Subgroups — #19148689

Order 5504.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583628	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583627	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583626	C₂	1	2	yes	maximal, complemented
4	#14583619	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583618	C₂	1	2	yes	maximal, complemented
6	#14583589	C₂	1	2	yes	maximal, complemented
7	#14583586	C₂	1	4	yes	maximal, complemented
8	D₄×Dic₈₆	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583511	C₂	1	2	yes	maximal, complemented
11	#14583506	C₂	1	4	yes	maximal, complemented
12	#14583456	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583451	C₂	1	2	yes	maximal, complemented
14	#14583430	C₂	1	2	yes	maximal
15	#14583376	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#529	C₂	1	1	yes	maximal, characteristic
18	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
19	C₂²×Dic₈₆	C₂²	1	2	yes	—
20	#13063325	C₂²	1	1	yes	characteristic
21	#13063325	C₂²	1	2	yes	—
22	#13063325	C₂²	1	1	yes	characteristic
23	#13063324	C₂²	1	2	yes	—
24	#13063324	C₂²	1	4	yes	—
25	#13063323	C₂²	1	2	yes	—
26	#13063318	C₂²	1	4	yes	—
27	#13063318	C₂²	1	4	yes	—
28	#13063318	C₂²	1	4	yes	—
29	#13063318	C₂²	1	4	yes	—
30	#13063317	C₂²	1	2	yes	—
31	#13063317	C₂²	1	2	yes	—
32	#13063316	C₂²	1	4	yes	—
33	#13063316	C₂²	1	2	yes	—
34	#13063315	C₂²	1	4	yes	—
35	#13063315	C₂²	1	4	yes	—
36	#13063315	C₂²	1	4	yes	—
37	#13063315	C₂²	1	4	yes	—
38	#13063312	C₂²	1	2	yes	—
39	#13063306	C₂²	1	4	yes	—
40	#13063304	C₂²	1	2	yes	—
41	#13063304	C₂²	1	2	yes	—
42	#13063304	C₂²	1	2	yes	—
43	#13063304	C₂²	1	2	yes	—
44	#13063302	C₂²	1	4	yes	—
45	#13063302	C₂²	1	4	yes	—
46	#13063302	C₂²	1	4	yes	—
47	Q₈×Dic₄₃	C₂²	1	2	yes	—
48	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
49	C₄×Dic₈₆	C₂²	1	2	yes	—
50	C₄×Dic₈₆	C₂²	1	2	yes	—
51	C₄×Dic₈₆	C₂²	1	2	yes	—
52	C₄×Dic₈₆	C₂²	1	2	yes	—
53	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
54	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
55	C₄×Dic₈₆	C₂²	1	2	yes	—
56	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
57	C₄×Dic₈₆	C₂²	1	2	yes	—
58	#13063290	C₂²	1	4	yes	—
59	#13063290	C₂²	1	2	yes	—
60	#13063290	C₂²	1	2	yes	—
61	#13063290	C₂²	1	4	yes	—
62	D₄×Dic₄₃	C₂²	1	4	yes	—
63	D₄×Dic₄₃	C₂²	1	2	yes	—
64	#13063284	C₂²	1	2	yes	—
65	#13063284	C₂²	1	2	yes	—
66	#13063281	C₂²	1	4	yes	—
67	#13063281	C₂²	1	4	yes	—
68	#13063281	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
70	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
71	C₂×C₄×Dic₄₃	C₂²	1	2	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	2	yes	—
85	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
90	C₂²×Dic₄₃	C₂³	1	2	yes	—
91	C₂²×Dic₄₃	C₂³	1	2	yes	—
92	C₂²×Dic₄₃	C₂³	1	4	yes	—
93	C₂×Dic₈₆	—	2	4	no	—
94	C₂×Dic₈₆	—	2	8	no	—
95	C₂×Dic₈₆	C₂³	1	2	yes	—
96	C₂×Dic₈₆	C₂³	1	4	yes	—
