Subgroups — #19149378

Order 5504.

1412 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583735	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063373	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583715	C₂	1	4	yes	maximal, complemented
4	#14583712	C₂	1	4	yes	maximal, complemented
5	#14583708	C₂	1	4	yes	maximal, complemented
6	#14583705	C₂	1	4	yes	maximal, complemented
7	#14583699	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583698	C₂	1	4	yes	maximal, complemented
9	#14583697	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063356	C₂	1	1	yes	maximal, characteristic, complemented
11	#137×D₄₃	C₂	1	4	yes	maximal, complemented
12	#14583665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#137×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#13063373	—	2	2	no	—
15	#13063373	—	2	2	no	—
16	#13063373	C₂²	1	4	yes	complemented
17	#13063373	C₂²	1	4	yes	complemented
18	#13063373	C₂²	1	2	yes	complemented
19	#13063372	—	2	1	no	—
20	#13063372	C₂²	1	2	yes	complemented
21	#13063371	—	2	1	no	—
22	#13063371	C₂²	1	2	yes	complemented
23	#13063370	—	2	2	no	—
24	#13063370	C₂²	1	2	yes	complemented
25	C₂×#10621902	—	2	1	no	—
26	C₂×#10621902	C₂²	1	2	yes	complemented
27	C₂×#10621898	—	2	2	no	—
28	C₂×#10621898	—	2	2	no	—
29	C₂×#10621898	C₂²	1	1	yes	characteristic
30	C₂×#10621898	C₂²	1	1	yes	characteristic
31	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
32	#41×D₄₃	—	2	2	no	—
33	#41×D₄₃	C₂²	1	4	yes	—
34	C₂×Q₈×D₄₃	—	2	1	no	—
35	C₂×Q₈×D₄₃	C₂²	1	2	yes	complemented
36	#13063358	C₂²	1	2	yes	complemented
37	#13063358	C₂²	1	2	yes	complemented
38	#13063357	C₂²	1	8	yes	complemented
39	#13063357	C₂²	1	8	yes	complemented
40	#13063356	C₂²	1	4	yes	complemented
41	#13063356	C₂²	1	4	yes	complemented
42	#13063356	C₂²	1	2	yes	complemented
43	#13063355	C₂²	1	2	yes	complemented
44	#13063354	C₂²	1	8	yes	complemented
45	#13063353	C₂²	1	2	yes	complemented
46	#13063353	C₂²	1	2	yes	complemented
47	#13063352	C₂²	1	8	yes	complemented
48	#13063351	C₂²	1	2	yes	complemented
49	#13063350	C₂²	1	2	yes	complemented
50	#13063348	C₂²	1	8	yes	complemented
51	#13063347	C₂²	1	4	yes	complemented
52	#13063346	C₂²	1	8	yes	complemented
53	#13063345	C₂²	1	4	yes	complemented
54	C₂×#10621885	C₂²	1	2	yes	complemented
55	Q₁₆×D₄₃	C₂²	1	8	yes	complemented
56	C₂×#10621884	C₂²	1	2	yes	complemented
57	SD₁₆×D₄₃	C₂²	1	8	yes	complemented
58	#13063333	C₂²	1	4	yes	complemented
59	#13063331	C₂²	1	4	yes	complemented
60	C₂×#10621877	C₂²	1	1	yes	characteristic, complemented
61	M₁₆×D₄₃	C₂²	1	4	yes	complemented
62	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
64	#137×C₄₃	C₂²	1	4	yes	complemented
65	#137×C₄₃	C₂²	1	4	yes	complemented
