Subgroups — #6628069

Order 512.

1709 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#39819	C₂	1	1	yes	maximal, characteristic, complemented
2	#34250	C₂	1	1	yes	maximal, characteristic
3	#32916	C₂	1	1	yes	maximal, characteristic
4	#32916	C₂	1	1	yes	maximal, characteristic
5	#32907	C₂	1	1	yes	maximal, characteristic
6	#29341	C₂	1	1	yes	maximal, characteristic, complemented
7	#29335	C₂	1	1	yes	maximal, characteristic, complemented
8	#29252	C₂	1	1	yes	maximal, characteristic, complemented
9	#29241	C₂	1	1	yes	maximal, characteristic, complemented
10	#27985	C₂	1	1	yes	maximal, characteristic, complemented
11	#27690	C₂	1	1	yes	maximal, characteristic, complemented
12	#27575	C₂	1	1	yes	maximal, characteristic, complemented
13	#27569	C₂	1	1	yes	maximal, characteristic, complemented
14	#27566	C₂	1	1	yes	maximal, characteristic, complemented
15	#27565	C₂	1	1	yes	maximal, characteristic, complemented
16	#26186	C₂	1	1	yes	maximal, characteristic, complemented
17	#26183	C₂	1	1	yes	maximal, characteristic, complemented
18	#26182	C₂	1	1	yes	maximal, characteristic, complemented
19	#26171	C₂	1	1	yes	maximal, characteristic, complemented
20	#26120	C₂	1	1	yes	maximal, characteristic, complemented
21	#26115	C₂	1	1	yes	maximal, characteristic, complemented
22	#24748	C₂	1	1	yes	maximal, characteristic, complemented
23	#24732	C₂	1	1	yes	maximal, characteristic, complemented
24	#23014	C₂	1	1	yes	maximal, characteristic, complemented
25	#23002	C₂	1	1	yes	maximal, characteristic, complemented
26	#22778	C₂	1	1	yes	maximal, characteristic, complemented
27	#22761	C₂	1	1	yes	maximal, characteristic, complemented
28	#22631	C₂	1	1	yes	maximal, characteristic, complemented
29	#21465	C₂	1	1	yes	maximal, characteristic
30	#21465	C₂	1	1	yes	maximal, characteristic
31	#21457	C₂	1	1	yes	maximal, characteristic
32	C₂×#520	C₂²	1	1	yes	characteristic
33	C₂×#520	C₂²	1	1	yes	characteristic
34	C₂×C₄×#41	C₂²	1	1	yes	characteristic
35	C₂×#462	C₂²	1	1	yes	characteristic
36	C₂×#462	C₂²	1	1	yes	characteristic
37	C₂×#462	C₂²	1	1	yes	characteristic
38	C₂×#461	C₂²	1	1	yes	characteristic
39	C₂×#461	C₂²	1	1	yes	characteristic
40	C₂×#461	C₂²	1	1	yes	characteristic
41	C₂×#452	C₂²	1	1	yes	characteristic
42	C₂×#452	C₂²	1	1	yes	characteristic
43	C₂×#452	C₂²	1	1	yes	characteristic
44	C₂×#441	C₂²	1	1	yes	characteristic
45	C₂×#440	C₂²	1	1	yes	characteristic
46	C₂×#440	C₂²	1	1	yes	characteristic
47	C₂×#440	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
50	#2857	C₂²	1	1	yes	characteristic
51	#2802	—	2	1	no	—
52	#2787	—	2	1	no	—
53	#2776	—	2	1	no	—
54	#2770	—	2	1	no	—
55	#2621	C₂²	1	1	yes	characteristic
56	#2621	C₂²	1	1	yes	characteristic
57	#2606	—	2	1	no	—
58	#2590	—	2	1	no	—
59	#2577	—	2	1	no	—
60	#2570	C₂²	1	1	yes	characteristic
61	#2546	C₂²	1	1	yes	characteristic
62	#2530	—	2	1	no	—
63	#2514	C₂²	1	1	yes	characteristic
64	#2511	C₂²	1	1	yes	characteristic
65	#2446	C₂²	1	1	yes	characteristic
66	#2446	C₂²	1	1	yes	characteristic
67	#2365	C₂²	1	1	yes	characteristic
68	#2356	C₂²	1	1	yes	characteristic
69	#2351	C₂²	1	1	yes	characteristic
70	#2351	C₂²	1	1	yes	characteristic
71	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	#2349	—	2	1	no	—
74	#2349	—	2	1	no	—
75	#2349	C₂²	1	1	yes	characteristic
