Subgroups — #25972842

Order 11008.

2656 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149374	C₂	1	2	yes	maximal, complemented
2	C₂×#14583701	C₂	1	1	yes	maximal, characteristic, complemented
3	#19146392	C₂	1	4	yes	maximal, complemented
4	#19146381	C₂	1	4	yes	maximal, complemented
5	#19146357	C₂	1	8	yes	maximal, complemented
6	#19145082	C₂	1	1	yes	maximal, characteristic, complemented
7	#19144325	C₂	1	2	yes	maximal, complemented
8	#19144311	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14583169	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143967	C₂	1	2	yes	maximal, complemented
11	#19143950	C₂	1	2	yes	maximal, complemented
12	#19143512	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143496	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13063371	C₂²	1	2	yes	complemented
16	#14583707	—	2	4	no	—
17	#14583707	C₂²	1	8	yes	complemented
18	#14583702	—	2	4	no	—
19	#14583702	C₂²	1	8	yes	complemented
20	#14583701	—	2	2	no	—
21	#14583701	—	2	2	no	—
22	#14583701	C₂²	1	4	yes	complemented
23	#14583701	C₂²	1	4	yes	complemented
24	#14583697	—	2	4	no	—
25	#14583697	C₂²	1	1	yes	characteristic
26	#14583697	C₂²	1	2	yes	complemented
27	C₂×#13063352	—	2	2	no	—
28	C₂×#13063350	—	2	4	no	—
29	C₂×#13063350	C₂²	1	2	yes	complemented
30	C₂×#13063350	C₂²	1	2	yes	complemented
31	C₂×#13063350	C₂²	1	2	yes	complemented
32	C₂×#13063348	—	2	1	no	—
33	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₈×D₄₃	—	2	1	no	—
35	#14583666	C₂²	1	2	yes	complemented
36	C₂×#13063331	C₂²	1	1	yes	characteristic, complemented
37	#14583463	C₂²	1	2	yes	complemented
38	#14583285	C₂²	1	4	yes	complemented
39	#14583284	C₂²	1	2	yes	complemented
40	#14583274	C₂²	1	2	yes	complemented
41	#14583171	C₂²	1	2	yes	complemented
42	#14583169	C₂²	1	4	yes	complemented
43	#14583169	C₂²	1	4	yes	complemented
44	#14583167	C₂²	1	8	yes	complemented
45	#14583166	C₂²	1	2	yes	complemented
46	#14583164	C₂²	1	8	yes	complemented
47	#14583159	C₂²	1	4	yes	complemented
48	#14583075	C₂²	1	8	yes	complemented
49	#14583072	C₂²	1	8	yes	complemented
50	#14583067	C₂²	1	8	yes	complemented
51	#14583065	C₂²	1	8	yes	complemented
52	#14583021	C₂²	1	4	yes	complemented
53	#14583019	C₂²	1	4	yes	complemented
54	#14583016	C₂²	1	4	yes	complemented
55	#14583014	C₂²	1	4	yes	complemented
56	#14582947	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13063261	C₂²	1	1	yes	characteristic, complemented
58	#14582916	C₂²	1	2	yes	complemented
59	#14582916	C₂²	1	1	yes	characteristic, complemented
60	#14582915	C₂²	1	1	yes	characteristic, complemented
61	#14582883	C₂²	1	2	yes	complemented
62	C₂×#13063241	C₂²	1	2	yes	complemented
63	#14582854	C₂²	1	1	yes	characteristic, complemented
64	C₄₃×#585	C₂²	1	2	yes	complemented
65	C₄₃×#578	—	2	1	no	—
66	C₄₃×#578	C₂²	1	2	yes	complemented
67	C₄₃×#577	—	2	2	no	—
68	C₄₃×#577	C₂²	1	4	yes	complemented
69	C₄₃×#576	—	2	1	no	—
70	C₄₃×#576	C₂²	1	2	yes	complemented
71	C₄₃×#575	—	2	2	no	—
72	C₄₃×#575	C₂²	1	2	yes	complemented
73	C₂×#135×C₄₃	—	2	2	no	—
74	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
75	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic, complemented
77	#13063371	—	2	4	no	—
78	#13063371	—	2	4	no	—
79	#13063371	—	4	2	no	—
80	#13063371	C₂³	1	8	yes	—
81	C₂×#10621902	—	2	2	no	—
82	C₂×#10621898	—	2	2	no	—
83	C₂×#10621898	C₂³	1	1	yes	characteristic
84	C₂²×D₁₇₂	—	2	2	no	—
85	C₂²×D₁₇₂	C₂³	1	2	yes	—
86	C₂×D₄×D₄₃	—	2	2	no	—
87	C₂×D₄×D₄₃	—	4	2	no	—
88	#13063356	—	2	8	no	—
89	#13063356	D₄	1	2	yes	complemented
90	#13063356	C₂³	1	4	yes	—
91	#13063355	—	2	2	no	—
92	#13063355	D₄	1	2	yes	complemented
93	#13063352	—	2	8	no	—
94	#13063352	—	2	8	no	—
95	#13063351	—	2	8	no	—
