Subgroups — #6699404

Order 512.

1535 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#42856	C₂	1	1	yes	maximal, characteristic, complemented
2	#35776	C₂	1	1	yes	maximal, characteristic
3	#33018	C₂	1	1	yes	maximal, characteristic
4	#32654	C₂	1	1	yes	maximal, characteristic, complemented
5	#32556	C₂	1	1	yes	maximal, characteristic, complemented
6	#32366	C₂	1	1	yes	maximal, characteristic, complemented
7	#31639	C₂	1	1	yes	maximal, characteristic, complemented
8	#31437	C₂	1	1	yes	maximal, characteristic, complemented
9	#31377	C₂	1	1	yes	maximal, characteristic, complemented
10	#31117	C₂	1	1	yes	maximal, characteristic, complemented
11	#31107	C₂	1	1	yes	maximal, characteristic, complemented
12	#30371	C₂	1	1	yes	maximal, characteristic, complemented
13	#30182	C₂	1	1	yes	maximal, characteristic, complemented
14	#29100	C₂	1	1	yes	maximal, characteristic, complemented
15	#28958	C₂	1	1	yes	maximal, characteristic, complemented
16	#27558	C₂	1	1	yes	maximal, characteristic, complemented
17	#27525	C₂	1	1	yes	maximal, characteristic
18	#27301	C₂	1	1	yes	maximal, characteristic, complemented
19	#27296	C₂	1	1	yes	maximal, characteristic, complemented
20	#26902	C₂	1	1	yes	maximal, characteristic, complemented
21	#26379	C₂	1	1	yes	maximal, characteristic, complemented
22	#26182	C₂	1	1	yes	maximal, characteristic, complemented
23	#25156	C₂	1	1	yes	maximal, characteristic
24	#24921	C₂	1	1	yes	maximal, characteristic
25	#24917	C₂	1	1	yes	maximal, characteristic
26	#24343	C₂	1	1	yes	maximal, characteristic, complemented
27	#24337	C₂	1	1	yes	maximal, characteristic, complemented
28	#23002	C₂	1	1	yes	maximal, characteristic, complemented
29	#22678	C₂	1	1	yes	maximal, characteristic, complemented
30	#22324	C₂	1	1	yes	maximal, characteristic, complemented
31	#21459	C₂	1	1	yes	maximal, characteristic
32	C₂×#554	C₂²	1	1	yes	characteristic
33	C₂×#518	C₂²	1	1	yes	characteristic
34	C₂×#485	C₂²	1	1	yes	characteristic
35	C₂×#479	C₂²	1	1	yes	characteristic, complemented
36	C₂×#475	C₂²	1	1	yes	characteristic, complemented
37	C₂×#461	C₂²	1	1	yes	characteristic
38	C₂×#450	C₂²	1	1	yes	characteristic
39	C₂×#450	C₂²	1	1	yes	characteristic
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×#440	C₂²	1	1	yes	characteristic
42	C₂×#440	C₂²	1	1	yes	characteristic
43	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
45	#2838	—	2	1	no	—
46	#2793	—	2	1	no	—
47	#2792	—	2	1	no	—
48	#2777	—	2	1	no	—
49	#2776	—	2	1	no	—
50	#2655	—	2	1	no	—
51	#2655	—	2	1	no	—
52	#2629	C₂²	1	1	yes	characteristic
53	#2626	—	2	1	no	—
54	#2625	C₂²	1	1	yes	characteristic
55	#2596	—	2	1	no	—
56	#2581	C₂²	1	1	yes	characteristic, complemented
57	#2581	C₂²	1	1	yes	characteristic, complemented
58	#2579	—	2	1	no	—
59	#2566	C₂²	1	1	yes	characteristic
60	#2538	C₂²	1	1	yes	characteristic
61	#2514	C₂²	1	1	yes	characteristic, complemented
62	#2509	C₂²	1	1	yes	characteristic, complemented
63	#2507	C₂²	1	1	yes	characteristic, complemented
64	#2494	C₂²	1	1	yes	characteristic
65	#2454	C₂²	1	1	yes	characteristic
66	#2452	C₂²	1	1	yes	characteristic
67	#2450	—	2	1	no	—
68	#2449	—	2	1	no	—
