Subgroups — C₄₃×#34874 #24954891

Order 11008.

1992 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2612	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#2610	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2609	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2574	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2555	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#2531	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2529	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2476	C₂	1	2	yes	maximal, complemented
10	C₄₃×#2474	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₃×#2392	C₂	1	2	yes	maximal, complemented
14	C₄×#124×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#124×C₄₃	C₂	1	2	yes	maximal, complemented
16	C₄×#121×C₄₃	C₂	1	2	yes	maximal, complemented
17	C₄₃×#2298	C₂	1	2	yes	maximal, complemented
18	C₄₃×#2290	C₂	1	2	yes	maximal, complemented
19	C₄×#117×C₄₃	C₂	1	2	yes	maximal, complemented
20	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₃	C₂²	1	2	yes	—
22	C₂×#121×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₃	C₂²	1	2	yes	—
30	C₂×#117×C₄₃	C₂²	1	2	yes	—
31	C₂×#117×C₄₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
33	C₄₃×#400	C₂²	1	1	yes	characteristic
34	C₄₃×#400	C₂²	1	1	yes	characteristic
35	C₄₃×#398	C₂²	1	1	yes	characteristic
36	C₄₃×#398	C₂²	1	2	yes	—
37	C₄₃×#398	C₂²	1	2	yes	—
38	C₄₃×#398	C₂²	1	1	yes	characteristic
39	C₄₃×#397	C₂²	1	2	yes	—
40	C₄₃×#397	C₂²	1	2	yes	—
41	C₄₃×#396	C₂²	1	2	yes	—
42	C₄₃×#396	C₂²	1	2	yes	—
43	C₄₃×#395	C₂²	1	2	yes	—
44	C₄₃×#395	C₂²	1	1	yes	characteristic
45	C₄₃×#395	C₂²	1	1	yes	characteristic
46	C₄₃×#394	C₂²	1	2	yes	—
47	C₄₃×#394	C₂²	1	1	yes	characteristic
48	C₄₃×#394	C₂²	1	2	yes	—
49	C₄₃×#394	C₂²	1	2	yes	—
50	C₄₃×#394	C₂²	1	1	yes	characteristic
51	C₄₃×#393	C₂²	1	2	yes	—
52	C₄₃×#392	C₂²	1	2	yes	—
53	C₄₃×#391	C₂²	1	2	yes	—
54	C₄₃×#391	C₂²	1	1	yes	characteristic
55	C₄₃×#390	C₂²	1	1	yes	characteristic
56	C₄₃×#390	C₂²	1	2	yes	—
57	C₄₃×#390	C₂²	1	2	yes	—
58	C₄₃×#389	C₂²	1	2	yes	—
59	C₄₃×#388	C₂²	1	2	yes	—
60	C₄₃×#388	C₂²	1	2	yes	—
61	C₄₃×#388	C₂²	1	2	yes	—
62	C₄₃×#388	C₂²	1	2	yes	—
63	C₄₃×#388	C₂²	1	2	yes	—
64	C₄₃×#388	C₂²	1	2	yes	—
65	C₄₃×#388	C₂²	1	2	yes	—
66	C₄₃×#388	C₂²	1	2	yes	—
67	C₄₃×#388	C₂²	1	2	yes	—
68	C₄₃×#388	C₂²	1	2	yes	—
69	C₄₃×#388	C₂²	1	2	yes	—
70	C₄₃×#388	C₂²	1	2	yes	—
