Subgroups — #6468433

Order 512.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	#34084	C₂	1	1	yes	maximal, characteristic
3	#29294	C₂	1	1	yes	maximal, characteristic, complemented
4	#29292	C₂	1	1	yes	maximal, characteristic, complemented
5	#29285	C₂	1	1	yes	maximal, characteristic, complemented
6	#29284	C₂	1	1	yes	maximal, characteristic, complemented
7	#29268	C₂	1	1	yes	maximal, characteristic, complemented
8	#29267	C₂	1	1	yes	maximal, characteristic, complemented
9	#29253	C₂	1	1	yes	maximal, characteristic, complemented
10	#29250	C₂	1	1	yes	maximal, characteristic, complemented
11	#29248	C₂	1	1	yes	maximal, characteristic
12	#29247	C₂	1	1	yes	maximal, characteristic
13	#28293	C₂	1	1	yes	maximal, characteristic, complemented
14	#28289	C₂	1	1	yes	maximal, characteristic, complemented
15	#27690	C₂	1	1	yes	maximal, characteristic, complemented
16	#27687	C₂	1	1	yes	maximal, characteristic
17	#24310	C₂	1	1	yes	maximal, characteristic, complemented
18	#24309	C₂	1	1	yes	maximal, characteristic
19	#23785	C₂	1	1	yes	maximal, characteristic, complemented
20	#23784	C₂	1	1	yes	maximal, characteristic, complemented
21	#23782	C₂	1	1	yes	maximal, characteristic, complemented
22	#23781	C₂	1	1	yes	maximal, characteristic, complemented
23	#21618	C₂	1	1	yes	maximal, characteristic, complemented
24	#21617	C₂	1	1	yes	maximal, characteristic, complemented
25	#21615	C₂	1	1	yes	maximal, characteristic, complemented
26	#21614	C₂	1	1	yes	maximal, characteristic, complemented
27	#21396	C₂	1	1	yes	maximal, characteristic
28	#21391	C₂	1	1	yes	maximal, characteristic
29	#21365	C₂	1	1	yes	maximal, characteristic, complemented
30	#21364	C₂	1	1	yes	maximal, characteristic, complemented
31	#20811	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#544	C₂²	1	1	yes	characteristic
33	C₂×#529	C₂²	1	1	yes	characteristic
34	C₂×#479	C₂²	1	1	yes	characteristic
35	C₂×#475	C₂²	1	1	yes	characteristic
36	C₂×#478	C₂²	1	1	yes	characteristic
37	C₂×#476	C₂²	1	1	yes	characteristic
38	C₂×#432	C₂²	1	1	yes	characteristic
39	C₂×#432	C₂²	1	1	yes	characteristic
40	#2335	—	2	1	no	—
41	#2335	—	2	1	no	—
42	#2334	—	2	1	no	—
43	#2334	—	2	1	no	—
44	#2331	—	2	1	no	—
45	#2331	C₂²	1	1	yes	characteristic
46	#2331	C₂²	1	1	yes	characteristic
47	#2330	—	2	1	no	—
48	#2330	C₂²	1	1	yes	characteristic
49	#2330	C₂²	1	1	yes	characteristic
50	#2330	C₂²	1	1	yes	characteristic
51	#2330	C₂²	1	1	yes	characteristic
52	#2329	—	2	1	no	—
53	#2329	—	2	1	no	—
54	#2326	C₂²	1	1	yes	characteristic
55	#2326	C₂²	1	1	yes	characteristic
56	#2324	C₂²	1	1	yes	characteristic
57	#2324	C₂²	1	1	yes	characteristic
58	#2323	C₂²	1	1	yes	characteristic
59	#2323	C₂²	1	1	yes	characteristic
60	#2317	C₂²	1	1	yes	characteristic
61	#2317	C₂²	1	1	yes	characteristic
62	#2316	C₂²	1	1	yes	characteristic
63	C₄×C₄⋊Q₈	—	2	1	no	—
64	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
66	C₄×#125	—	2	1	no	—
67	C₄×#125	C₂²	1	1	yes	characteristic
68	C₄×#125	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊Q₈	—	2	1	no	—
70	C₄×C₂²⋊Q₈	—	2	1	no	—
71	#2298	—	2	1	no	—
72	#2296	—	2	1	no	—
73	#2295	C₂²	1	1	yes	characteristic
74	#2293	—	2	1	no	—
75	#2293	C₂²	1	1	yes	characteristic
