Subgroups — #19149110

Order 5504.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583645	C₂	1	2	yes	maximal, complemented
2	#14583641	C₂	1	2	yes	maximal, complemented
3	#14583634	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583632	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583561	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583559	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583546	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583542	C₂	1	2	yes	maximal, complemented
9	#14583540	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583540	C₂	1	2	yes	maximal, complemented
11	D₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583533	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583523	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583488	C₂	1	2	yes	maximal, complemented
15	#14583488	C₂	1	2	yes	maximal, complemented
16	#14583485	C₂	1	2	yes	maximal, complemented
17	#14583468	C₂	1	1	yes	maximal, characteristic, complemented
18	#14583467	C₂	1	1	yes	maximal, characteristic, complemented
19	#14583460	C₂	1	2	yes	maximal, complemented
20	#14583450	C₂	1	1	yes	maximal, characteristic, complemented
21	#14583427	C₂	1	1	yes	maximal, characteristic, complemented
22	#124×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10621902	C₂²	1	1	yes	characteristic, complemented
25	C₂×#10621902	C₂²	1	2	yes	complemented
26	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
29	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
31	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
32	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
33	#13063322	C₂²	1	1	yes	characteristic
34	#13063322	C₂²	1	1	yes	characteristic, complemented
35	#13063321	C₂²	1	1	yes	characteristic
36	#13063320	C₂²	1	1	yes	characteristic, complemented
37	#13063320	C₂²	1	2	yes	complemented
38	#13063318	C₂²	1	1	yes	characteristic, complemented
39	#13063315	C₂²	1	1	yes	characteristic, complemented
40	#13063314	C₂²	1	1	yes	characteristic, complemented
41	#13063314	C₂²	1	1	yes	characteristic, complemented
42	#13063314	C₂²	1	2	yes	complemented
43	#13063314	C₂²	1	2	yes	complemented
44	#13063313	C₂²	1	1	yes	characteristic, complemented
45	#13063313	C₂²	1	2	yes	complemented
46	#13063313	C₂²	1	2	yes	complemented
47	#13063313	C₂²	1	1	yes	characteristic, complemented
48	#13063312	C₂²	1	1	yes	characteristic, complemented
49	#13063311	C₂²	1	2	yes	complemented
50	#13063311	C₂²	1	2	yes	complemented
51	#13063311	C₂²	1	1	yes	characteristic, complemented
52	#13063311	C₂²	1	2	yes	complemented
53	#13063311	C₂²	1	2	yes	complemented
54	#13063310	C₂²	1	2	yes	complemented
55	#13063310	C₂²	1	2	yes	complemented
56	#13063310	C₂²	1	2	yes	complemented
57	#13063310	C₂²	1	1	yes	characteristic, complemented
