Subgroups — #7304763

Order 512.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#45343	C₂	1	1	yes	maximal, characteristic, complemented
2	#42960	C₂	1	1	yes	maximal, characteristic
3	#32604	C₂	1	1	yes	maximal, characteristic, complemented
4	#32598	C₂	1	1	yes	maximal, characteristic, complemented
5	#32182	C₂	1	1	yes	maximal, characteristic, complemented
6	#32166	C₂	1	1	yes	maximal, characteristic, complemented
7	#32060	C₂	1	1	yes	maximal, characteristic, complemented
8	#32050	C₂	1	1	yes	maximal, characteristic, complemented
9	#31853	C₂	1	1	yes	maximal, characteristic, complemented
10	#31836	C₂	1	1	yes	maximal, characteristic, complemented
11	#31469	C₂	1	1	yes	maximal, characteristic, complemented
12	#31457	C₂	1	1	yes	maximal, characteristic, complemented
13	#31166	C₂	1	1	yes	maximal, characteristic, complemented
14	#31158	C₂	1	1	yes	maximal, characteristic, complemented
15	#30122	C₂	1	1	yes	maximal, characteristic
16	#29671	C₂	1	1	yes	maximal, characteristic
17	#29250	C₂	1	1	yes	maximal, characteristic, complemented
18	#27150	C₂	1	1	yes	maximal, characteristic, complemented
19	#27140	C₂	1	1	yes	maximal, characteristic, complemented
20	#26813	C₂	1	1	yes	maximal, characteristic, complemented
21	#26799	C₂	1	1	yes	maximal, characteristic, complemented
22	#26627	C₂	1	1	yes	maximal, characteristic, complemented
23	#26627	C₂	1	1	yes	maximal, characteristic, complemented
24	#26588	C₂	1	1	yes	maximal, characteristic, complemented
25	#26588	C₂	1	1	yes	maximal, characteristic, complemented
26	#26539	C₂	1	1	yes	maximal, characteristic, complemented
27	#26527	C₂	1	1	yes	maximal, characteristic, complemented
28	#24334	C₂	1	1	yes	maximal, characteristic, complemented
29	#24328	C₂	1	1	yes	maximal, characteristic, complemented
30	#24072	C₂	1	1	yes	maximal, characteristic, complemented
31	#23340	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#557	C₂²	1	1	yes	characteristic
33	C₂×#541	C₂²	1	1	yes	characteristic
34	C₂×#485	C₂²	1	1	yes	characteristic
35	C₂×#485	C₂²	1	1	yes	characteristic
36	C₂×#478	C₂²	1	1	yes	characteristic
37	C₂×#474	C₂²	1	1	yes	characteristic
38	C₂×#460	C₂²	1	1	yes	characteristic
39	C₂×#460	C₂²	1	1	yes	characteristic
40	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
42	#2837	—	2	1	no	—
43	#2725	—	2	1	no	—
44	#2719	—	2	1	no	—
45	#2719	—	2	1	no	—
46	#2716	—	2	1	no	—
47	#2706	—	2	1	no	—
48	#2705	—	2	1	no	—
49	#2696	—	2	1	no	—
50	#2693	—	2	1	no	—
51	#2663	—	2	1	no	—
52	#2649	—	2	1	no	—
53	#2619	C₂²	1	1	yes	characteristic
54	#2580	C₂²	1	1	yes	characteristic
55	#2571	C₂²	1	1	yes	characteristic
56	#2570	C₂²	1	1	yes	characteristic
57	#2568	C₂²	1	1	yes	characteristic
58	#2553	—	2	1	no	—
59	#2550	—	2	1	no	—
60	#2546	C₂²	1	1	yes	characteristic
61	#2538	C₂²	1	1	yes	characteristic
62	#2519	—	2	1	no	—
63	#2513	C₂²	1	1	yes	characteristic
64	#2512	C₂²	1	1	yes	characteristic
65	#2504	C₂²	1	1	yes	characteristic
66	#2501	C₂²	1	1	yes	characteristic
67	#2492	C₂²	1	1	yes	characteristic
