Subgroups — #25976409

Order 11008.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148188	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147433	C₂	1	2	yes	maximal, complemented
4	#19147418	C₂	1	2	yes	maximal, complemented
5	#19147407	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147396	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147385	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147374	C₂	1	1	yes	maximal, characteristic, complemented
9	#19147359	C₂	1	2	yes	maximal, complemented
10	#19147344	C₂	1	2	yes	maximal, complemented
11	#19147333	C₂	1	1	yes	maximal, characteristic, complemented
12	#19147322	C₂	1	1	yes	maximal, characteristic, complemented
13	#19147311	C₂	1	1	yes	maximal, characteristic, complemented
14	#19147300	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144938	C₂	1	2	yes	maximal, complemented
16	#19144918	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144383	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144381	C₂	1	2	yes	maximal, complemented
19	#19144050	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144046	C₂	1	2	yes	maximal, complemented
21	C₂×#14583029	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143391	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063345	C₂²	1	2	yes	—
25	#14583634	C₂²	1	1	yes	characteristic
26	#14583632	C₂²	1	2	yes	—
27	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic
28	#14583628	C₂²	1	1	yes	characteristic
29	#14583627	C₂²	1	1	yes	characteristic
30	#14583625	C₂²	1	2	yes	—
31	#14583621	C₂²	1	2	yes	—
32	#14583619	C₂²	1	1	yes	characteristic
33	#14583608	—	2	2	no	—
34	#14583608	C₂²	1	2	yes	—
35	#14583606	—	2	1	no	—
36	#14583606	C₂²	1	1	yes	characteristic
37	#14583598	—	2	2	no	—
38	#14583595	—	2	1	no	—
39	#14583570	C₂²	1	1	yes	characteristic
40	D₄×Dic₈₆	—	2	1	no	—
41	D₄×Dic₈₆	C₂²	1	1	yes	characteristic
42	#14583558	—	2	1	no	—
43	#14583456	—	2	1	no	—
44	#14583456	C₂²	1	1	yes	characteristic
45	#14583452	—	2	2	no	—
46	#14583452	C₂²	1	2	yes	—
47	#14583449	C₂²	1	1	yes	characteristic
48	#14583445	C₂²	1	2	yes	—
49	#14583433	—	2	1	no	—
50	#14583427	—	2	2	no	—
51	#41×Dic₄₃	C₂²	1	2	yes	—
52	C₄×#10621898	—	2	1	no	—
53	#14583367	C₂²	1	2	yes	—
54	C₂×C₄×Dic₈₆	—	2	1	no	—
55	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
56	#14583266	C₂²	1	2	yes	—
57	#14583266	C₂²	1	2	yes	—
58	#14583262	C₂²	1	2	yes	—
59	#14583262	C₂²	1	2	yes	—
60	#14583260	C₂²	1	2	yes	—
61	#14583260	C₂²	1	2	yes	—
62	#14583257	C₂²	1	2	yes	—
63	#14583257	C₂²	1	2	yes	—
64	#14583254	C₂²	1	2	yes	—
65	#14583254	C₂²	1	2	yes	—
66	#14583250	C₂²	1	1	yes	characteristic
67	#14583250	C₂²	1	1	yes	characteristic
68	#14583246	C₂²	1	1	yes	characteristic
69	#14583246	C₂²	1	1	yes	characteristic
70	#14583209	C₂²	1	2	yes	—
71	#14583206	C₂²	1	2	yes	—
72	#14583205	C₂²	1	2	yes	—
73	#14583202	C₂²	1	2	yes	—
74	#14583199	C₂²	1	2	yes	—
75	#14583198	C₂²	1	2	yes	—
76	#14583194	C₂²	1	1	yes	characteristic
77	#14583193	C₂²	1	2	yes	—
78	#14583189	C₂²	1	1	yes	characteristic
79	#14583188	C₂²	1	2	yes	—
80	#14583184	C₂²	1	1	yes	characteristic
81	#14583183	C₂²	1	2	yes	—
82	#14583179	C₂²	1	1	yes	characteristic
83	#14583178	C₂²	1	2	yes	—
84	#14583123	C₂²	1	2	yes	—
85	#14583121	C₂²	1	2	yes	—
86	#14583119	C₂²	1	2	yes	—
87	#14583116	C₂²	1	2	yes	—
88	#14583114	C₂²	1	2	yes	—
89	#14583112	C₂²	1	2	yes	—
90	#14583109	C₂²	1	1	yes	characteristic
91	#14583107	C₂²	1	2	yes	—
92	#14583104	C₂²	1	1	yes	characteristic
93	#14583102	C₂²	1	2	yes	—
94	#14583099	C₂²	1	1	yes	characteristic
95	#14583097	C₂²	1	2	yes	—
96	#14583094	C₂²	1	1	yes	characteristic
97	#14583092	C₂²	1	2	yes	—
98	#14583029	C₂²	1	1	yes	characteristic
99	#14583029	C₂²	1	1	yes	characteristic
100	#14583029	C₂²	1	1	yes	characteristic
