Subgroups — #6399158

Order 512.

1732 conjugacy classes of subgroups.

The subgroup lattice has 1211 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3344	C₂	1	1	yes	maximal, characteristic
2	#34462	C₂	1	1	yes	maximal, characteristic
3	#34299	C₂	1	1	yes	maximal, characteristic
4	#23166	C₂	1	1	yes	maximal, characteristic, complemented
5	#23144	C₂	1	1	yes	maximal, characteristic, complemented
6	#23136	C₂	1	1	yes	maximal, characteristic, complemented
7	#23070	C₂	1	1	yes	maximal, characteristic, complemented
8	#22970	C₂	1	1	yes	maximal, characteristic, complemented
9	#22947	C₂	1	1	yes	maximal, characteristic, complemented
10	#22940	C₂	1	1	yes	maximal, characteristic, complemented
11	#22927	C₂	1	1	yes	maximal, characteristic, complemented
12	#22927	C₂	1	1	yes	maximal, characteristic, complemented
13	#22779	C₂	1	1	yes	maximal, characteristic, complemented
14	#22712	C₂	1	1	yes	maximal, characteristic
15	#22623	C₂	1	1	yes	maximal, characteristic, complemented
16	#22615	C₂	1	1	yes	maximal, characteristic, complemented
17	#22502	C₂	1	1	yes	maximal, characteristic
18	#22499	C₂	1	1	yes	maximal, characteristic
19	#22255	C₂	1	1	yes	maximal, characteristic, complemented
20	#22197	C₂	1	1	yes	maximal, characteristic, complemented
21	#22188	C₂	1	1	yes	maximal, characteristic, complemented
22	#22129	C₂	1	1	yes	maximal, characteristic, complemented
23	#22089	C₂	1	1	yes	maximal, characteristic, complemented
24	#22083	C₂	1	1	yes	maximal, characteristic, complemented
25	#21621	C₂	1	1	yes	maximal, characteristic, complemented
26	#21585	C₂	1	1	yes	maximal, characteristic, complemented
27	#21579	C₂	1	1	yes	maximal, characteristic, complemented
28	#21127	C₂	1	1	yes	maximal, characteristic, complemented
29	#21038	C₂	1	1	yes	maximal, characteristic, complemented
30	#21033	C₂	1	1	yes	maximal, characteristic, complemented
31	#20564	C₂	1	1	yes	maximal, characteristic
32	C₂×#554	C₂²	1	1	yes	characteristic
33	C₂×#552	C₂²	1	1	yes	characteristic
34	#3344	C₄	1	16	yes	complemented
35	C₂×#501	C₂²	1	1	yes	characteristic
36	C₂×#484	C₂²	1	1	yes	characteristic
37	C₂×#485	C₂²	1	1	yes	characteristic
38	C₂×#483	C₂²	1	1	yes	characteristic
39	C₂×#483	C₂²	1	1	yes	characteristic
40	C₂×#479	C₂²	1	1	yes	characteristic
41	C₂×#475	C₂²	1	1	yes	characteristic
42	C₂×#470	C₂²	1	1	yes	characteristic
43	C₂×#467	C₂²	1	1	yes	characteristic
44	C₂×#441	C₂²	1	1	yes	characteristic
45	C₂×#436	C₂²	1	1	yes	characteristic
46	C₂×#435	C₂²	1	1	yes	characteristic
47	C₂×#428	C₂²	1	1	yes	characteristic
48	C₂²×#106	C₂²	1	1	yes	characteristic
49	#2383	—	2	1	no	—
50	#2376	—	2	1	no	—
51	#2371	—	2	1	no	—
52	#2370	—	2	1	no	—
53	#2370	C₂²	1	1	yes	characteristic
54	#2368	—	2	1	no	—
55	#2365	C₂²	1	1	yes	characteristic
56	#2362	—	2	1	no	—
57	#2362	C₂²	1	1	yes	characteristic
58	#2362	C₂²	1	1	yes	characteristic
59	#2362	C₂²	1	1	yes	characteristic
60	#2360	C₂²	1	1	yes	characteristic
61	#2356	C₂²	1	1	yes	characteristic
62	#2354	C₂²	1	1	yes	characteristic
63	#2353	—	2	1	no	—
64	#2352	C₂²	1	1	yes	characteristic