71	C₄₃×#388	C₂²	1	2	yes	—
72	C₄₃×#388	C₂²	1	2	yes	—
73	C₄₃×#387	C₂²	1	2	yes	—
74	C₄₃×#387	C₂²	1	2	yes	—
75	C₄₃×#387	C₂²	1	2	yes	—
76	C₄₃×#387	C₂²	1	2	yes	—
77	C₄₃×#387	C₂²	1	2	yes	—
78	C₄₃×#387	C₂²	1	2	yes	—
79	C₄₃×#386	C₂²	1	2	yes	—
80	C₄₃×#386	C₂²	1	2	yes	—
81	C₄₃×#386	C₂²	1	2	yes	—
82	C₄₃×#386	C₂²	1	2	yes	—
83	C₄₃×#385	C₂²	1	2	yes	—
84	C₄₃×#385	C₂²	1	2	yes	—
85	C₄₃×#382	C₂²	1	1	yes	characteristic
86	C₄₃×#382	C₂²	1	2	yes	—
87	C₄₃×#380	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
93	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
101	C₄₃×#376	C₂²	1	2	yes	—
102	C₄₃×#376	C₂²	1	1	yes	characteristic
103	C₄₃×#376	C₂²	1	1	yes	characteristic
104	C₄₃×#376	C₂²	1	2	yes	—
105	C₄³×C₄₃	C₂²	1	1	yes	characteristic
106	C₄³×C₄₃	C₂²	1	2	yes	—
107	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
117	#124×C₄₃	—	2	8	no	—
118	#124×C₄₃	—	2	4	no	—
119	#121×C₄₃	—	2	8	no	—
120	C₄×Q₈×C₄₃	—	4	2	no	—
121	C₄×Q₈×C₄₃	—	4	2	no	—
122	C₄×D₄×C₄₃	—	2	8	no	—
123	C₄×D₄×C₄₃	—	4	2	no	—
124	C₄×D₄×C₄₃	—	4	4	no	—
125	C₄×D₄×C₄₃	—	4	2	no	—
126	#117×C₄₃	—	2	8	no	—
127	#117×C₄₃	—	2	8	no	—
128	#117×C₄₃	—	2	8	no	—
129	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₄₃	—	2	8	no	—
167	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
183	#95×C₄₃	C₂³	1	2	yes	—
184	#95×C₄₃	C₂³	1	2	yes	—
185	#95×C₄₃	C₂³	1	2	yes	—
186	#95×C₄₃	C₂³	1	2	yes	—
187	#95×C₄₃	C₂³	1	2	yes	—
188	#95×C₄₃	C₂³	1	2	yes	—
189	#95×C₄₃	C₂³	1	2	yes	—
190	#95×C₄₃	C₂³	1	2	yes	—
191	#95×C₄₃	C₂³	1	1	yes	characteristic
192	#95×C₄₃	C₂³	1	2	yes	—
193	#95×C₄₃	C₂³	1	1	yes	characteristic
194	#95×C₄₃	C₂³	1	2	yes	—
195	#95×C₄₃	C₂³	1	1	yes	characteristic
196	#95×C₄₃	C₂³	1	1	yes	characteristic
197	#95×C₄₃	C₂³	1	2	yes	—
198	#95×C₄₃	C₂³	1	2	yes	—
199	#95×C₄₃	C₂³	1	2	yes	—
200	#95×C₄₃	C₂³	1	2	yes	—
201	#95×C₄₃	C₂³	1	2	yes	—
202	#95×C₄₃	C₂³	1	2	yes	—
203	#95×C₄₃	C₂³	1	2	yes	—
204	#95×C₄₃	C₂³	1	2	yes	—
205	#95×C₄₃	C₂³	1	2	yes	—
206	#95×C₄₃	C₂³	1	2	yes	—
207	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
208	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₄₃	—	2	4	no	—
210	C₂×Q₈×C₄₃	—	2	2	no	—
211	C₂×Q₈×C₄₃	—	4	1	no	—
212	C₂×Q₈×C₄₃	—	4	1	no	—
213	C₂×Q₈×C₄₃	—	4	1	no	—
214	C₂×D₄×C₄₃	—	2	4	no	—
215	C₂×D₄×C₄₃	—	2	4	no	—
216	C₂×D₄×C₄₃	—	2	2	no	—
217	C₂×D₄×C₄₃	—	2	4	no	—
218	C₂×D₄×C₄₃	—	2	4	no	—
219	C₂×D₄×C₄₃	—	2	4	no	—
