Subgroups — #19148478

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	#14583627	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583624	C₂	1	2	yes	maximal, complemented
3	#14583623	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583622	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583621	C₂	1	2	yes	maximal, complemented
6	#14583590	C₂	1	2	yes	maximal, complemented
7	#14583587	C₂	1	2	yes	maximal, complemented
8	#14583581	C₂	1	4	yes	maximal, complemented
9	#14583508	C₂	1	4	yes	maximal, complemented
10	#14583474	C₂	1	2	yes	maximal
11	#14583455	C₂	1	2	yes	maximal, complemented
12	#14583453	C₂	1	2	yes	maximal, complemented
13	#14583453	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583375	C₂	1	2	yes	maximal, complemented
16	C₄×#10621902	C₂	1	1	yes	maximal, characteristic
17	C₄₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621902	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₄₃	C₂²	1	2	yes	—
20	#13063325	C₂²	1	1	yes	characteristic
21	#13063324	C₂²	1	2	yes	—
22	#13063324	C₂²	1	2	yes	—
23	#13063324	C₂²	1	1	yes	characteristic
24	#13063323	C₂²	1	2	yes	—
25	#13063323	C₂²	1	2	yes	—
26	#13063323	C₂²	1	1	yes	characteristic
27	#13063320	C₂²	1	4	yes	—
28	#13063320	C₂²	1	4	yes	—
29	#13063320	C₂²	1	4	yes	—
30	#13063319	C₂²	1	4	yes	—
31	#13063317	C₂²	1	2	yes	—
32	#13063316	C₂²	1	4	yes	—
33	#13063315	C₂²	1	4	yes	—
34	#13063315	C₂²	1	4	yes	—
35	#13063315	C₂²	1	4	yes	—
36	#13063315	C₂²	1	2	yes	—
37	#13063314	C₂²	1	2	yes	—
38	#13063313	C₂²	1	2	yes	—
39	#13063310	C₂²	1	4	yes	—
40	#13063310	C₂²	1	4	yes	—
41	#13063305	C₂²	1	1	yes	characteristic
42	#13063305	C₂²	1	2	yes	—
43	#13063303	C₂²	1	2	yes	—
44	#13063303	C₂²	1	4	yes	—
45	#13063303	C₂²	1	4	yes	—
46	#13063303	C₂²	1	4	yes	—
47	#13063301	C₂²	1	1	yes	characteristic
48	#13063301	C₂²	1	2	yes	—
49	Q₈×Dic₄₃	C₂²	1	2	yes	—
50	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
51	C₄×Dic₈₆	C₂²	1	2	yes	—
52	C₄×Dic₈₆	C₂²	1	2	yes	—
53	C₄×Dic₈₆	C₂²	1	2	yes	—
54	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
55	C₄×Dic₈₆	C₂²	1	4	yes	—
56	#13063290	C₂²	1	4	yes	—
57	#13063290	C₂²	1	2	yes	—
58	#13063290	C₂²	1	4	yes	—
59	C₄×D₁₇₂	C₂²	1	2	yes	—
60	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
61	#13063287	C₂²	1	2	yes	—
62	#13063287	C₂²	1	1	yes	characteristic
63	#13063283	C₂²	1	4	yes	—
64	#13063283	C₂²	1	2	yes	—
65	#13063283	C₂²	1	2	yes	—
66	#13063283	C₂²	1	1	yes	characteristic
67	#13063283	C₂²	1	2	yes	—
68	#13063282	C₂²	1	4	yes	—
69	#13063282	C₂²	1	4	yes	—
70	#13063282	C₂²	1	2	yes	—
71	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
72	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
73	C₄²×D₄₃	C₂²	1	1	yes	characteristic
74	C₄²×D₄₃	C₂²	1	2	yes	—
75	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
76	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
77	#125×C₄₃	C₂²	1	4	yes	—
78	#125×C₄₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₄₃	C₂²	1	2	yes	—
80	C₄×Q₈×C₄₃	C₂²	1	2	yes	—
81	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
82	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
83	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
85	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	#10621902	—	2	4	no	—
87	Q₈×D₄₃	—	2	8	no	—
88	C₂×D₁₇₂	C₂³	1	2	yes	—