65	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	#2347	—	2	1	no	—
67	#2347	C₂²	1	1	yes	characteristic
68	#2345	C₂²	1	1	yes	characteristic
69	#2345	C₂²	1	1	yes	characteristic
70	#2344	C₂²	1	1	yes	characteristic
71	#2336	—	2	1	no	—
72	#2336	—	2	1	no	—
73	#2335	—	2	1	no	—
74	#2334	—	2	1	no	—
75	#2332	—	2	1	no	—
76	#2331	C₂²	1	1	yes	characteristic
77	#2330	C₂²	1	1	yes	characteristic
78	#2323	C₂²	1	1	yes	characteristic
79	#2323	C₂²	1	1	yes	characteristic
80	#2320	C₂²	1	1	yes	characteristic
81	#2316	C₂²	1	1	yes	characteristic
82	#2314	—	2	1	no	—
83	C₄×C₂²⋊Q₈	—	2	1	no	—
84	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
86	#2296	C₂²	1	1	yes	characteristic
87	#2290	—	2	1	no	—
88	#2290	C₂²	1	1	yes	characteristic
89	#2276	C₂²	1	1	yes	characteristic
90	#2274	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	#1991	C₂²	1	1	yes	characteristic
93	#1990	C₂²	1	1	yes	characteristic
94	#1989	C₂²	1	1	yes	characteristic
95	#1987	C₂²	1	1	yes	characteristic
96	#1949	C₂²	1	1	yes	characteristic
97	#1947	C₂²	1	1	yes	characteristic
98	#1944	C₂²	1	1	yes	characteristic
99	#1944	C₂²	1	1	yes	characteristic
100	#1944	C₂²	1	1	yes	characteristic
101	#1943	C₂²	1	1	yes	characteristic
102	#1941	C₂²	1	1	yes	characteristic
103	#1941	C₂²	1	1	yes	characteristic
104	#1935	C₂²	1	1	yes	characteristic
105	#1935	C₂²	1	1	yes	characteristic
106	#1935	C₂²	1	1	yes	characteristic
107	#1935	C₂²	1	1	yes	characteristic
108	#1933	C₂²	1	1	yes	characteristic
109	#1933	C₂²	1	1	yes	characteristic
110	#1928	C₂²	1	1	yes	characteristic
111	#1928	C₂²	1	1	yes	characteristic
112	#1928	C₂²	1	1	yes	characteristic
113	#1927	C₂²	1	1	yes	characteristic
114	#1927	C₂²	1	1	yes	characteristic
115	#1927	C₂²	1	1	yes	characteristic
116	#1921	C₂²	1	1	yes	characteristic
117	#1921	C₂²	1	1	yes	characteristic
118	#1921	C₂²	1	1	yes	characteristic
119	#1921	C₂²	1	1	yes	characteristic
120	#1920	C₂²	1	1	yes	characteristic
121	#1920	C₂²	1	1	yes	characteristic
122	#1920	C₂²	1	1	yes	characteristic
123	#1920	C₂²	1	1	yes	characteristic
124	#1920	C₂²	1	1	yes	characteristic
125	#1920	C₂²	1	1	yes	characteristic
126	#1920	C₂²	1	1	yes	characteristic
127	#1919	C₂²	1	1	yes	characteristic
128	#1919	C₂²	1	1	yes	characteristic
129	#1919	C₂²	1	1	yes	characteristic
130	#1919	C₂²	1	1	yes	characteristic
131	#1919	C₂²	1	1	yes	characteristic
132	#1919	C₂²	1	1	yes	characteristic
133	#1919	C₂²	1	1	yes	characteristic
134	#1919	C₂²	1	1	yes	characteristic
135	#1919	C₂²	1	1	yes	characteristic
136	#1918	C₂²	1	1	yes	characteristic
137	#1918	C₂²	1	1	yes	characteristic
138	#1918	C₂²	1	1	yes	characteristic
139	#1918	C₂²	1	1	yes	characteristic
140	#1894	C₂²	1	1	yes	characteristic
141	#1894	C₂²	1	1	yes	characteristic
142	#1894	C₂²	1	1	yes	characteristic
143	#1894	C₂²	1	1	yes	characteristic
144	#1878	C₂²	1	1	yes	characteristic
145	#1878	C₂²	1	1	yes	characteristic
146	#1878	C₂²	1	1	yes	characteristic
147	#1878	C₂²	1	1	yes	characteristic
148	#1873	C₂²	1	1	yes	characteristic
149	#1873	C₂²	1	1	yes	characteristic
