Subgroups — #19148925

Order 5504.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583640	C₂	1	4	yes	maximal, complemented
2	#14583634	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583571	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583570	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583545	C₂	1	2	yes	maximal, complemented
6	#14583540	C₂	1	2	yes	maximal, complemented
7	D₄×D₁₇₂	C₂	1	2	yes	maximal, complemented
8	D₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583533	C₂	1	2	yes	maximal, complemented
10	#14583505	C₂	1	2	yes	maximal, complemented
11	#14583504	C₂	1	2	yes	maximal, complemented
12	#14583468	C₂	1	2	yes	maximal, complemented
13	#14583467	C₂	1	2	yes	maximal, complemented
14	#14583460	C₂	1	4	yes	maximal, complemented
15	C₂×#13063322	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621902	C₂²	1	2	yes	complemented
19	C₂×#10621898	C₂²	1	2	yes	complemented
20	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
21	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
22	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
23	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
24	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
25	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
26	#13063322	C₂²	1	1	yes	characteristic
27	#13063322	C₂²	1	1	yes	characteristic, complemented
28	#13063322	C₂²	1	2	yes	complemented
29	#13063322	C₂²	1	2	yes	complemented
30	#13063322	C₂²	1	2	yes	complemented
31	#13063322	C₂²	1	2	yes	complemented
32	#13063321	C₂²	1	2	yes	complemented
33	#13063319	C₂²	1	2	yes	complemented
34	#13063317	C₂²	1	1	yes	characteristic, complemented
35	#13063314	C₂²	1	2	yes	complemented
36	#13063313	C₂²	1	2	yes	complemented
37	#13063313	C₂²	1	1	yes	characteristic, complemented
38	#13063310	C₂²	1	4	yes	complemented
39	#13063310	C₂²	1	4	yes	complemented
40	#13063310	C₂²	1	4	yes	complemented
41	#13063310	C₂²	1	4	yes	complemented
42	#13063308	C₂²	1	2	yes	complemented
43	#13063304	C₂²	1	1	yes	characteristic, complemented
44	#13063300	C₂²	1	4	yes	complemented
45	#13063300	C₂²	1	2	yes	complemented
46	#13063300	C₂²	1	4	yes	complemented
47	#13063300	C₂²	1	4	yes	complemented
48	#13063300	C₂²	1	4	yes	complemented
49	#13063300	C₂²	1	2	yes	complemented
50	#13063299	C₂²	1	1	yes	characteristic
51	#13063299	C₂²	1	2	yes	complemented
52	#13063299	C₂²	1	2	yes	complemented
53	#13063298	C₂²	1	4	yes	complemented
54	#13063298	C₂²	1	4	yes	complemented
55	#13063298	C₂²	1	4	yes	complemented
56	#13063298	C₂²	1	4	yes	complemented
57	#13063295	C₂²	1	4	yes	complemented
58	#13063295	C₂²	1	4	yes	complemented
59	#13063295	C₂²	1	4	yes	complemented
60	#13063295	C₂²	1	4	yes	complemented
61	#13063295	C₂²	1	4	yes	complemented
