Subgroups — #25148156

Order 11008.

860 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145090	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144332	C₂	1	2	yes	maximal, complemented
3	#19144311	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583175	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135876	C₂	1	2	yes	maximal, complemented
6	#19135656	C₂	1	2	yes	maximal, complemented
7	#19135510	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135386	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135147	C₂	1	2	yes	maximal, complemented
10	#19134396	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583697	C₂²	1	2	yes	—
13	C₂×#13063358	C₂²	1	2	yes	—
14	C₂×#13063355	C₂²	1	2	yes	—
15	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
16	C₂×#13063331	C₂²	1	1	yes	characteristic
17	#14583470	C₂²	1	2	yes	—
18	#14583290	—	2	2	no	—
19	#14583282	—	2	1	no	—
20	#14583277	—	2	1	no	—
21	#14583175	—	2	2	no	—
22	#14583175	—	2	2	no	—
23	#14583174	—	2	4	no	—
24	#14583171	—	2	1	no	—
25	#14583166	—	2	1	no	—
26	#14583162	—	2	4	no	—
27	#14583159	—	2	2	no	—
28	#14582948	C₂²	1	2	yes	—
29	C₂×#13063261	C₂²	1	1	yes	characteristic
30	#14582907	C₂²	1	2	yes	—
31	#14582883	C₂²	1	2	yes	—
32	#14582881	C₂²	1	1	yes	characteristic
33	C₂×#13063243	C₂²	1	2	yes	—
34	C₂×#13063243	C₂²	1	2	yes	—
35	#14582872	C₂²	1	1	yes	characteristic
36	#14582854	C₂²	1	1	yes	characteristic
37	#14582671	C₂²	1	2	yes	—
38	#14582671	C₂²	1	1	yes	characteristic
39	#14582669	C₂²	1	1	yes	characteristic
40	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#568	C₂²	1	2	yes	—
42	C₄₃×#444	—	2	2	no	—
43	C₄₃×#443	—	2	2	no	—
44	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#421	C₂²	1	2	yes	—
46	C₄₃×#405	C₂²	1	1	yes	characteristic
47	C₂×#10621898	C₂³	1	1	yes	characteristic
48	C₂²×Dic₈₆	C₂³	1	2	yes	—
49	#13063358	—	2	4	no	—
50	#13063358	—	4	2	no	—
51	#13063356	—	2	2	no	—
52	#13063355	—	2	2	no	—
53	#13063355	—	2	4	no	—
54	#13063355	—	4	2	no	—
55	#13063351	—	2	2	no	—
56	#13063350	—	2	2	no	—
57	#13063345	—	4	2	no	—
58	C₂×Dic₁₇₂	—	2	2	no	—
59	C₂×Dic₁₇₂	—	2	1	no	—
60	C₂×Dic₁₇₂	—	2	1	no	—
61	C₂×Dic₁₇₂	—	2	1	no	—
62	C₂×Dic₁₇₂	—	2	1	no	—
63	C₂×Dic₁₇₂	—	2	1	no	—
64	C₂×Dic₁₇₂	—	2	1	no	—
65	C₂×#10621885	—	2	2	no	—
66	C₂×#10621873	—	2	2	no	—
67	C₂×#10621883	—	2	2	no	—
68	#13063331	—	2	1	no	—
69	#13063331	—	2	1	no	—
70	#13063331	—	2	1	no	—
71	#13063331	—	2	1	no	—
72	C₂×#10621877	C₂³	1	1	yes	characteristic
73	C₂×#10621877	C₂³	1	2	yes	—
74	C₂×#10621877	C₂³	1	1	yes	characteristic
75	C₂×#10621872	—	2	1	no	—
76	C₂×C₈×D₄₃	—	2	1	no	—
77	#13063323	—	2	2	no	—
78	#13063312	—	2	2	no	—
79	#13063306	—	2	4	no	—
80	#13063304	—	4	2	no	—
81	#13063284	C₂³	1	1	yes	characteristic
82	#13063261	—	2	1	no	—
83	#13063261	—	2	1	no	—
84	#13063261	—	2	4	no	—
85	#13063248	—	4	2	no	—
86	#13063244	—	2	2	no	—
87	#13063243	—	2	4	no	—
88	#13063243	—	2	4	no	—
89	#13063243	D₄	1	2	yes	—
