Subgroups — #25969063

Order 11008.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148330	C₂	1	1	yes	maximal, characteristic
2	#19148000	C₂	1	1	yes	maximal, characteristic, complemented
3	#19145895	C₂	1	2	yes	maximal, complemented
4	#19145880	C₂	1	2	yes	maximal, complemented
5	#19145850	C₂	1	2	yes	maximal, complemented
6	#19145850	C₂	1	2	yes	maximal, complemented
7	#19145837	C₂	1	2	yes	maximal, complemented
8	#19145795	C₂	1	2	yes	maximal, complemented
9	#19145776	C₂	1	2	yes	maximal, complemented
10	#19145733	C₂	1	2	yes	maximal, complemented
11	#19145134	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145126	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144951	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144951	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144536	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144528	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144510	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14583224	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144459	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144448	C₂	1	1	yes	maximal, characteristic, complemented
21	#19144427	C₂	1	1	yes	maximal, characteristic, complemented
22	#19144427	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#14583612	—	2	1	no	—
25	#14583597	—	2	1	no	—
26	#14583593	—	2	1	no	—
27	#14583573	—	2	2	no	—
28	#14583550	—	2	1	no	—
29	#14583539	—	2	2	no	—
30	#14583530	—	2	1	no	—
31	#14583530	—	2	1	no	—
32	#14583527	C₂²	1	1	yes	characteristic
33	#14583527	C₂²	1	1	yes	characteristic
34	#14583527	C₂²	1	1	yes	characteristic
35	#14583527	C₂²	1	1	yes	characteristic
36	#14583527	C₂²	1	1	yes	characteristic
37	#14583527	C₂²	1	2	yes	complemented
38	#14583527	C₂²	1	2	yes	complemented
39	#14583525	—	2	2	no	—
40	#14583520	C₂²	1	2	yes	—
41	#14583504	C₂²	1	2	yes	—
42	#14583468	C₂²	1	1	yes	characteristic
43	#14583456	C₂²	1	2	yes	complemented
44	#14583456	C₂²	1	2	yes	complemented
45	#14583452	—	2	2	no	—
46	#14583452	—	2	1	no	—
47	#14583452	—	2	1	no	—
48	#14583449	C₂²	1	2	yes	—
49	#14583433	C₂²	1	2	yes	—
50	#14583410	C₂²	1	1	yes	characteristic
51	C₂×#13063299	C₂²	1	1	yes	characteristic
52	#14583379	C₂²	1	1	yes	characteristic
53	#14583373	C₂²	1	1	yes	characteristic
54	C₂×#13063284	C₂²	1	1	yes	characteristic
55	C₂×#13063284	C₂²	1	1	yes	characteristic
56	#14583308	C₂²	1	2	yes	complemented
57	#14583308	C₂²	1	2	yes	complemented
58	#14583308	C₂²	1	2	yes	complemented
59	#14583308	C₂²	1	2	yes	complemented
60	#14583304	C₂²	1	2	yes	complemented
61	#14583301	C₂²	1	2	yes	complemented
62	#14583301	C₂²	1	2	yes	complemented
63	#14583297	C₂²	1	2	yes	complemented
64	#14583264	C₂²	1	2	yes	complemented
65	#14583264	C₂²	1	2	yes	complemented
66	#14583259	C₂²	1	2	yes	complemented
67	#14583259	C₂²	1	2	yes	complemented
68	#14583254	C₂²	1	2	yes	complemented
69	#14583254	C₂²	1	2	yes	complemented
70	#14583246	C₂²	1	2	yes	complemented
71	#14583246	C₂²	1	2	yes	complemented
72	#14583241	C₂²	1	1	yes	characteristic, complemented
73	#14583241	C₂²	1	2	yes	complemented
74	#14583241	C₂²	1	1	yes	characteristic, complemented
75	#14583241	C₂²	1	2	yes	complemented
76	#14583235	C₂²	1	1	yes	characteristic, complemented
77	#14583230	C₂²	1	1	yes	characteristic, complemented
78	#14583224	C₂²	1	2	yes	—
79	#14583224	C₂²	1	2	yes	—
80	#14583224	C₂²	1	2	yes	—
81	#14583224	C₂²	1	2	yes	—
82	#14583224	C₂²	1	2	yes	—
83	#14583224	C₂²	1	2	yes	—
84	#14583224	C₂²	1	1	yes	characteristic, complemented
85	#14583224	C₂²	1	2	yes	complemented
86	#14583224	C₂²	1	1	yes	characteristic, complemented
87	#14583224	C₂²	1	2	yes	complemented
88	#14583218	C₂²	1	2	yes	—
89	#14583218	C₂²	1	1	yes	characteristic, complemented
90	#14583213	C₂²	1	2	yes	—
91	#14583213	C₂²	1	1	yes	characteristic, complemented
92	#14583207	C₂²	1	2	yes	complemented
93	#14583207	C₂²	1	2	yes	complemented
94	#14583200	C₂²	1	2	yes	complemented
95	#14583200	C₂²	1	2	yes	complemented
96	#14583200	C₂²	1	2	yes	complemented
97	#14583200	C₂²	1	2	yes	complemented
98	#14583200	C₂²	1	2	yes	complemented
99	#14583200	C₂²	1	2	yes	complemented
100	#14583195	C₂²	1	2	yes	complemented
101	#14583190	C₂²	1	2	yes	complemented
102	#14583190	C₂²	1	2	yes	complemented