97	C₂×Dic₈₆	C₂³	1	2	yes	—
98	C₂×Dic₈₆	C₂³	1	2	yes	—
99	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
100	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
101	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
102	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
103	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
105	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
107	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
108	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	C₄²×C₄₃	C₂³	1	1	yes	characteristic
114	C₄²×C₄₃	C₂³	1	1	yes	characteristic
115	C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₄²×C₄₃	C₂³	1	2	yes	—
117	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
118	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
119	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
121	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
122	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
123	C₄⋊Dic₄₃	C₂³	1	2	yes	—
124	C₄⋊Dic₄₃	C₂³	1	2	yes	—
125	C₄⋊Dic₄₃	C₂³	1	2	yes	—
126	C₄⋊Dic₄₃	C₂³	1	2	yes	—
127	C₄⋊Dic₄₃	C₂³	1	2	yes	—
128	C₄⋊Dic₄₃	C₂³	1	4	yes	—
129	C₄⋊Dic₄₃	C₂³	1	4	yes	—
130	Dic₄₃⋊C₄	C₂³	1	2	yes	—
131	Dic₄₃⋊C₄	C₂³	1	2	yes	—
132	Dic₄₃⋊C₄	C₂³	1	2	yes	—
133	Dic₄₃⋊C₄	C₂³	1	2	yes	—
134	Dic₄₃⋊C₄	C₂³	1	4	yes	—
135	Dic₄₃⋊C₄	C₂³	1	4	yes	—
136	Dic₄₃⋊C₄	C₂³	1	4	yes	—
137	Dic₄₃⋊C₄	C₂³	1	4	yes	—
138	Dic₄₃⋊C₄	C₂³	1	4	yes	—
139	Dic₄₃⋊C₄	C₂³	1	4	yes	—
140	Dic₄₃⋊C₄	C₂³	1	4	yes	—
141	Dic₄₃⋊C₄	C₂³	1	4	yes	—
142	C₄×Dic₄₃	C₂³	1	2	yes	—
143	C₄×Dic₄₃	C₂³	1	2	yes	—
144	C₄×Dic₄₃	C₂³	1	2	yes	—
145	C₄×Dic₄₃	C₂³	1	2	yes	—
146	C₄×Dic₄₃	C₂³	1	4	yes	—
147	C₄×Dic₄₃	C₂³	1	4	yes	—
148	C₄×Dic₄₃	C₂³	1	4	yes	—
149	C₄×Dic₄₃	C₂³	1	4	yes	—
150	C₂³×C₄₃	C₂⁴	1	2	yes	—
151	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
152	Q₈×C₄₃	—	2	2	no	—
153	D₄×C₄₃	—	2	4	no	—
154	D₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₄₃	—	2	4	no	—
169	C₂×Dic₄₃	—	2	4	no	—
170	C₂×Dic₄₃	—	2	8	no	—
171	C₂×Dic₄₃	C₂⁴	1	2	yes	—
172	C₂×Dic₄₃	C₂⁴	1	4	yes	—
173	C₂×Dic₄₃	C₂⁴	1	2	yes	—
174	C₂×Dic₄₃	C₂⁴	1	2	yes	—
175	C₂×Dic₄₃	C₂⁴	1	4	yes	—
176	C₂×Dic₄₃	C₂⁴	1	2	yes	—
177	Dic₈₆	—	2	2	no	—
178	Dic₈₆	—	2	4	no	—
179	Dic₈₆	—	2	4	no	—
180	Dic₈₆	—	2	8	no	—
181	Dic₈₆	—	2	4	no	—
182	Dic₈₆	#41	1	4	yes	—
183	C₂²×C₄₃	—	2	1	no	—
184	C₂²×C₄₃	—	2	1	no	—
185	C₂²×C₄₃	—	2	2	no	—
186	C₂²×C₄₃	—	2	2	no	—
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
189	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	—	2	1	no	—
192	C₄×C₄₃	—	2	1	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	2	2	no	—
197	C₄×C₄₃	C₂×#41	1	2	yes	—
198	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
199	Dic₄₃	—	2	4	no	—
200	Dic₄₃	—	2	2	no	—
201	Dic₄₃	—	2	4	no	—
202	Dic₄₃	—	2	2	no	—
203	Dic₄₃	—	2	2	no	—
204	Dic₄₃	C₂×#41	1	4	yes	—
205	#3523	—	43	1	no	maximal, Sylow
206	C₂×C₄₃	—	2	2	no	—
207	C₂×C₄₃	—	4	2	no	—
