Subgroups — #25961504

Order 11008.

2136 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143671	C₂	1	2	yes	maximal, complemented
2	#19143666	C₂	1	2	yes	maximal, complemented
3	#19143657	C₂	1	2	yes	maximal, complemented
4	#19143651	C₂	1	2	yes	maximal, complemented
5	#19143643	C₂	1	2	yes	maximal, complemented
6	#19143643	C₂	1	2	yes	maximal, complemented
7	#19143630	C₂	1	2	yes	maximal, complemented
8	#19143624	C₂	1	2	yes	maximal, complemented
9	#19143339	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143322	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143322	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143313	C₂	1	1	yes	maximal, characteristic, complemented
14	#19143299	C₂	1	1	yes	maximal, characteristic, complemented
15	#19143290	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14582971	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143261	C₂	1	1	yes	maximal, characteristic, complemented
18	#19143246	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143044	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143044	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14582866	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
24	C₂×#13063332	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13063332	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13063332	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13063332	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#10621877	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#10621877	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#10621877	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	#14582977	C₂²	1	2	yes	complemented
33	#14582977	C₂²	1	2	yes	complemented
34	#14582977	C₂²	1	2	yes	complemented
35	#14582977	C₂²	1	2	yes	complemented
36	#14582977	C₂²	1	2	yes	complemented
37	#14582977	C₂²	1	2	yes	complemented
38	#14582971	C₂²	1	1	yes	characteristic
39	#14582971	C₂²	1	1	yes	characteristic
40	#14582971	C₂²	1	2	yes	—
41	#14582971	C₂²	1	1	yes	characteristic, complemented
42	#14582971	C₂²	1	1	yes	characteristic, complemented
43	#14582971	C₂²	1	1	yes	characteristic, complemented
44	#14582971	C₂²	1	1	yes	characteristic, complemented
45	#14582971	C₂²	1	1	yes	characteristic, complemented
46	#14582971	C₂²	1	1	yes	characteristic, complemented
47	#14582971	C₂²	1	2	yes	complemented
48	#14582971	C₂²	1	2	yes	complemented
49	#14582971	C₂²	1	2	yes	complemented
50	#14582971	C₂²	1	2	yes	complemented
51	#14582971	C₂²	1	2	yes	complemented
52	#14582971	C₂²	1	2	yes	complemented
53	#14582971	C₂²	1	2	yes	complemented
54	#14582971	C₂²	1	2	yes	complemented
55	#14582971	C₂²	1	2	yes	complemented
56	#14582971	C₂²	1	2	yes	complemented
57	#14582971	C₂²	1	2	yes	complemented
58	#14582971	C₂²	1	2	yes	complemented
59	#14582971	C₂²	1	2	yes	complemented
60	#14582971	C₂²	1	2	yes	complemented
61	#14582971	C₂²	1	2	yes	complemented
62	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
63	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
64	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
65	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
66	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
67	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
68	#14582960	C₂²	1	2	yes	complemented
69	#14582960	C₂²	1	2	yes	complemented
70	#14582960	C₂²	1	2	yes	complemented
71	#14582960	C₂²	1	2	yes	complemented
72	#14582956	C₂²	1	2	yes	complemented
73	#14582956	C₂²	1	2	yes	complemented
74	#14582956	C₂²	1	2	yes	complemented
75	#14582952	C₂²	1	2	yes	complemented
76	#14582926	C₂²	1	1	yes	characteristic, complemented
77	#14582926	C₂²	1	1	yes	characteristic, complemented
78	#14582923	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
80	#14582866	C₂²	1	1	yes	characteristic
81	#14582866	C₂²	1	1	yes	characteristic
82	#14582866	C₂²	1	1	yes	characteristic
83	#14582866	C₂²	1	1	yes	characteristic
84	#14582866	C₂²	1	1	yes	characteristic, complemented
85	#14582866	C₂²	1	1	yes	characteristic, complemented
86	#14582866	C₂²	1	1	yes	characteristic, complemented
87	#14582866	C₂²	1	2	yes	complemented
88	#14582866	C₂²	1	2	yes	complemented
89	#14582866	C₂²	1	1	yes	characteristic, complemented
90	#14582866	C₂²	1	2	yes	complemented
91	#14582866	C₂²	1	2	yes	complemented
92	#14582866	C₂²	1	2	yes	complemented
93	#14582866	C₂²	1	2	yes	complemented
94	#14582866	C₂²	1	2	yes	complemented
95	#14582866	C₂²	1	2	yes	complemented
96	#14582863	C₂²	1	1	yes	characteristic, complemented
97	#14582863	C₂²	1	2	yes	complemented
98	#14582863	C₂²	1	2	yes	complemented
99	#14582863	C₂²	1	1	yes	characteristic, complemented
100	#14582863	C₂²	1	2	yes	complemented
101	#14582863	C₂²	1	2	yes	complemented
102	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
107	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
108	#14582855	C₂²	1	1	yes	characteristic, complemented
109	#14582855	C₂²	1	1	yes	characteristic, complemented
110	C₄×#10621877	C₂²	1	1	yes	characteristic, complemented
111	C₂×#13063236	C₂²	1	1	yes	characteristic, complemented
112	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
113	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
114	C₄₃×#550	C₄	1	1	yes	characteristic
115	D₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
116	C₄₃×#548	C₄	1	1	yes	characteristic
117	C₄₃×#548	C₄	1	1	yes	characteristic
118	C₄₃×#547	C₄	1	2	yes	—
119	C₄₃×#547	C₄	1	1	yes	characteristic
120	C₄₃×#546	C₄	1	2	yes	—
121	C₄₃×#546	C₄	1	2	yes	—
122	C₄₃×#546	C₄	1	1	yes	characteristic
123	C₄₃×#546	C₄	1	1	yes	characteristic
124	D₄²×C₄₃	C₄	1	1	yes	characteristic
125	D₄²×C₄₃	C₄	1	2	yes	—
126	C₄₃×#532	C₂²	1	1	yes	characteristic
127	C₄₃×#532	C₂²	1	2	yes	—
128	C₄₃×#525	C₂²	1	1	yes	characteristic
129	C₄₃×#525	C₂²	1	1	yes	characteristic
130	C₄₃×#525	C₂²	1	2	yes	—
131	C₄₃×#525	C₂²	1	2	yes	—
132	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
135	#13063332	—	4	2	no	—
136	#13063332	—	4	2	no	—
137	#13063332	—	4	2	no	—