101	#14583029	C₂²	1	1	yes	characteristic
102	#14583029	C₂²	1	2	yes	—
103	#14583029	C₂²	1	2	yes	—
104	#14583008	C₂²	1	2	yes	—
105	#14583008	C₂²	1	2	yes	—
106	#14583003	C₂²	1	2	yes	—
107	#14583003	C₂²	1	2	yes	—
108	#14583002	C₂²	1	2	yes	—
109	#14583002	C₂²	1	2	yes	—
110	#14582996	C₂²	1	2	yes	—
111	#14582996	C₂²	1	2	yes	—
112	#14582935	C₂²	1	2	yes	—
113	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
114	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
115	#14582896	C₂²	1	2	yes	—
116	#14582896	C₂²	1	2	yes	—
117	#14582895	C₂²	1	2	yes	—
118	#14582893	C₂²	1	2	yes	—
119	C₂×#13063235	C₂²	1	2	yes	—
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
123	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
131	C₄₃×#427	C₂²	1	1	yes	characteristic
132	C₄₃×#416	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	C₂³	1	2	yes	—
137	C₂²×Dic₈₆	—	2	1	no	—
138	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
139	#13063345	—	2	8	no	—
140	C₂×#10621885	C₂³	1	2	yes	—
141	C₂×#10621883	C₂³	1	2	yes	—
142	C₂×#10621884	C₂³	1	2	yes	—
143	C₂×#10621882	C₂³	1	2	yes	—
144	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
145	#13063325	—	2	1	no	—
146	#13063325	—	2	1	no	—
147	#13063325	C₂³	1	1	yes	characteristic
148	#13063325	C₂³	1	1	yes	characteristic
149	#13063325	C₂³	1	1	yes	characteristic
150	#13063324	—	2	2	no	—
151	#13063324	—	2	2	no	—
152	#13063324	C₂³	1	2	yes	—
153	#13063324	C₂³	1	2	yes	—
154	#13063323	C₂³	1	2	yes	—
155	#13063322	C₂³	1	1	yes	characteristic
156	#13063321	C₂³	1	2	yes	—
157	#13063320	—	2	2	no	—
158	#13063319	—	2	2	no	—
159	#13063318	—	2	2	no	—
160	#13063317	—	2	1	no	—
161	#13063317	—	2	2	no	—
162	#13063317	C₂³	1	2	yes	—
163	#13063316	—	2	2	no	—
164	#13063316	—	2	2	no	—
165	#13063316	C₂³	1	2	yes	—
166	#13063316	C₂³	1	2	yes	—
167	#13063315	—	2	2	no	—
168	#13063314	C₂³	1	2	yes	—
169	#13063313	—	2	1	no	—
170	#13063313	C₂³	1	2	yes	—
171	#13063312	C₂³	1	2	yes	—
172	#13063311	—	2	2	no	—
173	#13063310	—	2	2	no	—
174	#13063308	—	2	2	no	—
175	#13063307	—	2	2	no	—
176	#13063304	—	2	1	no	—
177	#13063304	—	2	1	no	—
178	#13063304	—	2	1	no	—
179	#13063304	—	2	1	no	—
180	#13063304	—	2	1	no	—
181	#13063304	—	2	2	no	—
182	#13063303	—	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	#13063299	—	2	1	no	—
190	#13063299	—	2	1	no	—
191	#13063299	—	2	1	no	—
192	#13063298	—	2	2	no	—
193	#13063297	—	2	2	no	—
194	#13063297	—	2	2	no	—
195	Q₈×Dic₄₃	C₂³	1	2	yes	—
196	Q₈×Dic₄₃	C₂³	1	2	yes	—
197	C₄×Dic₈₆	—	2	1	no	—
198	C₄×Dic₈₆	—	2	1	no	—
199	C₄×Dic₈₆	—	2	1	no	—
200	C₄×Dic₈₆	—	2	1	no	—
201	C₄×Dic₈₆	—	2	1	no	—
202	C₄×Dic₈₆	—	2	2	no	—
203	C₄×Dic₈₆	—	2	2	no	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	D₄	1	1	yes	characteristic
206	C₄×Dic₈₆	D₄	1	1	yes	characteristic
207	C₄×Dic₈₆	D₄	1	2	yes	—
208	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
209	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
210	C₄×Dic₈₆	C₂³	1	2	yes	—
211	#13063290	C₂³	1	2	yes	—
212	#13063290	C₂³	1	2	yes	—
213	C₄×D₁₇₂	—	2	1	no	—
214	C₄×D₁₇₂	—	2	1	no	—
215	C₄×D₁₇₂	—	2	1	no	—
216	D₄×Dic₄₃	—	2	2	no	—
217	D₄×Dic₄₃	—	2	2	no	—
218	D₄×Dic₄₃	C₂³	1	2	yes	—
219	D₄×Dic₄₃	C₂³	1	2	yes	—
220	#13063287	C₂³	1	2	yes	—
221	#13063287	C₂³	1	2	yes	—
222	C₄×C₂²⋊D₄₃	—	2	2	no	—
223	C₄×C₂²⋊D₄₃	—	2	2	no	—
224	C₄×C₂²⋊D₄₃	—	2	2	no	—
225	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
226	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
227	#13063284	—	2	1	no	—
228	#13063284	—	2	2	no	—
229	#13063284	C₂³	1	2	yes	—
230	#13063282	—	2	2	no	—
231	#13063282	—	2	2	no	—
232	C₂×C₄⋊Dic₄₃	—	2	1	no	—
233	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
234	C₂×Dic₄₃⋊C₄	—	2	2	no	—
235	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
236	C₂×C₄×Dic₄₃	—	2	2	no	—
