Subgroups — #21438390

Order 7552.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16838156	C₂	1	2	yes	maximal, complemented
2	#16838148	C₂	1	2	yes	maximal, complemented
3	#16838126	C₂	1	1	yes	maximal, characteristic, complemented
4	#16838110	C₂	1	2	yes	maximal, complemented
5	#16838100	C₂	1	1	yes	maximal, characteristic, complemented
6	#16838098	C₂	1	2	yes	maximal, complemented
7	#16838087	C₂	1	1	yes	maximal, characteristic, complemented
8	#16838065	C₂	1	1	yes	maximal, characteristic, complemented
9	#16838064	C₂	1	1	yes	maximal, characteristic, complemented
10	#16838061	C₂	1	1	yes	maximal, characteristic, complemented
11	#16838054	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838026	C₂	1	1	yes	maximal, characteristic, complemented
13	#16838025	C₂	1	2	yes	maximal, complemented
14	#16838010	C₂	1	1	yes	maximal, characteristic, complemented
15	#16838000	C₂	1	2	yes	maximal, complemented
16	#16837992	C₂	1	2	yes	maximal, complemented
17	#16837985	C₂	1	2	yes	maximal, complemented
18	#16837983	C₂	1	1	yes	maximal, characteristic, complemented
19	#16837975	C₂	1	1	yes	maximal, characteristic, complemented
20	#16837915	C₂	1	1	yes	maximal, characteristic, complemented
21	#16837911	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14273707	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11745689	C₂²	1	1	yes	characteristic
25	C₂×#11745685	C₂²	1	1	yes	characteristic
26	C₂×#11745685	C₂²	1	1	yes	characteristic, complemented
27	C₂²×Dic₁₁₈	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₅₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₅₉	C₂²	1	1	yes	characteristic
30	#14273726	C₂²	1	2	yes	complemented
31	#14273726	C₂²	1	2	yes	complemented
32	#14273725	C₂²	1	1	yes	characteristic, complemented
33	#14273722	C₂²	1	2	yes	—
34	#14273722	C₂²	1	2	yes	—
35	#14273722	C₂²	1	2	yes	—
36	#14273722	C₂²	1	2	yes	complemented
37	#14273722	C₂²	1	2	yes	complemented
38	#14273722	C₂²	1	2	yes	complemented
39	#14273721	C₂²	1	2	yes	—
40	#14273719	C₂²	1	2	yes	complemented
41	#14273718	C₂²	1	1	yes	characteristic, complemented
42	#14273717	C₂²	1	2	yes	complemented
43	#14273717	C₂²	1	2	yes	complemented
44	#14273716	C₂²	1	2	yes	—
45	#14273716	C₂²	1	2	yes	—
46	#14273715	C₂²	1	2	yes	—
47	#14273715	C₂²	1	1	yes	characteristic, complemented
48	#14273713	C₂²	1	2	yes	—
49	#14273713	C₂²	1	2	yes	complemented
50	#14273712	C₂²	1	2	yes	—
51	#14273712	C₂²	1	2	yes	—
52	#14273712	C₂²	1	1	yes	characteristic
53	#14273712	C₂²	1	2	yes	—
54	#14273712	C₂²	1	2	yes	—
55	#14273712	C₂²	1	2	yes	complemented
56	#14273710	C₂²	1	2	yes	—
57	#14273709	C₂²	1	1	yes	characteristic
58	#14273709	C₂²	1	2	yes	complemented
59	#14273709	C₂²	1	2	yes	complemented