69	#2446	C₂²	1	1	yes	characteristic, complemented
70	#2441	C₂²	1	1	yes	characteristic
71	#2439	C₂²	1	1	yes	characteristic
72	#2437	—	2	1	no	—
73	#2437	—	2	1	no	—
74	#2429	C₂²	1	1	yes	characteristic
75	#2423	C₂²	1	1	yes	characteristic
76	#2421	C₂²	1	1	yes	characteristic
77	#2417	—	2	1	no	—
78	#2396	C₂²	1	1	yes	characteristic
79	C₂×#396	—	2	1	no	—
80	#2365	C₂²	1	1	yes	characteristic, complemented
81	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	#2349	C₂²	1	1	yes	characteristic
83	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
84	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
85	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	#2323	C₂²	1	1	yes	characteristic
88	#2101	C₂²	1	1	yes	characteristic, complemented
89	#2101	C₂²	1	1	yes	characteristic, complemented
90	#2100	C₂²	1	1	yes	characteristic, complemented
91	#2099	C₂²	1	1	yes	characteristic, complemented
92	#2095	C₂²	1	1	yes	characteristic, complemented
93	#2093	C₂²	1	1	yes	characteristic
94	#2092	C₂²	1	1	yes	characteristic
95	#2088	C₂²	1	1	yes	characteristic, complemented
96	#2087	C₂²	1	1	yes	characteristic, complemented
97	#2086	C₂²	1	1	yes	characteristic, complemented
98	#2085	C₂²	1	1	yes	characteristic, complemented
99	#2084	C₂²	1	1	yes	characteristic, complemented
100	#2084	C₂²	1	1	yes	characteristic, complemented
101	#2083	C₂²	1	1	yes	characteristic, complemented
102	#2077	C₂²	1	1	yes	characteristic
103	#2076	C₂²	1	1	yes	characteristic
104	#2076	C₂²	1	1	yes	characteristic
105	#2075	C₂²	1	1	yes	characteristic
106	#2074	C₂²	1	1	yes	characteristic, complemented
107	#2073	C₂²	1	1	yes	characteristic
108	#2072	C₂²	1	1	yes	characteristic, complemented
109	#2067	C₂²	1	1	yes	characteristic
110	#2066	C₂²	1	1	yes	characteristic, complemented
111	#2065	C₂²	1	1	yes	characteristic
112	#2059	C₂²	1	1	yes	characteristic, complemented
113	#2059	C₂²	1	1	yes	characteristic, complemented
114	#2059	C₂²	1	1	yes	characteristic, complemented
115	#2058	C₂²	1	1	yes	characteristic, complemented
116	#2055	C₂²	1	1	yes	characteristic
117	#2055	C₂²	1	1	yes	characteristic
118	#2043	C₂²	1	1	yes	characteristic, complemented
119	#2036	C₂²	1	1	yes	characteristic
120	#2035	C₂²	1	1	yes	characteristic
121	#2035	C₂²	1	1	yes	characteristic
122	#2035	C₂²	1	1	yes	characteristic
123	#2026	C₂²	1	1	yes	characteristic, complemented
124	#2026	C₂²	1	1	yes	characteristic, complemented
125	#2026	C₂²	1	1	yes	characteristic, complemented
126	#2024	C₂²	1	1	yes	characteristic, complemented
127	#2013	C₂²	1	1	yes	characteristic
128	#1993	C₂²	1	1	yes	characteristic, complemented
129	#1991	C₂²	1	1	yes	characteristic, complemented
130	#1985	C₂²	1	1	yes	characteristic, complemented
131	#1984	C₂²	1	1	yes	characteristic, complemented
132	#1968	C₂²	1	1	yes	characteristic
133	#1956	C₂²	1	1	yes	characteristic, complemented
134	#1947	C₂²	1	1	yes	characteristic, complemented
135	#1943	C₂²	1	1	yes	characteristic, complemented
136	#1942	C₂²	1	1	yes	characteristic, complemented
137	#1942	C₂²	1	1	yes	characteristic, complemented
138	#1941	C₂²	1	1	yes	characteristic, complemented
139	#1936	C₂²	1	1	yes	characteristic
