Subgroups — #25079770

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145911	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144917	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143307	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134168	C₂	1	2	yes	maximal, complemented
5	#19134154	C₂	1	2	yes	maximal, complemented
6	#19134016	C₂	1	2	yes	maximal, complemented
7	#19134002	C₂	1	2	yes	maximal, complemented
8	C₂×#14582649	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133283	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133272	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3245	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063332	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	#14583253	—	2	1	no	—
15	#14583253	—	2	1	no	—
16	#14583249	C₂²	1	1	yes	characteristic
17	#14583249	C₂²	1	1	yes	characteristic
18	#14583245	C₂²	1	1	yes	characteristic
19	#14583245	C₂²	1	1	yes	characteristic
20	#14583189	C₂²	1	2	yes	—
21	#14583181	—	2	1	no	—
22	#14583126	—	2	2	no	—
23	#14583104	C₂²	1	2	yes	—
24	#14583096	—	2	1	no	—
25	#14582977	—	2	1	no	—
26	#14582977	C₂²	1	2	yes	—
27	D₄×C₄₃⋊C₈	—	2	1	no	—
28	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
29	#14582923	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	#14582895	—	2	1	no	—
32	#14582895	—	2	1	no	—
33	#14582866	—	2	1	no	—
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	#14582649	C₂²	1	2	yes	—
36	#14582649	C₂²	1	2	yes	—
37	#14582647	C₂²	1	2	yes	—
38	#14582646	C₂²	1	2	yes	—
39	#14582645	C₂²	1	2	yes	—
40	#14582643	C₂²	1	2	yes	—
41	C₄₃×#532	C₂²	1	1	yes	characteristic
42	C₄₃×#532	C₂²	1	1	yes	characteristic
43	C₄₃×#474	—	2	1	no	—
44	C₄₃×#474	C₂²	1	2	yes	—
45	C₄₃×#466	—	2	2	no	—
46	C₄₃×#459	—	2	1	no	—
47	C₄₃×#459	C₂²	1	2	yes	—
48	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×#10621883	—	2	2	no	—
50	#13063332	—	4	4	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621877	—	2	2	no	—
53	C₂²×C₄₃⋊C₈	—	2	1	no	—
54	C₂²×C₄₃⋊C₈	—	2	2	no	—
55	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
56	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
57	#13063325	C₂³	1	1	yes	characteristic
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063317	—	2	1	no	—
60	#13063304	—	2	1	no	—
61	#13063304	—	2	1	no	—
62	C₄×Dic₈₆	—	2	1	no	—
63	C₄×Dic₈₆	—	2	1	no	—
64	#13063284	—	2	1	no	—
65	#13063256	—	2	2	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
67	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
70	#13063249	—	2	1	no	—
71	#13063249	—	2	1	no	—
72	#13063249	—	2	1	no	—
73	#13063249	—	2	1	no	—
74	#13063248	—	2	2	no	—
75	#13063246	—	2	2	no	—
76	#13063246	—	2	1	no	—
77	#13063246	—	2	1	no	—
78	#13063246	—	2	1	no	—
79	#13063246	—	2	1	no	—
80	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
81	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
82	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×#41×C₄₃	—	2	1	no	—
87	C₂×#41×C₄₃	—	2	1	no	—
88	C₂×D₈×C₄₃	—	2	2	no	—
89	C₂²×C₈×C₄₃	—	2	1	no	—
90	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
91	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