60	#14273707	C₂²	1	2	yes	—
61	#14273707	C₂²	1	1	yes	characteristic
62	#14273707	C₂²	1	1	yes	characteristic
63	#14273707	C₂²	1	2	yes	—
64	#14273707	C₂²	1	1	yes	characteristic
65	#14273707	C₂²	1	1	yes	characteristic
66	#14273707	C₂²	1	2	yes	complemented
67	#14273707	C₂²	1	1	yes	characteristic, complemented
68	#14273707	C₂²	1	2	yes	complemented
69	#14273706	C₂²	1	1	yes	characteristic, complemented
70	#14273705	C₂²	1	1	yes	characteristic
71	#14273705	C₂²	1	2	yes	complemented
72	#14273705	C₂²	1	2	yes	complemented
73	#14273704	C₂²	1	1	yes	characteristic
74	#14273704	C₂²	1	2	yes	—
75	#14273703	C₂²	1	1	yes	characteristic
76	#14273703	C₂²	1	2	yes	complemented
77	#14273702	C₂²	1	2	yes	—
78	#14273702	C₂²	1	1	yes	characteristic
79	#14273702	C₂²	1	2	yes	—
80	#14273702	C₂²	1	1	yes	characteristic, complemented
81	#14273701	C₂²	1	1	yes	characteristic
82	#14273701	C₂²	1	2	yes	—
83	#14273701	C₂²	1	2	yes	—
84	#14273701	C₂²	1	2	yes	complemented
85	#14273700	C₂²	1	1	yes	characteristic
86	#14273700	C₂²	1	2	yes	—
87	#14273699	C₂²	1	1	yes	characteristic
88	#14273699	C₂²	1	2	yes	—
89	#14273697	C₂²	1	1	yes	characteristic
90	#14273697	C₂²	1	2	yes	—
91	#14273695	C₂²	1	1	yes	characteristic
92	Q₈×Dic₅₉	C₂²	1	2	yes	complemented
93	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic, complemented
94	#14273692	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
96	C₄×D₂₃₆	C₂²	1	2	yes	complemented
97	#14273689	C₂²	1	2	yes	—
98	#14273689	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	—
102	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	—
103	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	—
104	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	—
105	#14273686	C₂²	1	2	yes	complemented
106	#14273685	C₂²	1	1	yes	characteristic
107	#14273685	C₂²	1	1	yes	characteristic, complemented
108	#14273684	C₂²	1	1	yes	characteristic
109	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
110	C₄⋊C₄×D₅₉	C₂²	1	2	yes	complemented
111	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
113	#125×C₅₉	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
115	C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₅₉	C₂²	1	2	yes	—
121	C₂×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₅₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₅₉	C₂³	1	2	yes	—
126	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
130	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
137	C₂²×Dic₅₉	C₂³	1	2	yes	—
138	C₂²×Dic₅₉	C₂³	1	1	yes	characteristic
139	#11745689	—	4	2	no	—
140	Q₈×D₅₉	—	4	2	no	—
141	#11745685	—	4	2	no	—
142	#11745685	—	4	2	no	—
143	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
144	C₂×D₂₃₆	C₂³	1	2	yes	—