66	C₂×Q₁₆×C₄₃	C₂²	1	2	yes	complemented
67	C₂×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
68	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
69	#41×C₄₃	—	2	1	no	—
70	#41×C₄₃	—	2	1	no	—
71	#41×C₄₃	C₂³	1	2	yes	—
72	#41×C₄₃	C₂³	1	2	yes	—
73	C₂×Q₈×C₄₃	—	2	1	no	—
74	C₂×Q₈×C₄₃	—	2	1	no	—
75	C₂×Q₈×C₄₃	—	2	1	no	—
76	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
77	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
79	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
80	C₂×D₄×C₄₃	—	2	1	no	—
81	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊D₄₃	—	2	4	no	—
86	C₂×C₂²⋊D₄₃	—	2	1	no	—
87	C₂×C₂²⋊D₄₃	—	2	1	no	—
88	C₂×C₂²⋊D₄₃	D₄	1	2	yes	—
89	#10621902	—	2	2	no	—
90	#10621902	—	2	4	no	—
91	#10621902	—	2	4	no	—
92	#10621902	—	2	4	no	—
93	#10621902	C₂³	1	8	yes	—
94	#10621902	C₂³	1	4	yes	—
95	Q₈×D₄₃	—	2	4	no	—
96	Q₈×D₄₃	—	2	4	no	—
97	Q₈×D₄₃	—	2	4	no	—
98	Q₈×D₄₃	—	2	2	no	—
99	Q₈×D₄₃	C₂³	1	8	yes	—
100	Q₈×D₄₃	C₂³	1	4	yes	—
101	#10621900	—	2	4	no	—
102	#10621900	—	2	4	no	—
103	#10621900	—	2	2	no	—
104	#10621900	C₂³	1	4	yes	—
105	D₄×D₄₃	—	2	4	no	—
106	D₄×D₄₃	—	2	2	no	—
107	D₄×D₄₃	—	2	4	no	—
108	D₄×D₄₃	C₂³	1	4	yes	—
109	#10621898	—	2	1	no	—
110	#10621898	—	2	1	no	—
111	#10621898	—	2	1	no	—
112	#10621898	—	2	1	no	—
113	#10621898	—	2	4	no	—
114	#10621898	—	2	8	no	—
115	#10621898	—	2	8	no	—
116	#10621898	—	2	2	no	—
117	#10621898	—	2	4	no	—
118	#10621898	—	2	2	no	—
119	#10621898	D₄	1	2	yes	—
120	#10621898	D₄	1	2	yes	—
121	#10621898	C₂³	1	2	yes	—
122	#10621898	C₂³	1	2	yes	—
123	#10621898	C₂³	1	2	yes	—
124	#10621898	C₂³	1	2	yes	—
125	#10621898	C₂³	1	2	yes	—
126	#10621898	C₂³	1	2	yes	—
127	C₂×D₁₇₂	—	2	2	no	—
128	C₂×D₁₇₂	—	2	2	no	—
129	C₂×D₁₇₂	D₄	1	1	yes	characteristic
130	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
131	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₄₃	—	2	1	no	—
133	C₂×C₄×D₄₃	—	2	1	no	—
134	C₂×C₄×D₄₃	—	2	2	no	—
135	C₂×C₄×D₄₃	—	2	4	no	—
136	C₂×C₄×D₄₃	—	2	2	no	—
137	C₂×C₄×D₄₃	C₂³	1	2	yes	—
138	C₂×Dic₈₆	—	2	2	no	—
139	C₂×Dic₈₆	—	2	2	no	—
140	C₂×Dic₈₆	D₄	1	1	yes	characteristic
141	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
142	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
143	Q₁₆×C₄₃	C₂³	1	8	yes	—
144	SD₁₆×C₄₃	C₂³	1	8	yes	—
145	M₁₆×C₄₃	C₂³	1	2	yes	—
146	M₁₆×C₄₃	C₂³	1	2	yes	—
147	C₂×C₈×C₄₃	C₂³	1	2	yes	—
148	#10621885	C₂³	1	4	yes	—
149	#10621885	C₂³	1	8	yes	—
150	#10621884	C₂³	1	8	yes	—
151	#10621884	C₂³	1	4	yes	—
152	#10621883	C₂³	1	4	yes	—
153	#10621882	C₂³	1	4	yes	—
154	#10621877	C₂³	1	2	yes	—
155	#10621877	C₂³	1	2	yes	—
156	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
157	Dic₁₇₂	C₂³	1	4	yes	—
158	D₃₄₄	C₂³	1	4	yes	—
159	#10621873	C₂³	1	4	yes	—