76	#2349	C₂²	1	1	yes	characteristic
77	D₄×C₄⋊C₄	—	2	1	no	—
78	D₄×C₄⋊C₄	—	2	1	no	—
79	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	#2323	C₂²	1	1	yes	characteristic
82	#2323	C₂²	1	1	yes	characteristic
83	#2317	—	2	1	no	—
84	#2317	C₂²	1	1	yes	characteristic
85	#2316	—	2	1	no	—
86	#2316	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
88	#2296	—	2	1	no	—
89	#2296	C₂²	1	1	yes	characteristic
90	C₂×#389	—	2	1	no	—
91	C₂×#389	C₂²	1	1	yes	characteristic
92	#2101	C₂²	1	1	yes	characteristic
93	#2101	C₂²	1	1	yes	characteristic
94	#2101	C₂²	1	1	yes	characteristic
95	#2099	C₂²	1	1	yes	characteristic
96	#2099	C₂²	1	1	yes	characteristic
97	#2099	C₂²	1	1	yes	characteristic
98	#2097	C₂²	1	1	yes	characteristic
99	#2095	C₂²	1	1	yes	characteristic
100	#2088	C₂²	1	1	yes	characteristic
101	#2087	C₂²	1	1	yes	characteristic
102	#2087	C₂²	1	1	yes	characteristic
103	#2086	C₂²	1	1	yes	characteristic
104	#2074	C₂²	1	1	yes	characteristic
105	#2074	C₂²	1	1	yes	characteristic
106	#2072	C₂²	1	1	yes	characteristic
107	#2072	C₂²	1	1	yes	characteristic
108	#2068	C₂²	1	1	yes	characteristic
109	#2068	C₂²	1	1	yes	characteristic
110	#2068	C₂²	1	1	yes	characteristic
111	#2068	C₂²	1	1	yes	characteristic
112	#2043	C₂²	1	1	yes	characteristic
113	#2043	C₂²	1	1	yes	characteristic
114	#2043	C₂²	1	1	yes	characteristic
115	#2043	C₂²	1	1	yes	characteristic
116	#1960	C₂²	1	1	yes	characteristic
117	#1956	C₂²	1	1	yes	characteristic
118	#1949	C₂²	1	1	yes	characteristic
119	#1947	C₂²	1	1	yes	characteristic
120	#1940	C₂²	1	1	yes	characteristic
121	#1939	C₂²	1	1	yes	characteristic
122	#1935	C₂²	1	1	yes	characteristic
123	#1935	C₂²	1	1	yes	characteristic
124	#1935	C₂²	1	1	yes	characteristic
125	#1935	C₂²	1	1	yes	characteristic
126	#1935	C₂²	1	1	yes	characteristic
127	#1935	C₂²	1	1	yes	characteristic
128	#1933	C₂²	1	1	yes	characteristic
129	#1933	C₂²	1	1	yes	characteristic
130	#1921	C₂²	1	1	yes	characteristic
131	#1921	C₂²	1	1	yes	characteristic
132	#1921	C₂²	1	1	yes	characteristic
133	#1918	C₂²	1	1	yes	characteristic
134	#1917	C₂²	1	1	yes	characteristic
135	#1917	C₂²	1	1	yes	characteristic
136	#1917	C₂²	1	1	yes	characteristic
137	#1916	C₂²	1	1	yes	characteristic
138	#1878	C₂²	1	1	yes	characteristic
139	#1878	C₂²	1	1	yes	characteristic
140	#1878	C₂²	1	1	yes	characteristic
141	#1878	C₂²	1	1	yes	characteristic
142	#1878	C₂²	1	1	yes	characteristic
143	#1878	C₂²	1	1	yes	characteristic
144	#1878	C₂²	1	1	yes	characteristic
145	#1878	C₂²	1	1	yes	characteristic
146	#1878	C₂²	1	1	yes	characteristic
147	#1877	C₂²	1	1	yes	characteristic
148	#1877	C₂²	1	1	yes	characteristic
149	#1877	C₂²	1	1	yes	characteristic
150	#1877	C₂²	1	1	yes	characteristic
151	#1877	C₂²	1	1	yes	characteristic
152	#1877	C₂²	1	1	yes	characteristic
153	#1877	C₂²	1	1	yes	characteristic
154	#1877	C₂²	1	1	yes	characteristic
155	#1877	C₂²	1	1	yes	characteristic
156	#1873	C₂²	1	1	yes	characteristic
157	#1873	C₂²	1	1	yes	characteristic
158	#1873	C₂²	1	1	yes	characteristic
159	#1872	C₂²	1	1	yes	characteristic
160	#1872	C₂²	1	1	yes	characteristic
161	#1872	C₂²	1	1	yes	characteristic
162	#1872	C₂²	1	1	yes	characteristic
163	#1872	C₂²	1	1	yes	characteristic
164	#1872	C₂²	1	1	yes	characteristic
165	#1865	C₂²	1	1	yes	characteristic
166	#1864	C₂²	1	1	yes	characteristic