145	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
146	C₂×D₂₃₆	C₂³	1	2	yes	—
147	C₂×D₂₃₆	C₂³	1	2	yes	—
148	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₅₉	—	4	2	no	—
150	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅₉	C₂³	1	2	yes	—
154	C₂×C₄×D₅₉	C₂³	1	2	yes	—
155	C₂×C₄×D₅₉	C₂³	1	2	yes	—
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×Dic₁₁₈	—	4	2	no	—
160	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
161	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
162	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
163	C₂×Dic₁₁₈	C₂³	1	2	yes	—
164	C₂×Dic₁₁₈	C₂³	1	2	yes	—
165	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
167	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
169	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
176	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
178	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
179	C₄²×C₅₉	C₂³	1	2	yes	—
180	C₄²×C₅₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
184	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
195	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₅₉	C₂³	1	2	yes	—
210	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅₉	C₂³	1	2	yes	—
212	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₅₉⋊C₄	C₂³	1	2	yes	—
214	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
225	C₄×Dic₅₉	C₂³	1	2	yes	—
226	C₄×Dic₅₉	C₂³	1	2	yes	—
227	C₄×Dic₅₉	C₂³	1	2	yes	—
228	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₅₉	—	2	2	no	—
231	C₂²×D₅₉	—	4	1	no	—
232	C₂²×D₅₉	—	4	1	no	—
233	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₅₉	C₂⁴	1	2	yes	—
237	Q₈×C₅₉	—	2	2	no	—
238	Q₈×C₅₉	—	4	2	no	—
239	D₄×C₅₉	—	2	2	no	—
240	C₂×C₄×C₅₉	—	2	2	no	—
241	C₂×C₄×C₅₉	—	2	2	no	—
242	C₂×C₄×C₅₉	—	4	2	no	—
243	C₂×C₄×C₅₉	—	4	2	no	—
244	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
253	C₂²⋊D₅₉	—	2	4	no	—
254	C₂²⋊D₅₉	—	2	2	no	—
255	C₂²⋊D₅₉	—	4	2	no	—
256	C₂²⋊D₅₉	—	4	1	no	—
257	C₂²⋊D₅₉	—	4	1	no	—
258	C₂²⋊D₅₉	—	4	1	no	—
259	C₂×Dic₅₉	—	4	2	no	—
260	C₂×Dic₅₉	—	4	1	no	—
261	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₅₉	C₂⁴	1	2	yes	—
263	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₅₉	C₂⁴	1	2	yes	—
267	C₂×Dic₅₉	C₂⁴	1	2	yes	—
268	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
269	D₂₃₆	—	2	2	no	—
270	D₂₃₆	—	4	2	no	—
271	D₂₃₆	—	4	2	no	—
272	D₂₃₆	—	4	1	no	—
273	D₂₃₆	—	4	1	no	—
274	D₂₃₆	—	4	2	no	—
275	C₄×D₅₉	—	2	2	no	—
276	C₄×D₅₉	—	2	2	no	—
277	C₄×D₅₉	—	2	2	no	—
278	C₄×D₅₉	—	4	1	no	—
279	C₄×D₅₉	—	4	1	no	—
280	C₄×D₅₉	—	4	2	no	—
281	C₄×D₅₉	—	4	2	no	—
282	C₄×D₅₉	—	4	2	no	—
283	C₄×D₅₉	—	4	2	no	—
284	Dic₁₁₈	—	2	2	no	—
285	Dic₁₁₈	—	2	2	no	—
286	Dic₁₁₈	—	4	2	no	—
287	Dic₁₁₈	—	4	1	no	—