160	#10621873	C₂³	1	4	yes	—
161	#10621872	C₂³	1	8	yes	—
162	C₈×D₄₃	C₂³	1	8	yes	—
163	C₂³×C₄₃	—	2	1	no	—
164	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×D₄₃	—	2	1	no	—
166	C₂²×D₄₃	—	2	1	no	—
167	C₂²×D₄₃	—	2	4	no	—
168	C₂²×D₄₃	C₂×D₄	1	2	yes	—
169	Q₈×C₄₃	—	2	2	no	—
170	Q₈×C₄₃	—	2	2	no	—
171	Q₈×C₄₃	—	2	2	no	—
172	Q₈×C₄₃	—	2	1	no	—
173	Q₈×C₄₃	C₂⁴	1	4	yes	—
174	Q₈×C₄₃	C₂⁴	1	2	yes	—
175	D₄×C₄₃	—	2	2	no	—
176	D₄×C₄₃	—	2	2	no	—
177	D₄×C₄₃	—	2	1	no	—
178	D₄×C₄₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
191	C₂²⋊D₄₃	—	2	2	no	—
192	C₂²⋊D₄₃	—	2	2	no	—
193	C₂²⋊D₄₃	—	2	2	no	—
194	C₂²⋊D₄₃	—	2	2	no	—
195	C₂²⋊D₄₃	—	2	4	no	—
196	C₂²⋊D₄₃	—	2	4	no	—
197	C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
198	C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
199	C₂×Dic₄₃	—	2	1	no	—
200	C₂×Dic₄₃	—	2	1	no	—
201	C₂×Dic₄₃	—	2	4	no	—
202	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
203	D₁₇₂	—	2	4	no	—
204	D₁₇₂	—	2	8	no	—
205	D₁₇₂	—	2	1	no	—
206	D₁₇₂	—	2	1	no	—
207	D₁₇₂	C₂×D₄	1	2	yes	—
208	D₁₇₂	C₂×D₄	1	2	yes	—
209	D₁₇₂	C₂⁴	1	2	yes	—
210	D₁₇₂	C₂⁴	1	2	yes	—
211	C₄×D₄₃	—	2	4	no	—
212	C₄×D₄₃	—	2	8	no	—
213	C₄×D₄₃	—	2	2	no	—
214	C₄×D₄₃	—	2	2	no	—
215	C₄×D₄₃	—	2	2	no	—
216	C₄×D₄₃	—	2	2	no	—
217	C₄×D₄₃	—	2	4	no	—
218	C₄×D₄₃	—	2	8	no	—
219	C₄×D₄₃	C₂×D₄	1	4	yes	—
220	C₄×D₄₃	C₂⁴	1	4	yes	—
221	Dic₈₆	—	2	1	no	—
222	Dic₈₆	—	2	1	no	—
223	Dic₈₆	—	2	4	no	—
224	Dic₈₆	—	2	8	no	—
225	Dic₈₆	C₂×D₄	1	2	yes	—
226	Dic₈₆	C₂×D₄	1	2	yes	—
227	Dic₈₆	C₂⁴	1	2	yes	—
228	Dic₈₆	C₂⁴	1	2	yes	—
229	C₈×C₄₃	C₂⁴	1	4	yes	—
230	C₄₃⋊C₈	C₂⁴	1	4	yes	—
231	C₂²×C₄₃	—	2	2	no	—
232	C₂²×C₄₃	—	4	1	no	—
233	C₂²×C₄₃	—	8	1	no	—
234	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
235	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
236	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×D₄₃	—	2	2	no	—
238	C₂×D₄₃	—	2	2	no	—
239	C₂×D₄₃	—	4	2	no	—
240	C₂×D₄₃	—	4	2	no	—
241	C₂×D₄₃	—	8	4	no	—
242	C₂×D₄₃	—	8	1	no	—
243	C₂×D₄₃	C₂²×D₄	1	4	yes	—
244	C₄×C₄₃	—	2	2	no	—
245	C₄×C₄₃	—	2	4	no	—
246	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
248	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
249	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
250	Dic₄₃	—	2	2	no	—
251	Dic₄₃	—	2	2	no	—
252	Dic₄₃	C₂²×D₄	1	4	yes	—
253	#3586	—	43	1	no	maximal, Sylow
254	C₂×C₄₃	—	2	1	no	—
255	C₂×C₄₃	—	2	1	no	—
256	C₂×C₄₃	—	2	1	no	—
257	C₂×C₄₃	—	4	2	no	—
258	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
259	D₄₃	—	2	4	no	—
260	D₄₃	—	4	2	no	—
261	D₄₃	—	4	2	no	—
262	#585	—	43	1	no	—
263	C₂×2₋¹⁺⁴	—	43	1	no	—
264	#578	—	43	4	no	—
265	#578	—	43	4	no	—
266	#577	—	43	4	no	—
267	#577	—	43	4	no	—
268	#575	—	43	1	no	—
269	#575	—	43	4	no	—
270	#575	—	43	1	no	—