167	#1863	C₂²	1	1	yes	characteristic
168	#1863	C₂²	1	1	yes	characteristic
169	#1863	C₂²	1	1	yes	characteristic
170	#1863	C₂²	1	1	yes	characteristic
171	#1863	C₂²	1	1	yes	characteristic
172	#1863	C₂²	1	1	yes	characteristic
173	#1862	C₂²	1	1	yes	characteristic
174	#1862	C₂²	1	1	yes	characteristic
175	#1854	C₂²	1	1	yes	characteristic
176	#1852	C₂²	1	1	yes	characteristic
177	#1852	C₂²	1	1	yes	characteristic
178	#1836	C₂²	1	1	yes	characteristic
179	#1835	C₂²	1	1	yes	characteristic
180	#1805	C₂²	1	1	yes	characteristic
181	#1805	C₂²	1	1	yes	characteristic
182	#1805	C₂²	1	1	yes	characteristic
183	#1804	C₂²	1	1	yes	characteristic
184	#1804	C₂²	1	1	yes	characteristic
185	#1803	C₂²	1	1	yes	characteristic
186	#1803	C₂²	1	1	yes	characteristic
187	#1802	C₂²	1	1	yes	characteristic
188	#1798	C₂²	1	1	yes	characteristic
189	#1798	C₂²	1	1	yes	characteristic
190	#1797	C₂²	1	1	yes	characteristic
191	#1788	C₂²	1	1	yes	characteristic
192	#1771	C₂²	1	1	yes	characteristic
193	#1770	C₂²	1	1	yes	characteristic
194	#1763	C₂²	1	1	yes	characteristic
195	#1763	C₂²	1	1	yes	characteristic
196	#1763	C₂²	1	1	yes	characteristic
197	#1762	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	C₄×#102	C₂²	1	1	yes	characteristic
200	#1750	C₂²	1	1	yes	characteristic
201	#1750	C₂²	1	1	yes	characteristic
202	#1749	C₂²	1	1	yes	characteristic
203	C₂²×#41	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	#520	—	2	4	no	—
217	#520	—	2	4	no	—
218	#520	—	4	2	no	—
219	#520	—	4	2	no	—
220	C₄×#41	—	4	2	no	—
221	C₄×#41	—	4	2	no	—
222	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	—	2	1	no	—
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	—	2	1	no	—
237	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
243	C₂×#117	—	2	1	no	—
244	C₂×#117	—	2	1	no	—
245	C₂×#117	—	2	1	no	—
246	C₂×#117	C₂³	1	1	yes	characteristic
247	C₂×#117	C₂³	1	1	yes	characteristic
248	C₂×#117	C₂³	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	—	2	1	no	—
250	C₂²×C₄⋊C₄	—	2	1	no	—
251	C₂²×C₄⋊C₄	—	2	1	no	—
252	C₂²×C₄⋊C₄	—	2	1	no	—
253	C₂²×C₄⋊C₄	—	2	1	no	—
254	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂²×C₄²	—	2	1	no	—
257	C₂²×C₄²	C₂³	1	1	yes	characteristic
258	#462	—	2	4	no	—
259	#462	—	4	2	no	—
260	#462	—	4	2	no	—
261	#461	—	2	4	no	—
262	#461	—	4	2	no	—
263	#461	—	4	2	no	—
264	#452	—	2	4	no	—
265	#452	—	2	4	no	—
266	#452	—	2	4	no	—
267	#441	—	4	2	no	—
268	#440	—	2	4	no	—
269	#440	—	4	2	no	—
270	#440	—	4	2	no	—
271	C₄×Q₁₆	—	2	4	no	—
272	C₄×Q₁₆	—	4	2	no	—
273	C₂×#107	C₂³	1	1	yes	characteristic
274	C₂×#107	C₂³	1	1	yes	characteristic
275	C₂×#107	C₂³	1	1	yes	characteristic
276	C₂×#107	C₂³	1	1	yes	characteristic
277	C₂×#107	C₂³	1	1	yes	characteristic
278	C₂×#106	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#103	C₂³	1	1	yes	characteristic
295	C₂×#103	C₂³	1	1	yes	characteristic
296	C₂×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#103	C₂³	1	1	yes	characteristic
302	C₂×#103	C₂³	1	1	yes	characteristic
303	C₂×#103	C₂³	1	1	yes	characteristic
304	C₂×#103	C₂³	1	1	yes	characteristic
305	C₂×#103	C₂³	1	1	yes	characteristic
306	C₂×#103	C₂³	1	1	yes	characteristic
307	C₂×#103	C₂³	1	1	yes	characteristic
308	C₂×#102	C₂³	1	1	yes	characteristic
309	C₂×#102	C₂³	1	1	yes	characteristic
310	C₂×#102	C₂³	1	1	yes	characteristic