237	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
238	C₄²×D₄₃	—	2	2	no	—
239	#13063258	C₂³	1	2	yes	—
240	#13063258	C₂³	1	2	yes	—
241	#13063256	C₂³	1	2	yes	—
242	#13063256	C₂³	1	2	yes	—
243	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
244	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
245	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
246	Dic₄₃⋊C₈	C₂³	1	2	yes	—
247	Dic₄₃⋊C₈	C₂³	1	2	yes	—
248	Dic₄₃⋊C₈	C₂³	1	2	yes	—
249	Dic₄₃⋊C₈	C₂³	1	2	yes	—
250	#13063250	C₂³	1	2	yes	—
251	#13063250	C₂³	1	2	yes	—
252	#13063250	C₂³	1	2	yes	—
253	#13063250	C₂³	1	2	yes	—
254	#13063249	C₂³	1	2	yes	—
255	#13063249	C₂³	1	2	yes	—
256	#13063248	C₂³	1	2	yes	—
257	#13063248	C₂³	1	2	yes	—
258	#13063247	C₂³	1	2	yes	—
259	#13063247	C₂³	1	2	yes	—
260	#13063247	C₂³	1	2	yes	—
261	#13063247	C₂³	1	2	yes	—
262	#13063246	C₂³	1	2	yes	—
263	#13063246	C₂³	1	2	yes	—
264	#13063245	C₂³	1	2	yes	—
265	#13063245	C₂³	1	2	yes	—
266	#13063235	C₂³	1	2	yes	—
267	#13063235	C₂³	1	2	yes	—
268	#13063235	C₂³	1	2	yes	—
269	#13063235	C₂³	1	2	yes	—
270	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
272	#135×C₄₃	—	2	4	no	—
273	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₃	—	2	1	no	—
284	C₄×D₄×C₄₃	—	2	1	no	—
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
291	#117×C₄₃	—	2	1	no	—
292	#117×C₄₃	—	2	1	no	—
293	#117×C₄₃	C₂³	1	1	yes	characteristic
294	#117×C₄₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₃	—	2	1	no	—
296	C₂×C₄²×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#107×C₄₃	C₂³	1	1	yes	characteristic
300	#106×C₄₃	C₂³	1	1	yes	characteristic
301	#106×C₄₃	C₂³	1	1	yes	characteristic
302	#103×C₄₃	C₂³	1	1	yes	characteristic
303	#103×C₄₃	C₂³	1	1	yes	characteristic
304	#103×C₄₃	C₂³	1	1	yes	characteristic
305	#103×C₄₃	C₂³	1	1	yes	characteristic
306	#102×C₄₃	C₂³	1	1	yes	characteristic
307	#102×C₄₃	C₂³	1	1	yes	characteristic
308	#102×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	#41×C₄₃	—	2	2	no	—
315	#41×C₄₃	—	2	2	no	—
316	#41×C₄₃	—	2	2	no	—
317	#41×C₄₃	#41	1	4	yes	complemented
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₃	—	2	1	no	—
321	C₂×D₄×C₄₃	—	2	1	no	—
322	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₃	—	2	1	no	—
325	C₂²×C₄×C₄₃	—	2	1	no	—
326	C₂²×C₄×C₄₃	—	2	1	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₂²⋊D₄₃	—	2	2	no	—
334	C₂×C₂²⋊D₄₃	—	2	2	no	—
335	C₂×C₂²⋊D₄₃	—	2	2	no	—
336	C₂²×Dic₄₃	—	2	2	no	—
337	C₂²×Dic₄₃	—	2	2	no	—
338	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
339	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
340	#10621898	—	2	4	no	—
341	#10621898	—	2	4	no	—
342	#10621898	—	4	4	no	—
343	C₂×D₁₇₂	—	2	1	no	—
344	C₂×D₁₇₂	—	2	1	no	—
345	C₂×D₁₇₂	C₂⁴	1	2	yes	—
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	1	no	—
350	C₂×Dic₈₆	—	2	2	no	—
351	C₂×Dic₈₆	—	2	1	no	—
352	C₂×Dic₈₆	—	2	2	no	—
353	C₂×Dic₈₆	—	4	2	no	—
354	C₂×Dic₈₆	—	4	4	no	—
355	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
356	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
357	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
358	C₂×Dic₈₆	C₂⁴	1	2	yes	—
359	Q₁₆×C₄₃	—	2	2	no	—
360	SD₁₆×C₄₃	—	2	2	no	—
361	SD₁₆×C₄₃	—	2	2	no	—
362	D₈×C₄₃	—	2	2	no	—
363	C₂×C₈×C₄₃	—	2	2	no	—
364	C₂×C₈×C₄₃	—	2	2	no	—
365	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₄₃	—	2	1	no	—
370	C₄⋊C₄×C₄₃	—	2	1	no	—
371	C₄⋊C₄×C₄₃	—	2	1	no	—
372	C₄⋊C₄×C₄₃	—	2	1	no	—
373	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
377	C₂²⋊C₄×C₄₃	—	2	1	no	—
378	C₂²⋊C₄×C₄₃	—	2	1	no	—
379	C₂²⋊C₄×C₄₃	—	2	1	no	—
380	C₂²⋊C₄×C₄₃	—	2	1	no	—
381	C₂²⋊C₄×C₄₃	—	2	1	no	—
382	C₂²⋊C₄×C₄₃	—	2	1	no	—
383	C₄²×C₄₃	—	2	1	no	—
384	C₄²×C₄₃	—	2	1	no	—
385	C₄²×C₄₃	—	2	1	no	—
386	C₄²×C₄₃	—	2	1	no	—
387	C₄²×C₄₃	—	2	1	no	—
388	C₄²×C₄₃	—	2	1	no	—
