Subgroups — #21438138

Order 7552.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16838123	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838106	C₂	1	2	yes	maximal, complemented
3	#16838093	C₂	1	1	yes	maximal, characteristic, complemented
4	#16838092	C₂	1	1	yes	maximal, characteristic, complemented
5	#16838082	C₂	1	2	yes	maximal, complemented
6	#16838081	C₂	1	2	yes	maximal, complemented
7	Q₈×C₂²⋊D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#16838060	C₂	1	1	yes	maximal, characteristic, complemented
9	#16838052	C₂	1	1	yes	maximal, characteristic, complemented
10	#16838051	C₂	1	1	yes	maximal, characteristic, complemented
11	#16838041	C₂	1	2	yes	maximal, complemented
12	#16838016	C₂	1	2	yes	maximal, complemented
13	#16837998	C₂	1	2	yes	maximal, complemented
14	#16837997	C₂	1	2	yes	maximal, complemented
15	#16837956	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837931	C₂	1	1	yes	maximal, characteristic, complemented
17	#16837912	C₂	1	1	yes	maximal, characteristic, complemented
18	#16837909	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#14273703	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²⋊Q₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#16837881	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11745687	C₂²	1	2	yes	—
25	C₂×#11745687	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₅₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₅₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₅₉	C₂²	1	1	yes	characteristic
30	#14273726	C₂²	1	1	yes	characteristic, complemented
31	#14273725	C₂²	1	1	yes	characteristic, complemented
32	#14273725	C₂²	1	2	yes	complemented
33	#14273722	C₂²	1	2	yes	complemented
34	#14273721	C₂²	1	2	yes	complemented
35	#14273720	C₂²	1	2	yes	complemented
36	#14273720	C₂²	1	2	yes	complemented
37	#14273720	C₂²	1	2	yes	complemented
38	#14273719	C₂²	1	1	yes	characteristic, complemented
39	#14273717	C₂²	1	2	yes	complemented
40	#14273717	C₂²	1	2	yes	complemented
41	#14273717	C₂²	1	2	yes	complemented
42	#14273713	C₂²	1	2	yes	—
43	#14273713	C₂²	1	2	yes	complemented
44	#14273712	C₂²	1	2	yes	—
45	#14273710	C₂²	1	2	yes	complemented
46	#14273709	C₂²	1	2	yes	—
47	#14273709	C₂²	1	2	yes	complemented
48	#14273709	C₂²	1	2	yes	complemented
49	#14273708	C₂²	1	2	yes	—
50	#14273708	C₂²	1	2	yes	complemented
51	#14273708	C₂²	1	2	yes	complemented
52	#14273708	C₂²	1	2	yes	complemented
53	#14273707	C₂²	1	1	yes	characteristic
54	#14273706	C₂²	1	1	yes	characteristic, complemented
55	#14273706	C₂²	1	1	yes	characteristic, complemented
56	#14273706	C₂²	1	2	yes	complemented
57	#14273705	C₂²	1	2	yes	—
58	#14273705	C₂²	1	2	yes	—
