Subgroups — C₄₃×#14141 #24934158

Order 11008.

1938 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#388	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1440	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1439	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1437	C₂	1	2	yes	maximal, complemented
10	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
23	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#390	—	2	4	no	—
28	C₄₃×#390	—	2	4	no	—
29	C₄₃×#390	C₄	1	8	yes	complemented
30	C₄₃×#389	—	2	4	no	—
31	C₄₃×#388	—	2	8	no	—
32	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
33	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#95×C₄₃	C₂²	1	2	yes	—
37	C₂×#95×C₄₃	C₂²	1	2	yes	—
38	C₂×#95×C₄₃	C₂²	1	2	yes	—
39	C₂×#95×C₄₃	C₂²	1	2	yes	—
40	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
41	C₂⁵×C₄₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	—	2	2	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	—	2	2	no	—
47	C₂²×D₄×C₄₃	—	2	2	no	—
48	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
68	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
87	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
88	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
89	C₂×C₄²×C₄₃	—	2	2	no	—
90	C₂×C₄²×C₄₃	—	2	2	no	—
91	C₂×C₄²×C₄₃	—	2	4	no	—
92	C₂×C₄²×C₄₃	—	2	4	no	—
93	C₂×C₄²×C₄₃	—	2	2	no	—
94	C₂×C₄²×C₄₃	—	2	2	no	—
95	C₂×C₄²×C₄₃	—	2	2	no	—
96	C₂×C₄²×C₄₃	—	2	2	no	—
97	C₂×C₄²×C₄₃	—	2	2	no	—
98	C₂×C₄²×C₄₃	—	2	2	no	—
99	C₂×C₄²×C₄₃	—	4	2	no	—
100	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
101	#95×C₄₃	—	2	4	no	—
102	#95×C₄₃	—	2	4	no	—
103	#95×C₄₃	—	2	4	no	—
104	#95×C₄₃	—	2	2	no	—
105	#95×C₄₃	—	2	2	no	—
106	#95×C₄₃	—	2	2	no	—
107	#95×C₄₃	—	4	2	no	—
108	#95×C₄₃	D₄	1	4	yes	complemented
109	C₂⁴×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	2	no	—
112	C₂⁴×C₄₃	—	2	2	no	—
113	C₂⁴×C₄₃	—	2	2	no	—
114	C₂⁴×C₄₃	—	2	2	no	—
115	C₂⁴×C₄₃	—	2	2	no	—
116	C₂⁴×C₄₃	—	2	2	no	—
117	C₂⁴×C₄₃	—	2	2	no	—
118	C₂⁴×C₄₃	—	2	2	no	—
119	C₂⁴×C₄₃	—	2	2	no	—
120	C₂⁴×C₄₃	—	2	2	no	—
121	C₂⁴×C₄₃	—	2	2	no	—
122	C₂⁴×C₄₃	—	2	2	no	—
123	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
124	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂×D₄×C₄₃	—	2	8	no	—
126	C₂×D₄×C₄₃	—	2	8	no	—
127	C₂×D₄×C₄₃	—	2	8	no	—
128	C₂×D₄×C₄₃	—	4	4	no	—
129	C₂×D₄×C₄₃	—	4	4	no	—
130	C₂×D₄×C₄₃	—	4	4	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	2	1	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	—	2	1	no	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	1	no	—
156	C₂²×C₄×C₄₃	—	2	1	no	—
157	C₂²×C₄×C₄₃	—	2	1	no	—
158	C₂²×C₄×C₄₃	—	2	1	no	—
159	C₂²×C₄×C₄₃	—	2	2	no	—
160	C₂²×C₄×C₄₃	—	2	2	no	—
161	C₂²×C₄×C₄₃	—	2	2	no	—
162	C₂²×C₄×C₄₃	—	2	2	no	—
163	C₂²×C₄×C₄₃	—	2	2	no	—
164	C₂²×C₄×C₄₃	—	2	2	no	—
165	C₂²×C₄×C₄₃	—	2	2	no	—
166	C₂²×C₄×C₄₃	—	2	1	no	—
167	C₂²×C₄×C₄₃	—	2	1	no	—
168	C₂²×C₄×C₄₃	—	2	2	no	—
169	C₂²×C₄×C₄₃	—	2	2	no	—
170	C₂²×C₄×C₄₃	—	2	2	no	—
171	C₂²×C₄×C₄₃	—	2	2	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	1	no	—