96	#13063351	D₄	1	2	yes	complemented
97	#13063351	C₂³	1	4	yes	—
98	#13063350	—	2	4	no	—
99	#13063350	—	2	4	no	—
100	#13063350	—	2	2	no	—
101	#13063350	—	2	8	no	—
102	#13063350	—	2	8	no	—
103	#13063350	—	2	4	no	—
104	#13063350	—	2	4	no	—
105	#13063350	D₄	1	2	yes	complemented
106	#13063350	C₂³	1	8	yes	—
107	#13063350	C₂³	1	8	yes	complemented
108	#13063348	—	2	4	no	—
109	#13063348	—	2	4	no	—
110	#13063345	—	2	4	no	—
111	#13063345	—	2	8	no	—
112	#13063345	—	2	8	no	—
113	#13063345	C₂³	1	4	yes	—
114	C₂×#10621884	—	2	2	no	—
115	C₂×#10621884	—	2	2	no	—
116	C₂×#10621884	—	2	8	no	—
117	C₂×#10621884	C₂³	1	4	yes	complemented
118	C₂×D₃₄₄	—	2	1	no	—
119	C₂×D₃₄₄	—	2	1	no	—
120	C₂×D₃₄₄	—	2	1	no	—
121	C₂×D₃₄₄	—	2	1	no	—
122	C₂×D₃₄₄	C₂³	1	2	yes	—
123	C₂×D₃₄₄	C₂³	1	2	yes	—
124	C₂×#10621882	—	2	2	no	—
125	C₂×#10621882	—	2	2	no	—
126	C₂×#10621882	—	2	8	no	—
127	C₂×#10621882	C₂³	1	4	yes	complemented
128	D₈×D₄₃	—	2	4	no	—
129	D₈×D₄₃	—	2	4	no	—
130	#13063332	—	2	4	no	—
131	#13063332	C₂³	1	8	yes	complemented
132	#13063331	—	2	1	no	—
133	#13063331	—	2	1	no	—
134	#13063331	C₂³	1	2	yes	—
135	#13063331	C₂³	1	2	yes	—
136	C₂×#10621877	—	2	4	no	—
137	C₂×#10621877	C₂³	1	2	yes	—
138	C₂×#10621877	C₂³	1	1	yes	characteristic
139	C₂×#10621877	C₂³	1	1	yes	characteristic
140	C₂×#10621872	—	2	1	no	—
141	C₂×C₈×D₄₃	—	2	1	no	—
142	#13063321	C₂³	1	4	yes	complemented
143	#13063314	C₂³	1	4	yes	complemented
144	#13063299	—	4	2	no	—
145	#13063293	—	4	2	no	—
146	#13063284	C₂³	1	1	yes	characteristic
147	#13063261	C₂³	1	2	yes	complemented
148	#13063261	C₂³	1	2	yes	complemented
149	#13063260	C₂³	1	4	yes	complemented
150	#13063252	C₂³	1	8	yes	complemented
151	#13063252	C₂³	1	4	yes	complemented
152	#13063251	C₂³	1	4	yes	—
153	#13063244	C₂³	1	4	yes	complemented
154	#13063242	C₂³	1	4	yes	complemented
155	#13063241	C₂³	1	8	yes	complemented
156	#13063235	C₂³	1	2	yes	complemented
157	C₈×Dic₄₃	C₂³	1	2	yes	complemented
158	2₋¹⁺⁴×C₄₃	—	2	2	no	—
159	2₋¹⁺⁴×C₄₃	—	2	2	no	—
160	2₋¹⁺⁴×C₄₃	C₂³	1	4	yes	complemented
161	H(5,𝔽₂)×C₄₃	—	2	2	no	—
162	H(5,𝔽₂)×C₄₃	—	2	2	no	—
163	H(5,𝔽₂)×C₄₃	—	4	2	no	—
164	H(5,𝔽₂)×C₄₃	C₂³	1	4	yes	complemented
165	C₂×#41×C₄₃	—	2	4	no	—
166	C₂×#41×C₄₃	—	2	4	no	—
167	C₂×#41×C₄₃	—	4	2	no	—
168	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
169	C₂×#41×C₄₃	C₂³	1	2	yes	—
170	C₂×#41×C₄₃	C₂³	1	2	yes	—
171	#137×C₄₃	—	2	2	no	—
172	#137×C₄₃	—	2	4	no	—
173	#137×C₄₃	—	2	4	no	—
174	#137×C₄₃	C₂³	1	4	yes	complemented
175	AGL(1,ℤ/8)×C₄₃	—	2	2	no	—
176	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
177	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
178	AGL(1,ℤ/8)×C₄₃	C₂³	1	4	yes	complemented
179	#135×C₄₃	—	2	4	no	—
180	#135×C₄₃	—	2	2	no	—
181	#135×C₄₃	—	2	4	no	—
182	#135×C₄₃	—	2	2	no	—
183	#135×C₄₃	—	2	1	no	—
184	#135×C₄₃	—	2	1	no	—
185	#135×C₄₃	—	2	1	no	—
186	#135×C₄₃	—	2	1	no	—
187	#135×C₄₃	D₄	1	2	yes	complemented
188	#135×C₄₃	D₄	1	2	yes	complemented
189	#135×C₄₃	C₂³	1	2	yes	—
190	#135×C₄₃	C₂³	1	2	yes	—
191	C₂×Q₁₆×C₄₃	—	2	2	no	—
192	C₂×Q₁₆×C₄₃	D₄	1	1	yes	characteristic, complemented
193	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic, complemented
194	C₂×SD₁₆×C₄₃	—	2	4	no	—
195	C₂×SD₁₆×C₄₃	D₄	1	2	yes	complemented
196	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	complemented
197	C₂×D₈×C₄₃	—	2	2	no	—
198	C₂×D₈×C₄₃	D₄	1	1	yes	characteristic, complemented
199	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
200	#131×C₄₃	—	2	1	no	—
201	#131×C₄₃	—	2	1	no	—
202	#131×C₄₃	C₂³	1	2	yes	complemented
203	#131×C₄₃	C₂³	1	2	yes	complemented
204	C₂×M₁₆×C₄₃	—	2	1	no	—
205	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
206	C₂²×C₈×C₄₃	—	2	1	no	—
207	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