208	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
209	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
211	#557	—	43	2	no	—
212	#557	—	43	1	no	—
213	#557	—	43	1	no	—
214	#556	—	43	2	no	—
215	#556	—	43	1	no	—
216	#552	—	43	4	no	—
217	#552	—	43	2	no	—
218	D₄×Q₈	—	43	2	no	—
219	D₄×Q₈	—	43	1	no	—
220	#541	—	43	4	no	—
221	#541	—	43	2	no	—
222	#533	—	43	2	no	—
223	#533	—	43	1	no	—
224	#529	—	43	2	no	—
225	#529	D₄₃	1	1	yes	characteristic
226	#519	—	43	2	no	—
227	C₂×C₄×Q₈	—	43	1	no	—
228	C₄₃	#3523	1	1	yes	characteristic, complemented, Sylow
229	C₂²×Q₈	—	43	1	no	—
230	C₂²×Q₈	—	43	2	no	—
231	C₄⋊Q₈	—	43	2	no	—
232	C₄⋊Q₈	—	43	2	no	—
233	C₄⋊Q₈	—	43	4	no	—
234	C₄⋊Q₈	—	43	1	no	—
235	C₄⋊Q₈	—	43	1	no	—
236	C₄⋊Q₈	—	43	2	no	—
237	#126	—	43	4	no	—
238	#126	—	43	4	no	—
239	#126	—	43	4	no	—
240	#126	—	43	4	no	—
241	#126	C₂×D₄₃	1	2	yes	—
242	#125	—	43	2	no	—
243	#125	—	43	4	no	—
244	#125	—	43	4	no	—
245	#125	—	43	4	no	—
246	#125	—	43	4	no	—
247	#125	—	43	4	no	—
248	#125	—	43	2	no	—
249	#125	—	43	2	no	—
250	#125	C₂×D₄₃	1	1	yes	characteristic
251	#124	—	43	2	no	—
252	#124	C₂×D₄₃	1	1	yes	characteristic
253	#123	—	43	4	no	—
254	#123	C₂×D₄₃	1	2	yes	—
255	C₂²⋊Q₈	—	43	2	no	—
256	C₂²⋊Q₈	—	43	2	no	—
257	C₂²⋊Q₈	—	43	2	no	—
258	C₂²⋊Q₈	—	43	2	no	—
259	C₂²⋊Q₈	—	43	4	no	—
260	C₂²⋊Q₈	—	43	4	no	—
261	C₂²⋊Q₈	—	43	4	no	—
262	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
263	#121	C₂×D₄₃	1	1	yes	characteristic
264	C₄×Q₈	—	43	2	no	—
265	C₄×Q₈	—	43	4	no	—
266	C₄×Q₈	—	43	4	no	—
267	C₄×Q₈	—	43	2	no	—
268	C₄×Q₈	—	43	2	no	—
269	C₄×Q₈	—	43	1	no	—
270	C₄×Q₈	—	43	2	no	—
271	C₄×Q₈	—	43	1	no	—
272	C₄×Q₈	—	43	1	no	—
273	C₄×Q₈	—	43	2	no	—
274	C₄×Q₈	—	43	1	no	—
275	C₄×Q₈	—	43	2	no	—
276	C₄×Q₈	—	43	2	no	—
277	C₄×Q₈	—	43	2	no	—
278	C₄×Q₈	—	43	2	no	—
279	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
280	C₄×D₄	—	43	4	no	—
281	C₄×D₄	—	43	2	no	—
282	C₄×D₄	C₂×D₄₃	1	2	yes	—
283	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
284	#117	—	43	2	no	—
285	#117	—	43	2	no	—
286	#117	—	43	4	no	—
287	#117	—	43	4	no	—
288	#117	—	43	4	no	—
289	#117	C₂×D₄₃	1	2	yes	—
290	C₂×C₄⋊C₄	—	43	2	no	—
291	C₂×C₄⋊C₄	—	43	1	no	—
292	C₂×C₄²	—	43	2	no	—
293	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
294	C₂×Q₈	—	43	1	no	—
295	C₂×Q₈	—	43	2	no	—
296	C₂×Q₈	—	43	4	no	—
297	C₂×Q₈	—	43	2	no	—
298	C₂×Q₈	—	43	1	no	—
299	C₂×Q₈	—	43	2	no	—
300	C₂×Q₈	—	86	4	no	—
301	C₂×Q₈	—	86	8	no	—
302	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
303	C₂×D₄	C₂²×D₄₃	1	2	yes	—
304	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
305	C₂²×C₄	—	43	2	no	—
306	C₂²×C₄	—	43	2	no	—
307	C₂²×C₄	—	43	4	no	—
308	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
312	C₄⋊C₄	—	43	2	no	—
313	C₄⋊C₄	—	43	1	no	—
314	C₄⋊C₄	—	43	2	no	—
315	C₄⋊C₄	—	43	1	no	—
316	C₄⋊C₄	—	43	2	no	—
317	C₄⋊C₄	—	43	2	no	—
318	C₄⋊C₄	—	43	2	no	—
319	C₄⋊C₄	—	43	4	no	—
