Subgroups — #28493885

Order 15104.

886 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837360	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837358	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14273638	C₂	1	1	yes	maximal, characteristic
4	C₂×#16837166	C₂	1	1	yes	maximal, characteristic
5	#21423812	C₂	1	1	yes	maximal, characteristic
6	C₂×#16837162	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11745664	C₂²	1	1	yes	characteristic
9	C₂³×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#14273686	C₂²	1	1	yes	characteristic
12	#16837360	—	2	2	no	—
13	#16837360	C₄	1	4	yes	complemented
14	#16837358	—	2	2	no	—
15	#16837358	C₄	1	4	yes	complemented
16	C₂×#14273638	—	2	2	no	—
17	C₂×#14273638	—	2	2	no	—
18	C₂×#14273638	—	2	1	no	—
19	C₂×#14273638	C₄	1	4	yes	complemented
20	C₂×#14273637	—	2	1	no	—
21	C₂×C₄×C₅₉⋊C₈	—	2	1	no	—
22	C₂×C₈×Dic₅₉	—	2	1	no	—
23	#16837166	C₄	1	4	yes	complemented
24	#16837164	C₄	1	4	yes	complemented
25	#16837162	C₄	1	4	yes	complemented
26	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
29	C₅₉×#339	C₄	1	4	yes	complemented
30	C₂×#11745664	—	2	1	no	—
31	C₂×#11745664	—	2	1	no	—
32	C₂×#11745664	—	2	1	no	—
33	C₂×#11745664	C₂×C₄	1	2	yes	—
34	C₂×#11745664	C₂×C₄	1	2	yes	—
35	C₂×#11745664	C₂×C₄	1	2	yes	—
36	C₂²×C₅₉⋊C₈	—	2	1	no	—
37	C₂²×C₅₉⋊C₈	—	2	1	no	—
38	C₂²×C₅₉⋊C₈	—	2	1	no	—
39	C₂²×C₅₉⋊C₈	—	2	1	no	—
40	C₂²×C₅₉⋊C₈	—	2	1	no	—
41	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
46	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
48	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
49	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
50	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
51	C₂²×C₅₉⋊C₈	Q₈	1	2	yes	—
52	#14273686	—	2	1	no	—
53	#14273686	—	2	1	no	—
54	#14273686	C₂×C₄	1	2	yes	—
55	#14273686	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊Dic₅₉	—	2	1	no	—
58	C₂×C₄×Dic₅₉	—	2	1	no	—
59	#14273638	—	2	8	no	—
60	#14273638	—	2	4	no	—
61	#14273637	—	2	4	no	—
62	C₄×C₅₉⋊C₈	—	2	4	no	—
63	C₈×Dic₅₉	—	2	4	no	—
64	C₂³×C₄×C₅₉	—	2	1	no	—
65	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₅₉	—	2	1	no	—
67	C₂×M₁₆×C₅₉	—	2	1	no	—
68	C₂×M₁₆×C₅₉	—	2	1	no	—
69	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₅₉	—	2	1	no	—
73	#117×C₅₉	—	2	1	no	—
74	#117×C₅₉	—	2	1	no	—
75	#117×C₅₉	C₂×C₄	1	2	yes	—
76	#117×C₅₉	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
79	C₂×C₄²×C₅₉	—	2	1	no	—
80	C₂×C₄²×C₅₉	—	2	1	no	—
81	C₂×C₄²×C₅₉	—	2	1	no	—
82	C₂×C₄²×C₅₉	—	2	1	no	—
83	C₂×C₄²×C₅₉	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₅₉	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₅₉	C₂×C₄	1	2	yes	—
86	C₂⁴×C₅₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	—	2	2	no	—
88	C₂²×C₄×C₅₉	—	2	2	no	—
89	C₂²×C₄×C₅₉	—	2	2	no	—
90	C₂²×C₄×C₅₉	—	2	2	no	—
91	C₂²×C₄×C₅₉	—	4	4	no	—
92	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
106	C₂²×Dic₅₉	—	2	2	no	—
107	M₁₆×C₅₉	—	2	2	no	—
108	M₁₆×C₅₉	—	2	2	no	—
109	M₁₆×C₅₉	—	2	2	no	—
110	M₁₆×C₅₉	C₄²	1	4	yes	—
111	C₂×C₈×C₅₉	—	2	2	no	—
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₂×C₈×C₅₉	—	2	2	no	—
114	C₄⋊C₄×C₅₉	—	2	2	no	—
115	C₄⋊C₄×C₅₉	C₄²	1	4	yes	—
116	C₂²⋊C₄×C₅₉	—	2	2	no	—