103	#14583190	C₂²	1	2	yes	complemented
104	#14583185	C₂²	1	2	yes	complemented
105	#14583180	C₂²	1	2	yes	complemented
106	#14583180	C₂²	1	2	yes	complemented
107	#14583180	C₂²	1	2	yes	complemented
108	#14582941	C₂²	1	1	yes	characteristic
109	#14582941	C₂²	1	1	yes	characteristic
110	#14582941	C₂²	1	1	yes	characteristic
111	#14582941	C₂²	1	1	yes	characteristic
112	#14582937	C₂²	1	1	yes	characteristic
113	#14582937	C₂²	1	1	yes	characteristic
114	C₂×#13063259	C₂²	1	1	yes	characteristic
115	C₂×#13063257	C₂²	1	1	yes	characteristic
116	#14582905	C₂²	1	1	yes	characteristic
117	#14582905	C₂²	1	1	yes	characteristic
118	#14582901	C₂²	1	1	yes	characteristic
119	#14582901	C₂²	1	1	yes	characteristic
120	#14582896	C₂²	1	1	yes	characteristic
121	#14582896	C₂²	1	1	yes	characteristic
122	C₂×#13063247	C₂²	1	1	yes	characteristic
123	C₂×#13063247	C₂²	1	1	yes	characteristic
124	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
125	C₄₃×#433	C₂²	1	2	yes	complemented
126	C₄₃×#433	C₂²	1	2	yes	complemented
127	C₄₃×#432	C₂²	1	2	yes	complemented
128	C₄₃×#431	C₂²	1	2	yes	complemented
129	C₄₃×#424	C₂²	1	1	yes	characteristic
130	C₄₃×#424	C₂²	1	1	yes	characteristic
131	C₄₃×#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
133	C₄₃×#405	C₂²	1	1	yes	characteristic
134	C₄₃×#405	C₂²	1	1	yes	characteristic
135	C₂×#10621898	—	2	2	no	—
136	C₂×#10621898	C₂³	1	1	yes	characteristic
137	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
138	C₂²×C₂²⋊D₄₃	—	2	1	no	—
139	#13063325	C₂³	1	2	yes	—
140	#13063325	C₂³	1	2	yes	—
141	#13063325	C₂³	1	2	yes	—
142	#13063325	C₂³	1	2	yes	—
143	#13063325	C₂³	1	2	yes	—
144	#13063324	—	2	1	no	—
145	#13063324	—	2	1	no	—
146	#13063324	—	2	1	no	—
147	#13063324	—	2	1	no	—
148	#13063324	—	2	1	no	—
149	#13063324	—	2	2	no	—
150	#13063324	—	2	2	no	—
151	#13063322	C₂³	1	2	yes	—
152	#13063320	—	2	2	no	—
153	#13063319	—	2	2	no	—
154	#13063317	C₂³	1	2	yes	—
155	#13063317	C₂³	1	2	yes	—
156	#13063317	C₂³	1	2	yes	—
157	#13063317	C₂³	1	2	yes	—
158	#13063317	C₂³	1	2	yes	—
159	#13063316	—	2	1	no	—
160	#13063316	—	2	1	no	—
161	#13063316	—	2	1	no	—
162	#13063316	—	2	1	no	—
163	#13063316	—	2	1	no	—
164	#13063316	—	2	2	no	—
165	#13063316	—	2	2	no	—
166	#13063313	—	2	2	no	—
167	#13063313	C₂³	1	2	yes	—
168	#13063311	—	2	2	no	—
169	#13063310	—	2	2	no	—
170	#13063310	—	2	2	no	—
171	#13063308	—	2	1	no	—
172	#13063308	—	2	2	no	—
173	#13063307	—	2	2	no	—
174	#13063304	—	2	2	no	—
175	#13063304	—	2	2	no	—
176	#13063304	—	2	2	no	—
177	#13063304	—	2	2	no	—
178	#13063304	C₂³	1	1	yes	characteristic
179	#13063304	C₂³	1	1	yes	characteristic
180	#13063303	—	2	2	no	—
181	#13063302	—	2	2	no	—
182	#13063302	—	2	2	no	—
183	#13063302	—	2	2	no	—
184	#13063302	—	2	2	no	—
185	#13063302	—	2	2	no	—
186	#13063302	—	2	2	no	—
187	#13063302	—	2	2	no	—
188	#13063302	—	2	2	no	—
189	#13063302	—	2	2	no	—
190	#13063300	—	2	1	no	—
191	#13063300	—	2	1	no	—
192	#13063299	—	2	1	no	—
193	#13063299	—	2	1	no	—
194	#13063299	—	2	2	no	—
195	#13063299	C₂³	1	2	yes	—
196	#13063299	C₂³	1	2	yes	—
197	#13063299	C₂³	1	1	yes	characteristic
198	#13063299	C₂³	1	1	yes	characteristic
199	#13063298	—	2	2	no	—
200	#13063298	—	2	2	no	—
201	#13063295	—	2	2	no	—
202	#13063294	—	2	1	no	—
203	C₄×Dic₈₆	—	2	2	no	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	—	2	2	no	—
206	C₄×Dic₈₆	—	2	2	no	—
207	C₄×Dic₈₆	C₂³	1	2	yes	—
208	C₄×D₁₇₂	—	2	2	no	—
209	C₄×D₁₇₂	C₂³	1	2	yes	—
210	C₄×D₁₇₂	C₂³	1	2	yes	—
211	C₄×D₁₇₂	C₂³	1	2	yes	—
212	#13063287	—	2	1	no	—
213	#13063287	—	2	1	no	—
214	C₄×C₂²⋊D₄₃	—	2	1	no	—
215	C₄×C₂²⋊D₄₃	—	2	1	no	—
216	C₄×C₂²⋊D₄₃	—	2	2	no	—
217	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
218	#13063284	—	2	1	no	—
219	#13063284	—	2	1	no	—
220	#13063284	—	2	1	no	—
221	#13063284	—	2	1	no	—
222	#13063284	C₂³	1	1	yes	characteristic
223	#13063284	C₂³	1	1	yes	characteristic
224	#13063284	C₂³	1	2	yes	—
225	#13063284	C₂³	1	1	yes	characteristic
226	#13063284	C₂³	1	1	yes	characteristic
227	#13063284	C₂³	1	2	yes	—
228	#13063284	C₂³	1	1	yes	characteristic
229	#13063283	—	2	1	no	—
230	#13063282	—	2	2	no	—
231	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×D₄₃	—	2	1	no	—
237	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
238	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
