Subgroups — #19148862

Order 5504.

1058 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583642	C₂	1	2	yes	maximal, complemented
2	#14583638	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583635	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583633	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583616	C₂	1	2	yes	maximal, complemented
6	#14583613	C₂	1	2	yes	maximal, complemented
7	#14583572	C₂	1	2	yes	maximal, complemented
8	#14583555	C₂	1	2	yes	maximal, complemented
9	#14583538	C₂	1	2	yes	maximal, complemented
10	#14583517	C₂	1	2	yes	maximal, complemented
11	#14583516	C₂	1	2	yes	maximal, complemented
12	#14583515	C₂	1	2	yes	maximal, complemented
13	#14583486	C₂	1	2	yes	maximal, complemented
14	#14583481	C₂	1	2	yes	maximal, complemented
15	#14583471	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583462	C₂	1	1	yes	maximal, characteristic, complemented
17	#14583405	C₂	1	1	yes	maximal, characteristic, complemented
18	#14583405	C₂	1	2	yes	maximal, complemented
19	C₄₃×#560	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10621900	C₂²	1	2	yes	—
21	C₂×#10621900	C₂²	1	1	yes	characteristic
22	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
25	#13063324	C₂²	1	2	yes	complemented
26	#13063324	C₂²	1	2	yes	complemented
27	#13063321	C₂²	1	1	yes	characteristic
28	#13063320	C₂²	1	2	yes	complemented
29	#13063320	C₂²	1	2	yes	complemented
30	#13063320	C₂²	1	2	yes	complemented
31	#13063318	C₂²	1	2	yes	complemented
32	#13063318	C₂²	1	2	yes	complemented
33	#13063313	C₂²	1	1	yes	characteristic, complemented
34	#13063312	C₂²	1	2	yes	complemented
35	#13063312	C₂²	1	2	yes	complemented
36	#13063312	C₂²	1	2	yes	complemented
37	#13063312	C₂²	1	2	yes	complemented
38	#13063312	C₂²	1	1	yes	characteristic, complemented
39	#13063311	C₂²	1	2	yes	—
40	#13063311	C₂²	1	2	yes	—
41	#13063311	C₂²	1	2	yes	—
42	#13063311	C₂²	1	2	yes	complemented
43	#13063311	C₂²	1	2	yes	complemented
44	#13063311	C₂²	1	2	yes	complemented
45	#13063311	C₂²	1	2	yes	complemented
46	#13063311	C₂²	1	2	yes	complemented
47	#13063310	C₂²	1	2	yes	complemented
48	#13063309	C₂²	1	1	yes	characteristic
49	#13063309	C₂²	1	2	yes	complemented
50	#13063309	C₂²	1	1	yes	characteristic, complemented
51	#13063308	C₂²	1	1	yes	characteristic, complemented
52	#13063307	C₂²	1	2	yes	complemented
53	#13063306	C₂²	1	1	yes	characteristic, complemented
54	#13063306	C₂²	1	1	yes	characteristic, complemented
55	#13063306	C₂²	1	2	yes	complemented
56	#13063306	C₂²	1	2	yes	complemented
57	#13063305	C₂²	1	2	yes	complemented
58	#13063304	C₂²	1	2	yes	complemented
59	#13063303	C₂²	1	2	yes	complemented
60	#13063303	C₂²	1	2	yes	complemented
61	#13063302	C₂²	1	2	yes	complemented
