Subgroups — #7572031

Order 512.

1603 conjugacy classes of subgroups.

The subgroup lattice has 1269 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59771	C₂	1	1	yes	maximal, characteristic, complemented
2	#36456	C₂	1	1	yes	maximal, characteristic, complemented
3	#32655	C₂	1	1	yes	maximal, characteristic, complemented
4	#32589	C₂	1	1	yes	maximal, characteristic, complemented
5	#32351	C₂	1	1	yes	maximal, characteristic, complemented
6	#31547	C₂	1	1	yes	maximal, characteristic, complemented
7	#29304	C₂	1	1	yes	maximal, characteristic, complemented
8	#29156	C₂	1	1	yes	maximal, characteristic, complemented
9	#28958	C₂	1	1	yes	maximal, characteristic, complemented
10	#28779	C₂	1	1	yes	maximal, characteristic, complemented
11	#27321	C₂	1	1	yes	maximal, characteristic, complemented
12	#27316	C₂	1	1	yes	maximal, characteristic, complemented
13	#27019	C₂	1	1	yes	maximal, characteristic, complemented
14	#26490	C₂	1	1	yes	maximal, characteristic, complemented
15	#26411	C₂	1	1	yes	maximal, characteristic, complemented
16	#26388	C₂	1	1	yes	maximal, characteristic, complemented
17	#26385	C₂	1	1	yes	maximal, characteristic, complemented
18	#26373	C₂	1	1	yes	maximal, characteristic, complemented
19	#26341	C₂	1	1	yes	maximal, characteristic, complemented
20	#26061	C₂	1	1	yes	maximal, characteristic, complemented
21	#25951	C₂	1	1	yes	maximal, characteristic, complemented
22	#25951	C₂	1	1	yes	maximal, characteristic, complemented
23	#25837	C₂	1	1	yes	maximal, characteristic, complemented
24	#24341	C₂	1	1	yes	maximal, characteristic, complemented
25	#23238	C₂	1	1	yes	maximal, characteristic, complemented
26	#22981	C₂	1	1	yes	maximal, characteristic, complemented
27	#22877	C₂	1	1	yes	maximal, characteristic
28	#22857	C₂	1	1	yes	maximal, characteristic
29	#22673	C₂	1	1	yes	maximal, characteristic, complemented
30	#21456	C₂	1	1	yes	maximal, characteristic
31	#20872	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×Q₈²	C₂²	1	1	yes	characteristic
33	C₂×C₄×#41	C₂²	1	1	yes	characteristic
34	C₂×#498	C₂²	1	1	yes	characteristic
35	C₂×#475	C₂²	1	1	yes	characteristic
36	C₂×#475	C₂²	1	1	yes	characteristic
37	C₂×#474	C₂²	1	1	yes	characteristic
38	C₂×#449	C₂²	1	1	yes	characteristic
39	C₂×#442	C₂²	1	1	yes	characteristic
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×#440	C₂²	1	1	yes	characteristic
42	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
43	C₂×#427	C₂²	1	1	yes	characteristic
44	C₂×#416	C₂²	1	1	yes	characteristic
45	C₂×#416	C₂²	1	1	yes	characteristic
46	#2857	—	2	1	no	—
47	#2857	C₂²	1	1	yes	characteristic
48	#2804	—	2	1	no	—
49	#2780	—	2	1	no	—
50	#2589	—	2	1	no	—
51	#2587	—	2	1	no	—
52	#2580	C₂²	1	1	yes	characteristic
53	#2563	—	2	1	no	—
54	#2563	C₂²	1	1	yes	characteristic
55	#2546	C₂²	1	1	yes	characteristic
56	#2538	—	2	1	no	—
57	#2538	C₂²	1	1	yes	characteristic
58	#2509	C₂²	1	1	yes	characteristic
59	#2509	C₂²	1	1	yes	characteristic
60	#2492	—	2	1	no	—
61	#2452	—	2	1	no	—
62	#2452	—	2	1	no	—
63	#2452	—	2	1	no	—
64	#2452	C₂²	1	1	yes	characteristic
65	#2452	C₂²	1	1	yes	characteristic
66	#2452	C₂²	1	1	yes	characteristic
67	#2452	C₂²	1	1	yes	characteristic
68	#2450	—	2	1	no	—
69	#2439	—	2	1	no	—
