Subgroups — #21438024

Order 7552.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16838135	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838109	C₂	1	1	yes	maximal, characteristic, complemented
3	#16838098	C₂	1	2	yes	maximal, complemented
4	#16838096	C₂	1	1	yes	maximal, characteristic, complemented
5	#16838091	C₂	1	1	yes	maximal, characteristic, complemented
6	#16838081	C₂	1	2	yes	maximal, complemented
7	#16838078	C₂	1	2	yes	maximal, complemented
8	#16838057	C₂	1	1	yes	maximal, characteristic, complemented
9	#16838047	C₂	1	1	yes	maximal, characteristic, complemented
10	#16838046	C₂	1	1	yes	maximal, characteristic, complemented
11	#16838042	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#16838023	C₂	1	1	yes	maximal, characteristic, complemented
14	#16838003	C₂	1	1	yes	maximal, characteristic, complemented
15	#16837994	C₂	1	2	yes	maximal, complemented
16	#16837990	C₂	1	2	yes	maximal, complemented
17	#16837934	C₂	1	1	yes	maximal, characteristic, complemented
18	#16837930	C₂	1	1	yes	maximal, characteristic, complemented
19	#16837911	C₂	1	2	yes	maximal, complemented
20	C₂×#14273709	C₂	1	2	yes	maximal, complemented
21	#16837881	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11745685	C₂²	1	2	yes	complemented
25	C₂×#11745687	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₅₉	C₂²	1	2	yes	—
27	C₂×D₄×D₅₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₅₉	C₂²	1	2	yes	complemented
29	#14273727	C₂²	1	1	yes	characteristic, complemented
30	#14273723	C₂²	1	1	yes	characteristic
31	#14273722	C₂²	1	1	yes	characteristic, complemented
32	#14273722	C₂²	1	2	yes	complemented
33	#14273721	C₂²	1	2	yes	complemented
34	#14273720	C₂²	1	1	yes	characteristic, complemented
35	#14273720	C₂²	1	2	yes	complemented
36	#14273720	C₂²	1	2	yes	complemented
37	#14273719	C₂²	1	2	yes	complemented
38	#14273718	C₂²	1	1	yes	characteristic, complemented
39	#14273718	C₂²	1	1	yes	characteristic, complemented
40	#14273717	C₂²	1	1	yes	characteristic, complemented
41	#14273715	C₂²	1	1	yes	characteristic, complemented
42	#14273714	C₂²	1	1	yes	characteristic, complemented
43	#14273713	C₂²	1	1	yes	characteristic, complemented
44	#14273713	C₂²	1	2	yes	complemented
45	#14273713	C₂²	1	2	yes	complemented
46	#14273712	C₂²	1	1	yes	characteristic, complemented
47	#14273711	C₂²	1	2	yes	complemented
48	#14273710	C₂²	1	2	yes	complemented
49	#14273710	C₂²	1	2	yes	complemented
50	#14273709	C₂²	1	1	yes	characteristic
51	#14273709	C₂²	1	2	yes	—
52	#14273709	C₂²	1	2	yes	complemented
53	#14273709	C₂²	1	2	yes	complemented
54	#14273709	C₂²	1	2	yes	complemented
55	#14273709	C₂²	1	2	yes	complemented