288	Dic₁₁₈	—	4	2	no	—
289	C₂²×C₅₉	—	2	1	no	—
290	C₂²×C₅₉	—	2	1	no	—
291	C₂²×C₅₉	—	2	1	no	—
292	C₂²×C₅₉	—	2	1	no	—
293	C₂²×C₅₉	—	2	1	no	—
294	C₂²×C₅₉	2₋¹⁺⁴	1	2	yes	—
295	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
296	C₂×D₅₉	—	2	1	no	—
297	C₂×D₅₉	—	2	1	no	—
298	C₂×D₅₉	—	2	1	no	—
299	C₂×D₅₉	—	2	2	no	—
300	C₂×D₅₉	—	2	1	no	—
301	C₂×D₅₉	—	2	2	no	—
302	C₂×D₅₉	—	2	1	no	—
303	C₂×D₅₉	—	2	1	no	—
304	C₂×D₅₉	—	2	2	no	—
305	C₂×D₅₉	—	2	1	no	—
306	C₂×D₅₉	—	2	1	no	—
307	C₂×D₅₉	—	2	1	no	—
308	C₂×D₅₉	—	4	4	no	—
309	C₄×C₅₉	—	2	1	no	—
310	C₄×C₅₉	—	2	1	no	—
311	C₄×C₅₉	—	2	2	no	—
312	C₄×C₅₉	—	2	1	no	—
313	C₄×C₅₉	—	2	2	no	—
314	C₄×C₅₉	—	2	2	no	—
315	C₄×C₅₉	—	2	2	no	—
316	C₄×C₅₉	—	2	1	no	—
317	C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
318	Dic₅₉	—	2	2	no	—
319	Dic₅₉	—	2	2	no	—
320	Dic₅₉	—	2	1	no	—
321	Dic₅₉	—	2	1	no	—
322	Dic₅₉	—	2	1	no	—
323	Dic₅₉	—	2	1	no	—
324	Dic₅₉	—	2	2	no	—
325	Dic₅₉	—	2	1	no	—
326	#3541	—	59	1	no	maximal, Sylow
327	C₂×C₅₉	—	2	2	no	—
328	C₂×C₅₉	—	4	1	no	—
329	C₂×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂×C₅₉	#585	1	1	yes	characteristic
332	D₅₉	—	4	1	no	—
333	D₅₉	—	4	2	no	—
334	D₅₉	—	4	1	no	—
335	D₅₉	—	4	1	no	—
336	#563	—	59	2	no	—
337	#562	—	59	2	no	—
338	#556	—	59	1	no	—
339	#554	—	59	2	no	—
340	#554	D₅₉	1	1	yes	characteristic, complemented
341	#553	—	59	2	no	—
342	#553	—	59	1	no	—
343	#552	—	59	1	no	—
344	D₄×Q₈	—	59	1	no	—
345	#548	—	59	1	no	—
346	#548	—	59	1	no	—
347	#547	—	59	1	no	—
348	#542	—	59	1	no	—
349	#542	—	59	2	no	—
350	#541	—	59	1	no	—
351	#539	—	59	2	no	—
352	#538	—	59	2	no	—
353	#538	—	59	2	no	—
354	#537	—	59	1	no	—
355	#536	—	59	1	no	—
356	#525	—	59	1	no	—
357	#525	—	59	1	no	—
358	C₂×C₂²⋊Q₈	—	59	1	no	—
359	C₅₉	#3541	1	1	yes	characteristic, complemented, Sylow
360	C₂×#41	—	59	1	no	—
361	C₂×#41	—	59	1	no	—
362	C₂×#41	—	59	1	no	—
363	C₂²×Q₈	—	59	1	no	—
364	C₂²×Q₈	—	59	1	no	—
365	C₂³×C₄	—	59	1	no	—
366	C₄⋊Q₈	—	59	1	no	—
367	C₄⋊Q₈	—	59	2	no	—
368	C₄⋊Q₈	—	59	2	no	—
369	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
370	#126	—	59	2	no	—
371	#126	—	59	2	no	—
372	#126	—	59	2	no	—
373	#126	—	59	2	no	—
374	#126	—	59	2	no	—
375	#126	—	59	2	no	—
376	#126	—	59	2	no	—
377	#125	—	59	2	no	—
378	#125	—	59	1	no	—
379	#125	—	59	2	no	—
380	#125	—	59	2	no	—
381	#125	C₂×D₅₉	1	2	yes	complemented
382	#124	—	59	2	no	—
383	#124	—	59	2	no	—
384	#124	—	59	2	no	—
385	#124	—	59	2	no	—
386	#124	—	59	2	no	—
387	#124	—	59	1	no	—
388	#123	—	59	2	no	—
389	#123	—	59	1	no	—
390	#123	—	59	2	no	—
391	#123	—	59	2	no	—
392	#123	—	59	2	no	—
393	#123	—	59	2	no	—
394	#123	—	59	2	no	—
395	#123	—	59	1	no	—
396	#123	—	59	2	no	—
397	#123	—	59	2	no	—
398	C₂²⋊Q₈	—	59	1	no	—
399	C₂²⋊Q₈	—	59	2	no	—
