Subgroups — #25974970

Order 11008.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148506	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148388	C₂	1	1	yes	maximal, characteristic, complemented
3	#19146786	C₂	1	2	yes	maximal, complemented
4	#19146756	C₂	1	2	yes	maximal, complemented
5	#19146711	C₂	1	2	yes	maximal, complemented
6	#19146681	C₂	1	2	yes	maximal, complemented
7	#19146666	C₂	1	2	yes	maximal, complemented
8	#19146636	C₂	1	2	yes	maximal, complemented
9	#19146591	C₂	1	2	yes	maximal, complemented
10	#19146561	C₂	1	2	yes	maximal, complemented
11	C₂×#14583259	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144567	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144556	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144410	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144289	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144278	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144089	C₂	1	1	yes	maximal, characteristic, complemented
18	#19143906	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143895	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143314	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143124	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143117	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063372	C₂²	1	1	yes	characteristic
25	C₂×#13063371	C₂²	1	1	yes	characteristic
26	C₂×#13063355	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13063350	C₂²	1	1	yes	characteristic
28	C₂×#13063331	C₂²	1	1	yes	characteristic
29	C₂×#13063331	C₂²	1	1	yes	characteristic, complemented
30	#14583622	C₂²	1	2	yes	complemented
31	#14583614	C₂²	1	2	yes	complemented
32	#14583609	C₂²	1	2	yes	complemented
33	#14583595	—	2	2	no	—
34	#14583561	C₂²	1	2	yes	—
35	#14583561	C₂²	1	2	yes	—
36	#14583558	—	2	2	no	—
37	#14583554	C₂²	1	2	yes	complemented
38	#14583544	—	2	2	no	—
39	#14583544	—	2	2	no	—
40	#14583544	C₂²	1	2	yes	—
41	#14583544	C₂²	1	2	yes	—
42	#14583520	—	2	1	no	—
43	#14583520	—	2	1	no	—
44	#14583477	C₂²	1	1	yes	characteristic
45	#14583477	C₂²	1	1	yes	characteristic, complemented
46	#14583475	—	2	1	no	—
47	#14583475	C₂²	1	1	yes	characteristic
48	#14583468	—	2	1	no	—
49	#14583468	C₂²	1	1	yes	characteristic
50	#14583456	—	2	1	no	—
51	#14583449	—	2	1	no	—
52	#14583449	—	2	1	no	—
53	#14583449	C₂²	1	1	yes	characteristic
54	C₂×#13063325	C₂²	1	1	yes	characteristic, complemented
55	C₂×#13063313	—	2	1	no	—
56	C₂×#13063313	C₂²	1	1	yes	characteristic
57	#14583379	C₂²	1	1	yes	characteristic
58	#14583379	C₂²	1	1	yes	characteristic, complemented
59	#14583259	C₂²	1	2	yes	complemented
60	#14583259	C₂²	1	2	yes	complemented
61	#14583259	C₂²	1	2	yes	complemented
62	#14583259	C₂²	1	2	yes	complemented
63	#14583243	C₂²	1	2	yes	complemented
64	#14583242	C₂²	1	2	yes	complemented
65	#14583236	C₂²	1	2	yes	complemented
66	#14583231	C₂²	1	2	yes	complemented
67	#14583226	C₂²	1	2	yes	complemented
68	#14583225	C₂²	1	2	yes	complemented
69	#14583219	C₂²	1	2	yes	complemented
70	#14583214	C₂²	1	2	yes	complemented
71	#14583194	C₂²	1	2	yes	complemented
72	#14583189	C₂²	1	2	yes	complemented
73	#14583184	C₂²	1	2	yes	complemented
74	#14583179	C₂²	1	2	yes	complemented
75	#14583156	C₂²	1	2	yes	complemented
76	#14583151	C₂²	1	2	yes	complemented
77	#14583148	C₂²	1	2	yes	complemented
78	#14583144	C₂²	1	2	yes	complemented
79	#14583139	C₂²	1	2	yes	complemented
80	#14583134	C₂²	1	2	yes	complemented
81	#14583131	C₂²	1	2	yes	complemented
82	#14583127	C₂²	1	2	yes	complemented
83	#14583121	C₂²	1	2	yes	complemented
84	#14583121	C₂²	1	2	yes	complemented
85	#14583114	C₂²	1	2	yes	complemented
86	#14583114	C₂²	1	2	yes	complemented
87	#14583060	C₂²	1	2	yes	—
88	#14583058	C₂²	1	2	yes	complemented
89	#14583053	C₂²	1	2	yes	complemented
90	#14583048	C₂²	1	2	yes	—
91	#14583043	C₂²	1	2	yes	—
92	#14583041	C₂²	1	2	yes	complemented
93	#14583036	C₂²	1	2	yes	complemented
94	#14583031	C₂²	1	2	yes	—
95	#14582972	C₂²	1	2	yes	complemented
96	#14582972	C₂²	1	2	yes	complemented
97	#14582972	C₂²	1	2	yes	complemented
98	#14582972	C₂²	1	2	yes	complemented
99	#14582942	C₂²	1	1	yes	characteristic, complemented
100	#14582942	C₂²	1	1	yes	characteristic, complemented
101	#14582923	C₂²	1	1	yes	characteristic, complemented
102	#14582907	C₂²	1	1	yes	characteristic, complemented
103	#14582906	C₂²	1	2	yes	complemented
104	#14582903	C₂²	1	1	yes	characteristic
105	#14582902	C₂²	1	2	yes	—
106	#14582900	C₂²	1	1	yes	characteristic
107	#14582900	C₂²	1	1	yes	characteristic
108	#14582899	C₂²	1	2	yes	—
109	#14582897	C₂²	1	2	yes	complemented
110	#14582894	C₂²	1	2	yes	—
111	#14582892	C₂²	1	2	yes	complemented
112	C₂×#13063250	C₂²	1	1	yes	characteristic, complemented
113	C₂×#13063250	C₂²	1	1	yes	characteristic, complemented
114	#103×D₄₃	C₂²	1	2	yes	complemented