311	C₂×#102	C₂³	1	1	yes	characteristic
312	C₂×#102	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₂×#97	C₂³	1	1	yes	characteristic
318	C₂×#97	C₂³	1	1	yes	characteristic
319	C₂×#97	C₂³	1	1	yes	characteristic
320	C₂×#97	C₂³	1	1	yes	characteristic
321	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
322	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
323	#401	—	2	1	no	—
324	#400	—	2	1	no	—
325	#400	—	2	1	no	—
326	#400	—	2	1	no	—
327	#400	—	2	1	no	—
328	#400	—	2	1	no	—
329	#400	—	2	1	no	—
330	#398	—	2	1	no	—
331	#398	—	2	1	no	—
332	#398	—	2	1	no	—
333	#398	—	2	1	no	—
334	#398	—	2	1	no	—
335	#398	—	2	1	no	—
336	#398	—	2	1	no	—
337	#398	—	2	1	no	—
338	#398	—	2	1	no	—
339	#397	—	2	1	no	—
340	#397	—	2	1	no	—
341	#397	—	2	1	no	—
342	#397	—	2	1	no	—
343	#391	C₂³	1	1	yes	characteristic
344	#391	C₂³	1	1	yes	characteristic
345	#391	C₂³	1	1	yes	characteristic
346	#391	C₂³	1	1	yes	characteristic
347	#391	C₂³	1	1	yes	characteristic
348	#391	C₂³	1	1	yes	characteristic
349	#391	C₂³	1	1	yes	characteristic
350	#391	C₂³	1	1	yes	characteristic
351	#391	C₂³	1	1	yes	characteristic
352	#389	—	2	1	no	—
353	#389	—	2	1	no	—
354	#389	—	2	1	no	—
355	#389	—	2	1	no	—
356	#389	—	2	1	no	—
357	#389	—	2	1	no	—
358	#389	—	2	1	no	—
359	#389	—	2	1	no	—
360	#389	—	2	1	no	—
361	#389	—	2	1	no	—
362	#389	—	2	1	no	—
363	#389	—	2	1	no	—
364	#389	—	2	1	no	—
365	#389	—	2	1	no	—
366	#389	—	2	1	no	—
367	#389	—	2	1	no	—
368	#389	—	2	1	no	—
369	#389	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	—	2	1	no	—
372	#389	—	2	1	no	—
373	#389	D₄	1	1	yes	characteristic
374	#389	D₄	1	1	yes	characteristic
375	#389	D₄	1	1	yes	characteristic
376	#389	D₄	1	1	yes	characteristic
377	#389	C₂³	1	1	yes	characteristic
378	#389	C₂³	1	1	yes	characteristic
379	#389	C₂³	1	1	yes	characteristic
380	#389	C₂³	1	1	yes	characteristic
381	#389	C₂³	1	1	yes	characteristic
382	#389	C₂³	1	1	yes	characteristic
383	#389	C₂³	1	1	yes	characteristic
384	#389	C₂³	1	1	yes	characteristic
385	#389	C₂³	1	1	yes	characteristic
386	#389	C₂³	1	1	yes	characteristic
387	#389	C₂³	1	1	yes	characteristic
388	#388	—	2	1	no	—
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#387	—	2	1	no	—
398	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#387	—	2	1	no	—
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#385	—	2	1	no	—
409	#385	—	2	1	no	—
410	#385	—	2	1	no	—
411	#385	—	2	1	no	—
412	#385	—	2	1	no	—
413	#385	—	2	1	no	—
414	#385	—	2	1	no	—
415	#385	—	2	1	no	—
416	#385	—	2	1	no	—
417	#385	—	2	1	no	—
418	#385	—	2	1	no	—
419	#385	D₄	1	1	yes	characteristic
420	#385	D₄	1	1	yes	characteristic
421	#385	D₄	1	1	yes	characteristic
422	#385	D₄	1	1	yes	characteristic
423	#384	—	2	1	no	—
424	#384	—	2	1	no	—
425	#384	C₂³	1	1	yes	characteristic
426	#384	C₂³	1	1	yes	characteristic
427	#384	C₂³	1	1	yes	characteristic
428	#383	—	2	1	no	—
429	#383	—	2	1	no	—
430	#382	—	2	1	no	—
431	#382	—	2	1	no	—
432	#382	C₂³	1	1	yes	characteristic
433	#382	C₂³	1	1	yes	characteristic
434	#382	C₂³	1	1	yes	characteristic
435	#382	C₂³	1	1	yes	characteristic
436	#380	—	2	1	no	—
437	#380	—	2	1	no	—
438	#380	—	2	1	no	—
439	#380	—	2	1	no	—
440	#380	—	2	1	no	—
441	#380	—	2	1	no	—
442	#380	—	2	1	no	—
443	#380	—	2	1	no	—
444	#380	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	—	2	1	no	—