117	C₂²⋊C₄×C₅₉	—	2	2	no	—
118	C₄²×C₅₉	—	2	2	no	—
119	C₄²×C₅₉	—	2	2	no	—
120	C₄²×C₅₉	—	2	2	no	—
121	C₄²×C₅₉	—	2	2	no	—
122	C₄²×C₅₉	—	2	2	no	—
123	C₄²×C₅₉	C₄²	1	4	yes	—
124	C₂²⋊Dic₅₉	—	2	2	no	—
125	C₂²⋊Dic₅₉	—	2	2	no	—
126	C₄⋊Dic₅₉	—	2	2	no	—
127	C₄⋊Dic₅₉	C₄²	1	4	yes	—
128	C₄×Dic₅₉	—	2	2	no	—
129	C₄×Dic₅₉	—	2	2	no	—
130	#11745664	—	2	2	no	—
131	#11745664	—	2	2	no	—
132	#11745664	—	2	2	no	—
133	#11745664	C₄²	1	4	yes	—
134	C₂×C₅₉⋊C₈	—	2	2	no	—
135	C₂×C₅₉⋊C₈	—	2	2	no	—
136	C₂×C₅₉⋊C₈	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	2	2	no	—
138	C₂×C₅₉⋊C₈	—	2	2	no	—
139	C₂×C₅₉⋊C₈	—	2	2	no	—
140	C₂×C₅₉⋊C₈	—	2	2	no	—
141	C₂×C₅₉⋊C₈	—	2	2	no	—
142	C₂×C₅₉⋊C₈	—	2	2	no	—
143	C₂×C₅₉⋊C₈	C₄²	1	4	yes	—
144	C₂×C₅₉⋊C₈	C₄²	1	4	yes	—
145	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
146	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
147	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	4	yes	—
149	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	2	yes	—
150	C₂×C₅₉⋊C₈	C₄⋊C₄	1	2	yes	—
151	C₂×C₅₉⋊C₈	C₄⋊C₄	1	2	yes	—
152	C₂×C₅₉⋊C₈	C₄⋊C₄	1	4	yes	—
153	C₂×C₅₉⋊C₈	C₄⋊C₄	1	4	yes	—
154	C₂³×C₅₉	—	2	4	no	—
155	C₂³×C₅₉	#117	1	1	yes	characteristic
156	C₂³×C₅₉	#117	1	1	yes	characteristic
157	C₂³×C₅₉	#117	1	1	yes	characteristic
158	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
159	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₅₉	C₄×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₅₉	—	2	4	no	—
163	C₂×C₄×C₅₉	—	2	4	no	—
164	C₂×C₄×C₅₉	—	4	4	no	—
165	C₂×C₄×C₅₉	—	4	4	no	—
166	C₂×C₄×C₅₉	—	4	4	no	—
167	C₂×C₄×C₅₉	—	4	4	no	—
168	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
182	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
183	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
196	C₂×Dic₅₉	—	2	4	no	—
197	C₂×Dic₅₉	—	4	4	no	—
198	C₈×C₅₉	—	2	4	no	—
199	C₅₉⋊C₈	—	2	4	no	—
200	C₅₉⋊C₈	—	2	4	no	—
201	C₅₉⋊C₈	#95	1	4	yes	—
202	C₅₉⋊C₈	#95	1	4	yes	—
203	#10707	—	59	1	no	maximal, Sylow
204	C₂²×C₅₉	—	2	2	no	—
205	C₂²×C₅₉	—	2	2	no	—
206	C₂²×C₅₉	—	2	2	no	—
207	C₂²×C₅₉	—	2	2	no	—
208	C₂²×C₅₉	—	2	2	no	—
209	C₂²×C₅₉	—	2	2	no	—
210	C₂²×C₅₉	#376	1	1	yes	characteristic
211	C₂²×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×C₅₉	#444	1	4	yes	—
218	C₄×C₅₉	—	4	4	no	—
219	C₄×C₅₉	—	4	4	no	—
220	C₄×C₅₉	C₄³	1	1	yes	characteristic
221	C₄×C₅₉	C₂×#95	1	1	yes	characteristic
222	C₄×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
225	C₄×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
226	C₄×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
227	C₄×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
228	Dic₅₉	—	4	4	no	—
229	C₂×#405	—	59	1	no	—
230	C₂×#405	—	59	1	no	—
231	C₂²×#97	—	59	1	no	—
232	C₂×#341	—	59	1	no	—
233	#1735	—	59	1	no	—
234	C₂×#339	—	59	1	no	—
235	C₂×#339	D₅₉	1	1	yes	characteristic
236	C₂×C₅₉	—	2	1	no	—
237	C₂×C₅₉	—	2	1	no	—
238	C₂×C₅₉	—	2	1	no	—
239	C₂×C₅₉	—	2	1	no	—
240	C₂×C₅₉	C₄×#95	1	1	yes	characteristic
241	C₂×C₅₉	#1765	1	2	yes	—
242	C₂×C₅₉	#1765	1	2	yes	—
243	C₂×C₅₉	#1773	1	2	yes	—
244	C₂²×M₁₆	—	59	1	no	—
245	C₂²×M₁₆	C₂×D₅₉	1	1	yes	characteristic
246	C₂³×C₈	—	59	1	no	—
247	C₂³×C₈	—	59	1	no	—
248	C₂×#117	—	59	1	no	—
