Subgroups — #25107704

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582977	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582863	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135394	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135390	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135210	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135203	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135203	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135203	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134893	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134893	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134893	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134780	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134505	C₂	1	1	yes	maximal, characteristic, complemented
14	#19134379	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#120×C₄₃	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10621877	C₂²	1	1	yes	characteristic
17	C₂²×#10621877	C₂²	1	1	yes	characteristic
18	C₂²×#10621877	C₂²	1	1	yes	characteristic, complemented
19	#14582977	—	2	4	no	—
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
23	#14582863	—	2	4	no	—
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×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13063236	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	#14582654	C₂²	1	1	yes	characteristic, complemented
41	#14582654	C₂²	1	1	yes	characteristic, complemented
42	#14582654	C₂²	1	1	yes	characteristic, complemented
43	#14582654	C₂²	1	1	yes	characteristic, complemented
44	#14582654	C₂²	1	1	yes	characteristic, complemented
45	#14582654	C₂²	1	1	yes	characteristic, complemented
46	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#120×C₄₃	C₄	1	1	yes	characteristic
48	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
51	C₄₃×#386	C₄	1	1	yes	characteristic
52	C₄₃×#386	C₄	1	1	yes	characteristic
53	C₄₃×#386	C₄	1	1	yes	characteristic
54	C₄₃×#385	C₄	1	1	yes	characteristic
55	C₄₃×#385	C₄	1	1	yes	characteristic
56	C₄₃×#385	C₄	1	1	yes	characteristic
57	C₄₃×#379	C₄	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
61	C₂×#10621877	—	2	2	no	—
62	C₂×#10621877	—	2	2	no	—
63	C₂×#10621877	—	4	1	no	—
64	C₂×#10621877	—	4	1	no	—
65	C₂×#10621877	—	4	1	no	—
66	C₂×#10621877	—	4	1	no	—
67	C₂×#10621877	—	4	1	no	—
68	C₂×#10621877	—	4	1	no	—
69	C₂×#10621877	D₄	1	4	yes	complemented
70	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
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	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
79	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
80	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
81	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
82	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
