Subgroups — #19149068

Order 5504.

1022 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583646	C₂	1	4	yes	maximal, complemented
2	#14583634	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583631	C₂	1	2	yes	maximal, complemented
4	#14583628	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583605	C₂	1	2	yes	maximal, complemented
6	#14583570	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583558	C₂	1	2	yes	maximal, complemented
9	#14583554	C₂	1	2	yes	maximal, complemented
10	#14583522	C₂	1	2	yes	maximal, complemented
11	#14583520	C₂	1	2	yes	maximal, complemented
12	#14583502	C₂	1	2	yes	maximal, complemented
13	#14583490	C₂	1	4	yes	maximal, complemented
14	#14583475	C₂	1	2	yes	maximal, complemented
15	#14583456	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583449	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621898	C₂²	1	2	yes	—
19	C₂×#10621898	C₂²	1	2	yes	—
20	C₂²×Dic₈₆	C₂²	1	2	yes	—
21	#13063325	C₂²	1	2	yes	—
22	#13063325	C₂²	1	1	yes	characteristic
23	#13063325	C₂²	1	1	yes	characteristic
24	#13063325	C₂²	1	1	yes	characteristic
25	#13063324	C₂²	1	2	yes	—
26	#13063322	C₂²	1	1	yes	characteristic
27	#13063321	C₂²	1	2	yes	—
28	#13063320	C₂²	1	4	yes	—
29	#13063317	C₂²	1	2	yes	—
30	#13063316	C₂²	1	2	yes	—
31	#13063316	C₂²	1	4	yes	—
32	#13063314	C₂²	1	2	yes	—
33	#13063313	C₂²	1	2	yes	—
34	#13063313	C₂²	1	2	yes	—
35	#13063311	C₂²	1	4	yes	—
36	#13063311	C₂²	1	4	yes	—
37	#13063310	C₂²	1	4	yes	—
38	#13063309	C₂²	1	4	yes	—
39	#13063309	C₂²	1	4	yes	—
40	#13063307	C₂²	1	4	yes	—
41	#13063307	C₂²	1	4	yes	—
42	#13063307	C₂²	1	4	yes	—
43	#13063305	C₂²	1	4	yes	—
44	#13063305	C₂²	1	4	yes	—
45	#13063304	C₂²	1	1	yes	characteristic
46	#13063304	C₂²	1	2	yes	—
47	#13063304	C₂²	1	1	yes	characteristic
48	#13063304	C₂²	1	2	yes	—
49	#13063303	C₂²	1	4	yes	—
50	#13063303	C₂²	1	4	yes	—
51	#13063302	C₂²	1	4	yes	—
52	#13063299	C₂²	1	2	yes	—
53	#13063299	C₂²	1	2	yes	—
54	#13063299	C₂²	1	2	yes	—
55	#13063298	C₂²	1	4	yes	—
56	#13063297	C₂²	1	4	yes	—
57	#13063296	C₂²	1	4	yes	—
58	Q₈×Dic₄₃	C₂²	1	2	yes	—
59	C₄×Dic₈₆	C₂²	1	2	yes	—
60	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
61	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
62	C₄×Dic₈₆	C₂²	1	2	yes	—
63	C₄×D₁₇₂	C₂²	1	2	yes	—
64	C₄×D₁₇₂	C₂²	1	2	yes	—
65	C₄×D₁₇₂	C₂²	1	2	yes	—
66	D₄×Dic₄₃	C₂²	1	2	yes	—
67	#13063287	C₂²	1	2	yes	—
68	#13063287	C₂²	1	2	yes	—
69	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
70	#13063284	C₂²	1	2	yes	—
71	C₄⋊C₄×D₄₃	C₂²	1	4	yes	—
72	#126×C₄₃	C₂²	1	2	yes	—
73	#125×C₄₃	C₂²	1	1	yes	characteristic
74	#124×C₄₃	C₂²	1	1	yes	characteristic
75	#123×C₄₃	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
77	#121×C₄₃	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
79	C₄×D₄×C₄₃	C₂²	1	2	yes	—
80	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
81	#117×C₄₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
