Subgroups — #19148437

Order 5504.

1140 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583631	C₂	1	4	yes	maximal, complemented
2	#14583617	C₂	1	2	yes	maximal, complemented
3	#14583615	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583601	C₂	1	2	yes	maximal, complemented
5	#14583593	C₂	1	2	yes	maximal, complemented
6	#14583567	C₂	1	2	yes	maximal, complemented
7	#14583554	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583553	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583483	C₂	1	4	yes	maximal, complemented
10	#14583465	C₂	1	2	yes	maximal, complemented
11	#14583454	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583446	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583411	C₂	1	2	yes	maximal, complemented
14	#14583409	C₂	1	2	yes	maximal, complemented
15	#14583379	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621898	C₂²	1	2	yes	—
19	C₂×#10621898	C₂²	1	2	yes	complemented
20	C₂×#10621900	C₂²	1	2	yes	complemented
21	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
23	#13063325	C₂²	1	1	yes	characteristic, complemented
24	#13063324	C₂²	1	1	yes	characteristic, complemented
25	#13063321	C₂²	1	4	yes	—
26	#13063321	C₂²	1	1	yes	characteristic, complemented
27	#13063319	C₂²	1	4	yes	complemented
28	#13063318	C₂²	1	4	yes	complemented
29	#13063316	C₂²	1	2	yes	complemented
30	#13063314	C₂²	1	4	yes	complemented
31	#13063311	C₂²	1	4	yes	—
32	#13063311	C₂²	1	2	yes	complemented
33	#13063309	C₂²	1	4	yes	complemented
34	#13063309	C₂²	1	4	yes	complemented
35	#13063307	C₂²	1	4	yes	complemented
36	#13063307	C₂²	1	4	yes	complemented
37	#13063305	C₂²	1	2	yes	—
38	#13063305	C₂²	1	2	yes	complemented
39	#13063304	C₂²	1	2	yes	complemented
40	#13063301	C₂²	1	2	yes	—
41	#13063300	C₂²	1	2	yes	—
42	#13063300	C₂²	1	1	yes	characteristic
43	#13063300	C₂²	1	2	yes	complemented
44	#13063299	C₂²	1	2	yes	—
45	#13063298	C₂²	1	2	yes	—
46	#13063298	C₂²	1	4	yes	complemented
47	#13063297	C₂²	1	4	yes	complemented
48	#13063296	C₂²	1	2	yes	—
49	#13063296	C₂²	1	1	yes	characteristic
50	#13063295	C₂²	1	4	yes	—
51	#13063293	C₂²	1	4	yes	—
52	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
53	C₄×Dic₈₆	C₂²	1	4	yes	complemented
54	#13063290	C₂²	1	2	yes	complemented
55	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
56	C₄×D₁₇₂	C₂²	1	4	yes	—
57	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
58	C₄×D₁₇₂	C₂²	1	4	yes	complemented
59	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
60	D₄×Dic₄₃	C₂²	1	4	yes	complemented
61	#13063287	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
64	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
65	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
66	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
67	#13063283	C₂²	1	2	yes	—
68	#13063283	C₂²	1	2	yes	complemented
69	#13063283	C₂²	1	2	yes	complemented
70	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	—
74	C₄²×D₄₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