150	#1873	C₂²	1	1	yes	characteristic
151	#1872	C₂²	1	1	yes	characteristic
152	#1865	C₂²	1	1	yes	characteristic
153	#1863	C₂²	1	1	yes	characteristic
154	#1863	C₂²	1	1	yes	characteristic
155	#1863	C₂²	1	1	yes	characteristic
156	#1863	C₂²	1	1	yes	characteristic
157	#1863	C₂²	1	1	yes	characteristic
158	#1854	C₂²	1	1	yes	characteristic
159	#1854	C₂²	1	1	yes	characteristic
160	#1854	C₂²	1	1	yes	characteristic
161	#1852	C₂²	1	1	yes	characteristic
162	#1836	C₂²	1	1	yes	characteristic
163	#1825	C₂²	1	1	yes	characteristic
164	#1824	C₂²	1	1	yes	characteristic
165	#1823	C₂²	1	1	yes	characteristic
166	#1823	C₂²	1	1	yes	characteristic
167	#1809	C₂²	1	1	yes	characteristic
168	#1808	C₂²	1	1	yes	characteristic
169	#1805	C₂²	1	1	yes	characteristic
170	#1803	C₂²	1	1	yes	characteristic
171	#1776	C₂²	1	1	yes	characteristic
172	#1776	C₂²	1	1	yes	characteristic
173	#1776	C₂²	1	1	yes	characteristic
174	#1776	C₂²	1	1	yes	characteristic
175	#1776	C₂²	1	1	yes	characteristic
176	C₄×#107	C₂²	1	1	yes	characteristic
177	C₄×#107	C₂²	1	1	yes	characteristic
178	#1771	C₂²	1	1	yes	characteristic
179	#1770	C₂²	1	1	yes	characteristic
180	#1768	C₂²	1	1	yes	characteristic
181	#1763	C₂²	1	1	yes	characteristic
182	#1763	C₂²	1	1	yes	characteristic
183	#1763	C₂²	1	1	yes	characteristic
184	#1763	C₂²	1	1	yes	characteristic
185	C₄×#103	C₂²	1	1	yes	characteristic
186	C₄×#103	C₂²	1	1	yes	characteristic
187	C₄×#103	C₂²	1	1	yes	characteristic
188	C₄×#103	C₂²	1	1	yes	characteristic
189	#1753	C₂²	1	1	yes	characteristic
190	#1753	C₂²	1	1	yes	characteristic
191	#1753	C₂²	1	1	yes	characteristic
192	#1752	C₂²	1	1	yes	characteristic
193	#1750	C₂²	1	1	yes	characteristic
194	#1749	C₂²	1	1	yes	characteristic
195	#1746	C₂²	1	1	yes	characteristic
196	#1736	C₂²	1	1	yes	characteristic
197	#1736	C₂²	1	1	yes	characteristic
198	#1736	C₂²	1	1	yes	characteristic
199	#1736	C₂²	1	1	yes	characteristic
200	#1736	C₂²	1	1	yes	characteristic
201	#1735	C₂²	1	1	yes	characteristic
202	#1729	C₂²	1	1	yes	characteristic
203	#1728	C₂²	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂²×M₁₆	C₂³	1	1	yes	characteristic
207	C₂²×M₁₆	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	#554	—	2	4	no	—
210	#554	C₂×C₄	1	8	yes	—
211	#552	—	2	4	no	—
212	#552	C₂×C₄	1	8	yes	—
213	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×#126	—	2	1	no	—
215	C₂×#125	—	2	1	no	—
216	C₂×#125	—	2	1	no	—
217	C₂×#125	C₂³	1	1	yes	characteristic
218	C₂×#123	—	2	1	no	—
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	—	2	1	no	—
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₂×#117	—	2	1	no	—
235	C₂×#117	—	2	1	no	—
236	C₂×#117	C₂³	1	1	yes	characteristic
237	C₂×#117	C₂³	1	1	yes	characteristic
238	C₂×#117	C₂³	1	1	yes	characteristic
239	C₂×#117	C₂³	1	1	yes	characteristic
240	C₂×#117	C₂³	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂²×C₄²	—	2	1	no	—
246	C₂²×C₄²	C₂³	1	1	yes	characteristic
247	#501	C₂×C₄	1	8	yes	complemented
248	#485	C₂×C₄	1	8	yes	—
249	#484	C₂×C₄	1	8	yes	complemented
250	#483	C₂×C₄	1	8	yes	—
