Subgroups — #25102458

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143813	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583019	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583014	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143298	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134922	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134922	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134897	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134870	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134870	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134800	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134539	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134437	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134430	C₂	1	1	yes	maximal, characteristic, complemented
14	#19134376	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063345	C₂²	1	1	yes	characteristic
17	C₂×#13063345	C₂²	1	1	yes	characteristic
18	C₂×#13063331	C₂²	1	1	yes	characteristic, complemented
19	#14583410	C₂²	1	1	yes	characteristic
20	#14583061	C₄	1	1	yes	characteristic, complemented
21	#14583061	C₄	1	1	yes	characteristic, complemented
22	#14583055	C₄	1	1	yes	characteristic, complemented
23	#14583050	C₄	1	1	yes	characteristic, complemented
24	#14583044	C₄	1	1	yes	characteristic, complemented
25	#14583044	C₄	1	1	yes	characteristic, complemented
26	#14583038	C₄	1	1	yes	characteristic, complemented
27	#14583033	C₄	1	1	yes	characteristic, complemented
28	#14583019	—	2	4	no	—
29	#14583014	—	2	4	no	—
30	#14582975	—	2	1	no	—
31	#14582975	—	2	1	no	—
32	#14582968	—	2	1	no	—
33	#14582968	—	2	1	no	—
34	C₂×#13063260	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13063260	C₂²	1	1	yes	characteristic, complemented
36	#14582925	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13063252	C₂²	1	1	yes	characteristic
38	C₂×#13063252	C₂²	1	1	yes	characteristic
39	C₂×#13063252	C₂²	1	1	yes	characteristic
40	C₂×#13063252	C₂²	1	1	yes	characteristic
41	C₂×#13063251	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13063251	C₂²	1	1	yes	characteristic, complemented
43	#14582895	C₂²	1	1	yes	characteristic
44	#14582895	C₂²	1	1	yes	characteristic
45	#14582865	C₂²	1	1	yes	characteristic, complemented
46	#14582863	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
48	#14582854	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13063235	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
52	#14582663	C₂²	1	1	yes	characteristic, complemented
53	#14582663	C₂²	1	1	yes	characteristic, complemented
54	#14582660	C₂²	1	1	yes	characteristic, complemented
55	#14582660	C₂²	1	1	yes	characteristic, complemented
56	#14582653	C₂²	1	1	yes	characteristic, complemented
57	#14582653	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
59	C₄₃×#568	—	2	4	no	—
60	C₄₃×#568	—	2	4	no	—
61	C₂×#131×C₄₃	—	2	1	no	—
62	C₂×#131×C₄₃	—	2	1	no	—
63	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
64	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
65	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
66	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
67	C₂²×M₁₆×C₄₃	—	2	1	no	—
68	C₂²×M₁₆×C₄₃	—	2	1	no	—
69	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
