Subgroups — #7339798

Order 512.

1397 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32704	C₂	1	1	yes	maximal, characteristic, complemented
2	#32698	C₂	1	1	yes	maximal, characteristic, complemented
3	#32696	C₂	1	1	yes	maximal, characteristic, complemented
4	#32696	C₂	1	1	yes	maximal, characteristic, complemented
5	#32696	C₂	1	1	yes	maximal, characteristic, complemented
6	#31417	C₂	1	1	yes	maximal, characteristic, complemented
7	#31416	C₂	1	1	yes	maximal, characteristic, complemented
8	#31415	C₂	1	1	yes	maximal, characteristic, complemented
9	#31415	C₂	1	1	yes	maximal, characteristic, complemented
10	#31285	C₂	1	1	yes	maximal, characteristic, complemented
11	#31283	C₂	1	1	yes	maximal, characteristic, complemented
12	#30498	C₂	1	1	yes	maximal, characteristic, complemented
13	#30058	C₂	1	1	yes	maximal, characteristic, complemented
14	#30056	C₂	1	1	yes	maximal, characteristic, complemented
15	#29232	C₂	1	1	yes	maximal, characteristic, complemented
16	#29232	C₂	1	1	yes	maximal, characteristic, complemented
17	#25748	C₂	1	1	yes	maximal, characteristic, complemented
18	#25592	C₂	1	1	yes	maximal, characteristic, complemented
19	#25590	C₂	1	1	yes	maximal, characteristic, complemented
20	#25199	C₂	1	1	yes	maximal, characteristic, complemented
21	#25196	C₂	1	1	yes	maximal, characteristic, complemented
22	#24474	C₂	1	1	yes	maximal, characteristic, complemented
23	#24473	C₂	1	1	yes	maximal, characteristic, complemented
24	#24000	C₂	1	1	yes	maximal, characteristic, complemented
25	#23998	C₂	1	1	yes	maximal, characteristic, complemented
26	#23991	C₂	1	1	yes	maximal, characteristic, complemented
27	#23990	C₂	1	1	yes	maximal, characteristic, complemented
28	#23873	C₂	1	1	yes	maximal, characteristic, complemented
29	#23362	C₂	1	1	yes	maximal, characteristic, complemented
30	#22899	C₂	1	1	yes	maximal, characteristic, complemented
31	#21784	C₂	1	1	yes	maximal, characteristic, complemented
32	#3586	C₂²	1	1	yes	characteristic
33	#3510	C₂²	1	1	yes	characteristic
34	#3508	C₂²	1	1	yes	characteristic
35	#3500	C₂²	1	1	yes	characteristic
36	#3153	C₂²	1	1	yes	characteristic
37	#3140	C₂²	1	1	yes	characteristic, complemented
38	#3139	C₂²	1	1	yes	characteristic, complemented
39	#3069	C₂²	1	1	yes	characteristic
40	#3069	C₂²	1	1	yes	characteristic
41	#3068	C₂²	1	1	yes	characteristic
42	#3068	C₂²	1	1	yes	characteristic
43	#3040	C₂²	1	1	yes	characteristic, complemented
44	#3040	C₂²	1	1	yes	characteristic, complemented
45	#3039	C₂²	1	1	yes	characteristic, complemented
46	#3027	C₂²	1	1	yes	characteristic
47	#3022	C₂²	1	1	yes	characteristic, complemented
48	#3021	C₂²	1	1	yes	characteristic, complemented
49	#3019	C₂²	1	1	yes	characteristic
50	#3019	C₂²	1	1	yes	characteristic
51	#3018	C₂²	1	1	yes	characteristic
52	C₂×#456	C₂²	1	1	yes	characteristic
53	C₂×#454	C₂²	1	1	yes	characteristic
54	C₂×#455	C₂²	1	1	yes	characteristic, complemented
55	C₂×#453	C₂²	1	1	yes	characteristic, complemented
56	#2956	C₂²	1	1	yes	characteristic
57	#2956	C₂²	1	1	yes	characteristic
58	#2901	C₂²	1	1	yes	characteristic, complemented
59	#2901	C₂²	1	1	yes	characteristic, complemented
60	#2888	C₂²	1	1	yes	characteristic, complemented
61	#2883	C₂²	1	1	yes	characteristic, complemented
62	#2858	C₂²	1	1	yes	characteristic, complemented
63	#2102	C₂²	1	1	yes	characteristic, complemented
64	#2102	C₂²	1	1	yes	characteristic, complemented
65	#2102	C₂²	1	1	yes	characteristic, complemented
66	#2102	C₂²	1	1	yes	characteristic, complemented
67	#2082	C₂²	1	1	yes	characteristic, complemented
68	#2082	C₂²	1	1	yes	characteristic, complemented
69	#2082	C₂²	1	1	yes	characteristic, complemented
70	#2082	C₂²	1	1	yes	characteristic, complemented
71	#2082	C₂²	1	1	yes	characteristic, complemented
72	#2082	C₂²	1	1	yes	characteristic, complemented
73	#2081	C₂²	1	1	yes	characteristic, complemented
74	#2081	C₂²	1	1	yes	characteristic, complemented
75	#2069	C₂²	1	1	yes	characteristic, complemented
76	#2069	C₂²	1	1	yes	characteristic, complemented
77	#2050	C₂²	1	1	yes	characteristic
78	#2050	C₂²	1	1	yes	characteristic
79	#2049	C₂²	1	1	yes	characteristic, complemented
80	#2049	C₂²	1	1	yes	characteristic, complemented
81	#2049	C₂²	1	1	yes	characteristic, complemented
82	#2049	C₂²	1	1	yes	characteristic, complemented
83	#2048	C₂²	1	1	yes	characteristic, complemented
84	#2048	C₂²	1	1	yes	characteristic, complemented
85	#2031	C₂²	1	1	yes	characteristic, complemented
86	#2031	C₂²	1	1	yes	characteristic, complemented
87	#2031	C₂²	1	1	yes	characteristic, complemented
88	#2031	C₂²	1	1	yes	characteristic, complemented
89	#2031	C₂²	1	1	yes	characteristic, complemented
90	#2031	C₂²	1	1	yes	characteristic, complemented
91	#2031	C₂²	1	1	yes	characteristic, complemented