90	#13063242	—	2	2	no	—
91	#13063241	D₄	1	2	yes	—
92	#13063239	—	2	2	no	—
93	#13063235	—	2	1	no	—
94	C₈×Dic₄₃	—	2	1	no	—
95	C₂×#41×C₄₃	C₂³	1	2	yes	—
96	#135×C₄₃	—	2	1	no	—
97	#135×C₄₃	—	2	1	no	—
98	#135×C₄₃	—	2	1	no	—
99	#135×C₄₃	—	2	1	no	—
100	C₂×Q₁₆×C₄₃	D₄	1	1	yes	characteristic
101	C₂×SD₁₆×C₄₃	D₄	1	2	yes	—
102	C₂×D₈×C₄₃	D₄	1	1	yes	characteristic
103	#131×C₄₃	—	2	4	no	—
104	#131×C₄₃	—	2	4	no	—
105	C₂×M₁₆×C₄₃	—	4	2	no	—
106	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	#117×C₄₃	C₂³	1	1	yes	characteristic
110	#108×C₄₃	D₄	1	2	yes	—
111	#108×C₄₃	D₄	1	2	yes	—
112	#104×C₄₃	—	2	4	no	—
113	#97×C₄₃	—	2	1	no	—
114	C₄×C₈×C₄₃	—	2	1	no	—
115	#41×C₄₃	—	2	2	no	—
116	#41×C₄₃	—	2	2	no	—
117	#41×C₄₃	—	2	2	no	—
118	#41×C₄₃	—	2	2	no	—
119	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₃	—	2	1	no	—
125	C₂²×Dic₄₃	—	2	2	no	—
126	#10621898	—	2	1	no	—
127	#10621898	—	2	1	no	—
128	#10621898	—	2	1	no	—
129	#10621898	—	2	1	no	—
130	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₄₃	—	2	1	no	—
132	C₂×Dic₈₆	—	2	2	no	—
133	C₂×Dic₈₆	—	2	2	no	—
134	C₂×Dic₈₆	—	2	2	no	—
135	C₂×Dic₈₆	—	2	2	no	—
136	C₂×Dic₈₆	—	2	2	no	—
137	C₂×Dic₈₆	—	2	2	no	—
138	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
139	Q₁₆×C₄₃	—	2	1	no	—
140	Q₁₆×C₄₃	—	2	1	no	—
141	SD₁₆×C₄₃	—	2	2	no	—
142	SD₁₆×C₄₃	—	2	2	no	—
143	D₈×C₄₃	—	2	1	no	—
144	D₈×C₄₃	—	2	1	no	—
145	M₁₆×C₄₃	—	2	1	no	—
146	M₁₆×C₄₃	—	2	2	no	—
147	M₁₆×C₄₃	—	4	4	no	—
148	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
149	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
150	C₂×C₈×C₄₃	—	2	1	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	4	4	no	—
153	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
158	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₂²⋊C₄×C₄₃	—	2	1	no	—
161	C₄²×C₄₃	—	2	1	no	—
162	C₂²⋊Dic₄₃	—	4	4	no	—
163	C₂²⋊Dic₄₃	#41	1	2	yes	—
164	#10621885	—	4	4	no	—
165	#10621885	—	4	2	no	—
166	#10621884	—	4	2	no	—
167	#10621883	—	4	4	no	—
168	#10621883	—	4	2	no	—
169	#10621882	—	4	2	no	—
170	C₄⋊Dic₄₃	—	2	1	no	—
171	Dic₄₃⋊C₄	—	4	4	no	—
172	C₄×Dic₄₃	—	2	1	no	—
173	#10621877	—	2	1	no	—
174	#10621877	—	2	1	no	—
175	#10621877	—	2	2	no	—
176	#10621877	—	2	1	no	—
177	#10621877	—	2	2	no	—
178	#10621877	C₂×D₄	1	2	yes	—
179	C₂×C₄₃⋊C₈	—	2	1	no	—
180	C₂×C₄₃⋊C₈	—	2	1	no	—
181	C₂×C₄₃⋊C₈	—	2	2	no	—
182	Dic₁₇₂	—	4	4	no	—
183	Dic₁₇₂	—	4	1	no	—
184	Dic₁₇₂	—	4	1	no	—
185	Dic₁₇₂	—	4	1	no	—
186	Dic₁₇₂	—	4	1	no	—
187	#10621873	—	4	4	no	—
188	#10621872	—	4	1	no	—
189	#10621872	—	4	1	no	—
190	C₈×D₄₃	—	4	1	no	—
191	C₈×D₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂²×D₄₃	—	2	1	no	—
195	Q₈×C₄₃	—	2	2	no	—
196	Q₈×C₄₃	—	2	2	no	—
197	D₄×C₄₃	—	2	2	no	—
198	D₄×C₄₃	—	2	2	no	—
199	D₄×C₄₃	—	4	2	no	—
200	D₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²⋊D₄₃	—	4	1	no	—
212	C₂²⋊D₄₃	—	4	1	no	—
213	C₂×Dic₄₃	—	2	1	no	—
214	C₂×Dic₄₃	—	2	2	no	—
215	C₂×Dic₄₃	—	4	2	no	—
