Subgroups — #19148970

Order 5504.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 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	#14583593	C₂	1	2	yes	maximal, complemented
3	#14583571	C₂	1	2	yes	maximal, complemented
4	#14583571	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583552	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583542	C₂	1	2	yes	maximal, complemented
7	#14583540	C₂	1	2	yes	maximal, complemented
8	D₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583521	C₂	1	2	yes	maximal, complemented
10	#14583488	C₂	1	4	yes	maximal, complemented
11	#14583479	C₂	1	2	yes	maximal, complemented
12	#14583468	C₂	1	2	yes	maximal, complemented
13	#14583467	C₂	1	2	yes	maximal, complemented
14	#14583450	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583446	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583436	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621902	C₂²	1	2	yes	complemented
19	C₂×#10621902	C₂²	1	2	yes	complemented
20	C₂×#10621902	C₂²	1	2	yes	complemented
21	C₂×#10621898	C₂²	1	2	yes	complemented
22	C₂²×D₁₇₂	C₂²	1	2	yes	—
23	C₂×D₄×D₄₃	C₂²	1	2	yes	—
24	#13063324	C₂²	1	1	yes	characteristic, complemented
25	#13063322	C₂²	1	1	yes	characteristic
26	#13063322	C₂²	1	2	yes	complemented
27	#13063322	C₂²	1	4	yes	complemented
28	#13063321	C₂²	1	1	yes	characteristic
29	#13063320	C₂²	1	2	yes	complemented
30	#13063319	C₂²	1	4	yes	complemented
31	#13063316	C₂²	1	1	yes	characteristic, complemented
32	#13063314	C₂²	1	1	yes	characteristic
33	#13063314	C₂²	1	2	yes	complemented
34	#13063313	C₂²	1	4	yes	complemented
35	#13063311	C₂²	1	2	yes	complemented
36	#13063310	C₂²	1	4	yes	complemented
37	#13063310	C₂²	1	2	yes	complemented
38	#13063310	C₂²	1	4	yes	complemented
39	#13063307	C₂²	1	4	yes	complemented
40	#13063303	C₂²	1	4	yes	complemented
41	#13063301	C₂²	1	2	yes	complemented
42	#13063301	C₂²	1	1	yes	characteristic, complemented
43	#13063300	C₂²	1	2	yes	—
44	#13063300	C₂²	1	2	yes	—
45	#13063300	C₂²	1	1	yes	characteristic
46	#13063300	C₂²	1	1	yes	characteristic, complemented
47	#13063300	C₂²	1	2	yes	complemented
48	#13063300	C₂²	1	4	yes	complemented
49	#13063300	C₂²	1	4	yes	complemented
50	#13063300	C₂²	1	4	yes	complemented
51	#13063300	C₂²	1	2	yes	complemented
52	#13063300	C₂²	1	2	yes	complemented
53	#13063299	C₂²	1	2	yes	—
54	#13063298	C₂²	1	4	yes	complemented
55	#13063298	C₂²	1	2	yes	complemented
56	#13063298	C₂²	1	4	yes	complemented
57	#13063298	C₂²	1	4	yes	complemented
58	#13063296	C₂²	1	1	yes	characteristic
59	#13063295	C₂²	1	4	yes	—
60	#13063295	C₂²	1	4	yes	complemented
61	#13063295	C₂²	1	4	yes	complemented
62	#13063295	C₂²	1	4	yes	complemented
63	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
64	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₁₇₂	C₂²	1	4	yes	complemented
66	C₄×D₁₇₂	C₂²	1	2	yes	complemented
67	C₄×D₁₇₂	C₂²	1	2	yes	complemented
68	#13063287	C₂²	1	2	yes	complemented
69	#13063287	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
71	#13063282	C₂²	1	2	yes	complemented
72	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
74	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
