Subgroups — #19148945

Order 5504.

1060 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583653	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583643	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583641	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583613	C₂	1	2	yes	maximal, complemented
5	#14583576	C₂	1	2	yes	maximal, complemented
6	#14583576	C₂	1	2	yes	maximal, complemented
7	#14583572	C₂	1	2	yes	maximal, complemented
8	#14583546	C₂	1	2	yes	maximal, complemented
9	#14583541	C₂	1	2	yes	maximal, complemented
10	#14583522	C₂	1	2	yes	maximal, complemented
11	#14583517	C₂	1	2	yes	maximal, complemented
12	#14583486	C₂	1	2	yes	maximal, complemented
13	#14583485	C₂	1	2	yes	maximal, complemented
14	#14583472	C₂	1	2	yes	maximal, complemented
15	#14583457	C₂	1	2	yes	maximal, complemented
16	#14583434	C₂	1	1	yes	maximal, characteristic, complemented
17	#14583428	C₂	1	1	yes	maximal, characteristic, complemented
18	#124×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10621898	C₂²	1	2	yes	—
21	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
24	#13063324	C₂²	1	2	yes	complemented
25	#13063324	C₂²	1	2	yes	complemented
26	#13063320	C₂²	1	2	yes	complemented
27	#13063320	C₂²	1	2	yes	complemented
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	#13063317	C₂²	1	1	yes	characteristic, complemented
33	#13063314	C₂²	1	1	yes	characteristic
34	#13063314	C₂²	1	2	yes	complemented
35	#13063313	C₂²	1	1	yes	characteristic
36	#13063313	C₂²	1	1	yes	characteristic, complemented
37	#13063312	C₂²	1	1	yes	characteristic, complemented
38	#13063312	C₂²	1	2	yes	complemented
39	#13063311	C₂²	1	2	yes	complemented
40	#13063311	C₂²	1	2	yes	complemented
41	#13063311	C₂²	1	2	yes	complemented
42	#13063311	C₂²	1	2	yes	complemented
43	#13063311	C₂²	1	2	yes	complemented
44	#13063311	C₂²	1	2	yes	complemented
45	#13063310	C₂²	1	2	yes	—
46	#13063310	C₂²	1	2	yes	complemented
47	#13063310	C₂²	1	2	yes	complemented
48	#13063310	C₂²	1	2	yes	complemented
49	#13063309	C₂²	1	2	yes	complemented
50	#13063309	C₂²	1	2	yes	complemented
51	#13063307	C₂²	1	2	yes	complemented
52	#13063307	C₂²	1	2	yes	complemented
53	#13063307	C₂²	1	2	yes	complemented
54	#13063307	C₂²	1	2	yes	complemented
55	#13063305	C₂²	1	1	yes	characteristic, complemented
56	#13063305	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	#13063302	C₂²	1	2	yes	complemented
61	#13063301	C₂²	1	1	yes	characteristic, complemented
62	#13063301	C₂²	1	2	yes	complemented
63	#13063300	C₂²	1	1	yes	characteristic
64	#13063299	C₂²	1	2	yes	—
65	#13063298	C₂²	1	2	yes	complemented
66	#13063297	C₂²	1	2	yes	—
67	#13063297	C₂²	1	2	yes	complemented
68	#13063297	C₂²	1	2	yes	complemented
69	#13063296	C₂²	1	1	yes	characteristic
70	#13063296	C₂²	1	2	yes	complemented
71	#13063295	C₂²	1	2	yes	—
72	#13063295	C₂²	1	2	yes	—
73	#13063295	C₂²	1	2	yes	complemented
74	#13063293	C₂²	1	2	yes	—