59	#14273704	C₂²	1	2	yes	complemented
60	#14273704	C₂²	1	2	yes	complemented
61	#14273704	C₂²	1	2	yes	complemented
62	#14273703	C₂²	1	1	yes	characteristic
63	#14273703	C₂²	1	1	yes	characteristic
64	#14273703	C₂²	1	2	yes	—
65	#14273703	C₂²	1	2	yes	complemented
66	#14273703	C₂²	1	1	yes	characteristic, complemented
67	#14273703	C₂²	1	1	yes	characteristic, complemented
68	#14273703	C₂²	1	1	yes	characteristic, complemented
69	#14273703	C₂²	1	2	yes	complemented
70	#14273700	C₂²	1	2	yes	—
71	#14273699	C₂²	1	2	yes	—
72	#14273698	C₂²	1	1	yes	characteristic
73	#14273698	C₂²	1	1	yes	characteristic, complemented
74	#14273695	C₂²	1	2	yes	—
75	#14273695	C₂²	1	2	yes	—
76	Q₈×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₁₈	C₂²	1	2	yes	complemented
78	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic, complemented
79	#14273692	C₂²	1	2	yes	complemented
80	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
81	D₄×Dic₅₉	C₂²	1	1	yes	characteristic
82	D₄×Dic₅₉	C₂²	1	2	yes	complemented
83	D₄×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
84	#14273689	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	—
86	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	complemented
90	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	—
91	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₅₉)⋊C₄	C₂²	1	1	yes	characteristic
93	(C₂²⋊D₅₉)⋊C₄	C₂²	1	1	yes	characteristic
94	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	complemented
95	#14273686	C₂²	1	1	yes	characteristic, complemented
96	#14273685	C₂²	1	1	yes	characteristic, complemented
97	#14273684	C₂²	1	2	yes	—
98	#14273684	C₂²	1	2	yes	complemented
99	#14273683	C₂²	1	2	yes	complemented
100	#14273683	C₂²	1	2	yes	complemented
101	C₂×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic, complemented
102	C₂×Dic₅₉⋊C₄	C₂²	1	2	yes	complemented
103	C₂×Dic₅₉⋊C₄	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₅₉	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic, complemented
107	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₅₉	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₅₉	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₅₉	C₂²	1	1	yes	characteristic
111	C₄²×D₅₉	C₂²	1	1	yes	characteristic
112	C₂×#41×C₅₉	C₂²	1	1	yes	characteristic, complemented
113	C₂²×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
114	#124×C₅₉	C₂²	1	1	yes	characteristic, complemented
115	#124×C₅₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
118	#121×C₅₉	C₂²	1	2	yes	—
119	#121×C₅₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
122	C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