115	C₂×#13063247	C₂²	1	1	yes	characteristic
116	C₂×#13063247	C₂²	1	1	yes	characteristic
117	#102×D₄₃	C₂²	1	2	yes	—
118	#14582865	C₂²	1	1	yes	characteristic
119	#14582865	C₂²	1	1	yes	characteristic, complemented
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, complemented
123	C₄₃×#442	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#442	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#441	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#441	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#440	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#440	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#440	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#440	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
132	C₄₃×#416	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	#13063372	—	2	4	no	—
136	#13063372	—	4	2	no	—
137	#13063371	—	2	4	no	—
138	#13063371	—	4	2	no	—
139	C₂×#10621902	C₂³	1	2	yes	—
140	C₂×#10621898	—	2	1	no	—
141	C₂×#10621898	—	2	2	no	—
142	C₂×#10621898	—	2	1	no	—
143	C₂×#10621898	C₂³	1	1	yes	characteristic
144	C₂×#10621898	C₂³	1	1	yes	characteristic
145	C₂×#10621900	—	2	2	no	—
146	C₂×#10621900	C₂³	1	2	yes	—
147	C₂²×Dic₈₆	—	2	1	no	—
148	C₂²×Dic₈₆	—	2	1	no	—
149	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
150	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
151	C₂²×D₁₇₂	—	2	1	no	—
152	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
153	C₂×D₄×D₄₃	—	2	2	no	—
154	C₂×D₄×D₄₃	C₂³	1	2	yes	—
155	#13063355	—	4	2	no	—
156	#13063350	—	4	2	no	—
157	C₂×#10621885	C₂³	1	2	yes	—
158	C₂×#10621883	C₂³	1	2	yes	—
159	C₂×#10621884	C₂³	1	2	yes	—
160	C₂×#10621882	C₂³	1	2	yes	—
161	#13063331	—	4	2	no	—
162	#13063331	—	4	2	no	—
163	C₂×#10621877	C₂³	1	1	yes	characteristic
164	C₂×#10621877	C₂³	1	1	yes	characteristic
165	C₂×#10621872	C₂³	1	2	yes	—
166	C₂×#10621872	C₂³	1	2	yes	—
167	C₂×C₈×D₄₃	C₂³	1	2	yes	—
168	C₂×C₈×D₄₃	C₂³	1	2	yes	—
169	#13063325	—	2	1	no	—
170	#13063325	—	2	1	no	—
171	#13063325	—	2	1	no	—
172	#13063325	D₄	1	1	yes	characteristic
173	#13063325	C₂³	1	2	yes	—
174	#13063325	C₂³	1	2	yes	—
175	#13063322	—	2	1	no	—
176	#13063322	D₄	1	1	yes	characteristic
177	#13063320	—	2	2	no	—
178	#13063320	—	2	2	no	—
179	#13063317	—	2	2	no	—
180	#13063313	—	2	2	no	—
181	#13063313	—	2	1	no	—
182	#13063313	—	2	1	no	—
183	#13063313	—	2	1	no	—
184	#13063313	—	2	1	no	—
185	#13063313	—	2	2	no	—
186	#13063313	—	2	2	no	—
187	#13063313	D₄	1	1	yes	characteristic
188	#13063313	D₄	1	1	yes	characteristic
189	#13063313	C₂³	1	2	yes	—
190	#13063313	C₂³	1	2	yes	—
191	#13063311	—	2	2	no	—
192	#13063311	—	2	2	no	—
193	#13063309	—	2	2	no	—
194	#13063309	—	2	2	no	—
195	#13063309	—	2	2	no	—
196	#13063307	—	2	2	no	—
197	#13063307	—	2	2	no	—
198	#13063305	—	2	2	no	—
199	#13063305	—	2	2	no	—
200	#13063305	C₂³	1	2	yes	—
201	#13063305	C₂³	1	2	yes	—
202	#13063304	—	2	1	no	—
203	#13063304	—	2	1	no	—
204	#13063304	—	2	2	no	—
205	#13063303	—	2	2	no	—
206	#13063303	—	2	2	no	—
207	#13063301	C₂³	1	2	yes	—
208	#13063301	C₂³	1	2	yes	—
209	#13063300	—	2	2	no	—
210	#13063300	—	2	2	no	—
211	#13063300	C₂³	1	2	yes	—
212	#13063300	C₂³	1	2	yes	—
213	#13063299	—	2	2	no	—
214	#13063299	—	2	1	no	—
215	#13063299	—	2	1	no	—
216	#13063299	—	2	2	no	—
217	#13063299	—	2	2	no	—
218	#13063299	D₄	1	2	yes	—
219	#13063299	D₄	1	2	yes	—
220	#13063297	—	2	2	no	—
221	#13063297	—	2	2	no	—
222	#13063296	C₂³	1	2	yes	—
223	#13063296	C₂³	1	2	yes	—
224	#13063295	—	2	2	no	—
225	#13063295	—	2	2	no	—
226	#13063295	—	2	2	no	—
227	C₄×Dic₈₆	—	2	1	no	—
228	C₄×Dic₈₆	—	2	1	no	—
229	C₄×Dic₈₆	—	2	2	no	—
230	C₄×D₁₇₂	—	2	2	no	—
231	C₄×D₁₇₂	—	2	1	no	—
232	C₄×D₁₇₂	—	2	1	no	—
233	C₄×D₁₇₂	—	2	2	no	—
234	C₄×D₁₇₂	—	2	2	no	—
235	C₄×D₁₇₂	C₂³	1	2	yes	—
236	C₄×D₁₇₂	C₂³	1	2	yes	—
237	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
238	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
239	#13063284	—	2	2	no	—
240	#13063283	C₂³	1	2	yes	—
241	#13063283	C₂³	1	2	yes	—
242	C₂×C₄⋊Dic₄₃	—	2	1	no	—
243	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
246	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
247	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
248	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
249	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
250	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
251	#13063258	C₂³	1	2	yes	—
252	#13063258	C₂³	1	2	yes	—
253	#13063256	C₂³	1	2	yes	—
254	#13063256	C₂³	1	2	yes	—
255	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
256	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
257	#13063250	C₂³	1	2	yes	—
258	#13063250	C₂³	1	2	yes	—
259	#13063250	C₂³	1	2	yes	—
260	#13063250	C₂³	1	2	yes	—
261	#13063249	C₂³	1	2	yes	—
262	#13063249	C₂³	1	2	yes	—
263	#13063248	C₂³	1	2	yes	—
