²	1	1	yes	characteristic
36	#16837157	C₂²	1	1	yes	characteristic
37	#16837157	C₂²	1	1	yes	characteristic
38	#16837157	C₂²	1	1	yes	characteristic
39	#16837157	C₂²	1	1	yes	characteristic
40	#16837157	C₂²	1	1	yes	characteristic
41	#16837157	C₂²	1	1	yes	characteristic
42	#16837157	C₂²	1	1	yes	characteristic
43	#16837157	C₂²	1	1	yes	characteristic
44	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#388	C₄	1	1	yes	characteristic
46	C₅₉×#388	C₄	1	1	yes	characteristic
47	C₅₉×#388	C₄	1	1	yes	characteristic
48	C₅₉×#388	C₄	1	1	yes	characteristic
49	C₅₉×#387	C₄	1	1	yes	characteristic
50	C₅₉×#387	C₄	1	1	yes	characteristic
51	C₅₉×#387	C₄	1	1	yes	characteristic
52	C₅₉×#387	C₄	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
57	C₅₉×#376	C₂²	1	1	yes	characteristic
58	C₄³×C₅₉	C₂²	1	1	yes	characteristic
59	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
68	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
69	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
70	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
71	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
72	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
73	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
75	#14273638	—	2	2	no	—
76	#14273638	—	2	2	no	—
77	#14273638	—	2	2	no	—
78	#14273638	—	2	2	no	—
79	C₄×C₅₉⋊C₈	—	2	2	no	—
80	C₄×C₅₉⋊C₈	—	2	2	no	—
81	C₄×C₅₉⋊C₈	—	2	2	no	—
82	C₄×C₅₉⋊C₈	—	2	2	no	—
83	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
84	#117×C₅₉	—	2	2	no	—
85	#117×C₅₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₅₉	C₂³	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	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
108	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
109	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
110	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
111	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
112	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
113	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
114	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
115	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
116	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
117	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
118	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
119	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
120	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	1	no	—
123	C₂²×C₄×C₅₉	—	2	1	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	2	1	no	—
127	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
141	C₄⋊C₄×C₅₉	—	2	2	no	—
142	C₄⋊C₄×C₅₉	—	2	2	no	—
143	C₄⋊C₄×C₅₉	—	2	2	no	—
144	C₄⋊C₄×C₅₉	—	2	2	no	—
145	C₄⋊C₄×C₅₉	—	4	1	no	—
146	C₄⋊C₄×C₅₉	—	4	1	no	—