138	#13063332	—	4	2	no	—
139	C₂×#10621877	—	4	2	no	—
140	C₂×#10621877	—	4	2	no	—
141	C₂×#10621877	—	4	2	no	—
142	C₂×#10621877	C₂³	1	1	yes	characteristic
143	C₂×#10621877	C₂³	1	1	yes	characteristic
144	C₂×#10621877	C₂³	1	1	yes	characteristic
145	C₂×#10621877	C₂³	1	1	yes	characteristic
146	C₂×#10621877	C₂³	1	1	yes	characteristic
147	C₂×#10621877	C₂³	1	1	yes	characteristic
148	C₂×#10621877	C₂³	1	2	yes	—
149	C₂×#10621877	C₂³	1	2	yes	—
150	C₂×#10621877	C₂³	1	2	yes	—
151	C₂×#10621877	C₂³	1	2	yes	—
152	C₂×#10621877	C₂³	1	2	yes	—
153	C₂×#10621877	C₂³	1	1	yes	characteristic
154	C₂×#10621877	C₂³	1	1	yes	characteristic
155	C₂×#10621877	C₂³	1	2	yes	—
156	C₂²×C₄₃⋊C₈	—	4	2	no	—
157	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
158	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
159	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
164	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
165	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
166	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
167	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
168	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
169	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
170	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
171	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
172	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
173	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
174	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
175	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
176	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
177	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
178	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
179	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
180	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
181	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
182	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
183	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
184	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
185	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
186	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
187	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
188	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
189	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
190	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
191	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
192	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
193	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
194	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
195	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
196	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
197	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
198	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
199	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
200	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
201	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
202	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
203	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
204	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
205	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
206	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
207	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
208	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
209	#13063236	C₂³	1	1	yes	characteristic
210	#13063236	C₂³	1	1	yes	characteristic
211	#13063236	C₂³	1	1	yes	characteristic
212	#13063236	C₂³	1	1	yes	characteristic
213	#13063236	C₂³	1	2	yes	—
214	#13063236	C₂³	1	2	yes	—
215	#13063236	C₂³	1	2	yes	—
216	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
217	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
218	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
219	C₂×#41×C₄₃	—	4	2	no	—
220	C₂×#41×C₄₃	—	4	2	no	—
221	C₂×#41×C₄₃	—	4	2	no	—
222	C₂×#41×C₄₃	—	4	2	no	—
223	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
224	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
225	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
226	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
227	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
228	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
229	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
230	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
231	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
232	C₂×#41×C₄₃	C₂³	1	2	yes	—
233	C₂×#41×C₄₃	C₂³	1	2	yes	—
234	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
235	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
236	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
237	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
238	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
239	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
240	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
241	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
242	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
243	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
244	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
245	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
246	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
247	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
248	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
249	#127×C₄₃	C₂×C₄	1	2	yes	—
250	#124×C₄₃	C₂×C₄	1	1	yes	characteristic
251	#124×C₄₃	C₂×C₄	1	1	yes	characteristic
252	#124×C₄₃	C₂×C₄	1	2	yes	—
253	#124×C₄₃	C₂×C₄	1	2	yes	—
254	#123×C₄₃	C₂×C₄	1	2	yes	—
255	#123×C₄₃	C₂×C₄	1	2	yes	—
256	#123×C₄₃	C₂×C₄	1	2	yes	—
257	#123×C₄₃	C₂×C₄	1	2	yes	—
258	#123×C₄₃	C₂×C₄	1	2	yes	—
259	#123×C₄₃	C₂×C₄	1	2	yes	—
260	C₂²⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