70	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
71	C₂×#10621898	C₂³	1	1	yes	characteristic
72	#13063345	—	2	2	no	—
73	#13063345	—	2	2	no	—
74	#13063345	—	2	2	no	—
75	#13063345	—	2	2	no	—
76	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
77	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
78	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
79	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
80	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
81	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
82	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
83	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
84	#13063331	—	2	2	no	—
85	#13063331	—	2	2	no	—
86	C₂×#10621877	C₂³	1	1	yes	characteristic
87	C₂×#10621877	C₂³	1	1	yes	characteristic
88	C₂×#10621872	—	2	1	no	—
89	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₈×D₄₃	—	2	1	no	—
92	#13063308	—	2	1	no	—
93	#13063304	C₂×C₄	1	1	yes	characteristic
94	#13063304	C₂×C₄	1	1	yes	characteristic
95	#13063299	C₂×C₄	1	1	yes	characteristic
96	#13063299	C₂×C₄	1	1	yes	characteristic
97	#13063294	—	2	1	no	—
98	C₄×C₂²⋊D₄₃	—	2	1	no	—
99	C₄×C₂²⋊D₄₃	—	2	1	no	—
100	#13063284	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
102	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
104	#13063260	—	2	2	no	—
105	#13063260	—	2	2	no	—
106	Dic₄₃⋊C₈	—	2	1	no	—
107	Dic₄₃⋊C₈	—	2	1	no	—
108	#13063252	—	2	2	no	—
109	#13063252	—	2	2	no	—
110	#13063252	—	2	2	no	—
111	#13063252	—	2	2	no	—
112	#13063251	—	2	2	no	—
113	#13063251	—	2	2	no	—
114	#13063249	C₂×C₄	1	1	yes	characteristic
115	#13063249	C₂×C₄	1	1	yes	characteristic
116	#13063249	C₂×C₄	1	1	yes	characteristic
117	#13063249	C₂×C₄	1	1	yes	characteristic
118	#13063246	C₂×C₄	1	1	yes	characteristic
119	#13063246	C₂×C₄	1	1	yes	characteristic
120	#13063246	C₂×C₄	1	1	yes	characteristic
121	#13063246	C₂×C₄	1	1	yes	characteristic
122	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
123	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
124	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
127	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
128	(C₂×D₄₃)⋊C₈	—	2	1	no	—
129	(C₂×D₄₃)⋊C₈	—	2	1	no	—
130	#13063235	—	2	2	no	—
131	#13063235	—	2	1	no	—
132	C₈×Dic₄₃	—	2	2	no	—
133	C₈×Dic₄₃	—	2	1	no	—
134	C₄₃⋊#95	—	2	1	no	—
135	C₂×#41×C₄₃	—	2	2	no	—
136	C₂×#41×C₄₃	—	2	2	no	—
137	C₂×#41×C₄₃	—	2	2	no	—
138	C₂×#41×C₄₃	—	2	2	no	—
139	C₂×#41×C₄₃	—	2	1	no	—
140	C₂×#41×C₄₃	—	2	1	no	—
141	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
142	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
143	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
146	C₂²×D₄×C₄₃	—	2	1	no	—
147	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
148	C₂³×C₄×C₄₃	—	2	1	no	—
149	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
150	#131×C₄₃	—	2	8	no	—
151	#131×C₄₃	—	2	8	no	—
152	#131×C₄₃	—	2	2	no	—
153	#131×C₄₃	—	2	2	no	—
154	#131×C₄₃	—	2	2	no	—
155	#131×C₄₃	—	2	2	no	—
156	#131×C₄₃	—	2	2	no	—
157	#131×C₄₃	—	2	2	no	—
158	#131×C₄₃	D₄	1	4	yes	complemented
159	#131×C₄₃	D₄	1	4	yes	complemented
160	C₂×M₁₆×C₄₃	—	2	8	no	—
161	C₂×M₁₆×C₄₃	—	2	8	no	—
162	C₂×M₁₆×C₄₃	—	2	1	no	—
163	C₂×M₁₆×C₄₃	—	2	2	no	—
164	C₂×M₁₆×C₄₃	—	2	2	no	—
165	C₂×M₁₆×C₄₃	—	2	1	no	—
166	C₂×M₁₆×C₄₃	—	2	1	no	—
167	C₂×M₁₆×C₄₃	—	2	1	no	—
168	C₂×M₁₆×C₄₃	—	2	1	no	—
