Subgroups — #28610757

Order 15104.

720 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433880	C₂	1	1	yes	maximal, characteristic
2	#21433040	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432662	C₂	1	1	yes	maximal, characteristic
4	#21425071	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424870	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424844	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424843	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424695	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424694	C₂	1	1	yes	maximal, characteristic, complemented
10	#21424373	C₂	1	1	yes	maximal, characteristic
11	#21424371	C₂	1	1	yes	maximal, characteristic
12	C₄×Dic₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#21423934	C₂	1	1	yes	maximal, characteristic
14	#104×Dic₅₉	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1764	C₂	1	1	yes	maximal, characteristic
16	C₂×#14273734	C₂²	1	1	yes	characteristic
17	#16837955	C₂²	1	1	yes	characteristic
18	#41×Dic₅₉	C₂²	1	1	yes	characteristic
19	#16837711	C₄	1	1	yes	characteristic, complemented
20	#16837707	C₄	1	1	yes	characteristic, complemented
21	#16837704	C₄	1	1	yes	characteristic, complemented
22	#16837700	C₄	1	1	yes	characteristic, complemented
23	#16837695	C₄	1	1	yes	characteristic, complemented
24	#16837690	C₄	1	1	yes	characteristic, complemented
25	#16837685	C₄	1	1	yes	characteristic, complemented
26	#16837680	C₄	1	1	yes	characteristic, complemented
27	#16837532	—	2	1	no	—
28	#16837530	—	2	1	no	—
29	#16837530	—	2	1	no	—
30	C₈×Dic₁₁₈	—	2	1	no	—
31	C₂×#14273663	C₂²	1	1	yes	characteristic
32	C₂×#14273662	C₂²	1	1	yes	characteristic
33	#16837440	C₂²	1	1	yes	characteristic
34	#16837438	C₂²	1	1	yes	characteristic
35	#16837430	—	2	1	no	—
36	#16837430	C₂²	1	1	yes	characteristic
37	#16837429	C₂²	1	1	yes	characteristic
38	#16837428	—	2	1	no	—
39	#16837428	C₂²	1	1	yes	characteristic
40	#16837428	C₂²	1	1	yes	characteristic
41	#16837425	—	2	1	no	—
42	#16837425	C₂²	1	1	yes	characteristic
43	C₂×Dic₅₉⋊C₈	—	2	1	no	—
44	C₂×Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×#14273654	C₂²	1	1	yes	characteristic
47	#16837398	C₂²	1	1	yes	characteristic
48	#16837360	C₂²	1	1	yes	characteristic
49	M₁₆×Dic₅₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
51	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
52	#16837166	C₂²	1	1	yes	characteristic
53	#16837163	C₂²	1	1	yes	characteristic
54	#16837163	C₂²	1	1	yes	characteristic
55	#16837162	C₂²	1	1	yes	characteristic
56	#16837162	C₂²	1	1	yes	characteristic
57	#16837161	C₂²	1	1	yes	characteristic
58	#16837156	C₂²	1	1	yes	characteristic
59	#16837156	C₂²	1	1	yes	characteristic
60	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
61	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