140	#1936	C₂²	1	1	yes	characteristic
141	#1935	C₂²	1	1	yes	characteristic, complemented
142	#1935	C₂²	1	1	yes	characteristic, complemented
143	#1935	C₂²	1	1	yes	characteristic, complemented
144	#1934	C₂²	1	1	yes	characteristic
145	#1933	C₂²	1	1	yes	characteristic, complemented
146	#1926	C₂²	1	1	yes	characteristic
147	#1924	C₂²	1	1	yes	characteristic
148	#1924	C₂²	1	1	yes	characteristic
149	#1923	C₂²	1	1	yes	characteristic
150	#1923	C₂²	1	1	yes	characteristic
151	#1920	C₂²	1	1	yes	characteristic, complemented
152	#1919	C₂²	1	1	yes	characteristic, complemented
153	#1919	C₂²	1	1	yes	characteristic, complemented
154	#1917	C₂²	1	1	yes	characteristic, complemented
155	#1916	C₂²	1	1	yes	characteristic, complemented
156	#1916	C₂²	1	1	yes	characteristic, complemented
157	#1916	C₂²	1	1	yes	characteristic, complemented
158	#1880	C₂²	1	1	yes	characteristic
159	#1880	C₂²	1	1	yes	characteristic
160	#1880	C₂²	1	1	yes	characteristic
161	#1877	C₂²	1	1	yes	characteristic
162	#1877	C₂²	1	1	yes	characteristic
163	#1877	C₂²	1	1	yes	characteristic
164	#1877	C₂²	1	1	yes	characteristic
165	#1877	C₂²	1	1	yes	characteristic
166	#1877	C₂²	1	1	yes	characteristic
167	#1877	C₂²	1	1	yes	characteristic
168	#1877	C₂²	1	1	yes	characteristic
169	#1877	C₂²	1	1	yes	characteristic
170	#1873	C₂²	1	1	yes	characteristic
171	#1865	C₂²	1	1	yes	characteristic, complemented
172	#1864	C₂²	1	1	yes	characteristic
173	#1864	C₂²	1	1	yes	characteristic
174	#1864	C₂²	1	1	yes	characteristic
175	#1864	C₂²	1	1	yes	characteristic
176	#1864	C₂²	1	1	yes	characteristic
177	#1864	C₂²	1	1	yes	characteristic
178	#1863	C₂²	1	1	yes	characteristic, complemented
179	#1863	C₂²	1	1	yes	characteristic, complemented
180	#1863	C₂²	1	1	yes	characteristic, complemented
181	#1863	C₂²	1	1	yes	characteristic, complemented
182	#1862	C₂²	1	1	yes	characteristic
183	#1862	C₂²	1	1	yes	characteristic
184	#1862	C₂²	1	1	yes	characteristic
185	#1862	C₂²	1	1	yes	characteristic
186	#1862	C₂²	1	1	yes	characteristic
187	#1854	C₂²	1	1	yes	characteristic
188	#1847	C₂²	1	1	yes	characteristic, complemented
189	#1825	C₂²	1	1	yes	characteristic
190	#1818	C₂²	1	1	yes	characteristic
191	#1805	C₂²	1	1	yes	characteristic, complemented
192	#1804	C₂²	1	1	yes	characteristic
193	#1804	C₂²	1	1	yes	characteristic
194	#1802	C₂²	1	1	yes	characteristic
195	#1786	C₂²	1	1	yes	characteristic
196	#1786	C₂²	1	1	yes	characteristic
197	#1771	C₂²	1	1	yes	characteristic, complemented
198	#1770	C₂²	1	1	yes	characteristic, complemented
199	#1762	C₂²	1	1	yes	characteristic
200	C₄×#102	C₂²	1	1	yes	characteristic
201	C₄×#102	C₂²	1	1	yes	characteristic
202	#1750	C₂²	1	1	yes	characteristic
203	C₂³×D₄	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	#554	—	4	2	no	—
209	#554	—	4	2	no	—
210	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#125	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊Q₈	—	2	1	no	—
215	C₂×C₂²⋊Q₈	—	2	1	no	—
216	C₂×C₂²⋊Q₈	—	2	1	no	—
217	C₂×C₂²⋊Q₈	—	2	1	no	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	#518	—	4	2	no	—
222	#518	—	4	2	no	—
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×D₄	—	2	1	no	—
