Subgroups — #25979161

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148625	C₂	1	2	yes	maximal, complemented
2	#19147568	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147459	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147299	C₂	1	2	yes	maximal, complemented
5	#19147014	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146996	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146992	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146832	C₂	1	2	yes	maximal, complemented
9	#19146735	C₂	1	2	yes	maximal, complemented
10	#19146731	C₂	1	2	yes	maximal, complemented
11	#19146270	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146269	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146269	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145241	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145171	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144837	C₂	1	2	yes	maximal, complemented
17	#19144833	C₂	1	2	yes	maximal, complemented
18	#19144684	C₂	1	2	yes	maximal, complemented
19	#19143566	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143448	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143442	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
25	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
27	#14583613	C₂²	1	2	yes	complemented
28	#14583605	C₂²	1	2	yes	complemented
29	#14583602	C₂²	1	2	yes	complemented
30	#14583596	C₂²	1	2	yes	complemented
31	#14583594	—	2	2	no	—
32	#14583569	C₂²	1	2	yes	complemented
33	#14583546	—	2	2	no	—
34	#14583541	—	2	2	no	—
35	#14583538	—	2	2	no	—
36	#14583534	C₂²	1	2	yes	complemented
37	#14583533	C₂²	1	2	yes	complemented
38	#14583533	C₂²	1	2	yes	complemented
39	#14583500	C₂²	1	2	yes	complemented
40	#14583485	—	2	2	no	—
41	#14583481	—	2	2	no	—
42	#14583446	C₂²	1	2	yes	complemented
43	#14583427	C₂²	1	1	yes	characteristic
44	#14583407	—	2	2	no	—
45	#121×D₄₃	—	2	2	no	—
46	#14583373	C₂²	1	2	yes	complemented
47	#14583371	C₂²	1	2	yes	complemented
48	C₄×D₄×D₄₃	C₂²	1	2	yes	complemented
49	#14583303	C₂²	1	1	yes	characteristic, complemented
50	#14583300	C₂²	1	1	yes	characteristic, complemented
51	#14583274	C₂²	1	1	yes	characteristic, complemented
52	#14583274	C₂²	1	1	yes	characteristic, complemented
53	#14583262	C₂²	1	2	yes	complemented
54	#14583244	C₂²	1	2	yes	complemented
55	#14583225	C₂²	1	2	yes	complemented
56	#14583222	C₂²	1	2	yes	complemented
57	#14583220	C₂²	1	2	yes	complemented
58	#14583220	C₂²	1	2	yes	complemented
59	#14583219	C₂²	1	2	yes	complemented
60	#14583216	C₂²	1	2	yes	complemented
61	#14583201	C₂²	1	2	yes	complemented
62	#14583198	C₂²	1	2	yes	complemented
63	#14583196	C₂²	1	2	yes	complemented
64	#14583196	C₂²	1	2	yes	complemented
65	#14583188	C₂²	1	2	yes	complemented
66	#14583187	C₂²	1	2	yes	complemented
67	#14583151	C₂²	1	2	yes	complemented
68	#14583136	C₂²	1	1	yes	characteristic, complemented
69	#14583136	C₂²	1	1	yes	characteristic, complemented
70	#14583134	C₂²	1	2	yes	complemented
71	#14583132	C₂²	1	1	yes	characteristic, complemented
72	#14583132	C₂²	1	1	yes	characteristic, complemented
73	#14583093	C₂²	1	2	yes	complemented
74	#14583093	C₂²	1	2	yes	complemented
75	#14583092	C₂²	1	2	yes	complemented
76	#14583092	C₂²	1	2	yes	complemented
77	#14583091	C₂²	1	2	yes	complemented
78	#14583091	C₂²	1	2	yes	complemented
79	#14583034	C₂²	1	2	yes	complemented
80	#14583034	C₂²	1	2	yes	complemented
81	#14583032	C₂²	1	2	yes	complemented
82	#14583032	C₂²	1	2	yes	complemented
83	#14583031	C₂²	1	2	yes	complemented
84	#14583031	C₂²	1	2	yes	complemented
85	#14583027	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
87	#14583012	C₂²	1	2	yes	complemented
88	#14583012	C₂²	1	2	yes	complemented
89	#14583009	C₂²	1	2	yes	complemented
90	#14583009	C₂²	1	2	yes	complemented
91	#14583008	C₂²	1	2	yes	complemented
92	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
93	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
94	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
96	D₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
97	D₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
98	#14582981	C₂²	1	1	yes	characteristic
99	#14582981	C₂²	1	1	yes	characteristic
100	C₄×#10621882	C₂²	1	2	yes	complemented
101	C₄×#10621882	C₂²	1	2	yes	complemented
102	#14582979	C₂²	1	2	yes	complemented
103	#14582975	C₂²	1	1	yes	characteristic, complemented
104	#14582972	C₂²	1	1	yes	characteristic, complemented
105	#14582968	C₂²	1	1	yes	characteristic, complemented