62	C₅₉×#416	C₂²	1	1	yes	characteristic
63	C₅₉×#405	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
65	C₅₉×#341	C₂²	1	1	yes	characteristic
66	C₅₉×#339	C₂²	1	1	yes	characteristic
67	#14273734	—	2	2	no	—
68	#14273734	—	4	1	no	—
69	C₂×#11745664	—	2	1	no	—
70	C₂×#11745664	C₂³	1	1	yes	characteristic
71	C₂×#11745664	C₂³	1	1	yes	characteristic
72	C₂²×C₅₉⋊C₈	—	2	1	no	—
73	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
75	#14273726	C₂×C₄	1	1	yes	characteristic
76	#14273726	C₂×C₄	1	1	yes	characteristic
77	#14273718	C₂×C₄	1	1	yes	characteristic
78	#14273718	C₂×C₄	1	1	yes	characteristic
79	#14273704	—	2	1	no	—
80	#14273704	—	2	1	no	—
81	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
82	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₁₈	—	2	1	no	—
84	C₄×Dic₁₁₈	—	2	1	no	—
85	D₄×Dic₅₉	—	2	1	no	—
86	D₄×Dic₅₉	—	2	1	no	—
87	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
88	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
89	#14273686	—	2	1	no	—
90	#14273686	C₂³	1	1	yes	characteristic
91	#14273686	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₅₉	—	2	1	no	—
93	C₂×C₄×Dic₅₉	—	2	1	no	—
94	C₂×C₄×Dic₅₉	—	2	1	no	—
95	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
97	#14273663	—	4	1	no	—
98	#14273662	—	4	1	no	—
99	#14273661	C₂×C₄	1	1	yes	characteristic
100	#14273661	C₂×C₄	1	1	yes	characteristic
101	#14273660	C₂×C₄	1	1	yes	characteristic
102	#14273660	C₂×C₄	1	1	yes	characteristic
103	#14273659	C₂×C₄	1	1	yes	characteristic
104	#14273659	C₂×C₄	1	1	yes	characteristic
105	#14273658	C₂×C₄	1	1	yes	characteristic
106	#14273658	C₂×C₄	1	1	yes	characteristic
107	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
108	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
109	Dic₅₉⋊C₈	—	2	1	no	—
110	Dic₅₉⋊C₈	—	2	1	no	—
111	Dic₅₉⋊C₈	—	2	1	no	—
112	Dic₅₉⋊C₈	—	2	1	no	—
113	Dic₅₉⋊C₈	—	2	1	no	—
114	Dic₅₉⋊C₈	—	2	1	no	—
115	Dic₅₉⋊C₈	—	2	1	no	—
116	Dic₅₉⋊C₈	—	2	1	no	—
117	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
118	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
119	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
120	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
121	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
122	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
123	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
124	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
125	#14273654	—	2	2	no	—
126	#14273651	C₂×C₄	1	1	yes	characteristic
127	#14273651	C₂×C₄	1	1	yes	characteristic
128	#14273648	C₂×C₄	1	1	yes	characteristic
129	#14273648	C₂×C₄	1	1	yes	characteristic
130	#14273637	—	2	1	no	—
131	#14273637	—	2	1	no	—
132	C₄×C₅₉⋊C₈	—	4	1	no	—
133	C₈×Dic₅₉	—	2	1	no	—
134	C₈×Dic₅₉	—	2	1	no	—
135	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
136	#131×C₅₉	—	2	2	no	—
137	#131×C₅₉	—	4	1	no	—