176	C₂²×C₄×C₄₃	—	2	1	no	—
177	C₂²×C₄×C₄₃	—	2	1	no	—
178	C₂²×C₄×C₄₃	—	2	2	no	—
179	C₂²×C₄×C₄₃	—	2	2	no	—
180	C₂²×C₄×C₄₃	—	2	1	no	—
181	C₂²×C₄×C₄₃	—	2	1	no	—
182	C₂²×C₄×C₄₃	—	2	1	no	—
183	C₂²×C₄×C₄₃	—	2	1	no	—
184	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
185	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
188	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₄₃	#41	1	2	yes	—
196	C₂²×C₄×C₄₃	#41	1	2	yes	—
197	C₂²×C₄×C₄₃	#41	1	2	yes	—
198	C₂²×C₄×C₄₃	#41	1	2	yes	—
199	C₂²×C₄×C₄₃	#41	1	2	yes	—
200	C₂²×C₄×C₄₃	#41	1	2	yes	—
201	C₂²×C₄×C₄₃	#41	1	2	yes	—
202	C₄⋊C₄×C₄₃	—	2	8	no	—
203	C₄⋊C₄×C₄₃	—	2	8	no	—
204	C₄⋊C₄×C₄₃	—	2	8	no	—
205	C₄⋊C₄×C₄₃	—	4	8	no	—
206	C₂²⋊C₄×C₄₃	—	2	16	no	—
207	C₂²⋊C₄×C₄₃	—	4	8	no	—
208	C₂²⋊C₄×C₄₃	—	4	8	no	—
209	C₂²⋊C₄×C₄₃	—	4	8	no	—
210	C₂²⋊C₄×C₄₃	—	4	8	no	—
211	C₂²⋊C₄×C₄₃	—	4	8	no	—
212	C₄²×C₄₃	—	2	8	no	—
213	C₄²×C₄₃	—	4	8	no	—
214	C₄²×C₄₃	—	4	4	no	—
215	C₄²×C₄₃	—	4	4	no	—
216	C₂³×C₄₃	—	2	4	no	—
217	C₂³×C₄₃	—	2	4	no	—
218	C₂³×C₄₃	—	2	4	no	—
219	C₂³×C₄₃	—	2	4	no	—
220	C₂³×C₄₃	—	2	4	no	—
221	C₂³×C₄₃	—	2	4	no	—
222	C₂³×C₄₃	—	2	4	no	—
223	C₂³×C₄₃	—	4	2	no	—
224	C₂³×C₄₃	—	4	2	no	—
225	C₂³×C₄₃	—	4	2	no	—
226	C₂³×C₄₃	—	4	2	no	—
227	C₂³×C₄₃	—	4	2	no	—
228	C₂³×C₄₃	—	4	2	no	—
229	C₂³×C₄₃	—	4	2	no	—
230	C₂³×C₄₃	—	4	2	no	—
231	C₂³×C₄₃	—	4	2	no	—
232	C₂³×C₄₃	—	4	2	no	—
233	C₂³×C₄₃	—	4	2	no	—
234	C₂³×C₄₃	—	4	2	no	—
235	C₂³×C₄₃	—	4	2	no	—
236	C₂³×C₄₃	—	4	2	no	—
237	C₂³×C₄₃	—	4	2	no	—
238	C₂³×C₄₃	—	4	2	no	—
239	C₂³×C₄₃	—	4	2	no	—
240	C₂³×C₄₃	—	4	2	no	—
241	C₂³×C₄₃	—	4	2	no	—
242	C₂³×C₄₃	—	4	2	no	—
243	C₂³×C₄₃	—	4	2	no	—
244	C₂³×C₄₃	—	4	2	no	—
245	C₂³×C₄₃	—	4	2	no	—
246	C₂³×C₄₃	—	4	2	no	—
247	C₂³×C₄₃	—	4	2	no	—
248	C₂³×C₄₃	—	4	2	no	—
249	C₂³×C₄₃	—	4	2	no	—
250	C₂³×C₄₃	—	4	2	no	—
251	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
252	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
253	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
254	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
255	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
256	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
257	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
258	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
259	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
260	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
261	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
262	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
266	D₄×C₄₃	—	4	16	no	—
267	C₂×C₄×C₄₃	—	2	2	no	—
268	C₂×C₄×C₄₃	—	2	2	no	—
269	C₂×C₄×C₄₃	—	2	2	no	—
270	C₂×C₄×C₄₃	—	2	2	no	—
271	C₂×C₄×C₄₃	—	2	2	no	—
272	C₂×C₄×C₄₃	—	2	2	no	—
273	C₂×C₄×C₄₃	—	2	2	no	—
274	C₂×C₄×C₄₃	—	2	4	no	—
275	C₂×C₄×C₄₃	—	2	4	no	—
276	C₂×C₄×C₄₃	—	2	2	no	—
277	C₂×C₄×C₄₃	—	2	2	no	—
278	C₂×C₄×C₄₃	—	2	4	no	—
279	C₂×C₄×C₄₃	—	2	4	no	—
280	C₂×C₄×C₄₃	—	2	4	no	—
281	C₂×C₄×C₄₃	—	2	2	no	—
282	C₂×C₄×C₄₃	—	2	2	no	—
283	C₂×C₄×C₄₃	—	2	2	no	—
284	C₂×C₄×C₄₃	—	2	2	no	—
285	C₂×C₄×C₄₃	—	2	4	no	—
