Subgroups — #19148006

Order 5504.

1160 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583524	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583492	C₂	1	2	yes	maximal, complemented
3	#14583491	C₂	1	2	yes	maximal, complemented
4	#14583490	C₂	1	2	yes	maximal, complemented
5	#14583487	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583483	C₂	1	2	yes	maximal, complemented
7	#14583481	C₂	1	2	yes	maximal, complemented
8	#14583459	C₂	1	2	yes	maximal, complemented
9	#14583457	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583435	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583432	C₂	1	2	yes	maximal, complemented
12	#14583430	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583428	C₂	1	2	yes	maximal, complemented
14	#14583409	C₂	1	2	yes	maximal, complemented
15	#14583407	C₂	1	2	yes	maximal, complemented
16	#14583405	C₂	1	2	yes	maximal, complemented
17	C₂×(C₂²⋊D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₄₃	C₂	1	2	yes	maximal, complemented
19	C₄₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10621900	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₄₃	C₂²	1	2	yes	—
23	C₂³×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₄₃	C₂²	1	2	yes	complemented
26	#13063320	C₂²	1	2	yes	complemented
27	#13063319	C₂²	1	2	yes	complemented
28	#13063318	C₂²	1	2	yes	complemented
29	#13063318	C₂²	1	2	yes	complemented
30	#13063318	C₂²	1	2	yes	complemented
31	#13063317	C₂²	1	2	yes	complemented
32	#13063316	C₂²	1	1	yes	characteristic, complemented
33	#13063316	C₂²	1	1	yes	characteristic, complemented
34	#13063315	C₂²	1	2	yes	complemented
35	#13063314	C₂²	1	1	yes	characteristic, complemented
36	#13063312	C₂²	1	1	yes	characteristic, complemented
37	#13063311	C₂²	1	2	yes	complemented
38	#13063310	C₂²	1	2	yes	complemented
39	#13063309	C₂²	1	2	yes	complemented
40	#13063309	C₂²	1	2	yes	complemented
41	#13063308	C₂²	1	2	yes	complemented
42	#13063307	C₂²	1	2	yes	complemented
43	#13063307	C₂²	1	2	yes	complemented
44	#13063307	C₂²	1	2	yes	complemented
45	#13063307	C₂²	1	2	yes	complemented
46	#13063307	C₂²	1	2	yes	complemented
47	#13063306	C₂²	1	2	yes	complemented
48	#13063306	C₂²	1	2	yes	complemented
49	#13063305	C₂²	1	2	yes	complemented
50	#13063304	C₂²	1	2	yes	complemented
51	#13063304	C₂²	1	1	yes	characteristic, complemented
52	#13063303	C₂²	1	2	yes	complemented
53	#13063303	C₂²	1	2	yes	complemented
54	#13063303	C₂²	1	2	yes	complemented
55	#13063302	C₂²	1	2	yes	complemented
56	#13063302	C₂²	1	2	yes	complemented
57	#13063301	C₂²	1	2	yes	complemented
58	#13063299	C₂²	1	1	yes	characteristic
59	#13063298	C₂²	1	2	yes	—
60	#13063298	C₂²	1	2	yes	—
61	#13063298	C₂²	1	2	yes	complemented
62	#13063297	C₂²	1	2	yes	—
63	#13063297	C₂²	1	2	yes	complemented
64	#13063296	C₂²	1	2	yes	—
65	#13063296	C₂²	1	2	yes	—
66	#13063295	C₂²	1	2	yes	complemented
67	#13063294	C₂²	1	2	yes	complemented
68	#13063293	C₂²	1	2	yes	complemented
69	#13063293	C₂²	1	2	yes	complemented
70	#13063293	C₂²	1	2	yes	complemented