220	C₂×D₄×C₄₃	—	4	1	no	—
221	C₂×D₄×C₄₃	—	4	2	no	—
222	C₂×D₄×C₄₃	—	4	1	no	—
223	C₂×D₄×C₄₃	—	4	2	no	—
224	C₂×D₄×C₄₃	—	4	1	no	—
225	C₂²×C₄×C₄₃	—	2	4	no	—
226	C₂²×C₄×C₄₃	—	2	4	no	—
227	C₂²×C₄×C₄₃	—	2	4	no	—
228	C₂²×C₄×C₄₃	—	2	4	no	—
229	C₂²×C₄×C₄₃	—	2	4	no	—
230	C₂²×C₄×C₄₃	—	2	4	no	—
231	C₂²×C₄×C₄₃	—	2	4	no	—
232	C₂²×C₄×C₄₃	—	2	4	no	—
233	C₂²×C₄×C₄₃	—	2	4	no	—
234	C₂²×C₄×C₄₃	—	2	4	no	—
235	C₂²×C₄×C₄₃	—	2	4	no	—
236	C₂²×C₄×C₄₃	—	4	2	no	—
237	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₄⋊C₄×C₄₃	—	2	4	no	—
255	C₄⋊C₄×C₄₃	—	2	4	no	—
256	C₄⋊C₄×C₄₃	—	2	4	no	—
257	C₄⋊C₄×C₄₃	—	2	4	no	—
258	C₄⋊C₄×C₄₃	—	2	4	no	—
259	C₄⋊C₄×C₄₃	—	2	4	no	—
260	C₄⋊C₄×C₄₃	—	2	4	no	—
261	C₄⋊C₄×C₄₃	—	2	4	no	—
262	C₄⋊C₄×C₄₃	—	4	2	no	—
263	C₄⋊C₄×C₄₃	—	4	2	no	—
264	C₄⋊C₄×C₄₃	—	4	1	no	—
265	C₄⋊C₄×C₄₃	—	4	1	no	—
266	C₄⋊C₄×C₄₃	—	4	2	no	—
267	C₄⋊C₄×C₄₃	—	4	1	no	—
268	C₄⋊C₄×C₄₃	—	4	1	no	—
269	C₄⋊C₄×C₄₃	—	4	1	no	—
270	C₄⋊C₄×C₄₃	—	4	1	no	—
271	C₂²⋊C₄×C₄₃	—	2	4	no	—
272	C₂²⋊C₄×C₄₃	—	2	4	no	—
273	C₂²⋊C₄×C₄₃	—	2	4	no	—
274	C₂²⋊C₄×C₄₃	—	2	4	no	—
275	C₂²⋊C₄×C₄₃	—	2	4	no	—
276	C₂²⋊C₄×C₄₃	—	2	4	no	—
277	C₂²⋊C₄×C₄₃	—	2	4	no	—
278	C₂²⋊C₄×C₄₃	—	2	4	no	—
279	C₂²⋊C₄×C₄₃	—	2	4	no	—
280	C₂²⋊C₄×C₄₃	—	2	4	no	—
281	C₂²⋊C₄×C₄₃	—	2	4	no	—
282	C₂²⋊C₄×C₄₃	—	2	4	no	—
283	C₂²⋊C₄×C₄₃	—	2	4	no	—
284	C₂²⋊C₄×C₄₃	—	4	2	no	—
285	C₂²⋊C₄×C₄₃	—	4	2	no	—
286	C₂²⋊C₄×C₄₃	—	4	2	no	—
287	C₂²⋊C₄×C₄₃	—	4	2	no	—
288	C₂²⋊C₄×C₄₃	—	4	2	no	—
289	C₂²⋊C₄×C₄₃	—	4	2	no	—
290	C₂²⋊C₄×C₄₃	#41	1	8	yes	—
291	C₄²×C₄₃	—	2	4	no	—
292	C₄²×C₄₃	—	2	4	no	—
293	C₄²×C₄₃	—	2	4	no	—
294	C₄²×C₄₃	—	2	4	no	—
295	C₄²×C₄₃	—	2	4	no	—
296	C₄²×C₄₃	—	2	4	no	—
297	C₄²×C₄₃	—	2	4	no	—
298	C₄²×C₄₃	—	2	4	no	—
299	C₄²×C₄₃	—	2	2	no	—
300	C₄²×C₄₃	—	2	4	no	—
301	C₄²×C₄₃	—	2	2	no	—
302	C₄²×C₄₃	—	2	2	no	—
303	C₄²×C₄₃	—	4	1	no	—
304	C₄²×C₄₃	—	4	2	no	—
305	C₄²×C₄₃	#41	1	8	yes	—
306	C₄²×C₄₃	#41	1	4	yes	—
307	C₂³×C₄₃	—	2	2	no	—
308	C₂³×C₄₃	—	2	2	no	—
309	C₂³×C₄₃	—	2	2	no	—
310	C₂³×C₄₃	—	2	2	no	—
311	C₂³×C₄₃	—	2	2	no	—
312	C₂³×C₄₃	—	2	2	no	—
313	C₂³×C₄₃	—	2	2	no	—
314	C₂³×C₄₃	—	2	2	no	—
315	C₂³×C₄₃	—	2	2	no	—
316	C₂³×C₄₃	—	2	2	no	—
317	C₂³×C₄₃	—	2	2	no	—
318	C₂³×C₄₃	—	2	2	no	—
319	C₂³×C₄₃	—	2	2	no	—
320	C₂³×C₄₃	C₂×#41	1	4	yes	—
321	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
322	Q₈×C₄₃	—	4	4	no	—
323	Q₈×C₄₃	—	4	4	no	—
324	D₄×C₄₃	—	4	8	no	—
325	D₄×C₄₃	—	4	8	no	—
326	D₄×C₄₃	—	4	4	no	—
327	D₄×C₄₃	—	4	4	no	—
