Subgroups — #21438692

Order 7552.

912 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉⋊#564	C₂	1	2	yes	maximal, complemented
2	#16838151	C₂	1	2	yes	maximal, complemented
3	#16838130	C₂	1	1	yes	maximal, characteristic, complemented
4	#16838113	C₂	1	1	yes	maximal, characteristic, complemented
5	#16838112	C₂	1	1	yes	maximal, characteristic, complemented
6	#16838093	C₂	1	1	yes	maximal, characteristic, complemented
7	#16838093	C₂	1	2	yes	maximal, complemented
8	#16838093	C₂	1	1	yes	maximal, characteristic, complemented
9	#16838090	C₂	1	1	yes	maximal, characteristic, complemented
10	#16838090	C₂	1	1	yes	maximal, characteristic, complemented
11	#16838084	C₂	1	2	yes	maximal, complemented
12	#16838032	C₂	1	1	yes	maximal, characteristic, complemented
13	#16838029	C₂	1	2	yes	maximal, complemented
14	#16838029	C₂	1	1	yes	maximal, characteristic, complemented
15	#16838011	C₂	1	2	yes	maximal, complemented
16	#16838010	C₂	1	1	yes	maximal, characteristic, complemented
17	#16838010	C₂	1	2	yes	maximal, complemented
18	#16838010	C₂	1	1	yes	maximal, characteristic, complemented
19	#16838000	C₂	1	2	yes	maximal
20	#16837956	C₂	1	1	yes	maximal, characteristic, complemented
21	#16837939	C₂	1	1	yes	maximal, characteristic
22	#125×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
24	#14273727	C₂²	1	1	yes	characteristic
25	#14273726	C₂²	1	1	yes	characteristic
26	#14273726	C₂²	1	2	yes	—
27	#14273725	C₂²	1	2	yes	—
28	#14273725	C₂²	1	1	yes	characteristic
29	#14273725	C₂²	1	2	yes	—
30	#14273722	C₂²	1	2	yes	—
31	#14273722	C₂²	1	2	yes	—
32	#14273722	C₂²	1	1	yes	characteristic
33	#14273722	C₂²	1	1	yes	characteristic
34	#14273722	C₂²	1	2	yes	—
35	#14273722	C₂²	1	2	yes	—
36	#14273721	C₂²	1	2	yes	—
37	#14273721	C₂²	1	2	yes	—
38	#14273721	C₂²	1	2	yes	—
39	#14273721	C₂²	1	2	yes	—
40	#14273719	C₂²	1	2	yes	—
41	#14273719	C₂²	1	2	yes	—
42	#14273719	C₂²	1	1	yes	characteristic
43	#14273719	C₂²	1	2	yes	—
44	#14273719	C₂²	1	1	yes	characteristic
45	#14273718	C₂²	1	1	yes	characteristic
46	#14273718	C₂²	1	2	yes	—
47	#14273718	C₂²	1	2	yes	—
48	#14273718	C₂²	1	2	yes	—
49	#14273718	C₂²	1	1	yes	characteristic
50	#14273718	C₂²	1	1	yes	characteristic
51	#14273717	C₂²	1	2	yes	—
52	#14273717	C₂²	1	2	yes	—
53	#14273717	C₂²	1	2	yes	—
54	#14273717	C₂²	1	2	yes	—
55	#14273717	C₂²	1	2	yes	—
56	#14273717	C₂²	1	2	yes	—
57	#14273717	C₂²	1	2	yes	—
58	#14273717	C₂²	1	2	yes	—
59	#14273717	C₂²	1	2	yes	—
60	#14273717	C₂²	1	2	yes	—
61	#14273717	C₂²	1	2	yes	—
62	#14273716	C₂²	1	1	yes	characteristic
63	#14273712	C₂²	1	2	yes	—
64	#14273712	C₂²	1	2	yes	—
65	#14273712	C₂²	1	1	yes	characteristic
66	#14273712	C₂²	1	1	yes	characteristic
67	#14273712	C₂²	1	2	yes	—
68	#14273712	C₂²	1	2	yes	—
69	#14273707	C₂²	1	1	yes	characteristic
70	#14273707	C₂²	1	2	yes	—
71	#14273707	C₂²	1	1	yes	characteristic
72	#14273707	C₂²	1	1	yes	characteristic
73	#14273705	C₂²	1	2	yes	—