264	#13063248	C₂³	1	2	yes	—
265	#13063247	C₂³	1	2	yes	—
266	#13063247	C₂³	1	2	yes	—
267	#13063247	C₂³	1	2	yes	—
268	#13063247	C₂³	1	2	yes	—
269	#13063246	C₂³	1	2	yes	—
270	#13063246	C₂³	1	2	yes	—
271	#13063245	C₂³	1	2	yes	—
272	#13063245	C₂³	1	2	yes	—
273	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
274	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
275	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
276	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
277	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
279	#135×C₄₃	—	2	4	no	—
280	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
281	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
282	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
283	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	—	2	1	no	—
291	C₄×D₄×C₄₃	—	2	1	no	—
292	C₄×D₄×C₄₃	—	2	1	no	—
293	C₄×D₄×C₄₃	—	2	1	no	—
294	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
297	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
298	#117×C₄₃	—	2	1	no	—
299	#117×C₄₃	—	2	1	no	—
300	#117×C₄₃	C₂³	1	1	yes	characteristic
301	#117×C₄₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₄₃	—	2	1	no	—
303	C₂×C₄²×C₄₃	—	2	1	no	—
304	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
305	#107×C₄₃	C₂³	1	1	yes	characteristic
306	#107×C₄₃	C₂³	1	1	yes	characteristic
307	#106×C₄₃	C₂³	1	1	yes	characteristic
308	#106×C₄₃	C₂³	1	1	yes	characteristic
309	#103×C₄₃	C₂³	1	1	yes	characteristic
310	#103×C₄₃	C₂³	1	1	yes	characteristic
311	#103×C₄₃	C₂³	1	1	yes	characteristic
312	#103×C₄₃	C₂³	1	1	yes	characteristic
313	#102×C₄₃	C₂³	1	1	yes	characteristic
314	#102×C₄₃	C₂³	1	1	yes	characteristic
315	#102×C₄₃	C₂³	1	1	yes	characteristic
316	#102×C₄₃	C₂³	1	1	yes	characteristic
317	#97×C₄₃	C₂³	1	1	yes	characteristic
318	#97×C₄₃	C₂³	1	1	yes	characteristic
319	#97×C₄₃	C₂³	1	1	yes	characteristic
320	#97×C₄₃	C₂³	1	1	yes	characteristic
321	C₂³×D₄₃	—	2	1	no	—
322	C₂³×D₄₃	—	2	2	no	—
323	#41×C₄₃	—	2	2	no	—
324	#41×C₄₃	—	2	2	no	—
325	#41×C₄₃	—	2	2	no	—
326	#41×C₄₃	#41	1	4	yes	complemented
327	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₄₃	—	2	1	no	—
330	C₂×D₄×C₄₃	—	2	1	no	—
331	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₄₃	—	2	1	no	—
334	C₂²×C₄×C₄₃	—	2	1	no	—
335	C₂²×C₄×C₄₃	—	2	1	no	—
336	C₂²×C₄×C₄₃	—	2	1	no	—
337	C₂²×C₄×C₄₃	—	2	1	no	—
338	C₂²×C₄×C₄₃	—	2	1	no	—
339	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₂²⋊D₄₃	—	2	2	no	—
343	C₂×C₂²⋊D₄₃	—	2	2	no	—
344	C₂×C₂²⋊D₄₃	—	2	2	no	—
345	C₂×C₂²⋊D₄₃	—	2	2	no	—
346	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
347	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
348	C₂²×Dic₄₃	—	2	2	no	—
349	C₂²×Dic₄₃	—	2	1	no	—
350	C₂²×Dic₄₃	—	2	1	no	—
351	C₂²×Dic₄₃	—	2	1	no	—
352	#10621902	—	2	4	no	—
353	#10621902	—	4	2	no	—
354	Q₈×D₄₃	—	2	4	no	—
355	Q₈×D₄₃	—	4	2	no	—
356	#10621900	—	2	4	no	—
357	#10621900	—	4	2	no	—
358	#10621900	—	4	8	no	—
359	D₄×D₄₃	—	2	4	no	—
360	D₄×D₄₃	—	4	2	no	—
361	D₄×D₄₃	—	4	8	no	—
362	#10621898	—	2	2	no	—
363	#10621898	—	2	2	no	—
364	#10621898	—	2	2	no	—
365	#10621898	—	2	2	no	—
366	#10621898	—	4	4	no	—
367	#10621898	—	4	4	no	—
368	#10621898	—	8	4	no	—
369	C₂×D₁₇₂	—	2	1	no	—
370	C₂×D₁₇₂	—	2	2	no	—
371	C₂×D₁₇₂	—	2	2	no	—
372	C₂×D₁₇₂	—	2	2	no	—
373	C₂×D₁₇₂	—	2	2	no	—
374	C₂×D₁₇₂	—	2	2	no	—
375	C₂×D₁₇₂	—	4	4	no	—
376	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
377	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
378	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
379	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
380	C₂×D₁₇₂	C₂⁴	1	2	yes	—
381	C₂×C₄×D₄₃	—	2	2	no	—
382	C₂×C₄×D₄₃	—	2	2	no	—
383	C₂×C₄×D₄₃	—	2	2	no	—
384	C₂×C₄×D₄₃	—	2	2	no	—
385	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
386	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
387	C₂×Dic₈₆	—	2	2	no	—
388	C₂×Dic₈₆	—	2	2	no	—
389	C₂×Dic₈₆	—	2	2	no	—
390	C₂×Dic₈₆	—	2	1	no	—
391	C₂×Dic₈₆	—	2	2	no	—
392	C₂×Dic₈₆	—	2	2	no	—
393	C₂×Dic₈₆	—	4	4	no	—
394	C₂×Dic₈₆	—	8	2	no	—
395	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
396	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
397	C₂×Dic₈₆	C₂⁴	1	2	yes	—
398	Q₁₆×C₄₃	—	2	2	no	—
399	SD₁₆×C₄₃	—	2	2	no	—
400	SD₁₆×C₄₃	—	2	2	no	—
401	D₈×C₄₃	—	2	2	no	—
402	C₂×C₈×C₄₃	—	2	2	no	—
403	C₂×C₈×C₄₃	—	2	2	no	—
404	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₄₃	—	2	1	no	—
409	C₄⋊C₄×C₄₃	—	2	1	no	—
410	C₄⋊C₄×C₄₃	—	2	1	no	—
411	C₄⋊C₄×C₄₃	—	2	1	no	—
412	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₄₃	—	2	1	no	—
417	C₂²⋊C₄×C₄₃	—	2	1	no	—
418	C₂²⋊C₄×C₄₃	—	2	1	no	—
419	C₂²⋊C₄×C₄₃	—	2	1	no	—
420	C₂²⋊C₄×C₄₃	—	2	1	no	—
421	C₂²⋊C₄×C₄₃	—	2	1	no	—
422	C₄²×C₄₃	—	2	1	no	—
423	C₄²×C₄₃	—	2	1	no	—
424	C₄²×C₄₃	—	2	1	no	—
425	C₄²×C₄₃	—	2	1	no	—
426	C₄²×C₄₃	—	2	1	no	—
427	C₄²×C₄₃	—	2	1	no	—
