Subgroups — #19149097

Order 5504.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583651	C₂	1	2	yes	maximal, complemented
2	#14583651	C₂	1	2	yes	maximal, complemented
3	#14583632	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583631	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583626	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583625	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583621	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583618	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583608	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583605	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583588	C₂	1	2	yes	maximal, complemented
12	#14583582	C₂	1	2	yes	maximal, complemented
13	#14583522	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583517	C₂	1	2	yes	maximal, complemented
15	#14583516	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583514	C₂	1	2	yes	maximal, complemented
17	#14583509	C₂	1	1	yes	maximal, characteristic, complemented
18	#14583502	C₂	1	1	yes	maximal, characteristic
19	#14583492	C₂	1	2	yes	maximal, complemented
20	#14583491	C₂	1	2	yes	maximal, complemented
21	#14583456	C₂	1	1	yes	maximal, characteristic, complemented
22	#14583433	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	#13063325	C₂²	1	1	yes	characteristic
25	#13063325	C₂²	1	1	yes	characteristic
26	#13063324	C₂²	1	1	yes	characteristic
27	#13063324	C₂²	1	1	yes	characteristic
28	#13063324	C₂²	1	2	yes	—
29	#13063324	C₂²	1	2	yes	—
30	#13063323	C₂²	1	1	yes	characteristic
31	#13063321	C₂²	1	1	yes	characteristic
32	#13063320	C₂²	1	2	yes	—
33	#13063320	C₂²	1	2	yes	—
34	#13063319	C₂²	1	2	yes	—
35	#13063319	C₂²	1	2	yes	—
36	#13063318	C₂²	1	2	yes	—
37	#13063318	C₂²	1	2	yes	—
38	#13063318	C₂²	1	2	yes	—
39	#13063318	C₂²	1	2	yes	—
40	#13063318	C₂²	1	2	yes	—
41	#13063317	C₂²	1	1	yes	characteristic
42	#13063317	C₂²	1	1	yes	characteristic
43	#13063317	C₂²	1	2	yes	—
44	#13063317	C₂²	1	1	yes	characteristic
45	#13063316	C₂²	1	2	yes	—
46	#13063316	C₂²	1	1	yes	characteristic
47	#13063316	C₂²	1	1	yes	characteristic
48	#13063316	C₂²	1	2	yes	—
49	#13063315	C₂²	1	2	yes	—
50	#13063315	C₂²	1	2	yes	—
51	#13063315	C₂²	1	2	yes	—
52	#13063314	C₂²	1	1	yes	characteristic
53	#13063313	C₂²	1	1	yes	characteristic
54	#13063312	C₂²	1	1	yes	characteristic
55	#13063312	C₂²	1	2	yes	—
56	#13063311	C₂²	1	2	yes	—
57	#13063311	C₂²	1	2	yes	—
58	#13063311	C₂²	1	2	yes	—
59	#13063309	C₂²	1	2	yes	—
60	#13063309	C₂²	1	2	yes	—
61	#13063308	C₂²	1	2	yes	—
62	#13063308	C₂²	1	2	yes	—
63	#13063307	C₂²	1	2	yes	—
64	#13063307	C₂²	1	2	yes	—
65	#13063307	C₂²	1	2	yes	—
66	#13063307	C₂²	1	2	yes	—
67	#13063306	C₂²	1	2	yes	—
68	#13063305	C₂²	1	2	yes	—
