Subgroups — #19148790

Order 5504.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 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	#14583640	C₂	1	2	yes	maximal, complemented
3	#14583598	C₂	1	2	yes	maximal, complemented
4	#14583574	C₂	1	2	yes	maximal, complemented
5	#14583541	C₂	1	2	yes	maximal, complemented
6	#14583541	C₂	1	2	yes	maximal, complemented
7	#14583540	C₂	1	2	yes	maximal, complemented
8	D₄×D₁₇₂	C₂	1	2	yes	maximal, complemented
9	#14583505	C₂	1	2	yes	maximal, complemented
10	#14583497	C₂	1	2	yes	maximal, complemented
11	#14583489	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583485	C₂	1	2	yes	maximal, complemented
13	#14583480	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583460	C₂	1	2	yes	maximal, complemented
15	#14583457	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583412	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#13063310	C₂	1	1	yes	maximal, characteristic, complemented
18	#121×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10621902	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10621898	C₂²	1	2	yes	complemented
22	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
23	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
24	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
26	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
28	#13063322	C₂²	1	2	yes	complemented
29	#13063320	C₂²	1	2	yes	complemented
30	#13063319	C₂²	1	2	yes	complemented
31	#13063318	C₂²	1	2	yes	complemented
32	#13063315	C₂²	1	2	yes	complemented
33	#13063314	C₂²	1	2	yes	complemented
34	#13063311	C₂²	1	2	yes	complemented
35	#13063311	C₂²	1	2	yes	complemented
36	#13063310	C₂²	1	2	yes	complemented
37	#13063310	C₂²	1	2	yes	complemented
38	#13063310	C₂²	1	2	yes	complemented
39	#13063310	C₂²	1	2	yes	complemented
40	#13063310	C₂²	1	2	yes	complemented
41	#13063310	C₂²	1	2	yes	complemented
42	#13063310	C₂²	1	2	yes	complemented
43	#13063310	C₂²	1	2	yes	complemented
44	#13063310	C₂²	1	2	yes	complemented
45	#13063310	C₂²	1	2	yes	complemented
46	#13063308	C₂²	1	2	yes	complemented
47	#13063307	C₂²	1	2	yes	complemented
48	#13063305	C₂²	1	2	yes	complemented
49	#13063305	C₂²	1	2	yes	complemented
50	#13063303	C₂²	1	2	yes	complemented
51	#13063303	C₂²	1	2	yes	complemented
52	#13063301	C₂²	1	1	yes	characteristic, complemented
53	#13063300	C₂²	1	2	yes	—
54	#13063300	C₂²	1	1	yes	characteristic, complemented
55	#13063300	C₂²	1	2	yes	complemented
56	#13063300	C₂²	1	2	yes	complemented
57	#13063300	C₂²	1	1	yes	characteristic, complemented
58	#13063300	C₂²	1	2	yes	complemented
59	#13063300	C₂²	1	2	yes	complemented
60	#13063300	C₂²	1	2	yes	complemented
61	#13063300	C₂²	1	2	yes	complemented
62	#13063299	C₂²	1	2	yes	complemented
63	#13063299	C₂²	1	1	yes	characteristic, complemented
64	#13063299	C₂²	1	2	yes	complemented
