Subgroups — #19149370

Order 5504.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583734	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583711	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583710	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583709	C₂	1	3	yes	maximal, complemented
6	#14583706	C₂	1	3	yes	maximal, complemented
7	#14583703	C₂	1	3	yes	maximal, complemented
8	#14583702	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583700	C₂	1	3	yes	maximal, complemented
10	#14583696	C₂	1	3	yes	maximal, complemented
11	#14583695	C₂	1	3	yes	maximal, complemented
12	C₂×#13063349	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₄₃	C₂	1	3	yes	maximal, complemented
14	#14583664	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
16	#13063372	—	2	1	no	—
17	#13063372	C₂²	1	3	yes	complemented
18	#13063372	C₂²	1	1	yes	characteristic, complemented
19	#13063371	—	2	1	no	—
20	#13063371	C₂²	1	3	yes	complemented
21	#13063371	C₂²	1	1	yes	characteristic, complemented
22	#13063370	—	2	3	no	—
23	#13063370	—	2	3	no	—
24	#13063370	C₂²	1	3	yes	complemented
25	#13063370	C₂²	1	3	yes	complemented
26	C₂×#10621900	—	2	3	no	—
27	C₂×#10621900	C₂²	1	3	yes	complemented
28	#41×D₄₃	—	2	1	no	—
29	#41×D₄₃	—	2	1	no	—
30	#41×D₄₃	C₂²	1	1	yes	characteristic
31	#41×D₄₃	C₂²	1	3	yes	complemented
32	#41×D₄₃	C₂²	1	3	yes	complemented
33	C₂×D₄×D₄₃	—	2	3	no	—
34	C₂×D₄×D₄₃	C₂²	1	3	yes	complemented
35	#13063358	C₂²	1	3	yes	complemented
36	#13063357	C₂²	1	1	yes	characteristic, complemented
37	#13063357	C₂²	1	3	yes	complemented
38	#13063355	C₂²	1	3	yes	complemented
39	#13063354	C₂²	1	3	yes	complemented
40	#13063354	C₂²	1	3	yes	complemented
41	#13063353	C₂²	1	3	yes	complemented
42	#13063352	C₂²	1	3	yes	complemented
43	#13063352	C₂²	1	3	yes	complemented
44	#13063351	C₂²	1	3	yes	complemented
45	#13063351	C₂²	1	3	yes	complemented
46	#13063350	C₂²	1	3	yes	complemented
47	#13063349	C₂²	1	6	yes	complemented
48	#13063349	C₂²	1	3	yes	complemented
49	#13063349	C₂²	1	6	yes	complemented
50	#13063349	C₂²	1	6	yes	complemented
51	#13063349	C₂²	1	3	yes	complemented
52	#13063347	C₂²	1	3	yes	complemented
53	#13063346	C₂²	1	6	yes	complemented
54	#13063345	C₂²	1	3	yes	complemented
55	#13063345	C₂²	1	3	yes	complemented
