Subgroups — #6384604

Order 512.

1801 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3364	C₂	1	1	yes	maximal, characteristic
2	#34336	C₂	1	1	yes	maximal, characteristic, complemented
3	#34326	C₂	1	1	yes	maximal, characteristic
4	#23225	C₂	1	1	yes	maximal, characteristic
5	#23224	C₂	1	1	yes	maximal, characteristic
6	#23221	C₂	1	1	yes	maximal, characteristic, complemented
7	#23079	C₂	1	1	yes	maximal, characteristic
8	#23078	C₂	1	1	yes	maximal, characteristic, complemented
9	#23064	C₂	1	1	yes	maximal, characteristic, complemented
10	#23014	C₂	1	1	yes	maximal, characteristic, complemented
11	#23013	C₂	1	1	yes	maximal, characteristic
12	#23000	C₂	1	1	yes	maximal, characteristic
13	#22765	C₂	1	1	yes	maximal, characteristic
14	#22763	C₂	1	1	yes	maximal, characteristic, complemented
15	#22761	C₂	1	1	yes	maximal, characteristic, complemented
16	#22741	C₂	1	1	yes	maximal, characteristic, complemented
17	#22548	C₂	1	1	yes	maximal, characteristic
18	#22527	C₂	1	1	yes	maximal, characteristic, complemented
19	#21648	C₂	1	1	yes	maximal, characteristic
20	#21645	C₂	1	1	yes	maximal, characteristic, complemented
21	#21643	C₂	1	1	yes	maximal, characteristic
22	#21624	C₂	1	1	yes	maximal, characteristic
23	#21622	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#479	C₂	1	1	yes	maximal, characteristic, complemented
25	#21516	C₂	1	1	yes	maximal, characteristic, complemented
26	#21511	C₂	1	1	yes	maximal, characteristic
27	C₄×#464	C₂	1	1	yes	maximal, characteristic
28	#20521	C₂	1	1	yes	maximal, characteristic, complemented
29	#20507	C₂	1	1	yes	maximal, characteristic, complemented
30	#20506	C₂	1	1	yes	maximal, characteristic
31	C₄×#441	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#557	C₂²	1	1	yes	characteristic
33	C₂×#556	C₂²	1	1	yes	characteristic
34	#3364	C₄	1	16	yes	complemented
35	C₂×#488	C₂²	1	1	yes	characteristic
36	C₂×#488	C₂²	1	1	yes	characteristic
37	C₂×#487	C₂²	1	1	yes	characteristic
38	C₂×#479	C₂²	1	1	yes	characteristic
39	C₂×#479	C₂²	1	1	yes	characteristic
40	C₂×#474	C₂²	1	1	yes	characteristic
41	C₂×#464	C₂²	1	1	yes	characteristic
42	C₂×#464	C₂²	1	1	yes	characteristic
43	C₂×#462	C₂²	1	1	yes	characteristic
44	C₂×#446	C₂²	1	1	yes	characteristic
45	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic
46	C₂×#441	C₂²	1	1	yes	characteristic
47	C₂×#441	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
51	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
52	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
53	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
54	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
55	#2373	—	2	1	no	—
56	#2373	—	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	#2369	—	2	1	no	—
62	#2369	C₂²	1	1	yes	characteristic
63	#2368	—	2	1	no	—
64	#2367	C₂²	1	1	yes	characteristic
65	#2367	C₂²	1	1	yes	characteristic
66	#2365	C₂²	1	1	yes	characteristic
67	#2357	C₂²	1	1	yes	characteristic
68	#2356	C₂²	1	1	yes	characteristic
69	#2355	—	2	1	no	—
70	#2355	C₂²	1	1	yes	characteristic
71	#2355	C₂²	1	1	yes	characteristic
72	#2355	C₂²	1	1	yes	characteristic
73	#2351	C₂²	1	1	yes	characteristic
74	#2351	C₂²	1	1	yes	characteristic