83	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
84	C₂²⋊(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)	—	4	1	no	—
89	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
90	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
91	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
92	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
93	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
94	#13063236	—	4	1	no	—
95	C₄×C₄₃⋊C₈	—	2	2	no	—
96	C₄×C₄₃⋊C₈	—	4	1	no	—
97	C₂⁵×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₂³×C₄×C₄₃	—	2	2	no	—
102	C₂³×C₄×C₄₃	—	2	2	no	—
103	C₂³×C₄×C₄₃	—	4	1	no	—
104	C₂³×C₄×C₄₃	—	4	1	no	—
105	C₂³×C₄×C₄₃	—	4	1	no	—
106	C₂³×C₄×C₄₃	—	4	1	no	—
107	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
108	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
109	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
110	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
114	#120×C₄₃	—	2	4	no	—
115	C₄×D₄×C₄₃	—	2	2	no	—
116	C₄×D₄×C₄₃	—	2	2	no	—
117	C₄×D₄×C₄₃	—	4	1	no	—
118	C₄×D₄×C₄₃	—	4	1	no	—
119	C₄×D₄×C₄₃	—	4	1	no	—
120	C₄×D₄×C₄₃	—	4	1	no	—
121	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊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×C₄²×C₄₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
139	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
140	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
141	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
142	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
143	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
144	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
145	C₂⁴×C₄₃	—	2	2	no	—
146	C₂⁴×C₄₃	—	2	2	no	—
147	C₂⁴×C₄₃	—	2	2	no	—
148	C₂⁴×C₄₃	—	4	1	no	—
149	C₂⁴×C₄₃	—	4	1	no	—
150	C₂⁴×C₄₃	—	4	1	no	—
151	C₂⁴×C₄₃	—	4	1	no	—
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	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₄₃	—	2	2	no	—
157	C₂×D₄×C₄₃	—	2	2	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	—	4	1	no	—
162	C₂×D₄×C₄₃	—	4	1	no	—
163	C₂×D₄×C₄₃	—	4	1	no	—
164	C₂×D₄×C₄₃	—	4	1	no	—
165	C₂²×C₄×C₄₃	—	2	1	no	—
166	C₂²×C₄×C₄₃	—	2	1	no	—
167	C₂²×C₄×C₄₃	—	2	1	no	—
168	C₂²×C₄×C₄₃	—	2	1	no	—
169	C₂²×C₄×C₄₃	—	2	2	no	—
170	C₂²×C₄×C₄₃	—	2	2	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	1	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	1	no	—
183	C₂²×C₄×C₄₃	—	2	1	no	—
184	C₂²×C₄×C₄₃	—	2	1	no	—
185	C₂²×C₄×C₄₃	—	2	1	no	—
186	C₂²×C₄×C₄₃	—	2	1	no	—
187	C₂²×C₄×C₄₃	—	2	1	no	—
188	C₂²×C₄×C₄₃	—	2	1	no	—
189	C₂²×C₄×C₄₃	—	2	2	no	—
190	C₂²×C₄×C₄₃	—	4	1	no	—
191	C₂²×C₄×C₄₃	—	4	1	no	—
192	C₂²×C₄×C₄₃	—	4	1	no	—
193	C₂²×C₄×C₄₃	—	4	1	no	—
194	C₂²×C₄×C₄₃	—	4	1	no	—
195	C₂²×C₄×C₄₃	—	4	1	no	—
196	C₂²×C₄×C₄₃	—	4	4	no	—
197	C₂²×C₄×C₄₃	—	4	4	no	—
198	C₂²×C₄×C₄₃	—	4	4	no	—
199	C₂²×C₄×C₄₃	—	4	4	no	—