239	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
240	C₂²⋊C₄×D₄₃	—	2	2	no	—
241	C₂×C₄×Dic₄₃	—	2	1	no	—
242	C₂×C₄×Dic₄₃	—	2	1	no	—
243	#13063259	C₂³	1	1	yes	characteristic
244	#13063259	C₂³	1	2	yes	—
245	#13063259	C₂³	1	2	yes	—
246	#13063259	C₂³	1	2	yes	—
247	#13063259	C₂³	1	1	yes	characteristic
248	#13063259	C₂³	1	2	yes	—
249	#13063259	C₂³	1	2	yes	—
250	#13063259	C₂³	1	1	yes	characteristic
251	#13063259	C₂³	1	2	yes	—
252	#13063259	C₂³	1	1	yes	characteristic
253	#13063257	C₂³	1	1	yes	characteristic
254	#13063257	C₂³	1	2	yes	—
255	#13063257	C₂³	1	2	yes	—
256	#13063257	C₂³	1	2	yes	—
257	#13063257	C₂³	1	1	yes	characteristic
258	#13063257	C₂³	1	2	yes	—
259	#13063257	C₂³	1	2	yes	—
260	#13063257	C₂³	1	2	yes	—
261	#13063257	C₂³	1	1	yes	characteristic
262	#13063257	C₂³	1	1	yes	characteristic
263	#13063250	C₂³	1	1	yes	characteristic
264	#13063250	C₂³	1	1	yes	characteristic
265	#13063250	C₂³	1	1	yes	characteristic
266	#13063250	C₂³	1	1	yes	characteristic
267	#13063250	C₂³	1	2	yes	—
268	#13063250	C₂³	1	2	yes	—
269	#13063247	C₂³	1	2	yes	—
270	#13063247	C₂³	1	2	yes	—
271	#13063247	C₂³	1	2	yes	—
272	#13063247	C₂³	1	2	yes	—
273	#13063247	C₂³	1	1	yes	characteristic
274	#13063247	C₂³	1	1	yes	characteristic
275	#13063247	C₂³	1	1	yes	characteristic
276	#13063247	C₂³	1	1	yes	characteristic
277	#13063247	C₂³	1	2	yes	—
278	#13063247	C₂³	1	2	yes	—
279	#13063247	C₂³	1	2	yes	—
280	#13063247	C₂³	1	2	yes	—
281	#13063247	C₂³	1	2	yes	—
282	#13063247	C₂³	1	2	yes	—
283	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
284	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
285	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
288	#117×C₄₃	D₄	1	2	yes	—
289	#117×C₄₃	D₄	1	1	yes	characteristic
290	#117×C₄₃	D₄	1	1	yes	characteristic
291	#117×C₄₃	C₂³	1	1	yes	characteristic
292	#117×C₄₃	C₂³	1	1	yes	characteristic
293	#117×C₄₃	C₂³	1	2	yes	—
294	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
297	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
298	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
299	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
300	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
301	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
308	#97×C₄₃	C₂³	1	2	yes	—
309	#97×C₄₃	C₂³	1	2	yes	—
310	C₄×C₈×C₄₃	C₂³	1	2	yes	—
311	C₄×C₈×C₄₃	C₂³	1	2	yes	—
312	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
313	C₂³×D₄₃	—	2	1	no	—
314	C₂²×C₄×C₄₃	—	2	2	no	—
315	C₂²×C₄×C₄₃	—	2	2	no	—
316	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
320	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
321	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₂²⋊D₄₃	—	2	1	no	—
325	C₂×C₂²⋊D₄₃	—	2	1	no	—
326	C₂×C₂²⋊D₄₃	—	2	2	no	—
327	C₂×C₂²⋊D₄₃	—	2	1	no	—
328	C₂×C₂²⋊D₄₃	—	2	2	no	—
329	C₂×C₂²⋊D₄₃	—	8	2	no	—
330	C₂²×Dic₄₃	—	2	1	no	—
331	C₂²×Dic₄₃	—	2	1	no	—
332	C₂²×Dic₄₃	—	2	1	no	—
333	C₂²×Dic₄₃	—	2	1	no	—
334	C₂²×Dic₄₃	—	2	1	no	—
335	#10621898	—	2	2	no	—
336	#10621898	—	2	2	no	—
337	#10621898	—	8	4	no	—
338	C₂×D₁₇₂	—	2	1	no	—
339	C₂×D₁₇₂	—	2	2	no	—
340	C₂×D₁₇₂	—	2	2	no	—
341	C₂×D₁₇₂	—	2	2	no	—
342	C₂×D₁₇₂	—	2	2	no	—
343	C₂×D₁₇₂	C₂⁴	1	2	yes	—
344	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
345	C₂×C₄×D₄₃	—	2	1	no	—
346	C₂×C₄×D₄₃	—	2	2	no	—
347	C₂×C₄×D₄₃	—	2	2	no	—
348	C₂×C₄×D₄₃	—	2	2	no	—
349	C₂×Dic₈₆	—	2	2	no	—
350	C₂×Dic₈₆	—	2	2	no	—
351	C₂×Dic₈₆	—	2	2	no	—
352	C₂×Dic₈₆	—	2	2	no	—
353	C₂×Dic₈₆	—	2	2	no	—
354	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
355	M₁₆×C₄₃	—	2	2	no	—
356	M₁₆×C₄₃	—	2	2	no	—
357	C₂×C₈×C₄₃	—	2	2	no	—
358	C₂×C₈×C₄₃	—	2	2	no	—
359	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
367	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
368	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
369	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
371	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
372	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
373	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
374	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
375	C₄²×C₄₃	C₂×D₄	1	2	yes	—
376	C₄²×C₄₃	C₂×D₄	1	2	yes	—
377	C₄²×C₄₃	C₂⁴	1	2	yes	—
378	C₄²×C₄₃	C₂⁴	1	2	yes	—
379	C₂²⋊Dic₄₃	—	2	1	no	—