76	#2290	—	2	1	no	—
77	#2285	C₂²	1	1	yes	characteristic
78	C₄²×Q₈	C₂²	1	1	yes	characteristic
79	C₄²×D₄	C₂²	1	1	yes	characteristic
80	C₄×#117	C₂²	1	1	yes	characteristic
81	C₄×#117	C₂²	1	1	yes	characteristic
82	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	#2101	C₂²	1	1	yes	characteristic
84	#2101	C₂²	1	1	yes	characteristic
85	#2100	C₂²	1	1	yes	characteristic
86	#2099	C₂²	1	1	yes	characteristic
87	#2097	C₂²	1	1	yes	characteristic
88	#2095	C₂²	1	1	yes	characteristic
89	#2093	C₂²	1	1	yes	characteristic
90	#2092	C₂²	1	1	yes	characteristic
91	#2088	C₂²	1	1	yes	characteristic
92	#2088	C₂²	1	1	yes	characteristic
93	#2087	C₂²	1	1	yes	characteristic
94	#2087	C₂²	1	1	yes	characteristic
95	#2087	C₂²	1	1	yes	characteristic
96	#2086	C₂²	1	1	yes	characteristic
97	#2086	C₂²	1	1	yes	characteristic
98	#2086	C₂²	1	1	yes	characteristic
99	#2068	C₂²	1	1	yes	characteristic
100	#2067	C₂²	1	1	yes	characteristic
101	#2066	C₂²	1	1	yes	characteristic
102	#2066	C₂²	1	1	yes	characteristic
103	#2066	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	#2059	C₂²	1	1	yes	characteristic
109	#2058	C₂²	1	1	yes	characteristic
110	#2058	C₂²	1	1	yes	characteristic
111	#2026	C₂²	1	1	yes	characteristic
112	#2025	C₂²	1	1	yes	characteristic
113	#2024	C₂²	1	1	yes	characteristic
114	#2023	C₂²	1	1	yes	characteristic
115	#1989	C₂²	1	1	yes	characteristic
116	#1989	C₂²	1	1	yes	characteristic
117	#1989	C₂²	1	1	yes	characteristic
118	#1989	C₂²	1	1	yes	characteristic
119	#1989	C₂²	1	1	yes	characteristic
120	#1989	C₂²	1	1	yes	characteristic
121	#1988	C₂²	1	1	yes	characteristic
122	#1987	C₂²	1	1	yes	characteristic
123	#1983	C₂²	1	1	yes	characteristic
124	#1983	C₂²	1	1	yes	characteristic
125	#1983	C₂²	1	1	yes	characteristic
126	#1983	C₂²	1	1	yes	characteristic
127	#1949	C₂²	1	1	yes	characteristic
128	#1949	C₂²	1	1	yes	characteristic
129	#1948	C₂²	1	1	yes	characteristic
130	#1948	C₂²	1	1	yes	characteristic
131	#1948	C₂²	1	1	yes	characteristic
132	#1948	C₂²	1	1	yes	characteristic
133	#1947	C₂²	1	1	yes	characteristic
134	#1947	C₂²	1	1	yes	characteristic
135	#1947	C₂²	1	1	yes	characteristic
136	#1947	C₂²	1	1	yes	characteristic
137	#1947	C₂²	1	1	yes	characteristic
138	#1947	C₂²	1	1	yes	characteristic
139	#1921	C₂²	1	1	yes	characteristic
140	#1920	C₂²	1	1	yes	characteristic
141	#1920	C₂²	1	1	yes	characteristic
142	#1920	C₂²	1	1	yes	characteristic
143	#1919	C₂²	1	1	yes	characteristic
144	#1919	C₂²	1	1	yes	characteristic
145	#1919	C₂²	1	1	yes	characteristic
146	#1918	C₂²	1	1	yes	characteristic
147	#1875	C₂²	1	1	yes	characteristic
148	#1875	C₂²	1	1	yes	characteristic
149	#1874	C₂²	1	1	yes	characteristic
150	#1874	C₂²	1	1	yes	characteristic
151	#1873	C₂²	1	1	yes	characteristic
152	#1873	C₂²	1	1	yes	characteristic
153	#1872	C₂²	1	1	yes	characteristic
154	#1872	C₂²	1	1	yes	characteristic
155	#1865	C₂²	1	1	yes	characteristic
156	#1864	C₂²	1	1	yes	characteristic
157	#1863	C₂²	1	1	yes	characteristic
158	#1863	C₂²	1	1	yes	characteristic
159	#1863	C₂²	1	1	yes	characteristic
160	#1862	C₂²	1	1	yes	characteristic
161	#1862	C₂²	1	1	yes	characteristic
162	#1862	C₂²	1	1	yes	characteristic
163	#1854	C₂²	1	1	yes	characteristic
