Subgroups — #6448414

Order 512.

1557 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34954	C₂	1	1	yes	maximal, characteristic
2	C₄×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	#27564	C₂	1	1	yes	maximal, characteristic, complemented
4	#27553	C₂	1	1	yes	maximal, characteristic, complemented
5	#27136	C₂	1	1	yes	maximal, characteristic, complemented
6	#27129	C₂	1	1	yes	maximal, characteristic, complemented
7	#26698	C₂	1	1	yes	maximal, characteristic, complemented
8	#26691	C₂	1	1	yes	maximal, characteristic, complemented
9	#26523	C₂	1	1	yes	maximal, characteristic, complemented
10	#26332	C₂	1	1	yes	maximal, characteristic
11	#26173	C₂	1	1	yes	maximal, characteristic, complemented
12	#26169	C₂	1	1	yes	maximal, characteristic, complemented
13	#26123	C₂	1	1	yes	maximal, characteristic, complemented
14	#25944	C₂	1	1	yes	maximal, characteristic
15	#25291	C₂	1	1	yes	maximal, characteristic
16	#25008	C₂	1	1	yes	maximal, characteristic, complemented
17	#24747	C₂	1	1	yes	maximal, characteristic
18	#24348	C₂	1	1	yes	maximal, characteristic, complemented
19	#23826	C₂	1	1	yes	maximal, characteristic, complemented
20	#23821	C₂	1	1	yes	maximal, characteristic, complemented
21	#23784	C₂	1	1	yes	maximal, characteristic, complemented
22	#23781	C₂	1	1	yes	maximal, characteristic, complemented
23	#21656	C₂	1	1	yes	maximal, characteristic
24	#21618	C₂	1	1	yes	maximal, characteristic, complemented
25	#21508	C₂	1	1	yes	maximal, characteristic, complemented
26	#21508	C₂	1	1	yes	maximal, characteristic, complemented
27	#21505	C₂	1	1	yes	maximal, characteristic
28	#21346	C₂	1	1	yes	maximal, characteristic, complemented
29	#21124	C₂	1	1	yes	maximal, characteristic, complemented
30	#21124	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#441	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#557	C₂²	1	1	yes	characteristic
33	C₂×#490	C₂²	1	1	yes	characteristic
34	C₂×#479	C₂²	1	1	yes	characteristic
35	C₂×#464	C₂²	1	1	yes	characteristic
36	C₂×#464	C₂²	1	1	yes	characteristic
37	C₂×#460	C₂²	1	1	yes	characteristic
38	C₂×#441	C₂²	1	1	yes	characteristic
39	C₂×#441	C₂²	1	1	yes	characteristic
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×#440	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
43	#2593	—	2	1	no	—
44	#2593	—	2	1	no	—
45	#2582	C₂²	1	1	yes	characteristic
46	#2571	C₂²	1	1	yes	characteristic
47	#2548	C₂²	1	1	yes	characteristic
48	#2548	C₂²	1	1	yes	characteristic
49	#2513	—	2	1	no	—
50	#2513	C₂²	1	1	yes	characteristic
51	#2513	C₂²	1	1	yes	characteristic
52	#2448	—	2	1	no	—
53	#2448	C₂²	1	1	yes	characteristic
54	#2448	C₂²	1	1	yes	characteristic
55	#2395	—	2	1	no	—
56	#2395	—	2	1	no	—
57	#2370	—	2	1	no	—
58	#2370	—	2	1	no	—
59	#2370	C₂²	1	1	yes	characteristic
60	#2370	C₂²	1	1	yes	characteristic
61	#2365	—	2	1	no	—
62	#2365	C₂²	1	1	yes	characteristic
63	#2355	—	2	1	no	—
64	#2355	C₂²	1	1	yes	characteristic
65	#2351	C₂²	1	1	yes	characteristic
66	#2351	C₂²	1	1	yes	characteristic