106	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
107	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
108	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
109	#14582961	C₂²	1	1	yes	characteristic, complemented
110	#14582960	C₂²	1	1	yes	characteristic, complemented
111	#14582954	C₂²	1	1	yes	characteristic, complemented
112	#14582937	C₂²	1	1	yes	characteristic, complemented
113	#14582936	C₂²	1	1	yes	characteristic, complemented
114	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
115	#14582905	C₂²	1	2	yes	complemented
116	#14582902	C₂²	1	2	yes	complemented
117	#102×D₄₃	C₂²	1	2	yes	complemented
118	#14582853	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#540	C₂²	1	2	yes	complemented
121	C₄₃×#499	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#493	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#490	C₂²	1	2	yes	complemented
124	C₄₃×#469	C₂²	1	2	yes	complemented
125	C₄₃×#466	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#466	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#442	C₂²	1	2	yes	complemented
128	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621898	—	2	2	no	—
132	C₂×#10621900	—	2	2	no	—
133	C₂²×D₁₇₂	C₂³	1	2	yes	—
134	C₂×D₄×D₄₃	—	2	2	no	—
135	C₂×D₄×D₄₃	—	2	2	no	—
136	C₂×D₄×D₄₃	—	2	2	no	—
137	C₂×D₄×D₄₃	C₂³	1	2	yes	—
138	C₂×D₄×D₄₃	C₂³	1	2	yes	—
139	C₂²×C₄×D₄₃	—	2	2	no	—
140	C₂×D₃₄₄	—	2	4	no	—
141	C₂×D₃₄₄	C₂³	1	2	yes	—
142	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
143	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
144	C₂×#10621882	C₂³	1	2	yes	—
145	C₂×#10621882	C₂³	1	2	yes	—
146	C₂×#10621882	C₂³	1	2	yes	—
147	C₂×#10621882	C₂³	1	2	yes	—
148	D₈×D₄₃	—	2	4	no	—
149	D₈×D₄₃	—	2	4	no	—
150	C₂×#10621872	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
154	#13063324	C₂³	1	2	yes	—
155	#13063321	C₂³	1	2	yes	—
156	#13063321	C₂³	1	2	yes	—
157	#13063320	—	2	2	no	—
158	#13063320	D₄	1	1	yes	characteristic
159	#13063318	—	2	2	no	—
160	#13063318	D₄	1	1	yes	characteristic
161	#13063316	C₂³	1	2	yes	—
162	#13063315	D₄	1	1	yes	characteristic
163	#13063312	—	2	2	no	—
164	#13063311	—	2	2	no	—
165	#13063311	—	2	2	no	—
166	#13063311	D₄	1	1	yes	characteristic
167	#13063310	—	2	2	no	—
168	#13063310	D₄	1	1	yes	characteristic
169	#13063308	—	2	2	no	—
170	#13063307	—	2	2	no	—
171	#13063307	D₄	1	1	yes	characteristic
172	#13063306	—	2	2	no	—
173	#13063305	—	2	2	no	—
174	#13063303	—	2	2	no	—
175	#13063303	—	2	2	no	—
176	#13063303	D₄	1	1	yes	characteristic
177	#13063300	—	2	2	no	—
178	#13063300	C₂³	1	2	yes	—
179	#13063300	C₂³	1	2	yes	—
180	#13063299	—	2	2	no	—
181	#13063298	—	2	2	no	—
182	#13063298	—	2	2	no	—
183	#13063298	—	2	2	no	—
184	#13063298	—	2	2	no	—
185	#13063298	D₄	1	1	yes	characteristic
186	#13063297	—	2	2	no	—
187	#13063297	—	2	2	no	—
188	#13063297	—	2	2	no	—
189	#13063296	—	2	2	no	—
190	#13063296	—	2	2	no	—
191	#13063296	—	2	2	no	—
192	#13063296	C₂³	1	2	yes	—
193	#13063296	C₂³	1	2	yes	—
194	#13063295	—	2	2	no	—
195	#13063295	—	2	2	no	—
196	#13063293	—	2	2	no	—
197	#13063293	—	2	2	no	—
198	#13063293	—	2	2	no	—
199	#13063293	—	2	2	no	—
200	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
201	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
202	C₄×D₁₇₂	C₂³	1	2	yes	—
203	C₄×D₁₇₂	C₂³	1	2	yes	—
204	C₄×D₁₇₂	C₂³	1	2	yes	—
205	C₄×D₁₇₂	C₂³	1	2	yes	—
206	D₄×Dic₄₃	C₂³	1	2	yes	—
207	D₄×Dic₄₃	C₂³	1	2	yes	—
208	#13063287	—	2	2	no	—
209	#13063287	—	2	2	no	—
210	#13063287	—	2	2	no	—
211	#13063287	C₂³	1	2	yes	—
212	#13063287	C₂³	1	2	yes	—
213	C₄×C₂²⋊D₄₃	—	2	2	no	—
214	C₄×C₂²⋊D₄₃	—	2	2	no	—
215	C₄×C₂²⋊D₄₃	—	2	2	no	—
216	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
217	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
218	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
220	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
221	#13063284	C₂³	1	2	yes	—
222	#13063283	C₂³	1	2	yes	—
223	#13063282	C₂³	1	1	yes	characteristic
224	#13063281	—	2	2	no	—
225	C₄⋊C₄×D₄₃	—	2	2	no	—
226	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
227	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
228	C₂²⋊C₄×D₄₃	—	2	2	no	—
229	C₂²⋊C₄×D₄₃	—	2	2	no	—
230	C₂²⋊C₄×D₄₃	—	2	2	no	—
231	C₂²⋊C₄×D₄₃	—	2	2	no	—
232	C₄²×D₄₃	C₂³	1	1	yes	characteristic
233	#13063259	C₂³	1	1	yes	characteristic
234	#13063259	C₂³	1	1	yes	characteristic
235	#13063258	C₂³	1	2	yes	—
236	#13063258	C₂³	1	2	yes	—
237	#13063257	C₂³	1	2	yes	—
238	#13063256	C₂³	1	2	yes	—
239	#13063256	C₂³	1	2	yes	—