164	#1854	C₂²	1	1	yes	characteristic
165	#1854	C₂²	1	1	yes	characteristic
166	#1854	C₂²	1	1	yes	characteristic
167	#1853	C₂²	1	1	yes	characteristic
168	#1853	C₂²	1	1	yes	characteristic
169	#1852	C₂²	1	1	yes	characteristic
170	#1852	C₂²	1	1	yes	characteristic
171	#1843	C₂²	1	1	yes	characteristic
172	#1843	C₂²	1	1	yes	characteristic
173	#1832	C₂²	1	1	yes	characteristic
174	#1832	C₂²	1	1	yes	characteristic
175	#1805	C₂²	1	1	yes	characteristic
176	#1804	C₂²	1	1	yes	characteristic
177	#1803	C₂²	1	1	yes	characteristic
178	#1802	C₂²	1	1	yes	characteristic
179	#1798	C₂²	1	1	yes	characteristic
180	#1798	C₂²	1	1	yes	characteristic
181	#1798	C₂²	1	1	yes	characteristic
182	#1798	C₂²	1	1	yes	characteristic
183	#1776	C₂²	1	1	yes	characteristic
184	#1776	C₂²	1	1	yes	characteristic
185	#1776	C₂²	1	1	yes	characteristic
186	#1776	C₂²	1	1	yes	characteristic
187	#1776	C₂²	1	1	yes	characteristic
188	#1776	C₂²	1	1	yes	characteristic
189	#1776	C₂²	1	1	yes	characteristic
190	#1776	C₂²	1	1	yes	characteristic
191	#1767	C₂²	1	1	yes	characteristic
192	#1767	C₂²	1	1	yes	characteristic
193	#1767	C₂²	1	1	yes	characteristic
194	#1767	C₂²	1	1	yes	characteristic
195	#1763	C₂²	1	1	yes	characteristic
196	#1763	C₂²	1	1	yes	characteristic
197	#1763	C₂²	1	1	yes	characteristic
198	#1763	C₂²	1	1	yes	characteristic
199	#1762	C₂²	1	1	yes	characteristic
200	#1762	C₂²	1	1	yes	characteristic
201	#1762	C₂²	1	1	yes	characteristic
202	#1762	C₂²	1	1	yes	characteristic
203	#544	—	2	4	no	—
204	#544	—	2	4	no	—
205	C₂×C₄⋊Q₈	—	2	1	no	—
206	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
208	#529	—	2	4	no	—
209	#529	Q₈	1	8	yes	complemented
210	C₂×#126	—	2	1	no	—
211	C₂×#125	—	2	1	no	—
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#125	C₂³	1	1	yes	characteristic
214	C₂×#125	C₂³	1	1	yes	characteristic
215	C₂×#124	C₂³	1	1	yes	characteristic
216	C₂×#123	—	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×#121	C₂³	1	1	yes	characteristic
221	C₂×C₄×Q₈	—	2	1	no	—
222	C₂×C₄×Q₈	—	2	1	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×D₄	—	2	1	no	—
227	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×#117	—	2	1	no	—
231	C₂×#117	—	2	1	no	—
232	C₂×#117	—	2	1	no	—
233	C₂×#117	C₂³	1	1	yes	characteristic
234	C₂×#117	C₂³	1	1	yes	characteristic
235	C₂×#117	C₂³	1	1	yes	characteristic
236	C₂×#117	C₂³	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂²×C₄²	—	2	1	no	—
240	C₂²×C₄²	—	2	1	no	—
241	C₂²×C₄²	C₂³	1	1	yes	characteristic
242	#479	—	2	4	no	—
243	#478	—	2	4	no	—
244	#476	—	2	4	no	—
245	#475	—	2	4	no	—
246	#432	—	2	4	no	—
247	#432	—	2	4	no	—
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
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×#107	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×#106	C₂³	1	1	yes	characteristic
260	C₂×#106	C₂³	1	1	yes	characteristic
261	C₂×#106	C₂³	1	1	yes	characteristic
262	C₂×#106	C₂³	1	1	yes	characteristic
263	C₂×#106	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₈	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×#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×#102	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	#391	—	2	1	no	—
301	#391	—	2	1	no	—
