Subgroups — #6916641

Order 512.

1386 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#37888	C₂	1	1	yes	maximal, characteristic, complemented
2	#37493	C₂	1	1	yes	maximal, characteristic
3	#32827	C₂	1	1	yes	maximal, characteristic, complemented
4	#32754	C₂	1	1	yes	maximal, characteristic, complemented
5	#32489	C₂	1	1	yes	maximal, characteristic, complemented
6	#32475	C₂	1	1	yes	maximal, characteristic, complemented
7	#32225	C₂	1	1	yes	maximal, characteristic, complemented
8	#32195	C₂	1	1	yes	maximal, characteristic, complemented
9	#31993	C₂	1	1	yes	maximal, characteristic, complemented
10	#31973	C₂	1	1	yes	maximal, characteristic, complemented
11	#31507	C₂	1	1	yes	maximal, characteristic, complemented
12	#31495	C₂	1	1	yes	maximal, characteristic, complemented
13	#30390	C₂	1	1	yes	maximal, characteristic, complemented
14	#30194	C₂	1	1	yes	maximal, characteristic, complemented
15	#30163	C₂	1	1	yes	maximal, characteristic, complemented
16	#29956	C₂	1	1	yes	maximal, characteristic, complemented
17	#29929	C₂	1	1	yes	maximal, characteristic, complemented
18	#29360	C₂	1	1	yes	maximal, characteristic, complemented
19	#29167	C₂	1	1	yes	maximal, characteristic, complemented
20	#28110	C₂	1	1	yes	maximal, characteristic, complemented
21	#28100	C₂	1	1	yes	maximal, characteristic, complemented
22	#27869	C₂	1	1	yes	maximal, characteristic, complemented
23	#27650	C₂	1	1	yes	maximal, characteristic, complemented
24	#26015	C₂	1	1	yes	maximal, characteristic, complemented
25	#26013	C₂	1	1	yes	maximal, characteristic, complemented
26	#25263	C₂	1	1	yes	maximal, characteristic, complemented
27	#25245	C₂	1	1	yes	maximal, characteristic, complemented
28	#24492	C₂	1	1	yes	maximal, characteristic, complemented
29	#24492	C₂	1	1	yes	maximal, characteristic, complemented
30	#23628	C₂	1	1	yes	maximal, characteristic, complemented
31	#22699	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#482	C₂²	1	1	yes	characteristic
33	C₂×#482	C₂²	1	1	yes	characteristic
34	C₂×#436	C₂²	1	1	yes	characteristic
35	C₂×#435	C₂²	1	1	yes	characteristic
36	C₂×#418	C₂²	1	1	yes	characteristic
37	C₂×#418	C₂²	1	1	yes	characteristic
38	#2851	C₂²	1	1	yes	characteristic
39	#2829	—	2	1	no	—
40	#2828	—	2	1	no	—
41	#2781	—	2	1	no	—
42	#2781	—	2	1	no	—
43	#2770	—	2	1	no	—
44	#2770	—	2	1	no	—
45	#2661	—	2	1	no	—
46	#2648	—	2	1	no	—
47	#2647	C₂²	1	1	yes	characteristic, complemented
48	#2644	C₂²	1	1	yes	characteristic
49	#2641	C₂²	1	1	yes	characteristic
50	#2629	C₂²	1	1	yes	characteristic, complemented
51	#2624	C₂²	1	1	yes	characteristic
52	#2622	—	2	1	no	—
53	#2619	C₂²	1	1	yes	characteristic
54	#2617	—	2	1	no	—
55	#2525	—	2	1	no	—
56	#2525	—	2	1	no	—
57	#2524	—	2	1	no	—
58	#2524	—	2	1	no	—
59	#2513	C₂²	1	1	yes	characteristic
60	#2508	C₂²	1	1	yes	characteristic, complemented
61	#2508	C₂²	1	1	yes	characteristic, complemented
62	#2495	C₂²	1	1	yes	characteristic, complemented
63	#2495	C₂²	1	1	yes	characteristic, complemented
64	#2490	C₂²	1	1	yes	characteristic
65	#2485	C₂²	1	1	yes	characteristic
66	#2485	C₂²	1	1	yes	characteristic
67	#2445	C₂²	1	1	yes	characteristic
68	#2442	C₂²	1	1	yes	characteristic
69	#2433	C₂²	1	1	yes	characteristic
70	#2428	C₂²	1	1	yes	characteristic
71	#2424	—	2	1	no	—
72	#2418	—	2	1	no	—
73	#2416	C₂²	1	1	yes	characteristic
74	#2408	C₂²	1	1	yes	characteristic
75	#2347	C₂²	1	1	yes	characteristic
76	#2347	C₂²	1	1	yes	characteristic
77	#2330	C₂²	1	1	yes	characteristic, complemented