216	C₂×Dic₄₃	—	4	2	no	—
217	C₂×Dic₄₃	—	4	2	no	—
218	D₁₇₂	—	2	1	no	—
219	D₁₇₂	—	2	1	no	—
220	C₄×D₄₃	—	4	1	no	—
221	C₄×D₄₃	—	4	1	no	—
222	Dic₈₆	—	2	1	no	—
223	Dic₈₆	—	2	1	no	—
224	Dic₈₆	—	4	2	no	—
225	Dic₈₆	—	4	2	no	—
226	Dic₈₆	—	4	2	no	—
227	Dic₈₆	—	4	2	no	—
228	C₈×C₄₃	—	2	4	no	—
229	C₈×C₄₃	—	2	2	no	—
230	C₈×C₄₃	#121	1	1	yes	characteristic
231	C₈×C₄₃	#121	1	1	yes	characteristic
232	C₈×C₄₃	#121	1	1	yes	characteristic
233	C₈×C₄₃	#121	1	1	yes	characteristic
234	C₄₃⋊C₈	—	2	2	no	—
235	C₄₃⋊C₈	—	4	1	no	—
236	C₄₃⋊C₈	—	4	2	no	—
237	#25448	—	43	1	no	maximal, Sylow
238	C₂²×C₄₃	—	4	1	no	—
239	C₂²×C₄₃	—	4	2	no	—
240	C₂²×C₄₃	—	8	2	no	—
241	C₂²×C₄₃	#532	1	1	yes	characteristic
242	C₂²×C₄₃	#546	1	1	yes	characteristic
243	C₂²×C₄₃	#550	1	1	yes	characteristic
244	C₂×D₄₃	—	4	1	no	—
245	C₂×D₄₃	—	8	1	no	—
246	C₄×C₄₃	—	4	2	no	—
247	C₄×C₄₃	—	8	1	no	—
248	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
249	C₄×C₄₃	#540	1	1	yes	characteristic
250	C₄×C₄₃	D₄²	1	1	yes	characteristic
251	C₄×C₄₃	D₄²	1	1	yes	characteristic
252	Dic₄₃	—	4	2	no	—
253	Dic₄₃	—	4	1	no	—
254	Dic₄₃	—	8	2	no	—
255	#3156	—	43	1	no	—
256	#3069	—	43	2	no	—
257	#3067	—	43	1	no	—
258	C₂×#473	—	43	1	no	—
259	#2957	D₄₃	1	1	yes	characteristic, complemented
260	#2049	—	43	2	no	—
261	#2009	—	43	2	no	—
262	#1979	—	43	1	no	—
263	#1953	—	43	1	no	—
264	#1915	—	43	2	no	—
265	#1757	—	43	1	no	—
266	C₂×C₄₃	—	2	1	no	—
267	C₂×C₄₃	—	2	1	no	—
268	C₂×C₄₃	—	2	1	no	—
269	C₂×C₄₃	—	8	2	no	—
270	C₂×C₄₃	#2428	1	1	yes	characteristic
271	D₄₃	—	8	1	no	—
272	#575	—	43	2	no	—
273	C₂×#137	—	43	2	no	—
274	C₂×#137	—	43	2	no	—
275	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
276	C₂²×Q₁₆	—	43	1	no	—
277	#568	C₂×D₄₃	1	2	yes	—
278	C₂×#131	—	43	1	no	—
279	#536	—	43	2	no	—
280	#497	—	86	2	no	—
281	#495	—	86	1	no	—
282	#494	—	86	1	no	—
283	#473	—	86	4	no	—
284	#473	—	86	1	no	—
285	#473	—	86	2	no	—
286	#473	—	86	2	no	—
287	#472	—	86	1	no	—
288	#471	—	86	4	no	—
289	#471	—	86	2	no	—
290	#444	—	2	2	no	—
291	#443	—	2	2	no	—
292	#430	—	43	2	no	—
293	C₂×#108	—	43	1	no	—
294	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
295	#421	C₂×D₄₃	1	2	yes	—
296	#419	—	43	2	no	—
297	#413	—	43	1	no	—
298	#413	—	43	2	no	—
299	C₂×#101	—	43	2	no	—
300	C₂×#101	—	43	2	no	—
301	#410	—	43	1	no	—
302	#405	—	43	1	no	—
303	#405	C₂×D₄₃	1	1	yes	characteristic
304	#344	—	43	1	no	—
305	#344	—	43	2	no	—
306	#344	—	43	1	no	—
307	C₄₃	#25448	1	1	yes	characteristic, complemented, Sylow
308	C₂×#41	—	43	1	no	—
309	C₂×#41	C₂²×D₄₃	1	2	yes	—
310	C₂²×Q₈	—	43	2	no	—
311	#137	—	86	4	no	—
312	#137	—	86	2	no	—
313	#137	—	86	2	no	—
314	#137	—	86	4	no	—
315	#137	—	172	2	no	—
316	#137	—	172	2	no	—
317	AGL(1,ℤ/8)	—	86	2	no	—
318	AGL(1,ℤ/8)	—	86	2	no	—
319	#135	—	2	1	no	—
320	#135	—	2	1	no	—
321	#135	—	2	1	no	—
322	#135	—	2	1	no	—
323	#135	—	172	2	no	—
324	C₂×Q₁₆	—	86	2	no	—
325	C₂×Q₁₆	—	86	2	no	—
326	C₂×Q₁₆	—	86	1	no	—
327	C₂×Q₁₆	—	86	1	no	—