169	C₂×M₁₆×C₄₃	—	2	2	no	—
170	C₂×M₁₆×C₄₃	—	2	2	no	—
171	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
172	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
173	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
174	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
175	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₄₃	—	2	1	no	—
178	C₂²×C₈×C₄₃	—	2	1	no	—
179	C₂²×C₈×C₄₃	—	2	1	no	—
180	C₂²×C₈×C₄₃	—	2	1	no	—
181	C₂²×C₈×C₄₃	—	2	1	no	—
182	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
183	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
184	C₂⁴×C₄₃	—	2	1	no	—
185	C₂⁴×C₄₃	#41	1	1	yes	characteristic
186	#41×C₄₃	—	2	4	no	—
187	#41×C₄₃	—	2	4	no	—
188	#41×C₄₃	—	2	4	no	—
189	#41×C₄₃	—	2	4	no	—
190	#41×C₄₃	—	2	2	no	—
191	#41×C₄₃	—	2	2	no	—
192	#41×C₄₃	—	2	2	no	—
193	#41×C₄₃	—	2	2	no	—
194	#41×C₄₃	—	2	1	no	—
195	#41×C₄₃	—	2	1	no	—
196	#41×C₄₃	—	2	1	no	—
197	#41×C₄₃	—	2	1	no	—
198	#41×C₄₃	C₂×D₄	1	2	yes	—
199	#41×C₄₃	C₂×D₄	1	2	yes	—
200	#41×C₄₃	#41	1	2	yes	—
201	#41×C₄₃	#41	1	2	yes	—
202	C₂×Q₈×C₄₃	—	2	2	no	—
203	C₂×Q₈×C₄₃	—	2	2	no	—
204	C₂×Q₈×C₄₃	—	2	1	no	—
205	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
206	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×D₄×C₄₃	—	2	4	no	—
208	C₂×D₄×C₄₃	—	2	4	no	—
209	C₂×D₄×C₄₃	—	2	2	no	—
210	C₂×D₄×C₄₃	—	2	2	no	—
211	C₂×D₄×C₄₃	—	2	1	no	—
212	C₂×D₄×C₄₃	—	2	1	no	—
213	C₂×D₄×C₄₃	—	2	1	no	—
214	C₂×D₄×C₄₃	—	2	1	no	—
215	C₂×D₄×C₄₃	—	2	1	no	—
216	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
218	C₂²×C₄×C₄₃	—	2	4	no	—
219	C₂²×C₄×C₄₃	—	2	4	no	—
220	C₂²×C₄×C₄₃	—	2	1	no	—
221	C₂²×C₄×C₄₃	—	2	1	no	—
222	C₂²×C₄×C₄₃	—	2	1	no	—
223	C₂²×C₄×C₄₃	—	2	1	no	—
224	C₂²×C₄×C₄₃	—	2	1	no	—
225	C₂²×C₄×C₄₃	—	2	1	no	—
226	C₂²×C₄×C₄₃	—	2	1	no	—
227	C₂²×C₄×C₄₃	—	2	1	no	—
228	C₂²×C₄×C₄₃	—	2	1	no	—
229	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
234	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₂²⋊D₄₃	—	2	1	no	—
236	C₂×C₂²⋊D₄₃	—	2	1	no	—
237	C₂×C₂²⋊D₄₃	—	2	1	no	—
238	C₂²×Dic₄₃	—	2	1	no	—
239	C₂²×Dic₄₃	—	2	1	no	—
240	#10621898	—	2	1	no	—
241	#10621898	—	2	1	no	—
242	#10621898	—	2	1	no	—
243	#10621898	—	2	1	no	—
244	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₄×D₄₃	—	2	1	no	—
246	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
247	M₁₆×C₄₃	—	2	4	no	—
248	M₁₆×C₄₃	—	2	4	no	—
249	M₁₆×C₄₃	—	2	4	no	—
250	M₁₆×C₄₃	—	2	1	no	—
251	M₁₆×C₄₃	—	2	1	no	—
252	M₁₆×C₄₃	—	2	2	no	—
253	M₁₆×C₄₃	—	2	2	no	—
254	M₁₆×C₄₃	—	2	4	no	—
255	M₁₆×C₄₃	—	2	4	no	—
256	M₁₆×C₄₃	—	2	2	no	—
257	M₁₆×C₄₃	—	2	2	no	—
258	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
259	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
260	C₂×C₈×C₄₃	—	2	4	no	—
261	C₂×C₈×C₄₃	—	2	4	no	—
262	C₂×C₈×C₄₃	—	2	4	no	—
263	C₂×C₈×C₄₃	—	2	1	no	—
264	C₂×C₈×C₄₃	—	2	1	no	—
265	C₂×C₈×C₄₃	—	2	1	no	—
266	C₂×C₈×C₄₃	—	2	1	no	—
267	C₂×C₈×C₄₃	—	2	4	no	—
268	C₂×C₈×C₄₃	—	2	4	no	—
269	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
270	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
271	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
272	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
273	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
274	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
275	C₂²⋊Dic₄₃	—	2	1	no	—
276	C₂²⋊Dic₄₃	—	2	1	no	—
277	C₂²⋊Dic₄₃	—	2	1	no	—
278	C₂²⋊Dic₄₃	—	4	2	no	—