261	C₂²⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
262	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
263	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
264	C₂²⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
265	C₂²⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
266	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
267	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
268	#121×C₄₃	C₂×C₄	1	1	yes	characteristic
269	#121×C₄₃	C₂×C₄	1	1	yes	characteristic
270	#121×C₄₃	C₂×C₄	1	2	yes	—
271	#121×C₄₃	C₂×C₄	1	2	yes	—
272	#121×C₄₃	C₂×C₄	1	1	yes	characteristic
273	#121×C₄₃	C₂×C₄	1	1	yes	characteristic
274	#121×C₄₃	C₂×C₄	1	2	yes	—
275	#121×C₄₃	C₂×C₄	1	2	yes	—
276	#121×C₄₃	C₂×C₄	1	2	yes	—
277	#121×C₄₃	C₂×C₄	1	2	yes	—
278	#121×C₄₃	C₂×C₄	1	2	yes	—
279	#121×C₄₃	C₂×C₄	1	2	yes	—
280	#121×C₄₃	C₂×C₄	1	2	yes	—
281	#121×C₄₃	C₂×C₄	1	2	yes	—
282	#120×C₄₃	C₂×C₄	1	2	yes	—
283	#120×C₄₃	C₂×C₄	1	2	yes	—
284	#120×C₄₃	C₂×C₄	1	2	yes	—
285	#120×C₄₃	C₂×C₄	1	2	yes	—
286	#120×C₄₃	C₂×C₄	1	2	yes	—
287	#120×C₄₃	C₂×C₄	1	2	yes	—
288	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
289	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
291	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
292	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
293	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
294	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
295	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
296	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
297	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
298	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
299	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
300	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
301	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
302	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
303	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
304	C₄×D₄×C₄₃	C₂³	1	2	yes	—
305	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
306	C₄×D₄×C₄₃	C₂³	1	2	yes	—
307	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
308	C₄×D₄×C₄₃	C₂³	1	2	yes	—
309	C₄×D₄×C₄₃	C₂³	1	2	yes	—
310	C₄×D₄×C₄₃	C₂³	1	2	yes	—
311	C₄×D₄×C₄₃	C₂³	1	2	yes	—
312	#117×C₄₃	C₂³	1	1	yes	characteristic
313	#117×C₄₃	C₂³	1	2	yes	—
314	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
315	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
316	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
318	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
319	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
320	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
321	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
322	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
323	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
324	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
325	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
326	#41×C₄₃	—	2	2	no	—
327	#41×C₄₃	—	2	2	no	—
328	#41×C₄₃	—	2	2	no	—
329	#41×C₄₃	—	2	2	no	—
330	#41×C₄₃	—	2	2	no	—
331	#41×C₄₃	—	2	2	no	—
332	#41×C₄₃	—	4	2	no	—
333	#41×C₄₃	—	4	2	no	—
334	#41×C₄₃	—	4	2	no	—
335	#41×C₄₃	—	4	2	no	—
336	#41×C₄₃	—	4	4	no	—
337	#41×C₄₃	—	4	4	no	—
338	#41×C₄₃	—	4	2	no	—
339	#41×C₄₃	—	4	2	no	—
340	#41×C₄₃	—	4	2	no	—
341	#41×C₄₃	—	4	2	no	—
342	C₂×Q₈×C₄₃	—	4	2	no	—
343	C₂×Q₈×C₄₃	—	4	2	no	—
344	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
346	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
347	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
348	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
349	C₂×D₄×C₄₃	—	4	2	no	—
350	C₂×D₄×C₄₃	—	4	4	no	—
351	C₂×D₄×C₄₃	—	4	4	no	—
352	C₂×D₄×C₄₃	—	4	4	no	—
353	C₂×D₄×C₄₃	—	4	2	no	—
354	C₂×D₄×C₄₃	—	4	2	no	—
355	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
356	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
357	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
358	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
360	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
361	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
362	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
363	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
366	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
367	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
368	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
369	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
370	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
371	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
372	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
373	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
374	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
375	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
376	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
377	C₂²×C₄×C₄₃	—	2	2	no	—
378	C₂²×C₄×C₄₃	—	2	2	no	—
379	C₂²×C₄×C₄₃	—	2	2	no	—
380	C₂²×C₄×C₄₃	—	2	2	no	—
381	C₂²×C₄×C₄₃	—	4	2	no	—
382	C₂²×C₄×C₄₃	—	4	2	no	—
383	C₂²×C₄×C₄₃	—	4	2	no	—
384	C₂²×C₄×C₄₃	—	4	2	no	—
385	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
386	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
387	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
388	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
389	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
390	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
391	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
392	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
393	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
394	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
395	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
396	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
397	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
398	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