328	C₂×C₄×C₄₃	—	2	16	no	—
329	C₂×C₄×C₄₃	—	2	2	no	—
330	C₂×C₄×C₄₃	—	2	2	no	—
331	C₂×C₄×C₄₃	—	2	2	no	—
332	C₂×C₄×C₄₃	—	2	2	no	—
333	C₂×C₄×C₄₃	—	2	2	no	—
334	C₂×C₄×C₄₃	—	2	2	no	—
335	C₂×C₄×C₄₃	—	2	2	no	—
336	C₂×C₄×C₄₃	—	2	1	no	—
337	C₂×C₄×C₄₃	—	2	2	no	—
338	C₂×C₄×C₄₃	—	2	2	no	—
339	C₂×C₄×C₄₃	—	2	1	no	—
340	C₂×C₄×C₄₃	—	2	2	no	—
341	C₂×C₄×C₄₃	—	2	2	no	—
342	C₂×C₄×C₄₃	—	2	2	no	—
343	C₂×C₄×C₄₃	—	2	2	no	—
344	C₂×C₄×C₄₃	—	2	2	no	—
345	C₂×C₄×C₄₃	—	2	2	no	—
346	C₂×C₄×C₄₃	—	2	2	no	—
347	C₂×C₄×C₄₃	—	2	2	no	—
348	C₂×C₄×C₄₃	—	2	2	no	—
349	C₂×C₄×C₄₃	—	2	1	no	—
350	C₂×C₄×C₄₃	—	2	1	no	—
351	C₂×C₄×C₄₃	—	2	2	no	—
352	C₂×C₄×C₄₃	—	2	2	no	—
353	C₂×C₄×C₄₃	—	2	2	no	—
354	C₂×C₄×C₄₃	—	2	2	no	—
355	C₂×C₄×C₄₃	—	2	2	no	—
356	C₂×C₄×C₄₃	—	2	2	no	—
357	C₂×C₄×C₄₃	—	2	1	no	—
358	C₂×C₄×C₄₃	—	2	1	no	—
359	C₂×C₄×C₄₃	—	2	1	no	—
360	C₂×C₄×C₄₃	—	2	1	no	—
361	C₂×C₄×C₄₃	—	2	1	no	—
362	C₂×C₄×C₄₃	—	2	2	no	—
363	C₂×C₄×C₄₃	—	2	2	no	—
364	C₂×C₄×C₄₃	—	2	2	no	—
365	C₂×C₄×C₄₃	—	2	2	no	—
366	C₂×C₄×C₄₃	—	2	1	no	—
367	C₂×C₄×C₄₃	—	2	1	no	—
368	C₂×C₄×C₄₃	—	4	8	no	—
369	C₂×C₄×C₄₃	—	4	8	no	—
370	C₂×C₄×C₄₃	—	4	8	no	—
371	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
372	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
373	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
374	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
375	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
376	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
377	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
378	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
379	#34874	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
380	C₂²×C₄₃	—	2	4	no	—
381	C₂²×C₄₃	—	2	4	no	—
382	C₂²×C₄₃	—	2	4	no	—
383	C₂²×C₄₃	—	4	2	no	—
384	C₂²×C₄₃	—	4	2	no	—
385	C₂²×C₄₃	—	4	2	no	—
386	C₂²×C₄₃	—	4	2	no	—
387	C₂²×C₄₃	—	4	2	no	—
388	C₂²×C₄₃	—	4	2	no	—
389	C₂²×C₄₃	—	4	2	no	—
390	C₂²×C₄₃	—	4	2	no	—
391	C₂²×C₄₃	—	4	2	no	—
392	C₂²×C₄₃	—	4	2	no	—
393	C₂²×C₄₃	—	4	2	no	—
394	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₄₃	C₂²×#41	1	2	yes	—
396	C₂²×C₄₃	C₂²×#41	1	2	yes	—
397	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²×C₄₃	#585	1	1	yes	characteristic
399	C₄×C₄₃	—	2	4	no	—
400	C₄×C₄₃	—	2	4	no	—
401	C₄×C₄₃	—	2	2	no	—
402	C₄×C₄₃	—	2	4	no	—
403	C₄×C₄₃	—	2	4	no	—
404	C₄×C₄₃	—	2	4	no	—
405	C₄×C₄₃	—	4	2	no	—
406	C₄×C₄₃	—	4	2	no	—
