Subgroups — #25112661

Order 11008.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582971	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135536	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135532	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134893	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134888	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134888	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134888	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134666	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134663	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134579	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134361	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134292	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14582654	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10621877	C₂²	1	1	yes	characteristic
17	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	#14582971	—	2	4	no	—
21	D₄×C₄₃⋊C₈	—	2	4	no	—
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×#13063236	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
34	#14582654	C₂²	1	1	yes	characteristic
35	#14582654	C₂²	1	1	yes	characteristic
36	#14582654	C₂²	1	1	yes	characteristic
37	#14582654	C₂²	1	1	yes	characteristic
38	#14582654	C₂²	1	1	yes	characteristic
39	#14582654	C₂²	1	1	yes	characteristic
40	#14582654	C₂²	1	1	yes	characteristic
41	#14582654	C₂²	1	1	yes	characteristic
42	#14582654	C₂²	1	1	yes	characteristic
43	#14582654	C₂²	1	1	yes	characteristic
44	#14582654	C₂²	1	1	yes	characteristic
45	#14582654	C₂²	1	1	yes	characteristic
46	C₄₃×#529	—	2	4	no	—
47	C₄₃×#529	—	2	4	no	—
48	C₂×#126×C₄₃	C₄	1	1	yes	characteristic
49	C₂×#126×C₄₃	C₄	1	1	yes	characteristic
50	C₂×#125×C₄₃	C₄	1	1	yes	characteristic
51	C₂×#124×C₄₃	C₄	1	1	yes	characteristic
52	C₂×#123×C₄₃	C₄	1	1	yes	characteristic
53	C₂×#123×C₄₃	C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
55	C₂×#121×C₄₃	C₄	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
60	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
61	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
62	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
63	C₂×#10621877	—	2	2	no	—
64	C₂×#10621877	—	2	2	no	—
65	C₂×#10621877	—	4	1	no	—
66	C₂²×C₄₃⋊C₈	—	2	2	no	—
67	C₂²×C₄₃⋊C₈	—	2	2	no	—
68	C₂²×C₄₃⋊C₈	—	2	2	no	—
69	C₂²×C₄₃⋊C₈	—	2	2	no	—
70	C₂²×C₄₃⋊C₈	—	2	2	no	—
71	C₂²×C₄₃⋊C₈	—	2	2	no	—
72	C₂²×C₄₃⋊C₈	—	4	1	no	—
73	C₂²×C₄₃⋊C₈	—	4	1	no	—
74	C₂²×C₄₃⋊C₈	—	4	1	no	—
75	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
84	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
85	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