56	#13063344	C₂²	1	6	yes	complemented
57	C₂×#10621873	C₂²	1	3	yes	complemented
58	C₂×#10621883	C₂²	1	3	yes	complemented
59	SD₁₆×D₄₃	C₂²	1	6	yes	complemented
60	C₂×#10621882	C₂²	1	3	yes	complemented
61	D₈×D₄₃	C₂²	1	6	yes	complemented
62	#13063333	C₂²	1	3	yes	complemented
63	#13063332	C₂²	1	1	yes	characteristic, complemented
64	#13063331	C₂²	1	3	yes	complemented
65	C₂×#10621872	C₂²	1	3	yes	complemented
66	M₁₆×D₄₃	C₂²	1	3	yes	complemented
67	H(5,𝔽₂)×C₄₃	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₄₃	C₂²	1	1	yes	characteristic, complemented
69	AGL(1,ℤ/8)×C₄₃	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₄₃	C₂²	1	3	yes	complemented
71	#135×C₄₃	C₂²	1	3	yes	complemented
72	C₂×D₈×C₄₃	C₂²	1	3	yes	complemented
73	#131×C₄₃	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₄₃	—	2	3	no	—
75	#41×C₄₃	—	2	1	no	—
76	#41×C₄₃	—	2	1	no	—
77	#41×C₄₃	C₂³	1	3	yes	—
78	#41×C₄₃	C₂³	1	1	yes	characteristic
79	#41×C₄₃	C₂³	1	3	yes	complemented
80	C₂×D₄×C₄₃	—	2	3	no	—
81	C₂×D₄×C₄₃	—	2	3	no	—
82	C₂×D₄×C₄₃	C₂³	1	3	yes	—
83	C₂×D₄×C₄₃	C₂³	1	3	yes	complemented
84	C₂×C₂²⋊D₄₃	—	2	6	no	—
85	C₂×C₂²⋊D₄₃	—	2	6	no	—
86	C₂×C₂²⋊D₄₃	—	2	3	no	—
87	C₂×C₂²⋊D₄₃	—	2	3	no	—
88	C₂²×Dic₄₃	—	2	3	no	—
89	#10621902	—	2	1	no	—
90	#10621902	D₄	1	1	yes	characteristic
91	#10621902	C₂³	1	3	yes	—
92	#10621902	C₂³	1	1	yes	characteristic
93	Q₈×D₄₃	—	2	1	no	—
94	Q₈×D₄₃	D₄	1	1	yes	characteristic
95	Q₈×D₄₃	C₂³	1	1	yes	characteristic
96	Q₈×D₄₃	C₂³	1	3	yes	complemented
97	#10621900	—	2	3	no	—
98	#10621900	—	2	6	no	—
99	#10621900	—	2	3	no	—
100	#10621900	—	2	3	no	—
101	#10621900	—	2	3	no	—
102	#10621900	—	2	3	no	—
103	#10621900	—	2	3	no	—
104	#10621900	—	2	3	no	—
105	#10621900	D₄	1	3	yes	—
106	#10621900	C₂³	1	3	yes	—
107	#10621900	C₂³	1	3	yes	—
108	#10621900	C₂³	1	6	yes	complemented
109	D₄×D₄₃	—	2	3	no	—
110	D₄×D₄₃	—	2	6	no	—
111	D₄×D₄₃	—	2	3	no	—
112	D₄×D₄₃	—	2	3	no	—
113	D₄×D₄₃	—	2	3	no	—
114	D₄×D₄₃	—	2	3	no	—
115	D₄×D₄₃	—	2	3	no	—
116	D₄×D₄₃	—	2	3	no	—
117	D₄×D₄₃	D₄	1	3	yes	—
118	D₄×D₄₃	C₂³	1	6	yes	—
119	D₄×D₄₃	C₂³	1	3	yes	—
120	D₄×D₄₃	C₂³	1	3	yes	complemented
121	#10621898	—	2	3	no	—
122	#10621898	—	2	3	no	—
123	#10621898	—	2	3	no	—
124	#10621898	—	2	3	no	—
125	#10621898	C₂³	1	3	yes	—
126	#10621898	C₂³	1	3	yes	—
127	#10621898	C₂³	1	3	yes	complemented