75	#13063293	C₂²	1	2	yes	complemented
76	#13063293	C₂²	1	2	yes	complemented
77	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
78	#13063290	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₄₃	C₂²	1	2	yes	complemented
80	D₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
81	#13063287	C₂²	1	2	yes	complemented
82	#13063287	C₂²	1	2	yes	complemented
83	#13063287	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
86	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
87	#13063284	C₂²	1	2	yes	complemented
88	#13063283	C₂²	1	2	yes	complemented
89	#13063283	C₂²	1	2	yes	complemented
90	#13063281	C₂²	1	2	yes	complemented
91	#13063281	C₂²	1	2	yes	complemented
92	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
97	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
98	#125×C₄₃	C₂²	1	1	yes	characteristic, complemented
99	#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
100	#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
101	#123×C₄₃	C₂²	1	2	yes	complemented
102	#123×C₄₃	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
105	#121×C₄₃	C₂²	1	2	yes	complemented
106	#121×C₄₃	C₂²	1	2	yes	complemented
107	C₂³×D₄₃	C₂³	1	2	yes	—
108	C₂³×D₄₃	C₂³	1	2	yes	—
109	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
110	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
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	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
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	C₂²×Dic₄₃	C₂³	1	2	yes	—
124	C₂²×Dic₄₃	C₂³	1	2	yes	—
125	Q₈×D₄₃	—	4	2	no	—
126	D₄×D₄₃	—	4	2	no	—
127	D₄×D₄₃	—	4	4	no	—
128	#10621898	—	4	4	no	—
129	C₂×D₁₇₂	C₂³	1	2	yes	—
130	C₂×D₁₇₂	C₂³	1	2	yes	—
131	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
132	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₄₃	C₂³	1	2	yes	—
135	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₄₃	C₂³	1	2	yes	—
138	C₂×C₄×D₄₃	C₂³	1	2	yes	—
139	C₂×C₄×D₄₃	C₂³	1	2	yes	—
140	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
141	C₂×Dic₈₆	C₂³	1	2	yes	—
142	C₂×Dic₈₆	C₂³	1	2	yes	—
143	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
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	2	yes	—
154	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
156	C₄²×C₄₃	C₂³	1	1	yes	characteristic
157	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
163	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₄₃)⋊C₄	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	C₄⋊Dic₄₃	C₂³	1	2	yes	—
180	C₄⋊Dic₄₃	C₂³	1	2	yes	—
181	C₄⋊Dic₄₃	C₂³	1	2	yes	—
182	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₄₃	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	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
192	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
193	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
194	C₄×Dic₄₃	C₂³	1	2	yes	—
195	C₄×Dic₄₃	C₂³	1	2	yes	—