400	C₂²⋊Q₈	—	59	1	no	—
401	C₂²⋊Q₈	—	59	1	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	1	no	—
408	C₂²⋊Q₈	—	59	1	no	—
409	C₂²⋊Q₈	—	59	2	no	—
410	C₂²⋊Q₈	—	59	2	no	—
411	C₂²⋊Q₈	—	59	2	no	—
412	C₂²⋊Q₈	—	59	2	no	—
413	C₂²⋊Q₈	—	59	1	no	—
414	C₂²⋊Q₈	—	59	2	no	—
415	C₂²⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
416	C₂²⋊Q₈	C₂×D₅₉	1	2	yes	—
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	2	no	—
421	#121	—	59	1	no	—
422	#121	—	59	2	no	—
423	#121	—	59	2	no	—
424	#121	—	59	2	no	—
425	#121	—	59	1	no	—
426	#121	—	59	2	no	—
427	#121	—	59	1	no	—
428	#121	—	59	2	no	—
429	#121	—	59	1	no	—
430	#121	—	59	2	no	—
431	#120	—	59	1	no	—
432	#120	—	59	2	no	—
433	#120	—	59	1	no	—
434	C₄×Q₈	—	59	2	no	—
435	C₄×Q₈	—	59	1	no	—
436	C₄×Q₈	—	59	1	no	—
437	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
438	C₄×D₄	—	59	1	no	—
439	C₄×D₄	—	59	1	no	—
440	C₄×D₄	—	59	2	no	—
441	C₄×D₄	—	59	2	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	—	59	2	no	—
448	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
449	C₄×D₄	C₂×D₅₉	1	2	yes	—
450	#117	—	59	2	no	—
451	#117	—	59	1	no	—
452	#117	—	59	1	no	—
453	#117	—	59	1	no	—
454	C₂×C₄⋊C₄	—	59	2	no	—
455	C₂×C₄⋊C₄	—	59	2	no	—
456	C₂×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic, complemented
458	C₂×C₂²⋊C₄	—	59	2	no	—
459	C₂⁴	—	59	1	no	—
460	#41	—	236	2	no	—
461	#41	—	236	2	no	—
462	#41	—	236	2	no	—
463	C₂×Q₈	—	59	1	no	—
464	C₂×Q₈	—	59	1	no	—
465	C₂×Q₈	—	59	2	no	—
466	C₂×Q₈	—	59	1	no	—
467	C₂×Q₈	—	59	2	no	—
468	C₂×Q₈	—	236	2	no	—
469	C₂×Q₈	—	236	2	no	—
470	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₅₉	1	2	yes	—
472	C₂×D₄	—	59	1	no	—
473	C₂×D₄	—	59	2	no	—
474	C₂×D₄	—	59	1	no	—
475	C₂×D₄	—	59	1	no	—
476	C₂×D₄	—	59	1	no	—
477	C₂×D₄	—	59	2	no	—
478	C₂×D₄	—	59	1	no	—
479	C₂×D₄	—	59	2	no	—
480	C₂×D₄	—	59	1	no	—
481	C₂×D₄	—	59	2	no	—
482	C₂×D₄	—	59	1	no	—
483	C₂×D₄	—	59	2	no	—
484	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
485	C₂²×C₄	—	59	2	no	—
486	C₂²×C₄	—	59	1	no	—
487	C₂²×C₄	—	59	1	no	—
488	C₂²×C₄	—	59	1	no	—
489	C₂²×C₄	—	59	1	no	—
490	C₂²×C₄	—	59	2	no	—
491	C₂²×C₄	—	59	2	no	—
492	C₂²×C₄	—	59	2	no	—
493	C₂²×C₄	—	59	2	no	—
494	C₂²×C₄	—	59	1	no	—
495	C₂²×C₄	—	59	1	no	—
496	C₂²×C₄	—	236	2	no	—
497	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
500	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
501	C₄⋊C₄	—	59	1	no	—
502	C₄⋊C₄	—	59	2	no	—
503	C₄⋊C₄	—	59	2	no	—
504	C₄⋊C₄	—	59	2	no	—
505	C₄⋊C₄	—	59	2	no	—
506	C₄⋊C₄	—	59	2	no	—
507	C₄⋊C₄	—	59	1	no	—
508	C₄⋊C₄	—	59	1	no	—
509	C₄⋊C₄	—	59	1	no	—
510	C₄⋊C₄	—	59	2	no	—
511	C₄⋊C₄	—	59	1	no	—
512	C₄⋊C₄	—	59	2	no	—
513	C₄⋊C₄	—	59	2	no	—
514	C₄⋊C₄	—	59	1	no	—
515	C₄⋊C₄	—	59	2	no	—