62	#13063302	C₂²	1	2	yes	complemented
63	#13063302	C₂²	1	2	yes	complemented
64	#13063302	C₂²	1	2	yes	complemented
65	#13063298	C₂²	1	2	yes	—
66	#13063297	C₂²	1	2	yes	—
67	#13063297	C₂²	1	2	yes	—
68	#13063297	C₂²	1	2	yes	—
69	#13063297	C₂²	1	2	yes	complemented
70	#13063297	C₂²	1	2	yes	complemented
71	#13063296	C₂²	1	2	yes	complemented
72	#13063294	C₂²	1	1	yes	characteristic
73	#13063294	C₂²	1	2	yes	complemented
74	#13063293	C₂²	1	2	yes	—
75	#13063293	C₂²	1	2	yes	—
76	#13063293	C₂²	1	2	yes	—
77	#13063293	C₂²	1	2	yes	complemented
78	C₄×Dic₈₆	C₂²	1	2	yes	complemented
79	#13063290	C₂²	1	2	yes	complemented
80	#13063290	C₂²	1	2	yes	complemented
81	D₄×Dic₄₃	C₂²	1	2	yes	complemented
82	D₄×Dic₄₃	C₂²	1	2	yes	complemented
83	D₄×Dic₄₃	C₂²	1	2	yes	complemented
84	D₄×Dic₄₃	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
87	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
88	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
90	#13063284	C₂²	1	2	yes	complemented
91	#13063283	C₂²	1	2	yes	complemented
92	#13063282	C₂²	1	1	yes	characteristic, complemented
93	#13063281	C₂²	1	1	yes	characteristic, complemented
94	#13063281	C₂²	1	2	yes	complemented
95	#13063281	C₂²	1	1	yes	characteristic, complemented
96	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
98	#127×C₄₃	C₂²	1	1	yes	characteristic
99	#126×C₄₃	C₂²	1	2	yes	complemented
100	#123×C₄₃	C₂²	1	2	yes	complemented
101	#123×C₄₃	C₂²	1	1	yes	characteristic, complemented
102	#121×C₄₃	C₂²	1	2	yes	—
103	#121×C₄₃	C₂²	1	2	yes	complemented
104	#121×C₄₃	C₂²	1	2	yes	complemented
105	#120×C₄₃	C₂²	1	1	yes	characteristic, complemented
106	#120×C₄₃	C₂²	1	2	yes	complemented
107	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
108	C₂³×D₄₃	C₂³	1	2	yes	—
109	C₂×D₄×C₄₃	C₂³	1	2	yes	—
110	C₂×D₄×C₄₃	C₂³	1	2	yes	—
111	C₂×D₄×C₄₃	C₂³	1	2	yes	—
112	C₂×D₄×C₄₃	C₂³	1	2	yes	—
113	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
115	C₂×D₄×C₄₃	C₂³	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
126	C₂²×Dic₄₃	—	4	2	no	—
127	C₂²×Dic₄₃	C₂³	1	2	yes	—
128	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
129	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
130	C₂²×Dic₄₃	C₂³	1	2	yes	—
131	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₄₃	C₂³	1	2	yes	—
133	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
134	#10621900	—	4	4	no	—
135	#10621900	—	4	2	no	—
136	D₄×D₄₃	—	4	2	no	—
137	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₄₃	C₂³	1	2	yes	—
140	C₂×C₄×D₄₃	C₂³	1	2	yes	—
141	C₂×Dic₈₆	—	4	2	no	—
142	C₂×Dic₈₆	C₂³	1	2	yes	—
143	C₂×Dic₈₆	C₂³	1	2	yes	—
144	C₂×Dic₈₆	C₂³	1	2	yes	—
145	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