58	#13063310	C₂²	1	2	yes	complemented
59	#13063308	C₂²	1	2	yes	complemented
60	#13063307	C₂²	1	2	yes	complemented
61	#13063307	C₂²	1	2	yes	complemented
62	#13063307	C₂²	1	1	yes	characteristic, complemented
63	#13063305	C₂²	1	2	yes	complemented
64	#13063305	C₂²	1	1	yes	characteristic, complemented
65	#13063303	C₂²	1	2	yes	complemented
66	#13063303	C₂²	1	1	yes	characteristic, complemented
67	#13063301	C₂²	1	2	yes	complemented
68	#13063300	C₂²	1	1	yes	characteristic
69	#13063300	C₂²	1	1	yes	characteristic, complemented
70	#13063300	C₂²	1	1	yes	characteristic, complemented
71	#13063300	C₂²	1	2	yes	complemented
72	#13063300	C₂²	1	2	yes	complemented
73	#13063300	C₂²	1	2	yes	complemented
74	#13063300	C₂²	1	2	yes	complemented
75	#13063300	C₂²	1	2	yes	complemented
76	#13063299	C₂²	1	2	yes	complemented
77	#13063298	C₂²	1	1	yes	characteristic
78	#13063298	C₂²	1	2	yes	complemented
79	#13063298	C₂²	1	2	yes	complemented
80	#13063298	C₂²	1	2	yes	complemented
81	#13063298	C₂²	1	2	yes	complemented
82	#13063296	C₂²	1	2	yes	complemented
83	#13063295	C₂²	1	2	yes	complemented
84	#13063295	C₂²	1	2	yes	complemented
85	#13063295	C₂²	1	2	yes	complemented
86	#13063295	C₂²	1	2	yes	complemented
87	#13063295	C₂²	1	2	yes	complemented
88	#13063295	C₂²	1	2	yes	complemented
89	#13063295	C₂²	1	2	yes	complemented
90	#13063295	C₂²	1	2	yes	complemented
91	#13063293	C₂²	1	2	yes	complemented
92	#13063293	C₂²	1	2	yes	complemented
93	C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
94	#13063290	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₁₇₂	C₂²	1	2	yes	complemented
97	C₄×D₁₇₂	C₂²	1	2	yes	complemented
98	#13063287	C₂²	1	2	yes	complemented
99	#13063287	C₂²	1	1	yes	characteristic, complemented
100	#13063287	C₂²	1	1	yes	characteristic, complemented
101	#13063287	C₂²	1	1	yes	characteristic, complemented
102	#13063287	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
106	#13063282	C₂²	1	1	yes	characteristic, complemented
107	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
111	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
113	#126×C₄₃	C₂²	1	2	yes	complemented
114	#124×C₄₃	C₂²	1	2	yes	complemented
115	#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
116	#123×C₄₃	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
119	#121×C₄₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
122	#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₄₃	C₂³	1	2	yes	—
124	C₂³×D₄₃	C₂³	1	2	yes	—
125	C₂³×D₄₃	C₂³	1	2	yes	—
126	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
128	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₄₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
139	#10621902	—	4	4	no	—
140	#10621902	—	4	2	no	—
141	Q₈×D₄₃	—	4	2	no	—
142	D₄×D₄₃	—	4	4	no	—
143	D₄×D₄₃	—	4	2	no	—
144	D₄×D₄₃	—	4	2	no	—