123	C₂³×D₅₉	C₂³	1	1	yes	characteristic
124	C₂³×D₅₉	C₂³	1	1	yes	characteristic
125	#41×C₅₉	—	4	2	no	—
126	C₂×Q₈×C₅₉	—	4	2	no	—
127	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₅₉	C₂³	1	2	yes	—
130	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₅₉	C₂³	1	2	yes	—
132	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₅₉	C₂³	1	2	yes	—
134	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₅₉	C₂³	1	2	yes	—
144	C₂²×Dic₅₉	C₂³	1	2	yes	—
145	C₂²×Dic₅₉	C₂³	1	1	yes	characteristic
146	C₂²×Dic₅₉	C₂³	1	2	yes	—
147	C₂²×Dic₅₉	C₂³	1	1	yes	characteristic
148	Q₈×D₅₉	—	4	2	no	—
149	#11745687	—	2	8	no	—
150	#11745687	—	4	2	no	—
151	D₄×D₅₉	—	2	4	no	—
152	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅₉	—	4	2	no	—
154	C₂×C₄×D₅₉	—	4	2	no	—
155	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅₉	C₂³	1	2	yes	—
159	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₅₉	C₂³	1	2	yes	—
164	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
166	C₂×Dic₁₁₈	C₂³	1	2	yes	—
167	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
168	C₂×Dic₁₁₈	C₂³	1	2	yes	—
169	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
173	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
174	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₄²×C₅₉	C₂³	1	1	yes	characteristic
180	C₄²×C₅₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
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	2	yes	—
187	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
189	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
200	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₅₉	C₂³	1	2	yes	—
203	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₅₉	C₂³	1	2	yes	—
205	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅₉	C₂³	1	2	yes	—
207	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₅₉⋊C₄	C₂³	1	2	yes	—
210	Dic₅₉⋊C₄	C₂³	1	2	yes	—
211	Dic₅₉⋊C₄	C₂³	1	2	yes	—
212	Dic₅₉⋊C₄	C₂³	1	2	yes	—
213	Dic₅₉⋊C₄	C₂³	1	2	yes	—
214	Dic₅₉⋊C₄	C₂³	1	2	yes	—
215	Dic₅₉⋊C₄	C₂³	1	2	yes	—
216	Dic₅₉⋊C₄	C₂³	1	2	yes	—
217	Dic₅₉⋊C₄	C₂³	1	2	yes	—
218	Dic₅₉⋊C₄	C₂³	1	2	yes	—
219	Dic₅₉⋊C₄	C₂³	1	2	yes	—
220	Dic₅₉⋊C₄	C₂³	1	2	yes	—
221	Dic₅₉⋊C₄	C₂³	1	2	yes	—
222	Dic₅₉⋊C₄	C₂³	1	2	yes	—
223	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
226	C₄×Dic₅₉	C₂³	1	2	yes	—
227	C₄×Dic₅₉	C₂³	1	2	yes	—
228	C₄×Dic₅₉	C₂³	1	2	yes	—
229	C₄×Dic₅₉	C₂³	1	2	yes	—
230	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
231	C₂³×C₅₉	C₂⁴	1	2	yes	—
232	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₅₉	—	2	2	no	—
234	C₂²×D₅₉	—	2	2	no	—
235	C₂²×D₅₉	—	2	2	no	—
236	C₂²×D₅₉	—	2	2	no	—
237	C₂²×D₅₉	—	4	1	no	—
238	C₂²×D₅₉	—	4	1	no	—