446	C₄×C₄⋊C₄	—	2	1	no	—
447	C₄×C₄⋊C₄	—	2	1	no	—
448	C₄×C₄⋊C₄	—	2	1	no	—
449	C₄×C₄⋊C₄	—	2	1	no	—
450	C₄×C₄⋊C₄	—	2	1	no	—
451	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	—	2	1	no	—
459	#376	—	2	1	no	—
460	C₂×#95	—	2	1	no	—
461	C₂×#95	—	2	1	no	—
462	C₂×#95	—	2	1	no	—
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#340	C₂³	1	1	yes	characteristic
486	#340	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	#336	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	#336	C₂³	1	1	yes	characteristic
497	#336	C₂³	1	1	yes	characteristic
498	#336	C₂³	1	1	yes	characteristic
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	#41	1	4	yes	—
505	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
507	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
508	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	C₂⁴	1	1	yes	characteristic
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
521	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
522	C₂³×C₄	C₂⁴	1	1	yes	characteristic
523	C₂×Q₁₆	—	2	2	no	—
524	C₂×Q₁₆	—	2	2	no	—
525	C₂×Q₁₆	—	2	2	no	—
526	C₂×Q₁₆	—	2	2	no	—
527	C₂×Q₁₆	—	2	2	no	—
528	C₂×Q₁₆	—	2	2	no	—
529	C₂×Q₁₆	—	2	2	no	—
530	C₂×Q₁₆	—	2	2	no	—
531	C₂×Q₁₆	—	2	2	no	—
532	C₂×SD₁₆	—	2	2	no	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×SD₁₆	—	2	2	no	—
537	C₂×SD₁₆	—	2	2	no	—
538	C₂×SD₁₆	—	2	2	no	—
539	C₂×SD₁₆	—	2	2	no	—
540	C₂×SD₁₆	—	2	2	no	—
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₂²×C₈	C₂⁴	1	1	yes	characteristic
547	C₂²×C₈	C₂⁴	1	1	yes	characteristic
548	C₂²×C₈	C₂⁴	1	1	yes	characteristic
549	C₄⋊Q₈	—	2	2	no	—
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	—	4	1	no	—
552	C₄⋊Q₈	—	4	1	no	—
553	C₄⋊Q₈	—	4	1	no	—
554	C₄⋊Q₈	—	4	1	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	4	1	no	—
571	C₄×Q₈	—	4	1	no	—
572	C₄×Q₈	—	4	1	no	—
573	C₄×Q₈	—	4	1	no	—
574	C₄×Q₈	—	4	1	no	—
575	C₄×Q₈	—	4	1	no	—
576	C₄×Q₈	—	4	1	no	—
577	C₄×Q₈	—	4	1	no	—
578	C₄×Q₈	#41	1	4	yes	—
579	C₄×D₄	—	2	8	no	—
580	C₄×D₄	—	2	8	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	4	1	no	—
589	C₄×D₄	—	4	1	no	—
590	C₄×D₄	—	4	1	no	—
591	C₄×D₄	—	4	1	no	—
592	C₄×D₄	—	4	4	no	—
593	C₄×D₄	—	4	4	no	—
594	C₄×D₄	—	4	4	no	—
595	C₄×D₄	—	4	4	no	—
596	C₄×D₄	#41	1	4	yes	—
597	#117	—	2	8	no	—
598	#117	—	2	2	no	—
599	#117	—	2	2	no	—
600	#117	—	4	1	no	—
601	#117	—	4	1	no	—
602	#117	—	4	1	no	—
603	#117	—	4	1	no	—
604	#117	—	4	4	no	—
605	#117	—	4	4	no	—
606	C₂×C₄⋊C₄	—	2	8	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	2	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	4	1	no	—
647	C₂×C₄⋊C₄	—	4	1	no	—
648	C₂×C₄⋊C₄	—	4	4	no	—
649	C₂×C₄⋊C₄	—	8	2	no	—
650	C₂×C₄⋊C₄	—	8	2	no	—
651	C₂×C₄⋊C₄	—	8	2	no	—
652	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	1	no	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	—	2	1	no	—
692	C₂×C₄²	—	2	1	no	—
693	C₂×C₄²	—	2	1	no	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	—	2	1	no	—
696	C₂×C₄²	—	2	1	no	—
697	C₂×C₄²	—	2	1	no	—
698	C₂×C₄²	—	2	1	no	—
699	C₂×C₄²	—	2	1	no	—
700	C₂×C₄²	—	2	1	no	—
701	C₂×C₄²	—	2	1	no	—
702	C₂×C₄²	—	2	1	no	—
703	C₂×C₄²	—	4	1	no	—
704	C₂×C₄²	—	4	1	no	—
705	C₂×C₄²	—	4	4	no	—
706	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
707	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