138	C₂×M₁₆×C₅₉	—	2	1	no	—
139	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₅₉	—	2	1	no	—
142	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	#117×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
146	#104×C₅₉	Q₈	1	4	yes	complemented
147	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
148	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
149	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
150	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
151	#97×C₅₉	—	2	1	no	—
152	C₄×C₈×C₅₉	—	2	1	no	—
153	C₄×C₈×C₅₉	—	4	1	no	—
154	#41×C₅₉	—	2	1	no	—
155	#41×C₅₉	—	2	1	no	—
156	#41×C₅₉	C₂×Q₈	1	2	yes	—
157	#41×C₅₉	#41	1	2	yes	—
158	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₅₉	—	2	1	no	—
160	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅₉	—	2	1	no	—
162	C₂²×C₄×C₅₉	—	2	1	no	—
163	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
164	C₂²×Dic₅₉	—	2	1	no	—
165	C₂²×Dic₅₉	—	2	1	no	—
166	C₂²×Dic₅₉	—	2	1	no	—
167	C₂²×Dic₅₉	#41	1	1	yes	characteristic
168	C₂²×Dic₅₉	#41	1	1	yes	characteristic
169	C₂×Dic₁₁₈	—	2	1	no	—
170	C₂×Dic₁₁₈	—	2	1	no	—
171	M₁₆×C₅₉	—	2	1	no	—
172	M₁₆×C₅₉	—	2	1	no	—
173	M₁₆×C₅₉	—	2	1	no	—
174	M₁₆×C₅₉	—	4	2	no	—
175	M₁₆×C₅₉	C₂×Q₈	1	2	yes	—
176	C₂×C₈×C₅₉	—	2	1	no	—
177	C₂×C₈×C₅₉	—	2	1	no	—
178	C₂×C₈×C₅₉	—	2	1	no	—
179	C₂×C₈×C₅₉	—	2	1	no	—
180	C₂×C₈×C₅₉	—	2	1	no	—
181	C₂×C₈×C₅₉	—	2	1	no	—
182	C₂×C₈×C₅₉	—	4	2	no	—
183	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₅₉	—	2	1	no	—
190	C₄²×C₅₉	—	2	1	no	—
191	C₄²×C₅₉	—	2	1	no	—
192	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
193	C₂²⋊Dic₅₉	—	2	1	no	—
194	C₂²⋊Dic₅₉	—	2	1	no	—
195	C₂²⋊Dic₅₉	—	2	1	no	—
196	C₂²⋊Dic₅₉	—	2	1	no	—
197	C₄⋊Dic₅₉	—	2	1	no	—
198	C₄⋊Dic₅₉	—	2	1	no	—
199	C₄⋊Dic₅₉	—	2	1	no	—
200	C₄⋊Dic₅₉	—	2	1	no	—
201	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
205	Dic₅₉⋊C₄	—	2	1	no	—
206	Dic₅₉⋊C₄	—	2	1	no	—
207	Dic₅₉⋊C₄	—	2	1	no	—
208	Dic₅₉⋊C₄	—	2	1	no	—
209	C₄×Dic₅₉	—	2	4	no	—
210	C₄×Dic₅₉	—	2	1	no	—
211	C₄×Dic₅₉	—	2	1	no	—
212	C₄×Dic₅₉	—	2	1	no	—
213	C₄×Dic₅₉	—	2	1	no	—
214	C₄×Dic₅₉	—	2	1	no	—
215	C₄×Dic₅₉	—	2	1	no	—
216	C₄×Dic₅₉	—	4	2	no	—
217	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
218	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
219	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
220	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
221	#11745664	—	2	1	no	—
222	#11745664	—	2	1	no	—
223	#11745664	—	2	1	no	—
224	#11745664	—	2	1	no	—
225	#11745664	—	4	2	no	—
226	C₂×C₅₉⋊C₈	—	2	1	no	—
227	C₂×C₅₉⋊C₈	—	2	1	no	—
228	C₂×C₅₉⋊C₈	—	2	1	no	—
229	C₂×C₅₉⋊C₈	—	2	1	no	—
230	C₂×C₅₉⋊C₈	—	2	1	no	—
231	C₂×C₅₉⋊C₈	—	2	1	no	—
232	C₂×C₅₉⋊C₈	—	4	2	no	—
233	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
234	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