286	C₂×C₄×C₄₃	—	2	2	no	—
287	C₂×C₄×C₄₃	—	2	2	no	—
288	C₂×C₄×C₄₃	—	2	4	no	—
289	C₂×C₄×C₄₃	—	2	2	no	—
290	C₂×C₄×C₄₃	—	2	2	no	—
291	C₂×C₄×C₄₃	—	2	2	no	—
292	C₂×C₄×C₄₃	—	2	4	no	—
293	C₂×C₄×C₄₃	—	2	4	no	—
294	C₂×C₄×C₄₃	—	2	2	no	—
295	C₂×C₄×C₄₃	—	2	2	no	—
296	C₂×C₄×C₄₃	—	2	2	no	—
297	C₂×C₄×C₄₃	—	4	1	no	—
298	C₂×C₄×C₄₃	—	4	1	no	—
299	C₂×C₄×C₄₃	—	4	1	no	—
300	C₂×C₄×C₄₃	—	4	1	no	—
301	C₂×C₄×C₄₃	—	4	2	no	—
302	C₂×C₄×C₄₃	—	4	2	no	—
303	C₂×C₄×C₄₃	—	4	1	no	—
304	C₂×C₄×C₄₃	—	4	2	no	—
305	C₂×C₄×C₄₃	—	4	2	no	—
306	C₂×C₄×C₄₃	—	4	1	no	—
307	C₂×C₄×C₄₃	—	4	1	no	—
308	C₂×C₄×C₄₃	—	4	1	no	—
309	C₂×C₄×C₄₃	—	4	2	no	—
310	C₂×C₄×C₄₃	—	4	2	no	—
311	C₂×C₄×C₄₃	—	4	1	no	—
312	C₂×C₄×C₄₃	—	4	1	no	—
313	C₂×C₄×C₄₃	—	4	1	no	—
314	C₂×C₄×C₄₃	—	4	1	no	—
315	C₂×C₄×C₄₃	—	4	1	no	—
316	C₂×C₄×C₄₃	—	4	2	no	—
317	C₂×C₄×C₄₃	—	4	2	no	—
318	C₂×C₄×C₄₃	—	4	1	no	—
319	C₂×C₄×C₄₃	—	4	2	no	—
320	C₂×C₄×C₄₃	—	4	1	no	—
321	C₂×C₄×C₄₃	—	4	2	no	—
322	C₂×C₄×C₄₃	—	4	1	no	—
323	C₂×C₄×C₄₃	—	4	1	no	—
324	C₂×C₄×C₄₃	—	4	1	no	—
325	C₂×C₄×C₄₃	—	4	1	no	—
326	C₂×C₄×C₄₃	—	4	1	no	—
327	C₂×C₄×C₄₃	—	4	2	no	—
328	C₂×C₄×C₄₃	—	4	2	no	—
329	C₂×C₄×C₄₃	#117	1	4	yes	—
330	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
331	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
332	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
333	C₂×C₄×C₄₃	#121	1	4	yes	—
334	C₂×C₄×C₄₃	#123	1	4	yes	—
335	C₂×C₄×C₄₃	#124	1	4	yes	—
336	C₂×C₄×C₄₃	#126	1	4	yes	—
337	#14141	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂²×C₄₃	—	4	4	no	—
339	C₂²×C₄₃	—	4	4	no	—
340	C₂²×C₄₃	—	4	4	no	—
341	C₂²×C₄₃	—	4	4	no	—
342	C₂²×C₄₃	—	4	4	no	—
343	C₂²×C₄₃	—	4	4	no	—
344	C₂²×C₄₃	—	4	4	no	—
345	C₂²×C₄₃	—	8	2	no	—
346	C₂²×C₄₃	—	8	2	no	—
347	C₂²×C₄₃	—	8	2	no	—
348	C₂²×C₄₃	—	8	2	no	—
349	C₂²×C₄₃	—	8	2	no	—
350	C₂²×C₄₃	—	8	2	no	—
351	C₂²×C₄₃	—	8	2	no	—
352	C₂²×C₄₃	—	8	2	no	—
353	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
354	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
356	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
357	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
358	C₂²×C₄₃	#518	1	1	yes	characteristic
359	C₂²×C₄₃	#520	1	1	yes	characteristic
360	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
361	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
362	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
363	C₂²×C₄₃	C₂×#126	1	1	yes	characteristic
364	C₂²×C₄₃	#529	1	1	yes	characteristic
365	C₂²×C₄₃	#529	1	1	yes	characteristic
366	C₂²×C₄₃	#532	1	1	yes	characteristic
367	C₂²×C₄₃	#532	1	1	yes	characteristic
368	C₂²×C₄₃	#540	1	1	yes	characteristic
369	C₂²×C₄₃	#540	1	1	yes	characteristic
370	C₂²×C₄₃	#542	1	1	yes	characteristic
371	C₂²×C₄₃	#542	1	1	yes	characteristic
372	C₂²×C₄₃	D₄²	1	1	yes	characteristic
373	C₂²×C₄₃	D₄²	1	1	yes	characteristic
374	C₂²×C₄₃	#546	1	1	yes	characteristic
375	C₂²×C₄₃	#546	1	1	yes	characteristic
376	C₂²×C₄₃	#547	1	1	yes	characteristic
377	C₂²×C₄₃	#548	1	1	yes	characteristic
378	C₂²×C₄₃	#548	1	1	yes	characteristic