67	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊Q₈	—	2	1	no	—
69	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
70	C₄×#127	C₂²	1	1	yes	characteristic
71	C₄×#125	—	2	1	no	—
72	C₄×#125	—	2	1	no	—
73	C₄×#125	C₂²	1	1	yes	characteristic
74	C₄×#125	C₂²	1	1	yes	characteristic
75	C₄×#124	—	2	1	no	—
76	C₄×#124	C₂²	1	1	yes	characteristic
77	C₄×#124	C₂²	1	1	yes	characteristic
78	#2293	—	2	1	no	—
79	#2293	C₂²	1	1	yes	characteristic
80	#2293	C₂²	1	1	yes	characteristic
81	C₄²×Q₈	—	2	1	no	—
82	C₄²×Q₈	C₂²	1	1	yes	characteristic
83	C₄²×Q₈	C₂²	1	1	yes	characteristic
84	C₄²×Q₈	C₂²	1	1	yes	characteristic
85	C₄²×Q₈	C₂²	1	1	yes	characteristic
86	C₄²×Q₈	C₂²	1	1	yes	characteristic
87	#2101	C₂²	1	1	yes	characteristic
88	#2101	C₂²	1	1	yes	characteristic
89	#2101	C₂²	1	1	yes	characteristic
90	#2101	C₂²	1	1	yes	characteristic
91	#2101	C₂²	1	1	yes	characteristic
92	#2099	C₂²	1	1	yes	characteristic
93	#2093	C₂²	1	1	yes	characteristic
94	#2092	C₂²	1	1	yes	characteristic
95	#2088	C₂²	1	1	yes	characteristic
96	#2087	C₂²	1	1	yes	characteristic
97	#2087	C₂²	1	1	yes	characteristic
98	#2086	C₂²	1	1	yes	characteristic
99	#2074	C₂²	1	1	yes	characteristic
100	#2073	C₂²	1	1	yes	characteristic
101	#2072	C₂²	1	1	yes	characteristic
102	#2071	C₂²	1	1	yes	characteristic
103	#2067	C₂²	1	1	yes	characteristic
104	#2065	C₂²	1	1	yes	characteristic
105	#2065	C₂²	1	1	yes	characteristic
106	#2065	C₂²	1	1	yes	characteristic
107	#2059	C₂²	1	1	yes	characteristic
108	#2058	C₂²	1	1	yes	characteristic
109	#2042	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic
111	#2042	C₂²	1	1	yes	characteristic
112	#2042	C₂²	1	1	yes	characteristic
113	#2026	C₂²	1	1	yes	characteristic
114	#2025	C₂²	1	1	yes	characteristic
115	#2025	C₂²	1	1	yes	characteristic
116	#2024	C₂²	1	1	yes	characteristic
117	#2023	C₂²	1	1	yes	characteristic
118	#2023	C₂²	1	1	yes	characteristic
119	#1992	C₂²	1	1	yes	characteristic
120	#1989	C₂²	1	1	yes	characteristic
121	#1985	C₂²	1	1	yes	characteristic
122	#1985	C₂²	1	1	yes	characteristic
123	#1983	C₂²	1	1	yes	characteristic
124	#1983	C₂²	1	1	yes	characteristic
125	#1982	C₂²	1	1	yes	characteristic
126	#1961	C₂²	1	1	yes	characteristic
127	#1949	C₂²	1	1	yes	characteristic
128	#1949	C₂²	1	1	yes	characteristic
129	#1949	C₂²	1	1	yes	characteristic
130	#1947	C₂²	1	1	yes	characteristic
131	#1940	C₂²	1	1	yes	characteristic
132	#1940	C₂²	1	1	yes	characteristic
133	#1934	C₂²	1	1	yes	characteristic
134	#1934	C₂²	1	1	yes	characteristic
135	#1934	C₂²	1	1	yes	characteristic
136	#1934	C₂²	1	1	yes	characteristic
137	#1928	C₂²	1	1	yes	characteristic
138	#1928	C₂²	1	1	yes	characteristic
139	#1926	C₂²	1	1	yes	characteristic
140	#1926	C₂²	1	1	yes	characteristic
141	#1926	C₂²	1	1	yes	characteristic
142	#1926	C₂²	1	1	yes	characteristic
143	#1925	C₂²	1	1	yes	characteristic
144	#1925	C₂²	1	1	yes	characteristic
145	#1925	C₂²	1	1	yes	characteristic
146	#1925	C₂²	1	1	yes	characteristic