68	#2489	C₂²	1	1	yes	characteristic
69	#2469	—	2	1	no	—
70	#2453	—	2	1	no	—
71	#2453	C₂²	1	1	yes	characteristic
72	#2451	C₂²	1	1	yes	characteristic
73	#2445	C₂²	1	1	yes	characteristic
74	#2445	C₂²	1	1	yes	characteristic
75	#2429	C₂²	1	1	yes	characteristic
76	#2429	C₂²	1	1	yes	characteristic
77	#2396	C₂²	1	1	yes	characteristic
78	#2370	C₂²	1	1	yes	characteristic
79	#2365	C₂²	1	1	yes	characteristic
80	#2365	C₂²	1	1	yes	characteristic
81	#2363	C₂²	1	1	yes	characteristic
82	#2363	C₂²	1	1	yes	characteristic
83	#2323	C₂²	1	1	yes	characteristic
84	#2316	C₂²	1	1	yes	characteristic
85	#2101	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic
87	#2099	C₂²	1	1	yes	characteristic
88	#2097	C₂²	1	1	yes	characteristic
89	#2097	C₂²	1	1	yes	characteristic
90	#2096	C₂²	1	1	yes	characteristic
91	#2088	C₂²	1	1	yes	characteristic
92	#2087	C₂²	1	1	yes	characteristic
93	#2074	C₂²	1	1	yes	characteristic
94	#2074	C₂²	1	1	yes	characteristic
95	#2072	C₂²	1	1	yes	characteristic
96	#2072	C₂²	1	1	yes	characteristic
97	#2068	C₂²	1	1	yes	characteristic
98	#2067	C₂²	1	1	yes	characteristic
99	#2067	C₂²	1	1	yes	characteristic
100	#2066	C₂²	1	1	yes	characteristic
101	#2066	C₂²	1	1	yes	characteristic
102	#2066	C₂²	1	1	yes	characteristic
103	#2059	C₂²	1	1	yes	characteristic
104	#2059	C₂²	1	1	yes	characteristic
105	#2059	C₂²	1	1	yes	characteristic
106	#2058	C₂²	1	1	yes	characteristic
107	#2055	C₂²	1	1	yes	characteristic
108	#2055	C₂²	1	1	yes	characteristic
109	#2055	C₂²	1	1	yes	characteristic
110	#2055	C₂²	1	1	yes	characteristic
111	#2043	C₂²	1	1	yes	characteristic
112	#2043	C₂²	1	1	yes	characteristic
113	#2041	C₂²	1	1	yes	characteristic
114	#2034	C₂²	1	1	yes	characteristic
115	#2033	C₂²	1	1	yes	characteristic
116	#2025	C₂²	1	1	yes	characteristic
117	#2025	C₂²	1	1	yes	characteristic
118	#2025	C₂²	1	1	yes	characteristic
119	#2023	C₂²	1	1	yes	characteristic
120	#2014	C₂²	1	1	yes	characteristic
121	#2013	C₂²	1	1	yes	characteristic
122	#2013	C₂²	1	1	yes	characteristic
123	#2013	C₂²	1	1	yes	characteristic
124	#2013	C₂²	1	1	yes	characteristic
125	#2013	C₂²	1	1	yes	characteristic
126	#2013	C₂²	1	1	yes	characteristic
127	#2000	C₂²	1	1	yes	characteristic
128	#2000	C₂²	1	1	yes	characteristic
129	#2000	C₂²	1	1	yes	characteristic
130	#2000	C₂²	1	1	yes	characteristic
131	#2000	C₂²	1	1	yes	characteristic
132	#2000	C₂²	1	1	yes	characteristic
133	#1991	C₂²	1	1	yes	characteristic
134	#1990	C₂²	1	1	yes	characteristic
135	#1984	C₂²	1	1	yes	characteristic
136	#1984	C₂²	1	1	yes	characteristic
137	#1981	C₂²	1	1	yes	characteristic
138	#1981	C₂²	1	1	yes	characteristic
139	#1973	C₂²	1	1	yes	characteristic
140	#1968	C₂²	1	1	yes	characteristic
141	#1968	C₂²	1	1	yes	characteristic
142	#1968	C₂²	1	1	yes	characteristic
143	#1960	C₂²	1	1	yes	characteristic
144	#1956	C₂²	1	1	yes	characteristic
145	#1949	C₂²	1	1	yes	characteristic
146	#1948	C₂²	1	1	yes	characteristic
147	#1940	C₂²	1	1	yes	characteristic
148	#1939	C₂²	1	1	yes	characteristic
149	#1936	C₂²	1	1	yes	characteristic
