Subgroups — #19148571

Order 5504.

1014 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583624	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583607	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583605	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583600	C₂	1	2	yes	maximal, complemented
5	#14583591	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583587	C₂	1	2	yes	maximal, complemented
7	#14583587	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583585	C₂	1	2	yes	maximal, complemented
9	#14583581	C₂	1	2	yes	maximal, complemented
10	#14583552	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583551	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583551	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583507	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583497	C₂	1	2	yes	maximal, complemented
15	#14583490	C₂	1	2	yes	maximal, complemented
16	#14583453	C₂	1	1	yes	maximal, characteristic, complemented
17	#14583432	C₂	1	2	yes	maximal, complemented
18	#14583427	C₂	1	1	yes	maximal, characteristic, complemented
19	#125×D₄₃	C₂	1	2	yes	maximal, complemented
20	#14583381	C₂	1	1	yes	maximal, characteristic, complemented
21	#14583379	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#10621902	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10621902	C₂²	1	1	yes	characteristic
25	C₂×#10621902	C₂²	1	1	yes	characteristic
26	C₂×#10621898	C₂²	1	1	yes	characteristic
27	#13063324	C₂²	1	1	yes	characteristic
28	#13063323	C₂²	1	1	yes	characteristic
29	#13063323	C₂²	1	1	yes	characteristic
30	#13063320	C₂²	1	2	yes	—
31	#13063320	C₂²	1	2	yes	—
32	#13063320	C₂²	1	1	yes	characteristic
33	#13063320	C₂²	1	2	yes	—
34	#13063319	C₂²	1	2	yes	—
35	#13063318	C₂²	1	1	yes	characteristic
36	#13063317	C₂²	1	2	yes	—
37	#13063316	C₂²	1	2	yes	—
38	#13063316	C₂²	1	2	yes	—
39	#13063316	C₂²	1	2	yes	—
40	#13063316	C₂²	1	1	yes	characteristic
41	#13063315	C₂²	1	2	yes	—
42	#13063315	C₂²	1	2	yes	—
43	#13063315	C₂²	1	2	yes	—
44	#13063315	C₂²	1	2	yes	—
45	#13063315	C₂²	1	1	yes	characteristic
46	#13063315	C₂²	1	2	yes	—
47	#13063311	C₂²	1	1	yes	characteristic
48	#13063310	C₂²	1	2	yes	—
49	#13063310	C₂²	1	2	yes	—
50	#13063310	C₂²	1	2	yes	—
51	#13063310	C₂²	1	2	yes	—
52	#13063310	C₂²	1	2	yes	—
53	#13063310	C₂²	1	1	yes	characteristic
54	#13063309	C₂²	1	2	yes	—
55	#13063307	C₂²	1	2	yes	—
56	#13063307	C₂²	1	2	yes	—
57	#13063307	C₂²	1	1	yes	characteristic
58	#13063305	C₂²	1	2	yes	—
59	#13063305	C₂²	1	2	yes	—
60	#13063305	C₂²	1	1	yes	characteristic
61	#13063305	C₂²	1	1	yes	characteristic
62	#13063303	C₂²	1	1	yes	characteristic
63	#13063303	C₂²	1	2	yes	—
64	#13063303	C₂²	1	2	yes	—
65	#13063303	C₂²	1	2	yes	—
66	#13063302	C₂²	1	2	yes	—
67	#13063301	C₂²	1	1	yes	characteristic
68	#13063301	C₂²	1	1	yes	characteristic
69	#13063300	C₂²	1	2	yes	—
70	#13063298	C₂²	1	1	yes	characteristic