145	#10621898	—	4	2	no	—
146	C₂×D₁₇₂	—	4	4	no	—
147	C₂×D₁₇₂	—	4	2	no	—
148	C₂×D₁₇₂	C₂³	1	2	yes	—
149	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
150	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
151	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
152	C₂×D₁₇₂	C₂³	1	2	yes	—
153	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
154	C₂×D₁₇₂	C₂³	1	2	yes	—
155	C₂×D₁₇₂	C₂³	1	2	yes	—
156	C₂×D₁₇₂	C₂³	1	2	yes	—
157	C₂×D₁₇₂	C₂³	1	2	yes	—
158	C₂×D₁₇₂	C₂³	1	2	yes	—
159	C₂×D₁₇₂	C₂³	1	2	yes	—
160	C₂×D₁₇₂	C₂³	1	2	yes	—
161	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₄₃	C₂³	1	2	yes	—
166	C₂×C₄×D₄₃	C₂³	1	2	yes	—
167	C₂×C₄×D₄₃	C₂³	1	2	yes	—
168	C₂×C₄×D₄₃	C₂³	1	2	yes	—
169	C₂×C₄×D₄₃	C₂³	1	2	yes	—
170	C₂×C₄×D₄₃	C₂³	1	2	yes	—
171	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
172	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
173	C₂×Dic₈₆	C₂³	1	2	yes	—
174	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
176	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
179	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
180	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
182	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
188	C₄²×C₄₃	C₂³	1	1	yes	characteristic
189	C₄²×C₄₃	C₂³	1	1	yes	characteristic
190	C₄²×C₄₃	C₂³	1	2	yes	—
191	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
193	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
194	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
195	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
214	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
215	(C₂×D₄₃)⋊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	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
224	Dic₄₃⋊C₄	C₂³	1	2	yes	—
225	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
228	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
229	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₄₃	C₂³	1	2	yes	—
231	C₂³×C₄₃	C₂⁴	1	2	yes	—
232	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₄₃	—	2	4	no	—
234	C₂²×D₄₃	—	4	2	no	—
235	C₂²×D₄₃	—	4	2	no	—
236	C₂²×D₄₃	—	4	2	no	—
237	C₂²×D₄₃	—	4	2	no	—
238	C₂²×D₄₃	—	4	2	no	—
239	C₂²×D₄₃	—	4	2	no	—
240	C₂²×D₄₃	—	4	2	no	—
241	C₂²×D₄₃	—	4	2	no	—
242	C₂²×D₄₃	C₂⁴	1	2	yes	—
243	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₄₃	C₂⁴	1	2	yes	—
245	C₂²×D₄₃	C₂⁴	1	2	yes	—
246	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
247	Q₈×C₄₃	—	2	2	no	—
248	Q₈×C₄₃	—	4	2	no	—
249	D₄×C₄₃	—	2	2	no	—
250	D₄×C₄₃	—	4	2	no	—
251	C₂×C₄×C₄₃	—	2	2	no	—
252	C₂×C₄×C₄₃	—	4	2	no	—
253	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₄₃	—	2	2	no	—
263	C₂²⋊D₄₃	—	4	2	no	—
264	C₂²⋊D₄₃	—	4	2	no	—
265	C₂²⋊D₄₃	—	4	2	no	—
266	C₂²⋊D₄₃	—	4	2	no	—
267	C₂²⋊D₄₃	—	4	1	no	—
268	C₂²⋊D₄₃	—	4	2	no	—