239	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
240	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₅₉	—	2	2	no	—
243	Q₈×C₅₉	—	2	2	no	—
244	Q₈×C₅₉	—	4	2	no	—
245	D₄×C₅₉	—	2	2	no	—
246	D₄×C₅₉	—	2	4	no	—
247	D₄×C₅₉	—	2	2	no	—
248	D₄×C₅₉	—	4	2	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	2	no	—
251	C₂×C₄×C₅₉	—	4	2	no	—
252	C₂×C₄×C₅₉	—	4	2	no	—
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	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
257	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₅₉	—	2	4	no	—
262	C₂²⋊D₅₉	—	2	4	no	—
263	C₂²⋊D₅₉	—	2	2	no	—
264	C₂²⋊D₅₉	—	4	2	no	—
265	C₂²⋊D₅₉	#41	1	4	yes	complemented
266	C₂×Dic₅₉	—	2	4	no	—
267	C₂×Dic₅₉	—	2	4	no	—
268	C₂×Dic₅₉	—	4	1	no	—
269	C₂×Dic₅₉	—	4	1	no	—
270	C₂×Dic₅₉	—	4	2	no	—
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	C₂×Dic₅₉	C₂⁴	1	2	yes	—
278	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
280	D₂₃₆	—	2	2	no	—
281	C₄×D₅₉	—	2	4	no	—
282	C₄×D₅₉	—	2	2	no	—
283	C₄×D₅₉	—	2	2	no	—
284	C₄×D₅₉	—	2	2	no	—
285	C₄×D₅₉	—	2	2	no	—
286	C₄×D₅₉	—	2	2	no	—
287	C₄×D₅₉	—	4	1	no	—
288	C₄×D₅₉	—	4	1	no	—
289	C₄×D₅₉	—	4	1	no	—
290	C₄×D₅₉	—	4	1	no	—
291	C₄×D₅₉	—	4	2	no	—
292	Dic₁₁₈	—	2	2	no	—
293	Dic₁₁₈	—	2	4	no	—
294	Dic₁₁₈	—	4	2	no	—
295	C₂²×C₅₉	—	2	1	no	—
296	C₂²×C₅₉	—	2	1	no	—
297	C₂²×C₅₉	—	2	2	no	—
298	C₂²×C₅₉	—	2	1	no	—
299	C₂²×C₅₉	—	2	2	no	—
300	C₂²×C₅₉	—	2	1	no	—
301	C₂²×C₅₉	—	2	2	no	—
302	C₂²×C₅₉	—	2	1	no	—
303	C₂²×C₅₉	C₂×#41	1	2	yes	—
304	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
305	C₂×D₅₉	—	2	1	no	—
306	C₂×D₅₉	—	2	1	no	—
307	C₂×D₅₉	—	2	1	no	—
308	C₂×D₅₉	—	2	1	no	—
309	C₂×D₅₉	—	2	1	no	—
310	C₂×D₅₉	—	2	1	no	—
311	C₂×D₅₉	—	2	1	no	—
312	C₂×D₅₉	—	4	4	no	—
313	C₂×D₅₉	—	4	4	no	—
314	C₂×D₅₉	C₂×#41	1	2	yes	—
315	C₂×D₅₉	2₋¹⁺⁴	1	2	yes	—
316	C₄×C₅₉	—	2	2	no	—
317	C₄×C₅₉	—	2	1	no	—
318	C₄×C₅₉	—	2	2	no	—
319	C₄×C₅₉	—	2	1	no	—
320	C₄×C₅₉	—	2	1	no	—
321	C₄×C₅₉	—	2	2	no	—
322	C₄×C₅₉	—	2	1	no	—
323	C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
324	Dic₅₉	—	2	2	no	—
325	Dic₅₉	—	2	2	no	—
326	Dic₅₉	—	2	2	no	—
327	Dic₅₉	—	2	1	no	—
328	Dic₅₉	—	2	1	no	—
329	Dic₅₉	—	2	1	no	—
330	Dic₅₉	—	2	1	no	—
331	Dic₅₉	—	2	2	no	—
332	Dic₅₉	C₂×#41	1	2	yes	—
333	#3520	—	59	1	no	maximal, Sylow
334	C₂×C₅₉	—	2	2	no	—
335	C₂×C₅₉	—	4	1	no	—
336	C₂×C₅₉	—	4	2	no	—
337	C₂×C₅₉	C₂²×#41	1	1	yes	characteristic
338	C₂×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
340	D₅₉	—	2	2	no	—
341	D₅₉	—	2	2	no	—
342	D₅₉	—	4	1	no	—
343	#556	—	59	1	no	—
344	#554	—	59	2	no	—
345	#552	—	59	1	no	—
346	#552	—	59	1	no	—
347	#551	—	59	2	no	—
348	#551	—	59	2	no	—
349	D₄×Q₈	—	59	1	no	—
350	#548	—	59	1	no	—