240	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
241	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
242	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
246	#13063247	C₂³	1	2	yes	—
247	#13063247	C₂³	1	2	yes	—
248	#13063247	C₂³	1	2	yes	—
249	#13063247	C₂³	1	2	yes	—
250	#13063246	C₂³	1	2	yes	—
251	#13063246	C₂³	1	2	yes	—
252	#13063246	C₂³	1	2	yes	—
253	#13063246	C₂³	1	2	yes	—
254	#13063245	C₂³	1	2	yes	—
255	#13063245	C₂³	1	2	yes	—
256	#13063245	C₂³	1	2	yes	—
257	#13063245	C₂³	1	2	yes	—
258	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
259	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
260	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
263	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
264	#13063236	C₂³	1	1	yes	characteristic
265	#13063235	C₂³	1	1	yes	characteristic
266	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
272	C₂×D₈×C₄₃	C₂³	1	2	yes	—
273	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
275	#127×C₄₃	C₂³	1	2	yes	—
276	#125×C₄₃	C₂³	1	2	yes	—
277	#123×C₄₃	—	2	2	no	—
278	#123×C₄₃	—	2	2	no	—
279	#121×C₄₃	—	2	2	no	—
280	#121×C₄₃	—	2	2	no	—
281	#121×C₄₃	C₂³	1	2	yes	—
282	#121×C₄₃	C₂³	1	2	yes	—
283	C₄×D₄×C₄₃	C₂³	1	2	yes	—
284	C₄×D₄×C₄₃	C₂³	1	2	yes	—
285	#117×C₄₃	C₂³	1	1	yes	characteristic
286	#107×C₄₃	C₂³	1	1	yes	characteristic
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	#106×C₄₃	C₂³	1	2	yes	—
289	#102×C₄₃	C₂³	1	2	yes	—
290	#102×C₄₃	C₂³	1	2	yes	—
291	#102×C₄₃	C₂³	1	2	yes	—
292	#102×C₄₃	C₂³	1	2	yes	—
293	#97×C₄₃	C₂³	1	1	yes	characteristic
294	#97×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₂³×D₄₃	—	2	2	no	—
298	C₂³×D₄₃	—	2	2	no	—
299	C₂³×D₄₃	—	2	2	no	—
300	C₂×D₄×C₄₃	—	2	2	no	—
301	C₂×D₄×C₄₃	—	2	2	no	—
302	C₂×D₄×C₄₃	—	2	2	no	—
303	C₂×D₄×C₄₃	—	2	2	no	—
304	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
305	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₄₃	—	2	2	no	—
307	C₂²×C₄×C₄₃	—	2	2	no	—
308	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
309	C₂×C₂²⋊D₄₃	—	2	2	no	—
310	C₂×C₂²⋊D₄₃	—	2	2	no	—
311	C₂×C₂²⋊D₄₃	—	2	2	no	—
312	C₂×C₂²⋊D₄₃	—	2	2	no	—
313	C₂×C₂²⋊D₄₃	—	2	2	no	—
314	C₂×C₂²⋊D₄₃	—	2	2	no	—
315	C₂×C₂²⋊D₄₃	—	2	2	no	—
316	C₂×C₂²⋊D₄₃	—	2	2	no	—
317	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
318	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×Dic₄₃	—	2	2	no	—
320	C₂²×Dic₄₃	—	2	2	no	—
321	#10621900	—	8	4	no	—
322	D₄×D₄₃	—	2	4	no	—
323	D₄×D₄₃	—	2	4	no	—
324	D₄×D₄₃	—	4	2	no	—
325	D₄×D₄₃	—	4	2	no	—
326	D₄×D₄₃	—	8	4	no	—
327	D₄×D₄₃	—	8	4	no	—
328	D₄×D₄₃	—	8	4	no	—
329	#10621898	—	8	4	no	—
330	C₂×D₁₇₂	—	2	2	no	—
331	C₂×D₁₇₂	—	2	2	no	—
332	C₂×D₁₇₂	—	2	2	no	—
333	C₂×D₁₇₂	—	2	4	no	—
334	C₂×D₁₇₂	—	4	2	no	—
335	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
336	C₂×D₁₇₂	C₂⁴	1	2	yes	—
337	C₂×D₁₇₂	C₂⁴	1	2	yes	—
338	C₂×C₄×D₄₃	—	2	2	no	—
339	C₂×C₄×D₄₃	—	2	2	no	—
340	C₂×C₄×D₄₃	—	2	2	no	—
341	C₂×C₄×D₄₃	—	2	2	no	—
342	C₂×C₄×D₄₃	—	2	2	no	—
343	C₂×C₄×D₄₃	—	2	2	no	—
344	C₂×C₄×D₄₃	—	2	2	no	—
345	C₂×C₄×D₄₃	—	8	4	no	—
346	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
347	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
348	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
350	C₂×Dic₈₆	—	2	2	no	—
351	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
352	D₈×C₄₃	—	2	2	no	—
353	D₈×C₄₃	—	2	2	no	—
354	D₈×C₄₃	—	4	2	no	—
355	M₁₆×C₄₃	—	4	1	no	—
356	C₂×C₈×C₄₃	—	2	2	no	—
357	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₄₃	—	2	2	no	—
362	C₄⋊C₄×C₄₃	—	2	2	no	—
363	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
367	C₂²⋊C₄×C₄₃	—	2	2	no	—
368	C₂²⋊C₄×C₄₃	—	2	2	no	—
369	C₂²⋊C₄×C₄₃	—	2	2	no	—
370	C₂²⋊C₄×C₄₃	—	2	2	no	—
371	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
372	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₂²⋊Dic₄₃	—	2	2	no	—
376	C₂²⋊Dic₄₃	—	2	2	no	—
377	C₂²⋊Dic₄₃	—	2	2	no	—
378	C₂²⋊Dic₄₃	—	2	2	no	—
379	C₂²⋊Dic₄₃	—	2	2	no	—
380	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
381	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
382	#10621882	—	2	4	no	—
383	#10621882	—	2	4	no	—
384	#10621882	—	4	2	no	—
385	#10621882	—	4	2	no	—
386	(C₂×D₄₃)⋊C₄	—	2	2	no	—
387	(C₂×D₄₃)⋊C₄	—	2	2	no	—
388	(C₂×D₄₃)⋊C₄	—	2	2	no	—
389	(C₂×D₄₃)⋊C₄	—	2	2	no	—
390	(C₂×D₄₃)⋊C₄	—	2	2	no	—
391	(C₂×D₄₃)⋊C₄	—	2	2	no	—
392	(C₂×D₄₃)⋊C₄	—	2	2	no	—
393	(C₂×D₄₃)⋊C₄	—	2	2	no	—
394	(C₂×D₄₃)⋊C₄	—	2	2	no	—
395	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
396	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