320	C₄⋊C₄	—	43	2	no	—
321	C₄⋊C₄	—	43	4	no	—
322	C₄⋊C₄	—	43	4	no	—
323	C₄⋊C₄	—	43	4	no	—
324	C₄⋊C₄	—	43	2	no	—
325	C₄⋊C₄	—	43	4	no	—
326	C₄⋊C₄	—	43	2	no	—
327	C₄⋊C₄	—	43	2	no	—
328	C₄⋊C₄	—	43	4	no	—
329	C₄⋊C₄	—	43	4	no	—
330	C₄⋊C₄	—	43	4	no	—
331	C₄⋊C₄	—	43	4	no	—
332	C₄⋊C₄	—	43	4	no	—
333	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
334	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
335	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
336	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
337	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
339	C₂²⋊C₄	—	43	4	no	—
340	C₂²⋊C₄	—	43	4	no	—
341	C₂²⋊C₄	—	43	4	no	—
342	C₂²⋊C₄	—	43	4	no	—
343	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
345	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
346	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
347	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
348	C₄²	—	43	2	no	—
349	C₄²	—	43	2	no	—
350	C₄²	—	43	2	no	—
351	C₄²	—	43	2	no	—
352	C₄²	—	43	4	no	—
353	C₄²	—	43	4	no	—
354	C₄²	—	43	4	no	—
355	C₄²	—	43	4	no	—
356	C₄²	C₂²×D₄₃	1	1	yes	characteristic
357	C₄²	C₂²×D₄₃	1	1	yes	characteristic
358	C₄²	C₂²×D₄₃	1	1	yes	characteristic
359	C₄²	C₂²×D₄₃	1	1	yes	characteristic
360	C₄²	C₂²×D₄₃	1	2	yes	—
361	C₂³	C₂³×D₄₃	1	2	yes	—
362	C₂³	C₂³×D₄₃	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	43	4	no	—
365	Q₈	—	86	8	no	—
366	Q₈	—	86	4	no	—
367	Q₈	—	86	2	no	—
368	Q₈	—	86	4	no	—
369	Q₈	—	86	4	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	43	2	no	—
377	C₂×C₄	—	43	2	no	—
378	C₂×C₄	—	43	4	no	—
379	C₂×C₄	—	43	2	no	—
380	C₂×C₄	—	43	2	no	—
381	C₂×C₄	—	43	4	no	—
382	C₂×C₄	—	86	4	no	—
383	C₂×C₄	—	86	8	no	—
384	C₂×C₄	—	86	4	no	—
385	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
386	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₄₃	1	2	yes	—
388	C₂×C₄	C₂³×D₄₃	1	2	yes	—
389	C₂×C₄	C₂³×D₄₃	1	2	yes	—
390	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	#13063372	1	2	yes	—
400	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	43	4	no	—
409	C₄	—	86	2	no	—
410	C₄	—	86	4	no	—
411	C₄	—	86	2	no	—
412	C₄	—	86	2	no	—
413	C₄	—	86	4	no	—
414	C₄	#41×D₄₃	1	2	yes	—
415	C₄	#13063372	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
419	C₂	C₂×#13063372	1	1	yes	characteristic
420	C₂	C₂×#13063372	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	#3523
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. #14583628	C₂	semidirect
2. #14583627	C₂	semidirect
3. #14583626	C₂	semidirect
4. #14583619	C₂	semidirect
5. #14583618	C₂	semidirect
6. #14583589	C₂	semidirect
7. #14583586	C₂	semidirect
8. D₄×Dic₈₆	C₂	semidirect
9. D₄×Dic₈₆	C₂	semidirect
10. #14583511	C₂	semidirect
11. #14583506	C₂	semidirect
12. #14583456	C₂	semidirect
13. #14583451	C₂	semidirect
15. #14583376	C₂	semidirect
16. C₂×C₄×Dic₈₆	C₂	semidirect
228. C₄₃	#3523	semidirect