196	C₄×Dic₄₃	C₂³	1	2	yes	—
197	C₄×Dic₄₃	C₂³	1	2	yes	—
198	C₂³×C₄₃	C₂⁴	1	2	yes	—
199	C₂³×C₄₃	C₂⁴	1	2	yes	—
200	C₂²×D₄₃	—	2	4	no	—
201	C₂²×D₄₃	—	4	2	no	—
202	C₂²×D₄₃	—	4	2	no	—
203	C₂²×D₄₃	—	4	2	no	—
204	C₂²×D₄₃	—	4	2	no	—
205	C₂²×D₄₃	—	4	2	no	—
206	C₂²×D₄₃	C₂⁴	1	2	yes	—
207	C₂²×D₄₃	C₂⁴	1	2	yes	—
208	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
209	Q₈×C₄₃	—	4	1	no	—
210	Q₈×C₄₃	—	4	1	no	—
211	D₄×C₄₃	—	4	1	no	—
212	D₄×C₄₃	—	4	2	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
218	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
227	C₂²⋊D₄₃	—	4	2	no	—
228	C₂²⋊D₄₃	—	4	2	no	—
229	C₂²⋊D₄₃	—	4	2	no	—
230	C₂×Dic₄₃	—	4	2	no	—
231	C₂×Dic₄₃	—	4	2	no	—
232	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
233	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
234	C₂×Dic₄₃	C₂⁴	1	2	yes	—
235	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
236	C₂×Dic₄₃	C₂⁴	1	2	yes	—
237	C₂×Dic₄₃	C₂⁴	1	2	yes	—
238	C₂×Dic₄₃	C₂⁴	1	2	yes	—
239	D₁₇₂	—	2	4	no	—
240	D₁₇₂	—	4	1	no	—
241	D₁₇₂	—	4	2	no	—
242	D₁₇₂	—	4	1	no	—
243	C₄×D₄₃	—	2	4	no	—
244	C₄×D₄₃	—	2	2	no	—
245	C₄×D₄₃	—	4	2	no	—
246	C₄×D₄₃	—	4	1	no	—
247	C₄×D₄₃	—	4	1	no	—
248	C₄×D₄₃	—	4	2	no	—
249	C₄×D₄₃	—	4	2	no	—
250	Dic₈₆	—	4	1	no	—
251	Dic₈₆	—	4	2	no	—
252	Dic₈₆	—	4	1	no	—
253	Dic₈₆	—	4	2	no	—
254	C₂²×C₄₃	—	2	2	no	—
255	C₂²×C₄₃	—	2	2	no	—
256	C₂²×C₄₃	—	2	2	no	—
257	C₂²×C₄₃	—	2	2	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	2	2	no	—
260	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
261	C₂×D₄₃	—	2	1	no	—
262	C₂×D₄₃	—	2	1	no	—
263	C₂×D₄₃	—	2	2	no	—
264	C₂×D₄₃	—	2	2	no	—
265	C₂×D₄₃	—	2	2	no	—
266	C₂×D₄₃	—	2	2	no	—
267	C₂×D₄₃	—	2	2	no	—
268	C₂×D₄₃	—	2	2	no	—
269	C₂×D₄₃	—	8	4	no	—
270	C₂×D₄₃	—	8	4	no	—
271	C₂×D₄₃	H(5,𝔽₂)	1	2	yes	—
272	C₄×C₄₃	—	2	2	no	—
273	C₄×C₄₃	—	2	1	no	—
274	C₄×C₄₃	—	2	2	no	—
275	C₄×C₄₃	—	2	1	no	—
276	C₄×C₄₃	—	2	2	no	—
277	C₄×C₄₃	—	2	1	no	—
278	C₄×C₄₃	—	2	2	no	—
279	Dic₄₃	—	2	2	no	—
280	Dic₄₃	—	2	1	no	—
281	Dic₄₃	—	2	2	no	—
282	Dic₄₃	—	2	2	no	—
283	Dic₄₃	—	2	1	no	—
284	Dic₄₃	—	2	1	no	—
285	Dic₄₃	—	2	2	no	—
286	#3545	—	43	1	no	maximal, Sylow
287	C₂×C₄₃	—	4	2	no	—
288	C₂×C₄₃	—	4	2	no	—
289	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₄₃	#585	1	1	yes	characteristic
291	C₂×C₄₃	#585	1	1	yes	characteristic
292	D₄₃	—	2	2	no	—
293	D₄₃	—	4	2	no	—
294	D₄₃	—	4	2	no	—
295	#563	—	43	1	no	—
296	#562	—	43	1	no	—
297	#562	D₄₃	1	1	yes	characteristic, complemented
298	H(3,𝔽₄)	—	43	1	no	—
299	#555	—	43	2	no	—
300	#551	—	43	2	no	—
301	#551	—	43	2	no	—
302	#551	—	43	2	no	—
303	#546	—	43	2	no	—
304	#546	—	43	2	no	—
305	#542	—	43	2	no	—
306	#542	—	43	2	no	—
307	#538	—	43	2	no	—
308	#538	—	43	2	no	—
309	#536	—	43	2	no	—
310	#534	—	43	2	no	—
311	#529	—	43	1	no	—
312	#529	—	43	1	no	—
313	C₂×#124	—	43	1	no	—
314	C₄₃	#3545	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	43	2	no	—
316	C₂²×Q₈	—	43	1	no	—
317	C₂²×D₄	—	43	1	no	—
318	C₂²×D₄	—	43	2	no	—