397	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
398	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
399	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
400	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊Dic₄₃	—	2	2	no	—
402	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
403	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
404	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
405	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
406	Dic₄₃⋊C₄	—	2	2	no	—
407	Dic₄₃⋊C₄	—	2	2	no	—
408	Dic₄₃⋊C₄	—	2	2	no	—
409	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
411	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
412	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
413	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
414	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	—	2	2	no	—
416	C₄×Dic₄₃	—	2	2	no	—
417	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
419	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
420	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
425	D₃₄₄	—	2	4	no	—
426	D₃₄₄	—	2	2	no	—
427	D₃₄₄	#41	1	4	yes	complemented
428	#10621872	—	4	1	no	—
429	C₈×D₄₃	—	2	2	no	—
430	C₈×D₄₃	—	2	2	no	—
431	C₈×D₄₃	—	4	1	no	—
432	C₂³×C₄₃	—	2	2	no	—
433	C₂³×C₄₃	—	2	2	no	—
434	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
435	C₂²×D₄₃	—	2	2	no	—
436	C₂²×D₄₃	—	2	2	no	—
437	C₂²×D₄₃	—	4	4	no	—
438	C₂²×D₄₃	—	4	4	no	—
439	C₂²×D₄₃	—	4	4	no	—
440	C₂²×D₄₃	—	4	4	no	—
441	C₂²×D₄₃	—	8	2	no	—
442	C₂²×D₄₃	—	8	2	no	—
443	C₂²×D₄₃	—	8	2	no	—
444	C₂²×D₄₃	—	8	2	no	—
445	C₂²×D₄₃	—	8	2	no	—
446	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
447	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
448	D₄×C₄₃	—	2	2	no	—
449	D₄×C₄₃	—	2	2	no	—
450	D₄×C₄₃	—	2	2	no	—
451	D₄×C₄₃	—	2	2	no	—
452	D₄×C₄₃	—	8	2	no	—
453	D₄×C₄₃	—	8	2	no	—
454	D₄×C₄₃	—	8	2	no	—
455	D₄×C₄₃	—	8	2	no	—
456	C₂×C₄×C₄₃	—	2	1	no	—
457	C₂×C₄×C₄₃	—	2	1	no	—
458	C₂×C₄×C₄₃	—	2	2	no	—
459	C₂×C₄×C₄₃	—	2	2	no	—
460	C₂×C₄×C₄₃	—	8	2	no	—
461	C₂×C₄×C₄₃	—	8	2	no	—
462	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
468	C₂²⋊D₄₃	—	2	2	no	—
469	C₂²⋊D₄₃	—	2	2	no	—
470	C₂²⋊D₄₃	—	4	4	no	—
471	C₂²⋊D₄₃	—	4	4	no	—
472	C₂²⋊D₄₃	—	4	4	no	—
473	C₂²⋊D₄₃	—	4	4	no	—
474	C₂²⋊D₄₃	—	8	2	no	—
475	C₂²⋊D₄₃	—	8	2	no	—
476	C₂²⋊D₄₃	—	8	2	no	—
477	C₂²⋊D₄₃	—	8	2	no	—
478	C₂×Dic₄₃	—	2	2	no	—
479	C₂×Dic₄₃	—	2	2	no	—
480	C₂×Dic₄₃	—	4	4	no	—
481	C₂×Dic₄₃	—	8	2	no	—
482	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
488	D₁₇₂	—	2	2	no	—
489	D₁₇₂	—	2	2	no	—
490	D₁₇₂	—	2	2	no	—
491	D₁₇₂	—	2	2	no	—
492	D₁₇₂	—	4	4	no	—
493	D₁₇₂	—	4	4	no	—
494	D₁₇₂	—	8	2	no	—
495	D₁₇₂	C₂×#41	1	4	yes	—
496	C₄×D₄₃	—	2	2	no	—
497	C₄×D₄₃	—	2	1	no	—
498	C₄×D₄₃	—	2	1	no	—
499	C₄×D₄₃	—	2	1	no	—
500	C₄×D₄₃	—	2	1	no	—
501	C₄×D₄₃	—	2	2	no	—
502	C₄×D₄₃	—	4	4	no	—
503	C₄×D₄₃	—	8	2	no	—
504	C₄×D₄₃	—	8	2	no	—
505	C₄×D₄₃	—	8	2	no	—
506	C₄×D₄₃	—	8	2	no	—
507	C₄×D₄₃	—	8	2	no	—
508	C₄×D₄₃	—	8	2	no	—
509	Dic₈₆	—	2	2	no	—
510	Dic₈₆	—	8	2	no	—
511	C₈×C₄₃	—	2	1	no	—
512	C₈×C₄₃	—	2	1	no	—
513	C₈×C₄₃	—	2	1	no	—
514	C₈×C₄₃	C₂×#41	1	2	yes	—
515	C₄₃⋊C₈	—	2	1	no	—
516	C₄₃⋊C₈	—	2	1	no	—
517	C₄₃⋊C₈	—	2	1	no	—
518	C₄₃⋊C₈	—	2	1	no	—
519	#61480	—	43	1	no	maximal, Sylow
520	C₂²×C₄₃	—	2	1	no	—
521	C₂²×C₄₃	—	2	1	no	—
522	C₂²×C₄₃	—	2	1	no	—
523	C₂²×C₄₃	—	4	2	no	—
524	C₂²×C₄₃	—	4	2	no	—
525	C₂²×C₄₃	—	4	2	no	—
526	C₂²×C₄₃	—	4	2	no	—
527	C₂²×C₄₃	—	4	2	no	—
528	C₂²×C₄₃	—	4	2	no	—
529	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
530	C₂×D₄₃	—	2	1	no	—
531	C₂×D₄₃	—	2	1	no	—
532	C₂×D₄₃	—	2	4	no	—
533	C₂×D₄₃	—	2	1	no	—
534	C₂×D₄₃	—	2	1	no	—
535	C₂×D₄₃	—	2	1	no	—
536	C₂×D₄₃	—	4	2	no	—
537	C₂×D₄₃	—	4	2	no	—
538	C₂×D₄₃	—	4	2	no	—
539	C₂×D₄₃	—	4	2	no	—
540	C₂×D₄₃	—	4	2	no	—
541	C₂×D₄₃	—	8	8	no	—
542	C₂×D₄₃	—	16	4	no	—
543	C₂×D₄₃	—	16	4	no	—
544	C₂×D₄₃	#576	1	2	yes	—
545	C₄×C₄₃	—	2	1	no	—
546	C₄×C₄₃	—	2	1	no	—
547	C₄×C₄₃	—	2	1	no	—
548	C₄×C₄₃	—	2	1	no	—
549	C₄×C₄₃	—	2	1	no	—
550	C₄×C₄₃	—	4	2	no	—
551	C₄×C₄₃	—	4	2	no	—
552	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
553	C₄×C₄₃	#585	1	1	yes	characteristic
554	Dic₄₃	—	2	1	no	—
555	Dic₄₃	—	2	1	no	—
556	Dic₄₃	—	2	1	no	—
557	Dic₄₃	—	2	1	no	—
558	Dic₄₃	—	2	1	no	—
559	Dic₄₃	—	4	2	no	—
560	Dic₄₃	—	4	2	no	—
561	Dic₄₃	#576	1	2	yes	—
562	#3519	—	43	2	no	—
563	#3391	—	43	1	no	—
564	#3380	—	43	1	no	—
565	#3366	—	43	2	no	—
566	#3341	—	43	1	no	—
567	#3339	—	43	1	no	—
568	#3339	—	43	1	no	—
569	#3325	—	43	2	no	—