69	#13063305	C₂²	1	2	yes	—
70	#13063304	C₂²	1	2	yes	—
71	#13063304	C₂²	1	1	yes	characteristic
72	#13063304	C₂²	1	1	yes	characteristic
73	#13063304	C₂²	1	1	yes	characteristic
74	#13063304	C₂²	1	1	yes	characteristic
75	#13063304	C₂²	1	1	yes	characteristic
76	#13063303	C₂²	1	2	yes	—
77	#13063303	C₂²	1	2	yes	—
78	#13063303	C₂²	1	2	yes	—
79	#13063302	C₂²	1	2	yes	—
80	#13063302	C₂²	1	2	yes	—
81	#13063302	C₂²	1	2	yes	—
82	#13063302	C₂²	1	2	yes	—
83	#13063299	C₂²	1	1	yes	characteristic
84	#13063297	C₂²	1	2	yes	—
85	#13063296	C₂²	1	2	yes	—
86	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
87	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
88	C₄×Dic₈₆	C₂²	1	2	yes	—
89	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
90	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
91	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
92	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
93	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
94	#13063290	C₂²	1	2	yes	—
95	#13063290	C₂²	1	1	yes	characteristic
96	#13063290	C₂²	1	1	yes	characteristic
97	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
98	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
99	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
100	#13063287	C₂²	1	1	yes	characteristic
101	#13063287	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
104	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
105	#13063284	C₂²	1	1	yes	characteristic
106	#13063284	C₂²	1	1	yes	characteristic
107	#13063282	C₂²	1	2	yes	—
108	#13063282	C₂²	1	2	yes	—
109	#13063281	C₂²	1	2	yes	—
110	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
111	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
112	#126×C₄₃	C₂²	1	2	yes	—
113	#125×C₄₃	C₂²	1	1	yes	characteristic
114	#124×C₄₃	C₂²	1	1	yes	characteristic
115	#123×C₄₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
117	#121×C₄₃	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₄₃	C₂²	1	2	yes	—
121	#117×C₄₃	C₂²	1	2	yes	—
122	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₄₃	C₂³	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
133	C₂²×Dic₄₃	C₂³	1	2	yes	—
134	C₂²×Dic₄₃	C₂³	1	2	yes	—
135	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₄₃	C₂³	1	2	yes	—
137	C₂×C₄×D₄₃	C₂³	1	2	yes	—
138	C₂×C₄×D₄₃	C₂³	1	2	yes	—
139	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
140	C₂×Dic₈₆	C₂³	1	2	yes	—
141	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
142	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
143	C₂×Dic₈₆	C₂³	1	2	yes	—
144	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
145	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
150	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
157	C₄²×C₄₃	C₂³	1	1	yes	characteristic