279	#10621885	—	2	2	no	—
280	#10621885	—	2	2	no	—
281	#10621884	—	2	2	no	—
282	#10621884	—	2	2	no	—
283	#10621883	—	2	2	no	—
284	#10621883	—	2	2	no	—
285	#10621882	—	2	2	no	—
286	#10621882	—	2	2	no	—
287	(C₂×D₄₃)⋊C₄	—	2	1	no	—
288	(C₂×D₄₃)⋊C₄	—	2	1	no	—
289	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
290	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
291	Dic₄₃⋊C₄	—	2	1	no	—
292	Dic₄₃⋊C₄	—	2	1	no	—
293	C₄×Dic₄₃	—	2	1	no	—
294	C₄×Dic₄₃	—	2	1	no	—
295	C₄×Dic₄₃	—	2	1	no	—
296	C₄×Dic₄₃	—	2	1	no	—
297	C₄×Dic₄₃	—	2	1	no	—
298	#10621877	—	2	1	no	—
299	#10621877	—	2	1	no	—
300	#10621877	—	2	1	no	—
301	#10621877	—	2	1	no	—
302	C₂×C₄₃⋊C₈	—	2	1	no	—
303	C₂×C₄₃⋊C₈	—	2	1	no	—
304	C₂×C₄₃⋊C₈	—	2	1	no	—
305	C₂×C₄₃⋊C₈	—	2	1	no	—
306	C₂×C₄₃⋊C₈	—	2	1	no	—
307	C₂×C₄₃⋊C₈	—	2	1	no	—
308	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
309	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
310	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
311	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
312	#10621872	—	4	2	no	—
313	C₈×D₄₃	—	4	2	no	—
314	C₂³×C₄₃	—	2	4	no	—
315	C₂³×C₄₃	—	2	1	no	—
316	C₂³×C₄₃	—	2	1	no	—
317	C₂³×C₄₃	—	2	1	no	—
318	C₂³×C₄₃	—	2	1	no	—
319	C₂³×C₄₃	—	4	1	no	—
320	C₂³×C₄₃	—	4	1	no	—
321	C₂³×C₄₃	—	8	1	no	—
322	C₂³×C₄₃	—	8	1	no	—
323	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
324	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
325	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
326	C₂²×D₄₃	—	2	1	no	—
327	Q₈×C₄₃	—	2	4	no	—
328	Q₈×C₄₃	—	2	1	no	—
329	Q₈×C₄₃	—	2	1	no	—
330	Q₈×C₄₃	C₄×D₄	1	2	yes	—
331	Q₈×C₄₃	C₄×D₄	1	2	yes	—
332	D₄×C₄₃	—	2	4	no	—
333	D₄×C₄₃	—	2	4	no	—
334	D₄×C₄₃	—	2	4	no	—
335	D₄×C₄₃	—	2	2	no	—
336	D₄×C₄₃	—	2	2	no	—
337	D₄×C₄₃	—	2	2	no	—
338	D₄×C₄₃	—	2	2	no	—
339	D₄×C₄₃	—	2	1	no	—
340	D₄×C₄₃	—	2	1	no	—
341	D₄×C₄₃	C₄×D₄	1	2	yes	—
342	D₄×C₄₃	C₄×D₄	1	2	yes	—
343	C₂×C₄×C₄₃	—	2	4	no	—
344	C₂×C₄×C₄₃	—	2	4	no	—
345	C₂×C₄×C₄₃	—	2	4	no	—
346	C₂×C₄×C₄₃	—	2	1	no	—
347	C₂×C₄×C₄₃	—	2	1	no	—
348	C₂×C₄×C₄₃	—	2	1	no	—
349	C₂×C₄×C₄₃	—	2	1	no	—
350	C₂×C₄×C₄₃	—	2	1	no	—
351	C₂×C₄×C₄₃	—	2	1	no	—
352	C₂×C₄×C₄₃	—	2	1	no	—
353	C₂×C₄×C₄₃	—	2	1	no	—
354	C₂×C₄×C₄₃	—	2	2	no	—
355	C₂×C₄×C₄₃	—	2	2	no	—
356	C₂×C₄×C₄₃	—	2	1	no	—
357	C₂×C₄×C₄₃	—	2	1	no	—
358	C₂×C₄×C₄₃	—	2	1	no	—
359	C₂×C₄×C₄₃	—	2	2	no	—
360	C₂×C₄×C₄₃	—	2	2	no	—
361	C₂×C₄×C₄₃	—	2	1	no	—
362	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
363	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
364	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
365	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
369	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
370	C₂²⋊D₄₃	—	4	1	no	—
371	C₂²⋊D₄₃	—	4	1	no	—
372	C₂²⋊D₄₃	—	8	1	no	—
373	C₂²⋊D₄₃	—	8	1	no	—
374	C₂×Dic₄₃	—	2	2	no	—
375	C₂×Dic₄₃	—	2	1	no	—
376	C₂×Dic₄₃	—	2	1	no	—
377	C₂×Dic₄₃	—	2	1	no	—
378	C₂×Dic₄₃	—	4	1	no	—
379	C₂×Dic₄₃	—	4	1	no	—
380	C₂×Dic₄₃	—	4	1	no	—
381	C₂×Dic₄₃	—	4	1	no	—
382	C₂×Dic₄₃	—	4	1	no	—
383	D₁₇₂	—	2	1	no	—
384	D₁₇₂	—	2	1	no	—
385	C₄×D₄₃	—	4	1	no	—
386	C₄×D₄₃	—	4	1	no	—
387	Dic₈₆	—	2	1	no	—
388	Dic₈₆	—	2	1	no	—
389	C₈×C₄₃	—	2	2	no	—
390	C₈×C₄₃	—	2	2	no	—
391	C₈×C₄₃	—	2	1	no	—
392	C₈×C₄₃	—	2	1	no	—
393	C₈×C₄₃	#120	1	2	yes	—
394	C₈×C₄₃	#120	1	2	yes	—
395	C₄₃⋊C₈	—	2	1	no	—
396	C₄₃⋊C₈	—	2	1	no	—
397	C₄₃⋊C₈	—	2	1	no	—
