Subgroups — #7625001

Order 512.

1359 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62434	C₂	1	1	yes	maximal, characteristic, complemented
2	#62432	C₂	1	1	yes	maximal, characteristic, complemented
3	#33969	C₂	1	1	yes	maximal, characteristic, complemented
4	#33968	C₂	1	1	yes	maximal, characteristic, complemented
5	#33967	C₂	1	1	yes	maximal, characteristic, complemented
6	#33965	C₂	1	1	yes	maximal, characteristic, complemented
7	#33844	C₂	1	1	yes	maximal, characteristic, complemented
8	#33843	C₂	1	1	yes	maximal, characteristic, complemented
9	#33842	C₂	1	1	yes	maximal, characteristic, complemented
10	#33841	C₂	1	1	yes	maximal, characteristic, complemented
11	#33837	C₂	1	1	yes	maximal, characteristic, complemented
12	#33836	C₂	1	1	yes	maximal, characteristic, complemented
13	#33836	C₂	1	1	yes	maximal, characteristic, complemented
14	#33835	C₂	1	1	yes	maximal, characteristic, complemented
15	#33835	C₂	1	1	yes	maximal, characteristic, complemented
16	#33833	C₂	1	1	yes	maximal, characteristic, complemented
17	#33832	C₂	1	1	yes	maximal, characteristic, complemented
18	#33832	C₂	1	1	yes	maximal, characteristic, complemented
19	#33789	C₂	1	1	yes	maximal, characteristic, complemented
20	#33789	C₂	1	1	yes	maximal, characteristic, complemented
21	#33788	C₂	1	1	yes	maximal, characteristic, complemented
22	#33787	C₂	1	1	yes	maximal, characteristic, complemented
23	#33785	C₂	1	1	yes	maximal, characteristic, complemented
24	#33784	C₂	1	1	yes	maximal, characteristic, complemented
25	#33750	C₂	1	1	yes	maximal, characteristic, complemented
26	#33743	C₂	1	1	yes	maximal, characteristic, complemented
27	#33741	C₂	1	1	yes	maximal, characteristic, complemented
28	#33722	C₂	1	1	yes	maximal, characteristic, complemented
29	#33721	C₂	1	1	yes	maximal, characteristic, complemented
30	#33718	C₂	1	1	yes	maximal, characteristic, complemented
31	#33481	C₂	1	1	yes	maximal, characteristic, complemented
32	#3562	—	2	1	no	—
33	#3552	—	2	1	no	—
34	C₂×#510	C₂²	1	1	yes	characteristic
35	C₂×#510	C₂²	1	1	yes	characteristic
36	C₂×#510	C₂²	1	1	yes	characteristic
37	C₂×#510	C₂²	1	1	yes	characteristic
38	C₂×#510	C₂²	1	1	yes	characteristic, complemented
39	C₂×#510	C₂²	1	1	yes	characteristic, complemented
40	C₂×#510	C₂²	1	1	yes	characteristic, complemented
41	C₂×#509	C₂²	1	1	yes	characteristic
42	C₂×#508	C₂²	1	1	yes	characteristic
43	C₂×#508	C₂²	1	1	yes	characteristic
44	C₂²×Q₃₂	C₂²	1	1	yes	characteristic, complemented
45	C₂²×SD₃₂	C₂²	1	1	yes	characteristic
46	#3401	—	2	1	no	—
47	#3398	—	2	1	no	—
48	#3396	C₂²	1	1	yes	characteristic
49	#3395	C₂²	1	1	yes	characteristic, complemented
50	#3393	C₂²	1	1	yes	characteristic
51	#3393	C₂²	1	1	yes	characteristic, complemented
52	#3287	C₂²	1	1	yes	characteristic
53	D₄×Q₁₆	C₂²	1	1	yes	characteristic
54	D₄×Q₁₆	C₂²	1	1	yes	characteristic
55	D₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
56	#3285	C₂²	1	1	yes	characteristic
57	#3285	C₂²	1	1	yes	characteristic
58	#3285	C₂²	1	1	yes	characteristic
59	#3285	C₂²	1	1	yes	characteristic, complemented
60	#3283	C₂²	1	1	yes	characteristic
61	#3283	C₂²	1	1	yes	characteristic
62	#3280	C₂²	1	1	yes	characteristic
63	#3280	C₂²	1	1	yes	characteristic
64	#3276	—	2	1	no	—
65	#3275	—	2	1	no	—
66	#3271	—	2	1	no	—
67	#3270	—	2	1	no	—
68	#3270	—	2	1	no	—
69	#3267	—	2	1	no	—
70	#3223	—	2	1	no	—
71	#3223	—	2	1	no	—
72	#3222	—	2	1	no	—
73	#3221	—	2	1	no	—
74	#3219	—	2	1	no	—
75	#3218	—	2	1	no	—
76	#3177	C₂²	1	1	yes	characteristic
77	#3177	C₂²	1	1	yes	characteristic
78	#3177	C₂²	1	1	yes	characteristic, complemented
79	#3176	C₂²	1	1	yes	characteristic
80	#3168	C₂²	1	1	yes	characteristic
81	#3168	C₂²	1	1	yes	characteristic, complemented
82	#3156	C₂²	1	1	yes	characteristic
83	#3156	C₂²	1	1	yes	characteristic
84	#3156	C₂²	1	1	yes	characteristic, complemented
85	#3155	C₂²	1	1	yes	characteristic
86	#3147	C₂²	1	1	yes	characteristic
87	C₂×#494	C₂²	1	1	yes	characteristic, complemented
88	#2966	C₂²	1	1	yes	characteristic
89	#2253	C₂²	1	1	yes	characteristic, complemented
90	#2251	C₂²	1	1	yes	characteristic
91	#2251	C₂²	1	1	yes	characteristic
92	#2251	C₂²	1	1	yes	characteristic
93	#2251	C₂²	1	1	yes	characteristic
94	#2251	C₂²	1	1	yes	characteristic
95	#2251	C₂²	1	1	yes	characteristic
96	#2251	C₂²	1	1	yes	characteristic, complemented
97	#2251	C₂²	1	1	yes	characteristic, complemented
98	#2251	C₂²	1	1	yes	characteristic, complemented
99	#2251	C₂²	1	1	yes	characteristic, complemented
100	#2250	C₂²	1	1	yes	characteristic
101	#2250	C₂²	1	1	yes	characteristic
102	#2249	C₂²	1	1	yes	characteristic
103	#2249	C₂²	1	1	yes	characteristic
104	#2249	C₂²	1	1	yes	characteristic
105	#2248	C₂²	1	1	yes	characteristic
106	#2248	C₂²	1	1	yes	characteristic
107	#2248	C₂²	1	1	yes	characteristic
108	#2247	C₂²	1	1	yes	characteristic, complemented
109	#2247	C₂²	1	1	yes	characteristic, complemented
110	#2247	C₂²	1	1	yes	characteristic, complemented
111	#2245	C₂²	1	1	yes	characteristic, complemented
112	#2245	C₂²	1	1	yes	characteristic, complemented
113	#2245	C₂²	1	1	yes	characteristic, complemented
114	#2244	C₂²	1	1	yes	characteristic
115	#2242	C₂²	1	1	yes	characteristic