146	C₂×Dic₈₆	C₂³	1	2	yes	—
147	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
154	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
157	C₄²×C₄₃	C₂³	1	1	yes	characteristic
158	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
160	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
162	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
170	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
180	C₄⋊Dic₄₃	C₂³	1	2	yes	—
181	C₄⋊Dic₄₃	C₂³	1	2	yes	—
182	C₄⋊Dic₄₃	C₂³	1	2	yes	—
183	C₄⋊Dic₄₃	C₂³	1	2	yes	—
184	Dic₄₃⋊C₄	C₂³	1	2	yes	—
185	Dic₄₃⋊C₄	C₂³	1	2	yes	—
186	Dic₄₃⋊C₄	C₂³	1	2	yes	—
187	Dic₄₃⋊C₄	C₂³	1	2	yes	—
188	Dic₄₃⋊C₄	C₂³	1	2	yes	—
189	Dic₄₃⋊C₄	C₂³	1	2	yes	—
190	Dic₄₃⋊C₄	C₂³	1	2	yes	—
191	Dic₄₃⋊C₄	C₂³	1	2	yes	—
192	C₄×Dic₄₃	C₂³	1	2	yes	—
193	C₄×Dic₄₃	C₂³	1	2	yes	—
194	C₄×Dic₄₃	C₂³	1	2	yes	—
195	C₄×Dic₄₃	C₂³	1	2	yes	—
196	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₄₃	C₂³	1	2	yes	—
198	C₄×Dic₄₃	C₂³	1	2	yes	—
199	C₂³×C₄₃	—	4	1	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	C₂⁴	1	2	yes	—
202	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
203	C₂³×C₄₃	C₂⁴	1	2	yes	—
204	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
205	C₂²×D₄₃	—	4	2	no	—
206	C₂²×D₄₃	—	4	2	no	—
207	C₂²×D₄₃	—	4	2	no	—
208	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
209	C₂²×D₄₃	C₂⁴	1	2	yes	—
210	D₄×C₄₃	—	4	1	no	—
211	D₄×C₄₃	—	4	2	no	—
212	D₄×C₄₃	—	4	1	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	4	2	no	—
215	D₄×C₄₃	—	4	2	no	—
216	D₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	4	1	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
220	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
221	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
223	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
224	C₂²⋊D₄₃	—	2	4	no	—
225	C₂²⋊D₄₃	—	4	2	no	—
226	C₂²⋊D₄₃	—	4	1	no	—
227	C₂²⋊D₄₃	—	4	1	no	—
228	C₂²⋊D₄₃	—	4	2	no	—
229	C₂²⋊D₄₃	—	4	2	no	—
230	C₂²⋊D₄₃	—	4	2	no	—
231	C₂²⋊D₄₃	—	4	2	no	—
232	C₂×Dic₄₃	—	2	2	no	—
233	C₂×Dic₄₃	—	2	2	no	—
234	C₂×Dic₄₃	—	2	4	no	—
235	C₂×Dic₄₃	—	4	1	no	—
236	C₂×Dic₄₃	—	4	2	no	—
237	C₂×Dic₄₃	—	4	2	no	—
238	C₂×Dic₄₃	—	4	1	no	—
239	C₂×Dic₄₃	C₂⁴	1	2	yes	—
240	C₂×Dic₄₃	C₂⁴	1	2	yes	—
241	C₂×Dic₄₃	C₂⁴	1	2	yes	—
242	C₂×Dic₄₃	C₂⁴	1	2	yes	—
243	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₄₃	C₂⁴	1	2	yes	—
245	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
247	D₁₇₂	—	4	1	no	—
248	C₄×D₄₃	—	2	2	no	—
249	C₄×D₄₃	—	4	2	no	—
250	C₄×D₄₃	—	4	2	no	—
251	Dic₈₆	—	2	4	no	—
252	Dic₈₆	—	4	2	no	—
253	Dic₈₆	—	4	2	no	—
254	Dic₈₆	—	4	2	no	—
255	Dic₈₆	—	4	1	no	—
256	C₂²×C₄₃	—	2	2	no	—
257	C₂²×C₄₃	—	2	1	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	2	1	no	—