56	#14273709	C₂²	1	2	yes	complemented
57	#14273709	C₂²	1	2	yes	complemented
58	#14273709	C₂²	1	2	yes	complemented
59	#14273708	C₂²	1	2	yes	complemented
60	#14273707	C₂²	1	1	yes	characteristic, complemented
61	#14273706	C₂²	1	2	yes	complemented
62	#14273706	C₂²	1	2	yes	complemented
63	#14273706	C₂²	1	1	yes	characteristic, complemented
64	#14273705	C₂²	1	2	yes	complemented
65	#14273705	C₂²	1	1	yes	characteristic, complemented
66	#14273704	C₂²	1	2	yes	complemented
67	#14273704	C₂²	1	2	yes	complemented
68	#14273702	C₂²	1	1	yes	characteristic, complemented
69	#14273701	C₂²	1	1	yes	characteristic
70	#14273701	C₂²	1	2	yes	complemented
71	#14273701	C₂²	1	2	yes	complemented
72	#14273700	C₂²	1	1	yes	characteristic
73	#14273700	C₂²	1	2	yes	complemented
74	#14273700	C₂²	1	2	yes	complemented
75	#14273699	C₂²	1	2	yes	—
76	#14273699	C₂²	1	2	yes	complemented
77	#14273698	C₂²	1	1	yes	characteristic
78	#14273698	C₂²	1	1	yes	characteristic, complemented
79	#14273697	C₂²	1	2	yes	complemented
80	#14273696	C₂²	1	2	yes	—
81	#14273696	C₂²	1	2	yes	complemented
82	#14273695	C₂²	1	2	yes	—
83	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic, complemented
84	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic, complemented
85	#14273692	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₂₃₆	C₂²	1	2	yes	complemented
87	C₄×D₂₃₆	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₂₃₆	C₂²	1	1	yes	characteristic, complemented
89	D₄×Dic₅₉	C₂²	1	1	yes	characteristic
90	D₄×Dic₅₉	C₂²	1	1	yes	characteristic
91	#14273689	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	complemented
98	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	complemented
100	#14273686	C₂²	1	2	yes	complemented
101	#14273684	C₂²	1	2	yes	complemented
102	#14273684	C₂²	1	1	yes	characteristic, complemented
103	#14273683	C₂²	1	2	yes	complemented
104	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	complemented
105	C₂×Dic₅₉⋊C₄	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂²⋊Dic₅₉	C₂²	1	2	yes	complemented
109	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₅₉	C₂²	1	2	yes	complemented
111	C₄²×D₅₉	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₅₉	C₂²	1	1	yes	characteristic
113	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
114	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
115	C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
116	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
119	#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
120	#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
123	C₂⁴×C₅₉	C₂³	1	2	yes	—
124	C₂³×D₅₉	C₂³	1	2	yes	—