71	#13063298	C₂²	1	2	yes	—
72	#13063298	C₂²	1	2	yes	—
73	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
74	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
75	C₄×Dic₈₆	C₂²	1	2	yes	—
76	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
77	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
78	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
79	#13063290	C₂²	1	2	yes	—
80	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
81	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
82	C₄×D₁₇₂	C₂²	1	2	yes	—
83	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
84	C₄×D₁₇₂	C₂²	1	2	yes	—
85	#13063287	C₂²	1	2	yes	—
86	#13063287	C₂²	1	1	yes	characteristic
87	#13063287	C₂²	1	1	yes	characteristic
88	#13063287	C₂²	1	2	yes	—
89	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
91	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
93	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
94	#13063283	C₂²	1	2	yes	—
95	#13063283	C₂²	1	2	yes	—
96	#13063283	C₂²	1	2	yes	—
97	#13063283	C₂²	1	1	yes	characteristic
98	#13063282	C₂²	1	2	yes	—
99	#13063282	C₂²	1	2	yes	—
100	#13063282	C₂²	1	1	yes	characteristic
101	#13063281	C₂²	1	2	yes	—
102	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
104	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
105	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
107	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
108	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
109	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
110	C₄²×D₄₃	C₂²	1	2	yes	—
111	C₄²×D₄₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
113	#126×C₄₃	C₂²	1	2	yes	—
114	#126×C₄₃	C₂²	1	2	yes	—
115	#125×C₄₃	C₂²	1	2	yes	—
116	#125×C₄₃	C₂²	1	1	yes	characteristic
117	#125×C₄₃	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
122	#117×C₄₃	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
129	C₂²×Dic₄₃	C₂³	1	2	yes	—
130	#10621902	—	2	4	no	—
131	#10621902	—	2	4	no	—
132	#10621898	—	2	4	no	—
133	C₂×D₁₇₂	C₂³	1	2	yes	—
134	C₂×D₁₇₂	C₂³	1	2	yes	—
135	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
136	C₂×D₁₇₂	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	1	yes	characteristic
140	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₄₃	C₂³	1	2	yes	—
142	C₂×C₄×D₄₃	C₂³	1	2	yes	—
143	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₄₃	C₂³	1	2	yes	—
145	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₄₃	C₂³	1	2	yes	—
147	C₂×C₄×D₄₃	C₂³	1	2	yes	—
148	C₂×C₄×D₄₃	C₂³	1	2	yes	—
149	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
150	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₈₆	C₂³	1	2	yes	—
152	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
157	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
158	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
159	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