92	#2031	C₂²	1	1	yes	characteristic, complemented
93	#2009	C₂²	1	1	yes	characteristic
94	#2009	C₂²	1	1	yes	characteristic
95	#2009	C₂²	1	1	yes	characteristic
96	#2009	C₂²	1	1	yes	characteristic
97	#2008	C₂²	1	1	yes	characteristic
98	#2008	C₂²	1	1	yes	characteristic
99	#2005	C₂²	1	1	yes	characteristic, complemented
100	#2005	C₂²	1	1	yes	characteristic, complemented
101	#2004	C₂²	1	1	yes	characteristic
102	#2004	C₂²	1	1	yes	characteristic
103	#2004	C₂²	1	1	yes	characteristic
104	#2004	C₂²	1	1	yes	characteristic
105	#2004	C₂²	1	1	yes	characteristic, complemented
106	#2004	C₂²	1	1	yes	characteristic, complemented
107	#2003	C₂²	1	1	yes	characteristic, complemented
108	#2003	C₂²	1	1	yes	characteristic, complemented
109	#2002	C₂²	1	1	yes	characteristic
110	#2002	C₂²	1	1	yes	characteristic
111	#1994	C₂²	1	1	yes	characteristic, complemented
112	#1994	C₂²	1	1	yes	characteristic, complemented
113	#1967	C₂²	1	1	yes	characteristic, complemented
114	#1967	C₂²	1	1	yes	characteristic, complemented
115	#1965	C₂²	1	1	yes	characteristic, complemented
116	#1962	C₂²	1	1	yes	characteristic
117	#1932	C₂²	1	1	yes	characteristic, complemented
118	#1932	C₂²	1	1	yes	characteristic, complemented
119	#1932	C₂²	1	1	yes	characteristic, complemented
120	#1932	C₂²	1	1	yes	characteristic, complemented
121	#1932	C₂²	1	1	yes	characteristic, complemented
122	#1932	C₂²	1	1	yes	characteristic, complemented
123	#1914	C₂²	1	1	yes	characteristic
124	#1914	C₂²	1	1	yes	characteristic
125	#1914	C₂²	1	1	yes	characteristic
126	#1911	C₂²	1	1	yes	characteristic
127	#1911	C₂²	1	1	yes	characteristic
128	#1911	C₂²	1	1	yes	characteristic
129	#1911	C₂²	1	1	yes	characteristic
130	#1910	C₂²	1	1	yes	characteristic, complemented
131	#1909	C₂²	1	1	yes	characteristic, complemented
132	#1909	C₂²	1	1	yes	characteristic, complemented
133	#1909	C₂²	1	1	yes	characteristic, complemented
134	#1906	C₂²	1	1	yes	characteristic
135	#1906	C₂²	1	1	yes	characteristic
136	#1906	C₂²	1	1	yes	characteristic
137	#1906	C₂²	1	1	yes	characteristic
138	#1906	C₂²	1	1	yes	characteristic
139	#1906	C₂²	1	1	yes	characteristic
140	#1905	C₂²	1	1	yes	characteristic, complemented
141	#1905	C₂²	1	1	yes	characteristic, complemented
142	#1905	C₂²	1	1	yes	characteristic, complemented
143	#1905	C₂²	1	1	yes	characteristic, complemented
144	#1904	C₂²	1	1	yes	characteristic, complemented
145	#1904	C₂²	1	1	yes	characteristic, complemented
146	#1904	C₂²	1	1	yes	characteristic, complemented
147	#1904	C₂²	1	1	yes	characteristic, complemented
148	#1903	C₂²	1	1	yes	characteristic, complemented
149	#1903	C₂²	1	1	yes	characteristic, complemented
150	#1902	C₂²	1	1	yes	characteristic, complemented
151	#1902	C₂²	1	1	yes	characteristic, complemented
152	#1902	C₂²	1	1	yes	characteristic, complemented
153	#1902	C₂²	1	1	yes	characteristic, complemented
154	#1888	C₂²	1	1	yes	characteristic, complemented
155	#1887	C₂²	1	1	yes	characteristic, complemented
156	#1886	C₂²	1	1	yes	characteristic, complemented
157	#1885	C₂²	1	1	yes	characteristic, complemented
158	#1885	C₂²	1	1	yes	characteristic, complemented
159	#1885	C₂²	1	1	yes	characteristic, complemented
160	#1885	C₂²	1	1	yes	characteristic, complemented
161	#1885	C₂²	1	1	yes	characteristic, complemented
162	#1884	C₂²	1	1	yes	characteristic
163	#1884	C₂²	1	1	yes	characteristic
164	#1884	C₂²	1	1	yes	characteristic
165	#1861	C₂²	1	1	yes	characteristic, complemented
166	#1861	C₂²	1	1	yes	characteristic, complemented
167	#1861	C₂²	1	1	yes	characteristic, complemented
168	#1861	C₂²	1	1	yes	characteristic, complemented
169	#1861	C₂²	1	1	yes	characteristic, complemented
170	#1861	C₂²	1	1	yes	characteristic, complemented
171	#1841	C₂²	1	1	yes	characteristic, complemented
172	#1841	C₂²	1	1	yes	characteristic, complemented
173	#1841	C₂²	1	1	yes	characteristic, complemented
174	#1841	C₂²	1	1	yes	characteristic, complemented
175	#1829	C₂²	1	1	yes	characteristic, complemented
176	#1829	C₂²	1	1	yes	characteristic, complemented
177	#1827	C₂²	1	1	yes	characteristic, complemented
178	#1827	C₂²	1	1	yes	characteristic, complemented
179	#1827	C₂²	1	1	yes	characteristic, complemented
180	#1827	C₂²	1	1	yes	characteristic, complemented
181	#1796	C₂²	1	1	yes	characteristic
182	#1796	C₂²	1	1	yes	characteristic
183	#1796	C₂²	1	1	yes	characteristic
184	C₄×#104	C₂²	1	1	yes	characteristic, complemented
185	C₄×#104	C₂²	1	1	yes	characteristic, complemented
186	C₄×#104	C₂²	1	1	yes	characteristic, complemented
187	#585	C₂³	1	1	yes	characteristic
188	C₂×2₋¹⁺⁴	C₂³	1	1	yes	characteristic
189	C₂×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
190	#578	—	4	1	no	—
191	#578	—	4	1	no	—
192	#577	—	4	1	no	—
193	#577	—	4	1	no	—