78	#2314	C₂²	1	1	yes	characteristic, complemented
79	C₄×#121	C₂²	1	1	yes	characteristic
80	C₂×#390	C₂²	1	1	yes	characteristic
81	#2290	C₂²	1	1	yes	characteristic
82	#2285	C₂²	1	1	yes	characteristic
83	#2101	C₂²	1	1	yes	characteristic, complemented
84	#2101	C₂²	1	1	yes	characteristic, complemented
85	#2101	C₂²	1	1	yes	characteristic, complemented
86	#2092	C₂²	1	1	yes	characteristic
87	#2092	C₂²	1	1	yes	characteristic
88	#2092	C₂²	1	1	yes	characteristic, complemented
89	#2088	C₂²	1	1	yes	characteristic, complemented
90	#2088	C₂²	1	1	yes	characteristic, complemented
91	#2088	C₂²	1	1	yes	characteristic, complemented
92	#2088	C₂²	1	1	yes	characteristic, complemented
93	#2087	C₂²	1	1	yes	characteristic, complemented
94	#2087	C₂²	1	1	yes	characteristic, complemented
95	#2084	C₂²	1	1	yes	characteristic, complemented
96	#2083	C₂²	1	1	yes	characteristic, complemented
97	#2076	C₂²	1	1	yes	characteristic, complemented
98	#2075	C₂²	1	1	yes	characteristic, complemented
99	#2073	C₂²	1	1	yes	characteristic
100	#2073	C₂²	1	1	yes	characteristic
101	#2073	C₂²	1	1	yes	characteristic
102	#2073	C₂²	1	1	yes	characteristic
103	#2071	C₂²	1	1	yes	characteristic
104	#2071	C₂²	1	1	yes	characteristic
105	#2071	C₂²	1	1	yes	characteristic
106	#2071	C₂²	1	1	yes	characteristic
107	#2071	C₂²	1	1	yes	characteristic, complemented
108	#2071	C₂²	1	1	yes	characteristic, complemented
109	#2067	C₂²	1	1	yes	characteristic
110	#2067	C₂²	1	1	yes	characteristic
111	#2067	C₂²	1	1	yes	characteristic
112	#2067	C₂²	1	1	yes	characteristic
113	#2067	C₂²	1	1	yes	characteristic
114	#2067	C₂²	1	1	yes	characteristic
115	#2067	C₂²	1	1	yes	characteristic
116	#2067	C₂²	1	1	yes	characteristic
117	#2067	C₂²	1	1	yes	characteristic, complemented
118	#2065	C₂²	1	1	yes	characteristic
119	#2065	C₂²	1	1	yes	characteristic
120	#2065	C₂²	1	1	yes	characteristic
121	#2065	C₂²	1	1	yes	characteristic
122	#2065	C₂²	1	1	yes	characteristic, complemented
123	#2059	C₂²	1	1	yes	characteristic, complemented
124	#2059	C₂²	1	1	yes	characteristic, complemented
125	#2059	C₂²	1	1	yes	characteristic, complemented
126	#2041	C₂²	1	1	yes	characteristic
127	#2041	C₂²	1	1	yes	characteristic
128	#2041	C₂²	1	1	yes	characteristic
129	#2041	C₂²	1	1	yes	characteristic
130	#2034	C₂²	1	1	yes	characteristic
131	#2034	C₂²	1	1	yes	characteristic
132	#2034	C₂²	1	1	yes	characteristic, complemented
133	#2033	C₂²	1	1	yes	characteristic
134	#2033	C₂²	1	1	yes	characteristic
135	#2033	C₂²	1	1	yes	characteristic, complemented
136	#2025	C₂²	1	1	yes	characteristic
137	#2025	C₂²	1	1	yes	characteristic
138	#2025	C₂²	1	1	yes	characteristic, complemented
139	#1989	C₂²	1	1	yes	characteristic, complemented
140	#1989	C₂²	1	1	yes	characteristic, complemented
141	#1982	C₂²	1	1	yes	characteristic
142	#1982	C₂²	1	1	yes	characteristic
143	#1982	C₂²	1	1	yes	characteristic
144	#1982	C₂²	1	1	yes	characteristic
145	#1949	C₂²	1	1	yes	characteristic, complemented
146	#1949	C₂²	1	1	yes	characteristic, complemented
147	#1949	C₂²	1	1	yes	characteristic, complemented
148	#1949	C₂²	1	1	yes	characteristic, complemented
149	#1944	C₂²	1	1	yes	characteristic, complemented
150	#1942	C₂²	1	1	yes	characteristic, complemented
151	#1940	C₂²	1	1	yes	characteristic, complemented
152	#1939	C₂²	1	1	yes	characteristic, complemented
153	#1936	C₂²	1	1	yes	characteristic
154	#1936	C₂²	1	1	yes	characteristic
155	#1936	C₂²	1	1	yes	characteristic, complemented