302	#391	—	2	1	no	—
303	#391	—	2	1	no	—
304	#391	—	2	1	no	—
305	#391	—	2	1	no	—
306	#391	C₂³	1	1	yes	characteristic
307	#391	C₂³	1	1	yes	characteristic
308	#390	—	2	1	no	—
309	#390	—	2	1	no	—
310	#390	C₂³	1	1	yes	characteristic
311	#390	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
326	#389	—	2	1	no	—
327	#389	—	2	1	no	—
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	#389	C₂³	1	1	yes	characteristic
335	#389	C₂³	1	1	yes	characteristic
336	#389	C₂³	1	1	yes	characteristic
337	#389	C₂³	1	1	yes	characteristic
338	#389	C₂³	1	1	yes	characteristic
339	#389	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
350	#388	—	2	1	no	—
351	#388	—	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	#386	—	2	1	no	—
373	#386	—	2	1	no	—
374	#385	—	2	1	no	—
375	#385	—	2	1	no	—
376	#385	—	2	1	no	—
377	#385	—	2	1	no	—
378	#385	—	2	1	no	—
379	#385	—	2	1	no	—
380	#385	—	2	1	no	—
381	#385	—	2	1	no	—
382	#385	—	2	1	no	—
383	#385	—	2	1	no	—
384	#384	—	2	1	no	—
385	#384	C₂³	1	1	yes	characteristic
386	#384	C₂³	1	1	yes	characteristic
387	#384	C₂³	1	1	yes	characteristic
388	#384	C₂³	1	1	yes	characteristic
389	#382	—	2	1	no	—
390	#382	—	2	1	no	—
391	#382	C₂³	1	1	yes	characteristic
392	#382	C₂³	1	1	yes	characteristic
393	#380	—	2	1	no	—
394	#380	—	2	1	no	—
395	#380	—	2	1	no	—
396	#380	C₂³	1	1	yes	characteristic
397	#380	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
412	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
413	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
414	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
416	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
430	C₄×C₂²⋊C₄	—	2	1	no	—
431	C₄×C₂²⋊C₄	—	2	1	no	—
432	C₄×C₂²⋊C₄	—	2	1	no	—
433	C₄×C₂²⋊C₄	—	2	1	no	—
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
438	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
439	#376	—	2	1	no	—
440	#376	—	2	1	no	—
441	#376	C₂³	1	1	yes	characteristic
442	#376	C₂³	1	1	yes	characteristic
443	C₂×#95	—	2	1	no	—
444	C₄³	—	2	1	no	—
445	C₄³	—	2	1	no	—
446	C₄³	C₂³	1	1	yes	characteristic
447	C₄³	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#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	#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	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	C₂⁴	1	1	yes	characteristic
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	—	2	1	no	—
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
500	C₂³×C₄	C₂⁴	1	1	yes	characteristic
501	C₂²×C₈	C₂⁴	1	1	yes	characteristic
502	C₂²×C₈	C₂⁴	1	1	yes	characteristic
503	C₂²×C₈	C₂⁴	1	1	yes	characteristic
504	C₂²×C₈	C₂⁴	1	1	yes	characteristic
505	C₂²×C₈	C₂⁴	1	1	yes	characteristic
506	C₂²×C₈	C₂⁴	1	1	yes	characteristic
507	C₂²×C₈	C₂⁴	1	1	yes	characteristic
508	C₂²×C₈	C₂⁴	1	1	yes	characteristic
509	C₄⋊Q₈	—	2	8	no	—
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	#41	1	4	yes	—
514	#126	—	2	8	no	—
515	#125	—	2	8	no	—
516	#125	—	2	2	no	—
517	#125	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	C₂×Q₈	1	4	yes	—
521	#125	#41	1	4	yes	—
522	#124	—	2	2	no	—
523	#124	C₂×Q₈	1	4	yes	—
524	#123	—	2	8	no	—
525	C₂²⋊Q₈	—	2	8	no	—
526	C₂²⋊Q₈	—	2	8	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	C₂×Q₈	1	4	yes	—