236	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
237	C₂³×C₅₉	—	2	1	no	—
238	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
239	Q₈×C₅₉	—	2	1	no	—
240	Q₈×C₅₉	C₄×Q₈	1	2	yes	—
241	D₄×C₅₉	—	2	2	no	—
242	D₄×C₅₉	—	2	2	no	—
243	D₄×C₅₉	—	2	1	no	—
244	D₄×C₅₉	C₄×Q₈	1	2	yes	—
245	C₂×C₄×C₅₉	—	2	2	no	—
246	C₂×C₄×C₅₉	—	2	2	no	—
247	C₂×C₄×C₅₉	—	2	1	no	—
248	C₂×C₄×C₅₉	—	2	2	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	2	no	—
251	C₂×C₄×C₅₉	—	2	1	no	—
252	C₂×C₄×C₅₉	—	2	1	no	—
253	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
256	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
259	C₂×Dic₅₉	—	2	2	no	—
260	C₂×Dic₅₉	—	2	2	no	—
261	C₂×Dic₅₉	—	2	1	no	—
262	C₂×Dic₅₉	—	2	1	no	—
263	C₂×Dic₅₉	—	2	1	no	—
264	C₂×Dic₅₉	—	2	1	no	—
265	C₂×Dic₅₉	—	4	1	no	—
266	C₂×Dic₅₉	—	4	1	no	—
267	C₂×Dic₅₉	—	4	1	no	—
268	C₂×Dic₅₉	—	4	2	no	—
269	C₂×Dic₅₉	—	8	1	no	—
270	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
271	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
272	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
273	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
274	Dic₁₁₈	—	4	2	no	—
275	Dic₁₁₈	—	8	1	no	—
276	C₈×C₅₉	—	2	1	no	—
277	C₈×C₅₉	—	2	1	no	—
278	C₈×C₅₉	—	2	1	no	—
279	C₈×C₅₉	—	2	1	no	—
280	C₈×C₅₉	—	2	2	no	—
281	C₈×C₅₉	—	4	1	no	—
282	C₅₉⋊C₈	—	2	1	no	—
283	C₅₉⋊C₈	—	2	1	no	—
284	C₅₉⋊C₈	—	2	1	no	—
285	C₅₉⋊C₈	—	2	1	no	—
286	C₅₉⋊C₈	—	4	1	no	—
287	C₅₉⋊C₈	—	4	1	no	—
288	#22982	—	59	1	no	maximal, Sylow
289	C₂²×C₅₉	—	2	1	no	—
290	C₂²×C₅₉	—	2	1	no	—
291	C₂²×C₅₉	—	2	2	no	—
292	C₂²×C₅₉	—	4	1	no	—
293	C₂²×C₅₉	—	4	1	no	—
294	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×C₅₉	#552	1	1	yes	characteristic
296	C₂²×C₅₉	#554	1	1	yes	characteristic
297	C₄×C₅₉	—	2	4	no	—
298	C₄×C₅₉	—	2	2	no	—
299	C₄×C₅₉	—	4	1	no	—
300	C₄×C₅₉	—	4	1	no	—
301	C₄×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
302	C₄×C₅₉	#520	1	1	yes	characteristic
303	C₄×C₅₉	#546	1	1	yes	characteristic
304	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
305	Dic₅₉	—	2	1	no	—
306	Dic₅₉	—	2	1	no	—
307	Dic₅₉	—	2	1	no	—
308	Dic₅₉	—	4	2	no	—
309	Dic₅₉	—	4	1	no	—
310	Dic₅₉	—	4	1	no	—
311	Dic₅₉	—	4	1	no	—
312	Dic₅₉	—	4	1	no	—
313	Dic₅₉	#443	1	2	yes	—
314	#3076	—	59	1	no	—
315	#2962	—	59	1	no	—
316	#2906	—	59	1	no	—
317	#1994	—	59	1	no	—
318	#1950	—	59	1	no	—
319	#1945	—	59	1	no	—
320	#1945	—	59	1	no	—
321	#1922	—	59	1	no	—
322	#1922	—	59	1	no	—
323	#1866	—	59	1	no	—
324	#1866	—	59	1	no	—
325	C₄×C₄⋊C₈	—	59	1	no	—
326	#1764	—	59	1	no	—
327	#1764	D₅₉	1	1	yes	characteristic
328	C₄×#104	—	59	1	no	—
329	C₂×C₅₉	—	2	1	no	—
330	C₂×C₅₉	—	2	1	no	—
331	C₂×C₅₉	—	4	2	no	—
332	C₂×C₅₉	#2360	1	1	yes	characteristic
333	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
334	C₂×C₅₉	#2956	1	1	yes	characteristic
335	C₂×#131	—	59	1	no	—
336	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