147	#1921	C₂²	1	1	yes	characteristic
148	#1921	C₂²	1	1	yes	characteristic
149	#1921	C₂²	1	1	yes	characteristic
150	#1919	C₂²	1	1	yes	characteristic
151	#1918	C₂²	1	1	yes	characteristic
152	#1918	C₂²	1	1	yes	characteristic
153	#1916	C₂²	1	1	yes	characteristic
154	#1916	C₂²	1	1	yes	characteristic
155	#1916	C₂²	1	1	yes	characteristic
156	#1916	C₂²	1	1	yes	characteristic
157	#1880	C₂²	1	1	yes	characteristic
158	#1880	C₂²	1	1	yes	characteristic
159	#1880	C₂²	1	1	yes	characteristic
160	#1880	C₂²	1	1	yes	characteristic
161	#1880	C₂²	1	1	yes	characteristic
162	#1880	C₂²	1	1	yes	characteristic
163	#1880	C₂²	1	1	yes	characteristic
164	#1880	C₂²	1	1	yes	characteristic
165	#1878	C₂²	1	1	yes	characteristic
166	#1878	C₂²	1	1	yes	characteristic
167	#1865	C₂²	1	1	yes	characteristic
168	#1865	C₂²	1	1	yes	characteristic
169	#1865	C₂²	1	1	yes	characteristic
170	#1863	C₂²	1	1	yes	characteristic
171	#1863	C₂²	1	1	yes	characteristic
172	#1863	C₂²	1	1	yes	characteristic
173	#1836	C₂²	1	1	yes	characteristic
174	#1805	C₂²	1	1	yes	characteristic
175	#1805	C₂²	1	1	yes	characteristic
176	#1805	C₂²	1	1	yes	characteristic
177	#1803	C₂²	1	1	yes	characteristic
178	#1776	C₂²	1	1	yes	characteristic
179	#1776	C₂²	1	1	yes	characteristic
180	#1776	C₂²	1	1	yes	characteristic
181	#1776	C₂²	1	1	yes	characteristic
182	C₄×#106	C₂²	1	1	yes	characteristic
183	#1767	C₂²	1	1	yes	characteristic
184	#1767	C₂²	1	1	yes	characteristic
185	#1767	C₂²	1	1	yes	characteristic
186	#1763	C₂²	1	1	yes	characteristic
187	#1763	C₂²	1	1	yes	characteristic
188	#1763	C₂²	1	1	yes	characteristic
189	#1763	C₂²	1	1	yes	characteristic
190	#1763	C₂²	1	1	yes	characteristic
191	#1763	C₂²	1	1	yes	characteristic
192	#1762	C₂²	1	1	yes	characteristic
193	#1762	C₂²	1	1	yes	characteristic
194	#1762	C₂²	1	1	yes	characteristic
195	#1762	C₂²	1	1	yes	characteristic
196	#1762	C₂²	1	1	yes	characteristic
197	#1762	C₂²	1	1	yes	characteristic
198	C₄×#103	C₂²	1	1	yes	characteristic
199	C₄×#103	C₂²	1	1	yes	characteristic
200	#1745	C₂²	1	1	yes	characteristic
201	#1745	C₂²	1	1	yes	characteristic
202	C₄×#97	C₂²	1	1	yes	characteristic
203	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	#557	—	2	4	no	—
207	#557	—	2	4	no	—
208	C₂×C₄⋊Q₈	—	2	1	no	—
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#127	C₂³	1	1	yes	characteristic
211	C₂×#125	—	2	1	no	—
212	C₂×#125	—	2	1	no	—
213	C₂×#125	C₂³	1	1	yes	characteristic
214	C₂×#125	C₂³	1	1	yes	characteristic
215	C₂×#124	—	2	1	no	—
216	C₂×#124	C₂³	1	1	yes	characteristic
217	C₂×#124	C₂³	1	1	yes	characteristic
218	C₂×C₄×Q₈	—	2	1	no	—
219	C₂×C₄×Q₈	—	2	1	no	—
220	C₂×C₄×Q₈	—	2	1	no	—
221	C₂×C₄×Q₈	D₄	1	1	yes	characteristic
222	C₂×C₄×Q₈	D₄	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
238	C₂×#117	—	2	1	no	—
239	C₂×#117	—	2	1	no	—
240	#490	—	2	4	no	—
241	#479	—	2	4	no	—
242	#464	—	2	4	no	—
243	#464	—	2	4	no	—
244	#460	—	2	4	no	—
245	#441	—	2	4	no	—
246	#441	—	2	4	no	—
247	#440	—	2	4	no	—
248	#440	—	2	4	no	—
249	C₄×Q₁₆	—	2	4	no	—
