Subgroups — #28595633

Order 15104.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433812	C₂	1	1	yes	maximal, characteristic
2	#21432997	C₂	1	2	yes	maximal, complemented
3	#21432521	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424995	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424884	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424762	C₂	1	2	yes	maximal, complemented
7	#21424600	C₂	1	2	yes	maximal, complemented
8	#21424151	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423980	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423896	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₉×#444	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838200	C₂²	1	2	yes	—
13	C₂×#14273733	C₂²	1	1	yes	characteristic
14	C₂×#14273733	C₂²	1	1	yes	characteristic
15	C₄×#11745685	C₂²	1	1	yes	characteristic
16	#16837674	C₄	1	2	yes	complemented
17	#16837669	C₄	1	2	yes	complemented
18	#16837662	C₄	1	4	yes	complemented
19	#16837522	—	2	4	no	—
20	#16837517	—	2	4	no	—
21	#16837450	C₂²	1	2	yes	—
22	C₂×#14273663	C₂²	1	1	yes	characteristic
23	#16837440	C₂²	1	1	yes	characteristic
24	#16837419	C₂²	1	2	yes	—
25	#16837418	C₂²	1	2	yes	—
26	#16837386	C₂²	1	2	yes	—
27	#16837376	C₂²	1	2	yes	—
28	#16837359	—	2	1	no	—
29	#16837359	—	2	1	no	—
30	#16837357	C₂²	1	1	yes	characteristic
31	#16837357	C₂²	1	2	yes	—
32	#16837357	C₂²	1	1	yes	characteristic
33	C₄×#11745664	C₂²	1	1	yes	characteristic
34	#16837354	—	2	1	no	—
35	#97×D₅₉	—	2	1	no	—
36	#16837173	C₂²	1	2	yes	—
37	#16837173	C₂²	1	2	yes	—
38	#16837162	C₂²	1	2	yes	—
39	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#131×C₅₉	C₂²	1	2	yes	—
41	C₅₉×#444	—	2	1	no	—
42	C₅₉×#444	—	2	1	no	—
43	C₅₉×#444	—	2	1	no	—
44	C₅₉×#444	—	2	1	no	—
45	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×#104×C₅₉	C₂²	1	2	yes	—
47	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#11745685	C₂³	1	1	yes	characteristic
49	#14273758	C₂×C₄	1	4	yes	—
50	#14273757	—	2	2	no	—
51	#14273753	C₂×C₄	1	4	yes	—
52	#14273752	—	2	2	no	—
53	#14273747	—	2	4	no	—
54	#14273733	—	2	1	no	—
55	#14273733	—	2	1	no	—
56	#14273733	—	2	2	no	—
57	#14273733	C₂×C₄	1	2	yes	—
58	#14273733	C₂×C₄	1	2	yes	—
59	#14273733	D₄	1	4	yes	—
60	C₂×#11745664	C₂³	1	1	yes	characteristic
61	C₂×#11745664	C₂³	1	2	yes	—
62	C₂×#11745664	C₂³	1	1	yes	characteristic
63	C₂×#11745659	—	2	1	no	—
64	C₂×#11745659	—	2	1	no	—
65	C₂×C₈×D₅₉	—	2	1	no	—
66	C₂×C₈×D₅₉	—	2	1	no	—
67	C₄×Dic₁₁₈	—	2	1	no	—
68	C₄×D₂₃₆	—	2	1	no	—
69	C₄×C₂²⋊D₅₉	—	2	2	no	—
70	#14273686	C₂³	1	2	yes	—
71	#14273686	C₂³	1	1	yes	characteristic
72	#14273684	—	2	1	no	—
73	C₄²×D₅₉	—	2	1	no	—
74	#14273663	C₂×C₄	1	2	yes	complemented
75	#14273663	C₂×C₄	1	2	yes	complemented
76	#14273662	—	2	4	no	—
77	#14273661	—	2	1	no	—
78	#14273659	—	2	1	no	—
79	#14273654	—	2	4	no	—
80	#14273653	—	2	4	no	—
81	#14273646	C₂×C₄	1	4	yes	complemented
82	#14273644	C₂×C₄	1	4	yes	complemented
83	#14273642	—	2	4	no	—
84	#14273638	—	2	1	no	—
85	#14273637	—	2	2	no	—
86	#14273637	—	2	1	no	—
87	#14273637	—	2	1	no	—
88	C₄×C₅₉⋊C₈	—	2	1	no	—
89	C₈×Dic₅₉	—	2	2	no	—
90	C₈×Dic₅₉	—	2	1	no	—
91	C₈×Dic₅₉	—	2	1	no	—