260	C₂²×C₄₃	—	2	2	no	—
261	C₂²×C₄₃	—	2	2	no	—
262	C₂²×C₄₃	—	2	2	no	—
263	C₂²×C₄₃	—	2	2	no	—
264	C₂²×C₄₃	—	2	2	no	—
265	C₂²×C₄₃	—	2	2	no	—
266	C₂²×C₄₃	—	4	4	no	—
267	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
268	C₂×D₄₃	—	2	1	no	—
269	C₂×D₄₃	—	2	2	no	—
270	C₂×D₄₃	—	2	2	no	—
271	C₂×D₄₃	—	2	2	no	—
272	C₂×D₄₃	—	2	2	no	—
273	C₂×D₄₃	—	8	4	no	—
274	C₄×C₄₃	—	2	2	no	—
275	C₄×C₄₃	—	2	1	no	—
276	C₄×C₄₃	—	2	2	no	—
277	C₄×C₄₃	—	2	2	no	—
278	C₄×C₄₃	—	2	2	no	—
279	Dic₄₃	—	2	2	no	—
280	Dic₄₃	—	2	1	no	—
281	Dic₄₃	—	2	1	no	—
282	Dic₄₃	—	2	2	no	—
283	Dic₄₃	—	2	2	no	—
284	Dic₄₃	—	2	2	no	—
285	Dic₄₃	—	2	2	no	—
286	Dic₄₃	H(5,𝔽₂)	1	2	yes	—
287	#3540	—	43	1	no	maximal, Sylow
288	C₂×C₄₃	—	4	2	no	—
289	C₂×C₄₃	—	4	1	no	—
290	C₂×C₄₃	—	4	1	no	—
291	C₂×C₄₃	—	4	2	no	—
292	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₄₃	#585	1	2	yes	—
294	D₄₃	—	4	2	no	—
295	D₄₃	—	4	1	no	—
296	H(3,𝔽₄)	—	43	2	no	—
297	#560	—	43	1	no	—
298	#560	D₄₃	1	1	yes	characteristic, complemented
299	#559	—	43	1	no	—
300	#559	—	43	1	no	—
301	#556	—	43	2	no	—
302	#555	—	43	2	no	—
303	#551	—	43	2	no	—
304	#548	—	43	2	no	—
305	#546	—	43	2	no	—
306	#542	—	43	2	no	—
307	#542	—	43	2	no	—
308	#542	—	43	2	no	—
309	#538	—	43	2	no	—
310	#538	—	43	2	no	—
311	#536	—	43	1	no	—
312	#535	—	43	1	no	—
313	#525	—	43	1	no	—
314	#525	—	43	2	no	—
315	C₄₃	#3540	1	1	yes	characteristic, complemented, Sylow
316	C₂×#41	—	43	1	no	—
317	C₂×#41	—	43	2	no	—
318	C₂²×Q₈	—	43	1	no	—
319	C₂²×D₄	—	43	1	no	—
320	C₂³×C₄	—	43	1	no	—
321	C₄⋊Q₈	—	43	2	no	—
322	C₄⋊Q₈	—	43	2	no	—
323	#127	—	43	1	no	—
324	#127	C₂×D₄₃	1	1	yes	characteristic
325	#126	—	43	2	no	—
326	#126	—	43	2	no	—
327	#126	—	43	2	no	—
328	#126	—	43	2	no	—
329	#126	—	43	2	no	—
330	#126	C₂×D₄₃	1	2	yes	complemented
331	#124	—	43	1	no	—
332	#124	—	43	2	no	—
333	#124	—	43	2	no	—
334	#124	—	43	2	no	—
335	#124	—	43	2	no	—
336	#124	—	43	2	no	—
337	#124	—	43	2	no	—
338	#124	—	43	2	no	—
339	#124	—	43	2	no	—
340	#124	—	43	2	no	—
341	#124	—	43	2	no	—
342	#124	—	43	2	no	—
343	#124	—	43	2	no	—
344	#124	—	43	1	no	—
345	#123	—	43	2	no	—
346	#123	—	43	1	no	—
347	#123	—	43	1	no	—
348	#123	—	43	2	no	—
349	#123	—	43	1	no	—
350	#123	—	43	2	no	—
351	#123	—	43	2	no	—
352	#123	—	43	1	no	—
353	#123	—	43	1	no	—
354	#123	—	43	2	no	—
355	#123	C₂×D₄₃	1	1	yes	characteristic, complemented
356	#123	C₂×D₄₃	1	2	yes	complemented
357	C₂²⋊Q₈	—	43	2	no	—
358	C₂²⋊Q₈	—	43	2	no	—
359	C₂²⋊Q₈	—	43	2	no	—
360	C₂²⋊Q₈	—	43	2	no	—
361	C₂²⋊Q₈	—	43	2	no	—
362	C₂²⋊Q₈	—	43	2	no	—
363	C₂²⋊Q₈	—	43	2	no	—
364	C₂²⋊Q₈	—	43	2	no	—
365	#121	—	43	2	no	—
366	#121	—	43	2	no	—
367	#121	—	43	2	no	—
368	#121	—	43	2	no	—
369	#121	—	43	2	no	—
370	#121	—	43	2	no	—
