Subgroups — #19148227

Order 5504.

1900 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063370	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583541	C₂	1	4	yes	maximal, complemented
4	#14583538	C₂	1	4	yes	maximal, complemented
5	#14583533	C₂	1	4	yes	maximal, complemented
6	#14583531	C₂	1	4	yes	maximal, complemented
7	#14583464	C₂	1	2	yes	maximal, complemented
8	#14583460	C₂	1	2	yes	maximal, complemented
9	#14583458	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583407	C₂	1	2	yes	maximal, complemented
11	C₂×#13063295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063293	C₂	1	1	yes	maximal, characteristic, complemented
13	#120×D₄₃	C₂	1	2	yes	maximal, complemented
14	#14583372	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×D₄₃	C₂²	1	1	yes	characteristic, complemented
18	#13063370	—	2	8	no	—
19	C₂×#10621898	C₂²	1	2	yes	complemented
20	C₂×#10621900	C₂²	1	2	yes	complemented
21	C₂×#10621900	C₂²	1	2	yes	complemented
22	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
29	C₂×D₄×D₄₃	—	2	8	no	—
30	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
31	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
32	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
33	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
34	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
35	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
36	#13063321	C₂²	1	4	yes	complemented
37	#13063311	C₂²	1	4	yes	complemented
38	#13063310	C₂²	1	4	yes	complemented
39	#13063308	C₂²	1	2	yes	complemented
40	#13063306	C₂²	1	2	yes	complemented
41	#13063303	C₂²	1	4	yes	complemented
42	#13063300	C₂²	1	4	yes	complemented
43	#13063298	C₂²	1	4	yes	complemented
44	#13063298	C₂²	1	4	yes	complemented
45	#13063298	C₂²	1	4	yes	complemented
46	#13063297	C₂²	1	4	yes	complemented
47	#13063297	C₂²	1	4	yes	complemented
48	#13063295	C₂²	1	2	yes	complemented
49	#13063295	C₂²	1	4	yes	complemented
50	#13063295	C₂²	1	4	yes	complemented
51	#13063295	C₂²	1	2	yes	complemented
52	#13063295	C₂²	1	4	yes	complemented
53	#13063294	C₂²	1	2	yes	complemented
54	#13063293	C₂²	1	2	yes	complemented
55	#13063293	C₂²	1	4	yes	complemented
56	#13063293	C₂²	1	4	yes	complemented
57	#13063293	C₂²	1	2	yes	complemented
58	#13063293	C₂²	1	2	yes	complemented
59	#13063287	C₂²	1	4	yes	complemented
60	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
61	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
62	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
63	#13063281	C₂²	1	2	yes	complemented