379	C₂²×C₄₃	#550	1	1	yes	characteristic
380	C₂²×C₄₃	#550	1	1	yes	characteristic
381	C₂²×C₄₃	#550	1	1	yes	characteristic
382	C₂²×C₄₃	#553	1	1	yes	characteristic
383	C₂²×C₄₃	#553	1	1	yes	characteristic
384	C₂²×C₄₃	#555	1	1	yes	characteristic
385	C₂²×C₄₃	#556	1	1	yes	characteristic
386	C₂²×C₄₃	#559	1	1	yes	characteristic
387	C₂²×C₄₃	#559	1	1	yes	characteristic
388	C₄×C₄₃	—	2	4	no	—
389	C₄×C₄₃	—	4	2	no	—
390	C₄×C₄₃	—	4	4	no	—
391	C₄×C₄₃	—	4	2	no	—
392	C₄×C₄₃	—	4	4	no	—
393	C₄×C₄₃	—	4	2	no	—
394	C₄×C₄₃	—	4	4	no	—
395	C₄×C₄₃	—	4	2	no	—
396	C₄×C₄₃	—	4	2	no	—
397	C₄×C₄₃	#388	1	8	yes	complemented
398	C₂×#390	C₂×C₄₃	1	1	yes	characteristic
399	C₂×#390	C₂×C₄₃	1	1	yes	characteristic
400	C₂×#390	C₂×C₄₃	1	1	yes	characteristic
401	C₂×#389	C₂×C₄₃	1	1	yes	characteristic, complemented
402	C₂×#388	C₂×C₄₃	1	2	yes	complemented
403	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
404	#1440	C₂×C₄₃	1	2	yes	complemented
405	#1439	C₂×C₄₃	1	2	yes	complemented
406	#1437	C₂×C₄₃	1	2	yes	complemented
407	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic, complemented
408	C₄×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
409	C₂×C₄₃	—	8	4	no	—
410	C₂×C₄₃	C₂×#388	1	1	yes	characteristic
411	C₂×C₄₃	#2293	1	1	yes	characteristic
412	C₂×C₄₃	#2319	1	1	yes	characteristic
413	C₂×C₄₃	#2361	1	1	yes	characteristic
414	C₂×C₄₃	#2363	1	1	yes	characteristic
415	C₂×C₄₃	#2366	1	1	yes	characteristic
416	C₂×C₄₃	#2367	1	1	yes	characteristic
417	C₂×C₄₃	#2426	1	1	yes	characteristic
418	C₂×C₄₃	#2428	1	1	yes	characteristic
419	C₂×C₄₃	#2445	1	1	yes	characteristic
420	C₂×C₄₃	#2448	1	1	yes	characteristic
421	C₂×C₄₃	#2490	1	1	yes	characteristic
422	C₂×C₄₃	#2491	1	1	yes	characteristic
423	C₂×C₄₃	#2512	1	1	yes	characteristic
424	C₂×C₄₃	#2513	1	1	yes	characteristic
425	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
427	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
429	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
430	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
431	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
432	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
433	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
434	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
435	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
436	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
438	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
439	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
440	#390	—	2	4	no	—
441	#390	—	2	4	no	—
442	#390	C₄×C₄₃	1	8	yes	complemented
443	#389	—	2	4	no	—
444	#388	—	2	8	no	—
445	C₄×C₄⋊C₄	—	2	4	no	—
446	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
447	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
448	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
449	C₂×#95	C₂²×C₄₃	1	2	yes	—
450	C₂×#95	C₂²×C₄₃	1	2	yes	—
451	C₂×#95	C₂²×C₄₃	1	2	yes	—
452	C₂×#95	C₂²×C₄₃	1	2	yes	—
453	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