76	#126×C₄₃	C₂²	1	4	yes	complemented
77	#124×C₄₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
81	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
82	#117×C₄₃	C₂²	1	2	yes	complemented
83	C₂³×D₄₃	C₂³	1	4	yes	—
84	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
86	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
92	#10621902	—	4	4	no	—
93	#10621902	—	4	4	no	—
94	#10621902	—	4	4	no	—
95	D₄×D₄₃	—	4	4	no	—
96	#10621898	—	4	4	no	—
97	C₂×D₁₇₂	—	4	4	no	—
98	C₂×D₁₇₂	C₂³	1	2	yes	—
99	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
100	C₂×D₁₇₂	C₂³	1	2	yes	—
101	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
102	C₂×D₁₇₂	C₂³	1	2	yes	—
103	C₂×D₁₇₂	C₂³	1	2	yes	—
104	C₂×D₁₇₂	C₂³	1	4	yes	—
105	C₂×D₁₇₂	C₂³	1	4	yes	—
106	C₂×D₁₇₂	C₂³	1	4	yes	—
107	C₂×D₁₇₂	C₂³	1	4	yes	—
108	C₂×D₁₇₂	C₂³	1	4	yes	—
109	C₂×D₁₇₂	C₂³	1	2	yes	—
110	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₄₃	C₂³	1	2	yes	—
113	C₂×C₄×D₄₃	C₂³	1	2	yes	—
114	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
115	C₂×C₄×D₄₃	C₂³	1	4	yes	—
116	C₂×C₄×D₄₃	C₂³	1	4	yes	—
117	C₂×C₄×D₄₃	C₂³	1	4	yes	—
118	C₂×Dic₈₆	C₂³	1	2	yes	—
119	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
121	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
123	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
124	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
127	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
128	C₄²×C₄₃	C₂³	1	4	yes	—
129	C₄²×C₄₃	C₂³	1	1	yes	characteristic
130	C₄²×C₄₃	C₂³	1	2	yes	—
131	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
136	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
137	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
139	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
140	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
141	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
142	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
143	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
144	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₄₃	C₂³	1	2	yes	—
147	Dic₄₃⋊C₄	C₂³	1	4	yes	—
148	Dic₄₃⋊C₄	C₂³	1	2	yes	—
149	Dic₄₃⋊C₄	C₂³	1	2	yes	—
150	Dic₄₃⋊C₄	C₂³	1	2	yes	—
151	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
152	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
153	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄₃	C₂⁴	1	2	yes	—
155	C₂²×D₄₃	—	4	4	no	—
156	C₂²×D₄₃	—	4	4	no	—
157	C₂²×D₄₃	—	4	4	no	—
158	C₂²×D₄₃	C₂⁴	1	2	yes	—
159	C₂²×D₄₃	C₂⁴	1	4	yes	—
160	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
161	C₂²×D₄₃	C₂⁴	1	2	yes	—
162	Q₈×C₄₃	—	2	2	no	—
163	Q₈×C₄₃	—	2	4	no	—
164	D₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₄₃	C₂⁴	1	4	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	—	4	2	no	—
174	C₂²⋊D₄₃	—	4	2	no	—
175	C₂²⋊D₄₃	—	4	4	no	—
176	C₂²⋊D₄₃	—	4	2	no	—
177	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₄₃	C₂⁴	1	2	yes	—
181	C₂×Dic₄₃	C₂⁴	1	2	yes	—
182	D₁₇₂	—	2	2	no	—
183	D₁₇₂	—	2	4	no	—
184	D₁₇₂	—	2	4	no	—
185	D₁₇₂	—	2	2	no	—
186	D₁₇₂	—	4	4	no	—
187	D₁₇₂	—	4	2	no	—
188	D₁₇₂	—	4	2	no	—
189	D₁₇₂	—	4	4	no	—