319	C₄⋊Q₈	—	43	2	no	—
320	C₄⋊Q₈	—	43	2	no	—
321	#126	—	43	2	no	—
322	#126	—	43	2	no	—
323	#126	—	43	2	no	—
324	#126	—	43	2	no	—
325	#126	—	43	2	no	—
326	#126	—	43	2	no	—
327	#125	—	43	1	no	—
328	#125	C₂×D₄₃	1	1	yes	characteristic, complemented
329	#124	—	43	1	no	—
330	#124	—	43	2	no	—
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	1	no	—
340	#124	—	43	1	no	—
341	#124	C₂×D₄₃	1	1	yes	characteristic, complemented
342	#124	C₂×D₄₃	1	1	yes	characteristic, complemented
343	#123	—	43	2	no	—
344	#123	—	43	2	no	—
345	#123	—	43	2	no	—
346	#123	—	43	2	no	—
347	#123	—	43	2	no	—
348	#123	—	43	2	no	—
349	#123	—	43	2	no	—
350	#123	—	43	2	no	—
351	#123	—	43	2	no	—
352	#123	—	43	2	no	—
353	#123	C₂×D₄₃	1	2	yes	complemented
354	#123	C₂×D₄₃	1	2	yes	complemented
355	C₂²⋊Q₈	—	43	1	no	—
356	C₂²⋊Q₈	—	43	2	no	—
357	C₂²⋊Q₈	—	43	2	no	—
358	C₂²⋊Q₈	—	43	1	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	C₂×D₄₃	1	2	yes	complemented
364	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
365	#121	—	43	1	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	1	no	—
372	#121	—	43	2	no	—
373	#121	C₂×D₄₃	1	2	yes	complemented
374	#121	C₂×D₄₃	1	2	yes	complemented
375	#120	—	43	2	no	—
376	#120	—	43	2	no	—
377	#120	—	43	2	no	—
378	#120	—	43	2	no	—
379	#120	—	43	2	no	—
380	#120	—	43	2	no	—
381	C₄×Q₈	—	43	1	no	—
382	C₄×Q₈	—	43	1	no	—
383	C₄×D₄	—	43	1	no	—
384	C₄×D₄	—	43	2	no	—
385	C₄×D₄	—	43	2	no	—
386	C₄×D₄	—	43	2	no	—
387	C₄×D₄	—	43	1	no	—
388	C₄×D₄	—	43	2	no	—
389	C₄×D₄	—	43	2	no	—
390	C₄×D₄	—	43	2	no	—
391	#117	—	43	2	no	—
392	#117	—	43	2	no	—
393	#117	—	43	2	no	—
394	#117	—	43	2	no	—
395	#117	—	43	2	no	—
396	C₂×C₂²⋊C₄	—	43	2	no	—
397	C₂×C₂²⋊C₄	—	43	2	no	—
398	C₂×C₂²⋊C₄	—	43	2	no	—
399	C₂×C₂²⋊C₄	—	43	2	no	—
400	C₂×C₂²⋊C₄	—	43	2	no	—
401	C₂×C₄²	—	43	1	no	—
402	C₂⁴	—	43	2	no	—
403	C₂⁴	—	43	2	no	—
404	#41	—	172	4	no	—
405	C₂×Q₈	—	43	1	no	—
406	C₂×Q₈	—	43	2	no	—
407	C₂×Q₈	—	43	2	no	—
408	C₂×Q₈	—	43	1	no	—
409	C₂×Q₈	—	172	2	no	—
410	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
412	C₂×D₄	—	43	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	2	no	—
419	C₂×D₄	—	43	2	no	—
420	C₂×D₄	—	43	1	no	—
421	C₂×D₄	—	43	1	no	—
422	C₂×D₄	—	172	2	no	—
423	C₂×D₄	—	172	4	no	—
424	C₂×D₄	C₂²×D₄₃	1	2	yes	—
425	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
426	C₂×D₄	C₂²×D₄₃	1	2	yes	—
427	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
428	C₂²×C₄	—	43	2	no	—
429	C₂²×C₄	—	43	2	no	—
430	C₂²×C₄	—	43	1	no	—
431	C₂²×C₄	—	43	2	no	—
432	C₂²×C₄	—	43	1	no	—
433	C₂²×C₄	—	43	1	no	—
434	C₂²×C₄	—	43	2	no	—
435	C₂²×C₄	—	43	2	no	—
436	C₂²×C₄	—	43	2	no	—
437	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
438	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
439	C₄⋊C₄	—	43	2	no	—
440	C₄⋊C₄	—	43	2	no	—
441	C₄⋊C₄	—	43	2	no	—
442	C₄⋊C₄	—	43	2	no	—
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	1	no	—
448	C₄⋊C₄	—	43	1	no	—