249	C₂×#117	C₂×D₅₉	1	1	yes	characteristic
250	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
251	#405	—	59	4	no	—
252	#405	—	59	4	no	—
253	#405	—	118	2	no	—
254	#405	—	118	2	no	—
255	C₂×#97	—	59	4	no	—
256	C₂×#97	—	118	2	no	—
257	C₂×#97	—	118	2	no	—
258	C₂×#97	—	118	1	no	—
259	C₂×#97	—	118	1	no	—
260	C₂×C₄×C₈	—	118	1	no	—
261	C₂×C₄×C₈	—	118	1	no	—
262	#341	—	59	4	no	—
263	#340	—	59	4	no	—
264	#339	—	59	4	no	—
265	#339	Dic₅₉	1	4	yes	complemented
266	C₅₉	#10707	1	1	yes	characteristic, complemented, Sylow
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	59	2	no	—
273	C₂×M₁₆	—	59	2	no	—
274	C₂×M₁₆	—	59	2	no	—
275	C₂×M₁₆	—	118	1	no	—
276	C₂×M₁₆	—	118	1	no	—
277	C₂×M₁₆	—	118	1	no	—
278	C₂×M₁₆	C₄×D₅₉	1	2	yes	—
279	C₂×M₁₆	C₄×D₅₉	1	2	yes	—
280	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	59	2	no	—
283	C₂²×C₈	—	59	2	no	—
284	C₂²×C₈	—	59	2	no	—
285	C₂²×C₈	—	59	2	no	—
286	C₂²×C₈	—	59	2	no	—
287	C₂²×C₈	—	59	1	no	—
288	C₂²×C₈	—	59	1	no	—
289	C₂²×C₈	—	59	2	no	—
290	C₂²×C₈	—	59	2	no	—
291	C₂²×C₈	—	59	2	no	—
292	C₂²×C₈	—	59	2	no	—
293	C₂²×C₈	—	118	1	no	—
294	C₂²×C₈	—	118	1	no	—
295	C₂²×C₈	—	118	1	no	—
296	C₂²×C₈	—	118	1	no	—
297	C₂²×C₈	—	118	1	no	—
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	59	2	no	—
301	#117	—	59	2	no	—
302	#117	—	118	1	no	—
303	#117	—	118	1	no	—
304	#117	C₄×D₅₉	1	2	yes	—
305	#117	C₂×Dic₅₉	1	2	yes	—
306	C₂×C₄⋊C₄	—	59	2	no	—
307	C₂×C₄⋊C₄	C₄×D₅₉	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	118	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	118	1	no	—
315	C₂×C₄²	C₄×D₅₉	1	2	yes	—
316	C₂×C₄²	C₄×D₅₉	1	2	yes	—
317	C₂×C₄²	C₂×Dic₅₉	1	2	yes	—
318	#97	—	118	8	no	—
319	#97	—	118	4	no	—
320	#97	—	118	4	no	—
321	C₄×C₈	—	118	4	no	—
322	C₄×C₈	—	118	4	no	—
323	C₂⁴	#11745687	1	1	yes	characteristic
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	118	2	no	—
330	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
339	C₂²×C₄	#11745687	1	1	yes	characteristic
340	C₂²×C₄	#11745687	1	1	yes	characteristic
341	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
342	C₂²×C₄	#11745689	1	1	yes	characteristic
343	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	59	4	no	—
348	M₁₆	—	118	2	no	—
349	M₁₆	—	118	2	no	—
350	M₁₆	—	118	2	no	—
351	M₁₆	C₄×Dic₅₉	1	4	yes	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	59	4	no	—
356	C₂×C₈	—	59	2	no	—
357	C₂×C₈	—	59	2	no	—
358	C₂×C₈	—	59	4	no	—
359	C₂×C₈	—	59	2	no	—
360	C₂×C₈	—	59	2	no	—
361	C₂×C₈	—	59	4	no	—
362	C₂×C₈	—	59	4	no	—
363	C₂×C₈	—	59	2	no	—
364	C₂×C₈	—	59	2	no	—
365	C₂×C₈	—	59	4	no	—
366	C₂×C₈	—	118	2	no	—
367	C₂×C₈	—	118	2	no	—
368	C₂×C₈	—	118	2	no	—
369	C₂×C₈	—	118	2	no	—
370	C₂×C₈	—	118	2	no	—
371	C₂×C₈	—	118	2	no	—
372	C₂×C₈	—	118	2	no	—
373	C₂×C₈	—	118	2	no	—
374	C₂×C₈	—	118	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	59	4	no	—
377	C₄⋊C₄	—	118	2	no	—
378	C₄⋊C₄	C₄×Dic₅₉	1	4	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	118	2	no	—
382	C₂²⋊C₄	—	118	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	118	2	no	—
389	C₄²	—	118	2	no	—
390	C₄²	C₄×Dic₅₉	1	4	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	#14273683	1	1	yes	characteristic
393	C₂³	#14273683	1	1	yes	characteristic