351	#548	D₅₉	1	1	yes	characteristic, complemented
352	#547	—	59	1	no	—
353	#547	—	59	1	no	—
354	#546	—	59	2	no	—
355	#542	—	59	2	no	—
356	#539	—	59	2	no	—
357	#539	—	59	2	no	—
358	#533	—	59	1	no	—
359	#529	—	59	1	no	—
360	#525	—	59	1	no	—
361	#525	—	59	1	no	—
362	C₂×C₂²⋊Q₈	—	59	1	no	—
363	C₂×C₂²⋊Q₈	—	59	1	no	—
364	#520	—	59	2	no	—
365	C₂×C₄×D₄	—	59	1	no	—
366	C₅₉	#3520	1	1	yes	characteristic, complemented, Sylow
367	C₂×#41	—	59	2	no	—
368	C₂×#41	—	59	1	no	—
369	C₂×#41	C₂×D₅₉	1	1	yes	characteristic, complemented
370	C₂²×Q₈	—	59	1	no	—
371	C₂²×Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
372	C₂²×D₄	—	59	1	no	—
373	C₂³×C₄	—	59	1	no	—
374	C₂³×C₄	—	59	1	no	—
375	C₄⋊Q₈	—	59	1	no	—
376	C₄⋊Q₈	—	59	2	no	—
377	C₄⋊Q₈	—	59	1	no	—
378	#126	—	59	2	no	—
379	#126	—	59	2	no	—
380	#126	—	59	2	no	—
381	#126	—	59	2	no	—
382	#126	—	59	2	no	—
383	#125	—	59	2	no	—
384	#125	—	59	2	no	—
385	#125	—	59	2	no	—
386	#125	—	59	1	no	—
387	#124	—	59	2	no	—
388	#124	—	59	2	no	—
389	#124	C₂×D₅₉	1	1	yes	characteristic, complemented
390	#124	C₂×D₅₉	1	2	yes	complemented
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	1	no	—
401	C₂²⋊Q₈	—	59	1	no	—
402	C₂²⋊Q₈	—	59	2	no	—
403	C₂²⋊Q₈	—	59	1	no	—
404	C₂²⋊Q₈	—	59	1	no	—
405	C₂²⋊Q₈	—	59	2	no	—
406	C₂²⋊Q₈	—	59	1	no	—
407	C₂²⋊Q₈	—	59	2	no	—
408	C₂²⋊Q₈	—	59	1	no	—
409	C₂²⋊Q₈	—	59	1	no	—
410	C₂²⋊Q₈	—	59	2	no	—
411	C₂²⋊Q₈	—	59	1	no	—
412	C₂²⋊Q₈	—	59	2	no	—
413	C₂²⋊Q₈	—	59	2	no	—
414	C₂²⋊Q₈	—	59	2	no	—
415	C₂²⋊Q₈	—	59	2	no	—
416	C₂²⋊Q₈	—	59	2	no	—
417	C₂²⋊Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
418	C₂²⋊Q₈	C₂×D₅₉	1	2	yes	complemented
419	#121	—	59	1	no	—
420	#121	—	59	1	no	—
421	#121	—	59	2	no	—
422	#121	—	59	2	no	—
423	#121	C₂×D₅₉	1	2	yes	—
424	#121	C₂×D₅₉	1	1	yes	characteristic, complemented
425	#120	—	59	2	no	—
426	#120	—	59	2	no	—
427	C₄×Q₈	—	59	1	no	—
428	C₄×Q₈	—	59	2	no	—
429	C₄×Q₈	—	59	2	no	—
430	C₄×Q₈	—	59	1	no	—
431	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
432	C₄×D₄	—	59	1	no	—
433	C₄×D₄	—	59	2	no	—
434	C₄×D₄	—	59	1	no	—
435	C₄×D₄	—	59	1	no	—
436	C₄×D₄	—	59	1	no	—
437	C₄×D₄	—	59	2	no	—
438	C₄×D₄	—	59	2	no	—
439	C₄×D₄	—	59	2	no	—
440	C₄×D₄	—	59	1	no	—
441	C₄×D₄	—	59	1	no	—
442	C₄×D₄	—	59	1	no	—
443	C₄×D₄	—	59	2	no	—
444	C₄×D₄	—	59	2	no	—
445	C₄×D₄	—	59	2	no	—
446	C₄×D₄	—	59	1	no	—
447	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
448	C₄×D₄	C₂×D₅₉	1	2	yes	complemented
449	#117	—	59	1	no	—
450	#117	—	59	1	no	—
451	#117	—	59	2	no	—
452	#117	—	59	2	no	—
453	#117	—	59	2	no	—
454	#117	—	59	2	no	—
455	C₂×C₄⋊C₄	—	59	2	no	—
456	C₂×C₄⋊C₄	—	59	2	no	—
457	C₂×C₄⋊C₄	—	59	1	no	—
458	C₂×C₄⋊C₄	—	59	1	no	—
459	C₂×C₄⋊C₄	—	59	2	no	—