89	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
90	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×D₄₃	C₂³	1	2	yes	—
93	C₂×C₄×D₄₃	C₂³	1	2	yes	—
94	C₂×C₄×D₄₃	C₂³	1	2	yes	—
95	C₂×C₄×D₄₃	C₂³	1	4	yes	—
96	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
97	C₂×Dic₈₆	C₂³	1	2	yes	—
98	C₂×Dic₈₆	C₂³	1	4	yes	—
99	C₂×Dic₈₆	C₂³	1	2	yes	—
100	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
101	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
104	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
105	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
106	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
107	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
108	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
109	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
110	C₄²×C₄₃	C₂³	1	2	yes	—
111	C₄²×C₄₃	C₂³	1	4	yes	—
112	C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	C₄²×C₄₃	C₂³	1	2	yes	—
114	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
115	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
116	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
117	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
123	C₄⋊Dic₄₃	C₂³	1	2	yes	—
124	C₄⋊Dic₄₃	C₂³	1	2	yes	—
125	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₄₃	C₂³	1	2	yes	—
128	C₄⋊Dic₄₃	C₂³	1	4	yes	—
129	C₄⋊Dic₄₃	C₂³	1	2	yes	—
130	Dic₄₃⋊C₄	C₂³	1	4	yes	—
131	Dic₄₃⋊C₄	C₂³	1	4	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	2	yes	—
137	Dic₄₃⋊C₄	C₂³	1	4	yes	—
138	Dic₄₃⋊C₄	C₂³	1	2	yes	—
139	Dic₄₃⋊C₄	C₂³	1	4	yes	—
140	Dic₄₃⋊C₄	C₂³	1	2	yes	—
141	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
142	C₄×Dic₄₃	C₂³	1	2	yes	—
143	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
144	C₄×Dic₄₃	C₂³	1	2	yes	—
145	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
146	C₄×Dic₄₃	C₂³	1	4	yes	—
147	C₄×Dic₄₃	C₂³	1	4	yes	—
148	C₄×Dic₄₃	C₂³	1	2	yes	—
149	C₄×Dic₄₃	C₂³	1	4	yes	—
150	C₂²×D₄₃	C₂⁴	1	2	yes	—
151	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
152	Q₈×C₄₃	—	2	4	no	—
153	Q₈×C₄₃	—	2	2	no	—
154	Q₈×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
156	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
157	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
158	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
160	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
161	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₄₃	C₂⁴	1	2	yes	—
164	C₂×Dic₄₃	C₂⁴	1	2	yes	—
165	C₂×Dic₄₃	C₂⁴	1	2	yes	—
166	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
167	C₂×Dic₄₃	C₂⁴	1	4	yes	—
168	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
169	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
170	D₁₇₂	—	2	4	no	—
171	D₁₇₂	—	2	2	no	—
172	C₄×D₄₃	—	2	8	no	—
173	C₄×D₄₃	—	2	2	no	—
174	C₄×D₄₃	—	2	4	no	—
175	C₄×D₄₃	—	2	4	no	—
176	C₄×D₄₃	—	2	2	no	—
177	C₄×D₄₃	—	2	4	no	—
178	C₄×D₄₃	#41	1	4	yes	—
179	Dic₈₆	—	2	4	no	—
180	Dic₈₆	—	2	2	no	—
181	Dic₈₆	—	2	8	no	—
182	Dic₈₆	—	2	4	no	—
183	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
184	C₂×D₄₃	—	2	1	no	—
185	C₂×D₄₃	—	2	1	no	—
186	C₂×D₄₃	—	2	2	no	—
187	C₂×D₄₃	—	2	2	no	—
188	C₂×D₄₃	—	2	2	no	—
189	C₂×D₄₃	C₂×#41	1	2	yes	—
190	C₄×C₄₃	—	2	4	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	2	no	—