76	#124×C₄₃	C₂²	1	4	yes	complemented
77	#121×C₄₃	C₂²	1	2	yes	—
78	#121×C₄₃	C₂²	1	2	yes	complemented
79	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
81	#117×C₄₃	C₂²	1	2	yes	complemented
82	#117×C₄₃	C₂²	1	2	yes	complemented
83	C₂³×D₄₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
85	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₄₃	C₂³	1	4	yes	—
88	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
96	C₂²×Dic₄₃	C₂³	1	4	yes	—
97	C₂²×Dic₄₃	C₂³	1	2	yes	—
98	#10621900	—	4	4	no	—
99	D₄×D₄₃	—	2	4	no	—
100	#10621898	—	2	8	no	—
101	#10621898	—	4	4	no	—
102	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
103	C₂×D₁₇₂	C₂³	1	2	yes	—
104	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
105	C₂×D₁₇₂	C₂³	1	4	yes	—
106	C₂×C₄×D₄₃	—	4	4	no	—
107	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₄₃	C₂³	1	2	yes	—
109	C₂×C₄×D₄₃	C₂³	1	2	yes	—
110	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₄₃	C₂³	1	2	yes	—
112	C₂×C₄×D₄₃	C₂³	1	4	yes	—
113	C₂×C₄×D₄₃	C₂³	1	2	yes	—
114	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
115	C₂×Dic₈₆	C₂³	1	2	yes	—
116	C₂×Dic₈₆	C₂³	1	2	yes	—
117	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
120	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
122	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
125	C₄²×C₄₃	C₂³	1	4	yes	—
126	C₄²×C₄₃	C₂³	1	1	yes	characteristic
127	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
128	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
136	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
138	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂³	1	2	yes	—
140	C₄⋊Dic₄₃	C₂³	1	4	yes	—
141	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₄₃	C₂³	1	4	yes	—
143	C₄⋊Dic₄₃	C₂³	1	2	yes	—
144	Dic₄₃⋊C₄	C₂³	1	2	yes	—
145	Dic₄₃⋊C₄	C₂³	1	4	yes	—
146	Dic₄₃⋊C₄	C₂³	1	2	yes	—
147	Dic₄₃⋊C₄	C₂³	1	4	yes	—
148	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
150	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₄₃	C₂³	1	4	yes	—
152	C₄×Dic₄₃	C₂³	1	4	yes	—
153	C₂³×C₄₃	C₂⁴	1	2	yes	—
154	C₂³×C₄₃	C₂⁴	1	2	yes	—
155	C₂²×D₄₃	—	2	4	no	—
156	C₂²×D₄₃	—	4	2	no	—
157	C₂²×D₄₃	—	4	2	no	—
158	C₂²×D₄₃	C₂⁴	1	2	yes	—
159	C₂²×D₄₃	C₂⁴	1	2	yes	—
160	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
161	Q₈×C₄₃	—	4	2	no	—
162	D₄×C₄₃	—	2	2	no	—
163	D₄×C₄₃	—	2	2	no	—
164	D₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₄₃	—	2	4	no	—
174	C₂²⋊D₄₃	—	2	4	no	—
175	C₂²⋊D₄₃	—	2	4	no	—
176	C₂²⋊D₄₃	—	4	4	no	—
177	C₂²⋊D₄₃	—	4	4	no	—
178	C₂²⋊D₄₃	—	4	2	no	—
179	C₂×Dic₄₃	—	4	2	no	—
180	C₂×Dic₄₃	—	4	4	no	—
181	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₄₃	C₂⁴	1	2	yes	—
183	C₂×Dic₄₃	C₂⁴	1	2	yes	—
184	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₄₃	C₂⁴	1	4	yes	—
186	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
187	D₁₇₂	—	2	4	no	—
188	D₁₇₂	—	2	2	no	—
189	D₁₇₂	—	2	2	no	—
190	D₁₇₂	—	4	4	no	—
191	C₄×D₄₃	—	2	4	no	—
192	C₄×D₄₃	—	2	2	no	—