570	#3318	—	43	2	no	—
571	#3318	—	43	2	no	—
572	D₄×D₈	—	43	1	no	—
573	D₄×D₈	—	43	1	no	—
574	D₄×D₈	—	43	1	no	—
575	#3176	—	43	1	no	—
576	#3176	D₄₃	1	1	yes	characteristic, complemented
577	#3169	—	43	1	no	—
578	#3122	—	43	2	no	—
579	#3122	—	43	2	no	—
580	#3109	—	43	2	no	—
581	#2966	—	43	1	no	—
582	#2948	—	43	1	no	—
583	#2948	—	43	1	no	—
584	C₂×C₄×D₈	—	43	1	no	—
585	C₂×C₄₃	—	4	1	no	—
586	C₂×C₄₃	—	8	2	no	—
587	C₂×C₄₃	—	8	2	no	—
588	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
589	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
590	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
591	D₄₃	—	2	2	no	—
592	D₄₃	—	4	1	no	—
593	D₄₃	—	4	4	no	—
594	D₄₃	—	8	2	no	—
595	C₂²×D₈	—	43	1	no	—
596	C₂²×D₈	—	43	1	no	—
597	C₂²×D₈	—	43	1	no	—
598	#555	—	43	2	no	—
599	#554	—	43	2	no	—
600	#553	—	43	2	no	—
601	#553	—	43	2	no	—
602	#553	—	86	2	no	—
603	#550	—	43	2	no	—
604	#546	—	86	2	no	—
605	#546	—	86	2	no	—
606	#546	—	86	2	no	—
607	D₄²	—	43	2	no	—
608	D₄²	—	43	2	no	—
609	D₄²	—	43	2	no	—
610	#540	—	43	2	no	—
611	#540	C₂×D₄₃	1	2	yes	complemented
612	#538	—	86	2	no	—
613	#538	—	86	2	no	—
614	#532	—	43	2	no	—
615	#529	—	43	1	no	—
616	#525	—	86	2	no	—
617	C₂×#121	—	86	2	no	—
618	#518	—	43	2	no	—
619	#518	—	43	2	no	—
620	C₂×C₄×D₄	—	43	2	no	—
621	#500	—	43	1	no	—
622	#499	—	43	1	no	—
623	#499	C₂×D₄₃	1	1	yes	characteristic, complemented
624	#493	—	43	1	no	—
625	#493	—	43	1	no	—
626	#493	C₂×D₄₃	1	1	yes	characteristic, complemented
627	#490	—	43	2	no	—
628	#490	C₂×D₄₃	1	2	yes	complemented
629	#486	—	43	2	no	—
630	#482	—	43	2	no	—
631	#482	—	43	2	no	—
632	#482	—	43	2	no	—
633	#482	—	43	2	no	—
634	#481	—	43	2	no	—
635	#481	—	43	2	no	—
636	#478	—	43	2	no	—
637	#478	—	43	2	no	—
638	#478	—	43	2	no	—
639	#478	—	43	2	no	—
640	#476	—	43	2	no	—
641	#476	—	43	2	no	—
642	#469	—	43	2	no	—
643	#469	C₂×D₄₃	1	2	yes	complemented
644	#466	—	43	1	no	—
645	#466	—	43	1	no	—
646	#466	—	43	1	no	—
647	#466	—	43	1	no	—
648	#466	—	43	2	no	—
649	#466	C₂×D₄₃	1	1	yes	characteristic, complemented
650	#466	C₂×D₄₃	1	1	yes	characteristic, complemented
651	#459	—	43	2	no	—
652	#459	—	43	2	no	—
653	#459	—	43	2	no	—
654	#459	—	43	2	no	—
655	#459	—	43	2	no	—
656	#459	—	43	2	no	—
657	#447	—	43	2	no	—
658	#447	—	43	2	no	—
659	#447	—	43	2	no	—
660	#447	—	43	2	no	—
661	#447	—	43	2	no	—
662	#447	—	43	2	no	—
663	#446	—	43	1	no	—
664	C₈×Q₈	—	43	1	no	—
665	#442	—	43	2	no	—
666	#442	—	43	2	no	—
667	#442	—	43	2	no	—
668	#442	—	43	2	no	—
669	#442	—	43	2	no	—
670	#442	C₂×D₄₃	1	2	yes	complemented
671	C₄×D₈	—	43	1	no	—
672	C₄×D₈	—	43	1	no	—
673	C₄×D₈	—	43	2	no	—
674	C₄×D₈	—	43	2	no	—
675	C₄×D₈	—	43	1	no	—
676	C₄×D₈	—	43	1	no	—
677	C₄×D₈	—	43	2	no	—
678	C₄×D₈	—	43	1	no	—
679	C₄×D₈	—	43	1	no	—
680	C₄×D₈	—	43	1	no	—
681	C₄×D₈	—	43	1	no	—
682	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
683	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
684	#436	—	43	1	no	—
685	#435	—	43	1	no	—
686	#435	—	43	1	no	—
687	C₈×D₄	—	43	1	no	—
688	C₈×D₄	—	43	1	no	—
689	C₈×D₄	—	43	1	no	—
690	#433	—	43	1	no	—
691	#433	—	43	1	no	—
692	#432	—	43	1	no	—
693	#427	—	43	1	no	—
694	#427	—	43	1	no	—
695	C₂×#107	—	43	1	no	—
696	#418	—	43	2	no	—
697	#418	—	43	2	no	—
698	C₂×#102	—	43	2	no	—
699	#405	—	43	1	no	—
700	#405	C₂×D₄₃	1	1	yes	characteristic, complemented
701	C₂×C₄×C₈	—	43	1	no	—
702	C₄₃	#61480	1	1	yes	characteristic, complemented, Sylow
703	C₂×#41	—	86	2	no	—
704	C₂×#41	—	86	2	no	—
705	C₂²×D₄	—	43	2	no	—
706	C₂²×D₄	—	43	2	no	—
707	C₂²×D₄	—	43	2	no	—
708	C₂²×D₄	—	86	2	no	—
709	C₂²×D₄	—	86	2	no	—
710	C₂²×D₄	—	86	2	no	—
711	C₂³×C₄	—	86	2	no	—
712	C₂×D₈	—	43	2	no	—
713	C₂×D₈	—	43	2	no	—
714	C₂×D₈	—	43	2	no	—
715	C₂×D₈	—	43	2	no	—
716	C₂×D₈	—	43	1	no	—
717	C₂×D₈	—	43	1	no	—
718	C₂×D₈	—	43	2	no	—
719	C₂×D₈	—	86	4	no	—
720	C₂×D₈	—	86	4	no	—
721	C₂×D₈	—	86	4	no	—
722	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
723	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
724	C₂×D₈	C₂²×D₄₃	1	2	yes	—
725	C₂×M₁₆	—	43	1	no	—
726	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
727	C₂²×C₈	—	43	1	no	—
728	C₂²×C₈	—	43	1	no	—
729	C₂²×C₈	—	43	1	no	—
730	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
731	C₄⋊Q₈	—	43	2	no	—
732	#127	—	43	2	no	—
733	#127	—	43	2	no	—
734	#127	C₂²×D₄₃	1	2	yes	—
735	#126	—	43	1	no	—
736	#126	—	43	1	no	—
737	#126	—	86	2	no	—
738	#126	—	86	2	no	—
739	#125	—	43	1	no	—
740	#125	—	43	2	no	—
741	#125	C₂²×D₄₃	1	2	yes	—
742	#124	—	43	1	no	—
743	#124	—	86	2	no	—
744	#124	—	86	2	no	—
