Subgroups — #25979423

Order 11008.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148612	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148573	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147624	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147503	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147271	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147242	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147223	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147121	C₂	1	2	yes	maximal, complemented
9	#19146525	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146508	C₂	1	2	yes	maximal, complemented
11	#19146483	C₂	1	2	yes	maximal, complemented
12	#19146473	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146242	C₂	1	1	yes	maximal, characteristic, complemented
14	#19146150	C₂	1	2	yes	maximal, complemented
15	#19145259	C₂	1	2	yes	maximal, complemented
16	#19145181	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144892	C₂	1	2	yes	maximal, complemented
18	#19144853	C₂	1	2	yes	maximal, complemented
19	#19144757	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144757	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143570	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143431	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063354	C₂²	1	2	yes	—
25	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic
26	#14583627	C₂²	1	1	yes	characteristic
27	#14583619	—	2	1	no	—
28	#14583619	C₂²	1	1	yes	characteristic
29	#14583617	—	2	2	no	—
30	#14583617	C₂²	1	2	yes	—
31	#14583614	—	2	1	no	—
32	#14583614	C₂²	1	1	yes	characteristic
33	#14583609	C₂²	1	1	yes	characteristic
34	#14583606	C₂²	1	1	yes	characteristic
35	#14583595	—	2	1	no	—
36	#14583589	—	2	1	no	—
37	#14583588	C₂²	1	2	yes	—
38	#14583582	—	2	2	no	—
39	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic
40	#14583556	C₂²	1	2	yes	—
41	#14583553	C₂²	1	1	yes	characteristic
42	#14583548	C₂²	1	2	yes	—
43	#14583514	—	2	2	no	—
44	#14583514	C₂²	1	2	yes	—
45	#14583507	C₂²	1	2	yes	—
46	#14583491	—	2	2	no	—
47	#14583456	—	2	1	no	—
48	#14583456	C₂²	1	1	yes	characteristic
49	#14583456	C₂²	1	1	yes	characteristic
50	#14583433	—	2	1	no	—
51	#14583433	—	2	1	no	—
52	#14583433	C₂²	1	1	yes	characteristic
53	C₂×#13063317	—	2	1	no	—
54	#14583378	C₂²	1	2	yes	—
55	#14583375	C₂²	1	2	yes	—
56	#14583306	C₂²	1	2	yes	—
57	#14583304	C₂²	1	1	yes	characteristic
58	#14583290	C₂²	1	2	yes	—
59	#14583279	C₂²	1	1	yes	characteristic
60	#14583252	C₂²	1	2	yes	—
61	#14583250	C₂²	1	1	yes	characteristic
62	#14583250	C₂²	1	1	yes	characteristic
63	#14583248	C₂²	1	2	yes	—
64	#14583242	C₂²	1	2	yes	—
65	#14583240	C₂²	1	2	yes	—
66	#14583240	C₂²	1	2	yes	—
67	#14583239	C₂²	1	2	yes	—
68	#14583236	C₂²	1	2	yes	—
69	#14583211	C₂²	1	2	yes	—
70	#14583208	C₂²	1	2	yes	—
71	#14583205	C₂²	1	2	yes	—
72	#14583194	C₂²	1	1	yes	characteristic
73	#14583194	C₂²	1	1	yes	characteristic
74	#14583193	C₂²	1	2	yes	—
75	#14583189	C₂²	1	1	yes	characteristic
76	#14583189	C₂²	1	1	yes	characteristic
77	#14583177	C₂²	1	2	yes	—
78	#14583158	C₂²	1	2	yes	—
79	#14583142	C₂²	1	2	yes	—
80	#14583140	C₂²	1	2	yes	—
81	#14583140	C₂²	1	2	yes	—
82	#14583139	C₂²	1	2	yes	—
83	#14583127	C₂²	1	2	yes	—
84	#14583120	C₂²	1	2	yes	—
85	#14583112	C₂²	1	2	yes	—
86	#14583109	C₂²	1	1	yes	characteristic
87	#14583109	C₂²	1	1	yes	characteristic
88	#14583108	C₂²	1	2	yes	—
89	#14583107	C₂²	1	2	yes	—
90	#14583104	C₂²	1	1	yes	characteristic
91	#14583104	C₂²	1	1	yes	characteristic
92	#14583062	C₂²	1	2	yes	—
93	#14583061	C₂²	1	2	yes	—
94	#14583061	C₂²	1	2	yes	—
95	#14583056	C₂²	1	2	yes	—
96	#14583053	C₂²	1	2	yes	—
97	#14583041	C₂²	1	2	yes	—
98	#14583029	C₂²	1	1	yes	characteristic
99	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