116	#2242	C₂²	1	1	yes	characteristic, complemented
117	#2220	C₂²	1	1	yes	characteristic
118	#2220	C₂²	1	1	yes	characteristic
119	#2220	C₂²	1	1	yes	characteristic, complemented
120	#2220	C₂²	1	1	yes	characteristic, complemented
121	#2219	C₂²	1	1	yes	characteristic
122	#2219	C₂²	1	1	yes	characteristic
123	#2219	C₂²	1	1	yes	characteristic, complemented
124	#2218	C₂²	1	1	yes	characteristic
125	#2217	C₂²	1	1	yes	characteristic
126	#2217	C₂²	1	1	yes	characteristic, complemented
127	#2216	C₂²	1	1	yes	characteristic
128	#2216	C₂²	1	1	yes	characteristic
129	#2211	C₂²	1	1	yes	characteristic
130	#2211	C₂²	1	1	yes	characteristic
131	#2211	C₂²	1	1	yes	characteristic
132	#2211	C₂²	1	1	yes	characteristic
133	#2211	C₂²	1	1	yes	characteristic
134	#2211	C₂²	1	1	yes	characteristic, complemented
135	#2211	C₂²	1	1	yes	characteristic, complemented
136	#2211	C₂²	1	1	yes	characteristic, complemented
137	#2210	C₂²	1	1	yes	characteristic
138	#2210	C₂²	1	1	yes	characteristic
139	#2210	C₂²	1	1	yes	characteristic, complemented
140	#2210	C₂²	1	1	yes	characteristic, complemented
141	#2209	C₂²	1	1	yes	characteristic, complemented
142	#2209	C₂²	1	1	yes	characteristic, complemented
143	#2209	C₂²	1	1	yes	characteristic, complemented
144	#2209	C₂²	1	1	yes	characteristic, complemented
145	#2209	C₂²	1	1	yes	characteristic, complemented
146	#2209	C₂²	1	1	yes	characteristic, complemented
147	#2208	C₂²	1	1	yes	characteristic
148	#2208	C₂²	1	1	yes	characteristic
149	#2208	C₂²	1	1	yes	characteristic
150	#2208	C₂²	1	1	yes	characteristic, complemented
151	#2207	C₂²	1	1	yes	characteristic
152	#2207	C₂²	1	1	yes	characteristic
153	#2189	C₂²	1	1	yes	characteristic
154	#2189	C₂²	1	1	yes	characteristic
155	#2189	C₂²	1	1	yes	characteristic
156	#2189	C₂²	1	1	yes	characteristic
157	#2189	C₂²	1	1	yes	characteristic
158	#2189	C₂²	1	1	yes	characteristic
159	#2189	C₂²	1	1	yes	characteristic
160	#2189	C₂²	1	1	yes	characteristic, complemented
161	#2188	C₂²	1	1	yes	characteristic
162	#2188	C₂²	1	1	yes	characteristic
163	#2188	C₂²	1	1	yes	characteristic, complemented
164	#2188	C₂²	1	1	yes	characteristic, complemented
165	#2188	C₂²	1	1	yes	characteristic, complemented
166	#2188	C₂²	1	1	yes	characteristic, complemented
167	#2187	C₂²	1	1	yes	characteristic
168	#2187	C₂²	1	1	yes	characteristic
169	#2186	C₂²	1	1	yes	characteristic
170	#2186	C₂²	1	1	yes	characteristic
171	#2186	C₂²	1	1	yes	characteristic, complemented
172	#2186	C₂²	1	1	yes	characteristic, complemented
173	#2185	C₂²	1	1	yes	characteristic
174	#2185	C₂²	1	1	yes	characteristic
175	#2185	C₂²	1	1	yes	characteristic
176	#2185	C₂²	1	1	yes	characteristic, complemented
177	#2183	C₂²	1	1	yes	characteristic, complemented
178	#2183	C₂²	1	1	yes	characteristic, complemented
179	#2177	C₂²	1	1	yes	characteristic
180	#2176	C₂²	1	1	yes	characteristic, complemented
181	#2176	C₂²	1	1	yes	characteristic, complemented
182	#2176	C₂²	1	1	yes	characteristic, complemented
183	#2175	C₂²	1	1	yes	characteristic
184	#2175	C₂²	1	1	yes	characteristic
185	#2175	C₂²	1	1	yes	characteristic, complemented
186	#2175	C₂²	1	1	yes	characteristic, complemented
187	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
188	C₄×Q₃₂	C₂²	1	1	yes	characteristic, complemented
189	C₄×SD₃₂	C₂²	1	1	yes	characteristic
190	C₄×SD₃₂	C₂²	1	1	yes	characteristic, complemented
191	#2169	C₂²	1	1	yes	characteristic
192	#2169	C₂²	1	1	yes	characteristic, complemented
193	#2168	C₂²	1	1	yes	characteristic
194	#2168	C₂²	1	1	yes	characteristic
195	#2168	C₂²	1	1	yes	characteristic
196	#2168	C₂²	1	1	yes	characteristic, complemented
197	#2164	C₂²	1	1	yes	characteristic
198	#2164	C₂²	1	1	yes	characteristic, complemented
199	#2163	C₂²	1	1	yes	characteristic, complemented
200	#2108	C₂²	1	1	yes	characteristic
201	#2108	C₂²	1	1	yes	characteristic, complemented
202	C₄×M₃₂	C₂²	1	1	yes	characteristic, complemented
203	C₂×#137	—	2	1	no	—
204	C₂×#137	—	2	1	no	—
205	C₂×#137	—	2	1	no	—
206	C₂×AGL(1,ℤ/8)	—	2	1	no	—
207	C₂×#135	—	2	1	no	—
208	C₂×#135	C₂³	1	1	yes	characteristic
209	C₂×#135	C₂³	1	1	yes	characteristic
210	C₂×#135	C₂³	1	1	yes	characteristic
211	C₂×#135	C₂³	1	1	yes	characteristic
212	C₂×#135	C₂³	1	1	yes	characteristic
213	C₂×#135	C₂³	1	1	yes	characteristic
214	C₂²×Q₁₆	—	2	1	no	—
215	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
216	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
217	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
218	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
219	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
220	C₂²×D₈	C₂³	1	1	yes	characteristic
221	#563	—	4	1	no	—
222	#563	—	4	1	no	—
223	#562	—	4	1	no	—
224	#560	—	4	1	no	—
225	#559	—	2	1	no	—
226	#557	—	2	1	no	—
227	#556	—	2	1	no	—
228	#556	—	2	1	no	—
229	#554	—	4	1	no	—
230	#553	—	4	1	no	—
231	#553	—	4	1	no	—
232	#551	—	4	1	no	—
233	#550	—	2	1	no	—
234	D₄×Q₈	—	2	1	no	—
235	D₄×Q₈	—	2	1	no	—
236	D₄×Q₈	—	2	1	no	—
237	#548	—	2	1	no	—
238	#548	—	2	1	no	—
239	#548	—	2	1	no	—
240	#548	—	2	1	no	—
241	#547	—	2	1	no	—
242	#547	—	2	1	no	—
243	#546	—	2	1	no	—
244	#546	—	2	1	no	—
245	#544	—	4	1	no	—