193	C₄×D₄₃	—	2	4	no	—
194	C₄×D₄₃	—	4	2	no	—
195	C₄×D₄₃	—	4	2	no	—
196	C₄×D₄₃	—	4	1	no	—
197	C₄×D₄₃	—	4	4	no	—
198	C₄×D₄₃	#41	1	4	yes	complemented
199	Dic₈₆	—	2	4	no	—
200	Dic₈₆	—	2	4	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
208	C₂×D₄₃	—	2	1	no	—
209	C₂×D₄₃	—	2	1	no	—
210	C₂×D₄₃	—	2	2	no	—
211	C₂×D₄₃	—	2	2	no	—
212	C₂×D₄₃	—	2	2	no	—
213	C₂×D₄₃	—	2	2	no	—
214	C₂×D₄₃	—	2	2	no	—
215	C₂×D₄₃	—	2	2	no	—
216	C₂×D₄₃	—	4	8	no	—
217	C₂×D₄₃	C₂×#41	1	2	yes	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	4	no	—
222	C₄×C₄₃	C₂×#41	1	2	yes	—
223	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
224	Dic₄₃	—	2	2	no	—
225	Dic₄₃	—	2	4	no	—
226	Dic₄₃	—	2	1	no	—
227	Dic₄₃	—	2	2	no	—
228	Dic₄₃	—	2	1	no	—
229	Dic₄₃	C₂×#41	1	2	yes	—
230	#3506	—	43	1	no	maximal, Sylow
231	C₂×C₄₃	—	4	2	no	—
232	C₂×C₄₃	—	4	2	no	—
233	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
234	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄₃	#585	1	1	yes	characteristic
236	D₄₃	—	2	2	no	—
237	D₄₃	—	4	2	no	—
238	D₄₃	—	4	2	no	—
239	#559	—	43	4	no	—
240	#556	—	43	2	no	—
241	#555	—	43	1	no	—
242	#555	D₄₃	1	1	yes	characteristic, complemented
243	#553	—	43	2	no	—
244	#553	—	43	2	no	—
245	#550	—	43	2	no	—
246	#547	—	43	1	no	—
247	#547	—	43	1	no	—
248	#538	—	43	4	no	—
249	#535	—	43	2	no	—
250	#533	—	43	1	no	—
251	#532	—	43	1	no	—
252	#525	—	43	2	no	—
253	#525	—	43	2	no	—
254	#520	—	43	2	no	—
255	C₂×C₄×D₄	—	43	1	no	—
256	C₄₃	#3506	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	43	2	no	—
258	C₂×#41	—	43	2	no	—
259	C₂×#41	—	43	2	no	—
260	C₂²×D₄	—	43	1	no	—
261	C₂³×C₄	—	43	2	no	—
262	C₄⋊Q₈	—	43	1	no	—
263	C₄⋊Q₈	—	43	1	no	—
264	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
265	#127	—	43	1	no	—
266	#127	—	43	4	no	—
267	#126	—	43	4	no	—
268	#126	—	43	4	no	—
269	#125	—	43	2	no	—
270	#124	—	43	4	no	—
271	#124	—	43	2	no	—
272	#124	—	43	4	no	—
273	#124	C₂×D₄₃	1	4	yes	complemented
274	#123	—	43	4	no	—
275	#123	—	43	4	no	—
276	#123	—	43	4	no	—
277	#123	—	43	4	no	—
278	C₂²⋊Q₈	—	43	2	no	—
279	C₂²⋊Q₈	—	43	2	no	—
280	C₂²⋊Q₈	—	43	2	no	—
281	C₂²⋊Q₈	—	43	2	no	—
282	#121	—	43	1	no	—
283	#121	—	43	2	no	—
284	#121	—	43	4	no	—
285	#121	—	43	2	no	—
286	#121	—	43	1	no	—
287	#121	—	43	2	no	—
288	#121	—	43	2	no	—
289	#121	—	43	2	no	—
290	#121	—	43	4	no	—
291	#121	C₂×D₄₃	1	2	yes	—
292	#121	C₂×D₄₃	1	2	yes	complemented
293	#120	—	43	4	no	—
294	#120	—	43	4	no	—
295	C₄×Q₈	—	43	2	no	—
296	C₄×Q₈	—	43	2	no	—
297	C₄×Q₈	—	43	4	no	—
298	C₄×D₄	—	43	1	no	—
299	C₄×D₄	—	43	4	no	—
300	C₄×D₄	—	43	2	no	—
301	C₄×D₄	—	43	2	no	—
302	C₄×D₄	—	43	1	no	—
303	C₄×D₄	—	43	2	no	—
304	C₄×D₄	—	43	4	no	—
305	C₄×D₄	—	43	4	no	—
306	C₄×D₄	—	43	1	no	—
307	C₄×D₄	—	43	4	no	—
308	C₄×D₄	—	43	4	no	—
309	C₄×D₄	—	43	1	no	—
310	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
311	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
312	#117	—	43	2	no	—
313	#117	—	43	2	no	—
314	#117	—	43	2	no	—
315	#117	C₂×D₄₃	1	2	yes	complemented