337	#533	—	59	1	no	—
338	C₄×#41	—	59	1	no	—
339	#479	—	59	1	no	—
340	#479	—	59	1	no	—
341	#478	—	59	1	no	—
342	#478	—	59	1	no	—
343	#477	—	59	1	no	—
344	#476	—	59	1	no	—
345	#475	—	59	1	no	—
346	#474	—	59	1	no	—
347	#446	—	118	1	no	—
348	#446	—	118	1	no	—
349	#446	—	118	1	no	—
350	C₈×Q₈	—	118	1	no	—
351	C₂×#108	—	59	1	no	—
352	C₂×#108	—	59	1	no	—
353	#427	—	59	1	no	—
354	#427	—	59	1	no	—
355	#424	—	59	1	no	—
356	#424	—	59	1	no	—
357	#424	—	59	1	no	—
358	#424	—	59	1	no	—
359	#424	—	118	1	no	—
360	#424	—	118	1	no	—
361	#423	—	59	1	no	—
362	#423	—	118	1	no	—
363	C₂×C₄⋊C₈	—	59	1	no	—
364	C₂×C₄⋊C₈	—	59	1	no	—
365	C₂×C₄⋊C₈	—	118	1	no	—
366	C₂×#104	—	59	1	no	—
367	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
368	#416	—	59	1	no	—
369	#416	C₂×D₅₉	1	1	yes	characteristic
370	#405	—	59	1	no	—
371	#405	C₂×D₅₉	1	1	yes	characteristic
372	C₄×M₁₆	—	59	1	no	—
373	C₂×C₄×C₈	—	59	1	no	—
374	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
375	C₄³	—	59	1	no	—
376	#341	—	59	1	no	—
377	#341	C₂×D₅₉	1	1	yes	characteristic
378	#339	—	59	1	no	—
379	#339	—	59	1	no	—
380	#339	—	59	1	no	—
381	#339	—	59	1	no	—
382	#339	—	59	1	no	—
383	#339	C₂×D₅₉	1	1	yes	characteristic
384	#336	—	59	1	no	—
385	#336	—	59	1	no	—
386	C₅₉	#22982	1	1	yes	characteristic, complemented, Sylow
387	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
388	#131	—	2	2	no	—
389	#131	—	4	1	no	—
390	#131	—	118	2	no	—
391	#131	—	236	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	59	1	no	—
394	C₂×M₁₆	—	59	1	no	—
395	C₂×M₁₆	—	118	1	no	—
396	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
397	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	—	59	1	no	—
400	C₂²×C₈	—	59	1	no	—
401	C₂²×C₈	—	118	1	no	—
402	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
403	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
404	C₄⋊Q₈	—	59	1	no	—
405	C₄⋊Q₈	—	59	1	no	—
406	#125	—	59	1	no	—
407	#125	—	59	1	no	—
408	C₂²⋊Q₈	—	118	1	no	—
409	C₂²⋊Q₈	—	118	1	no	—
410	C₄×Q₈	—	59	1	no	—
411	C₄×Q₈	—	59	1	no	—
412	C₄×Q₈	—	118	1	no	—
413	C₄×Q₈	—	118	1	no	—
414	C₄×D₄	—	59	1	no	—
415	C₄×D₄	—	59	1	no	—
416	C₄×D₄	—	118	1	no	—
417	C₄×D₄	—	118	1	no	—
418	#117	—	59	1	no	—
419	#117	—	59	1	no	—
420	#117	—	118	1	no	—
421	#117	C₂²×D₅₉	1	1	yes	characteristic
422	C₂×C₄²	—	59	1	no	—
423	C₂×C₄²	—	59	1	no	—
424	C₂×C₄²	—	118	1	no	—
425	C₂×C₄²	—	118	1	no	—
426	C₂×C₄²	—	118	1	no	—
427	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
428	#108	—	236	1	no	—
429	#108	—	236	1	no	—
430	#107	—	59	1	no	—
431	#107	—	59	1	no	—
432	#107	—	59	1	no	—
433	#107	—	59	1	no	—
434	#106	—	59	1	no	—
435	#106	—	59	1	no	—
436	#106	—	59	1	no	—
437	#106	—	59	1	no	—
438	C₄⋊C₈	—	59	1	no	—
439	C₄⋊C₈	—	59	1	no	—
440	C₄⋊C₈	—	59	1	no	—
441	C₄⋊C₈	—	59	1	no	—
442	C₄⋊C₈	—	59	1	no	—
443	C₄⋊C₈	—	59	1	no	—
444	C₄⋊C₈	—	59	1	no	—