328	C₂×Q₁₆	—	86	1	no	—
329	C₂×Q₁₆	—	86	1	no	—
330	C₂×Q₁₆	—	86	1	no	—
331	C₂×Q₁₆	—	86	1	no	—
332	C₂×Q₁₆	D₁₇₂	1	1	yes	characteristic
333	C₂×SD₁₆	—	86	2	no	—
334	C₂×SD₁₆	—	86	2	no	—
335	C₂×SD₁₆	D₁₇₂	1	2	yes	—
336	C₂×D₈	D₁₇₂	1	1	yes	characteristic
337	#131	—	2	4	no	—
338	#131	—	2	4	no	—
339	#131	—	86	1	no	—
340	#131	—	86	1	no	—
341	#131	—	86	1	no	—
342	#131	—	86	1	no	—
343	C₂×M₁₆	—	4	2	no	—
344	C₂×M₁₆	—	43	1	no	—
345	C₂×M₁₆	—	43	1	no	—
346	C₂×M₁₆	—	43	2	no	—
347	C₂×M₁₆	—	86	1	no	—
348	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
349	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
350	C₂²×C₈	—	86	1	no	—
351	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
352	C₄⋊Q₈	—	86	2	no	—
353	#124	—	86	2	no	—
354	#123	—	86	4	no	—
355	C₂²⋊Q₈	—	172	2	no	—
356	#117	—	43	1	no	—
357	#117	C₂²×D₄₃	1	1	yes	characteristic
358	#108	—	86	4	no	—
359	#108	—	86	1	no	—
360	#108	—	86	1	no	—
361	#108	C₂²⋊D₄₃	1	2	yes	—
362	#108	C₂²⋊D₄₃	1	2	yes	—
363	#104	—	2	4	no	—
364	#103	—	172	2	no	—
365	#101	—	43	2	no	—
366	#101	—	86	2	no	—
367	#101	—	86	4	no	—
368	#101	—	86	4	no	—
369	#100	—	43	2	no	—
370	#100	—	86	2	no	—
371	#99	—	86	2	no	—
372	#97	—	2	1	no	—
373	#97	—	86	1	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	—	86	1	no	—
376	#41	—	2	2	no	—
377	#41	—	2	2	no	—
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	#41	—	86	1	no	—
381	#41	—	86	1	no	—
382	#41	—	86	1	no	—
383	#41	—	86	1	no	—
384	C₂×Q₈	—	43	1	no	—
385	C₂×Q₈	—	86	2	no	—
386	C₂×Q₈	—	86	2	no	—
387	C₂×Q₈	—	86	2	no	—
388	C₂×Q₈	—	86	2	no	—
389	C₂×Q₈	—	86	2	no	—
390	C₂×Q₈	—	86	2	no	—
391	C₂×Q₈	C₂×D₁₇₂	1	2	yes	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	43	1	no	—
394	C₂×D₄	—	86	1	no	—
395	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	86	1	no	—
398	C₂²×C₄	—	86	2	no	—
399	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
400	Q₁₆	—	2	1	no	—
401	Q₁₆	—	2	1	no	—
402	Q₁₆	—	172	4	no	—
403	Q₁₆	—	172	4	no	—
404	Q₁₆	—	172	2	no	—
405	Q₁₆	—	172	1	no	—
406	Q₁₆	—	172	1	no	—
407	Q₁₆	—	172	1	no	—
408	Q₁₆	—	172	1	no	—
409	SD₁₆	—	2	2	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	172	4	no	—
412	SD₁₆	—	172	4	no	—
413	SD₁₆	—	172	2	no	—
414	SD₁₆	—	172	2	no	—
415	D₈	—	2	1	no	—
416	D₈	—	2	1	no	—
417	D₈	—	172	2	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	4	4	no	—
421	M₁₆	—	43	2	no	—
422	M₁₆	—	86	1	no	—
423	M₁₆	—	86	2	no	—
424	M₁₆	—	86	1	no	—
425	M₁₆	—	86	1	no	—
426	M₁₆	—	86	2	no	—
427	M₁₆	—	172	1	no	—
428	M₁₆	—	172	1	no	—
429	M₁₆	D₄×D₄₃	1	2	yes	—
430	M₁₆	C₂×C₂²⋊D₄₃	1	4	yes	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	4	4	no	—
434	C₂×C₈	—	86	1	no	—
435	C₂×C₈	—	86	1	no	—
436	C₂×C₈	—	86	2	no	—
437	C₂×C₈	—	172	1	no	—
438	C₂×C₈	—	172	1	no	—
439	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
440	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
441	C₂×C₈	#10621898	1	1	yes	characteristic
442	C₂×C₈	#10621898	1	1	yes	characteristic