745	#124	—	86	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	43	1	no	—
749	#123	—	43	1	no	—
750	#123	—	86	2	no	—
751	#123	—	86	2	no	—
752	#123	—	86	2	no	—
753	#123	—	86	2	no	—
754	C₂²⋊Q₈	—	43	1	no	—
755	C₂²⋊Q₈	—	86	2	no	—
756	C₂²⋊Q₈	—	86	2	no	—
757	C₂²⋊Q₈	—	86	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	2	no	—
760	#121	—	43	1	no	—
761	#121	—	43	2	no	—
762	#121	—	43	2	no	—
763	#121	—	43	2	no	—
764	#121	—	43	2	no	—
765	#121	—	86	2	no	—
766	#121	—	86	2	no	—
767	#121	—	86	2	no	—
768	#121	—	86	2	no	—
769	#121	—	86	2	no	—
770	#121	—	86	2	no	—
771	#121	—	86	2	no	—
772	#121	—	86	2	no	—
773	#121	—	86	2	no	—
774	#121	—	86	2	no	—
775	#121	—	86	2	no	—
776	#121	—	86	2	no	—
777	#121	C₂²×D₄₃	1	2	yes	—
778	#121	C₂²×D₄₃	1	2	yes	—
779	#120	—	86	2	no	—
780	#120	—	86	2	no	—
781	#120	—	86	2	no	—
782	#120	—	86	2	no	—
783	#120	—	86	2	no	—
784	#120	—	86	2	no	—
785	C₄×Q₈	—	43	1	no	—
786	C₄×D₄	—	43	1	no	—
787	C₄×D₄	—	43	1	no	—
788	C₄×D₄	—	43	2	no	—
789	C₄×D₄	—	43	2	no	—
790	C₄×D₄	—	43	2	no	—
791	C₄×D₄	—	43	2	no	—
792	C₄×D₄	—	43	1	no	—
793	C₄×D₄	—	43	2	no	—
794	C₄×D₄	—	43	2	no	—
795	C₄×D₄	—	43	2	no	—
796	C₄×D₄	—	43	2	no	—
797	C₄×D₄	—	86	2	no	—
798	C₄×D₄	—	86	2	no	—
799	C₄×D₄	—	86	2	no	—
800	C₄×D₄	—	86	2	no	—
801	C₄×D₄	—	86	2	no	—
802	C₄×D₄	—	86	2	no	—
803	C₄×D₄	—	86	2	no	—
804	C₄×D₄	—	86	2	no	—
805	C₄×D₄	—	86	2	no	—
806	C₄×D₄	C₂²×D₄₃	1	2	yes	—
807	C₄×D₄	C₂²×D₄₃	1	2	yes	—
808	#117	—	43	1	no	—
809	#117	—	43	2	no	—
810	#117	—	43	2	no	—
811	#117	—	86	2	no	—
812	#117	C₂²×D₄₃	1	1	yes	characteristic
813	C₂×C₄⋊C₄	—	43	2	no	—
814	C₂×C₄⋊C₄	—	86	2	no	—
815	C₂×C₂²⋊C₄	—	86	2	no	—
816	C₂×C₂²⋊C₄	—	86	2	no	—
817	C₂×C₂²⋊C₄	—	86	2	no	—
818	C₂×C₂²⋊C₄	—	86	2	no	—
819	C₂×C₂²⋊C₄	—	86	2	no	—
820	C₂×C₄²	—	43	1	no	—
821	#107	—	43	1	no	—
822	#107	—	43	1	no	—
823	#107	—	43	2	no	—
824	#107	—	43	2	no	—
825	#107	C₂²×D₄₃	1	1	yes	characteristic
826	#107	C₂²×D₄₃	1	1	yes	characteristic
827	#106	—	43	2	no	—
828	#106	—	43	2	no	—
829	#106	—	43	2	no	—
830	#106	C₂²×D₄₃	1	2	yes	—
831	C₄⋊C₈	—	43	1	no	—
832	C₄⋊C₈	—	43	1	no	—
833	C₄⋊C₈	—	43	1	no	—
834	C₄⋊C₈	—	43	1	no	—
835	C₄⋊C₈	—	43	1	no	—
836	C₄⋊C₈	—	43	1	no	—
837	#102	—	43	2	no	—
838	#102	—	43	2	no	—
839	#102	—	43	2	no	—
840	#102	—	43	2	no	—
841	#102	—	43	2	no	—
842	#102	—	43	2	no	—
843	#102	—	43	2	no	—
844	#102	—	43	2	no	—
845	#102	—	43	2	no	—
846	#102	—	43	2	no	—
847	#102	—	43	2	no	—
848	#102	—	43	2	no	—
849	#102	C₂²×D₄₃	1	2	yes	—
850	#102	C₂²×D₄₃	1	2	yes	—
851	#102	C₂²×D₄₃	1	2	yes	—
852	#102	C₂²×D₄₃	1	2	yes	—
853	C₂²⋊C₈	—	43	1	no	—
854	C₂²⋊C₈	—	43	1	no	—
855	C₂²⋊C₈	—	43	1	no	—
856	C₂²⋊C₈	—	43	1	no	—
857	C₂²⋊C₈	—	43	1	no	—
858	C₂²⋊C₈	—	43	1	no	—
859	#97	—	43	1	no	—
860	#97	—	43	1	no	—
861	#97	C₂²×D₄₃	1	1	yes	characteristic
862	#97	C₂²×D₄₃	1	1	yes	characteristic
863	C₄×C₈	—	43	1	no	—
864	C₄×C₈	—	43	1	no	—
865	C₄×C₈	—	43	1	no	—
866	C₄×C₈	—	43	1	no	—
867	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
868	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
869	C₂⁴	—	86	2	no	—
870	C₂⁴	—	86	2	no	—
871	C₂⁴	—	86	2	no	—
872	#41	—	344	4	no	—
873	#41	—	344	4	no	—
874	C₂×Q₈	—	43	1	no	—
875	C₂×Q₈	—	86	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	43	1	no	—
881	C₂×D₄	—	43	1	no	—
882	C₂×D₄	—	43	1	no	—
883	C₂×D₄	—	43	2	no	—
884	C₂×D₄	—	43	2	no	—
885	C₂×D₄	—	86	4	no	—
886	C₂×D₄	—	86	2	no	—
887	C₂×D₄	—	86	2	no	—
888	C₂×D₄	—	86	2	no	—
889	C₂×D₄	—	86	2	no	—
890	C₂×D₄	—	86	2	no	—
891	C₂×D₄	—	86	2	no	—
892	C₂×D₄	—	86	2	no	—
893	C₂×D₄	—	86	2	no	—
894	C₂×D₄	—	86	4	no	—
895	C₂×D₄	—	86	4	no	—
896	C₂×D₄	—	86	2	no	—
897	C₂×D₄	—	86	2	no	—
898	C₂×D₄	—	86	2	no	—
899	C₂×D₄	—	344	4	no	—
900	C₂×D₄	—	344	4	no	—
901	C₂×D₄	—	344	4	no	—
902	C₂×D₄	—	172	2	no	—
903	C₂×D₄	—	172	2	no	—
904	C₂×D₄	—	172	2	no	—
905	C₂×D₄	C₂³×D₄₃	1	2	yes	—
906	C₂×D₄	C₂³×D₄₃	1	2	yes	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	43	1	no	—
910	C₂²×C₄	—	43	1	no	—
911	C₂²×C₄	—	43	1	no	—
912	C₂²×C₄	—	43	1	no	—
913	C₂²×C₄	—	86	2	no	—
914	C₂²×C₄	—	86	2	no	—
915	C₂²×C₄	—	86	2	no	—
916	C₂²×C₄	—	86	2	no	—
917	C₂²×C₄	—	86	2	no	—
918	C₂²×C₄	—	86	2	no	—
919	C₂²×C₄	—	86	2	no	—
920	C₂²×C₄	—	86	2	no	—
921	C₂²×C₄	—	86	2	no	—
922	C₂²×C₄	—	344	4	no	—
923	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
924	D₈	—	2	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	2	no	—
927	D₈	—	43	4	no	—
928	D₈	—	86	4	no	—
929	D₈	—	86	4	no	—
930	D₈	—	86	4	no	—
931	D₈	—	86	2	no	—
932	D₈	—	172	2	no	—
933	D₈	—	172	2	no	—
934	M₁₆	—	4	1	no	—
935	M₁₆	—	172	1	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	43	1	no	—