100	#14583005	C₂²	1	2	yes	—
101	#14583004	C₂²	1	2	yes	—
102	#14583004	C₂²	1	2	yes	—
103	#14583000	C₂²	1	2	yes	—
104	#14582999	C₂²	1	2	yes	—
105	#14582999	C₂²	1	2	yes	—
106	C₄×Dic₁₇₂	C₂²	1	2	yes	—
107	C₄×Dic₁₇₂	C₂²	1	2	yes	—
108	#14582991	C₂²	1	2	yes	—
109	#14582990	C₂²	1	2	yes	—
110	#14582978	C₂²	1	1	yes	characteristic
111	#14582970	C₂²	1	2	yes	—
112	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
113	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
114	#14582958	C₂²	1	2	yes	—
115	#14582956	C₂²	1	1	yes	characteristic
116	#14582938	C₂²	1	2	yes	—
117	#14582892	C₂²	1	2	yes	—
118	#103×D₄₃	C₂²	1	2	yes	—
119	#14582853	C₂²	1	2	yes	—
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
123	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
131	C₄₃×#427	C₂²	1	1	yes	characteristic
132	C₄₃×#416	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621900	C₂³	1	2	yes	—
136	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
137	#13063354	—	2	8	no	—
138	C₂×Dic₁₇₂	C₂³	1	2	yes	—
139	C₂×Dic₁₇₂	C₂³	1	2	yes	—
140	C₂×#10621885	C₂³	1	2	yes	—
141	C₂×#10621885	C₂³	1	2	yes	—
142	C₂×#10621883	C₂³	1	2	yes	—
143	C₂×#10621883	C₂³	1	2	yes	—
144	C₂×#10621872	C₂³	1	2	yes	—
145	C₂×C₈×D₄₃	C₂³	1	2	yes	—
146	#13063325	—	2	1	no	—
147	#13063325	—	2	1	no	—
148	#13063325	C₂³	1	1	yes	characteristic
149	#13063325	C₂³	1	1	yes	characteristic
150	#13063325	C₂³	1	1	yes	characteristic
151	#13063325	C₂³	1	1	yes	characteristic
152	#13063324	—	2	2	no	—
153	#13063324	C₂³	1	2	yes	—
154	#13063323	C₂³	1	2	yes	—
155	#13063320	—	2	2	no	—
156	#13063319	—	2	2	no	—
157	#13063319	—	2	2	no	—
158	#13063319	D₄	1	2	yes	—
159	#13063318	—	2	2	no	—
160	#13063318	—	2	2	no	—
161	#13063318	—	2	2	no	—
162	#13063318	—	2	2	no	—
163	#13063317	—	2	1	no	—
164	#13063317	—	2	1	no	—
165	#13063317	—	2	1	no	—
166	#13063317	—	2	1	no	—
167	#13063317	—	2	2	no	—
168	#13063317	—	2	2	no	—
169	#13063317	D₄	1	1	yes	characteristic
170	#13063316	C₂³	1	2	yes	—
171	#13063315	—	2	2	no	—
172	#13063315	—	2	2	no	—
173	#13063313	D₄	1	1	yes	characteristic
174	#13063312	—	2	2	no	—
175	#13063312	C₂³	1	2	yes	—
176	#13063311	—	2	2	no	—
177	#13063311	—	2	2	no	—
178	#13063311	—	2	2	no	—
179	#13063309	—	2	2	no	—
180	#13063308	—	2	2	no	—
181	#13063308	—	2	2	no	—
182	#13063308	D₄	1	2	yes	—
183	#13063307	—	2	2	no	—
184	#13063306	—	2	2	no	—
185	#13063305	—	2	2	no	—
186	#13063305	C₂³	1	2	yes	—
187	#13063305	C₂³	1	2	yes	—
188	#13063304	—	2	1	no	—
189	#13063304	—	2	1	no	—
190	#13063304	—	2	1	no	—
191	#13063304	—	2	1	no	—
192	#13063304	—	2	2	no	—
193	#13063304	—	2	2	no	—
194	#13063304	D₄	1	1	yes	characteristic
195	#13063304	C₂³	1	2	yes	—
196	#13063304	C₂³	1	2	yes	—
197	#13063303	—	2	2	no	—
198	#13063302	—	2	2	no	—
199	#13063301	C₂³	1	2	yes	—
200	#13063299	—	2	1	no	—
201	#13063299	—	2	1	no	—
202	#13063299	D₄	1	1	yes	characteristic
203	#13063297	—	2	2	no	—
204	#13063296	—	2	2	no	—
205	#13063296	C₂³	1	2	yes	—
206	Q₈×Dic₄₃	C₂³	1	2	yes	—
207	C₄×Dic₈₆	—	2	1	no	—
208	C₄×Dic₈₆	—	2	1	no	—
209	C₄×Dic₈₆	—	2	1	no	—
210	C₄×Dic₈₆	—	2	1	no	—
211	C₄×Dic₈₆	—	2	2	no	—
212	C₄×Dic₈₆	—	2	2	no	—
213	C₄×Dic₈₆	C₂³	1	2	yes	—
214	C₄×Dic₈₆	C₂³	1	2	yes	—
215	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
216	#13063290	—	2	2	no	—
217	#13063290	C₂³	1	2	yes	—
218	#13063290	C₂³	1	2	yes	—
219	C₄×D₁₇₂	—	2	1	no	—
220	C₄×D₁₇₂	—	2	1	no	—
221	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
222	D₄×Dic₄₃	C₂³	1	2	yes	—
223	C₄×C₂²⋊D₄₃	—	2	2	no	—
224	C₄×C₂²⋊D₄₃	—	2	2	no	—
225	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
226	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
227	#13063284	—	2	1	no	—
228	#13063284	—	2	1	no	—
229	#13063284	—	2	1	no	—
230	#13063284	—	2	1	no	—
231	#13063283	—	2	2	no	—
232	#13063283	C₂³	1	2	yes	—
233	#13063282	—	2	2	no	—
234	#13063282	—	2	2	no	—