454	C₄₃	#14141	1	1	yes	characteristic, direct product factor, Sylow
455	C₂⁵	C₂³×C₄₃	1	2	yes	—
456	C₂²×D₄	—	2	2	no	—
457	C₂²×D₄	—	2	2	no	—
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	—	2	2	no	—
460	C₂²×D₄	—	2	2	no	—
461	C₂²×D₄	—	2	2	no	—
462	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
463	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
464	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
466	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
468	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	—	2	2	no	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	—	2	2	no	—
476	C₂×C₄⋊C₄	—	2	2	no	—
477	C₂×C₄⋊C₄	—	2	2	no	—
478	C₂×C₄⋊C₄	—	2	2	no	—
479	C₂×C₄⋊C₄	—	2	4	no	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	4	2	no	—
482	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
483	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
484	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
485	C₂×C₂²⋊C₄	—	2	4	no	—
486	C₂×C₂²⋊C₄	—	2	4	no	—
487	C₂×C₂²⋊C₄	—	2	4	no	—
488	C₂×C₂²⋊C₄	—	2	4	no	—
489	C₂×C₂²⋊C₄	—	2	4	no	—
490	C₂×C₂²⋊C₄	—	2	4	no	—
491	C₂×C₂²⋊C₄	—	2	4	no	—
492	C₂×C₂²⋊C₄	—	2	4	no	—
493	C₂×C₂²⋊C₄	—	2	4	no	—
494	C₂×C₂²⋊C₄	—	2	4	no	—
495	C₂×C₂²⋊C₄	—	4	2	no	—
496	C₂×C₂²⋊C₄	—	4	2	no	—
497	C₂×C₂²⋊C₄	—	4	2	no	—
498	C₂×C₂²⋊C₄	—	4	2	no	—
499	C₂×C₂²⋊C₄	—	4	2	no	—
500	C₂×C₂²⋊C₄	—	4	2	no	—
501	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
502	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
503	C₂×C₄²	—	2	2	no	—
504	C₂×C₄²	—	2	2	no	—
505	C₂×C₄²	—	2	4	no	—
506	C₂×C₄²	—	2	4	no	—
507	C₂×C₄²	—	2	2	no	—
508	C₂×C₄²	—	2	2	no	—
509	C₂×C₄²	—	2	2	no	—
510	C₂×C₄²	—	2	2	no	—
511	C₂×C₄²	—	2	2	no	—
512	C₂×C₄²	—	2	2	no	—
513	C₂×C₄²	—	4	2	no	—
514	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
515	#95	—	2	4	no	—
516	#95	—	2	4	no	—
517	#95	—	2	4	no	—
518	#95	—	2	2	no	—
519	#95	—	2	2	no	—
520	#95	—	2	2	no	—
521	#95	—	4	2	no	—
522	#95	D₄×C₄₃	1	4	yes	complemented
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	2	no	—
531	C₂⁴	—	2	2	no	—
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	2	2	no	—
534	C₂⁴	—	2	2	no	—
535	C₂⁴	—	2	2	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
538	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
539	C₂×D₄	—	2	8	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	4	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
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	2	no	—
576	C₂²×C₄	—	2	2	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	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
599	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
600	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
601	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
602	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
603	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
604	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
605	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