86	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
87	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
88	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
89	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
90	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
91	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
92	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
93	#13063236	—	2	2	no	—
94	C₄×C₄₃⋊C₈	—	2	2	no	—
95	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
104	#126×C₄₃	—	2	4	no	—
105	#126×C₄₃	—	2	4	no	—
106	#125×C₄₃	—	2	4	no	—
107	#124×C₄₃	—	2	4	no	—
108	#123×C₄₃	—	2	4	no	—
109	#123×C₄₃	—	2	4	no	—
110	C₂²⋊Q₈×C₄₃	—	2	4	no	—
111	#121×C₄₃	—	2	4	no	—
112	C₄×Q₈×C₄₃	—	2	2	no	—
113	C₄×Q₈×C₄₃	—	2	2	no	—
114	C₄×D₄×C₄₃	—	2	2	no	—
115	C₄×D₄×C₄₃	—	2	2	no	—
116	C₄×D₄×C₄₃	—	2	2	no	—
117	C₄×D₄×C₄₃	—	2	2	no	—
118	C₄×D₄×C₄₃	D₄	1	4	yes	—
119	C₄×D₄×C₄₃	D₄	1	4	yes	—
120	#117×C₄₃	—	2	2	no	—
121	#117×C₄₃	—	2	2	no	—
122	#117×C₄₃	—	2	2	no	—
123	#117×C₄₃	—	2	2	no	—
124	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
144	C₂×C₄²×C₄₃	—	2	2	no	—
145	C₂×C₄²×C₄₃	—	2	2	no	—
146	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
147	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
148	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
152	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×Q₈×C₄₃	—	2	2	no	—
156	C₂×Q₈×C₄₃	—	2	2	no	—
157	C₂×Q₈×C₄₃	—	4	1	no	—
158	C₂×D₄×C₄₃	—	2	2	no	—
159	C₂×D₄×C₄₃	—	2	2	no	—
160	C₂×D₄×C₄₃	—	2	2	no	—
161	C₂×D₄×C₄₃	—	2	2	no	—
162	C₂×D₄×C₄₃	—	2	2	no	—
163	C₂×D₄×C₄₃	—	2	2	no	—
164	C₂×D₄×C₄₃	—	2	2	no	—
165	C₂×D₄×C₄₃	—	4	1	no	—
166	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
167	C₂²×C₄×C₄₃	—	2	1	no	—
168	C₂²×C₄×C₄₃	—	2	1	no	—
169	C₂²×C₄×C₄₃	—	2	1	no	—
170	C₂²×C₄×C₄₃	—	2	1	no	—
171	C₂²×C₄×C₄₃	—	2	1	no	—
172	C₂²×C₄×C₄₃	—	2	1	no	—
173	C₂²×C₄×C₄₃	—	2	1	no	—
174	C₂²×C₄×C₄₃	—	2	1	no	—
175	C₂²×C₄×C₄₃	—	2	2	no	—
176	C₂²×C₄×C₄₃	—	2	1	no	—
177	C₂²×C₄×C₄₃	—	2	1	no	—
178	C₂²×C₄×C₄₃	—	2	1	no	—
179	C₂²×C₄×C₄₃	—	2	1	no	—
180	C₂²×C₄×C₄₃	—	2	1	no	—
181	C₂²×C₄×C₄₃	—	2	1	no	—
182	C₂²×C₄×C₄₃	—	2	2	no	—
183	C₂²×C₄×C₄₃	—	2	2	no	—
184	C₂²×C₄×C₄₃	—	2	2	no	—
185	C₂²×C₄×C₄₃	—	2	2	no	—
186	C₂²×C₄×C₄₃	—	4	1	no	—
187	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
203	C₄⋊C₄×C₄₃	—	2	2	no	—
204	C₄⋊C₄×C₄₃	—	2	2	no	—
205	C₄⋊C₄×C₄₃	—	2	2	no	—
206	C₄⋊C₄×C₄₃	—	2	2	no	—
207	C₄⋊C₄×C₄₃	—	2	2	no	—
208	C₄⋊C₄×C₄₃	—	2	2	no	—
209	C₄⋊C₄×C₄₃	—	2	2	no	—
210	C₄⋊C₄×C₄₃	—	2	2	no	—
211	C₄⋊C₄×C₄₃	—	2	2	no	—
212	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
213	C₂²⋊C₄×C₄₃	—	2	2	no	—
214	C₂²⋊C₄×C₄₃	—	2	2	no	—
215	C₂²⋊C₄×C₄₃	—	2	2	no	—
216	C₂²⋊C₄×C₄₃	—	2	2	no	—
217	C₂²⋊C₄×C₄₃	—	2	2	no	—
218	C₂²⋊C₄×C₄₃	—	2	2	no	—