71	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
72	#13063290	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₁₇₂	C₂²	1	2	yes	complemented
74	D₄×Dic₄₃	C₂²	1	2	yes	complemented
75	D₄×Dic₄₃	C₂²	1	2	yes	complemented
76	D₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
77	#13063287	C₂²	1	2	yes	complemented
78	#13063287	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
81	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
82	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
83	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
84	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
85	(C₂²⋊D₄₃)⋊C₄	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	2	yes	complemented
89	#13063281	C₂²	1	2	yes	complemented
90	#13063281	C₂²	1	2	yes	complemented
91	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
97	C₄²×D₄₃	C₂²	1	2	yes	complemented
98	#126×C₄₃	C₂²	1	2	yes	complemented
99	#124×C₄₃	C₂²	1	2	yes	complemented
100	#123×C₄₃	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
102	#121×C₄₃	C₂²	1	1	yes	characteristic
103	#121×C₄₃	C₂²	1	2	yes	complemented
104	#120×C₄₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
108	C₂³×D₄₃	C₂³	1	2	yes	—
109	C₂³×D₄₃	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	2	yes	—
114	C₂×D₄×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	—	2	4	no	—
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	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
126	C₂²×Dic₄₃	—	4	2	no	—
127	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
128	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
129	C₂²×Dic₄₃	C₂³	1	2	yes	—
130	C₂²×Dic₄₃	C₂³	1	2	yes	—
131	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₄₃	C₂³	1	2	yes	—
133	#10621900	—	4	4	no	—
134	D₄×D₄₃	—	2	8	no	—
135	C₂×D₁₇₂	C₂³	1	2	yes	—
136	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₄₃	—	4	2	no	—
138	C₂×C₄×D₄₃	—	4	4	no	—
139	C₂×C₄×D₄₃	C₂³	1	2	yes	—
140	C₂×C₄×D₄₃	C₂³	1	2	yes	—
141	C₂×C₄×D₄₃	C₂³	1	2	yes	—
142	C₂×C₄×D₄₃	C₂³	1	2	yes	—
143	C₂×C₄×D₄₃	C₂³	1	2	yes	—
144	C₂×C₄×D₄₃	C₂³	1	2	yes	—
145	C₂×C₄×D₄₃	C₂³	1	2	yes	—
146	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
147	C₂×Dic₈₆	C₂³	1	2	yes	—
148	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
149	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
151	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
159	C₄²×C₄₃	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	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	(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	C₄⋊Dic₄₃	C₂³	1	2	yes	—
178	C₄⋊Dic₄₃	C₂³	1	2	yes	—
179	C₄⋊Dic₄₃	C₂³	1	2	yes	—
180	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₄₃	C₂³	1	2	yes	—
182	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
183	Dic₄₃⋊C₄	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	Dic₄₃⋊C₄	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	1	yes	characteristic
198	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄₃	—	2	2	no	—
201	C₂³×C₄₃	—	4	1	no	—
202	C₂³×C₄₃	—	4	1	no	—