389	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
392	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
393	C₂²⋊Dic₄₃	—	2	2	no	—
394	C₂²⋊Dic₄₃	—	2	2	no	—
395	C₂²⋊Dic₄₃	—	2	2	no	—
396	C₂²⋊Dic₄₃	—	2	2	no	—
397	C₂²⋊Dic₄₃	—	2	2	no	—
398	#10621885	—	2	4	no	—
399	#10621884	—	2	4	no	—
400	#10621883	—	2	4	no	—
401	#10621882	—	2	4	no	—
402	(C₂×D₄₃)⋊C₄	—	2	2	no	—
403	(C₂×D₄₃)⋊C₄	—	2	2	no	—
404	(C₂×D₄₃)⋊C₄	—	2	2	no	—
405	(C₂×D₄₃)⋊C₄	—	2	2	no	—
406	(C₂×D₄₃)⋊C₄	—	2	2	no	—
407	(C₂×D₄₃)⋊C₄	—	2	2	no	—
408	C₄⋊Dic₄₃	—	2	1	no	—
409	C₄⋊Dic₄₃	—	2	1	no	—
410	C₄⋊Dic₄₃	—	2	1	no	—
411	C₄⋊Dic₄₃	—	2	1	no	—
412	C₄⋊Dic₄₃	—	2	2	no	—
413	C₄⋊Dic₄₃	—	2	2	no	—
414	C₄⋊Dic₄₃	—	2	2	no	—
415	C₄⋊Dic₄₃	—	2	2	no	—
416	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
417	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
419	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
420	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
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	Dic₄₃⋊C₄	—	2	2	no	—
430	Dic₄₃⋊C₄	—	2	2	no	—
431	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
432	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
433	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
434	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
435	C₄×Dic₄₃	—	2	2	no	—
436	C₄×Dic₄₃	—	2	2	no	—
437	C₄×Dic₄₃	—	2	2	no	—
438	C₄×Dic₄₃	—	2	2	no	—
439	C₄×Dic₄₃	—	2	2	no	—
440	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
441	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
442	C₄×Dic₄₃	C₂⁴	1	2	yes	—
443	C₄×Dic₄₃	C₂⁴	1	2	yes	—
444	C₂×C₄₃⋊C₈	—	2	4	no	—
445	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
446	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
447	C₂³×C₄₃	—	2	1	no	—
448	C₂³×C₄₃	—	2	1	no	—
449	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
450	C₂²×D₄₃	—	2	2	no	—
451	Q₈×C₄₃	—	2	1	no	—
452	Q₈×C₄₃	—	2	1	no	—
453	Q₈×C₄₃	—	2	1	no	—
454	Q₈×C₄₃	C₂×#41	1	2	yes	—
455	D₄×C₄₃	—	2	4	no	—
456	D₄×C₄₃	—	2	1	no	—
457	D₄×C₄₃	—	2	1	no	—
458	D₄×C₄₃	—	2	1	no	—
459	D₄×C₄₃	—	4	2	no	—
460	D₄×C₄₃	C₂×#41	1	2	yes	—
461	C₂×C₄×C₄₃	—	2	1	no	—
462	C₂×C₄×C₄₃	—	2	4	no	—
463	C₂×C₄×C₄₃	—	2	2	no	—
464	C₂×C₄×C₄₃	—	2	1	no	—
465	C₂×C₄×C₄₃	—	2	1	no	—
466	C₂×C₄×C₄₃	—	2	1	no	—
467	C₂×C₄×C₄₃	—	2	1	no	—
468	C₂×C₄×C₄₃	—	2	1	no	—
469	C₂×C₄×C₄₃	—	4	1	no	—
470	C₂×C₄×C₄₃	—	4	2	no	—
471	C₂×C₄×C₄₃	—	4	2	no	—
472	C₂×C₄×C₄₃	—	4	2	no	—
473	C₂×C₄×C₄₃	—	8	1	no	—
474	C₂×C₄×C₄₃	—	8	1	no	—
475	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
481	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
482	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
483	C₂²⋊D₄₃	—	4	4	no	—
484	C₂²⋊D₄₃	—	4	4	no	—
485	C₂²⋊D₄₃	—	8	2	no	—
486	C₂×Dic₄₃	—	2	2	no	—
487	C₂×Dic₄₃	—	2	2	no	—
488	C₂×Dic₄₃	—	2	2	no	—
489	C₂×Dic₄₃	—	4	2	no	—
490	C₂×Dic₄₃	—	4	2	no	—
491	C₂×Dic₄₃	—	4	4	no	—
492	C₂×Dic₄₃	—	8	2	no	—
493	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
494	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
495	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
496	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
497	D₁₇₂	—	2	2	no	—
498	D₁₇₂	—	2	2	no	—
499	D₁₇₂	—	4	2	no	—
500	D₁₇₂	—	8	1	no	—
501	C₄×D₄₃	—	4	4	no	—
502	C₄×D₄₃	—	4	4	no	—
503	C₄×D₄₃	—	8	2	no	—
504	Dic₈₆	—	2	2	no	—
505	Dic₈₆	—	2	2	no	—
506	Dic₈₆	—	2	2	no	—
507	Dic₈₆	—	2	2	no	—
508	Dic₈₆	—	4	2	no	—
509	Dic₈₆	—	4	4	no	—
510	Dic₈₆	—	4	2	no	—
511	Dic₈₆	—	8	2	no	—
512	Dic₈₆	—	8	1	no	—
513	C₈×C₄₃	—	2	1	no	—
514	C₈×C₄₃	—	2	1	no	—
515	C₈×C₄₃	—	2	1	no	—
516	C₈×C₄₃	—	2	1	no	—
517	C₄₃⋊C₈	—	2	2	no	—
518	C₄₃⋊C₈	—	2	2	no	—
519	#61316	—	43	1	no	maximal, Sylow
520	C₂²×C₄₃	—	2	1	no	—
521	C₂²×C₄₃	—	2	1	no	—
522	C₂²×C₄₃	—	2	2	no	—
523	C₂²×C₄₃	—	4	1	no	—
524	C₂²×C₄₃	—	4	1	no	—
525	C₂²×C₄₃	—	4	1	no	—
526	C₂²×C₄₃	—	4	1	no	—