516	C₄⋊C₄	—	59	2	no	—
517	C₄⋊C₄	—	59	2	no	—
518	C₄⋊C₄	—	59	2	no	—
519	C₄⋊C₄	—	59	2	no	—
520	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
524	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
526	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
529	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
530	C₂²⋊C₄	—	59	1	no	—
531	C₂²⋊C₄	—	59	2	no	—
532	C₂²⋊C₄	—	59	1	no	—
533	C₂²⋊C₄	—	59	2	no	—
534	C₂²⋊C₄	—	59	2	no	—
535	C₂²⋊C₄	—	59	2	no	—
536	C₂²⋊C₄	—	59	2	no	—
537	C₂²⋊C₄	—	59	1	no	—
538	C₂²⋊C₄	—	59	2	no	—
539	C₂²⋊C₄	—	59	1	no	—
540	C₂²⋊C₄	—	59	2	no	—
541	C₂²⋊C₄	—	59	1	no	—
542	C₂²⋊C₄	—	59	1	no	—
543	C₂²⋊C₄	—	59	2	no	—
544	C₂²⋊C₄	—	59	1	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	2	no	—
552	C₂²⋊C₄	—	59	2	no	—
553	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
557	C₄²	—	59	2	no	—
558	C₄²	—	59	1	no	—
559	C₄²	—	59	2	no	—
560	C₄²	—	59	2	no	—
561	C₄²	—	59	2	no	—
562	C₄²	C₂²×D₅₉	1	1	yes	characteristic
563	C₄²	C₂²×D₅₉	1	2	yes	—
564	C₂³	—	59	1	no	—
565	C₂³	—	59	1	no	—
566	C₂³	—	59	1	no	—
567	C₂³	—	59	2	no	—
568	C₂³	—	118	2	no	—
569	C₂³	—	236	1	no	—
570	C₂³	—	236	1	no	—
571	C₂³	C₂³×D₅₉	1	1	yes	characteristic
572	C₂³	C₂³×D₅₉	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	4	2	no	—
575	Q₈	—	118	2	no	—
576	Q₈	—	118	2	no	—
577	Q₈	—	236	2	no	—
578	Q₈	—	236	2	no	—
579	Q₈	—	236	1	no	—
580	D₄	—	2	2	no	—
581	D₄	—	118	2	no	—
582	D₄	—	118	4	no	—
583	D₄	—	118	2	no	—
584	D₄	—	236	2	no	—
585	D₄	—	236	2	no	—
586	D₄	—	236	1	no	—
587	D₄	—	236	1	no	—
588	D₄	—	236	2	no	—
589	D₄	—	236	1	no	—
590	D₄	—	236	1	no	—
591	D₄	—	236	1	no	—
592	D₄	—	236	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	59	2	no	—
598	C₂×C₄	—	59	1	no	—
599	C₂×C₄	—	59	1	no	—
600	C₂×C₄	—	59	1	no	—
601	C₂×C₄	—	59	2	no	—
602	C₂×C₄	—	59	1	no	—
603	C₂×C₄	—	59	2	no	—
604	C₂×C₄	—	59	1	no	—
605	C₂×C₄	—	118	2	no	—
606	C₂×C₄	—	118	2	no	—
607	C₂×C₄	—	118	2	no	—
608	C₂×C₄	—	236	2	no	—
609	C₂×C₄	—	236	1	no	—
610	C₂×C₄	—	236	1	no	—
611	C₂×C₄	—	236	2	no	—
612	C₂×C₄	—	236	2	no	—
613	C₂×C₄	—	236	2	no	—
614	C₂×C₄	—	236	1	no	—
615	C₂×C₄	—	236	2	no	—
616	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₅₉	1	2	yes	—
618	C₂×C₄	C₂³×D₅₉	1	2	yes	—
619	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₅₉	1	2	yes	—
621	C₂×C₄	C₂³×D₅₉	1	2	yes	—
622	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	118	1	no	—
631	C₂²	—	118	1	no	—
632	C₂²	—	118	1	no	—
633	C₂²	—	118	2	no	—
634	C₂²	—	118	1	no	—
635	C₂²	—	118	2	no	—
636	C₂²	—	118	1	no	—
637	C₂²	—	118	1	no	—
638	C₂²	—	118	2	no	—
639	C₂²	—	118	1	no	—
640	C₂²	—	118	1	no	—
641	C₂²	—	118	1	no	—
642	C₂²	—	236	4	no	—
643	C₂²	#14273775	1	2	yes	—
644	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	118	1	no	—