235	#13063282	C₂³	1	2	yes	—
236	#13063281	—	2	2	no	—
237	C₂×C₄⋊Dic₄₃	—	2	1	no	—
238	C₂×C₄⋊Dic₄₃	—	2	1	no	—
239	C₂×Dic₄₃⋊C₄	—	2	2	no	—
240	C₂×Dic₄₃⋊C₄	—	2	2	no	—
241	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
242	#13063259	C₂³	1	2	yes	—
243	#13063259	C₂³	1	2	yes	—
244	#13063258	C₂³	1	2	yes	—
245	#13063258	C₂³	1	2	yes	—
246	#13063256	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₃⋊C₈	C₂³	1	2	yes	—
251	Dic₄₃⋊C₈	C₂³	1	2	yes	—
252	#13063250	C₂³	1	2	yes	—
253	#13063250	C₂³	1	2	yes	—
254	#13063250	C₂³	1	2	yes	—
255	#13063250	C₂³	1	2	yes	—
256	#13063249	C₂³	1	2	yes	—
257	#13063249	C₂³	1	2	yes	—
258	#13063248	C₂³	1	2	yes	—
259	#13063248	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063246	C₂³	1	2	yes	—
263	#13063246	C₂³	1	2	yes	—
264	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	#13063236	C₂³	1	2	yes	—
268	#13063235	C₂³	1	2	yes	—
269	C₈×Dic₄₃	C₂³	1	2	yes	—
270	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
272	#135×C₄₃	—	2	4	no	—
273	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₃	—	2	1	no	—
284	C₄×D₄×C₄₃	—	2	1	no	—
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
291	#117×C₄₃	—	2	1	no	—
292	#117×C₄₃	—	2	1	no	—
293	#117×C₄₃	C₂³	1	1	yes	characteristic
294	#117×C₄₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₃	—	2	1	no	—
296	C₂×C₄²×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#107×C₄₃	C₂³	1	1	yes	characteristic
300	#106×C₄₃	C₂³	1	1	yes	characteristic
301	#106×C₄₃	C₂³	1	1	yes	characteristic
302	#103×C₄₃	C₂³	1	1	yes	characteristic
303	#103×C₄₃	C₂³	1	1	yes	characteristic
304	#103×C₄₃	C₂³	1	1	yes	characteristic
305	#103×C₄₃	C₂³	1	1	yes	characteristic
306	#102×C₄₃	C₂³	1	1	yes	characteristic
307	#102×C₄₃	C₂³	1	1	yes	characteristic
308	#102×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	#41×C₄₃	—	2	2	no	—
315	#41×C₄₃	—	2	2	no	—
316	#41×C₄₃	—	4	1	no	—
317	#41×C₄₃	—	4	1	no	—
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₃	—	2	1	no	—
321	C₂×D₄×C₄₃	—	2	1	no	—
322	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₃	—	2	1	no	—
325	C₂²×C₄×C₄₃	—	2	1	no	—
326	C₂²×C₄×C₄₃	—	2	1	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₂²⋊D₄₃	—	2	2	no	—
334	C₂×C₂²⋊D₄₃	—	2	2	no	—
335	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
336	C₂²×Dic₄₃	—	2	2	no	—
337	C₂²×Dic₄₃	—	2	2	no	—
338	Q₈×D₄₃	—	2	4	no	—
339	Q₈×D₄₃	—	4	2	no	—
340	#10621900	—	2	4	no	—
341	#10621900	—	4	2	no	—
342	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
343	C₂×C₄×D₄₃	—	2	2	no	—
344	C₂×C₄×D₄₃	—	2	2	no	—
345	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
346	C₂×Dic₈₆	—	2	2	no	—
347	C₂×Dic₈₆	—	2	1	no	—
348	C₂×Dic₈₆	—	2	1	no	—
349	C₂×Dic₈₆	—	2	2	no	—
350	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
351	C₂×Dic₈₆	C₂⁴	1	2	yes	—
352	C₂×Dic₈₆	C₂⁴	1	2	yes	—
353	Q₁₆×C₄₃	—	2	2	no	—
354	SD₁₆×C₄₃	—	2	2	no	—
355	SD₁₆×C₄₃	#41	1	4	yes	—
356	D₈×C₄₃	—	2	2	no	—
357	C₂×C₈×C₄₃	—	2	2	no	—
358	C₂×C₈×C₄₃	—	4	1	no	—
359	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₄₃	—	2	1	no	—
364	C₄⋊C₄×C₄₃	—	2	1	no	—
365	C₄⋊C₄×C₄₃	—	2	1	no	—
366	C₄⋊C₄×C₄₃	—	2	1	no	—
367	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
371	C₂²⋊C₄×C₄₃	—	2	1	no	—
372	C₂²⋊C₄×C₄₃	—	2	1	no	—
373	C₂²⋊C₄×C₄₃	—	2	1	no	—
374	C₂²⋊C₄×C₄₃	—	2	1	no	—
375	C₂²⋊C₄×C₄₃	—	2	1	no	—
376	C₂²⋊C₄×C₄₃	—	2	1	no	—
377	C₄²×C₄₃	—	2	1	no	—
378	C₄²×C₄₃	—	2	1	no	—
379	C₄²×C₄₃	—	2	1	no	—
380	C₄²×C₄₃	—	2	1	no	—
381	C₄²×C₄₃	—	2	1	no	—
382	C₄²×C₄₃	—	2	1	no	—
383	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
386	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
387	C₂²⋊Dic₄₃	—	2	2	no	—
388	C₂²⋊Dic₄₃	—	2	2	no	—
389	C₂²⋊Dic₄₃	—	2	2	no	—
390	C₂²⋊Dic₄₃	—	2	2	no	—
391	C₂²⋊Dic₄₃	—	2	2	no	—
392	C₂²⋊Dic₄₃	—	2	2	no	—
393	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