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
238	C₂×#117	C₂³	1	1	yes	characteristic
239	C₂×#117	C₂³	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	—	2	1	no	—
241	C₂²×C₄⋊C₄	—	2	1	no	—
242	C₂²×C₄⋊C₄	—	2	1	no	—
243	C₂²×C₂²⋊C₄	—	2	1	no	—
244	C₂²×C₂²⋊C₄	—	2	1	no	—
245	C₂²×C₂²⋊C₄	—	2	1	no	—
246	C₂²×C₂²⋊C₄	—	2	1	no	—
247	#485	—	4	2	no	—
248	#479	—	4	2	no	—
249	#475	—	4	2	no	—
250	#461	—	2	4	no	—
251	#450	—	2	4	no	—
252	#450	—	4	2	no	—
253	#440	—	2	4	no	—
254	#440	—	4	2	no	—
255	#440	—	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×#107	C₂³	1	1	yes	characteristic
263	C₂×#107	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×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	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×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
302	C₂×#97	C₂³	1	1	yes	characteristic
303	C₂×#97	C₂³	1	1	yes	characteristic
304	C₂×#97	C₂³	1	1	yes	characteristic
305	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
306	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
308	#401	—	2	1	no	—
309	#401	—	2	1	no	—
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	—	2	1	no	—
331	#398	D₄	1	1	yes	characteristic
332	#398	D₄	1	1	yes	characteristic
333	#397	—	2	1	no	—
334	#397	—	2	1	no	—
335	#397	—	2	1	no	—
336	#397	—	2	1	no	—
337	#396	—	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	—	2	1	no	—
344	#396	—	2	1	no	—
345	#396	—	2	1	no	—
346	#396	—	2	1	no	—
347	#396	—	2	1	no	—
348	#396	D₄	1	1	yes	characteristic
349	#396	D₄	1	1	yes	characteristic
350	#395	—	2	1	no	—
351	#395	—	2	1	no	—
352	#395	D₄	1	1	yes	characteristic
353	#393	—	2	1	no	—
354	#393	—	2	1	no	—
355	#393	D₄	1	1	yes	characteristic
356	#391	—	2	1	no	—
357	#391	C₂³	1	1	yes	characteristic
358	#391	C₂³	1	1	yes	characteristic
359	#391	C₂³	1	1	yes	characteristic
360	#391	C₂³	1	1	yes	characteristic
361	#391	C₂³	1	1	yes	characteristic
362	#391	C₂³	1	1	yes	characteristic
363	#390	C₂³	1	1	yes	characteristic
364	#390	C₂³	1	1	yes	characteristic
365	#390	C₂³	1	1	yes	characteristic
366	#390	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
374	#389	—	2	1	no	—
375	#389	C₂³	1	1	yes	characteristic
376	#389	C₂³	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	#389	C₂³	1	1	yes	characteristic
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#388	—	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	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#386	—	2	1	no	—
413	#386	—	2	1	no	—
414	#386	—	2	1	no	—
415	#386	—	2	1	no	—
416	#385	—	2	1	no	—
417	#385	—	2	1	no	—
418	#385	—	2	1	no	—
419	#385	—	2	1	no	—
420	#385	—	2	1	no	—
421	#385	—	2	1	no	—
422	#385	—	2	1	no	—
423	#385	—	2	1	no	—
424	#385	—	2	1	no	—
425	#385	—	2	1	no	—
426	#384	—	2	1	no	—
427	#384	C₂³	1	1	yes	characteristic
428	#384	C₂³	1	1	yes	characteristic
429	#384	C₂³	1	1	yes	characteristic
430	#383	—	2	1	no	—
431	#382	C₂³	1	1	yes	characteristic
432	#382	C₂³	1	1	yes	characteristic
433	#382	C₂³	1	1	yes	characteristic
434	#380	—	2	1	no	—
435	#380	—	2	1	no	—
436	#380	—	2	1	no	—
437	#380	—	2	1	no	—
438	#380	—	2	1	no	—