219	C₂²⋊C₄×C₄₃	—	2	2	no	—
220	C₂²⋊C₄×C₄₃	—	2	2	no	—
221	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
222	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
223	C₄²×C₄₃	—	2	2	no	—
224	C₄²×C₄₃	—	2	2	no	—
225	C₄²×C₄₃	—	2	1	no	—
226	C₄²×C₄₃	—	2	1	no	—
227	C₄²×C₄₃	—	2	1	no	—
228	C₄²×C₄₃	—	2	1	no	—
229	C₄²×C₄₃	—	2	1	no	—
230	C₄²×C₄₃	—	2	1	no	—
231	C₄²×C₄₃	C₂×D₄	1	2	yes	—
232	C₄²×C₄₃	C₂×D₄	1	2	yes	—
233	#10621877	—	4	4	no	—
234	C₂×C₄₃⋊C₈	—	2	1	no	—
235	C₂×C₄₃⋊C₈	—	2	1	no	—
236	C₂×C₄₃⋊C₈	—	2	1	no	—
237	C₂×C₄₃⋊C₈	—	2	1	no	—
238	C₂×C₄₃⋊C₈	—	2	1	no	—
239	C₂×C₄₃⋊C₈	—	2	1	no	—
240	C₂×C₄₃⋊C₈	—	2	1	no	—
241	C₂×C₄₃⋊C₈	—	2	1	no	—
242	C₂×C₄₃⋊C₈	—	2	1	no	—
243	C₂×C₄₃⋊C₈	—	2	1	no	—
244	C₂×C₄₃⋊C₈	—	2	1	no	—
245	C₂×C₄₃⋊C₈	—	2	1	no	—
246	C₂×C₄₃⋊C₈	—	2	1	no	—
247	C₂×C₄₃⋊C₈	—	2	1	no	—
248	C₂×C₄₃⋊C₈	—	2	1	no	—
249	C₂×C₄₃⋊C₈	—	2	1	no	—
250	C₂×C₄₃⋊C₈	—	2	1	no	—
251	C₂×C₄₃⋊C₈	—	2	1	no	—
252	C₂×C₄₃⋊C₈	—	2	1	no	—
253	C₂×C₄₃⋊C₈	—	2	1	no	—
254	C₂×C₄₃⋊C₈	—	2	1	no	—
255	C₂×C₄₃⋊C₈	—	2	1	no	—
256	C₂×C₄₃⋊C₈	—	4	4	no	—
257	C₂×C₄₃⋊C₈	—	4	4	no	—
258	C₂×C₄₃⋊C₈	—	4	4	no	—
259	C₂×C₄₃⋊C₈	#41	1	2	yes	—
260	C₂×C₄₃⋊C₈	#41	1	2	yes	—
261	C₂³×C₄₃	—	2	1	no	—
262	C₂³×C₄₃	—	2	1	no	—
263	C₂³×C₄₃	—	2	1	no	—
264	C₂³×C₄₃	—	2	1	no	—
265	C₂³×C₄₃	—	2	1	no	—
266	C₂³×C₄₃	—	2	1	no	—
267	C₂³×C₄₃	—	2	1	no	—
268	C₂³×C₄₃	—	2	1	no	—
269	C₂³×C₄₃	—	2	1	no	—
270	C₂³×C₄₃	—	2	1	no	—
271	C₂³×C₄₃	—	2	1	no	—
272	C₂³×C₄₃	—	2	1	no	—
273	C₂³×C₄₃	—	2	1	no	—
274	C₂³×C₄₃	—	2	1	no	—
275	C₂³×C₄₃	—	2	1	no	—
276	C₂³×C₄₃	—	2	1	no	—
277	C₂³×C₄₃	—	2	1	no	—
278	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂³×C₄₃	#131	1	2	yes	—
281	C₂³×C₄₃	#131	1	2	yes	—
282	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
283	Q₈×C₄₃	—	4	4	no	—
284	D₄×C₄₃	—	2	8	no	—
285	D₄×C₄₃	—	4	4	no	—
286	D₄×C₄₃	—	4	4	no	—
287	C₂×C₄×C₄₃	—	2	1	no	—
288	C₂×C₄×C₄₃	—	2	1	no	—
289	C₂×C₄×C₄₃	—	2	1	no	—
290	C₂×C₄×C₄₃	—	2	1	no	—
291	C₂×C₄×C₄₃	—	2	1	no	—
292	C₂×C₄×C₄₃	—	2	1	no	—
293	C₂×C₄×C₄₃	—	2	1	no	—
294	C₂×C₄×C₄₃	—	2	1	no	—
295	C₂×C₄×C₄₃	—	2	1	no	—
296	C₂×C₄×C₄₃	—	2	1	no	—
297	C₂×C₄×C₄₃	—	2	2	no	—
298	C₂×C₄×C₄₃	—	2	2	no	—
299	C₂×C₄×C₄₃	—	2	2	no	—
300	C₂×C₄×C₄₃	—	2	2	no	—
301	C₂×C₄×C₄₃	—	2	2	no	—
302	C₂×C₄×C₄₃	—	2	2	no	—
303	C₂×C₄×C₄₃	—	2	2	no	—
304	C₂×C₄×C₄₃	—	2	2	no	—
305	C₂×C₄×C₄₃	—	2	1	no	—
306	C₂×C₄×C₄₃	—	2	1	no	—
307	C₂×C₄×C₄₃	—	2	1	no	—
308	C₂×C₄×C₄₃	—	2	1	no	—
309	C₂×C₄×C₄₃	—	2	1	no	—
310	C₂×C₄×C₄₃	—	2	1	no	—
311	C₂×C₄×C₄₃	—	2	1	no	—
312	C₂×C₄×C₄₃	—	2	1	no	—
313	C₂×C₄×C₄₃	—	2	1	no	—
314	C₂×C₄×C₄₃	—	2	1	no	—
315	C₂×C₄×C₄₃	—	2	1	no	—
316	C₂×C₄×C₄₃	—	2	1	no	—
317	C₂×C₄×C₄₃	—	2	1	no	—
318	C₂×C₄×C₄₃	—	2	1	no	—
319	C₂×C₄×C₄₃	—	2	1	no	—
320	C₂×C₄×C₄₃	—	2	1	no	—
321	C₂×C₄×C₄₃	—	2	1	no	—
322	C₂×C₄×C₄₃	—	2	1	no	—