407	C₄×C₄₃	—	4	1	no	—
408	C₄×C₄₃	—	4	1	no	—
409	C₄×C₄₃	—	4	2	no	—
410	C₄×C₄₃	—	4	2	no	—
411	C₄×C₄₃	—	4	2	no	—
412	C₄×C₄₃	—	4	1	no	—
413	C₄×C₄₃	—	4	1	no	—
414	C₄×C₄₃	—	4	1	no	—
415	C₄×C₄₃	#555	1	4	yes	—
416	#2612	C₂×C₄₃	1	1	yes	characteristic, complemented
417	#2610	C₂×C₄₃	1	2	yes	complemented
418	#2609	C₂×C₄₃	1	1	yes	characteristic, complemented
419	#2593	C₂×C₄₃	1	1	yes	characteristic, complemented
420	#2574	C₂×C₄₃	1	2	yes	complemented
421	#2555	C₂×C₄₃	1	1	yes	characteristic
422	#2531	C₂×C₄₃	1	2	yes	complemented
423	#2529	C₂×C₄₃	1	2	yes	complemented
424	#2476	C₂×C₄₃	1	2	yes	complemented
425	#2474	C₂×C₄₃	1	2	yes	complemented
426	#2399	C₂×C₄₃	1	1	yes	characteristic, complemented
427	#2398	C₂×C₄₃	1	1	yes	characteristic, complemented
428	#2392	C₂×C₄₃	1	2	yes	complemented
429	C₄×#124	C₂×C₄₃	1	1	yes	characteristic, complemented
430	C₄×#124	C₂×C₄₃	1	2	yes	complemented
431	C₄×#121	C₂×C₄₃	1	2	yes	complemented
432	#2298	C₂×C₄₃	1	2	yes	complemented
433	#2290	C₂×C₄₃	1	2	yes	complemented
434	C₄×#117	C₂×C₄₃	1	2	yes	complemented
435	C₂×C₄₃	—	4	4	no	—
436	C₂×C₄₃	—	8	2	no	—
437	C₂×C₄₃	#3444	1	2	yes	—
438	C₂×C₄₃	#3460	1	1	yes	characteristic
439	C₂×C₄₃	C₂×#555	1	1	yes	characteristic
440	C₂×C₄₃	#3475	1	2	yes	—
441	C₂×C₄₃	#3481	1	1	yes	characteristic
442	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
443	C₂×#124	C₂²×C₄₃	1	2	yes	—
444	C₂×#121	C₂²×C₄₃	1	2	yes	—
445	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
451	C₂×#117	C₂²×C₄₃	1	2	yes	—
452	C₂×#117	C₂²×C₄₃	1	2	yes	—
453	C₂×#117	C₂²×C₄₃	1	2	yes	—
454	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
455	#400	C₂²×C₄₃	1	1	yes	characteristic
456	#400	C₂²×C₄₃	1	1	yes	characteristic
457	#398	C₂²×C₄₃	1	2	yes	—
458	#398	C₂²×C₄₃	1	1	yes	characteristic
459	#398	C₂²×C₄₃	1	2	yes	—
460	#398	C₂²×C₄₃	1	1	yes	characteristic
461	#397	C₂²×C₄₃	1	2	yes	—
462	#397	C₂²×C₄₃	1	2	yes	—
463	#396	C₂²×C₄₃	1	2	yes	—
464	#396	C₂²×C₄₃	1	2	yes	—
465	#395	C₂²×C₄₃	1	2	yes	—
466	#395	C₂²×C₄₃	1	1	yes	characteristic
467	#395	C₂²×C₄₃	1	1	yes	characteristic
468	#394	C₂²×C₄₃	1	2	yes	—
469	#394	C₂²×C₄₃	1	1	yes	characteristic
470	#394	C₂²×C₄₃	1	2	yes	—
471	#394	C₂²×C₄₃	1	2	yes	—
472	#394	C₂²×C₄₃	1	1	yes	characteristic
473	#393	C₂²×C₄₃	1	2	yes	—
474	#392	C₂²×C₄₃	1	2	yes	—
475	#391	C₂²×C₄₃	1	1	yes	characteristic
476	#391	C₂²×C₄₃	1	2	yes	—
477	#390	C₂²×C₄₃	1	1	yes	characteristic