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#107	C₂³	1	1	yes	characteristic
253	C₂×#107	C₂³	1	1	yes	characteristic
254	C₂×#107	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×#106	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#103	C₂³	1	1	yes	characteristic
271	C₂×#103	C₂³	1	1	yes	characteristic
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	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×#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×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	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×#97	C₂³	1	1	yes	characteristic
292	C₂×#97	C₂³	1	1	yes	characteristic
293	C₂×#97	C₂³	1	1	yes	characteristic
294	C₂×#97	C₂³	1	1	yes	characteristic
295	C₂×#97	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#399	—	2	1	no	—
302	#399	—	2	1	no	—
303	#398	—	2	1	no	—
304	#398	—	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	#394	—	2	1	no	—
312	#394	—	2	1	no	—
313	#394	—	2	1	no	—
314	#394	—	2	1	no	—
315	#391	—	2	1	no	—
316	#391	—	2	1	no	—
317	#391	—	2	1	no	—
318	#391	—	2	1	no	—
319	#391	C₂³	1	1	yes	characteristic
320	#391	C₂³	1	1	yes	characteristic
321	#390	—	2	1	no	—
322	#390	—	2	1	no	—
323	#390	—	2	1	no	—
324	#390	—	2	1	no	—
325	#390	—	2	1	no	—
326	#390	C₂³	1	1	yes	characteristic
327	#390	C₂³	1	1	yes	characteristic
328	#390	C₂³	1	1	yes	characteristic
329	#390	C₂³	1	1	yes	characteristic
330	#390	C₂³	1	1	yes	characteristic
331	#390	C₂³	1	1	yes	characteristic
332	#390	C₂³	1	1	yes	characteristic
333	#390	C₂³	1	1	yes	characteristic
334	#389	—	2	1	no	—
335	#389	—	2	1	no	—
336	#389	—	2	1	no	—
337	#389	—	2	1	no	—
338	#389	—	2	1	no	—
339	#389	—	2	1	no	—
340	#389	—	2	1	no	—
341	#389	—	2	1	no	—
342	#389	—	2	1	no	—
343	#389	—	2	1	no	—
344	#389	—	2	1	no	—
345	#389	C₂³	1	1	yes	characteristic
346	#389	C₂³	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#389	C₂³	1	1	yes	characteristic
351	#389	C₂³	1	1	yes	characteristic
352	#389	C₂³	1	1	yes	characteristic
353	#389	C₂³	1	1	yes	characteristic
354	#389	C₂³	1	1	yes	characteristic
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#388	—	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	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#384	—	2	1	no	—
384	#384	C₂³	1	1	yes	characteristic
385	#384	C₂³	1	1	yes	characteristic
386	#382	—	2	1	no	—
387	#382	—	2	1	no	—
388	#382	—	2	1	no	—
389	#382	C₂³	1	1	yes	characteristic
390	#382	C₂³	1	1	yes	characteristic
391	#382	C₂³	1	1	yes	characteristic
392	#382	C₂³	1	1	yes	characteristic
393	C₄×C₄⋊C₄	—	2	1	no	—
394	C₄×C₄⋊C₄	—	2	1	no	—
395	C₄×C₄⋊C₄	—	2	1	no	—
396	C₄×C₄⋊C₄	—	2	1	no	—
397	C₄×C₄⋊C₄	—	2	1	no	—
398	C₄×C₄⋊C₄	—	2	1	no	—
399	C₄×C₄⋊C₄	—	2	1	no	—
400	C₄×C₄⋊C₄	—	2	1	no	—
401	C₄×C₄⋊C₄	—	2	1	no	—
402	C₄×C₄⋊C₄	—	2	1	no	—
403	C₄×C₄⋊C₄	—	2	1	no	—
404	C₄×C₄⋊C₄	—	2	1	no	—
405	C₄×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
417	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