62	#13063293	C₂²	1	4	yes	complemented
63	C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
64	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₁₇₂	C₂²	1	2	yes	complemented
66	C₄×D₁₇₂	C₂²	1	2	yes	complemented
67	#13063287	C₂²	1	2	yes	complemented
68	#13063287	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
70	#13063282	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
72	#126×C₄₃	C₂²	1	2	yes	complemented
73	#125×C₄₃	C₂²	1	1	yes	characteristic, complemented
74	#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
75	#123×C₄₃	C₂²	1	2	yes	complemented
76	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
77	#121×C₄₃	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
81	#117×C₄₃	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₄₃	C₂³	1	4	yes	—
84	C₂³×D₄₃	C₂³	1	4	yes	—
85	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₃	C₂³	1	2	yes	—
87	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
96	#10621902	—	4	4	no	—
97	D₄×D₄₃	—	4	8	no	—
98	D₄×D₄₃	—	4	4	no	—
99	#10621898	—	4	4	no	—
100	C₂×D₁₇₂	—	4	4	no	—
101	C₂×D₁₇₂	—	4	4	no	—
102	C₂×D₁₇₂	—	4	4	no	—
103	C₂×D₁₇₂	—	4	4	no	—
104	C₂×D₁₇₂	C₂³	1	2	yes	—
105	C₂×D₁₇₂	C₂³	1	2	yes	—
106	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
107	C₂×D₁₇₂	C₂³	1	2	yes	—
108	C₂×D₁₇₂	C₂³	1	2	yes	—
109	C₂×D₁₇₂	C₂³	1	4	yes	—
110	C₂×D₁₇₂	C₂³	1	4	yes	—
111	C₂×D₁₇₂	C₂³	1	2	yes	—
112	C₂×D₁₇₂	C₂³	1	4	yes	—
113	C₂×D₁₇₂	C₂³	1	4	yes	—
114	C₂×D₁₇₂	C₂³	1	4	yes	—
115	C₂×D₁₇₂	C₂³	1	4	yes	—
116	C₂×D₁₇₂	C₂³	1	2	yes	—
117	C₂×C₄×D₄₃	C₂³	1	2	yes	—
118	C₂×C₄×D₄₃	C₂³	1	4	yes	—
119	C₂×C₄×D₄₃	C₂³	1	4	yes	—
120	C₂×C₄×D₄₃	C₂³	1	4	yes	—
121	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
123	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
124	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
125	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
126	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
127	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
128	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
133	C₄²×C₄₃	C₂³	1	1	yes	characteristic
134	C₄²×C₄₃	C₂³	1	1	yes	characteristic
135	C₄²×C₄₃	C₂³	1	1	yes	characteristic
136	C₄²×C₄₃	C₂³	1	1	yes	characteristic
137	C₄²×C₄₃	C₂³	1	2	yes	—
138	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
139	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
141	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
142	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
143	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
144	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
145	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
146	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
147	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