208	C₂³×D₄₃	—	2	2	no	—
209	C₂³×D₄₃	—	4	2	no	—
210	#41×C₄₃	—	2	1	no	—
211	#41×C₄₃	—	2	2	no	—
212	#41×C₄₃	—	2	1	no	—
213	#41×C₄₃	—	2	2	no	—
214	#41×C₄₃	—	2	4	no	—
215	#41×C₄₃	—	2	4	no	—
216	#41×C₄₃	—	2	4	no	—
217	#41×C₄₃	—	2	4	no	—
218	#41×C₄₃	—	2	2	no	—
219	#41×C₄₃	—	2	2	no	—
220	#41×C₄₃	—	2	2	no	—
221	#41×C₄₃	—	2	2	no	—
222	#41×C₄₃	—	4	4	no	—
223	#41×C₄₃	—	4	4	no	—
224	#41×C₄₃	—	4	4	no	—
225	#41×C₄₃	—	4	4	no	—
226	#41×C₄₃	—	4	2	no	—
227	#41×C₄₃	—	4	2	no	—
228	#41×C₄₃	C₂×D₄	1	2	yes	—
229	#41×C₄₃	C₂×D₄	1	4	yes	—
230	#41×C₄₃	C₂⁴	1	2	yes	—
231	#41×C₄₃	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₄₃	—	2	4	no	—
233	C₂×Q₈×C₄₃	—	2	4	no	—
234	C₂×Q₈×C₄₃	—	4	2	no	—
235	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
237	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₄₃	—	2	1	no	—
239	C₂×D₄×C₄₃	—	2	2	no	—
240	C₂×D₄×C₄₃	—	2	2	no	—
241	C₂×D₄×C₄₃	—	2	4	no	—
242	C₂×D₄×C₄₃	—	2	4	no	—
243	C₂×D₄×C₄₃	—	4	4	no	—
244	C₂×D₄×C₄₃	—	4	4	no	—
245	C₂×D₄×C₄₃	—	4	4	no	—
246	C₂×D₄×C₄₃	—	4	2	no	—
247	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₄₃	—	2	1	no	—
251	C₂²×C₄×C₄₃	—	2	2	no	—
252	C₂²×C₄×C₄₃	—	2	2	no	—
253	C₂²×C₄×C₄₃	—	4	4	no	—
254	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₂²⋊D₄₃	—	2	1	no	—
256	C₂×C₂²⋊D₄₃	—	4	4	no	—
257	C₂×C₂²⋊D₄₃	—	4	2	no	—
258	#10621902	—	2	8	no	—
259	#10621902	—	4	4	no	—
260	D₄×D₄₃	—	2	8	no	—
261	D₄×D₄₃	—	4	8	no	—
262	D₄×D₄₃	—	4	4	no	—
263	D₄×D₄₃	—	4	8	no	—
264	#10621898	—	2	1	no	—
265	#10621898	—	2	1	no	—
266	#10621898	—	2	8	no	—
267	#10621898	—	4	4	no	—
268	#10621898	C₂×D₄	1	2	yes	—
269	#10621898	C₂⁴	1	2	yes	—
270	C₂×D₁₇₂	—	2	2	no	—
271	C₂×D₁₇₂	—	2	2	no	—
272	C₂×D₁₇₂	—	2	2	no	—
273	C₂×D₁₇₂	—	2	2	no	—
274	C₂×D₁₇₂	—	2	2	no	—
275	C₂×D₁₇₂	—	2	8	no	—
276	C₂×D₁₇₂	—	4	2	no	—
277	C₂×D₁₇₂	—	4	4	no	—
278	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
279	C₂×D₁₇₂	C₂⁴	1	4	yes	—
280	C₂×C₄×D₄₃	—	2	1	no	—
281	C₂×C₄×D₄₃	—	4	2	no	—
282	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
283	Q₁₆×C₄₃	—	2	4	no	—
284	Q₁₆×C₄₃	—	2	1	no	—
285	Q₁₆×C₄₃	—	2	1	no	—
286	Q₁₆×C₄₃	C₂×D₄	1	2	yes	—
287	Q₁₆×C₄₃	C₂×D₄	1	2	yes	—
288	SD₁₆×C₄₃	—	2	4	no	—
289	SD₁₆×C₄₃	—	2	4	no	—
290	SD₁₆×C₄₃	—	2	2	no	—
291	SD₁₆×C₄₃	—	2	2	no	—
292	SD₁₆×C₄₃	C₂×D₄	1	4	yes	—
293	SD₁₆×C₄₃	C₂×D₄	1	4	yes	—
294	D₈×C₄₃	—	2	4	no	—
295	D₈×C₄₃	—	2	1	no	—
296	D₈×C₄₃	—	2	1	no	—
297	D₈×C₄₃	C₂×D₄	1	2	yes	—
298	D₈×C₄₃	C₂×D₄	1	2	yes	—
299	M₁₆×C₄₃	—	2	1	no	—
300	M₁₆×C₄₃	—	2	2	no	—
301	M₁₆×C₄₃	—	2	2	no	—
302	M₁₆×C₄₃	C₂⁴	1	2	yes	—
303	C₂×C₈×C₄₃	—	2	1	no	—
304	C₂×C₈×C₄₃	—	2	2	no	—
305	C₂×C₈×C₄₃	—	2	2	no	—
306	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
307	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
308	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
309	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
310	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
312	C₂²⋊Dic₄₃	—	2	1	no	—
313	#10621885	—	2	4	no	—
314	#10621885	C₂×D₄	1	4	yes	—
315	#10621884	—	2	8	no	—
316	#10621884	—	2	8	no	—
317	#10621884	—	2	4	no	—
318	#10621884	—	2	8	no	—
319	#10621884	C₂×D₄	1	4	yes	—
320	#10621883	—	2	4	no	—
321	#10621883	C₂×D₄	1	4	yes	—
322	#10621882	—	2	8	no	—
323	#10621882	—	2	8	no	—
324	#10621882	—	2	4	no	—
325	#10621882	—	2	8	no	—
326	#10621882	C₂×D₄	1	4	yes	—
327	(C₂×D₄₃)⋊C₄	—	4	4	no	—
328	C₄⋊Dic₄₃	—	2	1	no	—
329	C₄×Dic₄₃	C₂⁴	1	2	yes	—
330	#10621877	—	2	2	no	—
331	#10621877	—	2	1	no	—
332	#10621877	—	2	8	no	—
333	#10621877	C₂×D₄	1	2	yes	—
334	#10621877	C₂×D₄	1	2	yes	—
335	#10621877	C₂⁴	1	4	yes	—
336	#10621877	C₂⁴	1	2	yes	—
337	C₂×C₄₃⋊C₈	—	2	1	no	—
338	C₂×C₄₃⋊C₈	—	2	2	no	—
339	C₂×C₄₃⋊C₈	—	2	8	no	—
340	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