371	#121	—	43	2	no	—
372	#121	C₂×D₄₃	1	2	yes	—
373	#121	C₂×D₄₃	1	2	yes	complemented
374	#121	C₂×D₄₃	1	2	yes	complemented
375	#120	—	43	2	no	—
376	#120	—	43	1	no	—
377	#120	—	43	2	no	—
378	#120	—	43	2	no	—
379	#120	—	43	2	no	—
380	#120	—	43	2	no	—
381	#120	C₂×D₄₃	1	1	yes	characteristic, complemented
382	#120	C₂×D₄₃	1	2	yes	complemented
383	C₄×Q₈	—	43	2	no	—
384	C₄×Q₈	—	43	2	no	—
385	C₄×Q₈	—	43	2	no	—
386	C₄×D₄	—	43	2	no	—
387	C₄×D₄	—	43	2	no	—
388	C₄×D₄	—	43	2	no	—
389	C₄×D₄	—	43	2	no	—
390	C₄×D₄	—	43	2	no	—
391	C₄×D₄	—	43	2	no	—
392	C₄×D₄	—	43	2	no	—
393	C₄×D₄	—	43	2	no	—
394	C₄×D₄	—	43	2	no	—
395	#117	—	43	2	no	—
396	#117	—	43	2	no	—
397	#117	—	43	1	no	—
398	#117	—	43	2	no	—
399	#117	—	43	1	no	—
400	#117	—	43	1	no	—
401	C₂×C₂²⋊C₄	—	43	2	no	—
402	C₂×C₂²⋊C₄	—	43	2	no	—
403	C₂⁴	—	43	2	no	—
404	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
405	#41	—	172	2	no	—
406	#41	—	172	4	no	—
407	C₂×Q₈	—	43	2	no	—
408	C₂×Q₈	—	43	2	no	—
409	C₂×Q₈	—	43	2	no	—
410	C₂×Q₈	—	43	2	no	—
411	C₂×Q₈	—	43	1	no	—
412	C₂×Q₈	—	172	2	no	—
413	C₂×D₄	—	43	2	no	—
414	C₂×D₄	—	43	2	no	—
415	C₂×D₄	—	43	2	no	—
416	C₂×D₄	—	43	2	no	—
417	C₂×D₄	—	43	2	no	—
418	C₂×D₄	—	43	1	no	—
419	C₂×D₄	—	43	1	no	—
420	C₂×D₄	—	43	2	no	—
421	C₂×D₄	—	43	1	no	—
422	C₂×D₄	—	172	2	no	—
423	C₂×D₄	C₂²×D₄₃	1	2	yes	—
424	C₂×D₄	C₂²×D₄₃	1	2	yes	—
425	C₂×D₄	C₂²×D₄₃	1	2	yes	—
426	C₂×D₄	C₂²×D₄₃	1	2	yes	—
427	C₂×D₄	C₂²×D₄₃	1	2	yes	—
428	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
430	C₂²×C₄	—	43	1	no	—
431	C₂²×C₄	—	43	2	no	—
432	C₂²×C₄	—	43	1	no	—
433	C₂²×C₄	—	43	2	no	—
434	C₂²×C₄	—	43	1	no	—
435	C₂²×C₄	—	43	1	no	—
436	C₂²×C₄	—	43	2	no	—
437	C₂²×C₄	—	43	1	no	—
438	C₂²×C₄	—	43	2	no	—
439	C₂²×C₄	—	43	2	no	—
440	C₂²×C₄	—	172	2	no	—
441	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
442	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
443	C₄⋊C₄	—	43	2	no	—
444	C₄⋊C₄	—	43	2	no	—
445	C₄⋊C₄	—	43	2	no	—
446	C₄⋊C₄	—	43	2	no	—
447	C₄⋊C₄	—	43	2	no	—
448	C₄⋊C₄	—	43	2	no	—
449	C₄⋊C₄	—	43	2	no	—
450	C₄⋊C₄	—	43	2	no	—
451	C₄⋊C₄	—	43	2	no	—
452	C₄⋊C₄	—	43	2	no	—
453	C₄⋊C₄	—	43	2	no	—
454	C₄⋊C₄	—	43	2	no	—
455	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
456	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
457	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
458	C₂²⋊C₄	—	43	2	no	—
459	C₂²⋊C₄	—	43	2	no	—
460	C₂²⋊C₄	—	43	2	no	—
461	C₂²⋊C₄	—	43	1	no	—
462	C₂²⋊C₄	—	43	1	no	—
463	C₂²⋊C₄	—	43	2	no	—
464	C₂²⋊C₄	—	43	2	no	—
465	C₂²⋊C₄	—	43	2	no	—
466	C₂²⋊C₄	—	43	2	no	—
467	C₂²⋊C₄	—	43	2	no	—
468	C₂²⋊C₄	—	43	2	no	—
469	C₂²⋊C₄	—	43	2	no	—
470	C₂²⋊C₄	—	43	2	no	—
471	C₂²⋊C₄	—	43	2	no	—
472	C₂²⋊C₄	—	43	2	no	—
473	C₂²⋊C₄	—	43	2	no	—
474	C₂²⋊C₄	—	43	2	no	—