128	C₂×D₁₇₂	—	2	3	no	—
129	C₂×D₁₇₂	C₂³	1	3	yes	—
130	C₂×C₄×D₄₃	—	2	3	no	—
131	C₂×C₄×D₄₃	—	2	3	no	—
132	C₂×C₄×D₄₃	C₂³	1	3	yes	—
133	C₂×Dic₈₆	—	2	3	no	—
134	C₂×Dic₈₆	C₂³	1	3	yes	complemented
135	Q₁₆×C₄₃	C₂³	1	1	yes	characteristic, complemented
136	SD₁₆×C₄₃	C₂³	1	3	yes	complemented
137	SD₁₆×C₄₃	C₂³	1	3	yes	complemented
138	D₈×C₄₃	C₂³	1	3	yes	complemented
139	D₈×C₄₃	C₂³	1	6	yes	complemented
140	M₁₆×C₄₃	C₂³	1	3	yes	complemented
141	C₂×C₈×C₄₃	C₂³	1	3	yes	complemented
142	#10621885	C₂³	1	1	yes	characteristic, complemented
143	#10621885	C₂³	1	3	yes	complemented
144	#10621884	C₂³	1	3	yes	complemented
145	#10621884	C₂³	1	1	yes	characteristic, complemented
146	#10621883	C₂³	1	6	yes	complemented
147	#10621883	C₂³	1	3	yes	complemented
148	#10621883	C₂³	1	3	yes	complemented
149	#10621882	C₂³	1	3	yes	complemented
150	#10621882	C₂³	1	6	yes	complemented
151	#10621882	C₂³	1	3	yes	complemented
152	#10621877	C₂³	1	3	yes	complemented
153	C₂×C₄₃⋊C₈	C₂³	1	3	yes	complemented
154	Dic₁₇₂	C₂³	1	3	yes	complemented
155	D₃₄₄	C₂³	1	3	yes	complemented
156	#10621873	C₂³	1	6	yes	complemented
157	#10621873	C₂³	1	3	yes	complemented
158	#10621873	C₂³	1	1	yes	characteristic, complemented
159	#10621872	C₂³	1	3	yes	—
160	#10621872	C₂³	1	1	yes	characteristic
161	#10621872	C₂³	1	3	yes	complemented
162	#10621872	C₂³	1	3	yes	complemented
163	C₈×D₄₃	C₂³	1	6	yes	complemented
164	C₂³×C₄₃	—	2	3	no	—
165	C₂³×C₄₃	—	2	3	no	—
166	C₂²×D₄₃	—	2	3	no	—
167	C₂²×D₄₃	—	2	3	no	—
168	C₂²×D₄₃	—	2	3	no	—
169	C₂²×D₄₃	—	2	6	no	—
170	C₂²×D₄₃	—	8	6	no	—
171	C₂²×D₄₃	C₂×D₄	1	3	yes	—
172	Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
173	Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
174	Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
175	D₄×C₄₃	—	2	3	no	—
176	D₄×C₄₃	—	2	3	no	—
177	D₄×C₄₃	—	2	3	no	—
178	D₄×C₄₃	—	2	3	no	—
179	D₄×C₄₃	C₂×D₄	1	3	yes	—
180	D₄×C₄₃	C₂⁴	1	3	yes	—
181	D₄×C₄₃	C₂⁴	1	3	yes	—
182	C₂×C₄×C₄₃	—	2	3	no	—
183	C₂×C₄×C₄₃	—	2	3	no	—
184	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
185	C₂²⋊D₄₃	—	2	3	no	—
186	C₂²⋊D₄₃	—	2	3	no	—
187	C₂²⋊D₄₃	—	2	3	no	—
188	C₂²⋊D₄₃	—	2	3	no	—
189	C₂²⋊D₄₃	—	2	6	no	—
190	C₂²⋊D₄₃	—	2	6	no	—
191	C₂²⋊D₄₃	—	2	3	no	—
192	C₂²⋊D₄₃	—	2	3	no	—
193	C₂²⋊D₄₃	C₂×D₄	1	6	yes	—