380	C₂²⋊Dic₄₃	—	2	2	no	—
381	C₂²⋊Dic₄₃	—	2	1	no	—
382	C₂²⋊Dic₄₃	—	2	1	no	—
383	C₂²⋊Dic₄₃	—	2	2	no	—
384	C₂²⋊Dic₄₃	—	2	1	no	—
385	C₂²⋊Dic₄₃	—	2	1	no	—
386	C₂²⋊Dic₄₃	—	2	1	no	—
387	C₂²⋊Dic₄₃	—	2	1	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	1	no	—
395	(C₂×D₄₃)⋊C₄	—	2	2	no	—
396	(C₂×D₄₃)⋊C₄	—	2	1	no	—
397	C₄⋊Dic₄₃	—	2	1	no	—
398	C₄⋊Dic₄₃	—	2	1	no	—
399	C₄⋊Dic₄₃	—	2	1	no	—
400	C₄⋊Dic₄₃	—	2	1	no	—
401	C₄⋊Dic₄₃	—	2	1	no	—
402	C₄⋊Dic₄₃	—	2	2	no	—
403	C₄⋊Dic₄₃	—	2	2	no	—
404	C₄⋊Dic₄₃	—	2	2	no	—
405	C₄⋊Dic₄₃	—	2	2	no	—
406	C₄⋊Dic₄₃	—	2	2	no	—
407	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
408	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
411	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
414	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
416	Dic₄₃⋊C₄	—	2	2	no	—
417	Dic₄₃⋊C₄	—	2	1	no	—
418	Dic₄₃⋊C₄	—	2	2	no	—
419	Dic₄₃⋊C₄	—	2	2	no	—
420	Dic₄₃⋊C₄	—	2	1	no	—
421	Dic₄₃⋊C₄	—	2	2	no	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	—	2	2	no	—
424	Dic₄₃⋊C₄	—	2	2	no	—
425	Dic₄₃⋊C₄	—	2	2	no	—
426	Dic₄₃⋊C₄	—	2	2	no	—
427	Dic₄₃⋊C₄	—	2	2	no	—
428	Dic₄₃⋊C₄	—	2	2	no	—
429	C₄×Dic₄₃	—	2	2	no	—
430	C₄×Dic₄₃	—	2	1	no	—
431	C₄×Dic₄₃	—	2	1	no	—
432	C₄×Dic₄₃	—	2	2	no	—
433	C₄×Dic₄₃	—	2	1	no	—
434	C₄×Dic₄₃	—	2	1	no	—
435	C₄×Dic₄₃	—	2	2	no	—
436	C₄×Dic₄₃	—	2	1	no	—
437	C₂³×C₄₃	—	2	2	no	—
438	C₂³×C₄₃	—	4	1	no	—
439	C₂³×C₄₃	—	4	1	no	—
440	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
442	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
443	C₂²×D₄₃	—	2	2	no	—
444	C₂²×D₄₃	—	2	1	no	—
445	C₂²×D₄₃	—	4	2	no	—
446	C₂²×D₄₃	—	8	1	no	—
447	C₂²×D₄₃	—	8	1	no	—
448	C₂×C₄×C₄₃	—	2	2	no	—
449	C₂×C₄×C₄₃	—	2	2	no	—
450	C₂×C₄×C₄₃	—	2	2	no	—
451	C₂×C₄×C₄₃	—	2	1	no	—
452	C₂×C₄×C₄₃	—	2	1	no	—
453	C₂×C₄×C₄₃	—	2	1	no	—
454	C₂×C₄×C₄₃	—	2	1	no	—
455	C₂×C₄×C₄₃	—	4	2	no	—
456	C₂×C₄×C₄₃	—	4	2	no	—
457	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
465	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
466	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
467	C₂²⋊D₄₃	—	4	2	no	—
468	C₂²⋊D₄₃	—	4	4	no	—
469	C₂²⋊D₄₃	—	4	2	no	—
470	C₂²⋊D₄₃	—	8	1	no	—
471	C₂²⋊D₄₃	—	8	2	no	—
472	C₂×Dic₄₃	—	2	2	no	—
473	C₂×Dic₄₃	—	2	1	no	—
474	C₂×Dic₄₃	—	2	1	no	—
475	C₂×Dic₄₃	—	2	2	no	—
476	C₂×Dic₄₃	—	2	1	no	—
477	C₂×Dic₄₃	—	2	1	no	—
478	C₂×Dic₄₃	—	2	1	no	—
479	C₂×Dic₄₃	—	2	1	no	—
480	C₂×Dic₄₃	—	2	2	no	—
481	C₂×Dic₄₃	—	2	1	no	—
482	C₂×Dic₄₃	—	8	1	no	—
483	C₂×Dic₄₃	—	8	1	no	—
484	C₂×Dic₄₃	—	8	1	no	—
485	C₂×Dic₄₃	—	8	1	no	—
486	C₂×Dic₄₃	—	8	1	no	—
487	D₁₇₂	—	2	2	no	—
488	D₁₇₂	—	2	2	no	—
489	D₁₇₂	—	2	1	no	—
490	D₁₇₂	—	2	1	no	—
491	D₁₇₂	—	4	2	no	—
492	D₁₇₂	—	8	2	no	—
493	D₁₇₂	—	8	2	no	—
494	C₄×D₄₃	—	4	2	no	—
495	C₄×D₄₃	—	8	2	no	—
496	C₄×D₄₃	—	8	2	no	—
497	C₄×D₄₃	—	8	2	no	—
498	Dic₈₆	—	2	1	no	—
499	Dic₈₆	—	2	1	no	—
500	Dic₈₆	—	8	2	no	—
501	Dic₈₆	—	8	2	no	—
502	Dic₈₆	—	8	2	no	—
503	Dic₈₆	—	8	2	no	—
504	Dic₈₆	—	8	2	no	—
505	C₈×C₄₃	—	2	1	no	—
506	C₈×C₄₃	—	2	1	no	—
507	C₈×C₄₃	—	2	1	no	—
508	C₈×C₄₃	—	2	1	no	—
509	C₈×C₄₃	—	2	2	no	—
510	C₈×C₄₃	—	2	2	no	—
511	#60875	—	43	1	no	maximal, Sylow
512	C₂²×C₄₃	—	2	1	no	—
513	C₂²×C₄₃	—	2	1	no	—
514	C₂²×C₄₃	—	2	1	no	—
515	C₂²×C₄₃	—	2	1	no	—
516	C₂²×C₄₃	—	2	1	no	—
517	C₂²×C₄₃	—	2	1	no	—
518	C₂²×C₄₃	—	2	1	no	—
519	C₂²×C₄₃	—	2	1	no	—
520	C₂²×C₄₃	—	8	2	no	—
521	C₂²×C₄₃	#536	1	2	yes	—
522	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
523	C₂×D₄₃	—	4	2	no	—
524	C₂×D₄₃	—	4	1	no	—
525	C₂×D₄₃	—	4	2	no	—
526	C₂×D₄₃	—	4	1	no	—
527	C₂×D₄₃	—	4	2	no	—
528	C₂×D₄₃	—	4	1	no	—
529	C₂×D₄₃	—	16	2	no	—
530	C₄×C₄₃	—	2	2	no	—
531	C₄×C₄₃	—	2	2	no	—
532	C₄×C₄₃	—	2	2	no	—
533	C₄×C₄₃	—	2	2	no	—
534	C₄×C₄₃	—	2	1	no	—
535	C₄×C₄₃	—	2	1	no	—
536	C₄×C₄₃	#536	1	2	yes	—
537	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
539	Dic₄₃	—	4	1	no	—
540	Dic₄₃	—	4	2	no	—
541	Dic₄₃	—	4	1	no	—
542	Dic₄₃	—	4	1	no	—
543	Dic₄₃	—	4	1	no	—
544	Dic₄₃	—	4	1	no	—
545	Dic₄₃	—	4	2	no	—
546	Dic₄₃	—	4	1	no	—
547	Dic₄₃	—	4	2	no	—
548	Dic₄₃	—	4	1	no	—
549	#3494	—	43	1	no	—
550	#3458	—	43	1	no	—
551	#3244	—	43	2	no	—
552	#3243	—	43	2	no	—
553	#3241	—	43	2	no	—
554	#3241	—	43	2	no	—
555	#3240	—	43	2	no	—
556	#3235	—	43	2	no	—
557	#3233	—	43	2	no	—
558	#3228	—	43	2	no	—
559	#3164	—	43	1	no	—
560	#3163	—	43	1	no	—