269	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₄₃	C₂⁴	1	2	yes	—
275	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
276	D₁₇₂	—	2	2	no	—
277	D₁₇₂	—	2	4	no	—
278	D₁₇₂	—	2	4	no	—
279	D₁₇₂	—	2	2	no	—
280	D₁₇₂	—	2	2	no	—
281	D₁₇₂	—	2	2	no	—
282	D₁₇₂	—	4	2	no	—
283	D₁₇₂	—	4	2	no	—
284	D₁₇₂	—	4	2	no	—
285	D₁₇₂	—	4	2	no	—
286	D₁₇₂	—	4	2	no	—
287	D₁₇₂	—	4	2	no	—
288	D₁₇₂	—	4	2	no	—
289	C₄×D₄₃	—	2	2	no	—
290	C₄×D₄₃	—	2	2	no	—
291	C₄×D₄₃	—	2	2	no	—
292	C₄×D₄₃	—	4	1	no	—
293	C₄×D₄₃	—	4	2	no	—
294	C₄×D₄₃	—	4	2	no	—
295	C₄×D₄₃	—	4	2	no	—
296	C₄×D₄₃	—	4	2	no	—
297	C₄×D₄₃	—	4	2	no	—
298	C₄×D₄₃	—	4	2	no	—
299	Dic₈₆	—	2	2	no	—
300	Dic₈₆	—	4	1	no	—
301	Dic₈₆	—	4	2	no	—
302	C₂²×C₄₃	—	2	2	no	—
303	C₂²×C₄₃	—	2	1	no	—
304	C₂²×C₄₃	—	2	1	no	—
305	C₂²×C₄₃	—	2	2	no	—
306	C₂²×C₄₃	—	2	2	no	—
307	C₂²×C₄₃	—	2	1	no	—
308	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
309	C₂×D₄₃	—	2	1	no	—
310	C₂×D₄₃	—	2	1	no	—
311	C₂×D₄₃	—	2	2	no	—
312	C₂×D₄₃	—	2	1	no	—
313	C₂×D₄₃	—	2	1	no	—
314	C₂×D₄₃	—	2	2	no	—
315	C₂×D₄₃	—	2	2	no	—
316	C₂×D₄₃	—	2	2	no	—
317	C₂×D₄₃	—	2	2	no	—
318	C₂×D₄₃	—	2	2	no	—
319	C₂×D₄₃	—	2	2	no	—
320	C₂×D₄₃	—	2	1	no	—
321	C₂×D₄₃	—	2	2	no	—
322	C₂×D₄₃	—	2	2	no	—
323	C₂×D₄₃	—	8	4	no	—
324	C₂×D₄₃	—	8	4	no	—
325	C₂×D₄₃	—	8	4	no	—
326	C₂×D₄₃	H(5,𝔽₂)	1	2	yes	—
327	C₄×C₄₃	—	2	2	no	—
328	C₄×C₄₃	—	2	1	no	—
329	C₄×C₄₃	—	2	2	no	—
330	C₄×C₄₃	—	2	1	no	—
331	C₄×C₄₃	—	2	2	no	—
332	C₄×C₄₃	—	2	1	no	—
333	C₄×C₄₃	—	2	1	no	—
334	C₄×C₄₃	—	2	1	no	—
335	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
336	Dic₄₃	—	2	2	no	—
337	Dic₄₃	—	2	1	no	—
338	Dic₄₃	—	2	1	no	—
339	Dic₄₃	—	2	1	no	—
340	Dic₄₃	—	2	1	no	—
341	Dic₄₃	—	2	1	no	—
342	Dic₄₃	—	2	1	no	—
343	#3558	—	43	1	no	maximal, Sylow
344	C₂×C₄₃	—	4	2	no	—
345	C₂×C₄₃	—	4	1	no	—
346	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₄₃	#585	1	1	yes	characteristic
349	D₄₃	—	2	2	no	—
350	D₄₃	—	4	2	no	—
351	D₄₃	—	4	2	no	—
352	D₄₃	—	4	2	no	—
353	D₄₃	—	4	1	no	—
354	#562	—	43	2	no	—
355	H(3,𝔽₄)	—	43	2	no	—
356	#559	—	43	1	no	—
357	#559	—	43	1	no	—
358	#548	—	43	1	no	—
359	#548	—	43	1	no	—
360	#546	—	43	2	no	—
361	#546	—	43	2	no	—
362	#546	—	43	1	no	—
363	#546	—	43	1	no	—
364	D₄²	—	43	1	no	—
365	D₄²	—	43	1	no	—
366	#542	—	43	1	no	—
367	#542	D₄₃	1	1	yes	characteristic, complemented
368	#538	—	43	2	no	—
369	#538	—	43	2	no	—
370	#538	—	43	2	no	—
371	#535	—	43	1	no	—
372	#535	—	43	1	no	—
373	#534	—	43	2	no	—
374	#532	—	43	1	no	—
375	#529	—	43	1	no	—
376	C₂×#124	—	43	1	no	—
377	C₄₃	#3558	1	1	yes	characteristic, complemented, Sylow
378	C₂×#41	—	43	2	no	—
379	C₂×#41	—	43	1	no	—
380	C₂×#41	—	43	1	no	—
381	C₂²×Q₈	—	43	1	no	—
382	C₂²×D₄	—	43	1	no	—
383	C₂²×D₄	—	43	2	no	—
384	C₂²×D₄	—	43	1	no	—
385	C₂²×D₄	—	43	2	no	—
386	C₂²×D₄	—	43	1	no	—
387	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