194	#575	—	4	1	no	—
195	#575	C₂³	1	1	yes	characteristic
196	#575	C₂³	1	1	yes	characteristic
197	#575	C₂³	1	1	yes	characteristic
198	#575	C₂³	1	1	yes	characteristic
199	C₂×#137	—	4	1	no	—
200	C₂×#137	C₂³	1	1	yes	characteristic
201	C₂×#137	C₂³	1	1	yes	characteristic
202	C₂×#137	C₂³	1	1	yes	characteristic
203	C₂×#137	C₂³	1	1	yes	characteristic
204	C₂×#137	C₂³	1	1	yes	characteristic
205	C₂×#137	C₂³	1	1	yes	characteristic
206	C₂×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
207	C₂×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
208	C₂×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
209	C₂×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
210	#568	C₂³	1	1	yes	characteristic
211	#568	C₂³	1	1	yes	characteristic
212	#568	C₂³	1	1	yes	characteristic
213	#568	C₂³	1	1	yes	characteristic
214	#568	C₂³	1	1	yes	characteristic
215	#559	—	4	1	no	—
216	#559	—	4	1	no	—
217	#556	—	4	1	no	—
218	#551	—	4	2	no	—
219	#550	—	4	1	no	—
220	#548	—	4	1	no	—
221	#546	—	4	2	no	—
222	#546	—	4	2	no	—
223	#546	—	4	1	no	—
224	#542	—	4	1	no	—
225	#540	—	4	1	no	—
226	#536	—	2	1	no	—
227	#536	C₂³	1	1	yes	characteristic
228	#536	C₂³	1	1	yes	characteristic
229	#535	—	2	1	no	—
230	#535	C₂³	1	1	yes	characteristic
231	#535	C₂³	1	1	yes	characteristic
232	#535	C₂³	1	1	yes	characteristic
233	#535	C₂³	1	1	yes	characteristic
234	#533	C₂³	1	1	yes	characteristic
235	#533	C₂³	1	1	yes	characteristic
236	#532	—	2	1	no	—
237	#532	—	4	1	no	—
238	#532	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₂×#127	C₂³	1	1	yes	characteristic
241	#529	—	4	1	no	—
242	C₂×#124	—	2	1	no	—
243	C₂×#124	C₂³	1	1	yes	characteristic
244	C₂×#124	C₂³	1	1	yes	characteristic
245	C₂×#124	C₂³	1	1	yes	characteristic
246	C₂×#124	C₂³	1	1	yes	characteristic
247	#519	C₂³	1	1	yes	characteristic
248	#518	C₂³	1	1	yes	characteristic
249	#518	C₂³	1	1	yes	characteristic
250	#518	C₂³	1	1	yes	characteristic
251	C₄×#41	C₂³	1	1	yes	characteristic
252	C₄×#41	C₂³	1	1	yes	characteristic
253	C₄×#41	C₂³	1	1	yes	characteristic
254	#497	—	2	1	no	—
255	#496	—	2	1	no	—
256	#495	—	2	1	no	—
257	#495	—	2	1	no	—
258	#491	—	4	1	no	—
259	#489	—	4	1	no	—
260	#488	—	4	1	no	—
261	#487	—	4	1	no	—
262	#473	—	4	1	no	—
263	#473	—	4	1	no	—
264	#472	—	4	1	no	—
265	#472	—	4	1	no	—
266	#471	—	4	1	no	—
267	#471	—	4	1	no	—
268	#471	—	4	1	no	—
269	#471	—	4	1	no	—
270	#464	—	4	1	no	—
271	#464	—	4	1	no	—
272	#463	—	4	1	no	—
273	#463	—	4	1	no	—
274	#462	—	4	1	no	—
275	#461	—	4	1	no	—
276	B(4,𝔽₂)	—	4	2	no	—
277	#456	—	2	1	no	—
278	#456	—	4	1	no	—
279	#456	—	4	1	no	—
280	#456	—	4	1	no	—
281	#455	—	2	1	no	—
282	#455	—	4	1	no	—
283	#455	—	4	1	no	—
284	#455	—	4	1	no	—
285	#455	—	4	1	no	—
286	#455	—	4	1	no	—
287	#454	—	2	1	no	—
288	#454	—	4	1	no	—
289	#454	—	4	1	no	—
290	#454	—	4	1	no	—
291	#453	—	2	1	no	—
292	#453	—	4	1	no	—
293	#453	—	4	1	no	—
294	#453	—	4	1	no	—
295	#453	—	4	1	no	—
296	#453	—	4	1	no	—
297	#444	—	4	1	no	—
298	#444	—	4	1	no	—
299	#443	—	4	1	no	—
300	#443	—	4	1	no	—
301	#430	C₂³	1	1	yes	characteristic
302	#430	C₂³	1	1	yes	characteristic
303	#430	C₂³	1	1	yes	characteristic
304	#430	C₂³	1	1	yes	characteristic
305	#430	C₂³	1	1	yes	characteristic
306	#430	C₂³	1	1	yes	characteristic
307	#423	C₂³	1	1	yes	characteristic
308	#423	C₂³	1	1	yes	characteristic
309	#423	C₂³	1	1	yes	characteristic
310	#421	—	4	1	no	—
311	#421	—	4	1	no	—
312	#421	C₂³	1	1	yes	characteristic
313	#421	C₂³	1	1	yes	characteristic
314	#421	C₂³	1	1	yes	characteristic
315	#421	C₂³	1	1	yes	characteristic
316	#421	C₂³	1	1	yes	characteristic
317	#421	C₂³	1	1	yes	characteristic
318	#421	C₂³	1	1	yes	characteristic
319	#421	C₂³	1	1	yes	characteristic
320	#421	C₂³	1	1	yes	characteristic
321	#421	C₂³	1	1	yes	characteristic
322	#421	C₂³	1	1	yes	characteristic
323	#421	C₂³	1	1	yes	characteristic
324	C₂×#104	—	4	1	no	—
325	C₂×#104	—	4	1	no	—
326	C₂×#104	C₂³	1	1	yes	characteristic
327	C₂×#104	C₂³	1	1	yes	characteristic
328	C₂×#104	C₂³	1	1	yes	characteristic
329	C₂×#104	C₂³	1	1	yes	characteristic
330	C₂×#104	C₂³	1	1	yes	characteristic
331	C₂×#104	C₂³	1	1	yes	characteristic
332	C₂×#104	C₂³	1	1	yes	characteristic
333	C₂×#104	C₂³	1	1	yes	characteristic
334	C₂×#104	C₂³	1	1	yes	characteristic
335	C₂×#104	C₂³	1	1	yes	characteristic
336	#419	C₂³	1	1	yes	characteristic
337	#419	C₂³	1	1	yes	characteristic
338	#419	C₂³	1	1	yes	characteristic
339	#419	C₂³	1	1	yes	characteristic
340	#419	C₂³	1	1	yes	characteristic
341	#419	C₂³	1	1	yes	characteristic
342	#419	C₂³	1	1	yes	characteristic
343	#419	C₂³	1	1	yes	characteristic
344	#419	C₂³	1	1	yes	characteristic
345	#419	C₂³	1	1	yes	characteristic
346	#418	C₂³	1	1	yes	characteristic
347	#418	C₂³	1	1	yes	characteristic
348	#418	C₂³	1	1	yes	characteristic