65	#13063299	C₂²	1	1	yes	characteristic, complemented
66	#13063298	C₂²	1	2	yes	complemented
67	#13063298	C₂²	1	2	yes	complemented
68	#13063298	C₂²	1	2	yes	complemented
69	#13063298	C₂²	1	2	yes	complemented
70	#13063297	C₂²	1	2	yes	complemented
71	#13063297	C₂²	1	2	yes	complemented
72	#13063296	C₂²	1	1	yes	characteristic, complemented
73	#13063295	C₂²	1	2	yes	—
74	#13063295	C₂²	1	2	yes	complemented
75	#13063295	C₂²	1	2	yes	complemented
76	#13063295	C₂²	1	2	yes	complemented
77	#13063295	C₂²	1	2	yes	complemented
78	#13063295	C₂²	1	2	yes	complemented
79	#13063295	C₂²	1	2	yes	complemented
80	#13063293	C₂²	1	2	yes	complemented
81	C₄×D₁₇₂	C₂²	1	2	yes	complemented
82	#13063287	C₂²	1	2	yes	complemented
83	#13063287	C₂²	1	2	yes	complemented
84	#13063287	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
86	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
87	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
88	#13063283	C₂²	1	1	yes	characteristic, complemented
89	#13063282	C₂²	1	2	yes	complemented
90	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
91	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
93	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
98	#126×C₄₃	C₂²	1	2	yes	complemented
99	#125×C₄₃	C₂²	1	2	yes	complemented
100	#123×C₄₃	C₂²	1	2	yes	complemented
101	#123×C₄₃	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
104	#121×C₄₃	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₄₃	C₂³	1	1	yes	characteristic
108	C₂³×D₄₃	C₂³	1	2	yes	—
109	C₂³×D₄₃	C₂³	1	1	yes	characteristic
110	C₂³×D₄₃	C₂³	1	2	yes	—
111	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₄₃	C₂³	1	2	yes	—
113	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	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	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
124	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
125	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
126	#10621902	—	4	2	no	—
127	D₄×D₄₃	—	4	2	no	—
128	D₄×D₄₃	—	4	4	no	—
129	D₄×D₄₃	—	4	4	no	—
130	#10621898	—	4	4	no	—
131	C₂×D₁₇₂	—	4	2	no	—
132	C₂×D₁₇₂	—	4	4	no	—
133	C₂×D₁₇₂	C₂³	1	2	yes	—
134	C₂×D₁₇₂	C₂³	1	2	yes	—
135	C₂×D₁₇₂	C₂³	1	2	yes	—
136	C₂×D₁₇₂	C₂³	1	2	yes	—
137	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
138	C₂×D₁₇₂	C₂³	1	2	yes	—
139	C₂×D₁₇₂	C₂³	1	2	yes	—
140	C₂×D₁₇₂	C₂³	1	2	yes	—
141	C₂×D₁₇₂	C₂³	1	2	yes	—
142	C₂×D₁₇₂	C₂³	1	2	yes	—
143	C₂×D₁₇₂	C₂³	1	2	yes	—
144	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₄₃	—	4	2	no	—
146	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₄₃	C₂³	1	2	yes	—
149	C₂×C₄×D₄₃	C₂³	1	2	yes	—
150	C₂×C₄×D₄₃	C₂³	1	2	yes	—
151	C₂×C₄×D₄₃	C₂³	1	2	yes	—
152	C₂×C₄×D₄₃	C₂³	1	2	yes	—
153	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₄₃	C₂³	1	2	yes	—
155	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