654	C₄	—	118	1	no	—
655	C₄	—	118	1	no	—
656	C₄	—	118	2	no	—
657	C₄	—	118	2	no	—
658	C₄	—	118	2	no	—
659	C₄	—	118	1	no	—
660	C₄	—	118	1	no	—
661	C₄	#14273773	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	236	1	no	—
665	C₂	—	236	1	no	—
666	C₂	—	236	1	no	—
667	C₂	—	236	2	no	—
668	C₂	C₂×#14273773	1	1	yes	characteristic
669	C₂	C₂×#14273775	1	1	yes	characteristic
670	C₂	#16838237	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₉
commutator, socle	C₂²×C₅₉	C₂⁵
Fitting	C₅₉×#554	C₂
hypercenter	#554	D₅₉
hypocenter	C₅₉	#3541
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #16838156	C₂	semidirect
2. #16838148	C₂	semidirect
3. #16838126	C₂	semidirect
4. #16838110	C₂	semidirect
5. #16838100	C₂	semidirect
6. #16838098	C₂	semidirect
7. #16838087	C₂	semidirect
8. #16838065	C₂	semidirect
9. #16838064	C₂	semidirect
10. #16838061	C₂	semidirect
11. #16838054	C₂	semidirect
12. #16838026	C₂	semidirect
13. #16838025	C₂	semidirect
14. #16838010	C₂	semidirect
15. #16838000	C₂	semidirect
16. #16837992	C₂	semidirect
17. #16837985	C₂	semidirect
18. #16837983	C₂	semidirect
19. #16837975	C₂	semidirect
20. #16837915	C₂	semidirect
21. #16837911	C₂	semidirect
22. C₂×#14273707	C₂	semidirect
23. C₅₉×#554	C₂	semidirect
26. C₂×#11745685	C₂²	semidirect
28. C₂×Q₈×D₅₉	C₂²	semidirect
30. #14273726	C₂²	semidirect
31. #14273726	C₂²	semidirect
32. #14273725	C₂²	semidirect
36. #14273722	C₂²	semidirect
37. #14273722	C₂²	semidirect
38. #14273722	C₂²	semidirect
40. #14273719	C₂²	semidirect
41. #14273718	C₂²	semidirect
42. #14273717	C₂²	semidirect
43. #14273717	C₂²	semidirect
47. #14273715	C₂²	semidirect
49. #14273713	C₂²	semidirect
55. #14273712	C₂²	semidirect
58. #14273709	C₂²	semidirect
59. #14273709	C₂²	semidirect
66. #14273707	C₂²	semidirect
67. #14273707	C₂²	semidirect
68. #14273707	C₂²	semidirect
69. #14273706	C₂²	semidirect
71. #14273705	C₂²	semidirect
72. #14273705	C₂²	semidirect
76. #14273703	C₂²	semidirect
80. #14273702	C₂²	semidirect
84. #14273701	C₂²	semidirect
92. Q₈×Dic₅₉	C₂²	semidirect
93. C₄×Dic₁₁₈	C₂²	semidirect
94. #14273692	C₂²	semidirect
96. C₄×D₂₃₆	C₂²	semidirect
98. #14273689	C₂²	semidirect
105. #14273686	C₂²	semidirect
107. #14273685	C₂²	semidirect
110. C₄⋊C₄×D₅₉	C₂²	semidirect
112. C₄⋊Q₈×C₅₉	C₂²	semidirect
113. #125×C₅₉	C₂²	semidirect
116. C₂²⋊Q₈×C₅₉	C₂²	semidirect
117. C₂²⋊Q₈×C₅₉	C₂²	semidirect
118. C₄×Q₈×C₅₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₅₉	C₂²	semidirect
340. #554	D₅₉	semidirect
359. C₅₉	#3541	semidirect
369. C₄⋊Q₈	C₂×D₅₉	semidirect
381. #125	C₂×D₅₉	semidirect
417. C₂²⋊Q₈	C₂×D₅₉	semidirect
418. C₂²⋊Q₈	C₂×D₅₉	semidirect
437. C₄×Q₈	C₂×D₅₉	semidirect
457. C₂×C₄⋊C₄	C₂×D₅₉	semidirect