349	#418	C₂³	1	1	yes	characteristic
350	#413	—	4	1	no	—
351	#413	C₂³	1	1	yes	characteristic
352	#413	C₂³	1	1	yes	characteristic
353	#413	C₂³	1	1	yes	characteristic
354	#413	C₂³	1	1	yes	characteristic
355	#413	C₂³	1	1	yes	characteristic
356	C₂×#101	C₂³	1	1	yes	characteristic
357	C₂×#101	C₂³	1	1	yes	characteristic
358	C₂×#101	C₂³	1	1	yes	characteristic
359	C₂×#101	C₂³	1	1	yes	characteristic
360	C₂×#100	—	4	1	no	—
361	C₂×#100	C₂³	1	1	yes	characteristic
362	C₂×#100	C₂³	1	1	yes	characteristic
363	C₂×#100	C₂³	1	1	yes	characteristic
364	C₂×#100	C₂³	1	1	yes	characteristic
365	C₂×#100	C₂³	1	1	yes	characteristic
366	C₂×#100	C₂³	1	1	yes	characteristic
367	C₂×#100	C₂³	1	1	yes	characteristic
368	C₂×#100	C₂³	1	1	yes	characteristic
369	#410	C₂³	1	1	yes	characteristic
370	#410	C₂³	1	1	yes	characteristic
371	#410	C₂³	1	1	yes	characteristic
372	#410	C₂³	1	1	yes	characteristic
373	#410	C₂³	1	1	yes	characteristic
374	#410	C₂³	1	1	yes	characteristic
375	#410	C₂³	1	1	yes	characteristic
376	C₂×#99	—	4	2	no	—
377	C₄×M₁₆	C₂³	1	1	yes	characteristic
378	C₄×M₁₆	C₂³	1	1	yes	characteristic
379	C₄×M₁₆	C₂³	1	1	yes	characteristic
380	#390	—	4	2	no	—
381	C₄³	C₂³	1	1	yes	characteristic
382	#344	C₂³	1	1	yes	characteristic
383	#344	C₂³	1	1	yes	characteristic
384	#344	C₂³	1	1	yes	characteristic
385	#344	C₂³	1	1	yes	characteristic
386	#344	C₂³	1	1	yes	characteristic
387	#344	C₂³	1	1	yes	characteristic
388	#344	C₂³	1	1	yes	characteristic
389	#344	C₂³	1	1	yes	characteristic
390	#344	C₂³	1	1	yes	characteristic
391	#344	C₂³	1	1	yes	characteristic
392	#344	C₂³	1	1	yes	characteristic
393	#344	C₂³	1	1	yes	characteristic
394	#344	C₂³	1	1	yes	characteristic
395	#344	C₂³	1	1	yes	characteristic
396	#339	C₂³	1	1	yes	characteristic
397	#339	C₂³	1	1	yes	characteristic
398	#339	C₂³	1	1	yes	characteristic
399	#339	C₂³	1	1	yes	characteristic
400	#339	C₂³	1	1	yes	characteristic
401	#339	C₂³	1	1	yes	characteristic
402	#339	C₂³	1	1	yes	characteristic
403	#339	C₂³	1	1	yes	characteristic
404	#339	C₂³	1	1	yes	characteristic
405	#339	C₂³	1	1	yes	characteristic
406	#339	C₂³	1	1	yes	characteristic
407	#339	C₂³	1	1	yes	characteristic
408	#339	C₂³	1	1	yes	characteristic
409	#339	C₂³	1	1	yes	characteristic
410	#338	C₂³	1	1	yes	characteristic
411	#338	C₂³	1	1	yes	characteristic
412	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
413	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
414	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
415	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
416	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
417	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
418	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
419	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
420	2₋¹⁺⁴	—	2	1	no	—
421	2₋¹⁺⁴	—	2	1	no	—
422	2₋¹⁺⁴	—	2	1	no	—
423	2₋¹⁺⁴	—	4	1	no	—
424	2₋¹⁺⁴	—	4	1	no	—
425	2₋¹⁺⁴	—	4	1	no	—
426	2₋¹⁺⁴	—	4	1	no	—
427	H(5,𝔽₂)	—	2	1	no	—
428	H(5,𝔽₂)	—	2	1	no	—
429	H(5,𝔽₂)	—	2	1	no	—
430	H(5,𝔽₂)	—	4	1	no	—
431	H(5,𝔽₂)	—	4	1	no	—
432	H(5,𝔽₂)	—	4	1	no	—
433	H(5,𝔽₂)	—	4	1	no	—
434	H(5,𝔽₂)	—	4	1	no	—
435	C₂×#41	—	2	1	no	—
436	C₂×#41	—	2	1	no	—
437	C₂×#41	—	2	1	no	—
438	C₂×#41	—	2	1	no	—
439	C₂×#41	—	4	1	no	—
440	C₂×#41	—	4	1	no	—
441	C₂×#41	—	4	1	no	—
442	C₂×#41	—	4	1	no	—
443	C₂×#41	—	4	2	no	—
444	C₂×#41	C₂⁴	1	1	yes	characteristic
445	C₂×#41	C₂⁴	1	1	yes	characteristic
446	C₂×#41	C₂⁴	1	1	yes	characteristic
447	C₂×#41	C₂⁴	1	1	yes	characteristic
448	C₂×#41	C₂⁴	1	1	yes	characteristic
449	C₂²×Q₈	—	2	1	no	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
452	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
453	C₂²×D₄	—	2	2	no	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	2	2	no	—
457	C₂²×D₄	C₂⁴	1	1	yes	characteristic
458	C₂²×D₄	C₂⁴	1	1	yes	characteristic
459	#137	—	2	1	no	—
460	#137	—	2	1	no	—
461	#137	—	2	1	no	—
462	#137	—	2	1	no	—
463	#137	—	2	1	no	—
464	#137	—	2	1	no	—
465	#137	—	2	1	no	—
466	#137	—	2	1	no	—
467	#137	—	4	1	no	—
468	#137	—	4	1	no	—
469	#137	—	4	1	no	—
470	#137	—	4	1	no	—
471	#137	—	4	1	no	—
472	#137	—	4	1	no	—
473	#137	—	4	1	no	—
474	#137	—	4	1	no	—
475	#137	—	4	1	no	—
476	#137	—	4	1	no	—
477	#137	—	4	1	no	—
478	#137	—	4	1	no	—
479	#137	—	4	2	no	—
480	#137	—	4	2	no	—
481	#137	—	4	2	no	—
482	AGL(1,ℤ/8)	—	2	1	no	—
483	AGL(1,ℤ/8)	—	2	1	no	—
484	AGL(1,ℤ/8)	—	2	1	no	—
485	AGL(1,ℤ/8)	—	2	1	no	—
486	AGL(1,ℤ/8)	—	2	1	no	—
487	AGL(1,ℤ/8)	—	2	1	no	—
488	AGL(1,ℤ/8)	—	2	1	no	—
489	AGL(1,ℤ/8)	—	2	1	no	—
490	AGL(1,ℤ/8)	—	4	1	no	—
491	AGL(1,ℤ/8)	—	4	1	no	—
492	AGL(1,ℤ/8)	—	4	1	no	—
493	AGL(1,ℤ/8)	—	4	1	no	—
494	AGL(1,ℤ/8)	—	4	1	no	—
495	AGL(1,ℤ/8)	—	4	1	no	—
496	AGL(1,ℤ/8)	—	4	1	no	—
497	AGL(1,ℤ/8)	—	4	1	no	—
498	AGL(1,ℤ/8)	—	4	2	no	—
499	#135	—	4	1	no	—