194	C₂×Dic₄₃	—	2	3	no	—
195	C₂×Dic₄₃	—	2	6	no	—
196	C₂×Dic₄₃	—	2	3	no	—
197	C₂×Dic₄₃	—	2	3	no	—
198	C₂×Dic₄₃	C₂×D₄	1	3	yes	—
199	D₁₇₂	—	2	3	no	—
200	D₁₇₂	—	2	1	no	—
201	D₁₇₂	—	2	3	no	—
202	D₁₇₂	C₂×D₄	1	3	yes	—
203	D₁₇₂	C₂⁴	1	3	yes	—
204	D₁₇₂	C₂⁴	1	1	yes	characteristic
205	C₄×D₄₃	—	2	1	no	—
206	C₄×D₄₃	—	2	3	no	—
207	C₄×D₄₃	—	2	3	no	—
208	C₄×D₄₃	—	2	3	no	—
209	C₄×D₄₃	—	2	1	no	—
210	C₄×D₄₃	—	2	3	no	—
211	C₄×D₄₃	C₂×D₄	1	3	yes	—
212	C₄×D₄₃	C₂×D₄	1	3	yes	—
213	C₄×D₄₃	C₂⁴	1	3	yes	—
214	C₄×D₄₃	C₂⁴	1	1	yes	characteristic
215	Dic₈₆	—	2	3	no	—
216	Dic₈₆	—	2	3	no	—
217	Dic₈₆	—	2	1	no	—
218	Dic₈₆	C₂×D₄	1	3	yes	—
219	Dic₈₆	C₂⁴	1	3	yes	—
220	Dic₈₆	C₂⁴	1	1	yes	characteristic
221	C₈×C₄₃	C₂⁴	1	3	yes	—
222	C₈×C₄₃	C₂⁴	1	1	yes	characteristic
223	C₄₃⋊C₈	C₂⁴	1	3	yes	—
224	C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄₃	—	2	3	no	—
226	C₂²×C₄₃	—	2	3	no	—
227	C₂²×C₄₃	—	8	3	no	—
228	C₂²×C₄₃	—	8	3	no	—
229	C₂²×C₄₃	C₂²×D₄	1	3	yes	—
230	C₂×D₄₃	—	2	3	no	—
231	C₂×D₄₃	—	2	1	no	—
232	C₂×D₄₃	—	4	3	no	—
233	C₂×D₄₃	—	4	6	no	—
234	C₂×D₄₃	—	8	3	no	—
235	C₂×D₄₃	—	8	6	no	—
236	C₂×D₄₃	—	8	3	no	—
237	C₂×D₄₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₄₃	C₂²×D₄	1	3	yes	—
239	C₄×C₄₃	—	2	1	no	—
240	C₄×C₄₃	—	2	1	no	—
241	C₄×C₄₃	C₂²×D₄	1	3	yes	—
242	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
243	Dic₄₃	—	2	3	no	—
244	Dic₄₃	—	2	1	no	—
245	Dic₄₃	C₂²×D₄	1	3	yes	—
246	Dic₄₃	C₂²×D₄	1	1	yes	characteristic
247	#3585	—	43	1	no	maximal, Sylow
248	C₂×C₄₃	—	2	3	no	—
249	C₂×C₄₃	—	4	3	no	—
250	C₂×C₄₃	—	4	3	no	—
251	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
252	D₄₃	—	2	1	no	—
253	D₄₃	—	2	3	no	—
254	D₄₃	—	4	3	no	—
255	D₄₃	—	4	1	no	—
256	#585	—	43	1	no	—
257	C₂×H(5,𝔽₂)	—	43	1	no	—
258	#577	—	43	1	no	—
259	#577	—	43	3	no	—
260	#577	—	43	3	no	—
261	#577	—	43	1	no	—
262	#576	—	43	1	no	—
263	#576	—	43	3	no	—
264	#576	—	43	3	no	—
265	#576	D₄₃	1	1	yes	characteristic, complemented
266	#575	—	43	3	no	—
267	#575	—	43	3	no	—
268	C₂×AGL(1,ℤ/8)	—	43	3	no	—
269	C₂×AGL(1,ℤ/8)	—	43	3	no	—
270	#568	—	43	1	no	—
271	C₄₃	#3585	1	1	yes	characteristic, complemented, Sylow
272	2₋¹⁺⁴	—	43	1	no	—
273	2₋¹⁺⁴	—	43	3	no	—
274	2₋¹⁺⁴	—	86	1	no	—
275	H(5,𝔽₂)	—	43	3	no	—
276	H(5,𝔽₂)	—	43	1	no	—
277	H(5,𝔽₂)	—	43	3	no	—
278	H(5,𝔽₂)	—	43	3	no	—