323	C₂×C₄×C₄₃	—	4	4	no	—
324	C₂×C₄×C₄₃	—	4	4	no	—
325	C₂×C₄×C₄₃	—	4	1	no	—
326	C₂×C₄×C₄₃	—	4	1	no	—
327	C₂×C₄×C₄₃	—	4	1	no	—
328	C₂×C₄×C₄₃	—	4	1	no	—
329	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
332	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
333	C₂×C₄×C₄₃	#131	1	2	yes	—
334	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
340	C₄₃⋊C₈	—	2	2	no	—
341	C₄₃⋊C₈	—	2	2	no	—
342	C₄₃⋊C₈	—	4	1	no	—
343	C₄₃⋊C₈	—	4	1	no	—
344	C₄₃⋊C₈	—	4	1	no	—
345	C₄₃⋊C₈	—	4	1	no	—
346	C₄₃⋊C₈	—	4	1	no	—
347	C₄₃⋊C₈	—	4	1	no	—
348	#22470	—	43	1	no	maximal, Sylow
349	C₂²×C₄₃	—	2	2	no	—
350	C₂²×C₄₃	—	2	2	no	—
351	C₂²×C₄₃	—	2	2	no	—
352	C₂²×C₄₃	—	2	2	no	—
353	C₂²×C₄₃	—	2	2	no	—
354	C₂²×C₄₃	—	2	2	no	—
355	C₂²×C₄₃	—	2	2	no	—
356	C₂²×C₄₃	—	2	2	no	—
357	C₂²×C₄₃	—	2	2	no	—
358	C₂²×C₄₃	—	4	1	no	—
359	C₂²×C₄₃	—	4	1	no	—
360	C₂²×C₄₃	—	4	1	no	—
361	C₂²×C₄₃	—	4	1	no	—
362	C₂²×C₄₃	—	4	1	no	—
363	C₂²×C₄₃	—	4	1	no	—
364	C₂²×C₄₃	—	4	1	no	—
365	C₂²×C₄₃	—	4	1	no	—
366	C₂²×C₄₃	—	4	1	no	—
367	C₂²×C₄₃	—	4	1	no	—
368	C₂²×C₄₃	—	4	1	no	—
369	C₂²×C₄₃	#408	1	4	yes	—
370	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
371	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
372	C₂²×C₄₃	#520	1	1	yes	characteristic
373	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
374	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
375	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
376	C₂²×C₄₃	#568	1	1	yes	characteristic
377	C₄×C₄₃	—	2	2	no	—
378	C₄×C₄₃	—	2	2	no	—
379	C₄×C₄₃	—	2	2	no	—
380	C₄×C₄₃	—	2	2	no	—
381	C₄×C₄₃	—	2	2	no	—
382	C₄×C₄₃	—	4	1	no	—
383	C₄×C₄₃	—	4	1	no	—
384	C₄×C₄₃	—	4	1	no	—
385	C₄×C₄₃	—	4	1	no	—
386	C₄×C₄₃	—	4	1	no	—
387	C₄×C₄₃	—	4	1	no	—
388	C₄×C₄₃	#546	1	1	yes	characteristic
389	C₄×C₄₃	#546	1	1	yes	characteristic
390	C₄×C₄₃	#547	1	1	yes	characteristic
391	C₄×C₄₃	#547	1	1	yes	characteristic
392	C₂×#529	D₄₃	1	1	yes	characteristic
393	C₂×#435	—	43	1	no	—
394	C₂×C₈×D₄	—	43	1	no	—
395	#1985	—	43	1	no	—
396	#1984	—	43	1	no	—
397	#1870	—	43	1	no	—
398	#1869	—	43	1	no	—
399	#1869	—	43	1	no	—
400	#1869	—	43	1	no	—
401	#1818	—	43	1	no	—
402	#1817	—	43	1	no	—
403	#1798	—	43	1	no	—
404	#1750	—	43	1	no	—
405	#1729	—	43	1	no	—
406	C₂×#336	—	43	1	no	—
407	C₂×C₄₃	—	2	4	no	—
408	C₂×C₄₃	—	4	2	no	—
409	C₂×C₄₃	—	8	1	no	—
410	C₂×C₄₃	#2339	1	1	yes	characteristic
411	C₂×C₄₃	C₂×#408	1	1	yes	characteristic
412	C₂×C₄₃	#2880	1	1	yes	characteristic
413	C₂×C₄₃	#2966	1	1	yes	characteristic
414	C₂×C₄₃	#2968	1	1	yes	characteristic
415	C₂×C₄₃	#2992	1	1	yes	characteristic
416	C₂×C₄₃	#2994	1	1	yes	characteristic
417	C₂²×M₁₆	—	43	1	no	—
418	C₂³×C₈	—	43	1	no	—
419	C₂³×C₈	—	43	1	no	—
420	C₂³×C₈	—	43	1	no	—
421	#529	—	2	4	no	—
422	#529	—	2	4	no	—