394	#10621885	—	2	4	no	—
395	#10621885	—	4	2	no	—
396	#10621883	—	2	4	no	—
397	#10621883	—	4	2	no	—
398	(C₂×D₄₃)⋊C₄	—	2	2	no	—
399	(C₂×D₄₃)⋊C₄	—	2	2	no	—
400	(C₂×D₄₃)⋊C₄	—	2	2	no	—
401	(C₂×D₄₃)⋊C₄	—	2	2	no	—
402	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
403	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
404	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
405	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
406	C₄⋊Dic₄₃	—	2	1	no	—
407	C₄⋊Dic₄₃	—	2	1	no	—
408	C₄⋊Dic₄₃	—	2	1	no	—
409	C₄⋊Dic₄₃	—	2	1	no	—
410	C₄⋊Dic₄₃	—	2	1	no	—
411	C₄⋊Dic₄₃	—	2	1	no	—
412	C₄⋊Dic₄₃	—	2	2	no	—
413	C₄⋊Dic₄₃	—	2	2	no	—
414	C₄⋊Dic₄₃	—	2	2	no	—
415	C₄⋊Dic₄₃	—	2	2	no	—
416	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
417	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
419	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
420	Dic₄₃⋊C₄	—	2	2	no	—
421	Dic₄₃⋊C₄	—	2	2	no	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	—	2	2	no	—
424	Dic₄₃⋊C₄	—	2	2	no	—
425	Dic₄₃⋊C₄	—	2	2	no	—
426	Dic₄₃⋊C₄	—	2	2	no	—
427	Dic₄₃⋊C₄	—	2	2	no	—
428	Dic₄₃⋊C₄	—	2	2	no	—
429	Dic₄₃⋊C₄	—	2	2	no	—
430	Dic₄₃⋊C₄	—	2	2	no	—
431	Dic₄₃⋊C₄	—	2	2	no	—
432	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
433	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
434	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
435	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
436	C₄×Dic₄₃	—	2	2	no	—
437	C₄×Dic₄₃	—	2	2	no	—
438	C₄×Dic₄₃	—	2	2	no	—
439	C₄×Dic₄₃	—	2	2	no	—
440	C₄×Dic₄₃	—	2	2	no	—
441	C₄×Dic₄₃	—	2	2	no	—
442	C₄×Dic₄₃	C₂⁴	1	2	yes	—
443	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
444	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
445	Dic₁₇₂	—	2	4	no	—
446	Dic₁₇₂	—	4	2	no	—
447	#10621872	—	2	4	no	—
448	C₈×D₄₃	—	4	2	no	—
449	C₂³×C₄₃	—	2	1	no	—
450	C₂³×C₄₃	—	2	1	no	—
451	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
452	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
453	Q₈×C₄₃	—	2	1	no	—
454	Q₈×C₄₃	—	2	1	no	—
455	Q₈×C₄₃	—	2	1	no	—
456	Q₈×C₄₃	C₂×#41	1	2	yes	—
457	D₄×C₄₃	—	2	1	no	—
458	D₄×C₄₃	—	2	1	no	—
459	D₄×C₄₃	—	2	1	no	—
460	D₄×C₄₃	—	4	2	no	—
461	D₄×C₄₃	—	4	2	no	—
462	D₄×C₄₃	C₂×#41	1	2	yes	—
463	C₂×C₄×C₄₃	—	2	1	no	—
464	C₂×C₄×C₄₃	—	2	2	no	—
465	C₂×C₄×C₄₃	—	2	1	no	—
466	C₂×C₄×C₄₃	—	2	1	no	—
467	C₂×C₄×C₄₃	—	2	1	no	—
468	C₂×C₄×C₄₃	—	2	1	no	—
469	C₂×C₄×C₄₃	—	2	1	no	—
470	C₂×C₄×C₄₃	—	2	1	no	—
471	C₂×C₄×C₄₃	—	2	1	no	—
472	C₂×C₄×C₄₃	—	4	1	no	—
473	C₂×C₄×C₄₃	—	4	2	no	—
474	C₂×C₄×C₄₃	—	4	2	no	—
475	C₂×C₄×C₄₃	—	4	2	no	—
476	C₂×C₄×C₄₃	—	4	2	no	—
477	C₂×C₄×C₄₃	—	8	1	no	—
478	C₂×C₄×C₄₃	—	8	1	no	—
479	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
485	C₂²⋊D₄₃	—	4	2	no	—
486	C₂²⋊D₄₃	—	4	4	no	—
487	C₂²⋊D₄₃	—	8	2	no	—
488	C₂×Dic₄₃	—	2	2	no	—
489	C₂×Dic₄₃	—	2	2	no	—
490	C₂×Dic₄₃	—	2	2	no	—
491	C₂×Dic₄₃	—	2	2	no	—
492	C₂×Dic₄₃	—	4	4	no	—
493	C₂×Dic₄₃	—	8	2	no	—
494	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
495	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
496	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
497	D₁₇₂	—	2	2	no	—
498	C₄×D₄₃	—	2	2	no	—
499	C₄×D₄₃	—	2	2	no	—
500	C₄×D₄₃	—	4	4	no	—
501	C₄×D₄₃	—	8	2	no	—
502	Dic₈₆	—	2	2	no	—
503	Dic₈₆	—	2	2	no	—
504	Dic₈₆	—	2	2	no	—
505	Dic₈₆	—	2	2	no	—
506	Dic₈₆	—	2	2	no	—
507	Dic₈₆	—	4	4	no	—
508	Dic₈₆	—	8	2	no	—
509	Dic₈₆	—	8	1	no	—
510	Dic₈₆	—	8	1	no	—
511	C₈×C₄₃	—	2	1	no	—
512	C₈×C₄₃	—	2	1	no	—
513	C₈×C₄₃	—	2	1	no	—
514	C₈×C₄₃	C₂×#41	1	2	yes	—
515	C₄₃⋊C₈	—	2	2	no	—
516	C₄₃⋊C₈	—	2	2	no	—
517	#61492	—	43	1	no	maximal, Sylow
518	C₂²×C₄₃	—	2	1	no	—
519	C₂²×C₄₃	—	2	2	no	—
520	C₂²×C₄₃	—	2	1	no	—
521	C₂²×C₄₃	—	2	1	no	—
522	C₂²×C₄₃	—	4	1	no	—
523	C₂²×C₄₃	—	4	1	no	—
524	C₂²×C₄₃	—	4	1	no	—
525	C₂²×C₄₃	—	4	1	no	—
526	C₂²×C₄₃	—	4	1	no	—
527	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