150	#1934	C₂²	1	1	yes	characteristic
151	#1933	C₂²	1	1	yes	characteristic
152	#1933	C₂²	1	1	yes	characteristic
153	#1928	C₂²	1	1	yes	characteristic
154	#1927	C₂²	1	1	yes	characteristic
155	#1926	C₂²	1	1	yes	characteristic
156	#1926	C₂²	1	1	yes	characteristic
157	#1926	C₂²	1	1	yes	characteristic
158	#1926	C₂²	1	1	yes	characteristic
159	#1926	C₂²	1	1	yes	characteristic
160	#1925	C₂²	1	1	yes	characteristic
161	#1924	C₂²	1	1	yes	characteristic
162	#1923	C₂²	1	1	yes	characteristic
163	#1923	C₂²	1	1	yes	characteristic
164	#1923	C₂²	1	1	yes	characteristic
165	#1920	C₂²	1	1	yes	characteristic
166	#1919	C₂²	1	1	yes	characteristic
167	#1919	C₂²	1	1	yes	characteristic
168	#1919	C₂²	1	1	yes	characteristic
169	#1917	C₂²	1	1	yes	characteristic
170	#1916	C₂²	1	1	yes	characteristic
171	#1916	C₂²	1	1	yes	characteristic
172	#1916	C₂²	1	1	yes	characteristic
173	#1880	C₂²	1	1	yes	characteristic
174	#1880	C₂²	1	1	yes	characteristic
175	#1880	C₂²	1	1	yes	characteristic
176	#1880	C₂²	1	1	yes	characteristic
177	#1877	C₂²	1	1	yes	characteristic
178	#1877	C₂²	1	1	yes	characteristic
179	#1877	C₂²	1	1	yes	characteristic
180	#1877	C₂²	1	1	yes	characteristic
181	#1873	C₂²	1	1	yes	characteristic
182	#1872	C₂²	1	1	yes	characteristic
183	#1872	C₂²	1	1	yes	characteristic
184	#1872	C₂²	1	1	yes	characteristic
185	#1865	C₂²	1	1	yes	characteristic
186	#1865	C₂²	1	1	yes	characteristic
187	#1865	C₂²	1	1	yes	characteristic
188	#1863	C₂²	1	1	yes	characteristic
189	#1863	C₂²	1	1	yes	characteristic
190	#1863	C₂²	1	1	yes	characteristic
191	#1863	C₂²	1	1	yes	characteristic
192	#1863	C₂²	1	1	yes	characteristic
193	#1854	C₂²	1	1	yes	characteristic
194	#1853	C₂²	1	1	yes	characteristic
195	#1818	C₂²	1	1	yes	characteristic
196	#1805	C₂²	1	1	yes	characteristic
197	#1805	C₂²	1	1	yes	characteristic
198	#1805	C₂²	1	1	yes	characteristic
199	#1803	C₂²	1	1	yes	characteristic
200	#1798	C₂²	1	1	yes	characteristic
201	#1776	C₂²	1	1	yes	characteristic
202	C₄×#107	C₂²	1	1	yes	characteristic
203	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	#557	—	4	2	no	—
210	#557	—	4	2	no	—
211	#541	—	4	2	no	—
212	#541	—	4	2	no	—
213	C₂×C₄⋊Q₈	—	2	1	no	—
214	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×#127	C₂³	1	1	yes	characteristic
219	C₂×#126	—	2	1	no	—
220	C₂×#126	—	2	1	no	—
221	C₂×#126	—	2	1	no	—
222	C₂×#125	—	2	1	no	—
223	C₂×#125	—	2	1	no	—
224	C₂×#125	—	2	1	no	—
225	C₂×#125	—	2	1	no	—
226	C₂×#125	C₂³	1	1	yes	characteristic
227	C₂×#125	C₂³	1	1	yes	characteristic
228	C₂×#123	—	2	1	no	—
229	C₂×#123	—	2	1	no	—
230	C₂×#123	—	2	1	no	—
231	C₂×#123	—	2	1	no	—
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
236	C₂×#121	C₂³	1	1	yes	characteristic
237	C₂×#121	C₂³	1	1	yes	characteristic
238	C₂×C₄×Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₄	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	C₂³	1	1	yes	characteristic
250	#485	—	4	2	no	—
251	#485	—	4	2	no	—
252	#478	—	4	2	no	—
253	#474	—	4	2	no	—
254	#460	—	4	2	no	—
255	#460	—	4	2	no	—