64	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
66	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
67	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
68	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
69	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
70	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
71	#123×C₄₃	C₂²	1	2	yes	complemented
72	#123×C₄₃	C₂²	1	2	yes	complemented
73	#121×C₄₃	C₂²	1	4	yes	complemented
74	#120×C₄₃	C₂²	1	2	yes	complemented
75	#120×C₄₃	C₂²	1	2	yes	complemented
76	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
78	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
79	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic, complemented
80	C₂³×D₄₃	—	2	4	no	—
81	C₂³×D₄₃	—	2	4	no	—
82	C₂³×D₄₃	—	4	4	no	—
83	C₂³×D₄₃	—	4	4	no	—
84	C₂³×D₄₃	C₂³	1	1	yes	characteristic
85	C₂³×D₄₃	C₂³	1	4	yes	—
86	C₂³×D₄₃	C₂³	1	2	yes	—
87	C₂³×D₄₃	C₂³	1	2	yes	—
88	C₂³×D₄₃	C₂³	1	1	yes	characteristic
89	C₂³×D₄₃	C₂³	1	1	yes	characteristic
90	C₂³×D₄₃	C₂³	1	1	yes	characteristic, complemented
91	C₂³×D₄₃	C₂³	1	2	yes	complemented
92	C₂×D₄×C₄₃	—	2	4	no	—
93	C₂×D₄×C₄₃	—	2	4	no	—
94	C₂×D₄×C₄₃	C₂³	1	2	yes	—
95	C₂×D₄×C₄₃	C₂³	1	2	yes	—
96	C₂×D₄×C₄₃	C₂³	1	2	yes	—
97	C₂×D₄×C₄₃	C₂³	1	2	yes	complemented
98	C₂×D₄×C₄₃	C₂³	1	4	yes	complemented
99	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic, complemented
101	C₂²×C₄×C₄₃	C₂³	1	2	yes	complemented
102	C₂×C₂²⋊D₄₃	—	2	8	no	—
103	C₂×C₂²⋊D₄₃	—	2	4	no	—
104	C₂×C₂²⋊D₄₃	—	2	4	no	—
105	C₂×C₂²⋊D₄₃	—	4	4	no	—
106	C₂×C₂²⋊D₄₃	D₄	1	8	yes	complemented
107	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
109	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
110	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
111	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
112	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	complemented
113	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	complemented
114	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	complemented
115	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	complemented
116	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	complemented
117	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
118	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic, complemented
119	C₂²×Dic₄₃	C₂³	1	2	yes	complemented
120	C₂²×Dic₄₃	C₂³	1	2	yes	complemented
121	#10621900	—	2	8	no	—
122	#10621900	—	2	8	no	—
123	D₄×D₄₃	—	2	16	no	—
124	D₄×D₄₃	—	2	16	no	—
125	D₄×D₄₃	—	2	8	no	—
126	D₄×D₄₃	—	2	8	no	—
127	D₄×D₄₃	—	4	8	no	—
128	#10621898	—	2	8	no	—