388	#127	—	43	1	no	—
389	#127	—	43	1	no	—
390	#127	—	43	1	no	—
391	#126	—	43	1	no	—
392	#126	—	43	2	no	—
393	#126	—	43	1	no	—
394	#126	C₂×D₄₃	1	2	yes	complemented
395	#125	—	43	1	no	—
396	#124	—	43	1	no	—
397	#124	—	43	2	no	—
398	#124	—	43	1	no	—
399	#124	—	43	2	no	—
400	#124	—	43	1	no	—
401	#124	—	43	2	no	—
402	#124	—	43	2	no	—
403	#124	—	43	1	no	—
404	#124	—	43	2	no	—
405	#124	—	43	2	no	—
406	#124	—	43	1	no	—
407	#124	—	43	1	no	—
408	#124	—	43	2	no	—
409	#124	—	43	2	no	—
410	#124	C₂×D₄₃	1	1	yes	characteristic, complemented
411	#124	C₂×D₄₃	1	2	yes	complemented
412	#123	—	43	2	no	—
413	#123	—	43	1	no	—
414	#123	—	43	2	no	—
415	#123	—	43	2	no	—
416	#123	—	43	2	no	—
417	#123	—	43	2	no	—
418	#123	—	43	1	no	—
419	#123	—	43	2	no	—
420	#123	—	43	2	no	—
421	#123	C₂×D₄₃	1	2	yes	complemented
422	C₂²⋊Q₈	—	43	2	no	—
423	C₂²⋊Q₈	—	43	1	no	—
424	C₂²⋊Q₈	—	43	2	no	—
425	C₂²⋊Q₈	—	43	2	no	—
426	C₂²⋊Q₈	—	43	1	no	—
427	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
428	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
429	#121	—	43	2	no	—
430	#121	—	43	2	no	—
431	#121	—	43	2	no	—
432	#121	—	43	1	no	—
433	#121	—	43	1	no	—
434	#121	—	43	2	no	—
435	#121	—	43	2	no	—
436	#121	—	43	2	no	—
437	#121	—	43	2	no	—
438	#121	—	43	1	no	—
439	#121	—	43	1	no	—
440	#121	—	43	2	no	—
441	#121	—	43	2	no	—
442	#121	—	43	2	no	—
443	#121	—	43	2	no	—
444	#121	C₂×D₄₃	1	1	yes	characteristic
445	#120	—	43	2	no	—
446	#120	—	43	2	no	—
447	#120	—	43	2	no	—
448	#120	—	43	2	no	—
449	#120	—	43	2	no	—
450	#120	—	43	2	no	—
451	#120	—	43	2	no	—
452	#120	—	43	2	no	—
453	#120	—	43	2	no	—
454	#120	—	43	2	no	—
455	C₄×Q₈	—	43	1	no	—
456	C₄×Q₈	—	43	1	no	—
457	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
458	C₄×D₄	—	43	1	no	—
459	C₄×D₄	—	43	1	no	—
460	C₄×D₄	—	43	2	no	—
461	C₄×D₄	—	43	2	no	—
462	C₄×D₄	—	43	1	no	—
463	C₄×D₄	—	43	1	no	—
464	C₄×D₄	—	43	2	no	—
465	C₄×D₄	—	43	1	no	—
466	C₄×D₄	—	43	1	no	—
467	C₄×D₄	—	43	2	no	—
468	C₄×D₄	—	43	2	no	—
469	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
470	#117	—	43	1	no	—
471	#117	C₂×D₄₃	1	1	yes	characteristic, complemented
472	C₂×C₂²⋊C₄	—	43	2	no	—
473	C₂×C₂²⋊C₄	—	43	2	no	—
474	C₂×C₂²⋊C₄	—	43	2	no	—
475	C₂×C₂²⋊C₄	—	43	2	no	—
476	C₂×C₄²	—	43	1	no	—
477	C₂⁴	—	43	2	no	—
478	C₂⁴	—	43	2	no	—
479	C₂⁴	—	43	2	no	—
480	#41	—	172	2	no	—
481	#41	—	172	4	no	—
482	#41	—	172	2	no	—
483	C₂×Q₈	—	43	1	no	—
484	C₂×Q₈	—	43	1	no	—
485	C₂×Q₈	—	43	2	no	—
486	C₂×Q₈	—	172	2	no	—
487	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
489	C₂×D₄	—	43	1	no	—
490	C₂×D₄	—	43	1	no	—
491	C₂×D₄	—	43	2	no	—
492	C₂×D₄	—	43	2	no	—
493	C₂×D₄	—	43	2	no	—
494	C₂×D₄	—	43	2	no	—
495	C₂×D₄	—	43	2	no	—
496	C₂×D₄	—	43	2	no	—
497	C₂×D₄	—	43	2	no	—
498	C₂×D₄	—	43	1	no	—
499	C₂×D₄	—	43	1	no	—
500	C₂×D₄	—	43	1	no	—
501	C₂×D₄	—	43	1	no	—