279	H(5,𝔽₂)	—	86	3	no	—
280	H(5,𝔽₂)	—	86	3	no	—
281	H(5,𝔽₂)	—	86	1	no	—
282	H(5,𝔽₂)	C₂×D₄₃	1	1	yes	characteristic, complemented
283	H(5,𝔽₂)	C₂×D₄₃	1	1	yes	characteristic, complemented
284	C₂×#41	—	43	1	no	—
285	C₂×#41	—	43	3	no	—
286	C₂×#41	—	43	3	no	—
287	C₂×#41	—	43	3	no	—
288	C₂×#41	—	86	3	no	—
289	C₂×#41	—	86	1	no	—
290	C₂×#41	—	86	1	no	—
291	C₂²×D₄	—	43	3	no	—
292	C₂²×D₄	—	86	3	no	—
293	#137	—	43	3	no	—
294	#137	—	43	1	no	—
295	#137	—	43	3	no	—
296	#137	—	43	3	no	—
297	#137	—	43	3	no	—
298	#137	—	43	3	no	—
299	AGL(1,ℤ/8)	—	43	3	no	—
300	AGL(1,ℤ/8)	—	43	3	no	—
301	AGL(1,ℤ/8)	—	43	3	no	—
302	AGL(1,ℤ/8)	—	43	3	no	—
303	AGL(1,ℤ/8)	—	43	3	no	—
304	AGL(1,ℤ/8)	—	43	6	no	—
305	AGL(1,ℤ/8)	—	43	3	no	—
306	AGL(1,ℤ/8)	—	43	6	no	—
307	AGL(1,ℤ/8)	—	43	6	no	—
308	AGL(1,ℤ/8)	—	43	3	no	—
309	AGL(1,ℤ/8)	—	43	3	no	—
310	AGL(1,ℤ/8)	C₂×D₄₃	1	3	yes	complemented
311	AGL(1,ℤ/8)	C₂×D₄₃	1	3	yes	complemented
312	#135	—	43	3	no	—
313	#135	—	43	3	no	—
314	#135	—	43	6	no	—
315	#135	—	43	6	no	—
316	#135	—	43	3	no	—
317	#135	C₂×D₄₃	1	3	yes	complemented
318	C₂×SD₁₆	—	43	3	no	—
319	C₂×SD₁₆	—	43	6	no	—
320	C₂×SD₁₆	—	43	3	no	—
321	C₂×D₈	—	43	3	no	—
322	C₂×D₈	—	43	6	no	—
323	C₂×D₈	C₂×D₄₃	1	3	yes	complemented
324	#131	—	43	1	no	—
325	#131	—	43	3	no	—
326	#131	—	43	3	no	—
327	#131	C₂×D₄₃	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	43	3	no	—
329	C₂×M₁₆	—	43	3	no	—
330	C₂⁴	—	86	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	1	no	—
333	#41	—	43	1	no	—
334	#41	—	43	3	no	—
335	#41	—	43	3	no	—
336	#41	—	43	3	no	—
337	#41	—	43	1	no	—
338	#41	—	43	6	no	—
339	#41	—	43	3	no	—
340	#41	—	43	3	no	—
341	#41	—	43	3	no	—
342	#41	—	43	3	no	—
343	#41	—	86	3	no	—
344	#41	—	86	3	no	—
345	#41	—	86	3	no	—
346	#41	—	86	3	no	—
347	#41	—	86	3	no	—
348	#41	—	86	3	no	—
349	#41	—	86	3	no	—
350	#41	—	86	3	no	—
351	#41	—	86	6	no	—
352	#41	—	86	3	no	—
353	#41	—	86	3	no	—
354	#41	—	86	1	no	—
355	#41	—	86	3	no	—
356	#41	C₂²×D₄₃	1	3	yes	—
357	#41	C₂²×D₄₃	1	1	yes	characteristic
358	#41	C₂²×D₄₃	1	3	yes	complemented
359	C₂×Q₈	—	43	1	no	—
360	C₂×Q₈	—	43	3	no	—
361	C₂×Q₈	—	43	1	no	—
362	C₂×Q₈	—	43	3	no	—
363	C₂×Q₈	—	86	3	no	—
364	C₂×Q₈	—	86	1	no	—
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	2	3	no	—
367	C₂×D₄	—	43	3	no	—
368	C₂×D₄	—	43	3	no	—