160	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
161	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
162	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
163	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
166	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
168	C₄²×C₄₃	C₂³	1	1	yes	characteristic
169	C₄²×C₄₃	C₂³	1	1	yes	characteristic
170	C₄²×C₄₃	C₂³	1	2	yes	—
171	C₄²×C₄₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
174	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₄₃	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	1	yes	characteristic
199	Dic₄₃⋊C₄	C₂³	1	2	yes	—
200	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
203	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₄₃⋊C₄	C₂³	1	2	yes	—
205	Dic₄₃⋊C₄	C₂³	1	2	yes	—
206	Dic₄₃⋊C₄	C₂³	1	2	yes	—
207	Dic₄₃⋊C₄	C₂³	1	2	yes	—
208	Dic₄₃⋊C₄	C₂³	1	2	yes	—
209	Dic₄₃⋊C₄	C₂³	1	2	yes	—
210	Dic₄₃⋊C₄	C₂³	1	2	yes	—
211	Dic₄₃⋊C₄	C₂³	1	2	yes	—
212	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₄₃⋊C₄	C₂³	1	2	yes	—
214	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₄₃⋊C₄	C₂³	1	2	yes	—
216	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₄₃	C₂³	1	2	yes	—
218	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₄₃	C₂³	1	2	yes	—
220	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₄₃	C₂³	1	2	yes	—
222	C₄×Dic₄₃	C₂³	1	2	yes	—
223	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₄₃	C₂³	1	2	yes	—
225	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₄₃	C₂⁴	1	2	yes	—
229	Q₈×C₄₃	—	2	2	no	—
230	Q₈×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	2	2	no	—
232	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
242	C₂²⋊D₄₃	—	2	4	no	—
243	C₂²⋊D₄₃	—	2	2	no	—
244	C₂²⋊D₄₃	—	4	1	no	—
245	C₂×Dic₄₃	—	4	2	no	—
246	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₄₃	C₂⁴	1	2	yes	—
248	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₄₃	C₂⁴	1	2	yes	—
250	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₄₃	C₂⁴	1	2	yes	—
253	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
255	D₁₇₂	—	2	4	no	—
256	D₁₇₂	—	2	4	no	—
257	D₁₇₂	—	4	1	no	—
258	D₁₇₂	#41	1	4	yes	—
259	C₄×D₄₃	—	2	4	no	—
260	C₄×D₄₃	—	2	4	no	—
261	C₄×D₄₃	—	2	4	no	—
262	C₄×D₄₃	—	2	2	no	—
263	C₄×D₄₃	—	2	2	no	—
264	C₄×D₄₃	—	2	4	no	—
265	C₄×D₄₃	—	2	2	no	—
266	C₄×D₄₃	—	4	1	no	—
267	C₄×D₄₃	—	4	2	no	—
268	C₄×D₄₃	—	4	2	no	—
269	C₄×D₄₃	—	4	2	no	—
270	C₄×D₄₃	—	4	2	no	—
271	Dic₈₆	—	2	2	no	—
272	Dic₈₆	—	2	2	no	—
273	Dic₈₆	—	4	2	no	—
274	C₂²×C₄₃	—	2	1	no	—
275	C₂²×C₄₃	—	2	1	no	—
276	C₂²×C₄₃	—	2	1	no	—
277	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
278	C₂×D₄₃	—	2	2	no	—
279	C₂×D₄₃	—	2	2	no	—
280	C₂×D₄₃	—	2	1	no	—
281	C₂×D₄₃	—	2	1	no	—
282	C₂×D₄₃	—	2	1	no	—
283	C₂×D₄₃	—	2	1	no	—
284	C₂×D₄₃	—	2	1	no	—
285	C₂×D₄₃	—	2	1	no	—
286	C₂×D₄₃	C₂×#41	1	4	yes	—
287	C₄×C₄₃	—	2	1	no	—
288	C₄×C₄₃	—	2	2	no	—
289	C₄×C₄₃	—	2	2	no	—