418	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
419	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
420	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
421	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
438	C₄×C₂²⋊C₄	—	2	1	no	—
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	C₄³	—	2	1	no	—
444	C₄³	—	2	1	no	—
445	C₄³	—	2	1	no	—
446	C₄³	—	2	1	no	—
447	C₄³	C₂³	1	1	yes	characteristic
448	C₄³	C₂³	1	1	yes	characteristic
449	C₄³	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	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
492	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	C₂⁴	1	1	yes	characteristic
497	C₂²×D₄	C₂⁴	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂×Q₁₆	—	2	2	no	—
501	C₂×Q₁₆	—	2	2	no	—
502	C₂×Q₁₆	#41	1	4	yes	—
503	C₂×SD₁₆	—	2	2	no	—
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	2	no	—
509	C₂²×C₈	C₂⁴	1	1	yes	characteristic
510	C₂²×C₈	C₂⁴	1	1	yes	characteristic
511	C₂²×C₈	C₂⁴	1	1	yes	characteristic
512	C₂²×C₈	C₂⁴	1	1	yes	characteristic
513	C₂²×C₈	C₂⁴	1	1	yes	characteristic
514	C₂²×C₈	C₂⁴	1	1	yes	characteristic
515	C₂²×C₈	C₂⁴	1	1	yes	characteristic
516	C₂²×C₈	C₂⁴	1	1	yes	characteristic
517	C₄⋊Q₈	—	2	8	no	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₄⋊Q₈	—	2	2	no	—
520	#127	—	2	2	no	—
521	#127	—	2	2	no	—
522	#125	—	2	8	no	—
523	#125	—	2	8	no	—
524	#125	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	—	2	2	no	—
527	#125	#41	1	4	yes	—
528	#124	—	2	2	no	—
529	#124	—	2	2	no	—
530	#124	—	4	1	no	—
531	#124	—	4	1	no	—
532	#124	—	4	4	no	—
533	C₄×Q₈	—	2	8	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	4	2	no	—
551	C₄×Q₈	—	4	2	no	—
552	C₄×Q₈	—	4	1	no	—
553	C₄×Q₈	—	4	1	no	—
554	C₄×Q₈	—	4	1	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×Q₈	—	4	4	no	—
557	C₄×Q₈	—	4	4	no	—
558	C₄×Q₈	#41	1	4	yes	—
559	C₄×Q₈	#41	1	4	yes	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	4	4	no	—
565	C₄×D₄	—	8	2	no	—
566	#117	—	8	2	no	—
567	#117	—	8	2	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	—	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	C₂×D₄	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
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	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
668	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
673	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	C₂×C₄²	C₂⁴	1	1	yes	characteristic
677	C₂×C₄²	C₂⁴	1	1	yes	characteristic
678	C₂×C₄²	C₂⁴	1	1	yes	characteristic
679	C₂×C₄²	C₂⁴	1	1	yes	characteristic
680	C₂×C₄²	C₂⁴	1	1	yes	characteristic
681	#107	—	2	2	no	—
682	#107	—	2	2	no	—
683	#107	—	2	2	no	—
684	#107	—	2	2	no	—
685	#107	—	4	1	no	—
686	#106	—	2	2	no	—
687	#106	—	2	2	no	—
688	#106	—	2	2	no	—
689	#106	—	4	1	no	—
690	C₄⋊C₈	—	2	2	no	—
691	C₄⋊C₈	—	2	2	no	—
692	C₄⋊C₈	—	2	2	no	—
693	C₄⋊C₈	—	2	2	no	—
694	C₄⋊C₈	—	4	1	no	—
695	C₄⋊C₈	—	4	1	no	—
696	#103	—	2	2	no	—
697	#103	—	2	2	no	—
698	#103	—	2	2	no	—
699	#103	—	2	2	no	—