439	#380	C₂³	1	1	yes	characteristic
440	#380	C₂³	1	1	yes	characteristic
441	#380	C₂³	1	1	yes	characteristic
442	#380	C₂³	1	1	yes	characteristic
443	#379	—	2	1	no	—
444	#379	—	2	1	no	—
445	C₄×C₄⋊C₄	—	2	1	no	—
446	C₄×C₄⋊C₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
454	C₂×#95	—	2	1	no	—
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	#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	#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	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	C₂⁵	—	2	1	no	—
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
496	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	—	4	1	no	—
504	C₂²×D₄	—	4	1	no	—
505	C₂²×D₄	C₂⁴	1	1	yes	characteristic
506	C₂²×D₄	C₂⁴	1	1	yes	characteristic
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	2	2	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×SD₁₆	—	4	1	no	—
527	C₂×SD₁₆	#41	1	4	yes	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	4	1	no	—
539	C₄⋊Q₈	—	4	1	no	—
540	#125	—	2	2	no	—
541	#125	—	4	1	no	—
542	#125	—	4	1	no	—
543	#125	—	4	1	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	4	4	no	—
546	C₂²⋊Q₈	—	4	4	no	—
547	C₂²⋊Q₈	—	4	1	no	—
548	C₂²⋊Q₈	—	4	4	no	—
549	C₂²⋊Q₈	—	4	1	no	—
550	C₂²⋊Q₈	—	4	1	no	—
551	C₂²⋊Q₈	—	8	2	no	—
552	C₂²⋊Q₈	—	8	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	4	1	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×Q₈	—	4	1	no	—
557	C₄×Q₈	—	4	1	no	—
558	C₄×Q₈	—	4	1	no	—
559	C₄×Q₈	—	4	1	no	—
560	C₄×Q₈	—	4	1	no	—
561	C₄×Q₈	—	4	1	no	—
562	C₄×Q₈	—	4	1	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	4	1	no	—
572	C₄×D₄	—	4	1	no	—
573	C₄×D₄	—	4	1	no	—
574	C₄×D₄	—	4	1	no	—
575	C₄×D₄	—	4	1	no	—
576	C₄×D₄	—	4	1	no	—
577	C₄×D₄	—	4	1	no	—
578	C₄×D₄	—	4	1	no	—
579	C₄×D₄	—	4	4	no	—
580	C₄×D₄	—	4	4	no	—
581	#117	—	2	2	no	—
582	#117	—	4	1	no	—
583	#117	—	4	1	no	—
584	#117	—	4	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	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	—	4	4	no	—
619	C₂×C₄⋊C₄	—	8	2	no	—
620	C₂×C₄⋊C₄	—	8	2	no	—
621	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂⁴	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×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
668	C₂×C₂²⋊C₄	—	4	4	no	—
669	C₂×C₂²⋊C₄	—	8	2	no	—
670	C₂×C₂²⋊C₄	—	8	2	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	C₂⁴	1	1	yes	characteristic
685	C₂×C₄²	C₂⁴	1	1	yes	characteristic
686	C₂×C₄²	C₂⁴	1	1	yes	characteristic
687	C₂×C₄²	C₂⁴	1	1	yes	characteristic
688	C₂×C₄²	C₂⁴	1	1	yes	characteristic
689	C₂×C₄²	C₂⁴	1	1	yes	characteristic
690	#107	—	2	2	no	—
691	#107	—	4	1	no	—
692	#107	—	4	1	no	—
693	#107	—	4	1	no	—
694	#107	—	4	1	no	—
695	#107	—	4	1	no	—
696	#106	—	2	2	no	—
697	#106	—	2	2	no	—
698	#106	—	4	1	no	—
699	#106	—	4	1	no	—
700	#106	—	4	1	no	—
701	#106	—	4	1	no	—
702	C₄⋊C₈	—	2	2	no	—
703	C₄⋊C₈	—	4	1	no	—
704	C₄⋊C₈	—	4	1	no	—
705	C₄⋊C₈	—	4	1	no	—
706	#103	—	2	2	no	—
707	#103	—	2	2	no	—
708	#103	—	2	2	no	—
709	#103	—	2	2	no	—
710	#103	—	2	2	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	#102	—	2	2	no	—
719	#102	—	2	2	no	—
720	#102	—	2	2	no	—
721	#102	—	2	2	no	—