251	#483	C₂×C₄	1	8	yes	complemented
252	#479	C₂×C₄	1	8	yes	complemented
253	#475	C₂×C₄	1	8	yes	complemented
254	#470	C₂×C₄	1	8	yes	—
255	#467	C₂×C₄	1	8	yes	complemented
256	#441	C₂×C₄	1	8	yes	complemented
257	#436	—	2	4	no	—
258	#435	C₂×C₄	1	8	yes	—
259	#428	C₂×C₄	1	8	yes	—
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×#107	C₂³	1	1	yes	characteristic
265	C₂×#107	C₂³	1	1	yes	characteristic
266	C₂×#107	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂×C₄	1	8	yes	complemented
268	C₂×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×#106	C₂³	1	1	yes	characteristic
271	C₂×#106	C₂³	1	1	yes	characteristic
272	C₂×#106	C₂³	1	1	yes	characteristic
273	C₂×#106	C₂³	1	1	yes	characteristic
274	C₂×#106	C₂³	1	1	yes	characteristic
275	C₂×#106	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₈	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×#97	C₂³	1	1	yes	characteristic
298	C₂×#97	C₂³	1	1	yes	characteristic
299	C₂×#97	C₂³	1	1	yes	characteristic
300	C₂×#97	C₂³	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
303	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
304	#391	—	2	1	no	—
305	#391	—	2	1	no	—
306	#391	—	2	1	no	—
307	#391	C₂³	1	1	yes	characteristic
308	#391	C₂³	1	1	yes	characteristic
309	#391	C₂³	1	1	yes	characteristic
310	#391	C₂³	1	1	yes	characteristic
311	#390	—	2	1	no	—
312	#389	—	2	1	no	—
313	#389	—	2	1	no	—
314	#389	—	2	1	no	—
315	#389	—	2	1	no	—
316	#389	—	2	1	no	—
317	#389	—	2	1	no	—
318	#389	—	2	1	no	—
319	#389	—	2	1	no	—
320	#389	—	2	1	no	—
321	#389	—	2	1	no	—
322	#389	C₂³	1	1	yes	characteristic
323	#389	C₂³	1	1	yes	characteristic
324	#389	C₂³	1	1	yes	characteristic
325	#389	C₂³	1	1	yes	characteristic
326	#389	C₂³	1	1	yes	characteristic
327	#389	C₂³	1	1	yes	characteristic
328	#389	C₂³	1	1	yes	characteristic
329	#389	C₂³	1	1	yes	characteristic
330	#389	C₂³	1	1	yes	characteristic
331	#389	C₂³	1	1	yes	characteristic
332	#389	C₂³	1	1	yes	characteristic
333	#389	C₂³	1	1	yes	characteristic
334	#388	—	2	1	no	—
335	#388	—	2	1	no	—
336	#388	—	2	1	no	—
337	#388	—	2	1	no	—
338	#388	—	2	1	no	—
339	#388	—	2	1	no	—
340	#388	—	2	1	no	—
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#388	—	2	1	no	—
348	#388	—	2	1	no	—
349	#388	D₄	1	1	yes	characteristic
350	#388	D₄	1	1	yes	characteristic
351	#387	—	2	1	no	—
352	#387	—	2	1	no	—
353	#387	—	2	1	no	—
354	#387	—	2	1	no	—
355	#387	—	2	1	no	—
356	#387	—	2	1	no	—
357	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#387	—	2	1	no	—
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#387	—	2	1	no	—
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#387	—	2	1	no	—
366	#387	—	2	1	no	—
367	#387	—	2	1	no	—
368	#387	—	2	1	no	—
369	#387	—	2	1	no	—
370	#387	—	2	1	no	—
371	#387	—	2	1	no	—
372	#387	—	2	1	no	—
373	#387	—	2	1	no	—
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	D₄	1	1	yes	characteristic
379	#387	D₄	1	1	yes	characteristic
380	#386	—	2	1	no	—
381	#386	D₄	1	1	yes	characteristic
382	#386	D₄	1	1	yes	characteristic
383	#385	—	2	1	no	—