399	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
400	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
401	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
408	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
410	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
411	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
415	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
419	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
420	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
421	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
422	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
425	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
426	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
428	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
430	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
432	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
435	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
436	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
443	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
446	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
447	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
448	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
449	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
451	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₄₃	C₂⁴	1	2	yes	—
453	#10621877	—	2	2	no	—
454	#10621877	—	2	2	no	—
455	#10621877	—	2	2	no	—
456	#10621877	—	2	2	no	—
457	#10621877	—	4	1	no	—
458	#10621877	—	4	1	no	—
459	#10621877	—	4	1	no	—
460	#10621877	—	4	1	no	—
461	#10621877	—	4	2	no	—
462	#10621877	—	4	2	no	—
463	#10621877	—	4	2	no	—
464	#10621877	—	4	2	no	—
465	#10621877	—	4	2	no	—
466	#10621877	—	4	2	no	—
467	C₂×C₄₃⋊C₈	—	2	2	no	—
468	C₂×C₄₃⋊C₈	—	2	2	no	—
469	C₂×C₄₃⋊C₈	—	2	2	no	—
470	C₂×C₄₃⋊C₈	—	2	2	no	—
471	C₂×C₄₃⋊C₈	—	4	1	no	—
472	C₂×C₄₃⋊C₈	—	4	1	no	—
473	C₂×C₄₃⋊C₈	—	4	1	no	—
474	C₂×C₄₃⋊C₈	—	4	1	no	—
475	C₂×C₄₃⋊C₈	—	4	2	no	—
476	C₂×C₄₃⋊C₈	—	4	2	no	—
477	C₂×C₄₃⋊C₈	—	4	2	no	—
478	C₂×C₄₃⋊C₈	—	4	2	no	—
479	C₂×C₄₃⋊C₈	—	4	2	no	—
480	C₂×C₄₃⋊C₈	—	4	2	no	—
481	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
482	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
483	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
484	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
485	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
486	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
487	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
488	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
489	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
490	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
491	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
492	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
493	C₂³×C₄₃	—	2	2	no	—
494	C₂³×C₄₃	—	2	2	no	—
495	C₂³×C₄₃	—	2	2	no	—
496	C₂³×C₄₃	—	2	4	no	—
497	C₂³×C₄₃	—	4	1	no	—
498	C₂³×C₄₃	—	4	2	no	—
499	C₂³×C₄₃	—	4	2	no	—
500	C₂³×C₄₃	—	4	1	no	—
501	C₂³×C₄₃	—	4	2	no	—
502	C₂³×C₄₃	—	4	2	no	—
503	C₂³×C₄₃	—	4	1	no	—
504	C₂³×C₄₃	—	4	2	no	—
505	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
506	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
507	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
508	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
509	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
510	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
511	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
512	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
513	Q₈×C₄₃	—	2	2	no	—
514	Q₈×C₄₃	—	2	2	no	—
515	Q₈×C₄₃	—	2	2	no	—
516	Q₈×C₄₃	—	4	2	no	—
517	Q₈×C₄₃	—	4	2	no	—
518	D₄×C₄₃	—	2	4	no	—
519	D₄×C₄₃	—	2	4	no	—
520	D₄×C₄₃	—	2	4	no	—
521	D₄×C₄₃	—	2	2	no	—
522	D₄×C₄₃	—	2	2	no	—
523	D₄×C₄₃	—	2	4	no	—
524	D₄×C₄₃	—	2	2	no	—
525	D₄×C₄₃	—	2	2	no	—
526	D₄×C₄₃	—	2	2	no	—
527	D₄×C₄₃	—	4	1	no	—
528	D₄×C₄₃	—	4	2	no	—
529	D₄×C₄₃	—	4	1	no	—
530	D₄×C₄₃	—	4	2	no	—
531	D₄×C₄₃	—	4	2	no	—
532	D₄×C₄₃	—	4	2	no	—
533	D₄×C₄₃	—	4	2	no	—
534	D₄×C₄₃	—	4	2	no	—
535	D₄×C₄₃	—	4	2	no	—
536	D₄×C₄₃	—	4	2	no	—
537	D₄×C₄₃	—	4	2	no	—
538	D₄×C₄₃	—	4	2	no	—
539	D₄×C₄₃	—	4	2	no	—
540	C₂×C₄×C₄₃	—	2	2	no	—
541	C₂×C₄×C₄₃	—	2	2	no	—
542	C₂×C₄×C₄₃	—	2	2	no	—
543	C₂×C₄×C₄₃	—	2	2	no	—
544	C₂×C₄×C₄₃	—	2	2	no	—
545	C₂×C₄×C₄₃	—	2	2	no	—
546	C₂×C₄×C₄₃	—	2	1	no	—
547	C₂×C₄×C₄₃	—	2	1	no	—
548	C₂×C₄×C₄₃	—	2	1	no	—
549	C₂×C₄×C₄₃	—	2	1	no	—
550	C₂×C₄×C₄₃	—	2	2	no	—
551	C₂×C₄×C₄₃	—	2	2	no	—
552	C₂×C₄×C₄₃	—	2	2	no	—
553	C₂×C₄×C₄₃	—	2	2	no	—
554	C₂×C₄×C₄₃	—	2	1	no	—
555	C₂×C₄×C₄₃	—	2	1	no	—
556	C₂×C₄×C₄₃	—	2	1	no	—
557	C₂×C₄×C₄₃	—	2	1	no	—
558	C₂×C₄×C₄₃	—	2	2	no	—
559	C₂×C₄×C₄₃	—	2	2	no	—
560	C₂×C₄×C₄₃	—	4	2	no	—
561	C₂×C₄×C₄₃	—	4	2	no	—
562	C₂×C₄×C₄₃	—	4	2	no	—
563	C₂×C₄×C₄₃	—	4	2	no	—
564	C₂×C₄×C₄₃	—	4	2	no	—
565	C₂×C₄×C₄₃	—	4	2	no	—
566	C₂×C₄×C₄₃	—	4	1	no	—
567	C₂×C₄×C₄₃	—	4	2	no	—
568	C₂×C₄×C₄₃	—	4	1	no	—
569	C₂×C₄×C₄₃	—	4	2	no	—
570	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
571	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
572	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
575	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
577	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
578	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
584	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
587	C₄₃⋊C₈	—	2	1	no	—
588	C₄₃⋊C₈	—	2	1	no	—
589	C₄₃⋊C₈	—	2	1	no	—
590	C₄₃⋊C₈	—	2	1	no	—
591	C₄₃⋊C₈	—	2	1	no	—
592	C₄₃⋊C₈	—	2	1	no	—
593	C₄₃⋊C₈	—	2	1	no	—
594	C₄₃⋊C₈	—	2	1	no	—
595	C₄₃⋊C₈	—	2	2	no	—
596	C₄₃⋊C₈	—	2	2	no	—
597	C₄₃⋊C₈	—	2	2	no	—
598	C₄₃⋊C₈	—	2	2	no	—
599	#60240	—	43	1	no	maximal, Sylow
600	C₂²×C₄₃	—	2	1	no	—
601	C₂²×C₄₃	—	2	1	no	—
602	C₂²×C₄₃	—	2	1	no	—
603	C₂²×C₄₃	—	2	1	no	—
604	C₂²×C₄₃	—	2	1	no	—
605	C₂²×C₄₃	—	2	1	no	—
606	C₂²×C₄₃	—	2	1	no	—
607	C₂²×C₄₃	—	2	2	no	—
608	C₂²×C₄₃	—	2	2	no	—
609	C₂²×C₄₃	—	2	2	no	—
610	C₂²×C₄₃	—	2	2	no	—