500	#135	—	4	1	no	—
501	#135	—	4	1	no	—
502	#135	—	4	1	no	—
503	#135	—	4	2	no	—
504	#135	—	4	2	no	—
505	C₂×Q₁₆	—	2	1	no	—
506	C₂×Q₁₆	—	2	1	no	—
507	C₂×Q₁₆	—	2	1	no	—
508	C₂×Q₁₆	—	2	1	no	—
509	C₂×Q₁₆	—	2	1	no	—
510	C₂×Q₁₆	—	2	1	no	—
511	C₂×Q₁₆	—	4	2	no	—
512	C₂×SD₁₆	—	2	1	no	—
513	C₂×SD₁₆	—	2	1	no	—
514	C₂×SD₁₆	—	2	1	no	—
515	C₂×SD₁₆	—	2	1	no	—
516	C₂×SD₁₆	—	2	1	no	—
517	C₂×SD₁₆	—	2	1	no	—
518	C₂×SD₁₆	—	2	1	no	—
519	C₂×SD₁₆	—	2	1	no	—
520	C₂×SD₁₆	—	2	1	no	—
521	C₂×SD₁₆	—	2	1	no	—
522	C₂×SD₁₆	—	4	2	no	—
523	C₂×D₈	—	2	1	no	—
524	C₂×D₈	—	2	1	no	—
525	C₂×D₈	—	2	1	no	—
526	C₂×D₈	—	2	1	no	—
527	#131	—	4	1	no	—
528	#131	—	4	1	no	—
529	#131	—	4	1	no	—
530	#131	—	4	1	no	—
531	#131	—	4	1	no	—
532	#131	—	4	1	no	—
533	#131	—	4	1	no	—
534	#131	—	4	1	no	—
535	#131	—	4	1	no	—
536	#131	—	4	1	no	—
537	C₂×M₁₆	—	4	1	no	—
538	C₂×M₁₆	—	4	1	no	—
539	C₂×M₁₆	—	4	1	no	—
540	C₂×M₁₆	—	4	1	no	—
541	C₂×M₁₆	—	4	1	no	—
542	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
543	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
544	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
545	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
546	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
547	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
548	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
549	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
550	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
551	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
552	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
553	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	4	1	no	—
561	C₄⋊Q₈	#41	1	1	yes	characteristic, complemented
562	#127	—	2	1	no	—
563	#127	—	2	1	no	—
564	#127	—	2	1	no	—
565	#127	—	2	1	no	—
566	#127	—	2	1	no	—
567	#127	—	2	1	no	—
568	#127	—	4	1	no	—
569	#127	#41	1	1	yes	characteristic, complemented
570	#126	—	4	2	no	—
571	#126	—	4	2	no	—
572	#125	—	2	1	no	—
573	#125	—	2	1	no	—
574	#124	—	2	1	no	—
575	#124	—	2	1	no	—
576	#124	—	2	1	no	—
577	#124	—	2	1	no	—
578	#124	—	2	1	no	—
579	#124	—	2	1	no	—
580	#124	—	2	1	no	—
581	#124	—	2	1	no	—
582	#124	—	2	1	no	—
583	#124	—	2	1	no	—
584	#124	—	2	1	no	—
585	#124	—	2	1	no	—
586	#124	—	2	1	no	—
587	#124	—	2	1	no	—
588	#124	—	4	1	no	—
589	#124	—	4	1	no	—
590	#124	—	4	1	no	—
591	#124	—	4	1	no	—
592	#124	—	4	2	no	—
593	#124	—	4	2	no	—
594	#124	—	4	2	no	—
595	#124	#41	1	1	yes	characteristic, complemented
596	#124	#41	1	1	yes	characteristic, complemented
597	#123	—	4	1	no	—
598	#123	—	4	1	no	—
599	#123	—	4	2	no	—
600	#123	—	4	2	no	—
601	#123	—	4	2	no	—
602	#123	—	4	2	no	—
603	#123	—	4	2	no	—
604	C₂²⋊Q₈	—	4	1	no	—
605	C₂²⋊Q₈	—	4	1	no	—
606	C₂²⋊Q₈	—	4	1	no	—
607	C₂²⋊Q₈	—	4	1	no	—
608	C₂²⋊Q₈	—	4	2	no	—
609	C₂²⋊Q₈	—	4	2	no	—
610	#121	—	4	1	no	—
611	#121	—	4	1	no	—
612	#121	—	4	1	no	—
613	#121	—	4	1	no	—
614	#121	—	4	1	no	—
615	#121	—	4	2	no	—
616	#121	—	4	2	no	—
617	#121	—	4	2	no	—
618	#121	—	4	2	no	—
619	#121	—	4	2	no	—
620	#120	—	2	2	no	—
621	#120	—	2	2	no	—
622	#120	—	2	2	no	—
623	#120	—	4	1	no	—
624	#120	—	4	2	no	—
625	C₄×Q₈	—	2	1	no	—
626	C₄×Q₈	—	2	1	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	—	4	1	no	—
629	C₄×Q₈	—	4	1	no	—
630	C₄×Q₈	—	4	1	no	—
631	C₄×Q₈	—	4	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	4	1	no	—
636	C₄×D₄	—	4	1	no	—
637	C₄×D₄	—	4	1	no	—
638	C₄×D₄	—	4	1	no	—
639	C₄×D₄	—	4	1	no	—
640	C₄×D₄	—	4	1	no	—
641	C₄×D₄	—	4	1	no	—
642	C₄×D₄	—	4	1	no	—
643	C₄×D₄	—	4	1	no	—
644	C₄×D₄	—	4	1	no	—
645	C₄×D₄	—	4	2	no	—
646	C₄×D₄	—	4	2	no	—
647	C₄×D₄	—	4	2	no	—
648	#117	—	2	1	no	—
649	#117	—	2	1	no	—
650	#117	—	2	1	no	—
651	#117	—	4	1	no	—
652	#117	—	4	2	no	—
653	#117	C₂⁴	1	1	yes	characteristic
654	#117	C₂⁴	1	1	yes	characteristic
655	#117	C₂⁴	1	1	yes	characteristic
656	#117	C₂⁴	1	1	yes	characteristic
657	#117	C₂⁴	1	1	yes	characteristic
658	#117	C₂⁴	1	1	yes	characteristic
659	#117	C₂⁴	1	1	yes	characteristic
660	C₂×C₄⋊C₄	—	4	1	no	—
661	C₂×C₂²⋊C₄	—	2	2	no	—
662	C₂×C₂²⋊C₄	—	2	2	no	—
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	—	4	1	no	—
666	C₂×C₂²⋊C₄	—	4	2	no	—
667	C₂×C₂²⋊C₄	—	4	1	no	—
668	C₂×C₂²⋊C₄	—	4	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	2	1	no	—
672	C₂×C₄²	—	4	1	no	—
673	C₂×C₄²	C₂⁴	1	1	yes	characteristic
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	#108	—	4	1	no	—
677	#108	—	4	1	no	—
678	#108	—	4	1	no	—
679	#108	—	4	1	no	—
680	#108	—	4	1	no	—
681	#108	—	4	1	no	—
682	C₄⋊C₈	—	4	1	no	—
683	C₄⋊C₈	—	4	1	no	—
684	C₄⋊C₈	—	4	1	no	—
685	#104	—	2	1	no	—
686	#104	—	2	1	no	—
687	#104	—	2	1	no	—
688	#104	—	2	1	no	—
689	#104	—	2	1	no	—
690	#104	—	2	1	no	—
691	#104	—	2	1	no	—
692	#104	—	2	1	no	—
693	#104	—	2	1	no	—
694	#104	—	2	1	no	—
695	#104	—	2	1	no	—