246	#542	—	4	1	no	—
247	#541	—	2	1	no	—
248	#541	—	2	1	no	—
249	#541	—	2	1	no	—
250	#540	—	2	1	no	—
251	#540	—	4	1	no	—
252	#539	—	4	1	no	—
253	#539	—	4	1	no	—
254	#539	—	4	1	no	—
255	#538	—	4	1	no	—
256	#538	—	4	1	no	—
257	#536	—	2	1	no	—
258	#536	—	2	1	no	—
259	#536	—	2	1	no	—
260	#535	—	2	1	no	—
261	#532	—	2	1	no	—
262	C₂×C₄⋊Q₈	—	2	1	no	—
263	#529	—	2	1	no	—
264	#529	—	2	1	no	—
265	#529	D₄	1	1	yes	characteristic
266	#510	—	4	2	no	—
267	#510	—	4	2	no	—
268	#510	—	4	2	no	—
269	#510	—	4	2	no	—
270	#510	—	4	2	no	—
271	#510	—	4	2	no	—
272	#510	—	4	2	no	—
273	#509	—	4	2	no	—
274	#508	—	4	2	no	—
275	#508	—	4	2	no	—
276	C₂×Q₃₂	—	4	2	no	—
277	C₂×Q₃₂	C₂³	1	1	yes	characteristic
278	C₂×Q₃₂	C₂³	1	1	yes	characteristic
279	C₂×Q₃₂	C₂³	1	1	yes	characteristic
280	C₂×Q₃₂	C₂³	1	1	yes	characteristic
281	C₂×Q₃₂	C₂³	1	1	yes	characteristic
282	C₂×Q₃₂	C₂³	1	1	yes	characteristic
283	C₂×Q₃₂	C₂³	1	1	yes	characteristic
284	C₂×Q₃₂	C₂³	1	1	yes	characteristic
285	C₂×Q₃₂	C₂³	1	1	yes	characteristic
286	C₂×Q₃₂	C₂³	1	1	yes	characteristic
287	C₂×Q₃₂	C₂³	1	1	yes	characteristic
288	C₂×Q₃₂	C₂³	1	1	yes	characteristic
289	C₂×Q₃₂	C₂³	1	1	yes	characteristic
290	C₂×Q₃₂	C₂³	1	1	yes	characteristic
291	C₂×Q₃₂	C₂³	1	1	yes	characteristic
292	C₂×SD₃₂	—	4	2	no	—
293	C₂×SD₃₂	C₂³	1	1	yes	characteristic
294	C₂×SD₃₂	C₂³	1	1	yes	characteristic
295	C₂×SD₃₂	C₂³	1	1	yes	characteristic
296	C₂×SD₃₂	C₂³	1	1	yes	characteristic
297	C₂×SD₃₂	C₂³	1	1	yes	characteristic
298	C₂×SD₃₂	C₂³	1	1	yes	characteristic
299	C₂×SD₃₂	C₂³	1	1	yes	characteristic
300	C₂×SD₃₂	C₂³	1	1	yes	characteristic
301	C₂×SD₃₂	C₂³	1	1	yes	characteristic
302	C₂×SD₃₂	C₂³	1	1	yes	characteristic
303	C₂×SD₃₂	C₂³	1	1	yes	characteristic
304	C₂×SD₃₂	C₂³	1	1	yes	characteristic
305	C₂×SD₃₂	C₂³	1	1	yes	characteristic
306	C₂×SD₃₂	C₂³	1	1	yes	characteristic
307	C₂×SD₃₂	C₂³	1	1	yes	characteristic
308	C₂×SD₃₂	C₂³	1	1	yes	characteristic
309	C₂×SD₃₂	C₂³	1	1	yes	characteristic
310	C₂×SD₃₂	C₂³	1	1	yes	characteristic
311	C₂×D₁₆	C₂³	1	1	yes	characteristic
312	C₂×D₁₆	C₂³	1	1	yes	characteristic
313	C₂×D₁₆	C₂³	1	1	yes	characteristic
314	C₂×M₃₂	C₂³	1	1	yes	characteristic
315	C₂×M₃₂	C₂³	1	1	yes	characteristic
316	C₂×M₃₂	C₂³	1	1	yes	characteristic
317	C₂×M₃₂	C₂³	1	1	yes	characteristic
318	C₂²×C₁₆	C₂³	1	1	yes	characteristic
319	C₂²×C₁₆	C₂³	1	1	yes	characteristic
320	#499	C₂³	1	1	yes	characteristic
321	#499	C₂³	1	1	yes	characteristic
322	#497	—	2	1	no	—
323	#497	—	2	1	no	—
324	#497	—	2	1	no	—
325	#497	—	2	1	no	—
326	#497	—	2	1	no	—
327	#497	—	2	1	no	—
328	#496	—	2	1	no	—
329	#496	—	2	1	no	—
330	#495	—	2	1	no	—
331	#495	C₂³	1	1	yes	characteristic
332	#495	C₂³	1	1	yes	characteristic
333	#495	C₂³	1	1	yes	characteristic
334	#495	C₂³	1	1	yes	characteristic
335	#495	C₂³	1	1	yes	characteristic
336	#495	C₂³	1	1	yes	characteristic
337	#495	C₂³	1	1	yes	characteristic
338	#495	C₂³	1	1	yes	characteristic
339	#494	—	2	1	no	—
340	#494	—	2	1	no	—
341	#494	C₂³	1	1	yes	characteristic
342	#494	C₂³	1	1	yes	characteristic
343	#494	C₂³	1	1	yes	characteristic
344	#494	C₂³	1	1	yes	characteristic
345	#494	C₂³	1	1	yes	characteristic
346	#494	C₂³	1	1	yes	characteristic
347	#494	C₂³	1	1	yes	characteristic
348	#494	C₂³	1	1	yes	characteristic
349	#493	C₂³	1	1	yes	characteristic
350	#493	C₂³	1	1	yes	characteristic
351	#492	—	2	1	no	—
352	#491	—	2	1	no	—
353	#491	—	2	1	no	—
354	#491	—	2	1	no	—
355	#490	—	2	1	no	—
356	#488	—	2	1	no	—
357	#488	—	2	1	no	—
358	#470	—	2	1	no	—
359	#470	—	2	1	no	—
360	#470	—	2	1	no	—
361	#469	—	2	1	no	—
362	#467	C₂³	1	1	yes	characteristic
363	#467	C₂³	1	1	yes	characteristic
364	#467	C₂³	1	1	yes	characteristic
365	#467	C₂³	1	1	yes	characteristic
366	#467	C₂³	1	1	yes	characteristic
367	#467	C₂³	1	1	yes	characteristic
368	#467	C₂³	1	1	yes	characteristic
369	#467	C₂³	1	1	yes	characteristic
370	#466	C₂³	1	1	yes	characteristic
371	#466	C₂³	1	1	yes	characteristic
372	#466	C₂³	1	1	yes	characteristic
373	#466	C₂³	1	1	yes	characteristic
374	#465	—	2	1	no	—
375	#465	—	2	1	no	—
376	#464	—	2	1	no	—
377	#464	—	2	1	no	—
378	#464	—	2	1	no	—
379	#464	—	2	1	no	—
380	#464	—	2	1	no	—
381	#464	—	2	1	no	—
382	#464	—	2	1	no	—
383	#464	—	2	1	no	—
384	#463	—	2	1	no	—
385	#463	—	2	1	no	—
386	#463	—	2	1	no	—
387	#463	—	2	1	no	—
388	#462	—	2	1	no	—
389	#462	—	2	1	no	—
390	#462	—	2	1	no	—
391	#462	—	2	1	no	—
392	#462	—	2	1	no	—
393	#462	—	2	1	no	—
394	#461	—	2	1	no	—
395	#461	—	2	1	no	—
396	#461	—	2	1	no	—
397	#461	—	2	1	no	—
398	#460	—	2	1	no	—
399	#460	—	2	1	no	—
400	#452	—	2	1	no	—
401	#452	—	2	1	no	—
402	#452	—	2	1	no	—
403	#452	—	2	1	no	—
404	#452	—	2	1	no	—
405	#452	—	2	1	no	—
406	#452	—	2	1	no	—
407	#452	—	2	1	no	—
408	#451	—	2	1	no	—
409	#451	—	2	1	no	—
410	#451	—	2	1	no	—
411	#451	—	2	1	no	—
412	#451	—	2	1	no	—
413	#451	—	2	1	no	—
414	#450	—	2	1	no	—
415	#450	—	2	1	no	—
416	#449	—	2	1	no	—
417	#449	—	2	1	no	—
418	#449	—	2	1	no	—
419	#449	—	2	1	no	—
420	#448	—	2	1	no	—
421	#448	—	2	1	no	—
422	#448	—	2	1	no	—
423	#448	—	2	1	no	—
424	#446	D₄	1	1	yes	characteristic
425	C₈×Q₈	C₂³	1	1	yes	characteristic
426	#442	—	2	1	no	—
427	#441	—	2	1	no	—
428	#441	—	2	1	no	—
429	#441	—	2	1	no	—
430	C₄×Q₁₆	C₂³	1	1	yes	characteristic