449	C₄⋊C₄	—	43	2	no	—
450	C₄⋊C₄	—	43	2	no	—
451	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
452	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
453	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
454	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
456	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
457	C₂²⋊C₄	—	43	2	no	—
458	C₂²⋊C₄	—	43	2	no	—
459	C₂²⋊C₄	—	43	2	no	—
460	C₂²⋊C₄	—	43	2	no	—
461	C₂²⋊C₄	—	43	2	no	—
462	C₂²⋊C₄	—	43	2	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	C₂²×D₄₃	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
485	C₄²	—	43	1	no	—
486	C₄²	—	43	1	no	—
487	C₄²	—	43	1	no	—
488	C₄²	—	43	2	no	—
489	C₄²	—	43	2	no	—
490	C₄²	—	43	2	no	—
491	C₄²	—	43	2	no	—
492	C₄²	C₂²×D₄₃	1	1	yes	characteristic
493	C₂³	—	43	1	no	—
494	C₂³	—	43	2	no	—
495	C₂³	—	43	2	no	—
496	C₂³	—	86	4	no	—
497	C₂³	—	172	2	no	—
498	C₂³	—	172	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	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	172	2	no	—
507	Q₈	—	172	1	no	—
508	Q₈	—	172	2	no	—
509	Q₈	—	172	1	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	1	no	—
514	D₄	—	86	4	no	—
515	D₄	—	86	4	no	—
516	D₄	—	172	1	no	—
517	D₄	—	172	2	no	—
518	D₄	—	172	1	no	—
519	D₄	—	172	2	no	—
520	D₄	—	172	2	no	—
521	D₄	—	172	2	no	—
522	D₄	—	172	2	no	—
523	D₄	—	172	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	43	1	no	—
527	C₂×C₄	—	43	1	no	—
528	C₂×C₄	—	43	2	no	—
529	C₂×C₄	—	43	2	no	—
530	C₂×C₄	—	43	1	no	—
531	C₂×C₄	—	43	2	no	—
532	C₂×C₄	—	43	2	no	—
533	C₂×C₄	—	86	2	no	—
534	C₂×C₄	—	86	4	no	—
535	C₂×C₄	—	172	2	no	—
536	C₂×C₄	—	172	2	no	—
537	C₂×C₄	—	172	2	no	—
538	C₂×C₄	—	172	1	no	—
539	C₂×C₄	—	172	1	no	—
540	C₂×C₄	—	172	2	no	—
541	C₂×C₄	—	172	2	no	—
542	C₂×C₄	C₂³×D₄₃	1	2	yes	—
543	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₄₃	1	2	yes	—
547	C₂×C₄	C₂³×D₄₃	1	2	yes	—
548	C₂×C₄	C₂³×D₄₃	1	2	yes	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	43	2	no	—
556	C₂²	—	86	1	no	—
557	C₂²	—	86	1	no	—
558	C₂²	—	86	2	no	—
559	C₂²	—	86	2	no	—
560	C₂²	—	86	2	no	—
561	C₂²	—	86	2	no	—
562	C₂²	—	86	2	no	—
563	C₂²	—	86	2	no	—
564	C₂²	—	344	4	no	—
565	C₂²	—	344	4	no	—
566	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	86	1	no	—
575	C₄	—	86	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	C₂	—	4	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	86	2	no	—
584	C₂	—	172	2	no	—
585	C₂	—	172	2	no	—
586	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
587	C₂	#14583734	1	1	yes	characteristic
588	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#562	C₂
hypercenter	#562	D₄₃
hypocenter	C₄₃	#3545
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #14583653	C₂	semidirect
2. #14583643	C₂	semidirect
3. #14583641	C₂	semidirect
4. #14583613	C₂	semidirect
5. #14583576	C₂	semidirect
6. #14583576	C₂	semidirect
7. #14583572	C₂	semidirect
8. #14583546	C₂	semidirect
9. #14583541	C₂	semidirect