92	#127×C₄₃	D₄	1	1	yes	characteristic
93	#127×C₄₃	C₂³	1	1	yes	characteristic
94	#124×C₄₃	—	2	1	no	—
95	#124×C₄₃	—	2	1	no	—
96	#121×C₄₃	—	2	1	no	—
97	#121×C₄₃	—	2	1	no	—
98	#121×C₄₃	—	2	1	no	—
99	#121×C₄₃	D₄	1	2	yes	—
100	C₄×D₄×C₄₃	—	2	1	no	—
101	C₄×D₄×C₄₃	—	2	1	no	—
102	C₄×D₄×C₄₃	—	2	1	no	—
103	C₄×D₄×C₄₃	C₂³	1	2	yes	—
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	#107×C₄₃	—	2	2	no	—
106	C₄⋊C₈×C₄₃	—	2	1	no	—
107	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
108	#102×C₄₃	—	2	2	no	—
109	#102×C₄₃	—	2	2	no	—
110	#41×C₄₃	—	4	2	no	—
111	#41×C₄₃	—	4	2	no	—
112	#41×C₄₃	—	4	2	no	—
113	#41×C₄₃	—	4	2	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	2	1	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	1	no	—
120	C₂×D₄×C₄₃	—	2	1	no	—
121	C₂×D₄×C₄₃	—	2	1	no	—
122	C₂×D₄×C₄₃	—	4	1	no	—
123	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	4	1	no	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
129	C₂×Dic₈₆	—	2	1	no	—
130	C₂×Dic₈₆	—	2	1	no	—
131	D₈×C₄₃	—	8	2	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	8	1	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₄₃	—	2	2	no	—
139	C₂²⋊C₄×C₄₃	—	2	2	no	—
140	C₂²⋊C₄×C₄₃	—	4	1	no	—
141	C₂²⋊C₄×C₄₃	—	4	1	no	—
142	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₃	#41	1	1	yes	characteristic
145	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
146	C₂²⋊Dic₄₃	—	4	1	no	—
147	#10621883	—	8	2	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	Dic₄₃⋊C₄	—	4	1	no	—
153	Dic₄₃⋊C₄	—	4	1	no	—
154	C₄×Dic₄₃	—	4	1	no	—
155	#10621877	—	4	4	no	—
156	#10621877	—	4	2	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	4	4	no	—
162	C₂×C₄₃⋊C₈	—	8	1	no	—
163	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₄₃	—	2	2	no	—
168	C₂³×C₄₃	—	4	1	no	—
169	C₂³×C₄₃	#121	1	1	yes	characteristic
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	4	1	no	—
172	Q₈×C₄₃	—	4	1	no	—
173	D₄×C₄₃	—	2	2	no	—
174	D₄×C₄₃	—	2	2	no	—
175	D₄×C₄₃	—	4	2	no	—
176	D₄×C₄₃	—	4	4	no	—
177	D₄×C₄₃	—	4	1	no	—
178	D₄×C₄₃	—	4	1	no	—
179	D₄×C₄₃	—	4	1	no	—
180	D₄×C₄₃	—	4	1	no	—
181	D₄×C₄₃	—	4	2	no	—
182	D₄×C₄₃	—	8	1	no	—
183	D₄×C₄₃	—	8	2	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	8	2	no	—
192	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₄₃	#135	1	2	yes	—
196	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
200	C₂×Dic₄₃	—	4	1	no	—
201	C₂×Dic₄₃	—	4	1	no	—
202	Dic₈₆	—	4	1	no	—
203	Dic₈₆	—	4	1	no	—
204	Dic₈₆	—	8	1	no	—
205	C₈×C₄₃	—	4	2	no	—
206	C₄₃⋊C₈	—	2	1	no	—
207	C₄₃⋊C₈	—	2	1	no	—
208	C₄₃⋊C₈	—	2	1	no	—
209	C₄₃⋊C₈	—	2	1	no	—
210	C₄₃⋊C₈	—	4	2	no	—
211	C₄₃⋊C₈	—	4	2	no	—
212	#19200	—	43	1	no	maximal, Sylow
213	C₂²×C₄₃	—	2	1	no	—
214	C₂²×C₄₃	—	2	1	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	8	1	no	—
219	C₂²×C₄₃	—	8	1	no	—
220	C₂²×C₄₃	—	8	1	no	—
221	C₂²×C₄₃	#463	1	2	yes	—
222	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	2	1	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	—	8	1	no	—
228	C₄×C₄₃	#463	1	2	yes	—
229	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
230	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₄₃	#577	1	1	yes	characteristic