70	#2439	—	2	1	no	—
71	#2439	C₂²	1	1	yes	characteristic
72	#2439	C₂²	1	1	yes	characteristic
73	#2439	C₂²	1	1	yes	characteristic
74	#2439	C₂²	1	1	yes	characteristic
75	#2369	C₂²	1	1	yes	characteristic
76	#2368	—	2	1	no	—
77	#2363	C₂²	1	1	yes	characteristic
78	#2363	C₂²	1	1	yes	characteristic
79	#2351	C₂²	1	1	yes	characteristic
80	#2351	C₂²	1	1	yes	characteristic
81	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	#2349	C₂²	1	1	yes	characteristic
83	#2341	C₂²	1	1	yes	characteristic
84	#2341	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊Q₈	—	2	1	no	—
86	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
87	C₄×#121	C₂²	1	1	yes	characteristic
88	#2296	C₂²	1	1	yes	characteristic
89	#2101	C₂²	1	1	yes	characteristic
90	#2100	C₂²	1	1	yes	characteristic
91	#2094	C₂²	1	1	yes	characteristic
92	#2092	C₂²	1	1	yes	characteristic
93	#2092	C₂²	1	1	yes	characteristic
94	#2092	C₂²	1	1	yes	characteristic
95	#2087	C₂²	1	1	yes	characteristic
96	#2086	C₂²	1	1	yes	characteristic
97	#2085	C₂²	1	1	yes	characteristic
98	#2085	C₂²	1	1	yes	characteristic
99	#2085	C₂²	1	1	yes	characteristic
100	#2085	C₂²	1	1	yes	characteristic
101	#2084	C₂²	1	1	yes	characteristic
102	#2083	C₂²	1	1	yes	characteristic
103	#2067	C₂²	1	1	yes	characteristic
104	#2065	C₂²	1	1	yes	characteristic
105	#2065	C₂²	1	1	yes	characteristic
106	#2065	C₂²	1	1	yes	characteristic
107	#2065	C₂²	1	1	yes	characteristic
108	#2065	C₂²	1	1	yes	characteristic
109	#2058	C₂²	1	1	yes	characteristic
110	#2058	C₂²	1	1	yes	characteristic
111	#2058	C₂²	1	1	yes	characteristic
112	#2058	C₂²	1	1	yes	characteristic
113	#2058	C₂²	1	1	yes	characteristic
114	#2057	C₂²	1	1	yes	characteristic
115	#2057	C₂²	1	1	yes	characteristic
116	#2057	C₂²	1	1	yes	characteristic
117	#2023	C₂²	1	1	yes	characteristic
118	#2023	C₂²	1	1	yes	characteristic
119	#2023	C₂²	1	1	yes	characteristic
120	#2023	C₂²	1	1	yes	characteristic
121	#1993	C₂²	1	1	yes	characteristic
122	#1993	C₂²	1	1	yes	characteristic
123	#1987	C₂²	1	1	yes	characteristic
124	#1985	C₂²	1	1	yes	characteristic
125	#1984	C₂²	1	1	yes	characteristic
126	#1972	C₂²	1	1	yes	characteristic
127	#1970	C₂²	1	1	yes	characteristic
128	#1949	C₂²	1	1	yes	characteristic
129	#1944	C₂²	1	1	yes	characteristic
130	#1944	C₂²	1	1	yes	characteristic
131	#1944	C₂²	1	1	yes	characteristic
132	#1944	C₂²	1	1	yes	characteristic
133	#1943	C₂²	1	1	yes	characteristic
134	#1943	C₂²	1	1	yes	characteristic
135	#1941	C₂²	1	1	yes	characteristic
136	#1941	C₂²	1	1	yes	characteristic
137	#1936	C₂²	1	1	yes	characteristic
138	#1934	C₂²	1	1	yes	characteristic
139	#1926	C₂²	1	1	yes	characteristic
140	#1925	C₂²	1	1	yes	characteristic
141	#1920	C₂²	1	1	yes	characteristic
142	#1920	C₂²	1	1	yes	characteristic
143	#1919	C₂²	1	1	yes	characteristic
144	#1918	C₂²	1	1	yes	characteristic
145	#1917	C₂²	1	1	yes	characteristic
146	#1917	C₂²	1	1	yes	characteristic
147	#1917	C₂²	1	1	yes	characteristic
148	#1916	C₂²	1	1	yes	characteristic
149	#1893	C₂²	1	1	yes	characteristic
150	#1893	C₂²	1	1	yes	characteristic
151	#1880	C₂²	1	1	yes	characteristic
152	#1880	C₂²	1	1	yes	characteristic
153	#1880	C₂²	1	1	yes	characteristic
154	#1879	C₂²	1	1	yes	characteristic