125	C₂×D₄×C₅₉	—	2	4	no	—
126	C₂×D₄×C₅₉	C₂³	1	2	yes	—
127	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
133	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅₉	—	4	4	no	—
135	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
144	C₂²×Dic₅₉	C₂³	1	2	yes	—
145	C₂²×Dic₅₉	C₂³	1	2	yes	—
146	C₂²×Dic₅₉	C₂³	1	2	yes	—
147	#11745687	—	2	4	no	—
148	D₄×D₅₉	—	2	4	no	—
149	#11745685	—	4	4	no	—
150	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
151	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
152	C₂×D₂₃₆	C₂³	1	2	yes	—
153	C₂×C₄×D₅₉	—	4	4	no	—
154	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₅₉	C₂³	1	2	yes	—
157	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₅₉	C₂³	1	2	yes	—
160	C₂×C₄×D₅₉	C₂³	1	2	yes	—
161	C₂×C₄×D₅₉	C₂³	1	2	yes	—
162	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
163	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
164	C₂×Dic₁₁₈	C₂³	1	2	yes	—
165	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₄²×C₅₉	C₂³	1	1	yes	characteristic
177	C₄²×C₅₉	C₂³	1	1	yes	characteristic
178	C₄²×C₅₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
188	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₅₉	C₂³	1	2	yes	—
205	C₄⋊Dic₅₉	C₂³	1	2	yes	—
206	C₄⋊Dic₅₉	C₂³	1	2	yes	—
207	C₄⋊Dic₅₉	C₂³	1	2	yes	—
208	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
209	Dic₅₉⋊C₄	C₂³	1	2	yes	—
210	Dic₅₉⋊C₄	C₂³	1	2	yes	—
211	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₅₉⋊C₄	C₂³	1	2	yes	—
213	Dic₅₉⋊C₄	C₂³	1	2	yes	—
214	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₅₉⋊C₄	C₂³	1	2	yes	—
216	Dic₅₉⋊C₄	C₂³	1	2	yes	—
217	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₅₉⋊C₄	C₂³	1	2	yes	—
220	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
222	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₅₉	C₂³	1	2	yes	—
226	C₄×Dic₅₉	C₂³	1	2	yes	—
227	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
228	C₂³×C₅₉	—	2	4	no	—
229	C₂³×C₅₉	—	4	2	no	—
230	C₂³×C₅₉	—	4	2	no	—
231	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₅₉	C₂⁴	1	2	yes	—
233	C₂³×C₅₉	C₂⁴	1	2	yes	—
234	C₂²×D₅₉	—	2	4	no	—
235	C₂²×D₅₉	—	2	4	no	—
236	C₂²×D₅₉	—	4	2	no	—
237	C₂²×D₅₉	C₂⁴	1	2	yes	—
238	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
240	D₄×C₅₉	—	2	4	no	—
241	D₄×C₅₉	—	2	2	no	—
242	D₄×C₅₉	#41	1	4	yes	complemented
243	C₂×C₄×C₅₉	—	2	2	no	—
244	C₂×C₄×C₅₉	—	4	2	no	—
245	C₂×C₄×C₅₉	—	4	2	no	—
246	C₂×C₄×C₅₉	—	4	2	no	—
247	C₂×C₄×C₅₉	—	4	2	no	—
248	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₅₉	—	2	4	no	—
257	C₂²⋊D₅₉	—	2	4	no	—
258	C₂²⋊D₅₉	—	2	4	no	—
259	C₂²⋊D₅₉	—	2	2	no	—
260	C₂²⋊D₅₉	—	4	2	no	—
261	C₂²⋊D₅₉	—	4	2	no	—
262	C₂²⋊D₅₉	—	4	2	no	—