158	C₄²×C₄₃	C₂³	1	1	yes	characteristic
159	C₄²×C₄₃	C₂³	1	1	yes	characteristic
160	C₄²×C₄₃	C₂³	1	1	yes	characteristic
161	C₄²×C₄₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
165	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
166	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
167	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
171	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
179	C₄⋊Dic₄₃	C₂³	1	2	yes	—
180	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
181	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₄₃	C₂³	1	2	yes	—
187	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₄₃	C₂³	1	2	yes	—
192	C₄⋊Dic₄₃	C₂³	1	2	yes	—
193	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
194	Dic₄₃⋊C₄	C₂³	1	2	yes	—
195	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
196	Dic₄₃⋊C₄	C₂³	1	2	yes	—
197	Dic₄₃⋊C₄	C₂³	1	2	yes	—
198	Dic₄₃⋊C₄	C₂³	1	2	yes	—
199	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₄₃⋊C₄	C₂³	1	2	yes	—
201	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₄₃⋊C₄	C₂³	1	2	yes	—
203	Dic₄₃⋊C₄	C₂³	1	2	yes	—
204	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₄₃⋊C₄	C₂³	1	2	yes	—
207	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₄₃⋊C₄	C₂³	1	2	yes	—
209	Dic₄₃⋊C₄	C₂³	1	2	yes	—
210	Dic₄₃⋊C₄	C₂³	1	2	yes	—
211	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₄₃⋊C₄	C₂³	1	2	yes	—
213	C₄×Dic₄₃	C₂³	1	2	yes	—
214	C₄×Dic₄₃	C₂³	1	2	yes	—
215	C₄×Dic₄₃	C₂³	1	2	yes	—
216	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₄₃	C₂³	1	2	yes	—
221	C₄×Dic₄₃	C₂³	1	2	yes	—
222	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
223	C₂³×C₄₃	C₂⁴	1	2	yes	—
224	C₂²×D₄₃	C₂⁴	1	2	yes	—
225	Q₈×C₄₃	—	2	2	no	—
226	D₄×C₄₃	—	2	2	no	—
227	D₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	2	2	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₄₃	—	4	2	no	—
242	C₂²⋊D₄₃	—	4	2	no	—
243	C₂²⋊D₄₃	—	4	2	no	—
244	C₂×Dic₄₃	—	4	2	no	—
245	C₂×Dic₄₃	—	4	2	no	—
246	C₂×Dic₄₃	C₂⁴	1	2	yes	—
247	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₄₃	C₂⁴	1	2	yes	—
252	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₄₃	C₂⁴	1	2	yes	—
255	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
257	D₁₇₂	—	2	2	no	—
258	C₄×D₄₃	—	4	2	no	—
259	C₄×D₄₃	—	4	2	no	—
260	C₄×D₄₃	—	4	2	no	—
261	Dic₈₆	—	2	2	no	—
262	Dic₈₆	—	4	2	no	—
263	Dic₈₆	—	4	2	no	—
264	Dic₈₆	—	4	1	no	—
265	Dic₈₆	—	4	1	no	—
266	Dic₈₆	—	4	1	no	—
267	Dic₈₆	—	4	1	no	—
268	C₂²×C₄₃	—	2	1	no	—
269	C₂²×C₄₃	—	2	2	no	—
270	C₂²×C₄₃	—	2	2	no	—
271	C₂²×C₄₃	—	2	2	no	—
272	C₂²×C₄₃	—	2	1	no	—
273	C₂²×C₄₃	—	2	1	no	—
274	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
275	C₂×D₄₃	—	2	2	no	—
276	C₂×D₄₃	—	2	2	no	—
277	C₂×D₄₃	—	2	2	no	—
278	C₄×C₄₃	—	2	1	no	—