722	#102	—	2	2	no	—
723	#102	—	2	2	no	—
724	#102	—	2	2	no	—
725	#102	—	2	2	no	—
726	#102	—	2	2	no	—
727	#102	—	4	1	no	—
728	#102	—	4	1	no	—
729	#102	—	4	1	no	—
730	C₂²⋊C₈	—	2	2	no	—
731	C₂²⋊C₈	—	4	1	no	—
732	C₂²⋊C₈	—	4	1	no	—
733	C₂²⋊C₈	—	4	1	no	—
734	#97	—	2	2	no	—
735	#97	—	4	1	no	—
736	#97	—	4	1	no	—
737	C₄×C₈	—	4	1	no	—
738	C₄×C₈	—	4	1	no	—
739	C₄×C₈	—	4	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	—	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	C₂×D₄	1	1	yes	characteristic
779	#95	C₂×D₄	1	1	yes	characteristic
780	#95	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	—	2	1	no	—
789	C₂⁴	—	2	4	no	—
790	C₂⁴	—	2	1	no	—
791	C₂⁴	—	4	2	no	—
792	C₂⁴	—	4	2	no	—
793	C₂⁴	—	8	1	no	—
794	C₂⁴	—	8	1	no	—
795	C₂⁴	—	8	1	no	—
796	C₂⁴	—	8	1	no	—
797	C₂⁴	C₂²×D₄	1	1	yes	characteristic
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	—	4	1	no	—
810	C₂×Q₈	—	4	1	no	—
811	C₂×Q₈	—	4	1	no	—
812	C₂×Q₈	—	4	2	no	—
813	C₂×Q₈	—	8	1	no	—
814	C₂×Q₈	—	8	1	no	—
815	C₂×Q₈	C₂×#41	1	2	yes	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	1	no	—
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	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	4	no	—
828	C₂×D₄	—	4	4	no	—
829	C₂×D₄	—	4	4	no	—
830	C₂×D₄	—	4	4	no	—
831	C₂×D₄	C₂×#41	1	2	yes	—
832	C₂×D₄	H(5,𝔽₂)	1	2	yes	—
833	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
834	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	4	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	—	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	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	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	—	8	1	no	—
872	C₂²×C₄	—	8	1	no	—
873	C₂²×C₄	—	8	1	no	—
874	C₂²×C₄	—	8	1	no	—
875	C₂²×C₄	—	8	1	no	—
876	C₂²×C₄	—	8	1	no	—
877	C₂²×C₄	—	8	1	no	—
878	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
888	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂⁵	1	1	yes	characteristic
893	SD₁₆	—	2	8	no	—
894	SD₁₆	—	4	4	no	—
895	SD₁₆	—	4	4	no	—
896	SD₁₆	—	8	2	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	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	C₂×#41	1	2	yes	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	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	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	4	1	no	—
947	C₄⋊C₄	—	4	1	no	—
948	C₄⋊C₄	—	4	1	no	—
949	C₄⋊C₄	—	4	1	no	—
950	C₄⋊C₄	—	4	1	no	—
951	C₄⋊C₄	—	4	1	no	—
952	C₄⋊C₄	—	4	1	no	—
953	C₄⋊C₄	—	4	1	no	—
954	C₄⋊C₄	—	4	1	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	—	8	1	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	—	8	1	no	—
980	C₄⋊C₄	—	8	1	no	—
981	C₄⋊C₄	—	8	1	no	—
982	C₄⋊C₄	—	8	1	no	—
983	C₄⋊C₄	—	8	1	no	—
984	C₄⋊C₄	—	8	1	no	—
985	C₄⋊C₄	—	8	1	no	—
986	C₄⋊C₄	—	8	1	no	—
987	C₄⋊C₄	—	8	1	no	—
988	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
989	C₂²⋊C₄	—	2	4	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	4	1	no	—
992	C₂²⋊C₄	—	4	1	no	—
993	C₂²⋊C₄	—	4	1	no	—
994	C₂²⋊C₄	—	4	1	no	—
995	C₂²⋊C₄	—	4	1	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	—	4	2	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	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	C₂²⋊C₄	—	8	1	no	—