611	C₂²×C₄₃	—	2	1	no	—
612	C₂²×C₄₃	—	2	2	no	—
613	C₂²×C₄₃	—	2	1	no	—
614	C₂²×C₄₃	—	2	1	no	—
615	C₂²×C₄₃	—	2	2	no	—
616	C₂²×C₄₃	—	2	1	no	—
617	C₂²×C₄₃	—	2	2	no	—
618	C₂²×C₄₃	—	2	1	no	—
619	C₂²×C₄₃	—	2	1	no	—
620	C₂²×C₄₃	—	2	2	no	—
621	C₂²×C₄₃	—	2	2	no	—
622	C₂²×C₄₃	—	4	4	no	—
623	C₂²×C₄₃	—	8	4	no	—
624	C₂²×C₄₃	—	8	2	no	—
625	C₂²×C₄₃	—	8	4	no	—
626	C₂²×C₄₃	#518	1	2	yes	—
627	C₂²×C₄₃	#568	1	2	yes	—
628	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
629	C₄×C₄₃	—	2	1	no	—
630	C₄×C₄₃	—	2	1	no	—
631	C₄×C₄₃	—	2	1	no	—
632	C₄×C₄₃	—	2	1	no	—
633	C₄×C₄₃	—	2	2	no	—
634	C₄×C₄₃	—	2	2	no	—
635	C₄×C₄₃	—	2	2	no	—
636	C₄×C₄₃	—	2	1	no	—
637	C₄×C₄₃	—	2	1	no	—
638	C₄×C₄₃	—	2	2	no	—
639	C₄×C₄₃	—	2	1	no	—
640	C₄×C₄₃	—	2	1	no	—
641	C₄×C₄₃	—	2	2	no	—
642	C₄×C₄₃	#518	1	2	yes	—
643	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
644	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
645	D₄×#41	D₄₃	1	1	yes	characteristic
646	#2981	—	43	2	no	—
647	#2980	—	43	2	no	—
648	#2978	—	43	2	no	—
649	#2977	—	43	2	no	—
650	#2976	—	43	2	no	—
651	#2976	—	43	2	no	—
652	#2974	—	43	2	no	—
653	#2973	—	43	2	no	—
654	#2935	—	43	1	no	—
655	D₄×M₁₆	—	43	1	no	—
656	#2933	—	43	1	no	—
657	#2933	—	43	1	no	—
658	#2932	—	43	1	no	—
659	#2930	—	43	1	no	—
660	#2929	—	43	1	no	—
661	C₂×#435	—	43	1	no	—
662	#2925	—	43	1	no	—
663	#2923	—	43	1	no	—
664	#2880	—	43	1	no	—
665	#2880	—	43	1	no	—
666	#2879	—	43	1	no	—
667	C₂×#408	—	43	1	no	—
668	C₂×C₄₃	—	2	2	no	—
669	C₂×C₄₃	—	2	2	no	—
670	C₂×C₄₃	—	4	1	no	—
671	C₂×C₄₃	—	4	1	no	—
672	C₂×C₄₃	—	4	2	no	—
673	C₂×C₄₃	—	4	2	no	—
674	C₂×C₄₃	—	4	2	no	—
675	C₂×C₄₃	—	4	1	no	—
676	C₂×C₄₃	C₂×#518	1	1	yes	characteristic
677	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
678	C₂×C₄₃	#3573	1	1	yes	characteristic
679	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
680	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
681	C₂×#131	—	43	1	no	—
682	C₂×#131	—	43	1	no	—
683	C₂×#131	—	43	1	no	—
684	C₂×#131	—	43	1	no	—
685	C₂²×M₁₆	—	43	1	no	—
686	C₂²×M₁₆	—	43	1	no	—
687	C₂²×M₁₆	—	43	1	no	—
688	C₂³×C₈	—	43	1	no	—
689	#550	Dic₄₃	1	1	yes	characteristic
690	D₄×Q₈	Dic₄₃	1	1	yes	characteristic
691	#548	Dic₄₃	1	1	yes	characteristic
692	#548	Dic₄₃	1	1	yes	characteristic
693	#547	Dic₄₃	1	2	yes	—
694	#547	Dic₄₃	1	1	yes	characteristic
695	#546	Dic₄₃	1	2	yes	—
696	#546	Dic₄₃	1	2	yes	—
697	#546	Dic₄₃	1	1	yes	characteristic
698	#546	Dic₄₃	1	1	yes	characteristic
699	D₄²	Dic₄₃	1	1	yes	characteristic
700	D₄²	Dic₄₃	1	2	yes	—
701	#532	C₂×D₄₃	1	1	yes	characteristic
702	#532	C₂×D₄₃	1	2	yes	—
703	#525	C₂×D₄₃	1	1	yes	characteristic
704	#525	C₂×D₄₃	1	1	yes	characteristic
705	#525	C₂×D₄₃	1	2	yes	—
706	#525	C₂×D₄₃	1	2	yes	—
707	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
708	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
709	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
710	#436	—	43	2	no	—
711	#436	—	43	2	no	—
712	#436	—	43	2	no	—
713	#436	—	43	2	no	—
714	#436	—	43	2	no	—
715	#436	—	43	2	no	—
716	#435	—	43	1	no	—
717	#435	—	43	1	no	—
718	#435	—	43	1	no	—
719	#435	—	43	1	no	—
720	#435	—	43	1	no	—
721	#435	—	43	1	no	—
722	#435	—	43	1	no	—
723	#435	—	43	1	no	—
724	#435	—	43	2	no	—
725	#435	—	43	2	no	—
726	#435	—	43	2	no	—
727	#435	—	43	2	no	—
728	#435	—	43	2	no	—
729	#435	—	43	2	no	—
730	#435	—	43	2	no	—
731	#435	—	43	2	no	—
732	#435	—	43	2	no	—
733	#435	—	43	2	no	—
734	#435	—	43	2	no	—
735	#435	—	43	2	no	—
736	#435	—	43	2	no	—
737	#435	—	43	2	no	—
738	#435	—	43	2	no	—
739	#435	—	43	2	no	—
740	C₈×D₄	—	43	2	no	—
741	C₈×D₄	—	43	2	no	—
742	C₈×D₄	—	43	2	no	—
743	C₈×D₄	—	43	2	no	—
744	C₈×D₄	—	43	2	no	—
745	C₈×D₄	—	43	2	no	—
746	#433	—	43	2	no	—
747	#433	—	43	2	no	—
748	#433	—	43	2	no	—
749	#433	—	43	2	no	—
750	#432	—	43	2	no	—
751	#432	—	43	2	no	—
752	#432	—	43	2	no	—
753	#431	—	43	2	no	—
754	#424	—	43	1	no	—
755	#424	—	43	1	no	—
756	#423	—	43	1	no	—
757	C₂×C₄⋊C₈	—	43	1	no	—
758	#408	—	43	1	no	—
759	#408	—	43	1	no	—
760	#408	—	43	1	no	—
761	#408	—	43	1	no	—
762	#408	—	43	2	no	—
763	#408	—	43	2	no	—
764	#408	—	43	1	no	—
765	#408	—	43	1	no	—
766	#408	—	43	1	no	—
767	#408	—	43	2	no	—
768	#408	—	43	2	no	—
769	#408	—	43	1	no	—
770	#408	—	43	2	no	—
771	#408	—	43	2	no	—
772	#408	—	43	2	no	—
773	#408	—	43	2	no	—
774	#407	—	43	2	no	—
775	#407	—	43	2	no	—
776	#407	—	43	1	no	—
777	#407	—	43	1	no	—
778	#407	—	43	2	no	—
779	#407	—	43	2	no	—
780	C₂×C₂²⋊C₈	—	43	2	no	—
781	C₂×C₂²⋊C₈	—	43	2	no	—
782	C₂×C₂²⋊C₈	—	43	1	no	—
783	C₂×C₂²⋊C₈	—	43	1	no	—
784	C₂×C₂²⋊C₈	—	43	2	no	—
785	C₂×C₂²⋊C₈	—	43	2	no	—
786	#405	—	43	1	no	—
787	#405	—	43	1	no	—
788	C₄×M₁₆	—	43	1	no	—
789	C₂×#97	—	43	1	no	—
790	C₄₃	#60240	1	1	yes	characteristic, complemented, Sylow
791	C₂×#41	—	4	2	no	—
792	C₂×#41	—	4	2	no	—
793	C₂×#41	—	4	2	no	—
794	C₂×#41	—	4	2	no	—
795	C₂×#41	C₂×Dic₄₃	1	2	yes	—
796	C₂×#41	C₂×Dic₄₃	1	2	yes	—
797	C₂×#41	C₂×Dic₄₃	1	1	yes	characteristic
798	C₂×#41	C₂×Dic₄₃	1	1	yes	characteristic
799	C₂×#41	C₂×Dic₄₃	1	1	yes	characteristic
800	C₂×#41	C₂×Dic₄₃	1	1	yes	characteristic
801	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
802	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
803	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
804	C₂×#41	C₂²×D₄₃	1	2	yes	—
805	C₂×#41	C₂²×D₄₃	1	2	yes	—
806	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
807	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
808	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
809	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
810	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
811	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
812	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
813	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
814	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
815	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
816	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
817	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
818	#131	—	172	2	no	—