200	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₄₃	#41	1	2	yes	—
212	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
213	C₄⋊C₄×C₄₃	—	2	2	no	—
214	C₄⋊C₄×C₄₃	—	4	1	no	—
215	C₄⋊C₄×C₄₃	—	4	1	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	—	4	1	no	—
222	C₂²⋊C₄×C₄₃	—	4	1	no	—
223	C₂²⋊C₄×C₄₃	—	4	1	no	—
224	C₂²⋊C₄×C₄₃	—	4	1	no	—
225	C₂²⋊C₄×C₄₃	—	4	1	no	—
226	C₂²⋊C₄×C₄₃	—	4	1	no	—
227	C₂²⋊C₄×C₄₃	M₁₆	1	4	yes	complemented
228	C₄²×C₄₃	—	2	1	no	—
229	C₄²×C₄₃	—	2	1	no	—
230	C₄²×C₄₃	—	2	1	no	—
231	C₄²×C₄₃	—	2	1	no	—
232	C₄²×C₄₃	—	2	1	no	—
233	C₄²×C₄₃	—	2	1	no	—
234	#10621877	—	4	4	no	—
235	#10621877	—	4	4	no	—
236	#10621877	—	4	4	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	—	2	1	no	—
257	C₂×C₄₃⋊C₈	—	2	1	no	—
258	C₂×C₄₃⋊C₈	—	2	1	no	—
259	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
260	C₂×C₄₃⋊C₈	C₂×D₄	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	—	2	1	no	—
279	C₂³×C₄₃	—	2	1	no	—
280	C₂³×C₄₃	—	2	1	no	—
281	C₂³×C₄₃	—	2	1	no	—
282	C₂³×C₄₃	—	2	1	no	—
283	C₂³×C₄₃	—	2	1	no	—
284	C₂³×C₄₃	—	2	1	no	—
285	C₂³×C₄₃	—	2	1	no	—
286	C₂³×C₄₃	—	4	4	no	—
287	C₂³×C₄₃	—	4	4	no	—
288	C₂³×C₄₃	—	4	4	no	—
289	C₂³×C₄₃	—	4	4	no	—
290	C₂³×C₄₃	—	4	4	no	—
291	C₂³×C₄₃	—	4	4	no	—
292	C₂³×C₄₃	—	4	4	no	—
293	C₂³×C₄₃	C₄×D₄	1	2	yes	—
294	C₂³×C₄₃	C₂×M₁₆	1	2	yes	—
295	C₂³×C₄₃	#131	1	2	yes	—
296	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
297	D₄×C₄₃	—	4	4	no	—
298	D₄×C₄₃	—	4	4	no	—
299	D₄×C₄₃	—	4	4	no	—
300	C₂×C₄×C₄₃	—	2	1	no	—
301	C₂×C₄×C₄₃	—	2	1	no	—
302	C₂×C₄×C₄₃	—	2	1	no	—
303	C₂×C₄×C₄₃	—	2	1	no	—
304	C₂×C₄×C₄₃	—	2	1	no	—
305	C₂×C₄×C₄₃	—	2	1	no	—
306	C₂×C₄×C₄₃	—	2	2	no	—
307	C₂×C₄×C₄₃	—	2	2	no	—
308	C₂×C₄×C₄₃	—	2	2	no	—
309	C₂×C₄×C₄₃	—	2	2	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	—	2	1	no	—
324	C₂×C₄×C₄₃	—	2	1	no	—
325	C₂×C₄×C₄₃	—	2	1	no	—
326	C₂×C₄×C₄₃	—	2	1	no	—
327	C₂×C₄×C₄₃	—	2	1	no	—
328	C₂×C₄×C₄₃	—	2	1	no	—
329	C₂×C₄×C₄₃	—	2	1	no	—
330	C₂×C₄×C₄₃	—	2	1	no	—
331	C₂×C₄×C₄₃	—	4	4	no	—
332	C₂×C₄×C₄₃	—	4	4	no	—
333	C₂×C₄×C₄₃	—	4	4	no	—
334	C₂×C₄×C₄₃	—	4	1	no	—
335	C₂×C₄×C₄₃	—	4	1	no	—
336	C₂×C₄×C₄₃	—	4	1	no	—
337	C₂×C₄×C₄₃	—	4	1	no	—
338	C₂×C₄×C₄₃	—	4	1	no	—
339	C₂×C₄×C₄₃	—	4	1	no	—
340	C₂×C₄×C₄₃	—	4	1	no	—
341	C₂×C₄×C₄₃	—	4	1	no	—
342	C₂×C₄×C₄₃	—	4	1	no	—
343	C₂×C₄×C₄₃	—	4	1	no	—
344	C₂×C₄×C₄₃	—	4	1	no	—
345	C₂×C₄×C₄₃	—	4	1	no	—
346	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
347	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
348	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
349	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
355	C₄₃⋊C₈	—	2	2	no	—
356	C₄₃⋊C₈	—	2	2	no	—
357	C₄₃⋊C₈	—	4	1	no	—
358	C₄₃⋊C₈	—	4	1	no	—
359	C₄₃⋊C₈	—	4	1	no	—
360	C₄₃⋊C₈	—	4	1	no	—
361	C₄₃⋊C₈	—	4	1	no	—
362	C₄₃⋊C₈	—	4	1	no	—
363	#22038	—	43	1	no	maximal, Sylow
364	C₂²×C₄₃	—	2	2	no	—
365	C₂²×C₄₃	—	2	2	no	—
366	C₂²×C₄₃	—	2	2	no	—
367	C₂²×C₄₃	—	2	2	no	—