1013	C₂²⋊C₄	—	8	1	no	—
1014	C₂²⋊C₄	—	8	1	no	—
1015	C₂²⋊C₄	—	8	1	no	—
1016	C₂²⋊C₄	—	8	1	no	—
1017	C₂²⋊C₄	—	8	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	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	4	2	no	—
1031	C₄²	—	4	2	no	—
1032	C₄²	—	8	1	no	—
1033	C₄²	—	8	1	no	—
1034	C₄²	—	8	1	no	—
1035	C₄²	—	8	1	no	—
1036	C₄²	—	8	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	2	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	4	8	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	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	—	8	4	no	—
1060	C₂³	—	8	4	no	—
1061	C₂³	—	16	2	no	—
1062	C₂³	—	16	2	no	—
1063	C₂³	—	16	2	no	—
1064	C₂³	—	16	2	no	—
1065	C₂³	C₂³×D₄	1	1	yes	characteristic
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	4	1	no	—
1069	Q₈	—	4	1	no	—
1070	Q₈	—	4	1	no	—
1071	Q₈	—	4	1	no	—
1072	Q₈	—	4	1	no	—
1073	Q₈	—	4	1	no	—
1074	Q₈	—	8	2	no	—
1075	Q₈	—	16	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	1	no	—
1083	D₄	—	4	1	no	—
1084	D₄	#539	1	4	yes	—
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	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	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	2	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	—	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	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	8	4	no	—
1170	C₂×C₄	—	8	4	no	—
1171	C₂×C₄	—	8	4	no	—
1172	C₂×C₄	—	16	2	no	—
1173	C₂×C₄	—	16	2	no	—
1174	C₂×C₄	—	16	2	no	—
1175	C₂×C₄	—	16	2	no	—
1176	C₂×C₄	—	16	2	no	—
1177	C₂×C₄	#577	1	2	yes	—
1178	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1179	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1180	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1181	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1182	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1183	C₂×C₄	#585	1	1	yes	characteristic
1184	C₈	—	2	2	no	—
1185	C₈	—	4	1	no	—
1186	C₈	—	4	1	no	—
1187	C₈	—	4	1	no	—
1188	C₈	—	4	1	no	—
1189	C₈	—	4	1	no	—
1190	C₈	—	4	1	no	—
1191	C₈	—	4	1	no	—
1192	C₂²	—	2	4	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	2	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	2	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	2	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	2	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	8	1	no	—
1210	C₂²	—	8	1	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	—	8	1	no	—
1213	C₂²	—	16	8	no	—
1214	C₂²	D₄×#41	1	1	yes	characteristic
1215	C₂²	#3484	1	1	yes	characteristic
1216	C₂²	#3486	1	1	yes	characteristic
1217	C₂²	C₂×#577	1	1	yes	characteristic
1218	C₂²	#3584	1	1	yes	characteristic
1219	C₂²	#3585	1	1	yes	characteristic
1220	C₂²	#3586	1	1	yes	characteristic
1221	C₄	—	2	2	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	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	2	no	—
1236	C₄	—	8	1	no	—
1237	C₄	—	8	1	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	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	C₂×#539	1	1	yes	characteristic