708	C₂×C₄²	C₂⁴	1	1	yes	characteristic
709	C₂×C₄²	C₂⁴	1	1	yes	characteristic
710	C₂×C₄²	C₂⁴	1	1	yes	characteristic
711	C₂×C₄²	C₂⁴	1	1	yes	characteristic
712	C₂×C₄²	C₂⁴	1	1	yes	characteristic
713	C₂×C₄²	C₂⁴	1	1	yes	characteristic
714	#107	—	2	2	no	—
715	#107	—	2	2	no	—
716	#107	—	4	1	no	—
717	#107	—	4	1	no	—
718	#107	—	4	1	no	—
719	#106	—	4	1	no	—
720	C₄⋊C₈	—	2	2	no	—
721	C₄⋊C₈	—	2	2	no	—
722	C₄⋊C₈	—	4	1	no	—
723	C₄⋊C₈	—	4	1	no	—
724	C₄⋊C₈	—	4	1	no	—
725	C₄⋊C₈	—	4	1	no	—
726	#103	—	2	2	no	—
727	#103	—	2	2	no	—
728	#103	—	2	2	no	—
729	#103	—	2	2	no	—
730	#103	—	2	2	no	—
731	#103	—	2	2	no	—
732	#103	—	2	2	no	—
733	#103	—	2	2	no	—
734	#103	—	2	2	no	—
735	#103	—	2	2	no	—
736	#103	—	2	2	no	—
737	#103	—	4	1	no	—
738	#103	—	4	1	no	—
739	#103	—	4	1	no	—
740	#103	—	4	1	no	—
741	#103	—	4	1	no	—
742	#103	—	4	1	no	—
743	#103	—	4	1	no	—
744	#103	—	4	1	no	—
745	#103	—	4	1	no	—
746	#103	—	4	1	no	—
747	#103	—	4	1	no	—
748	#103	—	4	1	no	—
749	#102	—	2	2	no	—
750	#102	—	2	2	no	—
751	#102	—	2	2	no	—
752	#102	—	2	2	no	—
753	#102	—	2	2	no	—
754	C₂²⋊C₈	—	2	2	no	—
755	C₂²⋊C₈	—	2	2	no	—
756	C₂²⋊C₈	—	2	2	no	—
757	C₂²⋊C₈	—	2	2	no	—
758	#97	—	2	2	no	—
759	#97	—	4	1	no	—
760	#97	—	4	1	no	—
761	#97	—	4	1	no	—
762	C₄×C₈	—	2	2	no	—
763	C₄×C₈	—	4	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	—	2	1	no	—
795	#95	—	2	1	no	—
796	#95	—	2	1	no	—
797	#95	—	2	1	no	—
798	#95	—	2	1	no	—
799	#95	—	2	1	no	—
800	#95	—	2	1	no	—
801	#95	—	2	1	no	—
802	#95	—	2	1	no	—
803	#95	—	2	1	no	—
804	#95	—	2	1	no	—
805	#95	C₂×D₄	1	1	yes	characteristic
806	#95	C₂×D₄	1	1	yes	characteristic
807	#95	C₂×D₄	1	1	yes	characteristic
808	#95	C₂×D₄	1	1	yes	characteristic
809	#95	C₂×D₄	1	1	yes	characteristic
810	#95	C₂×D₄	1	1	yes	characteristic
811	#95	C₂×D₄	1	1	yes	characteristic
812	#95	C₂×D₄	1	1	yes	characteristic
813	C₂⁴	—	2	1	no	—
814	C₂⁴	C₂²×D₄	1	1	yes	characteristic
815	#41	—	2	8	no	—
816	#41	—	2	8	no	—
817	#41	—	2	8	no	—
818	#41	—	2	8	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	1	no	—
827	C₂×Q₈	—	2	1	no	—
828	C₂×Q₈	—	2	1	no	—
829	C₂×Q₈	—	2	1	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	C₂×#41	1	2	yes	—
841	C₂×Q₈	C₂×#41	1	2	yes	—
842	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	4	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	C₂×#41	1	2	yes	—
850	C₂×D₄	C₂×#41	1	2	yes	—
851	C₂×D₄	H(5,𝔽₂)	1	2	yes	—
852	C₂²×C₄	—	2	4	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	4	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	1	no	—
880	C₂²×C₄	—	4	1	no	—
881	C₂²×C₄	—	4	1	no	—
882	C₂²×C₄	—	4	1	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	—	8	1	no	—
891	C₂²×C₄	—	8	1	no	—
892	C₂²×C₄	—	8	1	no	—
893	C₂²×C₄	—	8	1	no	—
894	C₂²×C₄	—	8	1	no	—
895	C₂²×C₄	—	8	1	no	—
896	C₂²×C₄	—	8	1	no	—
897	C₂²×C₄	—	8	1	no	—
898	C₂²×C₄	—	8	1	no	—
899	C₂²×C₄	—	8	1	no	—
900	C₂²×C₄	—	8	1	no	—
901	C₂²×C₄	—	8	1	no	—
902	C₂²×C₄	—	8	1	no	—
903	C₂²×C₄	—	8	1	no	—
904	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
906	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
909	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
910	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
911	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
912	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
913	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