561	#3136	—	43	1	no	—
562	#3136	—	43	1	no	—
563	#3094	—	43	1	no	—
564	#3093	—	43	1	no	—
565	#3091	—	43	1	no	—
566	C₂×#482	—	43	1	no	—
567	#3084	—	43	1	no	—
568	#3083	—	43	1	no	—
569	#3081	—	43	1	no	—
570	#3081	—	43	1	no	—
571	#2924	D₄₃	1	1	yes	characteristic, complemented
572	C₂×C₄₃	—	2	2	no	—
573	C₂×C₄₃	—	4	1	no	—
574	C₂×C₄₃	—	4	1	no	—
575	C₂×C₄₃	C₂×#536	1	1	yes	characteristic
576	C₂×C₄₃	#3584	1	1	yes	characteristic
577	C₂×C₄₃	#3585	1	1	yes	characteristic
578	D₄₃	—	8	1	no	—
579	D₄₃	—	8	2	no	—
580	#555	—	86	1	no	—
581	#553	—	86	1	no	—
582	#553	—	86	1	no	—
583	#551	—	86	2	no	—
584	#547	—	86	1	no	—
585	#546	—	86	2	no	—
586	#544	—	43	1	no	—
587	#544	—	43	1	no	—
588	#544	—	43	1	no	—
589	#544	—	43	1	no	—
590	#544	—	43	1	no	—
591	#544	—	43	2	no	—
592	#544	—	43	2	no	—
593	#544	—	86	1	no	—
594	#544	—	86	1	no	—
595	#543	—	86	2	no	—
596	#542	—	43	2	no	—
597	#540	—	43	2	no	—
598	#535	—	43	1	no	—
599	#533	—	43	2	no	—
600	#533	—	43	2	no	—
601	#533	—	86	2	no	—
602	#533	—	86	1	no	—
603	#533	—	86	1	no	—
604	#532	—	43	2	no	—
605	#529	—	43	2	no	—
606	#525	—	43	1	no	—
607	C₂×#121	—	43	1	no	—
608	#520	—	43	1	no	—
609	#518	—	43	1	no	—
610	C₂×#117	—	43	1	no	—
611	C₂×#117	—	43	1	no	—
612	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
613	#501	—	43	2	no	—
614	#501	—	43	2	no	—
615	#501	—	43	2	no	—
616	#501	—	43	2	no	—
617	#500	—	43	2	no	—
618	#499	—	43	2	no	—
619	#499	—	43	2	no	—
620	#498	—	43	2	no	—
621	#490	—	43	2	no	—
622	#490	—	43	2	no	—
623	#489	—	43	2	no	—
624	#489	—	43	2	no	—
625	#488	—	43	2	no	—
626	#488	—	43	2	no	—
627	#486	—	43	2	no	—
628	#486	—	43	2	no	—
629	#485	—	43	1	no	—
630	#485	—	43	1	no	—
631	#485	—	43	2	no	—
632	#485	—	43	2	no	—
633	#484	—	43	1	no	—
634	#483	—	43	1	no	—
635	#482	—	43	2	no	—
636	#482	—	43	2	no	—
637	#482	—	43	2	no	—
638	#482	—	43	2	no	—
639	#482	—	43	1	no	—
640	#482	—	43	1	no	—
641	#482	—	43	2	no	—
642	#482	—	43	2	no	—
643	#482	—	43	2	no	—
644	#482	—	43	2	no	—
645	#481	—	43	1	no	—
646	#481	—	43	2	no	—
647	#480	—	43	1	no	—
648	#480	—	43	2	no	—
649	#479	—	43	2	no	—
650	#479	—	43	2	no	—
651	#478	—	43	2	no	—
652	#478	—	43	2	no	—
653	#478	—	43	2	no	—
654	#478	—	43	2	no	—
655	#478	—	43	2	no	—
656	#478	—	43	2	no	—
657	#477	—	43	2	no	—
658	#476	—	43	2	no	—
659	#476	—	43	2	no	—
660	#476	—	43	2	no	—
661	#475	—	43	2	no	—
662	#474	—	43	2	no	—
663	#474	—	43	2	no	—
664	#474	—	43	2	no	—
665	#433	C₂×D₄₃	1	2	yes	complemented
666	#433	C₂×D₄₃	1	2	yes	complemented
667	#432	C₂×D₄₃	1	2	yes	complemented
668	#431	C₂×D₄₃	1	2	yes	complemented
669	#428	—	43	1	no	—
670	#428	—	43	1	no	—
671	#428	—	43	1	no	—
672	#428	—	43	1	no	—
673	#427	—	43	1	no	—
674	#427	—	43	1	no	—
675	C₂×#107	—	43	1	no	—
676	C₂×#106	—	43	1	no	—
677	#424	C₂×D₄₃	1	1	yes	characteristic
678	#424	C₂×D₄₃	1	1	yes	characteristic
679	#418	—	43	1	no	—
680	#418	—	43	1	no	—
681	#417	—	43	1	no	—
682	#417	—	43	1	no	—
683	#416	—	43	1	no	—
684	#416	—	43	1	no	—
685	C₂×#102	—	43	1	no	—
686	C₂×#102	—	43	1	no	—
687	#407	C₂×D₄₃	1	1	yes	characteristic
688	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
689	#405	C₂×D₄₃	1	1	yes	characteristic
690	#405	C₂×D₄₃	1	1	yes	characteristic
691	C₄₃	#60875	1	1	yes	characteristic, complemented, Sylow
692	C₂×#41	—	43	1	no	—
693	C₂×#41	—	86	2	no	—
694	C₂²×D₄	—	43	1	no	—
695	C₂²×D₄	—	86	1	no	—
696	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
697	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
698	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
699	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
700	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
701	C₄⋊Q₈	—	43	2	no	—
702	C₄⋊Q₈	—	43	2	no	—
703	C₄⋊Q₈	—	43	2	no	—
704	C₄⋊Q₈	—	43	2	no	—
705	C₄⋊Q₈	—	43	2	no	—
706	C₄⋊Q₈	—	86	1	no	—
707	C₄⋊Q₈	—	86	1	no	—
708	C₄⋊Q₈	—	86	1	no	—
709	C₄⋊Q₈	—	86	1	no	—
710	C₄⋊Q₈	—	86	2	no	—
711	C₄⋊Q₈	—	86	2	no	—
712	C₄⋊Q₈	—	86	1	no	—
713	#127	—	43	2	no	—
714	#126	—	86	2	no	—
715	#126	—	86	2	no	—
716	#125	—	43	2	no	—
717	#125	—	43	2	no	—
718	#125	—	43	2	no	—
719	#125	—	43	2	no	—
720	#125	—	43	2	no	—
721	#125	—	86	1	no	—
722	#125	—	86	1	no	—
723	#125	—	86	1	no	—
724	#125	—	86	1	no	—
725	#125	—	86	2	no	—
726	#125	—	86	2	no	—
727	#125	—	86	1	no	—
728	#124	—	43	2	no	—
729	#124	—	86	2	no	—
730	#124	—	86	2	no	—