938	C₂×C₈	—	43	1	no	—
939	C₂×C₈	—	43	1	no	—
940	C₂×C₈	—	43	1	no	—
941	C₂×C₈	—	86	2	no	—
942	C₂×C₈	—	86	2	no	—
943	C₂×C₈	—	172	1	no	—
944	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
945	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
946	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
947	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	43	1	no	—
951	C₄⋊C₄	—	43	1	no	—
952	C₄⋊C₄	—	43	1	no	—
953	C₄⋊C₄	—	43	1	no	—
954	C₄⋊C₄	—	43	1	no	—
955	C₄⋊C₄	—	43	1	no	—
956	C₄⋊C₄	—	43	1	no	—
957	C₄⋊C₄	—	43	1	no	—
958	C₄⋊C₄	—	43	2	no	—
959	C₄⋊C₄	—	43	2	no	—
960	C₄⋊C₄	—	86	2	no	—
961	C₄⋊C₄	—	86	2	no	—
962	C₄⋊C₄	—	86	2	no	—
963	C₄⋊C₄	—	86	2	no	—
964	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
965	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
967	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	43	1	no	—
973	C₂²⋊C₄	—	43	1	no	—
974	C₂²⋊C₄	—	43	1	no	—
975	C₂²⋊C₄	—	43	1	no	—
976	C₂²⋊C₄	—	43	1	no	—
977	C₂²⋊C₄	—	43	1	no	—
978	C₂²⋊C₄	—	43	1	no	—
979	C₂²⋊C₄	—	43	1	no	—
980	C₂²⋊C₄	—	86	2	no	—
981	C₂²⋊C₄	—	86	2	no	—
982	C₂²⋊C₄	—	86	2	no	—
983	C₂²⋊C₄	—	86	2	no	—
984	C₂²⋊C₄	—	86	2	no	—
985	C₂²⋊C₄	—	86	2	no	—
986	C₂²⋊C₄	—	86	2	no	—
987	C₂²⋊C₄	—	86	2	no	—
988	C₂²⋊C₄	—	86	2	no	—
989	C₂²⋊C₄	—	86	2	no	—
990	C₂²⋊C₄	—	86	2	no	—
991	C₂²⋊C₄	—	86	2	no	—
992	C₂²⋊C₄	—	86	2	no	—
993	C₂²⋊C₄	—	86	2	no	—
994	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
995	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
996	C₄²	—	43	1	no	—
997	C₄²	—	43	1	no	—
998	C₄²	—	43	1	no	—
999	C₄²	—	43	1	no	—
1000	C₄²	—	86	2	no	—
1001	C₄²	—	86	2	no	—
1002	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1003	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	43	1	no	—
1007	C₂³	—	43	1	no	—
1008	C₂³	—	86	2	no	—
1009	C₂³	—	86	2	no	—
1010	C₂³	—	344	2	no	—
1011	C₂³	—	344	2	no	—
1012	C₂³	—	344	2	no	—
1013	C₂³	—	344	2	no	—
1014	C₂³	—	344	2	no	—
1015	C₂³	—	172	4	no	—
1016	C₂³	—	172	4	no	—
1017	C₂³	—	172	4	no	—
1018	C₂³	—	172	4	no	—
1019	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1020	Q₈	—	86	2	no	—
1021	Q₈	—	344	2	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	8	2	no	—
1027	D₄	—	8	2	no	—
1028	D₄	—	8	2	no	—
1029	D₄	—	8	2	no	—
1030	D₄	—	43	4	no	—
1031	D₄	—	86	2	no	—
1032	D₄	—	86	2	no	—
1033	D₄	—	86	2	no	—
1034	D₄	—	86	2	no	—
1035	D₄	—	86	2	no	—
1036	D₄	—	86	2	no	—
1037	D₄	—	344	2	no	—
1038	D₄	—	344	2	no	—
1039	D₄	—	344	2	no	—
1040	D₄	—	344	2	no	—
1041	D₄	—	344	2	no	—
1042	D₄	—	172	4	no	—
1043	D₄	—	172	4	no	—
1044	D₄	—	172	4	no	—
1045	D₄	—	172	4	no	—
1046	D₄	—	172	4	no	—
1047	D₄	—	172	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	43	1	no	—
1055	C₂×C₄	—	43	1	no	—
1056	C₂×C₄	—	43	1	no	—
1057	C₂×C₄	—	43	1	no	—
1058	C₂×C₄	—	43	1	no	—
1059	C₂×C₄	—	43	1	no	—
1060	C₂×C₄	—	86	2	no	—
1061	C₂×C₄	—	86	2	no	—
1062	C₂×C₄	—	86	1	no	—
1063	C₂×C₄	—	86	1	no	—
1064	C₂×C₄	—	86	1	no	—
1065	C₂×C₄	—	86	1	no	—
1066	C₂×C₄	—	86	2	no	—
1067	C₂×C₄	—	86	2	no	—
1068	C₂×C₄	—	344	2	no	—
1069	C₂×C₄	—	344	2	no	—
1070	C₂×C₄	—	344	2	no	—
1071	C₂×C₄	—	344	2	no	—
1072	C₂×C₄	—	344	2	no	—
1073	C₂×C₄	—	344	2	no	—
1074	C₂×C₄	—	344	2	no	—
1075	C₂×C₄	—	172	4	no	—
1076	C₂×C₄	—	172	4	no	—
1077	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1078	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1079	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1080	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1081	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1082	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	86	1	no	—
1087	C₈	—	86	1	no	—
1088	C₈	—	86	1	no	—
1089	C₈	—	86	1	no	—
1090	C₈	#41×D₄₃	1	2	yes	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	43	2	no	—
1101	C₂²	—	86	1	no	—
1102	C₂²	—	86	1	no	—
1103	C₂²	—	86	1	no	—
1104	C₂²	—	86	1	no	—
1105	C₂²	—	86	1	no	—
1106	C₂²	—	86	4	no	—
1107	C₂²	—	344	8	no	—
1108	C₂²	—	172	2	no	—
1109	C₂²	—	172	2	no	—
1110	C₂²	—	172	2	no	—
1111	C₂²	—	172	2	no	—
1112	C₂²	—	172	2	no	—
1113	C₂²	—	688	4	no	—
1114	C₂²	—	688	4	no	—
1115	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	2	no	—
1123	C₄	—	43	2	no	—
1124	C₄	—	86	1	no	—
1125	C₄	—	86	1	no	—
1126	C₄	—	86	1	no	—
1127	C₄	—	86	1	no	—
1128	C₄	—	86	1	no	—
1129	C₄	—	172	2	no	—
1130	C₄	—	172	2	no	—
1131	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1132	C₄	#14583735	1	1	yes	characteristic
1133	C₂	—	4	1	no	—
1134	C₂	—	8	2	no	—
1135	C₂	—	8	2	no	—
1136	C₂	—	86	2	no	—
1137	C₂	—	344	2	no	—
1138	C₂	—	172	1	no	—