478	#390	C₂²×C₄₃	1	2	yes	—
479	#390	C₂²×C₄₃	1	2	yes	—
480	#389	C₂²×C₄₃	1	2	yes	—
481	#388	C₂²×C₄₃	1	2	yes	—
482	#388	C₂²×C₄₃	1	2	yes	—
483	#388	C₂²×C₄₃	1	2	yes	—
484	#388	C₂²×C₄₃	1	2	yes	—
485	#388	C₂²×C₄₃	1	2	yes	—
486	#388	C₂²×C₄₃	1	2	yes	—
487	#388	C₂²×C₄₃	1	2	yes	—
488	#388	C₂²×C₄₃	1	2	yes	—
489	#388	C₂²×C₄₃	1	2	yes	—
490	#388	C₂²×C₄₃	1	2	yes	—
491	#388	C₂²×C₄₃	1	2	yes	—
492	#388	C₂²×C₄₃	1	2	yes	—
493	#388	C₂²×C₄₃	1	2	yes	—
494	#388	C₂²×C₄₃	1	2	yes	—
495	#387	C₂²×C₄₃	1	2	yes	—
496	#387	C₂²×C₄₃	1	2	yes	—
497	#387	C₂²×C₄₃	1	2	yes	—
498	#387	C₂²×C₄₃	1	2	yes	—
499	#387	C₂²×C₄₃	1	2	yes	—
500	#387	C₂²×C₄₃	1	2	yes	—
501	#386	C₂²×C₄₃	1	2	yes	—
502	#386	C₂²×C₄₃	1	2	yes	—
503	#386	C₂²×C₄₃	1	2	yes	—
504	#386	C₂²×C₄₃	1	2	yes	—
505	#385	C₂²×C₄₃	1	2	yes	—
506	#385	C₂²×C₄₃	1	2	yes	—
507	#382	C₂²×C₄₃	1	2	yes	—
508	#382	C₂²×C₄₃	1	1	yes	characteristic
509	#380	C₂²×C₄₃	1	2	yes	—
510	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
512	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
515	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
516	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
517	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
523	#376	C₂²×C₄₃	1	2	yes	—
524	#376	C₂²×C₄₃	1	1	yes	characteristic
525	#376	C₂²×C₄₃	1	1	yes	characteristic
526	#376	C₂²×C₄₃	1	2	yes	—
527	C₄³	C₂²×C₄₃	1	1	yes	characteristic
528	C₄³	C₂²×C₄₃	1	2	yes	—
529	C₄₃	#34874	1	1	yes	characteristic, direct product factor, Sylow
530	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
533	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
534	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
537	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
538	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
540	#124	—	2	8	no	—
541	#124	—	2	4	no	—
542	#121	—	2	8	no	—
543	C₄×Q₈	—	4	2	no	—
544	C₄×Q₈	—	4	2	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	4	2	no	—
547	C₄×D₄	—	4	4	no	—
548	C₄×D₄	—	4	2	no	—
549	#117	—	2	8	no	—
550	#117	—	2	8	no	—
551	#117	—	2	8	no	—
552	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
589	C₂×C₄²	—	2	8	no	—
590	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
592	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
593	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
596	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