431	C₄×Q₁₆	C₂³	1	1	yes	characteristic
432	C₄×Q₁₆	C₂³	1	1	yes	characteristic
433	C₄×Q₁₆	C₂³	1	1	yes	characteristic
434	C₄×Q₁₆	C₂³	1	1	yes	characteristic
435	C₄×Q₁₆	C₂³	1	1	yes	characteristic
436	C₄×Q₁₆	C₂³	1	1	yes	characteristic
437	C₄×Q₁₆	C₂³	1	1	yes	characteristic
438	C₄×SD₁₆	—	2	1	no	—
439	C₄×SD₁₆	—	2	1	no	—
440	C₄×D₈	C₂³	1	1	yes	characteristic
441	C₄×D₈	C₂³	1	1	yes	characteristic
442	C₄×D₈	C₂³	1	1	yes	characteristic
443	C₄×D₈	C₂³	1	1	yes	characteristic
444	#436	D₄	1	1	yes	characteristic
445	#435	D₄	1	1	yes	characteristic
446	#435	D₄	1	1	yes	characteristic
447	C₈×D₄	C₂³	1	1	yes	characteristic
448	C₈×D₄	C₂³	1	1	yes	characteristic
449	C₈×D₄	C₂³	1	1	yes	characteristic
450	#433	D₄	1	1	yes	characteristic
451	#433	D₄	1	1	yes	characteristic
452	#432	D₄	1	1	yes	characteristic
453	#405	C₂³	1	1	yes	characteristic
454	#405	C₂³	1	1	yes	characteristic
455	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
456	#367	C₂³	1	1	yes	characteristic
457	#367	C₂³	1	1	yes	characteristic
458	#366	C₂³	1	1	yes	characteristic
459	#366	C₂³	1	1	yes	characteristic
460	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
461	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
462	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
463	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
464	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
465	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
466	#358	C₂³	1	1	yes	characteristic
467	#358	C₂³	1	1	yes	characteristic
468	#358	C₂³	1	1	yes	characteristic
469	#358	C₂³	1	1	yes	characteristic
470	#358	C₂³	1	1	yes	characteristic
471	#358	C₂³	1	1	yes	characteristic
472	#358	C₂³	1	1	yes	characteristic
473	#358	C₂³	1	1	yes	characteristic
474	#358	C₂³	1	1	yes	characteristic
475	#358	C₂³	1	1	yes	characteristic
476	#358	C₂³	1	1	yes	characteristic
477	#358	C₂³	1	1	yes	characteristic
478	#358	C₂³	1	1	yes	characteristic
479	#358	C₂³	1	1	yes	characteristic
480	#358	C₂³	1	1	yes	characteristic
481	#358	C₂³	1	1	yes	characteristic
482	#357	C₂³	1	1	yes	characteristic
483	#357	C₂³	1	1	yes	characteristic
484	#357	C₂³	1	1	yes	characteristic
485	#357	C₂³	1	1	yes	characteristic
486	#357	C₂³	1	1	yes	characteristic
487	#357	C₂³	1	1	yes	characteristic
488	#357	C₂³	1	1	yes	characteristic
489	#357	C₂³	1	1	yes	characteristic
490	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
491	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
492	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
493	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
494	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
495	C₂²⋊C₁₆	C₂³	1	1	yes	characteristic
496	#346	C₂³	1	1	yes	characteristic
497	#346	C₂³	1	1	yes	characteristic
498	#346	C₂³	1	1	yes	characteristic
499	#346	C₂³	1	1	yes	characteristic
500	#346	C₂³	1	1	yes	characteristic
501	#346	C₂³	1	1	yes	characteristic
502	C₄×C₁₆	C₂³	1	1	yes	characteristic
503	C₄×C₁₆	C₂³	1	1	yes	characteristic
504	C₄×C₁₆	C₂³	1	1	yes	characteristic
505	C₄×C₁₆	C₂³	1	1	yes	characteristic
506	C₂×#41	—	2	1	no	—
507	C₂×#41	—	2	1	no	—
508	C₂×#41	—	2	1	no	—
509	C₂×#41	—	2	1	no	—
510	C₂×#41	—	2	1	no	—
511	C₂×#41	—	2	1	no	—
512	C₂²×Q₈	—	2	1	no	—
513	C₂²×Q₈	—	2	1	no	—
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×Q₈	—	2	1	no	—
516	C₂²×Q₈	—	2	1	no	—
517	C₂²×D₄	—	2	1	no	—
518	#137	—	8	2	no	—
519	#137	—	8	2	no	—
520	#137	—	8	2	no	—
521	AGL(1,ℤ/8)	—	8	2	no	—
522	#135	—	4	1	no	—
523	#135	—	4	1	no	—
524	#135	—	4	1	no	—
525	#135	—	4	1	no	—
526	#135	—	4	1	no	—
527	#135	—	4	1	no	—
528	#135	—	4	1	no	—
529	#135	—	4	1	no	—
530	#135	—	4	1	no	—
531	#135	—	4	1	no	—
532	#135	—	4	1	no	—
533	#135	—	4	1	no	—
534	#135	—	8	2	no	—
535	C₂×Q₁₆	—	2	1	no	—
536	C₂×Q₁₆	—	2	1	no	—
537	C₂×Q₁₆	—	2	1	no	—
538	C₂×Q₁₆	—	2	1	no	—
539	C₂×Q₁₆	—	2	1	no	—
540	C₂×Q₁₆	—	2	1	no	—
541	C₂×Q₁₆	—	2	1	no	—
542	C₂×Q₁₆	—	2	1	no	—
543	C₂×Q₁₆	—	2	1	no	—
544	C₂×Q₁₆	—	2	1	no	—
545	C₂×Q₁₆	—	2	1	no	—
546	C₂×Q₁₆	—	2	1	no	—
547	C₂×Q₁₆	—	2	1	no	—
548	C₂×Q₁₆	—	4	1	no	—
549	C₂×Q₁₆	—	4	1	no	—
550	C₂×Q₁₆	—	4	1	no	—
551	C₂×Q₁₆	—	4	1	no	—
552	C₂×Q₁₆	—	4	1	no	—
553	C₂×Q₁₆	—	4	1	no	—
554	C₂×Q₁₆	—	4	1	no	—
555	C₂×Q₁₆	—	4	1	no	—
556	C₂×Q₁₆	—	4	1	no	—
557	C₂×Q₁₆	—	4	1	no	—
558	C₂×Q₁₆	—	8	2	no	—
559	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
560	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
561	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
562	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
563	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
564	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
565	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
566	C₂×Q₁₆	C₂⁴	1	1	yes	characteristic
567	C₂×SD₁₆	—	2	1	no	—
568	C₂×SD₁₆	—	2	1	no	—
569	C₂×SD₁₆	—	2	1	no	—
570	C₂×SD₁₆	—	2	1	no	—
571	C₂×SD₁₆	—	2	1	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	—	2	1	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	1	no	—
576	C₂×SD₁₆	—	2	1	no	—
577	C₂×SD₁₆	—	2	1	no	—
578	C₂×SD₁₆	—	2	1	no	—
579	C₂×SD₁₆	—	2	1	no	—
580	C₂×SD₁₆	—	2	1	no	—
581	C₂×D₈	—	2	1	no	—
582	C₂×D₈	—	2	1	no	—
583	C₂×D₈	—	2	1	no	—
584	C₂×D₈	—	4	1	no	—
585	C₂×D₈	—	4	1	no	—
