Subgroups — #6692791

Order 512.

1599 conjugacy classes of subgroups.

The subgroup lattice has 1288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#40031	C₂	1	1	yes	maximal, characteristic
2	#36435	C₂	1	1	yes	maximal, characteristic, complemented
3	#32906	C₂	1	1	yes	maximal, characteristic, complemented
4	#32608	C₂	1	1	yes	maximal, characteristic, complemented
5	#32601	C₂	1	1	yes	maximal, characteristic, complemented
6	#31828	C₂	1	1	yes	maximal, characteristic, complemented
7	#31820	C₂	1	1	yes	maximal, characteristic, complemented
8	#31664	C₂	1	1	yes	maximal, characteristic, complemented
9	#31655	C₂	1	1	yes	maximal, characteristic, complemented
10	#30888	C₂	1	1	yes	maximal, characteristic, complemented
11	#30880	C₂	1	1	yes	maximal, characteristic, complemented
12	#30202	C₂	1	1	yes	maximal, characteristic, complemented
13	#29958	C₂	1	1	yes	maximal, characteristic
14	#27559	C₂	1	1	yes	maximal, characteristic, complemented
15	#27556	C₂	1	1	yes	maximal, characteristic, complemented
16	#27274	C₂	1	1	yes	maximal, characteristic
17	#27272	C₂	1	1	yes	maximal, characteristic
18	#26433	C₂	1	1	yes	maximal, characteristic, complemented
19	#26429	C₂	1	1	yes	maximal, characteristic, complemented
20	#26189	C₂	1	1	yes	maximal, characteristic, complemented
21	#26183	C₂	1	1	yes	maximal, characteristic, complemented
22	#25937	C₂	1	1	yes	maximal, characteristic, complemented
23	#25931	C₂	1	1	yes	maximal, characteristic, complemented
24	#24746	C₂	1	1	yes	maximal, characteristic, complemented
25	#24741	C₂	1	1	yes	maximal, characteristic, complemented
26	#24369	C₂	1	1	yes	maximal, characteristic
27	#24369	C₂	1	1	yes	maximal, characteristic
28	#22869	C₂	1	1	yes	maximal, characteristic, complemented
29	#22869	C₂	1	1	yes	maximal, characteristic, complemented
30	#22289	C₂	1	1	yes	maximal, characteristic, complemented
31	#20926	C₂	1	1	yes	maximal, characteristic
32	C₂²×#137	C₂²	1	1	yes	characteristic
33	C₂×#557	C₂²	1	1	yes	characteristic
34	C₂²×C₄×Q₈	C₂²	1	1	yes	characteristic
35	C₂×#488	C₂²	1	1	yes	characteristic
36	C₂×#487	C₂²	1	1	yes	characteristic
37	C₂×#464	C₂²	1	1	yes	characteristic
38	C₂×#464	C₂²	1	1	yes	characteristic
39	C₂×#462	C₂²	1	1	yes	characteristic
40	C₂×#462	C₂²	1	1	yes	characteristic
41	C₂×#462	C₂²	1	1	yes	characteristic
42	C₂×#462	C₂²	1	1	yes	characteristic
43	C₂×#451	C₂²	1	1	yes	characteristic
44	C₂×#451	C₂²	1	1	yes	characteristic
45	C₂×#441	C₂²	1	1	yes	characteristic
46	C₂×#441	C₂²	1	1	yes	characteristic
47	C₂×#417	C₂²	1	1	yes	characteristic
48	C₂×#419	C₂²	1	1	yes	characteristic
49	#2857	C₂²	1	1	yes	characteristic
50	#2851	—	2	1	no	—
51	#2851	C₂²	1	1	yes	characteristic
52	#2781	—	2	1	no	—
53	#2779	—	2	1	no	—
54	#2741	—	2	1	no	—
55	#2702	—	2	1	no	—
56	#2652	—	2	1	no	—
57	#2592	C₂²	1	1	yes	characteristic
58	#2589	—	2	1	no	—
59	#2587	—	2	1	no	—
60	#2581	—	2	1	no	—
61	#2581	C₂²	1	1	yes	characteristic
62	#2568	C₂²	1	1	yes	characteristic
63	#2565	—	2	1	no	—
64	#2565	C₂²	1	1	yes	characteristic
65	#2546	C₂²	1	1	yes	characteristic
66	#2545	C₂²	1	1	yes	characteristic
67	#2512	C₂²	1	1	yes	characteristic
68	#2511	C₂²	1	1	yes	characteristic
69	#2453	—	2	1	no	—
70	#2453	C₂²	1	1	yes	characteristic
71	#2451	—	2	1	no	—
72	#2451	C₂²	1	1	yes	characteristic
73	#2448	C₂²	1	1	yes	characteristic
74	#2446	C₂²	1	1	yes	characteristic
75	#2442	—	2	1	no	—
76	#2442	C₂²	1	1	yes	characteristic
77	#2440	—	2	1	no	—
78	#2440	C₂²	1	1	yes	characteristic
79	#2432	C₂²	1	1	yes	characteristic
80	#2432	C₂²	1	1	yes	characteristic
81	#2362	C₂²	1	1	yes	characteristic
82	#2362	C₂²	1	1	yes	characteristic
83	#2351	C₂²	1	1	yes	characteristic