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	C₂×#41	1	2	yes	—
197	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
198	Dic₄₃	—	2	4	no	—
199	Dic₄₃	—	2	2	no	—
200	Dic₄₃	—	2	2	no	—
201	Dic₄₃	—	2	2	no	—
202	Dic₄₃	—	2	1	no	—
203	Dic₄₃	C₂×#41	1	2	yes	—
204	Dic₄₃	2₋¹⁺⁴	1	2	yes	—
205	#3509	—	43	1	no	maximal, Sylow
206	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
207	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
209	D₄₃	—	2	2	no	—
210	D₄₃	—	4	2	no	—
211	#557	—	43	2	no	—
212	#557	—	43	1	no	—
213	#557	D₄₃	1	1	yes	characteristic, complemented
214	#556	—	43	1	no	—
215	#556	—	43	2	no	—
216	#556	—	43	1	no	—
217	#552	—	43	4	no	—
218	#552	—	43	2	no	—
219	#552	—	43	2	no	—
220	#541	—	43	4	no	—
221	#536	—	43	2	no	—
222	#533	—	43	2	no	—
223	#533	—	43	1	no	—
224	#533	—	43	2	no	—
225	C₂×C₄⋊Q₈	—	43	1	no	—
226	#519	—	43	2	no	—
227	C₄×#41	—	43	1	no	—
228	C₄₃	#3509	1	1	yes	characteristic, complemented, Sylow
229	C₂×#41	—	43	1	no	—
230	C₂²×Q₈	—	43	2	no	—
231	C₄⋊Q₈	—	43	2	no	—
232	C₄⋊Q₈	—	43	1	no	—
233	C₄⋊Q₈	—	43	2	no	—
234	C₄⋊Q₈	—	43	2	no	—
235	C₄⋊Q₈	—	43	2	no	—
236	C₄⋊Q₈	—	43	1	no	—
237	C₄⋊Q₈	—	43	1	no	—
238	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
239	C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
240	#126	—	43	4	no	—
241	#126	—	43	4	no	—
242	#126	—	43	4	no	—
243	#126	—	43	4	no	—
244	#125	—	43	2	no	—
245	#125	—	43	4	no	—
246	#125	—	43	4	no	—
247	#125	—	43	4	no	—
248	#125	—	43	4	no	—
249	#125	—	43	2	no	—
250	#125	C₂×D₄₃	1	2	yes	—
251	#125	C₂×D₄₃	1	4	yes	—
252	#124	—	43	2	no	—
253	#124	—	43	2	no	—
254	#123	—	43	4	no	—
255	#123	—	43	4	no	—
256	C₂²⋊Q₈	—	43	1	no	—
257	C₂²⋊Q₈	—	43	2	no	—
258	C₂²⋊Q₈	—	43	4	no	—
259	C₂²⋊Q₈	—	43	4	no	—
260	C₂²⋊Q₈	—	43	2	no	—
261	C₂²⋊Q₈	—	43	1	no	—
262	C₂²⋊Q₈	—	43	4	no	—
263	C₂²⋊Q₈	—	43	2	no	—
264	C₄×Q₈	—	43	1	no	—
265	C₄×Q₈	—	43	2	no	—
266	C₄×Q₈	—	43	4	no	—
267	C₄×Q₈	—	43	2	no	—
268	C₄×Q₈	—	43	4	no	—
269	C₄×Q₈	—	43	4	no	—
270	C₄×Q₈	—	43	2	no	—
271	C₄×Q₈	—	43	2	no	—
272	C₄×Q₈	—	43	2	no	—
273	C₄×Q₈	—	43	1	no	—
274	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
275	C₄×Q₈	C₂×D₄₃	1	2	yes	—
276	C₄×Q₈	C₂×D₄₃	1	2	yes	—
277	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
278	C₄×D₄	—	43	2	no	—
279	C₄×D₄	—	43	1	no	—
280	C₄×D₄	—	43	2	no	—
281	C₄×D₄	—	43	1	no	—
282	#117	—	43	1	no	—
283	#117	—	43	2	no	—
284	#117	—	43	4	no	—
285	#117	—	43	2	no	—
286	#117	—	43	2	no	—
287	#117	—	43	2	no	—
288	#117	—	43	4	no	—
289	#117	—	43	4	no	—
290	C₂×C₄⋊C₄	—	43	2	no	—
291	C₂×C₄⋊C₄	—	43	2	no	—
292	C₂×C₄²	—	43	1	no	—
293	C₂×C₄²	—	43	2	no	—
294	#41	—	86	4	no	—
295	C₂×Q₈	—	43	2	no	—
296	C₂×Q₈	—	43	1	no	—
297	C₂×Q₈	—	43	4	no	—
298	C₂×Q₈	—	43	2	no	—
299	C₂×Q₈	—	86	8	no	—
300	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
301	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
302	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
303	C₂×D₄	—	43	2	no	—
304	C₂×D₄	—	43	1	no	—
305	C₂²×C₄	—	43	1	no	—
306	C₂²×C₄	—	43	1	no	—
307	C₂²×C₄	—	43	1	no	—
308	C₂²×C₄	—	43	2	no	—
309	C₂²×C₄	—	43	2	no	—
310	C₂²×C₄	—	43	2	no	—
311	C₂²×C₄	—	43	4	no	—
312	C₄⋊C₄	—	43	4	no	—
313	C₄⋊C₄	—	43	2	no	—
314	C₄⋊C₄	—	43	4	no	—
315	C₄⋊C₄	—	43	2	no	—
316	C₄⋊C₄	—	43	2	no	—
317	C₄⋊C₄	—	43	1	no	—
318	C₄⋊C₄	—	43	1	no	—
319	C₄⋊C₄	—	43	2	no	—