475	C₂²⋊C₄	—	43	2	no	—
476	C₂²⋊C₄	—	43	2	no	—
477	C₂²⋊C₄	—	43	2	no	—
478	C₂²⋊C₄	—	43	2	no	—
479	C₂²⋊C₄	—	43	2	no	—
480	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
483	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
484	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
487	C₄²	—	43	2	no	—
488	C₄²	—	43	2	no	—
489	C₄²	—	43	2	no	—
490	C₄²	—	43	2	no	—
491	C₄²	—	43	1	no	—
492	C₄²	—	43	2	no	—
493	C₄²	—	43	2	no	—
494	C₄²	C₂²×D₄₃	1	1	yes	characteristic
495	C₂³	—	4	1	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	43	1	no	—
498	C₂³	—	43	2	no	—
499	C₂³	—	172	2	no	—
500	C₂³	—	172	2	no	—
501	C₂³	—	172	2	no	—
502	C₂³	C₂³×D₄₃	1	2	yes	—
503	C₂³	C₂³×D₄₃	1	2	yes	—
504	C₂³	C₂³×D₄₃	1	1	yes	characteristic
505	C₂³	C₂³×D₄₃	1	1	yes	characteristic
506	Q₈	—	86	4	no	—
507	Q₈	—	172	2	no	—
508	Q₈	—	172	1	no	—
509	Q₈	—	172	2	no	—
510	Q₈	—	172	2	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	86	4	no	—
519	D₄	—	172	1	no	—
520	D₄	—	172	1	no	—
521	D₄	—	172	1	no	—
522	D₄	—	172	2	no	—
523	D₄	—	172	2	no	—
524	D₄	—	172	2	no	—
525	D₄	—	172	2	no	—
526	D₄	—	172	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	43	1	no	—
530	C₂×C₄	—	43	2	no	—
531	C₂×C₄	—	43	2	no	—
532	C₂×C₄	—	43	2	no	—
533	C₂×C₄	—	43	1	no	—
534	C₂×C₄	—	43	2	no	—
535	C₂×C₄	—	43	2	no	—
536	C₂×C₄	—	43	1	no	—
537	C₂×C₄	—	86	2	no	—
538	C₂×C₄	—	86	4	no	—
539	C₂×C₄	—	86	2	no	—
540	C₂×C₄	—	86	2	no	—
541	C₂×C₄	—	172	2	no	—
542	C₂×C₄	—	172	2	no	—
543	C₂×C₄	—	172	1	no	—
544	C₂×C₄	—	172	2	no	—
545	C₂×C₄	—	172	1	no	—
546	C₂×C₄	—	172	2	no	—
547	C₂×C₄	C₂³×D₄₃	1	2	yes	—
548	C₂×C₄	C₂³×D₄₃	1	2	yes	—
549	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₄₃	1	2	yes	—
551	C₂×C₄	C₂³×D₄₃	1	2	yes	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	86	1	no	—
564	C₂²	—	86	2	no	—
565	C₂²	—	86	2	no	—
566	C₂²	—	86	2	no	—
567	C₂²	—	86	2	no	—
568	C₂²	—	344	4	no	—
569	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	43	2	no	—
576	C₄	—	86	2	no	—
577	C₄	—	86	1	no	—
578	C₄	—	86	1	no	—
579	C₄	—	86	2	no	—
580	C₄	—	86	2	no	—
581	C₄	—	86	2	no	—
582	C₄	—	86	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	1	no	—
585	C₂	—	4	2	no	—
586	C₂	—	4	1	no	—
587	C₂	—	172	1	no	—
588	C₂	—	172	2	no	—
589	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
590	C₂	#14583734	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#560	C₂
hypercenter	#560	D₄₃
hypocenter	C₄₃	#3540
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #560

Complements

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

N	H ≅ G/N	type
1. #14583642	C₂	semidirect
2. #14583638	C₂	semidirect
3. #14583635	C₂	semidirect
4. #14583633	C₂	semidirect
5. #14583616	C₂	semidirect
6. #14583613	C₂	semidirect