1139	C₂	—	172	4	no	—
1140	C₂	#19148081	1	1	yes	characteristic
1141	C₂	#576×D₄₃	1	1	yes	characteristic
1142	C₂	#576×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3176	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3176	D₄₃
hypocenter	C₄₃	#61480
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3176

Complements

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

N	H ≅ G/N	type
1. #19148625	C₂	semidirect
2. #19147568	C₂	semidirect
3. #19147459	C₂	semidirect
4. #19147299	C₂	semidirect
5. #19147014	C₂	semidirect
6. #19146996	C₂	semidirect
7. #19146992	C₂	semidirect
8. #19146832	C₂	semidirect
9. #19146735	C₂	semidirect
10. #19146731	C₂	semidirect
11. #19146270	C₂	semidirect
12. #19146269	C₂	semidirect
13. #19146269	C₂	semidirect
14. #19145241	C₂	semidirect
15. #19145171	C₂	semidirect
16. #19144837	C₂	semidirect
17. #19144833	C₂	semidirect
18. #19144684	C₂	semidirect
19. #19143566	C₂	semidirect
20. #19143448	C₂	semidirect
21. #19143442	C₂	semidirect
22. C₄×D₈×D₄₃	C₂	semidirect
23. C₄₃×#3176	C₂	semidirect
27. #14583613	C₂²	semidirect
28. #14583605	C₂²	semidirect
29. #14583602	C₂²	semidirect
30. #14583596	C₂²	semidirect
32. #14583569	C₂²	semidirect
36. #14583534	C₂²	semidirect
37. #14583533	C₂²	semidirect
38. #14583533	C₂²	semidirect
39. #14583500	C₂²	semidirect
42. #14583446	C₂²	semidirect
46. #14583373	C₂²	semidirect
47. #14583371	C₂²	semidirect
48. C₄×D₄×D₄₃	C₂²	semidirect
49. #14583303	C₂²	semidirect
50. #14583300	C₂²	semidirect
51. #14583274	C₂²	semidirect
52. #14583274	C₂²	semidirect
53. #14583262	C₂²	semidirect
54. #14583244	C₂²	semidirect
55. #14583225	C₂²	semidirect
56. #14583222	C₂²	semidirect
57. #14583220	C₂²	semidirect
58. #14583220	C₂²	semidirect
59. #14583219	C₂²	semidirect
60. #14583216	C₂²	semidirect
61. #14583201	C₂²	semidirect
62. #14583198	C₂²	semidirect
63. #14583196	C₂²	semidirect
64. #14583196	C₂²	semidirect
65. #14583188	C₂²	semidirect
66. #14583187	C₂²	semidirect
67. #14583151	C₂²	semidirect
68. #14583136	C₂²	semidirect
69. #14583136	C₂²	semidirect
70. #14583134	C₂²	semidirect
71. #14583132	C₂²	semidirect
72. #14583132	C₂²	semidirect
73. #14583093	C₂²	semidirect
74. #14583093	C₂²	semidirect
75. #14583092	C₂²	semidirect
76. #14583092	C₂²	semidirect
77. #14583091	C₂²	semidirect
78. #14583091	C₂²	semidirect
79. #14583034	C₂²	semidirect
80. #14583034	C₂²	semidirect
81. #14583032	C₂²	semidirect
82. #14583032	C₂²	semidirect
83. #14583031	C₂²	semidirect
84. #14583031	C₂²	semidirect
85. #14583027	C₂²	semidirect
86. C₈×Dic₈₆	C₂²	semidirect
87. #14583012	C₂²	semidirect
88. #14583012	C₂²	semidirect
89. #14583009	C₂²	semidirect
90. #14583009	C₂²	semidirect
91. #14583008	C₂²	semidirect
94. C₄×D₃₄₄	C₂²	semidirect
95. C₄×D₃₄₄	C₂²	semidirect
96. D₈×Dic₄₃	C₂²	semidirect
97. D₈×Dic₄₃	C₂²	semidirect
100. C₄×#10621882	C₂²	semidirect
101. C₄×#10621882	C₂²	semidirect
102. #14582979	C₂²	semidirect
103. #14582975	C₂²	semidirect
104. #14582972	C₂²	semidirect
105. #14582968	C₂²	semidirect
106. C₈×D₁₇₂	C₂²	semidirect
107. C₈×C₂²⋊D₄₃	C₂²	semidirect
108. C₈×C₂²⋊D₄₃	C₂²	semidirect
109. #14582961	C₂²	semidirect
110. #14582960	C₂²	semidirect
111. #14582954	C₂²	semidirect
112. #14582937	C₂²	semidirect
113. #14582936	C₂²	semidirect
114. #107×D₄₃	C₂²	semidirect
115. #14582905	C₂²	semidirect
116. #14582902	C₂²	semidirect
117. #102×D₄₃	C₂²	semidirect
118. #14582853	C₂²	semidirect
119. C₄×C₈×D₄₃	C₂²	semidirect
120. C₄₃×#540	C₂²	semidirect
121. C₄₃×#499	C₂²	semidirect
122. C₄₃×#493	C₂²	semidirect
123. C₄₃×#490	C₂²	semidirect
124. C₄₃×#469	C₂²	semidirect
125. C₄₃×#466	C₂²	semidirect
126. C₄₃×#466	C₂²	semidirect
127. C₄₃×#442	C₂²	semidirect
128. C₄×D₈×C₄₃	C₂²	semidirect
129. C₄×D₈×C₄₃	C₂²	semidirect
130. C₄₃×#405	C₂²	semidirect
427. D₃₄₄	#41	semidirect
576. #3176	D₄₃	semidirect
611. #540	C₂×D₄₃	semidirect
623. #499	C₂×D₄₃	semidirect
626. #493	C₂×D₄₃	semidirect
628. #490	C₂×D₄₃	semidirect
643. #469	C₂×D₄₃	semidirect
649. #466	C₂×D₄₃	semidirect
650. #466	C₂×D₄₃	semidirect
670. #442	C₂×D₄₃	semidirect
682. C₄×D₈	C₂×D₄₃	semidirect
683. C₄×D₈	C₂×D₄₃	semidirect
700. #405	C₂×D₄₃	semidirect
702. C₄₃	#61480	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19148625	2
#19147568	2
#19147459	2
#19147299	2
#19147014	2
#19146996	2
#19146992	2
#19146832	2
#19146735	2
#19146731	2
#19146270	2
#19146269	2
#19145241	2
#19145171	2
#19144837	2
#19144833	2
#19144684	2
#19143566	2
#19143448	2
#19143442	2
C₄×D₈×D₄₃	2
C₄₃×#3176	2
#61480	43