445	C₄⋊C₈	—	59	1	no	—
446	C₄⋊C₈	—	118	1	no	—
447	C₄⋊C₈	—	118	1	no	—
448	C₄⋊C₈	—	118	1	no	—
449	C₄⋊C₈	—	118	1	no	—
450	C₄⋊C₈	—	118	1	no	—
451	C₄⋊C₈	—	118	1	no	—
452	C₄⋊C₈	—	118	1	no	—
453	C₄⋊C₈	—	118	1	no	—
454	C₄⋊C₈	—	118	1	no	—
455	C₄⋊C₈	—	118	1	no	—
456	#104	—	118	2	no	—
457	#104	Dic₁₁₈	1	4	yes	complemented
458	#103	—	59	1	no	—
459	#103	—	59	1	no	—
460	#103	C₄×D₅₉	1	1	yes	characteristic
461	#103	C₄×D₅₉	1	1	yes	characteristic
462	#102	—	59	1	no	—
463	#102	—	59	1	no	—
464	#102	C₄×D₅₉	1	1	yes	characteristic
465	#102	C₄×D₅₉	1	1	yes	characteristic
466	#97	—	2	1	no	—
467	#97	—	118	1	no	—
468	#97	—	118	1	no	—
469	C₄×C₈	—	2	1	no	—
470	C₄×C₈	—	4	1	no	—
471	C₄×C₈	—	118	1	no	—
472	C₄×C₈	—	118	1	no	—
473	C₄×C₈	—	236	1	no	—
474	#41	—	2	1	no	—
475	#41	—	2	1	no	—
476	#41	C₂×Dic₁₁₈	1	2	yes	—
477	#41	#11745685	1	2	yes	—
478	C₂×Q₈	—	118	1	no	—
479	C₂×Q₈	—	118	1	no	—
480	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	59	1	no	—
486	C₂²×C₄	—	59	1	no	—
487	C₂²×C₄	—	118	1	no	—
488	C₂²×C₄	—	118	1	no	—
489	C₂²×C₄	—	118	1	no	—
490	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	1	no	—
493	M₁₆	—	2	1	no	—
494	M₁₆	—	4	2	no	—
495	M₁₆	—	118	1	no	—
496	M₁₆	—	118	1	no	—
497	M₁₆	—	118	1	no	—
498	M₁₆	—	118	1	no	—
499	M₁₆	—	236	2	no	—
500	M₁₆	C₂×Dic₁₁₈	1	2	yes	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	4	2	no	—
508	C₂×C₈	—	59	1	no	—
509	C₂×C₈	—	59	1	no	—
510	C₂×C₈	—	59	1	no	—
511	C₂×C₈	—	59	1	no	—
512	C₂×C₈	—	118	1	no	—
513	C₂×C₈	—	118	1	no	—
514	C₂×C₈	—	118	1	no	—
515	C₂×C₈	—	118	1	no	—
516	C₂×C₈	—	118	1	no	—
517	C₂×C₈	—	118	1	no	—
518	C₂×C₈	—	236	2	no	—
519	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
520	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
521	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
522	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
523	C₄⋊C₄	—	59	1	no	—
524	C₄⋊C₄	—	59	1	no	—
525	C₄⋊C₄	—	59	1	no	—
526	C₄⋊C₄	—	59	1	no	—
527	C₄⋊C₄	—	118	1	no	—
528	C₄⋊C₄	—	118	1	no	—
529	C₄⋊C₄	—	118	1	no	—
530	C₄⋊C₄	—	118	1	no	—
531	C₄⋊C₄	—	118	1	no	—
532	C₄⋊C₄	—	118	1	no	—
533	C₄⋊C₄	—	118	1	no	—
534	C₄⋊C₄	—	118	1	no	—
535	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	118	1	no	—
539	C₂²⋊C₄	—	118	1	no	—
540	C₂²⋊C₄	—	118	1	no	—
541	C₂²⋊C₄	—	118	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	59	1	no	—
545	C₄²	—	59	1	no	—
546	C₄²	—	59	1	no	—
547	C₄²	—	59	1	no	—
548	C₄²	—	118	1	no	—
549	C₄²	—	118	1	no	—
550	C₄²	—	118	4	no	—
551	C₄²	—	118	1	no	—
552	C₄²	—	118	1	no	—
553	C₄²	—	118	1	no	—
554	C₄²	—	118	1	no	—
555	C₄²	—	236	2	no	—
556	C₄²	C₂×Dic₁₁₈	1	2	yes	—
557	C₂³	—	2	1	no	—
558	C₂³	#41×D₅₉	1	1	yes	characteristic
559	Q₈	—	2	1	no	—
560	Q₈	—	472	1	no	—
561	Q₈	—	236	2	no	—
562	Q₈	C₄×Dic₁₁₈	1	2	yes	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	1	no	—
566	D₄	C₄×Dic₁₁₈	1	2	yes	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	59	1	no	—