129	C₂×D₁₇₂	—	2	4	no	—
130	C₂×D₁₇₂	—	4	4	no	—
131	C₂×D₁₇₂	C₂³	1	4	yes	—
132	C₂×D₁₇₂	C₂³	1	4	yes	—
133	C₂×D₁₇₂	C₂³	1	2	yes	complemented
134	C₂×D₁₇₂	C₂³	1	4	yes	complemented
135	C₂×C₄×D₄₃	—	2	4	no	—
136	C₂×C₄×D₄₃	C₂³	1	4	yes	—
137	C₂×C₄×D₄₃	C₂³	1	2	yes	complemented
138	C₂×C₄×D₄₃	C₂³	1	2	yes	complemented
139	C₂×C₄×D₄₃	C₂³	1	4	yes	complemented
140	C₂×Dic₈₆	C₂³	1	2	yes	complemented
141	C₄⋊C₄×C₄₃	C₂³	1	4	yes	complemented
142	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	complemented
144	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	complemented
145	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	complemented
146	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
147	C₂²⋊Dic₄₃	C₂³	1	4	yes	complemented
148	C₂²⋊Dic₄₃	C₂³	1	2	yes	complemented
149	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
150	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
151	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
152	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
153	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
154	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
155	Dic₄₃⋊C₄	C₂³	1	4	yes	complemented
156	Dic₄₃⋊C₄	C₂³	1	4	yes	complemented
157	C₄×Dic₄₃	C₂³	1	4	yes	complemented
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	C₂×D₄	1	4	yes	complemented
164	C₂³×C₄₃	C₂⁴	1	2	yes	—
165	C₂³×C₄₃	C₂⁴	1	2	yes	—
166	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂²×D₄₃	—	2	2	no	—
170	C₂²×D₄₃	—	2	4	no	—
171	C₂²×D₄₃	—	2	2	no	—
172	C₂²×D₄₃	—	2	4	no	—
173	C₂²×D₄₃	—	2	4	no	—
174	C₂²×D₄₃	—	2	2	no	—
175	C₂²×D₄₃	—	2	8	no	—
176	C₂²×D₄₃	—	2	4	no	—
177	C₂²×D₄₃	—	2	8	no	—
178	C₂²×D₄₃	—	2	4	no	—
179	C₂²×D₄₃	—	2	4	no	—
180	C₂²×D₄₃	—	4	4	no	—
181	C₂²×D₄₃	—	4	2	no	—
182	C₂²×D₄₃	—	4	2	no	—
183	C₂²×D₄₃	—	4	2	no	—
184	C₂²×D₄₃	—	4	2	no	—
185	C₂²×D₄₃	—	4	2	no	—
186	C₂²×D₄₃	—	4	4	no	—
187	C₂²×D₄₃	—	4	16	no	—
188	C₂²×D₄₃	—	4	16	no	—
189	C₂²×D₄₃	C₂×D₄	1	4	yes	complemented
190	C₂²×D₄₃	C₂⁴	1	2	yes	—
191	C₂²×D₄₃	C₂⁴	1	2	yes	—
192	C₂²×D₄₃	C₂⁴	1	2	yes	—
193	C₂²×D₄₃	C₂⁴	1	2	yes	—
194	D₄×C₄₃	—	2	4	no	—
195	D₄×C₄₃	—	2	4	no	—
196	D₄×C₄₃	—	2	4	no	—
197	D₄×C₄₃	—	2	4	no	—
198	D₄×C₄₃	—	4	4	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
203	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
204	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
205	C₂²⋊D₄₃	—	2	4	no	—
206	C₂²⋊D₄₃	—	2	4	no	—
207	C₂²⋊D₄₃	—	2	4	no	—
208	C₂²⋊D₄₃	—	2	8	no	—
209	C₂²⋊D₄₃	—	2	8	no	—
210	C₂²⋊D₄₃	—	2	4	no	—
211	C₂²⋊D₄₃	—	4	4	no	—
212	C₂²⋊D₄₃	—	4	4	no	—