148	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
149	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
151	Dic₄₃⋊C₄	C₂³	1	2	yes	—
152	Dic₄₃⋊C₄	C₂³	1	2	yes	—
153	Dic₄₃⋊C₄	C₂³	1	2	yes	—
154	Dic₄₃⋊C₄	C₂³	1	2	yes	—
155	C₄×Dic₄₃	C₂³	1	2	yes	—
156	C₂³×C₄₃	C₂⁴	1	2	yes	—
157	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
158	C₂²×D₄₃	—	2	8	no	—
159	C₂²×D₄₃	—	4	4	no	—
160	C₂²×D₄₃	—	4	4	no	—
161	C₂²×D₄₃	—	4	4	no	—
162	C₂²×D₄₃	—	4	4	no	—
163	C₂²×D₄₃	—	4	4	no	—
164	C₂²×D₄₃	C₂⁴	1	4	yes	—
165	C₂²×D₄₃	C₂⁴	1	2	yes	—
166	C₂²×D₄₃	C₂⁴	1	4	yes	—
167	Q₈×C₄₃	—	2	2	no	—
168	D₄×C₄₃	—	2	4	no	—
169	D₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
180	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
181	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
183	C₂²⋊D₄₃	—	2	4	no	—
184	C₂²⋊D₄₃	—	4	4	no	—
185	C₂²⋊D₄₃	—	4	4	no	—
186	C₂²⋊D₄₃	—	4	4	no	—
187	C₂×Dic₄₃	C₂⁴	1	2	yes	—
188	C₂×Dic₄₃	C₂⁴	1	2	yes	—
189	C₂×Dic₄₃	C₂⁴	1	2	yes	—
190	D₁₇₂	—	2	2	no	—
191	D₁₇₂	—	2	4	no	—
192	D₁₇₂	—	2	4	no	—
193	D₁₇₂	—	2	4	no	—
194	D₁₇₂	—	2	4	no	—
195	D₁₇₂	—	4	4	no	—
196	D₁₇₂	—	4	2	no	—
197	D₁₇₂	—	4	4	no	—
198	D₁₇₂	—	4	2	no	—
199	D₁₇₂	—	4	4	no	—
200	D₁₇₂	—	4	4	no	—
201	D₁₇₂	—	4	4	no	—
202	D₁₇₂	—	4	4	no	—
203	C₄×D₄₃	—	2	4	no	—
204	C₄×D₄₃	—	4	4	no	—
205	C₄×D₄₃	—	4	4	no	—
206	C₄×D₄₃	—	4	4	no	—
207	Dic₈₆	—	2	2	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	2	2	no	—
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
214	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
215	C₂×D₄₃	—	2	4	no	—
216	C₂×D₄₃	—	2	4	no	—
217	C₂×D₄₃	—	2	2	no	—
218	C₂×D₄₃	—	2	4	no	—
219	C₂×D₄₃	—	2	2	no	—
220	C₂×D₄₃	—	2	4	no	—
221	C₂×D₄₃	—	2	2	no	—
222	C₂×D₄₃	—	2	4	no	—
223	C₂×D₄₃	—	2	4	no	—
224	C₂×D₄₃	—	8	8	no	—
225	C₂×D₄₃	—	8	8	no	—
226	C₄×C₄₃	—	2	2	no	—
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	2	2	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
234	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
235	Dic₄₃	—	2	2	no	—
236	Dic₄₃	—	2	2	no	—
237	Dic₄₃	—	2	2	no	—
238	#3543	—	43	1	no	maximal, Sylow
239	C₂×C₄₃	—	2	2	no	—
240	C₂×C₄₃	—	4	2	no	—
241	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	D₄₃	—	4	4	no	—
245	D₄₃	—	4	4	no	—
246	D₄₃	—	4	2	no	—
247	#560	—	43	4	no	—
248	#559	—	43	1	no	—
249	#550	—	43	1	no	—
250	#550	—	43	1	no	—
251	#546	—	43	2	no	—
252	#546	—	43	2	no	—
253	D₄²	—	43	2	no	—
254	D₄²	—	43	1	no	—
255	D₄²	—	43	2	no	—
256	#540	—	43	2	no	—
257	#540	—	43	2	no	—
258	#535	—	43	2	no	—
259	#535	—	43	2	no	—
260	#534	—	43	4	no	—
261	C₂×#127	—	43	1	no	—
262	#529	—	43	1	no	—
263	#529	D₄₃	1	1	yes	characteristic, complemented
264	C₄₃	#3543	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	—	43	2	no	—
266	C₂×#41	—	43	2	no	—
267	C₂²×D₄	—	43	4	no	—
268	C₂²×D₄	—	43	2	no	—