384	#385	—	2	1	no	—
385	#385	—	2	1	no	—
386	#385	—	2	1	no	—
387	#385	—	2	1	no	—
388	#385	D₄	1	1	yes	characteristic
389	#385	D₄	1	1	yes	characteristic
390	#384	—	2	1	no	—
391	#384	C₂³	1	1	yes	characteristic
392	#383	—	2	1	no	—
393	#383	—	2	1	no	—
394	#383	—	2	1	no	—
395	#382	—	2	1	no	—
396	#382	C₂³	1	1	yes	characteristic
397	#381	—	2	1	no	—
398	#380	—	2	1	no	—
399	#380	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	—	2	1	no	—
402	#380	C₂³	1	1	yes	characteristic
403	#380	C₂³	1	1	yes	characteristic
404	#380	C₂³	1	1	yes	characteristic
405	#380	C₂³	1	1	yes	characteristic
406	C₄×C₄⋊C₄	—	2	1	no	—
407	C₄×C₄⋊C₄	—	2	1	no	—
408	C₄×C₄⋊C₄	—	2	1	no	—
409	C₄×C₄⋊C₄	—	2	1	no	—
410	C₄×C₄⋊C₄	—	2	1	no	—
411	C₄×C₄⋊C₄	—	2	1	no	—
412	C₄×C₄⋊C₄	—	2	1	no	—
413	C₄×C₄⋊C₄	—	2	1	no	—
414	C₄×C₄⋊C₄	—	2	1	no	—
415	C₄×C₄⋊C₄	—	2	1	no	—
416	C₄×C₄⋊C₄	—	2	1	no	—
417	C₄×C₄⋊C₄	—	2	1	no	—
418	C₄×C₄⋊C₄	—	2	1	no	—
419	C₄×C₄⋊C₄	—	2	1	no	—
420	C₄×C₄⋊C₄	—	2	1	no	—
421	C₄×C₄⋊C₄	—	2	1	no	—
422	C₄×C₄⋊C₄	—	2	1	no	—
423	C₄×C₄⋊C₄	—	2	1	no	—
424	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
440	C₄×C₂²⋊C₄	—	2	1	no	—
441	C₄×C₂²⋊C₄	—	2	1	no	—
442	C₄×C₂²⋊C₄	—	2	1	no	—
443	C₄×C₂²⋊C₄	—	2	1	no	—
444	C₄×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
449	#376	—	2	1	no	—
450	#376	—	2	1	no	—
451	#376	C₂³	1	1	yes	characteristic
452	C₂×#95	—	2	1	no	—
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	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#340	C₂³	1	1	yes	characteristic
486	#340	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	#336	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	#336	C₂³	1	1	yes	characteristic
497	C₂²×Q₈	—	2	1	no	—
498	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
499	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
500	C₂²×D₄	C₂×D₄	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	—	2	1	no	—
505	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
506	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
507	C₂³×C₄	C₂⁴	1	1	yes	characteristic
508	C₂³×C₄	C₂⁴	1	1	yes	characteristic
509	C₂×Q₁₆	—	4	1	no	—
510	C₂×Q₁₆	—	4	1	no	—
511	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
512	C₂×M₁₆	—	2	2	no	—
513	C₂×M₁₆	—	2	2	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	C₂×M₁₆	—	4	1	no	—
520	C₂×M₁₆	C₂²×C₄	1	4	yes	—
521	C₂²×C₈	—	4	1	no	—
522	C₂²×C₈	—	4	1	no	—
523	C₂²×C₈	C₂²×C₄	1	4	yes	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
534	#126	—	2	8	no	—
535	#125	—	2	8	no	—
536	#125	—	2	8	no	—
537	#125	—	2	2	no	—
538	#125	C₂²×C₄	1	4	yes	—
539	#123	—	2	8	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	8	no	—
545	C₂²⋊Q₈	—	2	8	no	—
546	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
547	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
548	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
549	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	4	1	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	—	8	2	no	—
561	C₄×Q₈	C₂²×C₄	1	4	yes	—
562	C₄×Q₈	C₂²×C₄	1	4	yes	—