92	C₂×#41×C₅₉	C₂³	1	2	yes	—
93	#135×C₅₉	—	2	1	no	—
94	#135×C₅₉	—	2	1	no	—
95	#135×C₅₉	—	2	1	no	—
96	#135×C₅₉	—	2	1	no	—
97	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	complemented
99	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
100	#131×C₅₉	—	2	2	no	—
101	#131×C₅₉	—	2	2	no	—
102	#131×C₅₉	—	2	2	no	—
103	#131×C₅₉	—	2	2	no	—
104	C₂×M₁₆×C₅₉	—	2	2	no	—
105	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
106	C₂²×C₈×C₅₉	—	2	2	no	—
107	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
110	#108×C₅₉	—	2	1	no	—
111	#108×C₅₉	—	2	1	no	—
112	#104×C₅₉	—	2	2	no	—
113	#104×C₅₉	—	2	2	no	—
114	#97×C₅₉	D₄	1	1	yes	characteristic
115	#97×C₅₉	D₄	1	1	yes	characteristic
116	#97×C₅₉	D₄	1	1	yes	characteristic
117	#97×C₅₉	D₄	1	1	yes	characteristic
118	#41×C₅₉	—	2	2	no	—
119	#41×C₅₉	—	2	2	no	—
120	#41×C₅₉	—	2	2	no	—
121	#41×C₅₉	—	2	2	no	—
122	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
123	C₂×D₄×C₅₉	—	2	2	no	—
124	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	2	2	no	—
127	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₂²⋊D₅₉	—	2	1	no	—
129	#11745685	—	2	1	no	—
130	#11745685	—	2	1	no	—
131	#11745685	C₂²×C₄	1	2	yes	—
132	#11745685	C₂×D₄	1	2	yes	—
133	C₂×D₂₃₆	#41	1	1	yes	characteristic
134	C₂×C₄×D₅₉	—	2	1	no	—
135	C₂×C₄×D₅₉	—	2	2	no	—
136	C₂×Dic₁₁₈	#41	1	1	yes	characteristic
137	Q₁₆×C₅₉	—	2	1	no	—
138	Q₁₆×C₅₉	—	2	1	no	—
139	SD₁₆×C₅₉	—	2	2	no	—
140	SD₁₆×C₅₉	—	2	2	no	—
141	D₈×C₅₉	—	2	1	no	—
142	D₈×C₅₉	—	2	1	no	—
143	M₁₆×C₅₉	—	2	2	no	—
144	M₁₆×C₅₉	—	2	2	no	—
145	M₁₆×C₅₉	—	4	2	no	—
146	M₁₆×C₅₉	—	4	2	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₂×C₈×C₅₉	—	4	2	no	—
149	C₂×C₈×C₅₉	—	4	2	no	—
150	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
158	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
159	C₂×C₈×C₅₉	#41	1	2	yes	—
160	C₄²×C₅₉	—	2	1	no	—
161	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊Dic₅₉	—	2	2	no	—
164	C₂²⋊Dic₅₉	#41	1	2	yes	—
165	#11745672	—	2	4	no	—
166	#11745671	—	2	4	no	—
167	#11745670	—	2	4	no	—
168	#11745669	—	2	4	no	—
169	(C₂×D₅₉)⋊C₄	—	2	2	no	—
170	C₄⋊Dic₅₉	—	2	1	no	—
171	C₄⋊Dic₅₉	—	2	2	no	—
172	Dic₅₉⋊C₄	—	2	2	no	—
173	C₄×Dic₅₉	—	2	2	no	—
174	C₄×Dic₅₉	—	2	1	no	—
175	C₄×Dic₅₉	—	2	2	no	—
176	#11745664	—	2	1	no	—
177	#11745664	—	2	1	no	—
178	#11745664	—	2	2	no	—
179	#11745664	C₂²×C₄	1	2	yes	—
180	#11745664	C₂²×C₄	1	4	yes	—
181	#11745664	C₂×D₄	1	2	yes	—
182	C₂×C₅₉⋊C₈	—	2	1	no	—
183	C₂×C₅₉⋊C₈	—	2	1	no	—
184	C₂×C₅₉⋊C₈	—	2	2	no	—
185	#11745659	—	2	2	no	—
186	#11745659	—	2	2	no	—
187	#11745659	—	2	4	no	—
188	C₈×D₅₉	—	2	2	no	—
189	C₈×D₅₉	—	2	2	no	—
190	C₈×D₅₉	—	2	4	no	—
191	C₂³×C₅₉	—	2	2	no	—
192	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
193	C₂²×D₅₉	—	2	1	no	—
194	Q₈×C₅₉	—	2	2	no	—
195	Q₈×C₅₉	—	2	2	no	—
196	D₄×C₅₉	—	2	2	no	—
197	D₄×C₅₉	—	2	2	no	—
198	D₄×C₅₉	—	4	2	no	—
199	D₄×C₅₉	—	4	2	no	—
200	C₂×C₄×C₅₉	—	2	2	no	—
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	4	2	no	—
204	C₂×C₄×C₅₉	—	4	2	no	—
205	C₂×C₄×C₅₉	—	8	1	no	—
206	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
212	C₂²⋊D₅₉	—	2	2	no	—
213	C₂²⋊D₅₉	—	2	2	no	—
214	C₂×Dic₅₉	—	2	1	no	—