369	C₂×D₄	—	43	6	no	—
370	C₂×D₄	—	43	3	no	—
371	C₂×D₄	—	43	3	no	—
372	C₂×D₄	—	86	3	no	—
373	C₂×D₄	—	86	3	no	—
374	C₂×D₄	—	86	3	no	—
375	C₂×D₄	—	86	3	no	—
376	C₂×D₄	—	86	6	no	—
377	C₂×D₄	—	86	3	no	—
378	C₂×D₄	—	86	3	no	—
379	C₂×D₄	—	86	3	no	—
380	C₂×D₄	—	86	3	no	—
381	C₂×D₄	—	86	6	no	—
382	C₂×D₄	—	86	6	no	—
383	C₂×D₄	—	86	3	no	—
384	C₂×D₄	—	86	3	no	—
385	C₂×D₄	C₂²×D₄₃	1	3	yes	—
386	C₂×D₄	C₂²×D₄₃	1	3	yes	complemented
387	C₂²×C₄	—	43	3	no	—
388	C₂²×C₄	—	86	3	no	—
389	C₂²×C₄	—	86	3	no	—
390	C₂²×C₄	—	86	3	no	—
391	Q₁₆	—	43	3	no	—
392	Q₁₆	—	43	1	no	—
393	Q₁₆	—	43	3	no	—
394	Q₁₆	C₂²×D₄₃	1	1	yes	characteristic, complemented
395	SD₁₆	—	43	3	no	—
396	SD₁₆	—	43	1	no	—
397	SD₁₆	—	43	3	no	—
398	SD₁₆	—	43	6	no	—
399	SD₁₆	—	43	3	no	—
400	SD₁₆	—	43	6	no	—
401	SD₁₆	—	43	3	no	—
402	SD₁₆	—	43	1	no	—
403	SD₁₆	C₂²×D₄₃	1	3	yes	complemented
404	SD₁₆	C₂²×D₄₃	1	3	yes	complemented
405	D₈	—	43	3	no	—
406	D₈	—	43	3	no	—
407	D₈	—	43	6	no	—
408	D₈	—	43	3	no	—
409	D₈	C₂²×D₄₃	1	6	yes	complemented
410	D₈	C₂²×D₄₃	1	3	yes	complemented
411	M₁₆	—	43	3	no	—
412	M₁₆	—	43	3	no	—
413	M₁₆	—	43	1	no	—
414	M₁₆	—	43	3	no	—
415	M₁₆	—	43	3	no	—
416	M₁₆	C₂²×D₄₃	1	3	yes	complemented
417	C₂×C₈	—	43	3	no	—
418	C₂×C₈	—	43	6	no	—
419	C₂×C₈	C₂²×D₄₃	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	2	3	no	—
422	C₂³	—	43	3	no	—
423	C₂³	—	86	3	no	—
424	C₂³	—	86	6	no	—
425	C₂³	—	86	3	no	—
426	C₂³	—	86	3	no	—
427	C₂³	—	344	6	no	—
428	Q₈	—	43	3	no	—
429	Q₈	—	43	3	no	—
430	Q₈	—	43	1	no	—
431	Q₈	—	86	3	no	—
432	Q₈	—	86	1	no	—
433	Q₈	—	86	3	no	—
434	Q₈	D₄×D₄₃	1	1	yes	characteristic
435	Q₈	C₂³×D₄₃	1	1	yes	characteristic
436	Q₈	C₂³×D₄₃	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	2	3	no	—
441	D₄	—	43	6	no	—
442	D₄	—	43	3	no	—
443	D₄	—	43	1	no	—
444	D₄	—	43	3	no	—
445	D₄	—	86	3	no	—
446	D₄	—	86	1	no	—
447	D₄	—	86	3	no	—
448	D₄	—	86	6	no	—
449	D₄	—	86	3	no	—
450	D₄	—	86	3	no	—
451	D₄	—	86	3	no	—
452	D₄	—	86	6	no	—
453	D₄	—	86	3	no	—
454	D₄	—	86	3	no	—
455	D₄	—	86	3	no	—
456	D₄	D₄×D₄₃	1	3	yes	—
457	D₄	C₂³×D₄₃	1	3	yes	—
458	D₄	C₂³×D₄₃	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	43	3	no	—
462	C₂×C₄	—	43	3	no	—
463	C₂×C₄	—	43	3	no	—
464	C₂×C₄	—	43	3	no	—
465	C₂×C₄	—	43	1	no	—
466	C₂×C₄	—	86	1	no	—
467	C₂×C₄	—	86	3	no	—