84	#2351	C₂²	1	1	yes	characteristic
85	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
88	#2334	—	2	1	no	—
89	C₄×C₂²⋊Q₈	—	2	1	no	—
90	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
91	#2297	C₂²	1	1	yes	characteristic
92	#2101	C₂²	1	1	yes	characteristic
93	#2100	C₂²	1	1	yes	characteristic
94	#2100	C₂²	1	1	yes	characteristic
95	#2100	C₂²	1	1	yes	characteristic
96	#2097	C₂²	1	1	yes	characteristic
97	#2092	C₂²	1	1	yes	characteristic
98	#2088	C₂²	1	1	yes	characteristic
99	#2088	C₂²	1	1	yes	characteristic
100	#2074	C₂²	1	1	yes	characteristic
101	#2074	C₂²	1	1	yes	characteristic
102	#2073	C₂²	1	1	yes	characteristic
103	#2072	C₂²	1	1	yes	characteristic
104	#2068	C₂²	1	1	yes	characteristic
105	#2067	C₂²	1	1	yes	characteristic
106	#2066	C₂²	1	1	yes	characteristic
107	#2066	C₂²	1	1	yes	characteristic
108	#2066	C₂²	1	1	yes	characteristic
109	#2065	C₂²	1	1	yes	characteristic
110	#2056	C₂²	1	1	yes	characteristic
111	#2056	C₂²	1	1	yes	characteristic
112	#2055	C₂²	1	1	yes	characteristic
113	#2055	C₂²	1	1	yes	characteristic
114	#2043	C₂²	1	1	yes	characteristic
115	#2043	C₂²	1	1	yes	characteristic
116	#2043	C₂²	1	1	yes	characteristic
117	#2043	C₂²	1	1	yes	characteristic
118	#2042	C₂²	1	1	yes	characteristic
119	#2042	C₂²	1	1	yes	characteristic
120	#2026	C₂²	1	1	yes	characteristic
121	#2026	C₂²	1	1	yes	characteristic
122	#2026	C₂²	1	1	yes	characteristic
123	#2026	C₂²	1	1	yes	characteristic
124	#2026	C₂²	1	1	yes	characteristic
125	#2025	C₂²	1	1	yes	characteristic
126	#2024	C₂²	1	1	yes	characteristic
127	#2023	C₂²	1	1	yes	characteristic
128	#2016	C₂²	1	1	yes	characteristic
129	#2016	C₂²	1	1	yes	characteristic
130	#2015	C₂²	1	1	yes	characteristic
131	#2015	C₂²	1	1	yes	characteristic
132	#1989	C₂²	1	1	yes	characteristic
133	#1988	C₂²	1	1	yes	characteristic
134	#1984	C₂²	1	1	yes	characteristic
135	#1984	C₂²	1	1	yes	characteristic
136	#1969	C₂²	1	1	yes	characteristic
137	#1969	C₂²	1	1	yes	characteristic
138	#1960	C₂²	1	1	yes	characteristic
139	#1959	C₂²	1	1	yes	characteristic
140	#1940	C₂²	1	1	yes	characteristic
141	#1940	C₂²	1	1	yes	characteristic
142	#1936	C₂²	1	1	yes	characteristic
143	#1935	C₂²	1	1	yes	characteristic
144	#1935	C₂²	1	1	yes	characteristic
145	#1935	C₂²	1	1	yes	characteristic
146	#1934	C₂²	1	1	yes	characteristic
147	#1933	C₂²	1	1	yes	characteristic
148	#1927	C₂²	1	1	yes	characteristic
149	#1927	C₂²	1	1	yes	characteristic
150	#1921	C₂²	1	1	yes	characteristic
151	#1918	C₂²	1	1	yes	characteristic
152	#1917	C₂²	1	1	yes	characteristic
153	#1917	C₂²	1	1	yes	characteristic
154	#1916	C₂²	1	1	yes	characteristic
155	#1916	C₂²	1	1	yes	characteristic
156	#1894	C₂²	1	1	yes	characteristic
157	#1894	C₂²	1	1	yes	characteristic
158	#1894	C₂²	1	1	yes	characteristic
159	#1894	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	#1880	C₂²	1	1	yes	characteristic
166	#1878	C₂²	1	1	yes	characteristic
167	#1878	C₂²	1	1	yes	characteristic
168	#1878	C₂²	1	1	yes	characteristic
169	#1878	C₂²	1	1	yes	characteristic
170	#1878	C₂²	1	1	yes	characteristic
171	#1878	C₂²	1	1	yes	characteristic
172	#1878	C₂²	1	1	yes	characteristic
173	#1878	C₂²	1	1	yes	characteristic
174	#1878	C₂²	1	1	yes	characteristic
175	#1878	C₂²	1	1	yes	characteristic
176	#1878	C₂²	1	1	yes	characteristic
177	#1878	C₂²	1	1	yes	characteristic
178	#1878	C₂²	1	1	yes	characteristic
179	#1878	C₂²	1	1	yes	characteristic
180	#1872	C₂²	1	1	yes	characteristic
181	#1872	C₂²	1	1	yes	characteristic
182	#1863	C₂²	1	1	yes	characteristic
183	#1863	C₂²	1	1	yes	characteristic
184	#1863	C₂²	1	1	yes	characteristic
185	#1863	C₂²	1	1	yes	characteristic