156	C₂×Dic₈₆	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	1	yes	characteristic
161	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
162	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
163	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
170	C₄²×C₄₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₄₃	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	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
187	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₄₃)⋊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	2	yes	—
194	Dic₄₃⋊C₄	C₂³	1	2	yes	—
195	Dic₄₃⋊C₄	C₂³	1	2	yes	—
196	Dic₄₃⋊C₄	C₂³	1	2	yes	—
197	Dic₄₃⋊C₄	C₂³	1	2	yes	—
198	Dic₄₃⋊C₄	C₂³	1	2	yes	—
199	Dic₄₃⋊C₄	C₂³	1	2	yes	—
200	C₄×Dic₄₃	C₂³	1	2	yes	—
201	C₄×Dic₄₃	C₂³	1	2	yes	—
202	C₂³×C₄₃	C₂⁴	1	2	yes	—
203	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
204	C₂²×D₄₃	—	2	2	no	—
205	C₂²×D₄₃	—	2	2	no	—
206	C₂²×D₄₃	—	2	2	no	—
207	C₂²×D₄₃	—	2	4	no	—
208	C₂²×D₄₃	—	4	1	no	—
209	C₂²×D₄₃	—	4	1	no	—
210	C₂²×D₄₃	—	4	2	no	—
211	C₂²×D₄₃	—	4	2	no	—
212	C₂²×D₄₃	—	4	2	no	—
213	C₂²×D₄₃	—	4	2	no	—
214	C₂²×D₄₃	—	4	1	no	—
215	C₂²×D₄₃	—	4	2	no	—
216	C₂²×D₄₃	C₂⁴	1	2	yes	—
217	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
218	C₂²×D₄₃	C₂⁴	1	2	yes	—
219	C₂²×D₄₃	C₂⁴	1	2	yes	—
220	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
221	Q₈×C₄₃	—	4	1	no	—
222	D₄×C₄₃	—	2	4	no	—
223	D₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
229	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
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	C₂²⋊D₄₃	—	2	4	no	—
236	C₂²⋊D₄₃	—	2	4	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	C₂×Dic₄₃	—	4	1	no	—
242	C₂×Dic₄₃	—	4	1	no	—
243	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₄₃	C₂⁴	1	2	yes	—
245	C₂×Dic₄₃	C₂⁴	1	2	yes	—
246	C₂×Dic₄₃	C₂⁴	1	2	yes	—
247	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
248	D₁₇₂	—	2	4	no	—
249	D₁₇₂	—	2	4	no	—
250	D₁₇₂	—	4	2	no	—
251	D₁₇₂	—	4	2	no	—
252	D₁₇₂	—	4	2	no	—
253	D₁₇₂	—	4	2	no	—
254	D₁₇₂	—	4	2	no	—
255	D₁₇₂	—	4	2	no	—
256	D₁₇₂	—	4	1	no	—
257	D₁₇₂	—	4	2	no	—
258	D₁₇₂	—	4	2	no	—
259	D₁₇₂	—	4	1	no	—
260	C₄×D₄₃	—	2	2	no	—
261	C₄×D₄₃	—	2	2	no	—
262	C₄×D₄₃	—	4	1	no	—
263	C₄×D₄₃	—	4	1	no	—
264	C₄×D₄₃	—	4	2	no	—
265	C₄×D₄₃	—	4	2	no	—
266	C₄×D₄₃	—	4	2	no	—
267	C₄×D₄₃	—	4	2	no	—
268	C₄×D₄₃	—	4	2	no	—
269	C₄×D₄₃	—	4	2	no	—
270	Dic₈₆	—	4	2	no	—
271	C₂²×C₄₃	—	2	1	no	—
272	C₂²×C₄₃	—	2	1	no	—
273	C₂²×C₄₃	—	2	2	no	—
274	C₂²×C₄₃	—	2	2	no	—
275	C₂²×C₄₃	—	2	2	no	—
276	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
277	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
278	C₂×D₄₃	—	2	1	no	—
279	C₂×D₄₃	—	2	1	no	—
280	C₂×D₄₃	—	2	2	no	—
281	C₂×D₄₃	—	2	1	no	—
282	C₂×D₄₃	—	2	2	no	—
283	C₂×D₄₃	—	2	1	no	—
284	C₂×D₄₃	—	2	2	no	—
285	C₂×D₄₃	—	2	2	no	—
286	C₂×D₄₃	—	2	2	no	—