263	C₂²⋊D₅₉	—	4	1	no	—
264	C₂²⋊D₅₉	—	4	2	no	—
265	C₂×Dic₅₉	—	2	4	no	—
266	C₂×Dic₅₉	—	4	2	no	—
267	C₂×Dic₅₉	—	4	2	no	—
268	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅₉	C₂⁴	1	2	yes	—
272	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₅₉	C₂⁴	1	2	yes	—
275	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₅₉	C₂⁴	1	2	yes	—
277	D₂₃₆	—	2	2	no	—
278	D₂₃₆	—	2	2	no	—
279	D₂₃₆	—	4	2	no	—
280	C₄×D₅₉	—	2	2	no	—
281	C₄×D₅₉	—	2	4	no	—
282	C₄×D₅₉	—	2	2	no	—
283	C₄×D₅₉	—	2	2	no	—
284	C₄×D₅₉	—	4	2	no	—
285	C₄×D₅₉	—	4	2	no	—
286	C₄×D₅₉	—	4	1	no	—
287	C₄×D₅₉	—	4	2	no	—
288	Dic₁₁₈	—	2	2	no	—
289	Dic₁₁₈	—	4	1	no	—
290	Dic₁₁₈	—	4	2	no	—
291	C₂²×C₅₉	—	2	2	no	—
292	C₂²×C₅₉	—	2	2	no	—
293	C₂²×C₅₉	—	2	1	no	—
294	C₂²×C₅₉	—	2	2	no	—
295	C₂²×C₅₉	—	2	2	no	—
296	C₂²×C₅₉	—	2	1	no	—
297	C₂²×C₅₉	—	2	2	no	—
298	C₂²×C₅₉	—	2	1	no	—
299	C₂²×C₅₉	—	8	4	no	—
300	C₂²×C₅₉	C₂×#41	1	4	yes	—
301	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
302	C₂×D₅₉	—	2	1	no	—
303	C₂×D₅₉	—	2	1	no	—
304	C₂×D₅₉	—	2	1	no	—
305	C₂×D₅₉	—	2	2	no	—
306	C₂×D₅₉	—	2	1	no	—
307	C₂×D₅₉	—	2	2	no	—
308	C₂×D₅₉	—	2	1	no	—
309	C₂×D₅₉	—	2	2	no	—
310	C₂×D₅₉	—	4	8	no	—
311	C₂×D₅₉	H(5,𝔽₂)	1	2	yes	—
312	C₄×C₅₉	—	2	1	no	—
313	C₄×C₅₉	—	2	1	no	—
314	C₄×C₅₉	—	2	1	no	—
315	C₄×C₅₉	—	2	2	no	—
316	C₄×C₅₉	—	2	1	no	—
317	C₄×C₅₉	—	2	1	no	—
318	C₄×C₅₉	—	2	2	no	—
319	C₄×C₅₉	C₂×#41	1	2	yes	—
320	Dic₅₉	—	2	2	no	—
321	Dic₅₉	—	2	1	no	—
322	Dic₅₉	—	2	1	no	—
323	Dic₅₉	—	2	2	no	—
324	Dic₅₉	—	2	2	no	—
325	Dic₅₉	—	2	1	no	—
326	Dic₅₉	—	2	1	no	—
327	Dic₅₉	—	2	1	no	—
328	Dic₅₉	—	2	1	no	—
329	#3513	—	59	1	no	maximal, Sylow
330	C₂×C₅₉	—	2	4	no	—
331	C₂×C₅₉	—	4	2	no	—
332	C₂×C₅₉	—	4	1	no	—
333	C₂×C₅₉	C₂²×#41	1	1	yes	characteristic
334	C₂×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₅₉	#585	1	1	yes	characteristic
336	D₅₉	—	2	2	no	—
337	D₅₉	—	4	1	no	—
338	D₅₉	—	4	2	no	—
339	#559	—	59	1	no	—
340	#554	—	59	1	no	—
341	#553	—	59	2	no	—
342	#553	—	59	1	no	—
343	#552	—	59	1	no	—
344	#551	—	59	2	no	—
345	#551	—	59	2	no	—
346	#547	—	59	1	no	—
347	#546	—	59	1	no	—
348	#546	—	59	1	no	—
349	#546	—	59	2	no	—
350	D₄²	—	59	1	no	—
351	#542	—	59	1	no	—
352	#540	—	59	1	no	—
353	#539	—	59	2	no	—
354	#538	—	59	2	no	—
355	#529	—	59	1	no	—
356	#529	—	59	1	no	—
357	#525	—	59	2	no	—
358	C₂×#123	—	59	2	no	—
359	#520	—	59	1	no	—
360	#518	D₅₉	1	1	yes	characteristic, complemented
361	C₂×C₄×D₄	—	59	1	no	—
362	C₅₉	#3513	1	1	yes	characteristic, complemented, Sylow
363	C₂×#41	—	59	1	no	—
364	C₂×#41	—	59	2	no	—
365	C₂²×D₄	—	59	2	no	—
366	C₂²×D₄	—	59	1	no	—
367	C₂²×D₄	C₂×D₅₉	1	1	yes	characteristic
368	C₂³×C₄	—	59	2	no	—
369	C₄⋊Q₈	—	59	1	no	—
370	#127	—	59	1	no	—