428	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
429	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
431	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
432	C₂²⋊Dic₄₃	—	2	2	no	—
433	C₂²⋊Dic₄₃	—	2	2	no	—
434	#10621885	—	4	2	no	—
435	#10621884	—	4	2	no	—
436	#10621883	—	4	2	no	—
437	#10621882	—	4	2	no	—
438	(C₂×D₄₃)⋊C₄	—	2	2	no	—
439	(C₂×D₄₃)⋊C₄	—	2	2	no	—
440	(C₂×D₄₃)⋊C₄	—	2	2	no	—
441	(C₂×D₄₃)⋊C₄	—	2	2	no	—
442	(C₂×D₄₃)⋊C₄	—	2	2	no	—
443	(C₂×D₄₃)⋊C₄	—	2	2	no	—
444	(C₂×D₄₃)⋊C₄	—	2	2	no	—
445	(C₂×D₄₃)⋊C₄	—	2	2	no	—
446	(C₂×D₄₃)⋊C₄	—	2	2	no	—
447	(C₂×D₄₃)⋊C₄	—	2	2	no	—
448	(C₂×D₄₃)⋊C₄	—	2	2	no	—
449	(C₂×D₄₃)⋊C₄	—	2	2	no	—
450	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
451	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
452	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
453	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
454	C₄⋊Dic₄₃	—	2	2	no	—
455	C₄⋊Dic₄₃	—	2	2	no	—
456	C₄⋊Dic₄₃	—	2	1	no	—
457	C₄⋊Dic₄₃	—	2	1	no	—
458	C₄⋊Dic₄₃	—	2	2	no	—
459	C₄⋊Dic₄₃	—	2	2	no	—
460	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
461	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
462	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
463	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
464	Dic₄₃⋊C₄	—	2	2	no	—
465	Dic₄₃⋊C₄	—	2	2	no	—
466	Dic₄₃⋊C₄	—	2	2	no	—
467	Dic₄₃⋊C₄	—	2	2	no	—
468	C₄×Dic₄₃	—	2	2	no	—
469	C₄×Dic₄₃	—	2	2	no	—
470	#10621877	—	2	2	no	—
471	#10621877	—	2	2	no	—
472	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
473	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
474	#10621872	—	4	2	no	—
475	#10621872	—	4	2	no	—
476	C₈×D₄₃	—	4	2	no	—
477	C₈×D₄₃	—	4	2	no	—
478	C₂³×C₄₃	—	2	1	no	—
479	C₂³×C₄₃	—	2	1	no	—
480	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
481	C₂²×D₄₃	—	2	2	no	—
482	C₂²×D₄₃	—	4	4	no	—
483	C₂²×D₄₃	—	4	2	no	—
484	C₂²×D₄₃	—	8	2	no	—
485	C₂²×D₄₃	—	8	2	no	—
486	C₂²×D₄₃	—	8	1	no	—
487	C₂²×D₄₃	—	8	1	no	—
488	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
489	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
490	Q₈×C₄₃	—	2	1	no	—
491	Q₈×C₄₃	—	2	1	no	—
492	Q₈×C₄₃	—	2	1	no	—
493	Q₈×C₄₃	C₂×#41	1	2	yes	—
494	D₄×C₄₃	—	2	4	no	—
495	D₄×C₄₃	—	2	1	no	—
496	D₄×C₄₃	—	2	1	no	—
497	D₄×C₄₃	—	2	1	no	—
498	D₄×C₄₃	—	4	2	no	—
499	D₄×C₄₃	C₂×#41	1	2	yes	—
500	C₂×C₄×C₄₃	—	2	1	no	—
501	C₂×C₄×C₄₃	—	2	4	no	—
502	C₂×C₄×C₄₃	—	2	1	no	—
503	C₂×C₄×C₄₃	—	2	1	no	—
504	C₂×C₄×C₄₃	—	2	1	no	—
505	C₂×C₄×C₄₃	—	2	1	no	—
506	C₂×C₄×C₄₃	—	2	1	no	—
507	C₂×C₄×C₄₃	—	4	1	no	—
508	C₂×C₄×C₄₃	—	4	1	no	—
509	C₂×C₄×C₄₃	—	4	2	no	—
510	C₂×C₄×C₄₃	—	4	2	no	—
511	C₂×C₄×C₄₃	—	4	2	no	—
512	C₂×C₄×C₄₃	—	8	1	no	—
513	C₂×C₄×C₄₃	—	8	1	no	—
514	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
520	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
521	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
522	C₂²⋊D₄₃	—	2	4	no	—
523	C₂²⋊D₄₃	—	2	4	no	—
524	C₂²⋊D₄₃	—	4	4	no	—
525	C₂²⋊D₄₃	—	4	4	no	—
526	C₂²⋊D₄₃	—	8	2	no	—
527	C₂²⋊D₄₃	—	8	2	no	—
528	C₂×Dic₄₃	—	2	2	no	—
529	C₂×Dic₄₃	—	2	2	no	—
530	C₂×Dic₄₃	—	2	2	no	—
531	C₂×Dic₄₃	—	4	4	no	—
532	C₂×Dic₄₃	—	4	2	no	—
533	C₂×Dic₄₃	—	8	1	no	—
534	C₂×Dic₄₃	—	8	1	no	—
535	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
536	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
537	D₁₇₂	—	2	2	no	—
538	D₁₇₂	—	2	2	no	—
539	D₁₇₂	—	2	2	no	—
540	D₁₇₂	—	2	2	no	—
541	D₁₇₂	—	4	2	no	—
542	D₁₇₂	—	4	2	no	—
543	D₁₇₂	—	4	4	no	—
544	D₁₇₂	—	4	2	no	—
545	D₁₇₂	—	8	2	no	—
546	D₁₇₂	—	8	2	no	—
547	C₄×D₄₃	—	2	2	no	—
548	C₄×D₄₃	—	2	2	no	—
549	C₄×D₄₃	—	2	2	no	—
550	C₄×D₄₃	—	2	2	no	—
551	C₄×D₄₃	—	4	4	no	—
552	C₄×D₄₃	—	4	4	no	—
553	C₄×D₄₃	—	8	2	no	—
554	C₄×D₄₃	—	8	2	no	—
555	Dic₈₆	—	2	2	no	—
556	Dic₈₆	—	2	2	no	—
557	Dic₈₆	—	2	2	no	—
558	Dic₈₆	—	2	2	no	—
559	Dic₈₆	—	4	4	no	—
560	Dic₈₆	—	4	4	no	—
561	Dic₈₆	—	4	2	no	—
562	Dic₈₆	—	8	2	no	—
563	C₈×C₄₃	—	2	1	no	—
564	C₈×C₄₃	—	2	1	no	—
565	C₈×C₄₃	—	2	1	no	—
566	C₈×C₄₃	—	2	1	no	—
567	C₄₃⋊C₈	—	2	2	no	—
568	C₄₃⋊C₈	—	2	2	no	—
569	#61222	—	43	1	no	maximal, Sylow
570	C₂²×C₄₃	—	2	1	no	—
571	C₂²×C₄₃	—	2	1	no	—
572	C₂²×C₄₃	—	2	2	no	—
573	C₂²×C₄₃	—	4	1	no	—
574	C₂²×C₄₃	—	4	1	no	—
575	C₂²×C₄₃	—	4	1	no	—
576	C₂²×C₄₃	—	4	1	no	—
577	C₂²×C₄₃	—	4	1	no	—
578	C₂²×C₄₃	#546	1	2	yes	—
579	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
580	C₂×D₄₃	—	2	2	no	—
581	C₂×D₄₃	—	2	2	no	—
582	C₂×D₄₃	—	2	2	no	—
583	C₂×D₄₃	—	2	2	no	—
584	C₂×D₄₃	—	2	2	no	—
585	C₂×D₄₃	—	2	2	no	—
586	C₂×D₄₃	—	4	2	no	—
587	C₂×D₄₃	—	4	2	no	—
588	C₂×D₄₃	—	4	2	no	—
589	C₂×D₄₃	—	16	4	no	—
590	C₂×D₄₃	—	16	2	no	—
591	C₄×C₄₃	—	2	1	no	—
592	C₄×C₄₃	—	2	1	no	—
593	C₄×C₄₃	—	2	1	no	—
594	C₄×C₄₃	—	2	1	no	—
595	C₄×C₄₃	—	2	2	no	—
596	C₄×C₄₃	—	4	1	no	—
597	C₄×C₄₃	—	4	1	no	—
598	C₄×C₄₃	—	4	1	no	—
599	C₄×C₄₃	—	4	1	no	—
600	C₄×C₄₃	—	4	1	no	—
601	C₄×C₄₃	#546	1	2	yes	—