271	C₂×#137	—	43	1	no	—
272	C₂×#137	—	43	4	no	—
273	C₂×#137	D₄₃	1	1	yes	characteristic, complemented
274	#568	—	43	1	no	—
275	C₄₃	#3586	1	1	yes	characteristic, complemented, Sylow
276	2₋¹⁺⁴	—	43	2	no	—
277	2₋¹⁺⁴	—	43	4	no	—
278	2₋¹⁺⁴	—	43	4	no	—
279	2₋¹⁺⁴	—	43	2	no	—
280	2₋¹⁺⁴	—	86	2	no	—
281	2₋¹⁺⁴	—	86	2	no	—
282	2₋¹⁺⁴	—	86	1	no	—
283	H(5,𝔽₂)	—	43	2	no	—
284	H(5,𝔽₂)	—	43	2	no	—
285	H(5,𝔽₂)	—	86	2	no	—
286	H(5,𝔽₂)	—	86	1	no	—
287	C₂×#41	—	43	1	no	—
288	C₂×#41	—	43	4	no	—
289	C₂×#41	—	43	2	no	—
290	C₂×#41	—	43	1	no	—
291	C₂×#41	—	43	1	no	—
292	C₂×#41	—	86	2	no	—
293	C₂×#41	—	86	2	no	—
294	C₂×#41	—	86	1	no	—
295	C₂×#41	—	86	2	no	—
296	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
297	C₂²×Q₈	—	43	2	no	—
298	C₂²×Q₈	—	86	1	no	—
299	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
300	#137	—	43	2	no	—
301	#137	—	43	4	no	—
302	#137	—	43	4	no	—
303	#137	—	43	2	no	—
304	#137	—	43	8	no	—
305	#137	—	43	8	no	—
306	#137	—	43	8	no	—
307	#137	—	43	2	no	—
308	#137	—	43	2	no	—
309	#137	C₂×D₄₃	1	4	yes	complemented
310	#137	C₂×D₄₃	1	4	yes	complemented
311	AGL(1,ℤ/8)	—	43	2	no	—
312	AGL(1,ℤ/8)	—	43	2	no	—
313	AGL(1,ℤ/8)	—	43	8	no	—
314	AGL(1,ℤ/8)	—	43	2	no	—
315	AGL(1,ℤ/8)	—	43	2	no	—
316	#135	—	43	4	no	—
317	#135	—	43	8	no	—
318	#135	—	43	8	no	—
319	#135	—	43	4	no	—
320	C₂×Q₁₆	—	43	2	no	—
321	C₂×Q₁₆	—	43	8	no	—
322	C₂×Q₁₆	C₂×D₄₃	1	2	yes	complemented
323	C₂×SD₁₆	—	43	2	no	—
324	C₂×SD₁₆	—	43	8	no	—
325	C₂×SD₁₆	C₂×D₄₃	1	2	yes	complemented
326	#131	—	43	4	no	—
327	#131	—	43	4	no	—
328	C₂×M₁₆	—	43	1	no	—
329	C₂×M₁₆	—	43	4	no	—
330	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
331	#41	—	2	1	no	—
332	#41	—	2	1	no	—
333	#41	—	43	2	no	—
334	#41	—	43	2	no	—
335	#41	—	43	2	no	—
336	#41	—	43	2	no	—
337	#41	—	43	8	no	—
338	#41	—	43	4	no	—
339	#41	—	43	4	no	—
340	#41	—	43	2	no	—
341	#41	—	43	2	no	—
342	#41	—	43	2	no	—
343	#41	—	43	2	no	—
344	#41	—	86	4	no	—
345	#41	—	86	4	no	—
346	#41	—	86	2	no	—
347	#41	—	86	8	no	—
348	#41	—	86	8	no	—
349	#41	—	86	2	no	—
350	#41	—	86	4	no	—
351	#41	—	86	4	no	—
352	#41	—	86	4	no	—
353	#41	—	86	2	no	—
354	#41	—	86	2	no	—
355	#41	—	86	4	no	—
356	#41	—	86	4	no	—
357	#41	—	86	1	no	—
358	#41	—	86	1	no	—
359	#41	—	86	1	no	—
360	#41	—	86	1	no	—
361	#41	C₂²×D₄₃	1	2	yes	—
362	#41	C₂²×D₄₃	1	2	yes	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	43	1	no	—
367	C₂×Q₈	—	43	8	no	—
368	C₂×Q₈	—	43	4	no	—
369	C₂×Q₈	—	43	1	no	—
370	C₂×Q₈	—	43	1	no	—
371	C₂×Q₈	—	86	2	no	—
372	C₂×Q₈	—	86	2	no	—
373	C₂×Q₈	—	86	4	no	—
374	C₂×Q₈	—	86	4	no	—
375	C₂×Q₈	—	86	4	no	—
376	C₂×Q₈	—	86	2	no	—
377	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
378	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