10. #14583522	C₂	semidirect
11. #14583517	C₂	semidirect
12. #14583486	C₂	semidirect
13. #14583485	C₂	semidirect
14. #14583472	C₂	semidirect
15. #14583457	C₂	semidirect
16. #14583434	C₂	semidirect
17. #14583428	C₂	semidirect
18. #124×D₄₃	C₂	semidirect
19. C₄₃×#562	C₂	semidirect
21. C₂×Q₈×D₄₃	C₂²	semidirect
23. C₂×D₄×D₄₃	C₂²	semidirect
24. #13063324	C₂²	semidirect
25. #13063324	C₂²	semidirect
26. #13063320	C₂²	semidirect
27. #13063320	C₂²	semidirect
28. #13063320	C₂²	semidirect
29. #13063320	C₂²	semidirect
30. #13063320	C₂²	semidirect
31. #13063318	C₂²	semidirect
32. #13063317	C₂²	semidirect
34. #13063314	C₂²	semidirect
36. #13063313	C₂²	semidirect
37. #13063312	C₂²	semidirect
38. #13063312	C₂²	semidirect
39. #13063311	C₂²	semidirect
40. #13063311	C₂²	semidirect
41. #13063311	C₂²	semidirect
42. #13063311	C₂²	semidirect
43. #13063311	C₂²	semidirect
44. #13063311	C₂²	semidirect
46. #13063310	C₂²	semidirect
47. #13063310	C₂²	semidirect
48. #13063310	C₂²	semidirect
49. #13063309	C₂²	semidirect
50. #13063309	C₂²	semidirect
51. #13063307	C₂²	semidirect
52. #13063307	C₂²	semidirect
53. #13063307	C₂²	semidirect
54. #13063307	C₂²	semidirect
55. #13063305	C₂²	semidirect
56. #13063305	C₂²	semidirect
57. #13063305	C₂²	semidirect
58. #13063304	C₂²	semidirect
59. #13063303	C₂²	semidirect
60. #13063302	C₂²	semidirect
61. #13063301	C₂²	semidirect
62. #13063301	C₂²	semidirect
65. #13063298	C₂²	semidirect
67. #13063297	C₂²	semidirect
68. #13063297	C₂²	semidirect
70. #13063296	C₂²	semidirect
73. #13063295	C₂²	semidirect
75. #13063293	C₂²	semidirect
76. #13063293	C₂²	semidirect
77. Q₈×Dic₄₃	C₂²	semidirect
78. #13063290	C₂²	semidirect
79. D₄×Dic₄₃	C₂²	semidirect
80. D₄×Dic₄₃	C₂²	semidirect
81. #13063287	C₂²	semidirect
82. #13063287	C₂²	semidirect
83. #13063287	C₂²	semidirect
84. C₄×C₂²⋊D₄₃	C₂²	semidirect
85. C₄×C₂²⋊D₄₃	C₂²	semidirect
86. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
87. #13063284	C₂²	semidirect
88. #13063283	C₂²	semidirect
89. #13063283	C₂²	semidirect
90. #13063281	C₂²	semidirect
91. #13063281	C₂²	semidirect
92. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
93. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
94. C₂²⋊C₄×D₄₃	C₂²	semidirect
95. C₂²⋊C₄×D₄₃	C₂²	semidirect
96. C₂²⋊C₄×D₄₃	C₂²	semidirect
97. C₄²×D₄₃	C₂²	semidirect
98. #125×C₄₃	C₂²	semidirect
99. #124×C₄₃	C₂²	semidirect
100. #124×C₄₃	C₂²	semidirect
101. #123×C₄₃	C₂²	semidirect
102. #123×C₄₃	C₂²	semidirect
103. C₂²⋊Q₈×C₄₃	C₂²	semidirect
104. C₂²⋊Q₈×C₄₃	C₂²	semidirect
105. #121×C₄₃	C₂²	semidirect
106. #121×C₄₃	C₂²	semidirect
297. #562	D₄₃	semidirect
314. C₄₃	#3545	semidirect
328. #125	C₂×D₄₃	semidirect
341. #124	C₂×D₄₃	semidirect
342. #124	C₂×D₄₃	semidirect
353. #123	C₂×D₄₃	semidirect
354. #123	C₂×D₄₃	semidirect
363. C₂²⋊Q₈	C₂×D₄₃	semidirect
364. C₂²⋊Q₈	C₂×D₄₃	semidirect
373. #121	C₂×D₄₃	semidirect
374. #121	C₂×D₄₃	semidirect