423	C₂×#126	Dic₄₃	1	1	yes	characteristic
424	C₂×#126	Dic₄₃	1	1	yes	characteristic
425	C₂×#125	Dic₄₃	1	1	yes	characteristic
426	C₂×#124	Dic₄₃	1	1	yes	characteristic
427	C₂×#123	Dic₄₃	1	1	yes	characteristic
428	C₂×#123	Dic₄₃	1	1	yes	characteristic
429	C₂×C₂²⋊Q₈	Dic₄₃	1	1	yes	characteristic
430	C₂×#121	Dic₄₃	1	1	yes	characteristic
431	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
435	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
436	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
437	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
438	#435	—	86	4	no	—
439	C₈×D₄	—	86	4	no	—
440	C₂×C₄⋊C₈	—	43	1	no	—
441	C₂×C₄⋊C₈	—	43	1	no	—
442	C₂×C₂²⋊C₈	—	43	1	no	—
443	C₂×C₂²⋊C₈	—	43	1	no	—
444	C₂×C₂²⋊C₈	—	43	1	no	—
445	C₂×C₂²⋊C₈	—	43	1	no	—
446	C₂×C₂²⋊C₈	—	43	1	no	—
447	C₂×C₂²⋊C₈	—	43	1	no	—
448	C₂×C₂²⋊C₈	—	43	1	no	—
449	C₂×C₂²⋊C₈	—	43	1	no	—
450	C₂×#97	—	43	1	no	—
451	C₂×C₄×C₈	—	43	1	no	—
452	#336	—	43	1	no	—
453	#336	—	43	1	no	—
454	#336	—	43	1	no	—
455	#336	—	43	1	no	—
456	#336	—	43	1	no	—
457	#336	—	43	1	no	—
458	#336	—	43	1	no	—
459	#336	—	43	1	no	—
460	#336	—	43	1	no	—
461	#336	—	43	1	no	—
462	#336	—	43	1	no	—
463	#336	—	43	1	no	—
464	C₄₃	#22470	1	1	yes	characteristic, complemented, Sylow
465	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
466	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
467	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
468	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
469	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
470	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
471	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
472	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
473	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
474	C₂×M₁₆	—	86	2	no	—
475	C₂×M₁₆	—	86	2	no	—
476	C₂×M₁₆	—	172	1	no	—
477	C₂²×C₈	—	43	1	no	—
478	C₂²×C₈	—	43	1	no	—
479	C₂²×C₈	—	43	1	no	—
480	C₂²×C₈	—	43	1	no	—
481	C₂²×C₈	—	43	1	no	—
482	C₂²×C₈	—	43	1	no	—
483	C₂²×C₈	—	43	1	no	—
484	C₂²×C₈	—	43	1	no	—
485	C₂²×C₈	—	86	2	no	—
486	C₂²×C₈	—	86	2	no	—
487	C₂²×C₈	—	86	2	no	—
488	C₂²×C₈	—	86	2	no	—
489	C₂²×C₈	—	86	2	no	—
490	C₂²×C₈	—	86	2	no	—
491	C₂²×C₈	—	172	1	no	—
492	C₂²×C₈	—	172	1	no	—
493	C₂²×C₈	—	172	1	no	—
494	#126	—	2	4	no	—
495	#126	—	2	4	no	—
496	#125	—	2	4	no	—
497	#124	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	#121	—	2	4	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	C₂²⋊D₄₃	1	4	yes	—
509	C₄×D₄	C₂²⋊D₄₃	1	4	yes	—
510	#117	—	2	2	no	—
511	#117	—	2	2	no	—
512	#117	—	2	2	no	—
513	#117	—	2	2	no	—
514	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
534	C₂×C₄²	—	2	2	no	—
535	C₂×C₄²	—	2	2	no	—
536	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