156	#1934	C₂²	1	1	yes	characteristic
157	#1934	C₂²	1	1	yes	characteristic
158	#1934	C₂²	1	1	yes	characteristic, complemented
159	#1926	C₂²	1	1	yes	characteristic
160	#1926	C₂²	1	1	yes	characteristic
161	#1926	C₂²	1	1	yes	characteristic
162	#1926	C₂²	1	1	yes	characteristic
163	#1920	C₂²	1	1	yes	characteristic, complemented
164	#1920	C₂²	1	1	yes	characteristic, complemented
165	#1920	C₂²	1	1	yes	characteristic, complemented
166	#1918	C₂²	1	1	yes	characteristic, complemented
167	#1918	C₂²	1	1	yes	characteristic, complemented
168	#1918	C₂²	1	1	yes	characteristic, complemented
169	#1895	C₂²	1	1	yes	characteristic
170	#1895	C₂²	1	1	yes	characteristic
171	#1895	C₂²	1	1	yes	characteristic
172	#1895	C₂²	1	1	yes	characteristic
173	#1895	C₂²	1	1	yes	characteristic, complemented
174	#1893	C₂²	1	1	yes	characteristic
175	#1893	C₂²	1	1	yes	characteristic
176	#1893	C₂²	1	1	yes	characteristic, complemented
177	#1864	C₂²	1	1	yes	characteristic, complemented
178	#1862	C₂²	1	1	yes	characteristic, complemented
179	#1853	C₂²	1	1	yes	characteristic
180	#1852	C₂²	1	1	yes	characteristic
181	#1851	C₂²	1	1	yes	characteristic
182	#1851	C₂²	1	1	yes	characteristic
183	#1851	C₂²	1	1	yes	characteristic, complemented
184	#1850	C₂²	1	1	yes	characteristic, complemented
185	#1832	C₂²	1	1	yes	characteristic, complemented
186	#1825	C₂²	1	1	yes	characteristic
187	#1825	C₂²	1	1	yes	characteristic
188	#1809	C₂²	1	1	yes	characteristic
189	#1809	C₂²	1	1	yes	characteristic
190	#1809	C₂²	1	1	yes	characteristic, complemented
191	#1807	C₂²	1	1	yes	characteristic, complemented
192	#1804	C₂²	1	1	yes	characteristic, complemented
193	#1804	C₂²	1	1	yes	characteristic, complemented
194	#1798	C₂²	1	1	yes	characteristic, complemented
195	#1797	C₂²	1	1	yes	characteristic
196	#1786	C₂²	1	1	yes	characteristic
197	#1786	C₂²	1	1	yes	characteristic
198	#1768	C₂²	1	1	yes	characteristic, complemented
199	#1736	C₂²	1	1	yes	characteristic
200	#1736	C₂²	1	1	yes	characteristic
201	#1729	C₂²	1	1	yes	characteristic, complemented
202	#1728	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×M₁₆	C₂³	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂²×M₁₆	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	C₂×#127	C₂³	1	1	yes	characteristic
209	C₂×#127	C₂³	1	1	yes	characteristic
210	C₂×#125	C₂³	1	1	yes	characteristic
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#123	—	2	1	no	—
213	C₂×#121	—	2	1	no	—
214	C₂×#121	—	2	1	no	—
215	C₂×#121	C₂³	1	1	yes	characteristic
216	C₂×#121	C₂³	1	1	yes	characteristic
217	C₂×#121	C₂³	1	1	yes	characteristic
218	C₂×#121	C₂³	1	1	yes	characteristic
219	C₂×#120	—	2	1	no	—
220	C₂×#120	—	2	1	no	—
221	C₂×#120	—	2	1	no	—
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
225	C₂×#117	C₂³	1	1	yes	characteristic
226	C₂×#117	C₂³	1	1	yes	characteristic
227	C₂×#117	C₂³	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₂²⋊C₄	—	2	1	no	—
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	C₂²×C₄²	C₂³	1	1	yes	characteristic
232	#482	—	4	2	no	—
233	#482	—	4	2	no	—
234	#436	—	4	2	no	—
235	#435	—	4	2	no	—
236	C₂×#107	C₂³	1	1	yes	characteristic
237	C₂×#107	C₂³	1	1	yes	characteristic
238	C₂×#107	C₂³	1	1	yes	characteristic
239	C₂×#107	C₂³	1	1	yes	characteristic
240	C₂×#107	C₂³	1	1	yes	characteristic
241	C₂×#107	C₂³	1	1	yes	characteristic
242	C₂×#106	C₂³	1	1	yes	characteristic
243	C₂×#106	C₂³	1	1	yes	characteristic
244	C₂×#106	C₂³	1	1	yes	characteristic