563	C₄×D₄	—	2	8	no	—
564	C₄×D₄	C₂²×C₄	1	4	yes	—
565	C₄×D₄	#41	1	4	yes	—
566	#117	—	2	2	no	—
567	#117	—	2	8	no	—
568	#117	—	2	2	no	—
569	#117	—	4	1	no	—
570	#117	—	4	1	no	—
571	#117	—	4	1	no	—
572	#117	—	4	1	no	—
573	#117	—	4	1	no	—
574	#117	—	4	1	no	—
575	#117	—	4	1	no	—
576	#117	—	8	2	no	—
577	#117	C₂²×C₄	1	4	yes	—
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	—	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	2	no	—
591	C₂×C₄⋊C₄	—	2	2	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	2	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	—	4	1	no	—
614	C₂×C₄⋊C₄	C₂²×C₄	1	4	yes	—
615	C₂×C₄⋊C₄	C₂²×C₄	1	4	yes	—
616	C₂×C₄⋊C₄	C₂²×C₄	1	4	yes	—
617	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂⁴	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×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	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
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	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×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	2	1	no	—
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	4	1	no	—
681	C₂×C₄²	—	4	1	no	—
682	C₂×C₄²	—	8	2	no	—
683	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
684	C₂×C₄²	C₂×D₄	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	C₂²×C₄	1	4	yes	—
695	#107	C₂²×C₄	1	4	yes	—
696	#107	C₂²×C₄	1	4	yes	—
697	#106	—	4	1	no	—
698	#106	—	4	1	no	—
699	#106	C₂²×C₄	1	4	yes	—
700	#106	C₂²×C₄	1	4	yes	—
701	#106	C₂²×C₄	1	4	yes	—
702	#106	C₂²×C₄	1	4	yes	—
703	#106	C₂²×C₄	1	4	yes	—
704	#106	C₂²×C₄	1	4	yes	—
705	C₄⋊C₈	—	2	2	no	—
706	C₄⋊C₈	C₂²×C₄	1	4	yes	—
707	#103	—	2	2	no	—
708	#103	—	4	1	no	—
709	#103	—	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	C₂²×C₄	1	4	yes	—
716	#103	C₂²×C₄	1	4	yes	—
717	#103	C₂²×C₄	1	4	yes	—
718	#103	C₂²×C₄	1	4	yes	—
719	#103	C₂²×C₄	1	4	yes	—
720	#103	C₂²×C₄	1	4	yes	—
721	C₂²⋊C₈	—	2	2	no	—
722	C₂²⋊C₈	—	2	2	no	—
723	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
724	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
725	#97	—	4	1	no	—
726	#97	—	4	1	no	—
727	#97	—	4	1	no	—
728	#97	—	4	1	no	—
729	#97	C₂²×C₄	1	4	yes	—
730	C₄×C₈	—	2	2	no	—
731	C₄×C₈	—	4	1	no	—
732	C₄×C₈	—	4	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	—	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	C₂×D₄	1	1	yes	characteristic
774	#95	C₂×D₄	1	1	yes	characteristic
775	#95	C₂×D₄	1	1	yes	characteristic
776	#95	C₂×D₄	1	1	yes	characteristic
777	#95	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	C₂²×D₄	1	1	yes	characteristic
784	C₂⁴	C₂²×D₄	1	1	yes	characteristic
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	8	1	no	—
797	C₂×Q₈	—	8	1	no	—
798	C₂×Q₈	C₂³×C₄	1	2	yes	—
799	C₂×Q₈	C₂³×C₄	1	2	yes	—
800	C₂×D₄	—	4	1	no	—
801	C₂×D₄	—	4	1	no	—
802	C₂×D₄	C₄×D₄	1	4	yes	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	4	no	—
821	C₂²×C₄	—	2	4	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	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	—	4	1	no	—