696	#104	—	2	1	no	—
697	#104	—	2	1	no	—
698	#104	—	2	1	no	—
699	#104	—	2	1	no	—
700	#104	—	2	1	no	—
701	#104	—	2	1	no	—
702	#104	—	2	1	no	—
703	#104	—	2	1	no	—
704	#104	—	2	1	no	—
705	#104	—	4	1	no	—
706	#104	—	4	1	no	—
707	#104	—	4	1	no	—
708	#104	—	4	1	no	—
709	#104	—	4	1	no	—
710	#104	—	4	1	no	—
711	#104	—	4	1	no	—
712	#104	—	4	1	no	—
713	#104	—	4	1	no	—
714	#104	—	4	1	no	—
715	#104	—	4	1	no	—
716	#104	—	4	1	no	—
717	#103	—	4	1	no	—
718	#103	—	4	1	no	—
719	#103	—	4	1	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#103	—	4	1	no	—
724	#103	—	4	1	no	—
725	#103	—	4	1	no	—
726	#103	—	4	1	no	—
727	#102	—	4	1	no	—
728	#102	—	4	1	no	—
729	#102	—	4	1	no	—
730	#102	—	4	1	no	—
731	#101	—	2	1	no	—
732	#101	—	2	1	no	—
733	#101	—	2	1	no	—
734	#101	—	2	1	no	—
735	#101	—	2	1	no	—
736	#101	—	4	1	no	—
737	#101	—	4	1	no	—
738	#101	—	4	1	no	—
739	#101	—	4	1	no	—
740	#100	—	2	1	no	—
741	#100	—	2	1	no	—
742	#100	—	2	1	no	—
743	#100	—	2	1	no	—
744	#100	—	2	1	no	—
745	#100	—	4	1	no	—
746	#100	—	4	1	no	—
747	#100	—	4	1	no	—
748	#100	—	4	1	no	—
749	#100	—	4	1	no	—
750	#100	—	4	1	no	—
751	#100	—	4	1	no	—
752	#100	—	4	1	no	—
753	#99	—	4	1	no	—
754	#99	—	4	1	no	—
755	#99	—	4	1	no	—
756	#99	—	4	1	no	—
757	#99	—	4	1	no	—
758	#99	—	4	1	no	—
759	#99	—	4	1	no	—
760	#97	—	2	1	no	—
761	#97	—	2	1	no	—
762	#97	—	2	1	no	—
763	C₄×C₈	—	2	1	no	—
764	C₄×C₈	—	2	1	no	—
765	C₄×C₈	—	2	1	no	—
766	C₂⁴	—	2	2	no	—
767	C₂⁴	—	2	1	no	—
768	C₂⁴	H(5,𝔽₂)	1	2	yes	—
769	#41	—	2	1	no	—
770	#41	—	2	1	no	—
771	#41	—	2	1	no	—
772	#41	—	2	1	no	—
773	#41	—	2	1	no	—
774	#41	—	2	1	no	—
775	#41	—	2	1	no	—
776	#41	—	2	1	no	—
777	#41	—	2	1	no	—
778	#41	—	2	1	no	—
779	#41	—	2	1	no	—
780	#41	—	2	1	no	—
781	#41	—	2	1	no	—
782	#41	—	2	1	no	—
783	#41	—	2	1	no	—
784	#41	—	2	1	no	—
785	#41	—	2	1	no	—
786	#41	—	2	1	no	—
787	#41	—	2	1	no	—
788	#41	—	2	1	no	—
789	#41	—	4	1	no	—
790	#41	—	4	1	no	—
791	#41	—	4	1	no	—
792	#41	—	4	1	no	—
793	#41	—	4	1	no	—
794	#41	—	4	1	no	—
795	#41	—	4	2	no	—
796	#41	—	8	1	no	—
797	#41	—	8	1	no	—
798	#41	—	8	1	no	—
799	#41	—	8	1	no	—
800	#41	—	8	1	no	—
801	#41	—	8	1	no	—
802	#41	—	8	1	no	—
803	#41	—	8	2	no	—
804	#41	—	8	2	no	—
805	#41	—	8	1	no	—
806	#41	—	8	1	no	—
807	#41	—	8	1	no	—
808	#41	—	8	1	no	—
809	#41	—	16	4	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	4	1	no	—
823	C₂×Q₈	—	4	1	no	—
824	C₂×Q₈	—	4	1	no	—
825	C₂×Q₈	—	4	1	no	—
826	C₂×Q₈	—	4	1	no	—
827	C₂×Q₈	—	4	1	no	—
828	C₂×Q₈	—	4	2	no	—
829	C₂×Q₈	—	8	1	no	—
830	C₂×Q₈	—	8	1	no	—
831	C₂×Q₈	—	8	1	no	—
832	C₂×Q₈	C₂×#41	1	1	yes	characteristic
833	C₂×Q₈	C₂×#41	1	1	yes	characteristic
834	C₂×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
835	C₂×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
836	C₂×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
837	C₂×D₄	—	2	1	no	—
838	C₂×D₄	—	2	1	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	2	1	no	—
841	C₂×D₄	—	2	1	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	1	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	4	2	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	—	4	1	no	—
860	C₂×D₄	—	4	1	no	—
861	C₂×D₄	—	4	1	no	—
862	C₂×D₄	—	4	1	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂×D₄	—	8	1	no	—
868	C₂×D₄	—	8	1	no	—
869	C₂×D₄	—	8	1	no	—
870	C₂×D₄	—	8	1	no	—
871	C₂×D₄	—	8	4	no	—
872	C₂×D₄	—	8	2	no	—
873	C₂×D₄	—	8	2	no	—
874	C₂×D₄	—	8	1	no	—
875	C₂×D₄	—	8	1	no	—
876	C₂×D₄	—	8	1	no	—
877	C₂×D₄	C₂×#41	1	1	yes	characteristic
878	C₂×D₄	C₂×#41	1	1	yes	characteristic
879	C₂×D₄	H(5,𝔽₂)	1	1	yes	characteristic
880	C₂×D₄	H(5,𝔽₂)	1	1	yes	characteristic
881	C₂×D₄	H(5,𝔽₂)	1	1	yes	characteristic
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	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	—	4	1	no	—
894	C₂²×C₄	—	4	1	no	—
895	C₂²×C₄	—	4	1	no	—
896	C₂²×C₄	—	4	1	no	—
897	C₂²×C₄	—	4	1	no	—
898	C₂²×C₄	—	4	2	no	—
899	C₂²×C₄	—	4	2	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	—	8	1	no	—
902	C₂²×C₄	C₂⁵	1	1	yes	characteristic
903	Q₁₆	—	4	1	no	—
904	Q₁₆	—	4	1	no	—
905	Q₁₆	—	4	1	no	—
906	Q₁₆	—	4	1	no	—
907	Q₁₆	—	4	2	no	—
908	Q₁₆	—	4	2	no	—
909	Q₁₆	—	8	1	no	—
910	Q₁₆	—	8	1	no	—
911	Q₁₆	—	8	1	no	—
912	Q₁₆	—	8	1	no	—
913	SD₁₆	—	4	1	no	—
914	SD₁₆	—	4	1	no	—
915	SD₁₆	—	4	1	no	—
916	SD₁₆	—	4	1	no	—
917	SD₁₆	—	4	1	no	—
918	SD₁₆	—	4	1	no	—
919	SD₁₆	—	4	1	no	—
920	SD₁₆	—	4	1	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	8	1	no	—
924	SD₁₆	—	8	1	no	—
925	SD₁₆	—	8	1	no	—
926	SD₁₆	—	8	1	no	—
927	SD₁₆	—	8	1	no	—
928	SD₁₆	—	8	1	no	—
929	SD₁₆	—	8	1	no	—
930	SD₁₆	—	8	1	no	—
931	D₈	—	4	1	no	—
932	D₈	—	4	1	no	—
933	D₈	—	4	1	no	—
934	D₈	—	4	1	no	—
935	D₈	—	8	1	no	—
936	D₈	—	8	1	no	—
937	D₈	—	8	1	no	—
938	D₈	—	8	1	no	—
939	M₁₆	—	2	1	no	—
940	M₁₆	—	2	1	no	—