83	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₄₃	C₂³	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
93	C₂²×Dic₄₃	C₂³	1	4	yes	—
94	#10621898	—	4	4	no	—
95	#10621898	—	4	4	no	—
96	C₂×D₁₇₂	C₂³	1	2	yes	—
97	C₂×D₁₇₂	C₂³	1	2	yes	—
98	C₂×D₁₇₂	C₂³	1	2	yes	—
99	C₂×C₄×D₄₃	C₂³	1	4	yes	—
100	C₂×C₄×D₄₃	C₂³	1	4	yes	—
101	C₂×C₄×D₄₃	C₂³	1	4	yes	—
102	C₂×Dic₈₆	—	4	4	no	—
103	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
104	C₂×Dic₈₆	C₂³	1	2	yes	—
105	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
106	C₂×Dic₈₆	C₂³	1	2	yes	—
107	C₂×Dic₈₆	C₂³	1	4	yes	—
108	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
109	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
110	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
119	C₄²×C₄₃	C₂³	1	1	yes	characteristic
120	C₄²×C₄₃	C₂³	1	1	yes	characteristic
121	C₄²×C₄₃	C₂³	1	1	yes	characteristic
122	C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	C₄²×C₄₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
126	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
127	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
133	C₄⋊Dic₄₃	C₂³	1	4	yes	—
134	C₄⋊Dic₄₃	C₂³	1	2	yes	—
135	C₄⋊Dic₄₃	C₂³	1	2	yes	—
136	C₄⋊Dic₄₃	C₂³	1	2	yes	—
137	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₄₃	C₂³	1	2	yes	—
139	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₄₃	C₂³	1	2	yes	—
141	C₄⋊Dic₄₃	C₂³	1	4	yes	—
142	Dic₄₃⋊C₄	C₂³	1	2	yes	—
143	Dic₄₃⋊C₄	C₂³	1	4	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	2	yes	—
148	C₄×Dic₄₃	C₂³	1	2	yes	—
149	C₄×Dic₄₃	C₂³	1	2	yes	—
150	C₄×Dic₄₃	C₂³	1	4	yes	—
151	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₂³×C₄₃	C₂⁴	1	2	yes	—
153	C₂²×D₄₃	C₂⁴	1	4	yes	—
154	Q₈×C₄₃	—	2	2	no	—
155	D₄×C₄₃	—	2	2	no	—
156	D₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
170	C₂²⋊D₄₃	—	4	4	no	—
171	C₂²⋊D₄₃	—	4	4	no	—
172	C₂²⋊D₄₃	—	4	4	no	—
173	C₂×Dic₄₃	—	4	4	no	—
174	C₂×Dic₄₃	C₂⁴	1	2	yes	—
175	C₂×Dic₄₃	C₂⁴	1	2	yes	—
176	C₂×Dic₄₃	C₂⁴	1	2	yes	—
177	C₂×Dic₄₃	C₂⁴	1	4	yes	—
178	C₂×Dic₄₃	C₂⁴	1	2	yes	—
179	D₁₇₂	—	2	4	no	—
180	D₁₇₂	—	2	4	no	—
181	D₁₇₂	—	4	2	no	—
182	C₄×D₄₃	—	4	4	no	—
183	C₄×D₄₃	—	4	4	no	—
184	C₄×D₄₃	—	4	4	no	—
185	Dic₈₆	—	2	2	no	—
186	Dic₈₆	—	2	4	no	—
187	Dic₈₆	—	2	2	no	—
188	Dic₈₆	—	4	4	no	—
189	Dic₈₆	—	4	2	no	—
190	C₂²×C₄₃	—	2	2	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
197	C₂×D₄₃	—	2	4	no	—
198	C₂×D₄₃	—	2	4	no	—
199	C₂×D₄₃	—	2	4	no	—
200	C₄×C₄₃	—	2	2	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	—	2	2	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
208	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
209	Dic₄₃	—	2	2	no	—
210	Dic₄₃	—	2	4	no	—
211	Dic₄₃	—	2	2	no	—
212	Dic₄₃	—	2	2	no	—
213	Dic₄₃	—	2	2	no	—
214	#3554	—	43	1	no	maximal, Sylow
215	C₂×C₄₃	—	4	2	no	—
216	C₂×C₄₃	—	4	1	no	—
217	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×C₄₃	#585	1	1	yes	characteristic
220	D₄₃	—	4	4	no	—
221	#562	—	43	4	no	—
222	#559	—	43	2	no	—
223	#559	—	43	1	no	—
224	#557	—	43	1	no	—
225	#554	—	43	2	no	—