341	D₃₄₄	—	2	2	no	—
342	D₃₄₄	—	2	2	no	—
343	D₃₄₄	—	2	2	no	—
344	D₃₄₄	—	2	2	no	—
345	#10621872	—	2	2	no	—
346	#10621872	—	2	2	no	—
347	C₈×D₄₃	—	2	2	no	—
348	C₈×D₄₃	—	2	2	no	—
349	C₂³×C₄₃	—	2	2	no	—
350	C₂³×C₄₃	—	2	1	no	—
351	C₂³×C₄₃	—	2	2	no	—
352	C₂³×C₄₃	—	4	4	no	—
353	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×D₄₃	—	2	1	no	—
355	C₂²×D₄₃	—	2	4	no	—
356	C₂²×D₄₃	—	4	8	no	—
357	C₂²×D₄₃	—	4	2	no	—
358	C₂²×D₄₃	—	4	2	no	—
359	C₂²×D₄₃	—	16	4	no	—
360	C₂²×D₄₃	—	16	2	no	—
361	Q₈×C₄₃	—	2	2	no	—
362	Q₈×C₄₃	—	2	1	no	—
363	Q₈×C₄₃	—	2	2	no	—
364	Q₈×C₄₃	—	2	2	no	—
365	Q₈×C₄₃	—	4	4	no	—
366	Q₈×C₄₃	C₂²×D₄	1	2	yes	—
367	Q₈×C₄₃	C₂²×D₄	1	4	yes	—
368	D₄×C₄₃	—	2	4	no	—
369	D₄×C₄₃	—	2	2	no	—
370	D₄×C₄₃	—	2	4	no	—
371	D₄×C₄₃	—	2	2	no	—
372	D₄×C₄₃	—	2	2	no	—
373	D₄×C₄₃	—	2	1	no	—
374	D₄×C₄₃	—	2	2	no	—
375	D₄×C₄₃	—	2	2	no	—
376	D₄×C₄₃	—	4	4	no	—
377	D₄×C₄₃	—	4	4	no	—
378	D₄×C₄₃	—	4	4	no	—
379	D₄×C₄₃	—	4	2	no	—
380	D₄×C₄₃	—	4	2	no	—
381	D₄×C₄₃	C₂²×D₄	1	2	yes	—
382	D₄×C₄₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₄₃	—	2	2	no	—
384	C₂×C₄×C₄₃	—	2	1	no	—
385	C₂×C₄×C₄₃	—	2	4	no	—
386	C₂×C₄×C₄₃	—	2	2	no	—
387	C₂×C₄×C₄₃	—	2	4	no	—
388	C₂×C₄×C₄₃	—	2	2	no	—
389	C₂×C₄×C₄₃	—	2	2	no	—
390	C₂×C₄×C₄₃	—	4	4	no	—
391	C₂×C₄×C₄₃	—	4	4	no	—
392	C₂×C₄×C₄₃	—	4	4	no	—
393	C₂×C₄×C₄₃	—	4	2	no	—
394	C₂×C₄×C₄₃	—	4	2	no	—
395	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
400	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
401	C₂²⋊D₄₃	—	2	2	no	—
402	C₂²⋊D₄₃	—	2	2	no	—
403	C₂²⋊D₄₃	—	4	8	no	—
404	C₂²⋊D₄₃	—	16	4	no	—
405	C₂×Dic₄₃	—	2	1	no	—
406	C₂×Dic₄₃	—	2	2	no	—
407	D₁₇₂	—	2	1	no	—
408	D₁₇₂	—	2	4	no	—
409	D₁₇₂	—	2	4	no	—
410	D₁₇₂	—	4	8	no	—
411	D₁₇₂	—	4	2	no	—
412	D₁₇₂	—	4	2	no	—
413	D₁₇₂	C₂²×D₄	1	2	yes	—
414	C₄×D₄₃	—	2	2	no	—
415	C₄×D₄₃	—	2	2	no	—
416	C₄×D₄₃	—	4	8	no	—
417	Dic₈₆	—	2	1	no	—
418	Dic₈₆	C₂²×D₄	1	2	yes	—
419	C₈×C₄₃	—	2	2	no	—
420	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
421	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
422	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
423	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
424	C₄₃⋊C₈	—	2	2	no	—
425	C₄₃⋊C₈	—	2	4	no	—
426	C₄₃⋊C₈	C₂²×D₄	1	4	yes	—
427	#61106	—	43	1	no	maximal, Sylow
428	C₂²×C₄₃	—	2	4	no	—
429	C₂²×C₄₃	—	2	2	no	—
430	C₂²×C₄₃	—	4	1	no	—
431	C₂²×C₄₃	—	4	2	no	—
432	C₂²×C₄₃	—	8	2	no	—
433	C₂²×C₄₃	—	8	1	no	—
434	C₂²×C₄₃	—	8	2	no	—
435	C₂²×C₄₃	—	16	4	no	—
436	C₂²×C₄₃	D₄²	1	1	yes	characteristic
437	C₂²×C₄₃	D₄²	1	1	yes	characteristic
438	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×D₄₃	—	2	2	no	—
440	C₂×D₄₃	—	4	2	no	—
441	C₂×D₄₃	—	4	4	no	—
442	C₂×D₄₃	—	8	4	no	—
443	C₂×D₄₃	—	8	4	no	—
444	C₂×D₄₃	—	16	8	no	—
445	C₂×D₄₃	—	16	2	no	—
446	C₄×C₄₃	—	2	4	no	—
447	C₄×C₄₃	—	2	2	no	—
448	C₄×C₄₃	—	4	2	no	—
449	C₄×C₄₃	D₄²	1	1	yes	characteristic
450	C₄×C₄₃	D₄²	1	1	yes	characteristic
451	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
452	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
453	Dic₄₃	—	2	2	no	—
454	Dic₄₃	—	4	2	no	—
455	#3585	—	43	2	no	—
456	#3584	D₄₃	1	1	yes	characteristic, complemented
457	C₂×#576	—	43	1	no	—
458	#3292	—	43	4	no	—
459	#3290	—	43	4	no	—
460	#3288	—	43	8	no	—
461	#3155	—	43	1	no	—
462	#3068	—	43	2	no	—
463	#3067	—	43	1	no	—
464	C₂×#472	—	43	1	no	—
465	#3021	—	43	2	no	—
466	#3019	—	43	2	no	—
467	#2957	—	43	1	no	—
468	#2955	—	43	1	no	—
469	C₂×C₄₃	—	2	1	no	—
470	C₂×C₄₃	—	2	1	no	—
471	C₂×C₄₃	—	2	1	no	—
472	C₂×C₄₃	—	4	4	no	—
473	C₂×C₄₃	—	4	2	no	—
474	C₂×C₄₃	—	8	2	no	—
475	C₂×C₄₃	C₂×D₄²	1	1	yes	characteristic
476	D₄₃	—	4	2	no	—
477	D₄₃	—	8	4	no	—
478	#585	C₂×D₄₃	1	2	yes	complemented
479	C₂×H(5,𝔽₂)	—	43	2	no	—
480	#578	—	2	1	no	—
481	#578	C₂×D₄₃	1	2	yes	complemented