460	C₂×C₄⋊C₄	—	59	1	no	—
461	C₂×C₂²⋊C₄	—	59	2	no	—
462	C₂×C₂²⋊C₄	—	59	1	no	—
463	C₂×C₂²⋊C₄	—	59	1	no	—
464	C₂×C₂²⋊C₄	—	59	2	no	—
465	C₂×C₄²	—	59	1	no	—
466	C₂⁴	—	59	1	no	—
467	C₂⁴	—	59	1	no	—
468	#41	—	4	2	no	—
469	#41	—	118	8	no	—
470	#41	—	236	2	no	—
471	C₂×Q₈	—	4	2	no	—
472	C₂×Q₈	—	59	2	no	—
473	C₂×Q₈	—	59	1	no	—
474	C₂×Q₈	—	59	2	no	—
475	C₂×Q₈	—	236	2	no	—
476	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
477	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
478	C₂×Q₈	C₂²×D₅₉	1	2	yes	—
479	C₂×D₄	—	59	1	no	—
480	C₂×D₄	—	59	2	no	—
481	C₂×D₄	—	59	2	no	—
482	C₂×D₄	—	59	1	no	—
483	C₂×D₄	—	59	2	no	—
484	C₂×D₄	—	59	1	no	—
485	C₂×D₄	—	118	4	no	—
486	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₅₉	1	2	yes	—
488	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₅₉	1	2	yes	—
490	C₂²×C₄	—	59	2	no	—
491	C₂²×C₄	—	59	2	no	—
492	C₂²×C₄	—	59	1	no	—
493	C₂²×C₄	—	59	2	no	—
494	C₂²×C₄	—	59	1	no	—
495	C₂²×C₄	—	59	1	no	—
496	C₂²×C₄	—	59	1	no	—
497	C₂²×C₄	—	59	1	no	—
498	C₂²×C₄	—	59	2	no	—
499	C₂²×C₄	—	59	1	no	—
500	C₂²×C₄	—	59	1	no	—
501	C₂²×C₄	—	59	2	no	—
502	C₂²×C₄	—	59	1	no	—
503	C₂²×C₄	—	59	1	no	—
504	C₂²×C₄	—	59	1	no	—
505	C₂²×C₄	—	59	1	no	—
506	C₂²×C₄	—	236	2	no	—
507	C₂²×C₄	—	236	2	no	—
508	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
509	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
511	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
512	C₄⋊C₄	—	59	1	no	—
513	C₄⋊C₄	—	59	2	no	—
514	C₄⋊C₄	—	59	2	no	—
515	C₄⋊C₄	—	59	2	no	—
516	C₄⋊C₄	—	59	1	no	—
517	C₄⋊C₄	—	59	1	no	—
518	C₄⋊C₄	—	59	1	no	—
519	C₄⋊C₄	—	59	1	no	—
520	C₄⋊C₄	—	59	2	no	—
521	C₄⋊C₄	—	59	2	no	—
522	C₄⋊C₄	—	59	2	no	—
523	C₄⋊C₄	—	59	2	no	—
524	C₄⋊C₄	—	59	2	no	—
525	C₄⋊C₄	—	59	2	no	—
526	C₄⋊C₄	—	59	2	no	—
527	C₄⋊C₄	—	59	1	no	—
528	C₄⋊C₄	—	59	2	no	—
529	C₄⋊C₄	—	59	2	no	—
530	C₄⋊C₄	—	59	2	no	—
531	C₄⋊C₄	—	59	2	no	—
532	C₄⋊C₄	—	59	2	no	—
533	C₄⋊C₄	—	59	2	no	—
534	C₄⋊C₄	—	59	2	no	—
535	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
538	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
539	C₂²⋊C₄	—	59	1	no	—
540	C₂²⋊C₄	—	59	1	no	—
541	C₂²⋊C₄	—	59	2	no	—
542	C₂²⋊C₄	—	59	2	no	—
543	C₂²⋊C₄	—	59	2	no	—
544	C₂²⋊C₄	—	59	2	no	—
545	C₂²⋊C₄	—	59	2	no	—
546	C₂²⋊C₄	—	59	2	no	—
547	C₂²⋊C₄	—	59	2	no	—
548	C₂²⋊C₄	—	59	1	no	—
549	C₂²⋊C₄	—	59	2	no	—
550	C₂²⋊C₄	—	59	2	no	—
551	C₂²⋊C₄	—	59	1	no	—
552	C₂²⋊C₄	—	59	1	no	—
553	C₂²⋊C₄	—	59	1	no	—
554	C₂²⋊C₄	—	59	2	no	—
555	C₂²⋊C₄	—	59	2	no	—
556	C₂²⋊C₄	—	59	2	no	—
557	C₂²⋊C₄	—	59	2	no	—
558	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
559	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
564	C₄²	—	59	1	no	—
565	C₄²	—	59	1	no	—