586	C₂×D₈	C₂⁴	1	1	yes	characteristic
587	C₂×D₈	C₂⁴	1	1	yes	characteristic
588	C₂×D₈	C₂⁴	1	1	yes	characteristic
589	C₂×D₈	C₂⁴	1	1	yes	characteristic
590	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
591	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
592	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
593	C₂²×C₈	C₂⁴	1	1	yes	characteristic
594	C₂²×C₈	C₂⁴	1	1	yes	characteristic
595	C₂²×C₈	C₂⁴	1	1	yes	characteristic
596	C₄⋊Q₈	—	2	1	no	—
597	C₄⋊Q₈	—	2	1	no	—
598	C₄⋊Q₈	—	2	1	no	—
599	C₄⋊Q₈	—	2	1	no	—
600	C₄⋊Q₈	—	2	1	no	—
601	C₄⋊Q₈	—	2	1	no	—
602	C₄⋊Q₈	—	2	1	no	—
603	C₄⋊Q₈	—	2	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	#127	—	2	1	no	—
610	#127	—	2	1	no	—
611	#127	—	4	1	no	—
612	#126	—	4	1	no	—
613	#126	—	4	1	no	—
614	#126	—	4	1	no	—
615	#126	—	4	1	no	—
616	#126	—	4	1	no	—
617	#126	—	4	1	no	—
618	#126	—	4	1	no	—
619	#126	—	4	1	no	—
620	#126	—	4	1	no	—
621	#126	—	4	1	no	—
622	#126	—	4	1	no	—
623	#126	—	4	1	no	—
624	#126	D₈	1	1	yes	characteristic
625	#126	D₈	1	1	yes	characteristic
626	#125	—	2	1	no	—
627	#125	—	2	1	no	—
628	#125	—	4	1	no	—
629	#125	—	4	1	no	—
630	#125	—	4	1	no	—
631	#125	—	4	1	no	—
632	#125	—	4	1	no	—
633	#125	—	4	1	no	—
634	#125	—	4	1	no	—
635	#125	—	4	1	no	—
636	#125	—	4	1	no	—
637	#125	D₈	1	1	yes	characteristic
638	#124	—	2	1	no	—
639	#124	—	2	1	no	—
640	#124	—	2	1	no	—
641	#124	—	2	1	no	—
642	#124	—	2	1	no	—
643	#124	—	2	1	no	—
644	#124	—	2	1	no	—
645	#124	—	2	1	no	—
646	#124	—	4	1	no	—
647	#124	—	4	1	no	—
648	#124	—	4	1	no	—
649	#124	—	4	1	no	—
650	#124	—	4	1	no	—
651	#124	D₈	1	1	yes	characteristic
652	#123	—	4	1	no	—
653	#123	—	4	1	no	—
654	#123	—	4	1	no	—
655	#123	—	4	1	no	—
656	#123	—	4	1	no	—
657	#123	—	4	1	no	—
658	#123	—	4	1	no	—
659	#123	—	4	1	no	—
660	#123	—	4	1	no	—
661	#123	—	4	1	no	—
662	#123	—	4	1	no	—
663	#123	—	4	1	no	—
664	#123	—	4	1	no	—
665	#123	—	4	1	no	—
666	#123	—	4	1	no	—
667	#123	—	4	1	no	—
668	#123	—	4	1	no	—
669	#123	—	4	1	no	—
670	#123	D₈	1	1	yes	characteristic
671	#123	D₈	1	1	yes	characteristic
672	C₂²⋊Q₈	—	2	1	no	—
673	C₂²⋊Q₈	—	2	1	no	—
674	C₂²⋊Q₈	—	2	1	no	—
675	C₂²⋊Q₈	—	2	1	no	—
676	C₂²⋊Q₈	—	2	1	no	—
677	C₂²⋊Q₈	—	2	1	no	—
678	C₂²⋊Q₈	—	2	1	no	—
679	C₂²⋊Q₈	—	2	1	no	—
680	C₂²⋊Q₈	—	4	1	no	—
681	C₂²⋊Q₈	—	4	1	no	—
682	C₂²⋊Q₈	—	4	1	no	—
683	C₂²⋊Q₈	—	4	1	no	—
684	C₂²⋊Q₈	—	4	1	no	—
685	C₂²⋊Q₈	—	4	1	no	—
686	C₂²⋊Q₈	—	4	1	no	—
687	C₂²⋊Q₈	—	4	1	no	—
688	C₂²⋊Q₈	—	4	1	no	—
689	C₂²⋊Q₈	—	4	1	no	—
690	C₂²⋊Q₈	—	4	1	no	—
691	C₂²⋊Q₈	—	4	1	no	—
692	C₂²⋊Q₈	—	4	1	no	—
693	C₂²⋊Q₈	—	4	1	no	—
694	C₂²⋊Q₈	—	4	1	no	—
695	C₂²⋊Q₈	—	4	1	no	—
696	C₂²⋊Q₈	—	4	1	no	—
697	C₂²⋊Q₈	—	4	1	no	—
698	C₂²⋊Q₈	D₈	1	1	yes	characteristic
699	#121	—	2	1	no	—
700	#121	—	2	1	no	—
701	#121	—	2	1	no	—
702	#121	—	2	1	no	—
703	#121	—	4	1	no	—
704	#121	—	4	1	no	—
705	#121	—	4	1	no	—
706	#121	—	4	1	no	—
707	#121	—	4	1	no	—
708	#121	—	4	1	no	—
709	#121	—	4	1	no	—
710	#121	—	4	1	no	—
711	#121	—	4	1	no	—
712	#121	—	4	1	no	—
713	#121	—	4	1	no	—
714	#121	—	4	1	no	—
715	#121	—	4	1	no	—
716	#121	—	4	1	no	—
717	#121	—	4	1	no	—
718	#121	—	4	1	no	—
719	#121	D₈	1	1	yes	characteristic
720	#120	—	4	1	no	—
721	#120	—	4	1	no	—
722	#120	—	4	1	no	—
723	#120	—	4	1	no	—
724	C₄×Q₈	—	2	1	no	—
725	C₄×Q₈	—	2	1	no	—
726	C₄×Q₈	—	2	1	no	—
727	C₄×Q₈	—	2	1	no	—
728	C₄×Q₈	—	2	1	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	—	2	1	no	—
732	C₄×Q₈	—	4	1	no	—
733	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	—	2	1	no	—
738	C₄×D₄	—	4	1	no	—
739	C₄×D₄	—	4	1	no	—
740	C₄×D₄	—	4	1	no	—
741	C₄×D₄	—	4	1	no	—
742	C₄×D₄	—	4	1	no	—
743	C₄×D₄	—	4	1	no	—
744	C₄×D₄	—	4	1	no	—
745	C₄×D₄	—	4	1	no	—
746	C₄×D₄	—	4	1	no	—
747	C₄×D₄	—	4	1	no	—
748	C₄×D₄	—	4	1	no	—
749	C₄×D₄	—	4	1	no	—
750	C₄×D₄	—	4	1	no	—
751	C₄×D₄	C₂×D₄	1	1	yes	characteristic
752	C₄×D₄	C₂×D₄	1	1	yes	characteristic
753	C₄×D₄	C₂×D₄	1	1	yes	characteristic
754	#117	—	4	1	no	—
755	#117	—	4	1	no	—
756	#117	—	4	1	no	—
757	#117	—	4	1	no	—
758	#117	C₂×D₄	1	1	yes	characteristic
759	#117	C₂×D₄	1	1	yes	characteristic
760	C₂×C₄⋊C₄	—	4	1	no	—
761	C₂×C₄⋊C₄	—	4	1	no	—
762	C₂×C₄⋊C₄	—	4	1	no	—
763	C₂×C₄⋊C₄	—	4	1	no	—
764	C₂×C₂²⋊C₄	—	4	1	no	—
765	C₂×C₂²⋊C₄	—	4	1	no	—
766	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
767	Q₃₂	—	2	2	no	—
768	Q₃₂	—	2	2	no	—
769	Q₃₂	—	2	2	no	—
770	Q₃₂	—	2	2	no	—
771	Q₃₂	—	2	2	no	—
772	Q₃₂	—	4	1	no	—
773	Q₃₂	—	4	1	no	—
774	Q₃₂	—	4	1	no	—
775	Q₃₂	—	4	1	no	—
776	Q₃₂	—	4	1	no	—
777	Q₃₂	—	4	1	no	—
778	Q₃₂	—	4	1	no	—
779	Q₃₂	—	4	1	no	—
780	Q₃₂	—	4	1	no	—
781	Q₃₂	—	4	1	no	—
782	SD₃₂	—	2	2	no	—
783	SD₃₂	—	2	2	no	—
784	SD₃₂	—	2	2	no	—
785	SD₃₂	—	2	2	no	—
786	SD₃₂	—	2	2	no	—
787	SD₃₂	—	2	2	no	—
788	SD₃₂	—	4	1	no	—
789	SD₃₂	—	4	1	no	—
790	SD₃₂	—	4	1	no	—
791	SD₃₂	—	4	1	no	—
792	SD₃₂	—	4	1	no	—
793	SD₃₂	—	4	1	no	—
794	SD₃₂	—	4	1	no	—
795	SD₃₂	—	4	1	no	—
796	SD₃₂	—	4	1	no	—
797	SD₃₂	—	4	1	no	—
798	SD₃₂	—	4	1	no	—
799	SD₃₂	—	4	1	no	—
800	D₁₆	—	2	2	no	—
801	D₁₆	—	4	1	no	—
802	D₁₆	—	4	1	no	—
803	M₃₂	—	2	2	no	—
804	M₃₂	—	2	2	no	—
805	M₃₂	—	2	2	no	—
806	M₃₂	—	2	2	no	—
807	C₂×C₁₆	—	2	2	no	—
808	C₂×C₁₆	—	2	2	no	—
809	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
810	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