75	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	#2343	—	2	1	no	—
77	#2334	—	2	1	no	—
78	#2332	—	2	1	no	—
79	#2331	—	2	1	no	—
80	#2331	C₂²	1	1	yes	characteristic
81	#2330	—	2	1	no	—
82	#2330	C₂²	1	1	yes	characteristic
83	#2327	C₂²	1	1	yes	characteristic
84	#2326	C₂²	1	1	yes	characteristic
85	C₄×#125	—	2	1	no	—
86	C₄×#125	C₂²	1	1	yes	characteristic
87	C₄×#126	—	2	1	no	—
88	C₄×#124	C₂²	1	1	yes	characteristic
89	#2298	—	2	1	no	—
90	#2295	—	2	1	no	—
91	#2295	C₂²	1	1	yes	characteristic
92	#2276	C₂²	1	1	yes	characteristic
93	#2276	C₂²	1	1	yes	characteristic
94	#2276	C₂²	1	1	yes	characteristic
95	#2275	C₂²	1	1	yes	characteristic
96	C₄²×Q₈	C₂²	1	1	yes	characteristic
97	C₄²×Q₈	C₂²	1	1	yes	characteristic
98	#1993	C₂²	1	1	yes	characteristic
99	#1992	C₂²	1	1	yes	characteristic
100	#1991	C₂²	1	1	yes	characteristic
101	#1989	C₂²	1	1	yes	characteristic
102	#1989	C₂²	1	1	yes	characteristic
103	#1987	C₂²	1	1	yes	characteristic
104	#1983	C₂²	1	1	yes	characteristic
105	#1983	C₂²	1	1	yes	characteristic
106	#1981	C₂²	1	1	yes	characteristic
107	#1960	C₂²	1	1	yes	characteristic
108	#1959	C₂²	1	1	yes	characteristic
109	#1958	C₂²	1	1	yes	characteristic
110	#1949	C₂²	1	1	yes	characteristic
111	#1949	C₂²	1	1	yes	characteristic
112	#1949	C₂²	1	1	yes	characteristic
113	#1949	C₂²	1	1	yes	characteristic
114	#1948	C₂²	1	1	yes	characteristic
115	#1948	C₂²	1	1	yes	characteristic
116	#1936	C₂²	1	1	yes	characteristic
117	#1936	C₂²	1	1	yes	characteristic
118	#1936	C₂²	1	1	yes	characteristic
119	#1935	C₂²	1	1	yes	characteristic
120	#1935	C₂²	1	1	yes	characteristic
121	#1935	C₂²	1	1	yes	characteristic
122	#1935	C₂²	1	1	yes	characteristic
123	#1935	C₂²	1	1	yes	characteristic
124	#1934	C₂²	1	1	yes	characteristic
125	#1933	C₂²	1	1	yes	characteristic
126	#1933	C₂²	1	1	yes	characteristic
127	#1933	C₂²	1	1	yes	characteristic
128	#1928	C₂²	1	1	yes	characteristic
129	#1927	C₂²	1	1	yes	characteristic
130	#1927	C₂²	1	1	yes	characteristic
131	#1927	C₂²	1	1	yes	characteristic
132	#1926	C₂²	1	1	yes	characteristic
133	#1925	C₂²	1	1	yes	characteristic
134	#1921	C₂²	1	1	yes	characteristic
135	#1921	C₂²	1	1	yes	characteristic
136	#1920	C₂²	1	1	yes	characteristic
137	#1920	C₂²	1	1	yes	characteristic
138	#1918	C₂²	1	1	yes	characteristic
139	#1918	C₂²	1	1	yes	characteristic
140	#1880	C₂²	1	1	yes	characteristic
141	#1880	C₂²	1	1	yes	characteristic
142	#1878	C₂²	1	1	yes	characteristic
143	#1878	C₂²	1	1	yes	characteristic
144	#1878	C₂²	1	1	yes	characteristic
145	#1878	C₂²	1	1	yes	characteristic
146	#1865	C₂²	1	1	yes	characteristic
147	#1865	C₂²	1	1	yes	characteristic
148	#1865	C₂²	1	1	yes	characteristic
149	#1864	C₂²	1	1	yes	characteristic
150	#1863	C₂²	1	1	yes	characteristic
151	#1862	C₂²	1	1	yes	characteristic
152	#1835	C₂²	1	1	yes	characteristic
153	#1835	C₂²	1	1	yes	characteristic
154	#1834	C₂²	1	1	yes	characteristic
155	#1805	C₂²	1	1	yes	characteristic
156	#1805	C₂²	1	1	yes	characteristic
157	#1805	C₂²	1	1	yes	characteristic
158	#1804	C₂²	1	1	yes	characteristic
159	#1803	C₂²	1	1	yes	characteristic
160	#1803	C₂²	1	1	yes	characteristic
161	#1776	C₂²	1	1	yes	characteristic
162	#1776	C₂²	1	1	yes	characteristic
163	C₄×#107	C₂²	1	1	yes	characteristic
164	C₄×#107	C₂²	1	1	yes	characteristic