528	C₂×D₄₃	—	2	2	no	—
529	C₂×D₄₃	—	2	2	no	—
530	C₂×D₄₃	—	2	2	no	—
531	C₄×C₄₃	—	2	1	no	—
532	C₄×C₄₃	—	2	1	no	—
533	C₄×C₄₃	—	2	2	no	—
534	C₄×C₄₃	—	2	1	no	—
535	C₄×C₄₃	—	2	1	no	—
536	C₄×C₄₃	—	4	1	no	—
537	C₄×C₄₃	—	4	1	no	—
538	C₄×C₄₃	—	4	1	no	—
539	C₄×C₄₃	—	4	1	no	—
540	C₄×C₄₃	—	4	1	no	—
541	C₄×C₄₃	#578	1	2	yes	—
542	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
543	C₄×C₄₃	#585	1	1	yes	characteristic
544	Dic₄₃	—	2	2	no	—
545	Dic₄₃	—	2	2	no	—
546	Dic₄₃	—	2	2	no	—
547	Dic₄₃	—	4	2	no	—
548	Dic₄₃	—	4	2	no	—
549	Dic₄₃	—	4	2	no	—
550	Dic₄₃	—	4	2	no	—
551	#3518	—	43	1	no	—
552	#3515	—	43	1	no	—
553	#3398	—	43	1	no	—
554	#3385	—	43	1	no	—
555	#3363	—	43	1	no	—
556	#3360	—	43	1	no	—
557	#3357	—	43	1	no	—
558	#3349	—	43	2	no	—
559	#3303	—	43	1	no	—
560	#3302	—	43	2	no	—
561	#3300	—	43	2	no	—
562	#3299	—	43	1	no	—
563	#3276	—	43	1	no	—
564	#3269	—	43	2	no	—
565	#3178	—	43	2	no	—
566	#3170	—	43	1	no	—
567	#3127	—	43	2	no	—
568	#3124	—	43	2	no	—
569	#3116	—	43	1	no	—
570	#3116	—	43	1	no	—
571	#2966	—	43	1	no	—
572	#2947	—	43	2	no	—
573	C₄×#135	D₄₃	1	1	yes	characteristic, complemented
574	C₂×C₄₃	—	4	1	no	—
575	C₂×C₄₃	—	4	2	no	—
576	C₂×C₄₃	—	8	1	no	—
577	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
578	C₂×C₄₃	C₂×#578	1	1	yes	characteristic
579	C₂×C₄₃	#3584	1	1	yes	characteristic
580	D₄₃	—	4	2	no	—
581	C₂×#137	—	43	2	no	—
582	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
583	Q₈²	—	43	1	no	—
584	#557	—	43	1	no	—
585	#556	—	43	2	no	—
586	#556	—	43	1	no	—
587	#556	—	86	2	no	—
588	#556	—	86	1	no	—
589	#555	—	43	1	no	—
590	#555	—	86	1	no	—
591	#554	—	43	1	no	—
592	#554	—	43	1	no	—
593	#553	—	86	1	no	—
594	#552	—	43	2	no	—
595	#552	—	86	2	no	—
596	#552	—	86	1	no	—
597	D₄×Q₈	—	43	1	no	—
598	#548	—	43	2	no	—
599	#547	—	43	2	no	—
600	#547	—	43	1	no	—
601	#542	—	43	2	no	—
602	#542	—	86	2	no	—
603	#541	—	43	2	no	—
604	#539	—	86	2	no	—
605	#533	—	43	1	no	—
606	#533	—	43	1	no	—
607	#533	—	86	1	no	—
608	#529	—	43	1	no	—
609	#529	—	86	1	no	—
610	#529	—	86	1	no	—
611	C₂×#125	—	86	1	no	—
612	#520	—	43	2	no	—
613	#519	—	43	2	no	—
614	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
615	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
616	#501	—	43	2	no	—
617	#500	—	43	1	no	—
618	#497	—	43	2	no	—
619	#494	—	43	1	no	—
620	#488	—	43	2	no	—
621	#487	—	43	2	no	—
622	#487	—	43	1	no	—
623	#487	—	43	1	no	—
624	#485	—	43	2	no	—
625	#485	—	43	2	no	—
626	#485	—	43	2	no	—
627	#485	—	43	2	no	—
628	#484	—	43	2	no	—
629	#480	—	43	2	no	—
630	#479	—	43	2	no	—
631	#479	—	43	2	no	—
632	#477	—	43	1	no	—
633	#477	—	43	1	no	—
634	#477	—	43	2	no	—
635	#476	—	43	1	no	—
636	#476	—	43	1	no	—
637	#474	—	43	2	no	—
638	#470	—	43	2	no	—
639	#468	—	43	2	no	—
640	#467	—	43	2	no	—
641	#467	—	43	2	no	—
642	#467	—	43	2	no	—
643	#465	—	43	2	no	—
644	#464	—	43	2	no	—
645	#463	—	43	2	no	—
646	#462	—	43	2	no	—
647	#462	—	43	1	no	—
648	#462	—	43	1	no	—
649	#462	—	43	2	no	—
650	#461	—	43	1	no	—
651	#461	—	43	1	no	—
652	#452	—	43	2	no	—
653	#452	—	43	2	no	—
654	#452	—	43	2	no	—
655	#451	—	43	2	no	—
656	#451	—	43	2	no	—
657	#449	—	43	2	no	—
658	#446	—	43	1	no	—
659	C₈×Q₈	—	43	1	no	—
660	#441	—	43	2	no	—
661	#441	—	43	2	no	—
662	#441	—	43	2	no	—
663	#440	—	43	2	no	—
664	#440	—	43	2	no	—
665	#440	—	43	2	no	—
666	C₄×Q₁₆	—	43	2	no	—
667	C₄×Q₁₆	—	43	2	no	—
668	C₄×Q₁₆	—	43	2	no	—
669	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
670	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
671	C₄×SD₁₆	—	43	2	no	—
672	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
673	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
674	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
675	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
676	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