269	C₂²×D₄	—	43	2	no	—
270	C₂²×D₄	—	43	2	no	—
271	C₂²×D₄	—	43	2	no	—
272	C₂²×D₄	—	43	2	no	—
273	#127	—	43	2	no	—
274	#127	—	43	2	no	—
275	#127	—	43	2	no	—
276	#127	—	43	1	no	—
277	#127	—	43	1	no	—
278	#127	—	43	2	no	—
279	#127	—	43	2	no	—
280	#126	—	43	2	no	—
281	#126	C₂×D₄₃	1	2	yes	complemented
282	#125	—	43	1	no	—
283	#125	C₂×D₄₃	1	1	yes	characteristic, complemented
284	#124	—	43	2	no	—
285	#124	—	43	1	no	—
286	#124	—	43	2	no	—
287	#124	C₂×D₄₃	1	1	yes	characteristic, complemented
288	#123	—	43	2	no	—
289	#123	—	43	4	no	—
290	#123	—	43	4	no	—
291	#123	—	43	4	no	—
292	#123	—	43	4	no	—
293	#123	C₂×D₄₃	1	2	yes	complemented
294	C₂²⋊Q₈	—	43	1	no	—
295	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
296	#121	—	43	1	no	—
297	#121	—	43	2	no	—
298	#121	—	43	2	no	—
299	#121	—	43	4	no	—
300	#121	—	43	4	no	—
301	#121	—	43	4	no	—
302	#121	—	43	2	no	—
303	#121	—	43	2	no	—
304	#121	—	43	4	no	—
305	#121	—	43	4	no	—
306	#121	—	43	4	no	—
307	#121	—	43	4	no	—
308	#121	—	43	4	no	—
309	#121	C₂×D₄₃	1	1	yes	characteristic
310	#120	—	43	4	no	—
311	#120	—	43	4	no	—
312	#120	—	43	4	no	—
313	#120	—	43	4	no	—
314	#120	—	43	4	no	—
315	#120	—	43	4	no	—
316	C₄×Q₈	—	43	1	no	—
317	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
318	C₄×D₄	—	43	2	no	—
319	C₄×D₄	—	43	2	no	—
320	C₄×D₄	—	43	2	no	—
321	C₄×D₄	—	43	1	no	—
322	C₄×D₄	—	43	2	no	—
323	C₄×D₄	—	43	2	no	—
324	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
325	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
326	#117	—	43	2	no	—
327	#117	C₂×D₄₃	1	2	yes	complemented
328	C₂×C₂²⋊C₄	—	43	4	no	—
329	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic, complemented
330	C₂⁴	—	43	4	no	—
331	C₂⁴	—	43	4	no	—
332	#41	—	172	4	no	—
333	#41	—	172	4	no	—
334	C₂×Q₈	—	43	1	no	—
335	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
336	C₂×D₄	—	43	2	no	—
337	C₂×D₄	—	43	4	no	—
338	C₂×D₄	—	43	4	no	—
339	C₂×D₄	—	43	4	no	—
340	C₂×D₄	—	43	2	no	—
341	C₂×D₄	—	43	1	no	—
342	C₂×D₄	—	43	2	no	—
343	C₂×D₄	—	43	2	no	—
344	C₂×D₄	—	43	2	no	—
345	C₂×D₄	—	43	4	no	—
346	C₂×D₄	—	43	4	no	—
347	C₂×D₄	—	43	2	no	—
348	C₂×D₄	—	43	4	no	—
349	C₂×D₄	—	43	4	no	—
350	C₂×D₄	—	43	4	no	—
351	C₂×D₄	—	43	4	no	—
352	C₂×D₄	—	43	2	no	—
353	C₂×D₄	—	172	4	no	—
354	C₂×D₄	—	172	4	no	—
355	C₂×D₄	—	172	4	no	—
356	C₂×D₄	—	172	4	no	—
357	C₂×D₄	—	172	4	no	—
358	C₂×D₄	—	172	8	no	—
359	C₂×D₄	C₂²×D₄₃	1	2	yes	—
360	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
361	C₂²×C₄	—	43	2	no	—
362	C₂²×C₄	—	43	4	no	—
363	C₂²×C₄	—	43	4	no	—
364	C₂²×C₄	—	43	4	no	—
365	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
368	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
369	C₄⋊C₄	—	43	2	no	—
370	C₄⋊C₄	—	43	2	no	—
371	C₄⋊C₄	—	43	1	no	—
372	C₄⋊C₄	—	43	1	no	—
373	C₄⋊C₄	—	43	2	no	—