74	#14273705	C₂²	1	2	yes	—
75	#14273705	C₂²	1	2	yes	—
76	#14273705	C₂²	1	2	yes	—
77	#14273705	C₂²	1	2	yes	—
78	#14273703	C₂²	1	2	yes	—
79	#14273703	C₂²	1	2	yes	—
80	#14273703	C₂²	1	1	yes	characteristic
81	#14273703	C₂²	1	1	yes	characteristic
82	#14273703	C₂²	1	1	yes	characteristic
83	#14273703	C₂²	1	1	yes	characteristic
84	#14273703	C₂²	1	2	yes	—
85	#14273702	C₂²	1	1	yes	characteristic
86	C₄×Dic₁₁₈	C₂²	1	2	yes	—
87	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
89	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
90	#14273692	C₂²	1	2	yes	—
91	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
92	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
93	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
94	C₄×D₂₃₆	C₂²	1	2	yes	—
95	#14273689	C₂²	1	2	yes	—
96	#14273685	C₂²	1	2	yes	—
97	#14273685	C₂²	1	2	yes	—
98	#14273685	C₂²	1	1	yes	characteristic
99	#14273685	C₂²	1	1	yes	characteristic
100	#14273684	C₂²	1	1	yes	characteristic
101	#14273684	C₂²	1	1	yes	characteristic
102	#14273684	C₂²	1	2	yes	—
103	#14273684	C₂²	1	2	yes	—
104	#14273684	C₂²	1	2	yes	—
105	C₄⋊C₄×D₅₉	C₂²	1	2	yes	—
106	C₄⋊C₄×D₅₉	C₂²	1	2	yes	—
107	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₅₉	C₂²	1	1	yes	characteristic
111	C₄²×D₅₉	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
113	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
114	#125×C₅₉	C₂²	1	2	yes	—
115	#125×C₅₉	C₂²	1	1	yes	characteristic
116	#125×C₅₉	C₂²	1	2	yes	—
117	#125×C₅₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₅₉	C₂²	1	2	yes	—
121	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
122	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₅₉	C₂³	1	2	yes	—
125	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
126	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
127	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
128	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
129	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₅₉	C₂³	1	2	yes	—
132	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₅₉	C₂³	1	2	yes	—
136	C₂×C₄×D₅₉	C₂³	1	2	yes	—
137	C₂×C₄×D₅₉	C₂³	1	2	yes	—
138	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
139	C₂×Dic₁₁₈	C₂³	1	2	yes	—
140	C₂×Dic₁₁₈	C₂³	1	2	yes	—
141	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
148	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
151	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
152	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
153	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
154	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
155	C₄²×C₅₉	C₂³	1	1	yes	characteristic
156	C₄²×C₅₉	C₂³	1	2	yes	—
157	C₄²×C₅₉	C₂³	1	1	yes	characteristic
158	C₄²×C₅₉	C₂³	1	2	yes	—
159	C₄²×C₅₉	C₂³	1	1	yes	characteristic
160	C₄²×C₅₉	C₂³	1	2	yes	—
161	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