677	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
678	#436	—	43	1	no	—
679	#435	—	43	2	no	—
680	C₈×D₄	—	43	2	no	—
681	C₈×D₄	—	43	1	no	—
682	#433	—	43	2	no	—
683	#432	—	43	1	no	—
684	#428	—	43	2	no	—
685	#427	C₂×D₄₃	1	1	yes	characteristic
686	#416	—	43	2	no	—
687	#416	C₂×D₄₃	1	1	yes	characteristic
688	#416	C₂×D₄₃	1	1	yes	characteristic
689	C₂×#103	—	43	2	no	—
690	#405	—	43	2	no	—
691	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
692	C₄₃	#61492	1	1	yes	characteristic, complemented, Sylow
693	C₂×#41	—	43	2	no	—
694	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
695	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
696	C₂²×Q₈	—	43	2	no	—
697	#137	—	86	8	no	—
698	#135	—	2	4	no	—
699	C₂×Q₁₆	—	43	2	no	—
700	C₂×Q₁₆	—	43	2	no	—
701	C₂×Q₁₆	—	43	2	no	—
702	C₂×Q₁₆	—	43	2	no	—
703	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
704	C₂×SD₁₆	—	43	2	no	—
705	C₂×SD₁₆	—	43	2	no	—
706	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
707	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
708	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
709	C₂×M₁₆	—	43	2	no	—
710	C₂²×C₈	—	43	2	no	—
711	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
712	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
713	C₄⋊Q₈	—	43	2	no	—
714	C₄⋊Q₈	—	43	2	no	—
715	C₄⋊Q₈	—	43	1	no	—
716	C₄⋊Q₈	—	43	1	no	—
717	C₄⋊Q₈	—	43	1	no	—
718	C₄⋊Q₈	—	43	1	no	—
719	C₄⋊Q₈	—	86	1	no	—
720	C₄⋊Q₈	—	86	1	no	—
721	C₄⋊Q₈	—	86	2	no	—
722	#126	—	43	2	no	—
723	#126	—	86	2	no	—
724	#126	—	86	2	no	—
725	#126	—	86	2	no	—
726	#126	—	86	2	no	—
727	#126	—	86	2	no	—
728	#126	—	86	2	no	—
729	#126	—	86	2	no	—
730	#125	—	43	2	no	—
731	#125	—	43	1	no	—
732	#125	—	86	2	no	—
733	#125	—	86	2	no	—
734	#125	—	86	1	no	—
735	#125	—	86	1	no	—
736	#125	—	86	2	no	—
737	#125	—	86	2	no	—
738	#125	—	86	1	no	—
739	#125	—	86	1	no	—
740	#124	—	43	2	no	—
741	#124	—	43	1	no	—
742	#124	—	86	2	no	—
743	#124	—	86	2	no	—
744	#124	—	86	2	no	—
745	#124	—	86	2	no	—
746	#123	—	43	2	no	—
747	#123	—	86	2	no	—
748	#123	—	86	2	no	—
749	#123	—	86	2	no	—
750	#123	—	86	2	no	—
751	#123	—	86	2	no	—
752	C₂²⋊Q₈	—	43	1	no	—
753	C₂²⋊Q₈	—	43	2	no	—
754	C₂²⋊Q₈	—	43	2	no	—
755	C₂²⋊Q₈	—	43	2	no	—
756	C₂²⋊Q₈	—	43	2	no	—
757	C₂²⋊Q₈	—	43	2	no	—
758	C₂²⋊Q₈	—	86	2	no	—
759	C₂²⋊Q₈	—	86	2	no	—
760	C₂²⋊Q₈	—	86	2	no	—
761	C₂²⋊Q₈	—	86	2	no	—
762	C₂²⋊Q₈	—	86	2	no	—
763	C₂²⋊Q₈	—	86	1	no	—
764	C₂²⋊Q₈	—	86	1	no	—
765	C₂²⋊Q₈	—	86	1	no	—
766	C₂²⋊Q₈	—	86	1	no	—
767	#121	—	43	1	no	—
768	#121	—	43	2	no	—
769	#121	—	86	1	no	—
770	#121	—	86	1	no	—
771	#121	—	86	2	no	—
772	#121	—	86	2	no	—
773	C₄×Q₈	—	43	1	no	—
774	C₄×Q₈	—	43	2	no	—
775	C₄×Q₈	—	43	2	no	—
776	C₄×Q₈	—	43	2	no	—
777	C₄×Q₈	—	43	2	no	—
778	C₄×Q₈	—	43	2	no	—
779	C₄×Q₈	—	86	2	no	—
780	C₄×Q₈	—	86	2	no	—
781	C₄×Q₈	—	86	1	no	—
782	C₄×Q₈	—	86	1	no	—
783	C₄×Q₈	—	86	2	no	—
784	C₄×Q₈	—	86	1	no	—
785	C₄×Q₈	—	86	1	no	—
786	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
787	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
789	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	43	2	no	—
795	C₄×D₄	—	43	2	no	—
796	C₄×D₄	—	43	1	no	—
797	C₄×D₄	—	86	1	no	—
798	C₄×D₄	—	86	1	no	—
799	C₄×D₄	—	86	2	no	—
800	C₄×D₄	—	86	2	no	—
801	C₄×D₄	—	86	2	no	—
802	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
803	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
804	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
805	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	43	2	no	—
809	#117	—	43	2	no	—
810	#117	—	86	2	no	—
811	#117	—	86	2	no	—
812	#117	—	86	2	no	—
813	#117	—	86	2	no	—
814	#117	—	86	1	no	—
815	#117	—	86	1	no	—
816	#117	—	86	1	no	—
817	#117	—	86	1	no	—
818	#117	C₂²×D₄₃	1	1	yes	characteristic
819	#117	C₂²×D₄₃	1	1	yes	characteristic
820	C₂×C₄⋊C₄	—	43	2	no	—