819	#131	—	172	2	no	—
820	#131	—	172	2	no	—
821	#131	—	172	2	no	—
822	C₂×M₁₆	—	43	1	no	—
823	C₂×M₁₆	—	43	1	no	—
824	C₂×M₁₆	—	43	1	no	—
825	C₂×M₁₆	—	43	1	no	—
826	C₂×M₁₆	—	43	1	no	—
827	C₂×M₁₆	—	43	1	no	—
828	C₂×M₁₆	—	43	2	no	—
829	C₂×M₁₆	—	43	1	no	—
830	C₂×M₁₆	—	43	1	no	—
831	C₂×M₁₆	—	43	2	no	—
832	C₂×M₁₆	—	43	2	no	—
833	C₂×M₁₆	—	43	2	no	—
834	C₂×M₁₆	—	43	2	no	—
835	C₂×M₁₆	—	43	2	no	—
836	C₂×M₁₆	—	172	2	no	—
837	C₂×M₁₆	—	172	2	no	—
838	C₂×M₁₆	—	172	2	no	—
839	C₂²×C₈	—	43	1	no	—
840	C₂²×C₈	—	43	1	no	—
841	C₂²×C₈	—	43	1	no	—
842	C₂²×C₈	—	43	1	no	—
843	C₂²×C₈	—	43	1	no	—
844	C₂²×C₈	—	43	1	no	—
845	C₂²×C₈	—	43	1	no	—
846	C₂²×C₈	—	43	1	no	—
847	C₂²×C₈	—	43	2	no	—
848	C₂²×C₈	—	43	2	no	—
849	C₂²×C₈	—	43	2	no	—
850	C₂²×C₈	—	43	2	no	—
851	C₂²×C₈	—	43	2	no	—
852	C₂²×C₈	—	43	2	no	—
853	C₂²×C₈	—	172	2	no	—
854	C₄⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
855	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
856	#127	C₂×Dic₄₃	1	1	yes	characteristic
857	#127	C₂×Dic₄₃	1	2	yes	—
858	#124	C₂×Dic₄₃	1	1	yes	characteristic
859	#124	C₂×Dic₄₃	1	1	yes	characteristic
860	#124	C₂×Dic₄₃	1	2	yes	—
861	#124	C₂×Dic₄₃	1	2	yes	—
862	#123	C₂×Dic₄₃	1	2	yes	—
863	#123	C₂×Dic₄₃	1	2	yes	—
864	#123	C₂×Dic₄₃	1	2	yes	—
865	#123	C₂×Dic₄₃	1	2	yes	—
866	#123	C₂×Dic₄₃	1	2	yes	—
867	#123	C₂×Dic₄₃	1	2	yes	—
868	C₂²⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
869	C₂²⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
870	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
871	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
872	C₂²⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
874	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
875	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
876	#121	C₂×Dic₄₃	1	1	yes	characteristic
877	#121	C₂×Dic₄₃	1	1	yes	characteristic
878	#121	C₂×Dic₄₃	1	2	yes	—
879	#121	C₂×Dic₄₃	1	2	yes	—
880	#121	C₂×Dic₄₃	1	1	yes	characteristic
881	#121	C₂×Dic₄₃	1	1	yes	characteristic
882	#121	C₂×Dic₄₃	1	2	yes	—
883	#121	C₂×Dic₄₃	1	2	yes	—
884	#121	C₂×Dic₄₃	1	2	yes	—
885	#121	C₂×Dic₄₃	1	2	yes	—
886	#121	C₂×Dic₄₃	1	2	yes	—
887	#121	C₂×Dic₄₃	1	2	yes	—
888	#121	C₂×Dic₄₃	1	2	yes	—
889	#121	C₂×Dic₄₃	1	2	yes	—
890	#120	C₂×Dic₄₃	1	2	yes	—
891	#120	C₂×Dic₄₃	1	2	yes	—
892	#120	C₂×Dic₄₃	1	2	yes	—
893	#120	C₂×Dic₄₃	1	2	yes	—
894	#120	C₂×Dic₄₃	1	2	yes	—
895	#120	C₂×Dic₄₃	1	2	yes	—
896	C₄×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
897	C₄×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
898	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
899	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
900	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
901	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
902	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
903	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
904	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
905	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
906	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
907	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
908	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
909	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
910	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
911	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
912	C₄×D₄	C₂²×D₄₃	1	2	yes	—
913	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
914	C₄×D₄	C₂²×D₄₃	1	2	yes	—
915	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
916	C₄×D₄	C₂²×D₄₃	1	2	yes	—
917	C₄×D₄	C₂²×D₄₃	1	2	yes	—
918	C₄×D₄	C₂²×D₄₃	1	2	yes	—
919	C₄×D₄	C₂²×D₄₃	1	2	yes	—
920	#117	C₂²×D₄₃	1	1	yes	characteristic
921	#117	C₂²×D₄₃	1	2	yes	—
922	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
924	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
928	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
929	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
930	C₄⋊C₈	—	43	1	no	—
931	C₄⋊C₈	—	43	1	no	—
932	C₄⋊C₈	—	43	1	no	—
933	C₄⋊C₈	—	43	1	no	—
934	C₄⋊C₈	—	43	2	no	—
935	C₄⋊C₈	—	43	2	no	—
936	C₄⋊C₈	—	43	2	no	—
937	C₄⋊C₈	—	43	2	no	—
938	C₄⋊C₈	—	43	2	no	—
939	C₄⋊C₈	—	43	2	no	—
940	C₂²⋊C₈	—	43	1	no	—
941	C₂²⋊C₈	—	43	1	no	—
942	C₂²⋊C₈	—	43	2	no	—
943	C₂²⋊C₈	—	43	1	no	—
944	C₂²⋊C₈	—	43	2	no	—
945	C₂²⋊C₈	—	43	1	no	—
946	C₂²⋊C₈	—	43	2	no	—
947	C₂²⋊C₈	—	43	2	no	—
948	C₂²⋊C₈	—	43	2	no	—
949	C₂²⋊C₈	—	43	2	no	—
950	C₂²⋊C₈	—	43	2	no	—
951	C₂²⋊C₈	—	43	2	no	—
952	C₂²⋊C₈	—	43	2	no	—
953	C₂²⋊C₈	—	43	1	no	—
954	C₂²⋊C₈	—	43	2	no	—
955	C₂²⋊C₈	—	43	1	no	—
956	C₂²⋊C₈	—	43	1	no	—
957	C₂²⋊C₈	—	43	2	no	—
958	C₂²⋊C₈	—	43	2	no	—
959	C₂²⋊C₈	—	43	2	no	—
960	C₂²⋊C₈	—	43	1	no	—
961	C₂²⋊C₈	—	43	2	no	—
962	C₂²⋊C₈	—	43	2	no	—
963	C₂²⋊C₈	—	43	2	no	—
964	C₂²⋊C₈	—	43	2	no	—
965	C₂²⋊C₈	—	43	2	no	—
966	C₂²⋊C₈	—	43	2	no	—
967	C₂²⋊C₈	—	43	2	no	—
968	#97	—	43	1	no	—
969	#97	—	43	1	no	—
970	#97	—	43	1	no	—
971	#97	—	43	1	no	—
972	#97	—	43	2	no	—
973	#97	—	43	2	no	—
974	#97	—	43	2	no	—
975	C₄×C₈	—	43	2	no	—
976	C₄×C₈	—	43	2	no	—
977	C₄×C₈	—	43	2	no	—
978	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
979	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
980	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
981	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	2	2	no	—
986	#41	—	2	2	no	—
987	#41	—	2	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	2	no	—
990	#41	—	4	2	no	—
991	#41	—	4	2	no	—
992	#41	—	4	4	no	—
993	#41	—	4	4	no	—
994	#41	—	4	2	no	—
995	#41	—	4	2	no	—
996	#41	—	4	2	no	—
997	#41	—	4	2	no	—
998	C₂×Q₈	—	4	2	no	—
999	C₂×Q₈	—	4	2	no	—
1000	C₂×Q₈	C₂²×Dic₄₃	1	1	yes	characteristic
1001	C₂×Q₈	C₂²×Dic₄₃	1	1	yes	characteristic
1002	C₂×Q₈	C₂²×Dic₄₃	1	1	yes	characteristic
1003	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
1004	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
1005	C₂×D₄	—	4	2	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	4	4	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	4	no	—