731	#123	—	86	1	no	—
732	#123	—	86	2	no	—
733	#123	—	86	2	no	—
734	#123	—	86	2	no	—
735	#123	—	86	2	no	—
736	C₂²⋊Q₈	—	43	1	no	—
737	C₂²⋊Q₈	—	43	1	no	—
738	C₂²⋊Q₈	—	86	2	no	—
739	C₂²⋊Q₈	—	86	2	no	—
740	C₂²⋊Q₈	—	86	2	no	—
741	C₂²⋊Q₈	—	86	2	no	—
742	C₂²⋊Q₈	—	86	2	no	—
743	C₂²⋊Q₈	—	86	2	no	—
744	C₂²⋊Q₈	—	86	2	no	—
745	C₂²⋊Q₈	—	86	2	no	—
746	C₂²⋊Q₈	—	86	2	no	—
747	C₂²⋊Q₈	—	86	2	no	—
748	C₂²⋊Q₈	—	86	2	no	—
749	C₂²⋊Q₈	—	86	2	no	—
750	C₂²⋊Q₈	—	86	2	no	—
751	C₂²⋊Q₈	—	86	2	no	—
752	#121	—	43	2	no	—
753	#121	—	43	2	no	—
754	#121	—	43	1	no	—
755	#121	—	43	1	no	—
756	#121	—	86	1	no	—
757	#121	—	86	1	no	—
758	#121	—	86	2	no	—
759	#121	—	86	1	no	—
760	#121	—	86	1	no	—
761	#121	—	86	2	no	—
762	#121	—	86	2	no	—
763	#120	—	86	1	no	—
764	#120	—	86	2	no	—
765	C₄×Q₈	—	43	2	no	—
766	C₄×Q₈	—	86	2	no	—
767	C₄×Q₈	—	86	2	no	—
768	C₄×Q₈	—	86	2	no	—
769	C₄×Q₈	—	86	2	no	—
770	C₄×D₄	—	43	2	no	—
771	C₄×D₄	—	43	2	no	—
772	C₄×D₄	—	43	2	no	—
773	C₄×D₄	—	86	1	no	—
774	C₄×D₄	—	86	1	no	—
775	C₄×D₄	—	86	2	no	—
776	C₄×D₄	—	86	1	no	—
777	C₄×D₄	—	86	1	no	—
778	C₄×D₄	—	86	2	no	—
779	C₄×D₄	—	86	2	no	—
780	#117	—	43	2	no	—
781	#117	—	43	1	no	—
782	#117	—	43	1	no	—
783	#117	—	43	1	no	—
784	#117	—	43	1	no	—
785	#117	—	43	2	no	—
786	#117	—	43	1	no	—
787	#117	—	86	1	no	—
788	#117	—	86	1	no	—
789	#117	—	86	1	no	—
790	#117	—	86	1	no	—
791	#117	—	86	1	no	—
792	#117	—	86	2	no	—
793	#117	D₁₇₂	1	2	yes	—
794	#117	D₁₇₂	1	1	yes	characteristic
795	#117	D₁₇₂	1	1	yes	characteristic
796	#117	C₂²×D₄₃	1	1	yes	characteristic
797	#117	C₂²×D₄₃	1	1	yes	characteristic
798	#117	C₂²×D₄₃	1	2	yes	—
799	C₂×C₄⋊C₄	—	43	1	no	—
800	C₂×C₄⋊C₄	—	43	1	no	—
801	C₂×C₄⋊C₄	—	43	1	no	—
802	C₂×C₄⋊C₄	—	43	1	no	—
803	C₂×C₄⋊C₄	—	43	1	no	—
804	C₂×C₄⋊C₄	—	86	1	no	—
805	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
806	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
807	C₂×C₂²⋊C₄	—	86	1	no	—
808	C₂×C₂²⋊C₄	—	86	1	no	—
809	C₂×C₂²⋊C₄	—	86	1	no	—
810	C₂×C₂²⋊C₄	—	86	2	no	—
811	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
812	C₂×C₄²	—	86	1	no	—
813	C₂×C₄²	—	86	1	no	—
814	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
815	#107	—	43	2	no	—
816	#107	—	43	2	no	—
817	#107	—	43	1	no	—
818	#107	—	43	1	no	—
819	#107	—	43	1	no	—
820	#107	—	43	1	no	—
821	#107	—	43	2	no	—
822	#107	—	43	2	no	—
823	#107	—	43	2	no	—
824	#107	—	43	2	no	—
825	#106	—	43	2	no	—
826	#106	—	43	2	no	—
827	#106	—	43	1	no	—
828	#106	—	43	1	no	—
829	#106	—	43	1	no	—
830	#106	—	43	1	no	—
831	#106	—	43	2	no	—
832	#106	—	43	2	no	—
833	#106	—	43	2	no	—
834	#106	—	43	2	no	—
835	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
836	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
837	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
838	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
839	#103	—	43	1	no	—
840	#103	—	43	1	no	—
841	#103	—	43	1	no	—
842	#103	—	43	1	no	—
843	#103	—	43	2	no	—
844	#103	—	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	—	43	1	no	—
850	#102	—	43	1	no	—
851	#102	—	43	1	no	—
852	#102	—	43	1	no	—
853	#102	—	43	2	no	—
854	#102	—	43	2	no	—
855	#102	—	43	2	no	—
856	#102	—	43	2	no	—
857	#102	—	43	2	no	—
858	#102	—	43	2	no	—
859	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
860	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
861	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
862	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
863	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
864	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
865	#97	C₂²×D₄₃	1	2	yes	—
866	#97	C₂²×D₄₃	1	2	yes	—
867	C₄×C₈	C₂²×D₄₃	1	2	yes	—
868	C₄×C₈	C₂²×D₄₃	1	2	yes	—
869	C₂⁴	—	86	1	no	—
870	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
871	#41	—	86	2	no	—
872	#41	—	86	2	no	—
873	#41	—	344	4	no	—
874	C₂×Q₈	—	43	1	no	—
875	C₂×Q₈	—	86	2	no	—
876	C₂×Q₈	—	86	2	no	—
877	C₂×Q₈	—	86	2	no	—
878	C₂×Q₈	—	86	2	no	—
879	C₂×Q₈	—	86	2	no	—
880	C₂×D₄	—	43	2	no	—
881	C₂×D₄	—	43	1	no	—
882	C₂×D₄	—	86	1	no	—
883	C₂×D₄	—	86	2	no	—
884	C₂×D₄	—	86	1	no	—
885	C₂×D₄	—	86	1	no	—
886	C₂×D₄	—	86	2	no	—
887	C₂×D₄	—	86	2	no	—
888	C₂×D₄	—	86	2	no	—
889	C₂×D₄	—	86	1	no	—
890	C₂×D₄	—	86	2	no	—
891	C₂×D₄	—	86	2	no	—
892	C₂×D₄	—	344	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	86	1	no	—