279	C₄×C₄₃	—	2	2	no	—
280	C₄×C₄₃	—	2	1	no	—
281	C₄×C₄₃	—	2	1	no	—
282	C₄×C₄₃	—	2	2	no	—
283	C₄×C₄₃	—	2	2	no	—
284	C₄×C₄₃	—	2	1	no	—
285	C₄×C₄₃	—	2	1	no	—
286	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
287	Dic₄₃	—	2	2	no	—
288	Dic₄₃	—	2	1	no	—
289	Dic₄₃	—	2	1	no	—
290	Dic₄₃	—	2	1	no	—
291	Dic₄₃	—	2	1	no	—
292	Dic₄₃	—	2	2	no	—
293	Dic₄₃	—	2	1	no	—
294	Dic₄₃	—	2	1	no	—
295	Dic₄₃	—	2	2	no	—
296	Dic₄₃	—	2	1	no	—
297	Dic₄₃	—	2	1	no	—
298	#3557	—	43	1	no	maximal, Sylow
299	C₂×C₄₃	—	4	1	no	—
300	C₂×C₄₃	—	4	2	no	—
301	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₂×C₄₃	#585	1	1	yes	characteristic
303	C₂×C₄₃	#585	1	1	yes	characteristic
304	D₄₃	—	4	2	no	—
305	#563	—	43	2	no	—
306	#563	—	43	2	no	—
307	#559	—	43	1	no	—
308	#559	—	43	1	no	—
309	#557	—	43	1	no	—
310	#557	—	43	1	no	—
311	#556	—	43	1	no	—
312	#556	—	43	1	no	—
313	#554	—	43	1	no	—
314	#554	—	43	1	no	—
315	#552	—	43	2	no	—
316	#552	—	43	2	no	—
317	#542	—	43	2	no	—
318	#542	—	43	1	no	—
319	#542	—	43	1	no	—
320	#542	—	43	2	no	—
321	#541	—	43	1	no	—
322	#540	—	43	1	no	—
323	#539	—	43	2	no	—
324	#539	—	43	2	no	—
325	#533	—	43	1	no	—
326	#529	—	43	1	no	—
327	#529	D₄₃	1	1	yes	characteristic, complemented
328	C₄₃	#3557	1	1	yes	characteristic, complemented, Sylow
329	C₄⋊Q₈	—	43	1	no	—
330	C₄⋊Q₈	—	43	1	no	—
331	C₄⋊Q₈	—	43	1	no	—
332	C₄⋊Q₈	—	43	2	no	—
333	C₄⋊Q₈	—	43	2	no	—
334	C₄⋊Q₈	—	43	1	no	—
335	C₄⋊Q₈	—	43	1	no	—
336	#127	—	43	1	no	—
337	#126	—	43	2	no	—
338	#126	—	43	2	no	—
339	#126	—	43	2	no	—
340	#126	—	43	2	no	—
341	#126	—	43	2	no	—
342	#126	—	43	2	no	—
343	#126	—	43	2	no	—
344	#126	—	43	2	no	—
345	#126	—	43	2	no	—
346	#126	C₂×D₄₃	1	2	yes	—
347	#125	—	43	2	no	—
348	#125	—	43	2	no	—
349	#125	—	43	2	no	—
350	#125	—	43	1	no	—
351	#125	—	43	2	no	—
352	#125	—	43	2	no	—
353	#125	—	43	1	no	—
354	#125	—	43	1	no	—
355	#125	—	43	1	no	—
356	#125	—	43	1	no	—
357	#125	—	43	2	no	—
358	#125	C₂×D₄₃	1	1	yes	characteristic
359	#124	—	43	1	no	—
360	#124	—	43	2	no	—
361	#124	—	43	1	no	—
362	#124	—	43	2	no	—
363	#124	—	43	2	no	—
364	#124	—	43	2	no	—
365	#124	—	43	1	no	—
366	#124	C₂×D₄₃	1	1	yes	characteristic
367	#123	—	43	2	no	—
368	#123	—	43	2	no	—
369	#123	—	43	2	no	—
370	#123	—	43	2	no	—
371	#123	—	43	2	no	—
372	#123	—	43	2	no	—
373	#123	—	43	2	no	—
374	#123	—	43	2	no	—
375	#123	—	43	2	no	—
376	#123	C₂×D₄₃	1	2	yes	—
377	C₂²⋊Q₈	—	43	1	no	—
378	C₂²⋊Q₈	—	43	1	no	—
379	C₂²⋊Q₈	—	43	1	no	—
380	C₂²⋊Q₈	—	43	1	no	—
381	C₂²⋊Q₈	—	43	1	no	—
382	C₂²⋊Q₈	—	43	2	no	—
383	C₂²⋊Q₈	—	43	2	no	—
384	C₂²⋊Q₈	—	43	2	no	—
385	C₂²⋊Q₈	—	43	2	no	—
386	C₂²⋊Q₈	—	43	2	no	—
387	C₂²⋊Q₈	—	43	2	no	—
388	C₂²⋊Q₈	—	43	2	no	—
389	C₂²⋊Q₈	—	43	2	no	—
390	C₂²⋊Q₈	—	43	2	no	—
391	C₂²⋊Q₈	—	43	2	no	—
392	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