245	C₂×#106	C₂³	1	1	yes	characteristic
246	C₂×#106	C₂³	1	1	yes	characteristic
247	C₂×#106	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	#418	—	4	2	no	—
257	#418	—	4	2	no	—
258	C₂×#102	C₂³	1	1	yes	characteristic
259	C₂×#102	C₂³	1	1	yes	characteristic
260	C₂×#102	C₂³	1	1	yes	characteristic
261	C₂×#102	C₂³	1	1	yes	characteristic
262	C₂×#102	C₂³	1	1	yes	characteristic
263	C₂×#102	C₂³	1	1	yes	characteristic
264	C₂×#102	C₂³	1	1	yes	characteristic
265	C₂×#102	C₂³	1	1	yes	characteristic
266	C₂×#102	C₂³	1	1	yes	characteristic
267	C₂×#102	C₂³	1	1	yes	characteristic
268	C₂×#102	C₂³	1	1	yes	characteristic
269	C₂×#102	C₂³	1	1	yes	characteristic
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×#102	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×#97	C₂³	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
288	#400	—	2	1	no	—
289	#400	—	2	1	no	—
290	#400	—	2	1	no	—
291	#400	—	2	1	no	—
292	#400	—	2	1	no	—
293	#400	—	2	1	no	—
294	#400	—	2	1	no	—
295	#399	—	2	1	no	—
296	#398	—	2	1	no	—
297	#398	—	2	1	no	—
298	#398	—	2	1	no	—
299	#398	—	2	1	no	—
300	#398	—	2	1	no	—
301	#398	—	2	1	no	—
302	#398	—	2	1	no	—
303	#397	—	2	1	no	—
304	#397	—	2	1	no	—
305	#397	—	2	1	no	—
306	#397	—	2	1	no	—
307	#397	—	2	1	no	—
308	#397	—	2	1	no	—
309	#397	—	2	1	no	—
310	#397	—	2	1	no	—
311	#397	—	2	1	no	—
312	#397	—	2	1	no	—
313	#397	—	2	1	no	—
314	#396	—	2	1	no	—
315	#396	—	2	1	no	—
316	#396	—	2	1	no	—
317	#396	—	2	1	no	—
318	#394	—	2	1	no	—
319	#394	—	2	1	no	—
320	#394	—	2	1	no	—
321	#394	—	2	1	no	—
322	#394	—	2	1	no	—
323	#394	—	2	1	no	—
324	#394	—	2	1	no	—
325	#394	—	2	1	no	—
326	#394	—	2	1	no	—
327	#394	—	2	1	no	—
328	#394	—	2	1	no	—
329	#394	—	2	1	no	—
330	#394	—	2	1	no	—
331	#394	—	2	1	no	—
332	#394	—	2	1	no	—
333	#394	—	2	1	no	—
334	#392	—	2	1	no	—
335	#392	—	2	1	no	—
336	#392	—	2	1	no	—
337	#392	—	2	1	no	—
338	#392	—	2	1	no	—
339	#392	—	2	1	no	—
340	#390	—	2	1	no	—
341	#390	—	2	1	no	—
342	#390	—	2	1	no	—
343	#390	C₂³	1	1	yes	characteristic
344	#390	C₂³	1	1	yes	characteristic
345	#390	C₂³	1	1	yes	characteristic
346	#390	C₂³	1	1	yes	characteristic
347	#390	C₂³	1	1	yes	characteristic
348	#390	C₂³	1	1	yes	characteristic
349	#390	C₂³	1	1	yes	characteristic
350	#390	C₂³	1	1	yes	characteristic
351	#390	C₂³	1	1	yes	characteristic
352	#390	C₂³	1	1	yes	characteristic
353	#389	—	2	1	no	—
354	#389	—	2	1	no	—
355	#389	C₂³	1	1	yes	characteristic
356	#389	C₂³	1	1	yes	characteristic
357	#389	C₂³	1	1	yes	characteristic
358	#389	C₂³	1	1	yes	characteristic
359	#389	C₂³	1	1	yes	characteristic
360	#389	C₂³	1	1	yes	characteristic
361	#389	C₂³	1	1	yes	characteristic
362	#389	C₂³	1	1	yes	characteristic
363	#389	C₂³	1	1	yes	characteristic
364	#389	C₂³	1	1	yes	characteristic
365	#389	C₂³	1	1	yes	characteristic
366	#389	C₂³	1	1	yes	characteristic
367	#389	C₂³	1	1	yes	characteristic
368	#389	C₂³	1	1	yes	characteristic
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#388	—	2	1	no	—
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#388	—	2	1	no	—
377	#388	—	2	1	no	—
378	#388	—	2	1	no	—
379	#388	—	2	1	no	—
380	#388	—	2	1	no	—
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#388	D₄	1	1	yes	characteristic
384	#388	D₄	1	1	yes	characteristic
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	D₄	1	1	yes	characteristic
396	#387	D₄	1	1	yes	characteristic
397	#386	—	2	1	no	—
398	#386	—	2	1	no	—
399	#386	—	2	1	no	—
400	#386	—	2	1	no	—
401	#386	D₄	1	1	yes	characteristic