371	#126	—	59	1	no	—
372	#126	—	59	2	no	—
373	#126	—	59	2	no	—
374	#126	—	59	1	no	—
375	#126	—	59	2	no	—
376	#126	—	59	2	no	—
377	#125	—	59	1	no	—
378	#125	—	59	1	no	—
379	#125	—	59	1	no	—
380	#125	—	59	2	no	—
381	#124	—	59	1	no	—
382	#124	—	59	1	no	—
383	#124	—	59	2	no	—
384	#124	—	59	2	no	—
385	#124	—	59	1	no	—
386	#123	—	59	2	no	—
387	#123	—	59	2	no	—
388	#123	—	59	2	no	—
389	#123	—	59	1	no	—
390	#123	—	59	1	no	—
391	#123	—	59	2	no	—
392	#123	—	59	2	no	—
393	#123	—	59	2	no	—
394	#123	—	59	2	no	—
395	#123	—	59	2	no	—
396	#123	—	59	2	no	—
397	#123	—	59	2	no	—
398	#123	—	59	2	no	—
399	#123	—	59	2	no	—
400	C₂²⋊Q₈	—	59	2	no	—
401	C₂²⋊Q₈	—	59	2	no	—
402	C₂²⋊Q₈	—	59	1	no	—
403	C₂²⋊Q₈	—	59	2	no	—
404	C₂²⋊Q₈	—	59	1	no	—
405	C₂²⋊Q₈	—	59	1	no	—
406	C₂²⋊Q₈	—	59	2	no	—
407	C₂²⋊Q₈	—	59	2	no	—
408	#121	—	59	2	no	—
409	#121	—	59	1	no	—
410	#121	—	59	2	no	—
411	#121	—	59	1	no	—
412	#121	—	59	2	no	—
413	#121	—	59	2	no	—
414	#121	—	59	1	no	—
415	#121	—	59	1	no	—
416	#121	—	59	2	no	—
417	#121	—	59	1	no	—
418	#121	—	59	2	no	—
419	#120	—	59	2	no	—
420	#120	—	59	2	no	—
421	#120	—	59	2	no	—
422	#120	—	59	2	no	—
423	C₄×Q₈	—	59	1	no	—
424	C₄×Q₈	—	59	1	no	—
425	C₄×Q₈	—	59	1	no	—
426	C₄×D₄	—	59	1	no	—
427	C₄×D₄	—	59	1	no	—
428	C₄×D₄	—	59	2	no	—
429	C₄×D₄	—	59	2	no	—
430	C₄×D₄	—	59	2	no	—
431	C₄×D₄	—	59	1	no	—
432	C₄×D₄	—	59	2	no	—
433	C₄×D₄	—	59	1	no	—
434	C₄×D₄	—	59	1	no	—
435	C₄×D₄	—	59	2	no	—
436	C₄×D₄	—	59	2	no	—
437	C₄×D₄	—	59	1	no	—
438	C₄×D₄	—	59	2	no	—
439	C₄×D₄	—	59	1	no	—
440	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
441	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
442	C₄×D₄	C₂×D₅₉	1	2	yes	complemented
443	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic, complemented
444	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic, complemented
445	C₄×D₄	C₂×D₅₉	1	2	yes	complemented
446	#117	—	59	2	no	—
447	#117	—	59	2	no	—
448	#117	—	59	1	no	—
449	#117	—	59	2	no	—
450	#117	C₂×D₅₉	1	1	yes	characteristic, complemented
451	#117	C₂×D₅₉	1	1	yes	characteristic, complemented
452	C₂×C₄⋊C₄	—	59	2	no	—
453	C₂×C₄⋊C₄	—	59	2	no	—
454	C₂×C₄⋊C₄	—	59	1	no	—
455	C₂×C₄⋊C₄	—	59	1	no	—
456	C₂×C₂²⋊C₄	—	59	2	no	—
457	C₂×C₂²⋊C₄	—	59	2	no	—
458	C₂×C₂²⋊C₄	—	59	2	no	—
459	C₂×C₂²⋊C₄	C₂×D₅₉	1	2	yes	complemented
460	C₂×C₂²⋊C₄	C₂×D₅₉	1	2	yes	complemented
461	C₂×C₄²	—	59	1	no	—
462	C₂⁴	—	59	2	no	—
463	C₂⁴	C₂²×D₅₉	1	2	yes	—
464	#41	—	118	4	no	—
465	#41	—	236	4	no	—
466	C₂×Q₈	—	59	1	no	—
467	C₂×Q₈	—	59	1	no	—
468	C₂×Q₈	—	59	2	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	59	2	no	—
471	C₂×D₄	—	59	2	no	—
472	C₂×D₄	—	59	2	no	—
473	C₂×D₄	—	59	1	no	—
474	C₂×D₄	—	59	1	no	—