147	C₂²⋊C₄×C₅₉	—	2	2	no	—
148	C₂²⋊C₄×C₅₉	—	2	2	no	—
149	C₂²⋊C₄×C₅₉	—	2	2	no	—
150	C₂²⋊C₄×C₅₉	—	2	2	no	—
151	C₂²⋊C₄×C₅₉	—	4	1	no	—
152	C₂²⋊C₄×C₅₉	—	4	1	no	—
153	C₄²×C₅₉	—	2	2	no	—
154	C₄²×C₅₉	—	2	2	no	—
155	C₄²×C₅₉	—	2	1	no	—
156	C₄²×C₅₉	—	2	1	no	—
157	C₄²×C₅₉	—	2	1	no	—
158	C₄²×C₅₉	—	2	1	no	—
159	C₄²×C₅₉	—	2	1	no	—
160	C₄²×C₅₉	—	2	1	no	—
161	C₄²×C₅₉	—	2	1	no	—
162	C₄²×C₅₉	—	2	1	no	—
163	C₄²×C₅₉	—	2	1	no	—
164	C₄²×C₅₉	—	2	1	no	—
165	C₄²×C₅₉	—	4	1	no	—
166	C₄²×C₅₉	—	4	1	no	—
167	C₄²×C₅₉	#41	1	2	yes	—
168	C₄²×C₅₉	#41	1	2	yes	—
169	C₂×C₅₉⋊C₈	—	2	1	no	—
170	C₂×C₅₉⋊C₈	—	2	1	no	—
171	C₂×C₅₉⋊C₈	—	2	1	no	—
172	C₂×C₅₉⋊C₈	—	2	1	no	—
173	C₂×C₅₉⋊C₈	—	2	1	no	—
174	C₂×C₅₉⋊C₈	—	2	1	no	—
175	C₂×C₅₉⋊C₈	—	2	1	no	—
176	C₂×C₅₉⋊C₈	—	2	1	no	—
177	C₂×C₅₉⋊C₈	—	2	1	no	—
178	C₂×C₅₉⋊C₈	—	2	1	no	—
179	C₂×C₅₉⋊C₈	—	2	1	no	—
180	C₂×C₅₉⋊C₈	—	2	1	no	—
181	C₂×C₅₉⋊C₈	—	2	1	no	—
182	C₂×C₅₉⋊C₈	—	2	1	no	—
183	C₂×C₅₉⋊C₈	—	2	1	no	—
184	C₂×C₅₉⋊C₈	—	2	1	no	—
185	C₂×C₅₉⋊C₈	—	2	1	no	—
186	C₂×C₅₉⋊C₈	—	2	1	no	—
187	C₂×C₅₉⋊C₈	—	2	1	no	—
188	C₂×C₅₉⋊C₈	—	2	1	no	—
189	C₂×C₅₉⋊C₈	#41	1	2	yes	—
190	C₂×C₅₉⋊C₈	#41	1	2	yes	—
191	C₂×C₅₉⋊C₈	#41	1	2	yes	—
192	C₂×C₅₉⋊C₈	#41	1	2	yes	—
193	C₂³×C₅₉	—	2	1	no	—
194	C₂³×C₅₉	—	2	1	no	—
195	C₂³×C₅₉	—	2	1	no	—
196	C₂³×C₅₉	—	2	1	no	—
197	C₂³×C₅₉	—	2	1	no	—
198	C₂³×C₅₉	—	2	1	no	—
199	C₂³×C₅₉	—	2	1	no	—
200	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	2	1	no	—
204	C₂×C₄×C₅₉	—	2	1	no	—
205	C₂×C₄×C₅₉	—	2	1	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
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	—	2	1	no	—
218	C₂×C₄×C₅₉	—	2	1	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	1	no	—
222	C₂×C₄×C₅₉	—	2	1	no	—
223	C₂×C₄×C₅₉	—	2	1	no	—
224	C₂×C₄×C₅₉	—	2	1	no	—
225	C₂×C₄×C₅₉	—	2	1	no	—
226	C₂×C₄×C₅₉	—	2	1	no	—
227	C₂×C₄×C₅₉	—	2	1	no	—
228	C₂×C₄×C₅₉	—	2	1	no	—
229	C₂×C₄×C₅₉	—	2	1	no	—
230	C₂×C₄×C₅₉	—	2	1	no	—
231	C₂×C₄×C₅₉	—	2	1	no	—
232	C₂×C₄×C₅₉	—	2	1	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	4	1	no	—
237	C₂×C₄×C₅₉	—	4	1	no	—
238	C₂×C₄×C₅₉	—	4	1	no	—
239	C₂×C₄×C₅₉	—	4	1	no	—
240	C₂×C₄×C₅₉	#117	1	2	yes	—
241	C₂×C₄×C₅₉	#117	1	2	yes	—
242	C₂×C₄×C₅₉	#131	1	2	yes	—
243	C₂×C₄×C₅₉	#131	1	2	yes	—
244	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
250	C₅₉⋊C₈	—	2	2	no	—
251	C₅₉⋊C₈	—	2	2	no	—
252	C₅₉⋊C₈	—	2	2	no	—
253	C₅₉⋊C₈	—	2	2	no	—
254	C₅₉⋊C₈	—	4	1	no	—
255	C₅₉⋊C₈	—	4	1	no	—
256	C₅₉⋊C₈	—	4	1	no	—
257	C₅₉⋊C₈	—	4	1	no	—
258	#21436	—	59	1	no	maximal, Sylow
259	C₂²×C₅₉	—	4	1	no	—
260	C₂²×C₅₉	—	4	1	no	—
261	C₂²×C₅₉	—	4	1	no	—
262	C₂²×C₅₉	—	4	1	no	—
263	C₂²×C₅₉	—	4	1	no	—
264	C₂²×C₅₉	—	4	1	no	—
265	C₂²×C₅₉	—	4	1	no	—
266	C₂²×C₅₉	C₂×#117	1	1	yes	characteristic
267	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