700	#103	—	2	2	no	—
701	#103	—	2	2	no	—
702	#103	—	2	2	no	—
703	#103	—	2	2	no	—
704	#103	—	2	2	no	—
705	#103	—	2	2	no	—
706	#103	—	2	2	no	—
707	#103	—	2	2	no	—
708	#102	—	2	2	no	—
709	#102	—	2	2	no	—
710	#102	—	2	2	no	—
711	#102	—	2	2	no	—
712	#102	—	2	2	no	—
713	#102	—	2	2	no	—
714	#102	—	2	2	no	—
715	#102	—	2	2	no	—
716	#102	—	2	2	no	—
717	#102	—	2	2	no	—
718	#102	—	4	1	no	—
719	#102	—	4	1	no	—
720	#102	—	4	1	no	—
721	#102	—	4	1	no	—
722	#97	—	2	2	no	—
723	#97	—	2	2	no	—
724	#97	—	2	2	no	—
725	#97	—	2	2	no	—
726	#97	—	2	2	no	—
727	#97	—	2	2	no	—
728	C₄×C₈	—	2	2	no	—
729	C₄×C₈	—	4	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	—	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	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	#95	C₂×D₄	1	1	yes	characteristic
767	#95	C₂×D₄	1	1	yes	characteristic
768	#95	C₂×D₄	1	1	yes	characteristic
769	#95	C₂×D₄	1	1	yes	characteristic
770	C₂⁴	—	2	1	no	—
771	C₂⁴	—	2	1	no	—
772	C₂×Q₈	—	2	4	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	1	no	—
778	C₂×Q₈	—	2	1	no	—
779	C₂×Q₈	—	2	1	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	4	1	no	—
784	C₂×Q₈	—	4	2	no	—
785	C₂×Q₈	—	4	2	no	—
786	C₂×Q₈	C₂×#41	1	2	yes	—
787	C₂×Q₈	C₂×#41	1	2	yes	—
788	C₂×Q₈	C₂×#41	1	2	yes	—
789	C₂×Q₈	C₂×#41	1	2	yes	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	4	2	no	—
803	C₂×D₄	—	4	2	no	—
804	C₂×D₄	—	4	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	8	1	no	—
807	C₂×D₄	—	8	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	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
829	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
830	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
831	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
832	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
833	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
834	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
835	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
836	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
837	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
838	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
839	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
840	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
841	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
842	C₂²×C₄	C₂⁵	1	1	yes	characteristic
843	Q₁₆	—	2	8	no	—
844	SD₁₆	—	4	4	no	—
845	SD₁₆	—	4	4	no	—
846	C₂×C₈	—	2	1	no	—
847	C₂×C₈	—	2	1	no	—
848	C₂×C₈	—	2	1	no	—
849	C₂×C₈	—	2	1	no	—
850	C₂×C₈	—	2	1	no	—
851	C₂×C₈	—	2	1	no	—
852	C₂×C₈	—	2	1	no	—
853	C₂×C₈	—	2	1	no	—
854	C₂×C₈	—	2	1	no	—
855	C₂×C₈	—	2	1	no	—
856	C₂×C₈	—	2	1	no	—
857	C₂×C₈	—	2	1	no	—
858	C₂×C₈	—	2	1	no	—
859	C₂×C₈	—	2	1	no	—
860	C₂×C₈	—	2	1	no	—
861	C₂×C₈	—	2	1	no	—
862	C₂×C₈	—	2	1	no	—
863	C₂×C₈	—	2	1	no	—
864	C₂×C₈	—	2	1	no	—
865	C₂×C₈	—	2	1	no	—