226	#550	—	43	1	no	—
227	D₄×Q₈	—	43	1	no	—
228	#548	—	43	2	no	—
229	#547	—	43	2	no	—
230	#542	—	43	2	no	—
231	#542	—	43	2	no	—
232	#540	—	43	2	no	—
233	#539	—	43	4	no	—
234	#536	—	43	2	no	—
235	#533	—	43	1	no	—
236	#532	—	43	1	no	—
237	#529	D₄₃	1	1	yes	characteristic, complemented
238	C₄₃	#3554	1	1	yes	characteristic, complemented, Sylow
239	C₂×#41	—	43	2	no	—
240	C₂×#41	—	43	2	no	—
241	C₂²×Q₈	—	43	2	no	—
242	C₄⋊Q₈	—	43	2	no	—
243	C₄⋊Q₈	—	43	1	no	—
244	C₄⋊Q₈	—	43	1	no	—
245	C₄⋊Q₈	—	43	1	no	—
246	C₄⋊Q₈	—	43	2	no	—
247	#127	—	43	2	no	—
248	#127	—	43	1	no	—
249	#126	—	43	4	no	—
250	#126	C₂×D₄₃	1	2	yes	—
251	#125	—	43	4	no	—
252	#125	—	43	2	no	—
253	#125	—	43	2	no	—
254	#125	C₂×D₄₃	1	1	yes	characteristic
255	#124	—	43	2	no	—
256	#124	—	43	4	no	—
257	#124	—	43	4	no	—
258	#124	—	43	2	no	—
259	#124	—	43	2	no	—
260	#124	C₂×D₄₃	1	1	yes	characteristic
261	#123	—	43	4	no	—
262	#123	—	43	4	no	—
263	#123	—	43	4	no	—
264	#123	—	43	4	no	—
265	#123	—	43	4	no	—
266	#123	—	43	4	no	—
267	#123	C₂×D₄₃	1	2	yes	—
268	C₂²⋊Q₈	—	43	1	no	—
269	C₂²⋊Q₈	—	43	1	no	—
270	C₂²⋊Q₈	—	43	2	no	—
271	C₂²⋊Q₈	—	43	2	no	—
272	C₂²⋊Q₈	—	43	4	no	—
273	C₂²⋊Q₈	—	43	4	no	—
274	C₂²⋊Q₈	—	43	4	no	—
275	C₂²⋊Q₈	—	43	4	no	—
276	C₂²⋊Q₈	—	43	4	no	—
277	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
278	#121	—	43	4	no	—
279	#121	—	43	4	no	—
280	#121	—	43	2	no	—
281	#121	—	43	2	no	—
282	#121	—	43	2	no	—
283	#121	—	43	4	no	—
284	#121	C₂×D₄₃	1	1	yes	characteristic
285	C₄×Q₈	—	43	2	no	—
286	C₄×Q₈	—	43	1	no	—
287	C₄×Q₈	—	43	1	no	—
288	C₄×Q₈	—	43	2	no	—
289	C₄×Q₈	—	43	2	no	—
290	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
291	C₄×D₄	—	43	2	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	43	2	no	—
294	C₄×D₄	—	43	4	no	—
295	C₄×D₄	—	43	2	no	—
296	C₄×D₄	—	43	2	no	—
297	C₄×D₄	—	43	2	no	—
298	C₄×D₄	C₂×D₄₃	1	2	yes	—
299	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
300	#117	—	43	2	no	—
301	#117	C₂×D₄₃	1	2	yes	—
302	C₂×C₄⋊C₄	—	43	4	no	—
303	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
304	#41	—	172	4	no	—
305	#41	—	172	4	no	—
306	C₂×Q₈	—	43	1	no	—
307	C₂×Q₈	—	43	2	no	—
308	C₂×Q₈	—	43	1	no	—
309	C₂×Q₈	—	43	2	no	—
310	C₂×Q₈	—	43	4	no	—
311	C₂×Q₈	—	172	4	no	—
312	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
313	C₂×D₄	—	43	4	no	—
314	C₂×D₄	—	43	4	no	—
315	C₂×D₄	—	43	4	no	—
316	C₂×D₄	—	43	2	no	—
317	C₂×D₄	—	43	2	no	—
318	C₂×D₄	—	43	2	no	—
319	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
320	C₂×D₄	C₂²×D₄₃	1	2	yes	—
321	C₂²×C₄	—	43	4	no	—
322	C₂²×C₄	—	43	4	no	—
323	C₂²×C₄	—	43	4	no	—
324	C₂²×C₄	—	43	4	no	—
325	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
328	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
329	C₄⋊C₄	—	43	2	no	—
330	C₄⋊C₄	—	43	4	no	—
331	C₄⋊C₄	—	43	4	no	—
332	C₄⋊C₄	—	43	2	no	—
333	C₄⋊C₄	—	43	2	no	—
334	C₄⋊C₄	—	43	2	no	—
335	C₄⋊C₄	—	43	2	no	—
336	C₄⋊C₄	—	43	1	no	—
337	C₄⋊C₄	—	43	2	no	—
338	C₄⋊C₄	—	43	1	no	—
339	C₄⋊C₄	—	43	2	no	—