402	#386	D₄	1	1	yes	characteristic
403	#385	—	2	1	no	—
404	#385	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	D₄	1	1	yes	characteristic
407	#385	D₄	1	1	yes	characteristic
408	#384	C₂³	1	1	yes	characteristic
409	#384	C₂³	1	1	yes	characteristic
410	#383	—	2	1	no	—
411	#383	—	2	1	no	—
412	#383	—	2	1	no	—
413	#383	—	2	1	no	—
414	#382	—	2	1	no	—
415	#382	—	2	1	no	—
416	#382	C₂³	1	1	yes	characteristic
417	#382	C₂³	1	1	yes	characteristic
418	#382	C₂³	1	1	yes	characteristic
419	#382	C₂³	1	1	yes	characteristic
420	#380	—	2	1	no	—
421	#380	—	2	1	no	—
422	#380	—	2	1	no	—
423	#380	C₂³	1	1	yes	characteristic
424	#380	C₂³	1	1	yes	characteristic
425	#380	C₂³	1	1	yes	characteristic
426	#380	C₂³	1	1	yes	characteristic
427	#380	C₂³	1	1	yes	characteristic
428	#380	C₂³	1	1	yes	characteristic
429	#380	C₂³	1	1	yes	characteristic
430	#380	C₂³	1	1	yes	characteristic
431	#379	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
434	C₄×C₄⋊C₄	—	2	1	no	—
435	C₄×C₄⋊C₄	—	2	1	no	—
436	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₂²⋊C₄	—	2	1	no	—
443	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
445	#376	C₂³	1	1	yes	characteristic
446	#340	C₂³	1	1	yes	characteristic
447	#340	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	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	#336	C₂³	1	1	yes	characteristic
475	#336	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	C₂⁵	—	2	1	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
501	C₂²×D₄	C₂⁴	1	1	yes	characteristic
502	C₂²×D₄	C₂⁴	1	1	yes	characteristic
503	C₂²×D₄	C₂⁴	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	C₂⁴	1	1	yes	characteristic
509	C₂³×C₄	C₂⁴	1	1	yes	characteristic
510	C₂×M₁₆	—	2	2	no	—
511	C₂×M₁₆	—	2	2	no	—
512	C₂×M₁₆	—	4	1	no	—
513	C₂×M₁₆	—	4	1	no	—
514	C₂×M₁₆	—	4	1	no	—
515	C₂×M₁₆	—	4	1	no	—
516	C₂×M₁₆	—	4	1	no	—
517	C₂×M₁₆	—	4	1	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂²×C₈	—	4	1	no	—
520	C₂²×C₈	—	4	1	no	—
521	C₂²×C₈	—	4	1	no	—
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	#127	—	4	1	no	—
531	#127	—	4	1	no	—
532	#127	—	4	1	no	—
533	#127	—	4	1	no	—
534	#125	—	4	1	no	—
535	#125	—	4	1	no	—
536	#125	—	4	1	no	—
537	#125	—	4	1	no	—
538	#123	—	8	2	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	4	1	no	—
542	#121	—	4	1	no	—
543	#121	—	4	1	no	—
544	#121	—	4	1	no	—
545	#121	—	4	1	no	—
546	#121	—	4	1	no	—
547	#121	—	8	2	no	—
548	#121	—	8	2	no	—
549	#120	—	8	2	no	—
550	#120	—	8	2	no	—
551	#120	—	8	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	4	1	no	—
555	C₄×D₄	—	4	1	no	—
556	C₄×D₄	—	8	2	no	—
557	#117	—	2	2	no	—
558	#117	—	2	2	no	—
559	#117	—	2	2	no	—
560	#117	—	2	2	no	—
561	#117	—	4	1	no	—
562	#117	—	4	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	4	1	no	—
587	C₂×C₄⋊C₄	—	4	1	no	—
588	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	8	2	no	—
642	C₂×C₂²⋊C₄	—	8	2	no	—
643	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	4	1	no	—
659	C₂×C₄²	—	4	1	no	—
660	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂⁴	1	1	yes	characteristic
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴	1	1	yes	characteristic
665	C₂×C₄²	C₂⁴	1	1	yes	characteristic
666	C₂×C₄²	C₂⁴	1	1	yes	characteristic
667	#107	—	4	1	no	—
668	#107	—	4	1	no	—
669	#107	—	4	1	no	—
670	#107	—	4	1	no	—
671	#107	—	4	1	no	—
672	#107	—	4	1	no	—
673	#106	—	4	1	no	—
674	#106	—	4	1	no	—
675	#106	—	4	1	no	—
676	#106	—	4	1	no	—
677	#106	—	4	1	no	—
678	#106	—	4	1	no	—