482	#577	—	2	2	no	—
483	#577	—	43	8	no	—
484	#577	—	86	4	no	—
485	#577	C₂×D₄₃	1	4	yes	complemented
486	#576	—	2	1	no	—
487	#576	—	43	8	no	—
488	#576	—	43	4	no	—
489	#576	—	43	4	no	—
490	#576	—	86	4	no	—
491	#576	—	86	2	no	—
492	#576	—	86	2	no	—
493	#576	C₂×D₄₃	1	2	yes	complemented
494	#575	—	2	2	no	—
495	#575	—	43	1	no	—
496	#575	—	43	2	no	—
497	#575	—	86	4	no	—
498	#575	C₂×D₄₃	1	2	yes	complemented
499	C₂×AGL(1,ℤ/8)	—	43	2	no	—
500	C₂×AGL(1,ℤ/8)	—	43	2	no	—
501	C₂×AGL(1,ℤ/8)	—	43	2	no	—
502	C₂×AGL(1,ℤ/8)	—	86	4	no	—
503	C₂×AGL(1,ℤ/8)	—	86	2	no	—
504	C₂×#135	—	2	2	no	—
505	C₂×#135	—	86	1	no	—
506	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
507	C₂×#135	C₂×D₄₃	1	1	yes	characteristic, complemented
508	C₂²×D₈	—	43	1	no	—
509	C₂²×D₈	—	86	1	no	—
510	#568	—	43	2	no	—
511	C₂×#131	—	43	1	no	—
512	C₂×#131	C₂×D₄₃	1	1	yes	characteristic, complemented
513	#535	—	43	2	no	—
514	#496	—	43	4	no	—
515	#495	—	43	2	no	—
516	#493	—	43	2	no	—
517	#473	—	43	2	no	—
518	#472	—	43	8	no	—
519	#472	—	43	2	no	—
520	#472	—	43	4	no	—
521	#472	—	43	4	no	—
522	#471	—	43	8	no	—
523	#471	—	43	4	no	—
524	#455	—	43	8	no	—
525	#454	—	43	8	no	—
526	#453	—	43	8	no	—
527	#453	—	43	8	no	—
528	#444	—	43	4	no	—
529	#444	—	43	4	no	—
530	#443	—	43	4	no	—
531	#443	—	43	4	no	—
532	#430	—	43	1	no	—
533	C₂×#108	—	43	1	no	—
534	#421	—	43	1	no	—
535	#421	—	43	2	no	—
536	#421	—	43	1	no	—
537	#413	—	43	2	no	—
538	C₂×#100	—	43	2	no	—
539	#405	—	43	1	no	—
540	C₄₃	#61106	1	1	yes	characteristic, complemented, Sylow
541	2₋¹⁺⁴	—	2	2	no	—
542	2₋¹⁺⁴	—	2	2	no	—
543	2₋¹⁺⁴	C₂²×D₄₃	1	4	yes	complemented
544	H(5,𝔽₂)	—	2	2	no	—
545	H(5,𝔽₂)	—	2	2	no	—
546	H(5,𝔽₂)	—	4	2	no	—
547	H(5,𝔽₂)	—	43	8	no	—
548	H(5,𝔽₂)	—	86	4	no	—
549	H(5,𝔽₂)	—	86	4	no	—
550	H(5,𝔽₂)	—	172	2	no	—
551	H(5,𝔽₂)	C₂²×D₄₃	1	4	yes	complemented
552	C₂×#41	—	2	4	no	—
553	C₂×#41	—	2	4	no	—
554	C₂×#41	—	4	2	no	—
555	C₂×#41	—	43	1	no	—
556	C₂×#41	—	86	2	no	—
557	C₂×#41	—	86	2	no	—
558	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
559	C₂×#41	C₂²×D₄₃	1	2	yes	—
560	C₂×#41	C₂²×D₄₃	1	2	yes	—
561	C₂²×D₄	—	43	2	no	—
562	C₂²×D₄	—	86	2	no	—
563	C₂²×D₄	—	86	2	no	—
564	C₂²×D₄	—	172	2	no	—
565	#137	—	2	2	no	—
566	#137	—	2	4	no	—
567	#137	—	2	4	no	—
568	#137	—	43	2	no	—
569	#137	—	43	2	no	—
570	#137	—	43	4	no	—
571	#137	—	86	8	no	—
572	#137	—	86	2	no	—
573	#137	C₂²×D₄₃	1	4	yes	complemented
574	AGL(1,ℤ/8)	—	2	2	no	—
575	AGL(1,ℤ/8)	—	2	4	no	—
576	AGL(1,ℤ/8)	—	2	4	no	—
577	AGL(1,ℤ/8)	—	43	2	no	—
578	AGL(1,ℤ/8)	—	43	2	no	—
579	AGL(1,ℤ/8)	—	43	8	no	—
580	AGL(1,ℤ/8)	—	43	8	no	—
581	AGL(1,ℤ/8)	—	43	4	no	—
582	AGL(1,ℤ/8)	—	86	4	no	—
583	AGL(1,ℤ/8)	—	86	4	no	—
584	AGL(1,ℤ/8)	—	86	8	no	—
585	AGL(1,ℤ/8)	—	86	8	no	—
586	AGL(1,ℤ/8)	—	86	8	no	—
587	AGL(1,ℤ/8)	—	86	2	no	—
588	AGL(1,ℤ/8)	—	86	4	no	—
589	AGL(1,ℤ/8)	—	86	4	no	—
590	AGL(1,ℤ/8)	—	86	8	no	—
591	AGL(1,ℤ/8)	—	86	8	no	—
592	AGL(1,ℤ/8)	C₂²×D₄₃	1	4	yes	complemented
593	#135	—	2	4	no	—
594	#135	—	2	2	no	—
595	#135	—	2	4	no	—
596	#135	—	2	2	no	—
597	#135	—	2	1	no	—
598	#135	—	2	1	no	—
599	#135	—	2	1	no	—
600	#135	—	2	1	no	—
601	#135	—	43	4	no	—
602	#135	—	86	8	no	—
603	#135	—	86	8	no	—
604	#135	—	86	4	no	—
605	#135	—	86	4	no	—
606	#135	—	86	4	no	—
607	#135	C₂²⋊D₄₃	1	2	yes	complemented
608	#135	C₂²⋊D₄₃	1	2	yes	complemented
609	#135	C₂²×D₄₃	1	2	yes	—
610	#135	C₂²×D₄₃	1	2	yes	—
611	C₂×Q₁₆	—	2	2	no	—
612	C₂×Q₁₆	C₂²⋊D₄₃	1	1	yes	characteristic, complemented
613	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic, complemented
614	C₂×SD₁₆	—	2	4	no	—
615	C₂×SD₁₆	—	43	4	no	—
616	C₂×SD₁₆	—	86	8	no	—
617	C₂×SD₁₆	—	86	2	no	—
618	C₂×SD₁₆	—	86	2	no	—
619	C₂×SD₁₆	C₂²⋊D₄₃	1	2	yes	complemented