368	C₂²×C₄₃	—	2	2	no	—
369	C₂²×C₄₃	—	2	2	no	—
370	C₂²×C₄₃	—	2	2	no	—
371	C₂²×C₄₃	—	2	2	no	—
372	C₂²×C₄₃	—	2	2	no	—
373	C₂²×C₄₃	—	4	16	no	—
374	C₂²×C₄₃	—	4	1	no	—
375	C₂²×C₄₃	—	4	1	no	—
376	C₂²×C₄₃	—	4	1	no	—
377	C₂²×C₄₃	—	4	1	no	—
378	C₂²×C₄₃	—	4	1	no	—
379	C₂²×C₄₃	—	4	1	no	—
380	C₂²×C₄₃	—	4	1	no	—
381	C₂²×C₄₃	—	4	1	no	—
382	C₂²×C₄₃	—	4	1	no	—
383	C₂²×C₄₃	—	4	1	no	—
384	C₂²×C₄₃	—	4	1	no	—
385	C₂²×C₄₃	—	4	1	no	—
386	C₂²×C₄₃	—	4	1	no	—
387	C₂²×C₄₃	—	4	1	no	—
388	C₂²×C₄₃	—	4	1	no	—
389	C₂²×C₄₃	—	4	1	no	—
390	C₂²×C₄₃	—	4	1	no	—
391	C₂²×C₄₃	—	4	1	no	—
392	C₂²×C₄₃	—	4	1	no	—
393	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
394	C₂²×C₄₃	#518	1	1	yes	characteristic
395	C₂²×C₄₃	#518	1	1	yes	characteristic
396	C₂²×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
397	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
398	C₂²×C₄₃	#568	1	1	yes	characteristic
399	C₂²×C₄₃	#568	1	1	yes	characteristic
400	C₄×C₄₃	—	2	2	no	—
401	C₄×C₄₃	—	2	2	no	—
402	C₄×C₄₃	—	2	2	no	—
403	C₄×C₄₃	—	4	1	no	—
404	C₄×C₄₃	—	4	1	no	—
405	C₄×C₄₃	—	4	1	no	—
406	C₄×C₄₃	—	4	1	no	—
407	C₄×C₄₃	—	4	1	no	—
408	C₄×C₄₃	—	4	1	no	—
409	C₄×C₄₃	—	4	1	no	—
410	C₄×C₄₃	#534	1	1	yes	characteristic
411	C₄×C₄₃	#535	1	1	yes	characteristic
412	C₄×C₄₃	#538	1	1	yes	characteristic
413	C₄×C₄₃	#538	1	1	yes	characteristic
414	C₂×#436	—	43	1	no	—
415	C₂×#407	—	43	1	no	—
416	C₄×#120	D₄₃	1	1	yes	characteristic
417	#1955	—	43	1	no	—
418	#1954	—	43	1	no	—
419	#1924	—	43	1	no	—
420	#1923	—	43	1	no	—
421	#1923	—	43	1	no	—
422	#1923	—	43	1	no	—
423	#1870	—	43	1	no	—
424	#1870	—	43	1	no	—
425	#1870	—	43	1	no	—
426	#1851	—	43	1	no	—
427	#1779	—	43	1	no	—
428	#1753	—	43	1	no	—
429	C₂×C₄₃	—	4	2	no	—
430	C₂×C₄₃	—	4	2	no	—
431	C₂×C₄₃	—	4	2	no	—
432	C₂×C₄₃	—	8	1	no	—
433	C₂×C₄₃	#2321	1	1	yes	characteristic
434	C₂×C₄₃	#2933	1	1	yes	characteristic
435	C₂×C₄₃	D₄×M₁₆	1	1	yes	characteristic
436	C₂×C₄₃	#2974	1	1	yes	characteristic
437	C₂×C₄₃	#2975	1	1	yes	characteristic
438	C₂×C₄₃	#2976	1	1	yes	characteristic
439	C₂×C₄₃	#2978	1	1	yes	characteristic
440	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic
441	C₂²×M₁₆	—	43	1	no	—
442	C₂²×M₁₆	—	43	1	no	—
443	C₂²×M₁₆	—	43	1	no	—
444	C₂×#120	Dic₄₃	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
446	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
448	#436	—	86	4	no	—
449	C₂×C₄⋊C₈	—	43	1	no	—
450	C₂×C₄⋊C₈	—	43	1	no	—
451	C₂×C₄⋊C₈	—	43	1	no	—
452	#407	—	86	4	no	—
453	C₂×C₂²⋊C₈	—	43	1	no	—
454	C₂×C₂²⋊C₈	—	43	1	no	—
455	C₂×C₂²⋊C₈	—	43	1	no	—
456	C₂×C₂²⋊C₈	—	43	1	no	—
457	C₂×C₂²⋊C₈	—	43	1	no	—
458	C₂×C₂²⋊C₈	—	43	1	no	—
459	C₂×C₂²⋊C₈	—	43	1	no	—
460	C₂×C₂²⋊C₈	—	43	1	no	—
461	C₂×C₂²⋊C₈	—	43	1	no	—
462	C₂×C₂²⋊C₈	—	43	1	no	—
463	C₂×C₂²⋊C₈	—	43	1	no	—
464	C₂×C₂²⋊C₈	—	43	1	no	—
465	C₂×C₂²⋊C₈	—	43	1	no	—
466	C₂×#97	—	43	1	no	—
467	C₂×C₄×C₈	—	43	1	no	—
468	C₂×C₄×C₈	—	43	1	no	—