203	C₂³×C₄₃	C₂⁴	1	2	yes	—
204	C₂³×C₄₃	C₂⁴	1	2	yes	—
205	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
206	C₂²×D₄₃	—	2	4	no	—
207	C₂²×D₄₃	—	4	1	no	—
208	C₂²×D₄₃	—	4	2	no	—
209	C₂²×D₄₃	—	4	1	no	—
210	C₂²×D₄₃	—	4	2	no	—
211	C₂²×D₄₃	#41	1	4	yes	complemented
212	C₂²×D₄₃	C₂⁴	1	2	yes	—
213	C₂²×D₄₃	C₂⁴	1	2	yes	—
214	Q₈×C₄₃	—	4	1	no	—
215	D₄×C₄₃	—	2	4	no	—
216	D₄×C₄₃	—	4	2	no	—
217	D₄×C₄₃	—	4	1	no	—
218	D₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	4	1	no	—
222	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
225	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
226	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
227	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
228	C₂²⋊D₄₃	—	2	4	no	—
229	C₂²⋊D₄₃	—	2	4	no	—
230	C₂²⋊D₄₃	—	2	4	no	—
231	C₂²⋊D₄₃	—	2	4	no	—
232	C₂²⋊D₄₃	—	4	2	no	—
233	C₂²⋊D₄₃	—	4	2	no	—
234	C₂²⋊D₄₃	—	4	2	no	—
235	C₂×Dic₄₃	—	2	2	no	—
236	C₂×Dic₄₃	—	2	4	no	—
237	C₂×Dic₄₃	—	2	2	no	—
238	C₂×Dic₄₃	—	2	4	no	—
239	C₂×Dic₄₃	—	4	1	no	—
240	C₂×Dic₄₃	—	4	2	no	—
241	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₄₃	C₂⁴	1	2	yes	—
244	C₂×Dic₄₃	C₂⁴	1	2	yes	—
245	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₄₃	C₂⁴	1	2	yes	—
247	C₂×Dic₄₃	C₂⁴	1	2	yes	—
248	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
249	D₁₇₂	—	2	4	no	—
250	D₁₇₂	—	4	1	no	—
251	C₄×D₄₃	—	2	4	no	—
252	C₄×D₄₃	—	2	4	no	—
253	C₄×D₄₃	—	2	4	no	—
254	C₄×D₄₃	—	4	2	no	—
255	C₄×D₄₃	—	4	2	no	—
256	C₄×D₄₃	—	4	2	no	—
257	C₄×D₄₃	—	4	2	no	—
258	Dic₈₆	—	4	1	no	—
259	Dic₈₆	—	4	2	no	—
260	C₂²×C₄₃	—	2	1	no	—
261	C₂²×C₄₃	—	2	1	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	—	2	2	no	—
267	C₂²×C₄₃	—	2	2	no	—
268	C₂²×C₄₃	—	4	4	no	—
269	C₂²×C₄₃	C₂×#41	1	2	yes	—
270	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
271	C₂×D₄₃	—	2	2	no	—
272	C₂×D₄₃	—	2	2	no	—
273	C₂×D₄₃	—	2	2	no	—
274	C₂×D₄₃	—	2	2	no	—
275	C₂×D₄₃	—	2	2	no	—
276	C₂×D₄₃	—	4	4	no	—
277	C₂×D₄₃	—	4	8	no	—
278	C₂×D₄₃	C₂×#41	1	4	yes	—
279	C₄×C₄₃	—	2	2	no	—
280	C₄×C₄₃	—	2	2	no	—
281	C₄×C₄₃	—	2	2	no	—
282	C₄×C₄₃	—	2	1	no	—
283	C₄×C₄₃	—	2	2	no	—
284	C₄×C₄₃	—	2	1	no	—
285	Dic₄₃	—	2	2	no	—
286	Dic₄₃	—	2	1	no	—
287	Dic₄₃	—	2	1	no	—
288	Dic₄₃	—	2	2	no	—
289	Dic₄₃	—	2	2	no	—
290	Dic₄₃	—	2	1	no	—
291	Dic₄₃	—	2	2	no	—
292	Dic₄₃	H(5,𝔽₂)	1	2	yes	—
293	#3459	—	43	1	no	maximal, Sylow
294	C₂×C₄₃	—	2	2	no	—
295	C₂×C₄₃	—	4	2	no	—
296	C₂×C₄₃	—	4	2	no	—
297	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
298	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄₃	#585	1	1	yes	characteristic
300	D₄₃	—	2	4	no	—
301	D₄₃	—	4	2	no	—
302	#543	—	43	1	no	—
303	#539	—	43	2	no	—
304	#539	—	43	2	no	—
305	#539	—	43	2	no	—
306	#538	—	43	2	no	—
307	#538	—	43	2	no	—
308	#538	—	43	1	no	—
309	#538	D₄₃	1	1	yes	characteristic, complemented
310	#534	—	43	1	no	—
311	#534	—	43	2	no	—
312	#529	—	43	2	no	—
313	#529	—	43	2	no	—
314	#529	—	43	1	no	—
315	#529	—	43	1	no	—
316	#525	—	43	2	no	—
317	#525	—	43	2	no	—
318	#525	—	43	2	no	—
319	C₂×C₄×D₄	—	43	2	no	—
320	C₂×C₄×D₄	—	43	1	no	—