215	C₂×Dic₅₉	—	2	2	no	—
216	C₂×Dic₅₉	—	4	2	no	—
217	D₂₃₆	—	2	1	no	—
218	D₂₃₆	C₄×D₄	1	2	yes	—
219	C₄×D₅₉	—	2	2	no	—
220	C₄×D₅₉	—	2	2	no	—
221	C₄×D₅₉	—	8	2	no	—
222	Dic₁₁₈	—	2	1	no	—
223	Dic₁₁₈	C₄×D₄	1	2	yes	—
224	C₈×C₅₉	—	4	2	no	—
225	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
226	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
227	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
228	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
229	C₈×C₅₉	#121	1	2	yes	—
230	C₈×C₅₉	#121	1	2	yes	—
231	C₅₉⋊C₈	—	2	2	no	—
232	C₅₉⋊C₈	—	2	4	no	—
233	C₅₉⋊C₈	—	2	2	no	—
234	#21559	—	59	1	no	maximal, Sylow
235	C₂²×C₅₉	—	4	1	no	—
236	C₂²×C₅₉	—	4	2	no	—
237	C₂²×C₅₉	—	8	2	no	—
238	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
239	C₂²×C₅₉	#525	1	1	yes	characteristic
240	C₂²×C₅₉	#532	1	1	yes	characteristic
241	C₂×D₅₉	—	2	2	no	—
242	C₂×D₅₉	—	4	2	no	—
243	C₄×C₅₉	—	4	1	no	—
244	C₄×C₅₉	—	4	1	no	—
245	C₄×C₅₉	—	4	2	no	—
246	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
249	C₄×C₅₉	#529	1	1	yes	characteristic
250	Dic₅₉	—	2	2	no	—
251	Dic₅₉	—	4	2	no	—
252	Dic₅₉	—	8	2	no	—
253	#3067	—	59	1	no	—
254	#2955	—	59	2	no	—
255	C₂×#444	D₅₉	1	1	yes	characteristic, complemented
256	#2875	—	59	1	no	—
257	#1976	—	59	1	no	—
258	#1953	—	59	1	no	—
259	#1932	—	59	2	no	—
260	#1906	—	59	2	no	—
261	#1814	—	59	1	no	—
262	#1773	—	59	1	no	—
263	#1757	—	59	2	no	—
264	C₂×C₅₉	—	2	1	no	—
265	C₂×C₅₉	—	2	1	no	—
266	C₂×C₅₉	—	2	1	no	—
267	C₂×C₅₉	—	8	2	no	—
268	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
269	D₅₉	—	4	2	no	—
270	#575	—	59	2	no	—
271	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
272	C₂×#131	—	59	1	no	—
273	C₂×#131	—	59	1	no	—
274	C₂×#131	C₂×D₅₉	1	2	yes	—
275	C₄×#41	—	59	1	no	—
276	#473	—	59	2	no	—
277	#472	—	59	2	no	—
278	#471	—	59	4	no	—
279	#444	—	2	1	no	—
280	#444	—	2	1	no	—
281	#444	—	2	1	no	—
282	#444	—	2	1	no	—
283	#444	—	118	4	no	—
284	#443	—	118	4	no	—
285	#430	—	59	2	no	—
286	C₂×#108	—	59	1	no	—
287	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
288	#427	—	59	1	no	—
289	#421	—	59	2	no	—
290	#421	—	59	2	no	—
291	C₂×#104	C₂×D₅₉	1	2	yes	—
292	#413	—	59	2	no	—
293	#410	—	59	2	no	—
294	#405	—	59	1	no	—
295	#405	—	59	1	no	—
296	#405	—	59	2	no	—
297	#405	—	118	1	no	—
298	#405	—	118	1	no	—
299	C₄×M₁₆	—	59	1	no	—
300	C₄×M₁₆	—	118	1	no	—
301	C₂×#97	—	118	1	no	—
302	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
303	#344	—	59	2	no	—
304	#344	—	59	2	no	—
305	#339	—	59	2	no	—
306	C₅₉	#21559	1	1	yes	characteristic, complemented, Sylow
307	C₂×#41	—	59	1	no	—
308	C₂×#41	C₂²×D₅₉	1	2	yes	—
309	#137	—	59	4	no	—
310	#137	—	118	2	no	—
311	AGL(1,ℤ/8)	—	59	4	no	—
312	AGL(1,ℤ/8)	—	118	2	no	—
313	#135	—	2	1	no	—
314	#135	—	2	1	no	—
315	#135	—	2	1	no	—
316	#135	—	2	1	no	—
317	#135	—	118	4	no	—
318	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic, complemented
319	C₂×SD₁₆	C₄×D₅₉	1	2	yes	complemented
320	C₂×D₈	C₄×D₅₉	1	1	yes	characteristic, complemented
321	#131	—	2	2	no	—
322	#131	—	2	2	no	—
323	#131	—	2	2	no	—
324	#131	—	2	2	no	—
325	#131	—	59	2	no	—
326	#131	—	59	2	no	—
327	#131	—	59	4	no	—