213	C₂²⋊D₄₃	C₂×D₄	1	8	yes	complemented
214	C₂²⋊D₄₃	C₂×D₄	1	8	yes	complemented
215	C₂×Dic₄₃	—	2	2	no	—
216	C₂×Dic₄₃	—	2	4	no	—
217	C₂×Dic₄₃	—	4	2	no	—
218	C₂×Dic₄₃	C₂×D₄	1	4	yes	complemented
219	C₂×Dic₄₃	C₂⁴	1	4	yes	—
220	C₂×Dic₄₃	C₂⁴	1	2	yes	—
221	C₂×Dic₄₃	C₂⁴	1	2	yes	—
222	D₁₇₂	—	2	8	no	—
223	D₁₇₂	—	2	4	no	—
224	D₁₇₂	—	2	8	no	—
225	D₁₇₂	—	4	4	no	—
226	C₄×D₄₃	—	2	4	no	—
227	C₄×D₄₃	—	2	8	no	—
228	C₄×D₄₃	—	2	4	no	—
229	C₄×D₄₃	—	4	4	no	—
230	Dic₈₆	—	2	4	no	—
231	C₂²×C₄₃	—	2	2	no	—
232	C₂²×C₄₃	—	2	2	no	—
233	C₂²×C₄₃	—	2	2	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	2	4	no	—
237	C₂²×C₄₃	—	2	4	no	—
238	C₂²×C₄₃	—	4	4	no	—
239	C₂²×C₄₃	—	4	4	no	—
240	C₂²×C₄₃	—	8	2	no	—
241	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
242	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
243	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
244	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
245	C₂×D₄₃	—	2	8	no	—
246	C₂×D₄₃	—	2	2	no	—
247	C₂×D₄₃	—	2	2	no	—
248	C₂×D₄₃	—	2	4	no	—
249	C₂×D₄₃	—	2	2	no	—
250	C₂×D₄₃	—	2	2	no	—
251	C₂×D₄₃	—	2	2	no	—
252	C₂×D₄₃	—	2	2	no	—
253	C₂×D₄₃	—	2	4	no	—
254	C₂×D₄₃	—	4	4	no	—
255	C₂×D₄₃	—	4	16	no	—
256	C₂×D₄₃	—	4	8	no	—
257	C₂×D₄₃	—	4	8	no	—
258	C₂×D₄₃	—	4	4	no	—
259	C₂×D₄₃	—	8	4	no	—
260	C₂×D₄₃	—	8	2	no	—
261	C₂×D₄₃	C₂²×D₄	1	4	yes	—
262	C₂×D₄₃	H(5,𝔽₂)	1	4	yes	complemented
263	C₄×C₄₃	—	2	2	no	—
264	C₄×C₄₃	—	2	2	no	—
265	C₄×C₄₃	—	2	4	no	—
266	Dic₄₃	—	2	2	no	—
267	Dic₄₃	—	2	4	no	—
268	Dic₄₃	C₂²×D₄	1	4	yes	—
269	#3484	—	43	1	no	maximal, Sylow
270	C₂×C₄₃	—	2	2	no	—
271	C₂×C₄₃	—	2	2	no	—
272	C₂×C₄₃	—	2	2	no	—
273	C₂×C₄₃	—	4	2	no	—
274	C₂×C₄₃	—	4	2	no	—
275	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
276	C₂×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
277	D₄₃	—	2	4	no	—
278	D₄₃	—	2	4	no	—
279	D₄₃	—	4	2	no	—
280	D₄₃	—	4	2	no	—
281	C₂×H(5,𝔽₂)	—	43	1	no	—
282	C₂³×D₄	—	43	1	no	—
283	#546	—	43	4	no	—
284	#546	—	43	4	no	—
285	D₄²	—	43	4	no	—
286	D₄²	—	43	4	no	—
287	#535	—	43	2	no	—
288	#534	—	43	1	no	—
289	#534	—	43	2	no	—
290	#534	D₄₃	1	1	yes	characteristic, complemented
291	#525	—	43	2	no	—
292	C₂×#120	—	43	1	no	—
293	C₂×#120	—	43	2	no	—
294	C₂×#120	—	43	1	no	—
295	#518	—	43	1	no	—
296	C₄₃	#3484	1	1	yes	characteristic, complemented, Sylow
297	C₂⁵	—	43	1	no	—
298	C₂⁵	—	43	1	no	—
299	H(5,𝔽₂)	—	86	8	no	—
300	C₂×#41	—	43	2	no	—
301	C₂×#41	—	43	2	no	—
302	C₂×#41	—	43	2	no	—
303	C₂²×D₄	—	43	1	no	—
304	C₂²×D₄	—	43	1	no	—
305	C₂²×D₄	—	43	1	no	—
306	C₂²×D₄	—	43	2	no	—
307	C₂²×D₄	—	43	2	no	—
308	C₂²×D₄	—	43	2	no	—
309	C₂²×D₄	—	43	4	no	—