502	C₂×D₄	—	43	2	no	—
503	C₂×D₄	—	43	2	no	—
504	C₂×D₄	—	43	2	no	—
505	C₂×D₄	—	43	2	no	—
506	C₂×D₄	—	43	2	no	—
507	C₂×D₄	—	43	2	no	—
508	C₂×D₄	—	43	2	no	—
509	C₂×D₄	—	172	2	no	—
510	C₂×D₄	—	172	4	no	—
511	C₂×D₄	—	172	2	no	—
512	C₂×D₄	—	172	2	no	—
513	C₂×D₄	—	172	4	no	—
514	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
515	C₂×D₄	C₂²×D₄₃	1	2	yes	—
516	C₂²×C₄	—	43	1	no	—
517	C₂²×C₄	—	43	1	no	—
518	C₂²×C₄	—	43	1	no	—
519	C₂²×C₄	—	43	1	no	—
520	C₂²×C₄	—	43	2	no	—
521	C₂²×C₄	—	43	2	no	—
522	C₂²×C₄	—	43	2	no	—
523	C₂²×C₄	—	43	2	no	—
524	C₂²×C₄	—	43	2	no	—
525	C₂²×C₄	—	43	2	no	—
526	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
528	C₄⋊C₄	—	43	1	no	—
529	C₄⋊C₄	—	43	1	no	—
530	C₄⋊C₄	—	43	1	no	—
531	C₄⋊C₄	—	43	1	no	—
532	C₄⋊C₄	—	43	1	no	—
533	C₄⋊C₄	—	43	1	no	—
534	C₄⋊C₄	—	43	2	no	—
535	C₄⋊C₄	—	43	1	no	—
536	C₄⋊C₄	—	43	2	no	—
537	C₄⋊C₄	—	43	1	no	—
538	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
539	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
543	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
544	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
545	C₂²⋊C₄	—	43	1	no	—
546	C₂²⋊C₄	—	43	2	no	—
547	C₂²⋊C₄	—	43	2	no	—
548	C₂²⋊C₄	—	43	1	no	—
549	C₂²⋊C₄	—	43	1	no	—
550	C₂²⋊C₄	—	43	2	no	—
551	C₂²⋊C₄	—	43	2	no	—
552	C₂²⋊C₄	—	43	2	no	—
553	C₂²⋊C₄	—	43	2	no	—
554	C₂²⋊C₄	—	43	2	no	—
555	C₂²⋊C₄	—	43	2	no	—
556	C₂²⋊C₄	—	43	1	no	—
557	C₂²⋊C₄	—	43	1	no	—
558	C₂²⋊C₄	—	43	1	no	—
559	C₂²⋊C₄	—	43	1	no	—
560	C₂²⋊C₄	—	43	2	no	—
561	C₂²⋊C₄	—	43	1	no	—
562	C₂²⋊C₄	—	43	2	no	—
563	C₂²⋊C₄	—	43	2	no	—
564	C₂²⋊C₄	—	43	2	no	—
565	C₂²⋊C₄	—	43	2	no	—
566	C₂²⋊C₄	—	43	2	no	—
567	C₂²⋊C₄	—	43	2	no	—
568	C₂²⋊C₄	—	43	2	no	—
569	C₂²⋊C₄	—	43	2	no	—
570	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
575	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
577	C₄²	—	43	1	no	—
578	C₄²	—	43	1	no	—
579	C₄²	—	43	1	no	—
580	C₄²	—	43	1	no	—
581	C₄²	—	43	2	no	—
582	C₄²	C₂²×D₄₃	1	1	yes	characteristic
583	C₄²	C₂²×D₄₃	1	1	yes	characteristic
584	C₄²	C₂²×D₄₃	1	2	yes	—
585	C₂³	—	43	1	no	—
586	C₂³	—	43	2	no	—
587	C₂³	—	43	1	no	—
588	C₂³	—	43	2	no	—
589	C₂³	—	43	2	no	—
590	C₂³	—	86	4	no	—
591	C₂³	—	172	2	no	—
592	C₂³	—	172	2	no	—
593	C₂³	—	172	2	no	—
594	C₂³	—	172	2	no	—
595	C₂³	—	172	2	no	—
596	C₂³	—	172	2	no	—
597	C₂³	—	172	2	no	—
598	C₂³	—	172	2	no	—
599	C₂³	C₂³×D₄₃	1	2	yes	—
600	C₂³	C₂³×D₄₃	1	1	yes	characteristic
601	Q₈	—	2	2	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	86	2	no	—
604	Q₈	—	172	2	no	—
605	Q₈	—	172	1	no	—
606	D₄	—	2	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	86	2	no	—
609	D₄	—	86	4	no	—
610	D₄	—	86	4	no	—
611	D₄	—	86	2	no	—
612	D₄	—	86	2	no	—
613	D₄	—	86	2	no	—
614	D₄	—	86	2	no	—
615	D₄	—	172	2	no	—
616	D₄	—	172	2	no	—
617	D₄	—	172	2	no	—
618	D₄	—	172	2	no	—