256	C₄×SD₁₆	—	4	2	no	—
257	C₄×SD₁₆	—	4	2	no	—
258	C₂×#107	C₂³	1	1	yes	characteristic
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#107	C₂³	1	1	yes	characteristic
261	C₂×#107	C₂³	1	1	yes	characteristic
262	C₂×#106	C₂³	1	1	yes	characteristic
263	C₂×#106	C₂³	1	1	yes	characteristic
264	C₂×#106	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×#106	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	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×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×#102	C₂³	1	1	yes	characteristic
295	C₂×#102	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×#102	C₂³	1	1	yes	characteristic
299	C₂×#102	C₂³	1	1	yes	characteristic
300	C₂×#102	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂×#97	C₂³	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
308	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
310	#400	—	2	1	no	—
311	#400	—	2	1	no	—
312	#400	—	2	1	no	—
313	#400	—	2	1	no	—
314	#400	—	2	1	no	—
315	#400	—	2	1	no	—
316	#400	—	2	1	no	—
317	#400	—	2	1	no	—
318	#400	D₄	1	1	yes	characteristic
319	#399	—	2	1	no	—
320	#399	—	2	1	no	—
321	#399	—	2	1	no	—
322	#399	D₄	1	1	yes	characteristic
323	#398	—	2	1	no	—
324	#398	—	2	1	no	—
325	#398	—	2	1	no	—
326	#398	—	2	1	no	—
327	#398	—	2	1	no	—
328	#398	—	2	1	no	—
329	#398	—	2	1	no	—
330	#398	D₄	1	1	yes	characteristic
331	#398	D₄	1	1	yes	characteristic
332	#397	—	2	1	no	—
333	#397	—	2	1	no	—
334	#397	—	2	1	no	—
335	#397	—	2	1	no	—
336	#397	—	2	1	no	—
337	#397	—	2	1	no	—
338	#396	—	2	1	no	—
339	#396	—	2	1	no	—
340	#396	—	2	1	no	—
341	#396	—	2	1	no	—
342	#396	—	2	1	no	—
343	#396	D₄	1	1	yes	characteristic
344	#396	D₄	1	1	yes	characteristic
345	#395	—	2	1	no	—
346	#395	D₄	1	1	yes	characteristic
347	#394	—	2	1	no	—
348	#394	—	2	1	no	—
349	#394	—	2	1	no	—
350	#394	—	2	1	no	—
351	#394	—	2	1	no	—
352	#394	—	2	1	no	—
353	#393	—	2	1	no	—
354	#393	—	2	1	no	—
355	#393	D₄	1	1	yes	characteristic
356	#392	—	2	1	no	—
357	#392	—	2	1	no	—
358	#391	—	2	1	no	—
359	#391	—	2	1	no	—
360	#391	—	2	1	no	—
361	#391	C₂³	1	1	yes	characteristic
362	#391	C₂³	1	1	yes	characteristic
363	#391	C₂³	1	1	yes	characteristic
364	#391	C₂³	1	1	yes	characteristic
365	#391	C₂³	1	1	yes	characteristic
366	#391	C₂³	1	1	yes	characteristic
367	#391	C₂³	1	1	yes	characteristic
368	#390	—	2	1	no	—
369	#390	—	2	1	no	—
370	#390	C₂³	1	1	yes	characteristic
371	#390	C₂³	1	1	yes	characteristic
372	#390	C₂³	1	1	yes	characteristic
373	#390	C₂³	1	1	yes	characteristic
374	#390	C₂³	1	1	yes	characteristic
375	#390	C₂³	1	1	yes	characteristic
376	#390	C₂³	1	1	yes	characteristic
377	#390	C₂³	1	1	yes	characteristic
378	#389	—	2	1	no	—
379	#389	—	2	1	no	—
380	#389	—	2	1	no	—
381	#389	—	2	1	no	—
382	#389	—	2	1	no	—
383	#389	—	2	1	no	—
384	#389	—	2	1	no	—
385	#389	—	2	1	no	—
386	#389	—	2	1	no	—
387	#389	—	2	1	no	—
388	#389	—	2	1	no	—
389	#389	—	2	1	no	—
390	#389	C₂³	1	1	yes	characteristic
391	#389	C₂³	1	1	yes	characteristic
392	#389	C₂³	1	1	yes	characteristic