1249	C₄	#3520	1	1	yes	characteristic
1250	C₄	#3535	1	1	yes	characteristic
1251	C₄	#3541	1	1	yes	characteristic
1252	C₂	—	4	4	no	—
1253	C₂	—	8	1	no	—
1254	C₂	—	8	2	no	—
1255	C₂	#37721	1	1	yes	characteristic
1256	C₂	#61521	1	1	yes	characteristic
1257	C₂	#61550	1	1	yes	characteristic
1258	C₂	#61628	1	1	yes	characteristic
1259	C₂	#61680	1	1	yes	characteristic
1260	C₂	#61864	1	1	yes	characteristic
1261	C₂	#61873	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
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. #42856	C₂	semidirect
4. #32654	C₂	semidirect
5. #32556	C₂	semidirect
6. #32366	C₂	semidirect
7. #31639	C₂	semidirect
8. #31437	C₂	semidirect
9. #31377	C₂	semidirect
10. #31117	C₂	semidirect
11. #31107	C₂	semidirect
12. #30371	C₂	semidirect
13. #30182	C₂	semidirect
14. #29100	C₂	semidirect
15. #28958	C₂	semidirect
16. #27558	C₂	semidirect
18. #27301	C₂	semidirect
19. #27296	C₂	semidirect
20. #26902	C₂	semidirect
21. #26379	C₂	semidirect
22. #26182	C₂	semidirect
26. #24343	C₂	semidirect
27. #24337	C₂	semidirect
28. #23002	C₂	semidirect
29. #22678	C₂	semidirect
30. #22324	C₂	semidirect
35. C₂×#479	C₂²	semidirect
36. C₂×#475	C₂²	semidirect
56. #2581	C₂²	semidirect
57. #2581	C₂²	semidirect
61. #2514	C₂²	semidirect
62. #2509	C₂²	semidirect
63. #2507	C₂²	semidirect
69. #2446	C₂²	semidirect
80. #2365	C₂²	semidirect
81. Q₈×C₄⋊C₄	C₂²	semidirect
88. #2101	C₂²	semidirect
89. #2101	C₂²	semidirect
90. #2100	C₂²	semidirect
91. #2099	C₂²	semidirect
92. #2095	C₂²	semidirect
95. #2088	C₂²	semidirect
96. #2087	C₂²	semidirect
97. #2086	C₂²	semidirect
98. #2085	C₂²	semidirect
99. #2084	C₂²	semidirect
100. #2084	C₂²	semidirect
101. #2083	C₂²	semidirect
106. #2074	C₂²	semidirect
108. #2072	C₂²	semidirect
110. #2066	C₂²	semidirect
112. #2059	C₂²	semidirect
113. #2059	C₂²	semidirect
114. #2059	C₂²	semidirect
115. #2058	C₂²	semidirect
118. #2043	C₂²	semidirect
123. #2026	C₂²	semidirect
124. #2026	C₂²	semidirect
125. #2026	C₂²	semidirect
126. #2024	C₂²	semidirect
128. #1993	C₂²	semidirect
129. #1991	C₂²	semidirect
130. #1985	C₂²	semidirect
131. #1984	C₂²	semidirect
133. #1956	C₂²	semidirect
134. #1947	C₂²	semidirect
135. #1943	C₂²	semidirect
136. #1942	C₂²	semidirect
137. #1942	C₂²	semidirect
138. #1941	C₂²	semidirect
141. #1935	C₂²	semidirect
142. #1935	C₂²	semidirect
143. #1935	C₂²	semidirect
145. #1933	C₂²	semidirect
151. #1920	C₂²	semidirect
152. #1919	C₂²	semidirect
153. #1919	C₂²	semidirect
154. #1917	C₂²	semidirect
155. #1916	C₂²	semidirect
156. #1916	C₂²	semidirect
157. #1916	C₂²	semidirect
171. #1865	C₂²	semidirect
178. #1863	C₂²	semidirect
179. #1863	C₂²	semidirect
180. #1863	C₂²	semidirect
181. #1863	C₂²	semidirect
188. #1847	C₂²	semidirect
191. #1805	C₂²	semidirect
197. #1771	C₂²	semidirect
198. #1770	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#42856	2
#35776	2
#33018	2
#32654	2
#32556	2
#32366	2
#31639	2
#31437	2
#31377	2
#31117	2
#31107	2
#30371	2
#30182	2
#29100	2
#28958	2
#27558	2
#27525	2
#27301	2
#27296	2
#26902	2
#26379	2
#26182	2
#25156	2
#24921	2
#24917	2
#24343	2
#24337	2
#23002	2
#22678	2
#22324	2
#21459	2