165	C₄×#107	C₂²	1	1	yes	characteristic
166	C₄×#106	C₂²	1	1	yes	characteristic
167	C₄×#106	C₂²	1	1	yes	characteristic
168	C₄×#106	C₂²	1	1	yes	characteristic
169	C₄×#106	C₂²	1	1	yes	characteristic
170	#1771	C₂²	1	1	yes	characteristic
171	#1771	C₂²	1	1	yes	characteristic
172	#1770	C₂²	1	1	yes	characteristic
173	#1770	C₂²	1	1	yes	characteristic
174	#1770	C₂²	1	1	yes	characteristic
175	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
176	#1768	C₂²	1	1	yes	characteristic
177	#1768	C₂²	1	1	yes	characteristic
178	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic
179	#1763	C₂²	1	1	yes	characteristic
180	#1763	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	#1763	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	#1762	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	C₄×#103	C₂²	1	1	yes	characteristic
196	C₄×#103	C₂²	1	1	yes	characteristic
197	C₄×#103	C₂²	1	1	yes	characteristic
198	C₄×#103	C₂²	1	1	yes	characteristic
199	C₄×#103	C₂²	1	1	yes	characteristic
200	C₄×#102	C₂²	1	1	yes	characteristic
201	#1726	C₂²	1	1	yes	characteristic
202	#1726	C₂²	1	1	yes	characteristic
203	C₄×#97	C₂²	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	#557	—	2	4	no	—
208	#557	C₂×C₄	1	8	yes	complemented
209	#556	—	2	4	no	—
210	#556	C₂×C₄	1	8	yes	—
211	C₂×C₄⋊Q₈	—	2	1	no	—
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×#126	—	2	1	no	—
215	C₂×#126	—	2	1	no	—
216	C₂×#125	—	2	1	no	—
217	C₂×#125	—	2	1	no	—
218	C₂×#125	C₂³	1	1	yes	characteristic
219	C₂×#125	C₂³	1	1	yes	characteristic
220	C₂×#124	C₂³	1	1	yes	characteristic
221	C₂×#124	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₄×Q₈	—	2	1	no	—
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×Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
241	C₂×#117	—	2	1	no	—
242	#488	C₂×C₄	1	8	yes	—
243	#488	C₂×C₄	1	8	yes	—
244	#487	C₂×C₄	1	8	yes	complemented
245	#479	C₂×C₄	1	8	yes	complemented
246	#479	C₂×C₄	1	8	yes	complemented
247	#474	C₂×C₄	1	8	yes	—
248	#464	C₂×C₄	1	8	yes	—
249	#464	C₂×C₄	1	8	yes	—
250	#462	C₂×C₄	1	8	yes	complemented
251	#446	—	2	4	no	—
252	C₈×Q₈	C₂×C₄	1	8	yes	complemented
253	#441	—	2	4	no	—
254	#441	—	2	4	no	—
255	C₄×Q₁₆	—	2	4	no	—
256	C₄×Q₁₆	—	2	4	no	—
257	C₄×Q₁₆	C₂×C₄	1	8	yes	complemented
258	C₄×Q₁₆	C₂×C₄	1	8	yes	complemented
259	C₄×SD₁₆	—	2	4	no	—
260	C₄×SD₁₆	—	2	4	no	—
261	C₄×SD₁₆	C₂×C₄	1	8	yes	—
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×#106	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂³	1	1	yes	characteristic
268	C₂×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#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×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#103	C₂³	1	1	yes	characteristic
295	C₂×#103	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×#102	C₂³	1	1	yes	characteristic
299	C₂×#102	C₂³	1	1	yes	characteristic
300	C₂×#102	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×#102	C₂³	1	1	yes	characteristic
303	C₂×#97	C₂³	1	1	yes	characteristic
304	C₂×#97	C₂³	1	1	yes	characteristic
305	C₂×#97	C₂³	1	1	yes	characteristic
306	C₂×#97	C₂³	1	1	yes	characteristic
307	C₂×#97	C₂³	1	1	yes	characteristic
308	C₂×#97	C₂³	1	1	yes	characteristic