606	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
607	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
608	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
609	C₂²×C₄	#41×C₄₃	1	2	yes	—
610	C₂²×C₄	#41×C₄₃	1	2	yes	—
611	C₂²×C₄	#41×C₄₃	1	2	yes	—
612	C₂²×C₄	#41×C₄₃	1	2	yes	—
613	C₂²×C₄	#41×C₄₃	1	2	yes	—
614	C₂²×C₄	#41×C₄₃	1	2	yes	—
615	C₂²×C₄	#41×C₄₃	1	2	yes	—
616	C₄⋊C₄	—	2	8	no	—
617	C₄⋊C₄	—	2	8	no	—
618	C₄⋊C₄	—	2	8	no	—
619	C₄⋊C₄	—	4	8	no	—
620	C₂²⋊C₄	—	2	16	no	—
621	C₂²⋊C₄	—	4	8	no	—
622	C₂²⋊C₄	—	4	8	no	—
623	C₂²⋊C₄	—	4	8	no	—
624	C₂²⋊C₄	—	4	8	no	—
625	C₂²⋊C₄	—	4	8	no	—
626	C₄²	—	2	8	no	—
627	C₄²	—	4	8	no	—
628	C₄²	—	4	4	no	—
629	C₄²	—	4	4	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	4	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	4	2	no	—
638	C₂³	—	4	2	no	—
639	C₂³	—	4	2	no	—
640	C₂³	—	4	2	no	—
641	C₂³	—	4	2	no	—
642	C₂³	—	4	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	2	no	—
648	C₂³	—	4	2	no	—
649	C₂³	—	4	2	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	—	4	2	no	—
657	C₂³	—	4	2	no	—
658	C₂³	—	4	2	no	—
659	C₂³	—	4	2	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
667	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
668	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
669	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
670	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
671	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
672	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
673	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
674	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
675	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
676	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
677	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
678	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
679	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
680	D₄	—	4	16	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	#117×C₄₃	1	4	yes	—
744	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
745	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
746	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
747	C₂×C₄	#121×C₄₃	1	4	yes	—
748	C₂×C₄	#123×C₄₃	1	4	yes	—
749	C₂×C₄	#124×C₄₃	1	4	yes	—
750	C₂×C₄	#126×C₄₃	1	4	yes	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	8	2	no	—
759	C₂²	—	8	2	no	—
760	C₂²	—	8	2	no	—
761	C₂²	—	8	2	no	—
762	C₂²	—	8	2	no	—
763	C₂²	—	8	2	no	—
764	C₂²	—	8	2	no	—
765	C₂²	—	8	2	no	—
766	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
767	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
768	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
769	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
770	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
771	C₂²	C₄₃×#518	1	1	yes	characteristic
772	C₂²	C₄₃×#520	1	1	yes	characteristic
773	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
774	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