679	C₄⋊C₈	—	4	1	no	—
680	C₄⋊C₈	—	4	1	no	—
681	C₄⋊C₈	—	4	1	no	—
682	C₄⋊C₈	—	4	1	no	—
683	C₄⋊C₈	—	4	1	no	—
684	C₄⋊C₈	—	4	1	no	—
685	C₄⋊C₈	—	4	1	no	—
686	C₄⋊C₈	—	4	1	no	—
687	#102	—	4	1	no	—
688	#102	—	4	1	no	—
689	#102	—	4	1	no	—
690	#102	—	4	1	no	—
691	#102	—	4	1	no	—
692	#102	—	4	1	no	—
693	#102	—	4	1	no	—
694	#102	—	4	1	no	—
695	#102	—	4	1	no	—
696	#102	—	4	1	no	—
697	#102	—	4	1	no	—
698	#102	—	4	1	no	—
699	#102	—	4	1	no	—
700	#102	—	4	1	no	—
701	#102	—	4	1	no	—
702	#102	—	4	1	no	—
703	#102	—	4	1	no	—
704	#102	—	4	1	no	—
705	#102	—	4	1	no	—
706	#102	—	4	1	no	—
707	#102	—	4	1	no	—
708	#102	—	4	1	no	—
709	#102	—	4	1	no	—
710	#102	—	4	1	no	—
711	C₂²⋊C₈	—	2	2	no	—
712	C₂²⋊C₈	—	2	2	no	—
713	C₂²⋊C₈	—	4	1	no	—
714	C₂²⋊C₈	—	4	1	no	—
715	#97	—	4	1	no	—
716	C₄×C₈	—	4	1	no	—
717	#95	—	2	1	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
753	#95	C₂×D₄	1	1	yes	characteristic
754	#95	C₂×D₄	1	1	yes	characteristic
755	#95	C₂×D₄	1	1	yes	characteristic
756	#95	C₂×D₄	1	1	yes	characteristic
757	#95	C₂×D₄	1	1	yes	characteristic
758	#95	C₂×D₄	1	1	yes	characteristic
759	#95	C₂×D₄	1	1	yes	characteristic
760	#95	C₂×D₄	1	1	yes	characteristic
761	#95	C₂×D₄	1	1	yes	characteristic
762	C₂⁴	—	2	1	no	—
763	C₂⁴	—	2	1	no	—
764	C₂⁴	—	2	1	no	—
765	C₂⁴	—	4	2	no	—
766	C₂⁴	—	4	2	no	—
767	C₂⁴	—	4	2	no	—
768	C₂⁴	—	8	1	no	—
769	C₂⁴	—	8	1	no	—
770	C₂⁴	—	8	1	no	—
771	C₂⁴	—	8	1	no	—
772	C₂⁴	C₂²×D₄	1	1	yes	characteristic
773	C₂⁴	C₂²×D₄	1	1	yes	characteristic
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	4	4	no	—
794	C₂×D₄	—	4	4	no	—
795	C₂×D₄	—	4	1	no	—
796	C₂×D₄	—	4	1	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	8	2	no	—
802	C₂×D₄	—	8	2	no	—
803	C₂×D₄	—	8	1	no	—
804	C₂×D₄	—	8	1	no	—
805	C₂×D₄	—	8	1	no	—
806	C₂×D₄	—	8	1	no	—
807	C₂×D₄	—	8	1	no	—
808	C₂×D₄	—	8	1	no	—
809	C₂×D₄	—	8	1	no	—
810	C₂×D₄	—	8	1	no	—
811	C₂×D₄	—	8	1	no	—
812	C₂×D₄	—	8	1	no	—
813	C₂×D₄	—	8	1	no	—
814	C₂×D₄	—	8	1	no	—
815	C₂×D₄	—	8	1	no	—
816	C₂×D₄	—	8	1	no	—
817	C₂×D₄	—	8	1	no	—
818	C₂×D₄	—	8	1	no	—
819	C₂×D₄	—	8	1	no	—
820	C₂×D₄	—	8	1	no	—
821	C₂×D₄	—	8	1	no	—
822	C₂×D₄	—	8	1	no	—
823	C₂×D₄	—	8	1	no	—
824	C₂×D₄	—	8	1	no	—
825	C₂×D₄	—	8	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	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	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	8	1	no	—
858	C₂²×C₄	—	8	1	no	—
859	C₂²×C₄	—	8	1	no	—
860	C₂²×C₄	—	8	1	no	—
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
864	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
865	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
866	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
867	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
868	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
869	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
870	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
872	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂²×C₄	H(5,𝔽₂)	1	2	yes	—
874	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
875	C₂²×C₄	C₂⁵	1	1	yes	characteristic
876	M₁₆	—	8	2	no	—
877	M₁₆	—	8	2	no	—
878	M₁₆	—	8	2	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	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	—	8	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	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	—	4	1	no	—
932	C₄⋊C₄	—	4	1	no	—
933	C₄⋊C₄	—	4	1	no	—