374	C₄⋊C₄	—	43	2	no	—
375	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
376	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
377	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
378	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
380	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
381	C₂²⋊C₄	—	43	2	no	—
382	C₂²⋊C₄	—	43	4	no	—
383	C₂²⋊C₄	—	43	4	no	—
384	C₂²⋊C₄	—	43	2	no	—
385	C₂²⋊C₄	—	43	2	no	—
386	C₂²⋊C₄	—	43	2	no	—
387	C₂²⋊C₄	—	43	2	no	—
388	C₂²⋊C₄	—	43	4	no	—
389	C₂²⋊C₄	—	43	4	no	—
390	C₂²⋊C₄	—	43	4	no	—
391	C₂²⋊C₄	—	43	4	no	—
392	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
394	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
395	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
397	C₄²	—	43	2	no	—
398	C₄²	C₂²×D₄₃	1	1	yes	characteristic
399	C₄²	C₂²×D₄₃	1	1	yes	characteristic
400	C₄²	C₂²×D₄₃	1	1	yes	characteristic
401	C₄²	C₂²×D₄₃	1	1	yes	characteristic
402	C₄²	C₂²×D₄₃	1	2	yes	—
403	C₂³	—	43	2	no	—
404	C₂³	—	43	4	no	—
405	C₂³	—	43	4	no	—
406	C₂³	—	86	8	no	—
407	C₂³	—	172	4	no	—
408	C₂³	—	172	4	no	—
409	C₂³	—	172	4	no	—
410	C₂³	—	172	4	no	—
411	C₂³	—	172	4	no	—
412	C₂³	C₂³×D₄₃	1	2	yes	—
413	C₂³	C₂³×D₄₃	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	86	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	86	4	no	—
419	D₄	—	86	2	no	—
420	D₄	—	86	4	no	—
421	D₄	—	86	4	no	—
422	D₄	—	86	4	no	—
423	D₄	—	86	4	no	—
424	D₄	—	172	4	no	—
425	D₄	—	172	4	no	—
426	D₄	—	172	4	no	—
427	D₄	—	172	2	no	—
428	D₄	—	172	4	no	—
429	D₄	—	172	2	no	—
430	D₄	—	172	4	no	—
431	D₄	—	172	4	no	—
432	D₄	—	172	4	no	—
433	D₄	—	172	4	no	—
434	D₄	—	172	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	43	2	no	—
440	C₂×C₄	—	43	2	no	—
441	C₂×C₄	—	43	2	no	—
442	C₂×C₄	—	86	4	no	—
443	C₂×C₄	—	172	4	no	—
444	C₂×C₄	—	172	4	no	—
445	C₂×C₄	—	172	4	no	—
446	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
448	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
449	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₄₃	1	2	yes	—
451	C₂×C₄	C₂³×D₄₃	1	2	yes	—
452	C₂×C₄	C₂³×D₄₃	1	2	yes	—
453	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	86	2	no	—
461	C₂²	—	86	4	no	—
462	C₂²	—	86	4	no	—
463	C₂²	—	86	4	no	—
464	C₂²	—	86	2	no	—
465	C₂²	—	86	2	no	—
466	C₂²	—	86	4	no	—
467	C₂²	—	86	4	no	—
468	C₂²	—	86	4	no	—
469	C₂²	—	344	8	no	—
470	C₂²	—	344	8	no	—
471	C₂²	#13063371	1	2	yes	—
472	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	86	2	no	—
481	C₄	—	86	2	no	—
482	C₄	—	86	2	no	—
483	C₄	#13063371	1	2	yes	—
484	C₄	#13063371	1	2	yes	—
485	C₂	—	2	2	no	—
486	C₂	—	4	2	no	—
487	C₂	—	172	2	no	—
488	C₂	—	172	4	no	—
489	C₂	—	172	4	no	—
490	C₂	C₂×#13063371	1	1	yes	characteristic
491	C₂	C₂×#13063371	1	1	yes	characteristic