321	C₄₃	#3459	1	1	yes	characteristic, complemented, Sylow
322	C₂×#41	—	43	2	no	—
323	C₂²×D₄	—	43	1	no	—
324	C₂²×D₄	—	43	2	no	—
325	C₂³×C₄	—	43	1	no	—
326	C₂³×C₄	—	43	1	no	—
327	C₂³×C₄	—	43	2	no	—
328	#126	—	43	2	no	—
329	#126	—	43	2	no	—
330	#126	—	43	2	no	—
331	#126	—	43	2	no	—
332	#126	—	43	2	no	—
333	#126	C₂×D₄₃	1	2	yes	complemented
334	#125	—	43	2	no	—
335	#125	—	43	1	no	—
336	#125	—	43	1	no	—
337	#125	—	43	2	no	—
338	#124	—	43	1	no	—
339	#124	—	43	1	no	—
340	#124	—	43	2	no	—
341	#124	C₂×D₄₃	1	2	yes	complemented
342	#123	—	43	2	no	—
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	C₂²⋊Q₈	—	43	2	no	—
355	C₂²⋊Q₈	—	43	2	no	—
356	C₂²⋊Q₈	—	43	1	no	—
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	C₂×D₄₃	1	1	yes	characteristic, complemented
364	#121	—	43	2	no	—
365	#121	—	43	2	no	—
366	#121	—	43	2	no	—
367	#121	—	43	2	no	—
368	#121	—	43	1	no	—
369	#121	—	43	2	no	—
370	#121	—	43	2	no	—
371	#121	—	43	2	no	—
372	#121	C₂×D₄₃	1	1	yes	characteristic
373	#121	C₂×D₄₃	1	2	yes	complemented
374	#120	—	43	2	no	—
375	#120	—	43	2	no	—
376	#120	—	43	2	no	—
377	#120	—	43	2	no	—
378	#120	—	43	2	no	—
379	#120	C₂×D₄₃	1	2	yes	complemented
380	C₄×Q₈	—	43	1	no	—
381	C₄×Q₈	—	43	1	no	—
382	C₄×D₄	—	43	2	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	2	no	—
388	C₄×D₄	—	43	1	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	C₄×D₄	—	43	2	no	—
396	C₄×D₄	—	43	2	no	—
397	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
398	#117	—	43	2	no	—
399	#117	—	43	2	no	—
400	#117	—	43	2	no	—
401	C₂×C₄⋊C₄	—	43	1	no	—
402	C₂×C₄⋊C₄	—	43	2	no	—
403	C₂×C₂²⋊C₄	—	43	1	no	—
404	C₂×C₂²⋊C₄	—	43	2	no	—
405	C₂×C₂²⋊C₄	—	43	2	no	—
406	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
407	C₂×C₄²	—	43	1	no	—
408	C₂×C₄²	—	43	2	no	—
409	C₂⁴	—	43	1	no	—
410	C₂⁴	—	43	2	no	—
411	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
412	#41	—	172	4	no	—
413	C₂×Q₈	—	43	1	no	—
414	C₂×Q₈	—	43	2	no	—
415	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
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	2	no	—
421	C₂×D₄	—	43	2	no	—
422	C₂×D₄	—	43	2	no	—
423	C₂×D₄	—	43	2	no	—
424	C₂×D₄	—	43	1	no	—
425	C₂×D₄	—	86	8	no	—
426	C₂×D₄	—	86	4	no	—
427	C₂×D₄	C₂²×D₄₃	1	2	yes	—
428	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₄₃	1	2	yes	—
430	C₂×D₄	C₂²×D₄₃	1	2	yes	—
431	C₂²×C₄	—	43	1	no	—
432	C₂²×C₄	—	43	1	no	—
433	C₂²×C₄	—	43	2	no	—
434	C₂²×C₄	—	43	2	no	—
435	C₂²×C₄	—	43	1	no	—
436	C₂²×C₄	—	43	2	no	—
437	C₂²×C₄	—	43	2	no	—
438	C₂²×C₄	—	43	2	no	—
439	C₂²×C₄	—	43	2	no	—
440	C₂²×C₄	—	43	2	no	—
441	C₂²×C₄	—	43	2	no	—
442	C₂²×C₄	—	43	2	no	—
443	C₂²×C₄	—	43	2	no	—
444	C₂²×C₄	—	172	2	no	—
445	C₂²×C₄	—	172	4	no	—
446	C₂²×C₄	—	172	2	no	—
447	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
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	—	43	2	no	—
456	C₄⋊C₄	—	43	2	no	—
457	C₄⋊C₄	—	43	2	no	—
458	C₄⋊C₄	—	43	2	no	—
459	C₄⋊C₄	—	43	2	no	—
460	C₄⋊C₄	—	43	2	no	—
461	C₄⋊C₄	—	43	1	no	—
462	C₄⋊C₄	—	43	2	no	—
463	C₄⋊C₄	—	43	2	no	—
464	C₄⋊C₄	—	43	1	no	—