268	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
269	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
270	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
271	C₂²×C₅₉	#568	1	1	yes	characteristic
272	C₂²×C₅₉	#568	1	1	yes	characteristic
273	C₄×C₅₉	—	2	2	no	—
274	C₄×C₅₉	—	2	2	no	—
275	C₄×C₅₉	—	2	2	no	—
276	C₄×C₅₉	—	2	2	no	—
277	C₄×C₅₉	—	4	1	no	—
278	C₄×C₅₉	—	4	1	no	—
279	C₄×C₅₉	—	4	1	no	—
280	C₄×C₅₉	—	4	1	no	—
281	C₄×C₅₉	—	4	1	no	—
282	C₄×C₅₉	—	4	1	no	—
283	C₄×C₅₉	—	4	1	no	—
284	C₄×C₅₉	—	4	1	no	—
285	C₄×C₅₉	—	4	1	no	—
286	C₄×C₅₉	#529	1	1	yes	characteristic
287	C₄×C₅₉	#529	1	1	yes	characteristic
288	C₄×C₅₉	#529	1	1	yes	characteristic
289	C₄×C₅₉	#529	1	1	yes	characteristic
290	#2298	D₅₉	1	1	yes	characteristic
291	#1924	—	59	1	no	—
292	#1924	—	59	1	no	—
293	#1923	—	59	1	no	—
294	#1923	—	59	1	no	—
295	#1917	—	59	1	no	—
296	#1917	—	59	1	no	—
297	#1916	—	59	1	no	—
298	#1916	—	59	1	no	—
299	#1767	—	59	1	no	—
300	C₄×C₄⋊C₈	—	59	1	no	—
301	#1750	—	59	1	no	—
302	#1750	—	59	1	no	—
303	#1746	—	59	1	no	—
304	#1726	—	59	1	no	—
305	C₂×C₅₉	—	8	1	no	—
306	C₂×C₅₉	#2298	1	1	yes	characteristic
307	C₂×C₅₉	#2925	1	1	yes	characteristic
308	C₂×C₅₉	#2925	1	1	yes	characteristic
309	C₂×C₅₉	#2966	1	1	yes	characteristic
310	C₂×C₅₉	#2967	1	1	yes	characteristic
311	C₂×C₅₉	#2968	1	1	yes	characteristic
312	C₂×C₅₉	#2969	1	1	yes	characteristic
313	C₂×#117	C₂×D₅₉	1	1	yes	characteristic
314	C₂×C₄⋊C₈	—	59	1	no	—
315	C₂×C₄⋊C₈	—	59	1	no	—
316	C₂×C₄⋊C₈	—	59	1	no	—
317	C₂×C₄⋊C₈	—	59	1	no	—
318	C₂×C₂²⋊C₈	—	59	1	no	—
319	C₂×C₂²⋊C₈	—	59	1	no	—
320	C₂×C₂²⋊C₈	—	59	1	no	—
321	C₂×C₂²⋊C₈	—	59	1	no	—
322	C₂×#97	—	59	1	no	—
323	C₂×#97	—	59	1	no	—
324	C₂×#97	—	59	1	no	—
325	C₂×#97	—	59	1	no	—
326	C₂×C₄×C₈	—	59	1	no	—
327	C₂×C₄×C₈	—	59	1	no	—
328	C₂×C₄×C₈	—	59	1	no	—
329	C₂×C₄×C₈	—	59	1	no	—
330	#388	Dic₅₉	1	1	yes	characteristic
331	#388	Dic₅₉	1	1	yes	characteristic
332	#388	Dic₅₉	1	1	yes	characteristic
333	#388	Dic₅₉	1	1	yes	characteristic
334	#387	Dic₅₉	1	1	yes	characteristic
335	#387	Dic₅₉	1	1	yes	characteristic
336	#387	Dic₅₉	1	1	yes	characteristic
337	#387	Dic₅₉	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
339	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
340	C₄×C₂²⋊C₄	C₂×D₅₉	1	1	yes	characteristic
341	C₄×C₂²⋊C₄	C₂×D₅₉	1	1	yes	characteristic
342	#376	C₂×D₅₉	1	1	yes	characteristic
343	C₄³	C₂×D₅₉	1	1	yes	characteristic
344	#336	—	59	1	no	—
345	#336	—	59	1	no	—
346	#336	—	59	1	no	—
347	#336	—	59	1	no	—
348	#336	—	59	1	no	—
349	#336	—	59	1	no	—
350	#336	—	59	1	no	—
351	#336	—	59	1	no	—
352	#336	—	59	1	no	—
353	#336	—	59	1	no	—
354	#336	—	59	1	no	—
355	#336	—	59	1	no	—
356	C₅₉	#21436	1	1	yes	characteristic, complemented, Sylow
357	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
358	C₂²×C₈	—	59	1	no	—