811	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
812	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
813	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
814	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
815	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
816	C₂×C₁₆	C₂⁴	1	1	yes	characteristic
817	#107	C₂⁴	1	1	yes	characteristic
818	#107	C₂⁴	1	1	yes	characteristic
819	#107	C₂⁴	1	1	yes	characteristic
820	#107	C₂⁴	1	1	yes	characteristic
821	#106	—	2	1	no	—
822	#106	—	2	1	no	—
823	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
824	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
825	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
826	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
827	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
828	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
829	#103	—	2	1	no	—
830	#103	—	2	1	no	—
831	#103	—	2	1	no	—
832	#103	—	2	1	no	—
833	#103	—	2	1	no	—
834	#103	—	2	1	no	—
835	#103	—	2	1	no	—
836	#103	—	2	1	no	—
837	#103	—	2	1	no	—
838	#103	—	2	1	no	—
839	#103	—	2	1	no	—
840	#103	—	2	1	no	—
841	#103	—	2	1	no	—
842	#103	—	2	1	no	—
843	#103	—	2	1	no	—
844	#103	—	2	1	no	—
845	#102	—	2	1	no	—
846	#102	—	2	1	no	—
847	#102	—	2	1	no	—
848	#102	—	2	1	no	—
849	#102	—	2	1	no	—
850	#102	—	2	1	no	—
851	#102	—	2	1	no	—
852	#102	—	2	1	no	—
853	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
854	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
855	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
856	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
857	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
858	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
859	#97	C₂×D₄	1	1	yes	characteristic
860	#97	C₂×D₄	1	1	yes	characteristic
861	#97	C₂×D₄	1	1	yes	characteristic
862	#97	C₂×D₄	1	1	yes	characteristic
863	C₄×C₈	C₂×D₄	1	1	yes	characteristic
864	C₄×C₈	C₂×D₄	1	1	yes	characteristic
865	C₄×C₈	C₂⁴	1	1	yes	characteristic
866	C₄×C₈	C₂⁴	1	1	yes	characteristic
867	C₄×C₈	C₂⁴	1	1	yes	characteristic
868	C₄×C₈	C₂⁴	1	1	yes	characteristic
869	C₂⁴	—	4	1	no	—
870	#41	—	8	1	no	—
871	#41	—	8	1	no	—
872	#41	—	8	1	no	—
873	#41	—	8	1	no	—
874	#41	—	8	1	no	—
875	#41	—	8	1	no	—
876	#41	—	8	1	no	—
877	#41	—	8	1	no	—
878	#41	—	8	1	no	—
879	#41	—	8	1	no	—
880	#41	—	8	1	no	—
881	#41	—	8	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	4	1	no	—
891	C₂×Q₈	—	4	1	no	—
892	C₂×Q₈	—	4	1	no	—
893	C₂×Q₈	—	4	1	no	—
894	C₂×Q₈	—	4	1	no	—
895	C₂×Q₈	—	8	1	no	—
896	C₂×Q₈	—	8	1	no	—
897	C₂×Q₈	—	8	1	no	—
898	C₂×Q₈	—	8	1	no	—
899	C₂×Q₈	—	8	1	no	—
900	C₂×Q₈	—	8	1	no	—
901	C₂×Q₈	—	8	1	no	—
902	C₂×Q₈	—	8	1	no	—
903	C₂×Q₈	—	8	1	no	—
904	C₂×Q₈	—	8	1	no	—
905	C₂×Q₈	C₂×D₈	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	4	1	no	—
911	C₂×D₄	—	4	1	no	—
912	C₂×D₄	—	4	1	no	—
913	C₂×D₄	—	4	1	no	—
914	C₂×D₄	—	4	1	no	—
915	C₂×D₄	—	4	1	no	—
916	C₂×D₄	—	4	1	no	—
917	C₂×D₄	—	4	1	no	—
918	C₂×D₄	—	4	1	no	—
919	C₂×D₄	—	4	1	no	—
920	C₂×D₄	—	4	1	no	—
921	C₂×D₄	—	4	1	no	—
922	C₂×D₄	—	4	1	no	—
923	C₂×D₄	—	4	1	no	—
924	C₂×D₄	—	4	1	no	—
925	C₂×D₄	—	8	1	no	—
926	C₂×D₄	—	8	1	no	—
927	C₂×D₄	C₂×D₈	1	1	yes	characteristic
928	C₂×D₄	C₂×D₈	1	1	yes	characteristic
929	C₂×D₄	C₂×D₈	1	1	yes	characteristic
930	C₂²×C₄	—	4	1	no	—
931	C₂²×C₄	—	4	1	no	—
932	C₂²×C₄	—	4	1	no	—
933	C₂²×C₄	—	4	1	no	—
934	C₂²×C₄	—	4	1	no	—
935	C₂²×C₄	—	4	1	no	—
936	C₂²×C₄	—	4	1	no	—
937	C₂²×C₄	—	4	1	no	—
938	C₂²×C₄	—	4	1	no	—
939	C₂²×C₄	—	4	1	no	—
940	C₂²×C₄	—	4	1	no	—
941	C₂²×C₄	—	4	1	no	—
942	C₂²×C₄	—	4	1	no	—
943	C₂²×C₄	—	4	1	no	—
944	C₂²×C₄	—	4	1	no	—
945	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
947	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
948	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
949	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
950	Q₁₆	—	2	1	no	—
951	Q₁₆	—	2	1	no	—
952	Q₁₆	—	2	1	no	—
953	Q₁₆	—	2	1	no	—
954	Q₁₆	—	2	1	no	—
955	Q₁₆	—	2	1	no	—
956	Q₁₆	—	2	1	no	—
957	Q₁₆	—	2	1	no	—
958	Q₁₆	—	2	1	no	—
959	Q₁₆	—	2	1	no	—
960	Q₁₆	—	2	1	no	—
961	Q₁₆	—	2	1	no	—
962	Q₁₆	—	2	1	no	—
963	Q₁₆	—	2	1	no	—
964	Q₁₆	—	2	1	no	—
965	Q₁₆	—	2	1	no	—
966	Q₁₆	—	4	2	no	—
967	Q₁₆	—	4	2	no	—
968	Q₁₆	—	4	2	no	—
969	Q₁₆	—	8	1	no	—
970	Q₁₆	—	8	1	no	—
971	Q₁₆	—	8	1	no	—
972	Q₁₆	—	8	1	no	—
973	Q₁₆	—	8	1	no	—
974	Q₁₆	—	8	1	no	—
975	Q₁₆	—	8	1	no	—
976	Q₁₆	—	8	1	no	—
977	Q₁₆	—	8	1	no	—
978	Q₁₆	—	8	1	no	—
979	SD₁₆	—	4	2	no	—
980	SD₁₆	—	4	2	no	—
981	SD₁₆	—	8	1	no	—
982	SD₁₆	—	8	1	no	—
983	SD₁₆	—	8	1	no	—
984	SD₁₆	—	8	1	no	—
985	SD₁₆	—	8	1	no	—
986	SD₁₆	—	8	1	no	—
987	SD₁₆	—	8	1	no	—
988	SD₁₆	—	8	1	no	—
989	SD₁₆	—	8	1	no	—
990	SD₁₆	—	8	1	no	—
991	SD₁₆	—	8	1	no	—
992	SD₁₆	—	8	1	no	—
993	D₈	—	2	1	no	—
994	D₈	—	2	1	no	—
995	D₈	—	2	1	no	—
996	D₈	—	2	1	no	—
997	D₈	—	2	1	no	—
998	D₈	—	2	1	no	—
999	D₈	—	2	1	no	—
1000	D₈	—	2	1	no	—
1001	D₈	—	4	2	no	—
1002	D₈	—	8	1	no	—
1003	D₈	—	8	1	no	—
1004	M₁₆	—	2	2	no	—
1005	M₁₆	—	2	2	no	—
1006	C₂×C₈	—	2	2	no	—
1007	C₂×C₈	—	2	1	no	—
1008	C₂×C₈	—	2	1	no	—
1009	C₂×C₈	—	2	1	no	—
1010	C₂×C₈	—	2	1	no	—
1011	C₂×C₈	—	2	1	no	—
1012	C₂×C₈	—	2	1	no	—