934	C₄⋊C₄	—	4	1	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	4	2	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	—	8	1	no	—
945	C₄⋊C₄	—	8	1	no	—
946	C₄⋊C₄	—	8	1	no	—
947	C₄⋊C₄	—	8	1	no	—
948	C₄⋊C₄	—	8	1	no	—
949	C₄⋊C₄	—	8	1	no	—
950	C₄⋊C₄	—	8	1	no	—
951	C₄⋊C₄	—	8	1	no	—
952	C₄⋊C₄	—	8	1	no	—
953	C₄⋊C₄	—	8	1	no	—
954	C₄⋊C₄	—	8	1	no	—
955	C₄⋊C₄	—	8	1	no	—
956	C₄⋊C₄	—	8	1	no	—
957	C₄⋊C₄	—	8	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	4	1	no	—
961	C₂²⋊C₄	—	4	1	no	—
962	C₂²⋊C₄	—	4	1	no	—
963	C₂²⋊C₄	—	4	1	no	—
964	C₂²⋊C₄	—	4	1	no	—
965	C₂²⋊C₄	—	4	1	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	—	8	1	no	—
974	C₂²⋊C₄	—	8	1	no	—
975	C₂²⋊C₄	—	8	1	no	—
976	C₂²⋊C₄	—	8	1	no	—
977	C₂²⋊C₄	—	8	1	no	—
978	C₂²⋊C₄	—	8	1	no	—
979	C₂²⋊C₄	—	8	1	no	—
980	C₂²⋊C₄	—	8	1	no	—
981	C₂²⋊C₄	—	8	1	no	—
982	C₂²⋊C₄	—	8	1	no	—
983	C₂²⋊C₄	—	8	1	no	—
984	C₂²⋊C₄	—	8	1	no	—
985	C₂²⋊C₄	—	8	1	no	—
986	C₂²⋊C₄	—	8	1	no	—
987	C₂²⋊C₄	—	8	1	no	—
988	C₂²⋊C₄	—	8	1	no	—
989	C₂²⋊C₄	—	8	1	no	—
990	C₂²⋊C₄	—	8	1	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₂²⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	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	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	4	1	no	—
1012	C₄²	—	4	1	no	—
1013	C₄²	—	4	2	no	—
1014	C₄²	—	4	2	no	—
1015	C₄²	—	8	1	no	—
1016	C₄²	—	8	1	no	—
1017	C₄²	—	8	1	no	—
1018	C₄²	—	8	1	no	—
1019	C₄²	—	8	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	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	—	8	4	no	—
1055	C₂³	—	8	4	no	—
1056	C₂³	—	8	4	no	—
1057	C₂³	—	16	2	no	—
1058	C₂³	—	16	2	no	—
1059	C₂³	—	16	2	no	—
1060	C₂³	—	16	2	no	—
1061	C₂³	#537	1	2	yes	—
1062	C₂³	C₂³×D₄	1	1	yes	characteristic
1063	D₄	—	4	1	no	—
1064	D₄	—	4	1	no	—
1065	D₄	—	4	1	no	—
1066	D₄	—	4	1	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	1	no	—
1070	D₄	—	4	1	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	8	4	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	4	no	—
1078	D₄	—	16	2	no	—
1079	D₄	—	16	2	no	—
1080	D₄	—	16	2	no	—
1081	D₄	—	16	2	no	—
1082	D₄	—	16	2	no	—
1083	D₄	—	16	2	no	—
1084	D₄	—	16	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	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	1	no	—
1105	C₂×C₄	—	2	1	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	1	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	—	2	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	—	4	1	no	—
1167	C₂×C₄	—	8	2	no	—
1168	C₂×C₄	—	8	2	no	—
1169	C₂×C₄	—	16	2	no	—
1170	C₂×C₄	—	16	2	no	—
1171	C₂×C₄	#537	1	2	yes	—
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	C₂×C₄	#585	1	1	yes	characteristic
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	C₈	—	4	1	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	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	—	8	1	no	—
1207	C₂²	—	8	1	no	—
1208	C₂²	—	8	1	no	—
1209	C₂²	—	8	1	no	—
1210	C₂²	—	8	1	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	—	8	1	no	—
1213	C₂²	—	8	1	no	—
1214	C₂²	—	8	1	no	—
1215	C₂²	—	8	1	no	—
1216	C₂²	—	8	1	no	—
1217	C₂²	—	8	1	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	16	8	no	—
1222	C₂²	C₂×#537	1	1	yes	characteristic
1223	C₂²	#3485	1	1	yes	characteristic
1224	C₂²	#3500	1	1	yes	characteristic
1225	C₂²	#3584	1	1	yes	characteristic
1226	C₂²	#3585	1	1	yes	characteristic
1227	C₂²	#3585	1	1	yes	characteristic
1228	C₂²	#3585	1	1	yes	characteristic
1229	C₄	—	2	2	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	1	no	—