186	#1854	C₂²	1	1	yes	characteristic
187	#1854	C₂²	1	1	yes	characteristic
188	#1851	C₂²	1	1	yes	characteristic
189	#1851	C₂²	1	1	yes	characteristic
190	#1805	C₂²	1	1	yes	characteristic
191	#1803	C₂²	1	1	yes	characteristic
192	#1803	C₂²	1	1	yes	characteristic
193	#1803	C₂²	1	1	yes	characteristic
194	#1797	C₂²	1	1	yes	characteristic
195	#1788	C₂²	1	1	yes	characteristic
196	#1788	C₂²	1	1	yes	characteristic
197	C₄×#103	C₂²	1	1	yes	characteristic
198	C₄×#103	C₂²	1	1	yes	characteristic
199	#1753	C₂²	1	1	yes	characteristic
200	#1753	C₂²	1	1	yes	characteristic
201	#1736	C₂²	1	1	yes	characteristic
202	#1728	C₂²	1	1	yes	characteristic
203	C₂²×#41	C₂³	1	1	yes	characteristic
204	C₂³×Q₈	C₂³	1	1	yes	characteristic
205	C₂×#137	—	2	4	no	—
206	C₂×#137	—	4	2	no	—
207	C₂×#137	—	4	2	no	—
208	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
210	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
211	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
212	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
213	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
214	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
215	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
216	C₂²×M₁₆	C₂³	1	1	yes	characteristic
217	C₂²×M₁₆	C₂³	1	1	yes	characteristic
218	#557	—	4	2	no	—
219	#557	—	4	2	no	—
220	C₂×C₄⋊Q₈	—	2	1	no	—
221	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂×#126	—	2	1	no	—
226	C₂×#125	—	2	1	no	—
227	C₂×#125	—	2	1	no	—
228	C₂×#125	C₂³	1	1	yes	characteristic
229	C₂×#125	C₂³	1	1	yes	characteristic
230	C₂×#124	C₂³	1	1	yes	characteristic
231	C₂×#124	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₄×Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	—	2	1	no	—
238	C₂×C₄×Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	—	4	2	no	—
240	C₂×C₄×Q₈	—	4	2	no	—
241	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₂×#117	C₂³	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	—	2	1	no	—
254	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂²×C₄²	—	2	1	no	—
256	C₂²×C₄²	C₂³	1	1	yes	characteristic
257	#488	—	4	2	no	—
258	#487	—	4	2	no	—
259	#464	—	4	2	no	—
260	#464	—	4	2	no	—
261	#462	—	4	2	no	—
262	#462	—	4	2	no	—
263	#462	—	4	2	no	—
264	#462	—	4	2	no	—
265	#451	—	2	4	no	—
266	#451	—	2	4	no	—
267	#441	—	4	2	no	—
268	#441	—	4	2	no	—
269	C₂×#107	C₂³	1	1	yes	characteristic
270	C₂×#107	C₂³	1	1	yes	characteristic
271	C₂×#106	C₂³	1	1	yes	characteristic
272	C₂×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	#419	—	4	2	no	—
280	#417	—	4	2	no	—
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×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#103	C₂³	1	1	yes	characteristic
302	C₂×#103	C₂³	1	1	yes	characteristic
303	C₂×#103	C₂³	1	1	yes	characteristic
304	C₂×#103	C₂³	1	1	yes	characteristic
305	C₂×#103	C₂³	1	1	yes	characteristic
306	C₂×#103	C₂³	1	1	yes	characteristic
307	C₂×#102	C₂³	1	1	yes	characteristic
308	C₂×#102	C₂³	1	1	yes	characteristic
309	C₂×#102	C₂³	1	1	yes	characteristic
310	C₂×#102	C₂³	1	1	yes	characteristic
311	C₂×#102	C₂³	1	1	yes	characteristic
312	C₂×#102	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₂×#97	C₂³	1	1	yes	characteristic
316	C₂×#97	C₂³	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
319	#400	—	2	1	no	—
320	#400	—	2	1	no	—
321	#400	—	2	1	no	—
322	#400	—	2	1	no	—
323	#400	—	2	1	no	—
324	#400	—	2	1	no	—
325	#400	—	2	1	no	—
326	#400	—	2	1	no	—
327	#399	—	2	1	no	—
328	#398	—	2	1	no	—
329	#398	—	2	1	no	—
330	#398	—	2	1	no	—
331	#398	—	2	1	no	—
332	#398	—	2	1	no	—
333	#398	—	2	1	no	—
334	#398	—	2	1	no	—
335	#398	—	2	1	no	—