393	#121	—	43	2	no	—
394	#121	—	43	2	no	—
395	#121	—	43	1	no	—
396	#121	C₂×D₄₃	1	1	yes	characteristic
397	C₄×Q₈	—	43	1	no	—
398	C₄×Q₈	—	43	1	no	—
399	C₄×Q₈	—	43	1	no	—
400	C₄×Q₈	—	43	2	no	—
401	C₄×Q₈	—	43	1	no	—
402	C₄×Q₈	—	43	1	no	—
403	C₄×Q₈	—	43	1	no	—
404	C₄×Q₈	—	43	1	no	—
405	C₄×Q₈	—	43	1	no	—
406	C₄×Q₈	—	43	1	no	—
407	C₄×Q₈	—	43	2	no	—
408	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
409	C₄×D₄	—	43	1	no	—
410	C₄×D₄	—	43	1	no	—
411	C₄×D₄	—	43	2	no	—
412	C₄×D₄	—	43	2	no	—
413	C₄×D₄	—	43	1	no	—
414	C₄×D₄	—	43	1	no	—
415	C₄×D₄	—	43	2	no	—
416	C₄×D₄	—	43	1	no	—
417	C₄×D₄	C₂×D₄₃	1	2	yes	—
418	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
419	#117	—	43	1	no	—
420	#117	—	43	1	no	—
421	#117	—	43	2	no	—
422	#117	—	43	2	no	—
423	#117	—	43	2	no	—
424	#117	C₂×D₄₃	1	2	yes	—
425	C₂×C₄⋊C₄	—	43	2	no	—
426	C₂×C₄⋊C₄	—	43	2	no	—
427	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
428	C₂×Q₈	—	43	1	no	—
429	C₂×Q₈	—	43	1	no	—
430	C₂×Q₈	—	43	1	no	—
431	C₂×Q₈	—	43	2	no	—
432	C₂×Q₈	—	43	2	no	—
433	C₂×Q₈	—	43	1	no	—
434	C₂×Q₈	—	43	1	no	—
435	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
436	C₂×D₄	—	43	2	no	—
437	C₂×D₄	—	43	2	no	—
438	C₂×D₄	—	43	2	no	—
439	C₂×D₄	—	43	1	no	—
440	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
441	C₂×D₄	C₂²×D₄₃	1	2	yes	—
442	C₂²×C₄	—	43	2	no	—
443	C₂²×C₄	—	43	2	no	—
444	C₂²×C₄	—	43	2	no	—
445	C₂²×C₄	—	43	2	no	—
446	C₂²×C₄	—	43	2	no	—
447	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
451	C₄⋊C₄	—	43	1	no	—
452	C₄⋊C₄	—	43	1	no	—
453	C₄⋊C₄	—	43	2	no	—
454	C₄⋊C₄	—	43	2	no	—
455	C₄⋊C₄	—	43	2	no	—
456	C₄⋊C₄	—	43	2	no	—
457	C₄⋊C₄	—	43	2	no	—
458	C₄⋊C₄	—	43	1	no	—
459	C₄⋊C₄	—	43	1	no	—
460	C₄⋊C₄	—	43	2	no	—
461	C₄⋊C₄	—	43	1	no	—
462	C₄⋊C₄	—	43	1	no	—
463	C₄⋊C₄	—	43	2	no	—
464	C₄⋊C₄	—	43	2	no	—
465	C₄⋊C₄	—	43	1	no	—
466	C₄⋊C₄	—	43	1	no	—
467	C₄⋊C₄	—	43	1	no	—
468	C₄⋊C₄	—	43	1	no	—
469	C₄⋊C₄	—	43	1	no	—
470	C₄⋊C₄	—	43	1	no	—
471	C₄⋊C₄	—	43	2	no	—
472	C₄⋊C₄	—	43	1	no	—
473	C₄⋊C₄	—	43	1	no	—
474	C₄⋊C₄	—	43	2	no	—
475	C₄⋊C₄	—	43	2	no	—
476	C₄⋊C₄	—	43	1	no	—
477	C₄⋊C₄	—	43	1	no	—
478	C₄⋊C₄	—	43	2	no	—
479	C₄⋊C₄	—	43	2	no	—
480	C₄⋊C₄	—	43	1	no	—
481	C₄⋊C₄	—	43	1	no	—
482	C₄⋊C₄	—	43	2	no	—
483	C₄⋊C₄	—	43	2	no	—
484	C₄⋊C₄	—	43	2	no	—
485	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
486	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
487	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
491	C₂²⋊C₄	—	43	1	no	—
492	C₂²⋊C₄	—	43	1	no	—
493	C₂²⋊C₄	—	43	1	no	—
494	C₂²⋊C₄	—	43	1	no	—
495	C₂²⋊C₄	—	43	2	no	—
496	C₂²⋊C₄	—	43	2	no	—
497	C₂²⋊C₄	—	43	2	no	—
498	C₂²⋊C₄	—	43	2	no	—
499	C₂²⋊C₄	—	43	2	no	—
500	C₂²⋊C₄	—	43	2	no	—
501	C₂²⋊C₄	—	43	2	no	—
502	C₂²⋊C₄	—	43	2	no	—
503	C₂²⋊C₄	—	43	2	no	—