290	C₄×C₄₃	—	2	1	no	—
291	C₄×C₄₃	—	2	1	no	—
292	C₄×C₄₃	—	2	2	no	—
293	C₄×C₄₃	—	2	2	no	—
294	C₄×C₄₃	—	2	1	no	—
295	C₄×C₄₃	—	2	1	no	—
296	C₄×C₄₃	C₂×#41	1	2	yes	—
297	Dic₄₃	—	2	2	no	—
298	Dic₄₃	—	2	1	no	—
299	Dic₄₃	—	2	1	no	—
300	Dic₄₃	—	2	1	no	—
301	Dic₄₃	—	2	1	no	—
302	Dic₄₃	—	2	2	no	—
303	Dic₄₃	—	2	2	no	—
304	Dic₄₃	—	2	1	no	—
305	Dic₄₃	2₋¹⁺⁴	1	2	yes	—
306	#3515	—	43	1	no	maximal, Sylow
307	C₂×C₄₃	—	4	1	no	—
308	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
309	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂×C₄₃	#585	1	1	yes	characteristic
311	D₄₃	—	2	4	no	—
312	D₄₃	—	4	1	no	—
313	D₄₃	—	4	1	no	—
314	#557	—	43	1	no	—
315	#554	—	43	1	no	—
316	#554	—	43	1	no	—
317	#553	—	43	2	no	—
318	#552	—	43	2	no	—
319	#552	—	43	2	no	—
320	#552	—	43	1	no	—
321	#552	—	43	2	no	—
322	#552	—	43	1	no	—
323	#547	—	43	1	no	—
324	#547	—	43	1	no	—
325	#547	—	43	1	no	—
326	#541	—	43	1	no	—
327	#541	D₄₃	1	1	yes	characteristic, complemented
328	#539	—	43	2	no	—
329	#539	—	43	2	no	—
330	#533	—	43	1	no	—
331	#529	—	43	2	no	—
332	#529	—	43	1	no	—
333	C₂×#125	—	43	2	no	—
334	#520	—	43	1	no	—
335	#520	—	43	1	no	—
336	C₄×#41	—	43	1	no	—
337	C₄₃	#3515	1	1	yes	characteristic, complemented, Sylow
338	C₂×#41	—	43	1	no	—
339	C₂×#41	—	43	1	no	—
340	C₂×#41	—	43	1	no	—
341	C₄⋊Q₈	—	43	1	no	—
342	C₄⋊Q₈	—	43	1	no	—
343	C₄⋊Q₈	—	43	1	no	—
344	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
345	#126	—	43	1	no	—
346	#126	—	43	2	no	—
347	#126	—	43	2	no	—
348	#126	—	43	2	no	—
349	#126	—	43	1	no	—
350	#126	—	43	2	no	—
351	#126	C₂×D₄₃	1	2	yes	—
352	#126	C₂×D₄₃	1	2	yes	—
353	#125	—	43	1	no	—
354	#125	—	43	2	no	—
355	#125	—	43	2	no	—
356	#125	—	43	2	no	—
357	#125	—	43	2	no	—
358	#125	—	43	2	no	—
359	#125	—	43	2	no	—
360	#125	—	43	2	no	—
361	#125	—	43	2	no	—
362	#125	—	43	1	no	—
363	#125	—	43	2	no	—
364	#125	C₂×D₄₃	1	2	yes	—
365	#125	C₂×D₄₃	1	2	yes	—
366	#125	C₂×D₄₃	1	1	yes	characteristic
367	#124	—	43	1	no	—
368	#123	—	43	1	no	—
369	#123	—	43	2	no	—
370	#123	—	43	2	no	—
371	#123	—	43	2	no	—
372	#123	—	43	2	no	—
373	#123	—	43	2	no	—
374	#123	—	43	1	no	—
375	#123	—	43	2	no	—
376	#123	—	43	2	no	—
377	#123	—	43	2	no	—
378	C₂²⋊Q₈	—	43	1	no	—
379	C₂²⋊Q₈	—	43	1	no	—
380	C₂²⋊Q₈	—	43	1	no	—
381	C₂²⋊Q₈	—	43	2	no	—
382	C₂²⋊Q₈	—	43	2	no	—
383	C₂²⋊Q₈	—	43	1	no	—
384	C₂²⋊Q₈	—	43	2	no	—
385	C₂²⋊Q₈	—	43	2	no	—
386	C₂²⋊Q₈	—	43	2	no	—
387	C₂²⋊Q₈	—	43	1	no	—
388	C₂²⋊Q₈	—	43	2	no	—
389	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
390	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
391	#121	—	43	2	no	—
392	#121	—	43	2	no	—
393	#121	—	43	1	no	—
394	#121	—	43	2	no	—
395	C₄×Q₈	—	43	1	no	—
396	C₄×Q₈	—	43	1	no	—
397	C₄×Q₈	—	43	2	no	—
398	C₄×Q₈	—	43	1	no	—
399	C₄×Q₈	—	43	1	no	—
400	C₄×Q₈	—	43	1	no	—
401	C₄×Q₈	—	43	2	no	—
402	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
403	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