393	#389	C₂³	1	1	yes	characteristic
394	#389	C₂³	1	1	yes	characteristic
395	#389	C₂³	1	1	yes	characteristic
396	#389	C₂³	1	1	yes	characteristic
397	#389	C₂³	1	1	yes	characteristic
398	#389	C₂³	1	1	yes	characteristic
399	#388	—	2	1	no	—
400	#388	—	2	1	no	—
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#388	—	2	1	no	—
404	#388	—	2	1	no	—
405	#388	—	2	1	no	—
406	#388	—	2	1	no	—
407	#388	—	2	1	no	—
408	#388	—	2	1	no	—
409	#388	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#387	—	2	1	no	—
413	#387	—	2	1	no	—
414	#387	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	—	2	1	no	—
420	#387	—	2	1	no	—
421	#386	—	2	1	no	—
422	#386	—	2	1	no	—
423	#386	—	2	1	no	—
424	#386	—	2	1	no	—
425	#386	—	2	1	no	—
426	#386	—	2	1	no	—
427	#385	—	2	1	no	—
428	#385	—	2	1	no	—
429	#384	C₂³	1	1	yes	characteristic
430	#384	C₂³	1	1	yes	characteristic
431	#382	—	2	1	no	—
432	#382	—	2	1	no	—
433	#382	—	2	1	no	—
434	#382	C₂³	1	1	yes	characteristic
435	#382	C₂³	1	1	yes	characteristic
436	#382	C₂³	1	1	yes	characteristic
437	#380	—	2	1	no	—
438	#380	—	2	1	no	—
439	#380	—	2	1	no	—
440	#380	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	—	2	1	no	—
442	C₄×C₄⋊C₄	—	2	1	no	—
443	C₄×C₄⋊C₄	—	2	1	no	—
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	—	2	1	no	—
453	C₄×C₂²⋊C₄	—	2	1	no	—
454	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
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	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	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	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
492	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
494	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	C₂⁴	1	1	yes	characteristic
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	4	1	no	—
508	C₂×SD₁₆	—	4	1	no	—
509	C₂×SD₁₆	—	4	1	no	—
510	C₂×SD₁₆	—	4	1	no	—
511	C₂×SD₁₆	—	4	1	no	—
512	C₂×SD₁₆	—	4	1	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂×SD₁₆	—	4	1	no	—
516	C₂×SD₁₆	—	4	1	no	—
517	C₂×SD₁₆	—	4	1	no	—
518	C₂×SD₁₆	—	4	1	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	4	1	no	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	—	4	1	no	—
535	C₄⋊Q₈	—	4	1	no	—
536	C₄⋊Q₈	—	4	1	no	—
537	C₄⋊Q₈	—	4	1	no	—
538	C₄⋊Q₈	—	4	1	no	—
539	C₄⋊Q₈	—	4	4	no	—
540	#127	—	4	1	no	—
541	#127	—	4	1	no	—
542	#126	—	4	4	no	—
543	#126	—	4	4	no	—
544	#126	—	8	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	4	1	no	—
549	#125	—	4	4	no	—
550	#125	—	4	4	no	—
551	#125	—	4	4	no	—
552	#125	—	4	4	no	—
553	#123	—	8	2	no	—
554	#123	—	8	2	no	—
555	#123	—	8	2	no	—
556	#123	—	8	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	4	1	no	—
561	C₂²⋊Q₈	—	4	1	no	—
562	C₂²⋊Q₈	—	4	1	no	—
563	C₂²⋊Q₈	—	8	2	no	—
564	#121	—	4	1	no	—
565	#121	—	4	1	no	—
566	#121	—	4	1	no	—
567	#121	—	4	1	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	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	—	4	1	no	—
579	C₄×Q₈	—	4	1	no	—
580	C₄×Q₈	—	4	4	no	—
581	C₄×D₄	—	4	1	no	—
582	C₄×D₄	—	4	1	no	—