527	C₂²×C₄₃	—	4	1	no	—
528	C₂²×C₄₃	#548	1	2	yes	—
529	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
530	C₂×D₄₃	—	4	2	no	—
531	C₂×D₄₃	—	4	2	no	—
532	C₂×D₄₃	—	4	2	no	—
533	C₄×C₄₃	—	2	1	no	—
534	C₄×C₄₃	—	2	1	no	—
535	C₄×C₄₃	—	2	2	no	—
536	C₄×C₄₃	—	2	1	no	—
537	C₄×C₄₃	—	4	1	no	—
538	C₄×C₄₃	—	4	1	no	—
539	C₄×C₄₃	—	4	1	no	—
540	C₄×C₄₃	—	4	1	no	—
541	C₄×C₄₃	—	4	1	no	—
542	C₄×C₄₃	#548	1	2	yes	—
543	C₄×C₄₃	#575	1	2	yes	—
544	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
545	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
546	Dic₄₃	—	2	2	no	—
547	Dic₄₃	—	2	2	no	—
548	Dic₄₃	—	2	2	no	—
549	Dic₄₃	—	2	2	no	—
550	Dic₄₃	—	4	2	no	—
551	Dic₄₃	—	4	2	no	—
552	Dic₄₃	—	4	2	no	—
553	#3480	—	43	1	no	—
554	Q₈×#41	—	43	1	no	—
555	#3377	—	43	2	no	—
556	#3376	—	43	2	no	—
557	#3375	—	43	1	no	—
558	#3374	—	43	1	no	—
559	#3373	—	43	1	no	—
560	#3372	—	43	1	no	—
561	#3371	—	43	2	no	—
562	#3370	—	43	2	no	—
563	#3369	—	43	1	no	—
564	#3368	—	43	1	no	—
565	#3367	—	43	1	no	—
566	#3366	—	43	1	no	—
567	#3135	—	43	2	no	—
568	#3131	—	43	1	no	—
569	#3076	—	43	2	no	—
570	#3076	—	43	1	no	—
571	#3035	—	43	2	no	—
572	#3035	—	43	1	no	—
573	C₂×#446	—	43	1	no	—
574	#2943	—	43	2	no	—
575	C₄×#135	D₄₃	1	1	yes	characteristic, complemented
576	C₂×C₄₃	—	2	2	no	—
577	C₂×C₄₃	—	4	2	no	—
578	C₂×C₄₃	—	8	1	no	—
579	C₂×C₄₃	C₂×#548	1	1	yes	characteristic
580	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
581	C₂×C₄₃	#3584	1	1	yes	characteristic
582	D₄₃	—	8	2	no	—
583	C₂×#135	—	43	2	no	—
584	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
585	#559	—	43	1	no	—
586	#559	—	43	2	no	—
587	Q₈²	—	43	1	no	—
588	#557	—	43	1	no	—
589	#557	—	43	2	no	—
590	#557	—	43	1	no	—
591	#556	—	43	2	no	—
592	#556	—	43	1	no	—
593	#554	—	43	1	no	—
594	#554	—	43	2	no	—
595	#554	—	86	1	no	—
596	#554	—	86	2	no	—
597	#553	—	86	1	no	—
598	#553	—	86	2	no	—
599	#550	—	43	1	no	—
600	D₄×Q₈	—	43	1	no	—
601	D₄×Q₈	—	86	1	no	—
602	#548	—	86	1	no	—
603	#533	—	43	2	no	—
604	#533	—	43	1	no	—
605	#533	—	86	1	no	—
606	#533	—	86	2	no	—
607	#532	—	43	2	no	—
608	#532	—	43	1	no	—
609	#529	—	86	1	no	—
610	#529	—	86	2	no	—
611	C₄×#41	—	43	2	no	—
612	C₄×#41	—	43	2	no	—
613	C₄×#41	—	86	1	no	—
614	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
615	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
616	C₂×C₄×Q₈	—	43	1	no	—
617	C₂×C₄×Q₈	—	86	1	no	—
618	#491	—	43	2	no	—
619	#491	—	43	2	no	—
620	#490	—	43	2	no	—
621	#490	—	43	2	no	—
622	#489	—	43	2	no	—
623	#489	—	43	2	no	—
624	#489	—	43	2	no	—
625	#489	—	43	2	no	—
626	#488	—	43	2	no	—
627	#488	—	43	2	no	—
628	#487	—	43	1	no	—
629	#487	—	43	1	no	—
630	#486	—	43	1	no	—
631	#486	—	43	1	no	—
632	#479	—	43	2	no	—
633	#479	—	43	2	no	—
634	#479	—	43	2	no	—
635	#478	—	43	2	no	—
636	#478	—	43	2	no	—
637	#478	—	43	2	no	—
638	#477	—	43	1	no	—
639	#477	—	43	2	no	—
640	#476	—	43	1	no	—
641	#476	—	43	2	no	—
642	#475	—	43	1	no	—
643	#475	—	43	2	no	—
644	#474	—	43	1	no	—
645	#474	—	43	2	no	—
646	#464	—	43	2	no	—
647	#464	—	43	2	no	—
648	#464	—	43	2	no	—
649	#463	—	43	2	no	—
650	#463	—	43	2	no	—
651	#463	—	43	2	no	—
652	#462	—	43	2	no	—
653	#462	—	43	1	no	—
654	#461	—	43	2	no	—
655	#461	—	43	1	no	—
656	#460	—	43	2	no	—
657	#460	—	43	1	no	—
658	#459	—	43	2	no	—
659	#459	—	43	1	no	—
660	#446	—	43	1	no	—
661	#446	—	43	1	no	—
662	#446	—	43	1	no	—
663	#446	—	43	1	no	—
664	#446	—	43	2	no	—
665	#446	—	43	2	no	—
666	#442	—	43	2	no	—
667	#442	—	43	2	no	—
668	#441	—	43	2	no	—
669	#441	—	43	2	no	—
670	#440	—	43	2	no	—
671	#440	—	43	2	no	—
672	#440	—	43	2	no	—
673	#440	—	43	2	no	—
674	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
675	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
676	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