475	C₂×D₄	—	59	2	no	—
476	C₂×D₄	—	59	2	no	—
477	C₂×D₄	—	59	2	no	—
478	C₂×D₄	—	59	2	no	—
479	C₂×D₄	—	59	1	no	—
480	C₂×D₄	—	59	1	no	—
481	C₂×D₄	—	59	2	no	—
482	C₂×D₄	—	118	4	no	—
483	C₂×D₄	—	236	4	no	—
484	C₂×D₄	C₂²×D₅₉	1	2	yes	—
485	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
487	C₂²×C₄	—	59	2	no	—
488	C₂²×C₄	—	59	2	no	—
489	C₂²×C₄	—	59	2	no	—
490	C₂²×C₄	—	59	1	no	—
491	C₂²×C₄	—	59	1	no	—
492	C₂²×C₄	—	59	2	no	—
493	C₂²×C₄	—	59	1	no	—
494	C₂²×C₄	—	59	1	no	—
495	C₂²×C₄	—	59	2	no	—
496	C₂²×C₄	—	59	2	no	—
497	C₂²×C₄	—	59	2	no	—
498	C₂²×C₄	—	236	4	no	—
499	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
501	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
502	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
503	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
504	C₄⋊C₄	—	59	2	no	—
505	C₄⋊C₄	—	59	1	no	—
506	C₄⋊C₄	—	59	1	no	—
507	C₄⋊C₄	—	59	2	no	—
508	C₄⋊C₄	—	59	1	no	—
509	C₄⋊C₄	—	59	2	no	—
510	C₄⋊C₄	—	59	1	no	—
511	C₄⋊C₄	—	59	2	no	—
512	C₄⋊C₄	—	59	2	no	—
513	C₄⋊C₄	—	59	2	no	—
514	C₄⋊C₄	—	59	2	no	—
515	C₄⋊C₄	—	59	1	no	—
516	C₄⋊C₄	—	59	2	no	—
517	C₄⋊C₄	—	59	2	no	—
518	C₄⋊C₄	—	59	2	no	—
519	C₄⋊C₄	—	59	1	no	—
520	C₄⋊C₄	—	59	1	no	—
521	C₄⋊C₄	—	59	2	no	—
522	C₄⋊C₄	—	59	1	no	—
523	C₄⋊C₄	—	59	1	no	—
524	C₄⋊C₄	—	59	1	no	—
525	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
529	C₂²⋊C₄	—	59	1	no	—
530	C₂²⋊C₄	—	59	2	no	—
531	C₂²⋊C₄	—	59	2	no	—
532	C₂²⋊C₄	—	59	2	no	—
533	C₂²⋊C₄	—	59	2	no	—
534	C₂²⋊C₄	—	59	2	no	—
535	C₂²⋊C₄	—	59	2	no	—
536	C₂²⋊C₄	—	59	1	no	—
537	C₂²⋊C₄	—	59	2	no	—
538	C₂²⋊C₄	—	59	1	no	—
539	C₂²⋊C₄	—	59	2	no	—
540	C₂²⋊C₄	—	59	2	no	—
541	C₂²⋊C₄	—	59	2	no	—
542	C₂²⋊C₄	—	59	2	no	—
543	C₂²⋊C₄	—	59	2	no	—
544	C₂²⋊C₄	—	59	1	no	—
545	C₂²⋊C₄	—	59	1	no	—
546	C₂²⋊C₄	—	59	1	no	—
547	C₂²⋊C₄	—	59	1	no	—
548	C₂²⋊C₄	—	59	2	no	—
549	C₂²⋊C₄	—	59	2	no	—
550	C₂²⋊C₄	—	59	1	no	—
551	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
558	C₄²	—	59	1	no	—
559	C₄²	—	59	1	no	—
560	C₄²	—	59	1	no	—
561	C₄²	—	59	2	no	—
562	C₄²	—	59	2	no	—
563	C₄²	—	59	1	no	—
564	C₄²	C₂²×D₅₉	1	1	yes	characteristic
565	C₄²	C₂²×D₅₉	1	2	yes	—
566	C₄²	C₂²×D₅₉	1	1	yes	characteristic
567	C₂³	—	2	4	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	59	1	no	—
571	C₂³	—	59	2	no	—
572	C₂³	—	59	1	no	—
573	C₂³	—	118	4	no	—
574	C₂³	—	118	4	no	—
575	C₂³	—	236	2	no	—
576	C₂³	C₂³×D₅₉	1	1	yes	characteristic
577	C₂³	C₂³×D₅₉	1	2	yes	—
578	C₂³	C₂³×D₅₉	1	2	yes	—
579	Q₈	—	118	2	no	—
580	Q₈	—	236	1	no	—
581	Q₈	—	236	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	118	2	no	—
585	D₄	—	118	2	no	—
586	D₄	—	118	4	no	—
587	D₄	—	118	4	no	—
588	D₄	—	118	4	no	—
589	D₄	—	118	2	no	—