309	C₂×#97	C₂³	1	1	yes	characteristic
310	C₂×#97	C₂³	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
314	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
319	#391	—	2	1	no	—
320	#391	—	2	1	no	—
321	#391	—	2	1	no	—
322	#391	—	2	1	no	—
323	#391	—	2	1	no	—
324	#391	—	2	1	no	—
325	#391	D₄	1	1	yes	characteristic
326	#391	D₄	1	1	yes	characteristic
327	#391	C₂³	1	1	yes	characteristic
328	#391	C₂³	1	1	yes	characteristic
329	#391	C₂³	1	1	yes	characteristic
330	#391	C₂³	1	1	yes	characteristic
331	#390	C₂³	1	1	yes	characteristic
332	#390	C₂³	1	1	yes	characteristic
333	#389	—	2	1	no	—
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	D₄	1	1	yes	characteristic
346	#389	D₄	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	#388	—	2	1	no	—
354	#388	—	2	1	no	—
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	#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	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	D₄	1	1	yes	characteristic
388	#387	D₄	1	1	yes	characteristic
389	#387	D₄	1	1	yes	characteristic
390	#387	D₄	1	1	yes	characteristic
391	#385	—	2	1	no	—
392	#385	—	2	1	no	—
393	#385	—	2	1	no	—
394	#385	—	2	1	no	—
395	#384	—	2	1	no	—
396	#384	C₂³	1	1	yes	characteristic
397	#384	C₂³	1	1	yes	characteristic
398	#383	—	2	1	no	—
399	#382	—	2	1	no	—
400	#382	—	2	1	no	—
401	#382	—	2	1	no	—
402	#382	C₂³	1	1	yes	characteristic
403	#382	C₂³	1	1	yes	characteristic
404	#382	C₂³	1	1	yes	characteristic
405	#382	C₂³	1	1	yes	characteristic
406	#381	—	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	—	2	1	no	—
425	C₄×C₄⋊C₄	—	2	1	no	—
426	C₄×C₄⋊C₄	—	2	1	no	—
427	C₄×C₄⋊C₄	—	2	1	no	—
428	C₄×C₄⋊C₄	—	2	1	no	—
429	C₄×C₄⋊C₄	—	2	1	no	—
430	C₄×C₄⋊C₄	—	2	1	no	—
431	C₄×C₄⋊C₄	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	—	2	1	no	—
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	C₄×C₂²⋊C₄	—	2	1	no	—
457	C₄×C₂²⋊C₄	—	2	1	no	—
458	C₄×C₂²⋊C₄	—	2	1	no	—
459	C₄×C₂²⋊C₄	—	2	1	no	—
460	C₄×C₂²⋊C₄	—	2	1	no	—
461	#376	—	2	1	no	—
462	#376	—	2	1	no	—
463	#376	—	2	1	no	—
464	#376	—	2	1	no	—
465	#376	C₂³	1	1	yes	characteristic
466	#376	C₂³	1	1	yes	characteristic
467	C₂×#95	—	2	1	no	—
468	C₄³	—	2	1	no	—
469	C₄³	—	2	1	no	—
470	C₄³	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	#340	C₂³	1	1	yes	characteristic
488	#340	C₂³	1	1	yes	characteristic
489	#340	C₂³	1	1	yes	characteristic
490	#340	C₂³	1	1	yes	characteristic
491	#340	C₂³	1	1	yes	characteristic
492	#340	C₂³	1	1	yes	characteristic
493	#340	C₂³	1	1	yes	characteristic
494	#340	C₂³	1	1	yes	characteristic
495	#340	C₂³	1	1	yes	characteristic
496	#340	C₂³	1	1	yes	characteristic
497	#336	C₂³	1	1	yes	characteristic
498	#336	C₂³	1	1	yes	characteristic
499	#336	C₂³	1	1	yes	characteristic
500	#336	C₂³	1	1	yes	characteristic
501	#336	C₂³	1	1	yes	characteristic
502	#336	C₂³	1	1	yes	characteristic
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
505	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
507	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
508	C₂²×D₄	C₂⁴	1	1	yes	characteristic
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂×Q₁₆	—	2	2	no	—
513	C₂×Q₁₆	—	2	2	no	—
514	C₂×Q₁₆	—	2	2	no	—
515	C₂×Q₁₆	—	2	2	no	—
516	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