443	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
444	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	86	1	no	—
447	C₄⋊C₄	—	172	4	no	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	43	2	no	—
450	C₂²⋊C₄	—	172	4	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	86	1	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	86	1	no	—
455	C₂³	#41×D₄₃	1	1	yes	characteristic
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	86	1	no	—
459	Q₈	—	86	1	no	—
460	Q₈	—	172	2	no	—
461	Q₈	—	172	2	no	—
462	Q₈	—	172	2	no	—
463	Q₈	—	172	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	86	1	no	—
469	D₄	—	86	1	no	—
470	D₄	—	172	1	no	—
471	D₄	—	172	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	86	1	no	—
477	C₂×C₄	—	86	2	no	—
478	C₂×C₄	—	172	2	no	—
479	C₂×C₄	—	172	2	no	—
480	C₂×C₄	—	172	2	no	—
481	C₂×C₄	—	172	1	no	—
482	C₂×C₄	—	172	1	no	—
483	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
486	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
487	C₂×C₄	#13063370	1	1	yes	characteristic
488	C₂×C₄	#13063371	1	1	yes	characteristic
489	C₈	—	2	2	no	—
490	C₈	—	2	4	no	—
491	C₈	—	86	2	no	—
492	C₈	—	172	1	no	—
493	C₈	—	172	2	no	—
494	C₈	#13063299	1	1	yes	characteristic
495	C₈	#13063299	1	1	yes	characteristic
496	C₈	#13063299	1	1	yes	characteristic
497	C₈	#13063299	1	1	yes	characteristic
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	344	1	no	—
502	C₂²	—	172	1	no	—
503	C₂²	#14583446	1	1	yes	characteristic
504	C₂²	#14583544	1	1	yes	characteristic
505	C₂²	#14583568	1	1	yes	characteristic
506	C₄	—	4	2	no	—
507	C₄	—	8	1	no	—
508	C₄	—	344	2	no	—
509	C₄	—	172	2	no	—
510	C₄	—	172	1	no	—
511	C₄	C₂×#13063299	1	1	yes	characteristic
512	C₄	#14583500	1	1	yes	characteristic
513	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
514	C₄	D₄×D₁₇₂	1	1	yes	characteristic
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	2	1	no	—
518	C₂	—	8	2	no	—
519	C₂	—	344	1	no	—
520	C₂	#19138177	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19138177
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2957	C₂
socle	C₂×C₄₃	#2428
prime radical	#19144311	C₂
hypercenter	#2957	D₄₃
hypocenter	C₄₃	#25448
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2957

Complements

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

N	H ≅ G/N	type
1. #19145090	C₂	semidirect
2. #19144332	C₂	semidirect
4. C₂×#14583175	C₂	semidirect
5. #19135876	C₂	semidirect
6. #19135656	C₂	semidirect
7. #19135510	C₂	semidirect
8. #19135386	C₂	semidirect
9. #19135147	C₂	semidirect
10. #19134396	C₂	semidirect
11. C₄₃×#2957	C₂	semidirect
259. #2957	D₄₃	semidirect
307. C₄₃	#25448	semidirect

Maximal subgroups

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

subgroup	index
#19145090	2
#19144332	2
#19144311	2
C₂×#14583175	2
#19135876	2
#19135656	2
#19135510	2
#19135386	2
#19135147	2
#19134396	2
C₄₃×#2957	2
#25448	43