866	C₂×C₈	—	2	1	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	C₂×#41	1	2	yes	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	4	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	4	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	4	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	4	1	no	—
906	C₄⋊C₄	—	4	1	no	—
907	C₄⋊C₄	—	4	1	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₄⋊C₄	—	4	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	8	1	no	—
921	C₄⋊C₄	—	8	1	no	—
922	C₄⋊C₄	—	8	1	no	—
923	C₄⋊C₄	—	8	1	no	—
924	C₄⋊C₄	—	8	1	no	—
925	C₄⋊C₄	—	8	1	no	—
926	C₄⋊C₄	—	8	1	no	—
927	C₄⋊C₄	—	8	1	no	—
928	C₄⋊C₄	C₂×#41	1	2	yes	—
929	C₄⋊C₄	C₂×#41	1	2	yes	—
930	C₄⋊C₄	C₂×#41	1	2	yes	—
931	C₄⋊C₄	C₂×#41	1	2	yes	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	8	1	no	—
945	C₂²⋊C₄	—	8	1	no	—
946	C₂²⋊C₄	—	8	1	no	—
947	C₂²⋊C₄	—	8	1	no	—
948	C₂²⋊C₄	—	8	1	no	—
949	C₂²⋊C₄	—	8	1	no	—
950	C₂²⋊C₄	—	8	1	no	—
951	C₂²⋊C₄	—	8	1	no	—
952	C₂²⋊C₄	—	8	1	no	—
953	C₂²⋊C₄	—	8	1	no	—
954	C₄²	—	2	4	no	—
955	C₄²	—	2	4	no	—
956	C₄²	—	2	4	no	—
957	C₄²	—	2	4	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	4	1	no	—
971	C₄²	—	4	1	no	—
972	C₄²	—	4	1	no	—
973	C₄²	—	4	1	no	—
974	C₄²	—	4	1	no	—
975	C₄²	—	4	1	no	—
976	C₄²	—	4	1	no	—
977	C₄²	—	4	1	no	—
978	C₄²	—	4	1	no	—
979	C₄²	—	4	1	no	—
980	C₄²	—	4	2	no	—
981	C₄²	—	4	2	no	—
982	C₄²	—	4	2	no	—
983	C₄²	—	4	2	no	—
984	C₄²	—	4	2	no	—
985	C₄²	—	4	2	no	—
986	C₄²	—	4	2	no	—
987	C₄²	—	4	2	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	—	4	2	no	—
994	C₄²	—	8	1	no	—
995	C₄²	—	8	1	no	—
996	C₄²	—	8	1	no	—
997	C₄²	—	8	1	no	—
998	C₄²	C₂×#41	1	2	yes	—
999	C₄²	C₂×#41	1	2	yes	—
1000	C₄²	C₂×#41	1	2	yes	—
1001	C₄²	2₋¹⁺⁴	1	2	yes	—
1002	C₂³	—	4	1	no	—
1003	C₂³	—	4	1	no	—
1004	C₂³	—	4	1	no	—
1005	C₂³	—	4	1	no	—
1006	C₂³	—	4	1	no	—
1007	C₂³	—	4	1	no	—
1008	C₂³	—	4	1	no	—
1009	C₂³	—	4	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	1	no	—
1012	C₂³	—	4	1	no	—
1013	C₂³	—	4	1	no	—
1014	C₂³	—	4	1	no	—
1015	C₂³	—	4	1	no	—
1016	C₂³	C₂³×D₄	1	1	yes	characteristic
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	2	no	—
1022	Q₈	—	4	4	no	—
1023	Q₈	—	4	8	no	—
1024	Q₈	—	4	1	no	—
1025	Q₈	—	4	1	no	—
1026	Q₈	#529	1	4	yes	—
1027	D₄	—	4	1	no	—
1028	D₄	—	4	1	no	—
1029	D₄	—	4	1	no	—
1030	D₄	—	4	1	no	—
1031	D₄	—	4	1	no	—
1032	D₄	—	4	1	no	—
1033	D₄	—	4	1	no	—
1034	D₄	—	4	1	no	—
1035	D₄	—	8	4	no	—
1036	D₄	—	8	4	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	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	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	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	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	—	4	1	no	—
1082	C₂×C₄	—	4	1	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	1	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	—	8	4	no	—
1116	C₂×C₄	—	8	4	no	—
1117	C₂×C₄	#525	1	2	yes	—
1118	C₂×C₄	#525	1	2	yes	—
1119	C₂×C₄	#548	1	2	yes	—
1120	C₂×C₄	#548	1	2	yes	—
1121	C₂×C₄	#575	1	2	yes	—
1122	C₂×C₄	#575	1	2	yes	—