190	D₁₇₂	—	4	2	no	—
191	D₁₇₂	—	4	4	no	—
192	D₁₇₂	—	4	4	no	—
193	D₁₇₂	—	4	4	no	—
194	C₄×D₄₃	—	2	2	no	—
195	C₄×D₄₃	—	2	4	no	—
196	C₄×D₄₃	—	2	4	no	—
197	C₄×D₄₃	—	2	2	no	—
198	C₄×D₄₃	—	4	1	no	—
199	C₄×D₄₃	—	4	4	no	—
200	C₄×D₄₃	—	4	4	no	—
201	C₄×D₄₃	—	4	4	no	—
202	Dic₈₆	—	4	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	2	2	no	—
209	C₂×D₄₃	—	2	4	no	—
210	C₂×D₄₃	—	2	4	no	—
211	C₂×D₄₃	—	2	1	no	—
212	C₂×D₄₃	—	2	2	no	—
213	C₂×D₄₃	—	2	1	no	—
214	C₂×D₄₃	—	2	2	no	—
215	C₂×D₄₃	—	2	2	no	—
216	C₂×D₄₃	—	2	4	no	—
217	C₂×D₄₃	—	2	1	no	—
218	C₂×D₄₃	—	2	2	no	—
219	C₂×D₄₃	—	8	8	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	4	no	—
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	2	no	—
225	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
226	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
227	Dic₄₃	—	2	1	no	—
228	Dic₄₃	—	2	2	no	—
229	Dic₄₃	—	2	1	no	—
230	Dic₄₃	—	2	2	no	—
231	Dic₄₃	—	2	1	no	—
232	#3546	—	43	1	no	maximal, Sylow
233	C₂×C₄₃	—	4	2	no	—
234	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄₃	#585	1	1	yes	characteristic
237	D₄₃	—	4	1	no	—
238	D₄₃	—	4	2	no	—
239	D₄₃	—	4	4	no	—
240	D₄₃	—	4	2	no	—
241	#560	—	43	4	no	—
242	#556	D₄₃	1	1	yes	characteristic, complemented
243	#553	—	43	2	no	—
244	#550	—	43	2	no	—
245	#550	—	43	1	no	—
246	#547	—	43	1	no	—
247	#546	—	43	2	no	—
248	#546	—	43	2	no	—
249	D₄²	—	43	1	no	—
250	#542	—	43	2	no	—
251	#538	—	43	4	no	—
252	#537	—	43	2	no	—
253	#535	—	43	2	no	—
254	#535	—	43	2	no	—
255	#532	—	43	1	no	—
256	#532	—	43	1	no	—
257	#529	—	43	1	no	—
258	C₄₃	#3546	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	43	2	no	—
260	C₂×#41	—	43	2	no	—
261	C₂×#41	—	43	2	no	—
262	C₂×#41	—	43	2	no	—
263	C₂²×D₄	—	43	2	no	—
264	C₂²×D₄	—	43	2	no	—
265	C₄⋊Q₈	—	43	1	no	—
266	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
267	#127	—	43	1	no	—
268	#127	—	43	1	no	—
269	#127	—	43	2	no	—
270	#127	—	43	4	no	—
271	#126	—	43	2	no	—
272	#126	—	43	4	no	—
273	#126	C₂×D₄₃	1	4	yes	complemented
274	#125	—	43	1	no	—
275	#124	—	43	1	no	—
276	#124	—	43	2	no	—
277	#124	—	43	2	no	—
278	#124	—	43	4	no	—
279	#124	C₂×D₄₃	1	2	yes	—
280	#123	—	43	2	no	—
281	#123	—	43	4	no	—
282	#123	—	43	4	no	—
283	#123	—	43	4	no	—
284	C₂²⋊Q₈	—	43	1	no	—
285	C₂²⋊Q₈	—	43	2	no	—
286	C₂²⋊Q₈	—	43	4	no	—
287	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
288	#121	—	43	1	no	—
289	#121	—	43	2	no	—
290	#121	—	43	1	no	—
291	#121	—	43	2	no	—
292	#121	—	43	1	no	—
293	#121	—	43	2	no	—
294	#121	—	43	2	no	—
295	#121	—	43	2	no	—
296	#121	—	43	4	no	—
297	#121	—	43	4	no	—
298	#121	—	43	4	no	—
299	#121	—	43	2	no	—
300	#121	—	43	2	no	—
301	#121	—	43	4	no	—
302	#121	—	43	4	no	—
303	#121	—	43	4	no	—
304	#120	—	43	4	no	—
305	#120	—	43	4	no	—
306	#120	—	43	4	no	—
307	#120	—	43	4	no	—
308	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
309	C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
310	C₄×D₄	—	43	2	no	—
311	C₄×D₄	—	43	2	no	—
312	C₄×D₄	—	43	2	no	—
313	C₄×D₄	—	43	1	no	—
314	C₄×D₄	—	43	2	no	—
315	C₄×D₄	—	43	1	no	—
316	C₄×D₄	—	43	4	no	—
317	C₄×D₄	—	43	2	no	—
318	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