340	C₄⋊C₄	—	43	4	no	—
341	C₄⋊C₄	—	43	2	no	—
342	C₄⋊C₄	—	43	2	no	—
343	C₄⋊C₄	—	43	4	no	—
344	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
345	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
346	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
347	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
350	C₂²⋊C₄	—	43	2	no	—
351	C₂²⋊C₄	—	43	2	no	—
352	C₂²⋊C₄	—	43	4	no	—
353	C₂²⋊C₄	—	43	4	no	—
354	C₂²⋊C₄	—	43	4	no	—
355	C₂²⋊C₄	—	43	4	no	—
356	C₂²⋊C₄	—	43	4	no	—
357	C₂²⋊C₄	—	43	4	no	—
358	C₂²⋊C₄	—	43	4	no	—
359	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
360	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
361	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
362	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
364	C₄²	—	43	2	no	—
365	C₄²	—	43	2	no	—
366	C₄²	—	43	4	no	—
367	C₄²	C₂²×D₄₃	1	1	yes	characteristic
368	C₄²	C₂²×D₄₃	1	1	yes	characteristic
369	C₄²	C₂²×D₄₃	1	1	yes	characteristic
370	C₄²	C₂²×D₄₃	1	1	yes	characteristic
371	C₄²	C₂²×D₄₃	1	2	yes	—
372	C₂³	—	43	4	no	—
373	C₂³	C₂³×D₄₃	1	1	yes	characteristic
374	C₂³	C₂³×D₄₃	1	2	yes	—
375	Q₈	—	2	2	no	—
376	Q₈	—	86	2	no	—
377	Q₈	—	86	4	no	—
378	Q₈	—	86	2	no	—
379	Q₈	—	172	4	no	—
380	Q₈	—	172	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	86	4	no	—
384	D₄	—	86	4	no	—
385	D₄	—	172	2	no	—
386	D₄	—	172	4	no	—
387	D₄	—	172	4	no	—
388	D₄	—	172	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	43	2	no	—
394	C₂×C₄	—	43	2	no	—
395	C₂×C₄	—	43	2	no	—
396	C₂×C₄	—	43	4	no	—
397	C₂×C₄	—	43	2	no	—
398	C₂×C₄	—	172	4	no	—
399	C₂×C₄	—	172	4	no	—
400	C₂×C₄	—	172	4	no	—
401	C₂×C₄	—	172	4	no	—
402	C₂×C₄	C₂³×D₄₃	1	2	yes	—
403	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
406	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂³×D₄₃	1	2	yes	—
408	C₂×C₄	C₂³×D₄₃	1	2	yes	—
409	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	86	4	no	—
418	C₂²	—	86	4	no	—
419	C₂²	—	86	4	no	—
420	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	86	2	no	—
429	C₄	—	86	4	no	—
430	C₄	—	86	2	no	—
431	C₄	—	86	2	no	—
432	C₄	—	86	2	no	—
433	C₄	#13063371	1	2	yes	—
434	C₄	#13063372	1	2	yes	—
435	C₂	—	4	2	no	—
436	C₂	—	4	1	no	—
437	C₂	—	172	4	no	—
438	C₂	C₂×#13063371	1	1	yes	characteristic
439	C₂	C₂×#13063372	1	1	yes	characteristic
440	C₂	#14583735	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#529	C₂
hypercenter	#529	D₄₃
hypocenter	C₄₃	#3554
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #14583646	C₂	semidirect
2. #14583634	C₂	semidirect
3. #14583631	C₂	semidirect
4. #14583628	C₂	semidirect
5. #14583605	C₂	semidirect
6. #14583570	C₂	semidirect
7. D₄×Dic₈₆	C₂	semidirect
8. #14583558	C₂	semidirect
9. #14583554	C₂	semidirect
10. #14583522	C₂	semidirect
11. #14583520	C₂	semidirect
12. #14583502	C₂	semidirect
13. #14583490	C₂	semidirect
14. #14583475	C₂	semidirect
15. #14583456	C₂	semidirect
16. #14583449	C₂	semidirect
17. C₄₃×#529	C₂	semidirect
237. #529	D₄₃	semidirect
238. C₄₃	#3554	semidirect