398	C₄₃⋊C₈	—	2	1	no	—
399	C₄₃⋊C₈	—	4	1	no	—
400	C₄₃⋊C₈	—	4	1	no	—
401	#21468	—	43	1	no	maximal, Sylow
402	C₂²×C₄₃	—	2	1	no	—
403	C₂²×C₄₃	—	2	1	no	—
404	C₂²×C₄₃	—	2	1	no	—
405	C₂²×C₄₃	—	2	1	no	—
406	C₂²×C₄₃	—	2	1	no	—
407	C₂²×C₄₃	—	2	1	no	—
408	C₂²×C₄₃	—	2	1	no	—
409	C₂²×C₄₃	—	2	2	no	—
410	C₂²×C₄₃	—	2	2	no	—
411	C₂²×C₄₃	—	2	1	no	—
412	C₂²×C₄₃	—	4	1	no	—
413	C₂²×C₄₃	—	4	1	no	—
414	C₂²×C₄₃	—	4	1	no	—
415	C₂²×C₄₃	—	4	1	no	—
416	C₂²×C₄₃	—	8	1	no	—
417	C₂²×C₄₃	—	8	1	no	—
418	C₂²×C₄₃	—	8	4	no	—
419	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
420	C₂²×C₄₃	#525	1	1	yes	characteristic
421	C₂²×C₄₃	#525	1	1	yes	characteristic
422	C₂×D₄₃	—	4	1	no	—
423	C₂×D₄₃	—	4	1	no	—
424	C₂×D₄₃	—	4	1	no	—
425	C₄×C₄₃	—	2	1	no	—
426	C₄×C₄₃	—	2	2	no	—
427	C₄×C₄₃	—	2	2	no	—
428	C₄×C₄₃	—	2	1	no	—
429	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
430	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
431	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
432	C₄×C₄₃	#525	1	1	yes	characteristic
433	Dic₄₃	—	4	2	no	—
434	Dic₄₃	—	4	1	no	—
435	Dic₄₃	—	4	1	no	—
436	Dic₄₃	—	4	1	no	—
437	Dic₄₃	—	8	1	no	—
438	C₂×#568	D₄₃	1	1	yes	characteristic, complemented
439	#3002	—	43	1	no	—
440	C₂×#444	—	43	1	no	—
441	C₂×#443	—	43	1	no	—
442	#2930	—	43	1	no	—
443	#1876	—	43	1	no	—
444	#1876	—	43	1	no	—
445	#1871	—	43	1	no	—
446	#1866	—	43	1	no	—
447	#1866	—	43	1	no	—
448	#1855	—	43	1	no	—
449	#1789	—	43	1	no	—
450	#1765	—	43	1	no	—
451	#1764	—	43	1	no	—
452	#1753	—	43	1	no	—
453	C₂×C₄₃	—	2	1	no	—
454	C₂×C₄₃	—	2	1	no	—
455	C₂×C₄₃	—	4	1	no	—
456	C₂×C₄₃	—	4	1	no	—
457	C₂×C₄₃	—	4	2	no	—
458	C₂×C₄₃	—	4	2	no	—
459	C₂×C₄₃	C₄×#120	1	1	yes	characteristic
460	C₂×C₄₃	#2956	1	1	yes	characteristic
461	C₂×C₄₃	#2957	1	1	yes	characteristic
462	D₄₃	—	8	1	no	—
463	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
464	C₂×#135	—	43	1	no	—
465	C₂×#135	—	43	1	no	—
466	#568	—	2	4	no	—
467	#568	—	2	4	no	—
468	C₂×#131	—	2	1	no	—
469	C₂×#131	—	2	1	no	—
470	C₂×#131	—	43	1	no	—
471	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
472	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
473	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
474	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
475	C₂²×M₁₆	—	2	1	no	—
476	C₂²×M₁₆	—	2	1	no	—
477	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
478	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
479	#525	—	43	1	no	—
480	#452	—	43	1	no	—
481	#452	—	43	1	no	—
482	#451	—	43	1	no	—
483	#450	—	43	1	no	—
484	#449	—	43	1	no	—
485	#449	—	43	1	no	—
486	#448	—	43	1	no	—
487	#447	—	43	1	no	—
488	#444	—	86	4	no	—
489	#443	—	86	4	no	—
490	#436	—	86	1	no	—
491	#436	—	86	1	no	—
492	#435	—	86	1	no	—
493	#435	—	86	1	no	—
494	C₂×#108	—	43	1	no	—
495	C₂×#108	—	43	1	no	—
496	#424	—	43	1	no	—
497	C₂×#104	—	43	1	no	—
498	C₂×#104	—	43	1	no	—
499	C₂×#104	—	43	1	no	—
500	C₂×#104	—	43	1	no	—
501	C₂×#104	—	43	1	no	—
502	C₂×#104	—	43	1	no	—
503	#416	—	43	1	no	—
504	#416	—	43	1	no	—
505	#408	—	43	1	no	—
506	#407	—	43	1	no	—
507	C₂×C₂²⋊C₈	—	43	1	no	—
508	#405	—	43	1	no	—
509	C₂×#97	—	43	1	no	—
510	C₂×C₄×C₈	—	43	1	no	—
511	C₄×C₂²⋊C₄	—	43	1	no	—
512	#341	—	43	1	no	—
513	#341	—	43	1	no	—
514	#339	—	43	1	no	—
515	#339	—	43	1	no	—
516	#336	—	43	1	no	—
517	#336	—	43	1	no	—
518	C₄₃	#21468	1	1	yes	characteristic, complemented, Sylow