468	C₂×C₄	—	86	1	no	—
469	C₂×C₄	—	86	3	no	—
470	C₂×C₄	—	86	3	no	—
471	C₂×C₄	—	86	3	no	—
472	C₂×C₄	—	86	6	no	—
473	C₂×C₄	—	86	3	no	—
474	C₂×C₄	—	86	3	no	—
475	C₂×C₄	—	86	3	no	—
476	C₂×C₄	C₂³×D₄₃	1	3	yes	—
477	C₈	—	43	1	no	—
478	C₈	—	43	3	no	—
479	C₈	C₂³×D₄₃	1	3	yes	—
480	C₈	C₂³×D₄₃	1	1	yes	characteristic
481	C₂²	—	2	3	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	8	3	no	—
485	C₂²	—	43	1	no	—
486	C₂²	—	43	3	no	—
487	C₂²	—	86	1	no	—
488	C₂²	—	86	3	no	—
489	C₂²	—	344	3	no	—
490	C₂²	—	344	6	no	—
491	C₂²	—	344	3	no	—
492	C₂²	—	172	3	no	—
493	C₂²	—	172	6	no	—
494	C₂²	C₂×D₄×D₄₃	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	43	1	no	—
498	C₄	—	43	3	no	—
499	C₄	—	86	1	no	—
500	C₄	—	86	3	no	—
501	C₄	C₂×D₄×D₄₃	1	3	yes	—
502	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	3	no	—
506	C₂	—	86	3	no	—
507	C₂	—	86	1	no	—
508	C₂	—	172	3	no	—
509	C₂	—	172	1	no	—
510	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁵
Frattini	C₄	C₂⁴×D₄₃
Fitting	C₄₃×#576	C₂
socle	C₂×C₄₃	C₂³×D₄
hypercenter	#576	D₄₃
hypocenter	C₄₃	#3585
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. #14583734	C₂	semidirect
2. H(5,𝔽₂)×D₄₃	C₂	semidirect
3. #14583711	C₂	semidirect
4. #14583710	C₂	semidirect
5. #14583709	C₂	semidirect
6. #14583706	C₂	semidirect
7. #14583703	C₂	semidirect
8. #14583702	C₂	semidirect
9. #14583700	C₂	semidirect
10. #14583696	C₂	semidirect
11. #14583695	C₂	semidirect
12. C₂×#13063349	C₂	semidirect
13. AGL(1,ℤ/8)×D₄₃	C₂	semidirect
14. #14583664	C₂	semidirect
15. C₄₃×#576	C₂	semidirect
17. #13063372	C₂²	semidirect
18. #13063372	C₂²	semidirect
20. #13063371	C₂²	semidirect
21. #13063371	C₂²	semidirect
24. #13063370	C₂²	semidirect
25. #13063370	C₂²	semidirect
27. C₂×#10621900	C₂²	semidirect
31. #41×D₄₃	C₂²	semidirect
32. #41×D₄₃	C₂²	semidirect
34. C₂×D₄×D₄₃	C₂²	semidirect
35. #13063358	C₂²	semidirect
36. #13063357	C₂²	semidirect
37. #13063357	C₂²	semidirect
38. #13063355	C₂²	semidirect
39. #13063354	C₂²	semidirect
40. #13063354	C₂²	semidirect
41. #13063353	C₂²	semidirect
42. #13063352	C₂²	semidirect
43. #13063352	C₂²	semidirect
44. #13063351	C₂²	semidirect
45. #13063351	C₂²	semidirect
46. #13063350	C₂²	semidirect
47. #13063349	C₂²	semidirect
48. #13063349	C₂²	semidirect
49. #13063349	C₂²	semidirect