583	C₄×D₄	—	4	1	no	—
584	C₄×D₄	—	4	1	no	—
585	#117	—	4	1	no	—
586	#117	—	4	1	no	—
587	#117	—	4	1	no	—
588	#117	—	4	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	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	1	no	—
611	C₂×C₄⋊C₄	—	2	1	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	—	4	1	no	—
623	C₂×C₄⋊C₄	—	4	1	no	—
624	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	C₂⁴	1	1	yes	characteristic
689	C₂×C₄²	C₂⁴	1	1	yes	characteristic
690	C₂×C₄²	C₂⁴	1	1	yes	characteristic
691	C₂×C₄²	C₂⁴	1	1	yes	characteristic
692	C₂×C₄²	C₂⁴	1	1	yes	characteristic
693	C₂×C₄²	C₂⁴	1	1	yes	characteristic
694	#107	—	2	2	no	—
695	#107	—	2	2	no	—
696	#107	—	4	1	no	—
697	#107	—	4	1	no	—
698	#106	—	2	2	no	—
699	#106	—	2	2	no	—
700	#106	—	4	1	no	—
701	#106	—	4	1	no	—
702	#106	—	4	1	no	—
703	#106	—	4	1	no	—
704	C₄⋊C₈	—	4	1	no	—
705	C₄⋊C₈	—	4	1	no	—
706	C₄⋊C₈	—	4	1	no	—
707	C₄⋊C₈	—	4	1	no	—
708	C₄⋊C₈	—	4	1	no	—
709	C₄⋊C₈	—	4	1	no	—
710	#103	—	4	1	no	—
711	#103	—	4	1	no	—
712	#103	—	4	1	no	—
713	#103	—	4	1	no	—
714	#103	—	4	1	no	—
715	#103	—	4	1	no	—
716	#103	—	4	1	no	—
717	#103	—	4	1	no	—
718	#103	—	4	1	no	—
719	#103	—	4	1	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#103	—	4	1	no	—
724	#103	—	4	1	no	—
725	#103	—	4	1	no	—
726	#103	—	4	1	no	—
727	#103	—	4	1	no	—
728	#102	—	2	2	no	—
729	#102	—	2	2	no	—
730	#102	—	2	2	no	—
731	#102	—	2	2	no	—
732	#102	—	4	1	no	—
733	#102	—	4	1	no	—
734	#102	—	4	1	no	—
735	#102	—	4	1	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	C₂²⋊C₈	—	4	1	no	—
739	C₂²⋊C₈	—	4	1	no	—
740	C₂²⋊C₈	—	4	1	no	—
741	C₂²⋊C₈	—	4	1	no	—
742	#97	—	4	1	no	—
743	C₄×C₈	—	4	1	no	—
744	C₄×C₈	—	4	1	no	—
745	C₄×C₈	—	4	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
782	#95	C₂×D₄	1	1	yes	characteristic
783	#95	C₂×D₄	1	1	yes	characteristic
784	#95	C₂×D₄	1	1	yes	characteristic
785	#95	C₂×D₄	1	1	yes	characteristic
786	#95	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	C₂⁴	—	2	1	no	—
792	C₂⁴	—	2	1	no	—
793	C₂⁴	C₂²×D₄	1	1	yes	characteristic
794	C₂×Q₈	—	2	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	4	1	no	—
813	C₂×Q₈	—	4	1	no	—
814	C₂×Q₈	—	4	2	no	—
815	C₂×Q₈	—	4	2	no	—
816	C₂×Q₈	—	8	1	no	—
817	C₂×Q₈	2₋¹⁺⁴	1	2	yes	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	8	1	no	—
833	C₂×D₄	—	8	1	no	—
834	C₂×D₄	—	8	1	no	—
835	C₂×D₄	—	8	1	no	—
836	C₂×D₄	—	8	1	no	—
837	C₂×D₄	—	8	1	no	—
838	C₂×D₄	—	8	1	no	—
839	C₂×D₄	—	8	1	no	—
840	C₂×D₄	—	8	1	no	—
841	C₂×D₄	—	8	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	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	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	8	1	no	—
865	C₂²×C₄	—	8	1	no	—
866	C₂²×C₄	—	8	1	no	—
867	C₂²×C₄	—	8	1	no	—
868	C₂²×C₄	—	8	1	no	—
869	C₂²×C₄	—	8	1	no	—
870	C₂²×C₄	—	8	1	no	—
871	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
872	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
874	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂⁵	1	1	yes	characteristic
885	SD₁₆	—	4	4	no	—