155	#1879	C₂²	1	1	yes	characteristic
156	#1879	C₂²	1	1	yes	characteristic
157	#1875	C₂²	1	1	yes	characteristic
158	#1865	C₂²	1	1	yes	characteristic
159	#1865	C₂²	1	1	yes	characteristic
160	#1865	C₂²	1	1	yes	characteristic
161	#1865	C₂²	1	1	yes	characteristic
162	#1865	C₂²	1	1	yes	characteristic
163	#1865	C₂²	1	1	yes	characteristic
164	#1864	C₂²	1	1	yes	characteristic
165	#1864	C₂²	1	1	yes	characteristic
166	#1864	C₂²	1	1	yes	characteristic
167	#1864	C₂²	1	1	yes	characteristic
168	#1864	C₂²	1	1	yes	characteristic
169	#1864	C₂²	1	1	yes	characteristic
170	#1863	C₂²	1	1	yes	characteristic
171	#1863	C₂²	1	1	yes	characteristic
172	#1863	C₂²	1	1	yes	characteristic
173	#1863	C₂²	1	1	yes	characteristic
174	#1863	C₂²	1	1	yes	characteristic
175	#1862	C₂²	1	1	yes	characteristic
176	#1862	C₂²	1	1	yes	characteristic
177	#1862	C₂²	1	1	yes	characteristic
178	#1854	C₂²	1	1	yes	characteristic
179	#1854	C₂²	1	1	yes	characteristic
180	#1854	C₂²	1	1	yes	characteristic
181	#1854	C₂²	1	1	yes	characteristic
182	#1854	C₂²	1	1	yes	characteristic
183	#1850	C₂²	1	1	yes	characteristic
184	#1850	C₂²	1	1	yes	characteristic
185	#1846	C₂²	1	1	yes	characteristic
186	#1807	C₂²	1	1	yes	characteristic
187	#1807	C₂²	1	1	yes	characteristic
188	#1805	C₂²	1	1	yes	characteristic
189	#1805	C₂²	1	1	yes	characteristic
190	#1804	C₂²	1	1	yes	characteristic
191	#1788	C₂²	1	1	yes	characteristic
192	#1771	C₂²	1	1	yes	characteristic
193	#1770	C₂²	1	1	yes	characteristic
194	#1763	C₂²	1	1	yes	characteristic
195	#1763	C₂²	1	1	yes	characteristic
196	#1762	C₂²	1	1	yes	characteristic
197	C₄×#103	C₂²	1	1	yes	characteristic
198	#1752	C₂²	1	1	yes	characteristic
199	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
200	#1749	C₂²	1	1	yes	characteristic
201	#1735	C₂²	1	1	yes	characteristic
202	C₂×#336	C₂²	1	1	yes	characteristic
203	C₂²×#41	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×D₈	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	C₂³×C₈	C₂³	1	1	yes	characteristic
208	Q₈²	—	4	2	no	—
209	Q₈²	—	4	2	no	—
210	C₂×C₄⋊Q₈	—	2	1	no	—
211	C₂×C₄⋊Q₈	—	2	1	no	—
212	C₂×C₄⋊Q₈	—	2	1	no	—
213	C₂×C₄⋊Q₈	—	2	1	no	—
214	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	—	2	1	no	—
222	C₂×C₂²⋊Q₈	—	2	1	no	—
223	C₂×C₂²⋊Q₈	—	2	1	no	—
224	C₂×C₂²⋊Q₈	—	2	1	no	—
225	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
226	C₂×#121	C₂³	1	1	yes	characteristic
227	C₄×#41	—	4	2	no	—
228	C₄×#41	—	4	2	no	—
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₄	—	2	1	no	—
238	C₂×C₄×D₄	—	2	1	no	—
239	C₂×C₄×D₄	—	2	1	no	—
240	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
245	C₂×#117	—	2	1	no	—
246	C₂×#117	C₂³	1	1	yes	characteristic
247	C₂×#117	C₂³	1	1	yes	characteristic
248	C₂×#117	C₂³	1	1	yes	characteristic
249	C₂²×C₄²	—	2	1	no	—
250	C₂²×C₄²	C₂³	1	1	yes	characteristic
251	#498	—	4	2	no	—
252	#475	—	2	4	no	—
253	#475	—	4	2	no	—
254	#474	—	4	2	no	—
255	#449	Q₈	1	8	yes	complemented
256	#442	—	4	2	no	—
257	#440	—	4	2	no	—
258	#440	—	4	2	no	—
259	C₄×SD₁₆	—	2	4	no	—
260	#427	—	4	2	no	—
261	C₂×#107	C₂³	1	1	yes	characteristic
262	C₂×#107	C₂³	1	1	yes	characteristic
263	C₂×#107	C₂³	1	1	yes	characteristic
264	C₂×#107	C₂³	1	1	yes	characteristic
265	C₂×#107	C₂³	1	1	yes	characteristic