566	C₄²	—	59	1	no	—
567	C₄²	—	59	2	no	—
568	C₄²	—	59	2	no	—
569	C₄²	—	59	2	no	—
570	C₄²	—	59	2	no	—
571	C₄²	C₂²×D₅₉	1	1	yes	characteristic
572	C₄²	C₂²×D₅₉	1	2	yes	—
573	C₂³	—	59	1	no	—
574	C₂³	—	59	1	no	—
575	C₂³	—	59	1	no	—
576	C₂³	—	118	2	no	—
577	C₂³	—	118	2	no	—
578	C₂³	—	118	2	no	—
579	C₂³	—	118	2	no	—
580	C₂³	—	236	1	no	—
581	C₂³	—	236	1	no	—
582	C₂³	C₂³×D₅₉	1	1	yes	characteristic
583	C₂³	C₂³×D₅₉	1	2	yes	—
584	C₂³	C₂³×D₅₉	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	118	4	no	—
589	Q₈	—	118	2	no	—
590	Q₈	—	236	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	59	4	no	—
596	D₄	—	118	2	no	—
597	D₄	—	118	2	no	—
598	D₄	—	118	4	no	—
599	D₄	—	118	4	no	—
600	D₄	—	236	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	59	1	no	—
606	C₂×C₄	—	59	2	no	—
607	C₂×C₄	—	59	1	no	—
608	C₂×C₄	—	59	2	no	—
609	C₂×C₄	—	59	1	no	—
610	C₂×C₄	—	59	1	no	—
611	C₂×C₄	—	59	2	no	—
612	C₂×C₄	—	59	2	no	—
613	C₂×C₄	—	59	1	no	—
614	C₂×C₄	—	118	2	no	—
615	C₂×C₄	—	118	2	no	—
616	C₂×C₄	—	118	4	no	—
617	C₂×C₄	—	118	4	no	—
618	C₂×C₄	—	118	4	no	—
619	C₂×C₄	—	118	2	no	—
620	C₂×C₄	—	118	2	no	—
621	C₂×C₄	—	118	2	no	—
622	C₂×C₄	—	236	1	no	—
623	C₂×C₄	—	236	1	no	—
624	C₂×C₄	—	236	1	no	—
625	C₂×C₄	—	236	1	no	—
626	C₂×C₄	—	236	2	no	—
627	C₂×C₄	—	236	1	no	—
628	C₂×C₄	—	236	1	no	—
629	C₂×C₄	—	236	2	no	—
630	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₅₉	1	2	yes	—
633	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₅₉	1	2	yes	—
635	C₂×C₄	C₂³×D₅₉	1	2	yes	—
636	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	59	2	no	—
647	C₂²	—	59	2	no	—
648	C₂²	—	118	1	no	—
649	C₂²	—	118	1	no	—
650	C₂²	—	118	1	no	—
651	C₂²	—	118	1	no	—
652	C₂²	—	118	1	no	—
653	C₂²	—	118	1	no	—
654	C₂²	—	118	1	no	—
655	C₂²	—	236	4	no	—
656	C₂²	—	236	4	no	—
657	C₂²	#41×D₅₉	1	2	yes	—
658	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	59	2	no	—
667	C₄	—	118	2	no	—
668	C₄	—	118	2	no	—
669	C₄	—	118	1	no	—
670	C₄	—	118	1	no	—
671	C₄	—	118	1	no	—
672	C₄	—	118	2	no	—
673	C₄	—	118	1	no	—
674	C₄	—	118	2	no	—
675	C₄	#14273772	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	4	1	no	—
678	C₂	—	4	2	no	—
679	C₂	—	118	2	no	—
680	C₂	—	118	2	no	—
681	C₂	—	236	1	no	—
682	C₂	C₂×#41×D₅₉	1	1	yes	characteristic
683	C₂	C₂×#14273772	1	1	yes	characteristic
684	C₂	2₋¹⁺⁴×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₉
commutator, socle	C₂²×C₅₉	C₂⁵
Fitting	C₅₉×#548	C₂
hypercenter	#548	D₅₉
hypocenter	C₅₉	#3520
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #16838123	C₂	semidirect
2. #16838106	C₂	semidirect
3. #16838093	C₂	semidirect
4. #16838092	C₂	semidirect
5. #16838082	C₂	semidirect
6. #16838081	C₂	semidirect