336	#398	—	2	1	no	—
337	#397	—	2	1	no	—
338	#397	—	2	1	no	—
339	#397	—	2	1	no	—
340	#396	—	2	1	no	—
341	#396	—	2	1	no	—
342	#396	—	2	1	no	—
343	#395	—	2	1	no	—
344	#395	—	2	1	no	—
345	#395	—	2	1	no	—
346	#394	—	2	1	no	—
347	#394	—	2	1	no	—
348	#394	—	2	1	no	—
349	#394	—	2	1	no	—
350	#393	—	2	1	no	—
351	#391	—	2	1	no	—
352	#391	—	2	1	no	—
353	#391	—	2	1	no	—
354	#391	—	2	1	no	—
355	#391	—	2	1	no	—
356	#391	—	2	1	no	—
357	#391	D₄	1	1	yes	characteristic
358	#391	C₂³	1	1	yes	characteristic
359	#391	C₂³	1	1	yes	characteristic
360	#391	C₂³	1	1	yes	characteristic
361	#391	C₂³	1	1	yes	characteristic
362	#391	C₂³	1	1	yes	characteristic
363	#391	C₂³	1	1	yes	characteristic
364	#391	C₂³	1	1	yes	characteristic
365	#391	C₂³	1	1	yes	characteristic
366	#391	C₂³	1	1	yes	characteristic
367	#391	C₂³	1	1	yes	characteristic
368	#391	C₂³	1	1	yes	characteristic
369	#391	C₂³	1	1	yes	characteristic
370	#390	C₂³	1	1	yes	characteristic
371	#390	C₂³	1	1	yes	characteristic
372	#390	C₂³	1	1	yes	characteristic
373	#390	C₂³	1	1	yes	characteristic
374	#389	—	2	1	no	—
375	#389	—	2	1	no	—
376	#389	—	2	1	no	—
377	#389	—	2	1	no	—
378	#389	—	2	1	no	—
379	#389	—	2	1	no	—
380	#389	—	2	1	no	—
381	#389	—	2	1	no	—
382	#389	—	2	1	no	—
383	#389	—	2	1	no	—
384	#389	—	2	1	no	—
385	#389	D₄	1	1	yes	characteristic
386	#389	C₂³	1	1	yes	characteristic
387	#389	C₂³	1	1	yes	characteristic
388	#389	C₂³	1	1	yes	characteristic
389	#389	C₂³	1	1	yes	characteristic
390	#389	C₂³	1	1	yes	characteristic
391	#389	C₂³	1	1	yes	characteristic
392	#389	C₂³	1	1	yes	characteristic
393	#389	C₂³	1	1	yes	characteristic
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#388	—	2	1	no	—
398	#388	—	2	1	no	—
399	#388	—	2	1	no	—
400	#388	—	2	1	no	—
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#388	—	2	1	no	—
404	#388	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#387	—	2	1	no	—
413	#387	—	2	1	no	—
414	#387	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	D₄	1	1	yes	characteristic
420	#387	D₄	1	1	yes	characteristic
421	#386	—	2	1	no	—
422	#386	—	2	1	no	—
423	#385	—	2	1	no	—
424	#385	—	2	1	no	—
425	#385	—	2	1	no	—
426	#385	—	2	1	no	—
427	#385	—	2	1	no	—
428	#385	—	2	1	no	—
429	#385	—	2	1	no	—
430	#385	—	2	1	no	—
431	#385	D₄	1	1	yes	characteristic
432	#385	D₄	1	1	yes	characteristic
433	#384	—	2	1	no	—
434	#384	C₂³	1	1	yes	characteristic
435	#384	C₂³	1	1	yes	characteristic
436	#382	—	2	1	no	—
437	#382	—	2	1	no	—
438	#382	—	2	1	no	—
439	#382	C₂³	1	1	yes	characteristic
440	#382	C₂³	1	1	yes	characteristic
441	#380	—	2	1	no	—
442	#380	—	2	1	no	—
443	#380	—	2	1	no	—
444	#380	—	2	1	no	—
445	#380	—	2	1	no	—
446	#380	D₄	1	1	yes	characteristic
447	#380	C₂³	1	1	yes	characteristic
448	#380	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	—	2	1	no	—
450	C₄×C₄⋊C₄	—	2	1	no	—
451	C₄×C₄⋊C₄	—	2	1	no	—
452	C₄×C₄⋊C₄	—	2	1	no	—
453	C₄×C₄⋊C₄	—	2	1	no	—
454	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
456	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	—	2	1	no	—
460	C₄×C₂²⋊C₄	—	2	1	no	—
461	C₄×C₂²⋊C₄	—	2	1	no	—
462	C₄×C₂²⋊C₄	—	2	1	no	—
463	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
464	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	#336	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	#336	C₂³	1	1	yes	characteristic
497	#336	C₂³	1	1	yes	characteristic
498	#336	C₂³	1	1	yes	characteristic
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	4	1	no	—
502	C₂×#41	—	4	1	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	—	4	1	no	—
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×Q₈	—	2	2	no	—
508	C₂²×Q₈	—	2	2	no	—