287	C₂×D₄₃	—	2	2	no	—
288	C₂×D₄₃	—	2	2	no	—
289	C₂×D₄₃	—	2	2	no	—
290	C₂×D₄₃	—	2	1	no	—
291	C₂×D₄₃	—	2	2	no	—
292	C₂×D₄₃	—	4	4	no	—
293	C₂×D₄₃	—	8	4	no	—
294	C₂×D₄₃	—	8	2	no	—
295	C₂×D₄₃	—	8	4	no	—
296	C₂×D₄₃	H(5,𝔽₂)	1	2	yes	—
297	C₄×C₄₃	—	2	2	no	—
298	C₄×C₄₃	—	2	1	no	—
299	C₄×C₄₃	—	2	1	no	—
300	C₄×C₄₃	—	2	2	no	—
301	C₄×C₄₃	—	2	2	no	—
302	C₄×C₄₃	—	2	2	no	—
303	C₄×C₄₃	—	2	2	no	—
304	Dic₄₃	—	2	2	no	—
305	Dic₄₃	—	2	2	no	—
306	Dic₄₃	—	2	1	no	—
307	Dic₄₃	—	2	1	no	—
308	Dic₄₃	—	2	2	no	—
309	#3534	—	43	1	no	maximal, Sylow
310	C₂×C₄₃	—	2	2	no	—
311	C₂×C₄₃	—	4	2	no	—
312	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₄₃	#585	1	1	yes	characteristic
315	D₄₃	—	2	2	no	—
316	D₄₃	—	4	1	no	—
317	D₄₃	—	4	2	no	—
318	D₄₃	—	4	2	no	—
319	D₄₃	—	4	2	no	—
320	#562	—	43	2	no	—
321	#560	—	43	2	no	—
322	#553	—	43	2	no	—
323	#551	—	43	2	no	—
324	#546	—	43	2	no	—
325	#546	—	43	2	no	—
326	#546	—	43	2	no	—
327	D₄²	—	43	2	no	—
328	#540	—	43	2	no	—
329	#539	—	43	2	no	—
330	#539	D₄₃	1	1	yes	characteristic, complemented
331	#538	—	43	2	no	—
332	#538	—	43	1	no	—
333	#537	—	43	1	no	—
334	#534	—	43	2	no	—
335	#534	—	43	1	no	—
336	#525	—	43	1	no	—
337	C₂×#123	—	43	1	no	—
338	C₂×#121	—	43	1	no	—
339	C₄₃	#3534	1	1	yes	characteristic, complemented, Sylow
340	C₂×#41	—	43	1	no	—
341	C₂×#41	—	43	2	no	—
342	C₂²×D₄	—	43	1	no	—
343	C₂²×D₄	—	43	2	no	—
344	C₂²×D₄	—	43	2	no	—
345	C₂²×D₄	—	43	1	no	—
346	C₂²×D₄	—	43	2	no	—
347	C₂³×C₄	—	43	1	no	—
348	#127	—	43	2	no	—
349	#126	—	43	2	no	—
350	#126	—	43	2	no	—
351	#126	—	43	2	no	—
352	#126	C₂×D₄₃	1	2	yes	complemented
353	#125	—	43	2	no	—
354	#125	C₂×D₄₃	1	2	yes	complemented
355	#124	—	43	2	no	—
356	#124	—	43	2	no	—
357	#124	—	43	2	no	—
358	#123	—	43	2	no	—
359	#123	—	43	2	no	—
360	#123	—	43	2	no	—
361	#123	—	43	2	no	—
362	#123	—	43	2	no	—
363	#123	—	43	2	no	—
364	#123	—	43	2	no	—
365	#123	—	43	2	no	—
366	#123	—	43	2	no	—
367	#123	—	43	2	no	—
368	#123	—	43	2	no	—
369	#123	—	43	2	no	—
370	#123	C₂×D₄₃	1	2	yes	complemented
371	#123	C₂×D₄₃	1	2	yes	complemented
372	C₂²⋊Q₈	—	43	1	no	—
373	C₂²⋊Q₈	—	43	2	no	—
374	C₂²⋊Q₈	—	43	2	no	—
375	C₂²⋊Q₈	—	43	2	no	—
376	C₂²⋊Q₈	—	43	2	no	—
377	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
378	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
379	#121	—	43	1	no	—
380	#121	—	43	2	no	—
381	#121	—	43	2	no	—
382	#121	—	43	1	no	—
383	#121	—	43	1	no	—
384	#121	—	43	2	no	—
385	#121	—	43	2	no	—
386	#121	—	43	1	no	—
387	#121	—	43	1	no	—
388	#121	—	43	2	no	—
389	#121	—	43	2	no	—
390	#121	—	43	2	no	—
391	#121	—	43	2	no	—
392	#121	—	43	2	no	—
393	#121	—	43	2	no	—
394	#121	—	43	2	no	—
395	#121	—	43	2	no	—
396	#121	—	43	2	no	—
397	#121	—	43	2	no	—
398	#121	—	43	2	no	—
399	#121	C₂×D₄₃	1	1	yes	characteristic
400	#120	—	43	2	no	—
401	#120	—	43	2	no	—
402	#120	—	43	2	no	—
403	#120	—	43	2	no	—