7. Q₈×C₂²⋊D₅₉	C₂	semidirect
8. #16838060	C₂	semidirect
9. #16838052	C₂	semidirect
10. #16838051	C₂	semidirect
11. #16838041	C₂	semidirect
12. #16838016	C₂	semidirect
13. #16837998	C₂	semidirect
14. #16837997	C₂	semidirect
15. #16837956	C₂	semidirect
16. #16837931	C₂	semidirect
17. #16837912	C₂	semidirect
18. #16837909	C₂	semidirect
19. C₂×#14273703	C₂	semidirect
20. C₂²⋊Q₈×D₅₉	C₂	semidirect
21. #16837881	C₂	semidirect
22. C₄×D₄×D₅₉	C₂	semidirect
23. C₅₉×#548	C₂	semidirect
25. C₂×#11745687	C₂²	semidirect
26. C₂×Q₈×D₅₉	C₂²	semidirect
30. #14273726	C₂²	semidirect
31. #14273725	C₂²	semidirect
32. #14273725	C₂²	semidirect
33. #14273722	C₂²	semidirect
34. #14273721	C₂²	semidirect
35. #14273720	C₂²	semidirect
36. #14273720	C₂²	semidirect
37. #14273720	C₂²	semidirect
38. #14273719	C₂²	semidirect
39. #14273717	C₂²	semidirect
40. #14273717	C₂²	semidirect
41. #14273717	C₂²	semidirect
43. #14273713	C₂²	semidirect
45. #14273710	C₂²	semidirect
47. #14273709	C₂²	semidirect
48. #14273709	C₂²	semidirect
50. #14273708	C₂²	semidirect
51. #14273708	C₂²	semidirect
52. #14273708	C₂²	semidirect
54. #14273706	C₂²	semidirect
55. #14273706	C₂²	semidirect
56. #14273706	C₂²	semidirect
59. #14273704	C₂²	semidirect
60. #14273704	C₂²	semidirect
61. #14273704	C₂²	semidirect
65. #14273703	C₂²	semidirect
66. #14273703	C₂²	semidirect
67. #14273703	C₂²	semidirect
68. #14273703	C₂²	semidirect
69. #14273703	C₂²	semidirect
73. #14273698	C₂²	semidirect
76. Q₈×Dic₅₉	C₂²	semidirect
77. C₄×Dic₁₁₈	C₂²	semidirect
78. C₄×Dic₁₁₈	C₂²	semidirect
79. #14273692	C₂²	semidirect
82. D₄×Dic₅₉	C₂²	semidirect
83. D₄×Dic₅₉	C₂²	semidirect
89. C₄×C₂²⋊D₅₉	C₂²	semidirect
94. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
95. #14273686	C₂²	semidirect
96. #14273685	C₂²	semidirect
98. #14273684	C₂²	semidirect
99. #14273683	C₂²	semidirect
100. #14273683	C₂²	semidirect
101. C₂×C₄⋊Dic₅₉	C₂²	semidirect
102. C₂×Dic₅₉⋊C₄	C₂²	semidirect
103. C₂×Dic₅₉⋊C₄	C₂²	semidirect
105. C₄⋊C₄×D₅₉	C₂²	semidirect
106. C₄⋊C₄×D₅₉	C₂²	semidirect
112. C₂×#41×C₅₉	C₂²	semidirect
113. C₂²×Q₈×C₅₉	C₂²	semidirect
114. #124×C₅₉	C₂²	semidirect
115. #124×C₅₉	C₂²	semidirect
116. C₂²⋊Q₈×C₅₉	C₂²	semidirect
117. C₂²⋊Q₈×C₅₉	C₂²	semidirect
119. #121×C₅₉	C₂²	semidirect
120. C₄×Q₈×C₅₉	C₂²	semidirect
122. C₄×D₄×C₅₉	C₂²	semidirect
265. C₂²⋊D₅₉	#41	semidirect
351. #548	D₅₉	semidirect
366. C₅₉	#3520	semidirect
369. C₂×#41	C₂×D₅₉	semidirect
371. C₂²×Q₈	C₂×D₅₉	semidirect
389. #124	C₂×D₅₉	semidirect
390. #124	C₂×D₅₉	semidirect
417. C₂²⋊Q₈	C₂×D₅₉	semidirect
418. C₂²⋊Q₈	C₂×D₅₉	semidirect
424. #121	C₂×D₅₉	semidirect
431. C₄×Q₈	C₂×D₅₉	semidirect
448. C₄×D₄	C₂×D₅₉	semidirect