602	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
603	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	Dic₄₃	—	2	2	no	—
605	Dic₄₃	—	2	2	no	—
606	Dic₄₃	—	4	2	no	—
607	Dic₄₃	—	4	2	no	—
608	Dic₄₃	—	4	2	no	—
609	#3511	—	43	1	no	—
610	#3500	—	43	1	no	—
611	#3321	—	43	2	no	—
612	#3319	—	43	2	no	—
613	#3316	—	43	2	no	—
614	#3314	—	43	2	no	—
615	#3313	—	43	2	no	—
616	#3311	—	43	2	no	—
617	#3308	—	43	2	no	—
618	#3306	—	43	2	no	—
619	C₂×#489	—	43	1	no	—
620	#3097	—	43	1	no	—
621	#3096	—	43	1	no	—
622	#3079	—	43	1	no	—
623	#3063	—	43	1	no	—
624	#3062	—	43	1	no	—
625	#3040	—	43	1	no	—
626	#3013	—	43	1	no	—
627	#3012	—	43	1	no	—
628	#2943	D₄₃	1	1	yes	characteristic, complemented
629	#2932	—	43	1	no	—
630	#2898	—	43	1	no	—
631	#2897	—	43	1	no	—
632	C₂×C₄₃	—	2	2	no	—
633	C₂×C₄₃	—	4	2	no	—
634	C₂×C₄₃	—	8	1	no	—
635	C₂×C₄₃	C₂×#546	1	1	yes	characteristic
636	C₂×C₄₃	#3585	1	1	yes	characteristic
637	C₂×C₄₃	#3586	1	1	yes	characteristic
638	D₄₃	—	4	2	no	—
639	D₄₃	—	4	2	no	—
640	D₄₃	—	8	2	no	—
641	C₂×2₋¹⁺⁴	—	43	1	no	—
642	C₂×H(5,𝔽₂)	—	43	1	no	—
643	C₂×#137	—	43	1	no	—
644	C₂×AGL(1,ℤ/8)	—	43	1	no	—
645	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
646	C₂×#131	—	43	1	no	—
647	C₂×#131	—	43	1	no	—
648	#556	—	43	2	no	—
649	#555	—	43	2	no	—
650	#554	—	43	2	no	—
651	#553	—	86	2	no	—
652	#548	—	43	2	no	—
653	#548	—	43	2	no	—
654	#548	—	86	2	no	—
655	#547	—	43	2	no	—
656	#546	—	43	2	no	—
657	#546	—	43	2	no	—
658	#546	—	86	2	no	—
659	#546	—	86	2	no	—
660	#542	—	86	1	no	—
661	#542	—	86	1	no	—
662	#537	—	43	1	no	—
663	#537	—	43	1	no	—
664	#536	—	43	1	no	—
665	#536	—	86	1	no	—
666	#535	—	43	1	no	—
667	#535	—	86	1	no	—
668	#533	—	86	1	no	—
669	#532	—	43	1	no	—
670	#532	—	86	1	no	—
671	#532	—	86	1	no	—
672	C₂×C₄⋊Q₈	—	43	1	no	—
673	C₂×#124	—	43	1	no	—
674	C₂×#124	—	86	1	no	—
675	#520	—	43	1	no	—
676	#520	—	43	1	no	—
677	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
678	C₄×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
679	#489	—	43	2	no	—
680	#489	—	43	2	no	—
681	#489	—	43	2	no	—
682	#489	—	43	2	no	—
683	#485	—	43	2	no	—
684	#485	—	43	2	no	—
685	#484	—	43	2	no	—
686	#483	—	43	2	no	—
687	#482	—	43	2	no	—
688	#482	—	43	2	no	—
689	#481	—	43	2	no	—
690	#480	—	43	2	no	—
691	#477	—	43	2	no	—
692	#476	—	43	2	no	—
693	#475	—	43	2	no	—
694	#474	—	43	2	no	—
695	#470	—	43	2	no	—
696	#469	—	43	2	no	—
697	#468	—	43	2	no	—
698	#468	—	43	2	no	—
699	#467	—	43	2	no	—
700	#466	—	43	2	no	—
701	#465	—	43	2	no	—
702	#465	—	43	2	no	—
703	#464	—	43	2	no	—
704	#464	—	43	2	no	—
705	#463	—	43	2	no	—
706	#463	—	43	2	no	—
707	#452	—	43	2	no	—
708	#452	—	43	2	no	—
709	#451	—	43	2	no	—
710	#450	—	43	2	no	—
711	#449	—	43	2	no	—
712	#449	—	43	2	no	—
713	#448	—	43	2	no	—
714	#447	—	43	2	no	—
715	#442	C₂×D₄₃	1	1	yes	characteristic, complemented
716	#442	C₂×D₄₃	1	1	yes	characteristic, complemented
717	#441	C₂×D₄₃	1	1	yes	characteristic, complemented
718	#441	C₂×D₄₃	1	1	yes	characteristic, complemented
719	#440	C₂×D₄₃	1	1	yes	characteristic, complemented
720	#440	C₂×D₄₃	1	1	yes	characteristic, complemented
721	#440	C₂×D₄₃	1	1	yes	characteristic, complemented
722	#440	C₂×D₄₃	1	1	yes	characteristic, complemented
723	#435	—	43	2	no	—
724	#435	—	43	2	no	—
725	#435	—	43	2	no	—
726	#435	—	43	2	no	—
727	#428	—	43	1	no	—
728	#428	—	43	1	no	—
729	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
730	#423	—	43	1	no	—
731	#419	—	43	1	no	—
732	#419	—	43	2	no	—
733	#418	—	43	1	no	—
734	#418	—	43	2	no	—
735	#417	—	43	1	no	—
736	#417	—	43	1	no	—
737	#417	—	43	2	no	—
738	#417	—	43	2	no	—
739	#416	—	43	2	no	—
740	#416	—	43	2	no	—
741	#416	C₂×D₄₃	1	1	yes	characteristic
742	#416	C₂×D₄₃	1	1	yes	characteristic, complemented
743	C₂×#103	—	43	1	no	—
744	C₂×#103	—	43	1	no	—
745	C₂×#103	—	43	2	no	—
746	C₂×#102	—	43	1	no	—
747	C₂×#102	—	43	1	no	—
748	C₂×#102	—	43	2	no	—
749	#408	—	43	1	no	—
750	#408	—	43	1	no	—
751	C₂×#97	C₂×D₄₃	1	1	yes	characteristic, complemented
752	C₄₃	#61222	1	1	yes	characteristic, complemented, Sylow
753	2₋¹⁺⁴	—	86	4	no	—
754	2₋¹⁺⁴	—	172	2	no	—
755	H(5,𝔽₂)	—	86	4	no	—
756	H(5,𝔽₂)	—	172	2	no	—
757	C₂×#41	—	43	1	no	—
758	C₂×#41	—	43	1	no	—
759	C₂×#41	—	43	2	no	—
760	C₂×#41	—	43	2	no	—
761	C₂×#41	—	86	2	no	—
762	C₂×#41	—	86	1	no	—
763	C₂×#41	—	86	1	no	—
764	C₂×#41	—	86	2	no	—
765	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
766	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
767	C₂²×Q₈	—	43	2	no	—
768	C₂²×Q₈	—	43	1	no	—
769	C₂²×Q₈	—	86	1	no	—
770	C₂²×Q₈	—	86	1	no	—
771	C₂²×D₄	—	43	2	no	—
772	C₂²×D₄	—	43	1	no	—
773	C₂²×D₄	—	86	1	no	—
774	C₂²×D₄	—	86	2	no	—
775	#137	—	172	2	no	—
776	AGL(1,ℤ/8)	—	172	2	no	—
777	#135	—	2	4	no	—
778	C₂×Q₁₆	—	43	2	no	—
779	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
780	C₂×SD₁₆	—	43	2	no	—
781	C₂×SD₁₆	—	43	2	no	—