319	#117	—	43	2	no	—
320	#117	C₂×D₄₃	1	2	yes	complemented
321	C₂×C₄⋊C₄	—	43	2	no	—
322	C₂×C₂²⋊C₄	—	43	4	no	—
323	C₂×C₄²	—	43	1	no	—
324	C₂⁴	—	43	4	no	—
325	#41	—	172	4	no	—
326	#41	—	172	4	no	—
327	#41	—	172	4	no	—
328	#41	—	172	4	no	—
329	C₂×Q₈	—	43	2	no	—
330	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
331	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
332	C₂×D₄	—	43	2	no	—
333	C₂×D₄	—	43	2	no	—
334	C₂×D₄	—	43	2	no	—
335	C₂×D₄	—	43	4	no	—
336	C₂×D₄	—	43	1	no	—
337	C₂×D₄	—	43	2	no	—
338	C₂×D₄	—	43	2	no	—
339	C₂×D₄	—	43	1	no	—
340	C₂×D₄	—	43	2	no	—
341	C₂×D₄	—	43	2	no	—
342	C₂×D₄	—	43	4	no	—
343	C₂×D₄	—	43	4	no	—
344	C₂×D₄	—	43	4	no	—
345	C₂×D₄	—	43	4	no	—
346	C₂×D₄	—	43	4	no	—
347	C₂×D₄	—	43	2	no	—
348	C₂×D₄	—	172	4	no	—
349	C₂×D₄	—	172	4	no	—
350	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	—	43	1	no	—
352	C₂²×C₄	—	43	1	no	—
353	C₂²×C₄	—	43	2	no	—
354	C₂²×C₄	—	43	2	no	—
355	C₂²×C₄	—	43	1	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	C₄⋊C₄	—	43	1	no	—
361	C₄⋊C₄	—	43	4	no	—
362	C₄⋊C₄	—	43	2	no	—
363	C₄⋊C₄	—	43	2	no	—
364	C₄⋊C₄	—	43	1	no	—
365	C₄⋊C₄	—	43	2	no	—
366	C₄⋊C₄	—	43	2	no	—
367	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
368	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
370	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
372	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
373	C₂²⋊C₄	—	43	2	no	—
374	C₂²⋊C₄	—	43	2	no	—
375	C₂²⋊C₄	—	43	4	no	—
376	C₂²⋊C₄	—	43	2	no	—
377	C₂²⋊C₄	—	43	2	no	—
378	C₂²⋊C₄	—	43	2	no	—
379	C₂²⋊C₄	—	43	2	no	—
380	C₂²⋊C₄	—	43	4	no	—
381	C₂²⋊C₄	—	43	4	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	C₂²×D₄₃	1	4	yes	—
387	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
388	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
389	C₄²	—	43	1	no	—
390	C₄²	—	43	1	no	—
391	C₄²	—	43	1	no	—
392	C₄²	C₂²×D₄₃	1	1	yes	characteristic
393	C₄²	C₂²×D₄₃	1	2	yes	—
394	C₄²	C₂²×D₄₃	1	4	yes	—
395	C₂³	—	43	2	no	—
396	C₂³	—	43	4	no	—
397	C₂³	—	43	1	no	—
398	C₂³	—	43	2	no	—
399	C₂³	—	172	4	no	—
400	C₂³	—	172	4	no	—
401	C₂³	—	172	4	no	—
402	C₂³	C₂³×D₄₃	1	2	yes	—
403	Q₈	—	2	2	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	172	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	86	2	no	—
408	D₄	—	86	4	no	—
409	D₄	—	86	4	no	—
410	D₄	—	86	2	no	—
411	D₄	—	172	4	no	—
412	D₄	—	172	2	no	—
413	D₄	—	172	4	no	—
414	D₄	—	172	4	no	—
415	D₄	—	172	4	no	—
416	D₄	—	172	2	no	—
417	D₄	—	172	2	no	—
418	D₄	—	172	4	no	—
419	D₄	—	172	4	no	—
420	D₄	—	172	2	no	—
421	D₄	—	172	2	no	—
422	D₄	—	172	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	43	1	no	—
425	C₂×C₄	—	43	1	no	—
426	C₂×C₄	—	43	1	no	—
427	C₂×C₄	—	43	2	no	—
428	C₂×C₄	—	43	2	no	—
429	C₂×C₄	—	86	4	no	—
430	C₂×C₄	—	86	2	no	—
431	C₂×C₄	—	86	4	no	—
432	C₂×C₄	—	86	2	no	—
433	C₂×C₄	—	172	4	no	—
434	C₂×C₄	—	172	4	no	—
435	C₂×C₄	—	172	4	no	—
436	C₂×C₄	—	172	1	no	—
437	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₄₃	1	2	yes	—
439	C₂×C₄	C₂³×D₄₃	1	2	yes	—
440	C₂×C₄	C₂³×D₄₃	1	2	yes	—
441	C₂×C₄	C₂³×D₄₃	1	4	yes	—
442	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