509	C₂²×Q₈	—	2	2	no	—
510	C₂²×Q₈	—	4	1	no	—
511	C₂²×Q₈	—	4	1	no	—
512	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
513	C₂²×Q₈	#41	1	4	yes	—
514	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
515	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
516	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
517	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
518	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	C₂⁴	1	1	yes	characteristic
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	—	2	1	no	—
524	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
525	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
526	C₂³×C₄	C₂⁴	1	1	yes	characteristic
527	#137	—	4	16	no	—
528	C₂×Q₁₆	—	2	2	no	—
529	C₂×Q₁₆	—	2	2	no	—
530	C₂×Q₁₆	—	2	2	no	—
531	C₂×Q₁₆	—	2	2	no	—
532	C₂×Q₁₆	—	2	2	no	—
533	C₂×Q₁₆	—	2	2	no	—
534	C₂×Q₁₆	—	2	2	no	—
535	C₂×Q₁₆	—	2	2	no	—
536	C₂×Q₁₆	—	2	2	no	—
537	C₂×Q₁₆	—	2	2	no	—
538	C₂×Q₁₆	—	2	2	no	—
539	C₂×Q₁₆	—	2	2	no	—
540	C₂×Q₁₆	—	4	1	no	—
541	C₂×Q₁₆	—	4	1	no	—
542	C₂×Q₁₆	—	4	1	no	—
543	C₂×Q₁₆	—	4	1	no	—
544	C₂×Q₁₆	—	4	1	no	—
545	C₂×Q₁₆	—	4	1	no	—
546	C₂×SD₁₆	—	2	2	no	—
547	C₂×SD₁₆	—	2	2	no	—
548	C₂×SD₁₆	—	2	2	no	—
549	C₂×SD₁₆	—	2	2	no	—
550	C₂×SD₁₆	—	4	1	no	—
551	C₂×SD₁₆	—	4	1	no	—
552	C₂×M₁₆	—	2	2	no	—
553	C₂×M₁₆	—	2	2	no	—
554	C₂×M₁₆	—	4	1	no	—
555	C₂×M₁₆	—	4	1	no	—
556	C₂×M₁₆	—	4	1	no	—
557	C₂×M₁₆	—	4	1	no	—
558	C₂²×C₈	C₂⁴	1	1	yes	characteristic
559	C₂²×C₈	C₂⁴	1	1	yes	characteristic
560	C₂²×C₈	C₂⁴	1	1	yes	characteristic
561	C₂²×C₈	C₂⁴	1	1	yes	characteristic
562	C₂²×C₈	C₂⁴	1	1	yes	characteristic
563	C₂²×C₈	C₂⁴	1	1	yes	characteristic
564	C₂²×C₈	C₂⁴	1	1	yes	characteristic
565	C₂²×C₈	C₂⁴	1	1	yes	characteristic
566	C₄⋊Q₈	—	2	2	no	—
567	C₄⋊Q₈	—	4	1	no	—
568	C₄⋊Q₈	—	4	1	no	—
569	C₄⋊Q₈	—	4	1	no	—
570	C₄⋊Q₈	—	4	1	no	—
571	C₄⋊Q₈	—	4	1	no	—
572	C₄⋊Q₈	—	4	1	no	—
573	C₄⋊Q₈	—	4	1	no	—
574	C₄⋊Q₈	—	4	4	no	—
575	#126	—	4	4	no	—
576	#125	—	2	2	no	—
577	#125	—	4	1	no	—
578	#125	—	4	1	no	—
579	#125	—	4	1	no	—
580	#125	—	4	4	no	—
581	#125	—	4	4	no	—
582	#124	—	4	1	no	—
583	#124	—	4	1	no	—
584	#124	—	4	1	no	—
585	#124	—	4	1	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	4	2	no	—
591	C₂²⋊Q₈	—	4	4	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	4	1	no	—
601	C₄×Q₈	—	4	1	no	—
602	C₄×Q₈	—	4	1	no	—
603	C₄×Q₈	—	4	1	no	—
604	C₄×Q₈	—	4	1	no	—
605	C₄×Q₈	—	4	1	no	—
606	C₄×Q₈	—	4	1	no	—
607	C₄×Q₈	—	4	1	no	—
608	C₄×Q₈	—	4	1	no	—
609	C₄×Q₈	—	4	1	no	—
610	C₄×Q₈	—	4	4	no	—
611	C₄×Q₈	—	4	4	no	—
612	C₄×Q₈	—	4	1	no	—
613	C₄×Q₈	—	4	1	no	—
614	C₄×Q₈	—	4	1	no	—
615	C₄×Q₈	—	4	1	no	—
616	C₄×Q₈	—	4	4	no	—
617	#117	—	4	1	no	—
618	#117	—	4	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	4	1	no	—
657	C₂×C₄⋊C₄	—	4	4	no	—
658	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	1	no	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₂²⋊C₄	—	2	1	no	—
688	C₂×C₂²⋊C₄	—	2	1	no	—
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	1	no	—
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	1	no	—
693	C₂×C₂²⋊C₄	—	2	1	no	—
694	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
698	C₂×C₄²	—	2	1	no	—
699	C₂×C₄²	—	2	1	no	—
700	C₂×C₄²	—	2	1	no	—
701	C₂×C₄²	—	2	1	no	—
702	C₂×C₄²	—	2	1	no	—
703	C₂×C₄²	—	2	1	no	—
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	—	2	1	no	—
707	C₂×C₄²	—	2	1	no	—
708	C₂×C₄²	—	2	1	no	—
709	C₂×C₄²	—	2	1	no	—
710	C₂×C₄²	—	2	1	no	—
711	C₂×C₄²	—	4	1	no	—
712	C₂×C₄²	—	4	1	no	—
713	C₂×C₄²	—	4	4	no	—
714	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
715	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
716	C₂×C₄²	C₂⁴	1	1	yes	characteristic