782	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
783	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
784	C₂×D₈	—	43	2	no	—
785	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
786	#131	—	172	2	no	—
787	#131	—	172	2	no	—
788	C₂×M₁₆	—	43	1	no	—
789	C₂×M₁₆	—	43	1	no	—
790	C₂×M₁₆	—	43	2	no	—
791	C₂×M₁₆	—	43	2	no	—
792	C₂²×C₈	—	43	2	no	—
793	C₂²×C₈	—	43	2	no	—
794	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
795	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
796	C₄⋊Q₈	—	43	1	no	—
797	C₄⋊Q₈	—	43	2	no	—
798	C₄⋊Q₈	—	43	2	no	—
799	C₄⋊Q₈	—	86	1	no	—
800	C₄⋊Q₈	—	86	1	no	—
801	C₄⋊Q₈	—	86	1	no	—
802	#127	—	43	1	no	—
803	#127	—	86	1	no	—
804	#126	—	86	2	no	—
805	#126	—	86	2	no	—
806	#125	—	86	2	no	—
807	#124	—	43	1	no	—
808	#124	—	43	1	no	—
809	#124	—	43	2	no	—
810	#124	—	43	2	no	—
811	#124	—	86	2	no	—
812	#124	—	86	2	no	—
813	#124	—	86	1	no	—
814	#124	—	86	2	no	—
815	#124	—	86	1	no	—
816	#124	—	86	2	no	—
817	#124	—	86	2	no	—
818	#124	—	86	1	no	—
819	#124	—	86	1	no	—
820	#123	—	86	2	no	—
821	#123	—	86	2	no	—
822	#123	—	86	2	no	—
823	#123	—	86	2	no	—
824	#123	—	86	2	no	—
825	C₂²⋊Q₈	—	43	2	no	—
826	C₂²⋊Q₈	—	43	2	no	—
827	C₂²⋊Q₈	—	43	2	no	—
828	C₂²⋊Q₈	—	43	2	no	—
829	C₂²⋊Q₈	—	86	2	no	—
830	C₂²⋊Q₈	—	86	2	no	—
831	C₂²⋊Q₈	—	86	2	no	—
832	C₂²⋊Q₈	—	86	2	no	—
833	C₂²⋊Q₈	—	86	2	no	—
834	C₂²⋊Q₈	—	86	1	no	—
835	C₂²⋊Q₈	—	86	1	no	—
836	#121	—	43	2	no	—
837	#121	—	43	2	no	—
838	#121	—	43	2	no	—
839	#121	—	43	2	no	—
840	#121	—	43	2	no	—
841	#121	—	43	2	no	—
842	#121	—	86	2	no	—
843	#121	—	86	2	no	—
844	#121	—	86	2	no	—
845	#121	—	86	2	no	—
846	#121	—	86	1	no	—
847	#121	—	86	1	no	—
848	#121	—	86	2	no	—
849	#121	—	86	2	no	—
850	#121	—	86	2	no	—
851	#120	—	86	2	no	—
852	#120	—	86	2	no	—
853	#120	—	86	2	no	—
854	C₄×Q₈	—	86	2	no	—
855	C₄×Q₈	—	86	1	no	—
856	C₄×Q₈	—	86	1	no	—
857	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
858	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
859	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
860	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	43	2	no	—
866	C₄×D₄	—	43	2	no	—
867	C₄×D₄	—	86	2	no	—
868	C₄×D₄	—	86	2	no	—
869	C₄×D₄	—	86	1	no	—
870	C₄×D₄	—	86	1	no	—
871	C₄×D₄	—	86	2	no	—
872	C₄×D₄	—	86	2	no	—
873	C₄×D₄	—	86	2	no	—
874	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
875	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
876	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
877	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
878	#117	—	2	1	no	—
879	#117	—	2	1	no	—
880	#117	—	43	2	no	—
881	#117	—	43	2	no	—
882	#117	—	86	2	no	—
883	#117	C₂²×D₄₃	1	1	yes	characteristic
884	#117	C₂²×D₄₃	1	1	yes	characteristic
885	C₂×C₄⋊C₄	—	43	1	no	—
886	C₂×C₄⋊C₄	—	43	1	no	—
887	C₂×C₄⋊C₄	—	43	2	no	—
888	C₂×C₄⋊C₄	—	43	2	no	—
889	C₂×C₄⋊C₄	—	86	1	no	—
890	C₂×C₂²⋊C₄	—	86	2	no	—
891	C₂×C₂²⋊C₄	—	86	2	no	—
892	C₂×C₂²⋊C₄	—	86	1	no	—
893	C₂×C₂²⋊C₄	—	86	1	no	—
894	C₂×C₄²	—	2	1	no	—
895	C₂×C₄²	—	2	1	no	—
896	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
897	#107	—	43	2	no	—
898	#107	—	43	2	no	—
899	#107	C₂²×D₄₃	1	1	yes	characteristic
900	#107	C₂²×D₄₃	1	1	yes	characteristic
901	#106	—	43	2	no	—
902	#106	—	43	2	no	—
903	#106	C₂²×D₄₃	1	1	yes	characteristic
904	#106	C₂²×D₄₃	1	1	yes	characteristic
905	C₄⋊C₈	—	43	2	no	—
906	C₄⋊C₈	—	43	2	no	—
907	#103	—	43	2	no	—
908	#103	—	43	2	no	—
909	#103	—	43	2	no	—
910	#103	—	43	2	no	—
911	#103	—	43	2	no	—
912	#103	—	43	2	no	—
913	#103	—	43	2	no	—
914	#103	—	43	2	no	—
915	#103	C₂²×D₄₃	1	1	yes	characteristic
916	#103	C₂²×D₄₃	1	1	yes	characteristic
917	#103	C₂²×D₄₃	1	1	yes	characteristic
918	#103	C₂²×D₄₃	1	1	yes	characteristic
919	#102	—	43	2	no	—
920	#102	—	43	2	no	—
921	#102	—	43	2	no	—
922	#102	—	43	2	no	—
923	#102	—	43	2	no	—
924	#102	—	43	2	no	—
925	#102	—	43	2	no	—
926	#102	—	43	2	no	—
927	#102	C₂²×D₄₃	1	1	yes	characteristic
928	#102	C₂²×D₄₃	1	1	yes	characteristic
929	#102	C₂²×D₄₃	1	1	yes	characteristic
930	#102	C₂²×D₄₃	1	1	yes	characteristic
931	C₂²⋊C₈	—	43	2	no	—
932	C₂²⋊C₈	—	43	2	no	—
933	C₂²⋊C₈	—	43	2	no	—
934	C₂²⋊C₈	—	43	2	no	—
935	#97	C₂²×D₄₃	1	1	yes	characteristic
936	#97	C₂²×D₄₃	1	1	yes	characteristic
937	#97	C₂²×D₄₃	1	1	yes	characteristic
938	#97	C₂²×D₄₃	1	1	yes	characteristic
939	C₂⁴	—	86	2	no	—
940	C₂⁴	—	86	1	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	86	2	no	—
945	#41	—	86	2	no	—
946	#41	—	86	2	no	—
947	#41	—	86	2	no	—
948	#41	—	86	4	no	—
949	#41	—	86	4	no	—
950	#41	—	344	4	no	—
951	#41	—	172	4	no	—
952	#41	—	172	4	no	—
953	#41	—	172	2	no	—
954	#41	—	172	2	no	—
955	#41	—	172	8	no	—
956	#41	#10621898	1	4	yes	complemented
957	C₂×Q₈	—	43	1	no	—
958	C₂×Q₈	—	43	1	no	—
959	C₂×Q₈	—	43	2	no	—
960	C₂×Q₈	—	86	2	no	—
961	C₂×Q₈	—	86	2	no	—
962	C₂×Q₈	—	86	2	no	—
963	C₂×Q₈	—	86	1	no	—
964	C₂×Q₈	—	86	4	no	—
965	C₂×Q₈	—	86	2	no	—