266	C₂×#107	C₂³	1	1	yes	characteristic
267	C₂×#107	C₂³	1	1	yes	characteristic
268	C₂×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×#106	C₂³	1	1	yes	characteristic
271	C₂×#106	C₂³	1	1	yes	characteristic
272	C₂×#106	C₂³	1	1	yes	characteristic
273	C₂×#106	C₂³	1	1	yes	characteristic
274	C₂×#106	C₂³	1	1	yes	characteristic
275	C₂×#106	C₂³	1	1	yes	characteristic
276	C₂×#106	C₂³	1	1	yes	characteristic
277	C₂×#106	C₂³	1	1	yes	characteristic
278	C₂×#106	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	#416	—	2	4	no	—
284	#416	—	4	2	no	—
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×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×#102	C₂³	1	1	yes	characteristic
295	C₂×#102	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×#102	C₂³	1	1	yes	characteristic
299	C₂×#102	C₂³	1	1	yes	characteristic
300	C₂×#102	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×#102	C₂³	1	1	yes	characteristic
303	C₂×#102	C₂³	1	1	yes	characteristic
304	C₂×#102	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂×#97	C₂³	1	1	yes	characteristic
308	C₂×#97	C₂³	1	1	yes	characteristic
309	C₂×#97	C₂³	1	1	yes	characteristic
310	C₂×#97	C₂³	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
313	#400	—	2	1	no	—
314	#400	—	2	1	no	—
315	#400	—	2	1	no	—
316	#400	—	2	1	no	—
317	#399	—	2	1	no	—
318	#398	—	2	1	no	—
319	#398	—	2	1	no	—
320	#396	—	2	1	no	—
321	#396	—	2	1	no	—
322	#396	—	2	1	no	—
323	#396	—	2	1	no	—
324	#396	—	2	1	no	—
325	#396	—	2	1	no	—
326	#396	—	2	1	no	—
327	#396	—	2	1	no	—
328	#396	—	2	1	no	—
329	#396	—	2	1	no	—
330	#393	—	2	1	no	—
331	#393	—	2	1	no	—
332	#393	—	2	1	no	—
333	#393	—	2	1	no	—
334	#393	—	2	1	no	—
335	#393	—	2	1	no	—
336	#393	—	2	1	no	—
337	#393	—	2	1	no	—
338	#393	—	2	1	no	—
339	#393	—	2	1	no	—
340	#393	—	2	1	no	—
341	#391	—	2	1	no	—
342	#391	—	2	1	no	—
343	#391	—	2	1	no	—
344	#391	—	2	1	no	—
345	#391	—	2	1	no	—
346	#391	—	2	1	no	—
347	#391	—	2	1	no	—
348	#391	—	2	1	no	—
349	#391	D₄	1	1	yes	characteristic
350	#390	—	2	1	no	—
351	#390	—	2	1	no	—
352	#390	—	2	1	no	—
353	#390	—	2	1	no	—
354	#390	—	2	1	no	—
355	#390	—	2	1	no	—
356	#390	C₂³	1	1	yes	characteristic
357	#390	C₂³	1	1	yes	characteristic
358	#390	C₂³	1	1	yes	characteristic
359	#390	C₂³	1	1	yes	characteristic
360	#390	C₂³	1	1	yes	characteristic
361	#390	C₂³	1	1	yes	characteristic
362	#390	C₂³	1	1	yes	characteristic
363	#389	—	2	1	no	—
364	#389	—	2	1	no	—
365	#389	—	2	1	no	—
366	#389	—	2	1	no	—
367	#389	—	2	1	no	—
368	#389	—	2	1	no	—
369	#389	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	—	2	1	no	—
372	#389	—	2	1	no	—
373	#389	D₄	1	1	yes	characteristic
374	#389	C₂³	1	1	yes	characteristic
375	#389	C₂³	1	1	yes	characteristic
376	#389	C₂³	1	1	yes	characteristic
377	#389	C₂³	1	1	yes	characteristic
378	#389	C₂³	1	1	yes	characteristic
379	#389	C₂³	1	1	yes	characteristic
380	#389	C₂³	1	1	yes	characteristic
381	#389	C₂³	1	1	yes	characteristic
382	#389	C₂³	1	1	yes	characteristic
383	#389	C₂³	1	1	yes	characteristic
384	#389	C₂³	1	1	yes	characteristic
385	#389	C₂³	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	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#387	—	2	1	no	—
397	#387	—	2	1	no	—