310	C₂²×D₄	—	43	4	no	—
311	C₂²×D₄	—	43	2	no	—
312	C₂²×D₄	—	43	4	no	—
313	C₂²×D₄	—	43	1	no	—
314	C₂²×D₄	—	43	2	no	—
315	C₂²×D₄	—	86	8	no	—
316	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
317	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
318	C₂³×C₄	—	43	1	no	—
319	#127	—	43	4	no	—
320	#124	—	43	4	no	—
321	#123	—	43	2	no	—
322	#123	—	43	2	no	—
323	#123	—	43	4	no	—
324	#123	C₂×D₄₃	1	2	yes	complemented
325	#123	C₂×D₄₃	1	2	yes	complemented
326	C₂²⋊Q₈	—	43	4	no	—
327	#121	—	43	4	no	—
328	#121	—	43	4	no	—
329	#121	—	43	4	no	—
330	#121	—	43	4	no	—
331	#121	—	43	4	no	—
332	#121	—	43	4	no	—
333	#121	C₂×D₄₃	1	4	yes	complemented
334	#120	—	43	2	no	—
335	#120	—	43	2	no	—
336	#120	—	43	2	no	—
337	#120	—	43	2	no	—
338	#120	—	43	4	no	—
339	#120	—	43	4	no	—
340	#120	—	43	2	no	—
341	#120	—	43	2	no	—
342	#120	—	43	4	no	—
343	#120	—	43	4	no	—
344	#120	—	43	4	no	—
345	#120	C₂×D₄₃	1	2	yes	complemented
346	#120	C₂×D₄₃	1	2	yes	complemented
347	C₄×D₄	—	43	4	no	—
348	C₄×D₄	—	43	4	no	—
349	C₄×D₄	—	43	4	no	—
350	C₄×D₄	—	43	4	no	—
351	#117	—	43	2	no	—
352	C₂×C₂²⋊C₄	—	43	1	no	—
353	C₂×C₂²⋊C₄	—	43	2	no	—
354	C₂×C₂²⋊C₄	—	43	2	no	—
355	C₂×C₂²⋊C₄	—	43	2	no	—
356	C₂×C₂²⋊C₄	—	43	4	no	—
357	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
358	C₂⁴	—	43	1	no	—
359	C₂⁴	—	43	1	no	—
360	C₂⁴	—	43	4	no	—
361	C₂⁴	—	43	2	no	—
362	C₂⁴	—	43	2	no	—
363	C₂⁴	—	43	1	no	—
364	C₂⁴	—	43	2	no	—
365	C₂⁴	—	43	1	no	—
366	C₂⁴	—	86	4	no	—
367	C₂⁴	—	86	4	no	—
368	C₂⁴	—	172	4	no	—
369	C₂⁴	—	172	4	no	—
370	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
371	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
372	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic, complemented
373	#41	—	86	8	no	—
374	#41	—	86	8	no	—
375	#41	—	86	8	no	—
376	C₂×Q₈	—	43	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	43	8	no	—
380	C₂×D₄	—	43	2	no	—
381	C₂×D₄	—	43	2	no	—
382	C₂×D₄	—	43	4	no	—
383	C₂×D₄	—	43	2	no	—
384	C₂×D₄	—	43	2	no	—
385	C₂×D₄	—	43	2	no	—
386	C₂×D₄	—	43	4	no	—
387	C₂×D₄	—	43	2	no	—
388	C₂×D₄	—	43	4	no	—
389	C₂×D₄	—	43	4	no	—
390	C₂×D₄	—	43	4	no	—
391	C₂×D₄	—	43	2	no	—
392	C₂×D₄	—	43	4	no	—
393	C₂×D₄	—	43	4	no	—
394	C₂×D₄	—	86	4	no	—
395	C₂×D₄	—	86	4	no	—
396	C₂×D₄	—	86	16	no	—
397	C₂×D₄	—	86	16	no	—
398	C₂×D₄	—	86	8	no	—
399	C₂×D₄	—	86	8	no	—
400	C₂×D₄	—	86	8	no	—
401	C₂×D₄	—	86	4	no	—
402	C₂×D₄	—	172	4	no	—
403	C₂×D₄	—	172	8	no	—
404	C₂×D₄	—	172	4	no	—
405	C₂×D₄	C₂²×D₄₃	1	2	yes	—
406	C₂×D₄	C₂²×D₄₃	1	2	yes	—
407	C₂×D₄	C₂²×D₄₃	1	2	yes	—
408	C₂×D₄	C₂²×D₄₃	1	2	yes	complemented
409	C₂×D₄	C₂²×D₄₃	1	4	yes	complemented