469	#386	Dic₄₃	1	1	yes	characteristic
470	#386	Dic₄₃	1	1	yes	characteristic
471	#386	Dic₄₃	1	1	yes	characteristic
472	#385	Dic₄₃	1	1	yes	characteristic
473	#385	Dic₄₃	1	1	yes	characteristic
474	#385	Dic₄₃	1	1	yes	characteristic
475	#379	Dic₄₃	1	1	yes	characteristic
476	C₄×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
479	#336	—	43	1	no	—
480	#336	—	43	1	no	—
481	#336	—	43	1	no	—
482	#336	—	43	1	no	—
483	#336	—	43	1	no	—
484	#336	—	43	1	no	—
485	C₄₃	#22038	1	1	yes	characteristic, complemented, Sylow
486	C₂⁵	C₂×Dic₄₃	1	1	yes	characteristic
487	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
488	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
489	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
490	C₂³×C₄	—	2	2	no	—
491	C₂³×C₄	—	2	2	no	—
492	C₂³×C₄	—	4	1	no	—
493	C₂³×C₄	—	4	1	no	—
494	C₂³×C₄	—	4	1	no	—
495	C₂³×C₄	—	4	1	no	—
496	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
497	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
498	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
499	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
500	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
501	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
502	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
503	C₂×M₁₆	—	43	4	no	—
504	C₂×M₁₆	—	86	2	no	—
505	C₂×M₁₆	—	86	2	no	—
506	C₂×M₁₆	—	172	1	no	—
507	C₂×M₁₆	—	172	1	no	—
508	C₂×M₁₆	—	172	1	no	—
509	C₂×M₁₆	—	172	1	no	—
510	C₂×M₁₆	—	172	1	no	—
511	C₂×M₁₆	—	172	1	no	—
512	C₂²×C₈	—	43	1	no	—
513	C₂²×C₈	—	43	1	no	—
514	C₂²×C₈	—	43	1	no	—
515	C₂²×C₈	—	43	1	no	—
516	C₂²×C₈	—	43	1	no	—
517	C₂²×C₈	—	43	1	no	—
518	C₂²×C₈	—	43	1	no	—
519	C₂²×C₈	—	43	1	no	—
520	#120	—	2	4	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	4	1	no	—
524	C₄×D₄	—	4	1	no	—
525	C₄×D₄	—	4	1	no	—
526	C₄×D₄	—	4	1	no	—
527	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
529	C₂×C₄⋊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×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
542	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
543	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
544	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
545	C₄⋊C₈	—	86	2	no	—
546	C₄⋊C₈	—	172	1	no	—
547	C₄⋊C₈	—	172	1	no	—
548	C₂²⋊C₈	—	86	2	no	—
549	C₂²⋊C₈	—	86	2	no	—
550	C₂²⋊C₈	—	86	2	no	—
551	C₂²⋊C₈	—	86	2	no	—
552	C₂²⋊C₈	—	86	2	no	—
553	C₂²⋊C₈	—	86	2	no	—
554	C₂²⋊C₈	—	86	2	no	—
555	C₂²⋊C₈	—	172	1	no	—
556	C₂²⋊C₈	—	172	1	no	—
557	C₂²⋊C₈	—	172	1	no	—
558	C₂²⋊C₈	—	172	1	no	—
559	C₂²⋊C₈	—	172	1	no	—
560	C₂²⋊C₈	—	172	1	no	—
561	#97	—	172	1	no	—
562	C₄×C₈	—	86	2	no	—
563	C₄×C₈	—	172	1	no	—
564	#95	C₂×Dic₄₃	1	1	yes	characteristic
565	#95	C₂×Dic₄₃	1	1	yes	characteristic
566	#95	C₂×Dic₄₃	1	1	yes	characteristic
567	#95	C₂×Dic₄₃	1	1	yes	characteristic
568	#95	C₂×Dic₄₃	1	1	yes	characteristic