529	#121	—	2	2	no	—
530	#121	C₂×Q₈	1	4	yes	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	4	1	no	—
535	C₄×Q₈	—	4	1	no	—
536	C₄×Q₈	—	8	2	no	—
537	C₄×Q₈	—	8	2	no	—
538	C₄×Q₈	C₂×Q₈	1	4	yes	—
539	C₄×D₄	—	2	8	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	4	1	no	—
544	C₄×D₄	—	4	1	no	—
545	C₄×D₄	C₂×Q₈	1	4	yes	—
546	#117	—	2	2	no	—
547	#117	—	2	2	no	—
548	#117	—	2	8	no	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	—	4	1	no	—
552	#117	—	4	1	no	—
553	#117	—	4	1	no	—
554	#117	—	4	1	no	—
555	#117	—	8	2	no	—
556	#117	—	8	2	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	2	no	—
569	C₂×C₄⋊C₄	—	2	2	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	—	4	1	no	—
594	C₂×C₄⋊C₄	—	4	1	no	—
595	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×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×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	1	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	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	—	8	2	no	—
652	C₂×C₄²	—	8	2	no	—
653	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
654	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄²	C₂×Q₈	1	4	yes	—
664	C₂×C₄²	#41	1	4	yes	—
665	C₂×C₄²	C₂⁴	1	1	yes	characteristic
666	C₂×C₄²	C₂⁴	1	1	yes	characteristic
667	C₂×C₄²	C₂⁴	1	1	yes	characteristic
668	C₂×C₄²	C₂⁴	1	1	yes	characteristic
669	C₂×C₄²	C₂⁴	1	1	yes	characteristic
670	C₂×C₄²	C₂⁴	1	1	yes	characteristic
671	#107	—	2	2	no	—
672	#107	—	2	2	no	—
673	#107	—	4	1	no	—
674	#107	—	4	1	no	—
675	#107	—	4	1	no	—
676	#107	—	4	1	no	—
677	#107	—	4	1	no	—
678	#107	—	4	1	no	—
679	#106	—	2	2	no	—
680	#106	—	2	2	no	—
681	#106	—	2	2	no	—
682	#106	—	2	2	no	—
683	#106	—	2	2	no	—
684	#106	—	2	2	no	—
685	#106	—	4	1	no	—
686	#106	—	4	1	no	—
687	C₄⋊C₈	—	2	2	no	—
688	C₄⋊C₈	—	2	2	no	—
689	C₄⋊C₈	—	2	2	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	—	2	2	no	—
695	C₄⋊C₈	—	4	1	no	—
696	C₄⋊C₈	—	4	1	no	—
697	C₄⋊C₈	—	4	1	no	—
698	C₄⋊C₈	—	4	1	no	—
699	#103	—	2	2	no	—
700	#103	—	2	2	no	—
701	#103	—	2	2	no	—
702	#103	—	2	2	no	—
703	#103	—	4	1	no	—
704	#103	—	4	1	no	—
705	#103	—	4	1	no	—
706	#103	—	4	1	no	—
707	#102	—	2	2	no	—
708	#102	—	2	2	no	—
709	#102	—	2	2	no	—
710	#102	—	2	2	no	—
711	#102	—	4	1	no	—
712	#102	—	4	1	no	—
713	#102	—	4	1	no	—
714	#102	—	4	1	no	—
715	C₂²⋊C₈	—	2	2	no	—
716	C₂²⋊C₈	—	2	2	no	—
717	C₂²⋊C₈	—	2	2	no	—
718	C₂²⋊C₈	—	2	2	no	—
719	#97	—	2	2	no	—
720	#97	—	2	2	no	—
721	#97	—	2	2	no	—
722	#97	—	2	2	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	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	C₂×D₄	1	1	yes	characteristic
760	#95	C₂×D₄	1	1	yes	characteristic
761	#95	C₂×D₄	1	1	yes	characteristic
762	#95	C₂×D₄	1	1	yes	characteristic
763	#95	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	—	2	1	no	—
768	C₂⁴	C₂²×D₄	1	1	yes	characteristic
769	C₂×Q₈	—	2	4	no	—
770	C₂×Q₈	—	2	4	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	1	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	8	1	no	—
777	C₂×Q₈	—	8	1	no	—
778	C₂×Q₈	—	8	1	no	—
779	C₂×Q₈	—	8	1	no	—
780	C₂×Q₈	C₂²×Q₈	1	2	yes	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	8	1	no	—
788	C₂×D₄	—	8	1	no	—