914	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
915	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
916	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
917	C₂²×C₄	C₂×#41	1	2	yes	—
918	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
919	C₂²×C₄	C₂⁵	1	1	yes	characteristic
920	Q₁₆	—	4	4	no	—
921	Q₁₆	—	4	4	no	—
922	Q₁₆	—	4	4	no	—
923	SD₁₆	—	4	4	no	—
924	SD₁₆	—	4	4	no	—
925	SD₁₆	—	4	4	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	—	2	1	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₂×C₈	—	2	1	no	—
935	C₂×C₈	—	2	1	no	—
936	C₂×C₈	—	2	1	no	—
937	C₂×C₈	—	2	1	no	—
938	C₂×C₈	—	2	1	no	—
939	C₂×C₈	—	2	1	no	—
940	C₂×C₈	—	2	1	no	—
941	C₂×C₈	—	2	1	no	—
942	C₂×C₈	—	2	1	no	—
943	C₂×C₈	—	2	1	no	—
944	C₂×C₈	—	2	1	no	—
945	C₂×C₈	—	2	1	no	—
946	C₂×C₈	—	2	1	no	—
947	C₂×C₈	—	2	1	no	—
948	C₂×C₈	—	2	1	no	—
949	C₂×C₈	—	2	1	no	—
950	C₄⋊C₄	—	2	4	no	—
951	C₄⋊C₄	—	2	4	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	4	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	4	1	no	—
978	C₄⋊C₄	—	4	1	no	—
979	C₄⋊C₄	—	4	1	no	—
980	C₄⋊C₄	—	4	1	no	—
981	C₄⋊C₄	—	4	1	no	—
982	C₄⋊C₄	—	4	1	no	—
983	C₄⋊C₄	—	4	1	no	—
984	C₄⋊C₄	—	4	1	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₄⋊C₄	—	4	2	no	—
989	C₄⋊C₄	—	4	2	no	—
990	C₄⋊C₄	—	4	2	no	—
991	C₄⋊C₄	—	4	2	no	—
992	C₄⋊C₄	—	4	2	no	—
993	C₄⋊C₄	—	4	2	no	—
994	C₄⋊C₄	—	4	2	no	—
995	C₄⋊C₄	—	4	2	no	—
996	C₄⋊C₄	—	4	2	no	—
997	C₄⋊C₄	—	4	2	no	—
998	C₄⋊C₄	—	4	2	no	—
999	C₄⋊C₄	—	4	2	no	—
1000	C₄⋊C₄	—	8	1	no	—
1001	C₄⋊C₄	—	8	1	no	—
1002	C₄⋊C₄	—	8	1	no	—
1003	C₄⋊C₄	—	8	1	no	—
1004	C₄⋊C₄	—	8	1	no	—
1005	C₄⋊C₄	—	8	1	no	—
1006	C₄⋊C₄	—	8	1	no	—
1007	C₄⋊C₄	—	8	1	no	—
1008	C₄⋊C₄	—	8	1	no	—
1009	C₄⋊C₄	—	8	1	no	—
1010	C₄⋊C₄	—	8	1	no	—
1011	C₄⋊C₄	—	8	1	no	—
1012	C₄⋊C₄	—	8	1	no	—
1013	C₄⋊C₄	—	8	1	no	—
1014	C₄⋊C₄	—	8	1	no	—
1015	C₄⋊C₄	—	8	1	no	—
1016	C₄⋊C₄	—	8	1	no	—
1017	C₄⋊C₄	—	8	1	no	—
1018	C₄⋊C₄	—	8	1	no	—
1019	C₄⋊C₄	C₂×#41	1	2	yes	—
1020	C₄⋊C₄	C₂×#41	1	2	yes	—
1021	C₂²⋊C₄	—	2	4	no	—
1022	C₂²⋊C₄	—	2	4	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	4	1	no	—
1026	C₂²⋊C₄	—	4	1	no	—
1027	C₂²⋊C₄	—	4	2	no	—
1028	C₂²⋊C₄	—	4	2	no	—
1029	C₂²⋊C₄	—	4	2	no	—
1030	C₂²⋊C₄	—	4	2	no	—
1031	C₂²⋊C₄	—	4	2	no	—
1032	C₂²⋊C₄	—	4	2	no	—
1033	C₂²⋊C₄	—	4	2	no	—
1034	C₂²⋊C₄	—	4	2	no	—
1035	C₂²⋊C₄	—	8	1	no	—
1036	C₄²	—	2	4	no	—
1037	C₄²	—	2	4	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	4	1	no	—
1049	C₄²	—	4	1	no	—
1050	C₄²	—	4	2	no	—
1051	C₄²	—	4	2	no	—
1052	C₄²	—	4	2	no	—
1053	C₄²	—	4	2	no	—
1054	C₄²	—	4	2	no	—
1055	C₄²	—	4	2	no	—
1056	C₄²	—	4	2	no	—
1057	C₄²	—	8	1	no	—
1058	C₄²	—	8	1	no	—
1059	C₄²	—	8	1	no	—
1060	C₄²	—	8	1	no	—
1061	C₄²	C₂×#41	1	2	yes	—
1062	C₄²	C₂×#41	1	2	yes	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	2	2	no	—
1068	C₂³	—	2	2	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	2	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	#548	1	2	yes	—
1077	C₂³	C₂³×D₄	1	1	yes	characteristic
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	4	1	no	—
1082	Q₈	—	4	1	no	—
1083	Q₈	—	4	1	no	—
1084	Q₈	—	4	1	no	—
1085	Q₈	—	4	1	no	—
1086	Q₈	—	4	1	no	—
1087	Q₈	—	4	1	no	—
1088	Q₈	—	4	1	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	#553	1	4	yes	—
1094	D₄	—	2	16	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	2	no	—