232	C₄×C₄₃	#577	1	1	yes	characteristic
233	Dic₄₃	—	8	1	no	—
234	Dic₄₃	—	8	1	no	—
235	#3246	—	43	1	no	—
236	#3245	D₄₃	1	1	yes	characteristic
237	#3131	—	43	1	no	—
238	#2931	—	43	1	no	—
239	#1703	—	43	2	no	—
240	#1701	—	43	2	no	—
241	#1679	—	43	2	no	—
242	#1677	—	43	2	no	—
243	C₂×#334	—	43	1	no	—
244	#1550	—	43	1	no	—
245	#1547	—	43	1	no	—
246	C₂×C₄₃	—	2	2	no	—
247	C₂×C₄₃	—	8	2	no	—
248	C₂×C₄₃	—	16	1	no	—
249	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
250	C₂×C₄₃	#3060	1	1	yes	characteristic
251	C₂×C₄₃	#3067	1	1	yes	characteristic
252	C₂×#131	—	86	1	no	—
253	#533	—	43	1	no	—
254	#532	C₂×D₄₃	1	1	yes	characteristic
255	#532	C₂×D₄₃	1	1	yes	characteristic
256	#488	—	86	1	no	—
257	#488	—	86	1	no	—
258	#487	—	43	1	no	—
259	#487	—	43	1	no	—
260	#486	—	43	1	no	—
261	#486	—	43	1	no	—
262	#476	—	43	2	no	—
263	#475	—	86	1	no	—
264	#474	—	2	1	no	—
265	#474	C₂×D₄₃	1	2	yes	—
266	#466	—	2	2	no	—
267	#465	—	86	2	no	—
268	#461	—	43	2	no	—
269	#460	—	86	1	no	—
270	#459	—	2	1	no	—
271	#459	C₂×D₄₃	1	2	yes	—
272	#436	—	43	2	no	—
273	#436	—	86	1	no	—
274	C₈×D₄	—	43	2	no	—
275	C₈×D₄	—	86	1	no	—
276	#423	—	43	1	no	—
277	C₂×C₄⋊C₈	—	43	1	no	—
278	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
279	#416	—	86	1	no	—
280	#416	—	86	1	no	—
281	#408	—	86	1	no	—
282	C₂×C₄×C₈	—	43	1	no	—
283	#334	—	43	2	no	—
284	#334	—	43	2	no	—
285	#333	—	43	2	no	—
286	#332	—	43	2	no	—
287	#332	—	43	2	no	—
288	#331	—	43	2	no	—
289	C₄₃	#19200	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	2	1	no	—
292	C₂×SD₁₆	—	86	2	no	—
293	C₂×D₈	—	2	2	no	—
294	#131	—	172	4	no	—
295	C₂×M₁₆	—	86	2	no	—
296	C₂×M₁₆	—	86	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	43	1	no	—
299	C₂²×C₈	—	43	1	no	—
300	C₂²×C₈	—	86	2	no	—
301	C₂²×C₈	—	86	1	no	—
302	C₄⋊Q₈	—	43	1	no	—
303	C₄⋊Q₈	—	43	1	no	—
304	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
305	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
306	#127	C₂²⋊D₄₃	1	1	yes	characteristic
307	#127	C₂²×D₄₃	1	1	yes	characteristic
308	#125	—	86	1	no	—
309	#124	—	2	1	no	—
310	#124	—	2	1	no	—
311	C₂²⋊Q₈	—	86	1	no	—
312	C₂²⋊Q₈	—	86	1	no	—
313	#121	—	2	1	no	—
314	#121	—	2	1	no	—
315	#121	—	2	1	no	—
316	#121	C₂²⋊D₄₃	1	2	yes	—
317	C₄×Q₈	—	86	1	no	—
318	C₄×Q₈	—	86	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	C₂²×D₄₃	1	2	yes	—
323	#117	—	86	1	no	—
324	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
325	#107	—	2	2	no	—
326	#106	—	86	2	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	43	2	no	—
329	C₄⋊C₈	—	43	2	no	—
330	C₄⋊C₈	—	86	1	no	—
331	C₄⋊C₈	—	86	1	no	—
332	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
333	#103	—	86	1	no	—
334	#103	—	86	1	no	—
335	#103	—	86	1	no	—
336	#103	—	86	1	no	—
337	#103	—	86	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#102	—	86	1	no	—
341	#102	—	86	1	no	—
342	#102	—	86	1	no	—
343	#102	—	86	1	no	—
344	#102	—	86	2	no	—
345	C₂²⋊C₈	—	86	2	no	—
346	C₂²⋊C₈	—	86	2	no	—
347	C₄×C₈	—	43	1	no	—
348	C₄×C₈	—	43	1	no	—
349	C₄×C₈	—	43	1	no	—
350	C₄×C₈	—	43	1	no	—
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	#41	—	4	2	no	—