504	C₂²⋊C₄	—	43	2	no	—
505	C₂²⋊C₄	—	43	2	no	—
506	C₂²⋊C₄	—	43	2	no	—
507	C₂²⋊C₄	—	43	2	no	—
508	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
513	C₄²	—	43	2	no	—
514	C₄²	—	43	1	no	—
515	C₄²	—	43	1	no	—
516	C₄²	—	43	1	no	—
517	C₄²	—	43	1	no	—
518	C₄²	—	43	2	no	—
519	C₄²	—	43	2	no	—
520	C₄²	—	43	2	no	—
521	C₄²	—	43	2	no	—
522	C₄²	C₂²×D₄₃	1	1	yes	characteristic
523	C₄²	C₂²×D₄₃	1	1	yes	characteristic
524	C₄²	C₂²×D₄₃	1	1	yes	characteristic
525	C₄²	C₂²×D₄₃	1	1	yes	characteristic
526	C₄²	C₂²×D₄₃	1	2	yes	—
527	C₂³	—	43	2	no	—
528	C₂³	C₂³×D₄₃	1	1	yes	characteristic
529	C₂³	C₂³×D₄₃	1	2	yes	—
530	Q₈	—	2	2	no	—
531	Q₈	—	86	2	no	—
532	Q₈	—	172	2	no	—
533	Q₈	—	172	1	no	—
534	Q₈	—	172	1	no	—
535	Q₈	—	172	1	no	—
536	Q₈	—	172	1	no	—
537	Q₈	—	172	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	86	2	no	—
541	D₄	—	172	2	no	—
542	D₄	—	172	2	no	—
543	D₄	—	172	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	43	2	no	—
549	C₂×C₄	—	43	1	no	—
550	C₂×C₄	—	43	1	no	—
551	C₂×C₄	—	43	1	no	—
552	C₂×C₄	—	43	1	no	—
553	C₂×C₄	—	43	2	no	—
554	C₂×C₄	—	43	1	no	—
555	C₂×C₄	—	43	1	no	—
556	C₂×C₄	—	43	1	no	—
557	C₂×C₄	—	43	1	no	—
558	C₂×C₄	—	43	2	no	—
559	C₂×C₄	—	172	2	no	—
560	C₂×C₄	—	172	2	no	—
561	C₂×C₄	—	172	2	no	—
562	C₂×C₄	—	172	2	no	—
563	C₂×C₄	—	172	2	no	—
564	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₄₃	1	2	yes	—
566	C₂×C₄	C₂³×D₄₃	1	2	yes	—
567	C₂×C₄	C₂³×D₄₃	1	2	yes	—
568	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	86	2	no	—
580	C₂²	—	86	2	no	—
581	C₂²	—	86	2	no	—
582	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	86	2	no	—
592	C₄	—	86	1	no	—
593	C₄	—	86	1	no	—
594	C₄	—	86	2	no	—
595	C₄	—	86	1	no	—
596	C₄	—	86	1	no	—
597	C₄	—	86	2	no	—
598	C₄	—	86	1	no	—
599	C₄	—	86	1	no	—
600	C₄	—	86	1	no	—
601	C₄	—	86	1	no	—
602	C₄	#13063372	1	2	yes	—
603	C₂	—	4	1	no	—
604	C₂	—	4	2	no	—
605	C₂	—	172	2	no	—
606	C₂	C₂×#13063372	1	1	yes	characteristic
607	C₂	#14583735	1	1	yes	characteristic
608	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	#3557
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. #14583651	C₂	semidirect
2. #14583651	C₂	semidirect
3. #14583632	C₂	semidirect
4. #14583631	C₂	semidirect
5. #14583626	C₂	semidirect
6. #14583625	C₂	semidirect
7. #14583621	C₂	semidirect
8. #14583618	C₂	semidirect
9. #14583608	C₂	semidirect
10. #14583605	C₂	semidirect
11. #14583588	C₂	semidirect
12. #14583582	C₂	semidirect
13. #14583522	C₂	semidirect
14. #14583517	C₂	semidirect
15. #14583516	C₂	semidirect
16. #14583514	C₂	semidirect
17. #14583509	C₂	semidirect
19. #14583492	C₂	semidirect
20. #14583491	C₂	semidirect
21. #14583456	C₂	semidirect
22. #14583433	C₂	semidirect
23. C₄₃×#529	C₂	semidirect
327. #529	D₄₃	semidirect
328. C₄₃	#3557	semidirect