619	D₄	—	172	2	no	—
620	D₄	—	172	2	no	—
621	D₄	—	172	2	no	—
622	D₄	—	172	2	no	—
623	D₄	—	172	2	no	—
624	D₄	—	172	2	no	—
625	D₄	—	172	2	no	—
626	D₄	—	172	1	no	—
627	D₄	—	172	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	43	1	no	—
631	C₂×C₄	—	43	1	no	—
632	C₂×C₄	—	43	1	no	—
633	C₂×C₄	—	43	1	no	—
634	C₂×C₄	—	43	2	no	—
635	C₂×C₄	—	43	1	no	—
636	C₂×C₄	—	43	1	no	—
637	C₂×C₄	—	86	2	no	—
638	C₂×C₄	—	86	2	no	—
639	C₂×C₄	—	86	2	no	—
640	C₂×C₄	—	172	2	no	—
641	C₂×C₄	—	172	2	no	—
642	C₂×C₄	—	172	2	no	—
643	C₂×C₄	—	172	2	no	—
644	C₂×C₄	—	172	2	no	—
645	C₂×C₄	—	172	2	no	—
646	C₂×C₄	—	172	1	no	—
647	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₄₃	1	2	yes	—
650	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₄₃	1	2	yes	—
652	C₂×C₄	C₂³×D₄₃	1	2	yes	—
653	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	43	2	no	—
663	C₂²	—	86	1	no	—
664	C₂²	—	86	1	no	—
665	C₂²	—	86	2	no	—
666	C₂²	—	86	2	no	—
667	C₂²	—	86	2	no	—
668	C₂²	—	86	1	no	—
669	C₂²	—	86	1	no	—
670	C₂²	—	86	2	no	—
671	C₂²	—	86	2	no	—
672	C₂²	—	86	2	no	—
673	C₂²	—	86	2	no	—
674	C₂²	—	86	2	no	—
675	C₂²	—	86	2	no	—
676	C₂²	—	86	1	no	—
677	C₂²	—	344	4	no	—
678	C₂²	—	344	4	no	—
679	C₂²	—	344	4	no	—
680	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	86	1	no	—
690	C₄	—	86	1	no	—
691	C₄	—	86	1	no	—
692	C₄	—	86	1	no	—
693	C₄	—	86	2	no	—
694	C₄	—	86	1	no	—
695	C₄	—	86	1	no	—
696	C₄	#13063371	1	2	yes	—
697	C₂	—	4	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	86	2	no	—
700	C₂	—	172	2	no	—
701	C₂	—	172	1	no	—
702	C₂	—	172	2	no	—
703	C₂	—	172	2	no	—
704	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
705	C₂	C₂×#13063371	1	1	yes	characteristic
706	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#542	C₂
hypercenter	#542	D₄₃
hypocenter	C₄₃	#3558
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #14583645	C₂	semidirect
2. #14583641	C₂	semidirect
3. #14583634	C₂	semidirect
4. #14583632	C₂	semidirect
5. #14583561	C₂	semidirect
6. #14583559	C₂	semidirect
7. #14583546	C₂	semidirect
8. #14583542	C₂	semidirect
9. #14583540	C₂	semidirect
10. #14583540	C₂	semidirect
11. D₄×D₁₇₂	C₂	semidirect
12. #14583533	C₂	semidirect
13. #14583523	C₂	semidirect
14. #14583488	C₂	semidirect
15. #14583488	C₂	semidirect
16. #14583485	C₂	semidirect
17. #14583468	C₂	semidirect
18. #14583467	C₂	semidirect
19. #14583460	C₂	semidirect
20. #14583450	C₂	semidirect
21. #14583427	C₂	semidirect
22. #124×D₄₃	C₂	semidirect
23. C₄₃×#542	C₂	semidirect
24. C₂×#10621902	C₂²	semidirect
25. C₂×#10621902	C₂²	semidirect
26. C₂×#10621898	C₂²	semidirect
27. C₂×Q₈×D₄₃	C₂²	semidirect
28. C₂²×D₁₇₂	C₂²	semidirect
29. C₂²×D₁₇₂	C₂²	semidirect
31. C₂×D₄×D₄₃	C₂²	semidirect
32. C₂×D₄×D₄₃	C₂²	semidirect
34. #13063322	C₂²	semidirect
36. #13063320	C₂²	semidirect
37. #13063320	C₂²	semidirect