410	C₂²×C₄	—	43	1	no	—
411	C₂²×C₄	—	43	1	no	—
412	C₂²×C₄	—	43	2	no	—
413	C₂²×C₄	—	43	2	no	—
414	C₂²×C₄	—	43	2	no	—
415	C₂²×C₄	—	43	2	no	—
416	C₂²×C₄	—	43	4	no	—
417	C₂²×C₄	—	43	4	no	—
418	C₂²×C₄	—	86	4	no	—
419	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
420	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic, complemented
421	C₂²×C₄	C₂²×D₄₃	1	2	yes	complemented
422	C₄⋊C₄	—	43	4	no	—
423	C₄⋊C₄	—	43	4	no	—
424	C₄⋊C₄	C₂²×D₄₃	1	4	yes	complemented
425	C₂²⋊C₄	—	43	2	no	—
426	C₂²⋊C₄	—	43	2	no	—
427	C₂²⋊C₄	—	43	4	no	—
428	C₂²⋊C₄	—	43	4	no	—
429	C₂²⋊C₄	—	43	4	no	—
430	C₂²⋊C₄	—	43	4	no	—
431	C₂²⋊C₄	—	43	4	no	—
432	C₂²⋊C₄	—	43	4	no	—
433	C₂²⋊C₄	—	43	4	no	—
434	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
435	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	complemented
436	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	complemented
437	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	complemented
438	C₄²	—	43	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	43	2	no	—
445	C₂³	—	43	2	no	—
446	C₂³	—	43	4	no	—
447	C₂³	—	43	2	no	—
448	C₂³	—	43	2	no	—
449	C₂³	—	86	4	no	—
450	C₂³	—	86	4	no	—
451	C₂³	—	86	8	no	—
452	C₂³	—	86	4	no	—
453	C₂³	—	86	4	no	—
454	C₂³	—	86	8	no	—
455	C₂³	—	86	2	no	—
456	C₂³	—	86	2	no	—
457	C₂³	—	86	4	no	—
458	C₂³	—	86	4	no	—
459	C₂³	—	86	2	no	—
460	C₂³	—	172	2	no	—
461	C₂³	—	172	4	no	—
462	C₂³	—	172	2	no	—
463	C₂³	—	172	2	no	—
464	C₂³	—	172	2	no	—
465	C₂³	—	172	2	no	—
466	C₂³	—	172	4	no	—
467	C₂³	—	172	16	no	—
468	C₂³	—	172	16	no	—
469	C₂³	D₄×D₄₃	1	4	yes	complemented
470	C₂³	C₂³×D₄₃	1	2	yes	—
471	C₂³	C₂³×D₄₃	1	2	yes	—
472	C₂³	C₂³×D₄₃	1	1	yes	characteristic
473	C₂³	C₂³×D₄₃	1	1	yes	characteristic
474	C₂³	C₂³×D₄₃	1	1	yes	characteristic
475	Q₈	—	86	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	4	no	—
480	D₄	—	4	4	no	—
481	D₄	—	43	8	no	—
482	D₄	—	43	8	no	—
483	D₄	—	86	8	no	—
484	D₄	—	86	4	no	—
485	D₄	—	86	8	no	—
486	D₄	—	86	8	no	—
487	D₄	—	86	4	no	—
488	D₄	—	86	4	no	—
489	D₄	—	86	8	no	—
490	D₄	—	86	4	no	—
491	D₄	—	86	4	no	—
492	D₄	—	172	4	no	—
493	D₄	—	172	4	no	—
494	D₄	—	172	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	43	4	no	—
499	C₂×C₄	—	43	2	no	—
500	C₂×C₄	—	43	4	no	—
501	C₂×C₄	—	43	2	no	—
502	C₂×C₄	—	86	8	no	—
503	C₂×C₄	—	86	4	no	—
504	C₂×C₄	—	86	4	no	—
505	C₂×C₄	—	86	4	no	—
506	C₂×C₄	—	86	2	no	—
507	C₂×C₄	—	172	4	no	—
508	C₂×C₄	—	172	2	no	—
509	C₂×C₄	C₂³×D₄₃	1	4	yes	—
510	C₂×C₄	C₂³×D₄₃	1	2	yes	—
511	C₂×C₄	C₂³×D₄₃	1	2	yes	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	43	4	no	—