398	#387	—	2	1	no	—
399	#387	—	2	1	no	—
400	#387	D₄	1	1	yes	characteristic
401	#387	D₄	1	1	yes	characteristic
402	#386	—	2	1	no	—
403	#386	—	2	1	no	—
404	#386	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#385	—	2	1	no	—
409	#385	—	2	1	no	—
410	#385	—	2	1	no	—
411	#385	—	2	1	no	—
412	#385	—	2	1	no	—
413	#385	—	2	1	no	—
414	#385	—	2	1	no	—
415	#385	D₄	1	1	yes	characteristic
416	#385	D₄	1	1	yes	characteristic
417	#384	—	2	1	no	—
418	#384	C₂³	1	1	yes	characteristic
419	#382	—	2	1	no	—
420	#382	—	2	1	no	—
421	#382	C₂³	1	1	yes	characteristic
422	#382	C₂³	1	1	yes	characteristic
423	#382	C₂³	1	1	yes	characteristic
424	#382	C₂³	1	1	yes	characteristic
425	#380	—	2	1	no	—
426	#380	—	2	1	no	—
427	#380	—	2	1	no	—
428	#380	—	2	1	no	—
429	#380	—	2	1	no	—
430	#380	—	2	1	no	—
431	#380	—	2	1	no	—
432	#380	D₄	1	1	yes	characteristic
433	#380	C₂³	1	1	yes	characteristic
434	#380	C₂³	1	1	yes	characteristic
435	#380	C₂³	1	1	yes	characteristic
436	C₄×C₄⋊C₄	—	2	1	no	—
437	C₄×C₄⋊C₄	—	2	1	no	—
438	C₄×C₄⋊C₄	—	2	1	no	—
439	C₄×C₄⋊C₄	—	2	1	no	—
440	C₄×C₄⋊C₄	—	2	1	no	—
441	C₄×C₄⋊C₄	—	2	1	no	—
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	—	2	1	no	—
449	C₄×C₂²⋊C₄	—	2	1	no	—
450	C₄×C₂²⋊C₄	—	2	1	no	—
451	C₄×C₂²⋊C₄	—	2	1	no	—
452	C₄×C₂²⋊C₄	—	2	1	no	—
453	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
455	C₂×#95	—	2	1	no	—
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#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	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	4	1	no	—
498	C₂×#41	—	4	1	no	—
499	C₂×#41	C₂×Q₈	1	4	yes	—
500	C₂²×Q₈	—	2	1	no	—
501	C₂²×Q₈	—	2	1	no	—
502	C₂²×Q₈	—	2	1	no	—
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×Q₈	—	2	1	no	—
505	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
506	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	C₂⁴	1	1	yes	characteristic
510	C₂²×D₄	C₂⁴	1	1	yes	characteristic
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
518	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
519	C₂³×C₄	C₂⁴	1	1	yes	characteristic
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	C₂×Q₈	1	4	yes	—
523	C₂×D₈	—	4	1	no	—
524	C₂×D₈	—	4	1	no	—
525	C₂×D₈	C₂×Q₈	1	4	yes	—
526	C₂²×C₈	—	2	2	no	—
527	C₂²×C₈	—	2	2	no	—
528	C₂²×C₈	—	2	2	no	—
529	C₂²×C₈	—	4	1	no	—
530	C₂²×C₈	—	4	1	no	—
531	C₂²×C₈	—	4	1	no	—
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₂²×C₈	C₂⁴	1	1	yes	characteristic
537	C₂²×C₈	C₂⁴	1	1	yes	characteristic
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
539	C₂²×C₈	C₂⁴	1	1	yes	characteristic
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	4	1	no	—
544	C₄⋊Q₈	—	4	1	no	—
545	C₄⋊Q₈	—	4	1	no	—
546	C₄⋊Q₈	—	4	1	no	—
547	C₄⋊Q₈	—	4	1	no	—
548	C₄⋊Q₈	—	4	1	no	—
549	C₄⋊Q₈	—	4	1	no	—
550	C₄⋊Q₈	—	4	4	no	—
551	C₄⋊Q₈	—	4	4	no	—
552	C₄⋊Q₈	—	4	4	no	—
553	C₄⋊Q₈	—	8	2	no	—
554	C₂²⋊Q₈	—	4	2	no	—
555	C₂²⋊Q₈	—	4	4	no	—
556	C₂²⋊Q₈	—	4	4	no	—
557	C₂²⋊Q₈	—	8	2	no	—
558	C₂²⋊Q₈	—	8	2	no	—
559	C₂²⋊Q₈	—	8	2	no	—
560	C₂²⋊Q₈	—	8	2	no	—
561	#121	—	2	2	no	—
562	#121	C₂×Q₈	1	4	yes	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	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	1	no	—
575	C₄×Q₈	—	4	1	no	—
576	C₄×Q₈	—	4	1	no	—