537	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
538	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
539	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
540	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
541	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
542	C₄⋊C₈	—	86	2	no	—
543	C₄⋊C₈	—	86	2	no	—
544	C₂²⋊C₈	—	86	2	no	—
545	C₂²⋊C₈	—	86	2	no	—
546	C₂²⋊C₈	—	86	2	no	—
547	C₂²⋊C₈	—	86	2	no	—
548	C₂²⋊C₈	—	86	2	no	—
549	C₂²⋊C₈	—	86	2	no	—
550	C₂²⋊C₈	—	172	1	no	—
551	C₂²⋊C₈	—	172	1	no	—
552	#97	—	86	2	no	—
553	C₄×C₈	—	86	2	no	—
554	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
555	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
556	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	4	1	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	C₂²⋊Dic₄₃	1	4	yes	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
590	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
592	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
593	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
594	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
595	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
596	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
597	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
598	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
599	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
601	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
602	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
603	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
604	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
605	M₁₆	—	172	4	no	—
606	C₂×C₈	—	43	2	no	—
607	C₂×C₈	—	43	2	no	—
608	C₂×C₈	—	86	1	no	—
609	C₂×C₈	—	86	1	no	—
610	C₂×C₈	—	86	1	no	—
611	C₂×C₈	—	86	1	no	—
612	C₂×C₈	—	86	1	no	—
613	C₂×C₈	—	86	1	no	—
614	C₂×C₈	—	86	1	no	—
615	C₂×C₈	—	86	1	no	—
616	C₂×C₈	—	86	1	no	—
617	C₂×C₈	—	86	1	no	—
618	C₂×C₈	—	86	1	no	—
619	C₂×C₈	—	86	1	no	—
620	C₂×C₈	—	86	1	no	—
621	C₂×C₈	—	86	1	no	—
622	C₂×C₈	—	86	1	no	—
623	C₂×C₈	—	86	1	no	—
624	C₂×C₈	—	86	1	no	—
625	C₂×C₈	—	86	1	no	—
626	C₂×C₈	—	86	1	no	—
627	C₂×C₈	—	86	1	no	—
628	C₂×C₈	—	86	1	no	—
629	C₂×C₈	—	86	1	no	—
630	C₂×C₈	—	172	4	no	—
631	C₂×C₈	—	172	4	no	—
632	C₂×C₈	—	172	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	C₂²⋊Dic₄₃	1	4	yes	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	C₂²⋊Dic₄₃	1	4	yes	—
652	C₂²⋊C₄	C₂²⋊Dic₄₃	1	4	yes	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
662	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	C₂×C₂²⋊Dic₄₃	1	2	yes	—
681	C₂³	C₂×C₂²⋊Dic₄₃	1	2	yes	—
682	C₂³	#13063332	1	2	yes	—
683	C₂³	#13063332	1	2	yes	—