677	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
678	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
679	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
680	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
681	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
682	#427	—	43	2	no	—
683	#427	C₂×D₄₃	1	1	yes	characteristic
684	C₂×C₄⋊C₈	—	43	2	no	—
685	C₂×C₄⋊C₈	—	43	1	no	—
686	#416	—	43	2	no	—
687	#416	—	43	2	no	—
688	#416	—	43	2	no	—
689	#416	—	43	2	no	—
690	#416	C₂×D₄₃	1	1	yes	characteristic
691	#416	C₂×D₄₃	1	1	yes	characteristic
692	C₂×#97	—	43	2	no	—
693	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
694	C₄₃	#61316	1	1	yes	characteristic, complemented, Sylow
695	C₂×#41	—	43	2	no	—
696	C₂×#41	—	86	1	no	—
697	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
698	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
699	C₂²×Q₈	—	43	1	no	—
700	C₂²×Q₈	—	86	1	no	—
701	#135	—	2	4	no	—
702	#135	—	86	8	no	—
703	C₂×Q₁₆	—	43	2	no	—
704	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
705	C₂×SD₁₆	—	43	2	no	—
706	C₂×SD₁₆	—	43	2	no	—
707	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
709	C₂×D₈	—	43	2	no	—
710	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
711	C₂²×C₈	—	43	2	no	—
712	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
713	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
714	C₄⋊Q₈	—	43	2	no	—
715	C₄⋊Q₈	—	43	2	no	—
716	C₄⋊Q₈	—	43	2	no	—
717	C₄⋊Q₈	—	43	1	no	—
718	C₄⋊Q₈	—	43	1	no	—
719	C₄⋊Q₈	—	43	1	no	—
720	C₄⋊Q₈	—	86	1	no	—
721	C₄⋊Q₈	—	86	1	no	—
722	C₄⋊Q₈	—	86	2	no	—
723	C₄⋊Q₈	—	86	2	no	—
724	#127	—	43	2	no	—
725	#127	—	43	1	no	—
726	#126	—	86	2	no	—
727	#126	—	86	2	no	—
728	#126	—	86	2	no	—
729	#125	—	43	2	no	—
730	#125	—	43	2	no	—
731	#125	—	43	2	no	—
732	#125	—	86	1	no	—
733	#125	—	86	2	no	—
734	#125	—	86	2	no	—
735	#125	—	86	2	no	—
736	#125	—	86	2	no	—
737	#124	—	43	2	no	—
738	#124	—	43	2	no	—
739	#124	—	43	2	no	—
740	#124	—	86	1	no	—
741	#124	—	86	2	no	—
742	#123	—	86	2	no	—
743	#123	—	86	2	no	—
744	#123	—	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	C₂²⋊Q₈	—	86	1	no	—
753	C₂²⋊Q₈	—	86	2	no	—
754	C₂²⋊Q₈	—	86	1	no	—
755	C₂²⋊Q₈	—	86	1	no	—
756	C₂²⋊Q₈	—	86	1	no	—
757	C₂²⋊Q₈	—	86	1	no	—
758	#121	—	86	2	no	—
759	#121	—	86	1	no	—
760	#121	—	86	2	no	—
761	#121	—	86	2	no	—
762	#121	—	86	1	no	—
763	#121	—	86	1	no	—
764	C₄×Q₈	—	43	1	no	—
765	C₄×Q₈	—	43	1	no	—
766	C₄×Q₈	—	43	2	no	—
767	C₄×Q₈	—	43	1	no	—
768	C₄×Q₈	—	43	1	no	—
769	C₄×Q₈	—	43	2	no	—
770	C₄×Q₈	—	43	2	no	—
771	C₄×Q₈	—	43	2	no	—
772	C₄×Q₈	—	43	2	no	—
773	C₄×Q₈	—	43	2	no	—
774	C₄×Q₈	—	86	2	no	—
775	C₄×Q₈	—	86	2	no	—
776	C₄×Q₈	—	86	2	no	—
777	C₄×Q₈	—	86	1	no	—
778	C₄×Q₈	—	86	1	no	—
779	C₄×Q₈	—	86	1	no	—
780	C₄×Q₈	—	86	1	no	—
781	C₄×Q₈	—	86	1	no	—
782	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
783	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
784	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
785	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	43	2	no	—
791	C₄×D₄	—	43	2	no	—
792	C₄×D₄	—	43	2	no	—
793	C₄×D₄	—	43	2	no	—
794	C₄×D₄	—	86	1	no	—
795	C₄×D₄	—	86	2	no	—
796	C₄×D₄	—	86	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	1	no	—
803	C₄×D₄	—	86	1	no	—
804	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
805	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
806	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
807	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	—	43	2	no	—
811	#117	—	86	2	no	—
812	#117	—	86	2	no	—
813	#117	—	86	2	no	—
814	#117	—	86	1	no	—
815	#117	C₂²×D₄₃	1	1	yes	characteristic
816	#117	C₂²×D₄₃	1	1	yes	characteristic
817	C₂×C₄⋊C₄	—	43	2	no	—
818	C₂×C₄⋊C₄	—	43	1	no	—
819	C₂×C₄⋊C₄	—	86	2	no	—
820	C₂×C₄⋊C₄	—	86	1	no	—
821	C₂×C₄²	—	2	1	no	—
822	C₂×C₄²	—	2	1	no	—