1123	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1124	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1125	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1126	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1127	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1128	C₂×C₄	#585	1	1	yes	characteristic
1129	C₈	—	2	2	no	—
1130	C₈	—	4	1	no	—
1131	C₈	—	4	1	no	—
1132	C₈	—	4	1	no	—
1133	C₈	—	4	1	no	—
1134	C₈	—	4	1	no	—
1135	C₈	—	4	1	no	—
1136	C₈	—	4	1	no	—
1137	C₂²	—	8	1	no	—
1138	C₂²	—	8	1	no	—
1139	C₂²	—	8	1	no	—
1140	C₂²	—	8	1	no	—
1141	C₂²	—	8	1	no	—
1142	C₂²	—	8	1	no	—
1143	C₂²	—	8	1	no	—
1144	C₂²	—	8	1	no	—
1145	C₂²	—	8	1	no	—
1146	C₂²	—	8	1	no	—
1147	C₂²	—	8	1	no	—
1148	C₂²	—	8	1	no	—
1149	C₂²	—	8	1	no	—
1150	C₂²	—	8	1	no	—
1151	C₂²	C₂×#525	1	1	yes	characteristic
1152	C₂²	C₂×#548	1	1	yes	characteristic
1153	C₂²	D₄×#41	1	1	yes	characteristic
1154	C₂²	C₂×#575	1	1	yes	characteristic
1155	C₂²	C₂×#575	1	1	yes	characteristic
1156	C₂²	#3585	1	1	yes	characteristic
1157	C₂²	#3586	1	1	yes	characteristic
1158	C₄	—	2	2	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	4	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	2	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	2	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	8	1	no	—
1179	C₄	—	8	1	no	—
1180	C₄	—	8	1	no	—
1181	C₄	—	8	1	no	—
1182	C₄	—	8	1	no	—
1183	C₄	—	8	1	no	—
1184	C₄	—	8	1	no	—
1185	C₄	—	8	1	no	—
1186	C₄	C₂×#529	1	1	yes	characteristic
1187	C₄	#3461	1	1	yes	characteristic
1188	C₄	#3480	1	1	yes	characteristic
1189	C₄	#3482	1	1	yes	characteristic
1190	C₂	—	16	1	no	—
1191	C₂	—	16	1	no	—
1192	C₂	#34708	1	1	yes	characteristic
1193	C₂	#60563	1	1	yes	characteristic
1194	C₂	#60576	1	1	yes	characteristic
1195	C₂	#61320	1	1	yes	characteristic
1196	C₂	#61324	1	1	yes	characteristic
1197	C₂	#61458	1	1	yes	characteristic
1198	C₂	#61462	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#127	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄²×Q₈ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₄×#557	C₂	semidirect
3. #27564	C₂	semidirect
4. #27553	C₂	semidirect
5. #27136	C₂	semidirect
6. #27129	C₂	semidirect
7. #26698	C₂	semidirect
8. #26691	C₂	semidirect
9. #26523	C₂	semidirect
11. #26173	C₂	semidirect
12. #26169	C₂	semidirect
13. #26123	C₂	semidirect
16. #25008	C₂	semidirect
18. #24348	C₂	semidirect
19. #23826	C₂	semidirect
20. #23821	C₂	semidirect
21. #23784	C₂	semidirect
22. #23781	C₂	semidirect
24. #21618	C₂	semidirect
25. #21508	C₂	semidirect
26. #21508	C₂	semidirect
28. #21346	C₂	semidirect
29. #21124	C₂	semidirect
30. #21124	C₂	semidirect
31. C₄×#441	C₂	semidirect

Maximal subgroups

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

subgroup	index
#34954	2
C₄×#557	2
#27564	2
#27553	2
#27136	2
#27129	2
#26698	2
#26691	2
#26523	2
#26332	2
#26173	2
#26169	2
#26123	2
#25944	2
#25291	2
#25008	2
#24747	2
#24348	2
#23826	2
#23821	2
#23784	2
#23781	2
#21656	2
#21618	2
#21508	2
#21505	2
#21346	2
#21124	2
C₄×#441	2