775	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
776	C₂²	C₂×#126×C₄₃	1	1	yes	characteristic
777	C₂²	C₄₃×#529	1	1	yes	characteristic
778	C₂²	C₄₃×#529	1	1	yes	characteristic
779	C₂²	C₄₃×#532	1	1	yes	characteristic
780	C₂²	C₄₃×#532	1	1	yes	characteristic
781	C₂²	C₄₃×#540	1	1	yes	characteristic
782	C₂²	C₄₃×#540	1	1	yes	characteristic
783	C₂²	C₄₃×#542	1	1	yes	characteristic
784	C₂²	C₄₃×#542	1	1	yes	characteristic
785	C₂²	D₄²×C₄₃	1	1	yes	characteristic
786	C₂²	D₄²×C₄₃	1	1	yes	characteristic
787	C₂²	C₄₃×#546	1	1	yes	characteristic
788	C₂²	C₄₃×#546	1	1	yes	characteristic
789	C₂²	C₄₃×#547	1	1	yes	characteristic
790	C₂²	C₄₃×#548	1	1	yes	characteristic
791	C₂²	C₄₃×#548	1	1	yes	characteristic
792	C₂²	C₄₃×#550	1	1	yes	characteristic
793	C₂²	C₄₃×#550	1	1	yes	characteristic
794	C₂²	C₄₃×#550	1	1	yes	characteristic
795	C₂²	C₄₃×#553	1	1	yes	characteristic
796	C₂²	C₄₃×#553	1	1	yes	characteristic
797	C₂²	C₄₃×#555	1	1	yes	characteristic
798	C₂²	C₄₃×#556	1	1	yes	characteristic
799	C₂²	C₄₃×#559	1	1	yes	characteristic
800	C₂²	C₄₃×#559	1	1	yes	characteristic
801	C₄	—	2	4	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	4	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	4	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	4	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	C₄₃×#388	1	8	yes	complemented
811	C₂	—	8	4	no	—
812	C₂	C₂×C₄₃×#388	1	1	yes	characteristic
813	C₂	C₄₃×#2293	1	1	yes	characteristic
814	C₂	C₄₃×#2319	1	1	yes	characteristic
815	C₂	C₄₃×#2361	1	1	yes	characteristic
816	C₂	C₄₃×#2363	1	1	yes	characteristic
817	C₂	C₄₃×#2366	1	1	yes	characteristic
818	C₂	C₄₃×#2367	1	1	yes	characteristic
819	C₂	C₄₃×#2426	1	1	yes	characteristic
820	C₂	C₄₃×#2428	1	1	yes	characteristic
821	C₂	C₄₃×#2445	1	1	yes	characteristic
822	C₂	C₄₃×#2448	1	1	yes	characteristic
823	C₂	C₄₃×#2490	1	1	yes	characteristic
824	C₂	C₄₃×#2491	1	1	yes	characteristic
825	C₂	C₄₃×#2512	1	1	yes	characteristic
826	C₂	C₄₃×#2513	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₃×#389	C₂	semidirect
5. C₂×C₄₃×#388	C₂	semidirect
6. C₂×C₄×C₄⋊C₄×C₄₃	C₂	semidirect
7. C₄₃×#1440	C₂	semidirect
8. C₄₃×#1439	C₂	semidirect
9. C₄₃×#1437	C₂	semidirect
10. C₄₃×C₄⋊#95	C₂	semidirect
11. C₄×#95×C₄₃	C₂	semidirect
29. C₄₃×#390	C₄	semidirect
108. #95×C₄₃	D₄	semidirect
337. #14141	C₄₃	direct (N × H)
397. C₄×C₄₃	#388	semidirect
401. C₂×#389	C₂×C₄₃	semidirect
402. C₂×#388	C₂×C₄₃	semidirect
403. C₂×C₄×C₄⋊C₄	C₂×C₄₃	semidirect
404. #1440	C₂×C₄₃	semidirect
405. #1439	C₂×C₄₃	semidirect
406. #1437	C₂×C₄₃	semidirect
407. C₄⋊#95	C₂×C₄₃	semidirect
408. C₄×#95	C₂×C₄₃	semidirect
442. #390	C₄×C₄₃	semidirect
454. C₄₃	#14141	direct (N × H)
522. #95	D₄×C₄₃	semidirect
810. C₄	C₄₃×#388	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#390	2
C₂×C₄₃×#389	2
C₂×C₄₃×#388	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1440	2
C₄₃×#1439	2
C₄₃×#1437	2
C₄₃×C₄⋊#95	2
C₄×#95×C₄₃	2
#14141	43

Subgroups — C43×#14141 #24934158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#14141 #24934158