1011	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
1012	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
1013	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1014	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1015	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
1016	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1017	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1018	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
1019	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
1020	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
1021	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1022	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
1023	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1024	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1025	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1026	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1027	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1028	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1029	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1030	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1031	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1032	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	—	4	2	no	—
1041	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1048	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1049	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1050	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1051	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1052	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1053	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1054	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1055	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1056	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
1057	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
1058	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
1062	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
1063	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1065	M₁₆	—	86	2	no	—
1066	M₁₆	—	86	2	no	—
1067	M₁₆	—	86	2	no	—
1068	M₁₆	—	86	2	no	—
1069	M₁₆	—	172	1	no	—
1070	M₁₆	—	172	1	no	—
1071	M₁₆	—	172	1	no	—
1072	M₁₆	—	172	1	no	—
1073	M₁₆	—	172	2	no	—
1074	M₁₆	—	172	2	no	—
1075	M₁₆	—	172	2	no	—
1076	M₁₆	—	172	2	no	—
1077	M₁₆	—	172	2	no	—
1078	M₁₆	—	172	2	no	—
1079	C₂×C₈	—	43	1	no	—
1080	C₂×C₈	—	43	1	no	—
1081	C₂×C₈	—	43	2	no	—
1082	C₂×C₈	—	43	2	no	—
1083	C₂×C₈	—	43	2	no	—
1084	C₂×C₈	—	43	2	no	—
1085	C₂×C₈	—	43	1	no	—
1086	C₂×C₈	—	43	1	no	—
1087	C₂×C₈	—	43	1	no	—
1088	C₂×C₈	—	43	1	no	—
1089	C₂×C₈	—	43	1	no	—
1090	C₂×C₈	—	43	1	no	—
1091	C₂×C₈	—	86	2	no	—
1092	C₂×C₈	—	86	2	no	—
1093	C₂×C₈	—	86	2	no	—
1094	C₂×C₈	—	86	2	no	—
1095	C₂×C₈	—	172	1	no	—
1096	C₂×C₈	—	172	1	no	—
1097	C₂×C₈	—	172	1	no	—
1098	C₂×C₈	—	172	1	no	—
1099	C₂×C₈	—	172	2	no	—
1100	C₂×C₈	—	172	2	no	—
1101	C₂×C₈	—	172	2	no	—
1102	C₂×C₈	—	172	2	no	—
1103	C₂×C₈	—	172	2	no	—
1104	C₂×C₈	—	172	2	no	—
1105	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1106	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1107	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1108	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1109	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1110	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1111	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1112	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1113	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1114	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1116	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1117	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1118	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1119	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1123	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1125	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1127	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1128	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1129	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1132	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1133	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1134	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1135	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1136	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1137	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1138	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1139	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1140	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1141	C₂²⋊C₄	C₂²×Dic₄₃	1	2	yes	—
1142	C₄²	C₂²×Dic₄₃	1	2	yes	—
1143	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
1144	C₄²	C₂²×Dic₄₃	1	2	yes	—
1145	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
1146	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1147	C₄²	C₂³×D₄₃	1	2	yes	—
1148	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	4	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	2	no	—
1155	C₂³	—	4	2	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	1	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
1162	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
1163	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
1164	C₂³	C₂³×Dic₄₃	1	2	yes	—
1165	C₂³	C₂³×Dic₄₃	1	2	yes	—
1166	C₂³	C₂³×Dic₄₃	1	2	yes	—
1167	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
1168	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	2	no	—
1171	Q₈	—	2	2	no	—
1172	Q₈	—	4	2	no	—
1173	Q₈	—	4	2	no	—
1174	D₄	—	2	4	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	2	4	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	4	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	2	no	—