717	C₂×C₄²	C₂⁴	1	1	yes	characteristic
718	C₂×C₄²	C₂⁴	1	1	yes	characteristic
719	C₂×C₄²	C₂⁴	1	1	yes	characteristic
720	C₂×C₄²	C₂⁴	1	1	yes	characteristic
721	C₂×C₄²	C₂⁴	1	1	yes	characteristic
722	#107	—	4	1	no	—
723	#107	—	4	1	no	—
724	#106	—	4	1	no	—
725	#106	—	4	1	no	—
726	C₄⋊C₈	—	4	1	no	—
727	C₄⋊C₈	—	4	1	no	—
728	C₄⋊C₈	—	4	1	no	—
729	C₄⋊C₈	—	4	1	no	—
730	C₄⋊C₈	—	4	1	no	—
731	C₄⋊C₈	—	4	1	no	—
732	#103	—	2	2	no	—
733	#103	—	2	2	no	—
734	#103	—	2	2	no	—
735	#103	—	2	2	no	—
736	#103	—	2	2	no	—
737	#103	—	2	2	no	—
738	#103	—	2	2	no	—
739	#103	—	2	2	no	—
740	#103	—	2	2	no	—
741	#103	—	4	1	no	—
742	#103	—	4	1	no	—
743	#103	—	4	1	no	—
744	#103	—	4	1	no	—
745	#103	—	4	1	no	—
746	#103	—	4	1	no	—
747	#103	—	4	1	no	—
748	#103	—	4	1	no	—
749	#103	—	4	1	no	—
750	#103	—	4	1	no	—
751	#103	—	4	1	no	—
752	#103	—	4	1	no	—
753	#103	—	4	1	no	—
754	#103	—	4	1	no	—
755	#103	—	4	1	no	—
756	#103	—	4	1	no	—
757	#103	—	4	1	no	—
758	#102	—	2	2	no	—
759	#102	—	4	1	no	—
760	#102	—	4	1	no	—
761	#102	—	4	1	no	—
762	#102	—	4	1	no	—
763	#102	—	4	1	no	—
764	C₂²⋊C₈	—	2	2	no	—
765	C₂²⋊C₈	—	2	2	no	—
766	#97	—	4	1	no	—
767	#97	—	4	1	no	—
768	C₄×C₈	—	4	1	no	—
769	C₄×C₈	—	4	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	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	—	2	1	no	—
795	#95	—	2	1	no	—
796	#95	—	2	1	no	—
797	#95	—	2	1	no	—
798	#95	—	2	1	no	—
799	#95	—	2	1	no	—
800	#95	—	2	1	no	—
801	#95	—	2	1	no	—
802	#95	—	2	1	no	—
803	#95	—	2	1	no	—
804	#95	—	2	1	no	—
805	#95	—	2	1	no	—
806	#95	—	2	1	no	—
807	#95	—	2	1	no	—
808	#95	—	2	1	no	—
809	#95	—	2	1	no	—
810	#95	C₂×D₄	1	1	yes	characteristic
811	#95	C₂×D₄	1	1	yes	characteristic
812	#95	C₂×D₄	1	1	yes	characteristic
813	#95	C₂×D₄	1	1	yes	characteristic
814	#95	C₂×D₄	1	1	yes	characteristic
815	#95	C₂×D₄	1	1	yes	characteristic
816	#95	C₂×D₄	1	1	yes	characteristic
817	#95	C₂×D₄	1	1	yes	characteristic
818	#95	C₂×D₄	1	1	yes	characteristic
819	#95	C₂×D₄	1	1	yes	characteristic
820	C₂⁴	—	2	1	no	—
821	C₂⁴	C₂²×D₄	1	1	yes	characteristic
822	#41	—	4	4	no	—
823	#41	—	4	4	no	—
824	#41	—	8	2	no	—
825	#41	—	8	2	no	—
826	C₂×Q₈	—	2	4	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	—	2	1	no	—
829	C₂×Q₈	—	2	1	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	8	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	4	1	no	—
856	C₂×Q₈	—	4	1	no	—
857	C₂×Q₈	—	4	2	no	—
858	C₂×Q₈	—	4	2	no	—
859	C₂×Q₈	—	4	2	no	—
860	C₂×Q₈	—	4	4	no	—
861	C₂×Q₈	—	4	4	no	—
862	C₂×Q₈	—	4	4	no	—
863	C₂×Q₈	—	4	2	no	—
864	C₂×Q₈	—	8	1	no	—
865	C₂×Q₈	C₂×#41	1	2	yes	—
866	C₂×Q₈	C₂×#41	1	2	yes	—
867	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
868	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	4	2	no	—
876	C₂×D₄	—	8	1	no	—
877	C₂×D₄	—	8	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	4	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	4	1	no	—
900	C₂²×C₄	—	4	1	no	—
901	C₂²×C₄	—	4	1	no	—
902	C₂²×C₄	—	4	1	no	—
903	C₂²×C₄	—	4	1	no	—
904	C₂²×C₄	—	4	2	no	—
905	C₂²×C₄	—	4	2	no	—
906	C₂²×C₄	—	4	2	no	—
907	C₂²×C₄	—	4	2	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	8	1	no	—
910	C₂²×C₄	—	8	1	no	—
911	C₂²×C₄	—	8	1	no	—
912	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
913	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
914	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
915	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
916	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
917	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
918	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
919	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