789	C₂×D₄	C₂²×Q₈	1	2	yes	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	4	no	—
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	—	4	1	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	8	1	no	—
821	C₂²×C₄	—	8	1	no	—
822	C₂²×C₄	—	8	1	no	—
823	C₂²×C₄	—	8	1	no	—
824	C₂²×C₄	—	8	1	no	—
825	C₂²×C₄	—	8	1	no	—
826	C₂²×C₄	—	8	1	no	—
827	C₂²×C₄	—	8	1	no	—
828	C₂²×C₄	C₂²⋊Q₈	1	4	yes	—
829	C₂²×C₄	C₂²⋊Q₈	1	4	yes	—
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	C₂²×D₄	1	1	yes	characteristic
843	C₂²×C₄	C₂²×Q₈	1	2	yes	—
844	C₂²×C₄	C₂×#41	1	2	yes	—
845	C₂²×C₄	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
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	4	no	—
879	C₄⋊C₄	—	2	4	no	—
880	C₄⋊C₄	—	2	4	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	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	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	8	1	no	—
911	C₄⋊C₄	—	8	1	no	—
912	C₄⋊C₄	—	8	1	no	—
913	C₄⋊C₄	—	8	1	no	—
914	C₄⋊C₄	—	8	1	no	—
915	C₄⋊C₄	—	8	1	no	—
916	C₄⋊C₄	—	8	1	no	—
917	C₄⋊C₄	—	8	1	no	—
918	C₄⋊C₄	—	8	1	no	—
919	C₄⋊C₄	—	8	1	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	—	8	1	no	—
929	C₄⋊C₄	—	8	1	no	—
930	C₄⋊C₄	C₂²×Q₈	1	2	yes	—
931	C₄⋊C₄	C₂²×Q₈	1	2	yes	—
932	C₄⋊C₄	C₂×#41	1	2	yes	—
933	C₄⋊C₄	C₂×#41	1	2	yes	—
934	C₄⋊C₄	C₂×#41	1	2	yes	—
935	C₄⋊C₄	C₂×#41	1	2	yes	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	4	1	no	—
945	C₂²⋊C₄	—	4	1	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	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	C₂²⋊C₄	—	8	1	no	—
955	C₄²	—	2	4	no	—
956	C₄²	—	2	4	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	4	1	no	—
964	C₄²	—	4	1	no	—
965	C₄²	—	4	1	no	—
966	C₄²	—	4	1	no	—
967	C₄²	—	4	1	no	—
968	C₄²	—	4	1	no	—
969	C₄²	—	4	1	no	—
970	C₄²	—	4	1	no	—
971	C₄²	—	4	2	no	—
972	C₄²	—	4	2	no	—
973	C₄²	—	4	2	no	—
974	C₄²	—	4	2	no	—
975	C₄²	—	4	2	no	—
976	C₄²	—	4	2	no	—
977	C₄²	—	4	2	no	—
978	C₄²	—	4	2	no	—
979	C₄²	—	4	2	no	—
980	C₄²	—	8	1	no	—
981	C₄²	—	8	1	no	—
982	C₄²	—	8	1	no	—
983	C₄²	—	8	1	no	—
984	C₄²	—	8	1	no	—
985	C₄²	—	8	1	no	—
986	C₄²	—	8	1	no	—
987	C₄²	—	8	1	no	—
988	C₄²	C₂²⋊Q₈	1	4	yes	—
989	C₄²	C₂²⋊Q₈	1	4	yes	—
990	C₄²	C₂²×Q₈	1	2	yes	—
991	C₄²	C₂²×Q₈	1	2	yes	—
992	C₄²	C₂×#41	1	2	yes	—
993	C₄²	C₂×#41	1	2	yes	—
994	C₄²	C₂×#41	1	2	yes	—
995	C₄²	C₂×#41	1	2	yes	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	2	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	C₂×C₂²⋊Q₈	1	2	yes	—
1010	C₂³	C₂³×D₄	1	1	yes	characteristic
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	4	1	no	—
1014	Q₈	—	4	1	no	—
1015	Q₈	—	8	4	no	—
1016	Q₈	—	8	4	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	4	1	no	—
1020	D₄	—	4	1	no	—
1021	D₄	—	8	4	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	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	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	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	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	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	—	4	4	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	8	no	—