517	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₄⋊Q₈	—	2	8	no	—
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
533	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
534	#126	—	2	8	no	—
535	#126	—	2	8	no	—
536	#125	—	2	8	no	—
537	#125	—	2	8	no	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	C₂²×C₄	1	4	yes	—
541	#125	C₂²×C₄	1	4	yes	—
542	#124	—	2	2	no	—
543	#124	—	2	2	no	—
544	#124	C₂²×C₄	1	4	yes	—
545	#124	C₂²×C₄	1	4	yes	—
546	C₂²⋊Q₈	—	2	8	no	—
547	C₄×Q₈	—	2	8	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	4	1	no	—
564	C₄×Q₈	—	4	1	no	—
565	C₄×Q₈	—	4	1	no	—
566	C₄×Q₈	—	4	1	no	—
567	C₄×Q₈	—	4	1	no	—
568	C₄×Q₈	C₂²×C₄	1	4	yes	—
569	C₄×Q₈	C₂²×C₄	1	4	yes	—
570	C₄×Q₈	C₂²×C₄	1	4	yes	—
571	C₄×Q₈	C₂²×C₄	1	4	yes	—
572	C₄×Q₈	C₂²×C₄	1	4	yes	—
573	C₄×Q₈	C₂²×C₄	1	4	yes	—
574	C₄×Q₈	#41	1	4	yes	—
575	C₄×Q₈	#41	1	4	yes	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	4	1	no	—
581	C₄×D₄	C₂²×C₄	1	4	yes	—
582	#117	—	2	8	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	—	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	C₂×D₄	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	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×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	—	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	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
676	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
677	C₂×C₄²	C₂×D₄	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	C₂×C₄²	C₂⁴	1	1	yes	characteristic
682	C₂×C₄²	C₂⁴	1	1	yes	characteristic
683	C₂×C₄²	C₂⁴	1	1	yes	characteristic
684	C₂×C₄²	C₂⁴	1	1	yes	characteristic
685	#107	—	2	2	no	—
686	#107	—	2	2	no	—
687	#107	C₂²×C₄	1	4	yes	—
688	#107	C₂²×C₄	1	4	yes	—
689	#106	—	2	2	no	—
690	#106	—	2	2	no	—
691	#106	—	2	2	no	—
692	#106	—	2	2	no	—
693	#106	C₂²×C₄	1	4	yes	—
694	C₄⋊C₈	—	2	2	no	—
695	C₄⋊C₈	—	2	2	no	—
696	C₄⋊C₈	—	2	2	no	—
697	C₄⋊C₈	C₂²×C₄	1	4	yes	—
698	C₄⋊C₈	C₂²×C₄	1	4	yes	—
699	C₄⋊C₈	C₂²×C₄	1	4	yes	—
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	—	4	1	no	—
708	#103	—	4	1	no	—
709	#103	—	4	1	no	—
710	#103	—	4	1	no	—
711	#103	C₂²×C₄	1	4	yes	—
712	#103	C₂²×C₄	1	4	yes	—
713	#103	C₂²×C₄	1	4	yes	—
714	#103	C₂²×C₄	1	4	yes	—
715	#103	C₂²×C₄	1	4	yes	—
716	#103	C₂²×C₄	1	4	yes	—
717	#103	C₂²×C₄	1	4	yes	—
718	#103	#41	1	4	yes	—
719	#102	—	2	2	no	—
720	#102	—	2	2	no	—
721	#102	—	4	1	no	—
722	#102	—	4	1	no	—
723	#102	C₂²×C₄	1	4	yes	—
724	#102	C₂²×C₄	1	4	yes	—
725	#102	C₂²×C₄	1	4	yes	—
726	#97	—	2	2	no	—
727	#97	—	2	2	no	—
728	#97	—	2	2	no	—
729	#97	—	2	2	no	—
730	#97	—	2	2	no	—
731	#97	—	4	1	no	—
732	#97	—	4	1	no	—
733	#97	—	4	1	no	—
734	C₄×C₈	—	2	2	no	—
735	C₄×C₈	—	2	2	no	—
736	C₄×C₈	—	2	2	no	—
737	C₄×C₈	—	2	2	no	—
738	C₄×C₈	—	2	2	no	—
739	C₄×C₈	C₂²×C₄	1	4	yes	—
740	C₄×C₈	C₂²×C₄	1	4	yes	—
741	C₄×C₈	C₂²×C₄	1	4	yes	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	C₂×D₄	1	1	yes	characteristic
781	#95	C₂×D₄	1	1	yes	characteristic
782	#95	C₂×D₄	1	1	yes	characteristic
783	#95	C₂×D₄	1	1	yes	characteristic
784	#95	C₂×D₄	1	1	yes	characteristic
785	#95	C₂×D₄	1	1	yes	characteristic
786	#95	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	#95	C₂×D₄	1	1	yes	characteristic