831	C₂²×C₄	—	4	1	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	1	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	8	1	no	—
839	C₂²×C₄	—	8	1	no	—
840	C₂²×C₄	—	8	1	no	—
841	C₂²×C₄	—	8	1	no	—
842	C₂²×C₄	—	8	1	no	—
843	C₂²×C₄	—	8	1	no	—
844	C₂²×C₄	—	8	1	no	—
845	C₂²×C₄	C₂³×C₄	1	2	yes	—
846	C₂²×C₄	C₂³×C₄	1	2	yes	—
847	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
848	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂×#41	1	2	yes	—
860	C₂²×C₄	C₂×#41	1	2	yes	—
861	C₂²×C₄	C₂⁵	1	1	yes	characteristic
862	Q₁₆	—	4	4	no	—
863	M₁₆	—	4	4	no	—
864	M₁₆	—	8	2	no	—
865	M₁₆	—	8	2	no	—
866	C₂×C₈	—	2	1	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	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	—	4	4	no	—
887	C₂×C₈	C₂³×C₄	1	2	yes	—
888	C₂×C₈	C₂³×C₄	1	2	yes	—
889	C₂×C₈	C₂³×C₄	1	2	yes	—
890	C₂×C₈	C₂³×C₄	1	2	yes	—
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	4	no	—
893	C₄⋊C₄	—	2	4	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	4	no	—
897	C₄⋊C₄	—	2	4	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	2	4	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	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	—	4	1	no	—
925	C₄⋊C₄	—	4	1	no	—
926	C₄⋊C₄	—	4	1	no	—
927	C₄⋊C₄	—	4	1	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	—	4	2	no	—
931	C₄⋊C₄	—	4	2	no	—
932	C₄⋊C₄	—	4	2	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	—	8	1	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	C₄×D₄	1	4	yes	—
948	C₄⋊C₄	C₂³×C₄	1	2	yes	—
949	C₄⋊C₄	C₂³×C₄	1	2	yes	—
950	C₄⋊C₄	C₂³×C₄	1	2	yes	—
951	C₄⋊C₄	C₂³×C₄	1	2	yes	—
952	C₄⋊C₄	C₂³×C₄	1	2	yes	—
953	C₄⋊C₄	C₂³×C₄	1	2	yes	—
954	C₄⋊C₄	2₋¹⁺⁴	1	2	yes	—
955	C₂²⋊C₄	—	2	4	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	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	—	8	1	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	C₄×D₄	1	4	yes	—
974	C₂²⋊C₄	C₄×D₄	1	4	yes	—
975	C₄²	—	2	4	no	—
976	C₄²	—	2	4	no	—
977	C₄²	—	2	4	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	4	1	no	—
987	C₄²	—	4	1	no	—
988	C₄²	—	4	2	no	—
989	C₄²	—	4	2	no	—
990	C₄²	—	4	2	no	—
991	C₄²	—	4	2	no	—
992	C₄²	—	4	2	no	—
993	C₄²	—	8	1	no	—
994	C₄²	—	8	1	no	—
995	C₄²	—	8	1	no	—
996	C₄²	—	8	1	no	—
997	C₄²	—	8	1	no	—
998	C₄²	—	8	1	no	—
999	C₄²	—	8	1	no	—
1000	C₄²	—	8	1	no	—
1001	C₄²	—	8	1	no	—
1002	C₄²	—	8	1	no	—
1003	C₄²	—	8	1	no	—
1004	C₄²	—	8	1	no	—
1005	C₄²	—	8	1	no	—
1006	C₄²	—	8	1	no	—
1007	C₄²	—	8	1	no	—
1008	C₄²	—	8	1	no	—
1009	C₄²	C₂³×C₄	1	2	yes	—
1010	C₄²	C₂×#41	1	2	yes	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	C₂×C₄×D₄	1	2	yes	—
1024	C₂³	C₂×C₄×D₄	1	2	yes	—
1025	C₂³	C₂³×D₄	1	1	yes	characteristic
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	4	1	no	—
1031	Q₈	—	4	1	no	—
1032	Q₈	—	4	1	no	—
1033	Q₈	—	4	1	no	—
1034	Q₈	—	8	4	no	—
1035	D₄	—	4	4	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	8	4	no	—
1126	C₂×C₄	—	8	4	no	—
1127	C₂×C₄	—	8	4	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	4	no	—