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	2	no	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	43	1	no	—
526	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
527	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
528	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
529	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
530	C₂²×Q₈	C₄×D₄₃	1	1	yes	characteristic
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
533	C₂³×C₄	—	2	1	no	—
534	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
535	#135	—	86	2	no	—
536	#135	—	86	2	no	—
537	#135	—	86	2	no	—
538	#135	—	86	2	no	—
539	C₂×Q₁₆	—	43	1	no	—
540	C₂×Q₁₆	—	43	1	no	—
541	C₂×SD₁₆	—	43	1	no	—
542	C₂×SD₁₆	—	43	1	no	—
543	C₂×SD₁₆	—	43	1	no	—
544	C₂×SD₁₆	—	43	1	no	—
545	C₂×D₈	—	43	1	no	—
546	C₂×D₈	—	43	1	no	—
547	#131	—	2	8	no	—
548	#131	—	2	8	no	—
549	#131	—	2	2	no	—
550	#131	—	2	2	no	—
551	#131	—	2	2	no	—
552	#131	—	2	2	no	—
553	#131	—	2	2	no	—
554	#131	—	2	2	no	—
555	#131	—	86	2	no	—
556	#131	—	86	2	no	—
557	#131	C₂²⋊D₄₃	1	4	yes	complemented
558	#131	C₂²⋊D₄₃	1	4	yes	complemented
559	C₂×M₁₆	—	2	8	no	—
560	C₂×M₁₆	—	2	8	no	—
561	C₂×M₁₆	—	2	1	no	—
562	C₂×M₁₆	—	2	2	no	—
563	C₂×M₁₆	—	2	2	no	—
564	C₂×M₁₆	—	2	1	no	—
565	C₂×M₁₆	—	2	1	no	—
566	C₂×M₁₆	—	2	1	no	—
567	C₂×M₁₆	—	2	1	no	—
568	C₂×M₁₆	—	2	2	no	—
569	C₂×M₁₆	—	2	2	no	—
570	C₂×M₁₆	—	43	1	no	—
571	C₂×M₁₆	—	43	1	no	—
572	C₂×M₁₆	—	86	1	no	—
573	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
574	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
575	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
576	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
577	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
578	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
579	C₂²×C₈	—	2	1	no	—
580	C₂²×C₈	—	2	1	no	—
581	C₂²×C₈	—	2	1	no	—
582	C₂²×C₈	—	2	1	no	—
583	C₂²×C₈	—	2	1	no	—
584	C₂²×C₈	—	43	1	no	—
585	C₂²×C₈	—	43	1	no	—
586	C₂²×C₈	—	86	1	no	—
587	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
588	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
589	#123	—	86	1	no	—
590	C₂²⋊Q₈	—	43	1	no	—
591	C₂²⋊Q₈	—	43	1	no	—
592	#121	—	43	1	no	—
593	#121	—	43	1	no	—
594	#120	—	86	1	no	—
595	C₄×D₄	—	86	1	no	—
596	C₄×D₄	—	86	1	no	—
597	#117	—	43	1	no	—
598	C₂×C₂²⋊C₄	—	86	1	no	—
599	C₂×C₄²	—	43	1	no	—
600	C₂×C₄²	—	43	1	no	—
601	#108	—	86	2	no	—
602	#108	—	86	2	no	—
603	C₄⋊C₈	—	86	1	no	—
604	C₄⋊C₈	—	86	1	no	—
605	#104	—	86	2	no	—
606	#104	—	86	2	no	—
607	#104	—	86	2	no	—
608	#104	—	86	2	no	—
609	#104	—	86	2	no	—
610	#104	—	86	2	no	—
611	#103	—	43	1	no	—
612	#103	—	43	1	no	—
613	#103	—	43	1	no	—
614	#103	—	43	1	no	—
615	#102	—	43	1	no	—
616	#102	—	43	1	no	—
617	#102	—	43	1	no	—
618	#102	—	43	1	no	—
619	C₂²⋊C₈	—	43	1	no	—
620	C₂²⋊C₈	—	43	1	no	—
621	C₂²⋊C₈	—	43	1	no	—
622	C₂²⋊C₈	—	43	1	no	—
623	C₂²⋊C₈	—	86	1	no	—
624	C₂²⋊C₈	—	86	1	no	—
625	C₂²⋊C₈	—	86	1	no	—
626	C₂²⋊C₈	—	86	1	no	—
627	#97	—	86	2	no	—
628	#97	—	86	1	no	—
629	C₄×C₈	—	86	2	no	—
630	C₄×C₈	—	86	1	no	—
631	#95	—	86	1	no	—
632	C₂⁴	—	2	1	no	—
633	C₂⁴	#10621898	1	1	yes	characteristic
634	#41	—	2	4	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	2	4	no	—
638	#41	—	2	2	no	—
639	#41	—	2	2	no	—
640	#41	—	2	2	no	—
641	#41	—	2	2	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	2	1	no	—
645	#41	—	2	1	no	—