823	C₂×C₄²	—	43	2	no	—
824	C₂×C₄²	—	86	2	no	—
825	C₂×C₄²	—	86	2	no	—
826	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
827	#107	—	43	2	no	—
828	#107	—	43	2	no	—
829	#107	C₂²×D₄₃	1	1	yes	characteristic
830	#107	C₂²×D₄₃	1	1	yes	characteristic
831	#106	—	43	2	no	—
832	#106	—	43	2	no	—
833	#106	C₂²×D₄₃	1	1	yes	characteristic
834	#106	C₂²×D₄₃	1	1	yes	characteristic
835	C₄⋊C₈	—	43	2	no	—
836	C₄⋊C₈	—	43	2	no	—
837	C₄⋊C₈	—	43	2	no	—
838	C₄⋊C₈	—	43	2	no	—
839	C₄⋊C₈	—	43	1	no	—
840	C₄⋊C₈	—	43	1	no	—
841	C₄⋊C₈	—	43	2	no	—
842	#103	—	43	2	no	—
843	#103	—	43	2	no	—
844	#103	—	43	2	no	—
845	#103	—	43	2	no	—
846	#103	—	43	2	no	—
847	#103	—	43	2	no	—
848	#103	—	43	2	no	—
849	#103	—	43	2	no	—
850	#103	C₂²×D₄₃	1	1	yes	characteristic
851	#103	C₂²×D₄₃	1	1	yes	characteristic
852	#103	C₂²×D₄₃	1	1	yes	characteristic
853	#103	C₂²×D₄₃	1	1	yes	characteristic
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	#102	—	43	2	no	—
860	#102	—	43	2	no	—
861	#102	—	43	2	no	—
862	#102	C₂²×D₄₃	1	1	yes	characteristic
863	#102	C₂²×D₄₃	1	1	yes	characteristic
864	#102	C₂²×D₄₃	1	1	yes	characteristic
865	#102	C₂²×D₄₃	1	1	yes	characteristic
866	#97	—	43	2	no	—
867	#97	—	43	2	no	—
868	#97	—	43	2	no	—
869	#97	—	43	2	no	—
870	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
871	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
872	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
873	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
874	#41	—	2	2	no	—
875	#41	—	2	2	no	—
876	#41	—	2	2	no	—
877	#41	—	86	4	no	—
878	#41	—	86	4	no	—
879	#41	—	172	4	no	—
880	#41	#10621898	1	4	yes	complemented
881	C₂×Q₈	—	43	1	no	—
882	C₂×Q₈	—	43	1	no	—
883	C₂×Q₈	—	43	2	no	—
884	C₂×Q₈	—	43	2	no	—
885	C₂×Q₈	—	86	2	no	—
886	C₂×Q₈	—	86	2	no	—
887	C₂×Q₈	—	86	1	no	—
888	C₂×Q₈	—	86	1	no	—
889	C₂×Q₈	—	172	2	no	—
890	C₂×Q₈	—	172	4	no	—
891	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
892	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	43	2	no	—
896	C₂×D₄	—	86	2	no	—
897	C₂×D₄	—	86	2	no	—
898	C₂×D₄	—	86	2	no	—
899	C₂×D₄	—	86	1	no	—
900	C₂×D₄	—	86	1	no	—
901	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
902	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	43	2	no	—
910	C₂²×C₄	—	43	2	no	—
911	C₂²×C₄	—	86	2	no	—
912	C₂²×C₄	—	86	2	no	—
913	C₂²×C₄	—	86	2	no	—
914	C₂²×C₄	—	86	2	no	—
915	C₂²×C₄	—	86	2	no	—
916	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
917	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
918	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
919	Q₁₆	—	2	2	no	—
920	Q₁₆	—	86	4	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	86	4	no	—
924	SD₁₆	—	86	4	no	—
925	D₈	—	2	2	no	—
926	D₈	—	86	4	no	—
927	C₂×C₈	—	2	2	no	—
928	C₂×C₈	—	2	2	no	—
929	C₂×C₈	—	43	2	no	—
930	C₂×C₈	—	43	2	no	—
931	C₂×C₈	—	86	4	no	—
932	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
933	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
934	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
935	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	43	1	no	—
941	C₄⋊C₄	—	43	2	no	—
942	C₄⋊C₄	—	43	2	no	—
943	C₄⋊C₄	—	43	1	no	—
944	C₄⋊C₄	—	43	2	no	—
945	C₄⋊C₄	—	43	2	no	—
946	C₄⋊C₄	—	43	2	no	—
947	C₄⋊C₄	—	43	2	no	—
948	C₄⋊C₄	—	43	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	—	86	2	no	—
955	C₄⋊C₄	—	86	2	no	—
956	C₄⋊C₄	—	86	2	no	—
957	C₄⋊C₄	—	86	2	no	—
958	C₄⋊C₄	—	86	2	no	—
959	C₄⋊C₄	—	86	2	no	—
960	C₄⋊C₄	—	86	2	no	—
961	C₄⋊C₄	—	86	2	no	—
962	C₄⋊C₄	—	86	1	no	—
963	C₄⋊C₄	—	86	1	no	—
964	C₄⋊C₄	—	86	1	no	—
965	C₄⋊C₄	—	86	2	no	—
966	C₄⋊C₄	—	86	1	no	—
967	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
970	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	86	2	no	—
978	C₂²⋊C₄	—	86	2	no	—