316	#117	C₂×D₄₃	1	2	yes	complemented
317	C₂×C₄⋊C₄	—	43	2	no	—
318	C₂×C₄⋊C₄	—	43	1	no	—
319	C₂×C₄⋊C₄	—	43	2	no	—
320	C₂×C₂²⋊C₄	—	43	2	no	—
321	C₂×C₄²	—	43	1	no	—
322	C₂⁴	—	43	2	no	—
323	#41	—	86	8	no	—
324	#41	—	172	4	no	—
325	#41	—	172	4	no	—
326	C₂×Q₈	—	43	2	no	—
327	C₂×Q₈	—	43	2	no	—
328	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
329	C₂×D₄	—	43	2	no	—
330	C₂×D₄	—	43	2	no	—
331	C₂×D₄	—	43	2	no	—
332	C₂×D₄	—	43	2	no	—
333	C₂×D₄	—	43	4	no	—
334	C₂×D₄	—	43	4	no	—
335	C₂×D₄	—	43	2	no	—
336	C₂×D₄	—	43	1	no	—
337	C₂×D₄	—	43	1	no	—
338	C₂×D₄	—	43	4	no	—
339	C₂×D₄	—	86	4	no	—
340	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
341	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
342	C₂×D₄	C₂²×D₄₃	1	4	yes	—
343	C₂²×C₄	—	43	1	no	—
344	C₂²×C₄	—	43	4	no	—
345	C₂²×C₄	—	43	2	no	—
346	C₂²×C₄	—	43	1	no	—
347	C₂²×C₄	—	43	2	no	—
348	C₂²×C₄	—	43	2	no	—
349	C₂²×C₄	—	43	1	no	—
350	C₂²×C₄	—	43	2	no	—
351	C₂²×C₄	—	43	4	no	—
352	C₂²×C₄	—	43	2	no	—
353	C₂²×C₄	—	172	4	no	—
354	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
355	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
356	C₄⋊C₄	—	43	1	no	—
357	C₄⋊C₄	—	43	2	no	—
358	C₄⋊C₄	—	43	2	no	—
359	C₄⋊C₄	—	43	4	no	—
360	C₄⋊C₄	—	43	4	no	—
361	C₄⋊C₄	—	43	1	no	—
362	C₄⋊C₄	—	43	4	no	—
363	C₄⋊C₄	—	43	2	no	—
364	C₄⋊C₄	—	43	4	no	—
365	C₄⋊C₄	—	43	2	no	—
366	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
368	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
369	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
370	C₂²⋊C₄	—	43	2	no	—
371	C₂²⋊C₄	—	43	2	no	—
372	C₂²⋊C₄	—	43	4	no	—
373	C₂²⋊C₄	—	43	2	no	—
374	C₂²⋊C₄	—	43	2	no	—
375	C₂²⋊C₄	—	43	4	no	—
376	C₂²⋊C₄	—	43	4	no	—
377	C₂²⋊C₄	—	43	4	no	—
378	C₂²⋊C₄	—	43	2	no	—
379	C₂²⋊C₄	—	43	4	no	—
380	C₂²⋊C₄	—	43	2	no	—
381	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
382	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
383	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
384	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
385	C₄²	—	43	1	no	—
386	C₄²	—	43	1	no	—
387	C₄²	—	43	1	no	—
388	C₄²	—	43	4	no	—
389	C₄²	—	43	4	no	—
390	C₄²	C₂²×D₄₃	1	1	yes	characteristic
391	C₄²	C₂²×D₄₃	1	4	yes	—
392	C₂³	—	43	1	no	—
393	C₂³	—	43	2	no	—
394	C₂³	—	43	2	no	—
395	C₂³	—	86	4	no	—
396	C₂³	—	172	2	no	—
397	C₂³	—	172	2	no	—
398	C₂³	C₂³×D₄₃	1	2	yes	—
399	C₂³	C₂³×D₄₃	1	2	yes	—
400	Q₈	—	4	2	no	—
401	Q₈	—	86	4	no	—
402	Q₈	—	86	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	86	4	no	—
407	D₄	—	86	4	no	—
408	D₄	—	86	4	no	—
409	D₄	—	86	4	no	—
410	D₄	—	86	2	no	—
411	D₄	—	86	2	no	—
412	D₄	—	172	4	no	—
413	D₄	—	172	4	no	—
414	D₄	—	172	4	no	—
415	D₄	—	172	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	43	1	no	—
419	C₂×C₄	—	43	4	no	—
420	C₂×C₄	—	43	2	no	—
421	C₂×C₄	—	43	1	no	—
422	C₂×C₄	—	43	1	no	—
423	C₂×C₄	—	43	2	no	—
424	C₂×C₄	—	43	4	no	—
425	C₂×C₄	—	86	4	no	—
426	C₂×C₄	—	86	2	no	—
427	C₂×C₄	—	86	4	no	—
428	C₂×C₄	—	172	2	no	—