600	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
601	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
604	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
606	#95	C₂³×C₄₃	1	2	yes	—
607	#95	C₂³×C₄₃	1	2	yes	—
608	#95	C₂³×C₄₃	1	2	yes	—
609	#95	C₂³×C₄₃	1	2	yes	—
610	#95	C₂³×C₄₃	1	2	yes	—
611	#95	C₂³×C₄₃	1	2	yes	—
612	#95	C₂³×C₄₃	1	2	yes	—
613	#95	C₂³×C₄₃	1	2	yes	—
614	#95	C₂³×C₄₃	1	1	yes	characteristic
615	#95	C₂³×C₄₃	1	2	yes	—
616	#95	C₂³×C₄₃	1	1	yes	characteristic
617	#95	C₂³×C₄₃	1	2	yes	—
618	#95	C₂³×C₄₃	1	1	yes	characteristic
619	#95	C₂³×C₄₃	1	1	yes	characteristic
620	#95	C₂³×C₄₃	1	2	yes	—
621	#95	C₂³×C₄₃	1	2	yes	—
622	#95	C₂³×C₄₃	1	2	yes	—
623	#95	C₂³×C₄₃	1	2	yes	—
624	#95	C₂³×C₄₃	1	2	yes	—
625	#95	C₂³×C₄₃	1	2	yes	—
626	#95	C₂³×C₄₃	1	2	yes	—
627	#95	C₂³×C₄₃	1	2	yes	—
628	#95	C₂³×C₄₃	1	2	yes	—
629	#95	C₂³×C₄₃	1	2	yes	—
630	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
631	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
632	C₂×Q₈	—	2	4	no	—
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	4	1	no	—
635	C₂×Q₈	—	4	1	no	—
636	C₂×Q₈	—	4	1	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	1	no	—
645	C₂×D₄	—	4	1	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	1	no	—
687	C₄⋊C₄	—	4	1	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	#41×C₄₃	1	8	yes	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	4	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	4	no	—
721	C₄²	—	2	4	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	4	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	4	1	no	—
727	C₄²	—	4	2	no	—
728	C₄²	#41×C₄₃	1	8	yes	—
729	C₄²	#41×C₄₃	1	4	yes	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	C₂×#41×C₄₃	1	4	yes	—
744	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
745	Q₈	—	4	4	no	—
746	Q₈	—	4	4	no	—
747	D₄	—	4	8	no	—
748	D₄	—	4	8	no	—
749	D₄	—	4	4	no	—
750	D₄	—	4	4	no	—
751	C₂×C₄	—	2	16	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	8	no	—
794	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
795	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
796	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
797	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
798	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
799	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