404	C₄×D₄	—	43	1	no	—
405	C₄×D₄	—	43	1	no	—
406	C₄×D₄	—	43	1	no	—
407	C₄×D₄	—	43	2	no	—
408	C₄×D₄	—	43	2	no	—
409	C₄×D₄	—	43	1	no	—
410	C₄×D₄	—	43	2	no	—
411	C₄×D₄	—	43	2	no	—
412	C₄×D₄	—	43	2	no	—
413	C₄×D₄	—	43	1	no	—
414	C₄×D₄	—	43	2	no	—
415	C₄×D₄	—	43	1	no	—
416	C₄×D₄	—	43	2	no	—
417	C₄×D₄	—	43	1	no	—
418	#117	—	43	1	no	—
419	#117	—	43	2	no	—
420	#117	—	43	2	no	—
421	#117	—	43	2	no	—
422	#117	—	43	2	no	—
423	#117	—	43	1	no	—
424	#117	—	43	2	no	—
425	#117	—	43	2	no	—
426	#117	C₂×D₄₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	—	43	1	no	—
428	C₂×C₄⋊C₄	—	43	2	no	—
429	C₂×C₄⋊C₄	—	43	2	no	—
430	C₂×C₄⋊C₄	—	43	1	no	—
431	C₂×C₄⋊C₄	—	43	2	no	—
432	C₂×C₄⋊C₄	—	43	2	no	—
433	C₂×C₄⋊C₄	—	43	2	no	—
434	C₂×C₄⋊C₄	—	43	2	no	—
435	C₂×C₄²	—	43	2	no	—
436	C₂×C₄²	—	43	1	no	—
437	#41	—	86	4	no	—
438	#41	—	86	4	no	—
439	#41	—	86	4	no	—
440	C₂×Q₈	—	43	1	no	—
441	C₂×Q₈	—	43	1	no	—
442	C₂×Q₈	—	43	2	no	—
443	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
444	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
445	C₂×D₄	—	43	1	no	—
446	C₂×D₄	—	43	2	no	—
447	C₂×D₄	—	43	1	no	—
448	C₂×D₄	—	43	1	no	—
449	C₂×D₄	—	43	2	no	—
450	C₂×D₄	—	43	2	no	—
451	C₂×D₄	—	43	1	no	—
452	C₂²×C₄	—	43	2	no	—
453	C₂²×C₄	—	43	2	no	—
454	C₂²×C₄	—	43	2	no	—
455	C₂²×C₄	—	43	1	no	—
456	C₂²×C₄	—	43	1	no	—
457	C₂²×C₄	—	43	2	no	—
458	C₂²×C₄	—	43	2	no	—
459	C₂²×C₄	—	43	1	no	—
460	C₂²×C₄	—	43	2	no	—
461	C₂²×C₄	—	43	1	no	—
462	C₂²×C₄	—	43	2	no	—
463	C₂²×C₄	—	43	2	no	—
464	C₂²×C₄	—	43	2	no	—
465	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
466	C₄⋊C₄	—	43	1	no	—
467	C₄⋊C₄	—	43	2	no	—
468	C₄⋊C₄	—	43	2	no	—
469	C₄⋊C₄	—	43	1	no	—
470	C₄⋊C₄	—	43	1	no	—
471	C₄⋊C₄	—	43	1	no	—
472	C₄⋊C₄	—	43	1	no	—
473	C₄⋊C₄	—	43	1	no	—
474	C₄⋊C₄	—	43	2	no	—
475	C₄⋊C₄	—	43	2	no	—
476	C₄⋊C₄	—	43	2	no	—
477	C₄⋊C₄	—	43	2	no	—
478	C₄⋊C₄	—	43	1	no	—
479	C₄⋊C₄	—	43	2	no	—
480	C₄⋊C₄	—	43	2	no	—
481	C₄⋊C₄	—	43	2	no	—
482	C₄⋊C₄	—	43	2	no	—
483	C₄⋊C₄	—	43	2	no	—
484	C₄⋊C₄	—	43	2	no	—
485	C₄⋊C₄	—	43	2	no	—
486	C₄⋊C₄	—	43	1	no	—
487	C₄⋊C₄	—	43	2	no	—
488	C₄⋊C₄	—	43	2	no	—
489	C₄⋊C₄	—	43	1	no	—
490	C₄⋊C₄	—	43	1	no	—
491	C₄⋊C₄	—	43	2	no	—
492	C₄⋊C₄	—	43	2	no	—
493	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
496	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
497	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
504	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
505	C₂²⋊C₄	—	43	1	no	—
506	C₂²⋊C₄	—	43	1	no	—
507	C₂²⋊C₄	—	43	2	no	—
508	C₂²⋊C₄	—	43	1	no	—
509	C₂²⋊C₄	—	43	1	no	—
510	C₂²⋊C₄	—	43	2	no	—
511	C₂²⋊C₄	—	43	2	no	—
512	C₂²⋊C₄	—	43	2	no	—
513	C₂²⋊C₄	—	43	2	no	—
514	C₂²⋊C₄	—	43	1	no	—
515	C₂²⋊C₄	—	43	2	no	—
516	C₂²⋊C₄	—	43	2	no	—
517	C₂²⋊C₄	—	43	2	no	—
518	C₂²⋊C₄	—	43	2	no	—
519	C₂²⋊C₄	—	43	1	no	—
520	C₂²⋊C₄	—	43	1	no	—
521	C₂²⋊C₄	—	43	1	no	—
522	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
526	C₄²	—	43	1	no	—