620	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	complemented
621	C₂×D₈	—	2	2	no	—
622	C₂×D₈	—	43	4	no	—
623	C₂×D₈	—	43	2	no	—
624	C₂×D₈	—	43	2	no	—
625	C₂×D₈	—	86	8	no	—
626	C₂×D₈	—	86	2	no	—
627	C₂×D₈	—	86	2	no	—
628	C₂×D₈	—	86	4	no	—
629	C₂×D₈	—	86	4	no	—
630	C₂×D₈	—	86	1	no	—
631	C₂×D₈	—	86	1	no	—
632	C₂×D₈	—	86	1	no	—
633	C₂×D₈	—	86	1	no	—
634	C₂×D₈	C₂²⋊D₄₃	1	1	yes	characteristic, complemented
635	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
636	#131	—	2	1	no	—
637	#131	—	2	1	no	—
638	#131	—	43	8	no	—
639	#131	—	43	2	no	—
640	#131	—	43	2	no	—
641	#131	—	86	4	no	—
642	#131	—	86	1	no	—
643	#131	—	86	1	no	—
644	#131	C₂²×D₄₃	1	2	yes	complemented
645	#131	C₂²×D₄₃	1	2	yes	complemented
646	C₂×M₁₆	—	2	1	no	—
647	C₂×M₁₆	—	43	1	no	—
648	C₂×M₁₆	—	43	1	no	—
649	C₂×M₁₆	—	43	2	no	—
650	C₂×M₁₆	—	86	4	no	—
651	C₂×M₁₆	—	86	1	no	—
652	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
653	C₂²×C₈	—	2	1	no	—
654	C₂²×C₈	—	86	1	no	—
655	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
656	#127	—	43	4	no	—
657	#124	—	43	4	no	—
658	#121	—	172	2	no	—
659	#120	—	172	2	no	—
660	#117	—	43	1	no	—
661	#108	—	43	4	no	—
662	#108	—	43	2	no	—
663	#108	—	43	2	no	—
664	#104	—	43	4	no	—
665	#104	—	43	8	no	—
666	#104	—	43	4	no	—
667	#101	—	43	4	no	—
668	#100	—	43	4	no	—
669	#100	—	43	8	no	—
670	#97	—	43	2	no	—
671	C₄×C₈	—	43	2	no	—
672	C₂⁴	—	86	2	no	—
673	C₂⁴	—	172	2	no	—
674	#41	—	2	2	no	—
675	#41	—	2	1	no	—
676	#41	—	2	1	no	—
677	#41	—	2	2	no	—
678	#41	—	2	4	no	—
679	#41	—	2	4	no	—
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	2	2	no	—
683	#41	—	2	2	no	—
684	#41	—	2	2	no	—
685	#41	—	2	2	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	4	no	—
690	#41	—	4	2	no	—
691	#41	—	4	2	no	—
692	#41	—	43	2	no	—
693	#41	—	43	2	no	—
694	#41	—	86	8	no	—
695	#41	—	86	1	no	—
696	#41	—	86	1	no	—
697	#41	—	86	8	no	—
698	#41	—	172	4	no	—
699	#41	—	172	4	no	—
700	#41	D₄×D₄₃	1	2	yes	—
701	#41	C₂×C₂²⋊D₄₃	1	4	yes	—
702	#41	C₂³×D₄₃	1	2	yes	—
703	#41	C₂³×D₄₃	1	4	yes	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	4	2	no	—
707	C₂×Q₈	—	43	1	no	—
708	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
709	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
710	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	43	1	no	—
721	C₂×D₄	—	43	4	no	—
722	C₂×D₄	—	86	8	no	—
723	C₂×D₄	—	86	1	no	—
724	C₂×D₄	—	86	8	no	—
725	C₂×D₄	—	86	2	no	—
726	C₂×D₄	—	86	2	no	—
727	C₂×D₄	—	86	2	no	—
728	C₂×D₄	—	86	2	no	—
729	C₂×D₄	—	86	2	no	—
730	C₂×D₄	—	172	4	no	—
731	C₂×D₄	—	172	2	no	—
732	C₂×D₄	—	172	4	no	—
733	C₂×D₄	—	172	2	no	—
734	C₂×D₄	—	172	4	no	—
735	C₂×D₄	—	172	8	no	—
736	C₂×D₄	—	172	8	no	—
737	C₂×D₄	D₄×D₄₃	1	1	yes	characteristic
738	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
739	C₂×D₄	C₂³×D₄₃	1	2	yes	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	4	4	no	—
744	C₂²×C₄	—	86	1	no	—
745	C₂²×C₄	—	172	2	no	—
746	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
747	Q₁₆	—	2	4	no	—
748	Q₁₆	—	2	1	no	—
749	Q₁₆	—	2	1	no	—
750	Q₁₆	—	43	4	no	—
751	Q₁₆	—	86	4	no	—
752	Q₁₆	C₂×C₂²⋊D₄₃	1	2	yes	—
753	Q₁₆	C₂×C₂²⋊D₄₃	1	2	yes	—
754	SD₁₆	—	2	4	no	—
755	SD₁₆	—	2	4	no	—
756	SD₁₆	—	2	2	no	—
757	SD₁₆	—	2	2	no	—
758	SD₁₆	—	43	4	no	—
759	SD₁₆	—	43	4	no	—
760	SD₁₆	—	86	8	no	—
761	SD₁₆	—	86	4	no	—
762	SD₁₆	—	86	4	no	—
763	SD₁₆	—	86	8	no	—
764	SD₁₆	—	86	8	no	—
765	SD₁₆	C₂×C₂²⋊D₄₃	1	4	yes	—
766	SD₁₆	C₂×C₂²⋊D₄₃	1	4	yes	—
767	D₈	—	2	4	no	—
768	D₈	—	2	1	no	—
769	D₈	—	2	1	no	—
770	D₈	—	43	4	no	—
771	D₈	—	86	8	no	—
772	D₈	—	86	4	no	—
773	D₈	—	86	8	no	—
774	D₈	—	86	8	no	—
775	D₈	—	86	2	no	—
776	D₈	—	86	2	no	—
777	D₈	—	86	2	no	—
778	D₈	—	86	2	no	—
779	D₈	C₂×C₂²⋊D₄₃	1	2	yes	—
780	D₈	C₂×C₂²⋊D₄₃	1	2	yes	—