886	SD₁₆	—	4	4	no	—
887	SD₁₆	—	8	2	no	—
888	SD₁₆	—	8	2	no	—
889	SD₁₆	—	8	2	no	—
890	SD₁₆	—	8	2	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	—	2	1	no	—
895	C₂×C₈	—	2	1	no	—
896	C₂×C₈	—	2	1	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	1	no	—
899	C₂×C₈	—	2	1	no	—
900	C₂×C₈	—	2	1	no	—
901	C₂×C₈	—	2	1	no	—
902	C₂×C₈	—	2	1	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	4	1	no	—
941	C₄⋊C₄	—	4	1	no	—
942	C₄⋊C₄	—	4	1	no	—
943	C₄⋊C₄	—	4	1	no	—
944	C₄⋊C₄	—	4	1	no	—
945	C₄⋊C₄	—	4	1	no	—
946	C₄⋊C₄	—	4	1	no	—
947	C₄⋊C₄	—	4	1	no	—
948	C₄⋊C₄	—	4	2	no	—
949	C₄⋊C₄	—	4	2	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	4	2	no	—
953	C₄⋊C₄	—	4	2	no	—
954	C₄⋊C₄	—	4	2	no	—
955	C₄⋊C₄	—	4	2	no	—
956	C₄⋊C₄	—	4	2	no	—
957	C₄⋊C₄	—	4	2	no	—
958	C₄⋊C₄	—	4	2	no	—
959	C₄⋊C₄	—	4	2	no	—
960	C₄⋊C₄	—	4	2	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	—	8	1	no	—
970	C₄⋊C₄	—	8	1	no	—
971	C₄⋊C₄	—	8	1	no	—
972	C₄⋊C₄	—	8	1	no	—
973	C₄⋊C₄	—	8	1	no	—
974	C₄⋊C₄	—	8	1	no	—
975	C₄⋊C₄	—	8	1	no	—
976	C₄⋊C₄	—	8	1	no	—
977	C₄⋊C₄	—	8	1	no	—
978	C₄⋊C₄	—	8	1	no	—
979	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
980	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	4	1	no	—
984	C₂²⋊C₄	—	4	1	no	—
985	C₂²⋊C₄	—	4	1	no	—
986	C₂²⋊C₄	—	4	1	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	8	1	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	—	8	1	no	—
1004	C₂²⋊C₄	—	8	1	no	—
1005	C₂²⋊C₄	—	8	1	no	—
1006	C₂²⋊C₄	—	8	1	no	—
1007	C₂²⋊C₄	—	8	1	no	—
1008	C₂²⋊C₄	—	8	1	no	—
1009	C₂²⋊C₄	—	8	1	no	—
1010	C₂²⋊C₄	—	8	1	no	—
1011	C₂²⋊C₄	—	8	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	4	2	no	—
1025	C₄²	—	4	2	no	—
1026	C₄²	—	4	2	no	—
1027	C₄²	—	4	2	no	—
1028	C₄²	—	4	2	no	—
1029	C₄²	—	4	2	no	—
1030	C₄²	—	8	1	no	—
1031	C₄²	—	8	1	no	—
1032	C₄²	—	8	1	no	—
1033	C₄²	—	8	1	no	—
1034	C₄²	—	8	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	4	1	no	—
1044	C₂³	—	4	1	no	—
1045	C₂³	—	4	1	no	—
1046	C₂³	—	4	1	no	—
1047	C₂³	—	4	1	no	—
1048	C₂³	—	4	1	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	1	no	—
1055	C₂³	—	4	1	no	—
1056	C₂³	C₂³×D₄	1	1	yes	characteristic
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	4	1	no	—
1061	Q₈	—	4	1	no	—
1062	Q₈	—	4	1	no	—
1063	Q₈	—	4	1	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	4	1	no	—
1066	Q₈	—	4	1	no	—
1067	Q₈	—	4	1	no	—
1068	Q₈	—	4	1	no	—
1069	Q₈	—	8	2	no	—
1070	Q₈	—	8	4	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	1	no	—
1076	D₄	—	4	1	no	—
1077	D₄	—	4	1	no	—
1078	D₄	—	4	1	no	—
1079	D₄	—	16	2	no	—
1080	D₄	—	16	2	no	—
1081	D₄	—	16	2	no	—
1082	D₄	—	16	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	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	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	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	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	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	—	16	2	no	—
1167	C₂×C₄	—	16	2	no	—
1168	C₂×C₄	—	16	2	no	—
1169	C₂×C₄	#577	1	2	yes	—