576	C₂×C₄	—	59	1	no	—
577	C₂×C₄	—	59	1	no	—
578	C₂×C₄	—	59	1	no	—
579	C₂×C₄	—	118	2	no	—
580	C₂×C₄	—	118	2	no	—
581	C₂×C₄	—	118	1	no	—
582	C₂×C₄	—	118	1	no	—
583	C₂×C₄	—	118	1	no	—
584	C₂×C₄	—	118	1	no	—
585	C₂×C₄	—	472	1	no	—
586	C₂×C₄	—	236	2	no	—
587	C₂×C₄	—	236	1	no	—
588	C₂×C₄	—	236	1	no	—
589	C₂×C₄	—	236	1	no	—
590	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
591	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
592	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
593	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
594	C₂×C₄	#14273772	1	1	yes	characteristic
595	C₂×C₄	#14273774	1	1	yes	characteristic
596	C₈	—	2	1	no	—
597	C₈	—	2	1	no	—
598	C₈	—	2	2	no	—
599	C₈	—	2	1	no	—
600	C₈	—	2	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	118	1	no	—
603	C₈	—	118	1	no	—
604	C₈	—	118	1	no	—
605	C₈	—	118	1	no	—
606	C₈	—	236	1	no	—
607	C₈	—	236	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
614	C₂²	#16838085	1	1	yes	characteristic
615	C₂²	#16838111	1	1	yes	characteristic
616	C₄	—	2	4	no	—
617	C₄	—	2	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	59	2	no	—
621	C₄	—	118	1	no	—
622	C₄	—	118	1	no	—
623	C₄	—	118	1	no	—
624	C₄	—	236	2	no	—
625	C₄	—	236	1	no	—
626	C₄	—	236	1	no	—
627	C₄	—	236	1	no	—
628	C₄	—	236	1	no	—
629	C₄	C₂×C₄×Dic₁₁₈	1	1	yes	characteristic
630	C₄	#16837881	1	1	yes	characteristic
631	C₄	#16838042	1	1	yes	characteristic
632	C₄	D₄×Dic₁₁₈	1	1	yes	characteristic
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	4	2	no	—
636	C₂	#21427102	1	1	yes	characteristic
637	C₂	#443×D₅₉	1	1	yes	characteristic
638	C₂	#21433001	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1764	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂³
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1764	D₅₉
hypocenter	C₅₉	#22982
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1764

Complements

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

N	H ≅ G/N	type
2. #21433040	C₂	semidirect
4. #21425071	C₂	semidirect
5. #21424870	C₂	semidirect
6. #21424844	C₂	semidirect
7. #21424843	C₂	semidirect
8. #21424695	C₂	semidirect
9. #21424694	C₂	semidirect
12. C₄×Dic₅₉⋊C₈	C₂	semidirect
19. #16837711	C₄	semidirect
20. #16837707	C₄	semidirect
21. #16837704	C₄	semidirect
22. #16837700	C₄	semidirect
23. #16837695	C₄	semidirect
24. #16837690	C₄	semidirect
25. #16837685	C₄	semidirect
26. #16837680	C₄	semidirect
146. #104×C₅₉	Q₈	semidirect
386. C₅₉	#22982	semidirect
457. #104	Dic₁₁₈	semidirect

Maximal subgroups

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

subgroup	index
#21433880	2
#21433040	2
#21432662	2
#21425071	2
#21424870	2
#21424844	2
#21424843	2
#21424695	2
#21424694	2
#21424373	2
#21424371	2
C₄×Dic₅₉⋊C₈	2
#21423934	2
#104×Dic₅₉	2
C₅₉×#1764	2
#22982	59