162	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
164	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
166	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
167	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
168	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
170	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
171	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
172	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
180	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₅₉	C₂³	1	2	yes	—
183	C₄⋊Dic₅₉	C₂³	1	2	yes	—
184	C₄⋊Dic₅₉	C₂³	1	2	yes	—
185	C₄⋊Dic₅₉	C₂³	1	2	yes	—
186	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₅₉	C₂³	1	2	yes	—
188	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₅₉	C₂³	1	2	yes	—
191	Dic₅₉⋊C₄	C₂³	1	2	yes	—
192	Dic₅₉⋊C₄	C₂³	1	2	yes	—
193	Dic₅₉⋊C₄	C₂³	1	2	yes	—
194	Dic₅₉⋊C₄	C₂³	1	2	yes	—
195	Dic₅₉⋊C₄	C₂³	1	2	yes	—
196	Dic₅₉⋊C₄	C₂³	1	2	yes	—
197	Dic₅₉⋊C₄	C₂³	1	2	yes	—
198	Dic₅₉⋊C₄	C₂³	1	2	yes	—
199	Dic₅₉⋊C₄	C₂³	1	2	yes	—
200	Dic₅₉⋊C₄	C₂³	1	2	yes	—
201	Dic₅₉⋊C₄	C₂³	1	2	yes	—
202	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
203	Dic₅₉⋊C₄	C₂³	1	2	yes	—
204	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₅₉⋊C₄	C₂³	1	2	yes	—
208	Dic₅₉⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
215	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
216	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
217	C₄×Dic₅₉	C₂³	1	2	yes	—
218	C₄×Dic₅₉	C₂³	1	2	yes	—
219	C₄×Dic₅₉	C₂³	1	2	yes	—
220	C₄×Dic₅₉	C₂³	1	2	yes	—
221	C₄×Dic₅₉	C₂³	1	2	yes	—
222	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
223	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
224	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
225	Q₈×C₅₉	—	2	2	no	—
226	Q₈×C₅₉	—	4	1	no	—
227	Q₈×C₅₉	—	4	2	no	—
228	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
233	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
234	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
235	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
238	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₅₉	C₂⁴	1	2	yes	—
240	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
241	C₂×Dic₅₉	C₂⁴	1	2	yes	—
242	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₅₉	C₂⁴	1	2	yes	—
247	C₂×Dic₅₉	C₂⁴	1	2	yes	—
248	D₂₃₆	—	2	2	no	—
249	D₂₃₆	—	2	2	no	—
250	D₂₃₆	—	4	1	no	—
251	C₄×D₅₉	—	2	2	no	—
252	C₄×D₅₉	—	2	4	no	—
253	C₄×D₅₉	—	2	2	no	—
254	C₄×D₅₉	—	2	2	no	—
255	C₄×D₅₉	—	2	2	no	—
256	C₄×D₅₉	—	4	2	no	—
257	C₄×D₅₉	—	4	1	no	—
258	C₄×D₅₉	—	4	2	no	—
259	C₄×D₅₉	—	4	2	no	—
260	Dic₁₁₈	—	2	2	no	—
261	Dic₁₁₈	—	4	2	no	—
262	Dic₁₁₈	—	4	2	no	—
263	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
264	C₂×D₅₉	—	2	1	no	—
265	C₂×D₅₉	—	2	1	no	—
266	C₂×D₅₉	—	2	1	no	—
267	C₂×D₅₉	—	2	1	no	—
268	C₂×D₅₉	—	2	1	no	—
269	C₂×D₅₉	—	2	1	no	—
270	C₂×D₅₉	—	2	1	no	—
271	C₂×D₅₉	—	2	1	no	—
272	C₂×D₅₉	2₋¹⁺⁴	1	2	yes	—