979	C₂²⋊C₄	—	86	2	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	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	43	2	no	—
995	C₄²	—	43	2	no	—
996	C₄²	—	43	2	no	—
997	C₄²	—	43	2	no	—
998	C₄²	—	86	2	no	—
999	C₄²	—	86	2	no	—
1000	C₄²	—	86	2	no	—
1001	C₄²	—	86	2	no	—
1002	C₄²	—	86	2	no	—
1003	C₄²	D₄×D₄₃	1	1	yes	characteristic
1004	C₄²	D₄×D₄₃	1	1	yes	characteristic
1005	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1006	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	86	2	no	—
1010	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	86	2	no	—
1015	Q₈	—	86	2	no	—
1016	Q₈	—	86	2	no	—
1017	Q₈	—	86	2	no	—
1018	Q₈	—	344	1	no	—
1019	Q₈	—	344	2	no	—
1020	Q₈	—	172	2	no	—
1021	Q₈	—	172	4	no	—
1022	Q₈	—	172	2	no	—
1023	Q₈	C₂×#10621898	1	2	yes	—
1024	D₄	—	2	4	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	86	2	no	—
1030	D₄	—	86	2	no	—
1031	D₄	—	344	1	no	—
1032	D₄	—	344	2	no	—
1033	D₄	—	172	4	no	—
1034	D₄	—	172	4	no	—
1035	D₄	—	172	2	no	—
1036	D₄	C₂×#10621898	1	2	yes	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	8	1	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	—	43	2	no	—
1052	C₂×C₄	—	43	2	no	—
1053	C₂×C₄	—	43	2	no	—
1054	C₂×C₄	—	43	2	no	—
1055	C₂×C₄	—	86	2	no	—
1056	C₂×C₄	—	86	2	no	—
1057	C₂×C₄	—	86	2	no	—
1058	C₂×C₄	—	344	2	no	—
1059	C₂×C₄	—	344	2	no	—
1060	C₂×C₄	—	172	4	no	—
1061	C₂×C₄	—	172	2	no	—
1062	C₂×C₄	—	172	2	no	—
1063	C₂×C₄	—	172	4	no	—
1064	C₂×C₄	—	172	4	no	—
1065	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1066	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1067	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1068	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1069	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1070	C₂×C₄	C₂×#10621898	1	2	yes	—
1071	C₂×C₄	#13063372	1	2	yes	—
1072	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	86	2	no	—
1078	C₈	—	86	2	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	172	2	no	—
1088	C₂²	—	172	2	no	—
1089	C₂²	—	172	2	no	—
1090	C₂²	#14583558	1	2	yes	—
1091	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	86	2	no	—
1102	C₄	—	86	2	no	—
1103	C₄	—	86	2	no	—
1104	C₄	—	86	2	no	—
1105	C₄	—	172	2	no	—
1106	C₄	—	172	2	no	—
1107	C₄	—	172	2	no	—
1108	C₄	#14583558	1	2	yes	—
1109	C₄	#14583696	1	2	yes	—
1110	C₄	C₂²×#10621898	1	1	yes	characteristic
1111	C₄	C₂×#13063372	1	1	yes	characteristic
1112	C₂	—	2	2	no	—
1113	C₂	—	4	2	no	—
1114	C₂	—	8	1	no	—
1115	C₂	—	344	2	no	—
1116	C₂	C₂×#14583558	1	1	yes	characteristic
1117	C₂	C₂×#14583696	1	1	yes	characteristic
1118	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#135	D₄₃
hypocenter	C₄₃	#61316
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #19148188	C₂	semidirect
2. #41×Dic₈₆	C₂	semidirect
3. #19147433	C₂	semidirect
4. #19147418	C₂	semidirect
5. #19147407	C₂	semidirect
6. #19147396	C₂	semidirect
7. #19147385	C₂	semidirect
8. #19147374	C₂	semidirect
9. #19147359	C₂	semidirect
10. #19147344	C₂	semidirect
11. #19147333	C₂	semidirect
12. #19147322	C₂	semidirect
13. #19147311	C₂	semidirect
14. #19147300	C₂	semidirect
15. #19144938	C₂	semidirect
16. #19144918	C₂	semidirect
17. #19144383	C₂	semidirect
18. #19144381	C₂	semidirect
19. #19144050	C₂	semidirect
20. #19144046	C₂	semidirect
21. C₂×#14583029	C₂	semidirect
22. #19143391	C₂	semidirect
23. C₄×#135×C₄₃	C₂	semidirect
317. #41×C₄₃	#41	semidirect
575. C₄×#135	D₄₃	semidirect
694. C₄₃	#61316	semidirect
880. #41	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148188	2
#41×Dic₈₆	2
#19147433	2
#19147418	2
#19147407	2
#19147396	2
#19147385	2
#19147374	2
#19147359	2
#19147344	2
#19147333	2
#19147322	2
#19147311	2
#19147300	2
#19144938	2
#19144918	2
#19144383	2
#19144381	2
#19144050	2
#19144046	2
C₂×#14583029	2
#19143391	2
C₄×#135×C₄₃	2
#61316	43