781	M₁₆	—	2	1	no	—
782	M₁₆	—	2	2	no	—
783	M₁₆	—	2	2	no	—
784	M₁₆	—	43	2	no	—
785	M₁₆	—	43	2	no	—
786	M₁₆	—	43	4	no	—
787	M₁₆	—	43	2	no	—
788	M₁₆	—	86	8	no	—
789	M₁₆	—	86	2	no	—
790	M₁₆	—	86	1	no	—
791	M₁₆	—	86	2	no	—
792	M₁₆	—	86	2	no	—
793	M₁₆	C₂³×D₄₃	1	2	yes	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	2	2	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	43	2	no	—
798	C₂×C₈	—	86	8	no	—
799	C₂×C₈	—	86	2	no	—
800	C₂×C₈	—	86	1	no	—
801	C₂×C₈	—	86	2	no	—
802	C₂×C₈	—	86	2	no	—
803	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
804	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
805	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
806	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
807	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
808	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
809	C₄⋊C₄	—	86	1	no	—
810	C₂²⋊C₄	—	86	1	no	—
811	C₂²⋊C₄	—	172	4	no	—
812	C₄²	—	43	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	86	1	no	—
818	C₂³	—	86	4	no	—
819	C₂³	—	172	8	no	—
820	C₂³	—	172	2	no	—
821	C₂³	—	172	2	no	—
822	C₂³	—	688	2	no	—
823	C₂³	—	688	4	no	—
824	C₂³	#13063370	1	1	yes	characteristic
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	4	4	no	—
830	Q₈	—	43	2	no	—
831	Q₈	—	86	1	no	—
832	Q₈	C₂×D₄×D₄₃	1	2	yes	—
833	Q₈	C₂²×C₂²⋊D₄₃	1	4	yes	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	4	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	2	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	2	no	—
847	D₄	—	43	2	no	—
848	D₄	—	86	2	no	—
849	D₄	—	86	2	no	—
850	D₄	—	86	4	no	—
851	D₄	—	86	4	no	—
852	D₄	—	86	1	no	—
853	D₄	—	172	8	no	—
854	D₄	—	172	8	no	—
855	D₄	—	172	2	no	—
856	D₄	—	172	2	no	—
857	D₄	—	688	4	no	—
858	D₄	C₂×D₄×D₄₃	1	2	yes	—
859	D₄	C₂²×C₂²⋊D₄₃	1	4	yes	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	86	1	no	—
873	C₂×C₄	—	86	2	no	—
874	C₂×C₄	—	86	2	no	—
875	C₂×C₄	—	86	2	no	—
876	C₂×C₄	—	172	8	no	—
877	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
878	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
881	C₂×C₄	#13063370	1	1	yes	characteristic
882	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
883	C₈	—	2	2	no	—
884	C₈	—	43	4	no	—
885	C₈	—	86	4	no	—
886	C₈	—	86	2	no	—
887	C₈	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
888	C₈	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
889	C₈	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
890	C₈	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
891	C₂²	—	2	2	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	8	2	no	—
896	C₂²	—	8	1	no	—
897	C₂²	—	8	2	no	—
898	C₂²	—	16	4	no	—
899	C₂²	—	86	2	no	—
900	C₂²	—	344	4	no	—
901	C₂²	—	344	4	no	—
902	C₂²	—	172	2	no	—
903	C₂²	—	172	4	no	—
904	C₂²	—	688	2	no	—
905	C₂²	—	688	8	no	—
906	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
907	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
908	C₂²	C₂×#13063370	1	1	yes	characteristic
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	4	2	no	—
912	C₄	—	86	2	no	—
913	C₄	—	172	2	no	—
914	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
915	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
916	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
917	C₄	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
918	C₂	—	2	1	no	—
919	C₂	—	2	1	no	—
920	C₂	—	2	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	4	4	no	—
923	C₂	—	8	2	no	—
924	C₂	—	344	4	no	—
925	C₂	—	172	2	no	—
926	C₂	C₂×D₄×C₂²⋊D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3584	C₂
socle	C₂×C₄₃	C₂×D₄²
hypercenter	#3584	D₄₃
hypocenter	C₄₃	#61106
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #19149374	C₂	semidirect
2. C₂×#14583701	C₂	semidirect