523	C₂²	—	43	4	no	—
524	C₂²	—	86	8	no	—
525	C₂²	—	86	2	no	—
526	C₂²	—	86	4	no	—
527	C₂²	—	86	2	no	—
528	C₂²	—	86	2	no	—
529	C₂²	—	86	2	no	—
530	C₂²	—	86	4	no	—
531	C₂²	—	86	2	no	—
532	C₂²	—	86	2	no	—
533	C₂²	—	344	2	no	—
534	C₂²	—	344	4	no	—
535	C₂²	—	172	4	no	—
536	C₂²	—	172	8	no	—
537	C₂²	—	172	8	no	—
538	C₂²	—	172	4	no	—
539	C₂²	—	172	16	no	—
540	C₂²	C₂×D₄×D₄₃	1	2	yes	—
541	C₂²	C₂×D₄×D₄₃	1	2	yes	—
542	C₂²	C₂×D₄×D₄₃	1	2	yes	—
543	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	4	no	—
547	C₄	—	43	4	no	—
548	C₄	—	86	2	no	—
549	C₄	—	86	4	no	—
550	C₂	—	2	2	no	—
551	C₂	—	2	2	no	—
552	C₂	—	2	2	no	—
553	C₂	—	4	2	no	—
554	C₂	—	4	2	no	—
555	C₂	—	86	4	no	—
556	C₂	—	86	4	no	—
557	C₂	—	172	2	no	—
558	C₂	—	172	2	no	—
559	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic
560	C₂	H(5,𝔽₂)×D₄₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#534	C₂
hypercenter	#534	D₄₃
hypocenter	C₄₃	#3484
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. C₂×#13063370	C₂	semidirect
2. C₂²×D₄×D₄₃	C₂	semidirect
3. #14583541	C₂	semidirect
4. #14583538	C₂	semidirect
5. #14583533	C₂	semidirect
6. #14583531	C₂	semidirect
7. #14583464	C₂	semidirect
8. #14583460	C₂	semidirect
9. #14583458	C₂	semidirect
10. #14583407	C₂	semidirect
11. C₂×#13063295	C₂	semidirect
12. C₂×#13063293	C₂	semidirect
13. #120×D₄₃	C₂	semidirect
14. #14583372	C₂	semidirect
15. C₄₃×#534	C₂	semidirect
16. C₂⁴×D₄₃	C₂²	semidirect
17. C₂⁴×D₄₃	C₂²	semidirect
19. C₂×#10621898	C₂²	semidirect
20. C₂×#10621900	C₂²	semidirect
21. C₂×#10621900	C₂²	semidirect
22. C₂²×D₁₇₂	C₂²	semidirect
23. C₂²×D₁₇₂	C₂²	semidirect
25. C₂²×C₂²⋊D₄₃	C₂²	semidirect
26. C₂²×C₂²⋊D₄₃	C₂²	semidirect
27. C₂²×C₂²⋊D₄₃	C₂²	semidirect
28. C₂²×C₂²⋊D₄₃	C₂²	semidirect
30. C₂×D₄×D₄₃	C₂²	semidirect
31. C₂×D₄×D₄₃	C₂²	semidirect
32. C₂×D₄×D₄₃	C₂²	semidirect
33. C₂×D₄×D₄₃	C₂²	semidirect
34. C₂×D₄×D₄₃	C₂²	semidirect
35. C₂²×C₄×D₄₃	C₂²	semidirect
36. #13063321	C₂²	semidirect
37. #13063311	C₂²	semidirect
38. #13063310	C₂²	semidirect
39. #13063308	C₂²	semidirect
40. #13063306	C₂²	semidirect
41. #13063303	C₂²	semidirect
42. #13063300	C₂²	semidirect
43. #13063298	C₂²	semidirect
44. #13063298	C₂²	semidirect
45. #13063298	C₂²	semidirect
46. #13063297	C₂²	semidirect
47. #13063297	C₂²	semidirect
48. #13063295	C₂²	semidirect
49. #13063295	C₂²	semidirect
50. #13063295	C₂²	semidirect
51. #13063295	C₂²	semidirect
52. #13063295	C₂²	semidirect
53. #13063294	C₂²	semidirect
54. #13063293	C₂²	semidirect
55. #13063293	C₂²	semidirect
56. #13063293	C₂²	semidirect