50. #13063349	C₂²	semidirect
51. #13063349	C₂²	semidirect
52. #13063347	C₂²	semidirect
53. #13063346	C₂²	semidirect
54. #13063345	C₂²	semidirect
55. #13063345	C₂²	semidirect
56. #13063344	C₂²	semidirect
57. C₂×#10621873	C₂²	semidirect
58. C₂×#10621883	C₂²	semidirect
59. SD₁₆×D₄₃	C₂²	semidirect
60. C₂×#10621882	C₂²	semidirect
61. D₈×D₄₃	C₂²	semidirect
62. #13063333	C₂²	semidirect
63. #13063332	C₂²	semidirect
64. #13063331	C₂²	semidirect
65. C₂×#10621872	C₂²	semidirect
66. M₁₆×D₄₃	C₂²	semidirect
67. H(5,𝔽₂)×C₄₃	C₂²	semidirect
68. H(5,𝔽₂)×C₄₃	C₂²	semidirect
69. AGL(1,ℤ/8)×C₄₃	C₂²	semidirect
70. AGL(1,ℤ/8)×C₄₃	C₂²	semidirect
71. #135×C₄₃	C₂²	semidirect
72. C₂×D₈×C₄₃	C₂²	semidirect
73. #131×C₄₃	C₂²	semidirect
79. #41×C₄₃	C₂³	semidirect
83. C₂×D₄×C₄₃	C₂³	semidirect
96. Q₈×D₄₃	C₂³	semidirect
108. #10621900	C₂³	semidirect
120. D₄×D₄₃	C₂³	semidirect
127. #10621898	C₂³	semidirect
134. C₂×Dic₈₆	C₂³	semidirect
135. Q₁₆×C₄₃	C₂³	semidirect
136. SD₁₆×C₄₃	C₂³	semidirect
137. SD₁₆×C₄₃	C₂³	semidirect
138. D₈×C₄₃	C₂³	semidirect
139. D₈×C₄₃	C₂³	semidirect
140. M₁₆×C₄₃	C₂³	semidirect
141. C₂×C₈×C₄₃	C₂³	semidirect
142. #10621885	C₂³	semidirect
143. #10621885	C₂³	semidirect
144. #10621884	C₂³	semidirect
145. #10621884	C₂³	semidirect
146. #10621883	C₂³	semidirect
147. #10621883	C₂³	semidirect
148. #10621883	C₂³	semidirect
149. #10621882	C₂³	semidirect
150. #10621882	C₂³	semidirect
151. #10621882	C₂³	semidirect
152. #10621877	C₂³	semidirect
153. C₂×C₄₃⋊C₈	C₂³	semidirect
154. Dic₁₇₂	C₂³	semidirect
155. D₃₄₄	C₂³	semidirect
156. #10621873	C₂³	semidirect
157. #10621873	C₂³	semidirect
158. #10621873	C₂³	semidirect
161. #10621872	C₂³	semidirect
162. #10621872	C₂³	semidirect
163. C₈×D₄₃	C₂³	semidirect
265. #576	D₄₃	semidirect
271. C₄₃	#3585	semidirect
282. H(5,𝔽₂)	C₂×D₄₃	semidirect
283. H(5,𝔽₂)	C₂×D₄₃	semidirect
310. AGL(1,ℤ/8)	C₂×D₄₃	semidirect
311. AGL(1,ℤ/8)	C₂×D₄₃	semidirect
317. #135	C₂×D₄₃	semidirect
323. C₂×D₈	C₂×D₄₃	semidirect
327. #131	C₂×D₄₃	semidirect
358. #41	C₂²×D₄₃	semidirect
386. C₂×D₄	C₂²×D₄₃	semidirect
394. Q₁₆	C₂²×D₄₃	semidirect
403. SD₁₆	C₂²×D₄₃	semidirect
404. SD₁₆	C₂²×D₄₃	semidirect
409. D₈	C₂²×D₄₃	semidirect
410. D₈	C₂²×D₄₃	semidirect
416. M₁₆	C₂²×D₄₃	semidirect
419. C₂×C₈	C₂²×D₄₃	semidirect