941	M₁₆	—	2	1	no	—
942	M₁₆	—	2	1	no	—
943	M₁₆	—	2	1	no	—
944	M₁₆	—	2	1	no	—
945	M₁₆	—	2	1	no	—
946	M₁₆	—	2	1	no	—
947	M₁₆	—	2	1	no	—
948	M₁₆	—	2	1	no	—
949	M₁₆	—	2	1	no	—
950	M₁₆	—	2	1	no	—
951	M₁₆	—	2	1	no	—
952	M₁₆	—	2	1	no	—
953	M₁₆	—	2	1	no	—
954	M₁₆	—	2	1	no	—
955	M₁₆	—	2	1	no	—
956	M₁₆	—	2	1	no	—
957	M₁₆	—	2	1	no	—
958	M₁₆	—	2	1	no	—
959	M₁₆	—	2	1	no	—
960	M₁₆	—	2	1	no	—
961	M₁₆	—	2	1	no	—
962	M₁₆	—	2	1	no	—
963	M₁₆	—	4	2	no	—
964	M₁₆	—	8	1	no	—
965	M₁₆	—	8	1	no	—
966	M₁₆	—	8	1	no	—
967	M₁₆	—	8	1	no	—
968	C₂×C₈	—	2	1	no	—
969	C₂×C₈	—	2	1	no	—
970	C₂×C₈	—	2	1	no	—
971	C₂×C₈	—	2	1	no	—
972	C₂×C₈	—	2	1	no	—
973	C₂×C₈	—	2	1	no	—
974	C₂×C₈	—	2	1	no	—
975	C₂×C₈	—	2	1	no	—
976	C₂×C₈	—	2	1	no	—
977	C₂×C₈	—	2	1	no	—
978	C₂×C₈	—	2	1	no	—
979	C₂×C₈	—	2	1	no	—
980	C₂×C₈	—	4	2	no	—
981	C₂×C₈	—	8	1	no	—
982	C₂×C₈	—	8	1	no	—
983	C₂×C₈	—	8	1	no	—
984	C₂×C₈	—	8	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	4	1	no	—
993	C₄⋊C₄	—	4	1	no	—
994	C₄⋊C₄	—	4	1	no	—
995	C₄⋊C₄	—	4	1	no	—
996	C₄⋊C₄	—	4	1	no	—
997	C₄⋊C₄	—	4	2	no	—
998	C₄⋊C₄	—	4	1	no	—
999	C₄⋊C₄	—	4	1	no	—
1000	C₄⋊C₄	—	4	2	no	—
1001	C₄⋊C₄	—	4	1	no	—
1002	C₄⋊C₄	—	4	1	no	—
1003	C₄⋊C₄	—	4	1	no	—
1004	C₄⋊C₄	—	4	2	no	—
1005	C₄⋊C₄	—	8	1	no	—
1006	C₄⋊C₄	—	8	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	4	1	no	—
1015	C₂²⋊C₄	—	4	1	no	—
1016	C₂²⋊C₄	—	4	2	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	4	2	no	—
1019	C₂²⋊C₄	—	4	2	no	—
1020	C₂²⋊C₄	—	4	2	no	—
1021	C₂²⋊C₄	—	4	1	no	—
1022	C₂²⋊C₄	—	4	1	no	—
1023	C₂²⋊C₄	—	4	1	no	—
1024	C₂²⋊C₄	—	4	2	no	—
1025	C₂²⋊C₄	—	4	2	no	—
1026	C₂²⋊C₄	—	4	2	no	—
1027	C₂²⋊C₄	—	4	2	no	—
1028	C₂²⋊C₄	—	4	2	no	—
1029	C₂²⋊C₄	—	4	2	no	—
1030	C₂²⋊C₄	—	4	2	no	—
1031	C₂²⋊C₄	—	4	2	no	—
1032	C₂²⋊C₄	—	8	1	no	—
1033	C₂²⋊C₄	—	8	1	no	—
1034	C₂²⋊C₄	—	8	1	no	—
1035	C₂²⋊C₄	—	8	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	4	1	no	—
1047	C₄²	—	4	1	no	—
1048	C₄²	—	4	1	no	—
1049	C₄²	—	4	2	no	—
1050	C₄²	—	8	2	no	—
1051	C₄²	C₂×#41	1	1	yes	characteristic
1052	C₄²	C₂×#41	1	1	yes	characteristic
1053	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
1054	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
1055	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
1056	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	8	1	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	—	16	2	no	—
1073	C₂³	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1074	Q₈	—	2	1	no	—
1075	Q₈	—	2	1	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	1	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	2	1	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	1	no	—
1084	Q₈	—	4	1	no	—
1085	Q₈	—	4	1	no	—
1086	Q₈	—	4	1	no	—
1087	Q₈	—	4	1	no	—
1088	Q₈	—	4	1	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	8	2	no	—
1093	Q₈	—	8	1	no	—
1094	Q₈	—	8	2	no	—
1095	Q₈	—	16	1	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	1	no	—
1099	D₄	—	2	1	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	2	1	no	—
1106	D₄	—	4	1	no	—
1107	D₄	—	4	1	no	—
1108	D₄	—	4	1	no	—
1109	D₄	—	4	1	no	—
1110	D₄	—	4	1	no	—
1111	D₄	—	4	1	no	—
1112	D₄	—	4	1	no	—
1113	D₄	—	4	1	no	—
1114	D₄	—	4	1	no	—
1115	D₄	—	4	1	no	—
1116	D₄	—	4	1	no	—
1117	D₄	—	4	1	no	—
1118	D₄	—	4	1	no	—
1119	D₄	—	4	1	no	—
1120	D₄	—	4	1	no	—
1121	D₄	—	4	1	no	—
1122	D₄	—	4	1	no	—
1123	D₄	—	4	1	no	—
1124	D₄	—	8	4	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	1	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	1	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	16	1	no	—
1132	D₄	—	16	2	no	—
1133	D₄	—	16	2	no	—
1134	D₄	—	16	2	no	—
1135	D₄	—	16	2	no	—
1136	D₄	—	16	2	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	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	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	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	1	no	—
1177	C₂×C₄	—	8	1	no	—
1178	C₂×C₄	—	8	1	no	—
1179	C₂×C₄	—	8	2	no	—
1180	C₂×C₄	—	8	2	no	—
1181	C₂×C₄	—	16	1	no	—
1182	C₂×C₄	—	16	1	no	—
1183	C₂×C₄	—	16	2	no	—
1184	C₂×C₄	—	16	2	no	—
1185	C₂×C₄	—	16	2	no	—
1186	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1187	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1190	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1191	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₈	—	4	1	no	—
1193	C₈	—	4	1	no	—
1194	C₈	—	4	1	no	—
1195	C₈	—	4	1	no	—
1196	C₈	—	4	1	no	—
1197	C₈	—	4	1	no	—
1198	C₈	—	4	1	no	—
1199	C₈	—	4	1	no	—
1200	C₈	—	4	1	no	—
1201	C₈	—	4	1	no	—
1202	C₈	—	4	1	no	—
1203	C₈	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	—	8	2	no	—
1213	C₂²	—	8	1	no	—
1214	C₂²	—	8	2	no	—
1215	C₂²	—	8	1	no	—
1216	C₂²	—	8	1	no	—
1217	C₂²	—	8	2	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	2	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	16	1	no	—