273	C₄×C₅₉	—	2	1	no	—
274	C₄×C₅₉	—	2	2	no	—
275	C₄×C₅₉	—	2	1	no	—
276	C₄×C₅₉	—	2	1	no	—
277	C₄×C₅₉	—	2	2	no	—
278	C₄×C₅₉	—	2	1	no	—
279	C₄×C₅₉	—	2	2	no	—
280	C₄×C₅₉	—	2	2	no	—
281	C₄×C₅₉	—	2	1	no	—
282	C₄×C₅₉	—	2	1	no	—
283	C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
284	Dic₅₉	—	2	2	no	—
285	Dic₅₉	—	2	1	no	—
286	Dic₅₉	—	2	2	no	—
287	Dic₅₉	—	2	1	no	—
288	Dic₅₉	—	2	1	no	—
289	Dic₅₉	—	2	1	no	—
290	Dic₅₉	—	2	1	no	—
291	Dic₅₉	—	2	2	no	—
292	Dic₅₉	—	2	2	no	—
293	#3563	—	59	1	no	maximal, Sylow
294	C₂×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
296	C₂×C₅₉	#585	1	1	yes	characteristic
297	D₅₉	—	2	2	no	—
298	D₅₉	—	4	1	no	—
299	D₅₉	—	4	1	no	—
300	#564	—	59	2	no	—
301	#563	—	59	2	no	—
302	#557	—	59	1	no	—
303	#557	D₅₉	1	1	yes	characteristic, complemented
304	#554	—	59	1	no	—
305	#554	—	59	1	no	—
306	#552	—	59	2	no	—
307	#552	—	59	1	no	—
308	#552	—	59	1	no	—
309	#552	—	59	2	no	—
310	#552	—	59	1	no	—
311	#552	—	59	1	no	—
312	#544	—	59	2	no	—
313	#544	—	59	1	no	—
314	#544	—	59	1	no	—
315	#541	—	59	2	no	—
316	#541	—	59	1	no	—
317	#541	—	59	1	no	—
318	#541	—	59	2	no	—
319	#539	—	59	2	no	—
320	#533	—	59	1	no	—
321	#529	—	59	1	no	—
322	C₂×#125	—	59	1	no	—
323	C₅₉	#3563	1	1	yes	characteristic, complemented, Sylow
324	C₄⋊Q₈	—	59	1	no	—
325	C₄⋊Q₈	—	59	2	no	—
326	C₄⋊Q₈	—	59	2	no	—
327	C₄⋊Q₈	—	59	1	no	—
328	C₄⋊Q₈	—	59	2	no	—
329	C₄⋊Q₈	—	59	1	no	—
330	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
331	C₄⋊Q₈	C₂×D₅₉	1	2	yes	—
332	#126	—	59	1	no	—
333	#126	—	59	1	no	—
334	#126	—	59	2	no	—
335	#126	—	59	2	no	—
336	#126	—	59	2	no	—
337	#126	—	59	2	no	—
338	#126	—	59	2	no	—
339	#126	—	59	2	no	—
340	#126	—	59	2	no	—
341	#126	—	59	2	no	—
342	#125	—	59	2	no	—
343	#125	—	59	1	no	—
344	#125	—	59	1	no	—
345	#125	—	59	2	no	—
346	#125	—	59	1	no	—
347	#125	—	59	2	no	—
348	#125	—	59	2	no	—
349	#125	—	59	2	no	—
350	#125	—	59	2	no	—
351	#125	—	59	2	no	—
352	#125	—	59	2	no	—
353	#125	—	59	2	no	—
354	#125	—	59	2	no	—
355	#125	—	59	2	no	—
356	#125	—	59	2	no	—
357	#125	—	59	2	no	—
358	#125	—	59	2	no	—
359	#125	—	59	1	no	—
360	#125	—	59	2	no	—
361	#125	—	59	2	no	—
362	#125	—	59	2	no	—
363	#125	—	59	1	no	—
364	#125	C₂×D₅₉	1	1	yes	characteristic
365	#125	C₂×D₅₉	1	2	yes	—
366	#125	C₂×D₅₉	1	2	yes	—
367	#125	C₂×D₅₉	1	1	yes	characteristic
368	#124	—	59	1	no	—
369	#123	—	59	1	no	—
370	#123	—	59	1	no	—
371	#123	—	59	2	no	—
372	#123	—	59	2	no	—
373	#123	—	59	2	no	—
374	#123	—	59	2	no	—
375	C₂²⋊Q₈	—	59	1	no	—
376	C₂²⋊Q₈	—	59	1	no	—
377	C₂²⋊Q₈	—	59	1	no	—
378	C₂²⋊Q₈	—	59	1	no	—
379	C₂²⋊Q₈	—	59	2	no	—
380	C₂²⋊Q₈	—	59	2	no	—
381	C₂²⋊Q₈	—	59	2	no	—
382	C₂²⋊Q₈	—	59	2	no	—
383	C₂²⋊Q₈	—	59	1	no	—
384	C₂²⋊Q₈	—	59	2	no	—
385	C₂²⋊Q₈	—	59	2	no	—
386	C₂²⋊Q₈	—	59	1	no	—
387	C₂²⋊Q₈	—	59	1	no	—
388	C₂²⋊Q₈	—	59	2	no	—
389	C₂²⋊Q₈	—	59	2	no	—
390	C₂²⋊Q₈	—	59	2	no	—
391	#121	—	59	1	no	—
392	C₄×Q₈	—	59	2	no	—