1013	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1014	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1015	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1016	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1017	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1018	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1019	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1020	C₂×C₈	C₂⁵	1	1	yes	characteristic
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	4	1	no	—
1026	C₄⋊C₄	—	4	1	no	—
1027	C₄⋊C₄	—	4	1	no	—
1028	C₄⋊C₄	—	4	1	no	—
1029	C₄⋊C₄	—	4	1	no	—
1030	C₄⋊C₄	—	4	1	no	—
1031	C₄⋊C₄	—	4	1	no	—
1032	C₄⋊C₄	—	4	1	no	—
1033	C₄⋊C₄	—	4	1	no	—
1034	C₄⋊C₄	—	4	1	no	—
1035	C₄⋊C₄	—	4	1	no	—
1036	C₄⋊C₄	—	4	1	no	—
1037	C₄⋊C₄	—	4	1	no	—
1038	C₄⋊C₄	—	4	1	no	—
1039	C₄⋊C₄	—	4	1	no	—
1040	C₄⋊C₄	—	4	1	no	—
1041	C₄⋊C₄	—	4	1	no	—
1042	C₄⋊C₄	—	4	1	no	—
1043	C₄⋊C₄	—	4	1	no	—
1044	C₄⋊C₄	—	4	1	no	—
1045	C₄⋊C₄	—	4	1	no	—
1046	C₄⋊C₄	—	4	1	no	—
1047	C₄⋊C₄	—	4	1	no	—
1048	C₄⋊C₄	—	4	1	no	—
1049	C₄⋊C₄	—	4	1	no	—
1050	C₄⋊C₄	—	4	1	no	—
1051	C₄⋊C₄	—	4	1	no	—
1052	C₄⋊C₄	—	4	1	no	—
1053	C₄⋊C₄	—	4	1	no	—
1054	C₄⋊C₄	—	4	1	no	—
1055	C₄⋊C₄	—	4	1	no	—
1056	C₄⋊C₄	—	4	1	no	—
1057	C₄⋊C₄	—	4	1	no	—
1058	C₄⋊C₄	—	4	1	no	—
1059	C₄⋊C₄	—	4	1	no	—
1060	C₄⋊C₄	—	4	1	no	—
1061	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1068	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1069	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1070	C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
1071	C₂²⋊C₄	—	4	1	no	—
1072	C₂²⋊C₄	—	4	1	no	—
1073	C₂²⋊C₄	—	4	1	no	—
1074	C₂²⋊C₄	—	4	1	no	—
1075	C₂²⋊C₄	—	4	1	no	—
1076	C₂²⋊C₄	—	4	1	no	—
1077	C₂²⋊C₄	—	4	1	no	—
1078	C₂²⋊C₄	—	4	1	no	—
1079	C₂²⋊C₄	—	4	1	no	—
1080	C₂²⋊C₄	—	4	1	no	—
1081	C₂²⋊C₄	—	4	1	no	—
1082	C₂²⋊C₄	—	4	1	no	—
1083	C₂²⋊C₄	—	4	1	no	—
1084	C₂²⋊C₄	—	4	1	no	—
1085	C₂²⋊C₄	—	4	1	no	—
1086	C₂²⋊C₄	—	4	1	no	—
1087	C₂²⋊C₄	—	4	1	no	—
1088	C₂²⋊C₄	—	4	1	no	—
1089	C₂²⋊C₄	—	4	1	no	—
1090	C₂²⋊C₄	—	4	1	no	—
1091	C₂²⋊C₄	—	4	1	no	—
1092	C₂²⋊C₄	—	4	1	no	—
1093	C₂²⋊C₄	—	4	1	no	—
1094	C₂²⋊C₄	—	4	1	no	—
1095	C₂²⋊C₄	—	4	1	no	—
1096	C₂²⋊C₄	—	4	1	no	—
1097	C₂²⋊C₄	—	4	1	no	—
1098	C₂²⋊C₄	—	4	1	no	—
1099	C₂²⋊C₄	—	4	1	no	—
1100	C₂²⋊C₄	—	4	1	no	—
1101	C₂²⋊C₄	—	4	1	no	—
1102	C₂²⋊C₄	—	4	1	no	—
1103	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1104	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1105	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1106	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1107	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1108	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1109	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1110	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1112	C₂²⋊C₄	C₂×D₈	1	1	yes	characteristic
1113	C₄²	—	4	1	no	—
1114	C₄²	—	4	1	no	—
1115	C₄²	—	4	1	no	—
1116	C₄²	—	4	1	no	—
1117	C₄²	—	4	1	no	—
1118	C₄²	—	4	1	no	—
1119	C₄²	—	4	1	no	—
1120	C₄²	—	4	1	no	—
1121	C₄²	C₂×D₈	1	1	yes	characteristic
1122	C₄²	C₂×D₈	1	1	yes	characteristic
1123	C₄²	C₂²×D₄	1	1	yes	characteristic
1124	C₄²	C₂²×D₄	1	1	yes	characteristic
1125	C₄²	C₂²×D₄	1	1	yes	characteristic
1126	C₄²	C₂²×D₄	1	1	yes	characteristic
1127	C₁₆	—	2	1	no	—
1128	C₁₆	—	2	1	no	—
1129	C₁₆	—	2	1	no	—
1130	C₁₆	—	2	1	no	—
1131	C₁₆	—	2	1	no	—
1132	C₁₆	—	2	1	no	—
1133	C₁₆	H(5,𝔽₂)	1	2	yes	—
1134	C₁₆	H(5,𝔽₂)	1	2	yes	—
1135	C₂³	—	4	1	no	—
1136	C₂³	—	4	1	no	—
1137	C₂³	—	4	1	no	—
1138	C₂³	—	4	1	no	—
1139	C₂³	—	16	1	no	—
1140	C₂³	—	16	1	no	—
1141	C₂³	—	16	1	no	—
1142	C₂³	C₂²×D₈	1	1	yes	characteristic
1143	C₂³	C₂²×D₈	1	1	yes	characteristic
1144	C₂³	C₂²×D₈	1	1	yes	characteristic
1145	Q₈	—	4	1	no	—
1146	Q₈	—	4	1	no	—
1147	Q₈	—	4	1	no	—
1148	Q₈	—	4	1	no	—
1149	Q₈	—	4	1	no	—
1150	Q₈	—	4	1	no	—
1151	Q₈	—	4	1	no	—
1152	Q₈	—	4	1	no	—
1153	Q₈	—	4	1	no	—
1154	Q₈	—	4	1	no	—
1155	Q₈	—	4	1	no	—
1156	Q₈	—	4	1	no	—
1157	Q₈	—	4	1	no	—
1158	Q₈	—	4	1	no	—
1159	Q₈	—	4	1	no	—
1160	Q₈	—	4	1	no	—
1161	Q₈	—	4	1	no	—
1162	Q₈	—	16	1	no	—
1163	Q₈	—	16	1	no	—
1164	Q₈	—	16	1	no	—
1165	Q₈	—	16	1	no	—
1166	Q₈	—	16	1	no	—
1167	D₄	—	4	1	no	—
1168	D₄	—	4	1	no	—
1169	D₄	—	4	1	no	—
1170	D₄	—	4	1	no	—
1171	D₄	—	4	1	no	—
1172	D₄	—	4	1	no	—
1173	D₄	—	4	1	no	—
1174	D₄	—	4	1	no	—
1175	D₄	—	4	1	no	—
1176	D₄	—	4	1	no	—
1177	D₄	—	4	1	no	—
1178	D₄	—	8	2	no	—
1179	D₄	—	16	1	no	—
1180	D₄	—	16	1	no	—
1181	D₄	—	16	1	no	—
1182	D₄	—	16	1	no	—
1183	D₄	—	16	1	no	—
1184	D₄	—	16	1	no	—
1185	D₄	—	16	1	no	—
1186	D₄	—	16	1	no	—
1187	D₄	—	16	1	no	—
1188	D₄	—	16	1	no	—
1189	D₄	—	16	1	no	—
1190	D₄	—	16	1	no	—
1191	D₄	—	16	1	no	—
1192	D₄	—	16	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	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	—	4	1	no	—
1206	C₂×C₄	—	4	1	no	—
1207	C₂×C₄	—	4	1	no	—
1208	C₂×C₄	—	4	1	no	—
1209	C₂×C₄	—	4	1	no	—
1210	C₂×C₄	—	4	1	no	—
1211	C₂×C₄	—	4	1	no	—
1212	C₂×C₄	—	4	1	no	—
1213	C₂×C₄	—	8	2	no	—
1214	C₂×C₄	—	16	1	no	—
1215	C₂×C₄	—	16	1	no	—
1216	C₂×C₄	—	16	1	no	—
1217	C₂×C₄	—	16	1	no	—
1218	C₂×C₄	—	16	1	no	—
1219	C₂×C₄	—	16	1	no	—
1220	C₂×C₄	—	16	1	no	—
1221	C₂×C₄	—	16	1	no	—
1222	C₂×C₄	—	16	1	no	—
1223	C₂×C₄	—	16	1	no	—
1224	C₂×C₄	—	16	1	no	—
1225	C₂×C₄	—	16	1	no	—