379	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
380	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	43	2	no	—
383	C₂×D₄	—	43	4	no	—
384	C₂×D₄	—	43	1	no	—
385	C₂×D₄	—	43	1	no	—
386	C₂×D₄	—	43	1	no	—
387	C₂×D₄	—	86	2	no	—
388	C₂×D₄	—	86	2	no	—
389	C₂×D₄	—	86	4	no	—
390	C₂×D₄	—	86	2	no	—
391	C₂×D₄	—	86	4	no	—
392	C₂×D₄	—	86	4	no	—
393	C₂×D₄	—	86	1	no	—
394	C₂×D₄	—	86	1	no	—
395	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	43	2	no	—
399	C₂²×C₄	—	86	2	no	—
400	C₂²×C₄	—	86	4	no	—
401	C₂²×C₄	—	86	2	no	—
402	C₂²×C₄	—	86	1	no	—
403	C₂²×C₄	—	86	1	no	—
404	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
405	Q₁₆	—	43	4	no	—
406	Q₁₆	—	43	8	no	—
407	Q₁₆	—	43	4	no	—
408	Q₁₆	C₂²×D₄₃	1	8	yes	—
409	SD₁₆	—	43	8	no	—
410	SD₁₆	—	43	4	no	—
411	SD₁₆	—	43	4	no	—
412	SD₁₆	—	43	4	no	—
413	SD₁₆	—	43	4	no	—
414	SD₁₆	C₂²×D₄₃	1	8	yes	—
415	D₈	—	43	4	no	—
416	D₈	—	43	4	no	—
417	M₁₆	—	43	2	no	—
418	M₁₆	—	43	2	no	—
419	M₁₆	—	43	8	no	—
420	M₁₆	C₂²×D₄₃	1	2	yes	—
421	M₁₆	C₂²×D₄₃	1	2	yes	—
422	C₂×C₈	—	43	2	no	—
423	C₂×C₈	—	43	8	no	—
424	C₂×C₈	C₂²×D₄₃	1	2	yes	—
425	C₂³	—	2	1	no	—
426	C₂³	—	43	2	no	—
427	C₂³	—	86	4	no	—
428	C₂³	—	86	1	no	—
429	C₂³	—	86	1	no	—
430	C₂³	D₄×D₄₃	1	1	yes	characteristic
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	1	no	—
435	Q₈	—	43	2	no	—
436	Q₈	—	43	2	no	—
437	Q₈	—	43	2	no	—
438	Q₈	—	43	2	no	—
439	Q₈	—	86	8	no	—
440	Q₈	—	86	4	no	—
441	Q₈	—	86	1	no	—
442	Q₈	—	86	1	no	—
443	Q₈	C₂³×D₄₃	1	4	yes	—
444	Q₈	C₂³×D₄₃	1	2	yes	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	1	no	—
448	D₄	—	43	4	no	—
449	D₄	—	43	4	no	—
450	D₄	—	43	2	no	—
451	D₄	—	43	2	no	—
452	D₄	—	43	2	no	—
453	D₄	—	43	2	no	—
454	D₄	—	86	4	no	—
455	D₄	—	86	8	no	—
456	D₄	—	86	4	no	—
457	D₄	—	86	4	no	—
458	D₄	—	86	2	no	—
459	D₄	—	86	2	no	—
460	D₄	—	86	2	no	—
461	D₄	—	86	2	no	—
462	D₄	—	86	1	no	—
463	D₄	—	86	1	no	—
464	D₄	C₂³×D₄₃	1	2	yes	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	43	2	no	—
472	C₂×C₄	—	43	4	no	—
473	C₂×C₄	—	43	4	no	—
474	C₂×C₄	—	86	4	no	—
475	C₂×C₄	—	86	8	no	—
476	C₂×C₄	—	86	4	no	—
477	C₂×C₄	—	86	8	no	—
478	C₂×C₄	—	86	4	no	—
479	C₂×C₄	—	86	1	no	—
480	C₂×C₄	—	86	1	no	—
481	C₂×C₄	—	86	2	no	—
482	C₂×C₄	—	86	2	no	—
483	C₂×C₄	—	86	2	no	—
484	C₂×C₄	—	86	2	no	—
485	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
486	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
487	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
489	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
491	C₈	—	43	4	no	—
492	C₈	C₂³×D₄₃	1	4	yes	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	43	4	no	—
497	C₂²	—	86	2	no	—
498	C₂²	—	86	2	no	—
499	C₂²	—	344	1	no	—
500	C₂²	—	344	4	no	—