404	#120	—	43	2	no	—
405	#120	—	43	2	no	—
406	#120	—	43	2	no	—
407	#120	—	43	2	no	—
408	C₄×D₄	—	43	2	no	—
409	C₄×D₄	—	43	2	no	—
410	C₄×D₄	—	43	2	no	—
411	C₄×D₄	—	43	2	no	—
412	C₄×D₄	—	43	2	no	—
413	C₄×D₄	—	43	2	no	—
414	C₄×D₄	—	43	2	no	—
415	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
416	#117	—	43	1	no	—
417	#117	—	43	2	no	—
418	C₂×C₄⋊C₄	—	43	1	no	—
419	C₂×C₄⋊C₄	—	43	1	no	—
420	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	—	43	1	no	—
422	C₂×C₂²⋊C₄	—	43	1	no	—
423	C₂×C₂²⋊C₄	—	43	1	no	—
424	C₂×C₂²⋊C₄	—	43	2	no	—
425	C₂×C₂²⋊C₄	—	43	2	no	—
426	C₂×C₂²⋊C₄	—	43	2	no	—
427	C₂⁴	—	43	1	no	—
428	C₂⁴	—	43	2	no	—
429	C₂⁴	—	43	1	no	—
430	C₂⁴	—	43	2	no	—
431	#41	—	172	4	no	—
432	#41	—	172	2	no	—
433	C₂×Q₈	—	43	2	no	—
434	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
435	C₂×D₄	—	43	2	no	—
436	C₂×D₄	—	43	2	no	—
437	C₂×D₄	—	43	2	no	—
438	C₂×D₄	—	43	2	no	—
439	C₂×D₄	—	43	2	no	—
440	C₂×D₄	—	43	2	no	—
441	C₂×D₄	—	43	2	no	—
442	C₂×D₄	—	43	2	no	—
443	C₂×D₄	—	43	2	no	—
444	C₂×D₄	—	43	2	no	—
445	C₂×D₄	—	43	1	no	—
446	C₂×D₄	—	43	2	no	—
447	C₂×D₄	—	43	2	no	—
448	C₂×D₄	—	43	2	no	—
449	C₂×D₄	—	43	2	no	—
450	C₂×D₄	—	43	1	no	—
451	C₂×D₄	—	43	2	no	—
452	C₂×D₄	—	43	2	no	—
453	C₂×D₄	—	172	2	no	—
454	C₂×D₄	—	172	4	no	—
455	C₂×D₄	—	172	2	no	—
456	C₂×D₄	—	172	4	no	—
457	C₂×D₄	—	172	4	no	—
458	C₂×D₄	C₂²×D₄₃	1	2	yes	—
459	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
460	C₂²×C₄	—	43	1	no	—
461	C₂²×C₄	—	43	1	no	—
462	C₂²×C₄	—	43	1	no	—
463	C₂²×C₄	—	43	1	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	1	no	—
470	C₂²×C₄	—	43	2	no	—
471	C₂²×C₄	—	43	1	no	—
472	C₂²×C₄	—	172	2	no	—
473	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
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	1	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	C₂²×D₄₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
489	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
491	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
494	C₂²⋊C₄	—	43	2	no	—
495	C₂²⋊C₄	—	43	2	no	—
496	C₂²⋊C₄	—	43	2	no	—
497	C₂²⋊C₄	—	43	2	no	—
498	C₂²⋊C₄	—	43	2	no	—
499	C₂²⋊C₄	—	43	2	no	—
500	C₂²⋊C₄	—	43	2	no	—
501	C₂²⋊C₄	—	43	2	no	—
502	C₂²⋊C₄	—	43	2	no	—
503	C₂²⋊C₄	—	43	2	no	—
504	C₂²⋊C₄	—	43	2	no	—
505	C₂²⋊C₄	—	43	2	no	—
506	C₂²⋊C₄	—	43	2	no	—
507	C₂²⋊C₄	—	43	2	no	—
508	C₂²⋊C₄	—	43	2	no	—
509	C₂²⋊C₄	—	43	2	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	C₂²×D₄₃	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
519	C₄²	—	43	2	no	—
520	C₄²	—	43	2	no	—
521	C₄²	C₂²×D₄₃	1	2	yes	—
522	C₂³	—	43	1	no	—
523	C₂³	—	43	2	no	—
524	C₂³	—	43	1	no	—
525	C₂³	—	43	2	no	—
526	C₂³	—	43	2	no	—
527	C₂³	—	86	4	no	—
528	C₂³	—	86	2	no	—
529	C₂³	—	86	2	no	—
530	C₂³	—	86	2	no	—
531	C₂³	—	172	1	no	—
532	C₂³	—	172	2	no	—
533	C₂³	—	172	2	no	—
534	C₂³	—	172	2	no	—
535	C₂³	—	172	1	no	—