1226	C₂×C₄	—	16	1	no	—
1227	C₂×C₄	—	16	1	no	—
1228	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1229	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1230	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1231	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1232	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1233	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1234	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1235	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1236	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1237	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1238	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
1239	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1240	C₈	—	2	1	no	—
1241	C₈	—	2	1	no	—
1242	C₈	—	2	1	no	—
1243	C₈	—	2	1	no	—
1244	C₈	—	2	1	no	—
1245	C₈	—	2	1	no	—
1246	C₈	#576	1	2	yes	—
1247	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1248	C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	2	1	no	—
1252	C₂²	—	2	1	no	—
1253	C₂²	—	2	1	no	—
1254	C₂²	—	2	1	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	8	1	no	—
1259	C₂²	—	8	1	no	—
1260	C₂²	—	8	1	no	—
1261	C₂²	—	8	1	no	—
1262	C₂²	—	8	1	no	—
1263	C₂²	—	8	1	no	—
1264	C₂²	—	8	1	no	—
1265	C₂²	—	8	1	no	—
1266	C₂²	—	8	1	no	—
1267	C₂²	—	8	1	no	—
1268	C₂²	—	8	1	no	—
1269	C₂²	—	8	1	no	—
1270	C₂²	—	32	2	no	—
1271	C₂²	C₂³×D₈	1	1	yes	characteristic
1272	C₄	—	2	1	no	—
1273	C₄	—	2	1	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	2	1	no	—
1276	C₄	—	2	1	no	—
1277	C₄	—	2	1	no	—
1278	C₄	—	2	1	no	—
1279	C₄	—	2	1	no	—
1280	C₄	—	2	1	no	—
1281	C₄	—	2	1	no	—
1282	C₄	—	2	1	no	—
1283	C₄	—	8	1	no	—
1284	C₄	—	8	1	no	—
1285	C₄	—	8	1	no	—
1286	C₄	—	8	1	no	—
1287	C₄	—	8	1	no	—
1288	C₄	—	8	1	no	—
1289	C₄	—	8	1	no	—
1290	C₄	—	8	1	no	—
1291	C₄	—	8	1	no	—
1292	C₄	—	8	1	no	—
1293	C₄	—	8	1	no	—
1294	C₄	—	8	1	no	—
1295	C₄	#3498	1	1	yes	characteristic
1296	C₄	C₂×#576	1	1	yes	characteristic
1297	C₂	—	4	1	no	—
1298	C₂	—	4	1	no	—
1299	C₂	—	4	1	no	—
1300	C₂	—	16	1	no	—
1301	C₂	—	16	1	no	—
1302	C₂	—	16	1	no	—
1303	C₂	—	16	1	no	—
1304	C₂	#62415	1	1	yes	characteristic
1305	C₂	#62637	1	1	yes	characteristic
1306	C₂	#62637	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁵
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966 ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62434	C₂	semidirect
2. #62432	C₂	semidirect
3. #33969	C₂	semidirect
4. #33968	C₂	semidirect
5. #33967	C₂	semidirect
6. #33965	C₂	semidirect
7. #33844	C₂	semidirect
8. #33843	C₂	semidirect
9. #33842	C₂	semidirect
10. #33841	C₂	semidirect
11. #33837	C₂	semidirect
12. #33836	C₂	semidirect
13. #33836	C₂	semidirect
14. #33835	C₂	semidirect
15. #33835	C₂	semidirect
16. #33833	C₂	semidirect
17. #33832	C₂	semidirect
18. #33832	C₂	semidirect
19. #33789	C₂	semidirect
20. #33789	C₂	semidirect
21. #33788	C₂	semidirect
22. #33787	C₂	semidirect
23. #33785	C₂	semidirect
24. #33784	C₂	semidirect
25. #33750	C₂	semidirect
26. #33743	C₂	semidirect
27. #33741	C₂	semidirect
28. #33722	C₂	semidirect
29. #33721	C₂	semidirect
30. #33718	C₂	semidirect
31. #33481	C₂	semidirect
38. C₂×#510	C₂²	semidirect
39. C₂×#510	C₂²	semidirect
40. C₂×#510	C₂²	semidirect
44. C₂²×Q₃₂	C₂²	semidirect
49. #3395	C₂²	semidirect
51. #3393	C₂²	semidirect
55. D₄×Q₁₆	C₂²	semidirect
59. #3285	C₂²	semidirect
78. #3177	C₂²	semidirect
81. #3168	C₂²	semidirect
84. #3156	C₂²	semidirect
87. C₂×#494	C₂²	semidirect
89. #2253	C₂²	semidirect
96. #2251	C₂²	semidirect
97. #2251	C₂²	semidirect
98. #2251	C₂²	semidirect
99. #2251	C₂²	semidirect
108. #2247	C₂²	semidirect
109. #2247	C₂²	semidirect
110. #2247	C₂²	semidirect
111. #2245	C₂²	semidirect
112. #2245	C₂²	semidirect
113. #2245	C₂²	semidirect
116. #2242	C₂²	semidirect
119. #2220	C₂²	semidirect
120. #2220	C₂²	semidirect
123. #2219	C₂²	semidirect
126. #2217	C₂²	semidirect
134. #2211	C₂²	semidirect
135. #2211	C₂²	semidirect
136. #2211	C₂²	semidirect
139. #2210	C₂²	semidirect
140. #2210	C₂²	semidirect
141. #2209	C₂²	semidirect
142. #2209	C₂²	semidirect
143. #2209	C₂²	semidirect
144. #2209	C₂²	semidirect
145. #2209	C₂²	semidirect
146. #2209	C₂²	semidirect
150. #2208	C₂²	semidirect
160. #2189	C₂²	semidirect
163. #2188	C₂²	semidirect
164. #2188	C₂²	semidirect
165. #2188	C₂²	semidirect
166. #2188	C₂²	semidirect
171. #2186	C₂²	semidirect
172. #2186	C₂²	semidirect
176. #2185	C₂²	semidirect
177. #2183	C₂²	semidirect
178. #2183	C₂²	semidirect
180. #2176	C₂²	semidirect
181. #2176	C₂²	semidirect
182. #2176	C₂²	semidirect
185. #2175	C₂²	semidirect
186. #2175	C₂²	semidirect
187. C₄×Q₃₂	C₂²	semidirect
188. C₄×Q₃₂	C₂²	semidirect
190. C₄×SD₃₂	C₂²	semidirect
192. #2169	C₂²	semidirect
196. #2168	C₂²	semidirect
198. #2164	C₂²	semidirect
199. #2163	C₂²	semidirect
201. #2108	C₂²	semidirect
202. C₄×M₃₂	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#62434	2
#62432	2
#33969	2
#33968	2
#33967	2
#33965	2
#33844	2
#33843	2
#33842	2
#33841	2
#33837	2
#33836	2
#33835	2
#33833	2
#33832	2
#33789	2
#33788	2
#33787	2
#33785	2
#33784	2
#33750	2
#33743	2
#33741	2
#33722	2
#33721	2
#33718	2
#33481	2