393	C₄×Q₈	—	59	2	no	—
394	C₄×Q₈	—	59	1	no	—
395	C₄×Q₈	—	59	1	no	—
396	C₄×Q₈	—	59	1	no	—
397	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
398	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
399	C₄×Q₈	C₂×D₅₉	1	2	yes	—
400	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
401	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
402	C₄×D₄	—	59	2	no	—
403	C₄×D₄	—	59	1	no	—
404	C₄×D₄	—	59	1	no	—
405	C₄×D₄	—	59	1	no	—
406	C₄×D₄	—	59	2	no	—
407	#117	—	59	2	no	—
408	#117	—	59	1	no	—
409	#117	—	59	1	no	—
410	#117	—	59	2	no	—
411	#117	—	59	1	no	—
412	#117	—	59	1	no	—
413	#117	—	59	2	no	—
414	#117	—	59	2	no	—
415	#117	—	59	2	no	—
416	C₂×C₄⋊C₄	—	59	2	no	—
417	C₂×C₄⋊C₄	—	59	1	no	—
418	C₂×C₄⋊C₄	—	59	2	no	—
419	C₂×C₄⋊C₄	—	59	1	no	—
420	C₂×C₄⋊C₄	—	59	1	no	—
421	C₂×C₄⋊C₄	—	59	1	no	—
422	C₂×C₄²	—	59	1	no	—
423	C₂×Q₈	—	59	1	no	—
424	C₂×Q₈	—	59	2	no	—
425	C₂×Q₈	—	59	2	no	—
426	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
427	C₂×Q₈	C₂²×D₅₉	1	2	yes	—
428	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
429	C₂×D₄	—	59	1	no	—
430	C₂×D₄	—	59	1	no	—
431	C₂×D₄	—	59	1	no	—
432	C₂²×C₄	—	59	1	no	—
433	C₂²×C₄	—	59	1	no	—
434	C₂²×C₄	—	59	2	no	—
435	C₂²×C₄	—	59	1	no	—
436	C₂²×C₄	—	59	1	no	—
437	C₂²×C₄	—	59	1	no	—
438	C₂²×C₄	—	59	2	no	—
439	C₂²×C₄	—	59	2	no	—
440	C₂²×C₄	—	59	2	no	—
441	C₄⋊C₄	—	59	1	no	—
442	C₄⋊C₄	—	59	1	no	—
443	C₄⋊C₄	—	59	1	no	—
444	C₄⋊C₄	—	59	2	no	—
445	C₄⋊C₄	—	59	2	no	—
446	C₄⋊C₄	—	59	2	no	—
447	C₄⋊C₄	—	59	2	no	—
448	C₄⋊C₄	—	59	2	no	—
449	C₄⋊C₄	—	59	2	no	—
450	C₄⋊C₄	—	59	2	no	—
451	C₄⋊C₄	—	59	2	no	—
452	C₄⋊C₄	—	59	2	no	—
453	C₄⋊C₄	—	59	2	no	—
454	C₄⋊C₄	—	59	2	no	—
455	C₄⋊C₄	—	59	2	no	—
456	C₄⋊C₄	—	59	2	no	—
457	C₄⋊C₄	—	59	2	no	—
458	C₄⋊C₄	—	59	2	no	—
459	C₄⋊C₄	—	59	1	no	—
460	C₄⋊C₄	—	59	1	no	—
461	C₄⋊C₄	—	59	2	no	—
462	C₄⋊C₄	—	59	1	no	—
463	C₄⋊C₄	—	59	1	no	—
464	C₄⋊C₄	—	59	2	no	—
465	C₄⋊C₄	—	59	1	no	—
466	C₄⋊C₄	—	59	2	no	—
467	C₄⋊C₄	—	59	1	no	—
468	C₄⋊C₄	—	59	1	no	—
469	C₄⋊C₄	—	59	2	no	—
470	C₄⋊C₄	—	59	2	no	—
471	C₄⋊C₄	—	59	2	no	—
472	C₄⋊C₄	—	59	2	no	—
473	C₄⋊C₄	—	59	2	no	—
474	C₄⋊C₄	—	59	2	no	—
475	C₄⋊C₄	—	59	2	no	—
476	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
480	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
481	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
482	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
483	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
487	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
488	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
489	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
490	C₂²⋊C₄	—	59	2	no	—
491	C₂²⋊C₄	—	59	1	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	2	no	—
500	C₂²⋊C₄	—	59	1	no	—
501	C₂²⋊C₄	—	59	1	no	—
502	C₂²⋊C₄	—	59	2	no	—
503	C₂²⋊C₄	—	59	2	no	—
504	C₂²⋊C₄	—	59	2	no	—
505	C₂²⋊C₄	—	59	2	no	—
506	C₂²⋊C₄	—	59	1	no	—
507	C₂²⋊C₄	—	59	1	no	—
508	C₄²	—	59	1	no	—