569	#95	C₂×Dic₄₃	1	1	yes	characteristic
570	C₂⁴	—	2	2	no	—
571	C₂⁴	—	2	2	no	—
572	C₂⁴	—	2	2	no	—
573	C₂⁴	—	4	1	no	—
574	C₂⁴	—	4	1	no	—
575	C₂⁴	—	4	1	no	—
576	C₂⁴	—	4	1	no	—
577	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
578	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
579	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
580	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	4	1	no	—
618	C₂²×C₄	—	4	1	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	D₄×D₄₃	1	2	yes	—
626	C₂²×C₄	#10621900	1	2	yes	—
627	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
628	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
629	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
630	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
631	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
632	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
633	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
634	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
635	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
636	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
637	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
638	M₁₆	—	172	4	no	—
639	M₁₆	—	172	4	no	—
640	M₁₆	—	172	4	no	—
641	C₂×C₈	—	43	2	no	—
642	C₂×C₈	—	43	2	no	—
643	C₂×C₈	—	86	1	no	—
644	C₂×C₈	—	86	1	no	—
645	C₂×C₈	—	86	1	no	—
646	C₂×C₈	—	86	1	no	—
647	C₂×C₈	—	86	1	no	—
648	C₂×C₈	—	86	1	no	—
649	C₂×C₈	—	86	1	no	—
650	C₂×C₈	—	86	1	no	—
651	C₂×C₈	—	86	1	no	—
652	C₂×C₈	—	86	1	no	—
653	C₂×C₈	—	86	1	no	—
654	C₂×C₈	—	86	1	no	—
655	C₂×C₈	—	86	1	no	—
656	C₂×C₈	—	86	1	no	—
657	C₂×C₈	—	86	1	no	—
658	C₂×C₈	—	86	1	no	—
659	C₂×C₈	—	86	1	no	—
660	C₂×C₈	—	86	1	no	—
661	C₂×C₈	—	86	1	no	—
662	C₂×C₈	—	86	1	no	—
663	C₂×C₈	—	86	1	no	—
664	C₂×C₈	—	86	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	1	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	4	1	no	—
674	C₂²⋊C₄	—	4	1	no	—
675	C₂²⋊C₄	—	4	1	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	#10621877	1	4	yes	complemented
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	4	4	no	—
712	C₂³	—	4	4	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	4	no	—
718	C₂³	D₄×Dic₄₃	1	2	yes	—
719	C₂³	C₂×#10621877	1	2	yes	—
720	C₂³	#13063332	1	2	yes	—
721	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
722	D₄	—	4	4	no	—
723	D₄	—	4	4	no	—
724	D₄	—	4	4	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	4	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
772	C₂×C₄	C₂×#10621877	1	2	yes	—
773	C₂×C₄	C₂×#10621877	1	2	yes	—
774	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
775	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
776	C₂×C₄	#13063370	1	1	yes	characteristic
777	C₂×C₄	#13063370	1	1	yes	characteristic
778	C₂×C₄	#13063370	1	1	yes	characteristic
779	C₂×C₄	#13063370	1	1	yes	characteristic
780	C₈	—	86	2	no	—