821	C₂×C₄⋊C₄	—	86	2	no	—
822	C₂×C₄⋊C₄	—	86	2	no	—
823	C₂×C₄⋊C₄	—	86	1	no	—
824	C₂×C₄⋊C₄	—	86	1	no	—
825	C₂×C₄²	—	2	1	no	—
826	C₂×C₄²	—	2	1	no	—
827	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
828	#107	—	43	2	no	—
829	#107	—	43	2	no	—
830	#107	—	43	2	no	—
831	#107	—	43	2	no	—
832	#107	C₂²×D₄₃	1	1	yes	characteristic
833	#107	C₂²×D₄₃	1	1	yes	characteristic
834	#106	—	43	2	no	—
835	#106	—	43	2	no	—
836	#106	C₂²×D₄₃	1	1	yes	characteristic
837	#106	C₂²×D₄₃	1	1	yes	characteristic
838	C₄⋊C₈	—	43	2	no	—
839	C₄⋊C₈	—	43	2	no	—
840	C₄⋊C₈	—	43	1	no	—
841	C₄⋊C₈	—	43	1	no	—
842	#103	—	43	2	no	—
843	#103	—	43	2	no	—
844	#103	—	43	2	no	—
845	#103	—	43	2	no	—
846	#103	—	43	2	no	—
847	#103	—	43	2	no	—
848	#103	—	43	2	no	—
849	#103	—	43	2	no	—
850	#103	—	43	2	no	—
851	#103	—	43	2	no	—
852	#103	C₂²×D₄₃	1	1	yes	characteristic
853	#103	C₂²×D₄₃	1	1	yes	characteristic
854	#103	C₂²×D₄₃	1	1	yes	characteristic
855	#103	C₂²×D₄₃	1	1	yes	characteristic
856	#102	—	43	2	no	—
857	#102	—	43	2	no	—
858	#102	C₂²×D₄₃	1	1	yes	characteristic
859	#102	C₂²×D₄₃	1	1	yes	characteristic
860	#102	C₂²×D₄₃	1	1	yes	characteristic
861	#102	C₂²×D₄₃	1	1	yes	characteristic
862	C₂²⋊C₈	—	43	2	no	—
863	C₂²⋊C₈	—	43	2	no	—
864	C₂²⋊C₈	—	43	2	no	—
865	#97	—	43	2	no	—
866	#97	—	43	2	no	—
867	C₄×C₈	—	43	2	no	—
868	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
869	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
870	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
871	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
872	#41	—	2	2	no	—
873	#41	—	2	2	no	—
874	#41	—	4	1	no	—
875	#41	—	4	1	no	—
876	#41	—	86	4	no	—
877	#41	—	172	2	no	—
878	C₂×Q₈	—	43	1	no	—
879	C₂×Q₈	—	43	2	no	—
880	C₂×Q₈	—	43	2	no	—
881	C₂×Q₈	—	86	2	no	—
882	C₂×Q₈	—	86	2	no	—
883	C₂×Q₈	—	86	1	no	—
884	C₂×Q₈	—	86	1	no	—
885	C₂×Q₈	—	86	4	no	—
886	C₂×Q₈	—	172	2	no	—
887	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
888	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	43	2	no	—
892	C₂×D₄	—	43	1	no	—
893	C₂×D₄	—	86	2	no	—
894	C₂×D₄	—	86	2	no	—
895	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
896	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	43	2	no	—
904	C₂²×C₄	—	86	2	no	—
905	C₂²×C₄	—	86	2	no	—
906	C₂²×C₄	—	86	2	no	—
907	C₂²×C₄	—	86	2	no	—
908	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
909	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
910	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
911	Q₁₆	—	2	2	no	—
912	Q₁₆	—	86	4	no	—
913	Q₁₆	—	86	4	no	—
914	Q₁₆	—	172	2	no	—
915	Q₁₆	—	172	2	no	—
916	SD₁₆	—	2	2	no	—
917	SD₁₆	—	86	4	no	—
918	SD₁₆	—	172	2	no	—
919	SD₁₆	#10621898	1	4	yes	—
920	D₈	—	2	2	no	—
921	M₁₆	—	86	4	no	—
922	C₂×C₈	—	2	2	no	—
923	C₂×C₈	—	4	1	no	—
924	C₂×C₈	—	43	2	no	—
925	C₂×C₈	—	43	2	no	—
926	C₂×C₈	—	172	2	no	—
927	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
928	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
929	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
930	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	43	2	no	—
936	C₄⋊C₄	—	43	1	no	—
937	C₄⋊C₄	—	43	1	no	—
938	C₄⋊C₄	—	43	2	no	—
939	C₄⋊C₄	—	43	2	no	—
940	C₄⋊C₄	—	43	2	no	—
941	C₄⋊C₄	—	43	2	no	—
942	C₄⋊C₄	—	43	2	no	—
943	C₄⋊C₄	—	86	2	no	—
944	C₄⋊C₄	—	86	2	no	—
945	C₄⋊C₄	—	86	2	no	—
946	C₄⋊C₄	—	86	2	no	—
947	C₄⋊C₄	—	86	2	no	—
948	C₄⋊C₄	—	86	2	no	—
949	C₄⋊C₄	—	86	2	no	—
950	C₄⋊C₄	—	86	2	no	—
951	C₄⋊C₄	—	86	2	no	—
952	C₄⋊C₄	—	86	2	no	—
953	C₄⋊C₄	—	86	2	no	—
954	C₄⋊C₄	—	86	2	no	—
955	C₄⋊C₄	—	86	1	no	—
956	C₄⋊C₄	—	86	1	no	—
957	C₄⋊C₄	—	86	2	no	—
958	C₄⋊C₄	—	86	2	no	—
959	C₄⋊C₄	—	86	1	no	—
960	C₄⋊C₄	—	86	1	no	—
961	C₄⋊C₄	—	86	2	no	—
962	C₄⋊C₄	—	86	2	no	—
963	C₄⋊C₄	—	86	1	no	—
964	C₄⋊C₄	—	86	1	no	—
965	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	43	2	no	—
976	C₂²⋊C₄	—	43	2	no	—