3. #19146392	C₂	semidirect
4. #19146381	C₂	semidirect
5. #19146357	C₂	semidirect
6. #19145082	C₂	semidirect
7. #19144325	C₂	semidirect
8. #19144311	C₂	semidirect
9. C₂×#14583169	C₂	semidirect
10. #19143967	C₂	semidirect
11. #19143950	C₂	semidirect
12. #19143512	C₂	semidirect
13. #19143496	C₂	semidirect
14. C₄₃×#3584	C₂	semidirect
15. C₂×#13063371	C₂²	semidirect
17. #14583707	C₂²	semidirect
19. #14583702	C₂²	semidirect
22. #14583701	C₂²	semidirect
23. #14583701	C₂²	semidirect
26. #14583697	C₂²	semidirect
29. C₂×#13063350	C₂²	semidirect
30. C₂×#13063350	C₂²	semidirect
31. C₂×#13063350	C₂²	semidirect
33. C₂²×D₃₄₄	C₂²	semidirect
35. #14583666	C₂²	semidirect
36. C₂×#13063331	C₂²	semidirect
37. #14583463	C₂²	semidirect
38. #14583285	C₂²	semidirect
39. #14583284	C₂²	semidirect
40. #14583274	C₂²	semidirect
41. #14583171	C₂²	semidirect
42. #14583169	C₂²	semidirect
43. #14583169	C₂²	semidirect
44. #14583167	C₂²	semidirect
45. #14583166	C₂²	semidirect
46. #14583164	C₂²	semidirect
47. #14583159	C₂²	semidirect
48. #14583075	C₂²	semidirect
49. #14583072	C₂²	semidirect
50. #14583067	C₂²	semidirect
51. #14583065	C₂²	semidirect
52. #14583021	C₂²	semidirect
53. #14583019	C₂²	semidirect
54. #14583016	C₂²	semidirect
55. #14583014	C₂²	semidirect
56. #14582947	C₂²	semidirect
57. C₂×#13063261	C₂²	semidirect
58. #14582916	C₂²	semidirect
59. #14582916	C₂²	semidirect
60. #14582915	C₂²	semidirect
61. #14582883	C₂²	semidirect
62. C₂×#13063241	C₂²	semidirect
63. #14582854	C₂²	semidirect
64. C₄₃×#585	C₂²	semidirect
66. C₄₃×#578	C₂²	semidirect
68. C₄₃×#577	C₂²	semidirect
70. C₄₃×#576	C₂²	semidirect
72. C₄₃×#575	C₂²	semidirect
75. C₂×#135×C₄₃	C₂²	semidirect
76. C₂×#131×C₄₃	C₂²	semidirect
89. #13063356	D₄	semidirect
92. #13063355	D₄	semidirect
96. #13063351	D₄	semidirect
105. #13063350	D₄	semidirect
107. #13063350	C₂³	semidirect
117. C₂×#10621884	C₂³	semidirect
127. C₂×#10621882	C₂³	semidirect
131. #13063332	C₂³	semidirect
142. #13063321	C₂³	semidirect
143. #13063314	C₂³	semidirect
147. #13063261	C₂³	semidirect
148. #13063261	C₂³	semidirect
149. #13063260	C₂³	semidirect
150. #13063252	C₂³	semidirect
151. #13063252	C₂³	semidirect
153. #13063244	C₂³	semidirect
154. #13063242	C₂³	semidirect
155. #13063241	C₂³	semidirect
156. #13063235	C₂³	semidirect
157. C₈×Dic₄₃	C₂³	semidirect
160. 2₋¹⁺⁴×C₄₃	C₂³	semidirect
164. H(5,𝔽₂)×C₄₃	C₂³	semidirect
174. #137×C₄₃	C₂³	semidirect
178. AGL(1,ℤ/8)×C₄₃	C₂³	semidirect
187. #135×C₄₃	D₄	semidirect
188. #135×C₄₃	D₄	semidirect
192. C₂×Q₁₆×C₄₃	D₄	semidirect
193. C₂×Q₁₆×C₄₃	C₂³	semidirect
195. C₂×SD₁₆×C₄₃	D₄	semidirect
196. C₂×SD₁₆×C₄₃	C₂³	semidirect
198. C₂×D₈×C₄₃	D₄	semidirect
199. C₂×D₈×C₄₃	C₂³	semidirect
202. #131×C₄₃	C₂³	semidirect
203. #131×C₄₃	C₂³	semidirect
456. #3584	D₄₃	semidirect
478. #585	C₂×D₄₃	semidirect
481. #578	C₂×D₄₃	semidirect
485. #577	C₂×D₄₃	semidirect
493. #576	C₂×D₄₃	semidirect
498. #575	C₂×D₄₃	semidirect
507. C₂×#135	C₂×D₄₃	semidirect
512. C₂×#131	C₂×D₄₃	semidirect
540. C₄₃	#61106	semidirect
543. 2₋¹⁺⁴	C₂²×D₄₃	semidirect
551. H(5,𝔽₂)	C₂²×D₄₃	semidirect
573. #137	C₂²×D₄₃	semidirect
592. AGL(1,ℤ/8)	C₂²×D₄₃	semidirect
607. #135	C₂²⋊D₄₃	semidirect
608. #135	C₂²⋊D₄₃	semidirect
612. C₂×Q₁₆	C₂²⋊D₄₃	semidirect
613. C₂×Q₁₆	C₂²×D₄₃	semidirect
619. C₂×SD₁₆	C₂²⋊D₄₃	semidirect
620. C₂×SD₁₆	C₂²×D₄₃	semidirect
634. C₂×D₈	C₂²⋊D₄₃	semidirect
635. C₂×D₈	C₂²×D₄₃	semidirect
644. #131	C₂²×D₄₃	semidirect
645. #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
#19149374	2
C₂×#14583701	2
#19146392	2
#19146381	2
#19146357	2
#19145082	2
#19144325	2
#19144311	2
C₂×#14583169	2
#19143967	2
#19143950	2
#19143512	2
#19143496	2
C₄₃×#3584	2
#61106	43