800	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
801	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	4	no	—
804	C₂²	—	2	4	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	C₂²×#41×C₄₃	1	1	yes	characteristic
817	C₂²	C₂²×#41×C₄₃	1	2	yes	—
818	C₂²	C₂²×#41×C₄₃	1	2	yes	—
819	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
820	C₂²	C₄₃×#585	1	1	yes	characteristic
821	C₄	—	2	4	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	4	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	C₄₃×#555	1	4	yes	—
838	C₂	—	4	4	no	—
839	C₂	—	8	2	no	—
840	C₂	C₄₃×#3444	1	2	yes	—
841	C₂	C₄₃×#3460	1	1	yes	characteristic
842	C₂	C₂×C₄₃×#555	1	1	yes	characteristic
843	C₂	C₄₃×#3475	1	2	yes	—
844	C₂	C₄₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₃
socle	C₂³×C₄₃	C₂⁵
prime radical	C₄₃×#2555	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#2612	C₂	semidirect
2. C₄₃×#2610	C₂	semidirect
3. C₄₃×#2609	C₂	semidirect
4. C₄₃×#2593	C₂	semidirect
5. C₄₃×#2574	C₂	semidirect
7. C₄₃×#2531	C₂	semidirect
8. C₄₃×#2529	C₂	semidirect
9. C₄₃×#2476	C₂	semidirect
10. C₄₃×#2474	C₂	semidirect
11. C₄₃×#2399	C₂	semidirect
12. C₄₃×#2398	C₂	semidirect
13. C₄₃×#2392	C₂	semidirect
14. C₄×#124×C₄₃	C₂	semidirect
15. C₄×#124×C₄₃	C₂	semidirect
16. C₄×#121×C₄₃	C₂	semidirect
17. C₄₃×#2298	C₂	semidirect
18. C₄₃×#2290	C₂	semidirect
19. C₄×#117×C₄₃	C₂	semidirect
379. #34874	C₄₃	direct (N × H)
416. #2612	C₂×C₄₃	semidirect
417. #2610	C₂×C₄₃	semidirect
418. #2609	C₂×C₄₃	semidirect
419. #2593	C₂×C₄₃	semidirect
420. #2574	C₂×C₄₃	semidirect
422. #2531	C₂×C₄₃	semidirect
423. #2529	C₂×C₄₃	semidirect
424. #2476	C₂×C₄₃	semidirect
425. #2474	C₂×C₄₃	semidirect
426. #2399	C₂×C₄₃	semidirect
427. #2398	C₂×C₄₃	semidirect
428. #2392	C₂×C₄₃	semidirect
429. C₄×#124	C₂×C₄₃	semidirect
430. C₄×#124	C₂×C₄₃	semidirect
431. C₄×#121	C₂×C₄₃	semidirect
432. #2298	C₂×C₄₃	semidirect
433. #2290	C₂×C₄₃	semidirect
434. C₄×#117	C₂×C₄₃	semidirect
529. C₄₃	#34874	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#2612	2
C₄₃×#2610	2
C₄₃×#2609	2
C₄₃×#2593	2
C₄₃×#2574	2
C₄₃×#2555	2
C₄₃×#2531	2
C₄₃×#2529	2
C₄₃×#2476	2
C₄₃×#2474	2
C₄₃×#2399	2
C₄₃×#2398	2
C₄₃×#2392	2
C₄×#124×C₄₃	2
C₄×#121×C₄₃	2
C₄₃×#2298	2
C₄₃×#2290	2
C₄×#117×C₄₃	2
#34874	43

Subgroups — C43×#34874 #24954891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#34874 #24954891