57. #13063293	C₂²	semidirect
58. #13063293	C₂²	semidirect
59. #13063287	C₂²	semidirect
60. C₄×C₂²⋊D₄₃	C₂²	semidirect
61. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
62. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
63. #13063281	C₂²	semidirect
64. C₂×C₂²⋊Dic₄₃	C₂²	semidirect
65. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
66. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
67. C₂²⋊C₄×D₄₃	C₂²	semidirect
68. C₂²⋊C₄×D₄₃	C₂²	semidirect
69. C₂²×D₄×C₄₃	C₂²	semidirect
70. C₂²×D₄×C₄₃	C₂²	semidirect
71. #123×C₄₃	C₂²	semidirect
72. #123×C₄₃	C₂²	semidirect
73. #121×C₄₃	C₂²	semidirect
74. #120×C₄₃	C₂²	semidirect
75. #120×C₄₃	C₂²	semidirect
76. C₂×C₂²⋊C₄×C₄₃	C₂²	semidirect
79. C₂⁴×C₄₃	C₂³	semidirect
90. C₂³×D₄₃	C₂³	semidirect
91. C₂³×D₄₃	C₂³	semidirect
97. C₂×D₄×C₄₃	C₂³	semidirect
98. C₂×D₄×C₄₃	C₂³	semidirect
100. C₂²×C₄×C₄₃	C₂³	semidirect
101. C₂²×C₄×C₄₃	C₂³	semidirect
106. C₂×C₂²⋊D₄₃	D₄	semidirect
112. C₂×C₂²⋊D₄₃	C₂³	semidirect
113. C₂×C₂²⋊D₄₃	C₂³	semidirect
114. C₂×C₂²⋊D₄₃	C₂³	semidirect
115. C₂×C₂²⋊D₄₃	C₂³	semidirect
116. C₂×C₂²⋊D₄₃	C₂³	semidirect
118. C₂²×Dic₄₃	C₂³	semidirect
119. C₂²×Dic₄₃	C₂³	semidirect
120. C₂²×Dic₄₃	C₂³	semidirect
133. C₂×D₁₇₂	C₂³	semidirect
134. C₂×D₁₇₂	C₂³	semidirect
137. C₂×C₄×D₄₃	C₂³	semidirect
138. C₂×C₄×D₄₃	C₂³	semidirect
139. C₂×C₄×D₄₃	C₂³	semidirect
140. C₂×Dic₈₆	C₂³	semidirect
141. C₄⋊C₄×C₄₃	C₂³	semidirect
143. C₂²⋊C₄×C₄₃	C₂³	semidirect
144. C₂²⋊C₄×C₄₃	C₂³	semidirect
145. C₂²⋊C₄×C₄₃	C₂³	semidirect
147. C₂²⋊Dic₄₃	C₂³	semidirect
148. C₂²⋊Dic₄₃	C₂³	semidirect
151. (C₂×D₄₃)⋊C₄	C₂³	semidirect
152. (C₂×D₄₃)⋊C₄	C₂³	semidirect
153. (C₂×D₄₃)⋊C₄	C₂³	semidirect
154. (C₂×D₄₃)⋊C₄	C₂³	semidirect
155. Dic₄₃⋊C₄	C₂³	semidirect
156. Dic₄₃⋊C₄	C₂³	semidirect
157. C₄×Dic₄₃	C₂³	semidirect
163. C₂³×C₄₃	C₂×D₄	semidirect
189. C₂²×D₄₃	C₂×D₄	semidirect
213. C₂²⋊D₄₃	C₂×D₄	semidirect
214. C₂²⋊D₄₃	C₂×D₄	semidirect
218. C₂×Dic₄₃	C₂×D₄	semidirect
262. C₂×D₄₃	H(5,𝔽₂)	semidirect
290. #534	D₄₃	semidirect
296. C₄₃	#3484	semidirect
316. C₂²×D₄	C₂×D₄₃	semidirect
317. C₂²×D₄	C₂×D₄₃	semidirect
324. #123	C₂×D₄₃	semidirect
325. #123	C₂×D₄₃	semidirect
333. #121	C₂×D₄₃	semidirect
345. #120	C₂×D₄₃	semidirect
346. #120	C₂×D₄₃	semidirect
357. C₂×C₂²⋊C₄	C₂×D₄₃	semidirect
372. C₂⁴	C₂²×D₄₃	semidirect
408. C₂×D₄	C₂²×D₄₃	semidirect
409. C₂×D₄	C₂²×D₄₃	semidirect
420. C₂²×C₄	C₂²×D₄₃	semidirect
421. C₂²×C₄	C₂²×D₄₃	semidirect
424. C₄⋊C₄	C₂²×D₄₃	semidirect
435. C₂²⋊C₄	C₂²×D₄₃	semidirect
436. C₂²⋊C₄	C₂²×D₄₃	semidirect
437. C₂²⋊C₄	C₂²×D₄₃	semidirect
469. C₂³	D₄×D₄₃	semidirect