359	C₂²×C₈	—	59	1	no	—
360	C₂²×C₈	—	59	1	no	—
361	C₂²×C₈	—	59	1	no	—
362	C₂²×C₈	—	59	1	no	—
363	C₂²×C₈	—	59	1	no	—
364	C₂²×C₈	—	59	1	no	—
365	C₂²×C₈	—	59	1	no	—
366	#117	—	2	2	no	—
367	#117	—	2	2	no	—
368	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
380	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
381	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
382	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
383	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
384	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
385	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
386	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
387	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
388	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
389	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
390	C₄⋊C₈	—	118	2	no	—
391	C₄⋊C₈	—	118	2	no	—
392	C₄⋊C₈	—	118	2	no	—
393	C₄⋊C₈	—	118	2	no	—
394	C₂²⋊C₈	—	118	2	no	—
395	C₂²⋊C₈	—	118	2	no	—
396	C₂²⋊C₈	—	118	2	no	—
397	C₂²⋊C₈	—	118	2	no	—
398	#97	—	118	2	no	—
399	#97	—	118	2	no	—
400	#97	—	118	2	no	—
401	#97	—	118	2	no	—
402	C₄×C₈	—	118	2	no	—
403	C₄×C₈	—	118	2	no	—
404	C₄×C₈	—	118	2	no	—
405	C₄×C₈	—	118	2	no	—
406	#95	C₂×Dic₅₉	1	1	yes	characteristic
407	#95	C₂×Dic₅₉	1	1	yes	characteristic
408	#95	C₂×Dic₅₉	1	1	yes	characteristic
409	#95	C₂×Dic₅₉	1	1	yes	characteristic
410	#95	C₂×Dic₅₉	1	1	yes	characteristic
411	#95	C₂×Dic₅₉	1	1	yes	characteristic
412	#95	C₂×Dic₅₉	1	1	yes	characteristic
413	#95	C₂×Dic₅₉	1	1	yes	characteristic
414	#95	C₂×Dic₅₉	1	1	yes	characteristic
415	#95	C₂×Dic₅₉	1	1	yes	characteristic
416	#95	C₂×Dic₅₉	1	1	yes	characteristic
417	#95	C₂×Dic₅₉	1	1	yes	characteristic
418	C₂⁴	C₂²×Dic₅₉	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
426	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
427	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
428	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
432	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
433	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
434	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
436	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
437	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
438	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
439	C₂×C₈	—	59	2	no	—
440	C₂×C₈	—	59	2	no	—
441	C₂×C₈	—	59	2	no	—
442	C₂×C₈	—	59	2	no	—
443	C₂×C₈	—	118	1	no	—
444	C₂×C₈	—	118	1	no	—
445	C₂×C₈	—	118	1	no	—
446	C₂×C₈	—	118	1	no	—
447	C₂×C₈	—	118	1	no	—
448	C₂×C₈	—	118	1	no	—
449	C₂×C₈	—	118	1	no	—
450	C₂×C₈	—	118	1	no	—
451	C₂×C₈	—	118	1	no	—
452	C₂×C₈	—	118	1	no	—
453	C₂×C₈	—	118	1	no	—
454	C₂×C₈	—	118	1	no	—
455	C₂×C₈	—	118	1	no	—
456	C₂×C₈	—	118	1	no	—
457	C₂×C₈	—	118	1	no	—