590	D₄	—	236	2	no	—
591	D₄	—	236	1	no	—
592	D₄	—	236	2	no	—
593	D₄	—	236	2	no	—
594	D₄	—	236	2	no	—
595	D₄	—	236	2	no	—
596	D₄	#11745685	1	4	yes	complemented
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	59	1	no	—
603	C₂×C₄	—	59	2	no	—
604	C₂×C₄	—	59	1	no	—
605	C₂×C₄	—	59	1	no	—
606	C₂×C₄	—	59	1	no	—
607	C₂×C₄	—	59	2	no	—
608	C₂×C₄	—	59	1	no	—
609	C₂×C₄	—	59	1	no	—
610	C₂×C₄	—	59	2	no	—
611	C₂×C₄	—	118	2	no	—
612	C₂×C₄	—	118	4	no	—
613	C₂×C₄	—	118	4	no	—
614	C₂×C₄	—	118	2	no	—
615	C₂×C₄	—	118	2	no	—
616	C₂×C₄	—	236	1	no	—
617	C₂×C₄	—	236	2	no	—
618	C₂×C₄	—	236	2	no	—
619	C₂×C₄	—	236	2	no	—
620	C₂×C₄	—	236	2	no	—
621	C₂×C₄	—	236	2	no	—
622	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₅₉	1	2	yes	—
625	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₅₉	1	2	yes	—
628	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	8	4	no	—
639	C₂²	—	59	2	no	—
640	C₂²	—	118	1	no	—
641	C₂²	—	118	1	no	—
642	C₂²	—	118	1	no	—
643	C₂²	—	118	2	no	—
644	C₂²	—	118	1	no	—
645	C₂²	—	118	2	no	—
646	C₂²	—	118	1	no	—
647	C₂²	—	118	2	no	—
648	C₂²	—	236	8	no	—
649	C₂²	C₂×#11745685	1	4	yes	—
650	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	118	1	no	—
659	C₄	—	118	1	no	—
660	C₄	—	118	2	no	—
661	C₄	—	118	1	no	—
662	C₄	—	118	2	no	—
663	C₄	—	118	1	no	—
664	C₄	—	118	2	no	—
665	C₄	—	118	1	no	—
666	C₄	—	118	1	no	—
667	C₄	C₂×#11745685	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	4	2	no	—
671	C₂	—	118	2	no	—
672	C₂	—	236	2	no	—
673	C₂	—	236	1	no	—
674	C₂	C₂²×#11745685	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₅₉	1	1	yes	characteristic
676	C₂	#16838237	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₉
commutator, socle	C₂²×C₅₉	C₂⁵
Fitting	C₅₉×#518	C₂
hypercenter	#518	D₅₉
hypocenter	C₅₉	#3513
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. #16838135	C₂	semidirect
2. #16838109	C₂	semidirect
3. #16838098	C₂	semidirect
4. #16838096	C₂	semidirect
5. #16838091	C₂	semidirect
6. #16838081	C₂	semidirect
7. #16838078	C₂	semidirect
8. #16838057	C₂	semidirect
9. #16838047	C₂	semidirect
10. #16838046	C₂	semidirect
11. #16838042	C₂	semidirect
12. D₄×C₂²⋊D₅₉	C₂	semidirect
13. #16838023	C₂	semidirect
14. #16838003	C₂	semidirect
15. #16837994	C₂	semidirect
16. #16837990	C₂	semidirect
17. #16837934	C₂	semidirect
18. #16837930	C₂	semidirect
19. #16837911	C₂	semidirect
20. C₂×#14273709	C₂	semidirect
21. #16837881	C₂	semidirect
22. C₄×D₄×D₅₉	C₂	semidirect
23. C₅₉×#518	C₂	semidirect
24. C₂×#11745685	C₂²	semidirect
28. C₂²×C₄×D₅₉	C₂²	semidirect
29. #14273727	C₂²	semidirect
31. #14273722	C₂²	semidirect
32. #14273722	C₂²	semidirect
33. #14273721	C₂²	semidirect