577	C₄×Q₈	—	4	4	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	4	1	no	—
581	C₄×D₄	—	4	1	no	—
582	C₄×D₄	—	4	1	no	—
583	C₄×D₄	—	4	1	no	—
584	C₄×D₄	—	4	4	no	—
585	C₄×D₄	—	4	1	no	—
586	C₄×D₄	—	4	1	no	—
587	C₄×D₄	—	4	1	no	—
588	C₄×D₄	—	4	1	no	—
589	C₄×D₄	—	4	4	no	—
590	C₄×D₄	—	8	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	—	4	1	no	—
594	#117	—	4	1	no	—
595	#117	—	4	4	no	—
596	#117	—	4	1	no	—
597	#117	—	4	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	1	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	—	2	1	no	—
692	C₂×C₄²	—	4	1	no	—
693	C₂×C₄²	—	4	1	no	—
694	C₂×C₄²	—	4	4	no	—
695	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
696	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
697	C₂×C₄²	C₂⁴	1	1	yes	characteristic
698	C₂×C₄²	C₂⁴	1	1	yes	characteristic
699	C₂×C₄²	C₂⁴	1	1	yes	characteristic
700	C₂×C₄²	C₂⁴	1	1	yes	characteristic
701	C₂×C₄²	C₂⁴	1	1	yes	characteristic
702	C₂×C₄²	C₂⁴	1	1	yes	characteristic
703	#107	—	2	2	no	—
704	#107	—	4	1	no	—
705	#107	—	4	1	no	—
706	#107	—	4	1	no	—
707	#107	—	4	1	no	—
708	#107	—	4	1	no	—
709	#107	—	4	1	no	—
710	#106	—	2	2	no	—
711	#106	—	2	2	no	—
712	#106	—	2	2	no	—
713	#106	—	2	2	no	—
714	#106	—	2	2	no	—
715	#106	—	4	1	no	—
716	#106	—	4	1	no	—
717	#106	—	4	1	no	—
718	#106	—	4	1	no	—
719	#106	—	4	1	no	—
720	#106	—	4	1	no	—
721	C₄⋊C₈	—	2	2	no	—
722	C₄⋊C₈	—	4	1	no	—
723	C₄⋊C₈	—	4	1	no	—
724	C₄⋊C₈	—	4	1	no	—
725	#103	—	2	2	no	—
726	#103	—	2	2	no	—
727	#103	—	2	2	no	—
728	#103	—	2	2	no	—
729	#103	—	2	2	no	—
730	#103	C₂×Q₈	1	4	yes	—
731	#103	#41	1	4	yes	—
732	#102	—	2	2	no	—
733	#102	—	2	2	no	—
734	#102	—	2	2	no	—
735	#102	—	2	2	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	#102	—	4	1	no	—
739	#102	—	4	1	no	—
740	#102	—	4	1	no	—
741	#102	—	4	1	no	—
742	#102	—	4	1	no	—
743	#102	—	4	1	no	—
744	#102	C₂×Q₈	1	4	yes	—
745	C₂²⋊C₈	—	2	2	no	—
746	C₂²⋊C₈	C₂×Q₈	1	4	yes	—
747	#97	—	4	1	no	—
748	#97	—	4	1	no	—
749	#97	—	4	1	no	—
750	#97	—	4	1	no	—
751	C₄×C₈	—	2	2	no	—
752	C₄×C₈	—	4	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	C₂×D₄	1	1	yes	characteristic
785	#95	C₂×D₄	1	1	yes	characteristic
786	#95	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	#95	C₂×D₄	1	1	yes	characteristic
792	#95	C₂×D₄	1	1	yes	characteristic
793	#95	C₂×D₄	1	1	yes	characteristic
794	C₂⁴	—	2	1	no	—
795	C₂⁴	—	2	1	no	—
796	C₂⁴	C₂²×D₄	1	1	yes	characteristic
797	#41	—	2	8	no	—
798	#41	—	4	4	no	—
799	#41	—	4	4	no	—
800	#41	—	4	4	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	4	1	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	4	2	no	—
810	C₂×Q₈	—	4	2	no	—
811	C₂×Q₈	—	4	2	no	—
812	C₂×Q₈	—	8	1	no	—
813	C₂×Q₈	—	8	1	no	—
814	C₂×Q₈	—	8	1	no	—
815	C₂×Q₈	—	8	1	no	—
816	C₂×Q₈	—	8	1	no	—
817	C₂×Q₈	—	8	1	no	—
818	C₂×Q₈	—	8	1	no	—
819	C₂×Q₈	—	8	1	no	—
820	C₂×Q₈	—	8	1	no	—
821	C₂×Q₈	—	8	1	no	—
822	C₂×Q₈	C₂²×Q₈	1	2	yes	—
823	C₂×Q₈	C₂×#41	1	2	yes	—
824	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	8	1	no	—
840	C₂×D₄	—	8	1	no	—
841	C₂×D₄	C₂²×Q₈	1	2	yes	—
842	C₂×D₄	C₂²×Q₈	1	2	yes	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	1	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	8	1	no	—
878	C₂²×C₄	—	8	1	no	—
879	C₂²×C₄	—	8	1	no	—