1098	D₄	#553	1	4	yes	—
1099	C₂×C₄	—	2	16	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	—	8	4	no	—
1186	C₂×C₄	—	8	4	no	—
1187	C₂×C₄	—	8	4	no	—
1188	C₂×C₄	—	8	4	no	—
1189	C₂×C₄	—	8	2	no	—
1190	C₂×C₄	—	8	4	no	—
1191	C₂×C₄	—	16	2	no	—
1192	C₂×C₄	—	16	2	no	—
1193	C₂×C₄	—	16	2	no	—
1194	C₂×C₄	#525	1	2	yes	—
1195	C₂×C₄	#525	1	2	yes	—
1196	C₂×C₄	#548	1	2	yes	—
1197	C₂×C₄	#578	1	2	yes	—
1198	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1199	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1200	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1201	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1202	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1203	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1204	C₈	—	4	1	no	—
1205	C₈	—	4	1	no	—
1206	C₈	—	4	1	no	—
1207	C₈	—	4	1	no	—
1208	C₈	—	4	1	no	—
1209	C₈	—	4	1	no	—
1210	C₈	—	4	1	no	—
1211	C₈	—	4	1	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	4	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	C₂×#525	1	1	yes	characteristic
1227	C₂²	C₂×#548	1	1	yes	characteristic
1228	C₂²	#3484	1	1	yes	characteristic
1229	C₂²	C₂×#578	1	1	yes	characteristic
1230	C₂²	#3585	1	1	yes	characteristic
1231	C₂²	#3586	1	1	yes	characteristic
1232	C₂²	#3586	1	1	yes	characteristic
1233	C₄	—	2	2	no	—
1234	C₄	—	2	2	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	no	—
1237	C₄	—	2	4	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	2	no	—
1240	C₄	—	4	2	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	8	1	no	—
1250	C₄	—	8	1	no	—
1251	C₄	—	8	1	no	—
1252	C₄	—	8	1	no	—
1253	C₄	—	8	1	no	—
1254	C₄	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	—	8	1	no	—
1257	C₄	—	8	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	C₂×#553	1	1	yes	characteristic
1262	C₄	C₂×#553	1	1	yes	characteristic
1263	C₄	#3492	1	1	yes	characteristic
1264	C₄	#3492	1	1	yes	characteristic
1265	C₂	—	4	2	no	—
1266	C₂	—	4	4	no	—
1267	C₂	#36581	1	1	yes	characteristic
1268	C₂	#60575	1	1	yes	characteristic
1269	C₂	#60594	1	1	yes	characteristic
1270	C₂	#61338	1	1	yes	characteristic
1271	C₂	#61348	1	1	yes	characteristic
1272	C₂	#61622	1	1	yes	characteristic
1273	C₂	#61654	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2296 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #39819	C₂	semidirect
6. #29341	C₂	semidirect
7. #29335	C₂	semidirect
8. #29252	C₂	semidirect
9. #29241	C₂	semidirect
10. #27985	C₂	semidirect
11. #27690	C₂	semidirect
12. #27575	C₂	semidirect
13. #27569	C₂	semidirect
14. #27566	C₂	semidirect
15. #27565	C₂	semidirect
16. #26186	C₂	semidirect
17. #26183	C₂	semidirect
18. #26182	C₂	semidirect
19. #26171	C₂	semidirect
20. #26120	C₂	semidirect
21. #26115	C₂	semidirect
22. #24748	C₂	semidirect
23. #24732	C₂	semidirect
24. #23014	C₂	semidirect
25. #23002	C₂	semidirect
26. #22778	C₂	semidirect
27. #22761	C₂	semidirect
28. #22631	C₂	semidirect

Maximal subgroups

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

subgroup	index
#39819	2
#34250	2
#32916	2
#32907	2
#29341	2
#29335	2
#29252	2
#29241	2
#27985	2
#27690	2
#27575	2
#27569	2
#27566	2
#27565	2
#26186	2
#26183	2
#26182	2
#26171	2
#26120	2
#26115	2
#24748	2
#24732	2
#23014	2
#23002	2
#22778	2
#22761	2
#22631	2
#21465	2
#21457	2