896	C₂²×C₄	—	86	1	no	—
897	C₂²×C₄	—	86	1	no	—
898	C₂²×C₄	—	86	1	no	—
899	C₂²×C₄	—	86	1	no	—
900	C₂²×C₄	—	86	2	no	—
901	C₂²×C₄	—	86	2	no	—
902	C₂²×C₄	—	86	2	no	—
903	C₂²×C₄	—	86	1	no	—
904	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
905	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
907	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
908	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
909	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
910	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
911	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
912	M₁₆	—	2	2	no	—
913	M₁₆	—	2	2	no	—
914	C₂×C₈	—	2	2	no	—
915	C₂×C₈	—	2	2	no	—
916	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
917	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
918	C₂×C₈	C₂³×D₄₃	1	2	yes	—
919	C₂×C₈	C₂³×D₄₃	1	2	yes	—
920	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
921	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
922	C₄⋊C₄	—	43	2	no	—
923	C₄⋊C₄	—	43	1	no	—
924	C₄⋊C₄	—	43	1	no	—
925	C₄⋊C₄	—	43	2	no	—
926	C₄⋊C₄	—	43	1	no	—
927	C₄⋊C₄	—	43	1	no	—
928	C₄⋊C₄	—	43	2	no	—
929	C₄⋊C₄	—	43	1	no	—
930	C₄⋊C₄	—	43	1	no	—
931	C₄⋊C₄	—	86	1	no	—
932	C₄⋊C₄	—	86	1	no	—
933	C₄⋊C₄	—	86	1	no	—
934	C₄⋊C₄	—	86	1	no	—
935	C₄⋊C₄	—	86	1	no	—
936	C₄⋊C₄	—	86	2	no	—
937	C₄⋊C₄	—	86	1	no	—
938	C₄⋊C₄	—	86	2	no	—
939	C₄⋊C₄	—	86	2	no	—
940	C₄⋊C₄	—	86	2	no	—
941	C₄⋊C₄	—	86	1	no	—
942	C₄⋊C₄	—	86	2	no	—
943	C₄⋊C₄	—	86	2	no	—
944	C₄⋊C₄	—	86	2	no	—
945	C₄⋊C₄	—	86	2	no	—
946	C₄⋊C₄	—	86	2	no	—
947	C₄⋊C₄	—	86	2	no	—
948	C₄⋊C₄	—	86	2	no	—
949	C₄⋊C₄	—	86	2	no	—
950	C₄⋊C₄	—	86	2	no	—
951	C₄⋊C₄	—	86	2	no	—
952	C₄⋊C₄	—	86	2	no	—
953	C₄⋊C₄	—	86	2	no	—
954	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
957	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
958	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
959	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
960	C₂²⋊C₄	—	86	1	no	—
961	C₂²⋊C₄	—	86	2	no	—
962	C₂²⋊C₄	—	86	1	no	—
963	C₂²⋊C₄	—	86	1	no	—
964	C₂²⋊C₄	—	86	2	no	—
965	C₂²⋊C₄	—	86	1	no	—
966	C₂²⋊C₄	—	86	1	no	—
967	C₂²⋊C₄	—	86	1	no	—
968	C₂²⋊C₄	—	86	1	no	—
969	C₂²⋊C₄	—	86	2	no	—
970	C₂²⋊C₄	—	86	2	no	—
971	C₂²⋊C₄	—	86	2	no	—
972	C₂²⋊C₄	—	86	2	no	—
973	C₂²⋊C₄	—	86	2	no	—
974	C₂²⋊C₄	—	86	2	no	—
975	C₂²⋊C₄	—	86	1	no	—
976	C₂²⋊C₄	—	86	2	no	—
977	C₂²⋊C₄	—	86	1	no	—
978	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
979	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
980	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
981	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
982	C₄²	—	86	2	no	—
983	C₄²	—	86	1	no	—
984	C₄²	—	86	1	no	—
985	C₄²	—	86	2	no	—
986	C₄²	—	86	1	no	—
987	C₄²	—	86	1	no	—
988	C₄²	—	86	1	no	—
989	C₄²	—	86	2	no	—
990	C₄²	C₂×D₁₇₂	1	2	yes	—
991	C₄²	C₂×D₁₇₂	1	2	yes	—
992	C₄²	C₂³×D₄₃	1	2	yes	—
993	C₄²	C₂³×D₄₃	1	2	yes	—
994	C₂³	—	2	2	no	—
995	C₂³	—	4	1	no	—
996	C₂³	—	4	1	no	—
997	C₂³	—	86	2	no	—
998	C₂³	—	86	1	no	—
999	C₂³	—	344	1	no	—
1000	C₂³	—	344	1	no	—
1001	C₂³	—	172	2	no	—
1002	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
1003	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
1004	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
1005	Q₈	—	86	1	no	—
1006	Q₈	—	86	1	no	—
1007	Q₈	—	344	2	no	—
1008	Q₈	—	344	2	no	—
1009	Q₈	—	344	2	no	—
1010	Q₈	—	344	2	no	—
1011	Q₈	—	344	2	no	—
1012	D₄	—	86	2	no	—
1013	D₄	—	86	2	no	—
1014	D₄	—	86	1	no	—
1015	D₄	—	86	1	no	—
1016	D₄	—	344	2	no	—
1017	D₄	—	344	2	no	—
1018	D₄	—	344	2	no	—
1019	D₄	—	344	1	no	—
1020	D₄	—	172	4	no	—
1021	D₄	—	172	2	no	—
1022	D₄	—	172	2	no	—
1023	D₄	—	172	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	86	1	no	—
1034	C₂×C₄	—	86	2	no	—
1035	C₂×C₄	—	86	1	no	—
1036	C₂×C₄	—	86	1	no	—
1037	C₂×C₄	—	86	2	no	—
1038	C₂×C₄	—	86	1	no	—
1039	C₂×C₄	—	86	1	no	—
1040	C₂×C₄	—	86	1	no	—
1041	C₂×C₄	—	86	1	no	—
1042	C₂×C₄	—	86	2	no	—
1043	C₂×C₄	—	344	2	no	—
1044	C₂×C₄	—	344	2	no	—
1045	C₂×C₄	—	344	2	no	—
1046	C₂×C₄	—	344	1	no	—
1047	C₂×C₄	—	344	1	no	—
1048	C₂×C₄	—	344	1	no	—
1049	C₂×C₄	—	344	1	no	—
1050	C₂×C₄	—	344	1	no	—
1051	C₂×C₄	—	172	2	no	—
1052	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
1055	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