1248	C₄	—	8	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	#3533	1	1	yes	characteristic
1255	C₄	#3533	1	1	yes	characteristic
1256	C₄	#3564	1	1	yes	characteristic
1257	C₄	#3564	1	1	yes	characteristic
1258	C₂	—	4	2	no	—
1259	C₂	—	8	1	no	—
1260	C₂	—	16	1	no	—
1261	C₂	—	16	1	no	—
1262	C₂	—	16	1	no	—
1263	C₂	#41369	1	1	yes	characteristic
1264	C₂	#60920	1	1	yes	characteristic
1265	C₂	#60933	1	1	yes	characteristic
1266	C₂	#61749	1	1	yes	characteristic
1267	C₂	#61778	1	1	yes	characteristic
1268	C₂	#62564	1	1	yes	characteristic
1269	C₂	#62614	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#37493	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2290 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #37888	C₂	semidirect
3. #32827	C₂	semidirect
4. #32754	C₂	semidirect
5. #32489	C₂	semidirect
6. #32475	C₂	semidirect
7. #32225	C₂	semidirect
8. #32195	C₂	semidirect
9. #31993	C₂	semidirect
10. #31973	C₂	semidirect
11. #31507	C₂	semidirect
12. #31495	C₂	semidirect
13. #30390	C₂	semidirect
14. #30194	C₂	semidirect
15. #30163	C₂	semidirect
16. #29956	C₂	semidirect
17. #29929	C₂	semidirect
18. #29360	C₂	semidirect
19. #29167	C₂	semidirect
20. #28110	C₂	semidirect
21. #28100	C₂	semidirect
22. #27869	C₂	semidirect
23. #27650	C₂	semidirect
24. #26015	C₂	semidirect
25. #26013	C₂	semidirect
26. #25263	C₂	semidirect
27. #25245	C₂	semidirect
28. #24492	C₂	semidirect
29. #24492	C₂	semidirect
30. #23628	C₂	semidirect
31. #22699	C₂	semidirect
47. #2647	C₂²	semidirect
50. #2629	C₂²	semidirect
60. #2508	C₂²	semidirect
61. #2508	C₂²	semidirect
62. #2495	C₂²	semidirect
63. #2495	C₂²	semidirect
77. #2330	C₂²	semidirect
78. #2314	C₂²	semidirect
83. #2101	C₂²	semidirect
84. #2101	C₂²	semidirect
85. #2101	C₂²	semidirect
88. #2092	C₂²	semidirect
89. #2088	C₂²	semidirect
90. #2088	C₂²	semidirect
91. #2088	C₂²	semidirect
92. #2088	C₂²	semidirect
93. #2087	C₂²	semidirect
94. #2087	C₂²	semidirect
95. #2084	C₂²	semidirect
96. #2083	C₂²	semidirect
97. #2076	C₂²	semidirect
98. #2075	C₂²	semidirect
107. #2071	C₂²	semidirect
108. #2071	C₂²	semidirect
117. #2067	C₂²	semidirect
122. #2065	C₂²	semidirect
123. #2059	C₂²	semidirect
124. #2059	C₂²	semidirect
125. #2059	C₂²	semidirect
132. #2034	C₂²	semidirect
135. #2033	C₂²	semidirect
138. #2025	C₂²	semidirect
139. #1989	C₂²	semidirect
140. #1989	C₂²	semidirect
145. #1949	C₂²	semidirect
146. #1949	C₂²	semidirect
147. #1949	C₂²	semidirect
148. #1949	C₂²	semidirect
149. #1944	C₂²	semidirect
150. #1942	C₂²	semidirect
151. #1940	C₂²	semidirect
152. #1939	C₂²	semidirect
155. #1936	C₂²	semidirect
158. #1934	C₂²	semidirect
163. #1920	C₂²	semidirect
164. #1920	C₂²	semidirect
165. #1920	C₂²	semidirect
166. #1918	C₂²	semidirect
167. #1918	C₂²	semidirect
168. #1918	C₂²	semidirect
173. #1895	C₂²	semidirect
176. #1893	C₂²	semidirect
177. #1864	C₂²	semidirect
178. #1862	C₂²	semidirect
183. #1851	C₂²	semidirect
184. #1850	C₂²	semidirect
185. #1832	C₂²	semidirect
190. #1809	C₂²	semidirect
191. #1807	C₂²	semidirect
192. #1804	C₂²	semidirect
193. #1804	C₂²	semidirect
194. #1798	C₂²	semidirect
198. #1768	C₂²	semidirect
201. #1729	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#37888	2
#37493	2
#32827	2
#32754	2
#32489	2
#32475	2
#32225	2
#32195	2
#31993	2
#31973	2
#31507	2
#31495	2
#30390	2
#30194	2
#30163	2
#29956	2
#29929	2
#29360	2
#29167	2
#28110	2
#28100	2
#27869	2
#27650	2
#26015	2
#26013	2
#25263	2
#25245	2
#24492	2
#23628	2
#22699	2