977	C₂²⋊C₄	—	43	2	no	—
978	C₂²⋊C₄	—	43	2	no	—
979	C₂²⋊C₄	—	43	2	no	—
980	C₂²⋊C₄	—	86	2	no	—
981	C₂²⋊C₄	—	86	2	no	—
982	C₂²⋊C₄	—	86	2	no	—
983	C₂²⋊C₄	—	86	2	no	—
984	C₂²⋊C₄	—	86	2	no	—
985	C₂²⋊C₄	—	86	2	no	—
986	C₂²⋊C₄	—	86	2	no	—
987	C₂²⋊C₄	—	86	2	no	—
988	C₂²⋊C₄	—	86	2	no	—
989	C₂²⋊C₄	—	86	2	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	43	2	no	—
997	C₄²	—	86	2	no	—
998	C₄²	—	86	2	no	—
999	C₄²	—	86	2	no	—
1000	C₄²	—	86	2	no	—
1001	C₄²	—	86	2	no	—
1002	C₄²	—	86	2	no	—
1003	C₄²	D₄×D₄₃	1	1	yes	characteristic
1004	C₄²	D₄×D₄₃	1	1	yes	characteristic
1005	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1006	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	43	2	no	—
1010	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	86	2	no	—
1015	Q₈	—	86	2	no	—
1016	Q₈	—	86	2	no	—
1017	Q₈	—	86	2	no	—
1018	Q₈	—	86	2	no	—
1019	Q₈	—	344	1	no	—
1020	Q₈	—	344	1	no	—
1021	Q₈	—	344	2	no	—
1022	Q₈	—	172	4	no	—
1023	Q₈	C₂×#10621898	1	2	yes	—
1024	D₄	—	2	1	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	86	2	no	—
1030	D₄	—	344	2	no	—
1031	D₄	—	172	2	no	—
1032	D₄	—	172	4	no	—
1033	D₄	C₂×#10621898	1	2	yes	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	8	1	no	—
1049	C₂×C₄	—	8	1	no	—
1050	C₂×C₄	—	43	2	no	—
1051	C₂×C₄	—	43	2	no	—
1052	C₂×C₄	—	43	2	no	—
1053	C₂×C₄	—	86	2	no	—
1054	C₂×C₄	—	86	2	no	—
1055	C₂×C₄	—	86	2	no	—
1056	C₂×C₄	—	86	2	no	—
1057	C₂×C₄	—	86	2	no	—
1058	C₂×C₄	—	86	2	no	—
1059	C₂×C₄	—	344	2	no	—
1060	C₂×C₄	—	344	2	no	—
1061	C₂×C₄	—	172	4	no	—
1062	C₂×C₄	—	172	4	no	—
1063	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1064	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1065	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1066	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1067	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1068	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	1	no	—
1072	C₈	—	86	2	no	—
1073	C₈	—	86	2	no	—
1074	C₈	C₂×#10621898	1	2	yes	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	86	2	no	—
1085	C₂²	—	86	2	no	—
1086	C₂²	—	86	2	no	—
1087	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	86	2	no	—
1099	C₄	—	86	2	no	—
1100	C₄	—	86	2	no	—
1101	C₄	—	172	2	no	—
1102	C₄	—	172	2	no	—
1103	C₄	—	172	2	no	—
1104	C₄	—	172	2	no	—
1105	C₄	#14583713	1	2	yes	—
1106	C₄	C₂²×#10621898	1	1	yes	characteristic
1107	C₄	#14583735	1	1	yes	characteristic
1108	C₂	—	4	1	no	—
1109	C₂	—	4	2	no	—
1110	C₂	—	8	1	no	—
1111	C₂	—	172	2	no	—
1112	C₂	D₄×#10621898	1	1	yes	characteristic
1113	C₂	C₂×#14583713	1	1	yes	characteristic
1114	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#135	D₄₃
hypocenter	C₄₃	#61492
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #19148612	C₂	semidirect
2. #19148573	C₂	semidirect
3. #19147624	C₂	semidirect
4. #19147503	C₂	semidirect
5. #19147271	C₂	semidirect
6. #19147242	C₂	semidirect
7. #19147223	C₂	semidirect
8. #19147121	C₂	semidirect
9. #19146525	C₂	semidirect
10. #19146508	C₂	semidirect
11. #19146483	C₂	semidirect
12. #19146473	C₂	semidirect
13. #19146242	C₂	semidirect
14. #19146150	C₂	semidirect
15. #19145259	C₂	semidirect
16. #19145181	C₂	semidirect
17. #19144892	C₂	semidirect
18. #19144853	C₂	semidirect
19. #19144757	C₂	semidirect
20. #19144757	C₂	semidirect
21. #19143570	C₂	semidirect
22. #19143431	C₂	semidirect
23. C₄×#135×C₄₃	C₂	semidirect
573. C₄×#135	D₄₃	semidirect
692. C₄₃	#61492	semidirect

Maximal subgroups

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

subgroup	index
#19148612	2
#19148573	2
#19147624	2
#19147503	2
#19147271	2
#19147242	2
#19147223	2
#19147121	2
#19146525	2
#19146508	2
#19146483	2
#19146473	2
#19146242	2
#19146150	2
#19145259	2
#19145181	2
#19144892	2
#19144853	2
#19144757	2
#19143570	2
#19143431	2
C₄×#135×C₄₃	2
#61492	43