792	#95	C₂×D₄	1	1	yes	characteristic
793	#95	C₂×D₄	1	1	yes	characteristic
794	C₂⁴	—	2	1	no	—
795	C₂×Q₈	—	2	4	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	4	1	no	—
810	C₂×Q₈	—	4	1	no	—
811	C₂×Q₈	—	8	1	no	—
812	C₂×Q₈	—	8	1	no	—
813	C₂×Q₈	C₄×D₄	1	4	yes	—
814	C₂×Q₈	C₂³×C₄	1	2	yes	—
815	C₂×Q₈	C₂³×C₄	1	2	yes	—
816	C₂×Q₈	C₂³×C₄	1	2	yes	—
817	C₂×Q₈	C₂×#41	1	2	yes	—
818	C₂×Q₈	C₂×#41	1	2	yes	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	C₂³×C₄	1	2	yes	—
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	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	8	1	no	—
844	C₂²×C₄	—	8	1	no	—
845	C₂²×C₄	—	8	1	no	—
846	C₂²×C₄	—	8	1	no	—
847	C₂²×C₄	—	8	1	no	—
848	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
860	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂⁵	1	1	yes	characteristic
864	Q₁₆	—	2	8	no	—
865	Q₁₆	—	2	8	no	—
866	SD₁₆	—	2	8	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	C₂³×C₄	1	2	yes	—
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	C₂×#41	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	4	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	—	4	1	no	—
923	C₄⋊C₄	—	4	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	—	4	2	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	2	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	C₄×D₄	1	4	yes	—
946	C₄⋊C₄	C₄×D₄	1	4	yes	—
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	C₂×#41	1	2	yes	—
953	C₄⋊C₄	C₂×#41	1	2	yes	—
954	C₂²⋊C₄	—	2	4	no	—
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	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	8	1	no	—
963	C₂²⋊C₄	—	8	1	no	—
964	C₂²⋊C₄	—	8	1	no	—
965	C₄²	—	2	4	no	—
966	C₄²	—	2	4	no	—
967	C₄²	—	2	4	no	—
968	C₄²	—	2	4	no	—
969	C₄²	—	2	4	no	—
970	C₄²	—	2	4	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	4	1	no	—
978	C₄²	—	4	1	no	—
979	C₄²	—	4	1	no	—
980	C₄²	—	4	1	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	—	8	1	no	—
989	C₄²	—	8	1	no	—
990	C₄²	—	8	1	no	—
991	C₄²	—	8	1	no	—
992	C₄²	—	8	1	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	C₂³×C₄	1	2	yes	—
1005	C₄²	C₂³×C₄	1	2	yes	—
1006	C₄²	C₂³×C₄	1	2	yes	—
1007	C₄²	C₂×#41	1	2	yes	—
1008	C₄²	C₂×#41	1	2	yes	—
1009	C₄²	C₂×#41	1	2	yes	—
1010	C₄²	C₂×#41	1	2	yes	—
1011	C₄²	2₋¹⁺⁴	1	2	yes	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	4	1	no	—
1014	C₂³	—	4	1	no	—
1015	C₂³	—	4	1	no	—
1016	C₂³	—	4	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	C₂³×D₄	1	1	yes	characteristic
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	2	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	4	4	no	—
1028	Q₈	—	4	1	no	—
1029	Q₈	—	4	1	no	—
1030	Q₈	—	4	1	no	—
1031	Q₈	—	4	1	no	—
1032	Q₈	—	8	4	no	—
1033	Q₈	C₄×#41	1	4	yes	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	4	1	no	—
1037	D₄	—	4	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	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	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	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	1	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	2	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	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	8	4	no	—