458	C₂×C₈	—	118	1	no	—
459	C₂×C₈	—	118	1	no	—
460	C₂×C₈	—	118	1	no	—
461	C₂×C₈	—	118	1	no	—
462	C₂×C₈	—	118	1	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	—	4	1	no	—
489	C₄²	#11745685	1	2	yes	—
490	C₄²	#11745685	1	2	yes	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	C₂³×Dic₅₉	1	1	yes	characteristic
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	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	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	#14273686	1	2	yes	—
539	C₂×C₄	#14273686	1	2	yes	—
540	C₂×C₄	#14273734	1	2	yes	—
541	C₂×C₄	#14273734	1	2	yes	—
542	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
543	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
544	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
545	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
546	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
547	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
548	C₈	—	118	2	no	—
549	C₈	—	118	2	no	—
550	C₈	—	118	2	no	—
551	C₈	—	118	2	no	—
552	C₈	—	236	1	no	—
553	C₈	—	236	1	no	—
554	C₈	—	236	1	no	—
555	C₈	—	236	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂×#14273686	1	1	yes	characteristic
564	C₂²	#41×Dic₅₉	1	1	yes	characteristic
565	C₂²	#41×Dic₅₉	1	1	yes	characteristic
566	C₂²	C₂×#14273734	1	1	yes	characteristic
567	C₂²	C₂×#14273734	1	1	yes	characteristic
568	C₂²	#16838169	1	1	yes	characteristic
569	C₂²	#16838169	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	#16837930	1	1	yes	characteristic
584	C₄	#16837930	1	1	yes	characteristic
585	C₄	#16837930	1	1	yes	characteristic
586	C₄	#16837930	1	1	yes	characteristic
587	C₂	—	8	1	no	—
588	C₂	#21426594	1	1	yes	characteristic
589	C₂	#21432762	1	1	yes	characteristic
590	C₂	#21432762	1	1	yes	characteristic
591	C₂	#21433072	1	1	yes	characteristic
592	C₂	#21433083	1	1	yes	characteristic
593	C₂	#21433092	1	1	yes	characteristic
594	C₂	#21433101	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂³×C₄
Fitting	C₅₉×#2298	C₂
prime radical	C₂⁴×C₅₉	C₂²×C₄
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2298	D₅₉
hypocenter	C₅₉	#21436
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2298

Complements

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

N	H ≅ G/N	type
5. #21424662	C₂	semidirect
6. #21424662	C₂	semidirect
7. #21424655	C₂	semidirect
8. #21424655	C₂	semidirect
9. #21423949	C₂	semidirect
10. C₄×C₄⋊(C₅₉⋊C₈)	C₂	semidirect
13. #21423848	C₂	semidirect
14. #21423783	C₂	semidirect
356. C₅₉	#21436	semidirect

Maximal subgroups

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

subgroup	index
#21424711	2
#21424704	2
#21424662	2
#21424655	2
#21423949	2
C₄×C₄⋊(C₅₉⋊C₈)	2
#21423862	2
#21423848	2
#21423783	2
C₅₉×#2298	2
#21436	59