646	#41	—	86	1	no	—
647	#41	—	86	1	no	—
648	#41	—	86	1	no	—
649	#41	—	86	1	no	—
650	#41	#10621898	1	2	yes	—
651	#41	#10621898	1	2	yes	—
652	#41	C₂×C₂²⋊D₄₃	1	2	yes	—
653	#41	C₂×C₂²⋊D₄₃	1	2	yes	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	43	1	no	—
658	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
659	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	43	1	no	—
670	C₂×D₄	—	86	1	no	—
671	C₂×D₄	—	86	1	no	—
672	C₂×D₄	—	86	1	no	—
673	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
674	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	86	1	no	—
687	C₂²×C₄	—	86	1	no	—
688	C₂²×C₄	—	86	1	no	—
689	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
691	C₂²×C₄	#10621898	1	1	yes	characteristic
692	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
694	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
695	Q₁₆	—	86	2	no	—
696	Q₁₆	—	86	2	no	—
697	SD₁₆	—	86	2	no	—
698	SD₁₆	—	86	2	no	—
699	SD₁₆	—	86	2	no	—
700	SD₁₆	—	86	2	no	—
701	D₈	—	86	2	no	—
702	D₈	—	86	2	no	—
703	M₁₆	—	2	4	no	—
704	M₁₆	—	2	4	no	—
705	M₁₆	—	2	4	no	—
706	M₁₆	—	2	1	no	—
707	M₁₆	—	2	1	no	—
708	M₁₆	—	2	2	no	—
709	M₁₆	—	2	2	no	—
710	M₁₆	—	2	4	no	—
711	M₁₆	—	2	4	no	—
712	M₁₆	—	2	2	no	—
713	M₁₆	—	2	2	no	—
714	M₁₆	—	86	1	no	—
715	M₁₆	—	86	1	no	—
716	M₁₆	—	86	1	no	—
717	M₁₆	—	86	1	no	—
718	M₁₆	—	172	2	no	—
719	M₁₆	C₂×C₂²⋊D₄₃	1	2	yes	—
720	M₁₆	C₂×C₂²⋊D₄₃	1	2	yes	—
721	C₂×C₈	—	2	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	—	2	4	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	1	no	—
728	C₂×C₈	—	2	4	no	—
729	C₂×C₈	—	2	4	no	—
730	C₂×C₈	—	43	1	no	—
731	C₂×C₈	—	43	1	no	—
732	C₂×C₈	—	43	1	no	—
733	C₂×C₈	—	43	1	no	—
734	C₂×C₈	—	86	1	no	—
735	C₂×C₈	—	86	1	no	—
736	C₂×C₈	—	86	1	no	—
737	C₂×C₈	—	86	1	no	—
738	C₂×C₈	—	86	1	no	—
739	C₂×C₈	—	86	1	no	—
740	C₂×C₈	—	172	2	no	—
741	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
742	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
743	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
744	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
745	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
746	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
747	C₄⋊C₄	—	43	1	no	—
748	C₄⋊C₄	—	43	1	no	—
749	C₄⋊C₄	—	86	1	no	—
750	C₄⋊C₄	—	86	1	no	—
751	C₂²⋊C₄	—	86	1	no	—
752	C₂²⋊C₄	—	86	1	no	—
753	C₂²⋊C₄	—	86	1	no	—
754	C₂²⋊C₄	—	86	1	no	—
755	C₂²⋊C₄	—	86	1	no	—
756	C₂²⋊C₄	—	172	2	no	—
757	C₄²	—	86	1	no	—
758	C₄²	—	86	1	no	—
759	C₄²	—	86	1	no	—
760	C₄²	—	86	1	no	—
761	C₄²	—	86	1	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	—	86	1	no	—
772	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
773	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
774	C₂³	C₂×#10621898	1	1	yes	characteristic
775	Q₈	—	2	4	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	86	1	no	—
779	Q₈	—	86	1	no	—
780	Q₈	C₄×C₂²⋊D₄₃	1	2	yes	—
781	Q₈	C₄×C₂²⋊D₄₃	1	2	yes	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	4	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	86	1	no	—
792	D₄	—	86	1	no	—
793	D₄	—	344	1	no	—
794	D₄	—	344	1	no	—
795	D₄	—	172	1	no	—
796	D₄	—	172	1	no	—
797	D₄	C₄×C₂²⋊D₄₃	1	2	yes	—
798	D₄	C₄×C₂²⋊D₄₃	1	2	yes	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	86	2	no	—
819	C₂×C₄	—	86	1	no	—
820	C₂×C₄	—	86	1	no	—
821	C₂×C₄	—	86	1	no	—
822	C₂×C₄	—	172	1	no	—