328	#131	—	118	1	no	—
329	#131	—	118	1	no	—
330	#131	—	118	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	59	1	no	—
333	C₂×M₁₆	—	59	1	no	—
334	C₂×M₁₆	—	59	2	no	—
335	C₂×M₁₆	—	118	1	no	—
336	C₂×M₁₆	—	118	1	no	—
337	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	—	118	1	no	—
340	C₂²×C₈	—	118	1	no	—
341	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
342	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
343	C₄×Q₈	—	118	1	no	—
344	C₄×D₄	—	118	1	no	—
345	C₄×D₄	—	118	2	no	—
346	#117	—	59	1	no	—
347	#117	—	59	2	no	—
348	#117	—	118	1	no	—
349	C₂×C₄²	—	118	1	no	—
350	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
351	#108	—	2	1	no	—
352	#108	—	2	1	no	—
353	#108	—	59	2	no	—
354	#108	—	59	2	no	—
355	#108	—	118	4	no	—
356	#107	—	118	1	no	—
357	#106	—	118	1	no	—
358	#104	—	2	2	no	—
359	#104	—	2	2	no	—
360	#104	—	118	4	no	—
361	#104	—	118	4	no	—
362	#101	—	59	4	no	—
363	#100	—	59	4	no	—
364	#99	—	118	4	no	—
365	#97	—	118	2	no	—
366	#97	—	118	1	no	—
367	#97	—	118	1	no	—
368	#97	—	118	1	no	—
369	#97	C₂²⋊D₅₉	1	1	yes	characteristic
370	#97	C₂²⋊D₅₉	1	1	yes	characteristic
371	#97	C₂²⋊D₅₉	1	1	yes	characteristic
372	#97	C₂²⋊D₅₉	1	1	yes	characteristic
373	C₄×C₈	—	118	2	no	—
374	C₄×C₈	—	118	1	no	—
375	C₄×C₈	—	118	1	no	—
376	C₄×C₈	—	118	1	no	—
377	#41	—	2	2	no	—
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	#41	—	59	2	no	—
382	#41	—	59	2	no	—
383	#41	—	118	1	no	—
384	#41	—	118	1	no	—
385	C₂×Q₈	—	59	1	no	—
386	C₂×Q₈	C₂×C₄×D₅₉	1	2	yes	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	59	1	no	—
389	C₂×D₄	—	118	1	no	—
390	C₂×D₄	C₂×C₄×D₅₉	1	2	yes	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	118	2	no	—
394	C₂²×C₄	—	118	1	no	—
395	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
396	Q₁₆	—	2	1	no	—
397	Q₁₆	—	2	1	no	—
398	Q₁₆	—	118	4	no	—
399	SD₁₆	—	2	2	no	—
400	SD₁₆	—	2	2	no	—
401	SD₁₆	—	118	4	no	—
402	SD₁₆	—	118	4	no	—
403	D₈	—	2	1	no	—
404	D₈	—	2	1	no	—
405	D₈	—	118	4	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	4	2	no	—
409	M₁₆	—	4	2	no	—
410	M₁₆	—	59	2	no	—
411	M₁₆	—	59	4	no	—
412	M₁₆	—	59	2	no	—
413	M₁₆	—	118	2	no	—
414	M₁₆	—	118	1	no	—
415	M₁₆	—	118	1	no	—
416	M₁₆	—	118	2	no	—
417	M₁₆	—	118	2	no	—
418	M₁₆	—	118	4	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	4	2	no	—
422	C₂×C₈	—	118	2	no	—
423	C₂×C₈	—	118	1	no	—
424	C₂×C₈	—	118	1	no	—
425	C₂×C₈	—	118	2	no	—
426	C₂×C₈	—	118	2	no	—
427	C₂×C₈	—	118	4	no	—
428	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
429	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
430	C₂×C₈	#11745685	1	1	yes	characteristic
431	C₂×C₈	#11745685	1	1	yes	characteristic
432	C₂×C₈	D₄×D₅₉	1	2	yes	—
433	C₂×C₈	#11745687	1	2	yes	—
434	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
435	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
436	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
437	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
438	C₄⋊C₄	—	118	2	no	—
439	C₄⋊C₄	—	118	1	no	—
440	C₄⋊C₄	—	118	2	no	—
441	C₂²⋊C₄	—	59	2	no	—
442	C₂²⋊C₄	—	118	2	no	—
443	C₂²⋊C₄	—	118	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	118	2	no	—