1068	C₂×C₄	—	4	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	1	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	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	—	8	4	no	—
1107	C₂×C₄	—	8	4	no	—
1108	C₂×C₄	—	8	4	no	—
1109	C₂×C₄	—	8	4	no	—
1110	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1111	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1112	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1113	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1114	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1115	C₂×C₄	#525	1	2	yes	—
1116	C₂×C₄	#525	1	2	yes	—
1117	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
1118	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1119	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1120	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1121	C₂×C₄	#585	1	1	yes	characteristic
1122	C₂×C₄	#585	1	1	yes	characteristic
1123	C₈	—	4	1	no	—
1124	C₈	—	4	1	no	—
1125	C₈	—	4	1	no	—
1126	C₈	—	4	1	no	—
1127	C₈	—	4	1	no	—
1128	C₈	—	4	1	no	—
1129	C₈	—	4	1	no	—
1130	C₈	—	4	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	8	1	no	—
1142	C₂²	—	8	1	no	—
1143	C₂²	—	8	1	no	—
1144	C₂²	—	8	1	no	—
1145	C₂²	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
1146	C₂²	C₂×#525	1	1	yes	characteristic
1147	C₂²	#3449	1	1	yes	characteristic
1148	C₂²	#3585	1	1	yes	characteristic
1149	C₂²	#3585	1	1	yes	characteristic
1150	C₂²	#3586	1	1	yes	characteristic
1151	C₂²	#3586	1	1	yes	characteristic
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	8	1	no	—
1173	C₄	—	8	1	no	—
1174	C₄	—	8	1	no	—
1175	C₄	—	8	1	no	—
1176	C₄	—	8	1	no	—
1177	C₄	—	8	1	no	—
1178	C₄	—	8	1	no	—
1179	C₄	—	8	1	no	—
1180	C₄	Q₈×#41	1	1	yes	characteristic
1181	C₄	Q₈×#41	1	1	yes	characteristic
1182	C₄	#3480	1	1	yes	characteristic
1183	C₄	#3480	1	1	yes	characteristic
1184	C₂	—	4	2	no	—
1185	C₂	—	8	2	no	—
1186	C₂	#34952	1	1	yes	characteristic
1187	C₂	#60492	1	1	yes	characteristic
1188	C₂	#60493	1	1	yes	characteristic
1189	C₂	#60575	1	1	yes	characteristic
1190	C₂	#60576	1	1	yes	characteristic
1191	C₂	#60974	1	1	yes	characteristic
1192	C₂	#60975	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#121	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#117 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₄×#544	C₂	semidirect
3. #29294	C₂	semidirect
4. #29292	C₂	semidirect
5. #29285	C₂	semidirect
6. #29284	C₂	semidirect
7. #29268	C₂	semidirect
8. #29267	C₂	semidirect
9. #29253	C₂	semidirect
10. #29250	C₂	semidirect
13. #28293	C₂	semidirect
14. #28289	C₂	semidirect
15. #27690	C₂	semidirect
17. #24310	C₂	semidirect
19. #23785	C₂	semidirect
20. #23784	C₂	semidirect
21. #23782	C₂	semidirect
22. #23781	C₂	semidirect
23. #21618	C₂	semidirect
24. #21617	C₂	semidirect
25. #21615	C₂	semidirect
26. #21614	C₂	semidirect
29. #21365	C₂	semidirect
30. #21364	C₂	semidirect
31. #20811	C₂	semidirect
209. #529	Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#544	2
#34084	2
#29294	2
#29292	2
#29285	2
#29284	2
#29268	2
#29267	2
#29253	2
#29250	2
#29248	2
#29247	2
#28293	2
#28289	2
#27690	2
#27687	2
#24310	2
#24309	2
#23785	2
#23784	2
#23782	2
#23781	2
#21618	2
#21617	2
#21615	2
#21614	2
#21396	2
#21391	2
#21365	2
#21364	2
#20811	2