527	C₄²	—	43	2	no	—
528	C₄²	—	43	1	no	—
529	C₄²	—	43	2	no	—
530	C₄²	—	43	1	no	—
531	C₄²	—	43	2	no	—
532	C₄²	—	43	2	no	—
533	C₄²	—	43	2	no	—
534	C₄²	—	43	1	no	—
535	C₄²	C₂²×D₄₃	1	1	yes	characteristic
536	C₄²	C₂²×D₄₃	1	2	yes	—
537	C₄²	C₂²×D₄₃	1	2	yes	—
538	C₄²	C₂²×D₄₃	1	1	yes	characteristic
539	C₂³	—	43	2	no	—
540	C₂³	—	43	1	no	—
541	C₂³	—	43	1	no	—
542	C₂³	C₂³×D₄₃	1	1	yes	characteristic
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	86	2	no	—
546	Q₈	—	86	2	no	—
547	Q₈	—	172	2	no	—
548	D₄	—	43	4	no	—
549	D₄	—	86	4	no	—
550	D₄	—	86	4	no	—
551	D₄	—	86	2	no	—
552	D₄	—	86	4	no	—
553	D₄	—	172	1	no	—
554	D₄	—	172	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	43	1	no	—
557	C₂×C₄	—	43	1	no	—
558	C₂×C₄	—	43	2	no	—
559	C₂×C₄	—	43	1	no	—
560	C₂×C₄	—	43	1	no	—
561	C₂×C₄	—	43	2	no	—
562	C₂×C₄	—	43	2	no	—
563	C₂×C₄	—	43	1	no	—
564	C₂×C₄	—	43	1	no	—
565	C₂×C₄	—	86	4	no	—
566	C₂×C₄	—	86	2	no	—
567	C₂×C₄	—	86	4	no	—
568	C₂×C₄	—	86	4	no	—
569	C₂×C₄	—	86	4	no	—
570	C₂×C₄	—	86	2	no	—
571	C₂×C₄	—	86	2	no	—
572	C₂×C₄	—	172	2	no	—
573	C₂×C₄	—	172	1	no	—
574	C₂×C₄	—	172	2	no	—
575	C₂×C₄	—	172	2	no	—
576	C₂×C₄	—	172	2	no	—
577	C₂×C₄	—	172	2	no	—
578	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₄₃	1	2	yes	—
582	C₂×C₄	C₂³×D₄₃	1	2	yes	—
583	C₂×C₄	C₂³×D₄₃	1	2	yes	—
584	C₂×C₄	C₂³×D₄₃	1	2	yes	—
585	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	43	4	no	—
592	C₂²	—	86	2	no	—
593	C₂²	—	86	2	no	—
594	C₂²	—	86	1	no	—
595	C₂²	—	86	1	no	—
596	C₂²	—	86	1	no	—
597	C₂²	—	86	1	no	—
598	C₂²	—	86	1	no	—
599	C₂²	—	86	1	no	—
600	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	2	no	—
610	C₄	—	43	2	no	—
611	C₄	—	86	1	no	—
612	C₄	—	86	1	no	—
613	C₄	—	86	2	no	—
614	C₄	—	86	1	no	—
615	C₄	—	86	2	no	—
616	C₄	—	86	1	no	—
617	C₄	—	86	2	no	—
618	C₄	—	86	1	no	—
619	C₄	#41×D₄₃	1	2	yes	—
620	C₂	—	4	1	no	—
621	C₂	—	86	4	no	—
622	C₂	—	172	1	no	—
623	C₂	—	172	1	no	—
624	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
625	C₂	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
626	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#541	C₂
hypercenter	#541	D₄₃
hypocenter	C₄₃	#3515
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #14583624	C₂	semidirect
2. #14583607	C₂	semidirect
3. #14583605	C₂	semidirect
4. #14583600	C₂	semidirect
5. #14583591	C₂	semidirect
6. #14583587	C₂	semidirect
7. #14583587	C₂	semidirect
8. #14583585	C₂	semidirect
9. #14583581	C₂	semidirect
10. #14583552	C₂	semidirect
11. #14583551	C₂	semidirect
12. #14583551	C₂	semidirect
13. #14583507	C₂	semidirect
14. #14583497	C₂	semidirect
15. #14583490	C₂	semidirect
16. #14583453	C₂	semidirect
17. #14583432	C₂	semidirect
18. #14583427	C₂	semidirect
19. #125×D₄₃	C₂	semidirect
20. #14583381	C₂	semidirect
21. #14583379	C₂	semidirect
22. C₄×#10621902	C₂	semidirect
23. C₄₃×#541	C₂	semidirect
327. #541	D₄₃	semidirect
337. C₄₃	#3515	semidirect