684	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
685	Q₈	—	4	4	no	—
686	D₄	—	2	8	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	4	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
732	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
733	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
734	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
735	C₂×C₄	#13063332	1	2	yes	—
736	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
737	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
738	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
739	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
740	C₂×C₄	#13063371	1	1	yes	characteristic
741	C₂×C₄	#13063372	1	1	yes	characteristic
742	C₈	—	86	2	no	—
743	C₈	—	86	2	no	—
744	C₈	—	172	1	no	—
745	C₈	—	172	1	no	—
746	C₈	—	172	1	no	—
747	C₈	—	172	1	no	—
748	C₈	—	172	1	no	—
749	C₈	—	172	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	#14582866	1	4	yes	—
771	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
772	C₂²	#41×Dic₄₃	1	1	yes	characteristic
773	C₂²	#14583382	1	1	yes	characteristic
774	C₂²	C₂×#13063332	1	1	yes	characteristic
775	C₂²	C₂×#13063332	1	1	yes	characteristic
776	C₂²	C₂×#13063332	1	1	yes	characteristic
777	C₂²	#14583666	1	1	yes	characteristic
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	#14583537	1	1	yes	characteristic
790	C₄	#14583537	1	1	yes	characteristic
791	C₄	#14583548	1	1	yes	characteristic
792	C₄	#14583548	1	1	yes	characteristic
793	C₂	—	2	4	no	—
794	C₂	—	4	2	no	—
795	C₂	—	8	1	no	—
796	C₂	#19137425	1	1	yes	characteristic
797	C₂	C₂×#14582866	1	1	yes	characteristic
798	C₂	#19143044	1	1	yes	characteristic
799	C₂	#19143571	1	1	yes	characteristic
800	C₂	#19143591	1	1	yes	characteristic
801	C₂	#19143734	1	1	yes	characteristic
802	C₂	#19143755	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₂×C₄₃×#529	C₂
prime radical	C₂×#121×C₄₃	C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#529	D₄₃
hypocenter	C₄₃	#22470
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×#14582971	C₂	semidirect
2. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
3. #19135536	C₂	semidirect
4. #19135532	C₂	semidirect
5. #19134893	C₂	semidirect
6. #19134888	C₂	semidirect
7. #19134888	C₂	semidirect
8. #19134888	C₂	semidirect
9. #19134666	C₂	semidirect
10. #19134663	C₂	semidirect
11. #19134579	C₂	semidirect
12. #19134361	C₂	semidirect
13. #19134292	C₂	semidirect
14. C₂×#14582654	C₂	semidirect
464. C₄₃	#22470	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582971	2
C₂×D₄×C₄₃⋊C₈	2
#19135536	2
#19135532	2
#19134893	2
#19134888	2
#19134666	2
#19134663	2
#19134579	2
#19134361	2
#19134292	2
C₂×#14582654	2
C₂×C₄₃×#529	2
#22470	43