492	C₂	C₂×#13063371	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	#3543
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. #14583640	C₂	semidirect
2. #14583634	C₂	semidirect
3. #14583571	C₂	semidirect
4. #14583570	C₂	semidirect
5. #14583545	C₂	semidirect
6. #14583540	C₂	semidirect
7. D₄×D₁₇₂	C₂	semidirect
8. D₄×D₁₇₂	C₂	semidirect
9. #14583533	C₂	semidirect
10. #14583505	C₂	semidirect
11. #14583504	C₂	semidirect
12. #14583468	C₂	semidirect
13. #14583467	C₂	semidirect
14. #14583460	C₂	semidirect
15. C₂×#13063322	C₂	semidirect
16. #14583433	C₂	semidirect
17. C₄₃×#529	C₂	semidirect
18. C₂×#10621902	C₂²	semidirect
19. C₂×#10621898	C₂²	semidirect
20. C₂²×D₁₇₂	C₂²	semidirect
21. C₂²×D₁₇₂	C₂²	semidirect
22. C₂²×D₁₇₂	C₂²	semidirect
23. C₂²×D₁₇₂	C₂²	semidirect
24. C₂×D₄×D₄₃	C₂²	semidirect
25. C₂×D₄×D₄₃	C₂²	semidirect
27. #13063322	C₂²	semidirect
28. #13063322	C₂²	semidirect
29. #13063322	C₂²	semidirect
30. #13063322	C₂²	semidirect
31. #13063322	C₂²	semidirect
32. #13063321	C₂²	semidirect
33. #13063319	C₂²	semidirect
34. #13063317	C₂²	semidirect
35. #13063314	C₂²	semidirect
36. #13063313	C₂²	semidirect
37. #13063313	C₂²	semidirect
38. #13063310	C₂²	semidirect
39. #13063310	C₂²	semidirect
40. #13063310	C₂²	semidirect
41. #13063310	C₂²	semidirect
42. #13063308	C₂²	semidirect
43. #13063304	C₂²	semidirect
44. #13063300	C₂²	semidirect
45. #13063300	C₂²	semidirect
46. #13063300	C₂²	semidirect
47. #13063300	C₂²	semidirect
48. #13063300	C₂²	semidirect
49. #13063300	C₂²	semidirect
51. #13063299	C₂²	semidirect
52. #13063299	C₂²	semidirect
53. #13063298	C₂²	semidirect
54. #13063298	C₂²	semidirect
55. #13063298	C₂²	semidirect
56. #13063298	C₂²	semidirect
57. #13063295	C₂²	semidirect
58. #13063295	C₂²	semidirect
59. #13063295	C₂²	semidirect
60. #13063295	C₂²	semidirect
61. #13063295	C₂²	semidirect
62. #13063293	C₂²	semidirect
63. C₄×Dic₈₆	C₂²	semidirect
64. C₄×D₁₇₂	C₂²	semidirect
65. C₄×D₁₇₂	C₂²	semidirect
66. C₄×D₁₇₂	C₂²	semidirect
67. #13063287	C₂²	semidirect
68. #13063287	C₂²	semidirect
69. C₄×C₂²⋊D₄₃	C₂²	semidirect
70. #13063282	C₂²	semidirect
71. C₂²⋊C₄×D₄₃	C₂²	semidirect
72. #126×C₄₃	C₂²	semidirect
73. #125×C₄₃	C₂²	semidirect
74. #124×C₄₃	C₂²	semidirect
75. #123×C₄₃	C₂²	semidirect
76. C₂²⋊Q₈×C₄₃	C₂²	semidirect
78. C₄×Q₈×C₄₃	C₂²	semidirect
79. C₄×D₄×C₄₃	C₂²	semidirect
80. C₄×D₄×C₄₃	C₂²	semidirect
81. #117×C₄₃	C₂²	semidirect
82. C₂×C₄²×C₄₃	C₂²	semidirect
263. #529	D₄₃	semidirect
264. C₄₃	#3543	semidirect
281. #126	C₂×D₄₃	semidirect
283. #125	C₂×D₄₃	semidirect
287. #124	C₂×D₄₃	semidirect
293. #123	C₂×D₄₃	semidirect
295. C₂²⋊Q₈	C₂×D₄₃	semidirect
317. C₄×Q₈	C₂×D₄₃	semidirect
324. C₄×D₄	C₂×D₄₃	semidirect
325. C₄×D₄	C₂×D₄₃	semidirect
327. #117	C₂×D₄₃	semidirect
329. C₂×C₄²	C₂×D₄₃	semidirect