446	C₄²	—	118	1	no	—
447	C₄²	—	118	2	no	—
448	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
450	C₂³	—	2	2	no	—
451	C₂³	—	118	1	no	—
452	C₂³	#41×D₅₉	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	59	2	no	—
456	Q₈	—	118	1	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	59	2	no	—
462	D₄	—	118	2	no	—
463	D₄	—	118	2	no	—
464	D₄	—	118	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	118	1	no	—
472	C₂×C₄	—	118	2	no	—
473	C₂×C₄	—	118	2	no	—
474	C₂×C₄	—	118	2	no	—
475	C₂×C₄	—	472	2	no	—
476	C₂×C₄	—	236	2	no	—
477	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
479	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
480	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
481	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
482	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
483	C₈	—	4	2	no	—
484	C₈	—	118	2	no	—
485	C₈	—	118	4	no	—
486	C₈	—	118	2	no	—
487	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
488	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
489	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
490	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
491	C₈	#14273698	1	2	yes	—
492	C₈	#14273698	1	2	yes	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	118	2	no	—
497	C₂²	—	236	2	no	—
498	C₂²	C₄×#11745687	1	1	yes	characteristic
499	C₂²	#16837909	1	1	yes	characteristic
500	C₂²	#16837949	1	1	yes	characteristic
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	118	2	no	—
505	C₄	—	472	2	no	—
506	C₄	—	236	2	no	—
507	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
508	C₄	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
509	C₄	C₂×#14273698	1	1	yes	characteristic
510	C₄	#16837934	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	8	2	no	—
515	C₂	—	236	2	no	—
516	C₂	C₄×#14273698	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14273698
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₂×C₅₉×#444	C₂
socle	C₂×C₅₉	C₄×#121
prime radical	#21433812	C₂
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₂×#444	D₅₉
hypocenter	C₅₉	#21559
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. #21432997	C₂	semidirect
3. #21432521	C₂	semidirect
4. #21424995	C₂	semidirect
5. #21424884	C₂	semidirect
6. #21424762	C₂	semidirect
7. #21424600	C₂	semidirect
8. #21424151	C₂	semidirect
9. #21423980	C₂	semidirect
10. #21423896	C₂	semidirect
11. C₂×C₅₉×#444	C₂	semidirect
16. #16837674	C₄	semidirect
17. #16837669	C₄	semidirect
18. #16837662	C₄	semidirect
74. #14273663	C₂×C₄	semidirect
75. #14273663	C₂×C₄	semidirect
81. #14273646	C₂×C₄	semidirect
82. #14273644	C₂×C₄	semidirect
97. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
98. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
99. C₂×D₈×C₅₉	C₂×C₄	semidirect
255. C₂×#444	D₅₉	semidirect
306. C₅₉	#21559	semidirect
318. C₂×Q₁₆	C₄×D₅₉	semidirect
319. C₂×SD₁₆	C₄×D₅₉	semidirect
320. C₂×D₈	C₄×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21433812	2
#21432997	2
#21432521	2
#21424995	2
#21424884	2
#21424762	2
#21424600	2
#21424151	2
#21423980	2
#21423896	2
C₂×C₅₉×#444	2
#21559	59