1130	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1131	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1132	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1133	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1134	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1135	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1136	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1137	C₂×C₄	#585	1	1	yes	characteristic
1138	C₂×C₄	#585	1	1	yes	characteristic
1139	C₂×C₄	#585	1	1	yes	characteristic
1140	C₈	—	2	2	no	—
1141	C₈	—	2	2	no	—
1142	C₈	—	2	2	no	—
1143	C₈	—	2	2	no	—
1144	C₈	—	4	1	no	—
1145	C₈	—	4	1	no	—
1146	C₈	—	4	1	no	—
1147	C₈	—	4	1	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1163	C₂²	#3485	1	1	yes	characteristic
1164	C₂²	#3489	1	1	yes	characteristic
1165	C₂²	#3585	1	1	yes	characteristic
1166	C₂²	#3586	1	1	yes	characteristic
1167	C₂²	#3586	1	1	yes	characteristic
1168	C₂²	#3586	1	1	yes	characteristic
1169	C₄	—	2	2	no	—
1170	C₄	—	2	2	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	2	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	2	no	—
1175	C₄	—	4	2	no	—
1176	C₄	—	4	2	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	2	no	—
1190	C₄	—	8	1	no	—
1191	C₄	—	8	1	no	—
1192	C₄	—	8	1	no	—
1193	C₄	—	8	1	no	—
1194	C₄	—	8	1	no	—
1195	C₄	—	8	1	no	—
1196	C₄	—	8	1	no	—
1197	C₄	#3428	1	1	yes	characteristic
1198	C₄	C₄×2₋¹⁺⁴	1	1	yes	characteristic
1199	C₄	#3515	1	1	yes	characteristic
1200	C₄	#3521	1	1	yes	characteristic
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	#34289	1	1	yes	characteristic
1204	C₂	#60169	1	1	yes	characteristic
1205	C₂	#60174	1	1	yes	characteristic
1206	C₂	#61774	1	1	yes	characteristic
1207	C₂	#61781	1	1	yes	characteristic
1208	C₂	#62224	1	1	yes	characteristic
1209	C₂	#62234	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×D₄	C₂×D₄
LCS	G ▷ C₂×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
4. #23166	C₂	semidirect
5. #23144	C₂	semidirect
6. #23136	C₂	semidirect
7. #23070	C₂	semidirect
8. #22970	C₂	semidirect
9. #22947	C₂	semidirect
10. #22940	C₂	semidirect
11. #22927	C₂	semidirect
12. #22927	C₂	semidirect
13. #22779	C₂	semidirect
15. #22623	C₂	semidirect
16. #22615	C₂	semidirect
19. #22255	C₂	semidirect
20. #22197	C₂	semidirect
21. #22188	C₂	semidirect
22. #22129	C₂	semidirect
23. #22089	C₂	semidirect
24. #22083	C₂	semidirect
25. #21621	C₂	semidirect
26. #21585	C₂	semidirect
27. #21579	C₂	semidirect
28. #21127	C₂	semidirect
29. #21038	C₂	semidirect
30. #21033	C₂	semidirect
34. #3344	C₄	semidirect
247. #501	C₂×C₄	semidirect
249. #484	C₂×C₄	semidirect
251. #483	C₂×C₄	semidirect
252. #479	C₂×C₄	semidirect
253. #475	C₂×C₄	semidirect
255. #467	C₂×C₄	semidirect
256. #441	C₂×C₄	semidirect
267. C₂×#106	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3344	2
#34462	2
#34299	2
#23166	2
#23144	2
#23136	2
#23070	2
#22970	2
#22947	2
#22940	2
#22927	2
#22779	2
#22712	2
#22623	2
#22615	2
#22502	2
#22499	2
#22255	2
#22197	2
#22188	2
#22129	2
#22089	2
#22083	2
#21621	2
#21585	2
#21579	2
#21127	2
#21038	2
#21033	2
#20564	2