1170	C₂×C₄	#577	1	2	yes	—
1171	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1172	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1174	C₂×C₄	#585	1	1	yes	characteristic
1175	C₂×C₄	#585	1	1	yes	characteristic
1176	C₂×C₄	#585	1	1	yes	characteristic
1177	C₈	—	4	1	no	—
1178	C₈	—	4	1	no	—
1179	C₈	—	4	1	no	—
1180	C₈	—	4	1	no	—
1181	C₈	—	4	1	no	—
1182	C₈	—	4	1	no	—
1183	C₈	—	4	1	no	—
1184	C₈	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	8	1	no	—
1193	C₂²	—	8	1	no	—
1194	C₂²	—	8	1	no	—
1195	C₂²	—	8	1	no	—
1196	C₂²	—	8	1	no	—
1197	C₂²	—	8	1	no	—
1198	C₂²	—	8	1	no	—
1199	C₂²	—	8	1	no	—
1200	C₂²	—	8	1	no	—
1201	C₂²	—	8	1	no	—
1202	C₂²	—	8	1	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	1	no	—
1205	C₂²	—	8	1	no	—
1206	C₂²	#3484	1	1	yes	characteristic
1207	C₂²	#3487	1	1	yes	characteristic
1208	C₂²	#3489	1	1	yes	characteristic
1209	C₂²	C₂×#577	1	1	yes	characteristic
1210	C₂²	C₂×#577	1	1	yes	characteristic
1211	C₂²	#3584	1	1	yes	characteristic
1212	C₂²	#3586	1	1	yes	characteristic
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	2	no	—
1229	C₄	—	8	1	no	—
1230	C₄	—	8	1	no	—
1231	C₄	—	8	1	no	—
1232	C₄	—	8	1	no	—
1233	C₄	—	8	1	no	—
1234	C₄	—	8	1	no	—
1235	C₄	—	8	1	no	—
1236	C₄	—	8	1	no	—
1237	C₄	—	8	1	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	#3541	1	1	yes	characteristic
1241	C₄	#3541	1	1	yes	characteristic
1242	C₄	#3562	1	1	yes	characteristic
1243	C₄	#3562	1	1	yes	characteristic
1244	C₂	—	8	1	no	—
1245	C₂	—	16	1	no	—
1246	C₂	—	16	1	no	—
1247	C₂	#47837	1	1	yes	characteristic
1248	C₂	#61641	1	1	yes	characteristic
1249	C₂	#61692	1	1	yes	characteristic
1250	C₂	#61925	1	1	yes	characteristic
1251	C₂	#61933	1	1	yes	characteristic
1252	C₂	#62191	1	1	yes	characteristic
1253	C₂	#62213	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2619	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2396 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #45343	C₂	semidirect
3. #32604	C₂	semidirect
4. #32598	C₂	semidirect
5. #32182	C₂	semidirect
6. #32166	C₂	semidirect
7. #32060	C₂	semidirect
8. #32050	C₂	semidirect
9. #31853	C₂	semidirect
10. #31836	C₂	semidirect
11. #31469	C₂	semidirect
12. #31457	C₂	semidirect
13. #31166	C₂	semidirect
14. #31158	C₂	semidirect
17. #29250	C₂	semidirect
18. #27150	C₂	semidirect
19. #27140	C₂	semidirect
20. #26813	C₂	semidirect
21. #26799	C₂	semidirect
22. #26627	C₂	semidirect
23. #26627	C₂	semidirect
24. #26588	C₂	semidirect
25. #26588	C₂	semidirect
26. #26539	C₂	semidirect
27. #26527	C₂	semidirect
28. #24334	C₂	semidirect
29. #24328	C₂	semidirect
30. #24072	C₂	semidirect
31. #23340	C₂	semidirect

Maximal subgroups

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

subgroup	index
#45343	2
#42960	2
#32604	2
#32598	2
#32182	2
#32166	2
#32060	2
#32050	2
#31853	2
#31836	2
#31469	2
#31457	2
#31166	2
#31158	2
#30122	2
#29671	2
#29250	2
#27150	2
#27140	2
#26813	2
#26799	2
#26627	2
#26588	2
#26539	2
#26527	2
#24334	2
#24328	2
#24072	2
#23340	2