1182	D₄	—	2	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	1	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	1	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1227	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1228	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
1229	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
1230	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1231	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
1232	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1233	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1234	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1235	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1236	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1237	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
1238	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
1239	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
1240	C₂×C₄	#13063370	1	2	yes	—
1241	C₂×C₄	#13063370	1	2	yes	—
1242	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1243	C₈	—	86	1	no	—
1244	C₈	—	86	1	no	—
1245	C₈	—	86	1	no	—
1246	C₈	—	86	1	no	—
1247	C₈	—	86	1	no	—
1248	C₈	—	86	1	no	—
1249	C₈	—	86	1	no	—
1250	C₈	—	86	1	no	—
1251	C₈	—	86	2	no	—
1252	C₈	—	86	2	no	—
1253	C₈	—	86	2	no	—
1254	C₈	—	86	2	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	2	no	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	2	no	—
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	4	4	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	—	8	2	no	—
1280	C₂²	—	8	4	no	—
1281	C₂²	#14583374	1	2	yes	—
1282	C₂²	#14583666	1	2	yes	—
1283	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	2	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	1	no	—
1295	C₄	—	2	1	no	—
1296	C₄	—	2	2	no	—
1297	C₄	#14583374	1	2	yes	—
1298	C₄	C₂×#13063370	1	1	yes	characteristic
1299	C₄	C₂×#13063370	1	1	yes	characteristic
1300	C₂	—	2	2	no	—
1301	C₂	—	2	2	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	4	1	no	—
1306	C₂	—	4	2	no	—
1307	C₂	—	4	2	no	—
1308	C₂	C₂×#14583374	1	1	yes	characteristic
1309	C₂	C₂×#14583666	1	1	yes	characteristic
1310	C₂	#19149307	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting, prime radical	D₄×#41×C₄₃	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	D₄×#41	D₄₃
hypocenter	C₄₃	#60240
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. #19143671	C₂	semidirect
2. #19143666	C₂	semidirect
3. #19143657	C₂	semidirect
4. #19143651	C₂	semidirect
5. #19143643	C₂	semidirect
6. #19143643	C₂	semidirect
7. #19143630	C₂	semidirect
8. #19143624	C₂	semidirect
9. #19143339	C₂	semidirect
10. D₄×#10621877	C₂	semidirect
11. #19143322	C₂	semidirect
12. #19143322	C₂	semidirect
13. #19143313	C₂	semidirect
14. #19143299	C₂	semidirect
15. #19143290	C₂	semidirect
16. C₂×#14582971	C₂	semidirect
17. #19143261	C₂	semidirect
18. #19143246	C₂	semidirect
19. #19143044	C₂	semidirect
20. #19143044	C₂	semidirect
21. #19143040	C₂	semidirect
22. C₂×#14582866	C₂	semidirect
24. C₂×#13063332	C₂²	semidirect
25. C₂×#13063332	C₂²	semidirect
26. C₂×#13063332	C₂²	semidirect
27. C₂×#13063332	C₂²	semidirect
28. C₂²×#10621877	C₂²	semidirect
29. C₂²×#10621877	C₂²	semidirect
30. C₂²×#10621877	C₂²	semidirect
31. C₂³×C₄₃⋊C₈	C₂²	semidirect
32. #14582977	C₂²	semidirect
33. #14582977	C₂²	semidirect
34. #14582977	C₂²	semidirect
35. #14582977	C₂²	semidirect
36. #14582977	C₂²	semidirect
37. #14582977	C₂²	semidirect
41. #14582971	C₂²	semidirect
42. #14582971	C₂²	semidirect
43. #14582971	C₂²	semidirect
44. #14582971	C₂²	semidirect
45. #14582971	C₂²	semidirect
46. #14582971	C₂²	semidirect
47. #14582971	C₂²	semidirect
48. #14582971	C₂²	semidirect
49. #14582971	C₂²	semidirect
50. #14582971	C₂²	semidirect
51. #14582971	C₂²	semidirect
52. #14582971	C₂²	semidirect
53. #14582971	C₂²	semidirect
54. #14582971	C₂²	semidirect
55. #14582971	C₂²	semidirect
56. #14582971	C₂²	semidirect
57. #14582971	C₂²	semidirect
58. #14582971	C₂²	semidirect
59. #14582971	C₂²	semidirect
60. #14582971	C₂²	semidirect
61. #14582971	C₂²	semidirect
62. D₄×C₄₃⋊C₈	C₂²	semidirect
63. D₄×C₄₃⋊C₈	C₂²	semidirect
64. D₄×C₄₃⋊C₈	C₂²	semidirect
65. D₄×C₄₃⋊C₈	C₂²	semidirect
66. D₄×C₄₃⋊C₈	C₂²	semidirect
67. D₄×C₄₃⋊C₈	C₂²	semidirect
68. #14582960	C₂²	semidirect
69. #14582960	C₂²	semidirect
70. #14582960	C₂²	semidirect
71. #14582960	C₂²	semidirect
72. #14582956	C₂²	semidirect
73. #14582956	C₂²	semidirect
74. #14582956	C₂²	semidirect
75. #14582952	C₂²	semidirect
76. #14582926	C₂²	semidirect
77. #14582926	C₂²	semidirect
78. #14582923	C₂²	semidirect
79. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
84. #14582866	C₂²	semidirect
85. #14582866	C₂²	semidirect
86. #14582866	C₂²	semidirect
87. #14582866	C₂²	semidirect
88. #14582866	C₂²	semidirect
89. #14582866	C₂²	semidirect
90. #14582866	C₂²	semidirect
91. #14582866	C₂²	semidirect
92. #14582866	C₂²	semidirect
93. #14582866	C₂²	semidirect
94. #14582866	C₂²	semidirect
95. #14582866	C₂²	semidirect
96. #14582863	C₂²	semidirect
97. #14582863	C₂²	semidirect
98. #14582863	C₂²	semidirect
99. #14582863	C₂²	semidirect
100. #14582863	C₂²	semidirect
101. #14582863	C₂²	semidirect
102. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
103. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
104. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
105. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
106. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
107. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
108. #14582855	C₂²	semidirect
109. #14582855	C₂²	semidirect
110. C₄×#10621877	C₂²	semidirect
111. C₂×#13063236	C₂²	semidirect
790. C₄₃	#60240	semidirect

Maximal subgroups

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

subgroup	index
#19143671	2
#19143666	2
#19143657	2
#19143651	2
#19143643	2
#19143630	2
#19143624	2
#19143339	2
D₄×#10621877	2
#19143322	2
#19143313	2
#19143299	2
#19143290	2
C₂×#14582971	2
#19143261	2
#19143246	2
#19143044	2
#19143040	2
C₂×#14582866	2
D₄×#41×C₄₃	2
#60240	43