501	C₂²	—	172	2	no	—
502	C₂²	—	172	2	no	—
503	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
504	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
505	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	43	4	no	—
509	C₄	—	86	2	no	—
510	C₄	—	86	2	no	—
511	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
512	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
513	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
514	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	2	1	no	—
518	C₂	—	4	2	no	—
519	C₂	—	86	4	no	—
520	C₂	—	172	2	no	—
521	C₂	—	172	2	no	—
522	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	C₂×#137×C₄₃	C₂
socle	C₂×C₄₃	C₂³×D₄
hypercenter	C₂×#137	D₄₃
hypocenter	C₄₃	#3586
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#137

Complements

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

N	H ≅ G/N	type
1. #14583735	C₂	semidirect
2. C₂×#13063373	C₂	semidirect
3. #14583715	C₂	semidirect
4. #14583712	C₂	semidirect
5. #14583708	C₂	semidirect
6. #14583705	C₂	semidirect
7. #14583699	C₂	semidirect
8. #14583698	C₂	semidirect
9. #14583697	C₂	semidirect
10. C₂×#13063356	C₂	semidirect
11. #137×D₄₃	C₂	semidirect
12. #14583665	C₂	semidirect
13. C₂×#137×C₄₃	C₂	semidirect
16. #13063373	C₂²	semidirect
17. #13063373	C₂²	semidirect
18. #13063373	C₂²	semidirect
20. #13063372	C₂²	semidirect
22. #13063371	C₂²	semidirect
24. #13063370	C₂²	semidirect
26. C₂×#10621902	C₂²	semidirect
31. C₂×#10621898	C₂²	semidirect
35. C₂×Q₈×D₄₃	C₂²	semidirect
36. #13063358	C₂²	semidirect
37. #13063358	C₂²	semidirect
38. #13063357	C₂²	semidirect
39. #13063357	C₂²	semidirect
40. #13063356	C₂²	semidirect
41. #13063356	C₂²	semidirect
42. #13063356	C₂²	semidirect
43. #13063355	C₂²	semidirect
44. #13063354	C₂²	semidirect
45. #13063353	C₂²	semidirect
46. #13063353	C₂²	semidirect
47. #13063352	C₂²	semidirect
48. #13063351	C₂²	semidirect
49. #13063350	C₂²	semidirect
50. #13063348	C₂²	semidirect
51. #13063347	C₂²	semidirect
52. #13063346	C₂²	semidirect
53. #13063345	C₂²	semidirect
54. C₂×#10621885	C₂²	semidirect
55. Q₁₆×D₄₃	C₂²	semidirect
56. C₂×#10621884	C₂²	semidirect
57. SD₁₆×D₄₃	C₂²	semidirect
58. #13063333	C₂²	semidirect
59. #13063331	C₂²	semidirect
60. C₂×#10621877	C₂²	semidirect
61. M₁₆×D₄₃	C₂²	semidirect
63. C₂²×Q₈×C₄₃	C₂²	semidirect
64. #137×C₄₃	C₂²	semidirect
65. #137×C₄₃	C₂²	semidirect
66. C₂×Q₁₆×C₄₃	C₂²	semidirect
67. C₂×SD₁₆×C₄₃	C₂²	semidirect
68. C₂×M₁₆×C₄₃	C₂²	semidirect
273. C₂×#137	D₄₃	semidirect
275. C₄₃	#3586	semidirect
299. C₂²×Q₈	C₂×D₄₃	semidirect
309. #137	C₂×D₄₃	semidirect
310. #137	C₂×D₄₃	semidirect
322. C₂×Q₁₆	C₂×D₄₃	semidirect
325. C₂×SD₁₆	C₂×D₄₃	semidirect
330. C₂×M₁₆	C₂×D₄₃	semidirect