394	C₂³	#14273685	1	1	yes	characteristic
395	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
396	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
397	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
398	C₂³	#14273692	1	1	yes	characteristic
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	118	4	no	—
406	C₂×C₄	—	236	4	no	—
407	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
410	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
414	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
415	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
416	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
417	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
420	C₂×C₄	#14273683	1	1	yes	characteristic
421	C₂×C₄	#14273685	1	1	yes	characteristic
422	C₂×C₄	#14273685	1	1	yes	characteristic
423	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
424	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
425	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
426	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
427	C₂×C₄	#14273689	1	1	yes	characteristic
428	C₂×C₄	#14273689	1	1	yes	characteristic
429	C₂×C₄	#14273689	1	1	yes	characteristic
430	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
431	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
432	C₂×C₄	#14273692	1	1	yes	characteristic
433	C₂×C₄	#14273692	1	1	yes	characteristic
434	C₂×C₄	Q₈×Dic₅₉	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	—	59	4	no	—
437	C₈	—	59	4	no	—
438	C₈	—	118	4	no	—
439	C₈	—	118	4	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	#16837247	1	1	yes	characteristic
447	C₂²	#16837249	1	1	yes	characteristic
448	C₂²	C₂²⋊C₄×Dic₅₉	1	1	yes	characteristic
449	C₂²	C₂²⋊C₄×Dic₅₉	1	1	yes	characteristic
450	C₂²	#16837253	1	1	yes	characteristic
451	C₂²	#16837253	1	1	yes	characteristic
452	C₂²	C₄⋊C₄×Dic₅₉	1	1	yes	characteristic
453	C₂²	#16837521	1	4	yes	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	236	4	no	—
457	C₄	C₄²×Dic₅₉	1	1	yes	characteristic
458	C₄	#95×D₅₉	1	1	yes	characteristic
459	C₄	#16837249	1	1	yes	characteristic
460	C₄	#16837249	1	1	yes	characteristic
461	C₄	C₂²⋊C₄×Dic₅₉	1	1	yes	characteristic
462	C₄	#16837253	1	1	yes	characteristic
463	C₄	C₄⋊C₄×Dic₅₉	1	1	yes	characteristic
464	C₄	C₄⋊C₄×Dic₅₉	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	#95×Dic₅₉	1	1	yes	characteristic
470	C₂	#21423937	1	2	yes	—
471	C₂	#21423941	1	2	yes	—
472	C₂	#21423979	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₉
commutator	C₄×C₅₉	C₄³
Frattini	C₂³×C₄	C₂²×D₅₉
Fitting	C₂×C₅₉×#339	C₂
socle	C₂³×C₅₉	C₄×D₄
prime radical	C₂⁴×C₅₉	#41
cosocle	C₂³×C₄×C₅₉	C₂³
hypercenter	C₂×#339	D₅₉
hypocenter	C₅₉	#10707
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #16837360	C₄	semidirect
15. #16837358	C₄	semidirect
19. C₂×#14273638	C₄	semidirect
23. #16837166	C₄	semidirect
24. #16837164	C₄	semidirect
25. #16837162	C₄	semidirect
29. C₅₉×#339	C₄	semidirect
265. #339	Dic₅₉	semidirect
266. C₅₉	#10707	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837360	2
C₂×#16837358	2
C₂²×#14273638	2
C₂×#16837166	2
#21423812	2
C₂×#16837162	2
C₂×C₅₉×#339	2
#10707	59