443	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	86	1	no	—
448	C₂²	—	86	2	no	—
449	C₂²	—	86	1	no	—
450	C₂²	—	86	2	no	—
451	C₂²	—	86	2	no	—
452	C₂²	—	86	4	no	—
453	C₂²	—	86	4	no	—
454	C₂²	—	86	2	no	—
455	C₂²	—	86	1	no	—
456	C₂²	—	86	2	no	—
457	C₂²	—	86	4	no	—
458	C₂²	—	86	2	no	—
459	C₂²	—	344	8	no	—
460	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	4	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	2	no	—
466	C₄	—	86	1	no	—
467	C₄	—	86	2	no	—
468	C₄	—	86	2	no	—
469	C₄	—	86	1	no	—
470	C₄	—	86	1	no	—
471	C₄	#13063371	1	2	yes	—
472	C₄	#13063371	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	172	2	no	—
475	C₂	—	172	4	no	—
476	C₂	—	172	1	no	—
477	C₂	—	172	2	no	—
478	C₂	C₂×#13063371	1	1	yes	characteristic
479	C₂	C₂×#13063371	1	1	yes	characteristic
480	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#556	C₂
hypercenter	#556	D₄₃
hypocenter	C₄₃	#3546
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #14583640	C₂	semidirect
2. #14583593	C₂	semidirect
3. #14583571	C₂	semidirect
4. #14583571	C₂	semidirect
5. #14583552	C₂	semidirect
6. #14583542	C₂	semidirect
7. #14583540	C₂	semidirect
8. D₄×D₁₇₂	C₂	semidirect
9. #14583521	C₂	semidirect
10. #14583488	C₂	semidirect
11. #14583479	C₂	semidirect
12. #14583468	C₂	semidirect
13. #14583467	C₂	semidirect
14. #14583450	C₂	semidirect
15. #14583446	C₂	semidirect
16. #14583436	C₂	semidirect
17. C₄₃×#556	C₂	semidirect
18. C₂×#10621902	C₂²	semidirect
19. C₂×#10621902	C₂²	semidirect
20. C₂×#10621902	C₂²	semidirect
21. C₂×#10621898	C₂²	semidirect
24. #13063324	C₂²	semidirect
26. #13063322	C₂²	semidirect
27. #13063322	C₂²	semidirect
29. #13063320	C₂²	semidirect
30. #13063319	C₂²	semidirect
31. #13063316	C₂²	semidirect
33. #13063314	C₂²	semidirect
34. #13063313	C₂²	semidirect
35. #13063311	C₂²	semidirect
36. #13063310	C₂²	semidirect
37. #13063310	C₂²	semidirect
38. #13063310	C₂²	semidirect
39. #13063307	C₂²	semidirect
40. #13063303	C₂²	semidirect
41. #13063301	C₂²	semidirect
42. #13063301	C₂²	semidirect
46. #13063300	C₂²	semidirect
47. #13063300	C₂²	semidirect
48. #13063300	C₂²	semidirect
49. #13063300	C₂²	semidirect
50. #13063300	C₂²	semidirect
51. #13063300	C₂²	semidirect
52. #13063300	C₂²	semidirect
54. #13063298	C₂²	semidirect
55. #13063298	C₂²	semidirect
56. #13063298	C₂²	semidirect
57. #13063298	C₂²	semidirect
60. #13063295	C₂²	semidirect
61. #13063295	C₂²	semidirect
62. #13063295	C₂²	semidirect
64. C₄×D₁₇₂	C₂²	semidirect
65. C₄×D₁₇₂	C₂²	semidirect
66. C₄×D₁₇₂	C₂²	semidirect
67. C₄×D₁₇₂	C₂²	semidirect
68. #13063287	C₂²	semidirect
69. #13063287	C₂²	semidirect
70. C₄×C₂²⋊D₄₃	C₂²	semidirect
71. #13063282	C₂²	semidirect
72. C₄⋊C₄×D₄₃	C₂²	semidirect
73. C₂²⋊C₄×D₄₃	C₂²	semidirect
74. C₄²×D₄₃	C₂²	semidirect
75. C₄⋊Q₈×C₄₃	C₂²	semidirect
76. #126×C₄₃	C₂²	semidirect
78. C₂²⋊Q₈×C₄₃	C₂²	semidirect
79. C₄×Q₈×C₄₃	C₂²	semidirect
80. C₄×Q₈×C₄₃	C₂²	semidirect
82. #117×C₄₃	C₂²	semidirect
242. #556	D₄₃	semidirect
258. C₄₃	#3546	semidirect
266. C₄⋊Q₈	C₂×D₄₃	semidirect
273. #126	C₂×D₄₃	semidirect
287. C₂²⋊Q₈	C₂×D₄₃	semidirect
308. C₄×Q₈	C₂×D₄₃	semidirect
309. C₄×Q₈	C₂×D₄₃	semidirect
320. #117	C₂×D₄₃	semidirect