354	#41	—	4	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	86	1	no	—
358	C₂×Q₈	—	86	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
370	C₂²×C₄	#10621900	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
372	SD₁₆	—	344	2	no	—
373	D₈	—	8	2	no	—
374	M₁₆	—	172	4	no	—
375	M₁₆	—	172	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	8	1	no	—
378	C₂×C₈	—	43	1	no	—
379	C₂×C₈	—	43	1	no	—
380	C₂×C₈	—	43	1	no	—
381	C₂×C₈	—	43	1	no	—
382	C₂×C₈	—	86	2	no	—
383	C₂×C₈	—	86	2	no	—
384	C₂×C₈	—	86	2	no	—
385	C₂×C₈	—	86	2	no	—
386	C₂×C₈	—	344	1	no	—
387	C₂×C₈	—	172	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	86	1	no	—
392	C₄⋊C₄	—	86	1	no	—
393	C₄⋊C₄	—	86	1	no	—
394	C₄⋊C₄	—	86	1	no	—
395	C₄⋊C₄	—	172	1	no	—
396	C₄⋊C₄	—	172	1	no	—
397	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	172	1	no	—
403	C₄²	—	172	1	no	—
404	C₄²	D₄×D₄₃	1	1	yes	characteristic
405	C₄²	#10621900	1	1	yes	characteristic
406	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
407	C₄²	C₂³×D₄₃	1	1	yes	characteristic
408	C₂³	—	2	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	#13063297	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	344	1	no	—
415	Q₈	—	172	1	no	—
416	Q₈	—	172	1	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	—	172	1	no	—
437	C₂×C₄	—	172	1	no	—
438	C₂×C₄	#13063297	1	1	yes	characteristic
439	C₂×C₄	#13063297	1	1	yes	characteristic
440	C₂×C₄	#13063297	1	1	yes	characteristic
441	C₂×C₄	#13063344	1	2	yes	—
442	C₂×C₄	#13063349	1	2	yes	—
443	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
446	C₈	—	4	2	no	—
447	C₈	—	86	1	no	—
448	C₈	—	86	1	no	—
449	C₈	—	86	1	no	—
450	C₈	—	86	1	no	—
451	C₈	—	172	2	no	—
452	C₈	—	172	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	#14583112	1	2	yes	—
462	C₂²	C₂×#13063297	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	344	1	no	—
469	C₄	—	344	1	no	—
470	C₄	#14583112	1	2	yes	—
471	C₄	C₂×#13063344	1	1	yes	characteristic
472	C₄	C₂×#13063349	1	1	yes	characteristic
473	C₄	#14583707	1	1	yes	characteristic
474	C₄	#14583710	1	1	yes	characteristic
475	C₂	—	2	2	no	—
476	C₂	—	8	2	no	—
477	C₂	—	16	1	no	—
478	C₂	C₂×#14583112	1	1	yes	characteristic
479	C₂	#19144254	1	1	yes	characteristic
480	C₂	#19144312	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting, prime radical	C₄₃×#3245	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#3245	D₄₃
hypocenter	C₄₃	#19200
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3245

Complements

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

N	H ≅ G/N	type
1. #19145911	C₂	semidirect
2. #19144917	C₂	semidirect
3. #19143307	C₂	semidirect
4. #19134168	C₂	semidirect
5. #19134154	C₂	semidirect
6. #19134016	C₂	semidirect
7. #19134002	C₂	semidirect
8. C₂×#14582649	C₂	semidirect
9. #19133283	C₂	semidirect
10. #19133272	C₂	semidirect
289. C₄₃	#19200	semidirect

Maximal subgroups

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

subgroup	index
#19145911	2
#19144917	2
#19143307	2
#19134168	2
#19134154	2
#19134016	2
#19134002	2
C₂×#14582649	2
#19133283	2
#19133272	2
C₄₃×#3245	2
#19200	43