880	C₂²×C₄	—	8	1	no	—
881	C₂²×C₄	—	8	1	no	—
882	C₂²×C₄	—	8	1	no	—
883	C₂²×C₄	—	8	1	no	—
884	C₂²×C₄	—	8	1	no	—
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
888	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₂²×Q₈	1	2	yes	—
899	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
900	C₂²×C₄	C₂⁵	1	1	yes	characteristic
901	SD₁₆	—	2	8	no	—
902	D₈	—	4	4	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	4	4	no	—
925	C₂×C₈	—	8	2	no	—
926	C₂×C₈	C₂²×Q₈	1	2	yes	—
927	C₂×C₈	C₂²×Q₈	1	2	yes	—
928	C₂×C₈	C₂×#41	1	2	yes	—
929	C₄⋊C₄	—	2	4	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	4	1	no	—
956	C₄⋊C₄	—	4	1	no	—
957	C₄⋊C₄	—	4	1	no	—
958	C₄⋊C₄	—	4	1	no	—
959	C₄⋊C₄	—	4	1	no	—
960	C₄⋊C₄	—	4	1	no	—
961	C₄⋊C₄	—	4	1	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	2	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	4	2	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	8	1	no	—
981	C₄⋊C₄	—	8	1	no	—
982	C₄⋊C₄	—	8	1	no	—
983	C₄⋊C₄	—	8	1	no	—
984	C₄⋊C₄	—	8	1	no	—
985	C₄⋊C₄	—	8	1	no	—
986	C₄⋊C₄	—	8	1	no	—
987	C₄⋊C₄	—	8	1	no	—
988	C₄⋊C₄	—	8	1	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	—	8	1	no	—
991	C₄⋊C₄	C₂²×Q₈	1	2	yes	—
992	C₄⋊C₄	C₂×#41	1	2	yes	—
993	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
994	C₂²⋊C₄	—	2	4	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	4	1	no	—
997	C₂²⋊C₄	—	4	1	no	—
998	C₂²⋊C₄	—	4	1	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	—	4	2	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	8	1	no	—
1010	C₂²⋊C₄	—	8	1	no	—
1011	C₂²⋊C₄	—	8	1	no	—
1012	C₂²⋊C₄	—	8	1	no	—
1013	C₂²⋊C₄	—	8	1	no	—
1014	C₂²⋊C₄	—	8	1	no	—
1015	C₂²⋊C₄	—	8	1	no	—
1016	C₂²⋊C₄	—	8	1	no	—
1017	C₂²⋊C₄	—	8	1	no	—
1018	C₂²⋊C₄	—	8	1	no	—
1019	C₂²⋊C₄	—	8	1	no	—
1020	C₂²⋊C₄	—	8	1	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	1	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₄²	—	2	4	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	4	1	no	—
1038	C₄²	—	4	1	no	—
1039	C₄²	—	4	2	no	—
1040	C₄²	—	4	2	no	—
1041	C₄²	—	4	2	no	—
1042	C₄²	—	4	2	no	—
1043	C₄²	—	4	2	no	—
1044	C₄²	—	4	2	no	—
1045	C₄²	—	4	2	no	—
1046	C₄²	—	8	1	no	—
1047	C₄²	—	8	1	no	—
1048	C₄²	—	8	1	no	—
1049	C₄²	—	8	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	—	4	1	no	—
1060	C₂³	—	4	1	no	—
1061	C₂³	—	4	1	no	—
1062	C₂³	—	4	1	no	—
1063	C₂³	—	4	1	no	—
1064	C₂³	—	4	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	4	1	no	—
1069	C₂³	—	4	1	no	—
1070	C₂³	D₄×Q₈	1	2	yes	—
1071	C₂³	C₂³×D₄	1	1	yes	characteristic
1072	Q₈	—	2	2	no	—
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	4	4	no	—
1076	Q₈	—	16	2	no	—
1077	Q₈	—	16	2	no	—
1078	Q₈	—	16	2	no	—
1079	Q₈	—	16	2	no	—
1080	Q₈	—	16	2	no	—
1081	Q₈	#554	1	4	yes	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	4	8	no	—
1087	D₄	—	4	1	no	—
1088	D₄	—	4	1	no	—
1089	D₄	—	4	1	no	—
1090	D₄	—	4	1	no	—
1091	D₄	—	8	4	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	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	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	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	—	4	8	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	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	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	4	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	8	4	no	—