536	C₂³	—	172	2	no	—
537	C₂³	—	172	2	no	—
538	C₂³	—	172	1	no	—
539	C₂³	C₂³×D₄₃	1	2	yes	—
540	C₂³	C₂³×D₄₃	1	1	yes	characteristic
541	Q₈	—	4	1	no	—
542	Q₈	—	172	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	4	1	no	—
545	D₄	—	86	4	no	—
546	D₄	—	86	4	no	—
547	D₄	—	86	4	no	—
548	D₄	—	86	4	no	—
549	D₄	—	172	2	no	—
550	D₄	—	172	2	no	—
551	D₄	—	172	1	no	—
552	D₄	—	172	2	no	—
553	D₄	—	172	2	no	—
554	D₄	—	172	2	no	—
555	D₄	—	172	1	no	—
556	D₄	—	172	2	no	—
557	D₄	—	172	2	no	—
558	D₄	—	172	2	no	—
559	D₄	—	172	2	no	—
560	D₄	—	172	2	no	—
561	D₄	—	172	2	no	—
562	D₄	—	172	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	43	1	no	—
568	C₂×C₄	—	43	2	no	—
569	C₂×C₄	—	43	2	no	—
570	C₂×C₄	—	43	2	no	—
571	C₂×C₄	—	43	1	no	—
572	C₂×C₄	—	86	2	no	—
573	C₂×C₄	—	86	2	no	—
574	C₂×C₄	—	172	1	no	—
575	C₂×C₄	—	172	1	no	—
576	C₂×C₄	—	172	2	no	—
577	C₂×C₄	—	172	2	no	—
578	C₂×C₄	—	172	2	no	—
579	C₂×C₄	—	172	2	no	—
580	C₂×C₄	—	172	2	no	—
581	C₂×C₄	—	172	2	no	—
582	C₂×C₄	—	172	1	no	—
583	C₂×C₄	—	172	1	no	—
584	C₂×C₄	C₂³×D₄₃	1	2	yes	—
585	C₂×C₄	C₂³×D₄₃	1	2	yes	—
586	C₂×C₄	C₂³×D₄₃	1	2	yes	—
587	C₂×C₄	C₂³×D₄₃	1	2	yes	—
588	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₄₃	1	2	yes	—
590	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	43	2	no	—
597	C₂²	—	86	1	no	—
598	C₂²	—	86	1	no	—
599	C₂²	—	86	1	no	—
600	C₂²	—	86	2	no	—
601	C₂²	—	86	2	no	—
602	C₂²	—	86	2	no	—
603	C₂²	—	86	2	no	—
604	C₂²	—	86	2	no	—
605	C₂²	—	86	2	no	—
606	C₂²	—	86	1	no	—
607	C₂²	—	86	2	no	—
608	C₂²	—	86	2	no	—
609	C₂²	—	86	1	no	—
610	C₂²	—	86	2	no	—
611	C₂²	—	344	2	no	—
612	C₂²	—	344	4	no	—
613	C₂²	—	344	4	no	—
614	C₂²	—	172	4	no	—
615	C₂²	#13063371	1	2	yes	—
616	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	86	1	no	—
625	C₄	—	86	1	no	—
626	C₄	—	86	2	no	—
627	C₄	—	86	2	no	—
628	C₄	—	86	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	4	2	no	—
631	C₂	—	86	2	no	—
632	C₂	—	172	2	no	—
633	C₂	—	172	2	no	—
634	C₂	—	172	2	no	—
635	C₂	—	172	1	no	—
636	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
637	C₂	C₂×#13063371	1	1	yes	characteristic
638	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#539	C₂
hypercenter	#539	D₄₃
hypocenter	C₄₃	#3534
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #14583645	C₂	semidirect
2. #14583640	C₂	semidirect
3. #14583598	C₂	semidirect
4. #14583574	C₂	semidirect
5. #14583541	C₂	semidirect
6. #14583541	C₂	semidirect
7. #14583540	C₂	semidirect
8. D₄×D₁₇₂	C₂	semidirect
9. #14583505	C₂	semidirect
10. #14583497	C₂	semidirect
11. #14583489	C₂	semidirect
12. #14583485	C₂	semidirect
13. #14583480	C₂	semidirect
14. #14583460	C₂	semidirect
15. #14583457	C₂	semidirect
16. #14583412	C₂	semidirect
17. C₂×#13063310	C₂	semidirect
18. #121×D₄₃	C₂	semidirect
19. C₄₃×#539	C₂	semidirect
20. C₂×#10621902	C₂²	semidirect
21. C₂×#10621898	C₂²	semidirect