920	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
921	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
922	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
923	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
924	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
925	C₂²×C₄	C₂×#41	1	2	yes	—
926	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
927	C₂²×C₄	C₂⁵	1	1	yes	characteristic
928	Q₁₆	—	4	4	no	—
929	Q₁₆	—	4	4	no	—
930	Q₁₆	—	4	4	no	—
931	Q₁₆	—	4	4	no	—
932	Q₁₆	—	8	2	no	—
933	Q₁₆	—	8	2	no	—
934	SD₁₆	—	4	4	no	—
935	SD₁₆	—	4	4	no	—
936	M₁₆	—	4	4	no	—
937	M₁₆	—	8	2	no	—
938	C₂×C₈	—	2	1	no	—
939	C₂×C₈	—	2	1	no	—
940	C₂×C₈	—	2	1	no	—
941	C₂×C₈	—	2	1	no	—
942	C₂×C₈	—	2	1	no	—
943	C₂×C₈	—	2	1	no	—
944	C₂×C₈	—	2	1	no	—
945	C₂×C₈	—	2	1	no	—
946	C₂×C₈	—	2	1	no	—
947	C₂×C₈	—	2	1	no	—
948	C₂×C₈	—	2	1	no	—
949	C₂×C₈	—	2	1	no	—
950	C₂×C₈	—	2	1	no	—
951	C₂×C₈	—	2	1	no	—
952	C₂×C₈	—	2	1	no	—
953	C₂×C₈	—	2	1	no	—
954	C₂×C₈	—	2	1	no	—
955	C₂×C₈	—	2	1	no	—
956	C₂×C₈	—	2	1	no	—
957	C₂×C₈	—	2	1	no	—
958	C₂×C₈	—	2	1	no	—
959	C₂×C₈	—	2	1	no	—
960	C₂×C₈	—	2	1	no	—
961	C₂×C₈	—	2	1	no	—
962	C₄⋊C₄	—	2	4	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	4	1	no	—
986	C₄⋊C₄	—	4	1	no	—
987	C₄⋊C₄	—	4	1	no	—
988	C₄⋊C₄	—	4	1	no	—
989	C₄⋊C₄	—	4	1	no	—
990	C₄⋊C₄	—	4	1	no	—
991	C₄⋊C₄	—	4	2	no	—
992	C₄⋊C₄	—	4	2	no	—
993	C₄⋊C₄	—	4	2	no	—
994	C₄⋊C₄	—	4	2	no	—
995	C₄⋊C₄	—	4	2	no	—
996	C₄⋊C₄	—	4	2	no	—
997	C₄⋊C₄	—	4	2	no	—
998	C₄⋊C₄	—	4	2	no	—
999	C₄⋊C₄	—	4	2	no	—
1000	C₄⋊C₄	—	4	2	no	—
1001	C₄⋊C₄	—	4	2	no	—
1002	C₄⋊C₄	—	4	2	no	—
1003	C₄⋊C₄	—	4	2	no	—
1004	C₄⋊C₄	—	4	2	no	—
1005	C₄⋊C₄	—	4	2	no	—
1006	C₄⋊C₄	—	4	2	no	—
1007	C₄⋊C₄	—	4	2	no	—
1008	C₄⋊C₄	—	4	2	no	—
1009	C₄⋊C₄	—	4	2	no	—
1010	C₄⋊C₄	—	4	2	no	—
1011	C₄⋊C₄	—	4	2	no	—
1012	C₄⋊C₄	—	8	1	no	—
1013	C₄⋊C₄	—	8	1	no	—
1014	C₄⋊C₄	—	8	1	no	—
1015	C₄⋊C₄	—	8	1	no	—
1016	C₄⋊C₄	—	8	1	no	—
1017	C₄⋊C₄	—	8	1	no	—
1018	C₄⋊C₄	—	8	1	no	—
1019	C₄⋊C₄	—	8	1	no	—
1020	C₄⋊C₄	—	8	1	no	—
1021	C₄⋊C₄	—	8	1	no	—
1022	C₄⋊C₄	—	8	1	no	—
1023	C₄⋊C₄	—	8	1	no	—
1024	C₄⋊C₄	—	8	1	no	—
1025	C₄⋊C₄	—	8	1	no	—
1026	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	4	1	no	—
1029	C₂²⋊C₄	—	4	1	no	—
1030	C₂²⋊C₄	—	4	1	no	—
1031	C₂²⋊C₄	—	4	2	no	—
1032	C₂²⋊C₄	—	4	2	no	—
1033	C₂²⋊C₄	—	4	2	no	—
1034	C₂²⋊C₄	—	4	2	no	—
1035	C₂²⋊C₄	—	4	2	no	—
1036	C₂²⋊C₄	—	4	2	no	—
1037	C₂²⋊C₄	—	4	2	no	—
1038	C₂²⋊C₄	—	4	2	no	—
1039	C₂²⋊C₄	—	4	2	no	—
1040	C₂²⋊C₄	—	8	1	no	—
1041	C₂²⋊C₄	—	8	1	no	—
1042	C₂²⋊C₄	—	8	1	no	—
1043	C₂²⋊C₄	—	8	1	no	—
1044	C₂²⋊C₄	—	8	1	no	—
1045	C₂²⋊C₄	—	8	1	no	—
1046	C₂²⋊C₄	—	8	1	no	—
1047	C₂²⋊C₄	—	8	1	no	—
1048	C₄²	—	2	4	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	4	1	no	—
1062	C₄²	—	4	1	no	—
1063	C₄²	—	4	2	no	—
1064	C₄²	—	4	2	no	—
1065	C₄²	—	4	2	no	—
1066	C₄²	—	4	2	no	—
1067	C₄²	—	4	2	no	—
1068	C₄²	—	4	2	no	—
1069	C₄²	—	4	2	no	—
1070	C₄²	—	4	2	no	—
1071	C₄²	—	8	1	no	—
1072	C₄²	—	8	1	no	—
1073	C₄²	—	8	1	no	—
1074	C₄²	—	8	1	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	1	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	4	1	no	—
1082	C₂³	—	4	1	no	—
1083	C₂³	—	4	1	no	—
1084	C₂³	—	4	1	no	—
1085	C₂³	—	4	1	no	—
1086	C₂³	—	4	1	no	—
1087	C₂³	—	4	1	no	—
1088	C₂³	#548	1	2	yes	—
1089	C₂³	C₂³×D₄	1	1	yes	characteristic
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	2	2	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	2	2	no	—
1095	Q₈	—	4	8	no	—
1096	Q₈	—	4	1	no	—
1097	Q₈	—	4	1	no	—
1098	Q₈	—	4	1	no	—
1099	Q₈	—	4	1	no	—
1100	Q₈	—	4	1	no	—
1101	Q₈	—	4	1	no	—
1102	Q₈	—	4	1	no	—
1103	Q₈	—	4	1	no	—
1104	Q₈	—	4	1	no	—
1105	Q₈	—	4	1	no	—
1106	Q₈	—	4	1	no	—