429	C₂×C₄	—	172	2	no	—
430	C₂×C₄	—	172	4	no	—
431	C₂×C₄	—	172	1	no	—
432	C₂×C₄	—	172	2	no	—
433	C₂×C₄	—	172	4	no	—
434	C₂×C₄	C₂³×D₄₃	1	4	yes	—
435	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂³×D₄₃	1	2	yes	—
437	C₂×C₄	C₂³×D₄₃	1	2	yes	—
438	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	43	2	no	—
447	C₂²	—	86	1	no	—
448	C₂²	—	86	1	no	—
449	C₂²	—	86	2	no	—
450	C₂²	—	86	2	no	—
451	C₂²	—	86	2	no	—
452	C₂²	—	86	2	no	—
453	C₂²	—	86	2	no	—
454	C₂²	—	86	2	no	—
455	C₂²	—	172	8	no	—
456	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	4	no	—
461	C₄	—	43	2	no	—
462	C₄	—	86	2	no	—
463	C₄	—	86	1	no	—
464	C₄	—	86	2	no	—
465	C₄	—	86	4	no	—
466	C₄	—	86	1	no	—
467	C₄	#41×D₄₃	1	2	yes	—
468	C₄	#13063371	1	2	yes	—
469	C₂	—	4	2	no	—
470	C₂	—	4	2	no	—
471	C₂	—	86	2	no	—
472	C₂	—	172	2	no	—
473	C₂	—	172	2	no	—
474	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
475	C₂	C₂×#13063371	1	1	yes	characteristic
476	C₂	#14583734	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#555	C₂
hypercenter	#555	D₄₃
hypocenter	C₄₃	#3506
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #14583631	C₂	semidirect
2. #14583617	C₂	semidirect
3. #14583615	C₂	semidirect
4. #14583601	C₂	semidirect
5. #14583593	C₂	semidirect
6. #14583567	C₂	semidirect
7. #14583554	C₂	semidirect
8. #14583553	C₂	semidirect
9. #14583483	C₂	semidirect
10. #14583465	C₂	semidirect
11. #14583454	C₂	semidirect
12. #14583446	C₂	semidirect
13. #14583411	C₂	semidirect
14. #14583409	C₂	semidirect
15. #14583379	C₂	semidirect
16. C₄×D₄×D₄₃	C₂	semidirect
17. C₄₃×#555	C₂	semidirect
19. C₂×#10621898	C₂²	semidirect
20. C₂×#10621900	C₂²	semidirect
23. #13063325	C₂²	semidirect
24. #13063324	C₂²	semidirect
26. #13063321	C₂²	semidirect
27. #13063319	C₂²	semidirect
28. #13063318	C₂²	semidirect
29. #13063316	C₂²	semidirect
30. #13063314	C₂²	semidirect
32. #13063311	C₂²	semidirect
33. #13063309	C₂²	semidirect
34. #13063309	C₂²	semidirect
35. #13063307	C₂²	semidirect
36. #13063307	C₂²	semidirect
38. #13063305	C₂²	semidirect
39. #13063304	C₂²	semidirect
43. #13063300	C₂²	semidirect
46. #13063298	C₂²	semidirect
47. #13063297	C₂²	semidirect
52. Q₈×Dic₄₃	C₂²	semidirect
53. C₄×Dic₈₆	C₂²	semidirect
54. #13063290	C₂²	semidirect
57. C₄×D₁₇₂	C₂²	semidirect
58. C₄×D₁₇₂	C₂²	semidirect
60. D₄×Dic₄₃	C₂²	semidirect
63. C₄×C₂²⋊D₄₃	C₂²	semidirect
66. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
68. #13063283	C₂²	semidirect
69. #13063283	C₂²	semidirect
70. C₂×C₄⋊Dic₄₃	C₂²	semidirect
72. C₄⋊C₄×D₄₃	C₂²	semidirect
75. C₄⋊Q₈×C₄₃	C₂²	semidirect
76. #124×C₄₃	C₂²	semidirect
78. #121×C₄₃	C₂²	semidirect
80. C₄×D₄×C₄₃	C₂²	semidirect
81. #117×C₄₃	C₂²	semidirect
82. #117×C₄₃	C₂²	semidirect
198. C₄×D₄₃	#41	semidirect
242. #555	D₄₃	semidirect
256. C₄₃	#3506	semidirect
264. C₄⋊Q₈	C₂×D₄₃	semidirect
273. #124	C₂×D₄₃	semidirect
292. #121	C₂×D₄₃	semidirect
311. C₄×D₄	C₂×D₄₃	semidirect
315. #117	C₂×D₄₃	semidirect
316. #117	C₂×D₄₃	semidirect