1056	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
1057	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
1058	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1059	C₂×C₄	#13063372	1	2	yes	—
1060	C₂×C₄	#13063372	1	2	yes	—
1061	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1062	C₈	—	2	1	no	—
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	2	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	8	2	no	—
1077	C₂²	—	172	2	no	—
1078	C₂²	—	172	1	no	—
1079	C₂²	—	172	1	no	—
1080	C₂²	—	172	2	no	—
1081	C₂²	—	172	1	no	—
1082	C₂²	—	172	2	no	—
1083	C₂²	—	688	2	no	—
1084	C₂²	#14583475	1	2	yes	—
1085	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	172	1	no	—
1093	C₄	—	172	2	no	—
1094	C₄	—	172	1	no	—
1095	C₄	—	172	1	no	—
1096	C₄	—	172	2	no	—
1097	C₄	—	172	1	no	—
1098	C₄	—	172	2	no	—
1099	C₄	—	172	1	no	—
1100	C₄	—	172	1	no	—
1101	C₄	—	172	1	no	—
1102	C₄	#14583475	1	2	yes	—
1103	C₄	C₂×#13063372	1	1	yes	characteristic
1104	C₄	C₂×#13063372	1	1	yes	characteristic
1105	C₂	—	2	2	no	—
1106	C₂	—	4	1	no	—
1107	C₂	—	4	1	no	—
1108	C₂	—	344	2	no	—
1109	C₂	—	344	1	no	—
1110	C₂	C₂×#14583475	1	1	yes	characteristic
1111	C₂	#19149369	1	1	yes	characteristic
1112	C₂	#19149376	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#2924	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19148330	C₂
hypercenter	#2924	D₄₃
hypocenter	C₄₃	#60875
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ #2924

Complements

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

N	H ≅ G/N	type
2. #19148000	C₂	semidirect
3. #19145895	C₂	semidirect
4. #19145880	C₂	semidirect
5. #19145850	C₂	semidirect
6. #19145850	C₂	semidirect
7. #19145837	C₂	semidirect
8. #19145795	C₂	semidirect
9. #19145776	C₂	semidirect
10. #19145733	C₂	semidirect
11. #19145134	C₂	semidirect
12. #19145126	C₂	semidirect
13. #19144951	C₂	semidirect
14. #19144951	C₂	semidirect
15. #19144536	C₂	semidirect
16. #19144528	C₂	semidirect
17. #19144510	C₂	semidirect
18. C₂×#14583224	C₂	semidirect
19. #19144459	C₂	semidirect
20. #19144448	C₂	semidirect
21. #19144427	C₂	semidirect
22. #19144427	C₂	semidirect
23. C₄₃×#2924	C₂	semidirect
37. #14583527	C₂²	semidirect
38. #14583527	C₂²	semidirect
43. #14583456	C₂²	semidirect
44. #14583456	C₂²	semidirect
56. #14583308	C₂²	semidirect
57. #14583308	C₂²	semidirect
58. #14583308	C₂²	semidirect
59. #14583308	C₂²	semidirect
60. #14583304	C₂²	semidirect
61. #14583301	C₂²	semidirect
62. #14583301	C₂²	semidirect
63. #14583297	C₂²	semidirect
64. #14583264	C₂²	semidirect
65. #14583264	C₂²	semidirect
66. #14583259	C₂²	semidirect
67. #14583259	C₂²	semidirect
68. #14583254	C₂²	semidirect
69. #14583254	C₂²	semidirect
70. #14583246	C₂²	semidirect
71. #14583246	C₂²	semidirect
72. #14583241	C₂²	semidirect
73. #14583241	C₂²	semidirect
74. #14583241	C₂²	semidirect
75. #14583241	C₂²	semidirect
76. #14583235	C₂²	semidirect
77. #14583230	C₂²	semidirect
84. #14583224	C₂²	semidirect
85. #14583224	C₂²	semidirect
86. #14583224	C₂²	semidirect
87. #14583224	C₂²	semidirect
89. #14583218	C₂²	semidirect
91. #14583213	C₂²	semidirect
92. #14583207	C₂²	semidirect
93. #14583207	C₂²	semidirect
94. #14583200	C₂²	semidirect
95. #14583200	C₂²	semidirect
96. #14583200	C₂²	semidirect
97. #14583200	C₂²	semidirect
98. #14583200	C₂²	semidirect
99. #14583200	C₂²	semidirect
100. #14583195	C₂²	semidirect
101. #14583190	C₂²	semidirect
102. #14583190	C₂²	semidirect
103. #14583190	C₂²	semidirect
104. #14583185	C₂²	semidirect
105. #14583180	C₂²	semidirect
106. #14583180	C₂²	semidirect
107. #14583180	C₂²	semidirect
125. C₄₃×#433	C₂²	semidirect
126. C₄₃×#433	C₂²	semidirect
127. C₄₃×#432	C₂²	semidirect
128. C₄₃×#431	C₂²	semidirect
571. #2924	D₄₃	semidirect
665. #433	C₂×D₄₃	semidirect
666. #433	C₂×D₄₃	semidirect
667. #432	C₂×D₄₃	semidirect
668. #431	C₂×D₄₃	semidirect
691. C₄₃	#60875	semidirect

Maximal subgroups

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

subgroup	index
#19148330	2
#19148000	2
#19145895	2
#19145880	2
#19145850	2
#19145837	2
#19145795	2
#19145776	2
#19145733	2
#19145134	2
#19145126	2
#19144951	2
#19144536	2
#19144528	2
#19144510	2
C₂×#14583224	2
#19144459	2
#19144448	2
#19144427	2
C₄₃×#2924	2
#60875	43