465	C₄⋊C₄	—	43	2	no	—
466	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
467	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
468	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
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	—	43	2	no	—
481	C₂²⋊C₄	—	43	2	no	—
482	C₂²⋊C₄	—	43	2	no	—
483	C₂²⋊C₄	—	43	2	no	—
484	C₂²⋊C₄	—	43	2	no	—
485	C₂²⋊C₄	—	43	2	no	—
486	C₂²⋊C₄	—	43	2	no	—
487	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
494	C₄²	—	43	2	no	—
495	C₄²	—	43	1	no	—
496	C₄²	—	43	1	no	—
497	C₄²	—	43	2	no	—
498	C₄²	—	43	2	no	—
499	C₄²	—	43	1	no	—
500	C₄²	—	43	1	no	—
501	C₄²	C₂²×D₄₃	1	2	yes	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	43	2	no	—
506	C₂³	—	43	4	no	—
507	C₂³	—	43	2	no	—
508	C₂³	—	86	4	no	—
509	C₂³	—	172	1	no	—
510	C₂³	—	172	2	no	—
511	C₂³	—	172	1	no	—
512	C₂³	—	172	2	no	—
513	C₂³	C₂³×D₄₃	1	2	yes	—
514	C₂³	C₂³×D₄₃	1	2	yes	—
515	C₂³	C₂³×D₄₃	1	1	yes	characteristic
516	Q₈	—	4	1	no	—
517	Q₈	—	172	2	no	—
518	Q₈	—	172	1	no	—
519	D₄	—	2	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	2	no	—
523	D₄	—	86	4	no	—
524	D₄	—	86	4	no	—
525	D₄	—	86	4	no	—
526	D₄	—	86	4	no	—
527	D₄	—	86	4	no	—
528	D₄	—	172	1	no	—
529	D₄	—	172	2	no	—
530	D₄	—	172	2	no	—
531	D₄	—	172	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	43	1	no	—
536	C₂×C₄	—	43	2	no	—
537	C₂×C₄	—	43	1	no	—
538	C₂×C₄	—	43	2	no	—
539	C₂×C₄	—	43	1	no	—
540	C₂×C₄	—	43	1	no	—
541	C₂×C₄	—	43	2	no	—
542	C₂×C₄	—	43	2	no	—
543	C₂×C₄	—	86	4	no	—
544	C₂×C₄	—	86	4	no	—
545	C₂×C₄	—	86	4	no	—
546	C₂×C₄	—	86	2	no	—
547	C₂×C₄	—	86	4	no	—
548	C₂×C₄	—	86	4	no	—
549	C₂×C₄	—	86	2	no	—
550	C₂×C₄	—	172	2	no	—
551	C₂×C₄	—	172	2	no	—
552	C₂×C₄	—	172	2	no	—
553	C₂×C₄	—	172	2	no	—
554	C₂×C₄	—	172	2	no	—
555	C₂×C₄	—	172	1	no	—
556	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₄₃	1	2	yes	—
559	C₂×C₄	C₂³×D₄₃	1	2	yes	—
560	C₂×C₄	C₂³×D₄₃	1	2	yes	—
561	C₂×C₄	C₂³×D₄₃	1	2	yes	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	43	4	no	—
572	C₂²	—	86	2	no	—
573	C₂²	—	86	2	no	—
574	C₂²	—	86	2	no	—
575	C₂²	—	86	2	no	—
576	C₂²	—	86	2	no	—
577	C₂²	—	172	4	no	—
578	C₂²	—	172	8	no	—
579	C₂²	#41×D₄₃	1	2	yes	—
580	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	43	2	no	—
588	C₄	—	86	2	no	—
589	C₄	—	86	1	no	—
590	C₄	—	86	1	no	—
591	C₄	—	86	1	no	—
592	C₄	—	86	2	no	—
593	C₄	—	86	2	no	—
594	C₄	—	86	2	no	—
595	C₂	—	2	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	86	4	no	—
599	C₂	—	172	2	no	—
600	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
601	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
602	C₂	#14583734	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#538	C₂
hypercenter	#538	D₄₃
hypocenter	C₄₃	#3459
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #14583524	C₂	semidirect
2. #14583492	C₂	semidirect
3. #14583491	C₂	semidirect
4. #14583490	C₂	semidirect
5. #14583487	C₂	semidirect
6. #14583483	C₂	semidirect
7. #14583481	C₂	semidirect
8. #14583459	C₂	semidirect
9. #14583457	C₂	semidirect
10. #14583435	C₂	semidirect