23. C₂²×D₁₇₂	C₂²	semidirect
24. C₂×D₄×D₄₃	C₂²	semidirect
25. C₂×D₄×D₄₃	C₂²	semidirect
26. C₂×D₄×D₄₃	C₂²	semidirect
27. C₂²×C₄×D₄₃	C₂²	semidirect
28. #13063322	C₂²	semidirect
29. #13063320	C₂²	semidirect
30. #13063319	C₂²	semidirect
31. #13063318	C₂²	semidirect
32. #13063315	C₂²	semidirect
33. #13063314	C₂²	semidirect
34. #13063311	C₂²	semidirect
35. #13063311	C₂²	semidirect
36. #13063310	C₂²	semidirect
37. #13063310	C₂²	semidirect
38. #13063310	C₂²	semidirect
39. #13063310	C₂²	semidirect
40. #13063310	C₂²	semidirect
41. #13063310	C₂²	semidirect
42. #13063310	C₂²	semidirect
43. #13063310	C₂²	semidirect
44. #13063310	C₂²	semidirect
45. #13063310	C₂²	semidirect
46. #13063308	C₂²	semidirect
47. #13063307	C₂²	semidirect
48. #13063305	C₂²	semidirect
49. #13063305	C₂²	semidirect
50. #13063303	C₂²	semidirect
51. #13063303	C₂²	semidirect
52. #13063301	C₂²	semidirect
54. #13063300	C₂²	semidirect
55. #13063300	C₂²	semidirect
56. #13063300	C₂²	semidirect
57. #13063300	C₂²	semidirect
58. #13063300	C₂²	semidirect
59. #13063300	C₂²	semidirect
60. #13063300	C₂²	semidirect
61. #13063300	C₂²	semidirect
62. #13063299	C₂²	semidirect
63. #13063299	C₂²	semidirect
64. #13063299	C₂²	semidirect
65. #13063299	C₂²	semidirect
66. #13063298	C₂²	semidirect
67. #13063298	C₂²	semidirect
68. #13063298	C₂²	semidirect
69. #13063298	C₂²	semidirect
70. #13063297	C₂²	semidirect
71. #13063297	C₂²	semidirect
72. #13063296	C₂²	semidirect
74. #13063295	C₂²	semidirect
75. #13063295	C₂²	semidirect
76. #13063295	C₂²	semidirect
77. #13063295	C₂²	semidirect
78. #13063295	C₂²	semidirect
79. #13063295	C₂²	semidirect
80. #13063293	C₂²	semidirect
81. C₄×D₁₇₂	C₂²	semidirect
82. #13063287	C₂²	semidirect
83. #13063287	C₂²	semidirect
84. #13063287	C₂²	semidirect
85. C₄×C₂²⋊D₄₃	C₂²	semidirect
86. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
87. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
88. #13063283	C₂²	semidirect
89. #13063282	C₂²	semidirect
90. C₂×Dic₄₃⋊C₄	C₂²	semidirect
91. C₄⋊C₄×D₄₃	C₂²	semidirect
92. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
93. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
94. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
95. C₂²⋊C₄×D₄₃	C₂²	semidirect
96. C₂²⋊C₄×D₄₃	C₂²	semidirect
97. C₂²⋊C₄×D₄₃	C₂²	semidirect
98. #126×C₄₃	C₂²	semidirect
99. #125×C₄₃	C₂²	semidirect
100. #123×C₄₃	C₂²	semidirect
101. #123×C₄₃	C₂²	semidirect
102. C₂²⋊Q₈×C₄₃	C₂²	semidirect
103. C₂²⋊Q₈×C₄₃	C₂²	semidirect
105. C₄×D₄×C₄₃	C₂²	semidirect
106. C₂×C₄⋊C₄×C₄₃	C₂²	semidirect
330. #539	D₄₃	semidirect
339. C₄₃	#3534	semidirect
352. #126	C₂×D₄₃	semidirect
354. #125	C₂×D₄₃	semidirect
370. #123	C₂×D₄₃	semidirect
371. #123	C₂×D₄₃	semidirect
377. C₂²⋊Q₈	C₂×D₄₃	semidirect
378. C₂²⋊Q₈	C₂×D₄₃	semidirect
415. C₄×D₄	C₂×D₄₃	semidirect
420. C₂×C₄⋊C₄	C₂×D₄₃	semidirect