966	C₂×Q₈	—	86	2	no	—
967	C₂×Q₈	—	344	2	no	—
968	C₂×Q₈	—	172	4	no	—
969	C₂×Q₈	—	172	2	no	—
970	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
971	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	43	2	no	—
975	C₂×D₄	—	43	2	no	—
976	C₂×D₄	—	43	1	no	—
977	C₂×D₄	—	43	1	no	—
978	C₂×D₄	—	43	2	no	—
979	C₂×D₄	—	43	2	no	—
980	C₂×D₄	—	43	2	no	—
981	C₂×D₄	—	86	2	no	—
982	C₂×D₄	—	86	2	no	—
983	C₂×D₄	—	86	2	no	—
984	C₂×D₄	—	86	2	no	—
985	C₂×D₄	—	86	4	no	—
986	C₂×D₄	—	86	2	no	—
987	C₂×D₄	—	86	2	no	—
988	C₂×D₄	—	86	2	no	—
989	C₂×D₄	—	86	1	no	—
990	C₂×D₄	—	86	2	no	—
991	C₂×D₄	—	86	2	no	—
992	C₂×D₄	—	172	4	no	—
993	C₂×D₄	—	172	2	no	—
994	C₂×D₄	—	172	8	no	—
995	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
996	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	43	2	no	—
1004	C₂²×C₄	—	43	2	no	—
1005	C₂²×C₄	—	86	2	no	—
1006	C₂²×C₄	—	86	2	no	—
1007	C₂²×C₄	—	86	2	no	—
1008	C₂²×C₄	—	86	2	no	—
1009	C₂²×C₄	—	86	2	no	—
1010	C₂²×C₄	—	86	1	no	—
1011	C₂²×C₄	—	86	1	no	—
1012	C₂²×C₄	—	86	1	no	—
1013	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
1014	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1016	Q₁₆	—	2	2	no	—
1017	Q₁₆	—	172	2	no	—
1018	SD₁₆	—	2	2	no	—
1019	SD₁₆	—	2	2	no	—
1020	SD₁₆	—	172	2	no	—
1021	SD₁₆	—	172	2	no	—
1022	D₈	—	2	2	no	—
1023	D₈	—	172	2	no	—
1024	M₁₆	—	86	2	no	—
1025	M₁₆	—	86	2	no	—
1026	M₁₆	—	172	2	no	—
1027	M₁₆	—	172	2	no	—
1028	C₂×C₈	—	2	2	no	—
1029	C₂×C₈	—	2	2	no	—
1030	C₂×C₈	—	43	2	no	—
1031	C₂×C₈	—	43	2	no	—
1032	C₂×C₈	—	172	2	no	—
1033	C₂×C₈	—	172	2	no	—
1034	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1035	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1036	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1037	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	43	2	no	—
1043	C₄⋊C₄	—	43	2	no	—
1044	C₄⋊C₄	—	43	2	no	—
1045	C₄⋊C₄	—	43	2	no	—
1046	C₄⋊C₄	—	86	2	no	—
1047	C₄⋊C₄	—	86	2	no	—
1048	C₄⋊C₄	—	86	2	no	—
1049	C₄⋊C₄	—	86	2	no	—
1050	C₄⋊C₄	—	86	2	no	—
1051	C₄⋊C₄	—	86	2	no	—
1052	C₄⋊C₄	—	86	1	no	—
1053	C₄⋊C₄	—	86	1	no	—
1054	C₄⋊C₄	—	86	2	no	—
1055	C₄⋊C₄	—	86	2	no	—
1056	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1057	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1058	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	43	2	no	—
1067	C₂²⋊C₄	—	43	2	no	—
1068	C₂²⋊C₄	—	43	2	no	—
1069	C₂²⋊C₄	—	43	2	no	—
1070	C₂²⋊C₄	—	86	2	no	—
1071	C₂²⋊C₄	—	86	2	no	—
1072	C₂²⋊C₄	—	86	2	no	—
1073	C₂²⋊C₄	—	86	2	no	—
1074	C₂²⋊C₄	—	86	2	no	—
1075	C₂²⋊C₄	—	86	2	no	—
1076	C₂²⋊C₄	—	86	2	no	—
1077	C₂²⋊C₄	—	86	2	no	—
1078	C₂²⋊C₄	—	86	2	no	—
1079	C₂²⋊C₄	—	86	2	no	—
1080	C₂²⋊C₄	—	86	2	no	—
1081	C₂²⋊C₄	—	86	2	no	—
1082	C₂²⋊C₄	—	86	2	no	—
1083	C₂²⋊C₄	—	86	2	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	1	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	—	86	2	no	—
1091	C₄²	—	86	2	no	—
1092	C₄²	D₄×D₄₃	1	1	yes	characteristic
1093	C₄²	D₄×D₄₃	1	1	yes	characteristic
1094	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1095	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	1	no	—
1098	C₂³	—	43	2	no	—
1099	C₂³	—	43	2	no	—
1100	C₂³	—	86	2	no	—
1101	C₂³	—	344	1	no	—
1102	C₂³	—	344	1	no	—
1103	C₂³	—	344	2	no	—
1104	C₂³	—	344	2	no	—
1105	C₂³	—	172	4	no	—
1106	C₂³	—	172	2	no	—
1107	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	2	1	no	—
1111	Q₈	—	86	2	no	—
1112	Q₈	—	86	2	no	—
1113	Q₈	—	86	2	no	—
1114	Q₈	—	86	2	no	—
1115	Q₈	—	344	2	no	—
1116	Q₈	—	172	4	no	—
1117	Q₈	—	172	4	no	—
1118	Q₈	—	172	2	no	—
1119	Q₈	C₂×#10621898	1	2	yes	—
1120	D₄	—	2	4	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	1	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	86	4	no	—
1126	D₄	—	86	4	no	—
1127	D₄	—	86	2	no	—
1128	D₄	—	86	2	no	—
1129	D₄	—	86	2	no	—
1130	D₄	—	86	2	no	—
1131	D₄	—	344	2	no	—
1132	D₄	—	344	2	no	—
1133	D₄	—	344	2	no	—
1134	D₄	—	344	2	no	—
1135	D₄	—	172	2	no	—
1136	D₄	—	172	2	no	—
1137	D₄	—	172	4	no	—
1138	D₄	—	172	4	no	—
1139	D₄	—	172	4	no	—
1140	D₄	—	172	2	no	—
1141	D₄	C₂×#10621898	1	2	yes	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	4	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	8	1	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	43	2	no	—
1157	C₂×C₄	—	43	2	no	—
1158	C₂×C₄	—	86	2	no	—
1159	C₂×C₄	—	86	2	no	—
1160	C₂×C₄	—	86	2	no	—
1161	C₂×C₄	—	86	2	no	—
1162	C₂×C₄	—	86	2	no	—
1163	C₂×C₄	—	86	2	no	—
1164	C₂×C₄	—	86	2	no	—
1165	C₂×C₄	—	344	2	no	—
1166	C₂×C₄	—	344	2	no	—
1167	C₂×C₄	—	344	1	no	—
1168	C₂×C₄	—	344	1	no	—
1169	C₂×C₄	—	172	4	no	—
1170	C₂×C₄	—	172	4	no	—
1171	C₂×C₄	—	172	4	no	—
1172	C₂×C₄	—	172	2	no	—
1173	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1174	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1175	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1176	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1177	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1178	C₂×C₄	C₂×#10621898	1	2	yes	—