509	C₄²	—	59	1	no	—
510	C₄²	—	59	1	no	—
511	C₄²	—	59	2	no	—
512	C₄²	—	59	2	no	—
513	C₄²	—	59	2	no	—
514	C₄²	—	59	2	no	—
515	C₄²	—	59	2	no	—
516	C₄²	C₂²×D₅₉	1	1	yes	characteristic
517	C₄²	C₂²×D₅₉	1	2	yes	—
518	C₄²	C₂²×D₅₉	1	1	yes	characteristic
519	C₄²	C₂²×D₅₉	1	1	yes	characteristic
520	C₄²	C₂²×D₅₉	1	2	yes	—
521	C₄²	C₂²×D₅₉	1	2	yes	—
522	C₂³	—	59	1	no	—
523	C₂³	—	59	1	no	—
524	C₂³	—	59	1	no	—
525	Q₈	—	2	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	118	2	no	—
529	Q₈	—	236	2	no	—
530	Q₈	—	236	2	no	—
531	D₄	—	118	2	no	—
532	D₄	—	118	2	no	—
533	D₄	—	236	1	no	—
534	C₂×C₄	—	59	2	no	—
535	C₂×C₄	—	59	1	no	—
536	C₂×C₄	—	59	2	no	—
537	C₂×C₄	—	59	1	no	—
538	C₂×C₄	—	59	1	no	—
539	C₂×C₄	—	59	1	no	—
540	C₂×C₄	—	59	1	no	—
541	C₂×C₄	—	59	2	no	—
542	C₂×C₄	—	59	2	no	—
543	C₂×C₄	—	118	2	no	—
544	C₂×C₄	—	118	4	no	—
545	C₂×C₄	—	118	2	no	—
546	C₂×C₄	—	118	2	no	—
547	C₂×C₄	—	118	2	no	—
548	C₂×C₄	—	236	2	no	—
549	C₂×C₄	—	236	2	no	—
550	C₂×C₄	—	236	1	no	—
551	C₂×C₄	—	236	2	no	—
552	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
553	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₅₉	1	2	yes	—
556	C₂×C₄	C₂³×D₅₉	1	2	yes	—
557	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₅₉	1	2	yes	—
559	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
560	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
561	C₂×C₄	C₂³×D₅₉	1	2	yes	—
562	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
563	C₂²	—	59	2	no	—
564	C₂²	—	118	1	no	—
565	C₂²	—	118	1	no	—
566	C₂²	—	118	1	no	—
567	C₂²	—	118	1	no	—
568	C₂²	—	118	1	no	—
569	C₂²	—	118	1	no	—
570	C₂²	—	118	1	no	—
571	C₂²	—	118	1	no	—
572	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	118	1	no	—
584	C₄	—	118	2	no	—
585	C₄	—	118	1	no	—
586	C₄	—	118	1	no	—
587	C₄	—	118	1	no	—
588	C₄	—	118	2	no	—
589	C₄	—	118	2	no	—
590	C₄	—	118	1	no	—
591	C₄	—	118	2	no	—
592	C₄	#14273775	1	2	yes	—
593	C₂	—	118	2	no	—
594	C₂	—	236	1	no	—
595	C₂	—	236	1	no	—
596	C₂	2₋¹⁺⁴×D₅₉	1	1	yes	characteristic
597	C₂	C₂×#14273775	1	1	yes	characteristic
598	C₂	#16838238	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₉
commutator, socle	C₂²×C₅₉	C₂⁵
Fitting	C₅₉×#557	C₂
hypercenter	#557	D₅₉
hypocenter	C₅₉	#3563
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. C₅₉⋊#564	C₂	semidirect
2. #16838151	C₂	semidirect
3. #16838130	C₂	semidirect
4. #16838113	C₂	semidirect
5. #16838112	C₂	semidirect
6. #16838093	C₂	semidirect
7. #16838093	C₂	semidirect
8. #16838093	C₂	semidirect
9. #16838090	C₂	semidirect
10. #16838090	C₂	semidirect
11. #16838084	C₂	semidirect
12. #16838032	C₂	semidirect
13. #16838029	C₂	semidirect
14. #16838029	C₂	semidirect
15. #16838011	C₂	semidirect
16. #16838010	C₂	semidirect
17. #16838010	C₂	semidirect
18. #16838010	C₂	semidirect
20. #16837956	C₂	semidirect
22. #125×D₅₉	C₂	semidirect
23. C₅₉×#557	C₂	semidirect
303. #557	D₅₉	semidirect
323. C₅₉	#3563	semidirect