1179	C₂×C₄	—	16	2	no	—
1180	C₂×C₄	—	16	2	no	—
1181	C₂×C₄	—	16	2	no	—
1182	C₂×C₄	D₄×Q₈	1	2	yes	—
1183	C₂×C₄	#575	1	2	yes	—
1184	C₂×C₄	#577	1	2	yes	—
1185	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
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	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1190	C₂×C₄	#585	1	1	yes	characteristic
1191	C₈	—	2	2	no	—
1192	C₈	—	2	2	no	—
1193	C₈	—	2	2	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	C₂²	—	2	2	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	2	no	—
1207	C₂²	—	4	2	no	—
1208	C₂²	—	4	2	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	8	1	no	—
1213	C₂²	—	8	1	no	—
1214	C₂²	—	8	1	no	—
1215	C₂²	—	8	1	no	—
1216	C₂²	—	8	1	no	—
1217	C₂²	—	8	1	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	C₂×D₄×Q₈	1	1	yes	characteristic
1221	C₂²	D₄×#41	1	1	yes	characteristic
1222	C₂²	#3484	1	1	yes	characteristic
1223	C₂²	C₂×#575	1	1	yes	characteristic
1224	C₂²	C₂×#577	1	1	yes	characteristic
1225	C₂²	#3584	1	1	yes	characteristic
1226	C₂²	#3585	1	1	yes	characteristic
1227	C₄	—	2	2	no	—
1228	C₄	—	2	4	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	2	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	2	no	—
1243	C₄	—	4	2	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	1	no	—
1248	C₄	—	8	1	no	—
1249	C₄	—	8	1	no	—
1250	C₄	—	8	1	no	—
1251	C₄	—	8	1	no	—
1252	C₄	—	8	1	no	—
1253	C₄	—	8	1	no	—
1254	C₄	C₂×#554	1	1	yes	characteristic
1255	C₄	#3501	1	1	yes	characteristic
1256	C₄	#3520	1	1	yes	characteristic
1257	C₄	#3535	1	1	yes	characteristic
1258	C₂	—	4	2	no	—
1259	C₂	—	8	2	no	—
1260	C₂	—	8	2	no	—
1261	C₂	#59150	1	1	yes	characteristic
1262	C₂	#61365	1	1	yes	characteristic
1263	C₂	#61382	1	1	yes	characteristic
1264	C₂	#61462	1	1	yes	characteristic
1265	C₂	#61474	1	1	yes	characteristic
1266	C₂	#61594	1	1	yes	characteristic
1267	C₂	#61625	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#449	C₂²
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
1. #59771	C₂	semidirect
2. #36456	C₂	semidirect
3. #32655	C₂	semidirect
4. #32589	C₂	semidirect
5. #32351	C₂	semidirect
6. #31547	C₂	semidirect
7. #29304	C₂	semidirect
8. #29156	C₂	semidirect
9. #28958	C₂	semidirect
10. #28779	C₂	semidirect
11. #27321	C₂	semidirect
12. #27316	C₂	semidirect
13. #27019	C₂	semidirect
14. #26490	C₂	semidirect
15. #26411	C₂	semidirect
16. #26388	C₂	semidirect
17. #26385	C₂	semidirect
18. #26373	C₂	semidirect
19. #26341	C₂	semidirect
20. #26061	C₂	semidirect
21. #25951	C₂	semidirect
22. #25951	C₂	semidirect
23. #25837	C₂	semidirect
24. #24341	C₂	semidirect
25. #23238	C₂	semidirect
26. #22981	C₂	semidirect
29. #22673	C₂	semidirect
31. #20872	C₂	semidirect
255. #449	Q₈	semidirect

Maximal subgroups

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

subgroup	index
#59771	2
#36456	2
#32655	2
#32589	2
#32351	2
#31547	2
#29304	2
#29156	2
#28958	2
#28779	2
#27321	2
#27316	2
#27019	2
#26490	2
#26411	2
#26388	2
#26385	2
#26373	2
#26341	2
#26061	2
#25951	2
#25837	2
#24341	2
#23238	2
#22981	2
#22877	2
#22857	2
#22673	2
#21456	2
#20872	2