38. #13063318	C₂²	semidirect
39. #13063315	C₂²	semidirect
40. #13063314	C₂²	semidirect
41. #13063314	C₂²	semidirect
42. #13063314	C₂²	semidirect
43. #13063314	C₂²	semidirect
44. #13063313	C₂²	semidirect
45. #13063313	C₂²	semidirect
46. #13063313	C₂²	semidirect
47. #13063313	C₂²	semidirect
48. #13063312	C₂²	semidirect
49. #13063311	C₂²	semidirect
50. #13063311	C₂²	semidirect
51. #13063311	C₂²	semidirect
52. #13063311	C₂²	semidirect
53. #13063311	C₂²	semidirect
54. #13063310	C₂²	semidirect
55. #13063310	C₂²	semidirect
56. #13063310	C₂²	semidirect
57. #13063310	C₂²	semidirect
58. #13063310	C₂²	semidirect
59. #13063308	C₂²	semidirect
60. #13063307	C₂²	semidirect
61. #13063307	C₂²	semidirect
62. #13063307	C₂²	semidirect
63. #13063305	C₂²	semidirect
64. #13063305	C₂²	semidirect
65. #13063303	C₂²	semidirect
66. #13063303	C₂²	semidirect
67. #13063301	C₂²	semidirect
69. #13063300	C₂²	semidirect
70. #13063300	C₂²	semidirect
71. #13063300	C₂²	semidirect
72. #13063300	C₂²	semidirect
73. #13063300	C₂²	semidirect
74. #13063300	C₂²	semidirect
75. #13063300	C₂²	semidirect
76. #13063299	C₂²	semidirect
78. #13063298	C₂²	semidirect
79. #13063298	C₂²	semidirect
80. #13063298	C₂²	semidirect
81. #13063298	C₂²	semidirect
82. #13063296	C₂²	semidirect
83. #13063295	C₂²	semidirect
84. #13063295	C₂²	semidirect
85. #13063295	C₂²	semidirect
86. #13063295	C₂²	semidirect
87. #13063295	C₂²	semidirect
88. #13063295	C₂²	semidirect
89. #13063295	C₂²	semidirect
90. #13063295	C₂²	semidirect
91. #13063293	C₂²	semidirect
92. #13063293	C₂²	semidirect
93. C₄×Dic₈₆	C₂²	semidirect
94. #13063290	C₂²	semidirect
95. C₄×D₁₇₂	C₂²	semidirect
96. C₄×D₁₇₂	C₂²	semidirect
97. C₄×D₁₇₂	C₂²	semidirect
98. #13063287	C₂²	semidirect
99. #13063287	C₂²	semidirect
100. #13063287	C₂²	semidirect
101. #13063287	C₂²	semidirect
102. #13063287	C₂²	semidirect
103. C₄×C₂²⋊D₄₃	C₂²	semidirect
104. C₄×C₂²⋊D₄₃	C₂²	semidirect
105. C₄×C₂²⋊D₄₃	C₂²	semidirect
106. #13063282	C₂²	semidirect
107. C₂²⋊C₄×D₄₃	C₂²	semidirect
108. C₂²⋊C₄×D₄₃	C₂²	semidirect
109. C₂²⋊C₄×D₄₃	C₂²	semidirect
110. C₂²⋊C₄×D₄₃	C₂²	semidirect
111. C₄²×D₄₃	C₂²	semidirect
112. C₄⋊Q₈×C₄₃	C₂²	semidirect
113. #126×C₄₃	C₂²	semidirect
114. #124×C₄₃	C₂²	semidirect
115. #124×C₄₃	C₂²	semidirect
116. #123×C₄₃	C₂²	semidirect
117. C₂²⋊Q₈×C₄₃	C₂²	semidirect
118. C₂²⋊Q₈×C₄₃	C₂²	semidirect
120. C₄×Q₈×C₄₃	C₂²	semidirect
121. C₄×D₄×C₄₃	C₂²	semidirect
122. #117×C₄₃	C₂²	semidirect
367. #542	D₄₃	semidirect
377. C₄₃	#3558	semidirect
387. C₄⋊Q₈	C₂×D₄₃	semidirect
394. #126	C₂×D₄₃	semidirect
410. #124	C₂×D₄₃	semidirect
411. #124	C₂×D₄₃	semidirect
421. #123	C₂×D₄₃	semidirect
427. C₂²⋊Q₈	C₂×D₄₃	semidirect
428. C₂²⋊Q₈	C₂×D₄₃	semidirect
457. C₄×Q₈	C₂×D₄₃	semidirect
469. C₄×D₄	C₂×D₄₃	semidirect
471. #117	C₂×D₄₃	semidirect