7. #14583572	C₂	semidirect
8. #14583555	C₂	semidirect
9. #14583538	C₂	semidirect
10. #14583517	C₂	semidirect
11. #14583516	C₂	semidirect
12. #14583515	C₂	semidirect
13. #14583486	C₂	semidirect
14. #14583481	C₂	semidirect
15. #14583471	C₂	semidirect
16. #14583462	C₂	semidirect
17. #14583405	C₂	semidirect
18. #14583405	C₂	semidirect
19. C₄₃×#560	C₂	semidirect
22. C₂²×Dic₈₆	C₂²	semidirect
23. C₂×D₄×D₄₃	C₂²	semidirect
24. C₂³×Dic₄₃	C₂²	semidirect
25. #13063324	C₂²	semidirect
26. #13063324	C₂²	semidirect
28. #13063320	C₂²	semidirect
29. #13063320	C₂²	semidirect
30. #13063320	C₂²	semidirect
31. #13063318	C₂²	semidirect
32. #13063318	C₂²	semidirect
33. #13063313	C₂²	semidirect
34. #13063312	C₂²	semidirect
35. #13063312	C₂²	semidirect
36. #13063312	C₂²	semidirect
37. #13063312	C₂²	semidirect
38. #13063312	C₂²	semidirect
42. #13063311	C₂²	semidirect
43. #13063311	C₂²	semidirect
44. #13063311	C₂²	semidirect
45. #13063311	C₂²	semidirect
46. #13063311	C₂²	semidirect
47. #13063310	C₂²	semidirect
49. #13063309	C₂²	semidirect
50. #13063309	C₂²	semidirect
51. #13063308	C₂²	semidirect
52. #13063307	C₂²	semidirect
53. #13063306	C₂²	semidirect
54. #13063306	C₂²	semidirect
55. #13063306	C₂²	semidirect
56. #13063306	C₂²	semidirect
57. #13063305	C₂²	semidirect
58. #13063304	C₂²	semidirect
59. #13063303	C₂²	semidirect
60. #13063303	C₂²	semidirect
61. #13063302	C₂²	semidirect
62. #13063302	C₂²	semidirect
63. #13063302	C₂²	semidirect
64. #13063302	C₂²	semidirect
69. #13063297	C₂²	semidirect
70. #13063297	C₂²	semidirect
71. #13063296	C₂²	semidirect
73. #13063294	C₂²	semidirect
77. #13063293	C₂²	semidirect
78. C₄×Dic₈₆	C₂²	semidirect
79. #13063290	C₂²	semidirect
80. #13063290	C₂²	semidirect
81. D₄×Dic₄₃	C₂²	semidirect
82. D₄×Dic₄₃	C₂²	semidirect
83. D₄×Dic₄₃	C₂²	semidirect
84. D₄×Dic₄₃	C₂²	semidirect
85. C₄×C₂²⋊D₄₃	C₂²	semidirect
86. C₄×C₂²⋊D₄₃	C₂²	semidirect
88. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
90. #13063284	C₂²	semidirect
91. #13063283	C₂²	semidirect
92. #13063282	C₂²	semidirect
93. #13063281	C₂²	semidirect
94. #13063281	C₂²	semidirect
95. #13063281	C₂²	semidirect
96. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
97. C₂²⋊C₄×D₄₃	C₂²	semidirect
99. #126×C₄₃	C₂²	semidirect
100. #123×C₄₃	C₂²	semidirect
101. #123×C₄₃	C₂²	semidirect
103. #121×C₄₃	C₂²	semidirect
104. #121×C₄₃	C₂²	semidirect
105. #120×C₄₃	C₂²	semidirect
106. #120×C₄₃	C₂²	semidirect
298. #560	D₄₃	semidirect
315. C₄₃	#3540	semidirect
330. #126	C₂×D₄₃	semidirect
355. #123	C₂×D₄₃	semidirect
356. #123	C₂×D₄₃	semidirect
373. #121	C₂×D₄₃	semidirect
374. #121	C₂×D₄₃	semidirect
381. #120	C₂×D₄₃	semidirect
382. #120	C₂×D₄₃	semidirect