11. #14583432	C₂	semidirect
12. #14583430	C₂	semidirect
13. #14583428	C₂	semidirect
14. #14583409	C₂	semidirect
15. #14583407	C₂	semidirect
16. #14583405	C₂	semidirect
17. C₂×(C₂²⋊D₄₃)⋊C₄	C₂	semidirect
18. C₄×D₄×D₄₃	C₂	semidirect
19. C₄₃×#538	C₂	semidirect
20. C₂×#10621900	C₂²	semidirect
23. C₂³×Dic₄₃	C₂²	semidirect
25. C₂²×C₄×D₄₃	C₂²	semidirect
26. #13063320	C₂²	semidirect
27. #13063319	C₂²	semidirect
28. #13063318	C₂²	semidirect
29. #13063318	C₂²	semidirect
30. #13063318	C₂²	semidirect
31. #13063317	C₂²	semidirect
32. #13063316	C₂²	semidirect
33. #13063316	C₂²	semidirect
34. #13063315	C₂²	semidirect
35. #13063314	C₂²	semidirect
36. #13063312	C₂²	semidirect
37. #13063311	C₂²	semidirect
38. #13063310	C₂²	semidirect
39. #13063309	C₂²	semidirect
40. #13063309	C₂²	semidirect
41. #13063308	C₂²	semidirect
42. #13063307	C₂²	semidirect
43. #13063307	C₂²	semidirect
44. #13063307	C₂²	semidirect
45. #13063307	C₂²	semidirect
46. #13063307	C₂²	semidirect
47. #13063306	C₂²	semidirect
48. #13063306	C₂²	semidirect
49. #13063305	C₂²	semidirect
50. #13063304	C₂²	semidirect
51. #13063304	C₂²	semidirect
52. #13063303	C₂²	semidirect
53. #13063303	C₂²	semidirect
54. #13063303	C₂²	semidirect
55. #13063302	C₂²	semidirect
56. #13063302	C₂²	semidirect
57. #13063301	C₂²	semidirect
61. #13063298	C₂²	semidirect
63. #13063297	C₂²	semidirect
66. #13063295	C₂²	semidirect
67. #13063294	C₂²	semidirect
68. #13063293	C₂²	semidirect
69. #13063293	C₂²	semidirect
70. #13063293	C₂²	semidirect
71. Q₈×Dic₄₃	C₂²	semidirect
72. #13063290	C₂²	semidirect
73. C₄×D₁₇₂	C₂²	semidirect
74. D₄×Dic₄₃	C₂²	semidirect
75. D₄×Dic₄₃	C₂²	semidirect
76. D₄×Dic₄₃	C₂²	semidirect
77. #13063287	C₂²	semidirect
78. #13063287	C₂²	semidirect
79. C₄×C₂²⋊D₄₃	C₂²	semidirect
80. C₄×C₂²⋊D₄₃	C₂²	semidirect
81. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
82. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
83. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
84. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
85. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
86. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
87. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
88. #13063283	C₂²	semidirect
89. #13063281	C₂²	semidirect
90. #13063281	C₂²	semidirect
91. C₂×Dic₄₃⋊C₄	C₂²	semidirect
92. C₄⋊C₄×D₄₃	C₂²	semidirect
95. C₂²⋊C₄×D₄₃	C₂²	semidirect
96. C₂×C₄×Dic₄₃	C₂²	semidirect
97. C₄²×D₄₃	C₂²	semidirect
98. #126×C₄₃	C₂²	semidirect
99. #124×C₄₃	C₂²	semidirect
100. #123×C₄₃	C₂²	semidirect
101. C₂²⋊Q₈×C₄₃	C₂²	semidirect
103. #121×C₄₃	C₂²	semidirect
104. #120×C₄₃	C₂²	semidirect
105. C₄×D₄×C₄₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₄₃	C₂²	semidirect
211. C₂²×D₄₃	#41	semidirect
309. #538	D₄₃	semidirect
321. C₄₃	#3459	semidirect
333. #126	C₂×D₄₃	semidirect
341. #124	C₂×D₄₃	semidirect
353. #123	C₂×D₄₃	semidirect
363. C₂²⋊Q₈	C₂×D₄₃	semidirect
373. #121	C₂×D₄₃	semidirect
379. #120	C₂×D₄₃	semidirect
397. C₄×D₄	C₂×D₄₃	semidirect
406. C₂×C₂²⋊C₄	C₂×D₄₃	semidirect