781	C₈	—	86	2	no	—
782	C₈	—	172	1	no	—
783	C₈	—	172	1	no	—
784	C₈	—	172	1	no	—
785	C₈	—	172	1	no	—
786	C₈	—	172	1	no	—
787	C₈	—	172	1	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	4	16	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
818	C₂²	#14583374	1	1	yes	characteristic
819	C₂²	#14583374	1	1	yes	characteristic
820	C₂²	C₂²×#10621877	1	1	yes	characteristic
821	C₂²	C₂×#13063332	1	1	yes	characteristic
822	C₂²	#14583666	1	1	yes	characteristic
823	C₂²	#14583666	1	1	yes	characteristic
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	2	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	#14583459	1	1	yes	characteristic
835	C₄	#14583464	1	1	yes	characteristic
836	C₄	#14583484	1	1	yes	characteristic
837	C₄	#14583484	1	1	yes	characteristic
838	C₂	—	4	2	no	—
839	C₂	—	4	2	no	—
840	C₂	—	4	2	no	—
841	C₂	—	8	1	no	—
842	C₂	#19137256	1	1	yes	characteristic
843	C₂	#19143322	1	1	yes	characteristic
844	C₂	D₄×#10621877	1	1	yes	characteristic
845	C₂	#19143630	1	1	yes	characteristic
846	C₂	#19143636	1	1	yes	characteristic
847	C₂	#19143643	1	1	yes	characteristic
848	C₂	#19143657	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄×#120×C₄₃	C₂
prime radical	C₂×#120×C₄₃	C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#120	D₄₃
hypocenter	C₄₃	#22038
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#120

Complements

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

N	H ≅ G/N	type
1. C₂×#14582977	C₂	semidirect
2. C₂×#14582863	C₂	semidirect
3. #19135394	C₂	semidirect
4. #19135390	C₂	semidirect
5. #19135210	C₂	semidirect
6. #19135203	C₂	semidirect
7. #19135203	C₂	semidirect
8. #19135203	C₂	semidirect
9. #19134893	C₂	semidirect
10. #19134893	C₂	semidirect
11. #19134893	C₂	semidirect
12. #19134780	C₂	semidirect
13. #19134505	C₂	semidirect
14. #19134379	C₂	semidirect
18. C₂²×#10621877	C₂²	semidirect
20. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
21. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
22. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
34. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
35. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
36. C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
37. C₂×#13063236	C₂²	semidirect
38. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
39. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
40. #14582654	C₂²	semidirect
41. #14582654	C₂²	semidirect
42. #14582654	C₂²	semidirect
43. #14582654	C₂²	semidirect
44. #14582654	C₂²	semidirect
45. #14582654	C₂²	semidirect
69. C₂×#10621877	D₄	semidirect
227. C₂²⋊C₄×C₄₃	M₁₆	semidirect
485. C₄₃	#22038	semidirect
679. C₂²⋊C₄	#10621877	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582977	2
C₂×#14582863	2
#19135394	2
#19135390	2
#19135210	2
#19135203	2
#19134893	2
#19134780	2
#19134505	2
#19134379	2
C₄×#120×C₄₃	2
#22038	43