1118	C₂×C₄	—	16	2	no	—
1119	C₂×C₄	—	16	2	no	—
1120	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1121	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1122	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1123	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1124	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1125	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1126	C₂×C₄	#548	1	2	yes	—
1127	C₂×C₄	#548	1	2	yes	—
1128	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1129	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1130	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1131	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1132	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1133	C₂×C₄	#585	1	1	yes	characteristic
1134	C₈	—	2	2	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	2	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	4	1	no	—
1140	C₈	—	4	1	no	—
1141	C₈	—	4	1	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	8	1	no	—
1146	C₂²	—	8	1	no	—
1147	C₂²	—	8	1	no	—
1148	C₂²	—	8	1	no	—
1149	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1150	C₂²	C₂×#548	1	1	yes	characteristic
1151	C₂²	D₄×#41	1	1	yes	characteristic
1152	C₂²	#3584	1	1	yes	characteristic
1153	C₂²	#3584	1	1	yes	characteristic
1154	C₂²	#3586	1	1	yes	characteristic
1155	C₂²	#3586	1	1	yes	characteristic
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	4	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	2	no	—
1176	C₄	—	4	2	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	4	2	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	C₂×C₄×#41	1	1	yes	characteristic
1186	C₄	C₄×2₋¹⁺⁴	1	1	yes	characteristic
1187	C₄	#3480	1	1	yes	characteristic
1188	C₄	#3482	1	1	yes	characteristic
1189	C₂	—	8	2	no	—
1190	C₂	C₄×#548	1	1	yes	characteristic
1191	C₂	#60167	1	1	yes	characteristic
1192	C₂	#60175	1	1	yes	characteristic
1193	C₂	#61344	1	1	yes	characteristic
1194	C₂	#61350	1	1	yes	characteristic
1195	C₂	#61537	1	1	yes	characteristic
1196	C₂	#61538	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	C₂⁴
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2295 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #34336	C₂	semidirect
6. #23221	C₂	semidirect
8. #23078	C₂	semidirect
9. #23064	C₂	semidirect
10. #23014	C₂	semidirect
14. #22763	C₂	semidirect
15. #22761	C₂	semidirect
16. #22741	C₂	semidirect
18. #22527	C₂	semidirect
20. #21645	C₂	semidirect
23. #21622	C₂	semidirect
24. C₄×#479	C₂	semidirect
25. #21516	C₂	semidirect
28. #20521	C₂	semidirect
29. #20507	C₂	semidirect
31. C₄×#441	C₂	semidirect
34. #3364	C₄	semidirect
208. #557	C₂×C₄	semidirect
244. #487	C₂×C₄	semidirect
245. #479	C₂×C₄	semidirect
246. #479	C₂×C₄	semidirect
250. #462	C₂×C₄	semidirect
252. C₈×Q₈	C₂×C₄	semidirect
257. C₄×Q₁₆	C₂×C₄	semidirect
258. C₄×Q₁₆	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×#3364	2
#34336	2
#34326	2
#23225	2
#23224	2
#23221	2
#23079	2
#23078	2
#23064	2
#23014	2
#23013	2
#23000	2
#22765	2
#22763	2
#22761	2
#22741	2
#22548	2
#22527	2
#21648	2
#21645	2
#21643	2
#21624	2
#21622	2
C₄×#479	2
#21516	2
#21511	2
C₄×#464	2
#20521	2
#20507	2
#20506	2
C₄×#441	2