823	C₂×C₄	—	172	1	no	—
824	C₂×C₄	—	172	1	no	—
825	C₂×C₄	—	172	1	no	—
826	C₂×C₄	—	172	1	no	—
827	C₂×C₄	—	172	1	no	—
828	C₂×C₄	—	172	1	no	—
829	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
830	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
831	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
833	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
835	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
836	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	2	1	no	—
840	C₈	—	2	1	no	—
841	C₈	—	86	1	no	—
842	C₈	—	86	1	no	—
843	C₈	—	86	1	no	—
844	C₈	—	86	1	no	—
845	C₈	—	172	1	no	—
846	C₈	—	172	1	no	—
847	C₈	#13063294	1	2	yes	—
848	C₈	#13063294	1	2	yes	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	8	1	no	—
865	C₂²	—	8	4	no	—
866	C₂²	—	172	1	no	—
867	C₂²	—	172	1	no	—
868	C₂²	—	172	1	no	—
869	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
870	C₂²	#14583410	1	1	yes	characteristic
871	C₂²	#14583410	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	1	no	—
876	C₄	—	344	1	no	—
877	C₄	—	172	2	no	—
878	C₄	—	172	1	no	—
879	C₄	—	172	1	no	—
880	C₄	—	172	1	no	—
881	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
882	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
883	C₄	C₂×#13063294	1	1	yes	characteristic
884	C₄	#14583410	1	1	yes	characteristic
885	C₂	—	2	1	no	—
886	C₂	—	2	1	no	—
887	C₂	—	4	1	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	344	1	no	—
892	C₂	C₄×#13063294	1	1	yes	characteristic
893	C₂	#19143502	1	1	yes	characteristic
894	C₂	#19143510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#568	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19143813	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#568	D₄₃
hypocenter	C₄₃	#21468
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
2. C₂×#14583019	C₂	semidirect
3. C₂×#14583014	C₂	semidirect
4. #19143298	C₂	semidirect
5. #19134922	C₂	semidirect
6. #19134922	C₂	semidirect
7. #19134897	C₂	semidirect
8. #19134870	C₂	semidirect
9. #19134870	C₂	semidirect
10. #19134800	C₂	semidirect
11. #19134539	C₂	semidirect
12. #19134437	C₂	semidirect
13. #19134430	C₂	semidirect
14. #19134376	C₂	semidirect
15. C₂×C₄₃×#568	C₂	semidirect
18. C₂×#13063331	C₂²	semidirect
20. #14583061	C₄	semidirect
21. #14583061	C₄	semidirect
22. #14583055	C₄	semidirect
23. #14583050	C₄	semidirect
24. #14583044	C₄	semidirect
25. #14583044	C₄	semidirect
26. #14583038	C₄	semidirect
27. #14583033	C₄	semidirect
34. C₂×#13063260	C₂²	semidirect
35. C₂×#13063260	C₂²	semidirect
36. #14582925	C₂²	semidirect
41. C₂×#13063251	C₂²	semidirect
42. C₂×#13063251	C₂²	semidirect
45. #14582865	C₂²	semidirect
48. #14582854	C₂²	semidirect
49. C₂×#13063235	C₂²	semidirect
50. C₂×C₈×Dic₄₃	C₂²	semidirect
52. #14582663	C₂²	semidirect
53. #14582663	C₂²	semidirect
54. #14582660	C₂²	semidirect
55. #14582660	C₂²	semidirect
56. #14582653	C₂²	semidirect
57. #14582653	C₂²	semidirect
158. #131×C₄₃	D₄	semidirect
159. #131×C₄₃	D₄	semidirect
438. C₂×#568	D₄₃	semidirect
518. C₄₃	#21468	semidirect
557. #131	C₂²⋊D₄₃	semidirect
558. #131	C₂²⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19143813	2
C₂×#14583019	2
C₂×#14583014	2
#19143298	2
#19134922	2
#19134897	2
#19134870	2
#19134800	2
#19134539	2
#19134437	2
#19134430	2
#19134376	2
C₂×C₄₃×#568	2
#21468	43