1179	C₂×C₄	#13063371	1	2	yes	—
1180	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	86	2	no	—
1186	C₈	—	86	2	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	86	2	no	—
1196	C₂²	—	86	2	no	—
1197	C₂²	—	86	2	no	—
1198	C₂²	—	86	2	no	—
1199	C₂²	—	86	2	no	—
1200	C₂²	—	86	2	no	—
1201	C₂²	—	172	2	no	—
1202	C₂²	—	172	2	no	—
1203	C₂²	—	172	2	no	—
1204	C₂²	—	688	2	no	—
1205	C₂²	—	688	4	no	—
1206	C₂²	#14583545	1	2	yes	—
1207	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1208	C₄	—	2	2	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	86	2	no	—
1219	C₄	—	86	2	no	—
1220	C₄	—	172	2	no	—
1221	C₄	—	172	2	no	—
1222	C₄	—	172	2	no	—
1223	C₄	#14583545	1	2	yes	—
1224	C₄	C₂²×#10621898	1	1	yes	characteristic
1225	C₄	C₂×#13063371	1	1	yes	characteristic
1226	C₂	—	2	2	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	8	1	no	—
1229	C₂	—	344	2	no	—
1230	C₂	—	172	2	no	—
1231	C₂	—	172	2	no	—
1232	C₂	C₂×#14583545	1	1	yes	characteristic
1233	C₂	#19149372	1	1	yes	characteristic
1234	C₂	#19149379	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×#2943	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#2943	D₄₃
hypocenter	C₄₃	#61222
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
1. #19148506	C₂	semidirect
2. #19148388	C₂	semidirect
3. #19146786	C₂	semidirect
4. #19146756	C₂	semidirect
5. #19146711	C₂	semidirect
6. #19146681	C₂	semidirect
7. #19146666	C₂	semidirect
8. #19146636	C₂	semidirect
9. #19146591	C₂	semidirect
10. #19146561	C₂	semidirect
11. C₂×#14583259	C₂	semidirect
12. #19144567	C₂	semidirect
13. #19144556	C₂	semidirect
14. #19144410	C₂	semidirect
15. #19144289	C₂	semidirect
16. #19144278	C₂	semidirect
17. #19144089	C₂	semidirect
18. #19143906	C₂	semidirect
19. #19143895	C₂	semidirect
20. #19143314	C₂	semidirect
21. #19143124	C₂	semidirect
22. #19143117	C₂	semidirect
23. C₄₃×#2943	C₂	semidirect
26. C₂×#13063355	C₂²	semidirect
29. C₂×#13063331	C₂²	semidirect
30. #14583622	C₂²	semidirect
31. #14583614	C₂²	semidirect
32. #14583609	C₂²	semidirect
37. #14583554	C₂²	semidirect
45. #14583477	C₂²	semidirect
54. C₂×#13063325	C₂²	semidirect
58. #14583379	C₂²	semidirect
59. #14583259	C₂²	semidirect
60. #14583259	C₂²	semidirect
61. #14583259	C₂²	semidirect
62. #14583259	C₂²	semidirect
63. #14583243	C₂²	semidirect
64. #14583242	C₂²	semidirect
65. #14583236	C₂²	semidirect
66. #14583231	C₂²	semidirect
67. #14583226	C₂²	semidirect
68. #14583225	C₂²	semidirect
69. #14583219	C₂²	semidirect
70. #14583214	C₂²	semidirect
71. #14583194	C₂²	semidirect
72. #14583189	C₂²	semidirect
73. #14583184	C₂²	semidirect
74. #14583179	C₂²	semidirect
75. #14583156	C₂²	semidirect
76. #14583151	C₂²	semidirect
77. #14583148	C₂²	semidirect
78. #14583144	C₂²	semidirect
79. #14583139	C₂²	semidirect
80. #14583134	C₂²	semidirect
81. #14583131	C₂²	semidirect
82. #14583127	C₂²	semidirect
83. #14583121	C₂²	semidirect
84. #14583121	C₂²	semidirect
85. #14583114	C₂²	semidirect
86. #14583114	C₂²	semidirect
88. #14583058	C₂²	semidirect
89. #14583053	C₂²	semidirect
92. #14583041	C₂²	semidirect
93. #14583036	C₂²	semidirect
95. #14582972	C₂²	semidirect
96. #14582972	C₂²	semidirect
97. #14582972	C₂²	semidirect
98. #14582972	C₂²	semidirect
99. #14582942	C₂²	semidirect
100. #14582942	C₂²	semidirect
101. #14582923	C₂²	semidirect
102. #14582907	C₂²	semidirect
103. #14582906	C₂²	semidirect
109. #14582897	C₂²	semidirect
111. #14582892	C₂²	semidirect
112. C₂×#13063250	C₂²	semidirect
113. C₂×#13063250	C₂²	semidirect
114. #103×D₄₃	C₂²	semidirect
119. #14582865	C₂²	semidirect
122. C₄×#41×C₄₃	C₂²	semidirect
123. C₄₃×#442	C₂²	semidirect
124. C₄₃×#442	C₂²	semidirect
125. C₄₃×#441	C₂²	semidirect
126. C₄₃×#441	C₂²	semidirect
127. C₄₃×#440	C₂²	semidirect
128. C₄₃×#440	C₂²	semidirect
129. C₄₃×#440	C₂²	semidirect
130. C₄₃×#440	C₂²	semidirect
131. C₄₃×#427	C₂²	semidirect
133. C₄₃×#416	C₂²	semidirect
134. C₂×#97×C₄₃	C₂²	semidirect
326. #41×C₄₃	#41	semidirect
628. #2943	D₄₃	semidirect
678. C₄×#41	C₂×D₄₃	semidirect
715. #442	C₂×D₄₃	semidirect
716. #442	C₂×D₄₃	semidirect
717. #441	C₂×D₄₃	semidirect
718. #441	C₂×D₄₃	semidirect
719. #440	C₂×D₄₃	semidirect
720. #440	C₂×D₄₃	semidirect
721. #440	C₂×D₄₃	semidirect
722. #440	C₂×D₄₃	semidirect
729. #427	C₂×D₄₃	semidirect
742. #416	C₂×D₄₃	semidirect
751. C₂×#97	C₂×D₄₃	semidirect
752. C₄₃	#61222	semidirect
956. #41	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148506	2
#19148388	2
#19146786	2
#19146756	2
#19146711	2
#19146681	2
#19146666	2
#19146636	2
#19146591	2
#19146561	2
C₂×#14583259	2
#19144567	2
#19144556	2
#19144410	2
#19144289	2
#19144278	2
#19144089	2
#19143906	2
#19143895	2
#19143314	2
#19143124	2
#19143117	2
C₄₃×#2943	2
#61222	43