1107	Q₈	—	4	1	no	—
1108	Q₈	—	4	1	no	—
1109	Q₈	—	4	1	no	—
1110	Q₈	—	8	2	no	—
1111	Q₈	—	8	4	no	—
1112	Q₈	#538	1	4	yes	—
1113	D₄	—	4	1	no	—
1114	D₄	—	4	1	no	—
1115	D₄	—	4	1	no	—
1116	D₄	—	4	1	no	—
1117	D₄	—	8	4	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	4	8	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	4	1	no	—
1192	C₂×C₄	—	4	1	no	—
1193	C₂×C₄	—	4	1	no	—
1194	C₂×C₄	—	4	1	no	—
1195	C₂×C₄	—	4	1	no	—
1196	C₂×C₄	—	4	1	no	—
1197	C₂×C₄	—	4	1	no	—
1198	C₂×C₄	—	4	1	no	—
1199	C₂×C₄	—	4	1	no	—
1200	C₂×C₄	—	4	1	no	—
1201	C₂×C₄	—	4	1	no	—
1202	C₂×C₄	—	4	1	no	—
1203	C₂×C₄	—	4	1	no	—
1204	C₂×C₄	—	4	1	no	—
1205	C₂×C₄	—	8	4	no	—
1206	C₂×C₄	—	8	2	no	—
1207	C₂×C₄	—	8	4	no	—
1208	C₂×C₄	#548	1	2	yes	—
1209	C₂×C₄	#575	1	2	yes	—
1210	C₂×C₄	#578	1	2	yes	—
1211	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1212	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1213	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1214	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1215	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1216	C₂×C₄	#585	1	1	yes	characteristic
1217	C₈	—	4	1	no	—
1218	C₈	—	4	1	no	—
1219	C₈	—	4	1	no	—
1220	C₈	—	4	1	no	—
1221	C₈	—	4	1	no	—
1222	C₈	—	4	1	no	—
1223	C₈	—	4	1	no	—
1224	C₈	—	4	1	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	8	1	no	—
1233	C₂²	—	8	1	no	—
1234	C₂²	—	8	1	no	—
1235	C₂²	—	8	1	no	—
1236	C₂²	—	8	1	no	—
1237	C₂²	—	8	1	no	—
1238	C₂²	—	8	1	no	—
1239	C₂²	C₂×#548	1	1	yes	characteristic
1240	C₂²	#3484	1	1	yes	characteristic
1241	C₂²	#3488	1	1	yes	characteristic
1242	C₂²	C₂×#575	1	1	yes	characteristic
1243	C₂²	C₂×#578	1	1	yes	characteristic
1244	C₂²	#3586	1	1	yes	characteristic
1245	C₂²	#3586	1	1	yes	characteristic
1246	C₄	—	2	2	no	—
1247	C₄	—	2	4	no	—
1248	C₄	—	2	2	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	2	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	8	1	no	—
1263	C₄	—	8	1	no	—
1264	C₄	—	8	1	no	—
1265	C₄	—	8	1	no	—
1266	C₄	—	8	1	no	—
1267	C₄	—	8	1	no	—
1268	C₄	—	8	1	no	—
1269	C₄	—	8	1	no	—
1270	C₄	—	8	1	no	—
1271	C₄	—	8	1	no	—
1272	C₄	—	8	1	no	—
1273	C₄	—	8	1	no	—
1274	C₄	C₂×#538	1	1	yes	characteristic
1275	C₄	#3505	1	1	yes	characteristic
1276	C₄	#3535	1	1	yes	characteristic
1277	C₄	#3536	1	1	yes	characteristic
1278	C₂	—	4	2	no	—
1279	C₂	—	16	1	no	—
1280	C₂	#37703	1	1	yes	characteristic
1281	C₂	#61320	1	1	yes	characteristic
1282	C₂	#61342	1	1	yes	characteristic
1283	C₂	#61580	1	1	yes	characteristic
1284	C₂	#61612	1	1	yes	characteristic
1285	C₂	#61998	1	1	yes	characteristic
1286	C₂	#62086	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊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. #36435	C₂	semidirect
3. #32906	C₂	semidirect
4. #32608	C₂	semidirect
5. #32601	C₂	semidirect
6. #31828	C₂	semidirect
7. #31820	C₂	semidirect
8. #31664	C₂	semidirect
9. #31655	C₂	semidirect
10. #30888	C₂	semidirect
11. #30880	C₂	semidirect
12. #30202	C₂	semidirect
14. #27559	C₂	semidirect
15. #27556	C₂	semidirect
18. #26433	C₂	semidirect
19. #26429	C₂	semidirect
20. #26189	C₂	semidirect
21. #26183	C₂	semidirect
22. #25937	C₂	semidirect
23. #25931	C₂	semidirect
24. #24746	C₂	semidirect
25. #24741	C₂	semidirect
28. #22869	C₂	semidirect
29. #22869	C₂	semidirect
30. #22289	C₂	semidirect

Maximal subgroups

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

subgroup	index
#40031	2
#36435	2
#32906	2
#32608	2
#32601	2
#31828	2
#31820	2
#31664	2
#31655	2
#30888	2
#30880	2
#30202	2
#29958	2
#27559	2
#27556	2
#27274	2
#27272	2
#26433	2
#26429	2
#26189	2
#26183	2
#25937	2
#25931	2
#24746	2
#24741	2
#24369	2
#22869	2
#22289	2
#20926	2