1222	C₂²	—	16	1	no	—
1223	C₂²	—	32	1	no	—
1224	C₂²	—	32	2	no	—
1225	C₂²	#3490	1	1	yes	characteristic
1226	C₂²	#3532	1	1	yes	characteristic
1227	C₂²	#3532	1	1	yes	characteristic
1228	C₄	—	2	2	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	1	no	—
1248	C₄	#3519	1	1	yes	characteristic
1249	C₄	#3519	1	1	yes	characteristic
1250	C₄	#3532	1	1	yes	characteristic
1251	C₄	#3543	1	1	yes	characteristic
1252	C₂	—	2	1	no	—
1253	C₂	—	2	1	no	—
1254	C₂	—	2	1	no	—
1255	C₂	—	8	2	no	—
1256	C₂	—	8	1	no	—
1257	C₂	—	8	1	no	—
1258	C₂	—	8	1	no	—
1259	C₂	—	8	1	no	—
1260	C₂	—	8	1	no	—
1261	C₂	—	16	1	no	—
1262	C₂	#48088	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#48088
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #32704	C₂	semidirect
2. #32698	C₂	semidirect
3. #32696	C₂	semidirect
4. #32696	C₂	semidirect
5. #32696	C₂	semidirect
6. #31417	C₂	semidirect
7. #31416	C₂	semidirect
8. #31415	C₂	semidirect
9. #31415	C₂	semidirect
10. #31285	C₂	semidirect
11. #31283	C₂	semidirect
12. #30498	C₂	semidirect
13. #30058	C₂	semidirect
14. #30056	C₂	semidirect
15. #29232	C₂	semidirect
16. #29232	C₂	semidirect
17. #25748	C₂	semidirect
18. #25592	C₂	semidirect
19. #25590	C₂	semidirect
20. #25199	C₂	semidirect
21. #25196	C₂	semidirect
22. #24474	C₂	semidirect
23. #24473	C₂	semidirect
24. #24000	C₂	semidirect
25. #23998	C₂	semidirect
26. #23991	C₂	semidirect
27. #23990	C₂	semidirect
28. #23873	C₂	semidirect
29. #23362	C₂	semidirect
30. #22899	C₂	semidirect
31. #21784	C₂	semidirect
37. #3140	C₂²	semidirect
38. #3139	C₂²	semidirect
43. #3040	C₂²	semidirect
44. #3040	C₂²	semidirect
45. #3039	C₂²	semidirect
47. #3022	C₂²	semidirect
48. #3021	C₂²	semidirect
54. C₂×#455	C₂²	semidirect
55. C₂×#453	C₂²	semidirect
58. #2901	C₂²	semidirect
59. #2901	C₂²	semidirect
60. #2888	C₂²	semidirect
61. #2883	C₂²	semidirect
62. #2858	C₂²	semidirect
63. #2102	C₂²	semidirect
64. #2102	C₂²	semidirect
65. #2102	C₂²	semidirect
66. #2102	C₂²	semidirect
67. #2082	C₂²	semidirect
68. #2082	C₂²	semidirect
69. #2082	C₂²	semidirect
70. #2082	C₂²	semidirect
71. #2082	C₂²	semidirect
72. #2082	C₂²	semidirect
73. #2081	C₂²	semidirect
74. #2081	C₂²	semidirect
75. #2069	C₂²	semidirect
76. #2069	C₂²	semidirect
79. #2049	C₂²	semidirect
80. #2049	C₂²	semidirect
81. #2049	C₂²	semidirect
82. #2049	C₂²	semidirect
83. #2048	C₂²	semidirect
84. #2048	C₂²	semidirect
85. #2031	C₂²	semidirect
86. #2031	C₂²	semidirect
87. #2031	C₂²	semidirect
88. #2031	C₂²	semidirect
89. #2031	C₂²	semidirect
90. #2031	C₂²	semidirect
91. #2031	C₂²	semidirect
92. #2031	C₂²	semidirect
99. #2005	C₂²	semidirect
100. #2005	C₂²	semidirect
105. #2004	C₂²	semidirect
106. #2004	C₂²	semidirect
107. #2003	C₂²	semidirect
108. #2003	C₂²	semidirect
111. #1994	C₂²	semidirect
112. #1994	C₂²	semidirect
113. #1967	C₂²	semidirect
114. #1967	C₂²	semidirect
115. #1965	C₂²	semidirect
117. #1932	C₂²	semidirect
118. #1932	C₂²	semidirect
119. #1932	C₂²	semidirect
120. #1932	C₂²	semidirect
121. #1932	C₂²	semidirect
122. #1932	C₂²	semidirect
130. #1910	C₂²	semidirect
131. #1909	C₂²	semidirect
132. #1909	C₂²	semidirect
133. #1909	C₂²	semidirect
140. #1905	C₂²	semidirect
141. #1905	C₂²	semidirect
142. #1905	C₂²	semidirect
143. #1905	C₂²	semidirect
144. #1904	C₂²	semidirect
145. #1904	C₂²	semidirect
146. #1904	C₂²	semidirect
147. #1904	C₂²	semidirect
148. #1903	C₂²	semidirect
149. #1903	C₂²	semidirect
150. #1902	C₂²	semidirect
151. #1902	C₂²	semidirect
152. #1902	C₂²	semidirect
153. #1902	C₂²	semidirect
154. #1888	C₂²	semidirect
155. #1887	C₂²	semidirect
156. #1886	C₂²	semidirect
157. #1885	C₂²	semidirect
158. #1885	C₂²	semidirect
159. #1885	C₂²	semidirect
160. #1885	C₂²	semidirect
161. #1885	C₂²	semidirect
165. #1861	C₂²	semidirect
166. #1861	C₂²	semidirect
167. #1861	C₂²	semidirect
168. #1861	C₂²	semidirect
169. #1861	C₂²	semidirect
170. #1861	C₂²	semidirect
171. #1841	C₂²	semidirect
172. #1841	C₂²	semidirect
173. #1841	C₂²	semidirect
174. #1841	C₂²	semidirect
175. #1829	C₂²	semidirect
176. #1829	C₂²	semidirect
177. #1827	C₂²	semidirect
178. #1827	C₂²	semidirect
179. #1827	C₂²	semidirect
180. #1827	C₂²	semidirect
184. C₄×#104	C₂²	semidirect
185. C₄×#104	C₂²	semidirect
186. C₄×#104	C₂²	semidirect
561. C₄⋊Q₈	#41	semidirect
569. #127	#41	semidirect
595. #124	#41	semidirect
596. #124	#41	semidirect

Maximal subgroups

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

subgroup	index
#32704	2
#32698	2
#32696	2
#31417	2
#31416	2
#31415	2
#31285	2
#31283	2
#30498	2
#30058	2
#30056	2
#29232	2
#25748	2
#25592	2
#25590	2
#25199	2
#25196	2
#24474	2
#24473	2
#24000	2
#23998	2
#23991	2
#23990	2
#23873	2
#23362	2
#22899	2
#21784	2