320	C₄⋊C₄	—	43	2	no	—
321	C₄⋊C₄	—	43	2	no	—
322	C₄⋊C₄	—	43	4	no	—
323	C₄⋊C₄	—	43	4	no	—
324	C₄⋊C₄	—	43	4	no	—
325	C₄⋊C₄	—	43	4	no	—
326	C₄⋊C₄	—	43	4	no	—
327	C₄⋊C₄	—	43	2	no	—
328	C₄⋊C₄	—	43	2	no	—
329	C₄⋊C₄	—	43	2	no	—
330	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
331	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
332	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
333	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
334	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
335	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
336	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
337	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
338	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
339	C₂²⋊C₄	—	43	2	no	—
340	C₂²⋊C₄	—	43	2	no	—
341	C₂²⋊C₄	—	43	2	no	—
342	C₂²⋊C₄	—	43	2	no	—
343	C₂²⋊C₄	—	43	2	no	—
344	C₂²⋊C₄	—	43	4	no	—
345	C₂²⋊C₄	—	43	4	no	—
346	C₂²⋊C₄	—	43	4	no	—
347	C₂²⋊C₄	—	43	4	no	—
348	C₄²	—	43	1	no	—
349	C₄²	—	43	2	no	—
350	C₄²	—	43	1	no	—
351	C₄²	—	43	2	no	—
352	C₄²	—	43	1	no	—
353	C₄²	—	43	4	no	—
354	C₄²	—	43	4	no	—
355	C₄²	—	43	4	no	—
356	C₄²	—	43	2	no	—
357	C₄²	C₂²×D₄₃	1	2	yes	—
358	C₄²	C₂²×D₄₃	1	1	yes	characteristic
359	C₄²	C₂²×D₄₃	1	4	yes	—
360	C₄²	C₂²×D₄₃	1	2	yes	—
361	C₂³	—	43	1	no	—
362	C₂³	—	43	2	no	—
363	Q₈	—	2	4	no	—
364	Q₈	—	2	2	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	86	8	no	—
367	Q₈	—	86	4	no	—
368	Q₈	—	86	4	no	—
369	Q₈	—	86	2	no	—
370	D₄	—	86	4	no	—
371	D₄	—	86	2	no	—
372	C₂×C₄	—	43	1	no	—
373	C₂×C₄	—	43	1	no	—
374	C₂×C₄	—	43	4	no	—
375	C₂×C₄	—	43	2	no	—
376	C₂×C₄	—	43	2	no	—
377	C₂×C₄	—	43	2	no	—
378	C₂×C₄	—	43	1	no	—
379	C₂×C₄	—	43	4	no	—
380	C₂×C₄	—	86	4	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	86	4	no	—
383	C₂×C₄	—	86	8	no	—
384	C₂×C₄	—	86	2	no	—
385	C₂×C₄	—	86	4	no	—
386	C₂×C₄	C₂³×D₄₃	1	2	yes	—
387	C₂×C₄	C₂³×D₄₃	1	2	yes	—
388	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
389	C₂×C₄	C₂³×D₄₃	1	4	yes	—
390	C₂×C₄	C₂³×D₄₃	1	2	yes	—
391	C₂×C₄	C₂³×D₄₃	1	2	yes	—
392	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
394	C₂²	—	43	2	no	—
395	C₂²	—	86	1	no	—
396	C₂²	—	86	1	no	—
397	C₂²	—	86	2	no	—
398	C₂²	—	86	2	no	—
399	C₂²	—	86	2	no	—
400	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	43	2	no	—
408	C₄	—	43	2	no	—
409	C₄	—	86	4	no	—
410	C₄	—	86	2	no	—
411	C₄	—	86	2	no	—
412	C₄	—	86	1	no	—
413	C₄	—	86	2	no	—
414	C₄	#41×D₄₃	1	2	yes	—
415	C₄	#13063373	1	2	yes	—
416	C₂	—	86	2	no	—
417	C₂	—	172	2	no	—
418	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
419	C₂	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
420	C₂	C₂×#13063373	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#557	C₂
hypercenter	#557	D₄₃
hypocenter	C₄₃	#3509
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. #14583627	C₂	semidirect
2. #14583624	C₂	semidirect
3. #14583623	C₂	semidirect
4. #14583622	C₂	semidirect
5. #14583621	C₂	semidirect
6. #14583590	C₂	semidirect
7. #14583587	C₂	semidirect
8. #14583581	C₂	semidirect
9. #14583508	C₂	semidirect
11. #14583455	C₂	semidirect
12. #14583453	C₂	semidirect
13. #14583453	C₂	semidirect
14. C₄⋊Q₈×D₄₃	C₂	semidirect
15. #14583375	C₂	semidirect
17. C₄₃×#557	C₂	semidirect
213. #557	D₄₃	semidirect
228. C₄₃	#3509	semidirect