34. #14273720	C₂²	semidirect
35. #14273720	C₂²	semidirect
36. #14273720	C₂²	semidirect
37. #14273719	C₂²	semidirect
38. #14273718	C₂²	semidirect
39. #14273718	C₂²	semidirect
40. #14273717	C₂²	semidirect
41. #14273715	C₂²	semidirect
42. #14273714	C₂²	semidirect
43. #14273713	C₂²	semidirect
44. #14273713	C₂²	semidirect
45. #14273713	C₂²	semidirect
46. #14273712	C₂²	semidirect
47. #14273711	C₂²	semidirect
48. #14273710	C₂²	semidirect
49. #14273710	C₂²	semidirect
52. #14273709	C₂²	semidirect
53. #14273709	C₂²	semidirect
54. #14273709	C₂²	semidirect
55. #14273709	C₂²	semidirect
56. #14273709	C₂²	semidirect
57. #14273709	C₂²	semidirect
58. #14273709	C₂²	semidirect
59. #14273708	C₂²	semidirect
60. #14273707	C₂²	semidirect
61. #14273706	C₂²	semidirect
62. #14273706	C₂²	semidirect
63. #14273706	C₂²	semidirect
64. #14273705	C₂²	semidirect
65. #14273705	C₂²	semidirect
66. #14273704	C₂²	semidirect
67. #14273704	C₂²	semidirect
68. #14273702	C₂²	semidirect
70. #14273701	C₂²	semidirect
71. #14273701	C₂²	semidirect
73. #14273700	C₂²	semidirect
74. #14273700	C₂²	semidirect
76. #14273699	C₂²	semidirect
78. #14273698	C₂²	semidirect
79. #14273697	C₂²	semidirect
81. #14273696	C₂²	semidirect
83. C₄×Dic₁₁₈	C₂²	semidirect
84. C₄×Dic₁₁₈	C₂²	semidirect
85. #14273692	C₂²	semidirect
86. C₄×D₂₃₆	C₂²	semidirect
87. C₄×D₂₃₆	C₂²	semidirect
88. C₄×D₂₃₆	C₂²	semidirect
91. #14273689	C₂²	semidirect
93. C₄×C₂²⋊D₅₉	C₂²	semidirect
94. C₄×C₂²⋊D₅₉	C₂²	semidirect
95. C₄×C₂²⋊D₅₉	C₂²	semidirect
96. C₄×C₂²⋊D₅₉	C₂²	semidirect
97. C₄×C₂²⋊D₅₉	C₂²	semidirect
98. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
100. #14273686	C₂²	semidirect
101. #14273684	C₂²	semidirect
102. #14273684	C₂²	semidirect
103. #14273683	C₂²	semidirect
104. C₂×C₄⋊Dic₅₉	C₂²	semidirect
105. C₂×Dic₅₉⋊C₄	C₂²	semidirect
106. C₄⋊C₄×D₅₉	C₂²	semidirect
107. C₄⋊C₄×D₅₉	C₂²	semidirect
108. C₂×C₂²⋊Dic₅₉	C₂²	semidirect
109. C₂×(C₂×D₅₉)⋊C₄	C₂²	semidirect
110. C₂²⋊C₄×D₅₉	C₂²	semidirect
111. C₄²×D₅₉	C₂²	semidirect
115. C₄×D₄×C₅₉	C₂²	semidirect
116. C₄×D₄×C₅₉	C₂²	semidirect
117. C₄×D₄×C₅₉	C₂²	semidirect
118. C₄×D₄×C₅₉	C₂²	semidirect
119. #117×C₅₉	C₂²	semidirect
120. #117×C₅₉	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₅₉	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₅₉	C₂²	semidirect
242. D₄×C₅₉	#41	semidirect
360. #518	D₅₉	semidirect
362. C₅₉	#3513	semidirect
442. C₄×D₄	C₂×D₅₉	semidirect
443. C₄×D₄	C₂×D₅₉	semidirect
444. C₄×D₄	C₂×D₅₉	semidirect
445. C₄×D₄	C₂×D₅₉	semidirect
450. #117	C₂×D₅₉	semidirect
451. #117	C₂×D₅₉	semidirect
459. C₂×C₂²⋊C₄	C₂×D₅₉	semidirect
460. C₂×C₂²⋊C₄	C₂×D₅₉	semidirect
596. D₄	#11745685	semidirect